Answers
Answer:
A= 46°, a= 25.9, b=36
Step-by-step explanation:
A= 46°
all angles of a triangle add to 180, so since C=90° and B= 44°, A must be 46°
a= 25.9
b= 36
you can use the law of sines (sinA/a= sinB/b) to find a and c.
sin46/a= sin44/25
sin90/c= sin44/25
Related Questions
An eating disorder characterized by bingeing and purging is called The minimum amount of body fat needed for good health is Youris the amount of energy your body uses at complete rest. A term used to describe a person who is very overfat is People with extremely thin. see themselves as too fat even when they are A technique for assessing body fat levels that involves being weighed under water is called
Answers
An eating disorder characterized by bingeing and purging is called bulimia nervosa.
The minimum amount of body fat needed for good health is variable and can depend on factors such as age, gender, and individual circumstances. However, essential body fat is typically estimated to be around 3-5% for men and 8-12% for women.
The term used to describe a person who is very overfat is obese. Obesity refers to having excessive body fat, which can have negative effects on health.
People with anorexia nervosa, an eating disorder characterized by restrictive eating and an intense fear of gaining weight, often see themselves as too fat even when they are extremely thin. This distorted body image is a characteristic feature of anorexia nervosa.
A technique for assessing body fat levels that involves being weighed under water is called hydrostatic weighing or underwater weighing. It is considered one of the more accurate methods for determining body composition.
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Jessica hires ChromaLite Builders Corp. to construct a house. The contract specifies that grade A+ carpeting is to be installed on the entire second floor. ChromaLite Builders accidentally installs grade A carpeting instead. Few people, except for carpeting experts, can tell the difference. Jessica, however, refuses to pay for the construction citing that ChromaLite Builders has breached the contract. Which of the following statements is true in this scenario?a) The courts are likely to consider ChromaLite Builders’s performance as a substantial performance, and Jessica will have to pay something but not the full amount; i.e. she is entitled to monetary damagesb) Jessica has materially breached the contract by refusing to pay ChromaLite Builders; hence, she cannot sue ChromaLite Builders for the use of low-grade carpeting.c) Jessica can claim a breach of contract and refuse to pay ChromaLite Builders for the construction of the house.d) The courts are likely to declare that ChromaLite Builders has materially breached the contract and will ask Jessica to pay exactly half the cost originally mentioned in the contract.e) The courts are likely to consider ChromaLite Builders’s performance as complete performance, and Jessica will have to pay the full amount to ChromaLite Builders.
Answers
The correct answer in this scenario is a) The courts are likely to consider ChromaLite Builders's performance as a substantial performance, and Jessica will have to pay something but not the full amount; i.e. she is entitled to monetary damages.
This is because ChromaLite Builders did not fully comply with the contract by installing grade A carpeting instead of grade A+ carpeting, but the difference may not be significant to most people. As a result, the courts are likely to consider this a minor breach of contract and award Jessica some monetary damages but not the full cost of the contract.
It is important to note that if the difference between the two grades of carpeting was significant and clearly stated in the contract, Jessica may have had a stronger case for refusing to pay. However, in this scenario, it seems that the breach of contract was not significant enough to justify a complete refusal to pay.
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What is the area of the trapezoid?
A. 20 square units
B. 4√5 +4√/10 square units
C. 20√2 square units
D. 40 square units
Answers
The area of the trapezoid is 11 square units.
We are given that;
The coordinates of trapezoid= (-1,3) (-5, 1) (2, 2) (-2, 0) (4,-2) (1, -1)
Now,
The area of a trapezoid can be calculated using the formula A = (a + b)h/2, where a and b are the lengths of the parallel sides and h is the height of the trapezoid.
In this case, the coordinates you provided form a trapezoid with parallel sides of length 4 and 7, and a height of 2.
Plugging these values into the formula gives us an area of (4 + 7) * 2 / 2 = 11 square units.
Therefore, by the distance the answer will be 11 square units.
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A client is diagnosed with intermittent explosive disorder (IED). What drugs are likely to be prescribed for the client
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The prescription of drugs for a client diagnosed with intermittent explosive disorder (IED) may include selective serotonin reuptake inhibitors (SSRIs) and mood stabilizers.
SSRIs are commonly prescribed for IED as they help regulate serotonin levels in the brain, which can help with mood stability and control impulsive behaviors. These medications, such as fluoxetine (Prozac), sertraline (Zoloft), or escitalopram (Lexapro), may be prescribed to reduce aggressive outbursts and improve emotional regulation.
Mood stabilizers, such as lithium or anticonvulsant medications like divalproex sodium (Depakote) or carbamazepine (Tegretol), may also be prescribed to help stabilize mood swings and impulsive behaviors associated with IED. These medications work by regulating brain activity and may be beneficial in managing aggression and impulsivity.
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Pls give the CORRECT answer!!
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The exact value of sinθ in simplest radical form is sinθ = 1.
The terminal side of an angle in standard position is a line passing through the point (x,y).
To find the exact value of sinθ, use the trigonometric identity sinθ = y/r, where r is the distance or length of the line segment from the origin
r = √(x² + y²)
Given the point (-20, 21), the value of sinθ is 21/√(20² + 21²).
Simplifying, 21/√(441), sinθ = 21/21 = 1.
Therefore, the exact value of sinθ in simplest radical form is sinθ = 1.
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please help i need this
Answers
Step-by-step explanation:
point A (2,4) lies in first quadrant.
x coordinate is positive
Y coordinates is positive
Both coordinates are positive in the first quadrant.
exhibit 9-6 a random sample of 100 people was taken. eighty of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 75%. refer to exhibit 9-6. the p-value is . group of answer choices .05 .2112 .025 .1251
Answers
The correct answer is 0.1251. The proportion of the population in favor of candidate A is significantly more than 75% is 0.1251.
To determine the p-value for testing whether the proportion of the population in favor of candidate A is significantly more than 75%, we can perform a one-sample proportion test.
Let's denote the proportion of the population in favor of candidate A as p. The null hypothesis (H0) states that p = 0.75, and the alternative hypothesis (Ha) states that p > 0.75.
In Exhibit 9-6, we have a random sample of 100 people, and 80 of them favored candidate A. To test the hypothesis, we can use a normal approximation to the binomial distribution since the sample size is reasonably large.
The test statistic for a one-sample proportion test is calculated using the formula:
z = (p1 - p0) / √(p0 * (1 - p0) / n)
Here:
p1 is the sample proportion (80/100 = 0.8),
p0 is the hypothesized proportion under the null hypothesis (0.75),
n is the sample size (100).
Let's calculate the test statistic:
z = (0.8 - 0.75) / √(0.75 * (1 - 0.75) / 100)
= 0.05 / √(0.1875 / 100)
= 0.05 / √0.001875
= 0.05 / 0.04330127
≈ 1.1547
Now, we need to find the p-value associated with this test statistic. The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.
Since we are testing whether the proportion is significantly more than 75% (one-tailed test with the alternative hypothesis p > 0.75), we look for the area in the upper tail of the standard normal distribution.
Using a standard normal distribution table or a statistical software, we find that the p-value associated with z ≈ 1.1547 is approximately 0.1251.
Therefore, the correct answer is 0.1251.
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The poverty line is determined by ________. Group of answer choices the level of income needed to cover basic needs annual estimates based on a sampling of U.S. middle- and high-income households surveys completed on the elderly
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The poverty line is determined by the level of income needed to cover basic needs.
The poverty line is a threshold used to measure poverty and determine eligibility for various assistance programs. It represents the minimum income level required for individuals or households to meet their basic needs, such as food, shelter, clothing, and healthcare. The specific calculation of the poverty line varies from country to country and is often adjusted for factors like family size and location. To determine the poverty line, policymakers and researchers consider factors such as the cost of living, household expenses, and prevailing social standards. They assess the minimum income necessary to provide a decent standard of living and ensure that individuals and families are not living in extreme deprivation. The poverty line is not based on estimates from middle- or high-income households or surveys completed solely on the elderly. Instead, it is designed to reflect the income level below which individuals or households are considered to be living in poverty, indicating the need for targeted interventions and support to improve their economic well-being.
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Suppose an automobile maker producing a certain kind of car suddenly experiences an increase in the demand for the car. According to our definition of short-run and long-run, in the short run:
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In the short run, an automobile maker experiencing an increase in the demand for a certain kind of car will be limited in its ability to adjust its production capacity.
In economics, the short run refers to a period of time during which some factors of production are fixed, while others can be adjusted. In the context of the automobile maker facing increased demand for a specific car, the short run implies that certain aspects of production capacity cannot be changed immediately.
In the short run, the automobile maker may not have the flexibility to expand its production facilities or build new manufacturing plants. This means that the company is constrained by its existing resources and production capacity. Instead, the company can make temporary adjustments to production levels by utilizing existing resources more efficiently, such as adding additional shifts or optimizing the utilization of labor and machinery.
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After issuing its financial statements, a company discovered that its beginning inventory was overstated by $270,000. Its tax rate is 30%. As a result of this error, net income was:
Answers
As a result of the overstated beginning inventory by $270,000, the company's net income will decrease by $189,000 after considering the tax effect at a 30% tax rate.
The overstatement of the beginning inventory by $270,000 will affect the cost of goods sold (COGS) and ultimately impact the company's net income. Since the beginning inventory was overstated, the COGS will be adjusted to reflect the correct value, leading to an increase in expenses.
The adjustment to the COGS will result in a decrease in net income before taxes by $270,000. To determine the after-tax impact, the tax rate of 30% is applied. The tax effect is calculated by multiplying the adjustment ($270,000) by the tax rate (30%), resulting in a tax expense of $81,000.
Subtracting the tax expense from the decrease in net income before taxes, the net income after the error is calculated as $270,000 - $81,000 = $189,000. Therefore, the net income will decrease by $189,000 as a result of the $270,000 overstatement in the beginning inventory, considering the 30% tax rate.
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The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal sized stores is selected, with the following results:
Store Shelf Space(X) Weekly Sales(Y)
1 10 2.0
2 10 2.6
3 10 1.8
4 15 2.3
5 15 2.8
6 15 3.0
7 20 2.7
8 20 3.1
9 20 3.2
10 25 3.0
11 25 3.3
12 25 3.5
Using the equation of the regression line for these data, predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.
Answers
The regression line equation for predicting average weekly sales for stores with 13 feet of shelf space is:
[tex]Y = -0.63825 + 0.1938 * 13[/tex]
What is linear regression?
Linear regression is a statistical analysis technique used to model the relationship between a dependent variable (in this case, weekly sales) and one or more independent variables (in this case, store shelf space). It assumes a linear relationship between the variables and aims to find the best-fitting line that represents this relationship. The equation of the regression line allows for predicting the value of the dependent variable based on the given independent variable(s)
To predict the average weekly sales for stores with 13 feet of shelf space, we can use linear regression analysis. Let's calculate the regression line equation using the given data:
Store Shelf Space (X) | Weekly Sales (Y)
[tex]1 10 2.02 10 2.63 10 1.84 15 2.35 15 2.86 15 3.07 20 2.78 20 3.19 20 3.210 25 3.011 25 3.312 25 3.5[/tex]
Step 1: Calculate the mean of X and Y:
Mean[tex](X) = (10 + 10 + 10 + 15 + 15 + 15 + 20 + 20 + 20 + 25 + 25 + 25) / 12 = 17.5[/tex]
Mean[tex](Y) = (2.0 + 2.6 + 1.8 + 2.3 + 2.8 + 3.0 + 2.7 + 3.1 + 3.2 + 3.0 + 3.3 + 3.5) / 12 = 2.75[/tex]
Step 2: Calculate the deviations from the means:
X deviations: [tex]10 - 17.5, 10 - 17.5, 10 - 17.5, 15 - 17.5, 15 - 17.5, 15 - 17.5, 20 - 17.5, 20 - 17.5, 20 - 17.5, 25 - 17.5, 25 - 17.5, 25 - 17.5[/tex]
Y deviations: [tex]2.0 - 2.75, 2.6 - 2.75, 1.8 - 2.75, 2.3 - 2.75, 2.8 - 2.75, 3.0 - 2.75, 2.7 - 2.75, 3.1 - 2.75, 3.2 - 2.75, 3.0 - 2.75, 3.3 - 2.75, 3.5 - 2.75[/tex]
Step 3: Calculate the product of the deviations:
(X deviations * Y deviations):
[tex]-7.5 * -0.75 = 5.625-7.5 * 0.85 = -6.375-7.5 * -0.95 = 7.125-2.5 * -0.45 = 1.125-2.5 * 0.05 = -0.125-2.5 * 0.25 = -0.6252.5 * -0.05 = -0.1252.5 * 0.35 = 0.8752.5 * 0.45 = 1.1257.5 * 0.25 = 1.8757.5 * 0.55 = 4.1257.5 * 0.75 = 5.625[/tex]
Step 4: Calculate the sum of squared X deviations:
X deviations squared:
[tex](-7.5)^2 = 56.25(-7.5)^2 = 56.25[/tex]
Step 5: Calculate the sum of the product of X deviations and Y deviations:
Sum of (X deviations * Y deviations)[tex]= 5.625 + (-6.375) + 7.125 + 1.125 + (-0.125) + (-0.625) + (-0.125) + 0.875 + 1.125 + 1.875 + 4.125 + 5.625 = 21.75[/tex]
Step 6: Calculate the slope (b):
b = Sum of (X deviations * Y deviations) / Sum of X deviations squared = [tex]21.75 / (56.25 + 56.25) = 21.75 / 112.5 = 0.1938[/tex]
Step 7: Calculate the intercept (a):
a = Mean(Y) - b * Mean[tex](X) = 2.75 - 0.1938 * 17.5 = 2.75 - 3.38825 = -0.63825[/tex]
Step 8: Write the regression line equation:
Y = a + bX
Y = -0.63825 + 0.1938X
Therefore, the regression line equation for predicting average weekly sales for stores with 13 feet of shelf space is:
[tex]Y = -0.63825 + 0.1938 * 13[/tex]
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g Milk consumption and lactose digestion after weaning are exclusively human traits made possible by the continued production of the enzyme lactase in adulthood. In Europe and northwestern India, adult lactase persistence is considered a classic case of biocultural evolution since herders of Indian and European cattle share their predominant allele for lactase persistence and its presence in the human population appears to coincide with the presence of genes in the herded cattle for increased milk production. Multiple independent mutations in a 100-bp region-part of an enhancer-approximately 14-kb upstream of the LCT gene are associated with this trait in Europeans and pastoralists from Saudi Arabia and Africa. However, a single mutation of purported western Eurasian origin accounts for much of observed lactase persistence outside Africa. What is the dominant gene coding for adult lactase persistence in Europe and India? a. The south Asian -13910 C>T mutation has emerged as the dominant gene coding for adult lactase persistence in India and Europe. b. The west Eurasian -13910 C>T mutation accounts for nearly all the genetic variation observed in the 400- to 700-bp LCT regulatory region. c. None of the above. d. The north Atlantic -13910 C>T mutation is the basis for lactase persistence throughout the entire milk-drinking world. e. The east African -13910 C>T mutation diffused into Indian and then westward into Europe around 15 kya.
Answers
The dominant gene coding for adult lactase persistence in Europe and India is the east African -13910 C>T mutation diffused into Indian and then westward into Europe around 15 kya. The correct option is e.
In European popular and other areas population the lactase productions in body being continued throughout the life for lactase persistence. If we focus only on the European population a single -13,910×T genetic variant strongly associated with lactase persistence.
This genetic variant helps in natural adaptation. Enhancer region for the transcription of LCT is MCM6 which is upstream to LCT . In east Africa -13910 C>T mutation occurs which diffuse to India and western Europe. Option (a) is incorrect because this mutation indicate the high quantity of lactating animals and option (b) is incorrect because the mutation occurs in upstream region.
Therefore, option (e) is correct as mentioned above.
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y-4=-3(x+2)
y= -3/2x+1
y-1=-3x
3x+y=1
Answers
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line
m = [tex]\frac{-2-4}{2-(-2)}[/tex] = [tex]\frac{-6}{2+2}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]
the line crosses the y- axis at (0, 1 ) ⇒ c = 1
y = - [tex]\frac{3}{2}[/tex] x + 1 ← equation of line
Answer:
The second one: y = -3/2x + 1
Hope this helps!
Step-by-step explanation:
( -2, 4 ) : ( 2, -2 )
Slope = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]
Slope = [tex]\frac{-2-4}{2 - ( -2)} =\frac{-6}{4} = - \frac{3}{2}[/tex]
y = [tex]-\frac{3}{2}x[/tex] + 1 ( + 1 is the y-intercept, where the graph intercepts the y axis... )
Sara is very popular and has several suitors. She doesn't really care much for any of them. Which one is most likely to be angry that Sara does not return her feelings
Answers
Among the suitors pursuing Sara, the one who is most likely to be angry that she does not return her feelings would be the suitor who has developed strong emotional attachment and expectations towards Sara.
When someone has strong emotional attachment and expectations towards another person, they invest more of their feelings and desires into the relationship. In this scenario, if one of Sara's suitors has developed deep feelings for her and has invested significant emotional energy into pursuing her, they are more likely to feel hurt, disappointed, and angry if Sara does not reciprocate their feelings.
The suitor who may feel the strongest negative emotions could be the one who had the highest expectations or believed they had a special connection with Sara. They might have invested a lot of time, effort, and interest into their pursuit, leading to a sense of entitlement or disappointment if their feelings are not returned.
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Jolene counts the cracks in the sidewalk while she walks to/from work. As she nears the front door of her office, she fears that she has miscounted the number of cracks and so she feels compelled to return to her house to recount the cracks. What disorder is Jolene likely suffering from
Answers
Based on the given information, Jolene's behavior is suggestive of obsessive-compulsive disorder (OCD).
Obsessive-compulsive disorder(OCD) is a mental health condition characterized by the presence of obsessions and/or compulsions. Obsessions are intrusive and unwanted thoughts, images, or urges that cause distress and anxiety.
In Jolene's case, her obsession revolves around the fear of miscounting the cracks in the sidewalk. Compulsions, on the other hand, are repetitive behaviors or mental acts performed in response to obsessions, with the goal of reducing anxiety or preventing a feared outcome.
Jolene's compulsion is the urge to return home to recount the cracks, driven by her fear of having miscounted them.
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Margot missed 25% of the free throw shots in a season during the season she took a total of 90 free-throw shots find a number free throw shot Marco Mr. the nearest whole number
Answers
Answer:
She made 67 shots
She missed 23 shots
Step-by-step explanation:
Margot missed 90(0.25) = 22.5, or about 23 shots
Margot made 90-23 = 67
At the start of the week, Crystal’s bank account had a balance of $280. Each day from Monday to Friday, she used her debit card to pay $5 for parking. She wrote a check for $42, and made two deposits of $75 each. She also withdrew $200 in cash at an ATM. Which of the following expressions can be used to find the balance in Crystal’s account? Select all that apply.
Answers
The expressions used to find the balance in Crystal’s account are given as follows:
B) 280 + 5(–5) + (–42) + 2(75) + (–200)
C) 280 + 5(–5) – 42 + 2(75) – 200
How to obtain the balance?At the start of the week, Crystal’s bank account had a balance of $280. Each day from Monday to Friday, she used her debit card to pay $5 for parking, hence $5 was subtracted each day, that is:
280 - 5 x 5.
She wrote a check for $42, and made two deposits of $75 each, hence these amounts are also accounted, as follows:
280 - 5(5) -42 + 2(75)
$200 is withdrawn in cash, hence:
280 - 5(5) -42 + 2(75) - 200.
Missing InformationThe options are given as follows:
A) 280 + 5(5) + (–42) + 2(–75) + (–200)
B) 280 + 5(–5) + (–42) + 2(75) + (–200)
C) 280 + 5(–5) – 42 + 2(75) – 200
D) 280 + 5(–5) – 42 + 2(–75) – 200
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six baseball teams each have a certain amount of money to buy new baseballs and bats for the upcoming season baseballs cost $6 and bats cost $25. each inequality represents a team
situation in relation to the number of bats purchased. order the teams from teast to greatest based on the maximum number of baseballs they can purchase.
x. 2(125) 500
x + 6(125) 966
x 4(125) 1000
x + 4(125) 740
x + 3(125) 750
x + 3(125) 1200
Answers
The teams are ordered from least to greatest based on the maximum number of baseballs they can purchase as follows: Team 4, Team 5, Team 2, Team 1, Team 6, and Team 3.
In order to determine the order of the teams based on the maximum number of baseballs they can purchase, let's analyze the given inequalities.
The inequalities provided are:
x ≤ 2(125) + 500
x + 6(125) ≤ 966
x ≤ 4(125) + 1000
x + 4(125) ≤ 740
x + 3(125) ≤ 750
x + 3(125) ≤ 1200
To simplify the inequalities, we can perform the calculations:
x ≤ 750
x ≤ 366
x ≤ 1500
x ≤ 240
x ≤ 375
x ≤ 925
Now, let's order the teams based on the maximum number of baseballs they can purchase:
Team 4: The inequality x ≤ 240 indicates that this team can purchase a maximum of 240 baseballs.
Team 5: The inequality x ≤ 375 allows this team to buy up to 375 baseballs.
Team 2: With the inequality x ≤ 366, this team can purchase a maximum of 366 baseballs.
Team 1: The inequality x ≤ 750 allows this team to buy up to 750 baseballs.
Team 6: The inequality x ≤ 925 indicates that this team can purchase a maximum of 925 baseballs.
Team 3: With the inequality x ≤ 1500, this team has the highest capacity to buy baseballs, with a maximum of 1500.
Therefore, the teams are ordered from least to greatest based on the maximum number of baseballs they can purchase as follows: Team 4, Team 5, Team 2, Team 1, Team 6, and Team 3.
In summary, the teams are ordered from least to greatest based on the maximum number of baseballs they can purchase: Team 4, Team 5, Team 2, Team 1, Team 6, and Team 3. Team 4 can buy a maximum of 240 baseballs, Team 5 can buy up to 375 baseballs, Team 2 can purchase a maximum of 366 baseballs, Team 1 can buy up to 750 baseballs, Team 6 can purchase a maximum of 925 baseballs, and Team 3 has the highest capacity, being able to buy a maximum of 1500 baseballs.
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The Reagan doctrine of American activism in the Third World was most particularly exercised in a Grenada and Nicaragua b the Philippines and South Africa c Iran and Saudi Arabia d Venezuela and the Dominican Republic e Korea and Vietnam
Answers
The Reagan doctrine of American activism in the Third World was most particularly exercised in Nicaragua and Grenada. These countries became focal points of U.S. involvement and intervention.
The Reagan doctrine, implemented during the presidency of Ronald Reagan in the 1980s, aimed to counter Soviet influence and promote American interests in the Third World. This doctrine was characterized by a strong anti-communist stance and support for anti-communist governments and movements. Among the various countries where the Reagan doctrine was applied, Nicaragua and Grenada stand out as prime examples.
In Nicaragua, the Reagan administration actively supported the Contras, a rebel group fighting against the Sandinista government. The Contras were seen as a counterforce to the left-wing Sandinistas, who were aligned with the Soviet Union and Cuba. The United States provided financial and military assistance to the Contras, including covert operations, in an effort to undermine the Sandinista regime.
Grenada, a small island nation in the Caribbean, also witnessed American intervention under the Reagan doctrine. The United States launched Operation Urgent Fury, invading Grenada and overthrowing the government, with the stated objective of protecting American citizens and restoring democracy.
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the bottom of the inside of a rectangular prism is completely covered with the layers of the letter cubes are shown. The edges of a cube are 1 and 1/2 inches long. Please explain all and answer Part A and B.
Answers
Part A : The length and width of the bottom of the inside of the prism would be = 7½ in and 3.5 in
Part B : The total number of cubes of letter that can fit into the height of the prism = 6
How to calculate the length and width of the base of the given prism?For Part A:
The edges of each cube = 1½ in long
The number of cubes that makes up the base length of the prism = 5 cubes.
The length of the base of the prism = 1½×5 = 7.5 in
The number of cubes that makes up the base width of the prism = 3 cubes.
The width of the base of the prism = 1½×3 = 4.5 in
For Part B;
The total height of the prism = ¾ft
To convert to inches = ¾×12 = 9in
But 1 box = 1½ in
X box = 9 in
X box = 9/1.5
= 6 letter cube boxes
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if x=2 and t=4 what is the value of 1/8 (x^3 - 4) (t^2 + 8)?
Answers
Answer:
12
Step-by-step explanation:
Finding the 'value' means we need to calculate a number answer.
1/8 (x^3 - 4) (t^2 + 8)
Fill in 2 for x and 4 for t.
=1/8(2^3 - 4)(4^2 + 8)
inside of parenthesis we'll work on exponents first.
= 1/8 (8 - 4) (16 + 8)
Still inside of parenthesis, do the subtracting or adding next.
= 1/8 (4) (24)
This is all multiplying.
= 12
Who has the best conclusion?A.Joe said the average grade was a 75.B.Collin said almost 15% made between a 91 and a 100.C.Paulina said most of the class made between a 71 and a 80.D.Quannah said that most of the students understood the concepts that were not tested.
Answers
Based on the given grade distribution, Paulina's conclusion (C) that most of the class made between a 71 and an 80 is the best conclusion among the options provided.
What is the average?
This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
To determine who has the best conclusion among Joe, Collin, Paulina, and Quannah, let's evaluate each statement in relation to the given grade distribution:
A. Joe said the average grade was a 75.
Since we have the grade distribution, we can calculate the average grade to verify Joe's statement. However, the distribution alone is not sufficient to determine the average grade. We would need additional information such as the exact values within each grade range. Therefore, we cannot determine if Joe's conclusion is the best based solely on the given information.
B. Collin said almost 15% made between a 91 and a 100.
Based on the given grade distribution, we can calculate the percentage of students who fall within the range of 91-100. In this case, it is 10 students out of a total of 35 students. So, the percentage is approximately 28.6%, not close to 15%. Therefore, Collin's conclusion is not accurate based on the given information.
C. Paulina said most of the class made between a 71 and an 80.
Considering the grade distribution, the largest number of students (12) falls within the range of 71-80. Thus, Paulina's conclusion aligns with the data and can be considered the best conclusion based on the given information.
D. Quannah said that most of the students understood the concepts that were not tested.
The given grade distribution does not provide information about the understanding of concepts. It solely represents the distribution of grades. Therefore, Quannah's conclusion cannot be determined based on the given information.
hence, Based on the given grade distribution, Paulina's conclusion (C) that most of the class made between a 71 and an 80 is the best conclusion among the options provided.
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Two years from now, Country F hopes its GDP will be in the millions. If its present GDP is $975,875 and it has a growth rate of 11% annually, what will Country F's GDP be in 2 years
Answers
In two years, Country F's GDP is projected to be in the millions.
Currently, its GDP stands at $975,875, and it experiences an annual growth rate of 11%. Based on these figures, Country F's GDP in two years can be calculated.
To determine the GDP in two years, we need to calculate the growth rate for each year and apply it to the current GDP.
The growth rate is given as 11% annually, which means it is compounded over each year. To calculate the growth rate, we can use the formula:
GDP in two years = Current GDP × (1 + Growth Rate)^Number of Years
Plugging in the values, we get:
GDP in two years = $975,875 × (1 + 0.11)^2
Simplifying the equation, we have:
GDP in two years = $975,875 × 1.11^2
Evaluating the expression, we find:
GDP in two years ≈ $1,131,586
Therefore, based on the given growth rate of 11% annually, Country F's GDP is projected to be approximately $1,131,586 in two years.
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John purchased a vehicle for business and personal use. In 2021, he used the vehicle 70% for business (11,000 business miles incurred equally throughout the year) and calculated his vehicle expenses using the standard mileage rate. John also paid $1,800 in interest and $600 in county property tax on the car. What is the total business deduction related to business use of the car
Answers
The total business deduction related to the business use of the car would be $6,160, which represents the deductible vehicle expenses calculated based on the standard mileage rate.
To determine the total business deduction related to the business use of the car, we need to calculate the deductible expenses based on the percentage of business use.
First, let's calculate the deductible vehicle expenses using the standard mileage rate. In 2021, the standard mileage rate was $0.56 per mile.
John used the vehicle for 11,000 business miles (70% of total miles). Therefore, the deductible vehicle expenses can be calculated as follows:
Deductible Vehicle Expenses = Business Miles × Standard Mileage Rate
= 11,000 miles × $0.56 per mile
= $6,160
Next, let's consider the interest expense and county property tax paid on the car. Since these expenses are not directly related to the business use of the vehicle, they cannot be deducted as a business expense.
Therefore, the total business deduction related to the business use of the car would be $6,160, which represents the deductible vehicle expenses calculated based on the standard mileage rate.
It's important to note that tax deductions can be subject to specific rules and limitations, and it's advisable for John to consult with a tax professional or accountant to ensure accurate reporting and compliance with applicable tax laws and regulations.
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my cousin when in Vietnam was a personal banker for his Army buddies ... if they needed money mid-month he would give them $20 if you agreed to pay him $40 at month end on payday ... although he did not disclose his borrowing rate, what was the cost of money (APR) for his buddies who needed immediate gratification
Answers
The personal banker given lending arrangement, the APR for your cousin's buddies who borrowed $20 and repaid $40 at the end of the month would be 120%
The annual percentage rate (APR) for your cousin's lending arrangement, to make a few assumptions. That each lending transaction occurs on the first day of the month and is repaid on the last day of the same month. Based on these assumptions, calculate the effective APR as follows:
Calculate the interest charged for a $20 loan over one month:
Interest = $40 (repaid amount) - $20 (loaned amount) = $20
Divide the interest by the loan amount and multiply by 100 to get the monthly interest rate:
Monthly Interest Rate = (Interest / Loan Amount) ×100 = ($20 / $20) ×100 = 100%
Multiply the monthly interest rate by 12 to obtain the annual interest rate:
APR = Monthly Interest Rate ×12 = 100% ×12 = 120%
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convert 19.235ten to bicimals of 4 decimal places
Answers
The whole number part of 19.235 in base 2 is obtained by repeatedly dividing the number by 2 and recording the remainders until the quotient becomes 0.
19 divided by 2 equals 9 with a remainder of 1.
9 divided by 2 equals 4 with a remainder of 1.
4 divided by 2 equals 2 with a remainder of 0.
2 divided by 2 equals 1 with a remainder of 0.
1 divided by 2 equals 0 with a remainder of 1.
Reading the remainders from bottom to top, we get the whole number part in base 2 as 10011.
For the fractional part, we multiply the fractional part by 2 and record the whole number part of the result. We repeat this process until we achieve the desired number of decimal places.
0.235 * 2 = 0.47 (whole number part is 0)
0.47 * 2 = 0.94 (whole number part is 0)
0.94 * 2 = 1.88 (whole number part is 1)
0.88 * 2 = 1.76 (whole number part is 1)
Reading the whole number parts from left to right, we get the fractional part in base 2 as 0011.
Putting it all together, the bicimal representation of 19.235 to 4 decimal places is 10011.0011.
80 athletes are running a race. a gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. assume that there are no ties. in how many possible ways can the 3 medals be distributed?
Answers
Answer:
82160
combinations
Step-by-step explanation:
order doesn't matter since it is just who gets the medals not what order they get the medals in and pick 3 with no repetitions since no one ties or gets 2 medals at once
Part a. what is the main idea of sonia soto-mayor's opening statement? a.sonia feels the role of a judge is to fairly apply the law to benefit the public good b. sonia is most proud of her work as a judge for the southern district of new york c. sonia enjoys newfound popularity since being nominated for justice position. part b. what text best supports the answer to part a? a. "since president obama announced my nomination in may, i have received letters from people all over the country" b. "those decisions have not been made to serve the interests of any one litigant, but always to serve the larger interest of impartial justice." c. "as a trial judge, i did decide over 450 cases and presided over dozens of trials, with perhaps my most famous case being the major league baseball strike in 1995."
Answers
The main idea of Sonia Sotomayor's opening statement is that the role of a judge is to fairly apply the law to benefit the public good.
The text that best supports the answer to part a is option b: "those decisions have not been made to serve the interests of any one litigant, but always to serve the larger interest of impartial justice." This statement highlights Sonia Sotomayor's belief that the decisions she has made as a judge have been guided by the principle of impartial justice rather than favoring any specific party. This aligns with the main idea mentioned in part a, which states that Sonia believes the role of a judge is to fairly apply the law for the public good. By emphasizing that her decisions serve the larger interest of impartial justice, she underscores the importance of her commitment to fairness and the public's well-being. This reinforces the idea that Sonia's primary focus as a judge is on upholding the law for the benefit of society rather than personal or partisan interests.
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Simplify the following expression: (-5)^-4 x 3^-4
Answers
Answer:
1/50625
Step-by-step explanation:
First (5x3)^4
15^-4, which is 1/15^4
when multiplied out is 1/50625
What is the value of 22 11 + 11 × 3?
Answers
Answer:
= 2,244?
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