Answers
Answer:
See attachments.
Step-by-step explanation:
The quickest way to sketch the given functions, given that the coordinate plane is restricted to -5 ≤ x ≤ 5, is to substitute the values of x into the functions to find the points for the given interval. Plot these points on the given coordinate plane, and draw a continuous curve through the points.
Part (a)Given function:
[tex]y=\dfrac{5}{x}-2, \quad x > 0[/tex]
Substitute the values of x = 1, x = 2, x = 3, x = 4 and x = 5 into the function:
[tex]\begin{aligned}x=1 \implies y&=\dfrac{5}{1}-2\\&=5-2\\&=3\end{aligned}[/tex]
[tex]\begin{aligned}x=2 \implies y&=\dfrac{5}{2}-2\\&=2.5-2\\&=0.5\end{aligned}[/tex]
[tex]\begin{aligned}x=3 \implies y&=\dfrac{5}{3}-2\\&=-0.333...\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies y&=\dfrac{5}{4}-2\\&=1.25-2\\&=-0.75\end{aligned}[/tex]
[tex]\begin{aligned}x=5 \implies y&=\dfrac{5}{5}-2\\&=1-2\\&=-1\end{aligned}[/tex]
Plot the points (1, 3), (2, 0.5), (3, -0.333...), (4, -0.75) and (5, -1) on the given coordinate plane and draw a continuous curve through them.
End behaviour:
As x approaches 0 from the positive side, x tends to ∞.As x approaches ∞, y approaches -2.[tex]\hrulefill[/tex]
Part (b)Given function:
[tex]y=\dfrac{-2}{x+1}+3, \quad x < -1[/tex]
Substitute the values of x = -2, x = -3, x = -4 and x = -5 into the function:
[tex]\begin{aligned}x=-2 \implies y&=\dfrac{-2}{-2+1}+3\\&=2+3\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}x=-3 \implies y&=\dfrac{-2}{-3+1}+3\\&=1+3\\&=4\end{aligned}[/tex]
[tex]\begin{aligned}x=-4 \implies y&=\dfrac{-2}{-4+1}+3\\&=0.666...+3\\&=3.666...\end{aligned}[/tex]
[tex]\begin{aligned}x=-5 \implies y&=\dfrac{-2}{-5+1}+3\\&=0.5+3\\&=3.5\end{aligned}[/tex]
Plot the points (-2, 5), (-3, 4), (-4, 3.666...) and (-5, 3.5) on the given coordinate plane and draw a continuous curve through them.
End behaviour:
As x approaches -1 from the negative side, x tends to ∞.As x approaches -∞, y approaches 3.
Related Questions
¿De cuántas maneras es posible formar los grupos del torneo de liga de futbol de primera división? Recordemos que en la primera división del futbol en México participan 18 equipos, y para el torneo de la liga se forman dos grupos de cinco equipos y dos grupos de 4 equipos. Se sugiere que al resolverlo se vaya restando la cantidad de equipos que se han considerado para el primer grupo, después para el segundo grupo y así para cada grupo. Finalmente aplicar la regla del producto para encontrar las diferentes formas.
Answers
Note that his is solved using the principle of Combination, and there are 771, 891, 120 different ways to form the groups for the first division soccer league tournament in Mexico.
How is this so ?Let 's compute the number of ways to form the groups using combinations.
First group - 5 teams
C(18, 5) = 18! / (5! * (18-5)!) = 8568
Second group - 5 teams
C(13, 5) = 13! / (5! * (13-5)!) = 1,287
Third group - 4 teams
C(8, 4) = 8! / (4! * (8-4)!) = 70
Fourth group - 4 teams
C(4, 4) = 4! / (4! * (4-4)!) = 1
Now, applying the product rule
Total ways = 8568 x 1,287 x 70 x 1 = 771891120
Therefore, there are 771, 891, 120 different ways to form the groups for the first division soccer league tournament in Mexico.
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Translation
In how many ways is it possible to form the groups of the first division soccer league tournament? Let's remember that 18 teams participate in the first division of soccer in Mexico, and for the league tournament, two groups of five teams and two groups of 4 teams are formed. It is suggested that when solving it, the number of teams that have been considered for the first group be subtracted, then for the second group and so on for each group. Finally apply the product rule to find the different shapes.
In a class of 42 students, the number of boys is 2/5 of the girls. Find the number of boys and girls in the class.
Answers
Answer:
BOYS = 30.
GIRLS = 12.
Step-by-step explanation:
Boys: B
Girls: G
B = (2/5)G
B + G = 42.
(2/5)G + G = 42
2G + 5G = 210
7G = 210
G = 210/7
G = 30.
B = (2/5)G
B = (2/5)(30)
B = 60/5
B = 12.
Answer:
[tex]\Huge \boxed{\bold{\text{12 Boys}}}[/tex]
[tex]\Huge \boxed{\bold{\text{30 Girls}}}[/tex]
Step-by-step explanation:
Let the number of girls be [tex]g[/tex] and the number of boys be [tex]b[/tex].
According to the problem: [tex]b = \frac{2}{5} \times g[/tex]
We also know that the total number of students is 42, so [tex]b + g = 42[/tex].
Now, we have two equations with two variables:
[tex]b = \frac{2}{5} \times g[/tex] [tex]b + g = 42[/tex]We can solve these equations to find the values of [tex]b[/tex] and [tex]g[/tex].
Step 1: Solve for [tex]\bold{b}[/tex] in terms of [tex]\bold{g}[/tex]
From the first equation, we have[tex]b = \frac{2}{5} \times g[/tex]
Step 2: Substitute the expression for [tex]\bold{b}[/tex] into the second equation
Replace [tex]b[/tex] in the second equation with the expression we found in step 1.
[tex]\frac{2}{5} \times g + g = 42[/tex]
Step 3: Solve for [tex]\bold{g}[/tex]
Now, we have an equation with only one variable, [tex]g[/tex]:
[tex]\frac{2}{5} \times g + g = 42[/tex]
To solve for [tex]g[/tex], first find a common denominator for the fractions:
[tex]\frac{2}{5} \times g + \frac{5}{5} \times g = 42[/tex]
Combine the fractions:
[tex]\frac{7}{5} \times g = 42[/tex]
Now, multiply both sides of the equation by [tex]\frac{5}{7}[/tex] to isolate [tex]g[/tex]:
[tex]g = 42 \times \frac{5}{7}[/tex][tex]g = 30[/tex]Step 4: Find the value of [tex]\bold{b}[/tex]
Now that we have the value of [tex]g[/tex], we can find the value of [tex]b[/tex] using the first equation:
[tex]b = \frac{2}{5} \times g[/tex][tex]b = \frac{2}{5} \times 30[/tex][tex]b = 12[/tex]So, there are 12 boys and 30 girls in the class.
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you are riding your bike and notice the square sign above. You mentally draw a straight line from point A to C. Describe the angle relationship between DCA and BCA?
Answers
The angle relationship between DCA and BCA is that they are congruent.
What is an angle bisector?In Mathematics and Geometry, an angle bisector is a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
Generally speaking, the diagonals of a rhombus are angle bisectors. In this context, we can logically deduce that the two (2) angles that would result from the bisection of angle C by a straight line are congruent.
By applying the angle bisector theorem to the given square sign (rhombus ABCD) below, we would have the following congruent angles;
∠DCA ≅ ∠BCA
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The following is a parallelogram. What does A=, B=, X=, QR= and Angle QRS=
Answers
Answer:
a = 4
b=2
x=18
QR =16+1=17
Angle QRS =59
Step-by-step explanation:
4a+1 = 2a + 9
2a = 8
a = 4
6b = 11b-10
-5b=-10
-b= -2
b=2
6x+13 = 7x - 5 (opposite angles are equal)
-x=-18
x=18
QR =16+1=17
Angle QRS = 180 - 18•6+13 =59 (PQR + QRS = 180)
|x – 4| > –3 will have what type of solution set
Answers
Answer:
The inequality |x – 4| > –3 represents an absolute value inequality.
The absolute value of any real number is always non-negative, meaning it is greater than or equal to zero. Therefore, the left side of the inequality, |x – 4|, will always be greater than or equal to zero.
Since the right side of the inequality, -3, is also greater than or equal to zero, this means that the inequality |x – 4| > –3 holds true for all real numbers x. In other words, there are no restrictions on the value of x.
The solution set for this inequality is the set of all real numbers, often represented as (-∞, +∞).
Answer:
(−∞,∞)
Step-by-step explanation:
|x – 4| > – 3
Since |x – 4| is always positive and - 3 is negative, |x – 4| is always greater than - 3, so the inequality is always true for any value of x.
All real numbers
The result can be shown in multiple forms.
All real numbers
So, the answer is (−∞,∞)
NO LINKS!! URGENT HELP PLEASE!!!
4. Use the theorems for interior and exterior angles of a polygon to find:
a. The sum of the interior of a 73-gon.
b. The number of sides of a regular polygon if the sum of the interior angles is 2700°
c. The number of sides of a reguluar polygon if the exterior angle is 7.2°
Answers
Answer:
see explanation
Step-by-step explanation:
a
the sum of the interior angles of a polygon is calculated as
sum = 180° (n - 2) ← n is the number of sides
here n = 73 , then
sum = 180° × (73 - 2) = 180° × 71 = 12,780°
b
here sum of interior angles = 2700° , then
180° (n - 2) = 2700° ( divide both sides by 180° )
n - 2 = 15 ( add 2 to both sides )
n = 17
number of sides is 17
c
the sum of the exterior angles of a polygon = 360°
given the polygon is regular then each exterior angle is congruent , so
number of sides = 360° ÷ 7.2° = 50
Answer:
a) 12870°
b) 17
c) 50
Step-by-step explanation:
Part aThe Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.
The number of sides of a 73-gon is n = 73. Therefore, the sum of its interior angles is:
[tex]\begin{aligned}\textsf{Sum of the interior angles of a 73-agon}&=(73-2) \cdot 180^{\circ}\\&=71 \cdot 180^{\circ}\\&=12870^{\circ}\end{aligned}[/tex]
Therefore, the sum of the interior angles of a 73-gon is 12870°.
[tex]\hrulefill[/tex]
Part bThe Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.
Given the sum of the interior angles of a regular polygon is 2700°, then:
[tex]\begin{aligned} \textsf{Sum of the interior angles}&=2700^{\circ}\\\\\implies (n-2) \cdot 180^{\circ}&=2700^{\circ}\\n-2&=15\\n&=17\end{aligned}[/tex]
Therefore, the number of sides of the regular polygon is 17.
[tex]\hrulefill[/tex]
Part cAccording the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.
Therefore, to find the number of sides of a regular polygon given its exterior angle is 7.2°, divide 360° by the exterior angle.
[tex]\begin{aligned}\textsf{Number of sides}&=\dfrac{360^{\circ}}{\sf Exterior\;angle}\\\\&=\dfrac{360^{\circ}}{7.2^{\circ}}\\\\&=50\end{aligned}[/tex]
Therefore, the number of sides of the regular polygon is 50.
Multiply: −6ab3(a5b2−2a4b−10ab−7).
Answers
Answer:
--6a^6b^5+12a^5b^4+60a^2b^4+42ab^3
Step-by-step explanation:
6
a
6
b
5
+
12
a
5
b
4
+
60
a
2
b
4
+
42
a
b
3
solve the following system of equations (3x-5Y = -22) (4x +2y = 14)
Answers
The solution of the System of equation are,
⇒ x = 1
⇒ y = 5
We have to given that;
System of equation are,
⇒ 3x - 5y = - 22
⇒ 4x + 2y = 14
Now, We can simplify as;
From (ii);
2x + y = 7
y = 7 - 2x
Put above value in (i);
3x - 5 (7 - 2x) = - 22
3x - 35 + 10x = - 22
13x = - 22 + 35
13x = 13
x = 1
From (i);
⇒ 3x - 5y = - 22
⇒ 3 - 5y = - 22
⇒ 3 + 22 = 5y
⇒ 25 = 5y
⇒ y = 5
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2.2.3 State one reason why a student would choose to study in a province different from their home province
Answers
Answer:
Step-by-step explanation:
There are several reasons why a student would choose to study in a province different from their home province. Some of the reasons include:
To gain a new perspective and experience different cultures.
To take unique classes that are not available in their home province.
To learn history through immersive experiences.
To improve their ability to adapt.
To gain independence.
To gain international experience and a global network.
To immerse themselves in another language.
From 1980 to 2008, the number of federally insured banks could be approximated by B(t)=-328.2t+13716 where t is the year and t=0 corresponds to 1980.
How many federally insured banks were there in 1985?
Find the slope of the graph of B.
Interpret this slope as a rate of change. Choose the correct answer below.
The number of banks increased by 13716 banks per year
The number of banks decreased by 12075 banks per year
The number of banks increased by 328.2 banks per year
The number of banks increased by 12075 banks per year
The number of banks decreased by 328.2 banks per year
The number of banks decreased by 13716 banks per year
Find the y-intercept of the graph of B.
The y-intercept is
Interpret the y-intercept. Choose the correct answer below.
The y-intercept is the number of banks in 1985
The y-intercept is the maximum number of banks allowed in the country
The y-intercept is the minimum number of banks allowed in the country
The y-intercept is the number of banks in 2008
The y-intercept is the number of banks in 1980
Answers
Answer:
To find the number of federally insured banks in 1985, we need to substitute t = 1985 into the equation B(t) = -328.2t + 13716:
B(1985) = -328.2 * 1985 + 13716
B(1985) = -648537 + 13716
B(1985) = 7122
So, there were approximately 7122 federally insured banks in 1985.
The slope of the graph of B represents the rate of change. From the equation B(t) = -328.2t + 13716, we can see that the slope is -328.2. Therefore, the interpretation of the slope as a rate of change is: "The number of banks decreased by 328.2 banks per year."
The y-intercept of the graph of B represents the value of B when t = 0, which corresponds to the year 1980. From the equation B(t) = -328.2t + 13716, the y-intercept is 13716. Therefore, the interpretation of the y-intercept is: "The y-intercept is the number of banks in 1980."
What is the answer please
Answers
The volume of the cylinder with a height of 12 cm and a diameter of 8 cm is approximately 602.19 cm³.
How to find the volume of the cylinder of heightTo calculate the volume of a cylinder, you can use the formula:
Volume = π * (radius²) * height
Given that the diameter of the cylinder is 8 cm, the radius (r) can be calculated by dividing the diameter by 2:
radius (r) = 8 cm / 2 = 4 cm
The height (h) of the cylinder is 12 cm.
substitute these values into the formula:
Volume = π * (4 cm)² * 12 cm
Volume = π * 16 cm² * 12 cm
Volume ≈ 602.19 cm³ (rounded to two decimal places)
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D. Determining the best job to take based on the pay. when considering a new job. a. Job A is 40 hours per week and pays $15 per hour (gross pay) with no tips. b. Job B is 30 hours per week and pays $5 per hour (gross pay) plus tips (which average $350 per week).
Answers
The job A is the best job based on pay scale
Given data ,
a) Job A:
Hours per week: 40
Hourly rate: $15
On simplifying the equation , we get
Gross pay per week: 40 hours * $15/hour = $600
b) Job B:
Hours per week: 30
Hourly rate: $5
On simplifying the equation , we get
Gross pay per week: 30 hours * $5/hour = $150
In addition to the base pay, Job B also offers tips averaging $350 per week.
Considering the total compensation for each job:
Total compensation for Job A: $600 per week (base pay)
Total compensation for Job B: $150 per week (base pay) + $350 per week (tips) = $500 per week
Based on the total compensation, Job A offers a higher gross pay of $600 per week, while Job B offers a total compensation of $500 per week.
Hence , if the decision is solely based on pay, Job A would be the better choice.
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Find the inverse function Y = x² for x>0
Answers
Answer:
y= √x--------------
Given function:
y = x²In order to find its inverse, first swap x and y:
y = x² ⇒ x = y²Then solve for y:
y² = xy = √xThe inverse function is y= √x.
The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995.
Year Retail Sales
0 85.851
3 108.426
6 141.781
9 169.256
12 202.297
15 222.266
Let
be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t)= 9.44 t +84.182.
Use the above scatter plot to decide whether the linear model fits the data well.
The function is not a good model for the data
The function is a good model for the data.
Estimate the retails sales in the U. S. in 2016.
billions of dollars.
Use the model to predict the year that corresponds to retails sales of $241 billion.
Answers
The function is a good model for the data.
The retail sales in the U.S. in 2016 is estimated to be 282.24 billion dollars.
The year that corresponds to retail sales of $241 billion is 2020.
How to calculate the valueThe function F(t)= 9.44 t +84.182 is a linear model for the data. This means that the graph of the function is a straight line.
The scatter plot shows that the data points are close to a straight line. This means that the function is a good model for the data.
To estimate the retail sales in the U.S. in 2016, we need to find the value of F(11). F(11) = 9.44 * 11 + 84.182
= 282.24.
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To compare freshmen’s knowledge of mathematics in two departments of a university, a certain professor in Mathematics got a sample of Education and Nursing students and gave a special examination. A sample of 25 Education students has a mean score of 88.50 with standard deviation of 7.5. A sample of 29 Nursing students have a mean score of 90.25 with a standard deviation of 8.2. Is there a significant difference between the two sample means? Use α = .01 level of significance.
Answers
There is no significant difference between the mean scores of Education and Nursing students in mathematics.
Is there a significant difference between the mean scores?Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.
Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.
We will use significance level (α) of 0.01.
Given:
Sample mean for Education students (x₁) = 88.50
Sample mean for Nursing students (x₂) = 90.25
Standard deviation for the Education student sample (s₁) = 7.5
Standard deviation for the Nursing student sample (s₂) = 8.2
Sample size for Education students (n₁) = 25
Sample size for Nursing students (n₂) = 29
The t-test statistic for two independent samples is:
t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))
t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))
t ≈ -0.8187
In this case, df = 24.
The critical value for α = 0.01 and df = 24 is approximately ±2.797.
Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.
Therefore, we fail to reject the null hypothesis.
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which is larger the number of meters in the Milky Way or the number of cells in all humans
Answers
Answer:
the number of meters in the milky way
Step-by-step explanation:
becuse the world is infinite
Hi! I usually wouldn't ask for homework help but I have been stuck on this section for quite a few hours now and I'm really unsure as to how I should answer it. Thank you! :)
Answers
Answer:
1) 5/6
2) 19/30
3) They are mutually exclusive.
Step-by-step explanation:
Let's break the diagram down.
We have four types of smoothies:
Contains apple but not blueberry - 12
Contains blueberry but not apple - 7
Contains both blueberry and apple - 3
Doesn't contain either - 8
From here, we find that there are 30 smoothies in total.
In addition, we know that the number of smoothies containing an apple is 15, and the number of smoothies containing blueberry is 10.
Therefore,
[tex]P(\text{contains apple}) = \frac{\text{contains apple}}{\text{total}} = \frac{15}{30} = \frac12\\\\P(\text{contains blueberry}) = \frac{\text{contains blueberry}}{\text{total}} = \frac{10}{30} = \frac13\\\\\text{a) } P(\text{contains apple}) + P(\text{contains blueberry}) = \frac12 + \frac13 = \frac36 + \frac26 = \frac56[/tex]
Now, the probability of getting apple OR strawberry is given by adding the probabilities of getting one of the flavors but not the other.
[tex]P(\text{apple, no blueberry}) = \frac{12}{30}\\\\P(\text{blueberry, no apple}) = \frac{7}{30}\\\\P(\text{apple or blueberry}) = \frac{12}{30} + \frac7{30} = \frac{19}{30}[/tex]
We can check if the events are mutually exclusive using the formula:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In our case, A means contains apple, and B means contains blueberry.
[tex]P(A \cup B)[/tex] resembles the case for exclusively apple or exclusively blueberry (AKA our answer for b).
[tex]P(A \cap B)[/tex] resembles the case for both apple and blueberry (AKA the intersection), which is equal to 3/30 = 1/10.
If the two sides are equal, the cases are not mutually exclusive.
[tex]\frac{19}{30} = \frac{15}{30} + \frac{10}{30} - \frac{3}{30}\\\\\frac{19}{30} \ne \frac{22}{30}[/tex]
Therefore, the events are mutually exclusive.
There are 2 companies in town that seem to have a reasonable deal on fencing.
Company 1 will charge $200 for the first 150 ft of fencing and $18 for each additional
foot. Company 2 will charge you $450 for the first 75 ft of fencing and $15 for each
additional foot. Determine which company has the better deal. Provide evidence to
support your answer..
Answers
To determine which company offers the better deal, we compare the total costs for different amounts of fencing. Company 1 has a better deal for less than 608 ft of fencing, while Company 2 is more cost-effective for 608 ft or more.
To determine which company offers the better deal for fencing, we need to compare the total cost for a specific amount of fencing between the two companies.
Let's consider the amount of fencing required as "x" feet.
Company 1 charges $200 for the first 150 ft of fencing and $18 for each additional foot. So, the total cost for x feet of fencing with Company 1 can be calculated as:
Cost1 = $200 + $18 × (x - 150)
Company 2 charges $450 for the first 75 ft of fencing and $15 for each additional foot. Thus, the total cost for x feet of fencing with Company 2 is:
Cost2 = $450 + $15 × (x - 75)
To determine which company offers the better deal, we need to find the range of x values for which Cost1 is less than Cost2. Let's set up the inequality:
Cost1 < Cost2
$200 + $18 × (x - 150) < $450 + $15 × (x - 75)
Now, we can solve this inequality to find the range of x values where Company 1's cost is less than Company 2's cost.
$200 + $18x - $2700 < $450 + $15x - $1125
Combining like terms:
$18x - $2499 < $15x - $675
Subtracting $15x from both sides:
$3x - $2499 < - $675
Adding $2499 to both sides:
$3x < $1824
Dividing both sides by $3 (since x represents feet, we can ignore the currency):
x < $1824 / $3
x < 608
Therefore, for any value of x less than 608 feet, Company 1 has a better deal. However, when x is equal to or greater than 608 feet, Company 2 offers a better deal.
To provide evidence supporting this answer, let's consider an example:
Suppose we need 200 feet of fencing.
Using Company 1:
Cost1 = $200 + $18 × (200 - 150)
Cost1 = $200 + $18 × 50
Cost1 = $200 + $900
Cost1 = $1100
Using Company 2:
Cost2 = $450 + $15 × (200 - 75)
Cost2 = $450 + $15 × 125
Cost2 = $450 + $1875
Cost2 = $2325
In this example, Company 1's cost is $1100, while Company 2's cost is $2325. Hence, for 200 feet of fencing, Company 1 provides the better deal.
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The graph shows the number of weeks of practice () and the number of
shote missed in a free throw drill (). The equation of the trend line that best
fits the data is y- +6. Predict the number of missed shots after 8
weeks of practice.
A.3
B.2
C.4
D.5
Answers
Answer:
B. 2
Step-by-step explanation:
You want the predicted number of missed shots after 8 weeks if the trend line equation is ...
y = -1/2x +6
PredictionUsing x=8 in the given equation, we find the prediction to be ...
y = -1/2(8) +6 = -4 +6 = 2
The number of missed shots is predicted to be 2.
__
Additional comment
We can see that the trend line (red) goes through the point (8, 2). That tells you the prediction is 2 missed shots at 8 weeks of practice.
<95141404393>
Warm-Up
What is the approximate area of the shaded region?
Select the correct answer.
O 15.45 cm²
O69.53 cm²
128.54 cm²
18 cm
182.47 cm²
4
Answers
Answer:
The answer is 69.63cm²
Step-by-step explanation:
d=18
r=d/2=18/2=9cm
Area of shaded portion =Area of square -Area of circle
A=18²-pi×9²
A=69.53cm²
Answer:
69.53 centimeters squared.
Step-by-step explanation:
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
To solve for the area of the shaded region, we must figure out what the length and width is. Assuming this is a square, the length and width of the shape are 18cm. To solve for the area of a square, we can use the formula:
Area = [tex]side^{2}[/tex]Inserting 18 as our side length:
Area = [tex]18^{2}[/tex] = 324Therefore, the area of the square without the circular gap is 324 [tex]cm^{2}[/tex].
To solve for the area of a circle, we can use the formula:
Area = π[tex]r^{2}[/tex]But wait, we are given the diameter, not the radius!
No worries, the radius is simply half the size of the diameter, so we can just divide 18 by 2.
18 ÷ 2 = 9Inserting 9 into the formula for the radius:
Area = π × [tex]9^{2}[/tex] = 81π = 254.47 (Rounded to 2 decimal points)Now we can subtract this from the squares area.
324 - 254.47 = 69.53The closest to match this approximation is [tex]69.53cm^{2}[/tex].
Gift Wrapping A gift box has the shape of a rectangular prism. How much wrapping
paper do you need to cover the box?
You need
in.2 of paper to cover the box.
C
16 in
12 in
Answers
Answer:
608 in²
Step-by-step explanation:
To figure out how much wrapping paper we need to cover the box, we can find its surface area.
The surface area of a rectangular prism (a box) is defined as:
[tex]SA = 2A + (P \cdot d)[/tex]
where [tex]A[/tex] is the area of the base, [tex]P[/tex] is the perimeter of the base, and [tex]d[/tex] is the prism's depth.
From the diagram, we can identify the following values for these variables:
[tex]A=16\cdot 12 = 192 \text{ in}^2[/tex]
[tex]P = 16 + 12 + 16 + 12 = 56 \text{ in}[/tex]
[tex]d = 4\text{ in}[/tex]
Now, we can plug these values in for the variables in the above formula and solve for the prism's surface area.
[tex]SA = 2A + (P \cdot d)[/tex]
[tex]SA = 2(192) + (56 \cdot 4)[/tex]
[tex]SA = 384 + 224[/tex]
[tex]SA = 608 \text{ in}^2[/tex]
So, we need 608 in² of paper to cover the box.
What is the meaning of "[tex]ran(R)=\left \{ v:\exists u(u,v) \in R\right \}[/tex]"?
Answers
The meaning of ran R = { v : there exist u, (u, v) ∈ R} is,
⇒ Defined as v, there exist u such that an order pair (u, v) is belon in relation R
We have to given that;
The meaning of,
⇒ ran R = { v : there exist u, (u, v) ∈ R}
Since, WE know that;
''ran R'' is stand for range of relation R.
Which is defined as,
⇒ ran R = { v : there exist u, (u, v) ∈ R}
That's mean,
Let us defined as v, there exist u such that an order pair (u, v) is belon in relation R.
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Slope of Linear Equations
Which description best compares the graph given by the following equations:
5x-3y = -5
2x-y = 8
parallel
perpendicular
intersecting but not perpendicular
Answers
5x - 3y = -5
2x - y = 8
is "intersecting but not perpendicular."
A manufacturer has 576 square inches of material available to construct the 6 faces of a carton, which will be in the shape of a rectangular prism. To maximize the volume, the carton will have dimensions such that the length and width are each twice the height.
Answers
To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).
What is the dimension required to maximize the volume of the box?Assuming the height of the rectangular prism is h inches.
According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.
The total surface area of the rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the values, we have:
576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)
576 = 8h² + 4h² + 4h²
576 = 16h² + 4h²
576 = 20²
h² = 576/20
h² = 28.8
h = √28.8
h = 5.37
The height of the prism is approximately 5.37 inches.
The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.
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Solve for x
:
Sophie recently ran a marathon. It took her 5.2 hours to run the 26.2 miles required to complete a marathon.
Find her average speed in miles per hour. Then convert her speed to feet per second. (Hint: 1 mile = 5,280 feet).
(Round your answers to two decimal places)
4x+c=7d
Answers
The average speed of Sophie in miles per hour is 5.04 miles per hour.
The speed in feet per second is 7.39 feet per second.
Given that,
Sophie recently ran a marathon.
It took her 5.2 hours to run the 26.2 miles required to complete a marathon.
Total distance ran = 26.2 miles
Total time taken = 5.2 hours
Speed = Total distance / Total time
= 26.2 / 5.2
= 5.04 miles per hour
Speed in feet per second = (5.04 × 5280 feet) / 3600 seconds
= 7.39 feet per second
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How many ways can you arange 2 Letters picked
from A, B, C, D? order matters
Answers
When selecting 2 letters from the set {A, B, C, D}, considering that the order matters, we can use the concept of permutations to calculate the number of possible arrangements.
The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of items (in this case, 4) and r is the number of items being selected (in this case, 2).
Using this formula, the number of ways to arrange 2 letters from A, B, C, D is:
P(4, 2) = 4! / (4 - 2)!
= 4! / 2!
= (4 x 3 x 2 x 1) / (2 x 1)
= 24 / 2
= 12
Therefore, there are 12 possible ways to arrange 2 letters selected from A, B, C, D when considering that the order matters.
~~~Harsha~~~
Answer:
Step-by-step explanation:
When selecting 2 letters from the set {A, B, C, D} and considering that the order matters, we can determine the number of possible arrangements using the concept of permutations.
The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
where P(n, r) represents the number of permutations of r objects chosen from a set of n objects.
In this case, we have n = 4 (the total number of letters) and r = 2 (the number of letters to be selected).
Using the formula, we can calculate:
P(4, 2) = 4! / (4 - 2)!
= 4! / 2!
= (4 × 3 × 2 × 1) / (2 × 1)
= 24 / 2
= 12
Therefore, there are 12 different ways to arrange 2 letters chosen from the set {A, B, C, D} when the order matters.
sett up 12-5*9√49-5²
Answers
Answer:
-328
Step-by-step explanation:
Simply use BODMAS or BIDMAS; this is the order of your operations. It is an acronym that tells you what to do in what order
Brackets: there are no brackets, move on to indices/order
Indices/Order: for the first step, do 5^2, which is 25, and √49, which is 7. The equation is no 12-5*9(7)-25
Division/Multiplication: For this step, multiply 5, 9 and 7 to get 315. The equation is now 12-315-25
Addition/subtraction: For the final step, just solve 12-315-25 in the traditional left to right way, which is -328.
I have grouped addition and subtraction as well as division and multiplication together because they are done at the same time; if a question has either both addition and subtraction or division and multiplication, just solve these parts from left to right. Division is not superior to multiplication and, likewise, addition is not above subtraction.
classify the polynomial
Answers
The classification of the given polynomial is cubic polynomial, the correct option is C.
We are given that;
The equation=3x^3-x^2-x+4
Now,
Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
Degree of 3x^3=3
Degree of x^2=2
Degree of x=1
The heighest degree of the polynomial is three of 3x^3.
Therefore, by the polynomial the answer will be cubic polynomial.
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Derivative for 2/x is ?
Answers
Answer:
[tex]-2x^{-2} \ \text{or} \ -\frac{2}{x^2}[/tex]
Step-by-step explanation:
Find [tex]\frac{d}{dx}[\frac{2}{x} ][/tex].
(1) - Pull out the constant
[tex]\frac{d}{dx}[\frac{2}{x} ]\\\\\Longrightarrow 2\frac{d}{dx}[\frac{1}{x} ][/tex]
(2) - Flip the fraction
[tex]2\frac{d}{dx}[\frac{1}{x}]\\\\\Longrightarrow 2\frac{d}{dx}[x^{-1}][/tex]
(3) - Apply the power rule]
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right}\\\\\\2\frac{d}{dx}[x^{-1}]\\\\\Longrightarrow 2[(-1)x^{-1-1}]\\\\\Longrightarrow 2[-x^{-2}]\\\\\therefore \boxed{\boxed{\frac{d}{dx}[\frac{2}{x} ] =-2x^{-2} \ \text{or} \ -\frac{2}{x^2}}}[/tex]
Thus, the problem is solved.
What is the value of y?
A right triangle has a vertical leg labeled square root of 2 with its opposite angle labeled 45 degrees. A second right triangle has a leg that is the hypotenuse of the first right triangle. At the top of the leg is a 60 degree angle with opposite side labeled y and at the bottom of the leg is the right angle.
Enter your answer, as an exact value, in the box.
y =
Answers
The value of y is 2 * √3.
In the second right triangle, we have a 60-degree angle and a leg opposite to that angle labeled y. The hypotenuse of the first right triangle is equal to the leg of the second right triangle.
Let's denote the hypotenuse of the first right triangle as h. From the first right triangle, we know that the vertical leg is equal to the square root of 2.
Using trigonometric ratios, we can relate the sides of a right triangle as follows:
sin(angle) = opposite/hypotenuse
In the first right triangle, the angle is 45 degrees, and the opposite side is the square root of 2. Therefore, we have:
sin(45 degrees) = √2 / h
By rearranging the equation, we can solve for h:
h = √2 / sin(45 degrees)
Using the value of sin(45 degrees) = 1/√2, we can simplify the equation:
h = √2 / (1/√2) = √2 * √2 = 2
Now, we can find the value of y in the second right triangle. Since the hypotenuse of the first right triangle is equal to the leg of the second right triangle, we have:
y = 2 * √3
Therefore, the value of y is 2 * √3.
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