Therefore, the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.9732 or 97.32%.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.
Here,
Let μ be the mean tariff rate of all railroad-car shipments of ethanol, and let x be the mean tariff rate of a random sample of 600 railroad-car shipments of ethanol. We want to find the probability that x will be within $90 of μ.
The standard error of the mean (SE) can be calculated as:
SE = σ / √(n)
where σ is the standard deviation of the population, n is the sample size.
Substituting the given values, we get:
SE = 1150 / √(600)
≈ 47.03
The probability that x will be within $90 of μ can be calculated by standardizing x using the standard error and the z-score formula:
z = (x - μ) / SE
z = ($90) / 47.03
≈ 1.915
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.915 is approximately 0.9732.
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Jamie and Polly share £24 in the ratio 2:3. Work out how much money Jamie gets.
Answer:
Jamie gets £9.60
Step-by-step explanation:
sum the parts of the ratio, 2 + 3 = 5 parts
divide the amount by 5 to find the value of one part of the ratio.
£24 ÷ 5 = £4.80 ← value of 1 part of the ratio , then
2 parts = 2 × £4.80 = £9.60 ← amount Jamie gets
From a standard deck of 52 cards, in how many ways can 7 cards be drawn?
there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.
How to solve the question?
The number of ways to draw 7 cards from a standard deck of 52 cards can be calculated using the combination formula, which is:
C(52, 7) = 52! / (7! * (52-7)!)
where "!" represents the factorial function.
To simplify this expression, we can use the property that n! / k! = n * (n-1) * (n-2) * ... * (n-k+1) for positive integers n and k such that k ≤ n.
Using this property, we can rewrite the above expression as:
C(52, 7) = (52 * 51 * 50 * 49 * 48 * 47 * 46) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
Simplifying this expression, we get:
C(52, 7) = 133,784,560
Therefore, there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.
To understand why this is the case, we can think of each draw as a separate event with no replacement. The first card can be drawn in 52 ways, the second card can be drawn in 51 ways (since one card has already been drawn), the third card can be drawn in 50 ways (since two cards have already been drawn), and so on. Therefore, the total number of ways to draw 7 cards is the product of the number of ways to draw each individual card, which is 52 * 51 * 50 * 49 * 48 * 47 * 46. However, since the order in which the cards are drawn does not matter, we need to divide by the number of ways to arrange 7 cards, which is 7 * 6 * 5 * 4 * 3 * 2 * 1 (i.e., 7 factorial). This gives us the final answer of 133,784,560.
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poppy seed muffins 1
cinnamon rolls 3
bran muffins 2
apple fritters 2
croissants 2
Considering this data, how many of the next 20 pastries served should you expect to be bran muffins?
We can expect 4 of the next 20 pastries served to be bran muffins based on the given data.
What is meant by the term data?
Data refers to a collection of facts, statistics, measurements, or observations that are gathered and analyzed to gain insights or information about a particular topic or subject. Data can be both quantitative (numerical) and qualitative (descriptive) in nature, and it can be obtained from various sources, such as surveys, experiments, sensors, or records. The processing and interpretation of data can lead to new discoveries, trends, or predictions in various fields, including science, business, and technology.
According to the given information
The proportion of bran muffins out of the total pastries served can be calculated by dividing the number of bran muffins by the total number of pastries:
The proportion of bran muffins = 2 / (1 + 3 + 2 + 2 + 2) = 2 / 10 = 0.2
This means that 20% of the pastries served are bran muffins. To find out how many of the next 20 pastries served should be expected to be bran muffins, we can multiply 20% by 20:
The number of expected bran muffins = 0.2 * 20 = 4
Therefore, we can expect 4 of the next 20 pastries served to be bran muffins based on the given data.
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A checkout clerk at a department store is expected to complete 16 transactions every hour.
In the past 20 minutes, he completed 6 transactions.
Choose True or False for each statement.
Statements:
If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.
At his current rate, the clerk will complete 12 transactions in 1 hour.
At his current rate, the clerk will complete 9 transactions every half hour.
If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.
✓ - True If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.
➜ This is true. The clerk is currently going at 6 transactions per 1/3 hours. 6 * 3 = 18, and 18 > 16.
✗ - False At his current rate, the clerk will complete 12 transactions in 1 hour.
➜ This is false. As stated above, he will complete 18.
✓ - True At his current rate, the clerk will complete 9 transactions every half hour.
➜ Let us set up a proportion to check. Then we will cross-multiply and solve.
[tex]\frac{20\;min}{6} =\frac{30\;min}{x}[/tex]
180 = 20x
x = 9
➜ Yes, he will complete 9 every half hour.
✗ - False If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.
➜ We can utilize a proportion again. 6 hours is equal to 360 minutes. Then, we will cross-multiply and solve.
[tex]\frac{20\;min}{6} =\frac{360\;min}{x}[/tex]
20x = 2,120
x = 106
➜ He will complete 106 transactions, not 96. It depends on if they're asking for exactly 96 or at least 96.
EASY ALGEBRA 2 !! PLEASE HELP
according to the question the balance in the account earning compound interest after 6 years is $4,156.22.
what is interest ?Multiply the principal with the rate of interest, the time period, and various other factors to determine simple interest. Simple returns = money + interests + hours is the marketing formula. This approach makes calculating interest the simplest. The approach to calculating interest that is most usually employed is as a percentage over the principal sum. For instance, he will just pay his share of the interest at 100% when he borrows $100 with a friend and agrees to shell out it back with 5% interest. $100 has been reduced to $5 (0.05). Every time you borrow money, you must pay interest, which is applied to whatever loans you make. On the loan balance, interest is typically calculated using an annual percentage.
given,
To calculate the balance in the account earning compound interest after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the sum of money at the end of the period of time
P stands for the principle (beginning sum).
the decimal representation of the annual interest rate (r).
n represents how many times the interest rate is compounded annually.
t is the duration (in years).
In this case, we have:
P = $3500 (the principal)
r = 2.16% = 0.0216 (the annual interest rate)
Since interest is compounded four times a year (quarterly), n is equal to four.
t = 6 (the time period is 6 years)
With these values entered into the equation, we obtain:
A = 3500(1 + 0.0216/4)^(4*6)
A = $4,156.22
Therefore, the balance in the account earning compound interest after 6 years is $4,156.22.
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The balance in the account earning compound interest after 6 years when the principal is $3500 at an annual interest rate of 2.16% compounded quarterly is approximately $4,029.53.
What is compound interest?Compound interest is the term used to describe the interest that is calculated on both the initial investment and any accumulated interest. It is interest on top of interest, to put it another way.
We can use the formula for compound interest to find the balance in the account after 6 years:
A = P(1 + r/n)^(nt)
where:
A = balance after 6 years
P = principal = $3500
r = annual interest rate = 2.16%
n = number of compounded times per year = 4 (quarterly)
t = time in years = 6
Plugging in the values, we get:
A = 3500(1 + 0.0216/4)^(4×6)
A ≈ $4,029.53
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Addition Property of Equality:
If AB = CD, then AB + EF =
The Addition Property of Equality allows us to add EF to both sides of the equation without changing its truth, giving us AB + EF = CD + EF.
We have,
The Addition Property of Equality states that if we add the same quantity to both sides of an equation, the equation remains true.
In the given equation,
AB = CD, we can add the same quantity, EF, to both sides of the equation to obtain:
AB + EF = CD + EF
This is because if two quantities are equal, and we add the same amount to both of them, the result is still equal.
Therefore,
The Addition Property of Equality allows us to add EF to both sides of the equation without changing its truth, giving us AB + EF = CD + EF.
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Solve for x. I attached the image. Pls help :(
Based on the intersecting chords, the calculated value of x on the circle is 11
Calculating the value of x in the circleThe given shape in the question is a circle
As a general rule, a circle is a shape with all points on its boundary equidistant from a central point called the center
In this case, the center is point W
The sum of angles on the circumference is 360
So, we have
17x - 20 + 75 + 2 * 59 = 360
Evaluating the like terms, we have
17x = 187
Divide by 17
x = 11
Hence. the value of x is 11
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The circular bases of the traditional teepees of the Sioux and Cheyenne tribes have a diameter of about 15 ft. What is the area of the base? Round to the nearest square unit.
A. 707ft2
B. 47ft2
C. 24ft2
D.177ft2
Answer:
D. 177 ft²
Step-by-step explanation:
the area of a circle is
pi×r²
r is the radius which is half of the diameter, of course.
so, in our case
area = pi×(15/2)² = pi×7.5² = pi×56.25 =
= 176.7145868... ft² ≈ 177 ft²
The ratio of the weight of an object on earth to the weight of the same object on planet X is a 5 to 12 if an elephant weighs 3800 pounds on earth find the elephant weight on planet X ?
We can set up a proportion using the given ratio:
Weight on Earth : Weight on Planet X = 5 : 12
Let's let x be the weight of the elephant on Planet X. We can substitute the given weight on Earth to solve for x:
3800 : x = 5 : 12
We can cross-multiply to get:
3800 * 12 = 5 * x
Simplifying the right side, we get:
45600 = x * 5
Dividing both sides by 5, we get:
x = 9120
Therefore, the weight of the elephant on Planet X is 9120 pounds.
The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges 30 to mow a lawn that took him 1.5 hours to mow.
Which equation models the amount in dollars, d, Troy charges when it takes him h hours to mow a lawn?
The amount Troy (D, in dollars) charges to mow a lawn is proportional to the time (H, in hours) it takes him to mow the lawn.
Hence, we can write [tex]\text{D = kH}[/tex] ......... (1), where k is a constant.
Now, given that Troy charges $30 to mow a lawn that took him 1.5 hours to mow.
So, from equation (1) we get
[tex]{30 = 1.5\text{k}[/tex]
[tex]\rightarrow \text{k = 20}[/tex].
Therefore, equation (1) becomes
[tex]\boxed{\bold{D = 20H}}[/tex] (Answer)
Eastern Manufacturing is involved with several situations that possibly involve contingencies. Each is described below. Eastern’s fiscal year ends December 31, and the 2024 financial statements are issued on March 15, 2025.
The income statement, and stockholders equity are given below.
We have to show the income statement
The income statement for Coyote Corporation for the year ended December 31, 2024, is as follows:
Coyote Corporation
Income Statement
For the Year Ended December 31, 2024
Service Revenue $55,000
Less: Expenses
Salaries Expense $27,000
Rent Expense $6,000
Utilities Expense $6,000
Interest Expense $5,000
Total Expenses $44,000
Net Income $11,000
The statement of stockholders' equity for Coyote Corporation for the year ended December 31, 2024, is as follows:
Coyote Corporation
Statement of Stockholders' Equity
For the Year Ended December 31, 2024
Retained Earnings, December 31, 2023 $35,000
Add: Net Income for 2024 $11,000
Less: Dividends $0
Retained Earnings, December 31, 2024 $46,000
Classified Balance Sheet:
Assets
Current Assets
Cash $27,000
Accounts Receivable $26,000
Prepaid Rent $6,000
Supplies $5,000
Total Current Assets $64,000
Property, Plant, and Equipment
Land $55,000
Total Property, Plant, and Equipment $55,000
Total Assets $119,000
Liabilities and Stockholders' Equity
Current Liabilities
Accounts Payable $90,000
Salaries Payable $375,000
Interest Payable $6,000
Total Current Liabilities $471,000
Long-term Liabilities
Notes Payable (due in two years) $55,000
Total Liabilities $526,000
Stockholders' Equity
Common Stock $35,000
Retained Earnings $46,000
Total Stockholders' Equity $81,000
Total Liabilities and Stockholders' Equity $119,000
Therefore, the classified balance sheet for Coyote Corporation as of December 31, 2024, is as follows:
Coyote Corporation
Classified Balance Sheet
As of December 31, 2024
Assets
Current Assets
Cash $27,000
Accounts Receivable $26,000
Prepaid Rent $6,000
Supplies $5,000
Total Current Assets $64,000
Property, Plant, and Equipment
Land $55,000
Total Property, Plant, and Equipment $55,000
Total Assets $119,000
Liabilities and Stockholders' Equity
Current Liabilities
Accounts Payable $90,000
Salaries Payable $375,000
Interest Payable $6,000
Total Current Liabilities $471,000
Long-term Liabilities
Notes Payable (due in two years) $55,000
Total Liabilities $526,000
Stockholders' Equity
Common Stock $35,000
Retained Earnings $46,000
Total Stockholders' Equity $81,000
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complete question:
Kindly check if the photo below of income statement is wrong and correct which one is wrong in a excel or anything that makes it clear to me.
look at the picture below
The surface area of the composite solid is given as follows:
194 units squared.
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The prism in this problem is composed as follows:
Rectangular prism of dimensions 4, 7 and 3.Two right triangles of dimensions 4 and 3.One square of side length 5.One rectangle of dimensions 5 and 7.Hence the surface area of the prism is given as follows:
S = 2(4 x 7 + 4 x 3 + 3 x 7) + 4 x 3 + 5² + 5 x 7
S = 194 units squared.
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Q13
Steve receives £200 each month from his parents as an allowance.
20% of this amount is spent on his football magazine subscription, and the rest he spends on football stickers,
sweets, and fizzy drinks in the ratio of 5: 2: 1.
How much does Steve spend on football stickers?
Step-by-step explanation:
Steve spends 20% of £200 = 0.2 * £200 = £40 on his football magazine subscription.
The remaining amount he spends on football stickers, sweets, and fizzy drinks in the ratio of 5:2:1, which means that for every 5 parts he spends on football stickers, he spends 2 parts on sweets and 1 part on fizzy drinks.
So, let's call the amount he spends on football stickers "5x". Then, the amount he spends on sweets is "2x" and the amount he spends on fizzy drinks is "x".
The total amount he spends on these items is:
5x + 2x + x = 8x
We know that he has £200 - £40 = £160 left after paying for his magazine subscription. So, we can set up an equation:
8x = £160
Solving for x, we get:
x = £20
Therefore, Steve spends:
5x = 5 * £20 = £100
on football stickers.
Can you mark me asbrainliest if you appreciate my effort just for favor. Thank you^^
Answer:
5 : 2 : 1 = 100 : 40 : 20
Step-by-step explanation:
10% = 20 (200÷10=20)
20% = 40 (double both sides)
take away £40 from £200 = £160
£160 is left over after buying the magazine subscription
______________________________
add the radio all together = 5:2:1 = 8
divide 8 by 160 = £20
That now means 1 = 20
5 : 2 : 1
we already found 1, now to find 2 and 5
you times 2
1 = 20
2 = 40
and then do the same for 5
1 = 20
5 = 100
To know this is right, 100 + 40 + 20 = 160 the original number for the money left over.
Which ordered pair (x,y) could not be substituted in the relation below so that the relation is functional (6,7),(-2,9),(8,8),(-4,9),(x,y) a. (9,9) b. (2,9) c (7,8) d. (8,3)
None of the answer choices would result in an x-value being associated with two different y-values, the correct answer is:
e. None of the above.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To check whether the relation is functional, we need to make sure that each x-value is associated with only one y-value.
We can see that the pairs (6,7), (-2,9), (8,8), and (-4,9) all have different x-values, and therefore are associated with different y-values. This means that the relation is currently functional.
To determine which ordered pair could not be substituted so that the relation is functional, we need to find an x-value that is associated with two different y-values.
Let's look at each of the answer choices and see if they fit this criteria:
a. (9,9): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.
b. (2,9): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.
c. (7,8): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.
d. (8,3): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.
Since none of the answer choices would result in an x-value being associated with two different y-values, the correct answer is:
e. None of the above.
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Find the area of the regular polygon
Round to nearest tenth
On solving the provided question we can say that area of the polygon is 24 cm sq.
What is quadrilateral?A four-sided polygon having four edges and four corners is referred to as a quadrilateral. The word is derived from the Latin words quadri and latus, both of which imply "side". An object with a rectangle's four sides, four vertices, and four corners is a two-dimensional shape. There are essentially two sorts of concave and convex surfaces. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up the two-dimensional shape of a rectangle. There are many different shapes for quadrilaterals, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
Area of this polygon is -
A = 1/2 * 6* 8
A = 24 cm sq.
Hence, area of the polygon is 24 cm sq.
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Given f’(x)=-4x - 5 compute. F(3)- f(-1)
Answer:
-36
Step-by-step explanation:
To solve this problem, we need to integrate f'(x) to find f(x), and then evaluate f(3) and f(-1) to compute the expression f(3) - f(-1).
Integrating f'(x)=-4x - 5 with respect to x, we get:
f(x) = -2x^2 - 5x + C
Where C is the constant of integration.
To find the value of C, we can use the initial condition f(0) = 1. Substituting x = 0 and f(x) = 1 into the equation above, we get:
1 = -2(0)^2 - 5(0) + C
1 = C
So, we have:
f(x) = -2x^2 - 5x + 1
Now, we can evaluate f(3) and f(-1) and compute f(3) - f(-1):
f(3) = -2(3)^2 - 5(3) + 1 = -32
f(-1) = -2(-1)^2 - 5(-1) + 1 = 4
f(3) - f(-1) = (-32) - 4 = -36
Therefore, f(3) - f(-1) = -36.
Answer:
-36
Step-by-step explanation:
You want F(3) -F(1) given f'(x) = -4x -5.
IntegralThe desired difference is the definite integral ...
[tex]\displaystyle \int_{-1}^3{(-4x-5)}\,dx=\left[-2x^2-5x\right]_{-1}^3=-2(9-1)-5(3+1)\\\\=\boxed{-36}[/tex]
<95141404393>
. The formula 9x - 5y = -160 relates the
temperature in degrees Fahrenheit y to
the temperature in degrees Celsius x.
Tell whether the relationship is a direct
variation. Explain your answer.
The given formula 9x - 5y = -160 is not in the form of direct variation.
Calculating the type of variationThe given formula 9x - 5y = -160 relates the temperature in degrees Fahrenheit y to the temperature in degrees Celsius x.
To determine whether the relationship is a direct variation or not, we need to consider the definition of direct variation.
A relationship is said to be a direct variation if one variable is a constant multiple of the other variable, i.e., y = kx or x = ky, where k is a constant of proportionality.
However, the given formula is not in the form of direct variation. It is a linear equation in two variables, and there is no constant of proportionality present.
Hence, we can conclude that the given relationship is not a direct variation.
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What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.
A. 99 square meters
B. 122 square meters
C. 160 square meters
D. 553 square meters
The surface area of the cylinder to the nearest square meter include the following: C. 160 square meters.
How to calculate surface area of a cylinder?In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the formula for the surface area (SA) of a cylinder, we have the following;
Surface area = 2πrh + 2πr²
Surface area = 2(3.14)(2.8)(6.3) + 2(3.14)(2.8²)
Surface area = 160 square meters.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A car is purchased for $19,500. After each year, the resale value decreases by 20%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.
The resale value of the car after 3 years is $9,984.
How to find the resale value after 3 years?Since the resale value decreases by 20%. Thus, the resale value of the car will be 80% of its original value.
After the first year, the resale value of the car will be 80% of its original value:
Resale value after 1 year = 80/100 * $19,500 = $15,600
After the second year, the resale value of the car will be 80% of its value after the first year:
Resale value after 2 years = 80/100 * $15,600 = $12,480
After the third year, the resale value of the car will be 80% of its value after the second year:
Resale value after 3 years = 80/100 * $12,480 = $9,984
Therefore, the resale value of the car after 3 years will be $9,984.
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THE UNITE
VENOCH
Suppose you buy a $1000 bond with a 4.3% coupon that matures in 30 years.
1. First, how much do you earn off your bond every 6 months?
Type answer here...
SUBMIT
The amount (coupon interest) that is earned off the $1,000 bond with 4.3% coupon every 6 months is $21.50.
What is the coupon interest?The coupon interest represents the periodic payment received by a bondholder from the date of issuance until the date of maturity of a bond.
The coupon interest is computed by applying the coupon rate on the face value of the bond.
Face value of the bond = $1,000
Coupon interest rate = 4.3%
Maturity period = 30 years
Coupon (bond) interest for 6 months = $21.50 ($1,000 x 4.3% x 6/12)
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Mackenzie answered 72 questions correctly on her multiple choice math final that had a total of 160 problems. What percentage of questions did Mackenzie answer correctly on the final exam?
Answer:
45%
Step-by-step explanation:
72/160 = 0.45
0.45 x 100 = 45%
Find the circumference of a child swimming pool that has a radius of 3 feet
The circumference of a child swimming pool is 6π.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
Here, we have
Given: A child swimming pool that has a radius of 3 feet.
We have to find the circumference.
The circumference is diameter x π
The diameter is twice the radius
c = 2πr
c = 2π(3)
= 6π
Hence, the circumference of a child swimming pool is 6π.
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Springfield will be opening a new high school in the fall. The number of underclassmen (9th and 10th graders) must fall between 600 and 700
(inclusive), the number of upperclassmen (11th and 12th graders) must fall between 500 and 600 (inclusive), and the number of students cannot
exceed 1200. Let a represent the number of underclassmen and let b represent the number of upperclassmen. Write a set of inequalities that
models the constraints on the composition of the student body.
number of underclassmen:
number of upperclassmen:
Total number of students:
:: 600 < a < 700
000
:: 600 ≤ a ≤ 700
:: 500 ≤ b ≤ 600
:: a + b ≤ 1200
:: 500 < b < 600
:: a + b > 1200
= a + b < 1200
:: a + b > 1200
The correct set of inequalities that model the constraints on the composition of the student body are:
600 ≤ a ≤ 700, 500 ≤ b ≤ 600 and a + b ≤ 1200
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The correct set of inequalities that model the constraints on the composition of the student body are:
600 ≤ a ≤ 700 (the number of underclassmen must fall between 600 and 700, inclusive)
500 ≤ b ≤ 600 (the number of upperclassmen must fall between 500 and 600, inclusive)
a + b ≤ 1200 (the total number of students cannot exceed 1200)
Note that the inequalities 600 < a < 700 and 500 < b < 600 are not correct, as they do not take into account the inclusive limits of the ranges for the number of underclassmen and upperclassmen. Also, the inequality a + b > 1200 is not correct, as it contradicts the previous inequality a + b ≤ 1200.
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100 Points! Algebra question, photo attached. Only looking for an answer to B. Please show as much work as possible. Thank you!
Answer:f/g=29
Step-by-step explanation:
Answer: (f/g)=29
Hope this helps
Select all the correct answers. If the measure of angle is , which statements are true? The measure of the reference angle is . The measure of the reference angle is . The measure of the reference angle is . 0 =9/2
The statement cos(theta) = √3/2 is correct.
Which statement is correct?Angles are the angles formed by 2 bisecting lines or surfaces at or near their intersection.
The following information has been provided:
The angle (theta) = [tex]\frac{2\pi }{3}[/tex] measurement has been given to us.
We must determine which propositions are true by determining the measure of angle (theta) = [tex]\frac{2\pi }{3}[/tex]
cos(theta) = [tex]\frac{\sqrt{3} }{2}[/tex]
= cos30
theta = 30
tan(theta)= [tex]-\sqrt{3} = tan(90 + 30)[/tex]
tan(theta) = tan120
theta = 120
sin(theta) = [tex]-\frac{1}{2}[/tex] = [tex]cos(90 + 30)[/tex]
sin(theta) = sin120
theta = 120
Therefore the correct statement is cos(theta) = √3/2
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Complete question:
The measure of angle(theta) Is 2pi/3, which statements are true?
cos(theta) = √3/2
The measure of the reference angle is 30°.
The measure of the reference angle is 45°.
The measure of the reference angle is 60°.
tan(theta) = -√3
sin(theta)=-1/2
The product of 3 and the difference of a number and 8
The statement The product of 3 and the difference of a number and 8 as an expression is 3(x - 8)
From the question, we have the following parameters that can be used in our computation:
The product of 3 and the difference of a number and 8
Represent the number with x
So, we have
The product of 3 and the difference of x and 8
The difference of x and 8 means x - 8
So, we have
The product of 3 and x - 8
The product of 3 * (x - 8)
So, we have
3(x - 8)
Hence, the expression is 3(x - 8)
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the area of the parallelogram.
check the picture please.
Answer:
[tex]192[/tex] [tex]cm^2[/tex]
Step-by-step explanation:
Recall that the formula for the area of a parallelogram is:
[tex]A=bh[/tex]
Where b is the length of the base, and h is the length of the height.
We are given that the base is 24 cm.
So, b=24.
We are also given that the height is 8 cm.
So, h=8.
Let's plug these values into the formula:
[tex]A=bh=\\A=(24)(8)=\\A=192[/tex]
Since area is a two-dimensional measure, we need to label our answer using units squared.
Thus, the area is [tex]192[/tex] [tex]cm^2[/tex]
Area of a parallelogram => [tex]A=bh[/tex]
Where, b=24 cm and h=8 cm
Plug in the known values and solve.
[tex]\Longrightarrow A=bh \Longrightarrow A=(24 \ cm)(8 \ cm) \Longrightarrow A= \boxed{192 \ cm^2}[/tex]
can I ask for someone to help me please?
Here we have an exponential growth were the increase is of 26%, and it can be written as.
[tex]y = a*(1 + 0.26)^t[/tex]
How to rewrite the function?Here we want to rewrite the function
[tex]y = a*(2)^{t/3}[/tex]
In the given form for the general exponential, so let's do that.
We can expand the product to get:
[tex]y = a*(2)^{t/3}\\\\y = a*((2)^{1/3})^t\\\\y = a*(1.26)^t\\\\y = a*(1 + 0.26)^t[/tex]
To identify if it is a growth or a decay we need to see the sign of r (the thing we are adding to the 1) in this case is +0.26
When it is positive we have a growth, so here we have a growth.
And to get the percentage multiply that number by 100%, we will get:
0.25*100% = 26%
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(12, 6), (28, 8) slope
Step-by-step explanation:
slope, m = ( y1-y2) / (x1-x2) = ( 6-8) / (12-28) = -2 / -16 = 1/8
100 points and I will give brainlist but before I get released, I have to verify answers
A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.
The step in which Johnetta made her error include the following: A. step 1.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
Based on the information provided above, the division can be calculated as follows;
Fraction = (-5/8) ÷ (-3/4)
Fraction = -5/8 × (-4/3)
Fraction = -20/24
For Johnetta, we have:
Fraction = 7/9 ÷ 3/8
Fraction = 7/9 × 8/3
Fraction = 56/27
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