A line shape like a trapezoid has an area of 337. 5ft^2 if the length of the bases are 25 fr and 20 ft then the perpendicular distance between bases would be

Answers

Answer 1

The perpendicular distance between the bases of a trapezoid with an area of 337.5 ft² and base lengths of 25 ft and 20 ft is 15 ft.


Area = (1/2) * (Base1 + Base2) * Height

In this case, the area is 337.5 ft², Base1 is 25 ft, and Base2 is 20 ft. We need to solve for the height, which represents the perpendicular distance between the bases.

Plugging in the known values into the formula:

337.5 = (1/2) * (25 + 20) * Height

Simplifying the expression:

337.5 = (1/2) * (45) * Height

Multiplying both sides of the equation by 2 to get rid of the fraction:

675 = 45 * Height

Dividing both sides by 45 to solve for the height:

Height = 675 / 45

Height = 15 ft

Therefore, the perpendicular distance between the bases of the trapezoid is 15 ft.

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Related Questions

Some lemon, lime, and cherry lollipops are placed in a bowl. Some have a
chocolate center, and some do not. Suppose one of the lollipops is chosen
randomly from all the lollipops in the bowl. According to the table below, if it
is known to be lime, what is the probability that it does not have a chocolate
center?
OA. 35%
OB. 25%
O C. 45%
O D. 55%
See picture of diagram, I need this correct please help asap

Answers

Answer:

A (35%)

Step-by-step explanation:

Just divide what you want to find with the total. Does not have chocolate = 7. Total Lime = 20 (13 + 7) 7/20 = 0.35/35%

Ishaan tiene 2 veces la edad de Christopher.

Hace 35 años Ishaan tenía 7 veces la edad de

Christopher.

¿Cuántos años tiene Ishaan actualmente?

Answers

Ishaan's current age is 84.

How to solve for the current age

Let Ishaan's current age be I and Christopher's current age be C.

Given, I = 2C ...........(1) (Ishaan is twice the age of Christopher)

35 years ago, I - 35 = 7(C - 35) (Ishaan was 7 times the age of Christopher 35 years ago)

Simplifying the above equation, we get:

I - 35 = 7C - 245

I = 7C - 210 ...........(2)

Substituting equation (1) in equation (2), we get:

2C = 7C - 210

5C = 210

C = 42

Therefore, Christopher's current age is 42.

Substituting C = 42 in equation (1), we get:

I = 2C = 2(42) = 84

Therefore, Ishaan's current age is 84.

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The question is translated to English as

Ishaan is twice the age of Christopher. 35 years ago Ishaan was 7 times the age of Christopher. How old is Ishaan now?

In ΔMNO, the measure of ∠O=90°, OM = 1. 7 feet, and NO = 6. 7 feet. Find the measure of ∠N to the nearest degree

Answers

The measure of ∠N to the nearest degree is 82°.

Calculate the nearest degree?

To find the measure of ∠N, we can use the Pythagorean theorem and trigonometric functions.

First, we can use the Pythagorean theorem to find the length of MN:

MN² = NO² - OM²

MN² = (6.7 feet)² - (1.7 feet)²

MN² = 44.56 feet²

MN = 6.67 feet

Now, we can use the sine function to find the measure of ∠N:

sin(N) = MN/NO

sin(N) = 6.67 feet / 6.7 feet

sin(N) ≈ 0.994

N ≈ sin⁻¹(0.994)

N ≈ 82.4°

The measure of ∠N to the nearest degree is 82°.

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23. A triangular earring has side lengths of 1. 5 centimeters, 2 centimeters, and 3


centimeters. What is the approximate measure, in degrees, of the largest angle of the


triangular earring?


А


36. 3°


B.


45. 8°


C. 117. 3°


D.


134. 2°

Answers

Using cosine rule, the largest angle In the triangle is

C. 117. 3°

How to find the measure of the largest angle

The angle is found first using cosine rule by the formula

cos A = (b² + c² - a²) ÷ 2bc

Solving for the largest angle

substituting the values

cos γ = (2² + 1.5² - 3²) ÷ 2 * 1.5 * 2

< γ = arc cos ( -0.4583 )

< γ = 117.28 degrees

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How many people can fit in the passenger car of 70 feet and a width of 9 feet

Answers

Approximately 378 people can fit in a passenger car with a length of 70 feet and a width of 9 feet.

What is the volume of a car with a length of 70 feet and a width of 9 feet?

To determine the number of people who can fit in a passenger car with a length of 70 feet and a width of 9 feet, we need to consider the available space inside the car and the amount of space required per person.

Assuming that the passenger car is a rectangular box shape, the volume of the car can be calculated as follows:

Volume of car = Length x Width x Height

Since we are only interested in the number of people who can fit in the car, we will assume a standard height of 6 feet for simplicity. Therefore, the volume of the car can be calculated as follows:

Volume of car = 70 feet x 9 feet x 6 feet

Volume of car = 3,780 cubic feet

Next, we need to determine the amount of space required per person. This can vary depending on the seating arrangement and the size of the individuals, but as a general rule, we can estimate that each person requires approximately 10 to 12 cubic feet of space in a seated position.

Assuming we use the lower end of that estimate and allocate 10 cubic feet of space per person, we can calculate the number of people who can fit in the car as follows:

Number of people = Volume of car / Space per person

Number of people = 3,780 cubic feet / 10 cubic feet per person

Number of people = 378 people

Therefore, if we assume a standard height of 6 feet and allocate 10 cubic feet of space per person, approximately 378 people can fit in a passenger car with a length of 70 feet and a width of 9 feet. However, it is important to note that this is just an estimate and the actual number of people who can fit in the car will depend on factors such as the seating arrangement and the size of the individuals.

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andy can run 20 miles in 6 hours. how much miles can he run in 1 hour.

Answers

I see that this is a rate of change time of problem

If andy can run 20 miles in 6 hours, than our goal is to find out how much he runs in a hour

So, we just have to divide 20 by 6.

It's sorta hard to explain

Questions?

Anyhow, the answer is around 3.3 miles per hour

Answer:

3.33 miles

Step-by-step explanation:

We Know

Andy can run 20 miles in 6 hours.

How many miles can he run in 1 hour?

We Take

20 / 6 ≈ 3.33 miles

So, Andy can run about 3.33 miles in 1 hour.

Find the radius of the circle with equation x² + y² = 19²
r=0
Submit Answer

Answers

The radius of the circle of equation x² + y² = 19² is given as follows:

r = 19 units.

What is the equation of a circle?

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.

The equation of the circle in this problem is given as follows:

x² + y² = 19².

Hence the radius is obtained as follows, comparing to the general equation:

r² = 19²

r = 19 units.

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A person is working in the purchasing department of an appliance retailer. This month he is stocking up on washers and dryers. His


supervisor informs him that his budget this month is $12,000. He knows that the average wholesale cost of a washer over the past


year has been $250, while the average wholesale cost of a dryer has been $200. Complete parts a through h

Answers

a) What is the maximum number of washers the person can purchase within the budget?


To calculate the maximum number of washers the person can purchase within the budget, we divide the budget by the cost per washer:
$12,000 ÷ $250 = 48 washers

b) What is the maximum number of dryers the person can purchase within the budget?


To calculate the maximum number of dryers the person can purchase within the budget, we divide the budget by the cost per dryer:
$12,000 ÷ $200 = 60 dryers

c) If the person wants to purchase an equal number of washers and dryers, how many of each can he purchase?


To purchase an equal number of washers and dryers, we need to find the common factor of both 48 and 60:
48 = 2 x 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5

The common factor is 2 x 2 x 3 = 12. So, the person can purchase 12 washers and 12 dryers within the budget.

d) If the person purchases the maximum number of washers and dryers, what is the total cost of the purchase?


To calculate the total cost of the purchase, we multiply the maximum number of washers and dryers by their respective cost:
48 washers x $250 = $12,000
60 dryers x $200 = $12,000
The total cost of the purchase is $24,000.

e) If the person purchases an equal number of washers and dryers, what is the total cost of the purchase?


To calculate the total cost of the purchase, we multiply the number of washers and dryers by their respective cost:
12 washers x $250 = $3,000
12 dryers x $200 = $2,400
The total cost of the purchase is $5,400.

f) If the person wants to spend the entire budget on washers, how many washers can he purchase?


To spend the entire budget on washers, we divide the budget by the cost per washer:
$12,000 ÷ $250 = 48 washers

g) If the person wants to spend the entire budget on dryers, how many dryers can he purchase?


To spend the entire budget on dryers, we divide the budget by the cost per dryer:
$12,000 ÷ $200 = 60 dryers

h) If the person wants to spend the entire budget and purchase an equal number of washers and dryers, how many can he purchase?


To spend the entire budget and purchase an equal number of washers and dryers, we need to divide the budget by the sum of the cost per washer and cost per dryer, then find the common factor:

($12,000 ÷ ($250 + $200)) ÷ 2 = 18

The common factor of 18 is 2 x 3 = 6. So, the person can purchase 6 washers and 6 dryers within the budget.

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Use Newton's method to obtain the third approximation, X2, of the positive fourth root of 3 by calculating the third approximation of the right 0 of f(x)=x*- 3. Start with Xo = 1. The third approximation of the fourth root of 3 determined by calculating the third approximation of the right 0 of f(x) = x4 - 3, starting with Xo = 1, is (Round to four decimal places.) -

Answers

To use Newton's method to find the third approximation, X2, of the positive fourth root of 3, we follow these steps:

1. Define the function f(x) and its derivative, f'(x): f(x) = x^4 - 3 f'(x) = 4x^3

2. Start with an initial guess, X0 = 1.

3. Apply Newton's method formula to find the next approximations:

Xn+1 = Xn - f(Xn) / f'(Xn)

4. Calculate the first approximation, X1: X1 = X0 - f(X0) / f'(X0) X1 = 1 - (1^4 - 3) / (4 * 1^3) X1 = 1 - (-2) / 4 X1 = 1 + 0.5 X1 = 1.5

5. Calculate the second approximation, X2: X2 = X1 - f(X1) / f'(X1) X2 = 1.5 - (1.5^4 - 3) / (4 * 1.5^3) X2 = 1.5 - (5.0625 - 3) / 13.5 X2 = 1.5 - 2.0625 / 13.5 X2 = 1.5 - 0.15296 X2 ≈ 1.3470

So, the third approximation of the positive fourth root of 3, determined by calculating the third approximation of the right 0 of f(x) = x^4 - 3, starting with X0 = 1, is approximately 1.3470 (rounded to four decimal places).

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Your rate of pay is $36. Per hour and you bill by the quarter hour you spent four hour and 30 minutes on a client project how much would I bill for 162. Or 144

Answers

If your rate of pay is $36 per hour and you bill by the quarter hour, you would bill $162 for 4 hours and 30 minutes project.

Based on the given information, your rate of pay is $36 per hour, and you bill by the quarter hour. You spent 4 hours and 30 minutes on a client project.

To calculate the bill, first convert the 30 minutes into quarter hours: 30 minutes = 2 quarter hours. In total, you worked for 4 hours and 2 quarter hours (18 quarter hours).

Now, multiply your rate of pay ($36) by the number of quarter hours (18) and divide by 4 to account for the quarter hour billing: ($36 * 18) / 4 = $162. Therefore, you would bill the client $162 for the project.

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Drag each tile to the correct location, Determine the type of fee that will be charged In each situation. Joanne's brokerage firm charged her for providing investment information to help her make informed choices. Pete isn't a regular investor. He hasn't bought or sold any stock this year. His broker charged him an inacovity fee of $75 for the year. John's broker provided him with stock-trading software to manage his trading Lisa sold 50 shares of stock A on a given day. Her broker charged her $12 for this trade Reggie's broker charged him a front-end load of 2. 75% when he purchased a fund. Transaction Fee Non-transaction Fee 2021 Edmentum All rights reserved. ​

Answers

The type of fee that will be charged depends on the specific service provided by the broker to the client. Non-transaction fees are typically charged for account maintenance or access to investment tools, while transaction fees are charged for specific trades or transactions.

To determine the type of fee that will be charged in each situation, we need to consider the specific services that were provided by the broker to the client.

For Joanne, her brokerage firm charged her a fee for providing investment information to help her make informed choices. This type of fee is a non-transaction fee, as it is not related to a specific transaction or trade.

Pete, who hasn't bought or sold any stock this year, was charged an inactivity fee of $75 for the year by his broker. This fee is also a non-transaction fee, as it is not related to a specific trade but rather to the inactivity of the account.

John's broker provided him with stock trading software to manage his trading. This type of service is typically included in a brokerage firm's platform fee, which is a non-transaction fee that covers the cost of maintaining the software and other tools that clients can use to manage their investments.

Lisa sold 50 shares of stock A on a given day and her broker charged her $12 for this trade. This type of fee is a transaction fee, which is charged for each specific trade or transaction that a client makes.

Finally, Reggie's broker charged him a front-end load of 2.75% when he purchased a fund. This fee is a type of sales charge or commission that is applied to the initial investment and is considered a transaction fee.

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Question 10 > Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "DNE" 4 ( 1 -dz 22 +1 00

Answers

To determine the convergence of the integral 4(1-z)/(2^2 +1)² dz from 0 to infinity, we can use the comparison test.

First, note that (1-z) is bounded between 0 and 1, so we can compare it to the integral of 4/(2² +1)² dz from 0 to infinity, which is convergent since it is a constant times the convergent p-series with p=2.

Therefore, by the comparison test, the original integral is also convergent. To evaluate it, we can use partial fractions:

4(1-z)/(2² +1)^2 = A/(2+i)² + B/(2-i)²

Solving for A and B, we get A = (1+i)/5 and B = (1-i)/5.

Then, the integral becomes:

∫ 4(1-z)/(2² +1)² dz = A ∫ 1/(2+i)² dz + B ∫ 1/(2-i)² dz

= (1+i)/5 [-1/(2+i)] + (1-i)/5 [-1/(2-i)] from 0 to infinity

= [(1+i)(2-i) - (1-i)(2+i)]/25(2² +1)

= 0

Therefore, the integral is convergent and evaluates to 0.

To determine if an integral is convergent or divergent, you need to look at its limits and the function you are integrating. Convergent means that the integral has a finite value, while divergent means the integral does not have a finite value.

For example, if you have an integral like this:

∫(f(x) dx) from a to b,

you need to evaluate the limits 'a' and 'b' and the function 'f(x)'. If 'a' or 'b' is infinity (∞) or the function 'f(x)' behaves such that it leads to an infinite value for the integral, it is divergent. Otherwise, it is convergent.

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Select ALL the correct answers. Richard is renting a bike. The cost of renting a bike for the first hour is $7. He is charged $2.50 for every additional hour of renting the bike. Select all the functions that can be used to find the total amount that Richard is charged, f(n), for renting the bike for n hours. f ⁡ ( n ) = 2.5 ⁢ n + 7 f ⁡ ( n ) = 2.5 ⁢ n + 4.5 f ⁡ ( 1 ) = 7 ; f ⁡ ( n ) = f ⁡ ( n − 1 ) + 2.5 , for n ≥ 2 f ⁡ ( n ) = 4.5 ⁢ n + 2.5 f ⁡ ( 1 ) = 2.5 ; f ⁡ ( n ) = f ⁡ ( n − 1 ) + 7 , for n ≥ 2

Answers

The function that can be used to find the total amount is f(n) = 7 + (n - 1) * 2.5

Selecting the functions that can be used to find the total amount

From the question, we have the following parameters that can be used in our computation:

The cost of renting a bike for the first hour is $7. He is charged $2.50 for every additional hour of renting the bike.

This means that

f(n) = First hour + (n - 1) * Additional hour

Substitute the known values in the above equation, so, we have the following representation

f(n) = 7 + (n - 1) * 2.5

Hence, the function that can be used to find the total amount is f(n) = 7 + (n - 1) * 2.5

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Procter & Gamble reported that an American family of four washes an average of 1


ton (2000 pounds) of clothes each year. If the standard deviation of the distribution


is 187. 5 pounds, find the probability that the mean of a randomly selected sample of


50 families of four will be between 1980 and 1990 lbs.

Answers

The required probability is approximately 0.1253 or 12.53%.

We can use the central limit theorem to approximate the sampling distribution of the mean of the weights of clothes washed by 50 families of four. According to the central limit theorem, the sampling distribution of the mean will be approximately normal if the sample size is large enough (n > 30), regardless of the shape of the population distribution.

The mean of the sampling distribution of the mean will be equal to the population mean, which is 2000 lbs

[tex]SEM=\frac{\sigma}{\sqrt{n} }[/tex]

σ = population standard deviation

n = sample size.

[tex]SEM=\frac{187.5}{\sqrt{50} }[/tex]

= 26.5

Now we need to find the z-scores corresponding to the two values of the mean.

[tex]z_1=\frac{1980-2000}{26.5}[/tex]

= -0.75

[tex]z_2=\frac{1990-2000}{26.5}[/tex]

= -0.38

Using a standard normal table, we can find the probability that a z-score is between -0.75 and -0.38.

P(-0.75 < Z < -0.38) = 0.1253

Therefore, the required probability is approximately 0.1253 or 12.53%.

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A textbook company will ship a box of textbooks to college students. The weight of the box in pounds can be determined by the function w(x) = 7. 5x + 2, where x is the number of textbooks in the box. The company requires a student to order at least 2 books but not more than 6 books. What is the range of the function for this situation? *


A. 2 ≤ x ≤ 6


B. 17 ≤ y ≤ 47


C. {17, 24. 5, 32, 39. 5, 47}


D. {2, 3, 4, 5, 6}

Answers

The range of the function for this situation is {17, 24.5, 32, 39.5, 47}, The correct option is C.

To find the range of the function for this situation, we need to evaluate the function for x = 2, 3, 4, 5, and 6, since these are the only valid inputs based on the problem statement.

w(2) = 7.5(2) + 2 = 17

w(3) = 7.5(3) + 2 = 24.5

w(4) = 7.5(4) + 2 = 32

w(5) = 7.5(5) + 2 = 39.5

w(6) = 7.5(6) + 2 = 47

Therefore, the range of the function for this situation is {17, 24.5, 32, 39.5, 47}, which is option C.

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44 friends evenly divided up an

nn-slice pizza. One of the friends, Harris, ate
1
11 fewer slice than he received

Answers

The expression that denotes the number of slices of pizza eaten by Harris is: (N/4) - 1

How to solve Algebra Word Problems?

The parameters are given as:

Slices of pizza = n

Number of friends = 4

Slices of pizza evenly divided among friends = Total number of slices/number of friends = N/4

Now, this value will represent the number of slices each friend got.

Since, Harris had 1 slice lesser than what he received, then we can say that:

Number of slices of pizza eaten by Harris = (N/4) -1

This is because it's evenly divided into 4 people and as such we divide the total (N) by 4.

Since he at one less, you subtract one.

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Complete question is:

4 friends evenly divided up an n-slice pizza. One of the friends, Harris, ate 1 fewer slice than he received. How many slices of pizza did Harris eat? Write your answer as an expression.

Solve systems of Equation by substitution method
3(x-2) + y = 7

4x - 3(y-1) = 16

Answers

The values of the variables are x = 4 and y = 1

How to solve the equation

We have the equations as;

3(x-2) + y = 7

4x - 3(y-1) = 16

Using the substitution method

Make 'y' the subject of formula from equation (1), we have;

y = 7 - 3(x-2)

Now, substitute the expression as y in equation (2), we get;

4x - 3(7 -  3(x-2) - 1) = 16

expand the bracket, we have;

4x - 3(7 - 3x + 6 - 1) = 16

collect the like terms

4x - 3(12 - 3x) = 16

4x - 36 + 9x = 16

collect the like terms

13x = 52

x = 4

Substitute the value

y = 7 - 3(4 -2 )

y = 7 -3(2)

y = 1

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ANSWER ASAP PLEASE
The band club has $2,100 to spend on music stands and songs. Each music stand costs $15 and each song costs $350. Let x represent the number of music stands and let y represent the number of songs.

Part A
Write an equation that describes the number of music stands and songs the band club can buy.

x +
y =

Part B

What is the greatest number of each item that the club can buy?

greatest number of music stands =


greatest number of songs =

Answers

Part A: The equation that describes the amount of music stands and songs that the band club can purchase is 15x + 350y = 2100.

Part B: The greatest number of music stands the club can buy is 6, and the greatest number of songs the club can buy is 3.

Part A:

The cost of x music stands is 15x dollars, and the cost of y songs is 350y dollars. The total cost cannot exceed $2,100, so we can write the following equation:

15x + 350y = 2100

Therefore, the equation that describes the amount of music stands and songs that the band club can purchase is 15x + 350y = 2100.

Part B:

To find the greatest number of each item the club can buy, we can use the given equation and look for integer solutions for x and y that satisfy the equation.

We can rearrange the equation to solve for y:

y = (2100 - 15x) / 350

To get integer solutions for y, we need 2100 - 15x to be divisible by 350. The largest multiple of 350 that is less than or equal to 2100 is 6*350 = 2100. So, we can try x = 0, 1, 2, 3, ..., 6 and see which values give integer solutions for y.

When x = 0, y = 6, which is an integer solution.

When x = 1, y = 5, which is not an integer solution.

When x = 2, y = 4, which is not an integer solution.

When x = 3, y = 3, which is an integer solution.

When x = 4, y = 2, which is not an integer solution.

When x = 5, y = 1, which is not an integer solution.

When x = 6, y = 0, which is an integer solution.

So, the greatest number of music stands the club can buy is 6, and the greatest number of songs the club can buy is 3.

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Mrs. jones buys two toys for her son. the probability that the first toy is defective is , and the probability that the second toy is defective given that the first toy is defective is . what is the probability that both toys are defective? a. b. c. d.

Answers

The probability of the first toy being defective is 1/3 and the probability of both toys being defective is 1/15.

Hence, option 'a'.

Use the concept of probability defined as:

Probability is equal to the percentage of positive outcomes compared to all outcomes for the occurrence of an event.

Given that,

Mrs. Jones buys her son two toys.

The probability that the initial plaything is broken =  1/3.

The probability that the second toy has a problem.,

Also given the original toy is defective, is 1/5.

The goal is to calculate the probability that both toys are defective.

To calculate the probability that both toys are defective:

Multiply the individual probabilities.

Given that the probability of the first toy being defective = 1/3,

The probability of the second toy being defective given that the first toy is defective= 1/5,

Calculate the probability that,

Both toys have flaws, multiplying these probabilities together:

(1/3) x (1/5) = 1/15

Hence,

The probability that both toys are defective is [tex]1/15[/tex] which is option 'a'.

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The complete question is:

Mrs. Jones buys two toys for her son. the probability that the first toy is defective is 1/3, and the probability that the second toy is defective given /that the first toy is defective is 1/5. what is the probability that both toys are defective?

a.  1/15

b. 1/4

c. 1/8

d. 3/5

one serving of almonds is 1/3 cup. booker bought 2 and 2/3 cups of almonds how many servings of almonds did booker buy

Answers

Booker bought 8 servings of almonds.

How many servings of almonds did Booker buy if he purchased 2 and 2/3 cups of almonds, and one serving of almonds is 1/3 cup?

One serving of almonds is equal to 1/3 cup.

To find how many servings of almonds Booker bought, we can divide the total amount of almonds he purchased by the amount in one serving:

2 and 2/3 cups of almonds = 8/3 cups of almonds

Number of servings = (total amount of almonds purchased) / (amount in one serving)

Number of servings = (8/3) / (1/3)

Number of servings = 8/3 x 3/1

Number of servings = 8

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Write a division expression for each fraction 1/2

Answers

Answer: 1  ÷ 2

Step-by-step explanation: I think this is what you mean?

Ian stacks 5 glasses of juice. Each glass contains 185 milliliters of juice. Find the total volume of juice in the 5 glasses

Answers

The total volume of juice in the 5 glasses is 925 milliliters. To find the total volume of juice in the 5 glasses, we simply need to multiply the volume of juice in one glass by the number of glasses.

In this case, each glass contains 185 milliliters of juice and Ian has stacked 5 glasses, so we can use the formula:
Total volume of juice = Volume of juice per glass x Number of glasses
Plugging in the numbers, we get:
Total volume of juice = 185 ml/glass x 5 glasses
Total volume of juice = 925 ml


Therefore, the total volume of juice in the 5 glasses is 925 milliliters. This is a simple example of using multiplication to find the total quantity of something when we know the amount in one unit and the number of units. In this case, we were able to find the total volume of juice by multiplying the volume in one glass by the number of glasses.

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2-3 Consider the indefinite integral da. The substitution (3x - 2)2 u = 3x – 2 transforms the integral into: / None of these options are correct. 1-2 3 3 du 22 u 7 s". du 9u2 du u2 s " 0 7 u du u2

Answers

The substitution (3x - 2)2 u = 3x - 2 transforms the indefinite integral da into none of the given options. It should result in the integral of the function being expressed in terms of u rather than x.

This substitution is an example of using a change of variables to simplify an integral by transforming it into a more manageable form. This can be particularly useful when dealing with complicated integrals that are difficult to solve by other methods. Additionally, using such transforms can often provide insight into the underlying structure of the problem being studied.
 Based on your question, it appears that you want to perform a substitution to transform the indefinite integral of "da" using the substitution (3x - 2)² u = 3x - 2. However, the given integral "da" doesn't seem to be correct or complete. Please provide the complete integral, and I will be happy to help you with the transformation using the given substitution.

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5. Vanessa and Nancy plan to make a birthday cake. Working together, Vanessa and Nancy can complete the
birthday cake in 2 hours. If Nancy works alone, it will take her 3 times as long as it would take Vanessa to
complete the birthday cake. The equation below represents this situation.
2 2
-+-=1
3x
How many hours would it take Nancy to complete the birthday cake if she worked alone?
X

Answers

Using an equation, if Nancy worked alone, the number of hours it would take her to complete the birthday cake is 1 hour 30 minutes.

What is an equation?

An equation is a mathematical statement that proves the equality or equivalence of two or more mathematical expressions.

Equations use the equal symbol (=) unlike algebraic expressions, which combine variables with numbers, constants, and values using mathematical operands.

The number of hours for Vanessa and Nancy working together to make a birthday cake = 2 hours

The number of hours it takes Vanessa to complete the cake working alone = x

The number of hours it takes Nancy to complete the cake alone = 3x

Equation:

3x + x = 2

4x = 2

x = 0.5 = 30 minutes

The total time for Nancy to complete the cake = 3x = 1.5 (3 x 0.5)

= 1 hour 30 minutes

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Find the total surface area of the following


cone. Leave your answer in terms of a.


4 cm


3 cm


SA = [ ? ]7 cm


Hint: Surface Area of a Cone = tre + B


Where e = slant height, and B = area of the base

Answers

The total surface area of the cone is 44π cm², where π represents the mathematical constant pi.

We have,

To find the total surface area of a cone, we need to calculate the lateral surface area (denoted by L) and the base area (denoted by B), and then sum them.

The lateral surface area of a cone is given by L = πrℓ, where r is the radius of the base and ℓ is the slant height.

The base area is given by B = πr², where r is the radius of the base.

Given the dimensions:

Radius of the base (r) = 4 cm

Slant height (ℓ) = 7 cm

We can calculate the lateral surface area as L = π(4)(7) = 28π cm².

The base area can be calculated as B = π(4^2) = 16π cm².

Now, to find the total surface area (SA), we sum the lateral surface area and the base area:

SA = L + B = 28π + 16π = 44π cm².

Therefore,

The total surface area of the cone is 44π cm², where π represents the mathematical constant pi.

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I need help on this part, I don't even get it, please help me on this part​.

Here what it said:

"A store offers 3 brands of tee-shirts in 6 colors each in either long sleeve or short. How many different shirts are there?"

Answers

Answer:

36!

Step-by-step explanation:

There is 3 brands of clothing each brand has short and long sleeve, and both come in 6 different colors.

multiply 6*2 (because 6 different colors per long and short sleeve) get 12, then you multiply 12 times 3 because each one is from a different brand.

IT MAY BE A BI CONFUSING I SUCK AT EXPLAINING BUT

YEAHHH!

Answer:

18shirts

Step-by-step explanation:

3×6=18 shirts

NEED ANSWERS ASAP


Peter creates a square pyramid


model for History class. The


base of the pyramid has an


area of 20 square inches. Each


triangle has an area of 10


square inches. If Peter wants to


cover the entire pyramid with


gold paper, how much paper


will he need?


WILL GIVE BRAINLIEST TO THE CORRECT ANSWER

Answers

Peter will need 60 square inches of gold paper to cover the entire square pyramid for his History class.

You need to find the total surface area of the square pyramid that Peter creates for his History class to determine how much gold paper he will need. This can be done as follows.

1: Identify the given information.

Base area: 20 square inches

Triangle area: 10 square inches

2: Determine the number of triangles in a square pyramid.

A square pyramid has 4 triangular faces.

3: Calculate the total area of the triangular faces.

Multiply the area of one triangle by the number of triangles: 10 square inches x 4 = 40 square inches.

4: Calculate the total surface area of the pyramid.

Add the base area and the total area of the triangular faces: 20 square inches (base) + 40 square inches (triangles) = 60 square inches.

Hence, the gold paper to cover the entire square pyramid is 60 square inches.

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Find the volume of the cone in cubic feet. Use 3. 14 for π and round your answer to the nearest tenth.





(1 m ≈ 3. 2808 ft)


135,648 ft3


3,843. 8 ft3


4,790,189. 2 ft3


444,925. 4 ft3

Answers

The volume of the cone in cubic feet is approximately 0.0 cubic feet

We need to convert the given dimensions from inches to feet before calculating the volume in cubic feet.

The height of the cone is 6 inches, which is equivalent to 6/12 = 0.5 feet (since there are 12 inches in 1 foot).

The radius of the cone is 4.5 inches, which is equivalent to 4.5/12 = 0.375 feet.

Using the formula for the volume of a cone, which is:

V = (1/3) * π * r^2 * h

Substituting the given values, we get:

V = (1/3) * 3.14 * (0.375 feet)^2 * 0.5 feet

V ≈ 0.0221 cubic feet

Rounding this to the nearest tenth gives:

V ≈ 0.0 cubic feet

Therefore, the volume of the cone in cubic feet is approximately 0.0 cubic feet. None of the given options match this result.

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A researcher is studying life expectancy in different parts of the world using birth and death records she randomly selects a sample of 20 people from town a and a samle of 20 people form town b and records their lifespans in years.
mean lifespan in years standard deviation
town a 78.5 11.2
town b 74.4 12.3
the researhers wants to test the claim that there is a significant differnce in lifepan for people in the two towns. what are the null and alternative hypotheses that should be used to test this claim?
a. null: mu1 - mu2 is not equal to 0; alternative: mu1 - mu2 > 0 <---- a
b. null: mu1 - mu2 = 0; alternative: p1 - p2 is not equal to 0 <---- b
c. null: mu1 - mu2 = 0; alternative: mu1 - mu2 is not equal to 0 <---- c
d. null: p1 - p2 = 0; alternative: p1 - p2 < 0 <---- d

Answers

The correct answer is: c. null: mu1 - mu2 = 0; alternative: mu1 - mu2 is not equal to 0

The null hypothesis states that there is no significant difference in the mean lifespan of people in the two towns, while the alternative hypothesis states that there is a significant difference in the mean lifespan of people in the two towns.

Since we are comparing the means of two populations, we use the difference between the means as the test statistic. Therefore, the null hypothesis is mu1 - mu2 = 0 (there is no difference between the means) and the alternative hypothesis is mu1 - mu2 is not equal to 0 (there is a difference between the means).

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answer questions 2-20 please 1 and 5-7 are already answered no need to correct them does not need to be correct but please have relistic answers : )

Answers

The Pythagorean Theorem with regards to the relationships between the lengths of the sides of a right triangle indicates that we get;

2. x = 51

3. x = 50

4. x = 82

8. x = 2·√(77)

9. x = √(39)

10. x = 2·√(19)

11. x = 2·√(154)

12. x = 3·√3

13. x = 6·√(13)

16. A right triangle

17. A right triangle

18. The triangle is not a right triangle

19. An obtuse triangle

20. An obtuse triangle

What is the Pythagorean Theorem?

The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the lengths of the other two sides.  

2. x² = 45² + 24² = 2601

x = √(2601) = 51

3. x² = 30² + 40² = 2500

x = √(2500) = 50

x = 50

4. x² = 80² + 18² = 6724

x = √(6724) = 82

x = 82

8. According to the Pythagorean Theorem, in the right triangle we get;

x² = 18² - 4² = 308

x = 2·√(77)

9. x² = 8² - 5² = 39

x = √(39)

10. x² = 20² - 18²

x² = 76

x = √(76) = 2·√(19)

x = 2·√(19)

11. x² = 25² - 3² = 616

x = √(616) = 2·√(154)

x = 2·√(154)

12. x² = 6² - 3² = 27

x = √(27)

x = 3·√3

13. x² = 22² - 4² = 468

x = √(468) = 6·√(13)

x = 6·√(13)

16. A triangle is a right triangle if the square of the side that is the longest is equivalent to the square of the other two sides, therefore;

17² = 289

15² + 8² = 289

Therefore, the triangle is a right triangle

17. 45² = 2025

27² + 36² = 2025

Therefore, the triangle is a right triangle

18. 11² = 121

9² + 4² = 97

Therefore, the triangle is not a right triangle

19. 6² = 36

4² + 3² = 25

The square of the side that is longest is larger than the sum of the squares of the other two sides, which indicates that the angle facing the longest side is lar1ger than 90°, and the triangle is an obtuse triangle.

20. 16² = 256

9² + 11² = 202

16² > 9² + 11²; Therefore, the triangle is an obtuse triangle

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