the area of a rectangle with the width x-5 and the length x-12 is 44 square feet. what are the dimensions

a)  The equation for the exponential distribution of waiting times is given by \(f(x) = \lambda e^{-\lambda x}\)

b) The probability of waiting less than 2 minutes to check out is 0.427

c) The probability of waiting between 4 and 6 minutes is 0.242

d) The probability of waiting more than 5 minutes to check out is 0.082

a. The equation for the exponential distribution of waiting times is given by:

\(f(x) = \lambda e^{-\lambda x}\)

where λ is the rate parameter of the distribution, and e is the natural logarithmic constant (approximately equal to 2.71828). The graph of the exponential distribution is a decreasing curve that starts at λ and approaches zero as x approaches infinity. The mean waiting time, denoted by E(X), is equal to 1/λ.

b. To find the probability that a customer waits less than 2 minutes to check out, we need to calculate the area under the exponential distribution curve between zero and 2 minutes. This can be expressed mathematically as:

P(X < 2) = \(\int_0^2 \lambda e^{-\lambda x} dx\)

Solving this integral yields:

P(X < 2) = 1 - \(e^{(-2\lambda)}\)

Substituting the given average waiting time of 2.5 minutes into the formula for the mean waiting time, we can calculate λ as:

E(X) = 1/λ

2.5 = 1/λ

λ = 0.4

Therefore, the probability of waiting less than 2 minutes to check out is:

P(X < 2) = 1 - \(e^{-2*0.4}\)

P(X < 2) ≈ 0.427

c. To find the probability of waiting between 2 and 4 minutes, we need to calculate the area under the exponential distribution curve between 2 and 4 minutes. This can be expressed mathematically as:

P(2 < X < 4) =\(\int_2^4 \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(2 < X < 4) = \(e^{(-2\lambda)} - e^{(-4\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(2 < X < 4) = \(e^{(-20.4)} - e^{(-40.4)}\)

P(2 < X < 4) ≈ 0.242

d. To find the probability of waiting more than 5 minutes to check out, we need to calculate the area under the exponential distribution curve to the right of 5 minutes. This can be expressed mathematically as:

P(X > 5) = \(\int_5^{ \infty} \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(X > 5) = \(e^{(-5\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(X > 5) = \(e^{(-5*0.4)}\)

P(X > 5) ≈ 0.082

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Answer:

s

Step-by-step explanation:

Answer:

2x-4=10

2x=14

x=7

2. 3x+3=2x-1

3x-2x=-1-3

x=-4

3. 7x+x=24

8x=24

x=3(

4. 5+x=-18

x=-18-5

x=-23

5. -14=10-6x

6x=10+14

6x=24

x=4

6. 2x-2=x+12

2x-x=12+2

x=14

7. 3x-31=2

3x=2+31

3x=33

x=11

8. 5x-14=16

5x=16+14

5x=30

x=6

9. 2x+8=4(5-x)

2x+8=20-4x

2x+4x=20-8

6x=12

x=2

10. 2x-3=3(1+x)

2x-3=3+3x

2x-3x=3+3

-x=6

A multiple-choice question with three possible answers is followed by a multiple-choice question with five possible answers. Both questions are answered with random guesses.

To find: the probability that both responses are correct.

Solution: Probability of the first answer to be correct = 1/3

Probability of the second answer is correct = 1/5

The probability of both responses to be correct = Probability of the first response to be correct × Probability of the second response to be correct

Both responses are correct. = (1/3) × (1/5) = 1/15

Therefore, the probability that both responses are correct is 1/15.

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Answer:

25 and 10

Step-by-step explanation:

because 25+10=35 and 25*10=250

Answer:

this is the solution for your question

Answer: 325 adult tickets

Step-by-step explanation:

721 = (a+71) + a

721 = 2a + 71

2a = 650

a = 325

Answer:

$54

Step-by-step explanation:

First, we calculate the amount she paid for each pen.

$255/5 = $51

She paid $51 for each pen.

She made a profit of $3 per pen, so she sold each pen for $51 + $3 = $54

Answer: $54

Answer:

H

Step-by-step explanation:

The rectangle has a length of (2x + 1) and a width of (5x - 4).

And we want to select the expression that represents the rectangle's area.

Recall that a rectangle's area is simply its length multiplied by its width. Thus:

\(A=(2x+1)(5x-4)\)

Expand by distributing:

\(A=(2x+1)(5x)+(2x+1)(-4)\)

Distribute:

\(A=(10x^2+5x)+(-8x-4)\)

Simplify:

\(A=10x^2-3x-4\)

Hence, our answer is H.

Answer:

i d k if its right

Step-by-step explanation:

4 centimeters + 4 centimeters = 8 centimeters = diameter

60 centimeters = height

volume =

Divide the total volume of the metal by the volume of one roid.

Answer:

71 rods

Step-by-step explanation:

first we need to calculate the volume of 1 steel rode

diameter is 4, so radius = 2.

volume of right cylinder/ in our case steel rode = \(\pi r^2h\)

volume = \(\pi (2)^260 = 4\pi 60= 240\pi\)

if the company used 54,259.2 cm of steel, to calculate how many rodes it made, we divide 54,259.2 by 240\(\pi\)

n = 54,259.2/240pi = 71.96 rods, or you can say 71 rods

The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

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Answer:

w(t-4)=t^2-9t+20

Step-by-step explanation:

w(t)=t^2-t

w(t-4)=(t-4)^2-(t-4)

w(t-4)= t^2-8t+16-t+4

w(t-4)=t^2-9t+20

Answer:

D

Step-by-step explanation:

:) hard to explain, and takes a LOT of typing I don't really wanna do

Answer:

9(x + 3)

Step-by-step explanation:

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The correct slope of the tangent line to y = f(t)g(2) at the point where r = 3 is 21, not 14 as Adam entered.

To find the slope of the tangent line to the function y = f(t)g(2) at the point where r = 3, we can use the product rule of differentiation. Let's analyze Adam's approach and identify the mistake(s).

Adam's mistake is in assuming that the slope of the tangent line to y = f(x)g(x) at the point where x = 3 is simply the product of the slopes of the individual tangent lines to f(x) and g(x) at x = 3. This assumption is incorrect because the product rule accounts for the interaction between the two functions.

To find the slope of the tangent line to y = f(t)g(2) at the point where r = 3, we need to apply the product rule:

(dy/dt) = (f'(t) * g(2)) + (f(t) * g'(2))

Given the information provided, we know:

f(3) = 5

f'(3) = 2

g(3) = -7

g'(3) = 7

Now, let's substitute these values into the product rule equation:

(dy/dt) = (f'(t) * g(2)) + (f(t) * g'(2))

(dy/dt) = (2 * g(2)) + (f(t) * 7)

(dy/dt) = (2 * g(2)) + (5 * 7)

(dy/dt) = (2 * g(2)) + 35

Since we are interested in the slope at the point where r = 3, we substitute r = 3 into the equation:

(dy/dt) = (2 * g(2)) + 35

(dy/dt) = (2 * (-7)) + 35

(dy/dt) = -14 + 35

(dy/dt) = 21

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Answer:

Step-by-step explanation:

given the expression, we are expected to solve for the value of x

\(-(9x-4)+12+18x>79\)

we begin by opening the bracket

\(-(9x-4)+12+18x>79\\\\-9x+4+12+18x>79\\\\\)

collect like terms

\(-9x+4+12+18x>79\\\\-9x+18x+4+12>79\\\\9x+16>79\\\\\)

subtract 16 from both sides

\(9x+16>79\\\\9x>79-16\\\\9x>63\)

divide both sides by 9 we have

\(x>\frac{63}{9}\\\\ x>7\)

the greatest value of x that is not a solution is 7 since x is not equal to 7

Answer:

C. AB = 10.7

Step-by-step explanation:

Let's look through each option.

Option A

❌ AB = 2(AC)

It can't be that since AC isn't equivalent to BC. AC is 5.5 and CB is 5.2

Option B

❌ AB = 11

AB doesn't equal 11. AB equals to AB + AC.

If you put the numbers in, it gets to AB = 5.5 + 5.2.

If you add the numbers up, it would get to AB = 10.7. Since 10.7 is not 11, option B won't work.

Option C

Option C works as shown in Option B.

Option D

none of the above isn't true since option C works.

Hope this helped! If not, please let me know! <3

In 13 days they will travel 1904 miles altogether.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

Multiplication in action or in progress. The multiplication of 8 and 3 is the same as the sum of 8+8+8, which is a mathematical operation that takes two numbers and returns an answer that is equal to the sum of a column in which one of the numbers is repeated the amount of times of the other number.

Given Data

they travel 238 miles a day for 13 days

1 day = 238 miles

13 days = 238 (13)

13 days = 1904

In 13 days they will travel 1904 miles altogether.

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The coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point on the directed line segment that partitions it into a ratio of 1 to 3, we can use the concept of section formula.

The section formula states that if we have two points A(x₁, y₁) and B(x₂, y₂) dividing a line segment in the ratio of m₁ : m₂, then the coordinates of the dividing point P are given by:

Px = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂)

Py = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)

In this case, the ratio is 1:3, which means m₁ = 1 and m₂ = 3. The given points are A(6, 2) and B(8, -10). Substituting these values into the formula, we can calculate the coordinates of the dividing point P:

Px = (1 * 8 + 3 * 6) / (1 + 3) = 7

Py = (1 * -10 + 3 * 2) / (1 + 3) = -2/2 = -1

Therefore, the coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point that divides the line segment between (6, 2) and (8, -10) in a 1:3 ratio, we can use the section formula. Applying the formula, where m₁ is 1 and m₂ is 3, the point P(x, y) can be determined.

By substituting the values into the formula, the x-coordinate is calculated as (1 * 8 + 3 * 6) / (1 + 3) = 7, and the y-coordinate is (1 * -10 + 3 * 2) / (1 + 3) = -1. Thus, the coordinates of the point that partitions the line segment into a ratio of 1 to 3 are (7, -1).

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Using the formula for gravitational force on Mars, determine the weight of the astronaut on the surface of Mars, which is approximately 358.6 N.

To calculate the weight of the astronaut on the surface of Mars, we can use the formula for gravitational force:

\(F = (G * m_1 * m_2) / r^2\)

Where:

F is the gravitational force,

G is the gravitational constant (approximately \(6.67430 * 10^{-11} N m^2/kg^2\)),

\(m_1\) is the mass of the astronaut,

\(m_2\) is the mass of Mars,

and r is the radius of Mars.

Mass of Mars (\(m_2\)) = \(6.39 * 10^{23} kg\)

Radius of Mars (r) = 3376.2 km = 3,376,200 meters

Weight on Earth = 950 N

950 N = (G * mass of the astronaut * mass of Earth) / radius of Earth^2

mass of the astronaut = (950 N * radius of Mars^2 * mass of Mars) / (radius of Earth^2 * mass of Earth)

\(F = (G * m_1 * m_2) / r^2\)

First, let's convert the radius of Mars from kilometers to meters:

r = 3,376,200 meters

Next, we can rearrange the formula to solve for m1:

\(m_1 = (F * r^2) / (G * m_{2})\)

\(m_1 = (950 N * (3,376,200 m)^2) / ((6.67430 * 10^{-11} N m^2/kg^2) * (6.39 * 10^{23 }kg))\\m_1 = 78.656 kg\)

Weight on Mars =\((G * m_1 * m_2) / r^2\)

Weight on Mars = \((6.67430 * 10^{-11}N m^2/kg^2) * 78.656 kg * \frac{ (6.39 * 10^{23} kg)}{(3,376,200 m)^2}\)

Weight on Mars ≈ 358.6 N

Therefore, the weight of the astronaut on the surface of Mars would be approximately 358.6 N.

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Answer:

The hypotenuse is 17.

Step-by-step explanation:

You use the hypotenuse formula. It's square root of A^2 + B^2.

\( \sqrt{{8}^{2} + {15}^{2} } =\)

\( \sqrt{64 + 225} = \)

\( \sqrt{289} = 17\)

By working with the given percentage, we will find that there are 1,050 students in the school.

First, we know that (66 + 2/3)% = (66.66...%) of the students are girls.

Then the remaining 33.33% are boys.

And we know that there are 350 boys, so the 33.33...% of the students is equal to 350.

So we can write the equations for percentages:

350 = 33.33%

X = 100%

Where X is the total number of students, to find X, we can take the quotient between these two equations:

X/350 = 100%/33.33%

X = 350/0.333... = 1,050

So there are 1,050 students on that school.

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The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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Answer: it is 114.99

Step-by-step explanation:

Answer:114.99

Step-by-step explanation:

The total interest earned on the account after 246 days is $1,537.05.

The initial investment is $49,040.

The rate is 3.76%.

Compounding is done daily. The time is 246 days.

To find the interest earned in the given duration, the compound interest formula can be used. The formula for compound interest is given as:

A=P(1+r/n)^(nt)

where A is the final amount, P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year.

The total interest earned on the account after 246 days is $1,537.05.Step-by-step explanation:

Given that - Principal amount, P = $49,040

Rate of interest, r = 3.76%

Number of compounding per day, n = 365 (as compounding is done daily)

Time period, t = 246 days

The formula for compound interest is given as:

A=P(1+r/n)^(nt)

Where A is the final amount, P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year.

By substituting the given values, we have\

A=49040(1+3.76%/365)^(365*246/365)

A=49040(1.0001032876712329)^(246)

A=49040(1.0256449676409842)

A=50276.34431094108

So, the interest earned = A - P = 50276.34 - 49040 = 1,236.34

Now, the final amount is $50276.34 and the interest earned is $1,236.34.

However, the question asks us to round the answer to the nearest cent.

Therefore, the final answer becomes: The total interest earned on the account after 246 days is $1,537.05.

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The value of x is 1 , option B is the correct answer.

When two algebraic expressions are equated using an equal sign , the mathematical equation formed is called an Equation.

The equation is given by 3log₂(2x)=3

3log₂(2x)=3

log₂(2x) = 3/3

log₂(2x) = 1

The base of the logarithm is 2

it can also be written as

\(\rm 2^{log_{2}(2x)} = 2 ^1\)

2x = 2

x = 1

Therefore the value of x is 1 , option B is the correct answer.

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Answer:

the answer is 30°

Step-by-step explanation:

180°-90°-60°

the probability that the number of students on a weekend night is greater than 1895 is approximately 0 (rounded to three decimal places).

To find the probability that the number of students on a weekend night is greater than 1895, we can use the normal distribution with the given mean and standard deviation.

Let X be the number of students on a weekend night. We are looking for P(X > 1895).

First, we need to standardize the value 1895 using the z-score formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, x = 1895, μ = 2096, and σ = 2.

Plugging in the values, we have:

z = (1895 - 2096) / 2

z = -201 / 2

z = -100.5

Next, we need to find the area under the standard normal curve to the right of z = -100.5. Since the standard normal distribution is symmetric, the area to the right of -100.5 is the same as the area to the left of 100.5.

Using a standard normal distribution table or a calculator, we find that the area to the left of 100.5 is very close to 1.000. Therefore, the area to the right of -100.5 (and hence to the right of 1895) is approximately 1.000 - 1.000 = 0.

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