Refer to Exhibit 6-5. What is the probability that a randomly selected item will weigh between 11 and 12 ounces? a. 0.4772 b. 0.4332 c. 0.9104 d. 0.0440 Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces abla in this exneriment?

Answer:

p = 2

Step-by-step explanation:

Happy to help.

When we have numbers in parenthesis, we generally want to deal with those first. However, we can hit a rough patch when a variable is in there. Consider this:

2(3 + 4) = 2(7), or 14.

But, the two can also be distributed into both numbers in the parenthesis, like this:

2(3 + 4) = 2*3 + 2*4

That leaves us with the same answer—14! We can apply this to a variable, and that will help us figure out 9(p - 4), or the left side of your equation you presented.

9(p - 4) = -18

9*p - 9*4 = -18

9p - 36 = -18

Add 36 on both sides to isolate the variable (in this case, p)

9p = -18 + 36

You can also write it like this; 9p = 36 - 18

9p = 18

Divide 9 to isolate p

p = 2

So, we would get (p = 2). Make sure to practice a few more questions like these to really get the hang of it—you'll be using this a lot in the future!

Good luck!

Answer:

+, x, -

Step-by-step explanation:

8 + 6 x 4 - 2

8 + 24 - 2

32 - 2

30

Answer:

55+(12.50×5)=117.5

30+(15×\(x\))=?

say you were inviting 5 people to fannies you would need to invite 5 1/2 people to get basically the same amount

Answer:

1.8

2.16

3.-7

5.-702

I didn't understand the 4th one

Answer:

1) 8

2) 16

3) -7

4) 14

5) 243

Step-by-step explanation:

For number 4 i just assumed you meant 6 + 3 + 2 + 3

The value of (double)(5/2) is 2.0. In the expression (double)(5/2), the division operation 5/2 is performed using integer division because both 5 and 2 are integers.

Integer division truncates the decimal part of the result and returns the quotient as an integer. In this case, 5 divided by 2 is equal to 2.

However, by explicitly casting the result to a double (using the (double) operator), we convert the integer value 2 to a double value, which becomes 2.0.

Therefore, the value of (double)(5/2) is 2.0, as the division is performed as an integer division followed by a casting to a double.

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The area of 11.6 square inches is equivalent to approximately 74.84 square centimeters.

To convert square inches to square centimeters, we need to use the conversion factor 1 inch = 2.54 centimeters. Since we are dealing with areas, we need to square this conversion factor as well.

Convert inches to centimeters:

11.6 inches * 2.54 centimeters/inch = 29.464 centimeters

Square the conversion factor:

(2.54 centimeters/inch) * (2.54 centimeters/inch) = 6.4516 square centimeters/square inch

Calculate the area in square centimeters:

29.464 centimeters * 6.4516 square centimeters/square inch =  74.84 square centimeters.

Rounding this value to two decimal places, the area of 11.6 square inches is approximately 190.29 square centimeters.

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Using binomial distribution, the probability of

a. 5 will still be with the company after 1 year is 28%.

b. at most 6 will still be with the company after 1 year is 89%.

The probability of a new employee in a fast-food chain still being with the company at the end of the year is given to be 0.6, which can be taken as the success of the experiment, p.

We are finding probability for people, thus, our sample size, n = 8.

Thus, we can show the given experiment a binomial distribution, with n = 8, and p = 0.6.

(i) We are asked for the probability that 5 will still be with the company.

Thus, we take x = 5.

P(X = 5) = (8C5)(0.6⁵)((1 - 0.6)⁸⁻⁵),

or, P(X = 5) = (56)(0.07776)(0.064),

or, P(X = 5) = 0.27869184 ≈ 0.28 or 28%.

(ii) We are asked for the probability that at most 6 will still be with the company.

Thus, our x = 6, and we need to take all values below it also.

P(X ≤ 6)

= 1 - P(X > 6)

= 1 - P(X = 7) - P(X = 8)

= 1 - (8C7)(0.6)⁷((1 - 0.6)⁸⁻⁷) - (8C8)(0.6)⁸((1 - 0.6)⁸⁻⁸)

= 1 - 8*0.0279936*0.4 - 1*0.01679616*1

= 1 - 0.08957952 - 0.01679616

= 0.89362432 ≈ 0.89 or 89%.

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The provided question is incomplete. The complete question is:

If the probability of new employee in a fast-food chain still being with the company at the end of 1 year is 0.6, what is the probability that out of 8 newly hired people,

a. 5 will still be with the company after 1 year?

b. at most 6 will still be with the company after 1 year?

The value of principal payment is $97.26

To calculate the amount that goes toward the principal when making the minimum payment at the end of the first month, we need to subtract the interest portion from the minimum payment.

First, let's calculate the interest charged for the month. The interest can be calculated using the formula:

Interest = Principal * Monthly Interest Rate

where:

Principal = $958.62

Monthly Interest Rate = Annual Percentage Rate (APR) / 12

Annual Percentage Rate (APR) = 9.7%

Monthly Interest Rate = 0.097 / 12

Now, let's calculate the interest charged:

Interest = $958.62 * (0.097 / 12)

= $7.75

Next, we subtract the interest charged from the minimum payment to find the amount that goes toward the principal:

Principal Payment = Minimum Payment - Interest

Finally, we calculate the amount that goes toward the principal:

Principal Payment = $105.0 - (7.74)

= $ 97.26

Hence, the value of principal payment is $97.26

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Answer: C. y = 3x - 2.

Step-by-step explanation: The line that passes through the points (1, 7) and (-3, 4) has a slope of (4-7)/(-3-1) = -3/-4 = 3/4. Any line that is parallel to this line will have the same slope of 3/4. Therefore, the correct answer is C. y = 3x - 2.

- Lizzy ˚ʚ♡ɞ˚

Answer:

lol same but that's okay we can all for sure get better at it :)

Step-by-step explanation:

PART A

We were told that the price of a T-shirt is $50

T shirt and backpack is $100

T shirt, backpack and sportsball is $125

If If Brennan's parents give him a $ 75 donation, let x represent the amount of money that he would still need to win the prize of a T -shirt , backpack , and sports ball. It means that

t + 75 = 125

Thus, the equation ito

The surface area of the cylinder is approximately 401.92 square centimeters. To find the surface area of the cylinder, we need to add the area of the top and bottom circles to the area of the lateral surface.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where r is the radius of the base, h is the height of the cylinder, and π ≈ 3.14.

Given that the radius is 8 cm and the height is also 8 cm, we can plug in the values in the formula:

SA = 2π(8²) + 2π(8)(8)

SA = 401.92

Rounding to the nearest hundredth, we get:

SA ≈ 401.92 square centimeters

Therefore, the surface area of the cylinder is approximately 401.92 square centimeters.

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All of the vertical pairs of angles are; ∠HJE and ∠GJF, ∠UVS and ∠TVR, ∠DEB and ∠AEC, ∠JNM and ∠LNK.

All of the complementary pairs of angles are; ∠EJH and ∠IJH, ∠WVU and ∠SVU, ∠AEC and ∠FEC, ∠ONL and ∠KNL.

1) Vertical angles are defined as angles that are opposite of each other when two lines cross and as such they are congruent.

2) Complementary angles are defined as two angles that add up to form a right angle.

The vertical angles are ∠HJE and ∠GJF, ∠UVS and ∠TVR, ∠DEB and ∠AEC, ∠JNM and ∠LNK.

The complementary angles are ∠EJH and ∠IJH, ∠WVU and ∠SVU, ∠AEC and ∠FEC, ∠ONL and ∠KNL.

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The following angles are identified in their classes as follows:

7. m∠EJH and m∠IJH are complementary

8. m∠SVT and m∠SVU are adjacent angles

9. m∠AED and m∠BED supplementary

10. m∠KNL and m∠JNM are vertical angles

7. if two angles are said to be complementary, then the total of their sum is equal to 90° so m∠EJH and m∠IJH are complementary.

8. Adjacent angles are next to each other. When two adjacent angles are combined, they form a straight line and together they measure 180 degrees hences m∠SVT and m∠SVU are adjacent angles.

9. If two angles lie on a straight line, they add up to 180°, and are considered supplementary angles hence, m∠AED and m∠BED supplementary.

10. Vertical angles also called vertically opposite angles are formed when two lines intersect each other, thus m∠KNL and m∠JNM are vertical angles.

In conclusion the angles are identified as; m∠EJH and m∠IJH are complementary, m∠SVT and m∠SVU are adjacent angles, m∠AED and m∠BED supplementary, and m∠KNL and m∠JNM are vertical angles.

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Count is incremented by 1 before returning the result because we want to count the number of trials needed to achieve the first success.

To create a Geometric random variable with a probability of success equal to p, you can use the following algorithm:

Initialize a counter variable, let's call it count, to 0.

Generate a random number between 0 and 1, let's call it rand_num.

Set the initial probability of success, prob_success, to p.

While rand_num is greater than prob_success, do the following steps:

Increment count by 1.

Generate a new rand_num between 0 and 1.

Update prob_success by multiplying it with (1 - p).

Return count + 1 as the generated Geometric random variable.

This algorithm works by repeatedly generating random numbers until a success occurs. Each time a failure occurs (when rand_num is greater than prob_success), the probability of success is updated to account for the remaining trials.

Note that count is incremented by 1 before returning the result because we want to count the number of trials needed to achieve the first success.

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Answer:

A

Step-by-step explanation:

y = 9,958(0.972)x

Function which best models the given data is -150x + 9219.

A solution is an assignment of values to the unknown variables that makes the equality in the equation true.

According to the given question

y represents the number of bees.

and, x represents the number of days.

Since, we have to find the function to represent the given data.

As, we know the given data are the solution of any function, so they must satisfy the function. For this we will take any value of x and y and check whether it satisfy the given function or not.

From the given data,

Let check for the point (0, 1000).

Substitute (0, 1000) in the given function one by one.

For, y = 9,958(0.972)x

At, x = 0

We get y = 0

⇒ ( 0, 1000) is not the solution of the function 9958(0.72)x

For, y = 0.972(9,958)x

At, x = 0

we get y = 0

⇒ (0, 1000) is not the solution for the function 0.972(9958)x

For, y = 9219x - 150

At x = 0

we get y = -150

⇒ (0, 10000) is not the solution of function, 9219x -150

For, y = -150x + 9219

At x = 0

y = 9219 which is nearly equals to 10000 because y is the estimated number of bees.

⇒ (0, 10000) is the solution of the given function y = -150x + 9219 .

Hence, the function which best models the given data is -150x + 9219.

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If in a survey, 200 college students were asked whether they live on campus and if they own a car, 55% of college students in the survey don't own a car.

To find the percent of college students who don't own a car, we need to add up the number of students who don't own a car and divide it by the total number of students in the survey. In this case, the total number of students in the survey is 200.

From the table, we can see that there are 88 students who live on campus and don't own a car, and 22 students who don't live on campus and don't own a car. So the total number of students who don't own a car is 88 + 22 = 110.

To find the percentage, we divide the number of students who don't own a car by the total number of students in the survey and then multiply by 100 to get the percentage:

Percentage of students who don't own a car = (110/200) x 100% = 55%

When working with percentages, we need to divide the number we are interested in by the total and then multiply by 100 to get the percentage.

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Answer:

let common ratio between them be x

So, 5x,3x

5x-3x=18

2x=18

2x/2=18/2

x=9

Step-by-step explanation:

I hope it helps you☺️

If yes, do mark my answer as brainliest

Answer:

6c^2 + c

Step-by-step explanation:

8^2 - 2c^2= 6c^2

6c-5c = c

Answer:

true

Step-by-step explanation:

they cancel each other out.

Answer:

True

Step-by-step explanation:

The numbers 2.3 and -2.3 are opposites or additive inverses. They add to zero.

Answer: True

Answer:

9.75

Step-by-step explanation:

first we are going to subtract the bonus

142.25 -35 = 107.25

assuming that you are not takeing breaks you work a total of 11 hours (7+4)

so 11/107.25  = 9.75

so you would make 9.75 an hour before taxs

Answer:

7502040

Step-by-step explanation:

you can have 6 women,5 women and 1 men,4 women and 2 men,

in first case,you can place women in 15*14*13*12*11*10 ways

in second case

15*14*13*12*11*7

and in third case

15*14*13*12*7*6

and you need to sum all this numbers

Answer:

10

Step-by-step explanation:

a) The probability that the mean of the sample will fall between 50.5 and 52.3 is approximately 0.8623.

b) The probability that the sample standard deviation will exceed 10 is approximately 0.0244.

a) To find the probability that the mean of the sample falls between 50.5 and 52.3, we need to calculate the z-scores for these values and then use the z-table or a statistical calculator.

The formula to calculate the z-score is:

z = (x - μ) / (σ / √n)

Where:

x = the sample mean (in this case, the mean is between 50.5 and 52.3)

μ = the population mean (given as 51.4)

σ = the population standard deviation (given as 6.8)

n = the sample size (given as 64)

For 50.5:

z_1 = (50.5 - 51.4) / (6.8 / √64) = -0.15

For 52.3:

z_2 = (52.3 - 51.4) / (6.8 / √64) = 0.6625

Next, we use the z-table or a statistical calculator to find the probability associated with these z-scores. The probability of the mean falling between 50.5 and 52.3 is the difference between the cumulative probabilities at z_2 and z_1.

P(50.5 < x < 52.3) = P(z_1 < z < z_2)

Looking up the z-scores in the z-table or using a statistical calculator, we find that the probability associated with z_1 is approximately 0.4364 and the probability associated with z_2 is approximately 0.9454.

Therefore, the probability that the mean of the sample falls between 50.5 and 52.3 is approximately:

P(50.5 < x < 52.3) = 0.9454 - 0.4364 ≈ 0.8623

b) To find the probability that the sample standard deviation exceeds 10, we need to use the chi-square distribution.

The formula to calculate the chi-square statistic for sample standard deviation is:

χ² = (n - 1) * s² / σ²

Where:

n = sample size (given as 64)

s = sample standard deviation (in this case, we are interested in values exceeding 10)

σ = population standard deviation (given as 6.8)

To find the probability, we calculate the chi-square value and then use the chi-square distribution table or a statistical calculator.

χ² = (64 - 1) * 10² / 6.8² ≈ 121.5294

Using the chi-square distribution table or a statistical calculator, we find that the probability of the chi-square value exceeding 121.5294 is approximately 0.0244.

Therefore, the probability that the sample standard deviation exceeds 10 is approximately 0.0244.

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Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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Answer:

b = sp

Step-by-step explanation:

box = seeds per packet

The given relation can be used to find the total number of seeds in box b, using the equation b = sp. Hence, 3rd option is the right choice.

Equations are relations shown between two equal algebraic expressions.

We are given a box of sunflower seeds, containing p packets of seeds, each of which contains s number of seeds.

We are asked to write an equation that can be used to find the total number of seeds in the box, b.

We know that the box contains p packets of seeds.

In 1 packet we have s number of seeds.

∴ In p packets, we will have an s*p number of seeds or sp seeds.

Since the box contains p packets and the total number of seeds in the box is b, then we can say that

b = the number of seeds in p packets

or, b = sp, which is the required equation.

∴ The given relation can be used to find the total number of seeds in box b, using the equation b = sp. Hence, 3rd option is the right choice.

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The power series approximation of f(x)g(x) up to order 3 is:

\(e^56 sin 8x - 22(5x)sin 8x - 2e^56(5x) + 22(5x)^2 sin 8x\)

To find the power series expansion of the product f(x)g(x), we need to multiply the power series expansions of f(x) and g(x) and collect like terms.

First, let's find the power series expansion of f(x):

\(f(x) = e^56 - 2(5x)^"\)

Using the formula for the power series expansion of e^x:

\(e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...\)

We can write the power series expansion of f(x) as:

\(f(x) = e^56 - 2(5x)^"\)

\(= (1 + 56 + (56^2)/2! + (56^3)/3! + ...) - 2(5x)^(1)\)

= \(1 - 5x + (56 - 25x^2) +\)...

Now let's find the power series expansion of g(x):

g(x) = sin 8x

= (8x) - (8x)^3/3! + (8x)^5/5! - ...

Finally, we can multiply the power series expansions of f(x) and g(x) to get the power series expansion of f(x)g(x):

\(f(x)g(x) = (1 - 5x + (56 - 25x^2) + ...) * ((8x) - (8x)^3/3! + (8x)^5/5! - ...)\)

\(= (8x) - (40x^2) + (568x^2)/2! + ((56-8*8)/2!)x^4 + ...\)

Collecting like terms up to order 3, we get:

\(f(x)g(x) = (8x) - (40x^2) + (224x^3)/3! + ...\)

Therefore, the power series approximation of f(x)g(x) up to order 3 is:

\(e^56 sin 8x - 22(5x)sin 8x - 2e^56(5x) + 22(5x)^2 sin 8x\)

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Answer:

5 units

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

To solve you have to get x by itself on one side.

x/3+7=12

First, you move the seven over.

x/3+7-7=12-7

Simplify.

x/3=5

Now to get x by itself you can multiply both sides by 3.

x/3*3=5*3

Simplify.

x=15

Answer:

x = 15

Step-by-step explanation:

x/3 + 3⋅7/3 = 12

x+3⋅7/3=12

x+21/3

X=15

Answer:

Step-by-step explanation:

An Additive Verse is a pair of numbers whose sum is zero.

Example: the additive Inverse of -5 is +5

Therefore: the Additive Inverse of -10 1/4 would be +10 1/4

To find the solution to the given boundary value problem, we can solve the corresponding second-order linear homogeneous ordinary differential equation. The characteristic equation associated with the differential equation is obtained by substituting y = e^(rt) into the equation:

r² - 7r + 6 = 0

Factoring the quadratic equation, we have:

(r - 1)(r - 6) = 0

This gives us two roots: r = 1 and r = 6.

Therefore, the general solution to the differential equation is given by:

y(t) = c₁e^(t) + c₂e^(6t)

To find the particular solution that satisfies the given boundary conditions, we substitute y(0) = 1 and y(1) = 6 into the general solution:

y(0) = c₁e^(0) + c₂e^(6(0)) = c₁ + c₂ = 1

y(1) = c₁e^(1) + c₂e^(6(1)) = c₁e + c₂e^6 = 6

We can solve this system of equations to find the values of c₁ and c₂. Subtracting the first equation from the second, we have:

c₁e + c₂e^6 - c₁ - c₂ = 6 - 1

c₁(e - 1) + c₂(e^6 - 1) = 5

From this, we can determine the values of c₁ and c₂, and substitute them back into the general solution to obtain the particular solution that satisfies the boundary conditions.

In conclusion, the solution to the given boundary value problem is y(t) = c₁e^(t) + c₂e^(6t), where the values of c₁ and c₂ are determined by the boundary conditions y(0) = 1 and y(1) = 6.

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