What is the probability that a data value in a normal distribution is between a
z-score of -1.32 and a z-score of 0.94? Round your answer to the nearest
tenth of a percent.
A. 58.1%
B. 90.9%
C. 34.9%
D. 73.3%

If the paint gallon cost $12 and carton cost is $5 , then the amount saved per gallon buying the larger can is $8  .

We know that 1 gallon is = 4 quarts. So , a one-gallon can is equal to four one-quart cans.

To buy one gallon of paint, we need to buy 4 one-quart cans.

Each one-quart can costs $5, so 4 one-quart cans will cost:

⇒ 4 × $5 = $20 ,

Now, the cost of one gallon of paint if it is bought in one one-gallon can.

⇒ One one-gallon can costs $12.

So , if we buy the larger one-gallon can, we will save:

⇒ $20 - $12 = $8

Therefore, We will save $8 per gallon buying the larger can.

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The second guideline for evaluating a statistical study is to assess the validity and reliability of the data.

This means looking at the data sources and data collection methods used in the study, making sure they are appropriate and reliable. This includes considering the sample size and sampling methods used, any potential bias in the data, and the accuracy and precision of the measurements and analyses.

1. Review the data sources and data collection methods used in the study: This includes looking at the sample size and sampling methods used, any potential bias in the data, and the accuracy and precision of the measurements and analyses.

2. Assess the validity and reliability of the data: This means making sure that the data sources and data collection methods used are appropriate and reliable. This includes considering the sample size and sampling methods used, any potential bias in the data, and the accuracy and precision of the measurements and analyses.

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Answer: 2,916 inches³

Step-by-step explanation:

The volume of a box is:

= Length * Width * Height

But all of these have to have the same units for it to work. This means that the height of the box will have to be converted to inches :

1 ft is 12 inches so:

= 1¹/₂ * 12

= 3/2 * 12

= 18 inches

Volume is therefore:

= 18 * 9 * 18

= 2,916 inches³

Answer:

\(\frac{dy}{dx}\) = 2x + 3

Step-by-step explanation:

Differentiate each term using the power rule

\(\frac{d}{dx}\) (a\(x^{n}\) ) = na\(x^{n-1}\)

y = x² + 3x

\(\frac{dy}{dx}\) = 2\(x^{(2-1)}\) + 3\(x^{(1-1)}\)

   =  2x + 3\(x^{0}\)

   = 2x + 3

Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

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Answer:

Step 1: Obtain the mean and standard deviation of the weights of packs of chewing gum. The weights of packs of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation 2.- grams. Step 2: Obtain the z-score of the randomly selected pack of gum. The z-score of the randomly selected pack of gum is 3.11. Step 3: Determine which of the following statements is true: The weight of this pack of gum is lighter than the mean weight by 3.11 standard deviations The weight of this pack Of gum is heavier than the mean weight by 3.11 standard deviations The weight of this pack Of gum is lighter than the mean weight by 2.4 standard deviations The weight of this pack Of gum is heavier than the mean weight by 2.4 standard deviations

Answer:

54

Step-by-step explanation:

Multiply each number by 3

Answer: 1

Step-by-step explanation:

4)

\(\displaystyle\\\frac{(sin\theta+cos\theta)^2}{1+2sin\theta cos\theta}=\\\\\frac{sin^2\theta+2sin\theta cos\theta+cos^2\theta}{1+2sin\theta cos\theta} =\\\\\frac{sin^2\theta+cos^2\theta+2sin\theta cos\theta}{1+2sin\theta cos\theta} =\\\\\frac{1+2sin\theta cos\theta}{1+2sin\theta cos\theta} =\\\\1\)

Answer:

The answer is 1

Step-by-step explanation:

The solution is in the image below

The correct value of μ = 549 - (z * 26.5) and (549 - μ) / 26.5 = z

(a) To find the probability that a single student randomly chosen from all those taking the test scores 549 or higher, we need to calculate the z-score and then find the corresponding probability using the standard normal distribution.

The z-score formula is given by:

z = (x - μ) / σ

Where:

x = value we are interested in (549)

μ = mean of the distribution (unknown in this case)

σ = standard deviation of the distribution (26.5)

To find the z-score, we rearrange the formula:

z = (x - μ) / σ

(z * σ) + μ = x

μ = x - (z * σ)

Now we can substitute the values and calculate μ:

μ = 549 - (z * 26.5)

To find the probability, we need to calculate the z-score corresponding to the value 549. Since the distribution is normal, we can use a standard normal distribution table or a calculator to find the probability associated with that z-score.

(b) The mean and standard deviation of the sample mean score, Ł (pronounced "x-bar"), of 30 students can be calculated using the formulas:

Mean of the Sampling Distribution (Ł) = μ

Standard Deviation of the Sampling Distribution (σŁ) = σ / sqrt(n)

Where:

μ = population mean (unknown in this case)

σ = population standard deviation (26.5)

n = sample size (30)

(c) To find the z-score that corresponds to the mean score of 549, we use the same formula as in part (a):

z = (x - μ) / σ

Substituting the values:

z = (549 - μ) / 26.5

Since we are given the mean score and need to find the z-score, we rearrange the formula:

(549 - μ) / 26.5 = z

Now we can solve for z.

Please note that the solution to part (a) will provide the value of μ, which is needed to answer parts (b) and (c).

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The mean of the data set is equal to 13.

The median of the data set is equal to 14.

Mathematically, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data, we have;

Total, F(x) = 9 + 16 + 14 + 11 + 9 + 15 + 14 + 16

Total, F(x) = 104

Mean = 104/8

Mean = 13.

First of all, we would sort the observations (data set) from the least to greatest as follows:

Data set = 9, 9, 11, 14, 14, 15, 16, 16

Median = (14 + 14)/2.

Median = 14

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The company has an initial valuation of 1200

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

Falls = 40%

Increase = 25%

Final valuation = $900

The final valuation of the company can be calculated using

Final valuation = Initial valuation * (1 - Falls) * (1 + Increase)

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

900 = Initial valuation * (1 - 40%) * (1 + 25%)

This gives

900 = Initial valuation * 0.75

Divide both sides by 0.75

Initial valuation = 1200

Hence, the initial valuation is $1200

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Answer:

Below

Step-by-step explanation:

Y axis intercept occurs when x = 0

 put 0 in for x to compute y

      y = -32

x axis intercept occurs when y = 0

  put 0 in for y and compute x

    0 = 10x - 32

       10x = 32

          x = 3.2

Answer:

C

Step-by-step explanation:

Pythagorean theorem

√25²-20²=15

Answer:

C

Step-by-step explanation:

the figure is a rectangle with opposite equal sides

Consider the upper right triangle

using Pythagoras' identity

p² + 20² = 25²

p² + 400 = 625 ( subtract 400 from both sides )

p² = 225 ( take square root of both sides )

p = \(\sqrt{225}\) = 15

Answer:

Below.

Step-by-step explanation:

I assume you are referring to a system of equations.

Example:

2x - y =  4

x + y =  5

If we add these 2 equations then the y is eliminated because -y + y = 0:-

3x + 0 = 9

x = 3

Now we plug x = 3 into the first equation to find y:

2(3) - y = 4

-y = 4 - 6 = -2

y = 2.

If we cannot eliminate one of the variables we multiply one of the equations so that one of the variables so that it can be eliminated.

For example:

2x - 3y = 5       A

x  + y  =  6        B

We multiply the second equation B by 3 so that when we add -3y + 3y gets eliminated:

3x + 3y = 18

- so adding this to equation A

5x + 0 = 23.

In some cases we may have to multiply both equations by different values to get terms that can be eliminated.

Answer:

Step-by-step explanation:

5, -4

5-4=1

5(-4)=-20

Answer:

it is eather d or b

Step-by-step explanation:

Answer:

"23,520"

Step-by-step explanation:

one trip: 14 passengers

one day: 3 trips

passengers: 80

80x14= 1,120

1,120x3= 3,360

3,360x7= 23,520

Answer: 72

Step-by-step explanation:

12*6

The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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Answer:

Step-by-step explanation:

smplifying

7x + 11 = 25

Reorder the terms:

11 + 7x = 25

Solving

11 + 7x = 25

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.

11 + -11 + 7x = 25 + -11

Combine like terms: 11 + -11 = 0

0 + 7x = 25 + -11

7x = 25 + -11

Combine like terms: 25 + -11 = 14

7x = 14

Divide each side by '7'.

x = 2

Simplifying

x = 2

Answer: Inequality form: x<=-2

Interval notation: (-infinity,-2]

Answer:

(9x-2)(9x+2)

Step-by-step explanation:

81x^2 - 4

Rewriting as

(9x)^2 - 2^2

This is the difference of squares a^2 - b^2 = (a-b)(a+b)

(9x-2)(9x+2)

Answer:

(9x + 2)(9x - 2)

Step-by-step explanation:

To factor this expression, you can use a neat trick called difference of squares.

Difference of squares tells us:

a^2-b^2 = (a+b)(a-b)

Now look at the expression we have here:

81x^2 - 4

well, we know that 81 is 9^2, x^2 is literally x^2, and 4 is 2^2

So we can rewrite this as:

(9x)^2 - 2^2

By difference of squares that gives us:

(9x + 2)(9x - 2)

Answer:

-3

Step-by-step explanation:

Hope this helps!

Answer:

x= -9, x=9

Step-by-step explanation:

hope i helped if i did it wrong lmk i can try doing it better

Answer:

I think it's 6.9282032302755

Answer:

I did the best I could graphing it but it's weird. It's all I got. So here you go. I hope it helps! have a nice day!

Step-by-step explanation:

Answer:

LCM is 30.

Step-by-step explanation:

She forgot that they both can multiply into 30. She listed all their multiples and their LCM is 30. Not 60. That's her error.

Hope this helps and have a nice day!

Step-by-step explanation:

To determine if a system of two equations with two unknowns has infinite solutions using matrices, you can perform Gaussian elimination or row reduction on the augmented matrix of the system. If the reduced form of the matrix is the identity matrix, then the system has a unique solution. If the reduced form is a row of zeros except for the last column, then the system has no solution. If the reduced form has a row with all zeros except for the last column being non-zero, then the system has an infinite number of solutions.

In other words, the system has infinite solutions if the row reduced form of the augmented matrix has a row of the form [0 0 c], where c is a non-zero scalar. This means that there is a non-trivial solution that satisfies the equation, indicating that there are infinitely many solutions.