Snowy's Snowboard Co. manufactures snowboards. The company used the function P(x) = -5x2 -30% + 675 to model its profits, where P(x) is the profit in thousands of dollars and x is the number of snowboards sold in thousands. How many snowboards must be sold for the company to break even?

a) the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

a) To find the probability that a randomly selected Cobalt gets more than 34 MPG, we need to calculate the area under the normal distribution curve to the right of 34 MPG.

Using the z-score formula, we can convert the MPG value to a standard score (z-score) using the formula:

z = (x - μ) / σ,

where x is the given value (34 MPG), μ is the mean (32 MPG), and σ is the standard deviation (3.5 MPG).

Calculating the z-score:

z = (34 - 32) / 3.5 = 0.57

Using a standard normal distribution table or a statistical calculator, we can find the area to the right of the z-score 0.57.

Let's assume the standard normal distribution table gives us a value of 0.2851 for z = 0.57.

Since the total area under the normal curve is 1, the probability of getting more than 34 MPG is:

P(X > 34) = 1 - P(X ≤ 34) = 1 - 0.2851 = 0.7149

Therefore, the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) When selecting a sample of 10 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√10).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √10 ≈ 1.107

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 10 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

We can again convert the value of 34 MPG to a z-score:

z = (34 - 32) / 1.107 ≈ 1.805

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 1.805.

Let's assume the standard normal distribution table gives us a value of 0.035 for z = 1.805.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) When selecting a sample of 20 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√20).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √20 ≈ 0.78

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 20 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

Similarly, we can convert the value of 34 MPG to a z-score:

z = (34 - 32) / 0.78 ≈ 2.564

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 2.564.

Assuming the standard normal distribution table gives us a value of 0.005 for z = 2.564.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

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Answer:

d

Step-by-step

bc I did my times table

Answer:

A

Step-by-step explanation:

I think you forgot to add the closing ")" bit I'll assume it's supposed to go after the "4,000" or "40,000".

64,000÷ 10= 6,400

the first one should be your answer.

Mathematics is a fundamental subject in education that is essential in the development of an individual’s critical thinking and problem-solving skills. It is one of the primary subjects that are taught in elementary schools and must be taught appropriately for children to understand and gain the required skills. One true statement about mathematics teaching in elementary schools is that it should be student-centered.

Teachers should focus on the child's understanding, individual learning abilities and styles, and progress.The learning experience should not be centered on the teacher but on the students. Teachers should also make the subject engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject. Besides, teachers should develop a personalized learning approach that allows students to learn and understand the subject at their own pace while creating opportunities for individual and group learning. Through such learning approaches, students can develop the required mathematical concepts and competencies such as critical thinking, problem-solving, and decision-making skills that will be beneficial in their future endeavors.

In elementary schools, mathematics teaching should be student-centered. It should be engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject.

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In triangle XYZ, angle X Z Y is a right angle. The length of Z X is b, the length of Z Y is a, and the length of hypotenuse X Y is c. Then, the side XZ which is the perpendicular, is opposite to ∠Y. Side XZ is adjacent to the ∠Y, and side ZY, which is the base, is also adjacent to ∠Y. We can say that ∠Y has been formed by the sides XZ and ZY.

It is given that,

In triangle X Y Z, angle X Z Y is a right angle or 90°.

The length of the hypotenuse XY is c.

⇒ The side with length c is adjacent to ∠Y.

The sides XZ and ZY form the right angle, thus one is base and the other is perpendicular.

Now, in relation to ∠Y, side ZY of length a is the base (adjacent to angle Y)

Similarly, side XZ of length b forms the perpendicular and is opposite to ∠Y.

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Answer:

936 boxes

Step-by-step explanation:

The computation is shown below:

The red cars is

= 8,424 ÷ 3

= 2,808

The first method for the number of boxes is

= 8,424 ÷ 12 +  2,808 ÷ 12

= 702 + 234

= 936 boxes

And, the other method to solve the number of boxes is

= (8,424 + 2,808) ÷ 12

= 936 boxes

Hence, in this way it could be solved in these two ways

The sum of the interior angle of the triangle is 180°. Then the value of the variable x will be 12°.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The angles of the triangle are given below.

(8x - 1)°, (3x + 4)°, and (3x + 9)°

We know that the sum of the interior angle of the triangle is 180°. Then the equation will be

(8x - 1)° + (3x + 4)° + (3x + 9)° = 180°

14x + 12 = 180°

14x = 168°

x = 12°

The value of the variable x will be 12°.

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Answer:

40.82cm

Step-by-step explanation:

half of 26 is 13

the second's circle diameter is 13

the formula for circumference is C = 2πr

where r is the radius and π is 3.14

diameter =2r

13 = 2r

r = 6.5

2 x 6.5 x 3.14 = 40.82

40.82 cm  

Answer:

\( \sqrt{9 } = 3 \)

To solve for the Marshallian demands x1(p1, p2, m) and x2(p1, p2, m) in the consumer problem with utility function U(x1, x2) = min{x1, ax2}, we need to maximize the utility subject to the budget constraint p1x1 + p2x2 ≤ m, where p1 and p2 are the prices of goods 1 and 2 respectively, and m is the consumer's income.

To find the Marshallian demands, we need to solve the consumer's optimization problem. The objective is to maximize the utility function U(x1, x2) = min{x1, ax2} subject to the budget constraint p1x1 + p2x2 ≤ m.

The first step is to set up the Lagrangian function:

L(x1, x2, λ) = min{x1, ax2} + λ(m - p1x1 - p2x2)

Next, we take the first-order conditions by differentiating the Lagrangian with respect to x1, x2, and λ, and setting the derivatives equal to zero. This will give us the equations for the optimal values of x1, x2, and the Lagrange multiplier λ.

By solving these equations, we can find the specific values for x1(p1, p2, m) and x2(p1, p2, m) that maximize the utility function while satisfying the budget constraint. The resulting demands will depend on the prices (p1, p2) and the consumer's income (m).

Note that the specific calculations involved in solving the optimization problem can be quite involved and may require further mathematical manipulation.

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The expression that represents the word phrase of the product of 3 and 6 more than a number is 3(6 + x).

Let the given number be x.

Therefore, the expression that represents the word phrase the product of 3 and 6 more than a number will be:

= 3(6 + x)

In conclusion, the correct option will be 3(6 + x).

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To function effectively, a subtotal row must contain at least one aggregate function, which performs calculations on a group of values and produces a single, concise result that conveys the relevant information.

A subtotal row is an essential tool for data analysis in spreadsheets, allowing for easy organization and summarization of large datasets.

A subtotal row is a crucial element in organizing and analyzing data within spreadsheets, as it allows users to break down information into manageable sections. To achieve this, a subtotal row must contain at least one aggregate function. Aggregate functions perform calculations on a group of values, generating a single result that summarizes the data.
Examples of common aggregate functions include SUM, AVERAGE, COUNT, MIN, and MAX. These functions facilitate various mathematical operations, such as summing up values, finding the average, counting the number of instances, identifying the smallest value, and determining the largest value, respectively.
In practice, when creating a subtotal row in a spreadsheet, users typically sort the data by the desired category first. Then, they apply the appropriate aggregate function(s) to generate the desired summary statistics for each subset of data. This enables users to quickly gain insights into the data trends and make informed decisions based on the summarized information.

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To find the p-value for the test examining the positive linear relationship between speed and jump height, you need to calculate the Pearson correlation coefficient, determine the degrees of freedom, and then find the corresponding p-value.

To determine the p-value for this test, we would need to conduct a hypothesis test using a linear regression model. The null hypothesis would be that there is no linear relationship between speed and jump height, while the alternative hypothesis would be that there is a positive linear relationship between the two variables.

After running the regression model and performing the hypothesis test, we would look for the p-value associated with the slope coefficient for speed. If this p-value is less than the chosen significance level (usually 0.05), we can conclude that there is convincing evidence of a positive linear relationship between speed and jump height for students like these.

Without actually running the regression model and hypothesis test, it is not possible to provide an exact p-value for this scenario.

To determine if there is convincing evidence of a positive linear relationship between speed (mph) and jump height (in) for students like these, you need to conduct a correlation test, specifically a Pearson correlation test. The p-value will help you determine the significance of the relationship.

Step-by-step explanation:

1. Gather the data: Obtain the values for speed (mph) and jump height (in) for each student.

2. Calculate the Pearson correlation coefficient (r): This value will help you measure the strength and direction of the linear relationship between the two variables. You can use statistical software or a calculator for this.

3. Determine the degrees of freedom (df): Calculate this by subtracting 2 from the total number of data points (n). Formula: df = n - 2.

4. Calculate the p-value: Using the Pearson correlation coefficient (r) and the degrees of freedom (df), you can find the p-value in a t-distribution table or by using statistical software.

5. Interpret the p-value: If the p-value is less than your chosen significance level (commonly 0.05), there is convincing evidence of a positive linear relationship between speed and jump height. If the p-value is greater than 0.05, there is not enough evidence to suggest a significant positive linear relationship.

In summary, to find the p-value for the test examining the positive linear relationship between speed and jump height, you need to calculate the Pearson correlation coefficient, determine the degrees of freedom, and then find the corresponding p-value. Comparing this p-value to your chosen significance level will help you conclude if there is convincing evidence of a positive linear relationship between the two variables.

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Answer:

$29.70

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The Correct  option A: summarizing data.



- Summarizing data involves finding ways to represent the data in a concise and meaningful manner.
- Computing the average number of dollars college students have on their credit card balances is an example of summarizing data because it provides a single value that summarizes the data for this group.
- Generalizing data involves making conclusions or predictions about a larger population based on data collected from a smaller sample. Computing the average credit card balance for college students does not necessarily generalize to other populations, so it is not an example of generalizing data.
- Comparing data involves looking at differences or similarities between two or more sets of data. Computing the average credit card balance for college students does not involve comparing different sets of data, so it is not an example of comparing data.
- Relating data involves examining the relationship between two or more variables. Computing the average credit card balance for college students does not examine the relationship between credit card balances and other variables, so it is not an example of relating data.

Therefore, The correct option is A , computing the average number of dollars college students have on their credit card balances exemplifies summarizing data.

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if 15 x 1.8 = 27 then

45 x 1.8 = 81

so answer: B) 81

Answer: k = √27-i

Step-by-step explanation:

Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

The ratio of the number of unshaded to shaded squares is 7 : 3.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

It is also defined as the fraction of one quantity with respect to other.

The ratio of a and b is denoted as a : b.

Given is a grid of squares which is given below.

Total number of squares = 10

Of that,

Number of shaded squares = 3

Number of unshaded squares = 7

We have to find the ratio of unshaded to shaded squares in the grid which is 7 / 3 or 7 : 3.

Ratio of unshaded squares to shaded squares = 7 : 3

Hence 7 : 3 is the ratio of unshaded to shaded.

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To find a formula for the general term of the sequence 5, 6, 7, 8, 25, 125, 625, 3125. Let's break down the sequence and analyze the patterns.

The sequence can be divided into two parts:
1. The numerators: 5, 6, 7, 8
2. The denominators (as powers of 5): 5^0, 5^1, 5^2, 5^3

Now, let's analyze each part of the sequence.

Numerators: The numerators increase by 1 for each term. So, the nth term will have a numerator of n + 4.
Denominators: The denominators are powers of 5, so the nth term will have a denominator of 5^(n-1).

The signs of the terms are alternately positive and negative, so we need to multiply by a power of -1. Since we want to start with a positive term, we use (-1)^(n+1).

Therefore, the general term formula for this sequence is:
an = (-1)^(n+1) * (n + 4) / 5^(n-1)

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The number of rubber bands that Alana has to add to the ball to increase its diameter by 1 cm is 74.

Given that:

Alana is making a ball out of rubber bands.

The volume of the ball with 54 rubber bands is found as below:

Diameter of the ball = 3 cm

The radius of the ball is half of the diameter.

So, radius, r = 1.5 cm

So, the volume of the ball formed by 54 rubberbands is:

\(V=\frac{4}{3}\pi r^3\)

Substitute r = 1.5.

\(V=\frac{4}{3} \pi (1.5)^3\)

\(V=4.5\pi\)

Now, the volume of the ball formed by 1 rubber band or the volume of the rubber band is:

\(V(r)=\frac{4.5\pi }{54}\)

\(V(r)=\frac{\pi }{12}\)

When the diameter increased by 1 cm, the new diameter is 4 cm and thus the radius is 2 cm.

So, the increase in volume is:

\(\frac{4}{3} \pi (2)^3-\frac{4}{3} \pi (\frac{3}{2} )^3=\frac{37\pi }{6}\)

Now, divide this by the volume of one rubber band to get the number of rubber bands to be added.

\(\frac{\frac{37\pi }{6}}{\frac{\pi }{12} } =74\)

Hence, the number of bands added is 74.

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Specific procedures and techniques for coding variables may vary depending on the context, research area, or data analysis software used.

What is a Variable?

A variable is a quantity that can change in the context of a mathematical problem or experiment. We usually use one letter to represent a variable. The letters x, y, and z are common general symbols used for variables.

The procedure for identifying or indicating the value of cases on a variable is commonly known as data coding or data labeling. It involves assigning specific numerical or categorical values ​​to represent different categories or levels of a variable.

Here is the general procedure for encoding variables:

Define the variable: Start by clearly defining the variable you want to code. Understand its nature (eg nominal, ordinal, interval or ratio) and the categories or levels it covers.

Determine the encoding scheme: Decide on the encoding scheme you will use to represent the variable. For nominal variables (categories without their own order), you can assign numbers or labels to each category. For ordinal variables (categories with a meaningful order), you can assign numbers or labels that reflect the order. For interval or ratio variables, the numerical values ​​themselves can indicate the value of the variable.

Assign Codes: Assign specific codes or labels to represent each category or level of the variable. These codes can be numbers, letters, or any other symbol you choose. Make sure the codes are unique and do not overlap.

Apply Coding: Apply assigned codes to matching cases or observations in your dataset. Depending on the software or tool you are using, there are different ways to do this. You can manually enter codes, use syntax or programming commands, or use data transformation functions.

Verify your coding: Double-check your coding to ensure accuracy. Review a sample of the coded cases to ensure they match the intended coding scheme. This step is essential to avoid errors and inconsistencies in your data.

It is important to note that specific procedures and techniques for coding variables may vary depending on the context, research area, or data analysis software used.

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Answer:

the answer to this is

14 + 6√5

The data does not show a strong positive correlation. The data has a strong negative correlation.

Normal distribution is a function that represents the distribution of many random variables as a symmetrical bell-shaped graph. Mathematically -
\($f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}\)

Given is the interpretation of the graphing calculator display.

The value of r = - 0.99.

It shows a strong negative correlation and not a strong positive correlation.

Therefore, the data does not show a strong positive correlation. The data has a strong negative correlation.

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Answer:

A would make sense

Step-by-step explanation:

Answer:

pi ≈ 3,141593

Step-by-step explanation:

I think this is the right answer

Okay, so let's call B = the number of sandwiches Bill sells

and P = the number of sandwiches Pete sells

Since Bill sells 7 times as many sandwiches as Pete, then

B = 7P

And the difference between their sales is 414 sandwiches. Since we know that Bill sells more than Pete, then

B - P = 434

So, now we can substitute for B from the equation above B = 7P

x = bill's

y = pete's

x = 8y

B - P = 434

7P - P = 434

6P = 434

P = 72.33

Therefore, Pete sells 72.33 sandwiches

Bill sells 7 x 72.33 = 506 sandwiches.

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Answer:

The length of Midsegment = 9

Step-by-step explanation:

the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.

According to the Midsegment Theorem:

Thus,

The midsegment (x+4) is half the length of the third side (4x-2). so

\(\left(x+4\right)\:=\:\frac{1}{2}\:\left(4x\:-\:2\right)\)

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

Subtract 4 from both sides

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

\(x=2x-5\)

Subtract 2x from both sides

\(x-2x=2x-5-2x\)

Simplify

\(-x=-5\)

divide both sides by -1

\(\frac{-x}{-1}=\frac{-5}{-1}\)

Simplify

\(x=5\)

As

The length of Midsegment = x+4

                                             = (5) + 4        ∵ x = 5

                                             = 9

Therefore, the length of Midsegment = 9