A stack of one hundred fifty cards is placed next to a ruler, and the height of the stack is measured to be
3/4 inches.

How thick is one card?

The required expression that has a value of 15 is given as P + 3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Substitute the value of p in the expression,
= P + 3
= 12 + 3
= 15

When the value of p is put on another expression there output value is not 15.

Thus, the required expression that has a value of 15 is given as P + 3.

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Tony is not correct. The midway point between 4,000 and 5,000 is found by calculating the average of the two numbers, which is 4,500. Therefore, the halfway point is 4,500, not 4,400.

Tony states that 4,400 is halfway between 4,000 and 5,000. To determine if Tony is correct, we need to find the midpoint between the two numbers. The midpoint can be found by adding the two numbers together and dividing by 2:

(4,000 + 5,000) / 2 = 9,000 / 2 = 4,500.

Therefore, the exact halfway point between 4,000 and 5,000 is 4,500. This means that Tony's assertion that 4,400 is halfway between these two numbers is not correct; the correct halfway point is actually 4,500.

No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers, which is 4,500.

No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers. To find the average, we add the two numbers together and divide by 2. In this case, the average of 4,000 and 5,000 would be (4,000 + 5,000) / 2 = 9,000 / 2 = 4,500. Therefore, 4,400 is not halfway between 4,000 and 5,000.

There are 2 glasses of full water would be needed to fill the baking pan.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A drinking glass has height of 4 inches ,in a length of 2 inches and 2 inches in width.

And, A baking pan has a width of 4 inches length of 8 inches and a depth of 2 inches.

Now,

The volume of drinking water = 4 x 2 x 2

                                              = 16 inches³

And, The volume of baking pan = 4 x 8 x 2

                                                 = 64 inches³

So, Half depth of baking pan =  64 / 2

                                             = 32 inches³

Here, The volume of drinking water = 16 inches³

Thus, Number of glass of full water would be needed to fill the baking pan = 32 / 16 = 2

Therefore, There are 2 glasses of full water would be needed to fill the baking pan.

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product means multiply, sum means add

 so add 5+k = (5+k)

now multiply that by 6 to get

6(5+k)

The probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 can be calculated using the normal approximation to the binomial distribution.

To find the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02, we can use the normal approximation to the binomial distribution.

1. Calculate the mean of the sampling distribution using the formula:

μ = np = 50 * 0.02 = 1

2. Calculate the standard deviation using the formula:

σ = sqrt(npq)

where q = 1 - p = 1 - 0.02 = 0.98

σ = sqrt(50 * 0.02 * 0.98) ≈ 0.99

3. Convert p(hat) to a z-score using the formula:

z = (p(hat) - μ) / σ

z = (0.04 - 1) / 0.99 ≈ -0.96

4. Look up the z-score in the standard normal distribution table to find the corresponding probability.

P(z < -0.96) ≈ 0.166

Therefore, the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 is approximately 0.166.

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Complete question:

A random sample of 50 units is drawn from a production process every half hour. The fraction of non-conforming product manufactured is 0.02. What is the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02?

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Let the first integer be represented by: 2k

the second integer by: 2(k+1)

and the third by: 2(k+2)

Then, 2k + 2(k+1) = 2(k+2) + 30

2k + 2k + 2 = 2k + 4 + 30

4k + 2 = 2k + 34

2k = 32

k = 16

first integer: 2k = 2(16) = 32

second integer: 2(k+1) = 2(16+1) = 2(17) = 34

third integer: 2(k+2) = 2(16+2) = 2(18) = 36

Answer: 32, 34, 36

Let x denotes the number of days and y denotes the total change in gas price ( in dollars).

Given : During the past seven days the price of regular gas is decreased by $0.2 each day.

Rate of decrease =$0.2 per day

Then , Total change in gas price = Rate of decrease x Number of days

i.e.[tex]y= 0.2 \times x[/tex]

i.e. [tex]y=0.2x[/tex]         (1)

To find the total change in gas price in 7 days , we put x= 7 in (1) , we get

[tex]y=0.2(7)=1.4[/tex]    

Hence, the total change in gas price in 7 days = $1.4

Answer:

0.14

Step-by-step explanation:

Let t be the total reduction. Then ...  

t = daily change * number of days  

t = 7 * 0.02  

t = $0.14!

The value for x so that f(x) = 7 is at x = -3.

Using the equation of slope-intercept form (y = mx + b), where m is the gradient and b is the constant, we can find the value of x at which f(x) is equal to 7 as follows:

By observation on the graph, when x = 1, y = 3 and when x = 2, y = 2.

3 = m + b...(1)

2 = 2m + b...(2)

we multiply equation (1) by 2 and subtract equation (2) from the result;

6 - 2 = 2m - 2m + 2b - b

4 = b

putting 4 for b in equation (1) gives;

m = -1

Thus we have the equation for f(x) as

f(x) = (-1)x + 4

For f(x) = 7;

-x + 4 = 7

x = 4 - 7

x = -3.

Therefore, for f(x) to be equal to 7, the value of x is equal to -3.

The value of the x and y are 78° and 115°

Parallel lines are coplanar infinite straight lines that do not intersect at any point.

Parallel planes are planes in the same three-dimensional space that never meet.

Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

Given is a figure of parallel lines, m and n, we need to find the values of x and y,

x = 180°-102° [alternate interior angles and linear pair]

x = 78°

y = 115° [corresponding angle]

Hence, the value of the x and y are 78° and 115°

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Final answer:

To find the two numbers, we set up two equations, solve for one variable, and find the other. The numbers that satisfy the condition of one exceeding the other by 1 with their sum being 29 are 14 and 15.

Explanation:

The student's question involves finding two numbers where one number exceeds the other by 1 and their sum is 29. To solve this, let's set up a system of equations. We'll call the first number x and the second number y. Based on the question:

x = y + 1 (one number exceeds the other by 1)

x + y = 29 (the sum of the numbers is 29)

Substituting the first equation into the second gives us:

(y + 1) + y = 29

2y + 1 = 29

2y = 28

y = 14

Now that we have the value of y, we can find x:

x = y + 1

x = 14 + 1

x = 15

Therefore, the two numbers are 14 and 15.

The absolute value equation that represents the range of a category 1 hurricane's wind speed is |V - 84.5| ≤ 10.5. 84.5 is the average of the range and 10.5 is the difference from the range's center to the end.

The absolute value equation that represents the minimum and maximum sustained wind speeds of a category 1 hurricane can be written as |V - 84.5| ≤ 10.5. Here, V stands for the wind speed. The middle value of 74 and 95 is 84.5 (the average of 74 and 95). And the distance from 84.5 to either end of the range (74 or 95) is 10.5. So, the range of speeds is represented by the absolute difference from the center of the range is less than or equal to 10.5.

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Chase's model is only accurate if it shows starting at -4 on a number line and moving 3 units left to land at -7. Otherwise, the model requires correction to accurately portray the sum of -4 and -3.

The student's question relates to the operation of adding two negative numbers on a number line. When adding -4 and -3, you start at -4 on the number line and move 3 units to the left because you're adding another negative number. If Chase's model does not show starting at -4 and moving 3 units left to end at -7, then his model is inaccurate. To correct the model, ensure that the number line accurately reflects this movement and resulting position on the number line.

Final answer:

Sarah estimated that she could make at least 4,000 bracelets from 214 bags of beads by simplifying the calculation to 200 bags with enough beads for 20 bracelets each. Her estimate was conservative, as the calculation of 214 bags multiplied by 22 bracelets per bag totals 4,708 bracelets, which is greater than her estimate.

Explanation:

To critique Sarah's reasoning, we need to compare her estimate with the actual number of bracelets that can be made with the beads she has. She has 214 bags of beads, each with enough beads for 22 bracelets. To find the actual number of bracelets possible, we multiply the number of bags by the number of bracelets each bag can make:

214 bags × 22 bracelets per bag = 4,708 bracelets.

Sarah estimated that there were enough beads for at least 4,000 bracelets, based on the approximation that 200 bags with enough beads for 20 bracelets each would yield 4,000 bracelets. Although her estimation method simplifies the calculation by rounding down to manageable numbers, the actual total (4,708 bracelets) is greater than her estimate. By using this estimation method, Sarah has effectively ensured she will have more than enough beads for her classes, as her estimate is lower than the actual number.