2) Mr. Somers had twenty pieces of metal that were all the same length. If each piece of metal was 3 1/5 inches long and he put them side by side, what would be the total length of all the pieces together?

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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Answer:

i would say part to whole

Step-by-step explanation:

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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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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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:

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 written form of 7.007 is "seven and seven thousandths." It is derived from the digit 7 representing the units place, and the last digit 7 representing the thousandths place.

The written form of 7.007 is "seven and seven thousandths." To understand the structure of this decimal:

The digit 7 before the decimal point represents the units place, or 'seven'.

The first digit 0 after the decimal point represents the 'tenths' place, which is zero in this case.

The second digit 0 after the decimal point represents the 'hundredths' place, which is also zero.

The third digit 7 after the decimal point is in the 'thousandths' place, which means we have seven thousandths.

Combining these, we get the phrase "seven and seven thousandths," which is the written form of the number 7.007.

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

product means multiply, sum means add

 so add 5+k = (5+k)

now multiply that by 6 to get

6(5+k)

Matrix-chain-multiply is a recursive algorithm used to find the optimal matrix multiplication for a chain of matrices.

Matrix chain multiplication is a dynamic programming problem that aims to find the most efficient way to multiply a chain of matrices. We can solve this problem using a recursive algorithm called matrix-chain-multiply.

The algorithm takes four parameters: the matrix chain a, an array s to store the optimal split points, and indices i and j that determine the subchain to be multiplied. The base case of the recursive algorithm is when i and j are equal, in which case we simply return a[i].

For any other case, we iterate through all possible split points and recursively calculate the number of scalar multiplications required. We then select the split point that minimizes the required scalar multiplications. The overall complexity of the algorithm is O(n^3), where n is the number of matrices in the chain.

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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.

Dominic's total earnings for the week are calculated by adding his fixed salary of $285 to his commission, which is 8% of his sales. The commission on $4,213 worth of sales is $337.04, resulting in total earnings of $622.04.

The question requires us to calculate Dominic's total earnings for the week based on his fixed salary and the commission he makes from sales. Dominic earns a fixed amount of $285 per week plus an 8% commission from his sales. To find his total earnings, we need to calculate his commission from the $4,213 worth of merchandise he sells.

Firstly, we convert the 8% commission rate into decimal form by dividing by 100, which gives us 0.08. Then, we multiply the total sales amount by this decimal to find the commission amount:

Next, we add the commission to Dominic's fixed salary to get his total earnings for the week:

Therefore, Dominic's total earnings for the week will be $622.04.