Determine the equation of the line that goes through the points (-2, 1) and (1, -1).
The equation of the line is:

Answer:

Step-by-step explanation:

If I found the mean, the answer would be:

3+ 4+4+4+5+6+7+23= 56

56/ 8 = 7

If I found the average value using the median, the answer would be 4.5.

In this set of data, the anomaly is 23 as it is much higher than the other numbers.

The median is more accurate because it find the more ‘central’ number and is not affected as greatly with anomalies whereas the mean is affected greatly with anomalies as it raises the value significantly.

Therefore, the median is better to work out the average in this set of data.

:)

Answer:

55.68

Step-by-step explanation:

55.678 rounded to the nearest hundred would be 55.68.

Answer:

55.68

Step-by-step explanation:

because

Answer:

2/3

Step-by-step explanation:

.that's the answer

The 14.9% increase in Sylvia's lead lathe tech's hourly wage of $18.50 results in a $2.75 per hour increase. Assuming the lead lathe tech works 2,080 hours per year, the additional cost to Sylvia's annual wages budget would be approximately $5,720, excluding benefits or taxes.

First, we need to find the percentage increase in the lead lathe tech's hourly wage. The increase requested is $2.75, which is 14.9% of the current wage rate ($18.50). To calculate the percentage increase, we divide the increase by the current wage rate and multiply by 100: ($2.75 / $18.50) * 100 ≈ 14.9%.

To determine the additional cost to Sylvia's annual wages budget, we need to know the total number of hours worked by the lead lathe tech in a year. Let's assume the lead lathe tech works 40 hours per week and there are 52 weeks in a year, resulting in a total of 2,080 hours.

To calculate the annual cost of the wage increase, we multiply the hourly increase ($2.75) by the total number of hours worked (2,080): $2.75 * 2,080 ≈ $5,720.

Therefore, the 14.9% increase in the lead lathe tech's hourly wage will cost Sylvia an additional $5,720 in her annual wages budget, excluding benefits or taxes.

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The function is 130/2.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

According to question,

\(\int\limits^9_0 {f(x)} \, dx \\ \int\limits^7_0 {f(x)} \, dx+\int\limits^9_7 {f(x)} \, dx\\ \int\limits^7_0 {7} \, dx + \int\limits^9_7 {x} \, dx\\ (7x)^{7} _{0} + (\frac{x^{2} }{2})^{9} _{7}\)

7x7 - 7x0 + 81/4 - 49/4

49 + 32/2

130/2

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The factor of the \(18x^{2} -21x-15\) will be 3(3x-5)(2x+1).

Given quadratic equation is \(18x^{2} -21x-15\)

By taking 3 common from whole of the equation it becomes.

\(3(6x^{2} -7x-5)\)

now by factorization equation will be.

\(3(6x^{2} -10x+3x-5)\)

3[(2x(3x-5)+1(3x-5)]

Taking (3x-5) common from whole equation it will become

3(3x-5)(2x+1).

Hence the factor of the \(18x^{2} -21x-15\) will be 3(3x-5)(2x+1).

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Answer:

I think the sum of the first 10terms of each geometric series is

4x3=12

= 4+12

12x3=36

=4+12+36

36x3=108

=4+12+36+108

108x3=324

=4+12+36+108+324

324x3=972

=4+12+36+108+324+972

972x3=2916

= 4+12+36+108+324+972+2916

2916x3=8748

=4+12+36+108+324+972+2916+8748

8748x3=26244

=4+12+36+108+324+972+2916+8748+26244

26244x3=78732

=4+12+36+108+324+972+2916+8748+26244+78732=the sum of the geometric series which is = 118,096.

hope this helps I am not sure of the answer but I tried my best.

Answer:

the second one

Step-by-step explanation:

in order for it to be a function the x values CANNOT repeat.

in answer a the x value -6 repeats so that cannot be a function

in answer b none of the x values repeat so its probably this one but lets check the other ones just in case

in answer c the x value 8 repeats so it cannot be this one

in answer d the x value -2 repeats so it cant be this one \

b is the only one that does have repeating x values therefore it is the second one

There is sufficient data to infer that the valve does not operate as intended at the 0.1 level.

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

In inferential statistics, the null hypothesis states that two possibilities are equal.

The observed difference is thought to be the sole product of chance, which is the underlying premise.

Statistical tests can be used to calculate the likelihood that the null hypothesis is true.

So,

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

As the population standard deviation is given when n > 30

So, we'll run the Z test.

Formula: \(z=\frac{x-\mu}{\frac{a}{\sqrt{n}}}\)

Replace the values:

\(\begin{aligned}& z=\frac{7.7-7.6}{\frac{11.6}{\sqrt{160}}} \\& z=2.449\end{aligned}\)

For the p-value, see the z table.

Consequently, p = 0.9927.

The two-tailed nature of the test So, p = 2(1- 0.9927) = 0.0146

α = 0.1

p value< α

Thus, we disregard the null hypothesis.

Hence, at the 0.1 level, there is enough evidence to conclude that the valve does not function as intended.

Therefore, there is sufficient data to infer that the valve does not operate as intended at the 0.1 level.

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

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Answer:

48 pipes

Step-by-step explanation:

3/4 of 1 foot = 0.75 foot

36/0.75=48

The probability that exactly 4 out of the 5 randomly selected employees are cashiers is approximately 0.00549 or 0.549%

To calculate the probability that exactly 4 out of the 5 employees selected to work on Labor Day are cashiers, we need to use the concept of combinations and probabilities.

First, let's determine the total number of ways to select 5 employees out of the 22. This can be calculated using the combination formula:

C(n, k) = n! / (k!(n-k)!)

where n is the total number of employees (22) and k is the number of employees selected (5).

C(22, 5) = 22! / (5!(22-5)!)

= 22! / (5! * 17!)

= (22 * 21 * 20 * 19 * 18) / (5 * 4 * 3 * 2 * 1)

= 22,957

So, there are a total of 22,957 ways to select 5 employees out of the 22.

Next, let's determine the number of ways to select exactly 4 cashiers out of the 9 cashiers. This can also be calculated using combinations:

C(9, 4) = 9! / (4!(9-4)!)

= 9! / (4! * 5!)

= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)

= 126

Now, let's calculate the probability of selecting exactly 4 cashiers out of the 5 employees randomly selected for overtime pay:

P(4 cashiers) = Number of ways to select 4 cashiers out of 9 / Total number of ways to select 5 employees from 22

= C(9, 4) / C(22, 5)

= 126 / 22,957

≈ 0.00549

Therefore, the probability that exactly 4 out of the 5 randomly selected employees are cashiers is approximately 0.00549 or 0.549%

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Answer:

the smaller number is 18 and the larger number is 24

Given the expression that models the tip amount for a total bill of $102:

You know that "x" represents the dollar amount of the tax.

You also know that Mr. Jaxon tips $23.50.

Therefore, knowing all that information, you can set up the following equation to represent that situation:

Now you have to solve for "x" in order to find its value:

Hence, the answer is:

Answer:

5/3 would be the answer

Answer:

50

Step-by-step explanation:

you toss the ball 24 times, and of those 24 times, it lands 12 times on the yellow section, so 12/24= 0.5

Answer: 50

Step-by-step explanation:

Answer:

2x+3

Step-by-step explanation:

You have to combine your like terms then Subtract. I have tested my answer against an online Algebra Problem solver and this is 100% for sure the correct answer.

PLEASE MARK BRAINLIEST

Answer:

2x + 3

Step-by-step explanation:

i did the test

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

6 - n = 6 - (-#) = 6 + n

3 (6n) = greatest value

The length of the rectangular painting is equal to 76 cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of a rectangular painting is 4636 cm². The width of the painting is equal to 61 cm.

The length of the painting is calculated as,

Area of rectangle = Length x Width

4636 = Length x 61

Length = 4636 / 61

Length = 76 cm

The length is 76 cm for the rectangle.

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The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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The best order of integration for the given double integral is integrating with respect to y first and then with respect to x. The result of the integral will be 60xy.

The given double integral is 60x. To determine the best order of integration, we need to evaluate the integral using both the row-first order and the column-first order and compare the results.

Let's first consider integrating with respect to x first and then with respect to y. The limits of integration for x will depend on the outer integral with respect to y. Since there is no information provided about the limits of integration, we cannot proceed with this order.

Now, let's consider integrating with respect to y first and then with respect to x. The limits of integration for y will depend on the outer integral with respect to x. However, since the given function is 60x, the integral with respect to y will yield 60x times the integral of 1 with respect to y, which simplifies to 60xy.

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Answer: A. The compromise allowed California to join the United States as a free state but would allowed slavery in the southwestern territories.

Step-by-step explanation:

As the abolitionist North and the pro-slavery South saw their rivalry intensify with the lobbying by the South that slavery should be allowed in the western territories, Congress decided to pass the compromise of 1850 which was several acts that would calm both sides for the time being.

With this compromise, California was allowed to join the United States as a free state but in return, the Southwestern territories were allowed to decide their slavery status in an election which meant that if the territories so pleased, they could allow slavery in their territories.

To write an augmented matrix for a system of equations, you need to organize the equations into a matrix format.

This is done by writing each equation in terms of its coefficients, separating them with a comma, and placing them in a row. The coefficients for each equation should line up in the same columns. Then you need to include the constant terms of each equation in a separate column to the right of the coefficients.

For example, if you have the equations 2x + 3y = 8 and 5x + 7y = 10, the augmented matrix would be:

2, 3, 8
5, 7, 10

An augmented matrix for a system of equations is a matrix that represents the system of linear equations.

To write an augmented matrix for a system of equations, you can follow the following steps:

Step 1: Write the system of equations in matrix form.Example: Consider the following system of linear equations2x + 3y + 4z = 4x - 2y + 5z = 3x + y - z

Step 2: Write the matrix for the coefficients of the variables of the system of equations along with the matrix of the constant terms

Example: The matrix of the coefficients of the variables and the matrix of the constants for the above system of linear equations can be written as [2 3 4 | 4; 4 -2 5 | 3; 3 1 -1 | 2]

Step 3: Write the augmented matrix by combining the matrix of the coefficients and the matrix of the constants with a vertical line in between.

Example: The augmented matrix for the above system of linear equations is[2 3 4 | 4; 4 -2 5 | 3; 3 1 -1 | 2]

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Answer: 5

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

Step-by-step explanation:

That appears to be approximately 45 degrees, so to the nearest 10, I would put that at about a 50 degree angle.

Answer:

no solution with given parts of equation

Step-by-step explanation:

4(x-1)+3-2/2=n

4(x+1)+3-1=n

4(x+1)+2=n

4x+4+2=n

4x+6=n

Alternatively:

Slope = 4

x-intercept = -1.5

n-intercept = 6

Answer:

If you're looking for a simplified answer it would be: 4x-2

Step-by-step explanation:

Let L be the line in R^3 that consists of all scalar multiples of the vector `[3, 4, 5]`. Find the reflection of the vector v = `[1, 2, 3]` in the line L. A reflection is a transformation that takes an object and reflects it over a line. This transformation is called an isometry because the distance between points on the object is preserved.

Let's call the point of intersection between the line and the plane `P`. To find the reflection of `v` in the line `L`, we need to find the point `R` on `L` that is equidistant from `v` and `P`. We can do this by finding the projection of `v` onto `L`, and then doubling the distance between `v` and the projection. The projection of `v` onto `L` is given by:


where `u` is a unit vector in the direction of `L`. Since `L` consists of all scalar multiples of `[3, 4, 5]`, we can take `u` to be:

\(u = (1/√(3² + 4² + 5²))[3, 4, 5] = (1/√50)[3, 4, 5]\)

Then, we have:

Now, we need to double the distance between `v` and `projL(v)` to find `R`. We have:

R = v + 2(projL(v) - v) = [1, 2, 3] + 2([(29/50)3, (29/50)4, (29/50)5] - [1, 2, 3]) = [(58/25) - 1, (58/25) - 2, (58/25) - 3] = [(33/25), (8/25), (-7/25)]

Therefore, the reflection of `v` in the line `L` is `[33/25, 8/25, -7/25]`.

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The height  of the box that has the smallest possible surface area is  20m .

In the question ,

it is given that ,

the box has a square base ,

let the side of the box = "x" m

and let the height of the box = "y" m

volume of the box is given as 32000 m³,

So , x²y = 32000

y = 32000/x²

let the surface area of the box be "S" , that means

surface area(S) = area of base + total area of the 4 sides

= x²y + 4xy

Substituting the value of y = 32000/x² , we get

= x² + 4x(32000 / x²)

= x² + 128,000 / x,       x > 0

to minimize the area we differentiate it with respect to x,

we get ,

= 2x - 128,000 / x²

= (2x³ - 128,000) / x²

Substituting S' = 0 ,  we get , 2x³ = 128,000

x³ = 64,000

x = 40

and y = 32000/(40)² = 20 m .

Therefore , The height  of the box that has the smallest possible surface area is  20m .

The given question is incomplete , the complete question is

A box with a square base and open top must have a volume of 32,000 m³ . Find the height of the box that has the smallest possible surface area ?

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