When x = 1 then y equals

To get an average earnings of $1,000 for all nine salespeople, the ninth salesperson needs to earn $2,450.

The subject of this question is mathematics, specifically statistics, and it involves the concept of 'mean' or 'average'. To find out what the ninth person needs to earn to keep the average earn of $1,000, we first need to calculate the total earnings of all nine people. Since the average earnings of a salesperson is $1,000, we multiply $1,000 by 9, which gives us $9,000. Then we need to subtract the sum of the earnings of the first eight salespeople from $9,000 to find out the earnings of the ninth person.  

Here is the breakdown with the given figures:

So, the ninth person would need to earn $2,450 for the average earnings to remain at $1,000.

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Answer:

Step-by-step explanation:

1. The total amount of oil in the two tanks at the start is ...

  total oil = n + (n +150) + 0 = 2n+150 . . . . litres

The amount of oil in tank C at the end is 1/3 this amount, or

  oil in tank C = (total oil)/3 = (2n+150)/3 . . . . litres

The amount pumped into tank C was 500 litres, so we have ...

  (2n +150)/3 = 500

  2n +150 = 1500 . . . . . . multiply by 3

  2n = 1350 . . . . . . . . . . . subtract 150

  1350/2 = n = 675 . . . . . divide by the coefficient of n

___

2. Let x represent the amount remaining in container A. Then 4x is the amount in tank B. Before the transfer, the amount in each container was the same, so ...

  x +120 = 4x -120 . . . . . A had 120 more than remains; B had 120 less

  240 = 3x . . . . . . . . add 120-x

  240/3 = x = 80 . . . divide by the coefficient of x

The amount of liquid left in container A is 80 mL.

To find the area of the surface above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.

To find the area of the surface that lies above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The equation of the cylinder is y^2+z^2=9, and the vertices of the rectangle are (0,0), (4,0), (0,2), and (4,2). At the x=0 and x=4 cross sections, we can see that the y-coordinate ranges from 0 to 2 and the z-coordinate ranges from -3 to 3. Therefore, the surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.

The area of the rectangle is (4-0)(2-0) = 8 square units. The range of the z-coordinate is -3 to 3, so the surface area above the rectangle is 8 * (3 - (-3)) = 48 square units.

It takes Robert 13 minutes and 36 seconds to complete a 400 meter swimming race when he swims the first 50 meters in 1 minute and slows down by 12 seconds for each subsequent 50 meters.

In this mathematical problem, Robert swims the first 50 meters in 1 minute. He slows down by 12 seconds for each subsequent 50 meters of the race. The total distance Robert needs to swim is 400 meters. The 400 meters is split into eight 50 meter increments.

For the first increment, it takes Robert 1 minute (or 60 seconds). For the next seven increments, Robert swims each in 12 seconds slower than the previous increment.

Therefore, the total time in seconds for Robert to complete the 400 meters swimming race is:

60 + 72 + 84 + 96 + 108 + 120 + 132 + 144 = 816 seconds

This is equivalent to 13 minutes and 36 seconds.

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-5.25, -5.09, 1.002

hopes this help please mark me as brainliest. :)

Answer:

Yes, the number is correct.

Step-by-step explanation:

The cost of a hamburger is $2.50.

Each additional hamburger cost $2.00.

Sully wrote this explicit rule to explain the sequence of costs:

[tex]f(n) = 2+2.5(n-1)[/tex]

Using the rule, he found the cost of 12 hamburgers to be 29.50.

Lets check by putting n = 12.

[tex]f(12) = 2+2.5(12-1)[/tex]

= [tex]2+2.5(11)[/tex]

=  [tex]2+27.5 [/tex]

= $29.50

So, yes Sully is correct.

A unit test for the function addInventory() can be written in JavaScript using Jest. The test checks that the quantity of red sweaters increases correctly after calling addInventory(). If the test fails, an error message will be shown.

Based on the information given, you can create a unit test in many programming languages. Here we are going to illustrate with JavaScript and use the Jest testing framework.

Firstly, let's name the unit test file as redSweater.test.js. In this file, we call the addInventory() of the redSweater object with sweaterShipment as parameter.  Note that addInventory() is a method that increases the quantity of red sweaters in inventory by a certain amount provided by sweaterShipment.

Here is a sample unit test for your needs:

const redSweater = require('./redSweater'); // path to your redSweater.js file

test('addInventory() unit test', () => {

let initialQty = 10;

redSweater.qty = initialQty;

let shipmentQty = 50;

redSweater.addInventory(shipmentQty);

expect(redSweater.qty).toBe(initialQty + shipmentQty);

});

This script tests that the quantity of red sweaters increases correctly after calling the addInventory() method. If the quantity is not correct after the method call, the test will fail and show an error message.

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Final answer:

Using the formula for the confidence interval of a proportion, and after calculating standard error and margin of error, the 98% confidence interval for the proportion of 8th graders involved in after school activities is [0.799, 0.981]. Therefore, option a is correct.

Explanation:

To find the 98% confidence interval for the proportion of 8th graders involved in some type of after school activity, we can use the formula for the confidence interval of a proportion:

CI = ± z * √((p*(1-p))/n), where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the confidence level.

In this case, we have p = 0.89 (since 89% of the sample is involved in after school activities), n = 64, and for a 98% confidence interval, the z-score (from z-tables or statistical software) is approximately 2.33.

First, let's calculate the standard error (SE): SE = √((0.89*(1-0.89))/64) = √((0.89*0.11)/64) = √(0.0989/64) = 0.0392.

Next, calculate the margin of error (ME): ME = z * SE = 2.33 * 0.0392 = 0.09136.

Now we can calculate the confidence interval: the lower limit is p - ME = 0.89 - 0.09136 = 0.79864 and the upper limit is p + ME = 0.89 + 0.09136 = 0.98136.

After rounding to three decimal places, the 98% confidence interval for the proportion is [0.799, 0.981]. Hence, option a is correct.

Answer:

Option D

Step-by-step explanation:

The given function is

[tex]f(x)=4|x|[/tex]

It is given that the graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.

If a figure reflected across x-axis, then the rule of reflection is

[tex](x,y)\rightarrow (x,-y)[/tex]

Using the above rule, if the given function reflected across x-axis, then g(x)=-f(x).

[tex]g(x)=-(4|x|)[/tex]

[tex]g(x)=-4|x|[/tex]

The equation g(x)=-4|x| describes g(x).

Therefore, the correct option is D.

Answer:  The correct option is (B) 5.

Step-by-step explanation:  We are given to find the distance between the points (2, 5) and (6, 8).

We will be using the following formula :

DISTANCE FORMULA :  The distance between the points (a, b) and (c, d) is given by

[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]

Therefore, the distance between the points (2, 5) and (6, 8) is given by

[tex]D\\\\=\sqrt{(6-2)^2+(8-5)^2}\\\\=\sqrt{4^2+3^2}\\\\=\sqrt{16+9}\\\\=\sqrt{25}\\\\=5.[/tex]

Thus, the required distance between the given points is 5 units.

Option (B) is CORRECT.

Final answer:

The largest area for a rectangle with a fixed perimeter of 168 feet is achieved by a square, and the dimensions of that square are 42 feet by 42 feet.

Explanation:

To find the dimensions of a rectangle with the largest area given a fixed perimeter, we need to understand that the rectangle with the largest area for a given perimeter is a square.

In this problem, the perimeter is 168 feet, which can be expressed by the formula 2l + 2w = 168, where l is the length and w is the width of the rectangle. Knowing that a square has all four sides equal, we simply divide the perimeter by 4 to get the side length, which gives us l = w = 168/4 = 42 feet.

Therefore, the dimensions of the rectangle with the largest area, which in this case is a square, are 42 feet by 42 feet.

Answer:

the answer is .15

Step-by-step explanation:

The annual value of the employer's contribution towards Trina's health insurance plan is $5,580.

Here, we have to find the annual value of the employer's contribution, we need to determine how much the employer pays towards the health insurance plan in one month.

Trina's employer purchased a health insurance plan that costs $550 per month, and Trina pays $85 toward the plan each month.

Therefore, the employer's contribution is the difference between the total cost of the plan and what Trina pays:

Employer's contribution = Total cost of the plan - Trina's contribution

Employer's contribution = $550 - $85

Employer's contribution = $465 per month

Now, to find the annual value of the employer's contribution, we multiply the monthly contribution by 12 (since there are 12 months in a year):

Annual employer's contribution = $465 * 12

Annual employer's contribution = $5,580

So, the annual value of the employer's contribution towards Trina's health insurance plan is $5,580.

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Answer:

Option C is correct.

Step-by-step explanation:

The formula is = [tex](1+\frac{r}{n})^{n}-1[/tex]

r = rate of interest

n = number of times its compounded

1. 4.0784% compounded monthly

here n = 12

[tex](1+\frac{0.040784}{12})^{12} -1[/tex] = 1.0403-1 = 0.0403

2. 4.0798% compounded semiannually

here n = 2

[tex](1+\frac{0.040798}{12})^{2} -1[/tex] = 1.0066-1 = 0.0066

3. 4.0730% compounded daily

here n = 365

[tex](1+\frac{0.040730}{12})^{365}[/tex] = 3.328-1 = 2.328

The sample mean for the given 90% confidence interval (65, 77) is 71. The margin of error is 6. The sample standard deviation cannot be specifically calculated without the t-value, but presuming a common t-value for such datasets (1.96), it approximates to 3.072.

The subject at hand pertains to confidence intervals and basic statistics calculations. Given a 90% confidence interval of (65, 77), we can find the sample mean by adding the two limits and dividing by 2. So (65 + 77) / 2 equals 71.

The margin of error for the confidence interval is calculated by subtracting the sample mean from the upper limit. That gives us 77 - 71 equals 6.

Unfortunately, without knowing the value of the t-statistic, we can't calculate the sample standard deviation, as it's calculated via the formula: standard deviation = margin of error / (t-value/sqrt(sample size)). But, usually, for a sample size of 25 observations and a 90% confidence level, the t-value is about 1.96. Using that assumed t-value, the standard deviation calculation gives us 6/(1.96/sqrt(25)) equals approximately 3.072.

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The probability that both alternators fail is approximately 0.0004, the probability that neither fails is approximately 0.9612, and the probability that at least one fails is approximately 0.0388, all rounded to four decimal places.

(a) The probability that both Alternator will fail is calculated by multiplying the probabilities of each failing:
P(Both Fail) = P(Alternator 1 Fails) x P(Alternator 2 Fails) = 0.019 x 0.019 ≈ 0.000361 = 0.0004 (rounded to four decimal places).

(b) The probability that an alternator does not fail is 1 minus the probability that it fails.
P(Neither Fail) = (1 - P(Alternator Fails))^2 = (1 - 0.019)^2 ≈ 0.9612 (rounded to four decimal places).

(c) To find the probability of at least one alternator failing, we subtract the probability of neither failing from 1:
P(At Least One Fails) = 1 - P(Neither Fail) = 1 - 0.9612 ≈ 0.0388 (rounded to four decimal places)