The variable y varies jointly with x and w when y = - 42, x = 2, and w = -3.
1.) Find the constant of variation.
k=

Answer:

Linda starts the month with $15 in debt. Each hour, she makes 2.5 dollars. How many hours will it take for Linda to get out of debt?

A situation that can be represented by the expression 2.5x - 15 is given below.

Let's consider a situation where you are tracking the amount of money you earn from selling handmade crafts. In this scenario, the expression 2.5x - 15 can represent your net earnings after deducting the initial investment and expenses.

Suppose you invest a certain amount of money in materials and supplies to create your crafts. The variable x represents the number of crafts you sell. Each craft generates a profit of $2.50. Therefore, the term 2.5x represents the total profit you earn from selling x crafts.

However, running a business incurs expenses. In this case, the expression -15 represents $15, which is the total expense or cost associated with producing and selling your crafts.

So, 2.5x - 15 calculates your net earnings after subtracting the expenses from the profit. It provides you with a measure of how much money you've made after covering the costs.

By plugging in different values for x, you can evaluate the expression to determine your earnings for various levels of craft sales, allowing you to analyze your profitability and make informed decisions regarding your business.

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Option (c) 75% of Country A women weigh between 110 and 240 pounds.

What is the five-number summary?

When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

Given, the five-number summary of Country A:

92, 110, 120, 160, 240

Then, we get

Minimum value = 92, First quartile = 110, Median = 120, Third quartile=160,

Maximum value = 240

Between 110 and 240 pounds, data lies from the First quartile to Maximum value which represents 75% of the data.

Hence, Option (c) 75% of Country A women weigh between 110 and 240 pounds.

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The equation that represents the graph will be y = - (2)ˣ + 3.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation is given below.

y = A · (2)ˣ + k

At x = 0, the value of y is 2.

2 = A + k          ...1

At x = 1, the value of y is 1.

1 = 2A + k         ...2

Subtract equation 1 from equation 2, then we have

A = -1

Then the value of k is given as,

2 = -1 + k

k = 2 + 1

k = 3

The equation that represents the graph will be y = - (2)ˣ + 3.

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Answer:

Step-by-step explanation:

Answer:

22/25

Step-by-step explanation:

0.88 = 88/100

(88:4)/(100:4)

22/25

Answer:

F(x) = m1/5

Step-by-step explanation:

Answer:

4

Answer: yes, 1/3, 1/3x

Step-by-step explanation:

Does x vary directly with y?

This basically means is this a linear function and the answer is yes it is.

What is the constant of variation?

The constant of variation is 1/3 because you have to multiply each x value by 1/3 to get the y value

What is the function rule?

y = 1/3x

Answer:

Triangle PQR is a right triangle. First we have to find the length of each side of the triangle. This can be done using the points provided, along with the Pythagorean theorem, which is a^2+b^2=c^2. PR^2 = (7- -2)^2+(3-5)^2 = 85 => PR = sqrt(85) QR^2 = (7- -1)^2+(3-1)^2 = 68 => QR = sqrt(68) QP^2 = (1-5)^2+(-1 - -2)^2 =17 => QP = sqrt(17) Now that we have the sides of the triangle, we can put them into the Pythagorean theorem again to see that it works out: (Sqrt(17))^2 + (sqrt(68))^2 = (sqrt(85))^2 17 + 68 = 85 85 = 85 Since the Pythagorean theorem works for right triangles, the triangle is indeed a right triangle.

Step-by-step explanation:

The graph of the function f(x) = x² + 7x + 10 is attached.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix. The general equation of a parabola is -

y = a(x - h)² + k

We have the following equation of a quadratic equation representing parabola as -

f(x) = x² + 7x + 10

Refer to the graph of the function f(x) attached. It can be seen that it is a parabola opening upwards.

Therefore, the graph of the function f(x) attached.

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Answer:

-7 or 7

Step-by-step explanation:

|x|-2=5

Add 2 to each side:

|x|=7

Because it is the absolute value, x can be -7 or 7

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The average weight of a male Florida panther rounded to the nearest whole number is 53 kg

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Average weight = 52.6 kg

52.6

The number after decimal point is 6 which is more than 5.

So add  1 to the 52, we get 53

Thus, the average weight of a male Florida panther rounded to the nearest whole number is 53 kg

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Answer: The carbs in one glass of milk is 14 carbs and one snack bar is 10 carbs

Step-by-step explanation: Hope this helps!

Answer:

Step-by-step explanation:

78 and 10g

Answer:

[tex]\huge\boxed{\sf \$ \ 11.52}[/tex]

Step-by-step explanation:

12 bottles of juice = $8.64

Divide 12 to both sides

12/12 bottle of juice = $8.64/12

1 bottle of juice = $0.72

Multiply 16 to both sides

1 × 16 bottles of juice = $0.72 × 16

[tex]\rule[225]{225}{2}[/tex]

Answer: -$155

Step-by-step explanation:

Using this formula

New status=(-Account status-Cheque amount)-Bank charges

Let plug in the formula

New status= (-$112-$22)-$21-

New status=-$134-$21

New status=-$155

Inconclusion The new status of John's account at this point is -$155

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The required co-terminate angles of 1817° between 0° to 360° is 343°.

Co-terminal Angles are points who share similar introductory side and terminal sides. Finding co-terminal points is just about as straightforward as adding or taking away 360° or 2π to each point, contingent upon whether the given point is in degrees or radians. There are a boundless number of co-terminal  Angles that can be found.

For calculating co-terminal of angle 1817°,

We will subtract given angle 1817° from 2160°(multiple of 360°)

Then,

2160° - 1817°

343°

Thus, the co-terminating angle of 1817° is 343°.

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Applying the two-tangent theorem, the perimeter of the polygon = 70 cm.

To find the perimeter of a polygon, sum all the side lengths of the polygon all together.

If two tangent segment of a circle are drawn to meet at a point outside the circle, the two-tangent theorem says they are congruent together, that is, they have equal length.

Applying the two-tangent theorem, the following side lengths that are missing as labelled in the diagram attached below are:

a = 13 cm

b = 9 cm

c = 5 cm

d = 8 cm

Therefore:

Perimeter of the polygon = 13 + a + b + 9 + 5 + c + d + 8

Plug in the values

Perimeter of the polygon = 13 + 13 + 9 + 9 + 5 + 5 + 8 + 8 = 70 cm.

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Answer:

x=1/4k

Step-by-step explanation:

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Answer: Thousand  Liters

Step-by-step explanation:

a) The population of the confidence interval is given as follows: The temperature all days for that summer.

b) The point estimate of the interval is of: 80 degrees Fahrenheit.

c) The margin of error of the interval is of: 8 degrees Fahrenheit.

A confidence interval for a population parameter is built taking a sample of this population.

Then, the interval for the population mean is given as the sample mean plus/minus the margin of error.

The sample in this problem is given as follows:

The temperature for 10 days of summer.

Hence the population is of:

The temperature all days for that summer.

The interval in this problem is given as follows:

(72, 88).

The point estimate is the mean of the bounds, hence:

Point estimate = (72 + 88)/2 = 80.

The margin of error is half the difference of the two bounds, hence:

Margin of error = (88 - 72)/2 = 8.

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The fog(x) of the function will be 6x² -2x - 5 and gof(x) of the function will be 12x² + 62x - 80.

The collection of values that can be plugged into a function's domain is called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of numbers that the operator assumes is known as its range.

As per the given information in the question,

f(x) = 2x - 5 and,

g(x) = 3x² - x

fog(x) = 2x - 5 and,

gof(x) =  2x - 5

fog(x) = f(g(x))

= f (3x² - x) = 2(3x² - x) -5

= 6x² -2x - 5

gof(x) = g(f(x))

= g (2x - 5) = 3(2x - 5)² + 2x - 5

= 12x² - 75 + 60x + 2x -5

12x² + 62x - 80.

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Answer:

Step-by-step explanation:

(4,8)..Its the only one in which x doesnt repeat

120/15=f/18 is the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

Margie hands out 100 flyers in 2 hours.

Jaxon hands out 18 flyers in 15 minutes.

We need to find the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours.

Let us convert hours to minutes

2 hours=120 minutes.

Let f be the number of flyers Jaxon handed out in 2 hour.

18/15=f/120

Apply cross multiplication

120/f=15/18

120/15=f/18

Hence, 120/15=f/18 is the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours

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Answer:

y = 10, x = 18

Step-by-step explanation:

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The person who makes a basket more often, between Simon and Reina, is Simon

To find who makes the basket more, you need to find the percentage number of times the basket is made.

The percentage number of times the basket is made by Simon is :
= Number of baskets made / ( Number of baskets made + Number of baskets missed ) x 100 %

= 7 / ( 7 + 5 ) x 100%

= 7 / 12 x 100%

= 58.3%

The percentage number of times Reina makes the basket is :

= 9 / ( 9 + 7 ) x 100%

= 9 / 16 x 100%

= 56.25%

Simon therefore makes the basket more.

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Answer:

The total fare is $53, and the distance is 25

Step-by-step explanation:

The equation we can use for the first car would be:

28 + (1×k) = fare (f)

The equation we can use for the second car would be:

3 + (2×k) = f

If we were to plug in 20 into the equations, it would look like this:

28 + (1×20) = 48 (first car)

3 + (2×20) = 43 (second car)

As you can tell, the prices aren't matched up just yet.

Let's plug 25 into the equations.

28 + (1×25) = 53

3 + (2×25) = 53

The number of kilometers traveled is 25, and the price is $53

The total number of sandwiches they have in all on Sunday is 375 sandwiches.

The amount earned by the cafe if each sandwich cost $4.50 is $1,687.5

Total percentage of ham and turkey sandwiches = 35% + 25%

= 60%

So,

225 = 60% of x

225 = 0.60 × x

225 = 0.60x

divide both sides by 0.60

x = 225/0.60

x = 375

Hence,

Total number of sandwiches = 375

If the cafe sells all the sandwiches at $4.50 each

The total money earned by the cafe = cost of each sandwich × total number of sandwiches

= $4.50 × 375

= $1,687.5

Therefore, the total sandwiches sold in the cafe on Sunday is 375 sandwiches.

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Answer:100/10000000000

Step-by-step explanation:qazwsxeedcrfvtgbyhn