Write an equation of the line that passes through (2, 7) and (0, −5).

The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

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Step-by-step explanation:

Heron's formula when all 3 sides (a, b, c) are given :

s = (a + b + c)/2

A = sqrt(s(s-a)(s-b)(s-c))

in our case

s = (34+73+89)/2 = 98

A = sqrt(98(98-34)(98-73)(98-89)) =

= sqrt(98×64×25×9) = sqrt(98)×8×5×3 =

= sqrt(2×49)×120 = sqrt(2)×7×120 =

= sqrt(2)×840 = 1,187.939392... ≈ 1,188 in²

Answer:

Attached is an example of a circle with a radius of 5 and a diameter of 10.

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Have a GREAT day!!!

The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

A

Step-by-step explanation:

There is an x in all for terms that means that x = 0 is one of the factors and H is incorrect.

One of the remaining factors is x^2 - 9 which factors into (x - 3)(x + 3)

You are told that x = 1  is a zero which means x - 1 is a factor.

The answer is g(x) = x (x - 3)(x + 3) (x - 1) which is A

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

i think the answer is 60

Step-by-step explanation:i did the math

For only 4 wire transfers, Checking account A has a monthly fee of $54, while checking account B has a monthly fee of $55, so the correct option is D.

Checking account A charges a monthly fee of $12, plus $10.50 for each wire transfer, then the total cost if you make 4 wire transfers is:

C = $12 + $10.50*4 = $54

For checking account B, we have a fixed cost of $21, plus $8.50 per each wire transfer, then the total cost for 4 wire transfers is:

C'  = $21 + 4*$8.50  = $55

So, if you make only 4 wire transfers per month, checking account A is a better option.

Then we can see that the correct option is D.

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Maci and 2 appointments and Logan had 3 appointments.

The linear equation that represents the total amount earned by Maci is:

Total amount earned = (amount per appointment x number of appointments)  + tips

$170 = ($60 x a) + $50

$170 = $60a + $50

$170 - $50 = $60a

$120 = $60a

a = $120 / $60

a = 2

The linear equation that represents the total amount earned by Logan is:

Profit = total revenue - total cost

Profit = (fee per appointment  x number of appointments) + amount received in tips - (rental fee x number of appointments)

$235 = ($75 x a) + $40 - ($10 x a)

$235 = $75a + $40 - $10a

$235 = $65a + $40

$235 - $40 = $65a

$195 = $65a

a = $195 / 65

a = 3

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Answer:

c

Step-by-step explanation:

Answer:

201,376

Step-by-step explanation:

This is a combination because order doesn't matter

32 C 5 = 201,376

The number of different kinds of milkshakes that she can make will be 201,376.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Mary wants to make a milkshake by choosing 5 flavors of ice cream and putting a scoop of each in the blender. If mary has 32 flavors of ice cream available to her.

Then the number of the different kinds of milkshakes that she can make will be given by the combination formula.

Combination = ³²C₅

Combination = 32! / [(32 - 5)! x 5!]

Combination = 32 x 31 x 30 x 29 x 28 x 27! / (27! x 5 x 4 x 3 x 2 x 1)

Combination = 8 x 31 x 29 x 28

Combination = 201,376

The number of different kinds of milkshakes that she can make will be 201,376.

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Answer:

-5, 3

Step-by-step explanation:

The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

Rounding to the nearest hundredth, the area of the sector is approximately 49.06 cm².

To find the area of the sector of a circle, you can use the formula:

Area = (θ/360) * π * r²,

where θ is the central angle in degrees, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.

In this case, the central angle is 225° and the radius is 5 cm. Plugging these values into the formula, we get:

Area = (225/360) * 3.14 * (5 cm)²

Area = (0.625) * 3.14 * 25 cm²

Area ≈ 49.0625 cm²

Rounding to the nearest hundredth, the area of the sector is approximately 49.06 cm².

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Answer:

888

Step-by-step explanation:

The graph has an asymptote at y = 0 and is increasing as x approaches positive Infinity. Then the correct option is A.

An asymptote is a line that constantly reaches a given curve, but does not touch at any infinite distance.

Graph the given function.

f(x) = (7)ˣ

The graph of the function is given below.

From the graph, the graph has an asymptote at y = 0 and is increasing as x approaches positive Infinity.

Then the correct option is A.

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The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Using the z-distribution, as we have the standard deviation for the population, to test the hypothesis, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

At the null hypothesis, it is tested if the mean time is of 28 minutes, that is:

\(H_0: \mu = 28\)

At the alternative hypothesis, it is tested if the mean time is greater than 28 minutes, that is:

\(H_1: \mu > 28\).

The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

The parameters are:

In this problem, the values of the parameters are given by:

\(\overline{x} = 32, \mu = 28, \sigma = 5, n = 10\)

Hence:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{32 - 28}{\frac{5}{\sqrt{10}}}\)

\(z = 2.53\)

Considering that we have a right-tailed test, as we are testing if the mean is greater than a value, with a standard significance level of 0.05, the critical value is of \(z^\ast = 1.645\).

Since the test statistic is greater than the critical value, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

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Answer:

0 and -6

(0,-6)

Step-by-step explanation:

Can't really explain, but this is a guess on the actual question.

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

The rate of change of the height of the water in the pool when the depth of the water is 8 feet is equal to 602.84 cubic feet per minute.

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period.

The rate of change of the height of the water in the pool can be calculated by using the formula:
rate of change = (change in volume) / (change in time).

In this case, the change in volume is equal to the volume of the cylinder when the water is 8 feet deep minus the volume of the cylinder when the water is 0 feet deep. This is equal to (π*3^2*8) – (π*3^2*0), or 602.84 cubic feet. The change in time is equal to 1 minute.

Therefore, the rate of change of the height of the water in the pool when the depth of the water is 8 feet is equal to 602.84 cubic feet per minute.

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The two functions f and g are inverses of each other. Correct option is A. Yes

Inverse functions are functions which can be reversed in to another function.

Two functions f and g are inverses of each other if the composition of functions,

f (g(x)) = x and g(f(x)) = x

Given f(x) = 9x + 12 and g(x) = \(\frac{x-12}{9}\)

First, plug g(x) into f(x).

f [g(x) ] = f [ \(\frac{x-12}{9}\)]

           = 9 ( \(\frac{x-12}{9}\)) + 12

           = x - 12 + 12

           = x

Now plug f(x) into g(x).

g [f(x) ] = g [9x + 12]

           = \(\frac{9x+12-12}{9}\)

           = 9x / 9

           = x

Hence f and g are inverses of each other.

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The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.

To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:

Probability = possible outcome/ sample space

Where possible outcome = 2

sample space = A,B,B,B,C,C,D,D,D,E = 10

Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.

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The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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Answer:

(-2,5)

Step-by-step explanation:

Answer:

g(x)= ( \(\frac{1}{3}^{x}\)) − 2

Step-by-step explanation:

just took the quiz :D

the remainder when f(x) = x⁴ - 5x³ + 3x² - 2x +7 is divided by x - 1 is 4

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145