The surface area of a sphere is 275.56 1 cm? What is the approximate volume of the sphere?
A. 2,287.15 pi cm3
B. 762.38 pi cm3
C. 6,099.06 pi cm3
D. 381.19cm3

Answers

Answer 1

Answer:

[tex]V=430.19\ cm^3[/tex]  or  [tex]V=136.93\pi\ cm^3[/tex]

Step-by-step explanation:

The surface area of a sphere is:

[tex]A_s=4\pi r^2[/tex]

Where r is the radius of the sphere

In this case we know that [tex]A_s = 275.561\ cm^2[/tex]

So

[tex]4\pi r^2=275.561[/tex]

We solve the equation for r

[tex]4\pi r^2=275.561\\r^2 = \frac{275.561}{4\pi}\\\\r=\sqrt{ \frac{275.561}{4\pi}}\\\\r=4.683\ cm[/tex]

Now we know the radius of the sphere.

The volume of a sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

We substitute the value of the radius in the formula

[tex]V=\frac{4}{3}\pi (4.683)^3[/tex]

[tex]V=430.19\ cm^3[/tex]


Related Questions

what is the range of the reciprocal function ?

Answers

Answer:

B

Step-by-step explanation:

The range is the set of y-values for which the function is defined.

** Attached is the graph of the function

By looking at the graph, we can clearly see that there aren't any y-values that is not permitted in the graph. The function is defined for all y-values. Hence the range is set of all real numbers, or, the range is (-∞, +∞)

Answer choice B is right.

Final answer:

The range of the reciprocal function 1/x is all real numbers except zero, expressed in interval notation as (-∞, 0) ∪ (0, +∞).

Explanation:

The range of the reciprocal function, which is denoted as 1/x, can be understood by considering the behavior of the function as x approaches different values. As x approaches zero from the positive side (x → 0+), the reciprocal 1/x becomes increasingly larger, theoretically 'going to infinity' (∞). Similarly, as x approaches zero from the negative side (x → 0-), 1/x becomes increasingly negative, 'going to negative infinity' (-∞). Thus, the range of the reciprocal function excludes zero, but includes all other real numbers. In interval notation, the range is expressed as (-∞, 0) ∪ (0, +∞).

Please help, not understanding!​

Answers

Answer:

9 weeks.

Step-by-step explanation:

We need to find about how many weeks (w) it will take before Factory B has printed as many books (b) as Factory A.

In other words we need to find the value of week (w) when number of books from both factories are equal.

so set both equation equal

[tex]50w+650=100w+200[/tex]

[tex]50w-100w=200-650[/tex]

[tex]-50w=-450[/tex]

[tex]w=\frac{-450}{-50}[/tex]

[tex]w=9[/tex]

Hence final answer is 9 weeks.

It’s says factory a has printed 650 books and prints200 books just divide

Patti’s dance class starts at quarter past 4. At what time does her dance class start?

Answers

her dance class start at quater past 4

Patti's dance class starts at a quarter past 4, which is 4:15 p.m. This term refers to 15 minutes after the hour.

This question demands basic understanding of clocks and related concepts.

Patti's dance class starts at quarter past 4, which means it starts at 4:15 p.m.. In time telling, a quarter past the hour refers to 15 minutes after the hour mark. So when you're looking at a clock, this would be the time when the minute hand is on the 3 (as there are 60 minutes in an hour and 15 minutes is a quarter of that).

Therefore, as per the above explaination, the correct answer is  4:15 p.m.

Find the inverse of the given function.

Answers

For this case we must find the inverse of the following function:

[tex]f (x) = - \frac {1} {2} \sqrt {x + 3}[/tex]

We follow the steps below:

Replace f(x) with y:

[tex]y = -\frac {1} {2} \sqrt {x + 3}[/tex]

We exchange the variables:

[tex]x = - \frac {1} {2} \sqrt {y + 3}[/tex]

We solve for "y":

[tex]- \frac {1} {2} \sqrt {y + 3} = x[/tex]

Multiply by -2 on both sides of the equation:

[tex]\sqrt {y + 3} = - 2x[/tex]

We raise both sides of the equation to the square to eliminate the radical:

[tex](\sqrt {y + 3}) ^ 2 = (- 2x) ^ 2\\y + 3 = 4x ^ 2[/tex]

We subtract 3 from both sides of the equation:

[tex]y = 4x ^ 2-3[/tex]

We change y by f ^ {- 1} (x):

[tex]f ^ {- 1} (x) = 4x ^ 2-3[/tex]

Answer:[tex]f ^ {- 1} (x) = 4x ^ 2-3[/tex]

Answer:

[tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

Step-by-step explanation:

Given : [tex]f(x) =-\frac{1}{2}\sqrt{x+3}[/tex].

To find : Find the inverse of the given function.

Solution : We have given

[tex]f(x) =-\frac{1}{2}\sqrt{x+3}[/tex].

Step 1: take f(x) = y

[tex]y =-\frac{1}{2}\sqrt{x+3}[/tex].

Step 2 : Inter change y and x.

[tex]x =-\frac{1}{2}\sqrt{y+3}[/tex].

Step 3 : Solve for y

Taking square both sides

[tex]x^{2} = \frac{1}{4}(y+3)[/tex].

On multiply both sides by 4.

[tex]4x^{2} = (y+3)[/tex].

On subtraction both sides by 3.

[tex]4x^{2} -3 = y[/tex].

Here, [tex]f(x)^{-1}= y[/tex] is inverse of f(x)

[tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

Therefore, [tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

Please help I need it

Answers

There’s an app called Socratic it will help u with the steps

Question 1:

For this case we have to simplify the following expression:

[tex]\sqrt {54n ^ 7}[/tex]

We can rewrite the 54 as:

[tex]54 = 9 * 6 = 3 ^ 2 * 6[/tex]

In addition, we have to:

[tex]n ^ 7 = n ^ 6 * n[/tex] (According to the multiplication of powers of the same base)

Also, by definition of properties of powers and roots we have to:

\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})

Then, we can rewrite the expression as:

[tex]\sqrt {3 ^ 2 * n ^ 6 * 6 * n} =\\3n ^ 3 \sqrt {6n}[/tex]

Answer:

Option C

Question 2:

For this case we have by definition, that a perfect square is the result of multiplying a number by itself. Also, the perfect squares are the numbers that have exact square roots.

So:

2 and 10 are not perfect squares.

Answer:

Option A and D

Question 3:

For this case we must simplify the following expression:

[tex]\sqrt {75x ^ 2 * y ^ 4}[/tex]

We can rewrite the 75 as:[tex]75 = 25 * 3 = 5 ^ 2 * 3[/tex]

Also we have that by definition of properties of powers and roots that:

[tex]\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})[/tex]

So, we rewrite the expression:

[tex]\sqrt {5 ^ 2 * x ^ 2 * y ^ 4 * 3} =\\5xy ^ 2 \sqrt {3}[/tex]

Answer:

Option B

Write an equation of the line that passes through (2, -2) and is parallel to the line y=3x+9 . An equation of the parallel line is y=

Answers

Answer:

y = 3x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 9 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes, thus

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (2, - 2) into the partial equation

- 2 = 6 + c ⇒ c = - 2 - 6 = - 8

y = 3x - 8 ← equation of parallel line

A binomial event is one where there are 3 possible outcomes. A.True B.False

Answers

B. False

Bi = 2

Binomial = 2 possible outcomes

Find the volume of the square pyramid shown. Round to the nearest whole number. The diagrams are not drawn to scale.

Answers

the formula is 1/3 area of the base times height so

14*14=106

196*6=1176

1176/3=392

392cm^3 is the anwser

Answer:

Option A. 392 cm³

Step-by-step explanation:

Formula to get the volume of a pyramid is

[tex]V=\frac{1}{3}(l)(w)(h)[/tex]

Here l = length of the base

w = width of the base

h = height of the pyramid

From the figure attached

l = w = 14 cm

h = 6 cm

Therefore, [tex]V=\frac{1}{3}(14)(14)(6)[/tex]

V = 14×14×2 = 392 cm³

Option A. 392 cm³ is the answer.

whats 8.99 rounded to 1 decimal place??

Answers

Final answer:

8.99 rounded to 1 decimal place is 9.0, since the number after the decimal is 9, which is 5 or over, hence, the rounding up.

Explanation:

In mathematics, rounding means to replace a number with an approximate value that has a shorter, simpler, or more explicit representation. To round the number 8.99 to 1 decimal place, you need to look at the second number after the decimal point. Since that number is 9, which is 5 or over, we round up the first number after the decimal point, which is 8. Thus, 8.99 rounded to 1 decimal place is 9.0.

Learn more about Rounding Numbers here:

https://brainly.com/question/19166897

#SPJ2

It costs $19.00 to purchase 2 pounds of coffee and 3 pounds of tea. While it is $41.50 to purchase 5 pounds of coffee and 6 pounds and tea . how much per pound is the price of coffee?

Answers

It would be $3.5 per pound for the coffee and $4 per pound for tea.

Final answer:

The cost per pound of coffee is found to be $3.50 by setting up two equations from the given information and solving for the price of coffee.

Explanation:

To find out the price per pound of coffee, we need to set up two equations based on the given information and solve them using the method of substitution or elimination. Let's assume C is the cost per pound of coffee and T is the cost per pound of tea.

The first situation gives us the equation:

2C + 3T = $19.00

The second situation gives us the equation:

5C + 6T = $41.50

We can multiply the first equation by two, which gives:

4C + 6T = $38.00

By subtracting this equation from the second equation, we get:

(5C + 6T) - (4C + 6T) = $41.50 - $38.00

This leaves us with:

C = $3.50

Therefore, the cost of coffee per pound is $3.50.

Tim Worker receives the following income monthly from a second job.

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.
$200 $150 $250 $260 $285 $380 $200 $225 $200 $250 $220 $150
In dollars and cents the average pay will be?

Answers

Answer:

Step-by-step explanation:

$2.770,00. Hello friend, for reach that answer you have to add all values:

200+150+250+260+285+380+200+225+200+250+220+150= 2770.

It will be easier if you do ir by parts, like:

(200+150) + (250+260) + ...

Thank you for asking!

Have a nice day.

The average pay for Tim Worker's second job income monthly is $232.50.

To calculate the average, first, sum up all the monthly incomes:

200 + 150 + 250 + 260 + 285 + 380 + 200 + 225 + 200 + 250 + 220 + 150 = $2970

Next, divide the total income by the number of months (12 in this case) to find the average:

2970 / 12 = $232.50

So, the average monthly income from Tim Worker's second job is $232.50.

To find the average income, you add up all the monthly incomes and then divide by the total number of months. In this case, adding up Tim Worker's monthly incomes gives us $2970. Then, dividing by 12 (the number of months) gives us the average monthly income of $232.50. This method ensures that each month's income contributes equally to the overall average, regardless of fluctuations in individual months. So, despite variations in Tim Worker's monthly income, the average remains consistent at $232.50 per month.

Complete question:

Tim Worker receives the following income monthly from a second job.

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

$200 $150 $250 $260 $285 $380 $200 $225 $200 $250 $220 $150

In dollars and cents the average pay will be?

What equation results from completing the squre and then factoring x^2+10=15

Answers

For this case we must complete squares:

[tex]x ^ 2 + 10x = 15[/tex]

We add the square of half the coefficient of the term "x",

[tex](\frac {b} {2a}) ^ 2[/tex] on both sides of the equation:

[tex]x^2+10x+(\frac {10} {2 (1)}) ^ 2 = 25 + 15\\x ^ 2 + 10x + 5 ^ 2 = 25 + 15[/tex]

According to the perfect square trinomial we have:

[tex](a + b) ^ 2 = a ^2 + 2ab + b ^ 2[/tex]

Rewriting the expression we have:

[tex]a = x\\b = 5\\(x + 5) ^ 2 = 25 + 15\\(x + 5) ^ 2 = 40[/tex]

ANswer:

[tex](x + 5) ^ 2 = 40[/tex]

Look at the pie chart and table below.

What is the angle for the sector representing Somewhat Agree?

Answers

Answer:

150°

Step-by-step explanation:

To calculate the angle

angle = [tex]\frac{xsomewhatagree}{total}[/tex] × 360°

         = [tex]\frac{300}{720}[/tex] × 360° (cancel 360 and 720 by 2 )

         = [tex]\frac{300}{2}[/tex] = 150°

Select the correct answer from the drop-down menu. Find the missing term. On dividing both the numerator and the denominator of by , the result is .

Answers

On dividing both the numerator and the denominator of [tex]\frac{20a^2b}{5ab^2}[/tex] by 5b, the result is [tex]\frac{4a}{b}[/tex].

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Note: Let the variable x represent the unknown expression or missing term.

Based on the information provided, we can logically set up the following mathematical equation:

[tex]\frac{20a^2b}{5ab^2} \div \frac{x}{x} =\frac{4a}{b}[/tex]

Next, we would solve the equation in parts by using the numerators and denominators as follows;

[tex]20a^2b \div x = 4a\\\\\frac{20a^2b}{x} =4a\\\\x4a=20a^2b\\\\x=\frac{20a^2b}{4a} \\\\x=5a\\\\\\\\\frac{5ab^2}{x} =b\\\\xb=5ab^2\\\\x=\frac{5ab^2}{b} \\\\x=5a[/tex]

Complete Question:

Select the correct answer from the drop-down menu.

Find the missing term.

On dividing both the numerator and the denominator of [tex]\frac{20a^2b}{5ab^2}[/tex] by ___, the result is [tex]\frac{4a}{b}[/tex].

The volume of a right circular cone is 2,279.64 in cubed. If the height of the cone is 18 in, what is the diameter of the cone? (Use pi = 3.14)
A. 22 in
B. 60.5 in
C. 11 in
D. 121 in

Answers

ANSWER

A. 22 in

EXPLANATION

The volume of a cone is calculated using the formula:

[tex]Volume = \frac{1}{3} \times \pi {r}^{2} h[/tex]

It was given that: the volume is 2,279.64 in³

The height of the cylinder is also given as: h=18 in.

We substitute, the given values into the formula to get:

[tex]2279.64= \frac{1}{3} \times (3.14) \times {r}^{2} \times 18[/tex]

[tex]2279.64= 18.84 {r}^{2} [/tex]

[tex] {r}^{2} = \frac{2279.64}{18.84} [/tex]

[tex] {r}^{2} = 121[/tex]

We take positive square root to get;

[tex]r = \sqrt{121} [/tex]

[tex]r = 11in[/tex]

Therefore the diameter is 2(11) which is equal to 22 inches.

Please help !! A rider’s elevation on a Ferris wheel can be modeled by the function y=-16 cos(2pix)+18 where x is the time in minutes and y is the riders elevation in meters.

What is the riders elevation at the top of the Ferris wheel?

How often does the rider reach the reach the elevation?

What is the midline of the function?___what does it represent ?

Answers

Answer:

Step-by-step explanation:

Thomas has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many quarters does he have

Answers

Answer:

He has 11 quarters

Step-by-step explanation:

* Lets study the information in the problem to solve it

- The value of dimes and quarters is $6.35

- There are dimes and quarters

- The dime = 10 cents

- The quarter = 25 cents

* We must change the money from dollars to cents

∵ $1 = 100 cents

∴ $6.35 = 6.35 × 100 = 635 cents

- The number of dimes = 3 + 3 × number of quarters

* Let number of dimes is D and number of quarter is Q

∴ D = 3 + 3Q

∴ 10D + 25Q = 635

* Substitute the value of D from first equation in the second equation

∴ 10(3 + 3Q) + 25Q = 635 ⇒ open the bracket

∴ 10(3) + 10(3Q) + 25Q = 635

∴ 30 + 30Q + 25Q = 635 ⇒ collect like terms

∴ 30 + 55Q = 635 ⇒ subtract 30 from both sides

∴ 55Q = 605 ⇒ divide both sides by 55

∴ Q = 11

* He has 11 quarters

WILL GIVE BRAINLEST FOR ALL ANSWERED

Square root 36/81 simplified
1.1/3
2.2/3
3.3/3
4.4/3

Square root 121/144 simplified
1.1/12
2.5/12
3.7/12
4.11/12

SR 64/100 simplified
1.1/5
2.2/5
3.3/5
4.4/5

SR 4/9 simplified

1.1/3
2.2/3
3.3/3
4.4/3



Answers

Answer:

1. 2/3

2. 11/12

3. 4/5

4. 2/3

Step-by-step explanation:

28 is what percent to 31

Answers

if we take 31 to be the 100%, what is 28 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 31&100\\ 28&x \end{array}\implies \cfrac{31}{28}=\cfrac{100}{x}\implies 31x=2800\implies x=\cfrac{2800}{31} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x\approx 90.32~\hfill[/tex]

Write the equation of a line through points (5,5) and 1,0) in point slope form.

Answers

Hello!

The answer is:

The correct option is the first option,

[tex]y=\frac{5}{4} (x-1)[/tex]

Why?

To solve this problem, we need to remember that the point-slope form of a line is given by the following equation:

[tex]y-y_{1}=m(x-x_{1})\\\\y-0=\frac{5}{4}(x-1)[/tex]

We are given two points of the line,

[tex](5,5)\\(1,0)[/tex]

Where,

[tex]x=5\\x_{1}=1\\y=5\\y_{1}=0\\[/tex]

Then, substituting the given points into the equation ,to calculate m (slope), we have:

[tex]m=\frac{y-y_{1}}{x-x_{1}}[/tex]

[tex]m=\frac{5-0}{5-1}=\frac{5}{4}[/tex]

The slope of the function is [tex]\frac{5}{4}[/tex]

Now, substituting "x1" and "y1" and the slope in the point-slope equation, we have:

[tex](y-0)=\frac{5}{4} (x-1)[/tex]

[tex]y=\frac{5}{4} (x-1)[/tex]

Hence, the correct option is the first option,

[tex]y=\frac{5}{4} (x-1)[/tex]

Have a nice day!

Answer:

The correct answer is first option

y = 5/4(x - 1)

Step-by-step explanation:

It is given two coordinates (5, 5) and (1, 0)

To find the slope

Slope = (y₂ - y₁)/(x₂- x₁)

slope = (5 - 0)/(5 - 1) = 5/4

To find the equation

(y - y₁)/(x - x₁) = 5/4

(y - 0)/(x - 1) = 5/4

y = 5/4(x - 1)

The correct answer is first option

The dot plot shows the weights of ten calves, in pounds, born at Robert's farm this year.




What is the mean absolute deviation of the data set given in the dot plot?


A. 5

B. 1.28

C. 1.4

D. 64.2
P.S : I will mark brianliest. If I can, my brianliest don't work all the time. Sorry if I can't :(

Answers

Answer:

A. 5

Step-by-step explanation:

you need to bring the dot to the same value like this =10÷2

Find the volume of the cylinder.
Enter exact answer.

Answers

150.72 is the exact answer. Hope this helped!!

PLEASEEEEEEEEEEEEEEEEEEEEE answer this today thank u

Answers

Answer:

see explanation

Step-by-step explanation:

f(x) × g(x)

= 11(123x - 40) ← distribute

= 1353x - 440

Substitute x = - 4 into the product

= (1353 × - 4) - 440

= - 5412 - 440

= - 5852

If P= (2, 7) and Q= (2, -3), which could be the coordinates of R if triangle PQR is isosceles?
I (12, -3)
II (-6, -9)
III (-117, 2)

Answers

Answer is (-117, 2)

See photo

Final answer:

An isosceles triangle PQR with points P and Q sharing the same x-coordinate requires point R to also have this x-coordinate to have equal PR and QR sides. The y-coordinate of R should be the average of P and Q's y-coordinates. None of the provided options satisfy these conditions.

Explanation:

If we are looking for the coordinates of point R such that triangle PQR is isosceles, we should recall that in an isosceles triangle, two sides are of equal length. We can observe that whatever point we choose for R, one of the equal sides will be either PR or QR because points P and Q share the same x-coordinate (2).

Considering the coordinates of P (2, 7) and Q (2, -3), the vertical distance between P and Q is 10 units. For triangle PQR to be isosceles, the distance from R to either P or Q needs to be the same. This means point R must be horizontally aligned with P and Q to maintain its x-coordinate as 2, while the y-coordinate must be equidistant from P and Q's y-coordinates.

Since point P's y-coordinate is 7, and Q's is -3, the y-coordinate of R must be the average of 7 and -3, which is (7 + (-3))/2 = 2.

Therefore, the coordinates of R should be (2, 2), making triangle PQR isosceles with PR and QR as the equal sides. However, none of the given options (I, II, III) have an x-coordinate of 2, so none of these points could form an isosceles triangle with P and Q according to the given coordinates.

How do I Simplify (5x-2)4 using the distributive property?

Answers

Answer:

20x - 8

Step-by-step explanation:

using the distributive property to simplify (5x-2)4, you would multiply the outside term (4) by each inside term (5x-2).

for example:

4 × 5x = 20x

4 × -2 = -8

once you distribute the 4 into 5x-2, you are left with 20x - 8 which needs no further simplifying

Answer:

20x - 8

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

(5x - 2) · 4 = 4(5x - 2) = (4)(5x) + (4)(-2) = 20x - 8

According to Wikipedia, the population of China is about 1,362,080,000 and the population of the US is about 317,427,000.
Express the population of China in scientific notation.

Answers

1.36208 x 10^4, good luck

If y is directly proportional to x and y = 5 when x =2, what is the value of y when x=6

Answers

Answer:

y=15

Step-by-step explanation:

The formula for direct variation is

y = kx

5 =k*2

Solve for k

Divide by 2

5/2 = k

y = 5/2 x

Now we substitute x=6

y = 5/2(6)

y = 15

Answer:

y = 15

Step-by-step explanation:

If the variables are directly proportional, increasing one by a factor of 3 will mean the other one also increases by a factor of 3.

6 is 3 times 2, so the value of y will be 3 times 5, or 15.

___

You can write the relation as a proportion:

y/x = 5/2 = ?/6

Multiplying by 6 gives ...

(5/2)·6 = ? = 15

___

Or, you can bother with an equation relating x and y:

y = kx

5 = k·2 . . . plug in the given values and solve for k

5/2 = k . . . divide by 2

Then ...

y = (5/2)·6 = 15 . . . . same as the proportion, above.

If you rearrange this to y = 5·(6/2) then you see the relation described at the beginning of this solution. The new value of y is the old value multiplied by the factor by which x changes.

Find the lateral and surface area of each cone

Answers

Answer:

[tex]\large\boxed{L.A.=153\pi\ mm^2}\\\boxed{S.A.234\pi\ mm^2}[/tex]

Step-by-step explanation:

The formula of a lateral area of a cone:

[tex]L.A.=\pi rl[/tex]

r - radius

l - slant height

The formula of a surface area of a cone:

[tex]S.A.=\pi r^2+\pi rl[/tex]

We have r= 9mm and l = 17mm. Substitute:

[tex]L.A.=\pi(9)(17)=153\pi\ mm^2[/tex]

[tex]S.A.=\pi(9^2)+153\pi=81\pi+153\pi=234\pi\ mm^2[/tex]

If x = 8 units, y = 5 units, and h = 3 units, then what is the area of the parallelogram shown above?

A. 40 square units
B. 26 square units
C. 24 square units
D. 15 square units

I will give crown to best answer

Answers

The answer is C 24 square units.

Hope this helps!

Answer:

The answer is C.24 square units.

Step-by-step explanation:

A company manufactures and sells video games. A survey of video game stores indicated that at a price of $69 each, the demand would be 200 games, and at a price of $39 each, the demand would be 1,100 games. If a linear relationship between price and demand exists, which of the following equations models the price-demand relationship?

(Let x represent the price per video game and y represent the demand.)
(answers are in the snip)

Answers

Answer: If the equilibrium is such that only 12000 units are sold for $27, then the total earnings from the given scenario is $324,000. The supply equation would then be,

       supply: 324000 = 6p   ; p = 324000/6 = 54000

       demand: 324000 = 69p ; p = 324000/69 = 4695.65 ≈ 4696

The equation that models the price-demand relationship is:  [tex]\[ y = -30x + 2270 \][/tex]

The correct option is (C).

find the linear equation that models the price-demand relationship based on the given data points.

1. Given Data:

  - Price at which demand is 200 games:[tex]\(x_1 = 69\), \(y_1 = 200\)[/tex]

  - Price at which demand is 1,100 games: [tex]\(x_2 = 39\), \(y_2 = 1100\)[/tex]

2. Slope Calculation:

  The slope (m) of the linear equation can be found using the formula:

 [tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{1100 - 200}}{{39 - 69}} = \frac{{900}}{{-30}} = -30 \][/tex]

3. Y-Intercept Calculation:

  Using one of the data points [tex](let's use \(x_1 = 69\), \(y_1 = 200\))[/tex]:

  [tex]\[ y_1 = mx_1 + b \\ 200 = (-30)(69) + b \\ b = 2270 \][/tex]

4. Linear Equation:

  The equation that models the price-demand relationship is:

 [tex]\[ y = -30x + 2270 \][/tex]

Therefore, the correct answer is C. (y = -30x + 2270). This equation represents the linear relationship between the price per video game ((x)) and the demand ((y)) based on the given survey data.

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