A yoga studio sells monthly memberships. the function f(x) = −x2 50x − 264 models the profit in dollars, where x is the number of memberships sold. determine the zeros, and explain what these values mean in the context of the problem.

The Total surface area of the rectangular prism = 168 in.²

The Volume of the rectangular prism = 108 in.³

The total surface area of a rectangular prism is given as: SA = 2(wl + hl + hw), where:

w = width of the rectangular prism

h = height of the rectangular prism

l = length of the rectangular prism

The volume of a rectangular prism = l × w × h

Find the Total surface area of the rectangular prism:

Length (l) = 9 in.

Width (w) = 2 in.

Height (h) = 6 in.

Total surface area of the rectangular prism = 2(wl+hl+hw) = 2·(2·9+6·9+6·2) = 168 in.²

Find the volume of the rectangular prism:

Length (l) = 9 in.

Width (w) = 2 in.

Height (h) = 6 in.

Volume of the rectangular prism = l × w × h = 9 × 2 × 6

Volume of the rectangular prism = 108 in.³

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Answer:

$0.17425/Km

Step-by-step explanation:

8.5L/100Km*$2.05/L

= $0.17425/Km

3/12, or 1/4 is the probability that it is blue.

What is probability?

Probability = number of successes / total number of outcomes

Total marbels in bag = 4+ 3 + 5 = 12  

A total of 12 marbles are in the bag.

3 blue marbles are in the bag.

Therefore, the probability of picking a blue is 3/12, or 1/4.

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Answer:

Step-by-step explanation:

For missing hypotenuse: [tex]\sqrt({a^{2} + b^{2})[/tex]

Plug in the side lengths that are known to find the hypotenuse.

1. No, the angle is less than 18 degrees (closer to 15), so it is not safe

2. The length rounded to the nearest tenth is approximately 15.5 feet.

Answer:

100 miles

Cost = $63

Step-by-step explanation:

Let us assume that the distance driven for both plans when they both equal in cost is X miles

Plan 1

Cost = 48  + 0.15X

Plan2

Cost = 53 + 0.1X

If they are both equal then

48 + 0.15X = 53 + 0.10X

Collecting like terms

0.15X - 0.10X = 53 - 48

0.05X = 5

X 5/0.05 = 100 miles

Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63

Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63

The computation shows that the total distance will be 260.52km.

From the information given, it was stated that the race has 78 laps through the town of Monte Carlo and that each lap of the race has a distance of 3.34 km.

Therefore, the total distance will be:

= 78 × 3.34

= 260.52 km

Therefore, the distance is 260.52km.

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The term that is not possible in the domain of a sequence is:

-5.

The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexes of the terms, starting at 0 and going until the nth term.

For example, suppose we have the following sequence: 3, 5, 7, ...

From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:

-5.

Which is the only negative number of the options.

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In quadrant I, [tex]\cos(A)[/tex] is positive. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}[/tex]

The greatest common factor of the two expressions given as in the task content is; 3v².

It follows from the task content that the terms whose greatest common factor are to be determined are: 15v³ and 12 v².

15v³ and 12v²

= 3v²(5v) and 3v²(4)

= 3v²(5v) and (4)

Consequently, in a bid to factorise the two expressions by means of their greatest Common factor, the greatest common factor can be determined as; 3v².

The correct answer choice which therefore represents the greatest common factor as required in the task content is; 3v².

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The price of the board game before the markup is $21.50.

Percentage can be described as a fraction an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.

When the price of an item is marked up, it means that the price of the item has been increased by a predetermined percentage. In this question, the price of the board game is increased by 25%.

Price of the item before the mark up = price the retailer sells / ( 1 + percentage)

$26.88 / 1.25 = $21.50

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Solving a linear equation, we will see that after 9 days he cuts the last section.

We know that the initial length of the piece of cloth is 20m, and the taylor each day cuts a piece of 2 meters of it.

So, the length as a function on the number of days, is:

L(x) = 20m - 2m*x

Here we just need to solve:

L(x) = 2m

Because the last cut is when the long piece measures 4 meters (in that case he does one cut and has the two final pieces of 2 meters).

Solving that, we get:

20m - 2m*x = 2m

20m - 2m = 2m*x

18m/2m = x = 9

After 9 days he cuts the last section.

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The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.

According to the statement

we have given that the property of the hypotenuse of the triangle and we have to complete it.

So, For this purpose, we know that the

A hypotenuse is the longest side of a right-angled triangle, and The length of the hypotenuse can be found using the Pythagorean theorem.

Now we discuss about the properties of the hypotenuse;

And from these properties we have to complete the given property.

So, The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.

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Using the binomial distribution, we have that you would expected to draw a face card 8 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

For this problem, the parameters are given as follows:

Then the expected value is found as follows:

E(X) = np = 35 x 0.2308 = 8

You would expected to draw a face card 8 times.

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Answer:

Let Ji and Bi represent the initial amounts that Joe and Bill have at the start.  Number after J and B will be used to indicate subsequent steps in the problem.

We are told that "Joe has five times as much money as Bill," which we can write as:

   1)  Ji = 5Bi

We learn that "Joe pays Bill $5," which we can represent as:

   2)  J1 = Ji - 5

This would mean that Bill has added $5:

   3)  B1 = Bi + 5

We are then told that "Joe has just twice the amount Bill now has," which we can write as:

   4)  J1 = 2B1

===

We can rearrnage and substitute the above relationships to eliminate one of the two variables (B1 or J1)

J1 = Ji - 5                [from 2]

2B1 = Ji - 5              [Substitute 4 to eliminate J1]

Ji = 5Bi                    [from 1]

2B1 = 5Bi - 5           [Substitute 1 to eliminate Ji]

B1 = Bi + 5               [Rearrange]

2(Bi + 5) = 5Bi - 5    [Use the above expression in the previous equation to eliminate B1]

2Bi + 10 = 5Bi - 5    [Simplify]

-3Bi = -15                  [Simplify]

Bi = $5                       [Solve]

Ji = 5Bi                    [from 1]

Ji = 5*(5)                  [Since Bi = $5]

Ji = $25                    [Solve]  

===

CHECK:

Does Joe has five times as much money as Bill?

Ji = $25 and Bi = $5  YES

When Joe pays Bill $5 he owes him, does Joe has just twice the amount Bill now has?

J1 = $25 - $5 = $20

B1 = $5 + $5  = $10    YES

the expression is simplified to give - 39

Given the expression;

= 24- 4 to the power of 2 x 3+15

= 24 - (4^2 × 3 ) + 15

First, expand the bracket

= 24 - ( 16 × 3) + 15

Find the product of the bracket

= 24 - 48 + 15

From our knowledge of BODMAS, we add before we subtract

Now, let's add first

= 24 - 63

The, subtract

= - 39

The expression is simplified to - 39

Thus, the expression is simplified to give - 39

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Answer:

x - 4 = 2y

Step-by-step explanation:

"four less than a number x" therefore; x - 4

"is twice another number y" therefore; 2y

The probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.

Given A)Number of green marbles=5,number of red marbles=3, number of blue marbles=4,

B) Number of peaches=7,number of apples=3,

C) Number of red token=10, number of blue token=6,green tokens=4,

D)Number of golf balls=13, number of tennis balls=2.

We are required to find the following probabilities:

A) Probability of getting red marble=Number of red marbles/ Total marbles.

=3/12

=1/4

=0.25

B) Probability of getting peaches=Number of peaches/Total fruits.

=7/10

=0.7

C) Probability of getting green tokens=Number of green tokens/Total tokens

=4/20

=1/5

=0.2

D)Probability of getting golf balls= Number of golf balls/ Total balls.

=13/15

=0.867

The sequence will be from C-A-B-D.

Hence the probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.

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Answer:

The total selling price for the parcel is 1,524,600 dollars.

Step-by-step explanation:

We are given that 10 acre parcel was sold for $3.50.

First we need to figure out how many square foot is in 10 acres.

when we convert 10 acres we get 435600 square feet.

Since we know that parcel was sold for $3.50 per square foot we simply multiply 435600 by 3.5 = 1,524,600

Answer:

C. slope

Greetings !

The symbol for slope is "m". Slope can be calculated by taking any two locations along a line and calculating the ratio of the RISE to the RUN (the ratio of the difference between vertical positions of the locations to the difference between horizontal positions of the locations).

Answer: slope.

Step-by-step explanation:

The surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.

To find the total surface area of the 27 blocks:

A cube's surface area

Given that the box's side length is 15 inches:

Surface Area of 3-inch side length blocks:

Surface Area of 4-inch side length blocks:

Surface Area of 5-inch side length blocks:

Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.

To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:

So,

The side length of the blocks is 5 inches.

The total surface area of the 27 blocks is 4050 square inches.

This is 3 times the surface area of the box.

Therefore, the surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.

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Answer:

5

Step-by-step explanation:

y^1 = 5^1 (y = 5)

Anything raised to the power of 1 is just itself.

So, 5^1 = 5

Answer:

9

Step-by-step explanation:

when you divide 576 by 9 you get 64 which is a perfect cube

cbrt(64) = 4

so your answer is 9

Using a proportional relationship, it is found that the unit rate of change is of 9.

The relation d = 9t is graphed at the end of the answer.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, we have d as a function of t, hence the relationship is:

d = kt.

When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:

k = d/t = 1.8/0.2 = 9

The relation d = 9t is graphed at the end of the answer.

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The value of x in the system of equation is 6

The system of equations is given as:

y = 1/2 * 2^x

y = 5x + 2

Substitute y = 1/2 * 2^x in y = 5x + 2

1/2 * 2^x = 5x + 2

Multiply through by 2

2^x = 10x + 4

Next, we use the trial by error.

Set x = 6

This gives

2^6 = 10 * 6 + 4

Evaluate the product and the exponent

64 = 60 + 4

Evaluate the sum

64 = 64

Hence, the value of x in the system of equation is 6

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The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]

For given question,

We have been given a function g(x) = 4x / (x² + 2x - 3)

We need to find a power series for the function, centered at c, for c = 0.

First we factorize the denominator of function g(x), we have:

[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]

We can write g(x) as,

[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]

We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1

and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex]  if [tex]|\frac{x}{6}| < 1[/tex]

[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex]     if |x| < 1 and  if [tex]|\frac{x}{6}| < 1[/tex]

[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1

Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]

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The diagonals of the qudrilateral will not be perpendicular to each other.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. If two segments are perpendicular, the multiplication of their slopes is -1.

The slope of a coordinate pair is given by the change in y divided by the change in x, that is:

For the diagonal AD the slope will be:-

Slope = ( -5 + 3 ) / ( -2 - 4) = ( 1 / 3 )

For the diagonal BC, the slope will be:-

Slope= ( 1 - 3) / ( 4 - 2 ) = ( -2 / 2) = -1

The multiplication of the two slopes will be,

M  =  ( 1 / 3 ) x -1 = ( - 1 / 3 )

Therefore,  the diagonals of the quadrilateral will not be perpendicular to each other. Because the product of the slope is not equal to -1.

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Answer:

The product of the slopes of the diagonals is -1.

Step-by-step explanation:

I had the question and got it right.

The height of the tree and the building are 7.6 m and 28.6 m respectively.

An equation is an expression that shows the relationship between two or more variables and numbers.

Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Triangle BGD, CHD and AFD are similar triangles.

CH = 1.6, DH = 8, GH = 30,  GF = 105

FH = GF + GH = 105 + 30 = 135

FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38

Hence, using similar triangles:

BG/CH = GD / DH

BG / 1.6 = 38/8

BG = 7.6 m

Also:

building/CH = DF / DH

building / 1.6 = 143/8

building = 28.6 m

The height of the tree and the building are 7.6 m and 28.6 m respectively.

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Answer:

(a + b)(a + b - 2)

Step-by-step explanation:

(a + b)² - 2(a + b) ← factor out (a + b) from each term

= (a + b)(a + b - 2)