Which is the solution of the quadratic equation (4y – 3)^
2 = 72?

Answer: A

Step-by-step explanation:

c=number of crossings; Q=quarterly pass; S=semi-annual pass; P=pay as you go

P=$2.50c

Q=$12+$0.50c

S=$40

Compare single pay and quarterly ticket:

$2.50c=$12+$0.50c Subtract $0.50c from each side

$2.00c=$12 Divide each side by $2.

c=6 6 crossings is the break even for single pay and quarterly ticket: more crossings favor the ticket.

Compare quarterly and semi-annual tickets:

3 month pro-rated cost of semi annual ticket=$20

$20=$12+$0.50c Subtract 12 from each side

$8=$0.50c Divide each side by $0.50

16=c The break=even point between quarterly and semi annual tickets is 16 crossings per 3 months. More than this favors the semi annual ticket.

ANSWER: The three month pass is the best deal if you cross between 6 and 16 times during the three month period.

I hope this help you

Answer:

\(12-20x^{2}\)

Step-by-step explanation:

\(4(3-5x^{2}) = (4*3)-(4*5x^{2} )\)

\(4*3 = 12\)

\(4*5x^{2} =20x^{2}\) since you only multiply the numbers

\(12-20x^{2}\)

The volume of the sphere is approximately 137.1 cubic centimeters.

Volume is a physical quantity that measures the amount of space occupied by a three-dimensional object. It is typically measured in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal).

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.

Since the diameter of the sphere is given as 6.4 cm, the radius is half of this value:

r = 6.4 cm / 2 = 3.2 cm

Substituting this value into the formula for the volume of a sphere, we get:

V = (4/3)π(3.2 cm)^3

V = 4.1888 × (3.2 cm)^3

V = 4.1888 × 32.768 cm^3

V ≈ 137.0829 cm^3

Rounding to the nearest tenth of a cubic centimeter, we get:

V ≈ 137.1 cm^3

Therefore, the volume of the sphere is approximately 137.1 cubic centimeters.

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Answer:

the answer is 137.3

Answer:

twenty thousand four hundred and eight four one hundred and sixty four

Answer:

20,000,000 + 400,000 + 80,000 + 4,000 + 100 + 60 + 3

Step-by-step explanation:

You would have to add all the numbers together that makes 20,484,163 based on the place value. Expanded form for 20,484,163 is 20,000,000 + 400,000 + 80,000 + 4,000 + 100 + 60 + 3

Answer:

Step-by-step explanation:

\(x^{3}-2x^{2}-x+2\\ =x(x^{2}-2x-1)+2\\\)

We can clearly see here that x = 1 is one of the solution where this expression becomes zero

= x( (x-1)^2-2 ) + 2

Answers to be filled are rectangle, \(2\pi\) , equal, \(2\pi r^2\).

Given,

In the question:

Suppose the bottom surface, or base, of a cylinder is divided into 16 congruent sectors. then the sectors are rearranged as shown.

Open this GeoGebra activity to divide the circle into even more sectors and rearrange the sectors for yourself.

To complete the statement to compare the areas of the two figures and find the area of the base of the cylinder.

Now, According to the question:

To complete the statements

A circle of radius 'r' and rearranged figure out of sectors of the same circle.

When the sectors of the circle are rearranged , they are close to forming a rectangle with a length of 2\(\pi\)r units and a width of r units.

The area of the rearranged figure is equal to that of the circle. So, the area of the circular base 2\(\pi r^2\) sq. units

Hence, Answers to be filled are rectangle, \(2\pi\) , equal, \(2\pi r^2\).

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When the sectors of the circle are rearranged, they are close to forming a

rectangle with a length of 2*pi*r units and a width of r units. The area of the rearranged figure is equal to that of the circle. So, the area of the circular base 2*pi*r square units.

Answer:

25%

Step-by-step explanation:

If you start at 45% and it reduces by 20% you are just doing 45-20 which equals 25. (Please let me know if im wrong)

16 percent markup is the new retail price over the manufacturer price.

Here,

A store sells candles.

Retail price will be 45% marked-up

A month later, store reduced the retail price of the candles by 20%.

We have to find the percent markup.

What is the percentage?

The percentage is the value per hundred.

Now,

Consider the manufacturer price = 100x

Retail price will be 45% marked-up

Hence,  100x+45% of 100x = 145x

Reduced retail price of the ladder after one month = 145x-145x*20/100

Reduced retail price of the ladder after one month = 116x

Percentage markup of the reduced retail price over the manufacturer price will be:

={(reduced retail price - manufacturer price)/manufacturer price} *100

=[ (116x-100x)/100x ] *100 = 16%

Hence, 16 percent markup is the new retail price over the manufacturer price.

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Answer:

it is the 3rd one

Step-by-step explanation:

Answer:  The correct answer is the function domain is x<-7 or x>1

Your available options (a-d) appear to have some incorrect values, I am assuming the correct answer is "c. x1,x#-7" provided it matches "c. x>1, x<-7"

Step-by-step explanation:

The domain of a function is the set of input or argument values for which the function is real and defined.

Equation: x-8/x^2+6x-7

Define the domain of (x-8)/(x^2+6x-7)

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Answer:I believe is 18,000

Step-by-step explanation:

If the current population is 1000 in 27 weeks it would be 9000 because if they double every 3 weeks u have to divide 27 divided by 3 which is 9 and if they double you multiply 9x2 and that equals 18 now 18x1000 equals 18000

Assuming an equal probability of having a girl or a boy for each child, the probability that a couple does not have girls for all three children is 1/8 or approximately 0.125 (12.5%).

If we assume that the probability of having a girl or a boy for each child is equal (which is a simplifying assumption), then the probability of having a girl for each child is 1/2, and the probability of having a boy is also 1/2.

To find the probability that the couple does not have girls for all three children, we need to find the probability of having a boy for each child. Since the gender of each child is independent of the others, we can multiply the probabilities together.

So, the probability of having a boy for the first child is 1/2, for the second child is also 1/2, and for the third child is also 1/2.

Multiplying these probabilities together, we get:

(1/2) * (1/2) * (1/2) = 1/8

Therefore, the probability that the couple does not have girls for all three children is 1/8 or approximately 0.125 (12.5%).

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Answer: D

Step-by-step explanation:

Since a tadpole becomes a frog as it ages, it makes sense that the axis of the tail would go down as it ages since frogs don’t have tails. If you see the x axis as the tempature, and the coats as the y axis. It would make sense that as the tempature gets colder, more people would be buying coats. But basically, D is the only one that doesn’t have a cause and affect, so it wouldn’t have a very linear scatter plot. For example, I have the same letters in my name as someone I know who is 6‘ 4”, and I’m only 4’ 8”. So D wouldn’t make such a nicely formed scatter plot.

The domain and range are:

D: {2, 3, 6}

R: {70, 80, 90, 100}

And it is not a function.

A relation maps elements x into elements y using the notation (x, y).

The domain is the set of the inputs (set of the possible values of x) and the range is the set of the outputs (possible values of y).

And a relation is a function if each value in the domain is mapped into only one value of the range.

Here the relation is:

{ (6, 90), (2, 70), (6, 80), (3, 100)}

So the domain is:

D: {2, 3, 6}

The range is:

R: {70, 80, 90, 100}

And it is not a function because the input 6 is mapped into two different outputs.

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Answer:

-0.5x^3+700x^2-1,200x+500

Step-by-step explanation:

I answered it correctly

The profit function is equal to 0.5x³+700x²-1200x+500

COST PRICE  is the amount in which seller buys

Selling Price is the amount in which the consumer buys from the seller

Profit is the toal income earned after the investment.

C(x)=100x²+500x

R(x)=-0.5x³+800x²-700x+500

P(x)=R(x)-C(x)

      = -0.5x³+800x²-700x+500-100x²-500x

      =-0.5x³+700x²-1200x+500

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Answer:

3

Step-by-step explanation:

I think why but i think

number but

In this utility function, the term 6X represents the utility derived from consuming good X, while the term -Y represents the disutility or loss of satisfaction from consuming good Y. By subtracting Y from 6X, Chloe's preferences reflect the substitution relationship she perceives between the two goods.

A utility function describes an individual's preferences and the satisfaction they derive from consuming different goods. In Chloe's case, she believes that 6 units of good X can fully replace the satisfaction derived from consuming 1 unit of good Y. Therefore, we can construct a utility function based on this substitution ratio.

Let's denote the quantity of good X as X and the quantity of good Y as Y. Since Chloe believes that 6 units of X perfectly substitute 1 unit of Y, we can express her utility function as:

U(X, Y) = 6X - Y

It's important to note that utility functions are subjective and specific to an individual's preferences. Chloe's utility function captures her belief that 6 units of X are equivalent to 1 unit of Y, but it may not hold true for other individuals with different preferences or perceptions of substitutability between the goods.

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1. 13 hamsters

2. 66 legs

1. From the question, we are told that a hamster has 4 legs

Given that there are a total of 52 legs, so to find the total number of hamsters present, we simply go on to divide the number of total legs by the number of legs a hamster has

Mathematically; that would be 52/4 = 13 hamsters

2. Here, we want to the total number of legs present in a house where we have 4 bettles , 5 hamsters and 11 birds

1 bettle has 6 legs

so 4 bettles will have 4 * 6 = 24 legs

1 hamster has 4 legs

so 5 hamsters will have 5 * 4 = 20 legs

1 bird has two legs

so 11 birds will have 11 * 2 = 22 legs

So the total number of legs present in the house will be the addition of all the legs

That will be 24 + 20 + 22 = 66 legs

3. Here, we have a total of 32 legs , we now want to find the different combination of all the animals present

What is important here is that at any point, for any combination, the total number of legs must be eual to exactly 32

We proceed as follows;

1 bird

1 bettle

6 hamsters

Another can be;

2 birds

2 bettles

4 hamsters

Another combination can be

3 hamsters

3 bettles

1 bird

and so on

Answer:

5r+75≥300

Step-by-step explanation:

the money they plan to get from selling tikets: $5r all the money: $(75+5r) clothing costs' $300 so 54+75≥300

(if they want to make money then all the money ≥ clothing cost )

The solution of the inequality 5r + 75 ≥ 300 is greater than or equal to 45.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The pirouette dance group needs more than $300 to cover outfit costs. they have $75 and plan to sell pool tickets for $5 each to fund-raise.

Let 'r' be the number of raffle tickets the team needs to sell.

Then the equation is given as,

5r + 75 ≥ 300

Simplify the inequality, then we have

5r + 75 ≥ 300

5r ≥ 300 - 75

5r ≥ 225

r ≥ 225 / 5

r ≥ 45

The solution of the inequality 5r + 75 ≥ 300 is greater than or equal to 45.

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Step-by-step explanation:

(3-2)^2+y^2=4

(9-4)+y^2=2^2

the power of y and 2 should be cut now

5+y=2

5-2=y

3=y

y=3

:. the area of enclosed by a circle is 3 cm

Answer:

C, A, C

Step-by-step explanation:

1) Angle D corresponds to angle A, so since corresponding angles of similar triangles are congruent, it measures 64 degrees.

2) Angle E corresponds to angle B. To find the measure of angle B, we can start by using the fact that angles F and C correspond. This means that in triangle ABC, we have angles with measures of 64 degrees, 73 degrees, and angle B. It follows that angle B, and thus angle E, measures 43 degrees.

3) By the exterior angle theorem, the measure of angle G is equal to the measure of angles D and F combined. The measure of angle D is 64 degrees, and the measure of angle F is 73 degrees, so angle G measures 137 degrees.

The answer is A because it shows all of the terms

The domain of the function is -2, 2, 3, 4.

Option A is correct.

The domain of the function is defined as the all input values for which any function is defined.

From the given diagram, the input values are ,

                        -2 , 3 , 4 , 2

Hence, the domain of the function is -2, 2, 3, 4.

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Answer:

line m

Step-by-step explanation:

Answer:

The answer is  4×4+5×2−3.

Step-by-step explanation:

This is because, in the original amount, they had 4 tanks with 4 fish and 5 tanks with 2 fish. 4x4 is 16 and 5x2 is 10. Then you add them together to get 26. But, you have to subtract 3 because of the order of 3 fish, which equals 23. The equation 4×4+5×2−3 shows that.

Answer:

A. Proportional

B. Non-Proportional

C. Non-Proportional

D. Proportional

Step-by-step explanation:

1. For each graph divide the first cost by the number of apples

- 2.25 divided by 5 is .45 (price for one apple)

- 1.85 divided by 5 is .37 (price for one apple)

- 2.60 divided by 5 is .52 (price for one apple)

- 2.10 divided by 5 is .42 (price for one apple)

2. If you can multiply the price for one apple by the total # of apples and it matches the total cost throughout the entire graph then it's proportional.

To write an exponential decay function to represent this situation,  the initial value be 0.925

y=a(1-b)^x

decay factor is 1-b <- and the part we care about

b is 7.5%=0.075

1-0.075

=0.925

In mathematics, exponential decay function  describes the process of decreasing quantity at a constant rate over a period of time. It can be represented by the formula y = a(1-b)x. where y is the final volume, a is the initial volume, b is the decay factor, and x is the elapsed time.

exponential decay function  have his two types: exponential growth and exponential decay. For a function f(x) = bx, when b > 1, the function exhibits exponential growth. For the function f(x) = bx, the function exhibits an exponential decay when 0 < b < 1.

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Answer:

Step-by-step explanation:

\(4.5^{2}\) x \(pie\) =63.6\(cm^{2}\)

Answer:

20.25pi or about 63.62

Step-by-step explanation:

the formula for area of a circle is pi*r^2.

since the diameter is 9, the radius is half of that, which is 4.5

then, plugging this into our formula, we get 20.25pi. this rounds to 63.62.

To calculate the probability of selecting a boy or a red-haired person as a homeroom representative to student council, we need to find the probability of each event and then use the formula P(A or B) = P(A) + P(B) - P(A and B).

There are 31 students in total (16 girls + 15 boys). The probability of selecting a boy is 15/31.

There are 5 red-haired students (3 girls + 2 boys). The probability of selecting a red-haired person is 5/31.

However, we need to account for the overlap between boys and red-haired students. There are 2 red-haired boys, so the probability of selecting a red-haired boy is 2/31.

Now we can use the formula: P(boy or red-haired) = P(boy) + P(red-haired) - P(boy and red-haired) = (15/31) + (5/31) - (2/31) = 18/31.

So, the probability of selecting a boy or a red-haired person as a homeroom representative to student council is 18/31.

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