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You can buy 32 gumdrops at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece.

To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece, you need to compare the prices and calculate the equivalent quantity. Since the prices are different, you can set up a proportion to solve the problem:

2¢ / 8 = 8¢ / x

By cross-multiplying, you get:

2 * x = 8 * 8

Now, solve for x to find the number of gumdrops you can buy at 8¢ apiece:

x = (8 * 8) / 2

x = 32

Therefore, you can buy 32 gumdrops at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece.

To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money you spent on 8 gumdrops at 2¢ apiece, divide the total amount of money by the new price.

To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money you spent on 8 gumdrops at 2¢ apiece, divide the total amount of money by the new price:

Total amount of money = 8 gumdrops x 2¢ apiece = 16¢

Number of gumdrops you can buy at 8¢ apiece = Total amount of money / 8¢

Number of gumdrops you can buy = 16¢ / 8¢ = 2 gumdrops

So, for the same amount of money, you can buy 2 gumdrops at 8¢ apiece.

Answer:

37

Step-by-step explanation:

its 37

The value of a composite function (f•g)(x) at x = 10 is 37 if the function f(x) = x² + 1 and g(x) =x - 4 option (A) 37 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is:

If f(x) = x² + 1 and g(x) = x - 4, which value is equivalent to (f•g)(10)?

We have a function:

f(x) = x² + 1

g(x) =x - 4

Plug x = 10 in the function g(x)

g(10) = 10- 4

g(10) = 6

Plug the above value in the function f(x)

(f•g)(10) = f(g(10)) = (6)² + 1

(f•g)(10)  = 36 + 1

(f•g)(10)  = 37

Thus, the value of a composite function (f•g)(x) at x = 10 is 37 if the function f(x) = x² + 1 and g(x) =x - 4 option (A) 37 is correct.

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The order of the planets from least to greatest mass is Planet B, Planet D, Planet A, Planet C.

To determine the order of the planets from least to greatest mass, we need to compare the given masses:

Mass of Planet A: 5.97 × 1024 kg

Mass of Planet B: 3.30 × 1023 kg

Mass of Planet C: 1.89 × 1027 kg

Mass of Planet D: 4.87 × 1024 kg

These masses help us rank the planets:

Planet B: 3.30 × 1023 kg

Planet D: 4.87 × 1024 kg

Planet A: 5.97 × 1024 kg

Planet C: 1.89 × 1027 kg

Therefore, the order of the planets from least to greatest mass is Planet B, Planet D, Planet A, Planet C.

answers:

Describe the graph of the function at its roots.

f(x) = (x − 2)3(x + 6)2(x + 12)

At x = 2, the graph crosses the x–axis.

At x = −6, the graph touches the x–axis.

At x = −12, the graph crosses the x–axis.

The required solution of the given function, at x = 2 the graph crosses the x-axis.

Given that,
The graph of the function at its roots. f(x) = (x − 2)³(x + 6)²(x + 12)
To discuss At x = 2, the graph is the x-axis.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
The graph of the given function f(x) = (x − 2)³(x + 6)²(x + 12) is show,
From the graph, it is found that at x = 2, the graph passes through the x-axis.

Thus, the required solution of the given function, at x = 2 the graph crosses the x-axis.

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0.5 teaspoon of conditioner to 2.5 gallon of tank.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

Given

So, you need 2 teaspoons of conditioner for every 10 gallons of water.

2/10=x/2.5

Now, know for 10 gallons, you need 2 teaspoons. Divide, this means for every 1 teaspoon, you need 5 gallons. This here is a simplification.

x =0.5

2 teaspoons of conditioner for every 10 gallons

For 2.5 gallons, you need .5 teaspoons.

Hence 0.5 teaspoon of conditioner to 2.5 gallon of tank.

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Answer:

the answer is b 728

Step-by-step explanation:

The Perimeter of the isosceles trapezoid KLMN given the dimensions is;

3√2 + 2√5

We re given the lengths of the isosceles trapezoid KLMN as;

KL = 2√2; LM = √5; MN = √2

We don't have the length of KN but we have the coordinates as;

K(-2, -4) and N(-1, -2)

Length of KN = √[(-2 - (-4))² + (-1 - (-2))]

Length of KN = √5

Thus;

Perimeter = 2√2 + √5 + √2 + √5

Perimeter = 3√2 + 2√5

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Answer:

[tex]29\sqrt{5}.[/tex]

Step-by-step explanation:

The difference is

[tex]11\sqrt{45}-4\sqrt{5}[/tex]

To simplify let's try to covert [tex]\sqrt{45}[/tex] in terms of [tex]\sqrt{5}[/tex]:

45 = 9*5, then [tex]\sqrt{45} = \sqrt{9*5} = \sqrt{9}\sqrt{5} = 3\sqrt{5}[/tex]. So,

[tex]11\sqrt{45}-4\sqrt{5} = 11(3\sqrt{5})-4\sqrt{5} = 33\sqrt{5} -4\sqrt{5} = 29\sqrt{5}.[/tex]

Wolf population and compound interest are exponential functions because both functions are in the form of m x [tex]a^x[/tex] as given below.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

An exponential function is denoted as f(x) = [tex]a^x[/tex]

Where x is a variable and a is a constant.

Now,

Wolf population:

Suppose the wolf population initially is 10.

It grows double every year.

This means,

The population of wolves after 3 years.

x = 3

P = 10 x 2³ = 10 x 2 x 2 x 2 = 80

P = 10 x 2³ is an exponential function.

Now,

Compound interest:

Principal = 10

Rate = 10% per year

Time = 3

Amount = P [tex](1 + r/n)^{nt}[/tex]

A = 10 [tex](1 + 0.1)^3[/tex]

A = 10 x 1.1³

This is an exponential function.

Thus,

Wolf population and compound interest are exponential functions.

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The answer is (A) I find it very easy to see the relationships and why they are all exponential functions.

To see why a wolf population and compound interest both relate to exponential functions, follow these steps:

1. Understand exponential functions: An exponential function has the form [tex]\( f(t) = a \cdot b^t \)[/tex], where a is the initial amount, b is the growth (or decay) factor, and t is time.

2. Wolf population:

  - Suppose a wolf population grows at a constant rate of 5% per year.

  - If the initial population is [tex]\( P_0 \)[/tex], the population after t years is [tex]\( P(t) = P_0 \cdot (1.05)^t \)[/tex], showing exponential growth.

3. Compound interest:

  - For compound interest, if you invest P dollars at an annual interest rate of r, compounded annually, the amount after t years is [tex]\( A(t) = P \cdot (1 + r)^t \)[/tex], which is also an exponential function.

4. Conclusion:

  - Both scenarios involve quantities growing by a constant percentage over time, fitting the exponential model.

Thus, the answer is: A. I find it very easy to see the relationships and why they are all exponential functions.

Complete question:- A wolf population, and compound interest were both used as examples of exponential functions. How easy is it for you to see how these diverse examples relate to exponential functions?

A. I find it very easy to see the relationships and why they are all exponential functions.

B. I have some difficulty seeing the relationships but understand why they are both exponential functions.

C. I don't see the relationships and am not sure why they are both exponential functions.

D. I do not understand what an exponential function is.

Answer:

The number of real roots is 2.

Step-by-step explanation:

Given,

[tex]x^2 -18 = 0[/tex]

We will find the number of roots by Descartes' rule of signs.

Let,

[tex]f(x)=x^2-18[/tex]

Since,

[tex]f(x) = + x^2 - 18[/tex]

That is, the change in the sign shows, the given polynomial has one positive real root.

Now, by putting x = - x,

[tex]f(-x)=(-x)^2- 18 = x^2 - 18[/tex]

[tex]\implies f(-x) = + x^2 - 18[/tex]

That is, the change in the sign shows, the given polynomial has one negative real root.

We know that, given polynomial has degree 2,

⇒ It only has 2 roots one is positive real and another is negative real,

⇒ f(x) having 2 real roots.

The reflection of point E across the y-axis, point M, is at (5, 2). The distance between these two points is 10 units.

In the context of this problem, a reflection of a point across the y-axis inverts the sign of the x-coordinate while leaving the y-coordinate unchanged. Thus, if Point E is located at (-5, 2), the reflection of Point E, or Point M, would be located at (5, 2).

In terms of distance, it is important to remember that distance is always a positive value. Considering the x-coordinates, the distance from E to M is the absolute difference between their x-coordinates, which in this case is |-5 - 5| or 10 units.

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This was the correct answer, I even provided proof from my own test. Hope this helps!

81 = 9^2

100 = 10^2

121 = 11^2

n^2

=>

∞

∑ n^2

n=8

which means summation of n squared from n equals eight to infinity

10) Question 10. Find the sum of the arithmetic sequence.
17, 19, 21, 23, ..., 35

Answer: 260

Explanation:

The difference is 2:

The sum is: 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35.

You can use the formula for the sum of an arithmetic sequence:

(A1 + An) * n / 2 = (17 + 35)*10/2 = 260

11) Question 11. Find the sum of the geometric sequence. 

1, 1/2, 1/4, 1/8, 1/16

Answer: option D) 31/16

Explanation:

You can either sum the 5 terms or use the formula for the partial sum of a geometric sequence.

The formula is: Sum = A * ( 1 - r^n) / (1 - r)

Here A = 1, r = 1/2, and n = 5 => Sum = 1 * (1 - (1/2)^5 ) / (1 - 1/2) =

= [ 1 - 1/32] / [1/2] = [31/32] / [1/2] = 31 / 16