Bethany is a biologist who has been measuring and recording the rabbit population at a park over the last several years. She has noticed that a trigonometric function can model the population, which reaches a maximum population, m, each summer and a minimum population, n, each winter. If she uses to represent the rabbit population t years from the start of her study, what is the domain of function p?

∠A = 41.81°

To get measure of angle A, we would apply trigonometry ratio SOHCAHTOA:

opposite = side opposite the angle = 4

hypotenuse = 6

adjacent = base = AC = ?

Since we have been given the opposite and the hypotenuse, we would use the sine ratio:

Sin A = opposite/hypotenuse

Sin A = 4/6

sin A = 0.6667

A = 41.8129 degrees

To the nearest hundredth, ∠A = 41.81°

The unknown length of the similar figure is:

x = 15 units

Two figures are similar if they have the same shape but different sizes. The corresponding angles are equal and the ratios of their corresponding sides are also equal.

Using the above concept, we can equate the ratio of the corresponding sides and solve for the unknown lengths. That is:

TV/AC = TU/AB

x/10 = 6/4

x/10 = 1.5

x = 10 * 1.5

x = 15 units

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Answer:

c = 3 because 4 times 3 = 12

Answer:

12= 3+3+3+3 or 12= 3x4

Answer:

Step-by-step explanation:

C

Answer:   6.1% decrease

Note: It appears that your teacher doesn't want you to type in the percent sign, as that's already covered for you.

=========================================================

Explanation:

The salary decreased by 51500-48355 = 3145

Divide this over the initial salary to get 3145/51500 = 0.0611 which is approximate.

This converts to the percentage 6.11% and that rounds to 6.1%

----------------

As an alternative, you can use the formula method below

A = old value = 51500

B = new value = 48355

C = percent change when going from A to B

C = [ (B-A)/A ] * 100%

C = [ (48355-51500)/51500 ] * 100%

C = (-3145/51500)*100%

C = -0.0611*100%

C = -6.11%

C = -6.1%

The negative C value indicates a percent decrease.

Answer:

0.9544 = 95.44% probability of the resulting sample proportion being within .04 of the true proportion

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

20% of the residents in a certain state support an increase in the property tax. Sample of 400.

This means that \(p = 0.2, n = 400\)

Mean and standard deviation:

Mean \(\mu = p = 0.2\)

Standard deviation \(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.2*0.8}{400}} = 0.02\)

How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?

This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16. So

X = 0.24

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.24 - 0.2}{0.02}\)

\(Z = 2\)

\(Z = 2\) has a pvalue of 0.9772

X = 0.16

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.16 - 0.2}{0.02}\)

\(Z = -2\)

\(Z = -2\) has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability of the resulting sample proportion being within .04 of the true proportion

The length of the arc of a circle of radius 12 is 37.68.

The arc of a circle is defined as the part or segment of the circumference of a circle.

To calculate the arc of the circle, we the formula below.

Formula:

Where:

From the question,

Given:

Note: 360° = 2π radian

Substitute these values into equation 1

Hence, the length of the arc is 37.68.

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Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.

The equation can be set up as follows:

0.80x + 0.55(600 - x) = 0.60(600)

Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.

By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.

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Let x=amount of 80% solution needed

Then 600-x=amount of 30% solution needed

Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:

0.80x+0.30(600-x)=0.40*600 get rid of parens

0.80x+180-0.30x=240 subtract 180 from each side

0.80x+180-180-0.30x=240-180 collect like terms

0.50x=60 divide each side by 0.50

x=120 ml---------------------amount of 80% solution needed

600-x=600-120=480 ml---------------amount of 30% solution needed

CK

120*0.80+480*0.30=0.40*600

96+144=240

240=240

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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The exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

An exponential function is represented as:

\(y = b^x\)

The base is 3.

So, we have:

\(y = 3^x\)

It is stretched vertically by 2/3.

So, we have:

\(y = \frac23(3)^x\)

When reflected over the y-axis, we have:

\(y = \frac23(3)^{-x}\)

An asymptote of y = 2, makes the function becomes

\(y = \frac23(3)^{-x} + 2\)

Lastly, it passes through the point (0, 3.5).

So, we have:

\(y = \frac23(3)^{-x+h} + 2\)

This gives

\(3.5 = \frac23(3)^{-0+h} + 2\)

\(3.5 = \frac23(3)^{h} + 2\)

Subtract 2 from both sides

\(1.5 = \frac23(3)^{h}\)

Multiply by 3/2

\(2.25 = (3)^{h}\)

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in \(y = \frac23(3)^{-x+h} + 2\)

\(y = \frac23(3)^{-x+0.74} + 2\)

Hence, the exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

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To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

Answer:

Step-by-step explanation:

Answer:

  B)  15/17

Step-by-step explanation:

You want the sine of acute angle A in the right triangle shown.

The sine of the angle is the ratio ...

  Sin = Opposite/Hypotenuse

We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)

The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.

The value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.

Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.

The sine of angle A is 15/17.

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The expressions are evaluated to give;

a. 1/-6x²

b. 2/3

Note that index forms are models that are used to write numbers or variables that are too large or small in more convenient forms.

In indices, it is known that any number that is raised to the power or exponent 0 is 1.

For example:

x° = 1

y° = 1

z° = 1

Then, we have the expressions;

-6x⁻², this is represented as;

1/-6x²

Also, we have;

2x°/-3

Since x° = 1

substitute the value

2/3

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The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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The formula for the amount, A mg, of caffeine in the body t hours after drinking a cup of coffee is,

⇒ \(A = 100e^{0.17t}\)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A cup of coffee contains 100 mg of caffeine.

Now, The body at a continuous rate of 17% per hour.

Hence,

r = 17%

r = 17/100

r = 0.17

Therefore, The formula for the amount, A mg, of caffeine in the body t hours after drinking a cup of coffee is,

⇒ \(A = 100e^{0.17t}\)

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Answer:

= 13.51351351

Step-by-step explanation:

Sol:

(750×4)/222

= 3000/222

= 13.51351351

Step-by-step explanation:

hope it is helpful to you ☺️

Answer:

Subtraction property of equality

Step-by-step explanation:

In mathematics that are various types of properties that can be used to solve for questions

In the above question:

If 3x - 14 = 12

then 3x = 26

The property that is applied here is the Subtraction property of equality.

The subtraction property of equality states that when we subtract from one side of and algebraic expression, we must subtract from the other side

a = b

a - c = b - c

a = 3x

b = 26

c = 14

3x = 26

3x - 14 = 26 - 14

then 3x - 14 = 12

There are more types of corresponding angles because a line is equal to 180 degrees.

The required angle types would be corresponding angles has the most pairs of angles created when two parallel lines are intersected by a transversal.

Alternate Interior Angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles. These angles are always equal.

When two parallel lines are intersected by a transversal, the angle types with the most pairs of angles are corresponding angles.

Therefore, the angle types would be corresponding angles has the most pairs of angles created when two parallel lines are intersected by a transversal.

Hence, the correct answer would be an option (D).

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Answer:

60:90

Step-by-step explanation:

The ratio of girls (G) to boys (B) is 2 : 3.

Given the following data:

In this exercise, you're required to find the ratio of girls (G) to boys (B). In order to do this, we would divide the two values to the least.

\(G : B = 60 : 90\)

Dividing both sides by 30, we have;

\(G : B = \frac{60}{30} : \frac{90}{30} \\\\G : B = 2 : 3\)

Therefore, the ratio of girls (G) to boys (B) is 2 : 3.

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Answer:

55 minutes.

Step-by-step explanation:

1 2/3 - 3/4 = 11/12 hours

11/12 hours = 55 minutes.

Answer:

6 games

Step-by-step explanation:

Before the last game, Jonas had 88 points

In the last game, Jonas scored 23 points

Total points scored in the season = points before last game + point on last game

Total points of the season = 88 + 23

Total points of the season = 111 Points

Further ahead, we're told Jonas had a season average of 18.5 points. This means that he scored an average of 18.5 points in all the games in played in the season, each. We're then required to find the number of games he played.

To find the number of games he played, we divide the total number of points he scored in a season by the average points he scored in a game. Something like this

Number of games played = total points scored / average points scored

Number of games played = 111 / 18.5

Number of games played = 6.

Therefore, Jonas played 6 games during the season

Answer:

12, 3

Step-by-step explanation:

i think so but you could wait for another answer but im not sure of my own

Answer: 28 and 20

Step-by-step explanation:

52 - 44 = 8

44 - 36 = 8

36 - \(x_{1}\) = 8

\(x_{1}\) = 28

28 - \(x_{2}\) = 8

\(x_{2}\) = 20

please give me a brainliest answer

Answer:

\(9 {x}^{2} + 3 {x}^{3} \)

\(3 {x}^{2} (3 + x)\)

\(3 {x}^{2} (x + 3)\)

For the same value of x=3, y has two different values of 2 and 4, which is not allowed in a function. Therefore, third case is not a function.

What is function?

Functions cannot have different values of y for the same value of x. Now let us check each case one at a time.

First Case: For the same value of x=-1, y has two different values of 7 and 1, which is not allowed in a function. Therefore, the first case is not a function.

Second Case: For the same value of x=-1, y has two different values of -5 and 1, which is not allowed in a function. Therefore, the second case is not a function.

Third Case: For the same value of x=3, y has two different values of 2 and 4, which is not allowed in a function. Therefore, third case is not a function.

Fourth Case: In this case no value of x is same. So, this is a function.

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The model should visually represent that Ms. Duda's class hung 100 lanterns before lunch, which is 20% of the total 500 lanterns.

To draw a model showing what percent of 500 lanterns Ms. Duda's class hangs before lunch, we can use a rectangular bar model.

Draw a rectangular bar to represent the total number of lanterns, which is 500. Label it as "Total Lanterns."

Divide the rectangular bar into two parts. One part should represent the number of lanterns hung before lunch, which is 100. Label this section as "Lanterns Before Lunch."

Calculate the percentage of lanterns hung before lunch by dividing the number of lanterns hung before lunch by the total number of lanterns and multiplying by 100. In this case, (100/500) * 100 = 20%.

Draw an arrow pointing to the "Lanterns Before Lunch" section, and write "20%" next to it to represent the percentage.

The model should visually represent that Ms. Duda's class hung 100 lanterns before lunch, which is 20% of the total 500 lanterns.

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The sine of ∠I is represented by the ratio 63:65

First, let's draw the triangle (see the picture below.)

We need to use it here.

-sin = opposite/hypotenuse

-cos = adjacent/hypotenuse

-tan = opposite/adjacent.

Assuming that ∠I is Ф,

we can see that its opposite side is equal to 63 and the hypotenuse is 65. Therefore,

\(sin(I)=\frac{63}{65} \\\\sinI=75^0\)

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Answer:

0.18

Step-by-step explanation:

It’s right bc I got it correct with that answer