The heights, in feet, of 12 trees in a park are shown below.8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47Use the drop-down menus to explain the interquartile range of the data.

Basic geometry are formulars and properties of basic shapes like rectangle, square, circle, triangle, and solid shapes like cuboid, cube cylinder etc.

The area, perimeter and volume of solid shape are properties that can be determined from this shape.

Perimeter is the sum of the whole side of the figure. Example the perimeter of a rectangle with 2 length and 2 width can be calculated by adding the whole 2 length and width.

The perimeter of the rectangle above is by adding all the sides.

perimeter = 4 + 4 + 2 + 2 = 12 cm

The area of the figure below is the amount of space of the boundary. The area of the rectangle below is length * width = 4 * 2 = 8 cm squared.

The curve is given to be:

We can rewrite the equation in the form:

Using the Completing the Square method, we have the equation to be:

Therefore, the ellipse's center is (0, -6).

In this case, the information that is explicitly seen in the graph is that we have 2 pairs of equal sides.

The missing information, that can also be seen in the picture, is that we have a shared side that is QY.

If we applied the reflexive property, we know that:

and then we know that we have 3 pairs of equal sides, what proves that the triangles are congruent.

Answer: QY = QY (Option A).

Answer:

Aveage Rate of cCanege = 40

Explanation:

The line segment is drawn in the function below:

Using the line segment:

Therefore, the average rate of change will be:

The average rate of change is 40.

3 in the 9th power means that you have to make 3 to the power of 9.

The answer is 19,683.

The external angle formed by the secants equals one-half the difference of the intercepeted arcs. Therefore:

A  person weigh on the Mercury if they weigh 135 pounds on Earth is  43.94 pounds.

Weight of person on Earth = 145pounds

145 = mg

Weight of person on Mercury = 47.2pounds

47.2 = ma

145/47.2 = mg/ma

145/47.2 = g/a

a = 47.2g/145      .....1.

If weight of person on earth = 135pounds

135 = mg

  m = 135/g        .......2.

Then, Weight of person on Mercury = ma

using the above values of a and m we we get

= (135/g)x (47.2g/145 )

= 135 x 47.2 / 145

= 43.94 pounds

A  person weigh on the Mercury if they weigh 135 pounds on Earth is  43.94 pounds.

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The required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

The given starting weight for the diet program is 106 pounds. Because the weight is expected to be multiplied by 1.04 pounds each week, the weight will develop exponentially with an initial value of 106 pounds and a growth factor of 1.04 pounds. Then, for the weight after weeks, the exponential function is given by,

W  = W(n) = Pb'

Here P = 106 and b = 1.04

Hence the required formula is,

⇒ W = 106 × 1.04ⁿ

Thus, the required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.

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The question seems to be incomplete the correct question would be

A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week. Then, find the exponential function for the weight after weeks.

Answer:

2/3

Step-by-step explanation:

y = xk

6 = 72K  Solve for k  Divide both sides by 72

[tex]\frac{1}{12}[/tex] = k

y = xk

y = [tex]\frac{8}{1}[/tex] x [tex]\frac{1}{12}[/tex]

y = [tex]\frac{8}{12}[/tex]  I can simplify by dividing the numerator and denominator by 4

y = 2/3

For the given functions, we can write the sum as:

(f + g)(x) = 9x + 1

Here we want to find the sum between functions f(x) and g(x), and in this case, we have:

f(x)= x - 8

g(x) = 8x + 9

The sum can be written as:

(f + g)(x) = f(x) + g(x)

Replacing the functions there we get:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (x - 8) + (8x + 9)

(f + g)(x) = x + 8x - 8 + 9

(f + g)(x) = 9x + 1

That is the sum of the functions.

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y varies directly as x, y = 7 when x = 21. Determine x when y = 5.

Step 1

Let

y varies directly as x, it is y depends on x, in math terms

f(x)=y

y = 7 when x = 21

f(21)=7

Determine x when y = 5. f(?)=5

Step 2

there is a proportion, this must be equal, make a rule of three to find the value

so

x y

so , when y=5, x=15

Answer:

-4 +9i

Step-by-step explanation:

complex number in standard form.

(-2+6i)-(2-3i)=

Combine like terms

-2 -2  +6i +3i

Standard form is a+bi

-4 +9i

ticket sale on Saturday night is triple the ticket sale on Friday night.

Therefore

ticket sales on Saturday night = 3 x 12425 = 37275

Then

ticket sales for both nights = 12425 + 37275 = 49700

A ticket costs 35.

Let the number of people that attended the carnival on both nights be n.

Then, we have

Therefore 1420 people attended the carnival on both nights

The sentence in B uses the underlined word incorrectly. The kirt was clever in concocting a story about hossatye zot in trouble.

Here the word,

So here option B is vocabulary incorrect .

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By definition, a Right angle is an angle that measures 90 degrees.

Complementary angles are those angles that add up to 90 degrees.

For this case, you can identify that the angle 1 and the angle 2 are Complementary angles, because when you add them, you get 90 degrees (a Right angle).

Knowing the above, you can set up the following equation:

Since you know that:

You can substitute this value into the equation and the solve for the angle 1 in order to find its measure. You get that this is:

The answer is:

Step 1

Given the triangle, ABC translated to A'B'C'

Required to find the algebraic description that maps triangle ABC and A'B'C'

Step 2

The coordinates of points A, B,C are in the form ( x,y)

Hence

Step 3

Find the algebraic description that maps triangle ABS TO A'B'C'

The algebraic description is found using the following;

Hence,

Hence the answer is option B

The graph of (3, 2) is located 3 units to the right of the y-axis and 2 units above the x-axis, while the graphs of (-3, 2), (-3, -2) and (3, -2) are located 3 units to the left of the y-axis and 2 units below the x-axis, 3 units to the right of the y-axis, and 3 units to the bottom of the x-axis, respectively.

The ordinate of the point is the distance from the x-axis that it is placed at, and the abscissa of the point is the distance from the y-axis that it is located at. An algebraic equation of the type known as a linear equation.

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Answer:

45,000

Step-by-step explanation:

Hey! Let's help you with your question here!

So, let's think about this logically. The only limit we have here is that the leftmost digit cannot be zero. This makes sense because there would be no five-digit number if the leftmost is zero. In order to find the possible amount of even numbers, we need to take the possible numbers of each digit and have them multiplied to each other to get the total. (I will explain this soon).

First Digit:

Since, the rules state that the leftmost digit cannot be zero, this would be the digit that the rule affects. From here, we can have a possibility of the numbers 1 through 9 here. So, for the first digit, we have the possibility of 9 numbers that can be here.

Second, Third, Fourth Digit:

Now you're probably wondering as to why I've grouped up these 3 digits and not the last or the first one. We'll get to the last one in the next explanation, but we exclude the first digit because the rule that affects the first digit, does not affect these digits nor the last digit. With these 3 digits, we don't have that rule of it cannot be zero, so now our possibilities for what the numbers can be is 0 through 9. If we include 0 as a number too, then we have a possibility of 10 numbers that can be within these digits.

Fifth (Last) Digit:

For this last digit, there is an implicit rule being stated for the last digit. The question asks how many five-digit even numbers are possible if the leftmost digit cannot be zero. This rule affects the last digit only as that allows the whole five-digit number to be even and zero is included in this. So, the even numbers are 0, 2, 4, 6, and 8. In this case, we only have 5 possible numbers to choose from for the very last digit.

Answer Explanation:

Before I begin answering, back in the very first paragraph, I said we need to take the possible numbers of each digit and multiply them altogether to get the total amount of possible values. Why do we do this? This is the idea of possibility combination. We multiply because we are taking in account all of the possible values whereas if we just add, we're only taking in account the maximum possible value of each possibility. So, let's calculate the answer now! For the first digit, we have a possibility of 9 numbers being there (1-9). For the Second, Third, and Fourth digit, we have a possibility of 10 numbers being there (0-9). And finally for the last digit, we have a possibility of only 5 numbers (0, 2, 4, 6, and 8). So, the total possible combination is:

[tex]9*10*10*10*5[/tex]

[tex]=45,000[/tex]

Therefore, we get 45,000 total possible five-digit even numbers where the leftmost digit cannot be zero.

The expression (m⁻⁵n⁻³)⁻³ has an equivaent of m⁻¹⁵n⁹

From the question, the expression is represented as

(m−5n−3)−3

Rewrite the expression properly

This is done as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

This gives

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution is (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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The given expression (m⁻⁵n⁻³)⁻³ has an equivalent to the m⁻¹⁵n⁹

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is represented as (m−5n−3)−3

Rewrite the expression as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets , we have

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products, we have;

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution will be; (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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In a parallelogram opposite sides have the same length therefore, for figure EFGH to be a parallelogram we must have that:

Substituting we get:

Now, we solve for "z". First, we subtract "z" from both sides:

Therefore, the value of "z" is 10.

For finding y, we can replace the value of x in any equations.

Solution (-3,2)

Plot graphs

replace x with a for this exercise

we use this formula to factor

where a=5, b=-3 and c=-14

we have two roots

and

so the simplified equation is

now replace x for a

Answer:

12x-21

Explanation:

Given the expression

3 (4x-7)

On expanding using distributive law;

3(4x-7)

3(4x) - 3(7)

12x - 21

Hence the result required is 12x-21

The line passes through the points, (-6,-10) and (-2,-10)

We know equation of the line passing through points (x',y') and (x'',y'') is given by:

So the equation of the line is:

The equation of the line is y=-10

The break time is 2:15 pm.

The time interval for break is 45 min.

Determine the time at which interval ends.

So break ends (individual come back) at 3:00.

Given:

Total Number of ways = 54

Number of body styles = 3

Number of engine choices = 2

Let's find the number of colors available.

To find the number of colors available, we have:

Number of ways = Number of body styles x Number of engine choices x Number of colors

54 = 3 x 2 x c

Where c represent the available number of colors.

Let's find c.

54 = 3 x 2 x c

54 = 6c

Divide both sides by 6:

Therefore, there are 9 colors available to select from.

ANSWER:

9

Using the normal distribution and the central limit theorem, it is found that:

a) The distribution is: x¯ ~ N(22, 1.45).

b) The distribution is: ∑x ~ N(902, 59.55).

c) P( ¯x > 19.8214) = 0.9332 = 93.32%.

d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.

e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.

f) Q1 for the x¯distribution = 21 points a game.

g) P( ∑x > 829.0774) = 0.8888 = 88.88%.

Assumption of normality is not necessary, as the sample sizes are greater than 30.

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For a single game, the mean and the standard deviation of the number of points scored are given as follows:

[tex]\mu = 22, \sigma = 9.3[/tex]

For the average of 41 games, the standard error is:

[tex]s = \frac{9.3}{\sqrt{41}} = 1.45[/tex]

Hence the distribution is: x¯ ~ N(22, 1.45).

For the sum of the 41 games, the mean and the standard error are given as follows:

Hence the distribution is: ∑x ~ N(902, 59.55).

In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (19.8214 - 22)/1.45

Z = -1.5

Z = -1.5 has a p-value of 0.0668.

1 - 0.0668 = 0.9332 = 93.32%.

The 60th percentile for the distribution is X when Z = 0.253, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

0.253 = (X - 22)/1.45

X - 22 = 0.253 x 1.45

X = 22.37.

For item e, the probability is the p-value of Z when X = 23.2262 subtracted by the p-value of Z when X = 20.6214, hence:

X = 23.2262:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (23.2262 - 22)/1.45

Z = 0.85

Z = 0.85 has a p-value of 0.8023.

X = 20.6214:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (20.6214 - 22)/1.45

Z = -0.95

Z = -0.95 has a p-value of 0.1711.

0.8023 - 0.1711 = 0.6312 = 63.12%.

The first quartile for the distribution is X when Z = -0.675, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

-0.675 = (X - 22)/1.45

X - 22 = -0.675 x 1.45

X = 21.

For item g, the probability is one subtracted by the p-value of Z when X = 829.0774, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (829.0774 - 902)/59.55

Z = -1.22

Z = -1.22 has a p-value of 0.1112.

1 - 0.1112 = 0.8888 = 88.88%.

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Answer:

A

Step-by-step explanation: