What is the average rate of change for this function for the interval from x=3 to x=5

3 is correct, because for n more than 4 we must have node on x=4 too

ANSWER

[tex]2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) ) [/tex]

EXPLANATION

The complex number shown has coordinates (2,-2)

or

[tex]z = 2 - 2i[/tex]

The modulus is

[tex] |z| = \sqrt{ {2}^{2} + {( - 2)}^{2} } [/tex]

[tex]|z| = \sqrt{ 8} = 2 \sqrt{2} [/tex]

The argument is

[tex] \theta= \tan^{ - 1} ( \frac{ - 2}{2} )[/tex]

[tex] \theta= \tan^{ - 1} ( -1) = \frac{7\pi}{4} [/tex]

The polar form is

[tex]2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) ) [/tex]

The first option is correct.

Answer:

The first option (the one all the way at the top)

Step-by-step explanation:

a.pex

Mikah's assets increased by $1,500.

Answer: B

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

To complete the square

add ( half the coefficient of the b- term )² to b² + 16b

b² + 2(8)b + 8²

= b² + 16b + 64 = (b + 8)²

Answer:

19% of the total variation in the y-values is not explained by the regression line

Step-by-step explanation:

The correlation coefficient, r, is a measure of the degree of association between two variables. It gives information on the direction and strength of the relationship.

On the other hand, [tex]R^{2}[/tex] is the coefficient of determination and is a measure of the percent of the total variation in the y-values explained by the regression line.

[tex]R^{2}[/tex] is simply the square of r;

[tex]R^{2}=r^{2}=(-0.9)^{2}=0.81[/tex]

This implies that 81% of the total variation in the y-values is explained by the regression line. Therefore, only 19% is not explained.

Answer:

76.8

Step-by-step explanation:

40/250 = 0.16 (1 campers vote)

0.16 x 12 = 1.92

1.92 x 40 = 76.8

To estimate the number of campers who might be interested in tennis lessons, a proportion can be used based on a survey of 40 campers, 12 of whom were interested. Scaling this up to the total 250 campers, approximately 75 campers might be interested in the tennis lessons.

The question is asking us to estimate the number of campers who would be interested in taking tennis lessons at a summer camp. From a small survey of 40 campers, 12 said they would take tennis lessons. To find out how many campers out of the total 250 might be interested, we need to use proportion. The proportion of campers interested in the survey is 12 out of 40, which we can set as equal to x out of 250, where x is the number we want to find. The equation is set up as follows:

12 / 40 = x / 250

Multiply both sides by 250 to isolate x:

250 × (12 / 40) = x

Calculate x:

x = 250 × (12 / 40) = 75

Therefore, the counselors should plan on approximately 75 campers attending next week’s tennis lesson.

Answer:  C) the variance

Step-by-step explanation:

Variance is the "average" of the squared differences from the Mean.

Calculate the volume of each shape then add them together.

4 x 32 x 10 = 1280

12 x 16 x 10 = 1920

Total volume = 1280 + 1920 = 3,200 cubic in.

250

100 + 200 + 300 + 400 = 1000

1000/4 = 250

Answer:

250

Step-by-step explanation:

Answer:

Step-by-step explanation:

Mean, it is the average of all numbers and most accurately represents the data set.

The best measure of central tendency depends on the data set characteristics: the mean is suitable for outlier-free data, the median is better for skewed data or when outliers are present, and the mode indicates the most common value.

Choosing the Best Measure of Central Tendency

When analyzing a data set, selecting the appropriate measure of central tendency is crucial. The three main measures are the mean, median, and mode. The mean is the arithmetic average and is best used when the data set does not contain outliers that can skew the results. The median is the middle value when the data is ordered and offers a better representation when outliers are present. The mode is the most frequently occurring value and provides insight into the most common data point.

In a symmetrical data set where the data are evenly distributed, all three measures of central tendency—the mean, median, and mode—will be equal or close to each other. In a skewed distribution or when the data contains outliers, the median is generally the most reliable measure of the center, as it is unaffected by extreme values.

Answer : 72,000

Ex: Let x be his monthly salary.

The equation to set up would be

7920=0.11x

This equation represents 11% of monthly salary = 7920

To solve you divide 0.11x by 0.11 to get x by itself. then you do what you do to one side to the other. therefore you divide 7920 by 0.11 and you get 72,000

Answer:

25 ounces of water

Step-by-step explanation:

3/5 = 15

Cross multiplying this:

1 = x

3/5 = 15

3/5x=15

x=25

Answer:

The bottle hold 25 ounces of water

Step-by-step explanation:

To find the amount of water the bottle hold, we will follow the steps below;

let x be the number of ounces of water the bottle holds

3/5  of x  = 15 ounces

3/5  ×  x   = 15

[tex]\frac{3X}{5}[/tex]   = 15

Multiply both-side of the equation by 5

[tex]\frac{3X}{5}[/tex]  ×  5   =  15×5

At the left-hand side of the equation 5 will cancel-out 5 leaving us with 3x

3x = 75

Divide both-side of the equation by 3

[tex]\frac{3X}{3}[/tex]  =  [tex]\frac{75}{3}[/tex]

(On the left-hand side of the equation 3 at the numerator will cancel-out 3 at the denominator leaving us with x while on the right-hand side of the equation 75 will be divided by 3)

x = 25 ounce

Answer:

Total number of eggs in basket = 56

Step-by-step explanation:

Let z be the total number of eggs

Green eggs = [tex]\frac{2}{7}[/tex] × z   ........1

Blue eggs =  [tex]\frac{1}{4}[/tex] × z    .......2

Rest of eggs = 26  ........3

The addition of 1, 2 and 3 is equal to z  

[tex]\frac{2}{7}[/tex] × z + [tex]\frac{1}{4}[/tex] + 26 = z

[tex]\frac{8z + 7 z}{28}[/tex] + 26 = z                        ∵GCF for 4 and 7 is 28  

[tex]\frac{15z}{28}[/tex]  + 26 = z

15z + (26 × 28) = 28z                ∵ multiply both sides by 28

15z + 728 = 28z

28z - 15z = 728     .......... rearranging above equation

13z = 728  ⇒   z = [tex]\frac{728}{13}[/tex]   ⇒  z = 56

Total number of eggs = z = 56

Answer:  There are total 56 eggs in the basket.

Step-by-step explanation:  Given that an Easter basket contains eggs of three different colors, out of which [tex]\dfrac{2}{7}[/tex] are green, [tex]\dfrac{1}{4}[/tex] are blue and rest 26 eggs are red.

We are to find the total number of eggs in the basket.

Let x be the total number of eggs in the Easter basket.

Then, according to the given information, we have

[tex]\dfrac{2}{7}\times x+\dfrac{1}{4}\times x+26=x\\\\\\\Rightarrow \dfrac{8x+7x}{28}+26=x\\\\\\\Rightarrow \dfrac{15x}{28}+26=x\\\\\\\Rightarrow x-\dfrac{15x}{28}=26\\\\\\\Rightarrow \dfrac{28x-15x}{28}=26\\\\\\\Rightarrow \dfrac{13x}{28}=26\\\\\Rightarrow x=\dfrac{26\times 28}{13}\\\\\Rightarrow x=56.[/tex]

Thus, there are total 56 eggs in the basket.

Answer:

D) 14%

Step-by-step explanation:

Let the percent of the real fruit in the first brand = x

Given that number of gallons of  real fruit in the first brand = 9 gallons

Given that percent of the real fruit in the second brand = 48%

Given that number of gallons of  real fruit in the second brand = 8 gallons

Given that  percent of the real fruit in the mixture = 30%

then number of gallons of  real fruit in the mixture = (9+8) = 17 gallons

Then we get equation:

[x% of 9 gallons] + [48% of 8 gallons] = [30% of 17 gallons]

9x+48(8)=30(17)

9x+384=510

9x=510-384

9x=126

x=126/9

x=14

Hence final answer is D) 14%

Answer:D

Step-by-step explanation:jus took test

ANSWER

y=-1

EXPLANATION

The given line in the graph has equation

[tex]y = 2.5[/tex]

This line is a horizontal line.

All horizontal line has a slope of 0.

Let the equation of the line that is parallel to this line be

[tex]y = mx + b[/tex]

The slope of this line must also be zero.

We substitute the slope, m=0 and the point (3,-1) into this equation to get:

[tex] - 1 = 0(3) + b[/tex]

[tex] \therefore \: b = 0[/tex]

Hence the required equation is

[tex]y = - 1[/tex]

ANSWER

y= -1

Step-by-step explanation:

The given line in the graph has equation

This line is a horizontal line.

All horizontal line has a slope of 0.

Let the equation of the line that is parallel to this line be

The slope of this line must also be zero.

We substitute the slope, m=0 and the point (3,-1) into this equation to get:

Hence the required equation is

Kayla has mailed out 8 invitations

Final answer:

The odometer reads 2 miles for every 3 actual miles driven. To find the actual distance when the odometer shows 48 miles, a proportion is used, leading to the calculation that the automobile has driven 72 actual miles.

Explanation:

The student is dealing with a proportion problem in mathematics where the automobile's odometer is inaccurate. Given that the odometer registers 2 miles for every 3 miles driven, we can set up a proportion to find the actual distance driven. If the odometer indicates 48 miles, we can write the proportion as follows:

2 miles (odometer) / 3 miles (actual) = 48 miles (odometer) / x miles (actual)

Cross-multiply to solve for x: 2x = 48 × 3

Calculate x: 2x = 144

Divide both sides by 2 to isolate x: x = 144 / 2

Find the value of x: x = 72 miles

Therefore, the automobile has actually been driven 72 miles.

18 $20 Dollar Bills

5 Bills In 100

10 Bills In 200

15 Bills In 300

18 Bills In 360

Answer:

x=6.5

Step-by-step explanation:

This question is on intersecting cords and segments that intersect outside the circle

Forming an equation for this relation;

6(x+6)= 5(5+10)

6x+36=5(15)

6x+36=75.............................collect like terms

6x=75-36

6x=39...........................divide both sides by 6

x=6.5

ANSWER

B.

[tex]{f}^{ - 1} (x) = {x}^{2} - 3[/tex]

EXPLANATION

Given

[tex]f(x) = \sqrt{x + 3} [/tex]

Let

[tex]y= \sqrt{x + 3} [/tex]

Interchange x and y.

[tex]x= \sqrt{y + 3} [/tex]

Square both sides

[tex] {x}^{2} = y + 3[/tex]

Solve for y

[tex]y = {x}^{2} - 3[/tex]

Therefore the inverse of f(x) is

[tex] {f}^{ - 1} (x) = {x}^{2} - 3[/tex]

Answer:

5 miles apart

Step-by-step explanation:

(4,-6) is 5 units away from (9,-6)

To describe the situation, we can write a system of equations. The cost of a dozen chocolate cookies and a dozen oatmeal cookies can be found by solving the system of equations.

To write a system of equations to describe the situation, let's assign variables to the unknown quantities. Let's say the cost of a dozen chocolate cookies is x dollars and the cost of a dozen oatmeal cookies is y dollars.

The first equation represents the sale of 9 dozen chocolate cookies and 8 dozen oatmeal cookies for $110. This can be written as:

9x + 8y = 110

The second equation represents the sale of 9 dozen chocolate cookies and 5 dozen oatmeal cookies for $89. This can be written as:

9x + 5y = 89

We now have a system of two equations with two variables. We can solve this system using any method, such as substitution or elimination, to find the values of x and y.

Once we find the values of x and y, we can determine the cost of a dozen chocolate cookies and a dozen oatmeal cookies, respectively.

[tex]\bf \stackrel{\stackrel{\textit{net income}}{\textit{revenue}}}{f(x)}=9x^2-54x-144\implies \stackrel{\textit{revenue}}{0}=9x^2-54x-144 \\\\\\ 0=9(x^2-6x-16)\implies 0=x^2-6x-16 \\\\\\ 0=(x+2)(x-8)\implies x= \begin{cases} -2\\ 8&\checkmark \end{cases}[/tex]

since the units sold can't be negative, we can't use -2.

Answer:

I believe it is the third one (C)

Step-by-step explanation:

Hello There!

Your answer would be the first one.

f(x) = \x/

F of x has to equal f of -x

Answer:

[tex]5\frac{1}{2}\ mi[/tex]

Step-by-step explanation:

we know that

[tex]1\frac{3}{8}\ mi=\frac{1*8+3}{8}=\frac{11}{8}\ mi[/tex]

She drove from her house to the airport and back 2 times

so

Multiply the distance from her house to the airport by 4

[tex](4)*\frac{11}{8}=\frac{11}{2}=5\frac{1}{2}\ mi[/tex]

Hello There!

The answer would be 0.6

This is because you have to multiply the probability of each of these. First, I know that 0.5 is 1/2 in fraction form and that 0.3 is 3/10

Answer:

D. 150 metres

Step-by-step explanation:

speed = (60) times 5/18 = 50/3

lenght of the train = (speed x time)

lenght = 50/3 times (9)

   = 150 m.

No. There are two spots in the vertical line. (Vertical line test)

ANSWER

No, there are two points with the same x-coordinates.

EXPLANATION

The relation in the graph is not a function.

There are two points in the relation that have the same x-coordinates.

These points are (1,1) and (1,3).

As a result of this , a vertical line will intersect the graph of the relation at these two points.

Since the graph of the relation does not pass the vertical line test, it is not a function.

Step-by-step explanation:

l - 2 x l = 4

     2 x = 4

         x = 2

Answer:

Answer:

-2 & 2

( option C )

If you cross check with the answer , you’ll find option C to be the most appropriate option.

The difference between the first two terms is 9 and 9 is not a multiple of six, therefore first two are wrong.

Similarly, if you check option D for the first two terms , you get the second term as 27 which is false.

Therefore option C is the answer, also , it satisfies the series.

Final answer:

The correct expression to find the nth term of the given pattern is Option D: [tex]27(2/3)^{(n-1)}[/tex], as it accurately represents the geometric sequence of the provided numbers.

Explanation:

To find the nth term of the given pattern 27, 18, 12, 8, we will consider each option and see which one fits the sequence of numbers.

The first term (n=1) is 27.

The second term (n=2) is 18, which is 27 multiplied by ⅔ or 2/3.

The third term (n=3) is 12, which is the second term (18) multiplied by ⅔ or 2/3.

Similarly, the fourth term (n=4) is 8, which is the third term (12) multiplied by ⅔ or 2/3.

We can see that with each step, the term is being multiplied by a factor of ⅔ or 2/3. Therefore, an expression that uses multiplication by ⅔ repeatedly would likely represent the pattern.

Let's test the options:

Option A: 27-6n does not fit as it suggests a linear pattern with a constant subtraction, which does not match our sequence.

Option B: 27-6(n-1) also suggests a linear pattern and will not result in the given sequence when evaluated for n=1,2,3,4.

Option C: [tex]27(2/3)^n[/tex] represents a geometric sequence with a common ratio of ⅔, but for n=1, this expression gives us 27*⅔ which is not equal to 27.

Option D: [tex]27(2/3)^{(n-1)}[/tex] when evaluated for n=1 gives us 27*[tex](2/3)^{(1-1)}[/tex] = 27*1 = 27, which is the correct first term of our sequence. Applying this for subsequent terms also gives the correct sequence. Therefore, this is the correct expression for the nth term of the pattern.

Thus, the expression to find the nth term of the pattern is Option D: [tex]27(2/3)^{(n-1)}[/tex].