Consider the graphed function.

What are the domain and the range of this function?

The average rate of change of the function over −2 ≤ x ≤ 2 is 1/2

The function is given as:

[tex]h(x) = \frac 18x^3 - x^2[/tex]

The interval is given as:

−2 ≤ x ≤ 2

Calculate h(2) and h(-2)

[tex]h(2) = \frac 18 * 2^3 - (2)^2[/tex]

h(2) = -3

[tex]h(-2) = \frac 18 * (-2)^3 - (-2)^2[/tex]

h(-2) = -5

The average rate of change is then calculated as:

[tex]m = \frac{h(-2) - h(2)}{-2-2}[/tex]

This gives

[tex]m = \frac{-5 + 3}{-4}[/tex]

Evaluate

m = 1/2

Hence, the average rate of change of the function over −2 ≤ x ≤ 2 is 1/2

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Complete question

[tex]h(x) = \frac 18x^3 - x^2[/tex]

What is the average rate of change of h over the interval −2 ≤ x ≤ 2

The percentage form of given fraction is 60% and the hundredths form is 0.60

According to the statement

we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.

So, For this purpose,

The given fraction is 12/20.

Then the definition of the percentage is that

The Percentage, a relative value indicating hundredth parts of any quantity.

so, the percentage of given fraction is :

Percentage fraction = 12/20 * 100

After solving it, The percentage fraction will become:

Percentage fraction = 60%

and Now convert into the hundredths form then

In the hundredths form it will become

from 60% to 0.60.

So, The percentage form of given fraction is 60% and the hundredths form is 0.60

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There are 27720 strings.

Strings of 12 ternary digits, 3 possibilities for each digit in the string, gives a total of 3^12 = 531,441 ternary strings of length 12.

There are

C(12,3) = 12! / (9! 3!) = 12 * 11 * 10/ 3 * 2 = 220 possible combinations of positions for the three 0s.

Of the 9 remaining positions, there are

C(9,4) = 9! / (5! 4!)

= 9 * 8 * 7 * 6/ (4 * 3 * 2 * 1)

= 126 possible combinations of positions for the four 2s.

The remaining 5 places are, of course, occupied by the five 1s.

So there that contain exactly three 0s, five 1s, and 4 2s are 220 * 126= 27720 such strings.

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Step-by-step explanation:

20 gallons of gasoline

gas is $ 2.50 per gallons

2.50 × 20

{(2×2)(0×.5)(0)}

domain=200

range=2.5

The appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.

In this question,

The independent samples t test (also called the unpaired samples t test) is the most common form of the T test. It helps you to compare the means of two sets of data.

The Independent samples t test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.

The independent sample t-test is a useful statistical method of hypothesis testing when an organization wants to determine whether there is a statistical difference between two categories, groups, or items and, furthermore, if there is a statistical difference, whether that difference is significant.

From the definition, the independent sample t-test is the appropriate test for a comparison a group of 10 dogs and group of 10 cats.

Hence we can conclude that the appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.

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The solution to the inequality in discuss involving a rational expression as indicated in the task content is; t (9, infinity).

The inequality given in the task content as evident is; (2t +22)/(2t +2) <= 2.

On this note, the inequality can be solved by cross-multiplication as follows;

2t +22 <= 4t +4

Hence, we have;

-2t <= -18

t >= 9.

Hence, when expressed as an interval notation, we have; t (9, infinity).

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The option A is correct. A circle is the shape of the cross section taken parallel to the base of a cylinder.

According to the statement

We have given that the cylinder and we have to tell that the which shape required for the cross section taken parallel to the base of a cylinder.

So, For this purpose,

We know that the

A cylinder is a three-dimensional solid, one of the most basic geometric shapes.

In this shape the surface formed by the points at a fixed distance from a  line segment, which is  known as the axis of the cylinder.

As the bases of cylinder are two identical circles which are parallel to the curved surface.

The curved surface when we open will be circle rather than the circle.

So, Due to this reason the answer is a circle.

Therefore, a circle is the shape of the cross section taken parallel to the base of a cylinder.

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The Confidence interval for 95% who believes that the local businesses overcharge = (0.7026, 0.7574)

The range of values we see in our sample and hope to identify the value that most closely represents the population are referred to as a confidence interval.

Sample size n = 1000

73% of town residents believed that local businesses overcharged for their products over 1000 resident.

= (1000/100) x 73

= 730

Sample proportion p = 730/1000

                                    = .73

q = 1-p = 0.23

Std error of proportion = √(pq/n)

                                      = √((.73*0.27)/1000)

                                      = 0.0140

95% Z critical value = 1.96

Margin of error = 1.96*0.0140

                          = 0.0274

Confidence interval = sample proportion ±margin of error

(0.7026, 0.7574)

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Answer:

14×7=98 so multiply the same into 14×8=112

Answer:

112 watermelons

Step-by-step explanation:

7/8 = 7÷7/8÷7 = 1/1.14285714286

1 x 98/ 1.14285714286 x 98

98/112

Answer:

120.

Step-by-step explanation:

That would be factorial 5, written 5!.

That  is 5*4*3*2*1

= 120.

Answer:

120

Step-by-step explanation:

We have 5 digits that can be used to create different 5 digit numbers. We are also not allowed to repeat any numbers. Let's say we have 5 boxes to put the 5 numbers in.

Box 1

Box 2

Box 3

Box 4

Box 5

In the first box, we have 5 different choices. Since we aren't allowed to repeat any digits, the second box only has 4 different choices. And so on...

Box 1 --> 5 choices

Box 2 --> 4 choices

Box 3 --> 3 choices

Box 4 --> 2 choices

Box 5 --> 1 choice

Therefore the amount of 5 digit numbers that can be created is:

[tex]5\times4\times3\times2\times1[/tex] or 5 factorial (a factorial is all the product of all the positive integers equal to and less than the number), which is equivalent to:

120 5-digit numbers

Answer:

read below or other answer

Step-by-step explanation:

2 [{2-2(2÷2-2)} ÷2]÷2​

2 [ { 2 - 2 ( 1 - 2 ) } ÷ 2 ] ÷ 2

2 [ { 2 - 2 ( - 1 ) } ÷ 2 ] ÷ 2

2 [ { 2 + 2 } ÷ 2 ] ÷ 2

2 [ 4 ÷ 2 ] ÷ 2

2 ( 2 ) ÷ 2

4 ÷ 2

2 divided by 2

Answer: 2

Step-by-step explanation:

Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:

This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:

Me = (19 + 23)/2 = 21.

The first quartile is the median of 6, 7, 8, 8, 16, which is the third element of 8.

The third quartile is the median of 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.

The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.

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Answer: 21450

Step-by-step explanation:

That is the initial price.

The line cross the y axis at 21450.

The correct option is (C)

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Elise is buying a new car selling for $21,450.

The rate of depreciation on this type of car is 8% per year.

Using f(x) = A [tex](1+r)^x[/tex]

A= $21,450.  and r = -8% (depreciated)

So, f(x) = A [tex](1+r)^x[/tex]

f(x) = 21450 [tex](1- 8/100)^x[/tex]

= 21450 x [tex](0.92)^x[/tex]

Thus, the line cross the y axis at

= 21450 ( initial point)

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[tex]

\sin^{-1} \left(-\frac{1}{2} \right)=-\sin^{-1} \left(\frac{1}{2} \right)=\boxed{-\frac{\pi}{6}}[/tex]

Answer: [tex]\Large\boxed{a_n=6n-4}[/tex]

Step-by-step explanation:

Given sequence

2, 8, 14, 20, 26

Determine the pattern

2 + 6 = 8

8 + 6 = 14

14 + 6 =20

20 + 6 = 26

For each term, add 6 to get the next term

Determine the type of sequence

Since it continuously adds 6, the common difference is 6, which means it is an arithmetic sequence

Given the arithmetic sequence formula

aₙ = a₁ + d (n - 1)

Substitute values into the formula

aₙ = (2) + (6) (n - 1)

aₙ = 2 + 6 (n - 1)

aₙ = 2 + 6n - 6

aₙ = 2 - 6 + 6n

[tex]\Large\boxed{a_n=6n-4}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Given sequence :-

Solution :-

We need to calculate the nth term of the given sequence.

We know that,

Applying the values here.

>> tn = 2 + (n - 1) 6

>> tn = 2 + (n - 1) × 6

>> tn = 2 + 6n - 6

>> tn = 6n - 4

Therefore, nth term of the sequence is (6n - 4).

Answer:

option c

Step-by-step explanation:

option c is a correct answer

Answer:

204

Step-by-step explanation:

6*10=60

6*6=36

6*8=48

2((10*6)/2)=60

60+60+36+48=204

Answer:

2/3

Step-by-step explanation:

since they are just two colors of fish inside, since the probability is always 1.. so we have to minus 1/3 from 1,which is 1-1/3=2/3

The radius of the circle is 24 hectometers.

Remember that the circumference of a circle of radius R is given by the equation:

[tex]C = 2*\pi*R[/tex]

In this case, we know that the circumference is: C = 150.7968 hm

And π = 3.1416

Replacing that and solving for R, we get:

[tex]R = \frac{C}{2*\pi} = \frac{150.7968hm}{2*3.1416} = 24hm[/tex]

The radius of the circle is 24 hectometers.

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Answer:

65°

Step-by-step explanation:

JM = JK (all sides of a rhombus are equal)

Angle JKM = 25° (isosceles triangle)

Angle JKL = 50° (consecutive angles of rhombus)

Angle MKL = 25° (angle subtraction)

Angle MLK = 130° (opposite angles of a rhombus)

Angle KLN = 50° (angles on a straight line)

Angle LKN = 40° (angle sum of triangle)

Angle MKN = 65° (angle addition)

The ratio of the volume of a pyramid to the volume of a prism with the same base and height is 1 to 3; the formula for the volume of a pyramid is V = 1/3Bh.

where,

Volume of prism : Volume of pyramid

Bh : 1/3Bh

Therefore, the ratio of the volume of a pyramid to the volume of a prism with the same base and height is 1 to 3.

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So, 22, 23 are the two numbers.

There are two distinct but related ideas that are referred to as linear functions: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.

Consecutive numbers are preceding and following, hence we need two numbers so that

X+1=Y

or

X- Y = -1

In addition, we are aware of

4x + 3y = 157

Let's increase the top equation by 3 times.

We get

3x - 3y = -3

Then we combine that with the bottom equation.

4x + 3y = 157

      7x= 154

       x = 22

Afterward, we substitute x into the initial equation,

22+1 = 23

So, 22, 23 are the two numbers.

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Based on the given table which shows the number of years with a company in relation to the employee salary, the conclusion that can be drawn is There is a weak positive correlation between the variables.

When two variables are said to be positively correlated, then it means that when one variable increases, the other variable would increase as well.

If the correlation between them is strong, then the increase between the variables would be more uniform i.e. we can tell with higher accuracy, how the increase in one variable would affect the other.

In the table, we see that with every increase in the number of years with the company, there is an increase in the salary. This means that there is a positive correlation.

The increase is not uniform however. Sometimes it increases by $1,000, and other times by $7,000. As the increase is not uniform, it means that the correlation is weak.

In conclusion, there is a weak positive correlation between number of years and salary.

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The function that represents the amount of water is y = -2x + 10800 while the water in the pool after 187 seconds is 10426 gallons

An equation is an expression that shows the relationship between two or more numbers and variables.

A linear equation is in the form:

y = mx + b

Where m is the slope and b is the y intercept

Let y represent the amount of water in the pool after x seconds, hence:

y = -2x + 10800

After 187 s:

y = -2(187) + 10800 = 10426 gallons

The function that represents the amount of water is y = -2x + 10800 while the water in the pool after 187 seconds is 10426 gallons

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Answer:

"Unary Association" I believe

Answer:

x=1990

Step-by-step explanation:

x+10=2000

x=2000-10

x=1990

Answer:

therefore x = 1990

Step-by-step explanation:

x+10 = 2000

= x = 2000-10

= x = 1990

The values of b, h and k are (c) b = 2, h = -2 and k = -9

The logarithmic function is given as:

f(x) = log₂(x + 2) - 9

A logarithmic function is represented as:

f(x) = logb(x - h) + k

By comparing both equations, we have

b = 2

h = -2

k = -9

Hence, the values of b, h and k are (c) b = 2, h = -2 and k = -9

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Answer:

10724.29

Step-by-step explanation:

mean means average

so to find an average you add everything together then divide it by the amount of variables

m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7

m = 75070/7

m = 10724.2857143

m = 10724.29

Answer: 15.53

Step-by-step explanation:

Let the height of the goalpost be y. Then,

[tex]\frac{y}{10.65}=\frac{1.75}{1.2}\\\\y \approx 15.53[/tex]

Answer:

z = [tex]3\sqrt{13}[/tex]

Step-by-step explanation:

To find the measure of z we can use the Euclidian Theorem:

[tex]z^{2}[/tex] = 9(9+4) do the multiplication

[tex]z^{2}[/tex] = 117 find the root of both sides

z = [tex]3\sqrt{13}[/tex]