The graph of a function is shown on the coordinate plane below.

Which statement correctly describes the function on a given interval?

The Graph Of A Function Is Shown On The Coordinate Plane Below. Which Statement Correctly Describes The

Answers

Answer 1

Answer: D

Step-by-step explanation:

I did it

Answer 2

The statement that correctly describes the function is:

The function is decreasing and nonlinear from x = 4 to x = 11.

Option D is the correct answer.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the 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,

From the graph,

We see that,

The function is increasing and nonlinear from x = -7 to x = -4.

The function is constant and linear from x = -4 to x = 1.

The function is increasing and nonlinear from x = 1 to x = 4.

The function is decreasing and nonlinear from x = 4 to x = 11.

Thus,

The function is decreasing and nonlinear from x = 4 to x = 11.

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Related Questions

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

The time required to grow $5000 to $8300, if the rate of interest is 7.5 %, is 7 years.

What is interest?

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

The principal amount, p = $5000,

The amount, A = $8300

The rate of interest, r = 7.5 %,

Calculate the time as shown below,

[tex]A = p(1 + r / 400)^{4n}[/tex]

8300 = 5000 (1 + 7.5 / 400)⁴ⁿ

8300 / 5000 = (1 + 0.01875)⁴ⁿ

1.66  = (1.0188)⁴ⁿ

1.66 = (1.077)ⁿ

(1.077)⁷ = (1.077)ⁿ

n = 7

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Seventeen less than the product of 3 and a number is -50. what is the answer?

Answers

The number from the expression is 22. 3

What is an algebraic expression?

An algebraic expression can be defined as a mathematical expression that consists of variables, terms, constants, coefficients, and factors.

These expressions are also seen to be made up of mathematical or arithmetic operation, such as;

SubtractionAdditionMultiplicationDivisionBracketParentheses, etc

Some examples of algebraic expressions;

2x + 6

3x + 8

From the information given;

Let the number be x

Then'

3x - 17 = - 50

collect like terms

3x = 67

Make 'x' the subject

x = 22. 3

Hence, the value is 22. 3

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Find an equivalent fraction of 36/48
having denominator 6.

Answers

An equivalent fraction of 36/48 having denominator 6 could be 6/6 only.

What is a fraction?

A fraction represents a part of a number or any number of equal parts.

we are given a fraction as 36/48.

We can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.

We have to only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.

In this case we have a clue which is 48,

6 x 8 = 48

Then we would want to take the 6 and times it by the denominator which is 6

So 6 x 6 = 36

An equivalent fraction of 36/48 is 6/6.

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Luis has 60 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 216 square meters. Solve for the dimensions (length and width) of the field. The dimensions are __ meters by __ meters .

Answers

The dimensions are 12 meter by 18 meter .

what is perimeter of rectangle ?

perimeter of rectangle = 2(length + width)

length and width of the  Luis plot by L and W, respectively.

We know that the perimeter, is 60 meters. So we can write:

2L + 2W = 60

Simplifying this equation, we can divide both sides by 2:

L + W = 30

now , area of the plot is 216 square meters:

L x W = 216

use substitution to solve for one of the variables. Let's solve for L in the first equation:

L = 30 - W

We can substitute this expression for L into the second equation:

(30 - W) x W = 216

[tex]W^2 - 30W + 216 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

W = [30 ± [tex]\sqrt{30^2 - 4 * 1 * 216}[/tex] / 2

Simplifying:

W = [30 ± 6] / 2

So  W = 18 or W = 12.

If W = 18, then L = 30 - 18 = 12.

If W = 12, then L = 30 - 12 = 18.

Therefore, the dimensions  are 18 meters by 12 meters or 12 meters by 18 meters.

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NO LINKS!! Find the specified term of the geometric sequence.
a6: a1 = 3, a2= 18, a3= 108, . . .

a6=

Answers

Answer:

23328

Step-by-step explanation:

since it is a geometrics sequence we will use the formula

[tex] {ar}^{n - 1} [/tex]

The first term(a) = 3

The second term = ar = 18

divide the first term and second term to find the common ratio

[tex] \frac{t2}{t1} = \frac{ar}{a} = \frac{18}{3} [/tex]

r = 6

Now lets find the sixth term

[tex]t6 = {ar}^{6 - 1} [/tex]

[tex]t6 = {ar}^{5} [/tex]

by substituting for the values

[tex]t6 = 3 \times {6}^{5} [/tex]

= 3 × 7776

= 23328

i hope this helped

Answer:

[tex]a_{6} = 23,328[/tex]

Step-by-step explanation:

⭐ Geometric Progression formula: [tex]a_{n} = a_1(b)^{n-1}[/tex]

[tex]a_{1}[/tex] is the first term of the geometric progression[tex]b[/tex] is the common ratio (the number each term gets multiplied by)[tex]a_{n}[/tex] is the notation for which term you are finding, where n is the term number

We are given that [tex]a_{1}[/tex] = 3. Now, we need to find b.

b is the quotient of [tex]\frac{a__3}{a__2}[/tex].

[tex]\frac{a_3}{a_2}\\ \\\frac{108}{18}\\= 6[/tex][tex]b[/tex] = 6

Let's substitute the first term and common ratio into the formula.

[tex]a_n = 3(6)^{n-1}[/tex]

The problem wants us to solve for the 6th term, so we have to substitute 6 for n and solve.

[tex]a_6 = 3(6)^{6-1}\\a_6 = 3(6)^5\\a_6 = 3(7,776)\\a_6 = 23,328[/tex]

piecewise function.
Express the function graphed on the axes below as a
Please help me

Answers

The piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

How to express the function graphed?

On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).

On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).

That line passes through (-1, 0) and (0, 1), then the slope is:

a = (1 - 0)/(0 -(-1)) = 1

And the y-intercept is y = 1, then the equation of the line is:

y = x + 1

The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)

The slope is:

a = (0 - 7)/(6 -5) = -7

Then the line is something like:

y = -7*x + b

To find b, we use the point (6, 0)

0 = -7*6 + b

7*6 = 42 = b

Then this line is:

y = -7x + 42

Concluding, the piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

The complete question is : Help please!! Express the function graphed on the axes below as a piecewise function.

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Rick deposits $3 into his bank account. The following week, he deposits 3 times that amount. Each week after that, he deposits 3 times the amount he did the previous week. How much does he deposit in all during the first 3 weeks (THERE ARE 2 PAGES

Answers

Rick's deposit in first 3 weeks is  $39  

What is Rick's weekly deposit ?

1. Rick's deposit in the second week = 3  times($3)

                                                             = 3(3)

                                                             = 9

                                                             = [tex]3^{2}[/tex]

                                                           

The exponential expression for Rick's 2nd week deposit = [tex]3^{2}[/tex]

Where,  Base  = 3

              Exponent = 2                                

2. Rick's deposit in 1st week = $3  

   Rick's deposit in 2nd week = 3 (3) = $9

   Rick's deposit in 3rd week =  3 (9) = $27  

   Rick's deposit in first 3 weeks = 3+9+27

                                                      = $39      

  Rick's deposit in all in the first 3 weeks is  $39  

3.   Rick's deposit for 15 weeks = [tex]3^{15}[/tex]

                                                    = $1,43,48,907.

We know, no. of weeks in a year = 52

Rick's deposit for 52 weeks ( 1 year ) = 52 times of 3

                                                             [tex]=3^{52}\\= 6.4610819e+24[/tex]

                                                           

Since this is a huge number , Rick cannot keep up this savings plan for a year.

What is an exponential expression?Only a short version of a power can be expressed using an exponential expression. How frequently the base is employed as a factor is shown by the exponent. Any real or complex exponent is acceptable under the notion of exponentiation. For a large number of other algebraic structures, including matrices, exponentiation by integer exponents can also be defined.Compound interest, population expansion, chemical reaction kinetics, wave behaviour, and public-key cryptography are just a few examples of the many domains where exponentiation is widely utilized. It is also used extensively in fields including economics, biology, chemistry, physics, and computer science.

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A simple random sample of n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen. (A simple random sample is often called a random sample, but strictly speaking, a random sample has the weaker requirement that all members of the population have the same chance of being selected.) Determine whether each of the following is a simple random sample and a random sample. Complete parts a through c. .. a. In Major League Baseball, there are 30 teams, each with an active roster of 25 players. The names of the teams are printed on 30 separate index cards, the cards are shuffled, and one card is drawn. The sample consists of the 25 players on the active roster of the selected team. This sample a simple random sample. It v a random sample. b. For the same Major League Baseball population described in part (a), the 750 names of the players are printed on 750 separate index cards, and the cards are shuffled. Twenty-five different cards are selected from the top. The sample consists of the 25 selected players. This sample V a simple random sample. It v a random sample c. For the same Major League Baseball population described in part (a), a sample is constructed by selecting the 25 youngest players. This sample a simple random sample. It a random sample.

Answers

This sample a simple random sample. It v a random sample.

What is simple random sample?A selection of participants from a population is randomly chosen by the researcher using simple random sampling, a sort of probability sampling. The probability of getting chosen is the same for every person in the population.A simple random sample is a subset of people picked at random from a larger group, all with the same probability. It is the process of choosing a sample at random.Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main types of random (probability) sampling.This sample a simple random sample. It v a random sample.

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A tent pole that is 8 feet tall is secured to the ground with a piece of rope that is 17 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.

40 feet
30 feet
15 feet
9 feet

Answers

The distance between  the tent pole to the rope along the ground is 15 feet.

What is a cone?

A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.

Given that length of the tent pole is 8 feet.

The angle between the tent pole and the ground is 90°.

Thus the tent pole, the rope and the ground form a right angle triangle.

According too Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.

Here the legs of the right angle triangle is the tent pole and the the distance the tent pole to the rope along the ground.

Assume that the distance the tent pole to the rope along the ground be x.

The length of the rope is 17 feet which is hypotenuse of the right angle triangle.

Therefore,

x² + 8² = 17²

x² + 64 = 289

x²  = 225

x = 15

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Answer: 15 feet

Step-by-step explanation:

first we grab 17 feet a square it

17^2 = 289

then we square 8 feet

8^2 = 64

subtract

289-64= 225

what squared equals 225?

15 does

Can someone help me with this? I’m confused

Answers

Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

G(x) = 4x - 5, find g(3)

Answers

Step-by-step explanation:

this is a college question ? and you don't know how to do that ?

think back to elementary and middle school. and you had to use that all the way through high school as a very, VERY basic skill.

Focus !

g(3) just means that x = 3, and we need to replace every occurrence of x by 3. and then we calculate the result.

g(3) = 4×3 - 5 = 12 - 5 = 7

that's all to it.

30 POINTS. The county rummage sale arranges 250 tables in three groups. The group on the left has 75 tables. The group on the right has 80 tables. Write an equation to find the number of tables in the middle group. Then sovle your equation.

Answers

Answer: There are 95 tables in the middle group

Step-by-step explanation:

There are a total number of 250 tables.

There are three groups.

We know how many tables the left and right groups have

let x be the number of tables in the middle

75+80+x=250

155+x=250

x=95

27/22 as a decimal rounded to the nearest hundreth

Answers

The expression as a rounded decimal  is 1.23

How to evaluate the expression as a rounded decimal

From the question, we have the following parameters that can be used in our computation:

27/22

To start with, we evaluate the expression using a calculator

So, we have the following representation

27/22 = 1.22727272727

Next, we approximate to the nearest hundredth

So, we have the following representation

27/22 = 1.23

Hence, the approximated expression is 1.23

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Which pairs of rectangles are similar polygons? Select Similar or Not Similar for each pair of rectangles. Similar Not Similar A and B Similar – A and B Not Similar – A and B B and C Similar – B and C Not Similar – B and C A and C Similar – A and C Not Similar – A and C Three rectangles labeled A, B, and C. The length of rectangle A is labeled as 100 centimeters and the width is labeled as 80 centimeters. The length of rectangle B is labeled as 120 centimeters and the width is labeled as 100 centimeters. The length of rectangle C is labeled as 90 centimeters and the width is labeled as 72 centimeters.

Answers

A polygon is a plane shape with a minimum of three straight sides. Thus the appropriate answer are:

i. A and B Not Similar

ii. B and C Not Similar

iii. A and C Not Similar

Polygons are majorly plane shapes which have straight sides. They are named with respect to the number of their sides, and the minimum sides is three. Some common examples are: trigon (3 sides), octagon (8 sides), hexagon (6 sides), pentagon (5 sides) , etc.

Two or more shapes are said to be similar if and only if they have some common properties with respect to their sides or internal angles.

Considering the ratios of the sides of the given polygons, it can be deduced that:

i. A and B Not Similar

ii. B and C Not Similar

iii. A and C Not Similar

Thus none of the polygons are similar.

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PLEASE HELP god bless you /Barak Allah fic A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?

Answers

The required number of new boys in a sports team is 62.

As mentioned in the question,  A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Given that the number of men is now 60% of the total members, how many of the 50 new members were women is to be determined,
Percentage of women, in the team = 100 - 60 = 40%
40% of total members are women = 35 + 50

Total members = 85 / 40%
Total member = 212
Number of new member that are boys = 212 - 85 - 65 = 62 boys

Thus, the required number of new boys in a sports team is 62.

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Test the claim about the difference between two population means
μ1
and
μ2
at the level of significance
α.
Assume the samples are random and​ independent, and the populations are normally distributed.​Claim:
μ1=μ2​;
α=0.01
Population​ statistics:
σ1=3.6​,
σ2=1.4
Sample​ statistics:
x1=18​,
n1=27​,
x2=20​,
n2=26
Determine the alternative hypothesis.
Ha​:
μ1

greater than>
greater than or equals≥
less than<
less than or equals≤
not equals≠
μ2
Determine the standardized test statistic.
z=nothing
​(Round to two decimal places as​ needed.)
Determine the​ P-value.
​P-value=nothing
​(Round to three decimal places as​ needed.)
What is the proper​ decision?
A.Fail to reject
H0.
There is enough evidence at the
1​%
level of significance to reject the claim.
B.Reject
H0.
There is enough evidence at the
1​%
level of significance to reject the claim.
C.Fail to reject
H0.
There is not enough evidence at the
1​%
level of significance to reject the claim.
D.Reject
H0.
There is not enough evidence at the
1​%
level of significance to reject the claim

Answers

The correct answer is Option C. The proper decision, in this case, is  "Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim."

The alternative hypothesis, in this case, is "μ1 ≠ μ2", as the claim being tested is that the two population means are equal.

To calculate the standardized test statistic, we can use the following formula:

z = (x1 - x2) / sqrt(((σ1^2) / n1) + ((σ2^2) / n2))

Substituting in the values given in the problem, we get:

z = (18 - 20) / sqrt(((3.6^2) / 27) + ((1.4^2) / 26))

z = (-2) / sqrt((12.96 / 27) + (1.96 / 26))

z = (-2) / sqrt(0.481 + 0.075)

z = (-2) / sqrt(0.556)

z = (-2) / 0.746

z = -2.67

To calculate the P-value, we can use the standard normal table to look up the probability of getting a value of -2.67 or lower if the null hypothesis were true. The P-value in this case would be the probability of getting a value equal to -2.67 or lower, plus the probability of getting a value equal to 2.67 or higher.

Using the standard normal table, we find that the probability of getting a value equal to -2.67 or lower is 0.0039, and the probability of getting a value equal to 2.67 or higher is 0.9961. Therefore, the P-value is 0.0039 + 0.9961 = 1.0000.

Since the P-value is equal to 1.0000, which is greater than the level of significance α = 0.01, we fail to reject the null hypothesis.

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brett needs 2/3 cups of yogurt for one smoothie. He wants to know how many smoothies he can make with 2 4/6 cups of yogurt. which division expression can be used to represent the situation

Answers

Answer:

4

Step-by-step explanation:

2 4/6 = 16/6

Based on the given conditions, formulate:

16/6 ÷ 2/3

Divide a fraction by multiplying its reciprocal:

16/6 × 3/2

(16 × 3) ÷ (6 × 2)

48/12 = 4

Thus, Brett can make 4 smoothies with 2 4/6 cups of yogurt.

Which equations have the same value of X as 5/6x + 2/3=-9? Select three options

Answers

The equations have the same value of x are,

A) 5x + 4 = -54

B) 6(5/6x + 2/3) = -9(6)

C) 5x = -58

What is equation?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation

3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Consider the given equation

5/6 x + 2/3 = -9

Subtract 2/3 from both sides,

5/6x + 2/3 - 2/3 = -9 - 2/3

5/6x = -29/3

[tex]x = -\frac{29}{3}*\frac{6}{5}\\ x = -11.6[/tex]

The value of x is -11.6.

Hence, the equations have the same value of x are,

A) 5x + 4 = -54

B) 6(5/6x + 2/3) = -9(6)

C) 5x = -58

After solving above these equations we get the same value of x which is -11.6.

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Complete question:

Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options. 6(5/6x + 2/3) = -9

6(5/6x + 2/3) = -9(6)

5 x + 4 = -54 5 x + 4 = -9

5 x = -13

5 x = negative 58

Ester writes 6 x 7 = 42 to find
the number of students seated
at tables. Describe what each
factor represents.

Answers

Answer:

6 rows to 7 steal in each rows

Using three mixed numbers as side lengths draw an equilateral triangle with a perimeter of 8 and 1/4 feet.

Answers

The side of the equilateral triangle is 2 ³/4 feet, having perimeter 8 ¹/₄  feet.

What is an equilateral triangle?

If all three of a triangle's sides are the same length, the triangle is said to be equilateral. Congruent sides refer to sides that have the same length, and they characterize an equilateral triangle.

Given that,

The perimeter of equilateral triangle = 8 ¹/₄  feet.

Simplify the rational term.

8 ¹/₄ = (32 + 1) / 4 = 33 /4.

Let each side of an equilateral triangle is a feet.

The perimeter of the equilateral triangle = 3a

Since, 3a = 33/4

a = 11/4

a = 2 ³/4

The required side of the equilateral triangle is 2 ³/4.

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The display summarizes grades on a World History exam.

A vertical box plot is titled world history exams, with a minimum of 54, a maximum of 94, a lower quartile of 70, a median of 83, and an upper quartile of 88.

Which of the following describes the data set?

The data is univariate and categorical.
The data is univariate and numerical.
The data is bivariate and categorical.
The data is bivariate and numerical.

Answers

The option that best describes the data is The data is band numerical

What is univariate data?

This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.

In this case the one variable is World History scores exam

What are numerical data?

Data that is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.

Numerical data, also known as quantitative data, is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.

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3/4x + 2/3y - 3/8x + 1/2y

Answers

Answer:

[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].

Step-by-step explanation:

1. Write the expression.

[tex]3/4x + 2/3y - 3/8x + 1/2y[/tex]

2. Operate with like terms.

a) First, start by operating with the terms that contain the "x" variable.

[tex]3/4x- 3/8x\\ \\\frac{3}{4}x-\frac{3}{8}x\\ \\ \frac{3*2}{4*2}x-\frac{3}{8}x\\ \\\frac{6}{8}x-\frac{3}{8}x\\ \\x(\frac{6}{8} -\frac{3}{8} )\\ \\x(\frac{6-3}{8} )\\ \\x(\frac{3}{8} )\\ \\\frac{3}{8}x[/tex]

b) Start with terms containing "y".

[tex]2/3y+1/2y\\ \\\frac{2}{3}y +\frac{1}{2} y\\ \\\frac{2*2}{3*2}y +\frac{1*3}{2*3} y\\ \\\frac{4}{6}y +\frac{3}{6} y\\ \\y(\frac{4+3}{6})\\ \\y(\frac{7}{6})\\ \\\frac{7}{6} y[/tex]

3. Put the terms together.

[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].

Can someone answer this for me. I NEED HELPPP

Find the value of y if m∠3 =65° and m∠1 =(15y+5)°

Answers

Answer: 4 i think

Step-by-step explanation:

65=15y+5

65 - 5 = 15y +5 -5

60 = 15y

60/15 = 15y/15

4 = y

65=15y+5
65-5=15y+5-5
60=15y
60/15=15y/15=4y

Kate and Miley are selling girl scout cookies Kate sold 27 boxes in 45 minutes Miley sold 12 boxes in 30 minutes at the same rates how many total boxes will the girls have sold in one hour?

Answers

Kate and Miley sold 60 boxes of cookies in one hour.

What is ratio?

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b.

Given that,

Cookies sold by Kate in 45 minutes = 27 boxes.

Also,

Cookies sold by Miley in 30 minutes = 12 boxes.

To find the total boxes of cookies sold by girls in one hour,

Use ratio method,

Cookies sold by Kate in 3/4 hours = 27 boxes,

Cookies sold by Kate in 1 hour = 27 x (4/3) = 36

Cookies sold by Miley in 1/2 hours = 12 boxes,

Cookies sold by Miley in 1 hour = 12 x 2 = 24 boxes

Total cookies sold by Kate in Miley in one hour = 36 + 24 = 60

There are 60 boxes of cookies sold by the girls in one hour.

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A stage manager is trying to seat important guests in the front row of a theater. The row has seven seats, and she would like a diplomat in the first seat, a singer in the second seat, and a movie director in the third seat. After this, the remaining diplomats, singers, and movie directors will be seated in the last four seats, in no particular order. If there are 3 diplomats, 2 singers, and 2 directors attending the show, how many different front row plans are possible?

Answers

Answer:  12 row plans

The first seat has 2 possible options, the 2 directors. The second seat has another 2 options. With each director comes 2 options for the second seat, so 2 x 2=4 possible options for the 1st and 2nd seats. The third seat has 3 options. That means for each combination of the 1st and 2nd seat, there are 3 possible options. 4x3=12 combinations.

Step-by-step explanation:

9 more than the quantity of 6 less than a number n is 18

Answers

Answer: n = 15

Step-by-step explanation:

9 + n - 6 = 18

3 + n = 18

n = 15

Write a quadratic function h whose only zero is 2.
h(x) =

Answers

Answer:

h(x) = (x-2)^2

Step-by-step explanation:

Consider the polynomial g(x) = 4x³ - x² - 24x + 6
a. List all possible rational zeros of the polynomial. (Assume all numbers shown are both + and -).
O 1, 2, 4, 1/2, 1/3, 2/3, 4/3, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/3, 2/3, 4/3, 1/4, 3/4, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/4, 3/4
1, 2, 3, 6, 1/2, 3/2, 1/4, 3/4
b. List all actual zeros of the polynomial (rational, irrational, real, and complex).
Give exact answers, separated by commas as necessary.
Zeros:

Answers

a. The rational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 is 1/4.

b. The rational and irrational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 are 1/4 and ± √6.

What is a factor of a polynomial?

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A cubic polynomial function g(x) = 4x³ - x² - 24x + 6.

Therefore,

g(x) = 4x(x² - 6) - 1(x² - 6).

g(x) = (4x - 1)(x² - 6).

g(x) = (4x - 1)(x + √6)(x - √6).

Hence, x = 1/4, ± √6.

So, The roots of the polynomial are 1/4 and ± √6.

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Two angles are complementary. The measure of one angle is 17 degrees. What is the measure of the other angle?

Answers

The measure of the other angle is 73°.

What are complementary angles?

Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.

How do you find a complementary angle?

Two angles are said to be complimentary if their sum is 90 degrees. So, to find the complement of an angle, subtract it from 90.

Here, we have

Given

Two angles are complementary. If one measures 17 degrees.

Complementary angles are two angles that add up to exactly 90 °.

∠A + ∠B = 90°

17 + ∠B = 90°

∠B = 90 - 17

∠B = 73°

Hence, the measure of the other angle is 73°.

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A 41-year old woman has $398,100.00 in an IRA account. Due to medical concerns of a family member, she decided to make no additional contributions to the account but expect it to grow at 8% compounded every 4 months. How much does she expect to have in the account when she retires at age 65?

Answers

She expects to have $2710591.78 when she retires at age 65 with the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3 by the concept of compound interest.

What is compound interest?

Interest that is paid on the principal and interest at regular periods is known as compound interest. The interest is calculated for the new principal at regular intervals after the interest that has already accumulated has been combined with the existing principal amount. The initial principal plus the interest that has accrued thus far are added together to form the new principal.

Interest on the principal + periodic compound = compound interest.

According to the question the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3.

Here the interest is compounded every 4 months

So, the formula of compound interest is as follows:

A=p (1+ [tex]\frac{r}{n}[/tex]) ∧ (n× t)

Where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per year and t is the number of years.

Here the interest is compounded every 4 months hence the value of n is 12/4 which is equal too 3.

Insert the values of p, n, t, r in above equation,

A=398100(1+[tex]\frac{8}{300}[/tex]) ∧ (3×24)

A=398100× (1.027) ∧ (72)

A=398100×6.809

A=2710591.78

She expects to have amount $2710591.78 when she retires at age 65.

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