3. A triangle has an area of 6 square inches and a perimeter of 12 inches.
Suppose it is dilated by some scale factor, and the area and perimeter of
the image are calculated. Match each graph with the relationship it
represents.

A. Graph A
B. Graph B
C. Graph C
D. Graph D

1. Scale factor is the x-value; perimeter is the y-value
2. Scale factor is the x-value; area is the y-value
3. Perimeter is the x-value; scale factor is the y-value
4. Perimeter is the x-value; scale factor is the y-value

Answers

Answer 1

So, the correct graph should have the scale factor on the x-axis and the area on the y-axis. This is Graph B. The other graphs do not correctly represent the relationship between the scale factor, area, and perimeter.

What is graph?

There are different types of graphs, including directed graphs (also called digraphs), where each edge has a direction, and undirected graphs, where each edge has no direction. Graphs can also be weighted, meaning that each edge has a value associated with it, or unweighted, where all edges have the same value.

Graphs can be represented visually, using diagrams that show the vertices as points and the edges as lines or arrows connecting them. Graphs are used in a variety of applications, including computer algorithms, data analysis, and optimization problems.

by the question.

The area of the original triangle is 6 square inches, and the perimeter is 12 inches. Let the lengths of the sides be a, b, and c. Then, we have:

[tex]a + b + c = 12[/tex] (perimeter)

[tex]s = (a + b + c)/2 = 6[/tex] (semi perimeter)

[tex]A =\sqrt(s(s-a)(s-b)(s-c)) = 6[/tex] (area)

Simplifying the equations, we get:

[tex]a + b + c = 12[/tex]

[tex]a + b + c - 2a - 2b - 2c = 0[/tex]

[tex]-a - b - c = -12[/tex]

[tex]-a - b - c + 2a + 2b + 2c = 0[/tex]

[tex]a + b + c = 0[/tex]

Therefore, the centroid of the original triangle is at the origin (0,0).

When the triangle is dilated by a scale factor of k, the new area and perimeter are given by:

[tex]A' = k^2A = 6k^2[/tex]

[tex]P' = kP = 12k[/tex]

To learn more about scale factor:

https://brainly.com/question/30215044

#SPJ1


Related Questions

5my × 5ym = ?

Can you multiply two terms with the same 2 coefficients in different positions like the example above?​

Answers

Answer:

In the example given, 5my × 5ym, you can simplify it using the commutative property of multiplication as follows:

5my × 5ym = 5 × 5 × m × m × y × y

= 25m²y²

So, the answer is 25m²y².

This is the answer picture included

Find the total amount and total interest after six months if the interest is compounded every quarter. Principal =₹10 000 Rate of interest =20% per annum. ​

Answers

Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

Write down the smallest possible answer.

Answers

The answer of the given factor and multiplication term for the positive integers are 3.

What about integers?

Positive, negative, and zero digit whole numbers are all included in the category of integers. They can be stated without any fractional or decimal components and are a subset of the real numbers. On a number line, integers can be visualized as positive numbers to the right of zero and negative numbers to the left.

Define Multiplication term:

In mathematics, a multiplication term is a mathematical expression that involves the multiplication of two or more factors. The factors can be numbers, variables, or a combination of both. Multiplication terms are commonly represented using the multiplication symbol "×" or the dot "." symbol.

For example, in the expression 2x × 3y, the multiplication term is 2x × 3y, which involves the multiplication of the factors 2x and 3y.

According to the given information:

If you want to find the smallest possible value of the given term we have that,The smallest factor of 15 is 1.

The smallest multiple of 3 is 3so, the smallest answer is 1x3 = 3.

To know more about integers visit:

https://brainly.com/question/30161280

#SPJ1

Someone please help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly

Answers

Answer:

D

Step-by-step explanation:

First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.

Hope this helps.

Evaluate the expression

z + 3x4
A. 27

B. 32

C. 56

D. 1,304

Answers

The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.

The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.

z + 3x4 = 15 + 3x4

= 15 + 12

= 27

Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).

To know more about evaluating the expression:

https://brainly.com/question/2889219

#SPJ4

____The given question is incomplete , the complete question is given below:

Evaluate the expression, where z = 15

z + 3x4

A. 27

B. 32

C. 56

D. 1,304

The access code for a car's security system consist of six digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?

Answers

If an access code for a car's security system consist of six digits and the  first digit cannot be zero and the last digit must be even, then the number of different codes available are 4,500,000

Since the first digit cannot be zero, we have 9 choices for the first digit. For each of these 9 choices, there are 10 possibilities for the second digit (0-9).

Similarly, there are 10 possibilities for the third digit, 10 for the fourth digit, 10 for the fifth digit, and 5 (0, 2, 4, 6, 8) for the last digit.

Therefore, the total number of possible access codes is:

9 x 10 x 10 x 10 x 10 x 5 = 4,500,000

Learn more about possibilities here

brainly.com/question/28969499

#SPJ4

Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.

Answers

Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Exactly how many erasers did stefanie buy?

Answers

Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Stefanie bought total 10 erasers.

Equation:

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal.

According to the Question:

The number of erasers bought by Stefanie:

Let we denote the number of erasers bought by her by x (an unknown variable)

Then we will have:

Total amount before tax = cost of one package of pencil + cost of  erasers

   $4.25 = $1.75 + X × $0.25

⇒ 4.25 = 1.75 + 0.25x

Now,

we will perform subtraction by 1.75 and division by 0.25 on both sides.

4.25 = 1.75 + 0.25x

Subtracting 1.75 both side:

   4.25 -1.75 = 0.25x

⇒ 2.5 = 0.25x

Dividing by 0.25 on both sides:

   2.5/0.25 = 0.25x/0.25

⇒ x = 10

Thus, Stefanie bought total 10 erasers.

Learn more about Total:

https://brainly.com/question/29615374

#SPJ4

Tanya is making a scale drawing of her house. She is using a 6 inch line on her drawing to represent the 30 foot width of her house. Tanya's room is 12 feet by 12 feet. What will be the length of the lines she uses to represent her room on the scale drawing?

Answers

Answer:2.4 inches

Step-by-step explanation:

if 6 is for 30 feet, we can use a proportional statement to find what the length of the line will be for a room that is 12 feet.

At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?

Answers

Answer:

Step-by-step explanation:

Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:

999n = 727272

To solve for "n", we divide both sides by 999:

n = 727272/999

Using a calculator or long division, we get:

n ≈ 728.56

Therefore, each pizza has approximately 728 slices.

an urn contains p black balls, q white balls, and r red balls; and n balls are chosen without replacement. a. find the joint distribution of the numbers of black, white, and red balls in the sample. b. find the joint distribution of the numbers of black and white balls in the sample. c. find the marginal distribution of the number of white balls in the sample.

Answers

a. The joint distribution of the numbers of black, white, and red balls in the sample is given by P(x, y, z) = nCx * nCy * nCz / (p + q + r)Cn, where x is the number of black balls, y is the number of white balls, z is the number of red balls, and n is the total number of balls chosen.

b. The joint distribution of the numbers of black and white balls in the sample is given by P(x, y) = nCx * nCy / (p + q)Cn, where x is the number of black balls, y is the number of white balls, and n is the total number of balls chosen.

c. The marginal distribution of the number of white balls in the sample is given by P(y) = nCy / qCn, where y is the number of white balls, and n is the total number of balls chosen.

To learn more about distribution refer :

https://brainly.com/question/14310262

#SPJ11

a random sample of 15 recent college graduates found that starting salaries for attorneys in new york city had a mean of $102,342 and a standard deviation of $21,756. there are no outliers in the sample data set. construct a 95% confidence interval for the average starting salary of all attorneys in the city.

Answers

The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a p-value of 1-∝.

So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]

Now, find M as such

[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ

In which is the standard deviation of the population and n is the size of the sample.

[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.

The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.

So the correct answer is:

(91331.94, 113352.06)

Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.

Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.

To learn more about Standard deviation visit here:

brainly.com/question/23907081

#SPJ4

Complete Question:

A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices

A). (89869.82, 114814.18)

B). (90292.73, 114391.27)

C). (91331.94, 113352.06)

D). (90371.37, 114312.63)

find the volume of a pyramid with a square base, where the area of the base is 4.6 cm 2 4.6 cm 2 and the height of the pyramid is 2.3 cm 2.3 cm. round your answer to the nearest tenth of a cubic centimeter.

Answers

The volume of pyramid is 3.5 cm³.

To find the volume of a pyramid with a square base, where the area of the base is 4.6 cm² and the height of the pyramid is 2.3 cm, we can use the following formula:

V = (1/3)B*h

Where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid. Substitute the given values into the formula and solve:

V = (1/3)(4.6)(2.3)V = 3.53 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is 3.5 cm³. Therefore, the volume of pyramid is 3.5 cm³.

To learn more about volume of pyramid refer :

https://brainly.com/question/17615619

#SPJ11

Calculate the final value in cell D2 using the following formula: "price - price* discount". Use a formula with cell reference (B1, etc. ).


Product – Toys


Price - $114. 99


Discount – 12%

Answers

The final value in cell D2 using the following formula:

price - price× discount = $ 101.19

Take the original price. Multiply that by the discount percentage and divide the result by 100. Subtract the result from the original price. this is your final price

According to the Question:

The final value in cell D2 using the following formula:

(price - price) × discount.

Given that:

Price = $114.99

Discount = 12%

By the above formula:

(price - price) × discount.

= ($114.99 - $114.99) × 12%

= $101.19

Learn more about discount:

https://brainly.com/question/3541148

#SPJ4

16^(3x-1) = 32. pls help

Answers

Answer:x=33/4096=0.008

Step-by-step explanation: 1.1     16 = 24

(16)3 = (24)3 = 212

Equation at the end of step

1

:

 ((212 • x) -  1) -  32  = 0

STEP

2

:

Equation at the end of step 2

 4096x - 33  = 0

STEP

3

:

Solving a Single Variable Equation:

3.1      Solve  :    4096x-33 = 0

Add  33  to both sides of the equation :

                     4096x = 33

Divide both sides of the equation by 4096:

                    x = 33/4096 = 0.008

Use spherical coordinates to find the volume of the region outside the cone phi = pi /4 and inside the sphere rho = 4 cos phi. The volume is ____ . (Type an exact answer, using pi as needed.)

Answers

The volume is 63.717 cubic units

The limits of integration for rho are 0 and 4 cos phi, since the sphere has radius 4 cos phi. The limits for phi are π/4 and π/2, since we want to consider the region outside the cone but inside the sphere, and phi is the angle between the positive z-axis and the position vector of a point. Finally, the limits for theta are 0 and 2π, since theta is the azimuthal angle and we want to integrate over the entire azimuthal angle.

Thus, the volume of the region is given by:

V = 8 x ∫(0 to 2π) ∫(π/4 to π/2) ∫(0 to 4 cos phi) ρ² sin phi dρ dphi dtheta

Simplifying the integral using basic calculus, we get:

V = 8 x (64/3 - 16/3√2π) = 63.717

Therefore, the volume of the region outside the cone phi = π/4 and inside the sphere rho = 4 cos phi is 8(64/3 - 16/3√2π), which is an exact answer using π as needed.

To know more about volume here

https://brainly.com/question/11168779

#SPJ4

Calculate the area and perimeter of this rectangle.

Answers

Answer:

Area: 391.92 ft²

Perimeter: 84.4 ft

Step-by-step explanation:

Area of rectangle = L × W

We Take

13.8 × 28.4 = 391.92 ft²

Find the Perimeter of the Rectangle

We Take

28.4 + 13.8 + 28.4 + 13.8 = 84.4 ft

So, Area: 391.92 ft²

     Perimeter: 84.4 ft

Answer:

Area = 391.92 square feet

Perimeter = 84.4 feet

Step-by-step explanation:

The area of a rectangle is the product of its width and length.

The perimeter of a rectangle is twice the sum of its width and length.

Given the width of the rectangle is 28.4 feet and its length is 13.8 feet:

[tex]\begin{aligned}\textsf{Area of the rectangle}&=\sf width \times length\\&=28.4 \times 13.8\\&=391.92 \sf \;\;square\;feet\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=\sf 2(width +length)\\&=2(28.4 +13.8)\\&=2(42.2)\\&=84.4 \sf \;\;feet\end{aligned}[/tex]

How much greater is 0.05723 then 0.005?

Answers

0.05723 is 0.05223 greater than 0.005.

What is greater than?

"Greater than" is a comparison term used to indicate that one quantity or value is larger or more than another quantity or value. It is represented mathematically by the symbol ">".

What is lesser than?

"Lesser than" is a comparison term used to indicate that one quantity or value is smaller or less than another quantity or value. It is represented mathematically by the symbol "<".

In the given question,

To find out how much greater 0.05723 is than 0.005, we can subtract 0.005 from 0.05723:0.05723 - 0.005 = 0.05223

Therefore, 0.05723 is 0.05223 greater than 0.005.

To know more about comparison, visit:

https://brainly.com/question/29163855

#SPJ1

solve simultaneously 4x-y=3x+1y 4x+3y=x+6y​

Answers

(x, y) = (0,0) is the solution of the system of equations.

simultaneous equation

Simultaneous equations are a set of two or more equations that contain multiple variables, which must be solved at the same time. The solution to the system of equations is the set of values of the variables that satisfy all of the equations in the system simultaneously.

The given system of equations is:

4x - y = 3x + y

4x + 3y = x + 6y

Simplifying the first equation by moving all the y-terms to the left-hand side and all the x-terms to the right-hand side, we get:

4x - 3x = y + y

x = 2y

Substituting this value of x into the second equation, we get:

4(2y) + 3y = (2y) + 6y

8y + 3y = 8y

11y = 0

y = 0

Substituting y = 0 into the equation x = 2y, we get:

x = 2(0)

x = 0

Therefore, the solution to the system of equations is:

x = 0 and y = 0

Hence, (x, y) = (0,0) is the solution of the system of equations.

To know more about variables, visit:

https://brainly.com/question/17344045

#SPJ1

what is 1 half of 68 ?

Answers

Answer:

34

Step-by-step explanation:

1/2 multiplied by 68=34

34 is 1 half of 68 .

Here, we have,

given that,

what is 1 half of 68

we know that,

Half of a number can be found by dividing the number by 2.

i.e. we have to find half of 68,

for that, we need to divide 68 by 2

so, we get,

To find half of 68:

68 / 2 = 34

Therefore, half of 68 is 34.

To learn more on division click:

brainly.com/question/21416852

#SPJ6

phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch.Do these data give convincing evidence to support Phoebe’s hunch?

Answers

Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

What is p-value?

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

For more questions related to probability

https://brainly.com/question/25870256

#SPJ1

pls help Are the following lines parallel, perpendicular, or neither?

y = 2/3x − 4

y = −3/2x − 7

Responses


Parallel

Perpendicular

Neither

Answers

Answer:

Perpendicular.

Step-by-step explanation:

To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form

y = 2/3x - 4 ==> slope = 2/3

y = -3/2x - 7 ==> slope = -3/2

Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1

(2/3) * (-3/2) = -1

Since the product of the slopes is -1, the two lines are perpendicular.

Therefore, the answer is: perpendicular.

Find M BC using picture below

Answers

Based on the picture, we can use the Pythagorean theorem to find MBC. Therefore, MBC is equal to  [tex]7[/tex]√2.

What three categories of theorems are there?

Theorem of Linear Pairs Two angles are supplementary if they create a linear pair. Additional theorem, Two angles are congruent if they are supplements of the same angle.

Theorem of congruent complements an of thes., but it will be the first of a series of events that will result in a new set of rules and the.

First, we can find AB:

AB = √(AD² + BD²)

= √ [tex](3^2 + 4^2)[/tex]

= √[tex](9 + 16)[/tex]

= √ [tex]25[/tex]

[tex]= 5[/tex]

Next, we can find AC:

AC = √(AD² + CD²)

= √[tex](3^2 + 8^2)[/tex]

= √ [tex](9 + 64)[/tex]

= √[tex]73[/tex]

Finally, we can find BC:

[tex]BC = √(AB^2 + AC^2)[/tex]

= √(5² + (√73)²)

= √(25 + 73)

= √98

= 7√2

Therefore, m Bc is = 7√2

Learn more about theorem here:

https://brainly.com/question/30066983

#SPJ1

National Collegiate Athletic Association (NCAA) statistics show
that for every 75,000 high school seniors playing basketball, about 2250 play
college basketball as first-year students. Write the ratio of the number of first-
year students playing college basketball to the number of high school seniors
playing basketball.

Answers

Answer: 100:3

Step-by-step explanation:

Answer:

the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.

Step-by-step explanation:

The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.

The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.

To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.

So the ratio can be expressed as:

2,250/75,000

To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:

2,250/75,000 = 3/100

one number is 13 les then a certain number let g repersent the larger number. repersent the sum of the two numbers

Answers

J him
Cg sad h df da a

In Exercise 5.12 , we were given the following joint probability density function for the random variables Y1 and Y2, which were the proportions of two components in a sample from a mixture of insecticide: f(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhere
Are Y1 and Y2 independent?

Answers

The conclude that the Y1 and Y2 are not independent.

The joint probability density function for the random variables Y1 and Y2 for a mixture of insecticide isf(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhereTo verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Therefore, we need to find the marginal density functions of Y1 and Y2.Probability Density Function:We know that for a given joint probability density function, the probability density function of Y1 is given by integrating over all possible values of Y2, and vice versa.Mathematically,P(Y1)=∫0∫1f(y1,y2)dy2... (1)P(Y2)=∫0∫1f(y1,y2)dy1... (2)Using equation (1) to calculate P(Y1), we get,  P(Y1)=∫0∫1f(y1,y2)dy2=∫0∫1(2)dy2=2... (3)Similarly, we can use equation (2) to calculate P(Y2) as follows:P(Y2)=∫0∫1f(y1,y2)dy1=∫0∫1(2)dy1=2... (4)Product of marginal density functions:Now we can find the product of marginal density functions as follows:P(Y1)P(Y2)=2×2=4... (5)Thus, to verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Since 2 ≠ 4, Y1 and Y2 are not independent. Hence, we can conclude that the Y1 and Y2 are not independent.

Learn more about Conclude

brainly.com/question/2711657

#SPJ11

Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?

Answers

Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).

In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:

final amount = 5.00 - 5.00 - (5.00 * 0.045)

final amount = 5.00 - 5.00 - 0.225

final amount = 4.775

Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.

Suppose Elena has $5 and sells pens for $1.50 each. Her goal is to save $20 to buy a t-shirt. She does not spend any money while she is saving money.

Let p represent the number of pens Elena sells. Write an expression for how much money she saves in total after selling p pens.



Write an equation using your answer from question 1, showing that she saves exactly $20.



Solve the equation you wrote from question 2. What do you notice about your value for p?





What if Elena wants to have some money left over? Write an inequality using your expression from question 1 to show this.



Write down other values for p where Elena would have money left over.



Write an inequality using p, to describe the values of p where she would be able to buy the tshirt and still have money left over.

Answers

In conclusion  the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.  The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Why it is?

The expression for how much money Elena saves after selling p pens is:

Total money saved = 5 + (1.5)p

The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Solving the equation:

5 + (1.5)p = 20

(1.5)p = 15

p = 10

We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.

If Elena wants to have some money left over, we can write the inequality:

5 + (1.5)p > 20

Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.

To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:

5 + (1.5)p > 20

(1.5)p > 15

p > 10

Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.

To know more about Selling related questions, visit:

https://brainly.com/question/30615010

#SPJ1

Write and solve an equation to answer the following question. The Smith family rented a recreational vehicle for a seven-day vacation. The cost to rent the recreational vehicle was $80 plus $0.50 per mile. How many miles were driven if the total cost was $1350?

Answers

Answer: 2540

Step-by-step explanation: 1350-80=1270. 1270/0.5=2540

We will consider two cases: n is even and n is odd. In this step, you will complete the proof of the first case. Proof. Case 1: n is even Let n be an even integer. By the definition of even, for some integer k. This follows that nº + 17n - 1 = 2:( 2k )+1 Since is an integer, n^3+17n + 1 must be an integer. Since na +17n – 1 equals times an integer plus n+ 17n – 1 is 2

Answers

We will consider two cases: n is even and n is odd. In this step, you will complete the proof of the first case. Proof. Case 1: n is even Let n be an even integer. By the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`

Since is an integer, `n^3+17n + 1` must be an integer. Since `na +17n – 1` equals times an integer plus `n+ 17n – 1` is 2The solution explains the concept of even integer. Let n be an even integer, and by the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`.Since 2k is an integer, n^3 + 17n + 1 must also be an integer. This is because even times even is even and even times odd is even, which means that (2k + 1) is always odd. The integer n^3 can be written as (n*n*n). Given that n is an even integer, it follows that n*n is even. And since an even number times an even number is always even, it follows that (n*n*n) is even. Since the sum of an even number and an odd number is always odd, adding 1 to n^3 + 17n gives an odd number, and thus an integer, as desired. The equality `na +17n – 1 = 2` is not needed in this proof.

We will consider two cases: n is even and n is odd : https://brainly.com/question/31138563

Other Questions
in the story, the woken were already waiting for humankind to destroy itself due to the poor choices humans were making. what should the future look like? was there any truth to the woken's observations of humankind? is there anything we can do to prevent a similar outcome to the one in the story from happening? Consider points A(1,3) , B(4,-2) , and C(5,2). Let D be the midpoint of AB. How can you prove that C lies on the perpendicular bisector of AB? Complete each statement. Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ? How did systemic racism affect people politically? Isotopic dating of basement rocks in _________ suggest Earth has a long history because the oldest rocks, from the area of the Canadian Shield are more than 3 Billion years old A while loop reads characters from input. Write an expression that executes the while loop until character 'q' is read. Ex If the input is x n q, then the output is: Character is XCharacter is n Done #include using namespace std; int main() {char value: cinvalue; while (/*Your code goes here */){cout Hawks in both parties condemned Biden's compromise with Russia. First, they hoped that Washington could intervene with decisive military assistance; Then they were convinced that Putin would yield if the United States threatened to intervene militarily. However, the opposition of the Republicans is not as loud as before, because they still remember the controversial relationship between Trump and Russia. 5) What is the probability of picking a vowel, replacing itand then picking a consonant from the word "SLEEP"? The equilibrium constant expression for a reaction is [CO2]2/[SO2]2[O2]. What is the balanced chemical equation for the overall reaction if one of the reactants is Na2CO3(s). the idea of christian republicanism gained momentum after the american revolution. identify the statements that describe this concept if a firm believes that it will have sufficient cash flows to cover interest payments, it may consider using debt and equity, which implies a degree of financial leverage. a. more; less; lower b. more; less; higher c. less; more; higher d. none of these choices are correct. gerald corporation purchases inventory fob shipping point. the shipping costs are $300. the shipping costs are 1.President Roosevelt approved of the funding for the Manhattan Project to build the atomic bomb after receiving a letter from Albert Einstein Enrico Fermi Robert Oppenheimer Adolf Hitler2.Why was the second atomic bomb dropped on Nagasaki, Japan? The last major military base was located there. An airport used for Japanese bombers was there. Japan had not surrendered for three days following the bombing of Hiroshima. It was close to the approaching Soviet military and U.S. forces could not secure it.3.What two nations did Adolf Hitler force to unite in 1938? Austria and Germany Belgium and Netherlands Denmark and Norway Poland and Russia4.How did the British policy of appeasement impact Czechoslovakia? It bought it time to build up its military. It contained its loss of territory to the Sudetenland. It doomed it to domination by the Germans. It had no impact on Czechoslovakia.5.Which of the following countries entered World War I the last? Great Britain Russia Italy United States6.The assassination of Archduke Franz Ferdinand was the result of the combination of what two broad causes of World War I? Austrian alliances and Serbian militarism Austrian imperialism and Serbian nationalism Austrian militarism and Serbian imperialism Austrian militarism and Serbian alliances7.Which group was targeted by Slobodan Milosevic, the leader of Serbia in the 1990s? Jews Ethnic Bosniaks Roman Catholics Orthodox Christians8.What was the fundamental reason that people were killed during the Khmer Rouge? They were considered contributors to dividing society into classes, class divisions being the biggest problem in communism. They attempted to assassinate Pol Pot. They were communists. They had provided support to Allied forces during World War II.9.Why did the United States Senate refuse to ratify entry into the League of Nations? A majority believed it gave up too much American sovereignty. It was considered a return to an unwise isolationism. The general view was that it was a form of imperialism. Woodrow Wilson decided that it was not in America's best interest.10.Which of the following most distinguished World War I as a "total war"? The use of wartime propaganda The use of the draft The secret postwar plans of the major players The extraordinary demand and impact on civilians11.A German who supported the Nuremberg Laws would probably also have defended the Versailles Treaty euthanasia of the extreme elderly the rights of individuals free healthcare for the sick12.Use the map below to answer the following question:The map above illustrates what aspect of the Holocaust? The Nazis were haphazard in carrying out their "Final Solution." Switzerland was the home to many Jewish refugees escaping the Third Reich. It was organized and significantly centralized to the east of Germany. Jews and other prisoners were most likely sent from prison camps to ghettos.13.Benito Mussolin's fascist theory called for a union of the state, press, and major industries under a strong central government church and state all workers around the world from separate national socialist parties the Slavic peoples of the Dalmatian coast into their own nation-state14.The leader with the original idea for a communist, stateless society was ________, and the first leader of a country to put them into practice was ________. Vladimir Lenin; Joseph Stalin Leon Trotsky; Vladimir Lenin Karl Marx; Vladimir Lenin Adam Smith; Karl Marx15.Which of the following accurately describes the impact of the atomic bomb on Hiroshima, Japan? Its loss of life was much lower than military experts had projected. It killed tens of thousands instantly, and tens of thousands more from the blast and fire that followed. Though the initial blast was catastrophic, the survival rate after that was near 100 percent. It destroyed the entire city, which remains uninhabitable to this day. A negative point charge is placed next to an uncharged conducting sphere: An electric potential map is shown in the figure. Three regions (A,B , and C) are indicated on the map. Order the electric field in these regions from strongest at the top of the list to weakest at the bottom of the list. Which graph is the result of reflecting f(x) = 1/4(8) across the y-axis and then across the x-axis?OB765->32Shy-8-7-6-5-4-3-2-1 12 x A sample of 128g of an unknown substance has a half-life of 1,250years. Approximately how long will it take for 37 grams of the substanceto remain (to the nearest year)? 3. Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion.Test the claim that the mean lifetime of car engines of a particular type is greater than 220,000 miles. Sample data are summarized as n = 23.x=226,450 miles, and s- 11,500 miles. Use a significancea=0.01. Select the correct test statistic and critical value.Test statistic: t 2.6898. Critical value: t= -2.508.Test statistic: t=2.6898. Critical value: t = 2.508.Test statistic: t = -2.6898. Critical value: t = 12.508.All changeTest statistic: z = 2.6898. Critical value: z = +2.508. Of all the different types of U.S. interest groups, which of the following tends to have the most disproportionate amount of influence?A. labor unionsB. corporate and business interestsC. agricultural interest groupsD. trade and professional interestsE. environmental interest groups what is 7 in x 3 in x 6 in x 4 in x 15 in= which simple distillation resulted in a better separation of the two liquids- cyclohexane:toluene or cyclohexane:p-xylene? was this what you expected based on the boiling points of the liquids? explain.