Question 3
Joanne's Printing Services charges $49.95 to print 200 business cards. Each additional set of
100 cards costs $14. This is represented in the piecewise function below, where x is 1 set of
100 cards:
r(x) =
5 pts
29.95
when x is an integer and x < 2
29.95 + 14(x - 2) when x is an integer and x > 2
Determine the cost of 6 sets of cards.

The pair of functions are inverses, as their compositions result in x.

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

If two functions are inverse, the composites f(g(x)) and g(f(x)) both result in x.

The composite functions for this problem are given as follows:

Hence they are inverses.

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Answer: We can start by evaluating g(2):

g(2) = 2 + 9 = 11

Now we can use the definition of function composition to evaluate (f ∙ g)(2):

(f ∙ g)(2) = f(g(2)) = f(11)

To find f(11), we need to substitute 11 for x in the expression for f(x):

f(11) = (11 - 3)^2 + 1 = 8^2 + 1 = 65

Therefore, (f ∙ g)(2) = f(g(2)) = f(11) = 65.

Step-by-step explanation:

Jolie's working time increased by 20 %

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, Jolie’s time at work increases from 25 hours per week to 30 hours per week, we need to find that by  what percentage did the time at work per week increase,

Using the concept of percentage,

Initial working hours = 25 hours per week

Final working hours = 30 hours per week

Increased hour = 30 - 25 = 5 hours

Percentage increased = 5 / 25 x 100 = 20%

Hence, Jolie's working time increased by 20 %

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Answer:

5 3/4

Hope this is what you're looking for

We have no control over our cravings, affection, passion, or avarice. Humans and plants have many characteristics. You eat human flesh because you are a plant. Our way of life is represented by the plant.

Whether by hunting or scavenging, an animal or plant that consumes meat gets its food and energy needs from animal tissues (primarily muscle, fat, and other soft tissues).

The majority of the member species of the order Carnivora are known by the technical term "carnivoran," although confusion is often caused by the resemblance between the name of the order and the name of the diet.

So, in the given situation as the grows and as the money grows, it demonstrates that we are all looking out for one another.

In some ways, we are all carnivorous plants.

We all commit murder.

We are powerless against our hunger, love, passion, and greed. Plants and humans are similar in many ways.

What we desire is to live, and to exist in this world. You are a plant that consumes human flesh.

The plant represents our way of life.

Therefore, we have no control over our cravings, affection, passion, or avarice. Humans and plants have many characteristics. You eat human flesh because you are a plant. Our way of life is represented by the plant.

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Complete question:

Carnivorous plants have some unique and amazing characteristics. What do these characteristics suggest about life and the world that we live in? In other words, what can carnivorous plants teach us about the world?? Make a point and support it with an example from the text. Explain what your support shows.

Answer:6cm

Step-by-step explanation:You can use the formulas  or  to solve for diameter using volume. I will use the first forumla for this problem.

Substitute 113 for "V"

Multiply in the parenthesis

Divide by pi (3.14)

678 ÷ 3.14 = 215.923567

Apply the exponent

d = 5.99907...

d = 6 cm

The value of x in the chord is 2.8 units

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

The circle and the chords

Represent the radius of the circle with r

Next, we calculate the radius using each chord using the Pythagoras theorem

Using the above as a guide, we have the following:

r² = x² + (38/2)²

r² = 12² + (30/2)²

By substitution, we have

x² + (38/2)² = 12² + (30/2)²

So, we have

x² = -(38/2)² + 12² + (30/2)²

Evaluate

x² = 8

Take the square root of both sides

x = 2.8

Hence, the value of x is 2.8 units

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Answer:

B, C

Step-by-step explanation:

360 - 90 - 15 = 255

-90 - 15 = -105

Answer:

Step-by-step explanation:

To find the new population, we can substitute p = 4300 into the formula:

N = p + 0.04p

N = 4300 + 0.04(4300)

N = 4300 + 172

N = 4472

Therefore, the new population of the town is 4472 persons.

Answer:

-8

Step-by-step explanation:

4x - 9 + 3x = 8x - 1

7x - 9 = 8x - 1

7x = 8x + 8

x = -8

Therefore, the solution to the equation 4x - (9 - 3x) = 8x - 1 is x = -8.

Given:-

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Solution:-

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[tex] \: [/tex]

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[tex] \: [/tex]

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[tex] \: [/tex]

[tex] \: [/tex]

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hope it helps! :)

Answer:

20B

Step-by-step explanation:

Answer:

20B

Step-by-step explanation:

In the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.

An ellipse is a geometric shape that is a type of curve. In mathematics, an ellipse is defined as a set of points in a plane, such that the sum of the distances between any point on the curve and two fixed points is a constant which is known as foci.

To identify the major and minor axes of an ellipse, you can use both the graph and the equation of the ellipse.

Identify the major and minor axes using the graph: The major axis is the longest diameter of the ellipse, which passes through the center and touches the curve at two points called the vertices. The minor axis is the shortest diameter of the ellipse, which also passes through the center and touches the curve at two points called the co-vertices. On the graph, the major axis is the horizontal axis, while the minor axis is the vertical axis.

Identify the major and minor axes using the equation: The equation of an ellipse can be written in the standard form:

[tex]\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1[/tex]

where the ellipse's center is (h, k), the semi-major axis' length is a, and the semi-minor axis' length is b. The semi-major axis is half the length of the major axis, while the semi-minor axis is half the length of the minor axis. Therefore, you can identify the major and minor axes by looking at the denominators of the terms that contain x and y in the equation. The larger denominator corresponds to the semi-major axis, while the smaller denominator corresponds to the semi-minor axis.

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Answer: h(x) = 8x so choice A.

Step-by-step explanation:

f(x) = (x + 2)² - 1

g(x) = -(x - 2)² + 1

SOLVE:

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

——————————————

Step 1: Put together

((x + 2)² - 1) + (-(x - 2)² + 1)

Step 2: Positive and Negative 1 add to 0

((x + 2)² - ) + (-(x - 2)² + )

Step 3: Rewrite

(x + 2)² - (x - 2)²

Step 3: Expand the expression

(x + 2)(x + 2) - (x - 2)(x - 2)

Step 4: Distribute

(x² + 4x + 4) - (x² - 4x + 4)

Step 5: Remove Parentheses (don't forget to distribute the negative)

x² + 4x + 4 - x² + 4x - 4

Step 6: Collect Like Terms

x² and -x² add to 0

+ 4 and - 4 add up to 0

Leaving only + 4x and + 4x which add up to 8x

Therefore, h(x) = f(x) + g(x), h(x) = 8x

Graph Letter A:

The probability is approximately 0.129 or 12.9%.

Probability can also be used to describe more complex events, such as the likelihood of a stock price increasing by a certain amount in a given period of time, or the probability of a medical treatment being effective for a certain disease.

To calculate the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag, we need to use the binomial probability formula:

P(X >= 48) = 1 - P(X < 48)

Where

X is the number of orange Stattles in a 14 ounce bag

P(X < 48) is the probability of getting less than 48 orange Stattles in a 14 ounce bag

To calculate P(X < 48), we need to use the binomial probability formula:

[tex]P(X = x) = (nCx) * p^x * q^{(n-x)[/tex]

Where

n is the number of Stattles in a 14 ounce bag (we don't know this value)

x is the number of orange Stattles in a 14 ounce bag (we want to find the probability of getting less than 48)

p is the probability of getting an orange Stattle (0.4)

q is the probability of getting a non-orange Stattle (0.6)

nCx is the binomial coefficient

nCx is the binomial coefficient, which can be calculated using the formula:

nCx = n! / (x! * (n-x)!)

where ! denotes the factorial function.

We can use a cumulative binomial distribution table or a binomial calculator to find the probability of getting less than 48 orange Stattles in a 14 ounce bag. For example, using an online calculator, we find that:

P(X < 48) = 0.871

Therefore, the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag is:

P(X >= 48) = 1 - P(X < 48) = 1 - 0.871 = 0.129

So, the probability is approximately 0.129 or 12.9%.

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The population in thousands of a town in the year 2007 is 16.56 thousand.

In an exponential function, the base value controls how quickly the function increases or decreases. The function expands exponentially if the base value is more than 1, whereas it degrades exponentially if the base value is between 0 and 1. Faster growth or decay is indicated by a bigger base value.

Given that,

y = 8.5(1.1)ˣ

The value of x is calculated as:

x = 2007 - 2000 = 7 years.

Substitute the value of x in the given function:

y = 8.5(1.1)⁷

y = 16.56

Hence, the population in thousands of a town in the year 2007 is 16.56 thousand.

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The distance between points D(1,3) and H(9,8) found using the distance formula is 9.43 units.

To find the distance between two points, the coordinates of two points in space are used in the formula. In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula. The Pythagoras theorem is sometimes used to calculate the distance between two places. The length of the line segment bridging two points on a plane is known as the distance between the points.

d=√((x2 - x1)² + (y2 - y1)²) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

Assuming the question is the one given below.

The points given are:

D = (1,3) = (x1,y1)

H = (9,8) = (x2,y2)

The distance D between these two points can be found using the distance formula.

D = [tex]\sqrt{{(x_2-x_1)}^2 + {(y_2-y_1)}^2 } = \sqrt{{(9-1)}^2 + {(8-3)}^2 }[/tex] = √89 = 9.43 units

Therefore the distance between points D(1,3) and H(9,8) found using the distance formula is 9.43 units.

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Survey is a method used to collect the information from the group by asking  relevant questions.

It is simply how  likely the event can be occurred or in other words it is a likelihood of an event occurring

Let the events be:

A----Cooked food P(A)=10

B----washed dishes P(B)=13

C----- operated the cash register.

P(C)=25

P(A∩B)=5

(cooked + washed dishes)

P(A∩C)=5

(cooked & operated the cash register)

P(B∩C)=8

(washed dishes and operated the cash register)

P(A∩B∩C)=3 did All three jobs

P(A∩B∩C)'=3 did none of these jobs

P(AUBUC) = P(A) + P(B) + P(C) - P(A∩B)-P(A∩C)-P(B∩C) + P(A∩B∩C).

A.) How many employees were surveyed?

=P(A) + P(B) + P(C) - P(A∩B)-P(B∩C)-P(C∩A) + P(A∩B∩C)

=(10+13+25)-(5-5-8)+3

=48-(-8)+3

= 48 + 8 + 3

= 59

= 59+ 3 (members who did none of the jobs)

=62

62 employees were surveyed

x=A∩B∩C

=3

ab= A∩B-x

=5-3

=2

bc=B∩C-x

=8-3

=5

ca=A∩C-x

5-3

=2

b) only cooked food:

=A-(ab+x+ca)

= 10-(2+3+2)

=10-7

=3

3 employees only cooked food

c)only operated the cash register:

=C-(bc+x+ca)

=25-(5+3+2)

=25-10

=15

15 employees only operated the cash register

d) employees cooked food or operated the cash register:

P(A or C)=P(A)+P(C)

=10+25

=35

e) washed dishes or operated the cash register

P(B or C)= P(B)+P(C)

=13+25

=38

f)only washed dishes:

=B - P(bc+x+ab)

=13-(5+3+2)

=13-10

=3

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this question is incomplete

The complete question is:

In a survey of employees at a fast food​ restaurant, it was determined that 10 cooked​ food, 13 washed​ dishes, 25 operated the cash​ register, 5 cooked food and washed​ dishes, 5 cooked food and operated the cash​ register, 8 washed dishes and operated the cash​ register, 3 did all three​ jobs, and 3 did none of these jobs. Complete parts A) through F) below,

A.) How many employees were surveyed?

B.) How many of the employees only cooked food?

C.) How many of the employees only operated the cash register?

D.) How many of the employees washed dishes or operated the cash register?

E.) How many of the employees washed dishes or operated the cash register ?

F.) How many of the employees only washed dishes?

Answer:

Elsa's income tax for last year was 2,660 dollars.

Step-by-step explanation:

Answer:

30% i think

Step-by-step explanation:

For the polynomial 9x² - 49, the values of a and b include the following:

a = 3x

b = 7

In Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:

a² - b² = (a + b)(a - b).

Where:

a and b are numerical values (numbers or numerals).

Based on the information provided, we have the following polynomial function:

9x² - 49

By using the sum-product pattern, we have the following:

9x² + 21x - 21x - 49

By writing the common factor from the two pairs, we have the following:

(9x² + 21x) + (-21x - 49)

3x(3x + 7) - 7(3x + 7)

By rewriting in factored form, we have the following:

9x² - 49 = (3x - 7)(3x + 7)

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The DRD for Jazz Corporation on the dividend it received from Williams Corp. is $4,000.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate the dividends received deduction (DRD) for Jazz Corporation on the dividend it received from Williams Corp., we need to determine the taxable income limit for the deduction.

The taxable income limit is based on the percentage of ownership in the company. Since Jazz Corporation owns 10% of Williams Corp. stock, the taxable income limit is 50% of its taxable income, or $4,000 ($8,000 x 50%).

The DRD is then calculated as the lesser of the dividend received or the taxable income limit. In this case, Jazz Corporation received a dividend of $12,900, which exceeds the taxable income limit of $4,000.

Therefore, the DRD for Jazz Corporation on the dividend it received from Williams Corp. is $4,000.

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Answer:

a=50-40

a=10

lxb

answer

The profit made from Thembile selling the second hand sewing machine if the cost price is R5700 and the selling price is R8850 is R3150.

Profit/loss refers to the difference between the cost price and selling price of an item. When the difference is positive; it is profit. When the difference is negative; it is loss.

Cost profit = R5700

Selling price = R8850

Profit = Selling price - Cost price

= R8850 - R5700

= R3150

Ultimately, Thembile made a profit of R3150 on the second hand sewing machine.

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Answer: This is for college? lol the answer should be $2.75

Step-by-step explanation:

45.50-42.75= 2.75

The net price using the net price factor, complement method is $2958.75.

The complementary of the product of the market discount rates is represented by the net price factor, which is a decimal number. It is used to determine an item's final price after various trade discounts have been applied. By multiplying the complementary of the discount rates collectively and deducting the result from 1, we may determine the net price factor.

We use the complement method to calculate the net price using the net price factor.

For the given trade discount rates we have:

The complement of 35% is 65%

The complement of 30% is 70%

The complement of 5% is 95%

Multiply the values:

65% × 70% × 95% = 0.65 × 0.70 × 0.95 = 0.40825

The net price is obtained by:

1 - 0.40825 = 0.59175

Multiply the net price by the list price:

0.59175 × 5000 = $2958.75

Hence, the net price using the net price factor, complement method is $2958.75.

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Measure of ∠K in triangle KLM by open mouth theorem is ∠K < 90°.

The open mouth theorem states that if two sides of a triangle are congruent with two sides of another triangle, and the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.  

Given,

two triangles KLM and NOP

KL≅NO and KM≅NP

LM = 7, OP = 9

LM < OP

By open mouth theorem

m∠K < m∠N

m∠N = 90°

m∠K < 90°

Hence, m∠K < 90° is the value of angle K, in triangle KLM

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Answer:

5 miles / Maria's time = 4 miles / Gus's time

Since both Maria and Gus run for equal periods of time, we can set their times equal to each other:

5 miles / t = 4 miles / t

where t is the time it takes both of them to run.

Simplifying this equation, we can see that the distance Maria runs (M) is equal to the distance Gus runs (G) multiplied by 5/4:

M = (5/4)G

Therefore, the correct equation that relates the variables defined is:

M = (5/4)G

This means that Maria's distance is 1.25 times Gus's distance. So, the correct answer is option B: M = 1.25G.

Based on the information, we can infer that it is FALSE because it's not possible to construct a triangle with the measures of 4cm, 5cm and 9cm in length on its sides.

To find out if the statement is false or true, we must analyze the information on the lengths of the sides of the triangle and review the construction rules of a triangle to find out if its lengths have any condition.

In accordance with the above, we find that no triangle can be built with these lengths on its sides because, according to the Triangle Inequality Theorem, the sum of two of the sides of the triangle must be greater than the length of the third side. Therefore, if the sum of 4 + 5 results in 9, it is false that we can build a triangle with these measurements.

Note: This question is incomplete. Here is the complete information:

True or false.

Using this information, triangles can be constructed.

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PART 1: (a)The value of x in the pie graph is x = 30°

PART 2: (a)The value of x is 36°

(c) percentage of students for soccer is 25%

PART 3: (a)The value of Art is 165°

PART 1

(a) The value of x in the pie graph can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

x = 360 - 180 - 60 - 45 - 45 = 30°

(b) frequency = (angle of the part)/360 * 20

Baksket ball = 162/360 * 20 = 12

Bus        12

Car         4

Train       3

Walk       2

Bicycle   3

PART 2

(a) The value of x can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

x = 360 - 150 - 45 = 36°

(b) frequency = (angle of the part)/360 * 24

Basketball = 180/360 * 24 = 9

Basketball  9

Tennis        2

Hurling       4

Soccer       5

(c) percentage of student for soccer = 5/20 * 100 = 25%

PART 3

(a) The value of Art can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

Art = 360 - 162 - 90 - 72 = 165°

(b) frequency = (angle of the part)/360 * 120

Technology = 150/360 * 120 = 50

Technology  50

Music            15

Art                 55

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The solutions are given below.

Gross domestic product is a monetary measure of the market value or the market value of all the final goods and services produced and sold in a specific time period by a country or countries, generally "without double counting the intermediate goods and services used up to produce them".

here, we have,

1a. We can see immediate short run aggregate supply in North vaudeville in column A. This is because the price is fixed while output increases

1b. We can see short run aggregate supply in North vaudeville in column c. This is because output increases with price increase.

1c we can see long run aggregate supply in North vaudeville in column B. This is because output is constant with price increase.

Assuming output per hour of work decreases by 25% for column C then for each price, output is:

2A. Given price P= 110, output is 285(1-0.25) = 213.75

2B. Given price P = 100, output is 260(1-0.25) = 195

2C. Given price P = 95, output is 235(1-0.25) = 176.25

2D. Given price P = 90, output is 210(1-0.25) = 157.50

3. The new data from question 2 reflects a decrease in aggregate supply.

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