Mathematics College

Use the graph to answer the question. Determine the translation used to create the image.

A. 7 units to the right
B. 7 units to the left
C. 3 units to the right
D. 3 units to the left

Answers

Answer 1

Answer:

Step-by-step explanation:

Notice that the image of the point A(1,5) is A'(8,5).

Since the image and the original points have the same y-coordinates, so there is no vertical translation.

However, we do notice that the x-coordinate increases from x=1 to x=8.

So, there is a horizontal translation to the right by 8-1=7 units.

Related Questions

Luis scored 84 on the exam.
Find the z-score for Luis's exam grade. Round to two decimal places.

Answers

Mean: also known as the average is a measure of central tendency in a dataset. It is calculated by summing up all the values in the dataset and dividing the sum by the total number of values.

Standard deviation: The standard deviation is a measure of the dispersion of data around the mean in a dataset.t quantifies the average amount by which each data point in the dataset varies from the mean. A higher standard deviation indicates greater variability or dispersion of the data points, while a lower standard deviation suggests that the data points are closer to the mean. The standard deviation is typically represented by the symbol σ (sigma).

Z-Score: The z-score (also known as the standard score) is a statistical measurement that indicates how many standard deviations an individual data point is from the mean of a distribution. It allows you to compare and understand the relative position of a particular data point within a dataset.

The formula to calculate it is: Z = (x - μ) / σ where:

Z = Z-score

x = data point

μ = mean

σ = standard deviation

To calculate the z-score for Luis's exam grade, we can use the formula:

z = (x - μ) / σ

Where:

x = Luis's exam grade (84)

μ = Mean (81)

σ = Standard deviation (2.5)

Substituting the given values into the formula, we have:

z = (84 - 81) / 2.5

z = 3 / 2.5

z = 1.20

Rounding to two decimal places, the z-score for Luis's exam grade is 1.20.

Table of valúes y=8x-4

Answers

Here's a table of values for the equation y = 8x - 4:

The table below show the input and output values of the equation.

x y

0 -4

1 4

2 12

3 20

4 28

5 36

6 44

7 52

8 60

9 68

10 76

These values represent the corresponding values of y when you substitute different values of x into the equation y = 8x - 4.

Learn more about linear equation click;

https://brainly.com/question/12974594

#SPJ1

Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.

ln(14k)

Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*ln(h)

Answers

Answer:

[tex]\ln(14k)=\ln(14)+\ln(k)[/tex]

Step-by-step explanation:

Recall the following property of logarithmic function:

[tex]\ln(ab)=\ln(a)+\ln(b)[/tex]

By using the property above, we expand the given logarithmic expression as follows:

[tex]\ln(14k)=\ln(14)+\ln(k)[/tex]

Answer:

To expand the logarithm as much as possible, we need to use the properties of logarithms that allow us to rewrite the expression as a sum, difference, or product of logs. One such property is the product rule, which states that ln(ab) = ln(a) + ln(b) for any positive numbers a and b. Using this rule, we can rewrite ln(14k) as ln(14) + ln(k). This is the most simplified form of the expression, as we cannot further expand ln(14) or ln(k) using the properties of logarithms. Therefore, the final answer is:

ln(14k) = ln(14) + ln(k)

Note that we enclosed the arguments of the logarithm functions in parentheses and included a multiplication sign between 14 and k, as instructed.

MARK AS BRAINLIEST!!!

a cylindrical brass pipe is 600cm in length. Its outside diameter is 10cm, and its inside radius is 4. what is the total surface area of the pipe including the internal surface area

Answers

The total surface area of the cylindrical brass pipe, including the internal surface area, is approximately 34183.08 cm².

How to calculate the surface area

The formula for the surface area of a cylinder includes the curved surface area (CSA) and the two circular base areas.

1. Outer Surface Area:

The curved surface area (CSA) of a cylinder is given by the formula: CSA = 2πrh, where r is the radius and h is the height.

Given:

Outer diameter = 10 cm

Outer radius (R) = 10 cm / 2 = 5 cm

Height (h) = 600 cm

Outer CSA = 2π(5)(600) = 6000π cm²

The circular base areas can be calculated using the formula: Base area = πr², where r is the radius.

Outer base area = π(5)² = 25π cm²

Therefore, the total outer surface area is the sum of the curved surface area and the two circular base areas:

Total outer surface area = Outer CSA + 2 * Outer base area = 6000π + 2 * 25π = 6050π cm²

2. Inner Surface Area:

The inner radius (r) is given as 4 cm. We can use the same formulas to calculate the inner surface area.

Inner CSA = 2π(4)(600) = 4800π cm²

Inner base area = π(4)² = 16π cm²

Total inner surface area = Inner CSA + 2 * Inner base area = 4800π + 2 * 16π = 4832π cm²

Total surface area = Total outer surface area + Total inner surface area = 6050π + 4832π = 10882π cm²

To find the numerical value, we can use the approximation π ≈ 3.14:

Total surface area ≈ 10882 * 3.14 = 34183.08 cm²

Therefore, the total surface area of the cylindrical brass pipe, including the internal surface area, is approximately 34183.08 cm².

Learn more about surface area at https://brainly.com/question/16519513

#SPJ1

Today, interest rates on 1-year T-bonds yield 1.8%, interest rates on 2-year T-bonds yield 2.6%, and interest rates on 3-year T-bonds yield 3.7%.

A.) If the pure expectations theory is correct, what is the yield on 1-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.

B.) If the pure expectations theory is correct, what is the yield on 2-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.

C. If the pure expectations theory is correct, what is the yield on 1-year T-bonds two years from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.

Answers

The yield on 1-year T-bonds one year from now, based on the pure expectations Theory, is approximately 0.0349 or 3.49%. the yield on 2-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0443 or 4.43%.the yield on 1-year T-bonds two years from now, based on the pure expectations theory, is 5%.

The pure expectations theory, which suggests that the yield on a bond for a particular period is determined by the market's expectation of future interest rates. The theory assumes that investors are indifferent between investing in shorter-term bonds and rolling over their investments or investing in longer-term bonds.

A.) To calculate the yield on 1-year T-bonds one year from now, we need to find the geometric average of the current yield on 1-year T-bonds and the expected yield on 1-year T-bonds two years from now. Let's assume the current yield on 1-year T-bonds is 3% and the expected yield on 1-year T-bonds two years from now is 4%.

Using the geometric average formula, we can calculate the yield as follows:

Yield = sqrt((1 + Current Yield) * (1 + Expected Yield)) - 1

= sqrt((1 + 0.03) * (1 + 0.04)) - 1

= sqrt(1.03 * 1.04) - 1

≈ sqrt(1.0712) - 1

≈ 0.0349

Therefore, the yield on 1-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0349 or 3.49%.

B.) To calculate the yield on 2-year T-bonds one year from now, we need to find the geometric average of the current yield on 2-year T-bonds and the expected yield on 2-year T-bonds two years from now. Let's assume the current yield on 2-year T-bonds is 4% and the expected yield on 2-year T-bonds two years from now is 5%.

Using the geometric average formula, we can calculate the yield as follows:

Yield = sqrt((1 + Current Yield) * (1 + Expected Yield)) - 1

= sqrt((1 + 0.04) * (1 + 0.05)) - 1

= sqrt(1.04 * 1.05) - 1

≈ sqrt(1.092) - 1

≈ 0.0443

Therefore, the yield on 2-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0443 or 4.43%.

C.) To calculate the yield on 1-year T-bonds two years from now, we need to find the expected yield on 1-year T-bonds two years from now. Let's assume the expected yield on 1-year T-bonds two years from now is 5%.

The yield on 1-year T-bonds two years from now, based on the pure expectations theory, is equal to the expected yield, which is 5%.

Therefore, the yield on 1-year T-bonds two years from now, based on the pure expectations theory, is 5%.

To learn more about : yield

https://brainly.com/question/30841520

#SPJ8

In the diagram below, lines m and n are parallel, cut by transversal line p:

Label each of the following angle pairs based on this diagram:

<1 and <5 =
<3 and < 6 =
<4 and <6 =

Answers

Answer:

I assume you mean what they are called, if not please clarify

<1 and <5 = corresponding angles

<3 and < 6 = alternate interior angles

<4 and <6 = consecutive interior angles

Step-by-step explanation:

Leandra is renting a car for one week. The total cost to rent the car includes a weekly rate plus an additional charge per mile driven. Which graph shows the correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week?

Answers

The correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week is represented in option (B).

Explanation:

In the given scenario, we are given that Leandra is renting a car for one week. The total cost to rent the car includes a weekly rate plus an additional charge per mile driven.

We can make the following points to obtain the correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week

Let, x = Number of miles driven y = Total costLeandra is renting a car for one week.

Hence, we have the following given information:Total cost is a function of number of miles driven. Thus, the dependent variable is y, the Total cost.Weekly rate is a fixed cost and additional charge per mile driven is variable cost.

Hence, independent variable is x, the number of miles driven. Thus, x represents the number of miles driven and y represents the total cost to rent the car for one week.

The graph should show the number of miles driven on the x-axis and the corresponding total cost on the y-axis.The correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week is represented in option (B) which is given as follows:

x-axis represents the number of miles driven in the car during one week, and y-axis represents the total cost Leandra will pay to rent the car for one week.

To learn more about : total cost

https://brainly.com/question/25109150

#SPJ8

note the full question maybe:

Which graph correctly labels the axes for the total cost (y-axis) Leandra will pay to rent a car for one week based on the number of miles driven (x-axis)?

a bird flies at a speed of 50km/h. The bird then changes it's speed to 40km/h and continues for a further 2 hours. what is the average speed of the bird for the whole journey

Answers

Answer:There are several ways to calculate this.

The easiest way would be to determine the distance the bird flew.

40km/h x 4h = 160km

30km/h x 2,5h= 75km

Then add up the total distance: 160km + 75km = 235km

Next add up the total time: 4h + 2,5h = 6,5h

So in total the bird flew 235km in 6,5h. Now just divide both numbers by 6,5 as what you want to know is how far the bird got during an average hour.

Step-by-step explanation:

HELP NEEDED PLEASEEE

Answers

b) -x

explanation: The Middle Term of a Binomial Expansion is the term that comes in the middle of the expansion of the binomial, given by the Binomial Theorem. If the power of expansion of the sum or difference of two terms is an even number, then there is only one middle term. Otherwise, there are two middle terms.

QUESTION 25
Solve for a. Enter a number answer only.
25
a
24

Answers

Answer: 7

Step-by-step explanation:

We can use the Pythagorean theorem (a^2+b^2=c^2) so 25^2=625, and 24^2=576

576+b^2=625 b^2=49 b - (a)=7

Main Street Ice Cream Company uses a plantwide allocation method to allocate overhead based on direct labor-hours at a rate of $3 per labor-hour. Strawberry and vanilla flavors are produced in Department SV. Chocolate is produced in Department C. Sven manages Department SV and Charlene manages Department C. The product costs (per thousand gallons) follow.

Strawberry Vanilla Chocolate
Direct labor (per 1,000 gallons) $ 757 $ 832 $ 1,132
Raw materials (per 1,000 gallons) 807 507 607

Required:

a. If the number of hours of labor per 1,000 gallons is 60 for strawberry, 65 for vanilla, and 50 for chocolate, compute the total cost of 1,000 gallons of each flavor using plantwide allocation.

b. Charlene's department uses older, outdated machines. She believes that her department is being allocated some of the overhead of Department SV, which recently bought state-of-the-art machines. After she requested that overhead costs be broken down by department, the following information was discovered:

Department SV Department C
Overhead $ 90,972 $ 27,750
Machine-hours 25,270 36,700
Labor-hours 25,270 18,500

Using machine-hours as the department allocation base for Department SV and labor-hours as the department allocation base for Department C, compute the allocation rate for each.

c. Compute the cost of 1,000 gallons of each flavor of ice cream using the department allocation rates computed in requirement (b) if the number of machine-hours for 1,000 gallons of each of the three flavors of ice cream are as follows: strawberry, 60; vanilla, 65; and chocolate, 157. Direct labor-hours by product remain the same as in requirement (a).

Answers

a. Using plantwide allocation based on direct labor-hours at a rate of $3 per labor-hour:

Strawberry: $1,744 per 1,000 gallons

Vanilla: $1,534 per 1,000 gallons

Chocolate: $1,889 per 1,000 gallons

b. Allocation rates:

Department SV: $3.60 per machine-hour

Department C: $1.50 per labor-hour

c. Using department allocation rates:

Strawberry: $1,780 per 1,000 gallons

Vanilla: $1,573 per 1,000 gallons

Chocolate: $1,886 per 1,000 gallons

a. To compute the total cost of 1,000 gallons of each flavor using plantwide allocation, we need to allocate overhead based on direct labor-hours at a rate of $3 per labor-hour.

Strawberry:

Direct labor cost: $757 per 1,000 gallons

Labor-hours: 60 per 1,000 gallons

Overhead allocation: $3 per labor-hour * 60 labor-hours = $180

Raw materials cost: $807 per 1,000 gallons

Total cost of 1,000 gallons of strawberry flavor:

Direct labor cost + Overhead allocation + Raw materials cost = $757 + $180 + $807 = $1,744

Vanilla:

Direct labor cost: $832 per 1,000 gallons

Labor-hours: 65 per 1,000 gallons

Overhead allocation: $3 per labor-hour * 65 labor-hours = $195

Raw materials cost: $507 per 1,000 gallons

Total cost of 1,000 gallons of vanilla flavor:

Direct labor cost + Overhead allocation + Raw materials cost = $832 + $195 + $507 = $1,534

Chocolate:

Direct labor cost: $1,132 per 1,000 gallons

Labor-hours: 50 per 1,000 gallons

Overhead allocation: $3 per labor-hour * 50 labor-hours = $150

Raw materials cost: $607 per 1,000 gallons

Total cost of 1,000 gallons of chocolate flavor:

Direct labor cost + Overhead allocation + Raw materials cost = $1,132 + $150 + $607 = $1,889

b. To compute the allocation rate for each department, we will divide the overhead cost by the corresponding allocation base.

Allocation rate for Department SV:

Overhead: $90,972

Machine-hours: 25,270

Allocation rate = Overhead / Machine-hours = $90,972 / 25,270 = $3.60 per machine-hour

Allocation rate for Department C:

Overhead: $27,750

Labor-hours: 18,500

Allocation rate = Overhead / Labor-hours = $27,750 / 18,500 = $1.50 per labor-hour

c. To compute the cost of 1,000 gallons of each flavor using the department allocation rates, we will multiply the allocation rate by the corresponding allocation base for each flavor.

Strawberry:

Machine-hours: 60 per 1,000 gallons

Allocation rate for Department SV: $3.60 per machine-hour

Overhead allocation: $3.60 per machine-hour * 60 machine-hours = $216

Direct labor cost: $757 per 1,000 gallons

Raw materials cost: $807 per 1,000 gallons

Total cost of 1,000 gallons of strawberry flavor:

Direct labor cost + Overhead allocation + Raw materials cost = $757 + $216 + $807 = $1,780

Vanilla:

Machine-hours: 65 per 1,000 gallons

Allocation rate for Department SV: $3.60 per machine-hour

Overhead allocation: $3.60 per machine-hour * 65 machine-hours = $234

Direct labor cost: $832 per 1,000 gallons

Raw materials cost: $507 per 1,000 gallons

Total cost of 1,000 gallons of vanilla flavor:

Direct labor cost + Overhead allocation + Raw materials cost = $832 + $234 + $507 = $1,573

Chocolate:

Labor-hours: 157 per 1,000 gallons

Allocation rate for Department C: $1.50 per labor-hour

Overhead allocation: $1.50 per labor-hour * 157 labor-hours = $235

for such more question on total cost

https://brainly.com/question/25109150

#SPJ8

find the volume of the following solid figures

Answers

The volume of the solid figures are:

1. 480 cm³

2. 1000 m³

3. 141.43 cm³

4. 60.48 cm³

5. 16971.43 mm³

How to find the volume of solid figures?

1. The volume of a cuboid is given by the formula:

V = l * w * h

where l is the length, w is the width and h is the height

We have:

l = 12 cm

w = 5 cm

h = 8 cm

V = 12 * 5 * 8

V = 480 cm³

2. The volume of a cube is given by the formula:

V = l³

where l is the side length

We have:

l = 10m

V = 10³

V = 1000 m³

3. The volume of a cylinder is given by the formula:

V = πr²h

where r is the radius and h is the height

We have:

r = 3 cm

h = 5 cm

V = 22/7 * 3² * 5

V = 141.43 cm³

4. This is also a cuboid.

We have:

l = 4.5 cm

w = 3.2 cm

h = 4.2 cm

V = 4.5 * 3.2 * 4.2

V = 60.48 cm³

5. This is also a cylinder.

We have:

r = 30/2 = 15 mm

h = 24 mm

V = 22/7 * 15² * 24

V = 16971.43 mm³

Learn more about volume of solids on:

https://brainly.com/question/32071258

#SPJ1

Choose the function whose graph is given by

Answers

The function whose graph is given include the following: D. y = cosx + 1.

How to plot the graph of a cosine function?

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = acos(x - h) + k

Where:

a represents the amplitude.h represents the horizontal shift.k represents the vertical shift.

By critically observing the graph of the given cosine function, we can reasonably infer and logically deduce that the parent cosine function y = cosx was vertically shifted (translated) upward by 1 unit, in order to produce the transformed cosine function as follows;

y = cosx

g(x) = y + 1

g(x) = cosx + 1

Read more on cosine function here: brainly.com/question/26993851

#SPJ1

A
-2+
Which graph represents the
function y = tan x?
B
2T
2T
D
-2+1
21
4+
ㅠ
2T
2πT

Answers

The graph that represents the function y= tanx is Option A.

What is the description of the above function?

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and negative infinity, creating a wave- like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

Learn more about graph:
https://brainly.com/question/25184007
#SPJ1

Please helpppp

Which answers describe the shape below? Check all that apply. I put the attachment below

Answers

The given shape is a quadrilateral and a trapezoid.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

A trapezoid is a quadrilateral with at least one pair of parallel sides.

In a trapezoid, the parallel sides are called the bases of the trapezoid.

The other two sides are called the legs of the trapezoid.

The given shape is not a parallelogram because only one pair of sides are parallel and other sides are not.

Hence, the given shape is a quadrilateral and a trapezoid.

To learn more on Quadrilateral click:

https://brainly.com/question/29934291

#SPJ1

You pick 7 digits (0-9) at random without replacement, and write them in the order picked. What is the probability that you have written the first 7 digits of your phone number? Assume there are no repeats of digits in your phone number. Give your answer as a fraction.

Answers

The probability of writing the first 7 digits of your phone number is 1/604,800.

Given data ,

To determine the probability of writing the first 7 digits of your phone number, we need to consider the total number of possible outcomes and the favorable outcomes.

Total number of possible outcomes:

When picking 7 digits without replacement from the set of 10 digits (0-9), the total number of possible outcomes is given by 10P7 (permutations of 10 objects taken 7 at a time):

10P7 = 10! / (10 - 7)! = 10! / 3! = 10 * 9 * 8 * 7 * 6 * 5 * 4 = 604,800.

Favorable outcomes:

To have written the first 7 digits of your phone number, you need to pick those specific digits in the correct order. Since the phone number has no repeated digits, there is only one specific order that satisfies this condition.

Therefore, the number of favorable outcomes is 1.

Probability:

The probability is given by the ratio of favorable outcomes to total possible outcomes:

Probability = Favorable outcomes / Total possible outcomes

= 1 / 604,800.

Hence, the probability is 1/604,800.

To learn more about probability click :

https://brainly.com/question/17089724

#SPJ1

Mina has 462 flowers if she wants to put nine flowers in each phase how many for vases will she have how many flowers will she have left over

Answers

She will use 51 vases and have 3 flowers left

...................................................................................................

Answers

Answer:

Among them 4/5 Is correct answer.

Answer:

3/4

Step-by-step explanation:

..,...............

How many quarts of whipping cream that is 36% butterfat must be mixed with 4 quarts of half and half that is 12% butterfat to make light cream that is 18% butterfat.

Answers

Approximately 1.33 quarts of whipping cream should be mixed with 4 quarts of half and half to obtain a light cream with a 18% butterfat content.

Let's denote the number of quarts of whipping cream that needs to be mixed as "x". We know that the whipping cream has a butterfat percentage of 36% and the half and half has a butterfat percentage of 12%. We want to determine the quantity of whipping cream needed to create a mixture with a butterfat percentage of 18%.

To solve this problem, we can use the concept of weighted averages. The amount of butterfat contributed by the whipping cream is 0.36x, and the amount contributed by the half and half is 0.12 * 4 = 0.48.

The total amount of butterfat in the resulting mixture is 0.18 * (x + 4) since we are aiming for an 18% butterfat content in the final mixture.

Setting up an equation based on the butterfat content, we have:

0.36x + 0.48 = 0.18(x + 4)

Simplifying the equation:

0.36x + 0.48 = 0.18x + 0.72

0.36x - 0.18x = 0.72 - 0.48

0.18x = 0.24

x = 0.24 / 0.18

x = 1.33...

Therefore, approximately 1.33 quarts of whipping cream should be mixed with 4 quarts of half and half to obtain a light cream with a 18% butterfat content.

For more questions on quarts

https://brainly.com/question/29548067

#SPJ8

A water sample shows 0.016 grams of some trace element for every cubic centimeter of water. Adam uses a container in the shape of a right cylinder with a diameter of 11 cm and a height of 12 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Adam collected? Round your answer to the nearest tenth.

Answers

Answer:

18.2 grams

Step-by-step explanation:

Since the base diameter of the cylindrical container is d=11 cm, so its radius r is:

[tex]r=\frac{d}{2}=\frac{11}{2}=5.5[/tex]

Then, the volume V of the cylindrical container with radius r=5.5 cm and height h=12 cm is:

[tex]V=\pi r^{2}h=\pi \times 5.5^{2}\times 12=363\pi[/tex]

Since the water sample contains 0.016g of trace element for every cubic centimeter of water, so amount of trace element collected by the container of volume [tex]V=363\pi[/tex] cubic centimeters is:

[tex]0.016 g/cm^{3}\times 363\pi~cm^{3}=18.2g[/tex]

someone please help me solve this

Answers

Answer:

161.67 square feet

Step-by-step explanation:

The explanation is attached below.

Area of rectangle = length * width

=> Area of ABIJ = (7 * 6)ft^2 = 42 ft^2

=> Area of IJHG = (5 * 7)ft^2 = 35 ft^2
=> Area of HGCD = (7.81 * 7)ft^2 = 54.67 ft^2

=> Area of triangle = (EIH) = JFG = 1/2 * Base * height

EIH = 1/2 * 6 * 5 = 15 ft^2

JFG = 1/2 * 6 * 5 = 15 ft^2

Total area = (42 + 35 + 54.67 + 15 + 15)ft^2 = 161.67 ft^2

To learn more about Surface Area, Visit

https://brainly.com/question/30186087?referrer=searchResults

#SPJ1

Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A ∪ B' ? Your Answer:

Answers

Consequently, there are 5 elements in A B'.

Given the following definitions:

U = {1, 2, 3, 4, 5, 6, 7}A = {1, 2, 4, 5}B = {1, 3, 5, 7}

The complement of a set B is the set of all elements that belong to the universal set U but not to B.

A’ = {x | x ∈ U and x ∉ A} = {3, 6, 7}B’ = {x | x ∈ U and x ∉ B} = {2, 4, 6}

The union of sets A and B is the set of all elements that belong to set A or set B, or both.

A ∪ B = {x | x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 7}A ∪ B'

= {x | x ∈ A or x ∈ B’}

= {1, 2, 4, 5, 6}

Therefore, the number of elements in A ∪ B' is 5.

To learn more about : elements

https://brainly.com/question/25916838

#SPJ8

cos2theta + sin2theta = 0, solve for theta

Answers

Answer:

The solution for the original equation is:

theta = n pi and theta = (2n + 1)^pi/2, Where n is an integer.

Step-by-step explanation:

Rewrite the equation:

cos(2theta) + (sin(2theta) = 0

Use the double-angle formulas:

2 cos(theta) sin(theta) + 2 sin(theta) cos(theta) = 0

Factor out the common term:

2 sin(theta) cos(theta)(1 + 1) = 0

Simplify:

4 sin(theta) cos(theta) = 0

Set each factor to Zero:

For sin(theta) = 0.theta = n pi, Where n is an integer.

For cos(theta) = 0.theta = (2n + 1)^pi / 2, Where n is an integer

Draw a conclusion:

The solution for the original equation is:

theta = n pi, and theta = (2n + 1)^pi / 2, Where n is an integer.

Hope this helps!

Every year, the value of a condominium in Singapore appreciates by 15% of its value in the previous year. If the value of the condominium was $899300 in 2020, find its value in 2020.

Answers

Answer:

To find the value of the condominium in 2020, we can work backward from the given information. Since we know that the value appreciates by 15% each year, we can calculate the value for the previous year using the formula:

Value in previous year = Value in current year / (1 + appreciation rate)

Let's calculate the value of the condominium in 2020:

Value in 2021 = $899,300 / (1 + 0.15) ≈ $781,521.74

Value in 2020 = Value in 2021 / (1 + 0.15) ≈ $781,521.74 / (1 + 0.15) ≈ $678,309.34

Therefore, the value of the condominium in 2020 is approximately $678,309.34.

Step-by-step explanation:

The table shows the functions representing the height and base of a triangle for different values of x.
Height
Base
f(x)=x² + 3
g(x) = 2x
4
1
7
4
3
12
6
4
19
8
The area of the triangle when x = 2 is 14. Which equation can be used to represent the area of the triangle, A(x)?

Answers

Answer:

B) [tex]A=0.5(f\cdot g)(x)[/tex]

Step-by-step explanation:

[tex]\displaystyle A=\frac{1}{2}bh\\\\A=\frac{1}{2}(2x)(x^2+3)\\\\A=\frac{1}{2}g(x)f(x)\\\\A=\frac{1}{2}(f\cdot g)(x)[/tex]

Answer:

Option 2 is the correct answer.

Step-by-step explanation:

The equation that can be used to represent the area of the triangle is:

A(x) = 0.5 * (f ⋅ g)(x)

Let's break it down step by step:

Step 1: Understanding the equation components

f(x) represents the height of the triangle, given as x² + 3.

g(x) represents the base of the triangle, given as 2x.

(f ⋅ g)(x) represents the product of f(x) and g(x), or the multiplication of their respective values at a specific x.

Step 2: Evaluating the equation

To find the area of the triangle when x = 2, we substitute x = 2 into the equation.

A(2) = 0.5 * (f ⋅ g)(2)

Now, let's substitute the functions f(x) and g(x) with their corresponding values at x = 2.

f(2) = 2² + 3 = 4 + 3 = 7

g(2) = 2(2) = 4

Substituting these values into the equation:

A(2) = 0.5 * (7 ⋅ 4)

= 0.5 * 28

= 14

Therefore, when x = 2, the area of the triangle is 14.

Step 3: Interpretation and Conclusion

The equation A(x) = 0.5 * (f ⋅ g)(x) correctly represents the area of the triangle. It takes into account the height function f(x) = x² + 3 and the base function g(x) = 2x, multiplied together and multiplied by 0.5 (or divided by 2), which is a common factor in the formula for the area of a triangle.

Hence, the equation A(x) = 0.5 * (f ⋅ g)(x) can be used to represent the area of the triangle for any given value of x.

Please help with these two questions)l!!

Answers

The integral of xe^(7x) dx is equal to (1/7) xe^(7x) - (1/49) e^(7x) + C, where C is the constant of integration.

The integral of x cos(8x) dx is equal to (1/8) x sin(8x) + (1/64) * cos(8x) + C, where C is the constant of integration.

We have,

To solve the given integrals using integration by parts, we follow the formula:

∫u dv = uv - ∫v du

Let's solve each integral step by step:

∫xe^(7x) dx ; u = x, dv = e^(7x) dx

Taking the derivatives and integrals:

du = dx

v = ∫e^(7x) dx = (1/7) * e^(7x)

Applying the integration by parts formula:

∫xe^(7x) dx = uv - ∫v du

= x * (1/7) * e^(7x) - ∫(1/7) * e^(7x) dx

= (1/7) * xe^(7x) - (1/49) * e^(7x) + C

And,

∫x cos(8x) dx ; u = x, dv = cos(8x) dx

Taking the derivatives and integrals:

du = dx

v = ∫cos(8x) dx = (1/8) * sin(8x)

Applying the integration by parts formula:

∫x cos(8x) dx = uv - ∫v du

= x * (1/8) * sin(8x) - ∫(1/8) * sin(8x) dx

= (1/8) * x * sin(8x) + (1/64) * cos(8x) + C

Therefore,

The integral of xe^(7x) dx is equal to (1/7) xe^(7x) - (1/49) e^(7x) + C, where C is the constant of integration.

The integral of x cos(8x) dx is equal to (1/8) x sin(8x) + (1/64) * cos(8x) + C, where C is the constant of integration.

Learn more about integrations here:

https://brainly.com/question/31744185

#SPJ1

Someone please help me wit this

Answers

[tex](\sin \theta)^2+\left(\dfrac{9}{10}\right)^2=1\\\\(\sin \theta)^2+\dfrac{81}{100}=1\\\\(\sin \theta)^2=\dfrac{19}{100}\\\\\sin\theta=\sqrt{\dfrac{19}{100}}=\dfrac{\sqrt{19}}{10}[/tex]

What does 5^6 x 4=
.
Zzzzzzzzzz

Answers

62,500. Have a good day!!

62,000. I think. I could be wrong

surface area of prisms & cylinders homework 5 unit 11

Answers

1. The surface area of the rectangular prism is 872 square inches.

2. The surface area of the cylinder is 378o.56 square millimeters.

What is the surface area of a rectangular prism?

The rectangular prism has three pairs of equal faces: the top and bottom faces, the front and back faces, and the left and right faces.

The formula for the surface area of a rectangular prism is:

Surface Area = 2(length × width) + 2(length × height) + 2(width × height)

Surface Area = 2(8 in × 12 in) + 2(8 in × 17 in) + 2(12 in × 17 in)

Surface Area = 192 in² + 272 in² + 408 in²

Surface Area = 872 in².

What is the surface area of the cylinde?

The surface area of a cylinder consists of two circular bases and the curved surface area.

The formula for the surface area of a cylinder is: 2π(radius × height) + 2π(radius²).

Surface Area = 2π(14 mm × 29 mm) + 2π(14 mm)²

Surface Area = 2π(406 mm²) + 2π(196 mm²)

Surface Area = 812π mm² + 392π mm²

Surface Area = 1204π mm²

As π = 3.14:

Surface Area = 1204 × 3.14 mm²

Surface Area = 3780.56 mm²

Answers

Answer:

(a) x² + 6x + 8 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = 6, and c = 8

Substituting the values, we get:

x = (-6 ± sqrt(6² - 4(1)(8))) / 2(1)

x = (-6 ± sqrt(36 - 32)) / 2

x = (-6 ± sqrt(4)) / 2

x = (-6 ± 2) / 2

x = -4 or -2

Therefore, the solutions are x = -4 or x = -2.

(b) x² + 7x + 12 = 0