Translate triangle P by the vector​

The coordinates of A', B', C' and D' are obtained as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Hence the coordinates of the dilated figure are obtained multiplying it's respective coordinates on the original figure by the scale factor.

The problem is incomplete, hence the answer was given in general terms.

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

Step-by-step explanation:

[tex]3x - \frac{8}{2} = x - 6[/tex]

[tex] \frac{8}{2} = 4[/tex]

[tex]3x - 4 + 4 = x - 6 + 4[/tex]

[tex]3x = x - 6 + 4[/tex]

[tex]3x - x = - 6 + 4 - x[/tex]

[tex]3x - x = - 6 + 4[/tex]

[tex]2x = - 2[/tex]

[tex] \frac{2x}{2} = \frac{ - 2}{2} [/tex]

[tex]x = - 1[/tex]

The total value of the loan in simple interest is $59,625, which is the lowest amount and hence is the best option.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Compound interest is defined as the amount of interest which has been calculated on the principal amount and the amount accumulated over the previous period.

Principal amount, P = $50,000

Rate of interest, r = 5.25% = 0.0525

Time,t = 3 years 8 months = 3 + 0.6667 years = 3.6667 years

Part A :

For simple interest, total amount is,

A = P (1 + rt) = 50,000 ( 1 + (0.0525 × 3.6667 ))

                   = $59,625

Part B :

For compounded interest. total amount is,

A = P (1 + [tex]\frac{r}{n}[/tex])^(nt), where n is the number of times compounding is done in an year.

Here, n = 4, since compounding is quarterly

A = 50,000 [ 1 + [tex]\frac{0.0525}{4}[/tex]] ^(4 × 3.6667)

   = $60,537.9639 ≈ $60,537.96

Part C :

For continuously compounded interest, final amount is,

A = P [tex]e^r^t[/tex]

   = 50,000 [tex]e^{0.0525*3.6667[/tex]

   ≈ 60,613.83

Part D :

The option of simple interest is best for the small business owner since the total value of the loan is lowest for it.

Hence the value of the loan for simple interest is $59,625, value of the loan when compounded quarterly is $60,537.96 and the value of the loan when continuously compounded is 60,613.83. Simple interest is the best option since the value of the loan is lowest for it.

Learn more about Simple and Compound Interest here :

https://brainly.com/question/22621039

#SPJ1

Answer:

16

Step-by-step explanation:

You need to find 25% of 64.

To find a percent of a number, multiply the percent by the number.

25% of 64 = 25% × 64

To multiply a percent by a number, change the percent to a decimal by dividing the percent by 100. Move the decimal point two places to the left.

25% × 64 = 0.25 × 64 = 16

Answer:

.

Step-by-step explanation:.

The value of the standard deviation depends on the value of the mean.

As per the given data, we have to determine that the value of the standard deviation depends on the value of the mean

Yes, the value of the standard deviation depends on the value of the mean.

Because you have to know the mean to calculate the standard deviation.

The size of the standard deviation of a data set depends on what the mean is because the calculation of the mean is essential for calculating Standard Deviation.

The standard deviation determines how much the values deviate from the mean.

Besides, Standard deviation in simple terms means the deviation of data from the Mean.

The most popular way to assess dispersion is standard deviation, which is based on all values. As a result, even a small change in one value can modify the standard deviation's value.

Hence, Standard Deviation depends on the Mean.

For more questions on Standard Deviation and Mean

https://brainly.com/question/11965406

#SPJ4

The probability of getting exactly two heads when three coins are tossed is 25%, and the probability of getting one heads and one tail when three coins are tossed is 37.5%.

The probability of getting exactly two heads when three coins are tossed is 1/4 or 25%. This can be calculated using the formula for probability of an event: P(E) = Number of favorable outcomes / Total number of outcomes. In this case, the favorable outcome is two heads, and the total number of outcomes is 8 (2^3) since each coin has two possible outcomes (head or tail). So P(E) = 1/8 = 0.125 = 25%.

The probability of getting one heads and one tail when three coins are tossed is 3/8 or 37.5%. This can be calculated using the same formula as above. In this case, the favorable outcome is one heads and one tail, and the total number of outcomes is 8 (2^3). So P(E) = 3/8 = 0.375 = 37.5%.

The probability of getting exactly two heads when three coins are tossed is 25%, and the probability of getting one heads and one tail when three coins are tossed is 37.5%.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

Answer: One Half

Step-by-step explanation: 3 is half of 6 and  I took the test ;)

Answer:

14

Step-by-step explanation:

8/9 = 0.888888888......

<5 round down

[tex]\geq[/tex]5 round up

8/9 = 0.888888888....

larger than 0.5

the answer is 14

Answer:

3239609472 Km

Step-by-step explanation:

Answer:

Step-by-step explanation:

A cake recipe says to bake the cake until the center is 180°F, then let the cake cool to 120°F. The table shows

temperature readings for the cake.

a. Given a room temperature of 70°F, what is an

exponential model for this data set?

b. How long does it take the cake to cool to the desired

temperature?

Time (min)

a. The exponential model is y= 114.910(0.854) +70

(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)

b. The cake takes about ____ min to cool to 120°F

(Use the answer from part a to find this answer. Round to one decimal place as needed.)

Mar 7, 2019 · Do you know how to solve this? A cake recipe says to bake the c

ata set? How long does it take the cake to cool to the desired temperature? Follow • 1

Mar 7, 2019 · Do you know how to solve this? A cake recipe says to bake the cake until the center is 180° F, then let the cake cool to 100°F. The table shows temperature readings for the cake. Given a room temperature of 69 ° F, what is an exponential model for this data set? How long does it take the cake to cool to the desired temperature? Follow • 1

If you draw 2 cards, the probability of drawing 1 heart and 1 non-heart card are: 26/676.

It's crucial to keep in mind that your chances may change depending on the particular rules of the card game you're playing. B. The quantity of cards in the deck, the number of cards drawn, and whether or not the cards drawn after play were replaced.

A regular deck of 52 cards has a chance of producing exactly one heart depending on how many cards are drawn.

The likelihood of drawing a heart if you only draw one card is 13/52, or 1/4.

The probabilities of getting a card with a heart and a non-heart are:

(13/52) × (39/51) + (39/52) × (13/51) = 26/676

And if more cards are drawn, the odds of drawing exactly one heart are different.

To know more about probability visit:

brainly.com/question/30034780

#SPJ1

The diameter in inches of the small tire on the toy tractor is; 6 inches

The diameter is defined as the length of the line through the center that touches two points on the edge of the circle.

The parameters are;

Diameter of large tire = 5 ft

Diameter of small tire = 3.75 ft

The sizes are proportional, and as a result we have;

Toy size / actual size = (8 in)/(5 ft) = x/(3.75 ft)

Multiply both sides by 3.75 ft to get;

x = (8 in)(3.75/5)

x = (8 in)(0.75)

x = 6 in

The small tire on the toy is 6 inches in diameter.

Read more about Circle Diameter at; https://brainly.com/question/10907234

#SPJ1

Complete question is;

On tractor,the diameter of the large tire is 5 feet and the diameter of the small tire is 3.75 feet.

A toy tractor is made to scale from the actual tractor. On the toy tractor, the diameter of the large tire is 8 inches

What is the diameter in inches of the small tire on the toy tractor?

Answer:

14

Step-by-step explanation:

14 divided by -2 = -7

Answer:

6 1/2

Step-by-step explanation:

The difference between 13 9/20 and 6 7/8 can be found by converting both fractions to decimals and subtracting the two values.

13 9/20 can be expressed as a decimal as 13.45.

6 7/8 can be expressed as a decimal as 6.875.

So, the difference between 13 9/20 and 6 7/8 can be expressed as:

13.45 - 6.875 = 6.575

So the reasonable difference between 13 9/20 and 6 7/8 is 6.575.

The correct option for the true proportion is  AB/EF = CD/GH (option D)

Two figures are called similar if they have equal corresponding angles and their side are in same  ratios,

Given that, there are two similar polygons, ABCD and EFGH, we need to find the true proportion for the side of the polygons,

We know that, similar figure have equal ratios of the corresponding sides,

Therefore, we get,

AB/EF = CD/GH = BC/FG = AD/EH

From the options given, the true proportion is

AB/EF = CD/GH (option D)

Hence, the correct option for the true proportion is  AB/EF = CD/GH (option D)

Learn more about similar figures, click;

https://brainly.com/question/23637627

#SPJ1

The distance between the two corners of the garden is approximately equal to 3 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(5 - 8)² + (-3 - (-2))²]

Distance = √[(-3)² + (-3 + 2)²]

Distance = √[(-3)² + (-1)²]

Distance = √(9 + 1)

Distance = √10

Distance = 3.1623 ≈ 3 units.

Read more on distance here: brainly.com/question/12470464

#SPJ1

Answer: 324

Step-by-step explanation: Take 25% and enter it into a calculator with the percentage sign and times it by 480 and then subtract the number you get from 480, which is 360. Take 10% and enter it and times it by 360 and subtract that number from 360 and you should get 324. :)

The stated statement indicates that the item's new cost of goods sold is $37.7.

Exempt and non-exempt workers are the two basic categories into which employees fall. Your business may need to hire a variety of workers in order to function effectively and complete the task. This varies according to the type of organization.

A store manager gives his staff the order to mark up every item by 30%. The retailer paid $29 for the item, and 30% is shown in decimal form.

30/100 = 0.30

30% of the $29 = 0.30 × 29

                         = $8.7

Selling price of the item = Original price of item + 30% of the $29

                                       = $29 + $8.7

                                      = $ 37.7

Consequently, the item's new selling price is $37.7.

To know more about Employees visit:

https://brainly.com/question/27307326

#SPJ1

The value of an angle in radians that corresponds to a given trigonometric function value can be found using the inverse trigonometric functions.

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied.

In this case, since sinθ = 1/2, we can use the inverse sine function, denoted as sin^-1, to find the value of θ:

θ = sin^-1 (1/2)

Note that the inverse sine function returns an angle in the range of [−π/2, π/2].

The actual value of the angle may also lie in other ranges, depending on the context in which it is used.

Read more about trigonometry here:

https://brainly.com/question/24349828

#SPJ1

Answer:

143.2 L

Step-by-step explanation:

1 pm: 1870 L

Each hour, 14% is drained.

x - 14% of x = x - 0.14x = 0.86x

To decrease a number by 14%, multiply the number by 0.86

2 pm: 0.86 × 1870 L = 1608.2 L

3 pm: 0.86 × 1608.2 L = 1383.052 L

4 pm: 0.86 × 1383.052 L = 1189.4247 L

5 pm: 0.86 × 1189.4247 L = 1022.9052 L

6 pm: 0.86 × 1022.9052 L = 879.69847 L

From 5 pm to 6 pm, the volume decreased from 1022.9052 L to 879.69847 L:

1022.9052 L - 879.69847 L = 143.2068 L

Answer: 143.2 L

The option that would give the most money after 2 years would be Option 1.

The amount that Option 1 would give after 2 years is:

= Amount invested x ( 1 + rate / number of periods ) ^ number of periods in quarters

= 1, 000 x ( 1 + 12 % / 4 ) ⁴ ˣ ²

= $ 1, 267

The amount Option 2 would give after 2 years with continuous compounding is:

= Amount to invest x e ^ ( rate  x number of periods)

= 1, 000 x e ^ ( 6 % x 2 years )

= $1, 127 .50

Option 1 is the better option.

Find out more on compounding continuously at https://brainly.com/question/14303868

#SPJ1

By using the unitary method and dividing the time into equal intervals, the number of bacteria doubled every 3 hours, the final total of 32,000 bacteria after 14 hours.

Unitary method involves dividing the time interval into equal parts, and calculating the growth for each unit of time before adding them all up to get the total growth.

To start, let's divide the 14 hours into 3 hour intervals. We have

=> 14 hours / 3 hours = 4 intervals.

Next, we need to calculate the growth in each 3 hour interval. Since the number of bacteria doubles every 3 hours, we can find the growth by multiplying the initial number of bacteria by 2.

Starting with the first interval, we have 2000 bacteria * 2 = 4000 bacteria.

We can now repeat this calculation for each interval, multiplying the previous total by 2 each time.

For the second interval, we have 4000 bacteria * 2 = 8000 bacteria.

For the third interval, we have 8000 bacteria * 2 = 16,000 bacteria.

Finally, for the fourth interval, we have 16,000 bacteria * 2 = 32,000 bacteria.

So, at the end of 14 hours, there will be 32,000 bacteria in the culture.

To know more about unitary method here.

https://brainly.com/question/28276953

#SPJ4

Answer:

Step-by-step explanation: what you have to do is 36 divided by 3 because he used 3 scoops = 12 now 12 x 4( amount of how many scoops he used)= 48

* you times 4 by 12 because that's the amount he makes with 1 scoop

A graph of the solution (4, 4) for the system of linear equations is shown in the image attached below.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this context, we would replace the y-value of the first equation 4x - 2y = 8 with zero (0) as follows;

4x - 2(0) = 8

4x = 8

x = 2 ⇒ (2, 0).

For the y-intercept of the first equation 4x - 2y = 8, we would substitute the x-value with zero (0) as follows;

4(0) - 2y = 8

2y = -8

y = -4 ⇒ (0, -4).

For the y-intercept of the first equation y = 3x/2 - 2, we would substitute the x-value with zero (0) as follows;

y = 3(0)/2 - 2

y = -2 ⇒ (0, -2).

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of linear equations is at the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is equal to the ordered pair (4, 4).

Read more on equation here: brainly.com/question/19855458

#SPJ1

Answer:

34/50 or 68% or 0.68

Step-by-step explanation:

S= {16, 12, 22}

16 + 12 + 22 = 50

50 - 16 = 34

34/50

or

68%

or

0.68

The median daily electricity use is 1 kW-hr than the average (arithmetic mean) daily electricity use.

The median is the middle value of a set of data when the data is arranged in order. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

The data in ascending order is : 19 24 27 29 31

The median of the data is 27.

The mean, or average, is calculated by summing all the values in a set of data and dividing by the total number of observations.

Average of the data is

= ( 19 + 24 + 27 + 29 + 31)/ 5

= 26

The difference is therefore

= 27 - 26

= 1

To know more on median

https://brainly.com/question/28060453

#SPJ4

Answer:

as 92 is 2 std deviaiton above mean ; th

Step-by-step expla

Answer:

see below

Step-by-step explanation:

Put first equation into second

18x+3*(-6x+7) =21

open up the bracket

18x -18x+21=21

21 = 21

so infinite many solutions

The expression is solved with x = 6 to 62

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, factors and constants.

They are also composed of mathematical operations

From the information given, we have that;

1/2 x + 7.5 (x) + 11.4 + 2.6

Now, expand the bracket

1/2x + 7.5x + 11.4 + 2.6

Substitute the value of x as 6 , we get;

1/2(6) + 7.5(6) + 11.4 + 2.6

Multiply the values

3 + 45 + 11.4 + 2.6

Add the values

62

Hence, the value is 62

Learn about algebraic expressions on:

https://brainly.com/question/4344214

#SPJ1