Graph the image of W(10,1) after a rotation 90° counterclockwise around the origin.

For the 5th question, the length of the pool based on the information given will be 70ft.

The length of the pool can be described by the equation: length = 5x + 10, while the width of the pool can be portrayed through the equation: width = 2x + 12.

After weighing out the rationale for both sides of the expression, simplify it down to: x^3 + 12x^2 - 528x - 564 = 0. This can be broken up with synthetic division or a calculator and a possible solution to this problem is x = 12.

Further compounding the two equations, length = 70 ft and width = 36 ft emerge; presenting length being 70 ft and width claimed at 36 ft.

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The probability of coming out ahead after 30 spins is about 0.0732

The probability of winning on a single spin by betting on red (or black) is 18/38, which is approximately 0.4737.

Assuming each spin is independent of the others, the probability of winning exactly 15 times out of 30 is given by the binomial distribution with n=30 and p=0.4737. This can be calculated using the formula

P(X = k) = (n choose k) × [tex]p^k[/tex] × [tex](1-p)^{n-k}[/tex]

where X is the random variable representing the number of times we win in 30 spins, k is the number of times we win, "choose" denotes the binomial coefficient, and ^ denotes exponentiation.

Using a calculator or software that can calculate binomial probabilities, we find that

P(X = 15) = (30 choose 15) × 0.4737¹⁵ × 0.5263¹⁵ ≈ 0.0971

This means that the probability of winning exactly 15 times out of 30 is about 0.0971, or approximately 9.71%.

To find the probability of coming out ahead (winning more than you bet) after 30 spins, we need to consider all the possible outcomes. If we win exactly 15 times, we break even (winning 15 dollars and losing 15 dollars). If we win more than 15 times, we come out ahead. If we win less than 15 times, we come out behind.

The probability of winning more than 15 times can be calculated by adding up the probabilities of winning 16 times, 17 times, and so on, up to 30 times. This can be expressed as

P(X > 15) = P(X = 16) + P(X = 17) + ... + P(X = 30)

Using the same binomial distribution formula as before, we can calculate each term in this sum and add them up:

P(X > 15) ≈ 0.0732

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The give question is incomplete, the complete question is:

On an American roulette table, there are 38 squares that correspond to 38 slots in the roulette wheel. you can bet on single squares or combinations of squares. each square has a number and a color. eighteen of the squares are red, 18 are black, and 2 are green. one thing you can do is bet red (or black), and it pays even money. (you risk $1, but if the roulette lands on any red space, you get back your $1 plus $1 in winnings.) if you play 30 times, betting $1 on red each time, what is the probability you will come out ahead?

The surface area of the triangular prism is 125.25 square feet.

Given that:

Height, h = 8 ft

L₁ = 4 ft

L₂ = 4 ft

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and H be the height of the rectangle. Then the surface area of the triangular prism will be given as,

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (L₁ x L₂) + (L₁ + L₂ + L₃) x H

The length L₃ is calculated as,

L₁² + L₂² = L₃²

4² + 4² = L₃²

L₃ = 4√2

The surface area is calculated as,

SA = (4 x 4) + (4 + 4 + 4√2) x 8

SA = 16 + 109.25

SA = 125.25 square feet

The surface area is 125.25 square feet.

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Answer:

The point (a, b) would be in Quadrant III, where both the x-coordinate and y-coordinate are negative.

Answer:

The answer for the Area of the composite shape is 170.52in²

Step-by-step explanation:

Area of composite shape =area of square +area of parallelogram

L of square=9.8in

L of parallelogram =17.4-9.8=7.6

A=L²+L×B

A=9.8²+7.6×9.8

A=96.04+74.48

A=170.52in²

The surface area and volume of the prism is 204 in ²

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of the prism is calculated as ;

side 1 = 6 × 8

= 48 units²

side 2 = 48 in²

side 3 = 1/2( a+b) h

= 1/2 ( 2+10) 3

= 1/2 × 12 × 3

= 6 × 3

= 18 in²

side 4

= 18 in²

side 5

= 6 × 10

= 60 in²

side 6

= 6 × 2

= 12 in²

Surface area = 48+48+18+18+60+12

= 204 in²

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Answer:

1. neither

2. x axis

3. y axis

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

To solve this problem, you could either do this two ways: solve for x immediately and then multiply it by 2, or you could multiply the equation by two and solve for x.

I will be using the first option.

Step 1: Solve for x

[tex]-2x+7=-4x+11\\\\[/tex] - We can set these equal to each other because a square has all sides congruent, which means that this side and all the others are equal to each other

[tex]-2x+2x+7=-4x+2x+11\\\\7=-2x+11[/tex]- We add 2x to both sides so we can isolate all the variables on one side and all the constants on one

[tex]7-11=-2x+11-11\\\\-4=-2x[/tex]- We do this so all the constants are on one side

[tex]\frac{-4}{-2}=\frac{-2x}{-2} \\\\2=x[/tex]- We divide by the coefficient of x so that we can fully isolate it

So now we have what x is, so we have to reinsert x into the equations and multiply it by itself to find the original area, after that we multiply it by 2.

[tex]-2x+7\\\\-2(2)+7\\\\-4+7\\\\3*3=9\\\\9*2=18[/tex]

In the result of hypothesis testing, p-value < 0.1, so null hypothesis can't be rejected. Therefore, there is no evidence to support the claim that doors are either too long or too short.

We have, a carpenter is making doors, The height of door = 2058.0 millimeters. Consider a sample of doors with sample size, n = 25

Sample mean, μ = 2045 mili meters

Standard deviations, σ = 20

Level of significance, α = 0.1 for either too long or too short. Here, we considered population distribution is approximately normal. Using the hypothesis testing for support the claim, the null and alternative hypothesis are defined as

[tex]H_o: \mu = 2058[/tex]

[tex]H_a: \mu ≠ 2058[/tex]

Now, we z-test to determine test statistic value,

[tex]Z =\frac{ X - \mu}{\sigma}[/tex]

Substitute all known values in above formula,

[tex]=\frac{ 2045 - 2058}{20}[/tex]

= - 0.65

Using the normal distribution table the value of P value for z = - 0.65 is equals to 0.257846. So, p-value =0. 257846> 0.01.

Hence, the claim is not true.

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If Mike bought 4 "soft-pretzels" and 4 bottles of water for $15, Ling purchased 3 "soft-pretzels" and 2 bottles of water for $10, the each "soft-pretzels" cost $2.5 and each "water-bottle" cost 1.25.

Let the cost of a "soft-pretzel" be =  $x and

Let the cost of a bottle of water be = $y,

We know that, Mike purchased 4 "soft-pretzels" and 4 bottles of water for $15,

Ling purchased 3 "soft-pretzels" and 2 bottles of water for $10,

So, the equations are :

⇒ 4x + 4y = 15 ...(1)

⇒ 3x + 2y = 10 ...(2)

We solve this by using substitution method:

Solving equation (2),

We get,

⇒ 3x + 2y = 10,

⇒ x = (10 - 2y)/3,

Now we substitute this expression for "x" in equation(1),

⇒ 4x + 4y = 15,

⇒ 4[(10 - 2y)/3] + 4y = 15,

⇒ y = 5/4,

Substituting this "y" into equation(2),

We get,

⇒ 3x + 2y = 10,

⇒ 3x + 2(5/4) = 10,

⇒ x = 5/2 = 2.5,

Therefore, cost of a soft pretzel is $2.5 and cost of a bottle of water is $1.25.

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The graph represents the solution to the compound inequality is B; number line with an open circle at 2 with a bold line pointing to the right ending at the point at 7.

To solve for this inequality, we need to isolate "x" on one side of the inequality symbol (<) as;

–6 < 3x – 12 ≤ 9

Now add 12 from both sides:

6 < 3x ≤ 21

3x = 21

x = 7

Or 3x = 6

x = 2

To graph this inequality one needs to highlight all the real numbers of  number line with an open circle at 2 with a bold line pointing to the right ending at the point at 7.

The correct option is B.

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Answer:

B

Step-by-step explanation:

nvm

The land should be recorded at $52,000.

We are given that;

Amounts Due Victims = $110,000; $60,000; $103,000

Now,

Step 1: Find the total market value of the land and the building

The land is appraised at $100,000 and the building at $150,000, so the total market value is:

$100,000 + $150,000 = $250,000

Step 2: Divide the market value of each component by the total market value to get the percentage of each component

The percentage of the land is:

$100,000 / $250,000 = 0.4 or 40%

The percentage of the building is:

$150,000 / $250,000 = 0.6 or 60%

Step 3: Multiply the percentage of each component by the purchase price to get the allocated cost of each component

The allocated cost of the land is:

0.4 x $130,000 = $52,000

The allocated cost of the building is:

0.6 x $130,000 = $78,000

Therefore, by algebra the answer will be $52,000.

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The equation of the circle with center (-3, -7) and containing the point (-12, -19) is ( x + 3 )² + ( y + 7 )² = 225.

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Given that; the circle has a center of (-3, - 7) and containing the point (-12, -19).

First, find the radius of the circle using the distance formula.

r = √( (x₂ - x₁)² + (y₂ - y₁)² )

Plug in the points

r = √( ( -12 - (-3) )² + ( -19 - (-7) )² )

Simplify

r = √( ( -12 + 3 )² + ( -19 + 7 )² )

r = √( (-9)² + (-12)² )

r = √( 81 + 144 )

r = √( 225 )

r = 15

Next, plug the center (-3, -7) and radius 15 into the formula for equation of the circle:

(x - h)² + (y - k)² = r²

(x - (-3) )² + (y - (-7) )² = 15²

( x + 3 )² + ( y + 7 )² = 225

Therefore, the equation of the circle is ( x + 3 )² + ( y + 7 )² = 225.

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The piece of wood for the ramp should be about 4.27 feet long using Pythagorean theorem.

Define Pythagorean theorem ?

The Pythagorean theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right-angled triangle. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides).

We can use the Pythagorean theorem to find the length of the ramp.

First, we need to convert the height of the ramp from inches to feet:

18 inches = 1.5 feet

Let x be the length of the ramp in feet. Then, according to the Pythagorean theorem:

[tex]x^2 = 4^2 + 1.5^2[/tex]

[tex]x^2 = 16 + 2.25[/tex]

[tex]x^2 = 18.25[/tex]

x ≈ 4.27

Therefore, the piece of wood for the ramp should be about 4.27 feet long.

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The result integer is given by, -17 - (25) = -42.

The sign rules to do integer operation are:

Given the integer operation is,

- 17 - (+25)

= - 17 - 25 [Since the product of positive and negative signs gives negative]

= - (17 + 25) [Taking -1 as common]

= - 42

Hence the required integer is given by - 42.

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The experimental probability of drawing a heart is 0.35

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

Outcome Frequency

Heart 7

Spade 3

Club 6

Diamond 4

This means that

P(Heart) = Heart/Total

So, we have

P(Heart) = 7/(7 + 3 + 6 + 4)

Evaluate

P(Heart) = 0.35

Hence, the probability is 0.35

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An actor invested some money at 9​% simple​ interest, and ​$49,000 more than three times the amount at 10%. The total annual interest earned from the investment was ​$38,440. Then, the actor invested $307,000 at 10% simple interest.

Let's use the following variables to represent the amounts invested;

x; amount invested at 9% simple interest

3x + 49000: amount invested at 10% simple interest (as it is $49,000 more than three times the amount invested at 9%)

We know that the total annual interest earned from the investment was $38,440, so we can set up the following equation;

0.09x + 0.1(3x + 49000)

= 38440

Simplifying and solving for x, we get;

0.09x + 0.3x + 4900 = 38440

0.39x = 33540

x = 86000

So the actor invested $86,000 at 9% simple interest. Using this value, we can calculate the amount invested at 10%;

3x + 49000 = 3(86000) + 49000

= 307000

Therefore, the actor invested $307,000 amount.

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The true statements on the amount of money raised by the fundraiser would be:

The expression 319 - a shows that to find the number of children, you need to subtract the adults from 319 which shows that 319 attended.

If a adults attended and 319 - a children came, the system of equations would be:

a + b = 319

20a + 10 b = 5, 860

Solving this, we see that 52 children attended. This means that the adults contributed :

= ( ( 319 - 52) x 20 ) / ( 52 x 10 )

= 10.3

This shows that adults raised 10 times the total amount of money raised from children attending the fundraiser.

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Answer:

x=1/2, y=4

Step-by-step explanation:

2x+3y=13

or,y=(13-2x)/3 ........eq(i)

4x-y=-2

or,y=4x+2 ..............eq(ii)

From eq(i) and (ii),

(13-2x)/3=4x+2

or,13-2x=12x+6

or,13-6=12x+2x

or,7=14x

or,x= 7/14

x=1/2

y=4×(1/2)+2

y=4

Answer:

Step-by-step explanation:

Total cost of the food with delivery for Danielle is given by approximately $ 29.69.

Danielle ordered food for a party which costs = $118.75

Now she also gave the delivery person a 25% tip.

So the amount of tip which she paid to the delivery person is given by

= 25 percent of the amount $118.75

= 25% of the amount $118.75

= $(118.75*(25/100))

= $(118.75*(1/4)) [eliminating the similar terms from the numerator and denominator of the fraction 25/100]

= $ 29.6875

= $ 29.69 [Rounding off to the nearest cent]

Hence the total cost of food with the delivery is $ 29.69.

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Answer:

[tex]1.\\x=\frac{11}{4} \\y=-\frac{11}{3} \\2.\\x=-11\\y=-\frac{11}{5}[/tex]

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

(1+2)1-4)​

(3) - 3

-9

A blog is an online platform where we go to receive information that is neither too informal nor too formal. The difference between blog writing and academic writing are;

A blog can include informal language.

A blog can be written in first-person point of view.

A blog includes personal and emotional details.

Academic writing is a very formal style of writing where only facts are presented.

A blog is most times meant for entertainment. Its content could be informal. It uses the first-person point of view. Words such as I, Myself, We, etc., are used.

It is also subjective as the emotions of the author can be reflected in the text. Therefore, options B, D, and F are correct.

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complete question

How is writing a blog different from academic writing? Select three answer options. A blog is written in third-person point of view. A blog can include informal language. A blog uses formal language and structure. A blog can be written in first-person point of view. A blog is written with an objective viewpoint. A blog includes personal and emotional details.

A coin is to be tossed 1000 times, the probability that the 785th toss is heads is 1/2.

Hence option c is the correct answer.

A coin is to be tossed 1000 times and the probability of the outcome to be Heads oor Tails is recorded accordingly.

Probability of an event refers to the possibility of the event to occur or in other words, how likely is tthe event to occur. Probability ranges from 0 to 1 as number and 0% to 100% as percentage.

Probability can be calculated with the formula as,

Probability of an event to occur = (Nmber of favourable outcomes) / (Total number of outcomes possible)

Here, when tossing a coin we have two outcomes, Heads and Tails

The number of favourable outcome, that is the outcome is Heads is 1.

Thus the probability that the outcome is a Head = 1/2

When a coin is tossed for 785th time the probability that the head will come up = 1/2 (assuming that the coin is unbiased).

The probability remains unchanged for tossing the coin for the first time and for the 785th time since no number of times the coin is tossed the number of favourable outcome is 1 and total outcomes is 2.

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Answer:

m

Step-by-step explanation:

The correct order of the segments from least to greatest rate of increase in water level is

A - B - C

So we would drag segment A to the first box, segment B to the second box, and segment C to the third box.

To determine the order of the segments from least to greatest rate of increase in water level, we need to look at the slope of each segment. The slope represents the rate of change of the water level over time.

A steeper slope indicates a faster rate of increase in the water level, while a shallower slope indicates a slower rate of increase.

From the graph, we can see that

Segment A has a relatively shallow slope, indicating a slower rate of increase in water level.

Segment B has a steeper slope than segment A, indicating a faster rate of increase in water level.

Segment C has the steepest slope of all, indicating the fastest rate of increase in water level.

Therefore, the correct order of the segments from least to greatest rate of increase in water level is

A - B - C

So we would drag segment A to the first box, segment B to the second box, and segment C to the third box.

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Check the picture below.

a state accounting process in brief

The standard overhead rate for the Manuel Company is $13 per DLH, calculated as the total budgeted overhead divided by the standard allocation base at 80% capacity of 25,250 DLH.

The standard overhead rate is the total budgeted overhead divided by the standard allocation base at 80% capacity

Standard allocation base at 80% capacity = 50,500 units × 0.5 DLH per unit = 25,250 DLH

Standard overhead rate is equal to the total overhead divided by Standard allocation base at 80% capacity, mathematically

= $328,250 / 25,250 DLH

≈ $13 per DLH

Therefore, the standard overhead rate is approximately $13 per DLH.

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--The given question is incomplete, the complete question is given

" Manuel Company predicts it will operate at 80% of its productive capacity. Its overhead allocation base is DLH and its standard amount per allocation base is 0.5 DLH per unit. The company reports the following for this period.

Flexible Budget at 80% Capacity Actual Results

Production (in units) 50,500 44,800

Overhead  

Variable overhead $ 277,750

Fixed overhead 50,500

Total overhead $ 328,250 $ 311,600

Compute the standard overhead rate. Hint: Standard allocation base at 80% capacity is 25,250 DLH, computed as 50,500 units × 0.5 DLH per unit."--