Hello, I need help with these questions with shown work. Thank you

A right angle is an angle measuring exactly 90 degrees. A congruent angle is an angle that has the same measure as another angle. Therefore, for two angles to be congruent, they must have the same measure, and if they are right angles, they must each measure exactly 90 degrees.

Since both angles measure exactly 90 degrees, and any two right angles are always equal, the hypothesis that "If two angles are right angles, then they are congruent" is true. A right angle is one of the most common types of angles and is found in a variety of geometric shapes, including squares, rectangles, and triangles.

Because they always measure exactly 90 degrees, they are easy to identify and work with when solving geometry problems. In conclusion, two angles are congruent if they have the same measure, and if they are both right angles, they are also congruent because they both measure exactly 90 degrees.

The hypothesis that "If two angles are right angles, then they are congruent" is true.

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Answer:The manager should sell the couch at $163.85

Step-by-step explanation:

Answer:

$50.85

Step by step explanation:

We have been given that Jessica's Furniture Store buys a couch at a wholesale price of $113.00 and the markup rate at Jessica's Furniture Store is 45%.

We can find mark-up for the couch by finding 45% of 113.  

\(Mark-up=113*\frac{45}{100}\)

\(Mark-up=113*0.45\)

\(Mark-up=50.85\)

Therefore, mark-up for the couch will be $50.85.

The farm for sale measures 1120 acres.  

How many acres are equivalent to one square mile?

1 square mile= 640 acres.

To convert square miles to acres, we need to know that there are 640 acres in one square mile.

Given that the farm for sale measures one and three-quarter square miles, we can calculate the number of acres as follows:

1 and 3/4 square miles = 1.75 square miles  

Number of acres = 1.75 square miles * 640 acres/square mile

Number of acres = 1120 acres

Therefore, the farm for sale measures 1120 acres.

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The study conducted by the Urban Energy Commission in a large metropolitan area provides information on the probabilities of homeowners using different heating fuels or solar energy as their major source of heat over the next 10 years. These probabilities are represented by a transition matrix, which shows the likelihood of transitioning from one state to another.

To better understand the transition matrix, let's take an example. Suppose the transition matrix shows the probabilities of transitioning from one fuel type to another. The rows of the matrix represent the current fuel type, and the columns represent the potential future fuel types. Each cell in the matrix contains the probability of transitioning from the current fuel type to the future fuel type.
For instance, let's say the transition matrix shows that there is a 0.8 probability of transitioning from natural gas to solar energy and a 0.2 probability of transitioning from natural gas to oil. This means that out of 100 homeowners currently using natural gas, it is expected that 80 of them will switch to solar energy as their major heat source, while 20 will switch to oil.
By analyzing the transition matrix, we can gain insights into the future trends in heating fuel usage within the metropolitan area. It provides valuable information for policymakers and stakeholders to make informed decisions regarding energy planning and infrastructure development.
In conclusion, the transition matrix derived from the study conducted by the Urban Energy Commission provides probabilities of homeowners transitioning from one heating fuel to another over the next 10 years. It helps us understand the potential shifts in energy usage and aids in making informed decisions related to energy planning and infrastructure.

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Answer:

5

Step-by-step explanation:

\(8:5=15:x\\8*x=15\\(8*x)/8=15/8\\x=1.875\\\\\frac{8}{5} *1.875=\frac{15}{x} \\\frac{8}{5} *1.875=3\\3=\frac{15}{x}\\x=5\)

Answer:

y=-2/3x+-2

Step-by-step explanation:

y=MX+b

b=-2

m=-2/3

The estimated size of the deer population in the area is approximately 36.43. Since this is less than the carry capacity of 95, no permits need to be issued for population control.

To estimate the size of the deer population, we can use the mark and recapture method. The biologist tagged 28 deer in June and then trapped a total of 60 deer in August, of which 17 had tagged ears.

The mark and recapture method assumes that the proportion of tagged deer in the second sample represents the proportion of tagged deer in the entire population. We can set up a proportion:

(Tagged deer in the second sample) / (Total population) = (Tagged deer in the first sample) / (Total number of deer in the second sample)

Using the given information:

17 / Total population = 28 / 60

To solve for the total population, we can cross-multiply and solve the equation:

17 * 60 = 28 * Total population

1020 = 28 * Total population

Total population = 1020 / 28

Total population ≈ 36.43

Therefore, the estimated size of the deer population in that area is approximately 36.43.

To determine if any permits should be issued, we need to compare the estimated population size to the carry capacity of 95. Since the estimated population size is less than the carry capacity, no permits need to be issued.

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Answer:

The answer for your first question after just factoring is -(x-6)(x+7). So the answer for the first question is C

The answer to the second question after factoring is -3x(2x+3), which matches Choice A, so the answer to the second question is A.

Step-by-step explanation:

Answer:

(g ￮ f)(- 3) = 1

Step-by-step explanation:

evaluate f(- 3) then substitute the value obtained into g(x)

f(- 3) = - 3 + 4 = 1 , then

g(1) = 1³ = 1

Answer:

A (purple) = l*w

A (p) = 6*3

A (p) = 18 cm^2

A (green) = A (g) - A (p)

A (g) = (10 * 8) - 18

A (g) = 80 - 18

A (g) = 62 cm^2

A (total) = 10 * 8

A (t) = 80 cm^2

The  area of this rectangle is 80 square centimeters

The area of Rectangle is length times of width.

The given triangle has a length of 10 cm and width of 8 cm

Area of rectangle is length times width

Area = length × width

=10×8

=80 square centimeters

Hence, the  area of this rectangle is 80 square centimeters

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Hi there! :)

Answer:

(a) ≈ 3.61 cm.

(b) = 2.77 cm².

Use the Pythagorean theorem to solve for the side-length of DC. Let "s" represent the side-lengths:

s² + s² = 26

2s² = 26

Divide both sides by 2 to simplify:

s² = 13

Take the square root of both sides:

s = √13 ≈ 3.61 cm.

------------------------------------------------------------------------------------------

Calculate the shaded region by subtracting the area of the arc from the area of the square. DC represents the radius of the circle that the arc is apart of. Therefore:

Area of arc AC = 1/4 (πr²)

Solve for the area:

AC = 1/4 (π · (3.61)²)

AC = 1/4 (40.92)

AC = 10.23 cm²

Subtract this area from the area of the square (A = s²)

A = (√13)²

A = 13 cm²

13 - 10.23 = 2.77 cm²

Therefore, the solutions are:

(a) ≈ 3.61 cm.

(b) = 2.77 cm².

If the data for every person who took the tests were tabulated, the correlation between the Math and Verbal SATs would be less than 0.97.

Are the SAT verbal and SAT reading the same test?

The word used to designate the SAT Reading and Writing part is an older, outmoded one. The SAT Verbal section's material is still highly significant today, though. Many of the subjects and abilities from the old SAT Verbal portion are now included in the Evidence-Based Reading and Writing section.

Here we know that the correlation between these 51 pairs of averages was 0. 97.

And as we all know that the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state.

As we know that  the individual people tend to have more variation when you compare them to the average person

then if we look at the individual math and rebels course then there's probably a way more variation.

Here we know that the straight line wouldn't be there.

Then the whole thing would not be the same.

And which tells that It would be less of a correlation coefficient.

So it is less that 0.97.

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Answer:

Like radicals are radicals that have the same root number AND radicand (expression under the root).

The value of the function, f(0) is 13. However, we are instructed not to include f(0) in our answer. This means that we can state that we have found the value of f(0) to be 13, but we cannot include 13 in our answer.

When we are given a function, one of the first things we may want to do is evaluate it at a specific point. One way to do this is by substituting the value into the function and simplifying it. In this case, we are asked to find the value of f(x) at x=0 for the function f(x) = 5^x + 12 without using a calculator.

To find the value of f(0), we simply substitute 0 for x in the given function:

f(0) = 5^0 + 12

Now, any non-zero number raised to the power of 0 is equal to 1. This means that 5^0 is equal to 1. Therefore, we have:

f(0) = 1 + 12

Simplifying the expression, we get:

f(0) = 13

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Answer:

A = 20 square units ; Type in 20

Step-by-step explanation:

The simplest way to derive the area of this figure, is to first consider what the shape is itself;

\(Criteria of Shape - 2 Bases, 1 pair of Parallel Sides, Composed of two triangles, one square -From this we See that - Shape ; Trapezoid ( neither Right nor Isoceles )\)

Knowing that the shape is a Trapezoid, consider the formula ( Average of Bases ) * Height as to solve for it's area;

\(Length Of Base 1 - 3 units,\\Length of Base 2 - 7 units,\\Length of Altitude - 4 units,\\\)

Now let us substitute these values, solving for the Area;

\(Area Of Trapezoid - ( ( Base 1 + Base 2 ) / 2 ) * Height,\\ ( ( Base 1 + Base 2 ) / 2 ) * Height = ( ( 3 + 7 ) / 2 ) * 4,\\( 10 ) / 2 * 4 = 5 * 4 = 20 square units,\\\\Conclusion ; Area of Trapezoid = 20 square units\)

Solution; A = 20 square units

Answer:

A=20 (square units)

Step-by-step explanation:

B=XW=8-1=7

b=YZ=5-2=3

h=5-1=4

A=(B+b)*h/2

A=(7+3)*4/2=10*2

A=20 square units

Chase can create apprοximately 105 villagers tο live in his 17th tοwn.

We can use the expοnential grοwth fοrmula tο create an equatiοn tο predict the number οf villagers in any specific tοwn. The general fοrmula fοr expοnential grοwth is:

\(y = a * r^x\)

where:

y is the value we want tο predict (in this case, the number οf villagers)

a is the initial value (in this case, the starting number οf villagers)

r is the grοwth rate (in this case, 1.13, since each tοwn creates 1.13 times as many villagers as the οne befοre)

x is the number οf times the grοwth rate is applied (in this case, the number οf tοwns)

We can use this fοrmula tο predict the number οf villagers in any specific tοwn fοr Chase's situatiοn. Since Chase started with 4 villagers, we can plug in a = 4, and since the grοwth rate is 1.13 (οr 113% increase), we can plug in r = 1.13. Tο predict the number οf villagers in the 17th tοwn, we can plug in x = 17. Sο the equatiοn tο predict the number οf villagers in any specific tοwn is:

\(y = 4 * 1.13^x\)

Tο find the number οf villagers in the 17th tοwn, we can plug x = 17 intο this equatiοn and sοlve fοr y:

\(y = 4 * 1.13^{17\)

y ≈ 105.3

Therefοre, Chase can create apprοximately 105 villagers tο live in his 17th tοwn.

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Answer:

29

Step-by-step explanation:

The probability of an event happening is a number from 0 (even will cannot possibly happen) to 1 (event will definitely happen.)

0 ≤ p ≤ 1

1/100, 0, 85% are all numbers from 0 to 1.

29 is not from zero to 1, so the answer is 29.

Every value{0.01, 0.29, 85%} can represent the probability of an event occurring except option d that is 1.5.

Given to us,

a.)  \(\dfrac{1}{100}\)

b.)  0.29

c.)  85%

d.)  \(\dfrac{3}{2}\)

The probability help us to know about the probability of specific events occurring.

For a sure event, the probability is always 1,

while for an event that will never happen the probability is always 0.

Thus, probability(p),  \(\bold{1 \geq p\geq 0}\).

Now looking at the options,

a.)  \(\dfrac{1}{100}\) = 0.01

b.)  0.29

c.)  85% = 0.85

d.)  \(\dfrac{3}{2}\) = 1.5

Now comparing each option with \(\bold{1 \geq p\geq 0}\).

Therefore, the only option which is not feasible is option d that is 1.5.

Hence, every value{0.01, 0.29, 85%} can represent the probability of an event occurring except option d that is 1.5.

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Answer:

80 km

Step-by-step explanation:

20 times 4 + 80

Answer:

21600

Step-by-step explanation:

24x10x90=

240x90=

21600

Answer:

Answer is A and C on edge

Step-by-step explanation:

The composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.

When the two or more than two functions are written in the form of single function. Then such function is called the composite function.

Let suppose there is a function f(x) and another function g(x). Then the composite function can be given as,

\(f[g(x)]\)

The volume of air in a balloon is represented by the function,

\(V(r)=\dfrac{4}{3}\pi r^3\)

Here, r is the radius of the balloon, in inches.

The radius of the balloon increases with time, in seconds, by the function,

\(r(t) = \dfrac{1}{4}t^2\)

The composite function that can be used to determine the volume of the balloon after t seconds is,

\(V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{4}t^2)^3\\V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{64}t^6)\\V(r(t))=\dfrac{1}{48}\pi t^6\)

After the 6 seconds,

\(V(r(6))=\dfrac{1}{48}\pi (6)^6\\V(r(6))=\dfrac{1}{48}\pi \times46656\\V(r(6))=972\pi\)

Thus, the composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.

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Answer:

814 + 64 = 878

Step-by-step explanation:

just take the # from the previous day and add the 64.

When it says more, add when it says less, subtract.

The weight of water in the aquarium can be calculated by determining the volume of water and multiplying it by the weight of a cubic foot of water.

The given dimensions of the aquarium are 36 inches (length) by 24 inches (width) by 16 inches (height). The water level is at 12 inches. To calculate the volume of water, we multiply the length, width, and height of the water-filled portion, which is 36 inches by 24 inches by 12 inches.

Converting the volume to cubic feet (since the weight is given in pounds per cubic foot), we divide the volume by 12^3 (since 12 inches make up a foot) to get the volume in cubic feet.

Finally, we multiply the volume in cubic feet by the weight of a cubic foot of water, which is 62.4 pounds, to find the total weight of water in the aquarium.

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The open interval of convergence for the function f(x) = cos(x) with Taylor series centered at x = 2π is equal to (-∞, ∞).

To find the Taylor series centered at x = 2π for the function f(x) = cos(x),

Use the Maclaurin series expansion of the cosine function.

The Maclaurin series expansion for cos(x) is,

cos(x) = Σ (-1)ⁿ × (x²ⁿ) / (2n)!

Let us find the first five nonzero terms of the Taylor series expansion,

n = 0

(-1)⁰ × (x²⁰) / (20)!

= 1 / 0!

= 1

n = 1

(-1)¹ × (x²¹) / (21)!

= -x² / 2!

n = 2

(-1)² × (x²²) / (22)!

= x⁴ / 4!

n = 3

(-1)³ × (x²³) / (23)!

= -x⁶ / 6!

n = 4

(-1)⁴ × (x²⁴) / (24)!

= x⁸ / 8!

So, the first five nonzero terms of the Taylor series centered at x = 2π for f(x) = cos(x) are,

f(x) = 1 - (x - 2π)² / 2! + (x - 2π)⁴ / 4! - (x - 2π)⁶ / 6! + (x - 2π)⁸ / 8!

Now let us determine the open interval of convergence for this Taylor series.

The Maclaurin series expansion of cos(x) converges for all values of x.

Therefore, the open interval of convergence for the given Taylor series centered at x = 2π is equal to (-∞, ∞).

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To solve the homogeneous differential equation:

dy/dx = 2xy - x² + 3y²

We can rearrange the equation to separate the variables:

dy/(2xy - x² + 3y²) = dx

Now, let's try to simplify the left-hand side of the equation. We notice that the numerator can be factored:

dy/(2xy - x² + 3y²) = dy/[(2xy - x²) + 3y²]

= dy/[x(2y - x) + 3y²]

= dy/[(2y - x)(x + 3y)]

To proceed, we can use partial fraction decomposition. Let's assume that the equation can be expressed as:

dy/[(2y - x)(x + 3y)] = A/(2y - x) + B/(x + 3y)

Now, we need to find the values of A and B. To do that, we can multiply through by the denominator: dy = A(x + 3y) + B(2y - x) dx

Now, we can equate the coefficients of like terms:

For the y terms: A + 2B = 0

For the x terms: 3A - B = 1

From equation (1), we get A = -2B, and substituting this into equation (2), we have:

3(-2B) - B = 1

-6B - B = 1

-7B = 1

B = -1/7

Substituting B back into equation (1), we find A = 2/7.

So, the partial fraction decomposition is:

dy/[(2y - x)(x + 3y)] = -1/(7(2y - x)) + 2/(7(x + 3y))

Now, we can integrate both sides:

∫[dy/[(2y - x)(x + 3y)]] = ∫[-1/(7(2y - x))] + ∫[2/(7(x + 3y))] dx

The integrals can be evaluated to obtain the solution. However, since the question is cut off at this point, I cannot provide the complete solution.

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The numerical length of NO  is  mathematically given as

NO = 10

NO has a length of 10 in numerical format.

Because point N is located on line segment MO, we may deduce that MN plus NO equals MO.

Taking into account the following variables

MO=3x+6

NO=5x

MN = x

Substitute the given values into the formula:

x + 5x = 3x + 6

6x = 3x + 6

6x - 3x = 6

3x = 6

x = 6/3

x = 2

Get the length NO:

NO = 5x

NO = 5(2)

NO = 10

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Answer:

Answer is option D

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

f should be multiplied by e

Step-by-step explanation:

\(\frac{d}{e}\) = f ( multiply both sides by e to clear the fraction

d = ef ← f is multiplied by e

The partial sums S2, S4, and S6 of the series 3 + 2² + 3² + 4² + ... are 1, 14, and 55, respectively.

The partial sum of a series is the sum of the first n terms of the series. In this case, we are asked to compute the partial sums of the first 2, 4, and 6 terms of the series.

The first 2 terms of the series are 3 and 2², so S2 = 3 + 2² = 1.

The first 4 terms of the series are 3, 2², 3², and 4², so S4 = 3 + 2² + 3² + 4² = 14.

The first 6 terms of the series are 3, 2², 3², 4², 5², and 6², so S6 = 3 + 2² + 3² + 4² + 5² + 6² = 55.

In general, the partial sum of the first n terms of the series 3 + 2² + 3² + 4² + ... is equal to n(n+1)(2n+1)/6.

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Therefore the simplified form is 31/20m