simplify the following:

Simplify The Following:

Answers

Answer 1

Answer:

[tex]\dfrac{\left(12x-56\right)x}{\left(x-4\right)\left(-x^2+20x-32\right)}[/tex]

Step-by-step explanation:

Simplify

[tex]\dfrac{\dfrac{16}{x-2}-\dfrac{4}{x-4}}{\dfrac{16}{x}-\dfrac{x-4}{x-2}}[/tex]

The first-level numerator is
[tex]\dfrac{16}{x-4}-\dfrac{4}{x-2}\\\\\\= \dfrac{16(x-4) - 4(x - 2)}{(x-2)(x-4)}\\\\\\= \dfrac{16x -64 - 4x + 8}{(x-2)(x-4)}\\\\\\= \dfrac{12x -56}{(x-2)(x-4)}[/tex]

The first-level denominator is
[tex]\dfrac{16}{x}-\dfrac{x-4}{x-2}\\\\\\= \dfrac{16(x-2) - x(x-4)}{x(x-2)}\\\\\\\\= \dfrac{16x - 32 -x^2 +4x}{x(x-2)}[/tex]

[tex]= \dfrac{-x^2+20x-32}{x\left(x-2\right)}[/tex]

Therefore
[tex]\dfrac{\dfrac{16}{x-2}-\dfrac{4}{x-4}}{\dfrac{16}{x}-\dfrac{x-4}{x-2}}\\\\\\= \dfrac{12x -56}{(x-2)(x-4)} \div\dfrac{-x^2+20x-32}{x\left(x-2\right)} \\\\\\[/tex]

Use the fraction rule: [tex]\dfrac{a}{b} \div \dfrac{d}{c} = \dfrac{a}{b} \cdot \dfrac{d}{c}[/tex]

[tex]= \dfrac{12x -56}{(x-2)(x-4)} \cdot \dfrac{x(x-2)}{-x^2 +20x -32}}[/tex]

The (x-2) term cancels out resulting in:
[tex]\dfrac{\left(12x-56\right)x}{\left(x-4\right)\left(-x^2+20x-32\right)}[/tex]


Related Questions

Carl is buying a shirt that costs $24.00. It is on sale for 50% off. what will the price of the shirt be?
A. 19.00
B. 50.00
C. 12.00
D. 14.00
Please help I’ll give brainly if you explain :)

Answers

Answer: C

Step-by-step explanation:

We need to turn 50% into a fraction first to make it easier,

50% is equal to 1/2 because 50/100 is simplified to 1/2.

Now let's multiply!

24 x 1/2 = 24/2 = 12/1 = 12

f(25) = 80 , find the value of f(2022) and give proper method and the final answer ​

Answers

The value of f(2020) is 39/100.

Given function is,

f(25) = 80

And f(xy) = f(x)/y²   .....(i)

Since

f(25) = 80

Then we define function as

f(x) = x + 55   .....(ii)

Now we can write 2020 = 101 x 20

So f(2020) = f(101x20) = f(101)/20²                from (i)

                                    =  (101 + 55)/400       from(ii)

                                    = 156/400

                                    = 39/100

Hence, f(2020) = 39/100

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Simplify with steps. (Write each expression without using the absolute value symbol)
|x+3| if x>5​

Answers

The expression without the absolute value symbol is:

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

Since, An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

|(x + 3) | if x > 5

This can be written as,

= |x + 3|

Now,

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

Thus,

The expression without the absolute value symbol is:

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

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what are the answers to these questions

Answers

Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when the distance the cow must stand from the billboard x₀ = 26.

How to determine angle and distance?

To find Θ, use similar triangles. Let the distance from the cow to the top of the billboard be h. Then, using similar triangles:

h / x = 5 / (x - 13)

Solving for h:

h = 5x / (x - 13)

The vertical angle subtended by the billboard at the cow's eye is equal to the angle whose tangent is given by:

tan(Θ) = h / 4

Substituting for h:

tan(Θ) = 5x / (4(x - 13))

To maximize Θ, find the value of x that maximizes tan(Θ). Taking the derivative of tan(Θ) with respect to x and setting it equal to zero:

d/dx (tan(Θ)) = 5(52 - 26x) / (4(x - 13))² = 0

Solving for x:

x₀ = 26

Substituting x₀ into the expression for Θ:

Θ(x₀) = tan⁻¹(5(26) / 4(13)) = tan⁻¹(5/2)

Therefore, Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when x₀ = 26.

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Chandra needs to make 3 gallons of punch how many cups of strawberry are needed

Answers

The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.

How to solve

In this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch.

Thus, we would apply direct proportion.

Note: There are 16 cups of frozen strawberries in a gallon.

By direct proportion:

16 cups = 1 gallon

X cups = 3 gallons

Cross-multiplying, we have:

X = 16 × 3

X = 48 cups of frozen strawberries.

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CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars. Assume the standard deviation is 209 dollars. You take a simple random sample of 94 auto insurance policies. Assuming the original population forms a bell-shaped distribution, answer the following and round your answers to three decimals.

Find the probability that a single randomly selected value is more than 979 dollars.
P(X > 979) = ???

Find the probability that a sample of size
is randomly selected with a mean that is more than 979 dollars.
P(M > 979) = ???

Answers

1. The probability that P(X > 979) = 0.567

2. The probability that P(M > 979) = 0.956

How do you calculate probability?

To calculate the probability that  a single randomly selected value is more than 979 dollars.

 979-1016

= -37/209

= -0.177

P(X > -0.177) = 0.5675

Therefore P(X > 979) = 0.568

To calculate that a sample of size is randomly selected with a mean that is more than 979 dollars.

209 / √94 = 21.557

-37/ 21.557 = -1.7164

P(Z > -1.714) = 0.9564

therefore P(M > 979) = 0.956

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find - 4 - 2 1/2 expression on the number line by drawing an arrow

Answers

The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. Expressions can be simple or complex and are used to represent mathematical relationships and operations.

How to determine the expression?

To find -4 - 2 1/2 expression on the number line by drawing an arrow, we need to start at -4 and then move left by 2 1/2 units.

To do this, we can draw an arrow starting at -4 and then mark off 2 1/2 units to the left. One way to represent 2 1/2 units is to divide the space between -4 and -5 into two equal parts, and then mark off one of those parts.

The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

Here's an example of what the arrow would look like:

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In the xy-plane, what is the y-intercept of the graph of the equation y=6(x-1/2)(x+3)?

Answers

Answer:

The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Step-by-step explanation:

To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:

y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9

Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

13pi/6 terminal point

Answers

The terminal point of 13π/6 is (-√3/2, 1/2) by using unit circle.

What are the quadrants of a graph?

The quadrants of a graph are the four sections that divide the coordinate plane. The quadrants are numbered in a counterclockwise direction starting from the positive x-axis.

1. Quadrant I is located in the upper-right section and contains points with positive x and y-coordinates.

2. Quadrant II is located in the upper-left section and contains points with negative x-coordinates and positive y-coordinates.

3. Quadrant III is located in the lower-left section and contains points with negative x and y-coordinates.

4. Quadrant IV is located in the lower-right section and contains points with positive x-coordinates and negative y-coordinates.

The quadrants are useful for determining the signs of coordinates, angles, and for plotting points on a graph.

To find the terminal point of 13π/6, we can start by recognizing that this angle is greater than 2π, which is one complete revolution around the unit circle.

To bring the angle back within one revolution, we can subtract 2π, which gives us 13π/6 - 2π/1 = 13π/6 - 12π/6 = 1π/6.

The angle 1π/6 is in the standard position between the positive x-axis and the first quadrant. The reference angle is π/6, which is the angle between the terminal side and the x-axis.

Since the angle is in the 2nd quadrant, the x-coordinate will be negative and the y-coordinate will be positive. Using the unit circle, we can find the values of sine and cosine at π/6 and then negate the value of cosine since the angle is in the second quadrant.

cos(π/6) = √3/2

sin(π/6) = 1/2

Therefore, the terminal point of 13π/6 is (-√3/2, 1/2).

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A man drove 14 miles directly east from his home, made a left turn at an intersection, and then traveled 7 miles north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

Answers

We can use the Pythagorean theorem to find the distance between the man's home and his place of work.

The distance traveled east and the distance traveled north form the two legs of a right triangle, and the distance we want to find is the hypotenuse.

Using the Pythagorean theorem, we have:

distance^2 = (14 miles)^2 + (7 miles)^2
distance^2 = 196 + 49
distance^2 = 245
distance = sqrt(245)
distance = 15.62 miles (rounded to the nearest tenth)

Therefore, the distance between the man's home and his place of work, if a road was made directly between them, would be approximately 15.6 miles.

Use a net to find the surface area of the prism.

A. 469 in.2

B. 315 in.2

C. 539 in.2

D. 784 in.2

Answers

Answer:

2(1/2)(11)(7) + 11(14) + 14(8) + 14(9) = 469 in.^2

The correct answer is A.

If h = 7 feet, and r = 2 feet, then what is the volume of the cylinder? (Use = 3.14.)

Answers

Answer: 87.964594300514 feet3 or 87.96 feet3

Step-by-step explanation:

πr^2 h

=  π×2^2×7

=  28π

=  87.964594300514 feet3

Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 14 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is _?_.

Answers

P(X=2) &= {14\choose 2}(0.08)^2(0.92)^{12} \

&= \frac{14!}{2!(14-2)!}(0.08)^2(0.92)^{12} \

[tex]\sf\implies\:&=\frac{14\times13}{2\times1}(0.08)^2(0.92)^{12}[/tex]

&= 91(0.08)^2(0.92)^{12} \

&\approx \boxed{0.2166

[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]

please help me with this question thank you

Answers

The difference between the adjustable-rate mortgage (ARM) and the  fixed-rate mortgage is $176,494.80.

How to find the difference ?

First, find the total amount paid on the adjustable-rate mortgage would be :
= ( 5 years x 12 months x 2, 506.43 payment ) + ( 10 x 12 x 3, 059. 46 ) + ( 5 x 12 x 3, 646.76) + ( 5 x 12 x 3, 630.65 )

=  $ 1, 172, 971. 20

Then we can find the total payment for the fixed - rate mortgage :

= Monthly payment x Number of years

= 2, 767. 99 x 30 years x 12 months

= $ 996, 476. 40

The difference is:

= 1, 172, 971.20 - 996, 476. 40

= $ 176,494. 80.

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Answer this question soon

Answers

Answer:

CA - 144

AD - 98

ABD - 49

BC - 134

C - unsure

Step-by-step explanation:

g(x)=2x
h(x)=x^(2)+4
evaluate for g(h(-8))

Answers

The value of the function is 136

How to determine the function

It is important that we note that functions are described as expressions that are used to explain the relationship between two variables.

From the information given, we have that;

g(x)=2x

h(x)=x^(2)+4

To determine the composite function, we would need to substitute the value of h(-8) as x in the function g(x)

Then, we have that;

h(-8) = (-8)^2 + 4

Find the values

h(-8) = 68

Now, substitute the value as x , we have that;

g(h(-8)) = 2(68)

expand the bracket and multiply

g(h(-8)) = 136

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what are the answers to these questions_

Answers

The general formula for f'(x) would be f' (x) = - 8 sin (x) + C.

The most general formula based on the first would be f(x) = 8 cos ( x ) + Cx + D.

How to find the general formula ?

To find the most general formula for f ' ( x ), we need to integrate f'' ( x ) with respect to x:

f'' ( x ) = - 8 cos (x)

f' (x) = ∫ ( -8cos(x)) dx

f ' (x) = - 8 sin(x) + C, where C is an arbitrary constant.

We need to integrate f'( x ) with respect to x to find the most general formula for f ( x ):

f'(x) = - 8 sin(x) + C

f(x) = ∫ ( - 8sin ( x ) + C) dx

f(x) = 8 cos ( x ) + Cx + D, where D is another arbitrary constant.

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Maria has 56 flower seeds. She wants to put an equal amount of seeds into 8 bags How many seeds will go in each bag?

Answers

Answer:

7 seeds will go into each bag

Given:

56 flower seeds need to be put into 8 separate bags.

To find out how much go into each bag you will divide the number of seeds by the number of bags

56/8=7

So 7 seeds will go into each of the 8 bags

7. The towns of Washington, Franklin, and Springfield are
connected by straight roads. The towns wish to build an
airport to be shared by all of them.
a. Where should they build the airport if they want it to be the same distance from
each town's center? Describe how to find the precise location.
b. Where should they build the airport if they want it to be the same distance from
each of the roads connecting the towns? Describe how to find the precise
location.
They should build the airport at the
They should build the airport at the
n be found by locating the intersection of at least
which can be found by locating the intersection of a
a circumcenter
medians

Answers

a. To build the airport at the same distance from the center of each town, they should locate the intersection of the perpendicular bisectors of the segments connecting each pair of towns. The precise location of the airport will be the point where these perpendicular bisectors intersect. This point will be equidistant from the center of each town.

b. To build the airport at the same distance from each road connecting the towns, they should locate the intersection of the angle bisectors of the angles formed by the roads at each town. The precise location of the airport will be the point where these angle bisectors intersect. This point will be equidistant from each road connecting the towns.

Alternatively, they could locate the intersection of the medians of the triangle formed by the three towns. The medians are the segments connecting each vertex of the triangle with the midpoint of the opposite side. The precise location of the airport will be the point where these medians intersect, which is also the centroid of the triangle. This point will be equidistant from each of the three towns.

A pet store has 10 ​puppies, including 3 ​poodles, 3 ​terriers, and 4 retrievers. If Rebecka and​ Aaron, in that​ order, each select one puppy at random without​ replacement, find the probability that Aaron selects a​ retriever, given that Rebecka selects a poodle.

Answers

P(both poodle) = (3/10)(3/10) = 9/100

Answer: The probability of choosing the same puppy is 9/100

Work out the largest integer value that x could take if
x+7<13

Answers

Answer:

The answer is going to 5

Step-by-step explanation:

I hope this helps you

pls solve thank u
100 points for answer

Answers

Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .

what is radius ?

The radii of a circle in geometry is the separation between any two points on the circle's circumference. It is frequently used to describe how far apart two points are. One of a circle's most crucial characteristics is its radius, which is taken into account when calculating a circle's circumference, area, and diameter. The distance around a circle that passes through its centre, or its diameter, is equal to half of its radius. Other shapes like spheres, cylindrical, and cones can also be described using the radius. The radius here means the distance from the shape's centre to any point on its perimeter.

given

The following formula must be used to determine a sector's area:

A = (θ/360)[tex]\pi r^2[/tex]

where r is the circle's radius, is pi, or roughly 3.14, and is the sector's centre angle, expressed in degrees.

The circle's radius is 7 km, and the shaded sector's central angle is 154 degrees, according to the provided figure. When these values are added to the formula, we obtain:

[tex]A = (154/360)\pi (7)^2[/tex]

[tex]= 10.55 km^2[/tex]

Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .

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The complete question is:-  

154 degree

7 km

Find the area of the shaded sector.

A = __ km2

Solve.
13. A ferry shuttles from Seattle to Vancouver Island and back. Because of
head winds, the return trip is slower than the trip to the island. The
average speed of the, ferry, in miles per hour, is given by the
2d
expression:
What is the average speed of the ferry?
d
+
50 60

Answers

The average speed of the ferry is 54.54 miles per hour.

The expression for the average speed is given [tex]\frac{2d}{\frac{d}{50}+\frac{d}{60} }[/tex].

Now, the given expression can be solved as follows

2d÷ (6d/300 + 5d/300)

= 2d÷(11d/300)

= 2d×300/11d

= 600/11

= 54.54 miles per hour

Therefore, the average speed of the ferry is 54.54 miles per hour.

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Which expression is equivalent to 5/4x +33-2+2

Answers

The expression that is equivalent to 5/4x +33-2+2 is 5x + 132/4. Option C

How to determine the value

It is important to note that algebraic expressions are defined as expressions that consists of factors, variables, constants, coefficients and terms.

These expressions are also made up of arithmetic operations.

These operations are listed as;

AdditionBracketParenthesesMultiplicationDivisionSubtraction

From the information given, we have that;

5/4x +33-2+2

Add or subtract the values

5/4x + 33

Find the LCM, we have;

5x + 132/4

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Complete question:

Which expression is equivalent to 5/4x +33-2+2

5x + 132

6x + 132/4

5x + 132/4

6x + 132

Perimeter=8x-6 find the missing side of triangle

Answers

Answer:

Step-by-step explanation:

I'm sorry, but there isn't enough information to solve for the missing side of a triangle with just the perimeter given as 8x-6. We would need at least one more piece of information, such as the lengths of the other sides or angles of the triangle.

a) Close the following accounts. 9

K. Emmanuel

$

2020

$

640

360

2020

800

Feb. 10 Bank Cash

25

200

Feb. 1 15

Sales Sales

J. Amaze

$

$

2020

2020

260 1090

1350

Mar. 12

Returns inwards

Mar4

Sales

18

Bank

Z. Ventour

2020

$

2020

$

May 13

Cash

518

May 10

Purchases

518

FSampath

2020

$

2020

July 14 22

Returns outwards

Bank

$

220

July 3

Purchases Purchases

8

25

Bank

800

1500

830

350

Answers

Answer:

I dont know the answer I dont know  what it is I just needed points bye

Step-by-step explanation:

​7 centimeters = ​
millimeters

Answers

Answer: 7 centimeters equals 70 millimeters :)

If the dealership you are buying the car from is offering 6.3% interest on a 5 year loan, what will your monthly payment be? How am I able to solve this when the selling price is $56,937.

Answers

Answer:

Step-by-step explanation:

To calculate the monthly payment on a loan, you can use the formula for the monthly payment on an annuity: P = (r * PV) / (1 - (1 + r)^(-n)), where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (i.e., the amount borrowed), and n is the total number of monthly payments.

In this case, the amount borrowed is $56,937 and the interest rate is 6.3% per year. To convert this to a monthly interest rate, we divide by 12: r = 0.063 / 12 = 0.00525. The loan term is 5 years, so the total number of monthly payments is n = 5 * 12 = 60.

Substituting these values into our formula for the monthly payment, we get: P = (0.00525 * 56937) / (1 - (1 + 0.00525)^(-60)) ≈ $1102.53. So, the monthly payment on this loan would be approximately $1102.53.

If a coin is flipped five times the probability of getting heads all five times is ______. Mark all that are true.

Answers

Answer: 1/2, the same as getting tails 5 times

Step-by-step explanation:

hope this helps

If angle 3=61, what should angle 1 and angle 2 be?

Answers

Answer:

Step-by-step explanation:

so the entire angle sum is 180 degrees then subtract 61 from 180 and divide by 2. hope it helps :)

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Bystander video sparked it, with cellphone-bearing citizens capturing the killings of Eric Garner, Alton Sterling, George Floyd, and others. While those high-profile clips showed the extremes of police brutality, the ubiquity [popularity] of smart phones during nationwide protests in recent weeks has provided a window into protesters interactions with officers unimaginable to past generations of Americans. . . . . . . What is resonating [creating a response] most now are videos that offer evidence of police aggression that are helping to disprove police claims and show some Americans a side of law enforcement that Black communities have been complaining about for decades. "Black Lives Matter Movement: A Case for Camera Phones? Jake Seiner, June 17, 2020 How is the author primarily trying to shape public opinion? by explaining the history of protest movements in bringing about change by describing how protestors prepare to participate in marches and rallies by comparing opinions about several different Black Lives Matter protests by explaining why support for the Black Lives Matter movement has changed Alice gardener wants to build a rectangular enclosure with a dividing fence in the middle of the rectangle. On one side, she plans to put some goats, on the other side she wants to raise some vegetables. The fence along the outside of the rectangle costs $3 per foot, but the dividing fence costs $12 per foot. (a) Alice decides to spend $240 on the fencing, what is the maximum area she can enclose? Justify your answer. (b) If Alice decided she wants to enclose 300 square feet, what is the minimum cost? The process of tracking the evolution development and sequence of critical events that affects the survival and profitability of the future new business is called? O, come, Love, let us take a walk,Down the Way-of-Life together;Storms may come, but what care we,If be fair or foul the weather.When the sky overhead is blue,Balmy, scented winds will afterUs, adown the valley blowHaunting echoes of our laughter.When Life's storms upon us beatCrushing us with fury, afterAll is done, there'll ringing comeMocking echoes of our laughter.So we'll walk the Way-of-Life,You and I, Love, both together,Storm or sunshine, happy weIf be foul or fair the weather.Which line from the poem appeals to the reader's sense of smell? Balmy, scented winds will after us Mocking echoes of our laughter When the sky overhead is blue When life's storms upon us beat The world price of a pound of almonds is $4. 50. before uruguay allowed trade in almonds, the price of a pound of almonds there was $3. 0. once uruguay began allowing trade in almonds with other countries, uruguay began:. I need help finding the decimal for these equations. How does line 52 affect the reader's understanding of the story? use two details from "middle of nowhere to support your response, HELPPPPP ASAPPP I NEEDDD HELPPP!! PLEASE HELP ME IM IN NEEDDDD!!!! Describe what happens to the bonds between atom during a chemical reaction to help open up a restaurant Alonzo borrowed money from his Credit Union. he took out a personal amortized loan for $49,000 at an interest rate of 6.55% with monthly payments for a term of 6 years. is Alonso pays the monthly payment each month for the full term find his total amount to repay the loan There are four auto body shops in Bangor, Maine, and all claim to promptly repair cars. To check if there is any difference in repair times, customers are randomly selected from each repair shop and their repair times in days are recorded. The output from a statistical software package is: Is there evidence to suggest a difference in the mean waiting times at the four body shops? Use the 0. 05 significance level. Compute the critical value. (Round your answer to 2 decimal places. ) State the decision regarding the null hypothesis What is the perimeter of triangle abc? round answers to the nearest tenth.a1456 m45boa.20.5 metersob.b. 22.4 metersoc.12 metersod.18 meters Select the sentence that uses commas correctly? The stadium was well-managed, well-maintained, and popular.O He liked the new gym because it was clean, and comfortable.O The courts were smoothly finished and newly painted, with white lines.O He liked the new courts new gym, and new stadium.ploto the contence Five years ago, a county lottery official conducted a very extensive (and expensive) study to determine the average age of lottery players in the county. From the data, he estimated the true age to be about 50 years. Five years later, the lottery official wants to know if the average age is now different from 50 years. He plans to conduct a smaller (and less expensive) survey of lottery players. From a random sample of 81 players from the county, the average age is 48. 7 years with a standard deviation of 8. 5 years. (a) is there convincing evidence at the a = 0. 05 significance level that the present-day average age of all lottery players in the county is different from 50 years. (b) Referring to your conclusion in part fa), what type of error may have been made? Describe the error in the context of this study