A rectangle is 5√7+2√3 meters long and 6√7-3√3 meters wide.
a. Find the perimeter of the rectangle in simplest form.
b. Find the area of the rectanglè in simplest form

The length of XZ in circle C is equal to the √34. This can be found using the Pythagorean theorem and the fact that XZ is a radius of the circle.

As WZ and XR are diameters, they intersect at the center of the circle, which we'll call point O.

Since WX is a chord of the circle, we can use the perpendicular bisector of WX, which passes through O, to find the length of XZ.

Let's call the midpoint of WX point M. Then OM is perpendicular to WX and bisects it.

So we have two right triangles, OXM and MXZ. We know that OM = 5 and XM = 3 (half of WX).

Using the Pythagorean theorem, we can find the length of OX:

OX² = OM² + MX²

OX² = 5² + 3²

OX² = 34

OX = √(34)

Since XZ is also a radius of the circle, we have XZ = OX = √(34).

Therefore, the measure of XZ in circle C is √(34).

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They will need an additional 18/11 days to finish the job.

There are two sides to it—a left side and a right side—and an equals sign (=) divides them. The members of the equation are the expressions on either side of the equals sign.

From straightforward arithmetic equations like 2 + 2 = 4 to more intricate equations in algebra and calculus, equations can be used to represent a broad variety of mathematical connections.

By determining the values of the variables that make the equation true, equations are frequently employed to solve issues. This is usually accomplished by manipulating the equation with algebraic operations like addition, subtraction, multiplication, and division on both sides of the equation.

In a variety of disciplines, including physics, chemistry, and engineering, equations can also be used to simulate real-world occurrences. For instance, the equation [tex]d=1/2gt^2[/tex] can be used to represent the motion of an object falling, where d is the distance fallen, g is the acceleration caused by gravity, and t is the amount of time that has passed.

Assume that there are D total papers that need to be translated. Then, we can claim that Ann's daily translation rate is D/10 and that she can translate D documents in 10 days. Ben's daily translation pace is D/12 since he can translate D documents in 12 days.

While Ben is still waiting to start working, Ann begins translating the documents at her daily rate. The total amount of work that Ann has finished is (x/10)D after she has worked for x days. Now that Ben has joined them, they can finish the remaining (1 - x/10)D work jointly at a rate of (D/10 + D/12) papers per day. To find x, we can construct the following equation:

(x/10)D + [(1 - x/10)D]/[(D/10 + D/12)] = D

When we simplify the equation, we obtain:

x/10 + (12 - x)/15 = 1

When both sides are multiplied by the least common multiple of 10 and 15, or 30, we obtain:

3x + 2(12 - x) = 30

Solving for x, we get:

x = 6

So, before Ben starts working, Ann finishes (6/10)D = (3/5)D of the work, and the two of them together finish the remaining (2/5)D of the job at a combined rate of (D/10 + D/12) = (11/60)D per day. Therefore, the total number of days required to accomplish the work is:

(2/5)D / (11/60)D = 24/11 days

Ben and Ann will need to work an extra 24/11 - 6 = 18/11 days to finish the work because Ann has already put in 6 days of effort. As a result, they will need an additional 18/11 days to finish the job.

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We have shown that the left-hand side of the equation is equal to the right-hand side of the equation, and the trigonometric identity is proved.

We have,

(cos 2x + cos 4x)/(cos 2x - cos 4x)

We can use the identity cos 2A = 1 - 2sin² A to rewrite cos 4x as:

cos 4x = 1 - 2sin² 2x

Then, substituting this into the expression, we get:

(cos 2x + 1 - 2sin² 2x)/(cos 2x - 1 + 2sin² 2x)

Using the identity sin² A = 1 - cos^2 A, we can rewrite sin² 2x as:

sin² 2x = 1 - cos² 2x

Substituting this into the expression, we get:

(cos 2x + 1 - 2(1 - cos² 2x))/(cos 2x - 1 + 2(1 - cos² 2x))

Simplifying the numerator and denominator separately, we get:

(2cos² 2x + 1)/(2cos² 2x - 1)

Using the identity cot A = 1/tan A, we can rewrite tan 3x as:

tan 3x = sin 3x/cos 3x

We can then use the identity sin 3A = 3sin A - 4sin^3 A and

cos 3A = 4cos³ A - 3cos A to rewrite sin 3x and cos 3x as:

sin 3x = 3sin x - 4sin³ x

cos 3x = 4cos³ x - 3cos x

Substituting these expressions into the right-hand side of the equation, we get:

cot 3x/tan x = (cos x/sin x)/(3sin x - 4sin³ x)/(cos x)

Simplifying by multiplying the numerator and denominator by the reciprocal of the fraction in the denominator, we get:

cot 3x/tan x = (cos x/sin x) * (cos x)/(3sin x - 4sin^3 x)

Multiplying the two fractions together, we get:

cot 3x/tan x = cos^2 x/(sin x(3 - 4sin^2 x))

Using the identity 1 - cos^2 A = sin^2 A, we can rewrite cos^2 x as:

cos^2 x = 1 - sin^2 x

Substituting this into the expression, we get:

cot 3x/tan x = (1 - sin^2 x)/(sin x(3 - 4sin^2 x))

Simplifying the numerator and denominator separately, we get:

cot 3x/tan x = (1/sin x) x (1 + sin x)/(3 - 4sin^2 x)

Using the identity 1 + sin A = 1/cos A, we can rewrite the expression as:

cot 3x/tan x = (1/sin x) x (1/cos x)/(3 - 4sin^2 x)

Finally, using the identity cot A = cos A/sin A, we can rewrite the expression as:

cot 3x/tan x = cos x/(sin x(3 - 4sin^2 x))

Therefore,

We have shown that the left-hand side of the equation is equal to the right-hand side of the equation, and the trigonometric identity is proved.

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Answer: 3x²-2x+5=0

You subtract the 2x and add 9 from both sides to get 3x²-2x+9=0

Answer:

3x^2−2x+5=0

Step-by-step explanation:

3x^2-4=2x-9

first you gotta add 9 to both sides

3x^2+5=2x

then you gotta subtract 2x from both sides

3x^2-2x+5=0

-SpoOky

Therefore, C) The median for Felicia's data is bigger than the median for Gabriella's data is the claim best supported by the data in the box plots.

Basketball is a team sport played by two teams of five players each on a rectangular court. The objective of the game is to score points by shooting a ball through a hoop, which is located 10 feet high on a backboard at each end of the court.

In statistics, quartiles are values that divide a dataset into four equal parts, with each part comprising 25% of the data. The three quartiles that divide the data into four equal parts are the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). The second quartile (Q2) is the same as the median of the dataset.

From the given box plots, we can see that Felicia's maximum number of points scored in one game is 28 and Gabriella's maximum is 24. Therefore, statement A is false.

The range of the data for Felicia is from 6 to 28, which is 22. The range of the data for Gabriella is from 10 to 24, which is 14. Therefore, statement B is false.

The median for Felicia's data is approximately 19 and the median for Gabriella's data is approximately 16. Therefore, statement C is true.

The first quartile for Felicia's data is approximately 12 and the first quartile for Gabriella's data is approximately 11. Therefore, statement D is false.

Thus, the statement best supported by the information in the box plots is C) The median for Felicia’s data is greater than the median for Gabriella’s data.

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Answer:The discount would be 25%.

Step-by-Step explanation:

1.In order for us to find out the discount we need to find how much the original price got cut off.Let’s use 86.88-65.16 the answer would be 21.72.

2.Now for us to find the discount we need to find out what part of a hundred is the discount.Let’s use 86.88/21.72 the answer would be 4.

3.So now we have a fourth of a hundred and a fourth of a hundred would be 25%.

Discount given=25%=21.72

Answer:

127. my answer needs to be 20+ character sooooooooooooo

Answer:

Eqation a and 15

Step-by-step explanation:

because 5 pears all cut into thirds is 15 slices 5 times 3 is 15

Answer:

A. x<-5

Step-by-step explanation:

-0.4x - 1.2 > 0.8

-0.4x > 2

x < -5

So, the answer is A. x<-5

The image of point C(-3,0) after a 180° counterclockwise rotation around the origin is the point (3,0).

To graph the image of point C(-3,0) after a 180° counterclockwise rotation around the origin, we can use the following formula:

(x', y') = (-x, -y)

where (x, y) are the coordinates of the original point, and (x', y') are the coordinates of its image after rotation.

Using this formula, we get:

(x', y') = (-(-3), -(0)) = (3, 0)

So, the image of point C(-3,0) after a 180° counterclockwise rotation around the origin is the point (3,0).

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Answer:

the required answer is 1 and -5

Count the significant digits in the number.

Since there are no captive zeros or trailing zeros, only the two non-zero digits (3 and 6) are significant.

The time measurement 0.0036 seconds has 2 significant digits.

Significant digits in the time measurement 0.0036 seconds, let's first define what significant digits are and then determine the number of significant digits in the given measurement.
Significant digits are the meaningful digits in a number that contribute to its precision.

These digits help to reduce any ambiguity when reporting measurements.
To determine the significant digits in the number 0.0036 seconds:
Identify non-zero digits.
All non-zero digits (1-9) are always considered significant.

The non-zero digits are 3 and 6.
Identify leading zeros.
Leading zeros are the zeros that appear before the first non-zero digit.

These zeros are not considered significant.

The leading zeros are the three zeros before the 3.
Identify trailing zeros.
Trailing zeros are the zeros that appear after the last non-zero digit.

If the number has a decimal point, these zeros are considered significant.

There are no trailing zeros.
Identify captive zeros.
Captive zeros are the zeros that appear between non-zero digits.

These zeros are always considered significant.

There are no captive zeros.
Count the significant digits in the number.

Since there are no captive zeros or trailing zeros, only the two non-zero digits (3 and 6) are significant. So, the time measurement 0.0036 seconds has 2 significant digits.

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The table for the function f(x) = 2ˣ should be completed as follows;

x         -4      -3     -2    -1    0

f(x)      1/16   1/8    1/4   1/2  1

As x approaches negative infinity, f(x) decreases.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the negative power rule to the function based on each of the x-values, we have the following:

f(x) = 2⁰ = 1

f(x) = 2⁻¹ = 1/2

f(x) = 2⁻² = 1/2² = 1/4

f(x) = 2⁻³ = 1/2³ = 1/8

f(x) = 2⁻⁴ = 1/2⁴ = 1/16

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The distance that the fish was able to travel in all was 23. 9 meters .

The distance from Harry to the fish' s hole can be found by the Pythagorean theorem:

a ² + b ² = c ²

7 ² + 7 ² = c ²

49 + 49 = c²

98 = c²

c = 9. 9

The total distance that the fish traveled can then be found by summing the distance it already traveled with the distance to Harry's:

= 14 + 9. 9

= 23. 9 meters

The fish traveled approximately 23.9 meters in all, rounded to the nearest tenth.

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It takes the second marathoner 4 hours and 40 minutes to complete the marathon.

Let's assume the distance of the marathon is "d" miles.

The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:

speed = distance / time = d / 4

The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:

speed = 4(d / 4) = d

For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:

d / 2 = (3/4)(d / 4)(t)

Simplifying this equation, we get:

t = (2/3) hours

So the total time it takes the second marathoner to finish the race is:

4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.

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The total revenue between the two companies is $3,200

To find the Nash Equilibrium, we need to look for a situation where neither firm has an incentive to change their strategy. This occurs when both firms are charging a price of $8 per month and each has 200 customers, resulting in total revenue of $3,200.

At this price and quantity, neither firm can increase their revenue by changing their strategy. If Netflix were to increase its price above $8, some of its customers would switch to Flixbuster, and Netflix's revenue would decrease. Similarly, if Flixbuster were to decrease its price below $8, it would gain customers from Netflix, but its revenue would still decrease.

Therefore, the Nash Equilibrium in this scenario is a price of $8 and 200 customers for each firm, resulting in total revenue of $3,200 between the two companies.

In mathematical terms, the Nash Equilibrium is a solution to the following system of equations:

Qn = 300 - P

Qf = 300 - P

TRn = P(Qn)

TRf = P(Qf)

where Qn and Qf are the quantities demanded by Netflix and Flixbuster, respectively, P is the price, and TRn and TRf are the total revenues earned by Netflix and Flixbuster, respectively. Solving this system of equations, we get P = 8 and Qn = Qf = 200, which results in total revenue of $3,200.

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Complete Question:

The following table shows a small community's demand for monthly subscriptions to a streaming movie service. Assume that only two firms (Nextflix and Flixbuster) sell in this market, that each firm offers the same quality of service and movie selection, and that each firm's marginal cost is constant and equal to 0 (zero) due to excess capacity.

Price/Month    Number of Total (P) Customers (Q)        Revenue/Month(TR)

$10                                                     0                                                         $0

9                                                      100                                                     900

8                                                      200                                                1,600

7                                                      300                                               2,100

If the two companies are behaving in each best interest, and the market is able to reach a Nash Equilibrium. What is the total revenue between the two companies?

Answer:

C. -1.7

Step-by-step explanation:

-4.2 - x = -2 2/4

-2 2/4 = -10/4 = -2.5

-4.2 - x = -2.5

-x = 1.7

x = -1.7

So, the answer is C. -1.7

The  equation that shows the number of calories, c, in terms of the number servings, n  where Han wants to know how many calories he gets from the fruit snacks is  c = 90n.

Based on the provided information from the question, whereby Han wants to know how many calories he gets from the fruit snacks,  and was able to find the multilication of  number of servings, n, with calories per serving.

Therfore, we  can write the equation  as c = 90n since it is about the multiplication of the variables.

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complete question;

Each serving of a certain fruit snack contains 90 calories. Han wants to know how many calories he gets from the fruit snacks. Write an equation that shows the number of calories, c, in terms of the number servings, n. Complete the equation below c=______ Use n as your variable.

Jessie will cover a distance of about 486 yards.

The distance that Jessie will ride around the circular track can be calculated as the circumference of the circle.

The formula for the circumference of a circle is:

C = 2πr

Where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In this case, the radius of the circle is 25.8 yards.

We can substitute that into the formula and simplify:

C = 2πr

C = 2 × 3.14 × (25.8)

C = 162.024 yds

Since the circumference of the circular track is approximately 162.024 yards.

If Jessie rides around the track 3 times, the total distance she will ride is:

3 × 162.024 = 486 yards.

Therefore, option D) 486 yards is the correct answer.

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The length of the longer leg of this 30-60-90 triangle is 6.93 units.

In a 30-60-90 triangle, the length of the shorter leg is opposite to the 30-degree angle. The longer leg is opposite to the 60-degree angle, and the hypotenuse is opposite to the 90-degree angle.

The ratio of the sides in a 30-60-90 triangle is always the same. The length of the shorter leg is half of the length of the hypotenuse. The longer leg is the square root of three times the length of the shorter leg.

Let's use this information to solve a problem. Suppose you have a 30-60-90 triangle with a shorter leg of length 4 units. We can use the ratio to find the length of the longer leg.

The length of the hypotenuse is twice the length of the shorter leg, which is 2 times 4 units = 8 units.

The longer leg is the square root of three times the length of the shorter leg, which is the square root of three times 4 units = 6.93 units.

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Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer:

The annual percentage yield (APY) is a measure of the return on an investment that takes into account the effect of compounding interest. To calculate the APY for an investment of $8000 at an interest rate of 4.75% compounded daily, you can use the formula:

APY = (1 + r/n)^(n*t) - 1

where r is the annual interest rate as a decimal (0.0475 in this case), n is the number of times the interest is compounded per year (365 for daily compounding), and t is the number of years (1 in this case).

Plugging these values into the formula gives:

APY = (1 + 0.0475/365)^(365*1) - 1 APY ≈ 0.0486

So, the APY for this investment is approximately 4.86%.

Step-by-step explanation:

The polynomial equation with roots -26, -2, and 4.39 is:

x³ + 15.22x² - 239.44x + 1049.44 = 0

The given root of 0.11 is not a root of this equation.

Any equation with a sum of terms that includes constant coefficients multiplied by one or more variables raised to a non-negative integer power constitutes a polynomial equation.

If the roots of a polynomial equation are -26, -2, and 4.39, then the factored form of the polynomial equation can be written as:

(x + 26)(x + 2)(x - 4.39) = 0

Expanding this equation gives us:

(x + 26)(x² - 2x - 8.78x + 8.78×2) = 0

Simplifying further, we get:

(x + 26)(x² - 10.78x + 38.44) = 0

Multiplying out the second factor, we get:

x³ - 10.78x² + 38.44x + 26x² - 277.88x + 1049.44 = 0

Combining like terms, we get:

x³ + 15.22x² - 239.44x + 1049.44 = 0

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For given data, Carrie threw the ball highest = 35ft and ball stayed in the air longest = 3s for Carrie as well.

Any object that is fired into the air and travels in that direction is referred to as a projectile. Gravitation, however, is another force that an object experiences after the first force that pushes it.

Three distinct individuals, Alberto, Ben, and Carrie, each toss a ball straight up into the air.

Following equation may be used to explain Alberto's throw.

[tex]H = -16t^2 + 32t + 4[/tex]

Now , to find the maximum height, we solve for first derivative w.r.t.t,

[tex]-32t + 32 = 0[/tex]

[tex]32t=32\\t = 1s[/tex]

Using t=1, we can find maximum height as

[tex]H =-16(1)^2 + 32(1) + 4\\\\H=(-16)+32+4[/tex]

[tex]H= 20[/tex] ft

Thus, when Alberto threw ball, maximum height attained= 20 ft and total time duration ball was in air = 1s.

From the given table( refer to attached image),

Fom given table,

we can drive the function for maximum height as,

[tex]H=at^2+bt+c[/tex]

now, putting values of t, to get values of H,

from table, for t=0,H=6

6=[tex]a(0)+b(0)+c[/tex]

[tex]c=6[/tex]

[tex]H=at^2+bt+6[/tex]

for t=1,H=14

[tex]14=a(1)^2+b.1+6\\\\8=a+b............(1)[/tex]

similarly,for t=2,H=14

[tex]14=a(2)^2+b.2+6\\\\8=4a+2b........(2)[/tex]

solving equation 1 and 2,

a=(-4) and b=12

∴[tex]H=-4t^2+12t+6[/tex]

we know, [tex]t=\frac{-b}{2a}\\\\t=\frac{-12}{-8}=3/2=1.5s[/tex]

When Ben threw ball, the maximum height ball attained was 14 ft and total time duration for which ball was in air was 1.5 seconds.

From the given graph(refer to attached image),When Carrie threw the ball Maximum Height attained = 35ft and Time duration ball was afloat is 3s

Thus,When Carrie threw the ball attained Maximum Height 35ft  and ball stayed in the air longest.

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Complete Question: A ball is thrown straight up into the air by three different people, Alberto, Ben and Carrie. Below are different representations of their throws. Alberto’s throw can be described by the equation height=−16(time)^2+32(time)+4 Ben's throw can be described by the following table(refer to attached image).Who threw the ball highest and for whom the ball was in air for the longest?

The best description of the area under the normal curve that would be used to approximate binomial probability is 'Area to the left of 46.5'.

To approximate the binomial probability, we can use the normal distribution as an approximation for the binomial distribution when the sample size is large enough, and the probability of success is not too close to 0 or 1. The mean of the normal distribution is equal to the mean of the binomial distribution, which is np, and the standard deviation of the normal distribution is equal to the square root of npq, where q is the probability of failure.

In this case, the number of DVDs that may malfunction follows a binomial distribution with parameters n = 319 and p = 1/100, where 1/100 is the probability of a DVD malfunctioning. Therefore, the mean of the binomial distribution is np = 3.19, and the standard deviation is [tex]\sqrt{npq}[/tex] = [tex]\sqrt{3.19*0.99}[/tex] ≈ 1.77.

To find the probability that at most 46 out of 319 DVDs will malfunction, we need to find the area under the normal curve to the left of 46.5 (since we are interested in the probability of at most 46 malfunctions, which includes 46.5 as well). Therefore, the answer is 'Area to the left of 46.5'.

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Answer:

Set your calculator to degree mode.

sin(72°) = x/25

x = 25sin(72°) = about 23.8 feet

Answer:

Step-by-step explanation:

the fewer jumps=the jumps Ronaldo did - the jumps Ahanu did

                          = 1080-1050

                          = 30

If a random sample of 20 gas stations was selected to estimate the gas prices. The type of error that could have occurred is a type I error, which is the rejection of a true null hypothesis. The probability of making a type I error is equal to the level of significance (α), which is 10% in this case. So, there is a 10% chance of making a type I error in this test.

To test if the true average gas price is under $3.50, we can use a one-tailed t-test with a null hypothesis of:

H0: μ >= $3.50

And an alternative hypothesis of:

Ha: μ < $3.50

where μ is the true population mean gas price.

Using a t-test with a sample size of 20, we can calculate the t-value as:

t = (x -bar - μ) / (s / sqrt(n))

where x-bar is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (3.40 - 3.50) / (0.22 / sqrt(20))

t = -2.03

Looking up the t-distribution table with degrees of freedom (df) = 19 and a 10% alpha level (α = 0.10), we find the critical t-value as -1.325.

Since our calculated t-value (-2.03) is less than the critical t-value (-1.325), we reject the null hypothesis in favor of the alternative hypothesis. Therefore, we can conclude that there is sufficient evidence to suggest that the true average gas price is under $3.50.

The type of error that could have occurred is a Type I error, which is rejecting a true null hypothesis. In this case, it means that we conclude that the true average gas price is under $3.50 when it's actually not. The probability of making a Type I error is equal to the alpha level, which is 10% in this case. So there's a 10% chance that we falsely reject the null hypothesis.

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Answer: 7x+4y=12 answer is x = (12/7, 0) and y (0,3) and the x+2y=-4 is

x intercepts (-4,0) and y intercepts is (0,-2)

Step-by-step explanation:

Add to one side and then divide

Answer:

blank is 4

Step-by-step explanation:

We can set up the equation:

[tex]\frac{1}{8} *x = \frac{1}{2}[/tex]

To solve, multiply both sides by 8.

[tex]\frac{1}{2}*8 = 4[/tex]

This checks out with the other statement.