which of the following is an incorrect statement? if a density curve is skewed to the right, the mean will be larger than the median. in a symmetric density curve, the mean is equal to the median. the mean of a skewed distribution is pulled toward the long tail. the median is the balance point in a density curve.

Answers

Answer 1

In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.

what is mean ?

The median, a statistician's measure of central tendency, divides a dataset into two equally sized half. When the data is organized from smallest to largest, it is the midway value (or largest to smallest). The median is the average of the two middle values when there are an even number of values. Since it is unaffected by extreme values, the median is frequently employed as a measure of central tendency when a dataset contains outliers or is skewed.

given

None of the claims are untrue.

The mean will be greater than the median if a density curve is tilted to the right.

The mean and median are equal in a density curve that is symmetric.

In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.

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Related Questions

Can anyone help with this math problem please? Thanks!

Answers

New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

How to find reduced area?

The area of the tennis court is given by:

A = lw

where l is the length of the court and w is the width of the court.

Substituting the given values, we have:

[tex]$$260.7569 = l \cdot 10.97$$[/tex]

Solving for l, we get:

[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]

To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:

w' = w - 0.25w = 0.75w

Substituting the given values, we have:

[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]

where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:

[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]

Therefore, the new area of the court is reduced by 25%.

To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:

[tex]$w' = 0.75w$$[/tex]

Dividing both sides by w, we get:

[tex]$\frac{w'}{w} = 0.75$$[/tex]

This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

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5. {MCC.6.RP.A.3B} How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes?
*
1 point

Answers

Answer:

Step-by-step explanation:

It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.

Answer:

120 minutes / 2 hours

Step-by-step explanation:

time = distance / velocity

[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]

Please help me and all my other questions imma fr fail 10th and I need help (Find the perimeter of a Regular Pentagon with consecutive vertices at (-3,4) and (2, 6)

Answers

Answer: 25

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is______. A) 0.24 B) 0.34 C) 0.41 D) 0.66

Answers

The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.

Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.

Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.

Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.

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When a homeowner has a 25-year variable-rate mortgage loan, the monthly payment R is a function of the amount of the loan A and the current interest rate i (as a percent); that is, R = f(A). Interpret each of the following. (a) R140,000, 7) - 776.89 For a loan of $140,000 at 7% interest, the monthly payment is $776.89. For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan. For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan. For a loan of $140,000 at 7.7689% interest, the monthly payment is $700.

Answers

The monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89 is the correct statement(A).

The statement given is describing a function that relates the monthly payment R of a 25-year variable-rate mortgage loan to the loan amount A and the current interest rate i.

The given values are R = $776.89 and A = $140,000, with an interest rate of 7%. This means that the monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89.

However, the other statements are incorrect interpretations. For instance, the statement "For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan" is incorrect.

This is because the number of payments required to pay off a loan depends not only on the loan amount and interest rate, but also on the term of the loan.

Similarly, the statement "For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan" is also incorrect, as the number of payments required would be determined by the term of the loan.

Finally, the statement "For a loan of $140,000 at 7.7689% interest, the monthly payment is $700" is also incorrect. This is because, for the given loan amount and interest rate, the monthly payment required would be $776.89, as calculated above.

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Stephanie puts thirty cubes in a box. The cubes are 1\2 inches on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?

Answers

If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

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What are the zeros of g(x) = x3 + 6x2 − 9x − 54?

Answers

Answer:

Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.

Can some one solve this and show their work please

Answers

Answer:

m = 2n = 7

Step-by-step explanation:

we solve with two equations between the corresponding sides

9m = 7m + 4

9m - 7m = 4

2m = 4

m = 2

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

check

9 x 2 = 7 x 2 + 4

18 = 18

this answer is good

n + 6 = 2n - 1

n + 7 = 2n

7 = n

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

7 + 6 = 2 x 7 - 1

13 = 13

this answer is good

f of x is equals to 3 - 2 x and g of x is equals to X Minus x square + 1 where x is an element of I have set of numbers find the inverse of G and the value for X for which f of G is equals to g of f​.

Answers

The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x))​ is 1

Calculating the inverse of g(x)

Given that

f(x) = 3 - 2x

Rewrite as

g(x) = -x² + x + 1

Express as vertex form

g(x) = -(x - 0.5)² + 1.25

Express as equation and swap x & y

x = -(y - 0.5)² + 1.25

Make y the subject

y = 0.5 + √(1.25 - x)

So, the inverse is

g⁻¹(x) = 0.5 + √(1.25 - x)

Calculating the value of x

Here, we have

f(g(x)) = g(f(x))​

This means that

f(g(x)) = 3 - 2(-x² + x + 1)

g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1

Using a graphing tool, we have

f(g(x)) = g(f(x))​ when x = 1

Hence, the value of x is 1

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Complete question

f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers

Find the inverse of G and the value for x for which f(g(x)) = g(f(x))​.

how can you convert a given number of fluid ounces to find equivalent number of cups explian

Answers

Step-by-step explanation:

There are 8 fluid ounces in a cup....

   divide the number of ounces by 8 to find the number of cups

# ounces /  8 ounces/cup    =    cups

Write the given third order linear equation as an equivalent system of first order equations with initial values. (t - 2t^2)y' - 4y'" = -2t with y(3) = -2, y'(3) = 2, y"(3) = -3 Use x_1 = y, x_2 = y', and x_3 = y". with initial values If you don't get this in 2 tries, you can get a hint.

Answers

The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.

We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:

x_1 = y

x_2 = y'

x_3 = y''

with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.

The resulting system of equations is:

x_1' = x_2

x_2' = x_3

x_3' = (2t^2 - t)x_2 - 4x_3 + 2t

This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.

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If an excise tax is levied on the suppliers of tobacco, will the incidence fall mostly on consumers or mostly on producers? Will there be a large amount or small amount of deadweight loss? Will tax revenue from the tobacco tax fall or rise?

Answers

As the demand for tobacco is inelastic so the consumers are the group who are less responsive to a higher price as an outcome of it the consumers will have to bear the largest share of the tobacco tax.

This inelasticity of demand will lead to only a small decline in the quantity demanded after the tax have been leived , therefore the deadloss weight will be in really small degree. the percentage increase in price of any amount will overcome a smaller decline in the quantity which eventually would lead to a rise in the tax revenue collection.

Inelasticity of demand refers to the degree to which the quantity demanded of a particular good or service changes in response to a change in its price. When demand is inelastic, a change in price will result in a proportionally smaller change in quantity demanded. This is typically the case for goods or services that are considered necessities or have few substitutes available.

For example, if the price of insulin, a life-saving medication for diabetics, increases by 10%, it is unlikely that the quantity demanded will decrease by 10%. People with diabetes require insulin to manage their condition, and there are few substitutes available, so they are willing to pay a higher price to maintain their health.

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Complete Question: -

Suppose the supply of tobacco is elastic and the demand for tobacco is inelastic. If an excise tax is levied on the suppliers of tobacco, will the incidence fall mostly on consumers or mostly on producers? Will there be a large amount or small amount of deadweight loss? Will tax revenue from the tobacco tax fall or rise?

What is the value of this expression when x = -6 and y=-1/2

Answers

The resultant value of the given expression 4(x²+3)-2y is 157 respectively.

What are expressions?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra.

Here, we refer to these letters as variables.

An expression is a group of words with operators between them.

The equation is the union of two expressions joined by the symbol "equal to" (=).

For instance, 3x-8. Ex: 3x-8 = 16.

So, the value would be:

4(x²+3)-2y

Insert values as follows:

=4((-6)²+3)-2(-1/2)

=4(36+3)+1=157


Therefore, the resultant value of the given expression 4(x²+3)-2y is 157 respectively.

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Complete question:

What is the value of this expression when x= -6 and y= -1/2? 4(x2+3)-2y

Can you guys please help me with this question I think it’s A. but I’m not sure if it’s correct?!PLEASEEE

Answers

Answer:

A is correct

Step-by-step explanation:

Whatever value you put in for "y" will keep both of the equations equal

I’m pretty sure your right.

cindy and tom, working together, can rake the yard in 8 hours. working alone, tom takes twice as long as cindy. how many hours does it take cindy to rake the yard alone?

Answers

Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours

How do we calculate the time it takes Cindy?

To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.

Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.

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In the morning 134 books were checked out from the library.in the afternoon 254 books were checked out and 188 books were checked out in the evening.how many books were checked out in the library that day?

Answers

Answer:

576 books.

Step-by-step explanation:

134+254+188=576 books in total.

Hopefully this helps!

Which of the following are equations of straight lines? Select all that apply. Please keep in mind that for questions like this where there are one or more correct answers, Canvas will deduct points for incorrect selections. yhat = 23 + 4w yhat = 2c +34 yhat = 2h yhat= d2 + 3 yhat = 23r+ 4 yhat=2s + 3t yhat= 3

Answers

The equations of straight lines are \hat{y} = 2h, \hat{y} = 23r + 4 and \hat{y}= 2s + 3t. Option(A),(B) and (F) are correct.

A line in the coordinate plane can be described with the help of a linear equation, that is, an equation that has a first-degree expression, like y = 2x – 3.

There are many ways to put the equation of a line in the form y = mx + b,

where m is the slope and

b is the y-intercept,

but they all require the use of algebraic properties of equations, such as addition, subtraction, multiplication, division, and substitution.

The equations of straight lines among the following are:  \hat{y} = 2h,  \hat{y} = 23r + 4 and \hat{y}= 2s + 3t

Hence, the correct options are:Option A: \hat{y} = 2h , Option B: \hat{y} = 23r + 4  and Option F: \hat{y}= 2s + 3t.

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What is the measure of ∠D? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠D= ° A right triangle B C D. Angle C is marked as a right angle. Side B C is labeled as 25 feet. Side C D is labeled as 45 feet.

Answers

Therefore, the measure of ∠D is approximately 60.96 degrees.

What is measure?

A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.

by the question.

To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:

[tex]tan(∠D) = opposite/adjacent = CD/BC = 45/25[/tex]

Taking the inverse tangent of both sides, we get:

[tex]∠D = tan⁻¹(45/25) = 60.95 degrees[/tex]

Rounding this to the nearest hundredth, we get:

[tex]angleD = 60.95 degrees =60.96 degree.[/tex]

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A function is shown in the box. What is the value of this function for f(-8)?

(Write the answer as an improper fraction in lowest terms.)

Answers

Answer:

f(x) = (5/6)x - (1/4)

f(-8) = (5/6)(-8) - (1/4)

f(-8) = (5/3)(-4) - (1/4)

f(-8) = (-20/3) - (1/4)

f(-8) = (-80-3)/12

f(-8) = -83/12

Construct the first three Fourier approximations to the square wave function f(x) = {1 - pi lessthanorequalto x < 0 -1 0 lessthanorequalto x < pi F_1(x) = -(4/pi)*(sin(x)) F_2(x) = (4/pi)*(sin(x)) F_3(x) = (4/pi)*((sin(x))-(1/3)*(sin(3x)))

Answers

The Fourier series for f(x) is f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...].

The square wave function can be defined as:

f(x) = {1 -π ≤ x < 0

-1 0 ≤ x < π

To find the Fourier series for this function, we first need to determine the coefficients a_n and b_n.

a_n = (1/π) ∫_0^π f(x) cos(nx) dx

= (1/π) ∫_0^π (-1) cos(nx) dx + (1/π) ∫_(-π)^0 cos(nx) dx

= (2/π) ∫_0^π cos(nx) dx

= (2/π) [sin(nπ) - sin(0)]

= 0

b_n = (1/π) ∫_0^π f(x) sin(nx) dx

= (1/π) ∫_0^π (-1) sin(nx) dx + (1/π) ∫_(-π)^0 sin(nx) dx

= -(2/π) ∫_0^π sin(nx) dx

= -(2/π) [cos(nπ) - cos(0)]

= (2/π) [1 - (-1)^n]

Therefore, the Fourier series for f(x) is:

f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...]

To find the first three Fourier approximations, we truncate this series at the third term.

F_1(x) = -(4/π) sin(x)

F_2(x) = (4/π) sin(x) + (4/3π) sin(3x)

F_3(x) = (4/π) sin(x) + (4/3π) sin(3x) - (4/5π) sin(5x)

These are the first three Fourier approximations of the square wave function f(x). The more terms we include in the Fourier series, the closer the approximations will be to the original function.

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a:b=1:6
a:c=3:1
How many times is b bigger than c?

Answers

Answer:

18 times bigger

Step-by-step explanation:

Compute the value of the expression without using a calculator

Answers

Answer:

Using the property of logarithms that says log_a(a^b) = b, we can simplify the expression:

7^(log_7(12)) = 12

Therefore, the value of the expression is 12.

Given that m∠A=​(16​x)°​, m∠C=(8x+20)°​, and m∠D=128°​, what is m∠B

Answers

The value of m∠B is 212 - 24x.

How did we get the value?

The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.

As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.

To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.

Thus,

m∠A + m∠B + m∠C + m∠D = 360

Substituting the given values, we get:

(16x)° + m∠B + (8x+20)° + 128° = 360

Simplifying and solving for m∠B, we get:

m∠B = 360 - (16x)° - (8x+20)° - 128°

m∠B = 212 - 24x

Therefore, the value of m∠B is 212 - 24x.

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Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)a. 81stb. 19thc. 76thd. 24the. 10 th

Answers

The percentiles for the standard normal distribution

a. 0.93

b. -0.88

c. 0.67

d. -0.65

e. -1.28

To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.

The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.

Step 1: Write down the given percentiles as a decimal and round to two decimal places.

For example, for the 81st percentile, 0.81 will be used.

Step 2: Use the standard normal distribution table to find the corresponding z-score.

Step 3: Round off the obtained answer to two decimal places.

a) 81st percentile:

The area to the left of the z-score is 0.81.

The corresponding z-score is 0.93.

Hence, the 81st percentile for the standard normal distribution is 0.93.

b) 19th percentile:

The area to the left of the z-score is 0.19.

The corresponding z-score is -0.88.

Hence, the 19th percentile for the standard normal distribution is -0.88.

c) 76th percentile:

The area to the left of the z-score is 0.76.

The corresponding z-score is 0.67.

Hence, the 76th percentile for the standard normal distribution is 0.67.

d) 24th percentile:

The area to the left of the z-score is 0.24.

The corresponding z-score is -0.65.

Hence, the 24th percentile for the standard normal distribution is -0.65.

e) 10th percentile:

The area to the left of the z-score is 0.10.

The corresponding z-score is -1.28.

Hence, the 10th percentile for the standard normal distribution is -1.28.

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3gh2x4g3h3 help me please

Answers

Answer:

Step-by-step explanation:

To find the product

Its gonna be

12g^4h^5

HHHHEEEEELLLPPPPPP

Solve for x. using the tangent lines.
50 deg
X
x =[?]^

Answers

from the given circle having tangents, the value of x is 130°.

What does a tangent line mean?

A line that touches a curve at one point, y = f(x), is said to be the curve's tangent line. (x0, y0). The point at which it is drawn is substituted into the derivative f'(x) to find its slope (m), and y - y0 = m is used to find its equation. (x - x0).

In geometry, a tangent is a straight line that touches a curve or a surface at a single point, without intersecting it at that point. In the case of a curve, the tangent line at a point on the curve has the same slope as the curve at that point.

In trigonometry, the tangent is a mathematical function that relates the angles of a right triangle to the ratio of the length of the opposite side to the length of the adjacent side.

From the given figure,

We know that

50 + AB = 180

AB = 180 - 50

AB = 130

The value of x or arc AB is 130°.

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the picture pls answer my picture.

Answers

Answer:

$63 more in tax

Step-by-step explanation:

Takis is 5.25 in tax  

PlayStation is 68.25

well, we know the tax is 10.5% so let's get them for both.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]

[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]

A triangle has a side that is 5 inches long that is adjacent to an angle of 61. In addition, the side oppositethe 61 angle is 4,8 inches long. There are two triangles with these measurements. For each one,determine the other two angles of the triangle and the length of the third side..acute:(a) The triangle in which the angle opposite the 5-inch side-The angle between the two given sides measuresnearest tenth of a degree.)The third angle measuresThe remaining side is approximatelyan inch.)(b) The triangle in which the angle opposite the 5-inch side is obtuse:The angle between the two given sides measuresnearest tenth of andegree.)WThe third angle measuresThe remaining side is approximatelyan inch.)degrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)Ainches long. (Round to the nearest tenth ofdegrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)inches long. (Round to the nearest tenth of an inch

Answers

The two remaining angles are 58°, and the length of the third side of the triangle is 6.5 inch.

In order to determine the other two angles of each triangle as well as the length of the third side, we need to use the Cosine Rule. According to the Cosine Rule, for any triangle with sides of length a, b, and c, and angles of A, B, and C, the following equation holds:



[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]



For the first triangle, we are given that the side of length 5 is adjacent to an angle of 61°. Therefore, a = 5, C = 61°. Using the information provided, we can also determine that b = 4.8. Substituting these values into the Cosine Rule equation, we get:



[tex]c^2 = (5)^2 + (4.8)^2 - 2(5)(4.8) cos(61°)[/tex]



We can solve this equation to get c = 6.5. Therefore, the length of the third side in the first triangle is 6.5. Additionally, we can use the Triangle Angle Sum theorem to determine the other two angles. According to this theorem, the sum of the three angles of a triangle is 180°. Therefore, for the first triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.



For the second triangle, we use the same process, but with the given side lengths reversed. That is, we set a = 4.8, b = 5, and C = 61°. Again, substituting these values into the Cosine Rule equation, we get:



[tex]c^2 = (4.8)^2 + (5)^2 - 2(4.8)(5) cos(61°)[/tex]

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the second triangle is also 6.5. We can use the Triangle Angle Sum theorem again to determine the other two angles. Again, for the second triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.



In conclusion, for each triangle, the two remaining angles are 58°, and the length of the third side is 6.5 inch.

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Kelly took three days to travel from City A to City B by automobile. On the first day, Kelly traveled 2/5 of the distance from City A to City B and on the second day, she traveled 2/3 of the remaining distance. Which of the following is equivalent to the fraction of the distance from City A to City B that Kelly traveled on the third day.A) 1−2/5−2/3B) 1−2/5−2/3(2/5)C) 1−2/5−2/5(1−2/3)D) 1−2/5−2/3(1−2/5)E) 1−2/5−2/3(1−2/5−2/3)

Answers

The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).

What is the fraction?

The fraction represents a portion or part of a whole.

There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.

The fractional distance traveled on day one = ²/₅

The remaining fractional distance = ³/₅ (1 - ²/₅)

The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)

The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)

Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.

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4) Ella drives 60 miles per hour. How far will she drive in 2% hours?​

Answers

Answer: 1.2 miles

Step-by-step explanation:

1 hour = 60 min

60 x 0.02 = 1.2         1 minute and 20 seconds has elapsed

60 miles/ every 60 minutes or 1 mile a minute

1 x 1.2 = 1.2

she has traveled 1.2 miles

Answer: The answer is 120 mph (miles per hour)

Step-by-step explanation:

The one thing you need to do is to figure out how many mph did Ella drive for 2 hours.

So, you need to do 60 x 2, and you will get the answer 120.

And there's your answer!

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