Complete the final two columns in the following frequency distribution table and then find the percentiles
and percentile ranks requested:
X f cf c%
5 2
4 5
3 6
2 4
1 3

Answer:)Angle FIH and GIE after keeping angle EIH at 140° is 40° while ∠FIG will is the opposite angle of ∠EIH so it will remain the same as 140°.

Step-by-step explanation:We need to intersect both lines and make ∠EIH > 135°

So,Let's keep ∠EIH = 140°

Then,∠FIG = 140° (opposite angle)∠FIH = ∠GIE = x (opposite angle)

Now,The Sum of all angles around I will be 360 degrees.

So,140 + x + 140 +  x = 360 ,2x + 280 = 360, 2x = 80 ⇒ x = 40°.

The expression 3^(3/2) is equal to ²√27. The 4th option is the answer

Index is the power or exponent which is raised to a number or a variable e.g in number 3⁵, 5 is the index of 3. The 3 is called the base. The plural form of index is indices.

The expression 3^(3/2) can be written in form of root and power. That is:

3^(3/2) = ²√3³

3^(3/2) = ²√27

Therefore, the expression 3^(3/2) is equal to ²√27

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Answer:

y intercept is 4

Step-by-step explanation:

Answer:

1. 13

2. 15

Step-by-step explanation:

all you have to do is add and subtract.

Step-by-step explanation:

f(x)=x^2-4x-9

g(x)=-3x-5

so when f(g(x)) that x is a number

-3x-5 equals the number in f(x) so that x is -3x-5

f(-3x-5) and if f(x)=x^2-4x-9

then inserting in -3x-5 for x in f(x) and distrubute

(-3x-5)^2-4(-3x-5)-9

9x^2+42x+36

I hope that helps :)

Answer:

9x^2 + 42x + 16

Step-by-step explanation:

f(g(x))

Plug in the expression for g(x)

f(g(x)) = f(-3x - 5)

f(x) = x^2 - 4x - 9

For every x in f(x) replace it with -3x - 5

f(-3x - 5) = (-3x - 5)^2 - 4(-3x -5) -9

Expand

f(-3x - 5) =  (9x^2 + 30x + 25) + (12x + 20) - 9

Combine like terms

f(-3x - 5) = 9x^2 + 42x + 16

f(g(x)) = 9x^2 + 42x + 16

From greatest to least5.25, 1, 3/4 (or 0.75), -5/2 (or -2.5), -8.345

To sort these numbers from largest to smallest, we must establish a consistent format for swift comparison.

Among the various numbers included are whole figures, fractions and decimals, causing us to mix them uniformly first so that they match— in decimals.

-5/2 = -2.5

5.25 = 5.25 (no alteration required)

1 = 1.0 (to simplify analysis, only adding decimal points)

3/4 = 0.75

-8.345 = -8.345 (essentially unchanged)

At this point, we can effortlessly contrast and compare the numbers.

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Answer:

A 180 degree rotation.

Step-by-step explanation:

I took the quiz.

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Size of the house should be 2900 ft².

Correct option is B.

We have,

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

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complete question:

A house is listed for sale at $235,000, but the listing does not include square

footage of the house. Based on the comps, the line of best fit is

y=0.06x + 60.5. If the price is fair, what size (in square feet) should the house

be?

OA. 2850 ft2

OB. 2900 ft2

OC. 20,000 ft²

OD. 2350 ft²

The quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2  - 20.25.

We are given a quadratic function:

h (x) = x^2 + 3x − 18

We need to rewrite the function by completing the square.

We can see the coefficient of x is 3.

So, we will add and subtract the square of half that.

So, find the square of half of 3, we will get;

(3 / 2)^2 = 9 / 4 = 2.25

add and subtract the square of half of 3 from the given function, we will get;

h(x) = x^2 +3x + -18 2.25 -2.25

arrange the expression, we will get;

h(x) = (x^2 +3x +2.25) -18 -2.25

write the expression in parentheses as a square, and simplify the constant, we will get;

h(x) = (x + 1.5)^2  - 20.25

So, the square function is written as h(x) = (x + 1.5)^2  - 20.25.

Thus, the quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2  - 20.25.

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Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Answer:

122

Step-by-step explanation:

61 x 2 = 122 hope this helps:)

Answer:

113.1

Step-by-step explanation:

The way to find the circle's area is A=πr^2:

The radius is diameter/2, so the radius is 12/2, which is 6

Therefore, A=3.14*6^2 ≈ 113.09734

Now to round to the nearest tenth, it would be 113.1, the final answer.

Answer:

d

Step-by-step explanation:

Answer:

For the first question is 8y, and the second question would be 80

Step-by-step explanation:

The perimeter of a shape is calculated by adding it's sides together, and 2y+2y+2y+2y=8y. If y=10, we can substitute y for 10 in which 8*10 is 80.

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Solution:

Given:

Let the principal invested at 8% rate be x

Let the principal invested at 16% rate be y

Hence, using the simple interest formula;

The relationship between the number of years that Simon's money is invested and the account balance can be described as 4:The relationship is linear. His account increases each year by a constant value of $28.

The simple interest due to Simon's account every year is:
= Simple interest rate x Amount invested

= 0.4% x 7, 000

= $28

This means that every year, Simon's account would increase by a value of $28.

This represents a linear relationship because in linear relationships, the value of the variables increases by a constant amount each year or period.

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The number of tablets that should be taken each day by the patient who needs Synthroid is 1 tablet.

To find the number of tablets of Synthroid that should be taken, you convert the requirements from micrograms ( μg ) to milligrams ( mg).

1 milligram = 1, 000 micrograms ( μg )

25. 0 μg in milligrams is therefore:

= 25 / 1, 000

= 0. 025 mg

This means that the number of tablet to take is:

= Mg requirement / Mg of tablet

= 0. 025 / 0. 025

= 1 tablet

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Answer:

The original cost was $90.

Step-by-step explanation:

"Judy bought a coat at the office of $72, which is 20% off the original price. what was the original cost of the coat?"

Your equation contains an error that will lead to an incorrect answer.

This is the correct way to write the equation.

We don't know the original price, so we let x = the original price.

The discount was 20% off the original price, so the discount is 20% of x.

20% of x is the same as 20% * x = 0.2x. The discount is 0.2x. We now subtract the discount from the original price.

x - 0.2x

She paid the discounted price of x - 0.2x. We are told that amount is $72, so we let our expression of the discounted price equal the discounted price we are told she paid.

x - 0.2x = 72

Now we solve for x, the original price.

x - 0.2x = 72

Combine like terms on the left side.

0.8x = 72

Divide both sides by 0.8

0.8x/0.8 = 72/0.8

x = 90

Answer: The original cost was $90.

P.S.

You must be careful when writing the equation. What you wrote was

x - 20%

on the left side. Notice that 20% is simply equal to 0.2; it is not 20% of the original price. By writing

x - 20% = 72

you are in fact writing

x - 0.2 = 72

meaning that the discount was $0.20

A discount of 20% on $90 is really $18, not $0.20.

There is a big difference there.

If you have any questions, just ask in the comments.

The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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Answer:

77.40

Step-by-step explanation:

Answer:

The expected number of tests necessary for the entire group of 304 people is 180.0325

Step-by-step explanation:

Probability of person being positive = p = 0.04

Probability of person being negative = q = 1-0.04=0.96

Number of people in each group = 19

We will use binomial over here

Probability of no test positive :

\(P(x=0) = ^{19}C_0 (0.04)^0 (0.96)^{19} =0.460419201958\)

P( at least one tests positive) = 1-P( no one tests positive)= 1-0.460419201958= 0.539580798042

Expected number of tests for each group = 1(0.460419201958)+20(0.539580798042) = 11.2520351628

Number of groups =\(\frac{\text{Total population}}{\text{no. of people in each group}}=\frac{304}{19}=16\)

Expected number of tests necessary for the entire group of 304 people:

=\(\text{Expected number of tests for each group} \times \text{No. of groups}\)

=\(11.2520351628 \times 16\)

=180.0325

Hence The expected number of tests necessary for the entire group of 304 people is 180.0325

9514 1404 393

Answer:

Step-by-step explanation:

In scientific notation, the decimal point is placed immediately to the right of the most-significant digit. The exponent of 10 is the number of digits to the right of the most significant digit.

  186,000 mi/s = 1.86×10^5 mi/s

  671,000,000 mi/h = 6.71×10^8 mi/h

Answer:

30

Step-by-step explanation:

is mrs. jones is 40, her son is 10, sum = 50.

ten years before son was 0, mrs. jones was 30

The slope of a line that passes through the points (1,−2) and (2,2) is 4.

The two given points are (1,-2) and (2,2).

We have to find out the slope of the line that passes through the two given points.

We know that the slope of a line passing through two points (\(x_{1} ,y_{1}\)) and (\(x_{2} ,y_{2}\)) is -

\(m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

Using this formula for the given points (1,-2) and (2,2), we can find out the slope of the line passing through them as -

\(m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\= > m = \frac{2-(-2)}{2-1}\\ = > m = \frac{4}{1}\\ = > m = 4\)

Thus, the slope of a line that passes through the points (1,−2) and (2,2) is 4.

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The number of rounds that can be played is given by the product of three

and the least number of tokens a player has at the start.

A round is when the player with the most tokens gives one token to each of the other players, and one placed in the discard pile, we have;

17 - 3 = 14

16 + 1 = 17

15 + 1 = 16

17 - 3 = 14

14 + 1 = 15

16 + 1 = 17

17 - 3 = 14

14 + 1 = 15

15 + 1 = 16

The above values follow a number series such that we have;

4 - 3 = 1

2 + 1 = 3

3 + 1 = 4

4 - 3 = 1

1 + 1 = 2

3 + 1 = 4

4 - 3 = 1

2 + 1 = 3

1 + 1 = 2

3 - 3 = 0

1 + 1 = 2

2 + 1 = 3

3 - 3 = 0

0 + 1 = 1

2 + 1 = 3

3 - 3 = 0

0 + 1 = 1

1 + 1 = 2

Therefore, after the fifteenth three rounds, which is 15 × 3 = 45 rounds Ava runs out of token, ending the game.

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Answer: a rotation 180 degrees about Z’

Step-by-step explanation: I just took the assignment :)

Answer:

a rotation 180 degrees about Z

Step-by-step explanation:

Correct answer on Edg.