Right triangles and trigonometry

The option (A) 63 inches to 81 inches is correct after using the empirical Rule.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

We have:

The mean height of the population is 72 inches and the standard deviation is 3 inches, 99.7% of the population will have a height

99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean.

The lower range = 72 – 3(3) = 63 inches

The upper range = 72 + 3(3) = 81 inches

Thus, the option (A) 63 inches to 81 inches is correct after using the empirical Rule.

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Answer:

Step-by-step explanation:

1[tex]\frac{1}{2}[/tex]=1×[tex]\frac{2}{2}[/tex], +[tex]\frac{1}{2}[/tex]

(-[tex]\frac{3}{2}[/tex])÷[tex]\frac{3}{4}[/tex]×(-[tex]\frac{2}{3}[/tex])

[tex]\frac{3}{2}[/tex]×[tex]\frac{4}{3}[/tex]×[tex]\frac{2}{3}[/tex]

[tex]\frac{1}{2}[/tex]×4×[tex]\frac{1}{3}[/tex]

4×[tex]\frac{1}{3}[/tex]=[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]

=[tex]\frac{4}{3}[/tex]

Answer:

lol

Step-by-step explanation:

To write 28 + 24 as a product of two factors, we need to determine the HCF of the addends (28 and 24). This can be done by listing the factors of the addends. The greatest factor that is common in 28 and 24 is the HCF.

If the number is in bolded text, the number is a common factor.

Since 4 > 2 > 1, the HCF is 4.

Now, let us put the provided expression between parentheses.

Finally, factor four out of the expression, as it is the GCF of 28 and 24.

Therefore, 28 + 24 as a product of two factors is 4(7 + 6).

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The possible number represented by the 9 counter is 27

The counters are given as:

12 counters and 15 counters

When added, we get a number that can be represented by 9 counters.

This means that:

12 + 15 = 9x

Evaluate the sum

27 = 9x

Divide by 9

x = 3

When subtracted, you need more than 9 counters.

This means that:

x = 15 - 12 = 3

So, we conclude that the number is a multiple of 3 and 9

In other words, the decimal number is a multiple of 9 (i.e. 27)

Hence, the possible number is 27

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Answer:

I would edit this answer and tell you what I hope would be the correct answer if you give me the problem you are confused with

Step-by-step explanation:

I can't help you otherwise

Sorry

Answer: C ≈ 25.1

Step-by-step explanation:

      The circumference of a circle can be found with the following formula. We will plug in the diameter given, and solve.

C = dπ

C = (8)π

C ≈ 25.1

a) Line AE, and Line BC are parallel

b) Line ED, and Line CD

c) 3

Step-by-step explanation:

Answer:

Graph D

Step-by-step explanation:

Graph D is the graph of -2x + y < 5

Since the variable x is the numerator of the fraction, we first need to multiply each side by 6, since the denominator is 6. After doing this, the equation should now look like this: [tex]18 = x + 31[/tex]. Next, we subtract 31 from 18 following the rule. 18 - 31 = -13. x is equal to -13.

For shown work in order:

[tex](6) 3 = x +31[/tex]

[tex]18 = x + 31[/tex]

[tex]18 - 31 = x[/tex]

[tex]x = -13[/tex]

The names of this polygon include:

The polygon given has three sides which means that it is a triangle. It is an acute triangle because the angles are all less than 90°.

It is also a scalene triangle because all the sides have different lengths from each other.

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Answer:

Step-by-step explanation:

I: acute triangle

L: Isosceles triange

(sorry if im wrong i have not done this in a good few years lol)

Answer:

C) 26

Simplify using the FOIL method--used to multiply binomials--and then combine real and imaginary parts of the problem.

5 × 5 = 25 + positive 1(i) = 26

Answer:

option c, 26

Step-by-step explanation:

(5 + i)(5 - i)

Apply complex arithmetic rule: (a + bi)(a - bi) = a^2 + b^2

a = 5, b =1

(5)^2 + (1)^2

(5)^2 = 25

(1)^2 = 1

25 + 1

A rectangular fence is to a total perimeter of 200 feet. If the length is twice the width, find the measurements of the length and width of the rectangular fence.

In this question we are provided with the perimeter of a rectangle fence that is 200 feet. It is also given that the length of the fence is twice its breadth. We are asked to calculate it's dimensions.

First we will form an equation.

Let us assume the breadth as x

Then, length = 2x

It is given that the perimeter is 200 feet.

We know,

[tex] \bull \: \small\boxed{ \rm{ Perimeter_{(rectangle)} = 2(length + breadth)}}[/tex]

Substituting the values we get

[tex] \small\sf{ 200 = 2(2x + x)}[/tex]

Now we will solve this equation and find out the value of x.

[tex] \small\sf{ 200 = 2(2x + x)}[/tex]

[tex] \longmapsto \small\rm{ 200 = 2(3x )}[/tex]

[tex] \longmapsto \small\rm{200 = 6x} [/tex]

[tex] \longmapsto \small\rm{ \dfrac{ \cancel{200} \: \: 33.33}{ \cancel{6}} = x } [/tex]

[tex] \small\sf{x = 33.33} [/tex]

We will substitute the value of x = 33.33.

Length = 2x = 2 × 33.33 = 66.66 feet

Breadth = x = 33.33 feet

Answer:

Step-by-step explanation:

Area of a triangle is a*b divided by 2

Lets assume a = 8 and b= 9

8 *

9=72

72/2=36

Answer:

15%

Step-by-step explanation:

Percent increase in the original price of jacket = 15%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Original price of jacket = $110

Increased price of jacket = $126.5

Increased amount = $126.5 - $110

                               = $16.5

Increased amount in percentage = ($16.5/$110) × 100

                                                       = 0.15 × 100

                                                       = 15%

Hence, 15% is increase in the original price of jacket.

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Answer: The formula for area of a triangle is area equals base times height divided by 2. the height is 5 units.

Step-by-step explanation:

Answer:

[tex]0 \leqslant x \leqslant 20[/tex]

Answer:

8 and 48

Step-by-step explanation:

Here is how to find it mathematically

x = one number     6x = other number    ( because 3x is 1/2 of x)

(x + 6x) /2 = 28

7x = 56

x = 8     then 6x = 48

Step-by-step explanation:

If you agree that increasing age (for elementary school children) causes increasing foot size, and therefore increasing shoe size, then you expect a correlation between age and shoe size. Correlation is symmetric, so shoe size and age are correlated.

Answer:

The value of the rational expression when x = -3 is undefined.

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Rational Functions

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \frac{x}{x^2 - 9} ,\ x = -3[/tex]

Step 2: Find Value

∴ since we can't divide by 0, our rational expression when x = -3 will have to be undefined.

___

Topic: Algebra II

Based on the longitudes of Quito and Singapore, the shortest distance between the two areas is 19,702.5 km .

Because both cities are close to the equator, you use the longitudinal difference method to find the shortest distance.

First find the difference in longitudes:

= Singapore - Quito

= 104 - (-78.5) because Quito is west

= 104 + 78.5

= 182.5°

Then subtract this from 360°:
= 360 - 182.5

= 177.5°

Every 1° longitude along the Equator is 111 km so the shortest distance is:

= 177.5 x 111

= 19,702.5 km

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Answer:

y = 5x-17

Step-by-step explanation:

point slope form would be

y- -2   =  5(x-3)        or  re-arrange to:    y = 5x -17

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

[tex] log_{4}x = k \\ \\ \longrightarrow \: log_{4}x = log_{2 {}^{2} }x \\ \\ \longrightarrow \: 2 log_{2}x \\ \\ now , \\ \\ log_{2}x = k \\ \\ \therefore \: 2( log_{2}x) = 2(k) \\ \\ \longrightarrow \: 2k[/tex]

hope helpful ~

Answer:

see attached image

Step-by-step explanation:

Answer:

B. None of these

Step-by-step explanation:

There are a total of 12 coins in your pocket.

The probability of drawing a nickel first is 5/12

Since you return the coin, the total number of coins in your pocket doesn't change.

The probability of drawing a dime second is 7/12

Since this is a compound probability problem, multiply the two probabilities together.

5/12 x 7/12 = 35/144

35/144  = 0.243

Answer:

The answer should be $1127.74

The expression that can be use to find the difference between the fraction of money Amar put in the bank and the fraction he spent on the book is 4 / 7 x - 1 / 3 x

Amar put 4/7 of the money he earned raking leaves in the bank. Therefore,

let the money she earned = x

Hence,

amount put in bank = 4 / 7 x

She spent 1 / 3 of the money on books. Therefore,

money spent on books = 1 / 3 x

Therefore, the expression that can be use to find the difference between the fraction of money Amar put in the bank and the fraction he spent on the book is as follow:

4 / 7 x - 1 / 3 x

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