Find the median of the table below. NUMBER OF ¡NCHES 20 22 24 26 FREQUENCY 3 2 1 3

Simplify negative 2 and 1 over 9 – negative 4 and 1 over 3.

Ugo [173]

Answer:

The correct answer is

$2\frac{2}{9}$

Step-by-step explanation:

Method 1

We want to simplify,

$-2\frac{1}{9} -(-4\frac{1}{3})$

The double negatives becomes positive,

$=-2\frac{1}{9} +4\frac{1}{3}$

We now add the whole number parts and the fractions separately

$=-2+4-\frac{1}{9} +\frac{1}{3}$

This will give us,

$=2-\frac{1}{9} +\frac{1}{3}$

The least common denominator for the fractional parts is 9.

$=2+\frac{-1+3\times1}{9}$

$=2+\frac{-1+3}{9}$

$=2+\frac{2}{9}$

$=2\frac{2}{9}$

Method 2

We want to simplify,

$-2\frac{1}{9} -(-4\frac{1}{3})$

The double negatives becomes positive,

$=-2\frac{1}{9} +4\frac{1}{3}$

We first convert the mixed numbers to improper fractions to obtain,

$=-\frac{2\times9+1}{9} +\frac{4\times3+1}{3}$

We carry out the multiplication in the numerator to get,

$=-\frac{18+1}{9} +\frac{12+1}{3}$

We add in the numerator to get,

$=-\frac{19}{9} +\frac{13}{3}$

The least common denominator is $9$ .

$=\frac{-19+13\times3}{9}$

$=\frac{-19+39}{9}$

$=\frac{20}{9}$

We convert back to mixed numbers to get,

$=2\frac{2}{9}$

4 0

3 years ago

Certain items are purchased jointly. If each person pays 8 coins, the surplus is 3 coins, and if each person gives 7 coins, the

Karo-lina-s [1.5K]

Answer:

7 people purchase the items and they used 53 coins

Step-by-step explanation:

Let x represent the number of people.

Let y be the number of coins needed to purchase the items.

If each person pays 8 coins, the surplus is 3 coins. This is illustrated below:

8x = y + 3 (1)

if each person gives 7 coins, the deficiency is 4 coins. This is illustrated below:

7x = y — 4 (2)

Solving by elimination method: subtract equation(2) from equation (1). This is illustrated below:

8x = y + 3 (1)

— (7x = y — 4) (2)

x = 7.

Next, Substituting the value of x into any of the equation to obtain y. In this case I will be using equation 1 as illustrated below:

8x = y + 3 (1)

8(7) = y + 3

56 = y + 3

Collect like terms

y = 56 — 3

y = 53

Therefore, 7 people purchase the items and they used 53 coins

7 0

3 years ago

Azarai is looking to purchase a new pair of basketball shorts costing $40. The New Jersey state tax rate is 7.5 percent. What fi

ratelena [41]

Answer:

$43.00

Step-by-step explanation:

final price = marked price + tax

= marked price + (tax rate) · (marked price)

= (marked pric) · (1 + tax rate)

= $40.00 · 1.075

= $43.00

7 0

4 years ago

4) The line -3x + 4y = 8 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

Dimas [21]

Answer:

4) The linear equation which could represent its image is y = $\frac{3}{4}$ x + 8 ⇒ (2)

5) The equation of the image of the line is y = $\frac{3}{2}$ x - 3 ⇒ (4)

Step-by-step explanation:

Dilation does not change the slope of a line but changes the y-intercept

Dilation of a line segment is longer or shorter by ratio that equal to the scale factor of dilation

4)

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b its y-intercept

Let us put the given equation in the slope-intercept form to find its slope

∵ The line -3x + 4y = 8 is transformed by a dilation centered at

the origin

- Add 3x to both sides

∴ 4y = 3x + 8

- Divide both sides by 4

∴ y = $\frac{3}{4}$ x + 2 ⇒ the equation of the line before dilation

- By comparing it with the form above, then m = $\frac{3}{4}$ , so the

equation after dilation has the same slope

∵ The slope of the line before dilation is $\frac{3}{4}$

∴ The slope of the line after dilation is $\frac{3}{4}$

∵ The equation that has the slope $\frac{3}{4}$ is y =

∴ The equation of the image of the line is y = $\frac{3}{4}$ x + 8

The linear equation which could represent its image is y = $\frac{3}{4}$ x + 8

5)

∵ The equation of the line is y = $\frac{3}{2}$ x - 4

∵ The scale factor of dilation is $\frac{3}{4}$

- Dilation dose not change the slope of the line

∴ The slope of the image after dilation is $\frac{3}{2}$

- Dilation changes the y-intercept, to find it multiply the scale

factor of dilation by the y-intercept of the line before dilation

∵ The y-intercept of the line is (0 , -4)

- Multiply it by $\frac{3}{4}$

∵ $\frac{3}{4}$ × -4 = -3

∴ The y-intercept of the image is (0 , -3)

∴ The equation of the image of the line is y = $\frac{3}{2}$ x - 3

3 0

3 years ago

Write a recursive formula for the arithmetic sequence below. What is the value of the 8th term?

Bumek [7]

To find the answer,

Multiply the term with 4 then subtract with 3

Lets take the term as 'n'

Formula = 4n-3

Value of 8th term = (4*8)-3
= 32-3
= 29

The value of 8th term is 29

4 0

4 years ago

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Find the median of the table below. NUMBER OF ¡NCHES 20 22 24 26 FREQUENCY 3 2 1 3​

Find the median of the table below. NUMBER OF ¡NCHES 20 22 24 26 FREQUENCY 3 2 1 3