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2 years ago

Which of the following graphs shows the solution set to 2x < 6 and 3x + 2 > -4?

Mathematics

1 answer:

Ilya [14]2 years ago

5 0

Answer:

The third picture

Step-by-step explanation:

Solve for x in both equations

2x<6

Divide both sides by 2:

x<3

3x+2>-4

Subtract 2 from both sides:

3x>-6

Divide both sides by 3:

x>-2

There is this trick you can use when x is on the left side of the equation to find out which way to shade in you graph. Keep in mind this is only for the left side, it will not work if your variable is on the right.

When the symbol is facing left < then shade left, imagine it is pointing which way to shade. x<3 is represented by the 3 picture on the left. When the symbol is facing right > then shade right, again it is pointing which way to shade. x>-2 is represented by the 3 picture on the right.

The circles are not filled in because the symbol is < and > rather than $\leq and \geq$ . When it is greater than or equal to or less than and equal to (represented by the line under the symbol), then the circle is shaded in.

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3 years ago

Based on historical data, your manager believes that 41% of the company's orders come from first-time customers. A random sample

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Answer:

The probability that the sample proportion is between 0.35 and 0.5 is 0.7895

Step-by-step explanation:

To calculate the probability that the sample proportion is between 0.35 and 0.5 we need to know the z-scores of the sample proportions 0.35 and 0.5.

z-score of the sample proportion is calculated as

z= $\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }$ where

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p is the proportion of first time customers based on historical data

N is the sample size

For the sample proportion 0.35:

z(0.35)= $\frac{0,35-0.41}{\sqrt{\frac{0.41*0.59}{72} } }$ ≈ -1.035

For the sample proportion 0.5:

z(0.5)= $\frac{0,5-0.41}{\sqrt{\frac{0.41*0.59}{72} } }$ ≈ 1.553

The probabilities for z of being smaller than these z-scores are:

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3 years ago

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wariber [46]

Answer:

First figure: $954cm^3$

Second figure: $1,508yd^3$

Third figure:

Height= q
Side length = r

Fourth figure:  $726cm^3$

Explanation:

A. First figure:

1. Formula:

$\text{Volume of a cylinder}=\pi \times radius^2\times length$

2. Data:

radius = 9cm / 2 = 4.5cm

length = 15 cm

3. Substitute in the formula and compute:

$Volume=\pi \times (4.5cm)^2\times (15cm)\approx 954cm^3\approx 954cm^3$

B. Second figure

1. Formula:

$\text{Volume of a leaned cylinder}=\pi \times radius^2\times height$

2. Data:

radius = 12yd

height = 40 yd

3. Substitute and compute:

$Volume=\pi \times (12yd)^2\times (40yd)\approx 1,507.96yd^3\approx 1,508yd^3$

C) Third figure

a) The height is the segment that goes vertically upward from the center of the base to the apex of the pyramid, i.e. q .

The apex is the point where the three leaned edges intersect each other.

b) The side length is the measure of the edge of the base, i.e. r .

When the base of the pyramid is a square the four edges of the base have the same side length.

D) Fourth figure

1. Formula

The volume of a square pyramide is one third the product of the area of the base (B) and the height H).

$Volume=(1/3)B\times H$

2. Data:

height: H = 18cm

side length of the base: 11 cm

3. Calculations

a) Calculate the area of the base.

The base is a square of side length equal to 11 cm:

$\text{Area of the base}=B=(11cm)^2=121cm^2$

b) Volume of the pyramid:

$Volume=(1/3)B\times H=(1/3)\times 121cm^2\times 18cm=726cm^3$

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