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3 years ago

Subtraction property of equality

1 answer:

7 0

It tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same.

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Solve 5n – 7p + 3n = 25p for n.

saul85 [17]

5n – 7p + 3n = 25p

Combine like terms

8n - 7p = 25p

Add (7p) to both sides

8n - 7p + 7p = 25p + 7p

Simplifying

8n = 32p

Divide both sides by 8

8n / 8 = 32p / 8

Simplifying

n = 4p

7 0

3 years ago

Read 2 more answers

The volume of a cone is 3πx3 cubic units and its height is x units. Which expression represents the radius of the cone’s base, i

dalvyx [7]

Answer:

Step-by-step explanation:

<u>The Volume of a Cone</u>

The volume of a cone of radius r and height h is:

$\displaystyle V=\frac{1}{3}\pi hr^2$

We are given the volume of a cone is

$V=3\pi x^3$

Equating:

$\displaystyle \frac{1}{3}\pi hr^2=3\pi x^3$

Multiplying by 3:

$\pi hr^2=9\pi x^3$

Simplifying by pi:

$hr^2=9 x^3$

Since h=x:

$xr^2=9 x^3$

Dividing by x:

$r^2=9 x^2$

Taking square roots:

$r=\sqrt{9 x^2}=3x$

Thus: r=3x

5 0

2 years ago

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The lines below are perpendicular if the slope of the solid line is 4 what is the slope of the dashed line

const2013 [10]

Answer:

The slope of the dashed line is $-\frac{1}{4}$

Step-by-step explanation:

Perpendicular lines and slopes:

If two lines are perpendicular, the multiplication of their slopes is -1.

What is the slope of the dashed line

Perpendicular to a line with slope 4, so:

$4m = -1$

$m = -\frac{1}{4}$

The slope of the dashed line is $-\frac{1}{4}$

8 0

2 years ago

A random sample of 100 observations from a quantitative population produced a sample mean of 22.8 and a sample standard deviatio

natima [27]

Answer:

We conclude that the population mean is 24.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 24

Sample mean, $\bar{x}$ = 22.8

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 8.3

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 24\\H_A: \mu \neq 24$

We use Two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{22.8 - 24}{\frac{8.3}{\sqrt{100}} } = -1.44$

We calculate the p-value with the help of standard z table.

P-value = 0.1498

Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.

Now, $z_{critical} \text{ at 0.05 level of significance } = \pm 1.96$

Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.

7 0

2 years ago

The table below shows data for a class's mid-term and final exams:

lina2011 [118]

Mid term :
Q1 = (88 + 85)/2 = 86.5
Q2 = (92 + 95)/2 = 93.5
Q3 = 100
IQR = Q3 - Q1 = 100 - 86.5 = 13.5

final exams :
Q1 = (65 + 78)/2 = 71.5
Q2 = (88 + 82)/2 = 85
Q3 = (95 + 93)/2 = 94
IQR = Q3 - Q1 = 94 - 71.5 = 22.5

so the final exams has the largest IQR

5 0

2 years ago

Read 2 more answers

Subtraction property of equality​

Subtraction property of equality