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3 years ago

I need help on number 10 urgently.

Mathematics

2 answers:

grigory [225]3 years ago

6 0

Answer: Option A. 288 cubic inches

uranmaximum [27]3 years ago

4 0

The formula for the volume of a cylinder is

V = π · R² · Height .

The formula for the volume of a sphere is

V = 4/3 · π · R³ .

We know the volume of the cylinder, so let's work with that formula, and see if we can squeeze anything out of it that can help us with the sphere.

Cylinder: V = π · R² · Height .

Wow ! Look at the picture for a second ! The radius of the cylinder is the same as the radius of the sphere, AND the height of the cylinder is double the radius ! This should really help.

Cylinder: V = π · R² · (2R) .

V = π · (2R³)

But we know the volume of the cylinder. It's 432π inch³ .

432π in³ = π · 2R³

Divide each side by 2 :

π R³ = 216 in³

We could use this to find the radius, but why bother ? Why not just keep (π R³) and stuff it straight into the formula for the volume of the sphere ! ?

Sphere: V = 4/3 · (π · R³)

V = 4/3 · (216 in³)

V = (4/3 · 216) in³

V = 288 in³

Ahhh ... the sweet feeling of knowing that you're right !

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When lines intersect in one place, what are they called?

Deffense [45]

Independent
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7 0

3 years ago

Read 2 more answers

M×10-m×2=8 fill in the blanks as m

son4ous [18]

M*10-m*2=8
10m-2m=8
8m=8
Divide both sides by 8:
m=8

Fill in the m's:
1*10-1*2=8
10-2=8
8=8

Hope this helps :)

5 0

3 years ago

Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. assume that σ is known to be 36.8

Delvig [45]

We are given the following data:

Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22

We are to find the confidence intervals for 90%, 95% and 98% confidence level.

Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.

Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.645* \frac{36.8}{ \sqrt{22}}=110.69$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.645* \frac{36.8}{ \sqrt{22}}=136.51$

Thus the 90% confidence interval will be (110.69, 136.51)

Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.96* \frac{36.8}{ \sqrt{22}}=108.22$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.96* \frac{36.8}{ \sqrt{22}}=138.98$

Thus the 95% confidence interval will be (108.22, 138.98)

Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-2.327* \frac{36.8}{ \sqrt{22}}=105.34$
Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+2.327* \frac{36.8}{ \sqrt{22}}=141.86$

Thus the 98% confidence interval will be (105.34, 141.86)

Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)

As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.

3 0

3 years ago

Please help explain how to solve problem 16?

Anarel [89]

Here is the problem.....√(15x + 10) = 2x+3

to remove the square root, we do the opposite which is to square everything.

(√(15x + 10))² = (2x + 3)² (the square negates the square root)
15x + 10 = (2x +3)(2x + 3) (use the distributive property to continue)
15x + 10 = 4x² + 6x + 6x + 9 (combine like terms)
15x + 10 = 4x² + 12x + 9 (subtract 15x and 10 from each side)
-15x - 10 -15x - 10
0 = 4x² - 3x - 1 (factor completely)
(x - 1) (4x + 1) (set each to equal 0)

x - 1 = 0 4x + 1 = 0
x = 1 4x = -1
x = -1/4

place both into the equation to check for reasonableness...we see the negative number is not reasonable, but the x value of 1 is a solution.

answer is 1

4 0

3 years ago

Oliver purchased 11.3 gallons of gasoline. There are approximately 3.8 liters

m_a_m_a [10]

Answer:b

Step-by-step explanation:

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3 years ago