1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Stolb23 [73]
1 year ago
5

Find the volume of the composite figure.First, find the volume of the cylinder.Use 3.14 for it.CylinderVolume = [?] cm9 cm9 cmCu

be6 cmVolume = [ ]cm4 cmTotal Volume ofComposite Figure = [] cm3=9 cm

Mathematics
1 answer:
skad [1K]1 year ago
6 0

Solution

- The question gives us a composite figure made up of a cylinder and a cube.

- We are required to find the volume of the cylinder and the cube and then use the results to find the volume of the composite figure.

- The formulas needed for this calculation are:

\begin{gathered} Volume\text{ of Cylinder}=\pi\times r^2\times h \\ where, \\ r=radius\text{ of the cylinder} \\ h=height\text{ of the cylinder} \\  \\ Volume\text{ of Cube}=l^3 \\ where, \\ l=dimension\text{ of the cube} \\  \\ Volume\text{ of Composite figure}=Volume\text{ of Cylinder }+Volume\text{ of Cube} \\  \end{gathered}

- With the information above, we can proceed to solve the question

Volume of the Cylinder:

\begin{gathered} V=\pi\times r^2\times h \\ r=\frac{6}{2}=3\text{  \lparen Since 6cm is the diameter of the cylinder\rparen} \\ h=4 \\  \\ \therefore V=\pi\times3^2\times4 \\  \\ V=36\pi cm^3 \end{gathered}

Volume of Cube:

\begin{gathered} V=l^3 \\ l=9 \\ \therefore V=9^3=729cm^3 \end{gathered}

Volume of Composite Figure:

\begin{gathered} V=36\pi+729 \\ use\text{ }\pi=3.14 \\  \\ V=36\left(3.14\right)+729 \\  \\ V=842.04cm^3 \end{gathered}

Final Answer

The volume of the composite shape is 842.04 cm³

You might be interested in
If you want to create a perfect curve, which tool would be most helpful?
luda_lava [24]
The most usfull tool would be a compas
4 0
3 years ago
Read 2 more answers
For f(x) = 2x – 3 find f(-1/4)
Firdavs [7]

9514 1404 393

Answer:

  -3 1/2

Step-by-step explanation:

Put the argument where the variable is and do the arithmetic.

  f(-1/4) = 2(-1/4) -3 = -1/2 -3

  f(-1/4) = -(3 1/2)

5 0
3 years ago
An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberr
Sliva [168]

Answer:

A) Option B is correct.

H₀: μ₁ = μ₂

Hₐ: μ₁ - μ₂ < 0

B) t = -2.502

p-value = 0.0112

C) Option A is correct.

Reject H₀. The data suggests that cola has a higher average compression strength than the strawberry drink.

D) Option A is correct.

The distributions of compression strengths are approximately normal.

Step-by-step explanation:

The complete Question is presented in the two attached images to this answer.

A) To perform this test we first define the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to test if the extra carbonation of cola results in a higher average compression strength. That is, that cola has a higher average compression strength than the strawberry drink.

Hence, the null hypothesis would be that there isn't significant evidence to suggest that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

The alternative hypothesis is that there is significant evidence to suggest that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

Mathematically, if the average compression strength of strawberry drink is μ₁, the average compression strength of cola is μ₂ and the difference in compression strengths is μ = μ₁ - μ₂

The null hypothesis is represented as

H₀: μ = 0 or μ₁ = μ₂

The alternative hypothesis is represented as

Hₐ: μ < 0 or μ₁ - μ₂ < 0

B) So, to perform this test, we need to compute the test statistic

Test statistic for 2 sample mean data is given as

Test statistic = (μ₁ - μ₂))/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = average compression strength of strawberry drink = 537

n₁ = sample size of the sample of strawberry drink in cans surveyed = 10

s₁ = standard deviation of the compression strength of strawberry drink in cans surveyed= 22

μ₂ = average compression strength of cola = 559

n₂ = sample size of the sample of cola in cans surveyed = 10

s₂ = standard deviation of the compression strength of strawberry drink in cans surveyed = 17

σ = [(17²/10) + (22²/10)] = 77.5903160379 = 8.792

We will use the t-distribution as no information on population standard deviation is provided

t = (537 - 559) ÷ 8.792

= -2.502 = -2.50

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n₁ + n₂ - 2 = 10 + 10- 2 = 18

Significance level = 0.05

The hypothesis test uses a one-tailed condition because we're testing in only one direction (whether compression strength of cola in can is greater).

p-value (for t = -2.50, at 0.05 significance level, df = 18, with a one tailed condition) = 0.011154 = 0.0112 to 4 d.p.

C) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.0112

0.0112 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis accept the alternative hypothesis & say that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

D) The necessary conditions required before a t-test is deemed valid include.

- The samples used must be a random sample of the population distribution with each variable in the sample independent of other one.

- The distribution of the population where the samples were extracted from must be normal or approximately normal to ensure some degree of normality for the samples.

Hence, the necessary assumption for this t-test among the options is that the distributions of compression strengths are approximately normal.

Hope this Helps!!!

7 0
3 years ago
The measure of angle θ is 7pi/4 . The measure of its reference angle is *Blank* °, and tan θ is *blank*
sukhopar [10]

Since the measure of angle \Theta is \frac{7\Pi }{4}

The measure of its reference angle = \frac{7\times 180^{\circ}}{4}

==315^{\circ}

Now we have to compute the value of \tan \Theta

\tan \Theta = \tan \frac{7\Pi }{4}

= \tan (2\Pi -\frac{\Pi }{4})

The value of ((2\Pi -\frac{\Pi }{4})) lies in the fourth quadrant. In fourth quadrant, the value of tan is always negative.

So, \tan (2\Pi -\frac{\Pi }{4})

= -\tan (\frac{\Pi }{4})

= -1.

5 0
3 years ago
What is the mathematical sentence of "A number increasd by 7 is 15?
svet-max [94.6K]

Answer:

B

Step-by-step explanation:

A number increased by 7 means, 7 was added to the number and the result is 15

6 0
2 years ago
Other questions:
  • Two car-rental agencies are competing for business. Mertz charges $35 a day and $0.15 per mile, and Mavis charges $20 a day and
    13·1 answer
  • Is eight a multiple of 8
    7·2 answers
  • What is the exterior angle of 20-gon
    14·1 answer
  • Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a t
    14·1 answer
  • Which choice could be the equation of a line parallel to the line represented by this equation? y=7/4x - 6
    6·1 answer
  • Solve for the variable: 3.5x=32.2 <br> What’s the variable?
    14·1 answer
  • What is the simplified value of the expression below? One-third divided by two-thirds 0 One-third One-half 1
    13·2 answers
  • The Nelson family lives in a town where there is a swim club. At the beginning of the summer, they pay a membership fee of $40 a
    15·1 answer
  • Evaluate the function<br> Find f(2)<br> f(2) =
    11·1 answer
  • Express the following as percentage 9/20​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!