Multiple choice/ please help!!!

What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi

Sphinxa [80]

Answer:

$15,000\:\mathrm{mm^3}$

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by $V=s^2\cdot h$ , where $s$ is the base length and $h$ is the height. Substituting given values, we have: $V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}$

The volume of a trapezoidal prism is given by $V=\frac{b_1+b_2}{2}\cdot l\cdot h$ , where $b_1$ and $b_2$ are bases of the trapezoid, $l$ is the length of the height of the trapezoid and $h$ is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ( $\frac{b_1+b_2}{2}$ ) multiplied by the trapezoid's height ( $l$ ).

Substituting given values, we get:

$V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}$

Therefore, the total volume of the composite figure is $5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}$ (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

$V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark$

8 0

3 years ago

Solve 4 + 2 sinx= 14-8 sinx for 0° ≤ x ≤ 180

Oduvanchick [21]

<h2>Answer:</h2>

<u>x= 90°</u>.

<h2>Step-by-step explanation:</h2>

<h3>1. Write the expression.</h3>

$4 + 2 sin(x)= 14-8 sin(x)$

<h3>2. Subtract "4" from both sides of the equation.</h3>

$-4+4 + 2 sin(x)= 14-8 sin(x)-4\\ \\2 sin(x)= 10-8 sin(x)$

<h3>3. Add "8sin(x)" to both sides of the equation.</h3>

$2 sin(x)+8 sin(x)= 10-8 sin(x)+8 sin(x)\\ \\10 sin(x)= 10$

<h3>4. Divide both sides by 10.</h3>

$\frac{10 sin(x)}{10} = \frac{10}{10} \\ \\sin(x)=1$

<h3>5. Apply the arcsin of sin^-1 to both sides of the equation.</h3>

$arcsin(sin(x))=arcsin(1)\\ \\x=90$

<h3>6. Conclude.</h3>

<u>x= 90°</u>.

3 0

2 years ago

URGENT DUE BY 1:00 FOR MY FINAL GRADE PLEASE HELP OR I WILL FAIL SEMESTER WILL RATE GOOD THX BLESS YOU!!!!

Lesechka [4]

F(x) = 3x + 11
Is the function used to show this.

when you know this, you are able to do the following:
f(10) = 30 + 11 = $41
That would be the allowance of the 10th week.

The question, however wants the total.

This again, can be done like this:
f(1) + f(2) + f(3) + f(4) + f(5) + f(6) + f(7) + f(8) + f(9) + f(10) = $275 :)
14 + 17 + 20 + 23 + 26 + 29 + 32 + 35 + 38 + 41 = $275

Sure there is a better formula, but i couldnt seem to make it, sorry.

HUGE UPDATE: The sum is $275 not 200..

3 0

3 years ago

Read 2 more answers

Pschological tests are often used to determine the hostility levels in people. High scores on the HLT pschological test correspo

algol13

Answer: the correct answer is we are 95% confident that there is no statistically significant difference in the mean treatment methods for hostility.

Step-by-step explanation:

1) Test for the equality of variances in the two groups to choose the appropriate t-test.

H0: σ (1)^2 = σ (2)^2

Ha: σ (1)^2 ≠ σ (2)^2

Larger variance = 64

Smaller variance = 49

F = 1.30612

Degrees of freedom 15 and 9

Critical F from the table (with alpha=0.05) = 2.58

Calculated F is smaller than critical F, so we use the pooled variance t-test.

Sample 1 size 7

Sample 2 size 8

Sample 1 mean 79

Sample 2 mean 84

Sample 1 S.D. 7

Sample 2 S.D. 8

Pooled S.D = [(n1-1)s1^2+(n2-1)s2^2]/(n1+n2-2)

Pooled variance s = [(6)(49)+(7)(64))] / (13) = (294+448)/13=742/13=57.076923

Pooled variance s^2 = 57.076923

Standard error of difference in means = sqrt(1/n1+1/n2) times sqrt(s^2)

Standard error of difference in means = (0.517549)(7.554927) = 3.910046 (denominator of t)

Confidence interval = (mean1-mean2) +/- t SE

t is the critical t with 24 degrees of freedom = 2.056

(79 - 84) +/- (2.056) (3.910046)

= (-13.04, 3.04)

Interval encloses 0

We are 95% confident that there is no statistically significant difference in the mean treatment methods for hostility.

4 0

3 years ago

A piggy bank contains a total of 84 coins in nickels and quarters worth $12.80.

Kitty [74]

Let's make a system of equations to solve for this:

n + q = 84

0.05n + 0.25q = 12.80

where n = nickels and q = quarters.

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Solve for n in the first equation by subtracting q from both sides.

n = 84 - q

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Plug n into the second equation.

0.05(84 - q) + 0.25q = 12.80

Distribute 0.05 inside the parentheses.

4.2 - 0.05q + 0.25q = 12.80

Combine like terms.

4.2 + 0.2q = 12.80

Subtract 4.2 from both sides.

0.2q = 8.6

Divide both sides by 0.2.

q = 43

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Plug 43 for q in the first equation.

n + (43) = 84

Subtract 43 from both sides.

n = 41

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There are 41 nickels and 43 quarters in the piggy bank. ✅

8 0

3 years ago