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mestny
5 days ago
7

An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid h

as base lengths of x and 2 x, and a height of x. The distance between the 2 trapezoid bases is 20. The vertical height of the prism is 10. Which expression represents the volume of the prism? 10x3 cubic units 15x2 cubic units 20x3 cubic units 30x2 cubic units
Mathematics
1 answer:
Svet_ta [9.4K]5 days ago
5 0

Response:

Volume of the trapezoidal prism = 15x^2 cubic units

Detailed explanation:

First, let’s calculate the area of the trapezoidal bases.

The lengths of the parallel sides are x and 2x, averaging to 1.5x.

The height stands at x

Consequently, area of the trapezoidal base comes out to be 1.5x * x = 1.5x^2

The volume of this prism is computed as area of the base multiplied by height

(the length is not a factor, but height certainly is)

Thus, 1.5x^2 * 10 yields 15x^2

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Each 16-ounce serving contains 330 mg of caffeine. For 8-ounce servings:
330 mg divided by 2 equals 165 mg.
The limit for caffeine intake is capped at 600 mg.
Calculating for three servings: 165 mg * 3 = 495 mg, which is under the limit.
Calculating for four servings: 165 mg * 4 = 660 mg, exceeding the maximum amount.
Thus, a person can consume 3 full 8-ounce servings daily while remaining within the safety limit.
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23 days ago
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Miguel buys a large bottle and a small bottle of juice. The amount of juice that the manufacturer puts in the large bottle is a
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Pr(X>1540.2) = 0.0655. Step-by-step explanation: The expected value indicated for the large bottle is E(Large) = 1016, and for the small bottle, E(small) = 510. This leads to an expected total E(total) = 1016 + 510 = 1526. The new mean calculated is thus 1526. To find the standard deviation, we derive the variance of each bottle. The variance for the large bottle is v(large) = 8^2 = 64, while for the small bottle it's v(small) = 5^2 = 25. Hence, the total variance is v(total) = 64+25 = 89, resulting in a new standard deviation sd(new) = sqrt(89) = 9.434. To find the probability, we compute using the new mean and standard deviation. The z score is derived as z = (x - mean)/sd = (1540.2 - 1526)/9.434 = 1.505. Looking up this z score gives P(z<1.51) = 0.9345. Consequently, for x > 1540.2, we have P(z > 1.51) = 1 - 0.9345 = 0.0655.
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10 days ago
Two window washers start at the heights shown. (A: 21 ft high rising 8 in per second. The other is 50 feet high descending 11inc
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To address this problem, let's start by formulating the general motion equation along the vertical direction.

This gives us:

h = \frac {1} {2} gt ^ 2 + vo * t + h0

Where,

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  • vo: initial velocity
  • h0: starting height

For the first individual:

h1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21

For the second individual:

h2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

When both individuals reach the identical altitude, the following holds:

h1 = h2\\

\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

Rearranging results in:

\frac {8} {12} * t + 21 = - \frac {11} {12} * t + 50

\frac {8} {12} * t + \frac {11} {12} * t = 50 - 21

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Solving for time:

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Result:

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6 0
1 month ago
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A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue b
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Answer:

The likelihood of selecting a blue block is 7/11.

Step-by-step explanation:

To find the probability of selecting a blue block,

Odds:

The odds of a given event is the ratio of the probability of that event occurring to the probability of its absence. This means it compares favorable outcomes to those that are unfavorably likely.

The odds of not selecting a blue block being 4/7 means that out of 11 scenarios, there will be 4 occasions when the block is not blue, and 7 when it is blue.

Thus, the probability of not selecting the blue block is 4/11.

Probability of selecting the blue block is the complement of 4/11 which equals 7/11.

(b) Amanda plays a role-playing game with her friends. She will roll dice to decide if her character accesses a treasure chest. The chance of her character unlocking this chest is 13/20. Determine the odds in favor of her character unlocking the treasure chest.

Answer:

The odds in favor of her character unlocking the treasure chest equal 13/7.

Step-by-step explanation:

The probability of Amanda's character unlocking the treasure chest is given as 13/20.

This indicates that in a total of 20 chances, there will be 13 instances where the character successfully opens the treasure chest, while the remaining 7 times, they will not succeed.

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Unfavorable outcomes: 7

Consequently, the odds in favor of her character unlocking the treasure chest are 13/7.

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Answer:

Step-by-step explanation:

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\vec{i}\times \vec{j}=\vec{k}

\vec{j}\times \vec{k}=\vec{i}

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(a) \left [ \left ( \hat{i}+\hat{j}\right )\times \hat{i}\right ]\times \hat{j}

=\left [ \hat{i}\times \hat{i}+\hat{j}\times \hat{i}\right ]\times \hat{j}

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=0+\hat{i}+\hat{i}-0

=2\hat{i}

6 0
1 month ago
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