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irinina [24]
2 years ago
10

The volume of the right triangular prism is 91.8ft. The height of the prism is 10.8ft. What is the area of each base? Show your

work
Mathematics
1 answer:
kaheart [24]2 years ago
4 0

Answer:

8.5 ft.

Step-by-step explanation:

We'll use this right triangular prism volume formula: base area x height = volume

base area = ?

length = 10.8

volume = 91.8

base area x 10.8 = 91.8

Divide both sides by 10.8

base area x 10.8/10.8 = 91.8/10.8

base area = 8.5

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If (6^2]^p = 6^10, what is the value of p? <br> A.) 2 <br> B.) 3<br> C.) 4<br> D.) 5
kvv77 [185]
If u raise a power to another power, then u multiply the powers. In this case, u can simplify to 6^2p =6^10

Now you have like bases, so you can set the powers equal to each other. So now, 2p=10. Now p=5
5 0
2 years ago
A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has fa
gayaneshka [121]

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) = \dfrac{1}{6}

P (4 | green dice) = \dfrac{3}{6} =\dfrac{1}{2}

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = \dfrac{1}{2}

The probability of two 1's and two 4's in the first dice can be calculated as:

= \begin {pmatrix}  \left \begin{array}{c}4\\2\\ \end{array} \right  \end {pmatrix} \times  \begin {pmatrix} \dfrac{1}{6}  \end {pmatrix}  ^4

= \dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4

= \dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4

= 6 \times ( \dfrac{1}{6})^4

= (\dfrac{1}{6})^3

= \dfrac{1}{216}

The probability of two 1's and two 4's in the second  dice can be calculated as:

= \begin {pmatrix}  \left \begin{array}{c}4\\2\\ \end{array} \right  \end {pmatrix} \times  \begin {pmatrix} \dfrac{1}{6}  \end {pmatrix}  ^2  \times  \begin {pmatrix} \dfrac{3}{6}  \end {pmatrix}  ^2

= \dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times  ( \dfrac{3}{6})^2

= 6 \times ( \dfrac{1}{6})^2 \times  ( \dfrac{3}{6})^2

= ( \dfrac{1}{6}) \times  ( \dfrac{3}{6})^2

= \dfrac{9}{216}

∴

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = \dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}

The probability of two 1's and two 4's in both die = \dfrac{1}{432}  + \dfrac{1}{48}

The probability of two 1's and two 4's in both die = \dfrac{5}{216}

By applying  Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's )  = \dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}

P(second die (green) | two 1's and two 4's )  = \dfrac{0.5 \times 0.04166666667}{0.02314814815}

P(second die (green) | two 1's and two 4's )  = 0.9

Thus; the probability the die chosen was green is 0.9

8 0
3 years ago
Am i right on this math problem?
Minchanka [31]

Answer:

Step-by-step explanation:

8 0
3 years ago
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Marcia sells bracelets. She sells each one for $1.50. This year she spent $32.76 on supplies. At the end of the year, she made $
Marianna [84]

Answer:

$1.5b - $32.76 = $292.74

Step-by-step explanation:

Profit = total revenue - total cost

total revenue = price per unit x total unit of bracelet sold

total revenue = $1.50  x b = $1.50b

b = total units of bracelets sold

total cost = $32.76

$1.5b - $32.76 = $292.74

3 0
3 years ago
In the sequence below, a, = 9. Which of the following would be the correct way to label the 3 in the
zysi [14]

Answer:

Step-by-step explanation:3,9,27,81 because this is multiplication

8 0
3 years ago
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