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MrMuchimi
2 years ago
6

Select the correct answer.

Mathematics
1 answer:
Afina-wow [57]2 years ago
5 0

Answer:

d)\ \frac{81}{m^{7}}

Step-by-step explanation:

(3m^-4)^3(3m^5)

First, simplify (3m^{-4})^3:

(3m^{-4})^3\\\\3^3*m^{-4*3}\\\\27m^{-12}

27m^{-12}*3m^5\\\\27*3 *m^{-12+5}\\\\81m^{-7}\\\\81*\frac{1}{m^{7}} \\\\\frac{81}{m^{7}}

Hope this helps!

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You help your dad build a dog house for your dog. You tell him that it would be easy to build a dog house in the shape of a tent
Effectus [21]
3 feet tall
If it is in the shape of a tent and the floor is 8 feet across half of it cut down the middle would be 4 ft, you create a right triangle and can use the Pythagorean theorem to solve for the height. 5 is the hypotenuse and 4 is a leg.
a^2 + b^2 = c^2
Plug in  the values known
4^2 +b^2 = 5^2
simplify
16+b^2=25
subtract 16 from both sides
b^2=9
take the square root of both sides
b=3 the hight is 3 ft

6 0
3 years ago
Calculate the probability of each of the following events. (a) {at most three lines are in use} .72 Correct: Your answer is corr
andre [41]

Answer:

(a) The Probability that at most three lines are in use is 0.70.

(b) The Probability that fewer than three lines are in use is 0.45.

(c) The Probability that at least three lines are in use is 0.55.

(d) The Probability that between two and five lines, inclusive, are in use is 0.70.

(e) The Probability that between two and four lines, inclusive, are not in use is 0.35.

(f) The Probability that at least four lines are not in use is 0.70.

Step-by-step explanation:

<u>The complete question is: </u>A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.

X    0          1       2       3          4             5               6

P(X)  0.10      0.15      0.20       0.25         0.20      0.05         0.05  

Calculate the probability of each of the following events.

(a) {at most three lines are in use}

(b) {fewer than three lines are in use}  

(c) {at least three lines are in use}  

(d) {between two and five lines, inclusive, are in use}

(e) {between two and four lines, inclusive, are not in use}

(f) {at least four lines are not in use}

Now considering the above probability distribution;

(a) The Probability that at most three lines are in use is given by = P(X \leq 3)

    P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 0.10 + 0.15 + 0.20 + 0.25

                  = 0.70

(b) The Probability that fewer than three lines are in use is given by = P(X < 3)

    P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

                  = 0.10 + 0.15 + 0.20

                  = 0.45

(c) The Probability that at least three lines are in use is given by = P(X \geq 3)

    P(X \geq 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

                  = 0.25 + 0.20 + 0.05 + 0.05

                  = 0.55

(d) The Probability that between two and five lines, inclusive, are in use is given by = P(2 \leq X \leq 5)

    P(2 \leq X \leq 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

                         = 0.20 + 0.25 + 0.20 + 0.05

                         = 0.70

(e) The Probability that between two and four lines, inclusive, are not in use is given by = 1 - P(2 \leq X \leq 4)

    1 - P(2 \leq X \leq 4) = 1 - [P(X = 2) + P(X = 3) + P(X = 4)]

                             = 1 - [0.20 + 0.25 + 0.20]

                             = 1 - 0.65 = 0.35

(f) The Probability that at least four lines are not in use is given by = 1 - Probability that at least four lines are in use = 1 - P(X \geq 4)

    1 - P(X \geq 4) = 1 - [P(X = 4) + P(X = 5) + P(X = 6)]

                       = 1 - [0.20 + 0.05 + 0.05]

                       = 1 - 0.30 = 0.70

5 0
3 years ago
Tina's user ID is a 5-digit number.
Olin [163]

Answer:

98547

Step-by-step explanation:

6 0
2 years ago
The cost, C. of producing coolers, x, is modeled by the equation C = 0.005x2 - 0.3x + 17. How many coolers are
melamori03 [73]

Answer:

66 coolers

Step-by-step explanation:

C = 0.005x² - 0.3x + 17

When C = $19

19 = 0.005x² - 0.3x + 17

19 - 17 = 0.005x² - 0.3x

2 = 0.005x² - 0.3x

0.005x² - 0.3x - 2 = 0

x = -b ± √b² - 4ac / 2a

= -(-0.3) ± √-0.3² - 4*0.005*-2 / 2*0.005

= 0.3 ± √ 0.09 - (-0.04) / 0.01

= 0.3 ± √ 0.09 + 0.04 / 0.01

= 0.3 ± √ 0.13 / 0.01

= 0.3/0.01 ± √0.13/0.01

= 30 ± 0.36/0.01

x = 30 ± 36

x = 30 + 36 or 30 - 36

x = 66 or -6

Number of coolers can not be negative

Therefore, number of coolers produced when the cost is $19

is 66 coolers

3 0
2 years ago
For the function y=x^2+5, find the average rate of change over the interval -2≤x≤6
Ahat [919]
7 - 8 = -1
the rate of change is -1
Hope this is right,
Batgirl12
5 0
3 years ago
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