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2 years ago

The diameter of the Sun is about 1.4 × 10^6 km. The diameter of Mars is about 7000 km.

Mathematics

2 answers:

Vladimir79 [104]2 years ago

6 0

The answer should be C

Liula [17]2 years ago

4 0

Answer:

C.) 2×10²

Step-by-step explanation:

(Sun dia) / (Mars dia) = (1.4 x 10⁶ km) / (0.7 × 10⁴ km) = (1.4/0.7) × 10²

The ratio of diameters is about 2 × 10².

_____

The applicable rule of exponents is ...

(a^b)/(a^c) = a^(b-c)

The diameter of Mars can be expressed several ways.

7000 = 7×1000 = 0.7×10,000 = 0.7×10⁴

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What is the constant proportionality of 3 cans and 9 balls

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The constant proportionality is whats left over

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3 years ago

Given f(x) = 9-3x and g(x) = - 6x + 3, find (f + g)(x).

disa [49]

Answer:4

Step-by-step explanation:

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3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

Mrs. Carter baked 100 muffins for a bake sale. The muffins were sold in packages of 2. There were 12 muffins left. Write an equa

Sindrei [870]

<u>Answer:</u>

2n + 12 = 100 (Equation)
2n = 88 (Solving)
n = 44 people bought muffins at the bake sale. (Solving)

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

100 muffins, and 2 in each package. Therefore, there are 50 packages. However, in the end, there are 12 left, so there must have been 6 packages left.

5 0

3 years ago

Read 2 more answers

The shop sold 12,789 chocolate and 9,324 cookie dough cones. It sold 1078 more peanut butter cones than cookie dough cones. And

Brut [27]

Answer:

46,303

Step-by-step explanation:

12789+9324+9324+1078+12789+999= 46,303

5 0

3 years ago