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3 years ago

X 12 = 6 10 give your answer as an improper fraction in its simplest form.

Mathematics

1 answer:

Alika [10]3 years ago

3 0

Answer:

41/6

Step-by-step explanation:

Take the root of both sides and solve.

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"There are 15 questions on an exam. In how many ways can the exam be answered with exactly 8 answers correct?"

erastovalidia [21]

Answer:

The exam can be answered with exactly 8 answers correct in 6435 ways.

Step-by-step explanation:

The order is not important.

For example, answering correctly the questions 1,2,3,4,5,6,7,8 is the same outcome as answering 2,1,3,4,5,6,7,8. So we use the combinations formula to solve this problem.

Combinations formula:

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

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

"There are 15 questions on an exam. In how many ways can the exam be answered with exactly 8 answers correct?"

Combinations of 8 questions from a set of 15. So

$C_{15,8} = \frac{15!}{8!(15-8)!} = 6435$

The exam can be answered with exactly 8 answers correct in 6435 ways.

5 0

3 years ago

Let the abbreviation PSLT stand for the percent of the gross family income that goes into paying state and local taxes. Suppose

gavmur [86]

Answer:

Number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.

Step-by-step explanation:

We are given that one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000.

If sigma equals 2.0, we have to find that how many families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5.

Here, we will use the concept of Margin of error as the statement "true mean PSLT within 0.5" represents the margin of error we want.

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<u>SO, Margin of error formula is given by;</u>

Margin of error = $Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }$

where, $\alpha$ = significance level = 10%

$\sigma$ = standard deviation = 2.0

n = number of families

Now, in the z table the critical value of x at 5% ( $\frac{0.10}{2} = 0.05$ ) level of significance is 1.645.

SO, Margin of error = $Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }$

0.5 = $1.645 \times \frac{2}{\sqrt{n} }$

$\sqrt{n} =\frac{2\times 1.645 }{0.5}$

$\sqrt{n} =6.58$

n = $6.58^{2}$

= 43.3 ≈ 43

Therefore, number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.

4 0

3 years ago

Use the given information to find the length of a circular arc. Round to two decimal places.the arc of a circle of radius 11 inc

sattari [20]

Answer:

The length of the circular arc is 8.64 inches

Step-by-step explanation:

Length of circular arc (L) = central angle/360° × 2πr

central angle = pie/4 = 45°, r (radius) = 11 inches

L = 45°/360° × 2 × 3.142 × 11 = 8.64 inches (to two decimal places)

7 0

3 years ago