What is the circumference of a circle with a diameter of 8 feet? Use 3.14 for ON d=80 O A. 25.12 ft B. 12.56 ft C. 50.24 ft D. 11.14 ft​

Answer:

8. 8/9 is not the multiplicative inverse of –1⅛

9. 0.3 is the multiplicative inverse of 3⅓

Step-by-step explanation:

To answer the above questions, we must understand the meaning of multiplicative inverse. This is illustrated below:

Let y be the number.

The multiplicative inverse of y denoted by y¯¹ (or 1/y) when multiplied with y will give an identity of 1 i.e

y × y¯¹ = 1

Or

y × 1/y = 1

Now, let us answer the questions given above by calculating the multiplicative inverse.

8. The number (y) = –1⅛ = –9/8

Multiplicative inverse (y¯¹) =?

y × y¯¹ = 1

–9/8 × y¯¹ = 1

Divide both side by –9/8

y¯¹ = 1 ÷ –9/8

y¯¹ = 1 × –8/9

y¯¹ = –8/9

Thus, 8/9 is not the multiplicative inverse of –1⅛

9. The number (y) = 3⅓ = 10/3

Multiplicative inverse (y¯¹) =?

y × y¯¹ = 1

10/3 × y¯¹ = 1

Divide both side by 10/3

y¯¹ = 1 ÷ 10/3

y¯¹ = 1 × 3/10

y¯¹ = 3/10

y¯¹ = 0.3

Thus, 0.3 is the multiplicative inverse of 3⅓.

Answer:

[tex](f\ o\ g)(x) = 3x[/tex]

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

Given

[tex]f(x) = ln(x^2)[/tex]

[tex]g(x)=\sqrt{e^{3x}}[/tex]

Solving (a): (f o g)(x)

This is calculated as:

[tex](f\ o\ g)(x) = f(g(x))[/tex]

We have:

[tex]f(x) = ln(x^2)[/tex]

[tex]f(g(x)) = \ln((g(x))^2)[/tex]

Substitute: [tex]g(x)=\sqrt{e^{3x}}[/tex]

[tex]f(g(x)) = \ln(\sqrt{e^{3x}})^2[/tex]

Evaluate the square

[tex]f(g(x)) = \ln(e^{3x})[/tex]

Using laws of natural logarithm:

[tex]\ln(e^{ax}) = ax[/tex]

So:

[tex]f(g(x)) = \ln(e^{3x})[/tex]

[tex]f(g(x)) = 3x[/tex]

Hence:

[tex](f\ o\ g)(x) = 3x[/tex]

Solving (b): The domain

We have:

[tex]f(g(x)) = 3x[/tex]

The above function has does not have any undefined points and domain constraints.

Hence, the domain is: [tex]-\infty < x < \infty[/tex]

Answer:

0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 34.6, standard deviation of 10.2

This means that [tex]\mu = 34.6, \sigma = 10.2[/tex]

Sample of 36

This means that [tex]n = 36, s = \frac{10.2}{\sqrt{36}} = 1.7[/tex]

What is the probability that the average duration of unemployment was between 30 and 37 weeks?

This is the pvalue of Z when X = 37 subtracted by the pvalue of Z when X = 30.

X = 37

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{37 - 34.6}{1.7}[/tex]

[tex]Z = 1.41[/tex]

[tex]Z = 1.41[/tex] has a pvalue of 0.9207

X = 30

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{30 - 34.6}{1.7}[/tex]

[tex]Z = -2.71[/tex]

[tex]Z = -2.71[/tex] has a pvalue of 0.0034

0.9207 - 0.0034 = 0.9173

0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.

Answer:

A (the first answer)

Step-by-step explanation:

Answer:

y = 12     x = 12√2     z  = 12√3

Step-by-step explanation:

The 45° triangle will also have a height of y so....

    y² + y² = x²          2y²  = x²     y² = x²/2       y = √(x²/2)

The 30°  triangle

    y² + z² = 24²                          y² = 24² - z²          y = √(24² - z²)

sin 30 = y/24          1/2 = y/24      y = 12    

          y² = x²/2

         12² = x²/2²

    2(144)  = x²         x = √(288)       x = 12√2  

      y² + z² = 24²

           z² = 24² - y²

           z² = 24² - 12²

           z² = 576 - 144

            z² = 432      

                =  √(16·9·3)

            z  =  4·3√3

            z  = 12√3

     y² + z² = 24²

    12² + (12√3)² = 24²

    144 + 144·3    =   576

     2y²  = x²

     2(12)²  = x²

      288  =  (12√2)  = 144·2  = 288

Answer:

-7x^2 +9x-ki

Step-by-step explanation:

Answer:

x = 115

Step-by-step explanation:

The chord- chord angle x is half the sum of the arcs intercepted by the angle and its vertical angle, then

x = [tex]\frac{1}{2}[/tex] (145 + 85 ) = 0.5 × 230 = 115

Step-by-step explanation:

answer is 115 you should solve it also your answer will be same

Answer:

Two distinct lines intersecting each other at 90° or a right angle are called perpendicular lines. Here, AB is perpendicular to XY because AB and XY intersect each other at 90°. The two lines are parallel and do not intersect each other. They can never be perpendicular to each other.

Step-by-step explanation:

hope it helps:)

9514 1404 393

Answer:

  a.  -4

Step-by-step explanation:

When using the "diamond method" for factoring quadratics, the bottom number is the coefficient of the linear term. In this quadratic, it is -4.

The bottom number is -4.

Answer:

Step-by-step explanation:

D

Answer:

x > 2

Step-by-step explanation:2 and under

Answer:

what are the statements

Step-by-step explanation:

Answer:

This is an equation.

Step-by-step explanation:

An expression would mean that there is no equal sign, but since there is, that makes it an equation.

Answer:

59.8%

Step-by-step explanation:

599 - 300 = 299. Now we need to find the percentage 299 is of 500.

299 / 500 = 0.598

0.598 as a percent is 59.8%.

Answer: 59.8%

Hope this helps!

Answer:

180km

Step-by-step explanation:

1hour48mins =108mins

108÷18=6

6×30=180km

Answer:

PQ=36

Step-by-step explanation:

If the triangles are similar, then they must have a common ratio between them.

RQ corresponds with CB, so [tex]\frac{84}{18}=\frac{14}{3}[/tex]

If the ratio is [tex]\frac{14}{3}[/tex], then [tex]\frac{168}{\frac{14}{3}}=36[/tex], so PQ=36.

Answer:

1/6

Step-by-step explanation:

To solve this, multiply the denominator by 2, which would be 2x3 which would be 6.

Answer:

B.

[tex] \frac{5}{8} [/tex]

GPS.....................GPS..............................................................................................

Answer:

Step-by-step explanation:

Number of nickels = $1 * 1 nickel/$0.05 = 20 nickels

Thickness of 20 nickels = 20 nickels * 1.95 mm = 39 mm

Let's do the same for the quarters. Each quarter is worth $0.25.

Number of quarters = $1 * 1 quarter/$0.25 = 4 quarters

Thickness of 4 quarters = 4 quarters * 1.75 mm = 7 mm

Find the ratio of the two:

39 mm/7 mm = 5.57

Answer:

The calculated value Z = 1.5950 < 1.96 at 0.05 level of significance

The null hypothesis is accepted at a 0.05 level of significance

The proportion of cell phone owners in that country who have a smartphone has not increased over time

Step-by-step explanation:

Step(i):-

Given that the random sample size 'n' = 934

Given that the population proportion P = 0.51

                                                            Q= 1-P

                                                           Q = 1- 0.51 = 0.49

The sample proportion

                                   [tex]p = \frac{x}{n} = \frac{501}{934} = 0.5364[/tex]

Level of significance = 0.05

Critical value Z₀.₀₅ = 1.96

Step(ii):-

Null hypothesis:  P < 0.51

Alternative Hypothesis : P > 0.51

  Test statistic

                    [tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]

                   [tex]Z = \frac{0.536-0.51}{\sqrt{\frac{0.51 x 0.49}{934} } }[/tex]

                  Z =  1.5950

Final answer:-

Given that P-value 0. 0532

P-value > 0.05

Rejected Alternative Hypothesis and accepted null hypothesis

               ( OR)

The calculated value Z = 1.5950 < 1.96 at 0.05 level of significance

The null hypothesis is accepted at a 0.05 level of significance

The proportion of cell phone owners in that country who have a smartphone has not increased over time

Answer:

Step-by-step explanation:

[tex]sin ~a=\frac{12}{13} ,\frac{\pi}{2} <a<\pi\\a ~is~in~2nd~quadrant.\\sin~b=\frac{3}{5} ,0<b<\frac{\pi}{2} \\b~is~in~1st~quadrant.\\cos~b=\sqrt{1-sin ^2b} \\=\sqrt{1-(\frac{3}{5} )^2} \\=\sqrt{\frac{25-9}{25} } \\=\sqrt{\frac{16}{25} } \\=\frac{4}{5} ,\\cos~a=-\sqrt{1-sin^2 a} \\=-\sqrt{1-(\frac{12}{13} )^2} \\=-\sqrt{\frac{169-144}{169} } \\=-\sqrt{\frac{25}{169} } \\=-\frac{5}{13} \\cos(a-b)=cos~acos~b+sin~a sin~b\\=\frac{-5}{13}* \frac{4}{5} +\frac{12}{13}* \frac{3}{5} \\=?[/tex]

Answer:

The length of each lap around the lake was of 3.3 miles.

Step-by-step explanation:

Given that Josh cycled 8 laps on a bicycle path surrounding a lake, and each lap was the same length, to determine what was the length of each lap around the lake if he cycled a total of 26.4 miles, the following calculation must be performed:

26.4 / 8 = X

3.3 = X

Thus, the length of each lap around the lake was 3.3 miles.

Answer:

10/6 or 5/3

Step-by-step explanation:

1/2 ---> 3/6

1/3 ---> 2/6

5/6 ---> 5/6

Add those new fractions together:

(3/6) + (2/6) + (5/6) = 10/6 or 5/3

Answer:

10/6 or 5/3

Step-by-step explanation:

Hope it help's :)

Answer:

he would have to work 28 hours

Step-by-step explanation:

Answer:

Cole have to work 28 hours

Answer:

the answer is 4.6

Step-by-step explanation:

the explanation is shown in the following attachment below...

hope this helps...

Answer:

Step-by-step explanation:

He eats 1/6 or 1/5 of the original cake.

All  you need to do to get the answer is multiply the denominators.

1/5 * 1/6 = 1/30

If there was something in the numerators. you would multiply them too.

So suppose the two fractions were 3/5 and 2/7

The answer would be 3 * 2 / 5 * 7 = 6 / 35

General rule

When multiplying two fractions, multiply numerator * numerator / (denominator * denominator).