solve the system by substitution......

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:

A (the first answer)

Step-by-step explanation:

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).

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

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:

the answer is 4.6

Step-by-step explanation:

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

hope this helps...

Answer:

1/6

Step-by-step explanation:

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

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:

180km

Step-by-step explanation:

1hour48mins =108mins

108÷18=6

6×30=180km

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:

-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:

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:

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:)

Answer:

what are the statements

Step-by-step explanation:

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:

he would have to work 28 hours

Step-by-step explanation:

Answer:

Cole have to work 28 hours

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:

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:

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.

Solution :

A logical expression may be defined as those equation or expression which is either viable or inviable.

In the context, translating each statement into a logical expression using the predicates, the quantifiers, and the logical connectives.

Let P(x) be the propositional function "x is perfect"

Let F(x) be the propositional function "x is your friend"

And the domain is all the people

a). No one is perfect

     [tex]$\forall \ x \rightharpoondown P(x)$[/tex]

b). Not everyone is perfect.

     [tex]$\rightharpoondown \forall \ x\ P(x)$[/tex]

c). All your friends are perfect.

    [tex]$\forall \ x (F(x)\rightarrow P(x))$[/tex]

d). At least one of your friends is perfect.

   [tex]$\exists \ x \ (F(x) \wedge P(x))$[/tex]

e) Everyone is your friend and is perfect.

    [tex]$\forall \ x \ F(x) \wedge \ \forall \ x \ P(x)$[/tex]

f). Not everybody is your friend or someone is not perfect.

    [tex]$(\rightharpoondown \ \forall \ x \ F(x) ) \ \wedge (\exists \ x \ \rightharpoondown \ A (x))$[/tex]

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:

B.

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

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:

1436.8 in³

Step-by-step explanation:

Volume of sphere = (4/3)πr³

r = 7

---> (4/3)π(7)³ = 1436.8 in³

Have a great day :)

Answer:

The volume of the sphere is A.

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]