The usual price of a clock was $60. At a sale, it was
sold at a discount of 20%.

a) How much was the discount?
b) Find the selling price of the clock.

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:

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:

what are the statements

Step-by-step explanation:

Answer: Neither

Step-by-step explanation:

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:

-7x^2 +9x-ki

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Slope = (-3 - 2) / (1 - 2) = -5 / -1 = 5

Hi there!

[tex]\large\boxed{\text{slope =} 6}[/tex]

We can calculate slope using the following formula:

[tex]slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Plug in the corresponding points:

[tex]slope = \frac{-9-(-3)}{2-1}[/tex]

Simplify:

[tex]slope = \frac{-6}{1} = -6[/tex]

Answer:

1/6

Step-by-step explanation:

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

Answer:  Jenny was faster by 116.17

Step-by-step explanation: Jenny: 809.03 meters a minute

Johnny: 692.86 meters a minute

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:

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:

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:

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:

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:

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).

Answer:

B.

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

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:

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:

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:

(b). 3.5

(c). 28 cubes

Step-by-step explanation:

Answer:

he would have to work 28 hours

Step-by-step explanation:

Answer:

Cole have to work 28 hours

Answer:

180km

Step-by-step explanation:

1hour48mins =108mins

108÷18=6

6×30=180km

Answer:

A (the first answer)

Step-by-step explanation:

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:

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:

im sure its c

Step-by-step explanation:

:)