1. find x and y 2. find the measure of each side of LMN

Answer:

Option C is the correct option

Step-by-step explanation:

[tex] \frac{x}{3x - 1} \div \frac{x - 2}{2x} [/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \frac{x}{3x - 1} \times \frac{2x}{x - 2} [/tex]

Multiply the fractions

[tex] \frac{2 {x}^{2} }{(3x - 1)(x - 2)} [/tex]

Multiply the parentheses

[tex] \frac{2 {x}^{2} }{3x(x - 2) - 1(x - 2)} [/tex]

[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 6x - x + 2 } [/tex]

Collect like terms

[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 7x + 2 } [/tex]

Hope this helps...

Best regards!!

Answer:

Step-by-step explanation:

In computer programming relational operators are used to check conditions, that is if one conditions matches another and returns true if the condition is met or satisfied.

Answer:

The zeros are x=-3,-2,1

end behavior is one up one down

Step-by-step explanation:

The zeros are x=-3,-2,1

The end behaviors are one up one down because the function is of degree 3 meaning it is odd function and has opposite end directions.

Answer:

Step-by-step explanation:

There is no algebraic way to solve such an equation. It can be simplified to ...

  [tex]-2x-6=-2^x-6\\\\2x-2^x=0\qquad\text{add $2x+6$}[/tex]

This has solutions at x=1 and x=2 as shown in the attached graph.

__

The second attachment shows the functions graphed on the same graph.

Answer: 14384 ways

Step-by-step explanation:

With 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:

E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.

The marble arrangements are: (7,0,0,0) in 4!/3! = 4 ways, (6,1,0,0) in 4!/2! = 12 ways, (5,2,0,0) in 4!/2! = 12 ways, (5,1,1,0) in 4!/2! = 12 ways, (4,3,0,0) in 4!/2! = 12 ways, (4,2,1,0) in 4! = 24 ways, (4,1,1,1) in 4!/3! = 4 ways, (3,3,1,0) in 4!/2! = 12 ways, (3,2,2,0) in 4!/2! = 12 ways, (3,2,1,1) in 4!/2! = 12 ways, (2,2,2,1) in 4!/3! = 4 ways.

Total of ways = 4+12+12+12+12+24+4+12+12+12+4 = 120 as previously determined above for identical marbles and distinct jars.

Taking into account distinct colored marbles, the number of ways of marble distribution into 4 jars becomes as follows:

For (7,0,0,0) = 4*(7!/7!) =4. For (6,1,0,0) = 12*[7!/(6!)(1!)] = 84. For (5,2,0,0) =

12*[7!/(5!)(2!)] = 252. For (5,1,1,0) = 12*[7!/(5!)(1!)(1!)] = 504. For (4,3,0,0) =

12*[7!/(4!)(3!)] = 420. for (4,2,1,0) = 24*[7!/(4!)(2!)(1!)] = 2,520. For (4,1,1,1) =

4*7!/(4!)(1!)(1!)(1!)] = 840. For (3,3,1,0) = 12*]7!/(3!)(3!)(1!) = 1,680. For (3,2,20) = 12*]7!/(3!)(2!)(2!) = 2,520. For (3,2,1,1) = 12*]7!/(3!)(2!)(1!)(1!) = 5,040. For (2,2,2,1) = 4*]7!/(2!)(2!)(2!)(1!) = 2,520.

Total of ways as requested for distinct colored marbles and distinct jars = 4+84+252+504+420+2,520+840+1,680+2,520+5,040+2,520 = 14,384.

Answer:

If [tex]r >> h[/tex], the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

[tex]A = \pi \cdot r^{2} + 2\pi\cdot s[/tex]

Where:

[tex]r[/tex] - Base radius of the cone, measured in inches.

[tex]s[/tex] - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

[tex]s = \sqrt{r^{2}+h^{2}}[/tex]

Where [tex]h[/tex] is the altitude of the cone, measured in inches. If [tex]r >> h[/tex], then:

[tex]s \approx r[/tex]

And:

[tex]A = \pi\cdot r^{2} +2\pi\cdot r[/tex]

Given that [tex]A = 1885.7143\,in^{2}[/tex], the following second-order polynomial is obtained:

[tex]\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2} = 0[/tex]

Roots can be found by the Quadratic Formula:

[tex]r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}[/tex]

[tex]r_{1,2} \approx -1\,in \pm 24.521\,in[/tex]

[tex]r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in[/tex]

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

Complete Question:

Which statement about the following equation is true?

[tex]2x^2-9x+2 = -1[/tex]

A) The discriminant is less than 0, so there are two real roots

B) The discriminant is less than 0, so there are two complex roots

C) The discriminant is greater than 0, so there are two real roots

D) The discriminant is greater than 0, so there are two complex roots

Answer:

C) The discriminant is greater than 0, so there are two real roots

Step-by-step explanation:

The given equation is [tex]2x^2-9x+2 = -1[/tex] which by simplification becomes

[tex]2x^2 - 9x + 3 = 0[/tex]

For a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex], the discriminant is given by the equation, [tex]D = b^2 - 4ac[/tex]

If the discriminant D is greater than 0, the roots are real and different

If the discriminant D is equal to 0, the roots are real and equal

If the discriminant D is less than 0, the roots are imaginary

For the quadratic equation under consideration, a = 2, b = -9, c = 3

Let us calculate the discriminant D

D = (-9)² - 4(2)(3)

D = 81 - 24

D = 57

Since the Discriminant D is greater than 0, the roots are real and different.

Answer:

Step-by-step explanation:

C) The discriminant is greater than 0, so there are two real roots

The answer is 3,240

Explanation:

To calculate the total income tax, it is necessary to calculate what is the 15% of 8000, and 17% for the remaining money, which is 12.000 (20,000 - 8,000= 12,000). Considering the statement specifies the 15% is paid for the first 8,000 and from this, the 17% is paid. Now to know the percentages you can use a simple rule of three, by considering 8000 and 12000 as the 100%. The process is shown below:

1. Write the values

[tex]8000 = 100[/tex]

[tex]x = 15[/tex] (the percentage you want to know)

2. Use cross multiplication

[tex]x =\frac{8000 x 15 }{100}[/tex]

[tex]x = 1200[/tex]

This means for the first 8000 the money Rafael needs to pay is 1,200

Now, let's repeat the process for the remaining money (12,000)

[tex]12000 = 100\\\\[/tex]

[tex]x = 17[/tex]

[tex]x = \frac{12000 x 17}{100}[/tex]

[tex]x = 2040[/tex]

Finally, add the two values [tex]1200 + 2040 = 3240[/tex]

Answer:

29.4 degrees

Step-by-step explanation:

i divided sin by 55 degrees

Answer: t = 10

Step-by-step explanation:m

 Given that; n₁ = 10, n₂ = 10

ж₁ = 50, ж₂ = 30

Sˣ₁ = 20, Sˣ₂ = 20

Now using TEST STATISTICS

t = (ж₁ - ж₂) / √ ( Sˣ₁/n₁ + Sˣ₂/n₂ )

so we substitute our figures

t = ( 50 - 30 ) / √ ( 20/10 + 20/10 )

t = 20 / √4

t = 10

Answer:

There are many combinations based on the number you chose to subtract from both sides.

Step-by-step explanation:

Let the number be x.

According to the question,

3 x+7 > 4 x

We get, 3 x+1=4 x-6, after subtracting 6 from both sides.

3 x+1=4 x-6

4 x- 3 x=6+1

x=7

You will get the same answer if you subtract 3 x or 7 or any other number from both sides.

Thank you!

We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.

4(5+3) = 2(22-6)

4(8) = 2(16)

32 = 32

Once you finish distributing each side, you can check to see if it is equal on both sides.

In our case it is since they both equal 32 after distributing the terms.

Answer:

{58.02007 , 61.97993]

Step-by-step explanation:

Data are given in the question

Sample of cars = n = 121

Average speed = sample mean = 60

Standard deviation = sd = 11

And we assume

95% confidence t-score = 1.97993

Therefore

Confidence interval is

[tex]= [60 - \frac{1.97993 \times 11}{\sqrt{121} }] , [60 + \frac{1.97993 \times 11}{\sqrt{121} }][/tex]

=  {58.02007 , 61.97993]

Basically we applied the above formula to determine the confidence interval

Answer:

A perfect square

Answer:

square

Step-by-step explanation:

An example of a perfect square is 9.

9 squared is 3.

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The  standard deviation is  [tex]\sigma = 2.45[/tex]  

Step-by-step explanation:

From the given data we can compute the expected mean for each random values as follows

          [tex]E(X) = \sum [ X * P(X = x )]\\\\ X \ \ \ \ \ \ X* P(X =x )\\ 0 \ \ \ \ \ \ \ \ \ \ 0* 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2 * 0.3 = 0.6 \\ 4 \ \ \ \ \ \ \ \ \ \ 4 * 0.2 = 0.8\\ 6 \ \ \ \ \ \ \ \ \ \ 6* 0.1 = 0.6[/tex]

So  

          [tex]E(x) = 0 + 0.6 + 0.8 + 0.6[/tex]

          [tex]E(x) = 2[/tex]

The  

             [tex]E(X^2) = \sum [ X^2 * P(X = x )]\\\\ X \ \ \ \ \ \ \ \ \ \ X^2 * P(X=x ) \\ 0 \ \ \ \ \ \ \ \ \ \ 0^2 * 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2^2 * 0.3 = 12 \\ 4 \ \ \ \ \ \ \ \ \ \ 4^2 * 0.2 = 3.2 \\ 6 \ \ \ \ \ \ \ \ \ \ 6^2 * 0.1 = 3.6[/tex]

So  

        [tex]E(X^2) = 0 + 1.2 + 3.2 + 3.6[/tex]

        [tex]E(X^2) = 8[/tex]

Now  the variance is  mathematically evaluated as

         [tex]Var (X) = E(X^2 ) -[E(X]^2[/tex]

Substituting value  

        [tex]Var (X) = 8-4[/tex]

        [tex]Var (X) = 6[/tex]

The standard deviation is mathematically evaluated as

       [tex]\sigma = \sqrt{Var(x)}[/tex]

      [tex]\sigma = \sqrt{4}[/tex]

      [tex]\sigma = 2[/tex]

Answer:

The likelihood is [tex]P(X < 25.2) = 0.91668[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 24.7 \ years[/tex]

      The standard deviation is  [tex]\sigma = 2.8 \ years[/tex]

      The sample size is [tex]n = 60 \ men[/tex]

       The  consider random value is  x =  25.2  years

Given that mean age is normally distributed, the likelihood that the age when they were first married is less than x is mathematically represented as

          [tex]P(X < x) = P( \frac{X - \mu }{\sigma_{\= x }} < \frac{x - \mu }{\sigma_{\= x }} )[/tex]

Generally  [tex]\frac{X - \mu }{ \sigma_{\= x}} = Z (The \ standardized \ value \ of \ X )[/tex]

So

      [tex]P(X < x) = P(Z< \frac{x - \mu }{\sigma_{\= x }} )[/tex]

Where [tex]\sigma_{\= x }[/tex] is the standard error of the sample mean which mathematically evaluated as

       [tex]\sigma_{\= x } = \frac{ \sigma }{\sqrt{n} }[/tex]

substituting values

      [tex]\sigma_{\= x } = \frac{ 2.8 }{\sqrt{ 60 } }[/tex]

      [tex]\sigma_{\= x } = 0.3615[/tex]

So  

     [tex]P(X < 25.2) = P(Z< \frac{ 25.2 - 24.7 }{0.3615} )[/tex]

     [tex]P(X < 25.2) = P(Z< 1.3831 )[/tex]

From z-table the value for  P(Z<    1.3831  ) is [tex]P(Z < 1.3831 ) = 0.91668[/tex]

  So

        [tex]P(X < 25.2) = 0.91668[/tex]

Answer:

Answer:

The  probability is  [tex]P(J|B) = 0.36[/tex]

Step-by-step explanation:

B =business

J=jumbo

Or =ordinary

From the question we are told that  

     The proportion of the passenger on business in the ordinary jet  is [tex]P(B| Or) = 0.25[/tex]

     The proportion of the passenger on business in the jumbo jet  is  [tex]P(B|J) = 0.30[/tex]

     The  proportion of the passenger on jumbo jets is  [tex]P(j) = 0.40[/tex]

      The   proportion of the passenger on ordinary jets is evaluated as

         [tex]1 - P(J) = 1- 0.40 = 0.60[/tex]

According to  Bayer's theorem the probability a randomly chosen business customer flying with Global is on a jumbo jet is mathematically represented as

        [tex]P(J|B) = \frac{P(J) * P(B|J)}{P(J ) * P(B|J) + P(Or ) * P(B|Or)}[/tex]

substituting values

         [tex]P(J|B) = \frac{ 0.4 * 0.25}{0.4 * 0.25 + 0.6 * 0.3}[/tex]

         [tex]P(J|B) = 0.36[/tex]

Step-by-step explanation:

Answer:

The Hudson Record Store

1. As a fraction, discount rate = $3/$18 = 0.167

2. As a percentage, discount rate = 16.67%

3. Selling price during 2nd week = $13.50

4. The rate of the new selling price to the old is $13.50/$18 = 75%

Step-by-step explanation:

Selling price of CDs = $18

1st Week, sold CDs at $15

Discount = $3 ($18 - $15)

As a fraction, discount rate = $3/$18 = 0.167

As a percentage, discount rate = 16.67%

2nd Week, sold CDs at $13.50 ($18 - (25% of $18))

Discount = $4.50 ($18 - $13.50)

Price during the second week of the sale = $13.50

The rate of discount = $4.50/$18 = 25%

Answer:

18

Step-by-step explanation:

since you want the difference in scores, you want to take the absolute value of the difference

9 - (-9) = 9+9 = 18

The difference in scores between Player A and Player B is 18.

The difference between two numbers is found by subtracting the smaller number from the greater number.

We are informed that Player A finished first in a tournament at a golf club with a score of −9 or nine strokes under par. Tied for 46th place was player B, with a score of +9, or 9 strokes over par.

We are asked for the difference in scores between Player A and Player B.

The score of Player A = -9.

The score of Player B = 9

Since Player B's score > Player A's score,

To calculate the difference in their scores, we subtract player A's score from player B's score.

∴ Difference = 9 - (-9)

or,  Difference = 9 + 9

Difference = 18.

∴ The difference in scores between Player A and Player B is 18.

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Answer: Experimental probability.

Step-by-step explanation:

This starts as "based on past experience."

So we can suppose that this estimation is obtained by looking at the mean of the number of guests on the past N weekday evenings. (With N a large number, as larger is N, more data points we have, and a better estimation can be made)

Then, this would be an experimental probability, because it is obtained by repeating an experiment (counting the number of guests on weekday evenings) and using that information to make an estimation.

Answer:

x = - 4, y = 7

Step-by-step explanation:

Given the 2 equations

- 7x - 2y = 14 → (1)

6x + 6y = 18 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate the y- term

- 21x - 6y = 42 → (3)

Add (2) and (3) term by term to eliminate y

- 15x = 60 ( divide both sides by 15 )

x = - 4

Substitute x = - 4 into either of the 2 equations and evaluate for y

Substituting into (2)

6(- 4) + 6y = 18

- 24 + 6y = 18 ( add 24 to both sides )

6y = 42 ( divide both sides by 6 )

y = 7

Answer:

1 ): 3x-2y=-1,-x+2y=3 (1,2)

2): 4x-3y=-1 , -3x+4y=6       (2,3)

3x+6y=6, 2x+4y=-4 ( no solution)

-3x+6y=-3, 5x-10y=5 infinite

Step-by-step explanation:

4x-3y=-1

-3x+4y=6  ( multiply first by 3 and second equation by 4)

12x-9y=-3

-12x+16y=24 subtract

7y=21

y=21/7=3

x=2, y=3 (2,3)

3x-2y=-1

-x+2y=3

solve by addition/elimination ( same as other equation):

multiply second equation by 3

3x-2y=-1

-3x+6y=9

4y=8

y=2

x=1

3x+6y=6, 2x+4y=-4 ( no solution)

-3x+6y=-3, 5x-10y=5 infinite

Answer:

true

Step-by-step explanation:

Answer:

~0.3158

Step-by-step explanation:

Number of even numbers in the range of 1 - 38 is 38/2 = 19

=> P(E) = 19/38 = 1/2

Having: 38 = 3 x 12 + 2, then the number of numbers that is a multiple of 3 in the range of 1 - 38 is 12

=> P(M) = 12/38 = 6/19

Having: 38 = 6 x 6 + 2, then the number of numbers that is a multiple of 6 (or multiple of 2 and 3) is 6

=> P(E and M) = 6/38 = 3/19

Applying the conditional probability formula:

P(M|E) = P(E and M)/P(E) = (3/19)/(1/2) = 6/19 = ~0.3158

Answer:

7/9

Step-by-step explanation:

P(blue or odd) = P(blue) + P(odd) − P(blue and odd)

P(blue or odd) = 4/9 + 5/9 − 2/9

P(blue or odd) = 7/9

Alternatively:

P(blue or odd) = 1 − P(not blue and not odd)

P(blue or odd) = 1 − 2/9

P(blue or odd) = 7/9

Answer: 7299, 7301

Step-by-step explanation:

x + x + 2= 14,600

2x = 14,598

x = 7,299

Therefore, the office numbers are 7299 and 7301

Answer:

Don

Step-by-step explanation:

1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

David says he has 2/3 of a line length left, while Wear says he has 11/16 of a length left.

Convert the fraction numbers 2/3 and 11/16 into the decimal number. Then we have

2/3 = 0.6667

11/16 = 0.6875

The decimal number 0.6875 is greater than 0.6667. Then the fraction number 11/16 is greater than the fraction number 2/3.

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

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Answer:

The 95% confidence interval for the mean score, , of all students taking the test is

        [tex]28.37< L\ 30.63[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is [tex]n = 59[/tex]

    The mean score is  [tex]\= x = 29.5[/tex]

     The standard deviation [tex]\sigma = 5.2[/tex]

Generally the standard deviation of mean is mathematically represented as

                [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]

             [tex]\sigma _{\= x} = 0.677[/tex]

The degree of freedom is mathematically represented as

          [tex]df = n - 1[/tex]

substituting values

        [tex]df = 59 -1[/tex]

        [tex]df = 58[/tex]

Given that the confidence interval is 95%  then the level of significance is mathematically represented as

         [tex]\alpha = 100 -95[/tex]

        [tex]\alpha =[/tex]5%

        [tex]\alpha = 0.05[/tex]

Now the critical value at  this significance level and degree of freedom is

       [tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]

Obtained from the critical value table  

    So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as

      [tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]

substituting value

      [tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]

       [tex]28.37< L\ 30.63[/tex]

Answer: (-2,-7)

Step-by-step explanation:

A function f(x-c) , where c>0 , represents the horizontal shift of original function to the right c units.

The function f(x-c) is going to add c to the x value, while keeping the y value the same.

Similarly,

The function f(x-5) is going to add 5 to the x value, while keeping the y value the same.

So, the corresponding point to (-7,-7) on f(x-5) = (-7+5,-7)

= (-2,-7)

hence, the corresponding point to (-7,-7) on f(x-5)  =  (-2,-7)

Answer:

a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

b) The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Step-by-step explanation:

Step(i):-

Sample size 'n' =75

Mean of the sample x⁻ = 17.8

standard deviation of the sample (S) = 5.9

Mean of the Population = 15

Null hypothesis:H₀:μ = 15 years

Alternative Hypothesis :H₁:μ≠15 years

Step(ii):-

Test statistic

                         [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

                        [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]

                    t = 4.111

Degrees of freedom

ν = n-1 = 75-1=74

t₀.₀₂₅ = 1.9925

The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

P-value:-

The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years