Which inequality represents all the solutions of 8(6x - 7) < 5(9x - 4)?
A. x> 12
B. x< 12
C. x> 20
D. x < 20

Answer:

18

Step-by-step explanation:

3x+1=55

(alternate angle theorem)

3x=55-1

3x=54

x=54/3

x=18

Answer:

d

Step-by-step explanation:

3x + 1 and 55 are alternate angles and congruent, thus

3x + 1 = 55 ( subtract 1 from both sides )

3x = 54 ( divide both sides by 3 )

x = 18 → d

Angle 2 is the same as the given angle of 70 degrees so we can solve for y:

4y-30 = 70

Add 30 to both sides:

4y = 100

Divide both sides by 4:

Y = 25

Angle 1 and angle two are supplementary angles and when added together need to equal 180:

We know angle 2 = 70, so angle 1 must equal 180-70 = 110

2x + 10 = 110

Subtract 10 from both sides:

2x = 100

Divide both sides by 2:

X = 50

The answer is:

X = 50, y = 25

If you look at the figure, the angle marked red is equal to 70° because vertical angles are equal. So, that also means that the opposite angle 2 is also 70°. So, the first equation is:

70 = 5x + y

Next, the green angle as marked is equal to

Green angle = 180 - 70 = 110

Being vertical angles, angle 1 is then equal to 110°. So,the second equation is

110 = 5x + 3y

Subtract the two equations:

   5x + y = 70

-  5x + 3y = 110

________________

          -3y = -40

             y = -40/-3 = 13.33°

Substituting y to either one of the equations,

5x + 13.33 = 70

Solving for x,

x = 11.33°

Answer:

17x

Step-by-step explanation:

Combine terms with like variables. Like terms are terms with the same amount of variables as well as the same variable. Combine their coefficients:

20x - 4x = 16x

16x + (1)x = 17x

17x is your answer.

~

Answer:

17x

Step-by-step explanation:

20x-4x = 16x

16x + x = 17x

17x

Answer:

118°

Step-by-step explanation:

Line b is a perpendicular bisector so 90°+28°=118°

Answer:

B, C, and E

Step-by-step explanation:

A is incorrect because 4 is in it twice, D is wrong because 14 is also there twice, F is wrong because there are two y-points on a single x-poiny.

Answer:

the answer is 64 because you need to multiply all of them together to get the cubic volume. first you multiply 8 x 4 and that leaves you with 32. 32 x 2 is 64 and there are no numbers left to that means 64 is the cubic volume.

Answer:

12 in

Step-by-step explanation:

15^2 = 9^2 + h^2

225-81 =h^2

h^2 = 144

h = 12 inches

Answer:

They will play again together in 84 days, on October 10, only if it is the year 2029.

Step-by-step explanation:

I used the mode of the least common denominator. Hope this helps!

Answer:

When a question like this shows up, i suggest you do the following:

Check if the variable squared is less than or equal to.

IF so, take the square root of the number greater than or equal to x.

In this case,  root 36 is 6, so any value equal to and below 6 works.

Answer:

Christopher Columbus introduced horses, sugar plants, and disease to the New World, while facilitating the introduction of New World commodities like sugar, tobacco, chocolate, and potatoes to the Old World. The process by which commodities, people, and diseases crossed the Atlantic is known as the Columbian Exchange.

Answer:

See below

Step-by-step explanation:

Answer:

a

[tex]0.0028  < p_1 - p_2  < 0.0288[/tex]

b

The  interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack  and the non-Vioxx users (the placebo group  ) who suffered from heart attack  lie within the interval

The  use of Vioxx drug should be stopped

Step-by-step explanation:

From the question we are told that

   The sample size for Vioxx users is  [tex]n_1 = 3025[/tex]

   The second sample size for placebo is  [tex]n_2 =  2875[/tex]

   The number of Vioxx users that suffered heart attack is  [tex]k  = 334[/tex]

     The number of non-Vioxx users that suffered heart attack is  [tex]g  = 272[/tex]

    Generally the  sample proportion for Vioxx users is mathematically represented as

      [tex]\r p_1 =  \frac{k}{n_1}[/tex]

=>   [tex]\r p_1 =  \frac{334}{3025}[/tex]

=>   [tex]\r p_1 =  0.11041 [/tex]

    Generally the  sample proportion for placebo users is mathematically represented as

       [tex]\r p_2 =  \frac{g}{n_2}[/tex]

=>   [tex]\r p_2 =  \frac{272}{2875}[/tex]

=>   [tex]\r p_2 =  0.09461 [/tex]  

Generally the confidence level is 90% , then the level of significance is  [tex]\alpha =  (100-90)\%[/tex]

=>   [tex]\alpha =  0.10[/tex]

Generally the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  is  

     [tex]Z_{\frac{\alpha }{2} } =  1.645[/tex]

Generally the standard error is mathematically represented as

      [tex]SE =  \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }[/tex]

=>  [tex]SE =  \sqrt{\frac{0.11041 (1- 0.11041)}{3025} + \frac{0.09461 (1-0.09461)}{2875} }[/tex]

=>  [tex]SE = 0.0079[/tex]

Generally the margin of error is mathematically represented as

    [tex] E=  Z_{\frac{\alpha }{2} } *  SE[/tex]

=>  [tex] E=  1.645  *  0.0079[/tex]  

=>  [tex] E=  0.013[/tex]  

Generally the 90%  confidence interval is mathematically represented as

     [tex]0.11041 - 0.09461- 0.013 < p_1 - p_2  < 0.11041 - 0.09461+ 0.013 [/tex]

=>       [tex]0.0028  < p_1 - p_2  < 0.0288[/tex]

The  interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack  and the non-Vioxx users (the placebo group  )  lie within the interval

Looking at the interval we see that proportion of Vioxx users who suffered is  more compared to  non-Vioxx users (the placebo group  )[i.e the both limit of the interval is  positive ] hence the  use of Vioxx drug should be stopped

Answer: The answer is B, 23,483

Step-by-step explanation:

If you multiply 23,000 times 1.021 you get 23,483. Your welcome

The Lily's estimate population in 8 years is 187864.

It is required to find the population in 8 years.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

The function f(x)= 23,000(1.021) X( power) to model the future annual population growth of the city.

According to given question we have,

To put x= 8 years

Lily's estimate population in 8 years are

f(x)= 23,000*(1.021) *8

f(x)= 187864

Therefore, the Lily's estimate population in 8 years is 187864.

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Answer:

1.1102 * 10^4

Step-by-step explanation:

11102

= 1.1102 * 10^4

Answer:

14

Step-by-step explanation:

The base two number one one one zero is equal to one times eight, plus one times four, plus one times two, plus zero times one, which simplifies to fourteen.

Answer:

It has a steady line the entire way

Step-by-step explanation:

Answer:

The value of x is 63° ⇒ B

Step-by-step explanation:

The rule for finding the sum of the interior angles of a polygon with n sides is S = (n - 2) × 180°

In the given figure

There is a polygon with 5 sides

∵ n = 5

∴ S = (5 - 2) × 180°

∴ S = 3 × 180°

∴ S = 540°

→ We have the measure of 4 angles of them    

∵ The sum of the 4 given angles =  119° + 100° + 88° + 116°

∴ The sum of the 4 given angles = 423°

→ To find the 5th angle subtract 423° from 540°

∵ The measure of the fifth angle = 540° - 423°

∴ The measure of the fifth angle = 117°

→ x and 117° are linear pair angles, then their sum is 180°

∵ x + 117° = 180° ⇒ linear pair angles

→ Subtract 117 from both sides to find x

∴ x + 117 - 117 = 180 - 117

∴ x = 63°

Answer:

A

The probability of obtaining a simple random sample of 20 students whose mean IQ score is greater than 108 is

    [tex]P(\= X > 108) = 0.0084242[/tex]

B

Comparing the p-value obtained with a low level of significance  (say ∝= 0.01 ) we see that the p-value  is  less than ∝ which implies that the null hypothesis is  rejected hence  we can state that there is sufficient evidence to conclude that the mean IQ for all students at the school is greater than 100

Step-by-step explanation:

From the question we are told that

  The standard deviation is  [tex]\sigma = 15[/tex]

  The population mean is  [tex]\mu = 100[/tex]

  The sample size n  =  20

Generally the standard deviation of the sample mean (standard error ) is mathematically represented as

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

=>   [tex]\sigma_{\= x} = \frac{15 }{\sqrt{20} }[/tex]

=>   [tex]\sigma_{\= x} = 3.35[/tex]

Generally the probability of obtaining a simple random sample of 20 students whose mean IQ score is greater than 108 is mathematically represented as

      [tex]P(\= X > 108) = P(\frac{\=X - \mu}{\sigma_{\= x} } > \frac{108 - 100}{3.35} )[/tex]

=>   [tex]P(\= X > 108) = P(Z > \frac{108 - 100}{3.35} )[/tex]

=>   [tex]P(\= X > 108) = P(Z > \frac{108 - 100}{3.35} )[/tex]

=>   [tex]P(\= X > 108) = P(Z >2.39 )[/tex]

From the z-table  

      [tex]P(z > 2.39) = 0.0084242[/tex]

So

      [tex]P(\= X > 108) = 0.0084242[/tex]

The null hypothesis is  [tex]H_o : \mu = 100[/tex]

The alternative hypothesis is  [tex]H_a : \mu > 100[/tex]

The sample mean is  [tex]\= x = 108[/tex]

Generally the test statistics is  =  2.39

  Generally the p-value is  equal  to 0.0084242

Now comparing the  p-value with a low level of significance  (say ∝= 0.01 ) we see that the p-value  is  less than ∝ which implies that the null hypothesis is  rejected  and we can conclude that there is sufficient evidence to conclude that the mean IQ for all students at the school is greater than 100

Answer:

Step-by-step explanation:

Given that:

The null hypothesis:

[tex]H_0: p = 0.50[/tex]

The alternative hypothesis:

[tex]H_a : p> 0.50[/tex]

Suppose the number of samples n from the population is 16

The observed value x of the test statistics for testing the hypothesis for this study is x = 14

However, if the null hypothesis is true, then the distribution of the test statistics follows a binomial distribution which is expressed as:

bin(n=16, p = 0.5) distribution

The p-value for this test statistics can be computed as:

p-value = P(X ≥ 14)

p-value = 1 - P (X ≤ 13)

p-value = [tex]1- \sum _{x=0^{x-1}} (n^C \ _x)p^x(q)^{(n-x)}[/tex]

p-value = [tex]1- \sum _{x=0^{x-1}} \dfrac{n!}{r!(n-r)! } p^x(q)^{(n-x)}[/tex]

p-value = 0.00209

Answer:

A) W = 28 + H

B) W * H = 52

A) Height = W -28

B) W * (W -28) = 52

B) W^2 -28W = 52

W^2 - 28W - 52 = 0

Width = 29.748

Height = 1.748

Step-by-step explanation:

Answer:

Your answer is: 1/80 or -1/729

Simplify the expression.

↓

Step-by-step explanation:

Hope this helped : )

Answer: 33

======================================================

Explanation:

The exclamation mark means factorial.

Factorial's are operations in which we start with the given number, then count our way down to 1, multiplying along the way.

Examples:

The original number must be a positive whole number (side note: other inputs are possible but we have to involve more complicated math which I'll ignore for this solution).

Let's expand out the first few terms. I'll leave them in factored form and not multiply out the values

1! = 1

2! = 2*1

3! = 3*2*1

4! = 4*3*2*1

5! = 5*4*3*2*1 ... note the 3 and 5 in bold

6! = 6*5*4*3*2*1

7! = 7*6*5*4*3*2*1

This keeps going until we reach 100!

As you can see in the factors above, we have 3 and 5 show up as soon as we reach 5! which means we'll have 3*5 = 15 as a factor of the following items: {5!, 6!, 7!, 8!, ..., 99!, 100!}

Each higher factorial just builds in the last factorial so to speak.

So what this means is that we can write this

15q = 5!+6!+7!+...+99!+100!

where q is some integer. We don't need to worry about what q is

--------------

Therefore,

1!+2!+3!+4!+5!+6!+7!+...+99!+100!

1!+2!+3!+4!+( 5!+6!+7!+...+99!+100! )

1!+2!+3!+4! + 15q

1+2+6+24 + 15q

33+15q

15q+33

--------------

Recall that if we divide integers x and y, then

x/y = q remainder r

x/y = q + r/y

x = yq+r

Where q and r are the quotient and remainder.

Since 1!+2!+3!...100! = 15q+33, we're in the form yq+r showing that r = 33 is the remainder.

Answer:

People on the cover are usually there for outstanding performances. Because they are so far from the​ mean, the performance in the next year is likely to be closer to the mean.

Step-by-step explanation:

We are told that frequently, their performances then falter​ somewhat, after they are pictured on the cover of Sports Illustrated."

Also, we are told it's common for phenomenal rookies to have less stellar second​ seasons, which is called "sophomore​ slump."

Now, this could be due to pressure and the need to prove themselves.

Now, someone to be on the cover of Sports Illustrated, it doesn't neccesarily imply that such a person is the absolute best. It just implies that their performance was far better than how they normally perform. This may be due to either real skill, heavy training or a luck.

However, the most comprehensive reason is that;

People on the cover are usually make it there due to their outstanding performances. Thus, because they are so far from the​ mean, the performance in the following year is likely to be closer to the mean.

Answer:

C. 12 square units

Step-by-step explanation:

Length of side E'F' = EF*scale factor = 3*2 = 6 units

Length of side D'E' = DE*scale factor = 1*2 = 2 units

Area of rectangle = length * width

Therefore, area of rectangle D’E’F’G’ = length of side E'F' * length of side D'E' = 6*2

area of rectangle D’E’F’G’ = 12 square units

Answer:

(-2, -3)

Step-by-step explanation:

To solve this problem, we use the midpoint formula.

M = [tex]\frac{x1 + x2}{2} , \frac{y1+ y2}{2}[/tex]

Plug your coordinates in:

M = [tex]\frac{-7 + 3}{2} , \frac{-8 + 2}{2}[/tex]

Simplify:

M = [tex]\frac{-4}{2} , \frac{-6}{2}[/tex]

M = (-2,-3)

Answer:

[tex](3x+4)(3x-4)(9x^2+16)[/tex]

Step-by-step explanation:

Given [tex]p(x)=81x^4-256[/tex]

Factor using difference of squares

[tex]p(x)=(9x^2-16)(9x^2+16)[/tex]

Note that the factor [tex](9x^2-16)[/tex] can still be factored using, again, difference of squares. Thus,

[tex]p(x)=(3x+4)(3x-4)(9x^2+16)[/tex]

Answer:

y=x-10

Step-by-step explanation:

explain how crime contributes to social injustices

The difference between the range will be 5.

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

Given that last year, the highest value of temperature is 29 and the lowest is 6. After two years the maximum temperature is 25 and the lowest is 7.

The range difference will be calculated as,

Range = ( 29 - 6 ) - ( 25 - 7 )

Range = ( 23 - 18 )

Range = 5

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Answer:

the terms are 3v+7

Step-by-step explanation:

hope this helps

Answer:

2100 mg

Step-by-step explanation:

two can be multiplied by six to get 12 cleanly, so just multiply the amount for two tablets by six to get the amount for 12 tablets

350 x 6 = 2100 mg