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Answer:

Multiply using the distributive property.

D is the best answer.

Step-by-step explanation:

The simplified form of expression 3x (4x - 3) is 12x² - 9x.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

3x (4x - 3).

Simplify the expression by solving bracket term,

3x × (4x) - 3 x (3x)

12x² - 9x

The given expression can be simplified as 12x² - 9x.

Hence, option (D) is correct.

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Answer:

8 (19) or  8 (18 +1)

Step-by-step explanation:

Distributive property means to distribute.

HCF of 144 and 8.

=> 8 is the HCF of 144 and 8

8 (18 + 1)

=> 8 (19)

Answer:

y=-2x+1

Step-by-step explanation:

The slope of the line is (y(2)-y(1))/(2-1)=(-3+1)/1=-2. The equation of the line is y=mx+(y intercept), y=-2x+1

The complete equation describes how x and y are related y=-2x+1.

We have given, the equation,

We have to determine the complete equation describing how x and y are related.

The slope of the line is(m)=y2-y1/x2-x1

Where m is the slope,

Therefore we get,

(y(2)-y(1))/(2-1)

=(-3+1)/1

=-2.

The equation of the line is y=mx+(y-intercept), y=-2x+1.

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Answer:

T-test

Step-by-step explanation:

Significance of correlation between two variables x and y measures the strength and direction of their relationship. This is used to make future forecasts of the behaviour of a variable under study.

Correlation coefficient can be used to measure significance of correlation, but we can also use the t-test.

T-test is a statistics that is inferential. It measures the significance of difference between the means of two groups.

T-test is the statistic of choice when carrying out hypothesis testing.

T distribution values and degrees of freedom are used to determine statistical significance.

For example the means of two samples can be compared to determine of the come from the same population

Answer:

cos 60° = 1/2 because the angles are complements.

Step-by-step explanation:

[tex]f(x)=18(0.8)=14.4[/tex]

is a constant function, so it will be a straight line parallel to x axis and passing through y axis at $14.4$

Answer:

The correct option is  D

Step-by-step explanation:

From the question we are told that

    The standard deviation is  [tex]\sigma = 16[/tex]

     The sample size is  n =  64

The standard error of mean is mathematically evaluated as

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

substituting values

        [tex]\sigma _{\= x } = \frac{16 }{\sqrt{64} }[/tex]

        [tex]\sigma _{\= x } = 2[/tex]

Generally the probability that the sample mean will be within 2 of the population mean is mathematically represented as

              [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < \frac{ \= x - \mu }{\sigma_{\= x }} < \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]

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

So

         [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < Z< \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]

         [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( -2 }{\sigma_{\= x }} < Z< \frac{ 2 }{\sigma_{\= x }} )[/tex]

substituting values

        [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{-2 }{2} < Z< \frac{ 2 }{2} )[/tex]

        [tex]P( \mu - 2 < \= x < \mu + 2) = P(-1< Z< 1 )[/tex]

=>     [tex]P( \mu - 2 < \= x < \mu + 2) = P(Z < 1) - P(Z < -1)[/tex]

From the normal distribution table [tex]P(Z < 1 ) = 0.84134[/tex]

                                                          [tex]P(Z < - 1) = 0.15866[/tex]

=>  [tex]P( \mu - 2 < \= x < \mu + 2) = 0.84134 - 0.15866[/tex]

=>   [tex]P( \mu - 2 < \= x < \mu + 2) = 0.6826[/tex]

Answer:

4(4x-16)

Step-by-step explanation:

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Answer:

it doesnt add up. the question doesnt make sense.

Step-by-step explanation:

Answer:

157

Step-by-step explanation:

To find the average score, add all individual scores and divide the sum by the number of individual scores.

She has 5 individual scores. Let's say her scores are A, B, C, D, and E.

average score = (A + B + C + D + E)/5

Now we plug in the average and the 4 known scores for A through D, and we solve for E.

average score = (A + B + C + D + E)/5

136.8 = (135 + 144 + 116 + 132 + E)/5

E = 157

Answer: 157

Answer:

1.25 dollars per quart

Step-by-step explanation:

There are 4 quarts per gallon

3 gallons * 4 quarts/ gallon = 12 quarts

15 dollars/ 12 quarts

1.25 dollars per quart

Answer:

-2 > x

Step-by-step explanation:

14 <-7x

Divide each side by -7, remembering to flip the inequality

14/ -7 > -7x/-7

-2 > x

Answer:

x = 1

Step-by-step explanation:

First, move all the variables to one side by subtracting 5x on both sides:

5x + 2 = 12x - 5

2 = 7x - 5

Add 5 to both sides:

7 = 7x

1 = x

Answer:

x=1

Step-by-step explanation:

5x + 2 =12x- 5

Subtract 5x from each side

5x-5x + 2 =12x-5x- 5

2 = 7x-5

Add 5 to each side

2+5 = 7x-5+5

7 = 7x

Divide each side by 7

7/7 = 7x/7

1 =x

Answer:16

Step-by-step explanation:

Answer:

x = 2/3 or x = -2/5

Step-by-step explanation:

15x^2 - 4x - 4 = ?

factor the left side of the expression and set factors equal to zero:

(3x-2)(5x+2)=0

3x - 2 =0 or 5x + 2 =0

3x =2 or 5x = -2

x = 2/3 or x = -2/5

Answer: The new slope is -(2/3)

Step-by-step explanation:

Ok, we know that our line can be written as:

y = (2/3)*x + b

where b is the y-intercept, and here does not really matter.

Ok, remember that if we have a point (x, y) and we reflect it over the x-axis, the new point will be (x, -y).

For our linear equation, the point (x, y) can be written as:

(x, y = (2/3)*x + b) = (x,  (2/3)*x + b)

Now, after the reflection, our point is:

(x, - ( (2/3)*x + b)) = (x, -(2/3)*x - b)

Then our new line is y = -(2/3)*x - b

The new slope is -(2/3)

Answer:

y(x)=6^(x)-3

Step-by-step explanation:

Let the exponential function be y(x) = ab^(x) but since the graph is translated 3 units down, y(x) = ab^(x)-3. Now, y(0)=-2=a*b^(0)-3. a=1. The equation is nearly complete but we need b, we can find it by using the point y(1)=3. y(x)=b^(x) - 3. y(1)=3=b-3, b=6. The equation of the function is y(x)=6^(x)-3

Answer:

I agree with the first one

Answer:

Yes it can be concluded that state employees earn on average less than federal employees

  The critical value is  [tex]Z_{\alpha } = - 2.33[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = \$ 59593[/tex]

   The sample size is  n =  30

    The  sample mean is [tex]\= x = \$ 58800[/tex]

     The  standard deviation is  [tex]\sigma = \$ 1500[/tex]

     The significance level is  [tex]\alpha = 0.01[/tex]

The null hypothesis is  [tex]H_o : \mu = \$ 59593[/tex]

 The  alternative hypothesis is  [tex]H_a : \mu < \$ 59593[/tex]

The critical value of [tex]\alpha[/tex] from the normal distribution table is  [tex]Z_{\alpha } = - 2.33[/tex]

 Generally the test statistics is  mathematically evaluated as

            [tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]

=>         [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]  

=>          [tex]t = -2.896[/tex]

The  p-value is obtained from the z-table

   [tex]p-value = P(t < -2.896) = 0.0018898[/tex]

Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees  

Answer:

A. -f(1/2 x)

Step-by-step explanation:

Reflextion about the x-axis is

f(x) -> -f(x)

and horizontal dilation is

f(x) -> f(-x/b) where b is the factor of dilation.

so the proper answwer is

A. -f(1/2 x)

Answer: 2 years

Step-by-step explanation:

The exponential growth function is given by :-

[tex]y=A(1+r)^x[/tex] (i)

, where A = initial value , r = rate of growth and  x= time period.

As per given ,

A= 242

r= 12% = 0.12

To find : t when y= 300.

Put all the values in (i)

[tex]300=242(1+0.12)^x\\\\\Rightarrow\ \dfrac{300}{242}=(1.12)^x\\\\\Rightarrow\ 1.23967=(1.12)^x[/tex]

Taking log on both sides , we get

[tex]\log (1.2396) = t \log (1.12)\\\\\Rightarrow\ 0.09328=t(0.049218)\\\\\Rightarrow t=\dfrac{0.09328}{0.049218}=\approx2[/tex]

hence, it will take 2 years.

Answer:

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.

Statistics is maths.

Why:-

Statistics is related to maths because we study, use and even consider statistic problems with reference to mathematics.

• It is mostly used to find the census, which is maths.

• It is used to find interest rates and other banking terms using statistics, which is again related to math.

• It is also used to find the average people living in a village or panchayat, which is also math.

Therefore I strongly believe that Statistics is Maths.

Thank You!

Answer:

A. The median does not change.

Step-by-step explanation:

Original data set,

Put the numbers in order from smallest to largest

2,2, 4, 5, 5, 6,6, 8  

Median is the middle number

2,2, 4, 5,     5, 6,6, 8  

It is between the two 5's

(5+5)/2 = 10/2 = 5

New data set

Put the numbers in order from smallest to largest

2,2, 4, 5, 5, 6,6, 8,10  

Median is the middle number

2,2, 4, 5,     5,    6,6, 8,10  

The middle number is 5

Answer:

The answer is A

Step-by-step explanation:

Answer:

(D) 48​

Step-by-step explanation:

Let English book = x

Let french book = y

In 1995 x= 10

Y= 7

In 1996

Y = 2x

Total book read in the two years

0.6(Total) = y

0.4(total) = x

We don't know the exact amount of books read in 1996.

Total = 10 + 7 +x +2x

Total = 17+3x

0.6(total) = 7+2x

0.6(17+3x) = 7+2x

10.2 +1.8x= 7+2x

10.2-7= 2x-1.8x

3.2= 0.2x

3.2/0.2= x

16= x

So she read 16 English book

And 16*2 = 32 french book Making it a total of 16+32= 48 books in 1996

Step-by-step explanation:

Hi there!

Please see attached picture for your answer.

Hope it helps!

Answer:

Explained below.

Step-by-step explanation:

(a)

The first and third quartiles of bowling scores are as follows:

Q₁ = 125 and Q₃ = 156

Then the inter quartile range will be:

IQR = Q₁ - Q₃

      = 156 - 125

      = 31

Any value lying outside the range (Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) are considered as unusual.

The range is:

(Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) = (125 - 1.5×31, 156 + 1.5×31)

                                               = (78.5, 202.5)

The bowling score of 200 lies in this range.

Thus, the bowling score of 200 is usual.

(b)

Compute the probability that the mean bowling score will be smaller than 150 as follows:

[tex]P(\bar X<150)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{150-155}{16/\sqrt{40}})[/tex]

                  [tex]=P(Z<-1.98)\\=1-P(Z<1.98)\\=1-0.97615\\=0.02385\\\approx 0.024[/tex]

Thus, the probability that in a sample of 40 bowling scores, the mean will be smaller than 150 is 0.024.

(c)

It is provided that, the lower the golf score the better.  

So, the best 5% of scores would be the bottom 5%.

That is, P (X > x) = 0.05.

⇒ P (Z > z) = 0.05

⇒ P (Z < z) = 0.95

⇒ z = 1.645

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\1.645=\frac{x-77}{3}\\\\x=77+(3\times 1.645)\\\\x=81.935\\\\x\approx 82[/tex]

Thus, the score is 82.

(d)

A z-scores outside the range (-2, +2) are considered as mild outlier and the z-scores outside the range (-3, +3) are considered as extreme outlier.

Compute the z-score for the golf score of 70 as follows:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

  [tex]=\farc{70-77}{3}\\\\=\frac{-7}{3}\\\\=-2.33[/tex]

As the z-score for the golf score of 70 is less than -2, it is considered as a mild outlier.

Answer: 247.92 euros

Step-by-step explanation:

Given:  Varia is required pay $3,500 (in US dollars) per year to the university.

So, [tex]$3500\div 12 \approx\$291.67[/tex]

i.e. She will pay $ 291.67 per month.

Recent currency value: 1 US dollar = 0.85 euro

∴ $291.67 = ( 0.85 ×291.67) euros

= 247.92 euros  [Round to the nearest cent]

∴ She can expect 247.92 euros to pay per month to the university.

Answer D

Step-by-step explanation:

looks right

Step-by-step explanation:

Find the z-score.

z = (x − μ) / σ

z = (109.8 − 106.9) / 14.5

z = 0.2

Use a chart or calculator to find the probability.

P(Z < 0.2) = 0.5793

Find the mean and standard deviation of the sampling distribution.

μ = 106.9

σ = 14.5 / √20 = 3.242

Find the z-score.

z = (x − μ) / σ

z = (109.8 − 106.9) / 3.242

z = 0.894

Use a calculator to find the probability.

P(Z < 0.894) = 0.8145

Answer:

-50

Step-by-step explanation:

Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)

-50(0)+100 (0,100)  Y₂-Y₁/X₂-X₁ 50-100/1-0

Rate of change per month = -$50