Translate each phrase into a variable expression. Use n for the variable.

Nine increased by twice a number ​

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

Explanation:

The equation y = 3x-1 is in slope-intercept form y = mx+b

Parallel lines have equal slopes, but different y intercepts.

The answer will also have a slope of m = 3.

Plug that slope value, and the coordinates of the given point [tex](x_1,y_1) = (1,5)[/tex] , into the point-slope formula below.

Solve for y.

[tex]y - y_1 = m(x - x_1)\\\\y - 5 = 3(x - 1)\\\\y - 5 = 3x - 3\\\\y = 3x - 3+5\\\\y = 3x + 2\\\\[/tex]

That's how we arrive at the answer of y = 3x+2

As a check, plugging x = 1 into that answer should get us y = 5.

It confirms that the point (1,5) is on this line.

The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = [tex]\frac{1}{2}[/tex] and passing through    (-7, -7)

   [tex]y +7 = \frac{1}{2}(x +7)\\[/tex]

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by [tex]y - y_1 = m(x - x_1)[/tex] , [tex](x_1, y_1)[/tex] is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  [tex]y = 3 \times 0 -9\\y = -9[/tex]

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   [tex]y = -9 \times 0 -68\\y = -68[/tex]

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    [tex]y = 5 \times 0 + 2\\y = 2[/tex]

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = [tex]\frac{1}{2}[/tex]

      The line passes through (5, -3)

     Point slope equation

       [tex]y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\[/tex]

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Answer:

In the first one you should write: 6, because the test tells you that in 6 minutes she runs 3/4miles.

So in 12 minutes she runs (3/4miles)*2. (basically 3/4 miles in the first 6 minutes, and other 3/4 miles in the remaining 6munutes).

So in the second space you can write 12, and on the right 2*(3/4), which is... (3/2).

To find the equation:

3/4 = 6

(3/4)*2= 6*2

so we know that in 1 minute we do 1/8miles, and now we have our formula. (1/8)*6=1*6

the formula is: y(miles) =(1/8)*x

in fact is x=6 minutes, y= (1/8)*6, so y=3/4.

N × (-5/6) ≥ -1/2 is the inequality for the statement

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given the statement: negative one half is a minimum of the product of a number and negative five sixths.

This statement can also be written as the product of a number and negative five sixths is greater than or equal to negative one half

Let N represent the number. Thus, the inequality of the statement is:

N × (-5/6) ≥ -1/2    

Note: The symbol ≥ is pronounced as greater than or equal to

Therefore, the inequality for the statement is N × (-5/6) ≥ -1/2

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The value of the function f(a+4) is  [tex]\frac{7}{a^{2} +8a+11}[/tex]

function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable called the dependent variable.

if f(x) = [tex]\frac{7}{x^{2} - 5}[/tex], which means this equation is a function of x,

To find another equation whose function is f(a + 4)

We substitute x for a + 4 in the above equation

f(a+4) = [tex]\frac{7}{(a+4) ^{2} - 5 }[/tex]

expanding [tex](a + 4)^{2}[/tex], and simplifying the denominator, we have

[tex]a^{2}[/tex] +8a + 16 - 5 = [tex]a^{2}[/tex] + 8a + 11

so the simplified form of the new function would be  [tex]\frac{7}{a^{2} +8a+11}[/tex]

In conclusion, the function f(a +4) =  [tex]\frac{7}{a^{2} +8a+11}[/tex]

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Answer:

The cost would be $99 with each artist if the job took Eva 1 hour

Step-by-step explanation:

99=10x+89

subtract 89 from both sides

10=10x

1=x

After solving the value of x is -1/6.

Given:

[tex]25^3^x^+^2[/tex] = 125

[tex]5^{2(3x+2)}[/tex] = [tex]5^3[/tex]

2(3x+2) = 3

6x + 4 = 3

6x = 3-4

6x = -1

divide by 6 on both sides

6x/6 = -1/6

x = -1/6.

Therefore after solving the value of x is -1/6.

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Answer:  The correct answer is $15.06 is remaining after 71 minutes

Step-by-step explanation:

What we need to find out:

What we know:

If we convert the minutes (m) and remaining credits (c) to (x,y) data sets, they would look like the following:

  x       y

 41    19.26       (41, 19.26)

 57   17.02       (57, 17.02)

Plugging the x, y values into a linear equation, we get:

y - 19.26 = (17.02 - 19.26) / (57 - 41) * (x-41)

Solve the equation for y by adding 19.26 to both sides:

y − 19.26 + 19.26 = −0.14x + 5.74 + 19.26

y = −0.14x + 25

Resulting standard slope-intercept format:

y = −0.14x + 25

Now plug in 71 for the x value (minutes):

y = (-0.14*71) + 25

y = 15.06

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The types of variation and their constants are;

1) Direct variation with constant of variation as -1/4

2) Direct variation with constant of variation as ³/₂

A variation is defined as a relation that exists between a set of values of one variable and then a set of values of other variables.

In variation, if the variables change proportionately that is they either increase together or decrease together, then they are said to vary directly.

1) We are given the equation;

4y = -x

Now, y is the output while x is the input and so we make y the subject to get; y = -¹/₄x

Now, writing the relationship between y and x as a variation, we will have; y ∝ x

For this to be equal, there has to be a constant of proportionality which means; y = kx

Comparing with our equation tells us that;

This is a direct variation with constant of variation as -1/4

2) We are given the equation;

3x = 2y - 7

Rearranging gives;

2y = 3x + 7

y = ³/₂x + 7

Now, the greater the value of x, the greater the value of y and as such this is also a direct variation with the constant of variation being 3/2.

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Since the researcher randomly selected 100 people who exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on average: C. the study is an observational study.

An observational study can be defined as a type of scientific study in which a researcher observes and measures the effect of a diagnostic test, risk factors, and specific treatments on individuals without intervening, manipulating, altering, or changing those who are or aren't exposed to it (controlled conditions).

In Science, a controlled variable must always be held constant and unchanged in an experiment in order to prevent it from affecting or influencing the result, which is not applicable to this research.

In conclusion, we can logically deduce that this research is an observational study because people (participants) were chosen through an appropriate process, however, no attempt was made to control any aspect of the people (participants), even though the variable of interest (exercise) was recorded for one of the group.

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Answer:

y=-1/4x+4

Step-by-step explanation:

The graph starts on 4 so that is your y-intercept

Use slope formula to get the slop (y2-y1 over x2-x1)

Use 2 coordinates for formuls (In your case (0,4) and (4,3))

3-4=-1 4-0=4

slope is -1/4

y= -1/4x+4

The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]

Given,

In the question:

The function is:
f(x) =  [tex]x^4(5x^4+4)[/tex]

Differentiate the function with respect to x.

Now, According to the question:

f(x) = [tex]x^4(5x^4+4)[/tex]

Expand the expression:

f(x) = [tex]5x^8+4x^4[/tex]

Calculate the derivative

f'(x) =  [tex]\frac{d}{dx}(5x^8+4x^4)[/tex]

f'(x) = [tex]\frac{d}{dx}(5x^8)+\frac{d}{dx} (4x^4)[/tex]

Isolate Coefficients

f'(x) = 5 x [tex]\frac{d}{dx}(x^8)+4 \frac{d}{dx} (x^4)[/tex]

Apply the power rule

f'(x) = 5x [tex]8x^7+4[/tex] x[tex]4x^3[/tex]

f'(x) = [tex]40x^7 + 16x^3[/tex]

Hence, The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]

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The average rate of change in the number of cars the manufacturer sold between 2002 and 2006 is B. 225 cars per year.

The average rate of change shows the slope line over the stated interval.

We can find the average rate of change by dividing the change in y-values by the change in x-values.

Year        No. of cars sold

                in (hundreds)

2000                 45

2002                 51

2004                53

2006                60

2008                77

The total number of cars sold between 2002 and 2006 = 16,400

The number of cars sold in 2002 = 5,100

The number of cars sold in 2006 = 6,000

The increase in car sold between 2002 and 2006 = 900 (6,000 - 5,100)

OR:

Increase in the number of cars sold in 2004 = 200 (5,300 - 5,100)

Increase in the number of cars sold in 2006 = 700 (6,000 - 5,300)

Total change in y-values = 900 (6,000 - 5,100)

Total change in x-values = 4 (2006 - 200)2

Average rate of change = 225 (900/4)

Thus, we can conclude that for 4 years, car sales increased on, average, by 225 each year.

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The probability that Pat’s second pick will be a blue marble is the fracion 5/3 considering choosing marbles without replacement.

Probability of an event without replacement simply means once an item is drawn, then we do not replace it back to the sample space before drawing a second item.

For the fact that a red marble was first drawn without replacement with the probability of 55/100, given that there are 55 red marbles and a total of 100 marbles in the Urn.

Hence, there will be 99 samples left for the second draw to be made.

The probability that the second pick will be a blue marble = 15/99.

Therefore, the probability that the second pick is a blue marble after the first pick without replacement is the fraction 5/33 reduced to its lowest term from 15/99.

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If you do not pay anything on that loan during the year and assuming there is no compounding, the total sum owing is $1,216.50.

When money is given to someone else with the knowledge that it would be returned with interest, it is referred to as a loan. . Lenders will consider a borrower's income, credit rating, and level of debt before deciding to grant a loan.

Money borrowed from a bank or other financial organization is known as a loan. The borrower consents to repay the loan's principal plus interest. There are many different kinds of loans, such as auto loans, student loans, and mortgages.

The amount is 1000(1 + 0.0765), or 1000 x 1.0765, or 1,076.50.

Punishment equals 12(0.02 x 1000) = 12(20) = 240.

The total sum owing is $1,216.50 (1,076.50 plus 240).

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The probability that exactly two of the four live in elderly care facilities is; 0.244

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula of binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

Px = the probability of exactly x events occurring.

x = the number of expected successful outcomes.

p is probability of success

n is sample size

We are given;

p = 72% = 0.72

n = 4

Thus;

P(X = 2) = 4C2 * (0.72)^(2) * (1 - 0.72)^(4 - 2)

P(X = 2) = 0.244

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Step-by-step explanation:

Percentage means to be out of 100 . So, 20% is equivalent of being 20100 . That evaluates out to 0.20 . Removing the unnecessary 0 at the end gives us the decimal 0.2 , which is the correct answer.

The value of the larger number and the smaller number are 25 and 8 respectively.

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.

They are called simultaneous equations because the equations are solved at the same time.

If the bigger value is represented by x and the smaller value is represented by then

x+y= 33 equation 1

3x+ 4y= 107 equation 2

using Elimination method,

we multiply the coefficients of x by opposite equation

3x+3y=99 equation 3

3x+4y= 107 equation4

subtracting equation 3 from 4

y=107- 99

y= 8

substituting 8 for y in equation 1

x+8= 33

x= 33-8=25

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The solution of the given statement will be inequality c > -60.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

We have been given the statement "number c divided by 3 is greater than -20".

As per the given statement, we can represent this algebraic form with inequality as:

⇒ c / 3 > -20

Inequality by multiplying both sides of the inequality by 3:

⇒ 3 × c / 3 > 3 × -20

⇒ c > -60

Thus, the solution of the given statement will be inequality c > -60.

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The question seems to be incomplete the correct question would be

Find the solution if a number c divided by 3 is greater than -20.

Step-by-step explanation:

1/2 miles in 1/4 day (Given)

Find the distance of the road built in 1 day:

1/4 day = 1/2 miles

4/4 days 1/2 x 4 = 2 miles =

Answer: The rate is 2 miles per day.

Step-by-step explanation:

the area of a triangle is

base × height / 2

in our case

base × height / 2 = 196 mm²

base × height = 392

base = height / 2

so, using that in our main equation :

(height / 2) × height = 392

height² = 784

height = sqrt(784) = 28 mm

base = height / 2 = 28/2 = 14 mm

The highest value you would still hold the stock is $23.97

From the question, the given parameters about the distribution are

Mean value of the set of data = $26.94

Standard deviation value of the set of data = $3.54

Proportion = Highest 20%

This means that the p value is

p = 20%

Express as decimal

p = 0.2

At a p value of 0.2, the z-score is

z = -0.84

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

-0.84 = (x - 26.94)/3.54

Cross multiply in the above equation

So, we have

x - 26.94 = -0.84 * 3.54

Evaluate the products

x - 26.94 = -2.97

Add 26.94 to both sides of the equation

So, we have the following representation

x = 26.94 -2.97

Evaluate the difference

x = 23.97

Hence, the highest value is 23.97

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Answer:

[tex]y+10=\frac{13}{8}(x-20)[/tex]

Step-by-step explanation:

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].

Answer:

(-2/5,0)

Step-by-step explanation:

if y=0,

5/12 x + 1/6 = 0

5x + 2 = 0

x = -2/5

or, multiply by 6 to get the intercept form:

6y = 5/2 x + 1

-5/2 x + 6y = 1

x/(-2/5) + y/(1/6) = 1

For the two similar cuboids A and B,

surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.

As given in the question,

Given : Two similar cuboids A and B,

Let x , y , and z be the length , width and height of cuboid A

And l, b, h be the length , width , and height of cuboid B.

As both the cuboids are similar their sides are in proportion.

k is the constant of proportionality then,

x= kl , y = kb, z = kh

Surface area of A : Surface area of B = 16 :2

⇒2k²(lb +bh +hl) : 2(lb +bh +hl) = 16 : 2

⇒k² = 16 :2

⇒k = 4 : √2

Now volume of A : Volume of B

= xyz : lbh

= k³lbh : lbh

= k³

=( 4 : √2)³

=64 : 2√2

= 64√2 : 4

= 16√2 : 1

Therefore, for the two similar cuboids A and B,

surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.

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Answer:

9. 4/5

10. 3/4

11. 1/4

12. 1/8

13. 1/11

14. 1/9

15. 9/10

16. 1/10

Step-by-step explanation:

ur welcome

If three of the patients are randomly selected, then the probability that none of the patients reacted favorable is 21/506.

In the given question,

A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients.

After the study was concluded, it was concluded it was determined that 15 patients reacted favorably to the medicine, 7 reacted unfavorably, and 2 were unaffected.

If three of the patients are randomly selected, then we have to determine the probability that none of the patients reacted favorable.

Total patient are 24.

The patients reacted favorably to the medicine is 15.

The patients reacted unfavorably to the medicine is 7.

The patients unaffected to the medicine is 2.

Randomly selected patients are 3.

So the probability that none of the patients reacted favorable

P(E) = 9/24 × 8/23 × 7/22

Simplifying

P(E) = 9/3 × 1/23 × 7/22

P(E) = 3 × 1/23 × 7/22

P(E) = 21/506

Hence, if three of the patients are randomly selected, then the probability that none of the patients reacted favorable is 21/506.

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The right question is

"A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients. After the study was concluded, it was concluded it was determined that 15 patients reacted favorably to the medicine, 7 reacted unfavorably, and 2 were unaffected. If three of the patients are randomly selected, then we have to determine the probability that none of the patients reacted favorable."

Using the z-distribution to test the hypothesis, it is found that:

1. You would not like to continue the game, as in each trial you are losing.

2. The p-value is of 0.0023.

3. The low p-value means that there is enough evidence to conclude that the coin is biased.

At the null hypothesis, it is tested if there is not enough evidence that the coin is biased, that is, the proportion of heads is of 0.5, hence:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the coin is biased, that is, it has a proportion of heads lower than 0.5, hence:

[tex]H_1: p_1 < 0.5[/tex]

The test statistic is given by the equation as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the variables are listed and explained as follows:

The values of these parameters are given as follows:

[tex]\overline{p} = \frac{0}{8} = 0, n = 8, p = 0.5[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0 - 0.5}{\sqrt{\frac{0.5(0.5)}{8}}}[/tex]

z = -2.83.

Using a z-distribution calculator, and considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -2.83, the p-value is of 0.0023.

Since this p-value is less than the standard significance level of 0.05, it means that there is enough evidence to conclude that the coin is biased towards tails.

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The measurements 15, 17, 22 do not form a right triangle.

In this question, we have the measurements 15, 17, 22

We check whether the measurements 15, 17, 22 is Pythagorean triple.

22^2 = 484

15^2 = 225

17^2 = 289

15^ + 17^2 = 225 + 289

                = 514

                ≠ 484

i.e., 15^ + 17^2 ≠ 22^2

This means, these measurements do not form a right triangle.  

Therefore, the measurements 15, 17, 22 do not form a right triangle.

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Answer:

a: 0.3125kg

b: 4

Step-by-step explanation:

for a we simply calculate 5 * 0.5 ^ 4.
we then see that the weight after 4 minutes is smaller than 0.5kg, but if we go back to 3 minutes (by multiplying our solution to a by 2), giving us 0.625kg, which is now bigger than 0.5kg. meaning 4 minutes is the first whole amount that will give us a weight smaller than 0.5kg.