In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Paul has scored 75, 80, and 91 on the first three. What range of scores on the fourth test will give Paul a C for the semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.

Answer:

D: All real numbers except x=-1 and x=1

Step-by-step explanation:

Step-by-step explanation:

The domain of the rational expression is when the denominator is defined. (non-zero)

When the denominator is 0,

4x² - 4 = 0.

=> x² - 1 = 0, (x + 1)(x - 1) = 0, x = -1 or x = 1.

Hence the answer is all real numbers except x = -1 and x = 1.

Remember to follow the order of operation, PEMDAS. PEMDAS stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

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5. 9(7x - 4) = 27

First, distribute 9 to all terms within the parenthesis:

9(7x - 4) = 27

(9 * 7x) - (9 * 4) = 27

63x - 36 = 27

Next, isolate the variable, x. Do the opposite of PEMDAS.

First, add 36 to both sides:

63x - 36 (+36) = 27 (+36)

63x = 27 + 36

63x = 63

Isolate the variable, x. Divide 63 from both sides:

(63x)/63 = (63)/63

x = 63/63 = 1

x = 1

~

6. 5(3x + 8) = 175

First, distribute 5 to all terms within the parenthesis:

5(3x + 8) = (5 * 3x) + (5 * 8) = 15x + 40

15x + 40 = 175

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 40 from both sides:

15x + 40 (-40) = 175 (-40)

15x = 175 - 40

15x = 135

Next, divide 15 from both sides of the equation:

(15x)/15 = (135)/15

x = 135/15 = 9

x = 9

~

Answer:

5) I=1848. total=3248

Step-by-step explanation:

interest = principal x rate x time /100

I=prt/100

p=1400

r=16.5%

t=8

i=1400*16.5*8/100

i=14*16.5*8

I=112*16.5

I=1848

your answer is a

and x equals 20

Answer:

8 is your answer

Step-by-step explanation:

Hope this helps sorry if I'm wrong

Answer:

8

Step-by-step explanation:

I'm doing the quiz rn.

Answer:

Step-by-step explanation:

5!=5×4×3×2×1=120

so there are 5 distinct objects.

Answer:

The correct answer is option C. 5

Step-by-step explanation:

N=120

N=5

Answer:

The standard deviation is 17.5

Step-by-step explanation:

Let S be the sum of X and Y

S = X + Y

So we want to calculate the standard deviation of S

The standard deviation of S will be the square root of the sum of the variances of X and Y

Kindly recall that variance is the square of standard deviation

The variance of X will be 15^2 = 225

The variance of Y will be 9^2 = 81

So the standard deviation of the sum will be

√(81 + 225)

= √(306)

= 17.5

The standard deviation of X + Y is 17.5

The given parameters are:

[tex]\bar x =120[/tex] --- the mean of X

[tex]\sigma_x =15[/tex] -- the standard deviation of X

[tex]\bar y = 100[/tex] --- the mean of Y

[tex]\sigma_y = 9[/tex] --- the standard deviation of Y

The standard deviation of X + Y is then calculated as:

[tex]\sigma_{x +y} = \sqrt{\sigma_x^2 + \sigma_y^2}[/tex]

This gives

[tex]\sigma_{x +y} = \sqrt{15^2 + 9^2}[/tex]

Evaluate the exponents

[tex]\sigma_{x +y} = \sqrt{225 + 81}[/tex]

[tex]\sigma_{x +y} = \sqrt{306}[/tex]

Take the square root of 306

[tex]\sigma_{x +y} = 17.5[/tex]

Hence, the standard deviation of X + Y is 17.5

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Answer:

27 cubic feet

Step-by-step explanation:

Answer:

27ft

Step-by-step explanation:

Multiply Height, Width, and Length

Answer: 486

Step-by-step explanation:

Answer:

x= -3/4 + y/4

Step-by-step explanation:

Move all terms that don't contain

x to the right side and solve.

Answer:

[tex]x = - \frac{3}{4} + \frac{1}{4} y[/tex]

Step-by-step explanation:

[tex] - 4x + y = 3[/tex]

[tex] - 4x = 3 - y[/tex]

[tex]x = - \frac{3}{4} + \frac{1}{4} y[/tex]

[tex]x = - \frac{3}{4} + \frac{1}{4} y[/tex]

Hello there, and welcome to Brainly!

In the following equation, you are solving for the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 14 to both sides of the equation:

7x - 14 (+14) = 35 (+14)

7x = 35 + 14

7x = 49

Next, divide 7 from both sides:

(7x)/7 = (49)/7

x = 49/7

x = 7

7 is the value for x that will make the equation true.

~

Answer:

Oslo

Berlin

Glasgow

London

Nice

Answer: she will need 2.8 days to finish the work.

Step-by-step explanation:

Let's define:

D = number of days.

B = rate at which Barbara paints a barn

S = rate at which Sara paints a barn

We know that Barbara can paint a barn in 5 days, then:

B*5 days = 1 barn

B = 1/5 barns per day.

And we know that Sara can paint it in 8 days, then:

S*8 days = 1 barn

S = 1/8 barns per day.

Now, when they work together, their rates are added.

Then if they work together for two days, they paint a total of:

(1/5 barns per day + 1/8 barns per day)*2 days

(8/40 barns per day + 5/40 barns per day)*2 days

(13/40 barns per day)*days = 26/40 barns

Now Sara needs to paint he other 14/40 barns in her own, she will need D days, then:

(1/8 barns per day)*D = 14/40 barns

D = (14/40 barns)/(1/8 barns per day) = (14*8/40) = 2.8 days.

So she will need 2.8 days to finish the work.

Answer:

y = -3x + 4

Step-by-step explanation:

slope = -3 or -3/1

y - intercept: (0,4)

slope intercept form equation: y = -3x + 4

Answer:

600 students

Step-by-step explanation:

there were 20 students surveyed because 6 + 6 + 8 = 20 there were 8/20 who picked snickers then you have to find the proportions 20 * 75 = 1500 you then multiply 8 * 75 which equals 600 so in the end out of 1500 students 600 will pick snickers

Answer: the correct answer would be A!

Step-by-step explanation:

Taking this test as well ☺️

Answer:

1. 68%

2. 50%

3. 15/100

Step-by-step explanation:

Here, we want to use the empirical rule

1. % waiting between 15 and 25 minutes

From what we have in the question;

15 is 1 SD below the mean

25 is 1 SD above the mean

So practically, we want to calculate the percentage between;

1 SD below and above the mean

According to the empirical rule;

1 SD above the mean we have 34%

1 SD below, we have 34%

So between 1 SD below and above, we have

34 + 34 = 68%

2. Percentage above the mean

Mathematically, the percentage above the mean according to the empirical rule for the normal distribution is 50%

3. Probability that someone waits less than 5 minutes

Less than 5 minutes is 3 SD below the mean

That is 0.15% according to the empirical rule and the probability is 15/100

Answer:

9 houses

Step-by-step explanation:

45% of 20 is 9 so the answer is 9

Total 9 houses have decoration on Rainbow Street.

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

Given that,

Total number of houses on Rainbow Street = 20,

The percentage of the houses which have decorations = 45%

The number of houses which have decoration

= 20×(45/100)

= 9

There are 9 houses that have decorations.

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Answer: 2 pounds in each bag

Step-by-step explanation:

12 = pounds of almonds

6 = number of bags

12 / 6 = 2

Answer:

The 12 means it's how many pounds of almonds she has and the 6 means how many bags she has.

Step-by-step explanation:

12 divided by 6 is 2. (Hope this helps!)

Answer:

15

Step-by-step explanation:

Plug in 3 as x:

3x + 6

3(3) + 6

9 + 6

= 15

So, the simplified expression if x = 3 is 15

Answer:

D-6/25

Step-by-step explanation:

Answer:

it is an acute scalene triangle

Answer:

Since the lengths of the triangle are 4,5, and 6, which are almost equal, then the triangle cannot be obtuse. It's right triangle

Answer:

100 POINTS! (50 split up) PLSSSSSSSSSS HELP!!! I REALLY NEED IT SO MUCH :( I PROMICE TO GIVE BRAINLIEST AND FIVE STARS AND A THANKS! 6TH GRADE SCIENCE! i used all my points for this!

You measure the mass of an apple using a balance. You get these three measurements:

Trial 1: 167.0 g

Trial 2: 166.9 g

Trial 3: 167.2 g

You know that the true mass of the apple is 172 g. Describe your results in terms of precision and accuracy. Explain your answer in a paragraph for the best grade.

Step-by-step explanation:

Answer:

75 boys

Step-by-step explanation:

60 / 4 = 15

5 × 15 = 75