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Problem 5.1
A publisher wants to know the thickness of a new book.
The book has a front cover and a back cover, each with a
thickness of of an inch.
The paper has a thickness of
inch per 100 pages.
Write an equation that represents the total width of the
book, y, for every 100 pages of paper, x.

Answer:

[tex]Suppose~that~two~numbers~are~x~and~y.\\From~the~first~condition,\\x+y=4.........(1)\\or, y=4-x.......(2)\\From~the~second~condition,\\x^2+y^2-3xy=76\\or, (x+y)^2-2xy-3xy=76\\or, 4^2-5xy=76\\or, -5xy = 76-16\\or, -5xy = 60\\or, xy = -12\\From~eq^n~(2),\\x(4-x)=-12\\or, 4x-x^2=-12\\or, x^2-4x-12=0\\or, x^2 +2x-6x-12=0\\or, x(x+2)-6(x+2) = 0\\or,(x+2)(x-6) = 0\\i.e. x = -2 ~or ~6\\When~ x=-2, y=4-(-2) = 4+2 =6\\When~x=6, y=4-6 = 4-6 = -2\\So,~the~two~numbers~are~-2~and~6.[/tex]

Answer:

-2 and 6

Step-by-step explanation:

Mark the first number as x

and the second number as y

Since x + y = 4

y = 4 - x

// substitute the given value of y into the equation

[tex]x^{2} + y^{2}[/tex] - 3xy = 76

[tex]x^{2}[/tex] + [tex](4-x)^{2}[/tex] - 3 * x * (4 - x) = 76

[tex]x^{2}[/tex]  + 16 - 8x + [tex]x^{2}[/tex]  - 12x + 3[tex]x^{2}[/tex] = 76

[tex]x^{2}[/tex]  + [tex]x^{2}[/tex]  + 3[tex]x^{2}[/tex]  - 20x = 76 - 16

5[tex]x^{2}[/tex]  - 20x = 60

5[tex]x^{2}[/tex]  - 20x - 60 = 0

// divide both sides by 5

[tex]x^{2}[/tex] - 4x - 12 = 0

// write -4 x as a difference, this way it is faster than calculating discriminant

[tex]x^{2}[/tex] + 2x - 6x - 12 = 0

// factor out x and -6 from the expression

x (x +2) - 6 (x +2) = 0

(x - 6) * (x + 2) = 0

// there are two possible cases

1) x - 6 = 0

2) x + 2 = 0

1) x = -2

2) x = 6

// substitute the given value of x into the equation

1) y = 4 - x = 4 - (-2) = 6

2) y = 4 - x = 4 - 6 = -2

Now we get two pairs (-2; 6) and (6; -2), which are the solutions to the system

Since their sequence as the question suggests is irrelevant, the numbers are -2 and 6

Answer:

A A one-sample t-interval for a population mean

Step-by-step explanation:

The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.

In a confidence interval, we take the data from the sample and want to estimate it for the entire population, so the interval is for a population mean.

The standard deviation will be taken from the sample, which means that the t-interval is used.

We want for one population, so it is a one sample for the population mean, and the correct answer is given by option A.

Answer:

10x^2 or 10x because you are adding x

Answer:

(0,4)

Step-by-step explanation:

y intercept is where the line crosses the y axis

Answer:

4

Step-by-step explanation:

Answer:

It must be 3/2.........

Answer: -2/3

Step-by-step explanation:

I wrote the equation y-3=3/2(x-4) in slope-intercept form. It's y=3/2x-5, so the slope is 3/2.

To find the perpendicular slope, I found the opposite reciprocal. The reciprocal of 3/2 is 2/3 and the opposite of 2/3 is -2/3

Step-by-step explanation:

bence 27 cunkku yuzd sordugu icin kolaylıklar dilerim iyi günler

Answer:

E.

H0 : mu D = 0

Ha : mu d < 0

Step-by-step explanation:

The hypothesis is to test if there is a reduction in blood pressure for those who complete the program, this means if the mean difference in blood pressure (that is after - before) is less than 0. Here, the hypothesis is the alternative side while the opposite, that is, there is no difference in blood pressure before and after is the null.

This means :

H0 : μD = 0

Ha : μD < 0

You can use the definitions for null and alternate hypotheses  

The correct set of hypothesis is given by:

Option E.  [tex]H_0: \mu_D = 0[/tex]

[tex]H_a: \mu_D < 0[/tex]

There are two hypotheses. First one is  called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

Since the test is to test the effectiveness of the exercise program, thus the wish of the tester is to get the result that effectiveness is there. This will be the alternate hypothesis and the null hypothesis will be that there is no difference in the blood pressure before and after the exercise. Thus, we will test against the null hypothesis.

Since the evidence is to be found for all of the people who completed the program, thus it is hypothesis about population perimeter. The average blood pressure difference of the population is denoted by [tex]\mu_D[/tex] and that of the sample is denoted by [tex]\overline{x}_D[/tex]

Thus, we have:

Null hypothesis = the difference in average blood pressure before and after the program of the population is not changed(thus 0 is the difference) = [tex]H_0: \mu_D = 0[/tex]

Alternate hypothesis = the difference in average blood pressure is reduced(since the test is for seeing if the blood pressure is reduced or not) = [tex]H_a: \mu_D < 0[/tex]

Thus,

The correct set of hypothesis is given by:

Option E.  [tex]H_0: \mu_D = 0[/tex]

[tex]H_a: \mu_D < 0[/tex]

Learn more about null and alternative hypothesis here:

https://brainly.com/question/18831983

Given:

The two numbers are 19.8 and 5.

To find:

The estimated product of given numbers by rounding each factor to nearest whole number.

Solution:

Two number are 19.8 and 5.

On rounding the given numbers to the nearest whole number, we get 20 and 5.

Now, the estimated product is

[tex]20\times 5=100[/tex]

Therefore, the estimated product of given numbers is 100.

Answer:

Brothers Sorry I don't

Step-by-step explanation:

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Answer:

5. 1/29

Step-by-step explanation:

1/. and the bottom numbers says 30-1 which is 29 soooo 1/29

Answer:

7/18

Step-by-step explanation:

4 2/3=14/3

(14/3)/12=14/36

reduces to

7/18

Step-by-step explanation:

first distribute the first equation

8(2x) - 8(14) +13 = 4x -27

16x - 112 +13 = 4x -27

then combine like terms

16x - 99 = 4x -27

subtract 4x from both sides

12x - 99 = -27

add 99 to both sides

12x = 72

divide both sides 12 to isolate the x

x = 72/12 = 6

Answer:   b

Step-by-step explanation:

x= 5+√35 and 5-√35

Answer:

whats the graph???

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

When it’s an absolute value no matter what it’s inside the braces ( “ | # | “ ) it’s a positive. While the signs outsides can stay the same

Answer:

2/5=6/15

Step-by-step explanation:

2/5

3x2=6

3x5=15

compare they are same

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The equal sign completes the give incomplete mathematical statement.

The given incomplete expression is -

2/5 _____ 6/15

The given expression is -

2/5  ____  6/15

2/5  ____ 2/5

0.4  ____ 0.4

0.4 = 0.4

Therefore, the equal sign completes the give incomplete mathematical statement.

To solve more questions on functions, expressions and polynomials, visit the link below -

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Answer:

the answer is 10832

Step-by-step explanation:

you can use a calculator

Answer:

10832

Step-by-step explanation:

Add one digit at the time (from right to left):

1 + 1 = 2

0 + 3 = 3

8 + 0 = 8

8 + 2 = 10

Now we get 10832

Answer:

[tex]\frac{4}{25}[/tex]

Step-by-step explanation:

22/200 simpilfy is 4/25

The experimental probability that a person selected at random is going to city C is P ( C ) = 4/25 = 0.16

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the experimental probability that a person selected at random is going to city C is P ( C )

Now , the total number of people in the city = 100

The number of people going to city C = 16

So , P ( C ) = number of people going to city C / total number of people in the city

On simplifying , we get

P ( C ) = 16 / 100

P ( C ) = 4/25

P ( C ) = 0.16

Hence , the probability is 0.16

To learn more about probability click :

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Answer:

Step-by-step explanation:

This would be 500 x 250/100 = 125000/100 = 1250

Answer:

Step-by-step explanation:

Slope-intercept form:

Take two points from the graph:

Find the slope:

The y-intercept is b = 5

The line is:

Answer:

Step-by-step explanation:

Answer:

the y intercept would be at (0,-6)

Answer:

(0, 3)

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, when x = 0, we see that y = 3. Therefore, our y-intercept is (0, 3).

Answer:

The LCD is 3x²

The other two denominators can be factors of 3x²

Step-by-step explanation:

To get the equivalent fractions, divide the original denominator into the LCD, then multiply the original numerator by the quotient.

For the first term: 1/x²

3x² ÷ x² = 3 3×1=3 The equivalent is 3/3x²

Second term: Leave it as it is.

For the third term: 15x

The implied denominator is 1

3x² ÷ 1 = 3x² 3x² × 15 = 135x²

The equivalent is 135x²/3x²

To check the validity, substitute a value for x and calculate the numbers.

For example let x = 3

The original expression becomes

1/3² + 4/3(3²) - 15(3)

1/9 + 4/27 - 45

With the LCD it is

3/27 + 4/27 - 1215/27

Answer:

3x^2(x+5)

Step-by-step explanation:

hope this helps

Answer: the answer is 2.64 or 264

Explanation: if you multiply 3.3 × 0.8=264 but if you mulyiply 33×8=264

Step-by-step explanation:

step 1. I assume i is imaginary

step 2. i^2 = -1, i^3 = -i, i^4 = 1, i^5 = I. . . . and so on

step 3. i - 1 - i + 1 + i - 1 - i + 1 + i - 1

step 4. the result is i - 1.

Answer:

76 cases

Step-by-step explanation:

original 51 plus the 21 new is equal to 76 total