15 books are placed on a library shelf. 5 of them are paperback. a person takes 3 books at random, what is the probability of getting at least 1 paperback?

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 115 grams of a radioactive isotope

If we start with 115g of the isotope, after one half-life the quantity will diminish to [tex]\frac{115g}{2} = 57.5[/tex] which is half the original quantity.

This can be written mathematically as: [tex]115g(\frac{1}{2})^{1}[/tex]

After the second half life: [tex]\frac{57.5g}{2} = 28.75 = \frac{115g}{4} = (115g)\frac{1}{2}^{2}[/tex]

After the third half life: [tex]\frac{28.75g}{2} = 14.37g = \frac{115g}{8} = (115g)(\frac{1}{2}) ^{3}[/tex]

But now we can see a pattern developing, because for each new half-life we are dividing the quantity by 2 to a power that increases as the number of half-lives.

Then we can take the original quantity and quickly compute for 6 half-lives:

[tex](115g)(\frac{1}{2})^{6} = (115g)(\frac{1}{64}) = \frac{115g}{64} = 1.79g[/tex]

The time it takes for the isotope to do this will depend on the isotope in question. For some it will be microsecond, and for others it will be years and decades. The isotope will typically decay to become another element or isotope.

To learn more about radioactive isotope click here https://brainly.com/question/18640165

#SPJ4

The answer of the problem is -48.

The evaluation:

given that m = -32, n = 2, p= -8, and r = 4

∴ we have to find the value of pr/n + m

⇒ pr/n + m

⇒ -8×4/2 + (-32)

⇒ -8×2 - 32

⇒ -16 - 32

⇒ -48

So the value of the figure is -48.

Answer: 18

Step-by-step explanation:

a. The function to represent the situation y = 420x.

b. The store charge for each tablet to maximize its profit is $408

c. The  domain is [0, ∞) and the range is [0, ∞).

Function:

Basically, the term function means the relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given,

Last year, an office supply store sold 220 computer tablets for $420 each. This year its manager is considering reducing the price to increase sales. She estimates that for each $12 decrease in price, the store will sell 20 additional tablets.

Here we need to find the following:

a. The function to represent the situation

b. The store charge for each tablet to maximize its profit

c. The domain and range

While we looking into the given question as have identified that,

Price of each tablet = $420

Number of tablet sold = 220

Let us consider x be the number of tablet sold and y be the total amount.

So, the function that is used to calculate the sold tablet numbers is written as,

=> y = 420x

Here the store charge for each tablet to maximize its profit is $12.

So, the current price for the tablet is $408.

Here the domain is [0, ∞) and the range is [0, ∞).

To know more about Function here.

https://brainly.com/question/28193995

#SPJ1

The form of the equation y − 2 = 58(x + 16) is the (b) Point Slope Form

From the question, we have the equation to be

y − 2 = 58(x + 16)

The above equation is a linear equation

A  linear equation can be represented in three forms:

When the above forms are compared to y − 2 = 58(x + 16), we have the form to be y − Y = 58(x - X)

Hence, the equation is in its Point Slope Form

Read more about linear equations at

https://brainly.com/question/4074386

#SPJ1

Answer:

1/3 ; 10/21

Step-by-step explanation:

total sweets = 4+3+5+7+2 = 21

3.1.1

7/21 = (7:7)/(21:7) = 1/3

3.1.2

(5+3+2)/21

10/21

The answer is;

''If you know two corresponding angles are congruent in two triangles, then the third angles would have to be congruent too. The degrees in a triangle add up to 180 degrees.''

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The angle- angle criterion (AA) is sufficient to establish similarity in triangles

Now,

We know two corresponding angle are congruent in two triangles,

then the third angle would have to be congruent too.

Thus, The degree in a triangle add up to 180 degrees .

So, The answer is;

''If you know two corresponding angles are congruent in two triangles, then the third angles would have to be congruent too. The degrees in a triangle add up to 180 degrees.''

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The work done in stretching the spring from 40 cm to 44 cm is 0.28 J while the extension by the 20 N force is by 0.058 m.

Hooke's law states that, as long as the elastic limit is not exceeded the force that is exerted on an elastic material is directly proportional to the length of the material.

Given that;

W = 1/2Ke^2

W = elastic potential energy

K = force constant

e = extension

Given that the extension is obtained from; (49 - 32) * 10^-2

= 0.17 m

5 = 0.5 * K * (0.17)^2

K = 5/0.5 *  (0.17)^2

K = 346

a) To stretch the spring from 40 cm to 44;

e = (44 - 40) * 10^-2

= 0.04 m

W = 0.5 * 346 * (0.04)^2

= 0.28 J

b) The spring is stretched;

F = Ke

F =force

K = force constant

e = extension

20 = 346 * e

e = 20/346

e = 0.058 m

Learn ore about Hooke's law:https://brainly.com/question/13348278

#SPJ1

The multiplication of the given expression in the simplified is 5000/ 729 and in mixed form is [tex]6\frac{626}{729}[/tex].

To multiply fractions with mixed numbers, first convert the mixed number into an improper fraction. Then, multiply the numerators of the fractions separately, and then multiply the denominators separately and simplify the result to obtain the answer.

A whole number and a legal fraction are combined to form a mixed number. An improper fraction is created by multiplying a mixed number by its denominator, keeping the denominator, and adding the resulting number to the proper fraction's numerator.

The given expression is

3 × (5/9) ×(5/3) × (8/9) ×[tex]1\frac{6}{9}[/tex] × [tex]1\frac{2}{3}[/tex]

= 3 × (5/9) ×(5/3) × (8/9) × (1×(9/6))/9 × ((1×3)+2))/3

= 3 × (5/9) ×(5/3) × (8/9) × (15/9) × (5/3)

= 45000/6561

= 5000/729

= [tex]6\frac{626}{729}[/tex]

To know more about the multiplication of fractions and mixed numbers, visit:

https://brainly.com/question/26671298

#SPJ13

The complete question is:

"Multiply the whole number and fraction. Simplify your answer and write it as a mixed number  3 × (5/9) ×(5/3) × (8/9) ×[tex]1\frac{6}{9}[/tex] × [tex]1\frac{2}{3}[/tex]"

There are 19 randomly selected Americans must be surveyed, if we want to estimate 99% confidence interval for the true proportion of Americans who support the gun control in 2018 with a 0.36 margin of error

randomly selected americans must be surveyed can be calculate as follows:

If the prior population proportion is unavailable then the formula to find the sample size is given by :

[tex]n= 0.25(\frac{z*}{E} )^{2}[/tex]where,

z* = Critical z-value

E = margin of error

Let p be the proportion of Americans who support the gun control in 2018.

As per given , we have

Confidence level = 92%

The critical z-value for 92% confidence interval is 1.75 ( BY z-table)

Margin of error : E= 0.2

Since there no  prior information about the proportion of Americans who support the gun control in 2018.

So , the required sample size  to estimate 99% confidence interval would be:

[tex]n= 0.25(\frac{1.75}{0,2} )^{2}\\n= 0.25(8.75)^{2} \\n= 0.25 (76.5625)\\n= 19.14[/tex]or 19

Hence,  19 Americans should be surveyed.

lern more about confidence interval here: https://brainly.com/question/28546024

#SPJ4

Answer: a=2, b=3

Step-by-step explanation:

Answer:

3y+3y-12

Step-by-step explanation:

when they have the same variable with same power you can just combine the coefficient

3y+3y-12

6y-12

Hopes this helps please mark brainliest

Answer:3y+3y-12

Step-by-step explanation:

3y+3y=6y

-12

6y-12=3y+3y-12

For a Regression Analysis that the value of R is 0.42, the value of the Coefficient of Non-Determination is 0.8236.

Coefficient of non-determination is the variation recorded in the dependent variable which is not counted by the changes in the explanatory variable. This is calculated by subtracting Coefficient of Determination from 1.

Coefficient of Non-Determination explains the amount of unexplained, or unaccounted for, variance among two variables, or among a set of variables (predictors) in an outcome variable.

The formula for the Coefficient of Non-Determination is 1 – R².

So, in this case:

1 – R²

= 1 – (0.42)²

= 1 – 0.1764

= 0.8236

Hence, the value of the Coefficient of Non-Determination is 0.8236.

Learn more about Coefficient of Non-Determination at: https://brainly.com/question/14841877

#SPJ4

If a dinner theater charges $20 per person and a table can hold a maximum of five people, the situation represents a function.

In mathematics, function refers to an expression, law or rule that describes a relationship between the independent variable and the dependent variable. A function defines a relation between a set of inputs and a set of potential outputs with the quality property that each input is associated to exactly one output. The provided information can be represented as y = 20x where y is the total charge and x is the number of people, which is a linear function. As the number of people, a table can hold is 5 the domain is represented as 0 ≤ x ≤ 5 and the range is 0 ≤ x ≤ 100 (y = 20*5 = 100).

Note: The question is incomplete. The complete question is A dinner theater charges $20 per person. Your table can hold a maximum of five people. Does the situation represent a function? If so, find the domain and range.

Learn more about Function:

https://brainly.com/question/1415456

#SPJ4

Answer:

The meaning of life according to some people is to party and have fun all ur life. The reason we exist is God created us.

Step-by-step explanation:

The probability is that the married couple watches the show is 0.35.

According to the statement

We have to find the probability is that the probability that married couple watches the show is 0.35.

For this purpose, we know that the

Probability is the ratio of the number of outcomes to the total number of possible outcomes.

With the given information

a married man watches a certain television show is 0.4

the probability that a married woman watches the show is 0.5.

the probability that a man watches the show, given that his wife does, is 0.7

Then

Let M be the event that a married man watches a certain T.V.

And N be the event that a married woman watches the show.

The probability become

[tex]P(M)=0.4[/tex]   [tex]P(F)=0.5[/tex]

and the

[tex]P(\frac{M}{F} )=0.7[/tex]

Then

The probability become is the

P(M∩F)=0.7*0.5

And

[tex]P=0.7*0.5[/tex]

[tex]P=3.5[/tex]

So, The probability is that the married couple watches the show is 0.35.

Learn more about probability here

https://brainly.com/question/24756209

Disclaimer:

This question was incomplete. Please find the full content below.

Question:

The probability that a married man watches a certain TV show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Then

the probability that married couple watches the show.

#SPJ4

Answer:

i the anserw is b than c

Step-by-step explanation:

Answer:

Based on the information given, the SuperFast Deluxe machine is the faster copier. This can be determined by calculating the rate of copies for both machines at each time interval. For Quick Copies, we can calculate the rate using the equation c = 1.5t. For the SuperFast Deluxe, it can be simply observed that the number of copies produced increases by 8 each interval. We can then determine that the SuperFast Deluxe creates copies more quickly than the Quick Copies machine. Therefore, the principal should choose the SuperFast Deluxe.

We conclude that less than 30% of teen girls smoke to stay thin.

Let p be the percentage of teen girls who smoke to stay thin.

So, the Null Hypothesis,([tex]H_{0}[/tex]):

p≥ 30%

This means that at least 30% of teen girls smoke to stay thin

Alternate Hypothesis,([tex]H_{A}[/tex]) :

p < 30%

This means that less than 30% of teen girls smoke to stay thin.

The test statistics that would be used here

One sample z proportion statistics:

T.S = p' - p/ [tex]\sqrt{p'(1-p')/n}[/tex] ≈N( 0,1)

Here p'= sample percent of teen girls who smoke to stay thin = 63/ 273 = 0.231

n = number of sample of teen girls = 273

Now putting these values we have:

Test statistics = 0.231 - 0.30/ [tex]\sqrt{0.231( 1- 0.231)/ 273}[/tex]

                      = -2.705

So we get the value of z-test statistics as - 2.705.

As there is not provided in the question that the level of significance so we assume it to be 5%. Now at a 5% significance level, the z table gives the critical value of -1.645 for left- the tailed test.

As test statistics is less than the critical value of z that is -2.705< -1.645. So we reject our null hypothesis as will fall in reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore we get that less than 30% of teen girls smoke to stay thin.

To know more about the test statistics refer to the link given below:

https://brainly.com/question/15110538

#SPJ4

Main answer:

She bought 5 coach tickets and 6 first class tickets.

Step-by-step explanation:

Given:

Total tickets = 11

Let's First class tickets =f, Coach tickets = c.

Total tickets = f + c

     f + c = 11  

⇒  f = 11 - c  →   equation 1

Cost she used to purchase coach tickets = $260

Cost she used to purchase First class tickets = $1130

Total budget for airfare = $8080

260c + 1130f = 8080  →  equation 2

Substitute equation 1 in equation 2;

260c + 1130(11-c) = 8080

260c + 12430 - 1130c = 8080

12430 - 8080 = 1130c- 260c

870c = 4350

c = 5 peoples

Now, Substitute c in equation 1;

f + c = 11

f = 11 - 5

f = 6 peoples

Hence, She bought 5 coach tickets and 6 first class tickets.

To know more about equations check below given:

https://brainly.in/question/47134002

#SPJ13

The evaluation of the fraction, [tex]\dfrac{x^3-5\cdot x^2+ 2\cdot x-6}{x - 1}[/tex], using the long division method is the option;

The expression can be presented as follows;

[tex]\dfrac{x^3-5\cdot x^2+ 2\cdot x-6}{x - 1}[/tex]

The numerator x³ - 5·x² + 2·x - 6  does not have (x - 1) as a factor
However, dividing x³ - 5·x² + 2·x - 6 by (x - 1), gives;

        x² - 4·x -2

(x - 1)|x³ - 5·x² + 2·x - 6

  [tex]{}[/tex]      x³ - x²

[tex]{}[/tex]             -4·x² + 2·x - 6

[tex]{}[/tex]             -4·x² + 4·x

[tex]{}[/tex]                        -2·x - 6

[tex]{}[/tex]                      -2·x  + 2

[tex]{}[/tex]                                 -8

The quotient from the division is x² -4·x  -2, the remainder is -8, therefore, the result from the division x³ - 5·x² + 2·x - 6 by (x - 1) is the option;

Learn more about the long division method for dividing polynomials here:

https://brainly.com/question/25777560

#SPJ1

When we are interested in deviations greater than or less than the hypothesized value, we do a two-sided test.

A two-tailed or two-sided test determines whether a sample is greater than or less than a specific range of values by using a two-sided critical area of distribution.

This test tests the null hypothesis. This test determines whether there is a statistically significant difference between the sample and population mean.

This test also determines whether a claim is true or not.

This test differs from a one-tailed test because one-tailed tests permit the potential for a one-directional effect. But the two-tailed tests examine the potential for two-directional (positive and negative directions) effects.

To know more about the two-tailed test:

https://brainly.com/question/8170655

#SPJ4

Answer:

Below

Step-by-step explanation:

Realize  ----    Angle 3 = Angle 7

  from this , you should be able to see that angle 3 and angle 6 are supplementary ( they add to 180 degrees....straight line)

Answer:

x + 100 = 4x +49

x= 17

158+148+32+x = 360

338+x= 360

x= 22

let me know if you need more help

Answer:

15.04

Step-by-step explanation:

7.77−1.66x+16.7x

Combine −1.66x and 16.7x to get 15.04x.

d/dx (7.77+15.04x)

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n is nax^n-1.

15.04x^1-1

Subtract 1 from 1.

15.04x ^0

For any term t except 0, t ^0 =1.

15.04×1

For any term t, t×1=t and 1t=t.

and that leaves us with 15.04 as your answer

hopes this helps

Answer: 369.

Step-by-step explanation:

We need to do trial and error to do this.

I'm going to try 3 because I know 4 is too high.

3, 6, and 9.

3 + 6 is 9.

9 + 9 is 18.

This means that the answer is 369.

Step-by-step explanation:i went on half of 84 wich was 42 so i found another problem that can equal into 84 wich was 63 green marbles 21 red             

If the ANOVA test is statistically significant, then we can determine which groups are different by means of the F statistic, which is defined by the ratio of the mean sum square to the average square error (none of the options are correct).

The ANOVA test can be defined as a strategy to assess when differences between two or even more groups and or populations in the same are statistically significant.

Moreover, the F statistic refers to the results of the ANOVA, which is used to show statistically significant differences between groups in the sample.

Therefore, with this data, we can see that the ANOVA test is used to determine when differences between groups in the sample are significant enough to explain a given working hypothesis, and it is associated with the F statistics.

Complete question:

Your ANOVA is statistically significant. How will you determine which groups are different?

Use planned or unplanned comparisons.

Look at what the means in each group are.

Conduct Levene's test.

None of the above

Learn more about the Anova test here:

https://brainly.com/question/15084465

#SPJ1