Which rule describes the translation

Answer:

The cost of making 60 calls a month is $20.

Step-by-step explanation:

There was a small typing mistake there. If the fixed charge is $14, the cost of n calls is given by the following equation:

[tex]C(n) = 0.1n + 14[/tex]

Find the cost of making 60 calls a month.

This is C(60), that is, C when n = 60. So

[tex]C(n) = 0.1n + 14[/tex]

[tex]C(60) = 0.1*60 + 14 = 20[/tex]

The cost of making 60 calls a month is $20.

Subtract 20 from the total weight and divide by 4:

200 - 20 = 180

180/4 = 45

Each other crate weighs 45 pounds each.

Answer:

(-3, 3)

Step-by-step explanation:

Answer:

Liability

Step-by-step explanation:

Ap3x

Answer:

The correct answer is m=8

Answer:

There are 536,878,650 ways to place the order.

Step-by-step explanation:

The order in which the cases are put is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

8 varieties from a set of 50. So

[tex]C_{50,8} = \frac{50!}{8!(50-8)!} = 536878650[/tex]

There are 536,878,650 ways to place the order.

Answer:

[tex]\displaystyle \int {xsinx} \, dx = -xcosx + sinx + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Integration

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration by Parts:                                                                                               [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int {xsinx} \, dx[/tex]

Step 2: Integrate Pt. 1

Identify variables for integration by parts using LIPET.

Step 3: Integrate Pt. 2

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

Step-by-step explanation:

(Parentheses) 6 + -5.8 = 0.2

(Multiplication) 3.4 - 5 x 0.2

(Subtraction) 3.4 - 1 = 2.4

2.4

I'm always happy to help :)

Answer:

3024

Step-by-step explanation:

Find the area of the isosceles triangles, and add then with the three rectangles to get surface area.

14*24/2 * 2 = 336, and you have 25*42 * 2 = 2100, and finally you have 14*42 = 588. so the sum should be 3024

Answer:

There is enough evidence to support the claim that the proportions are not equal. (P-value: 0.048).

Step-by-step explanation:

The question is incomplete:

"A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are different."

This is a hypothesis test for the difference between proportions.

The claim is that the proportions are not equal.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=1000 has a proportion of p1=0.031.

[tex]p_1=X_1/n_1=31/1000=0.031[/tex]

The sample 2, of size n2=1200 has a proportion of p2=0.018.

[tex]p_2=X_2/n_2=22/1200=0.018[/tex]

The difference between proportions is (p1-p2)=0.013.

[tex]p_d=p_1-p_2=0.031-0.018=0.013[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{31+22}{1000+1200}=\dfrac{53}{2200}=0.024[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.024*0.976}{1000}+\dfrac{0.024*0.976}{1200}}\\\\\\s_{p1-p2}=\sqrt{0+0}=\sqrt{0}=0.007[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.013-0}{0.007}=\dfrac{0.013}{0.007}=1.98[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=2\cdot P(z>1.98)=0.048[/tex]

As the P-value (0.048) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions are not equal.

Answer:

(1) The sample mean is = 6.98, the standard deviation is = 4.53 (2) The pint estimate difference is = 20.2 (3) The confidence interval limits are $ 15943.6 and $24456.4

Step-by-step explanation:

Solution

(A) The first step is to compute the mean sample and the standard deviation for private and public colleges.

Thus,

The mean and private colleges is computed as follows:

The mean and private colleges = The sum of derivation/The total number of observation

x= 42.5

The standard deviation is S₁ = 6.9806 = √∈ (xi - x)²/n-1

The mean of public colleges y =22.3

Standard deviation  S₂ = 4.5323 = √∈ (yi - y)²/n-1

Thus,

S₁ = 6.98

S₂  =4.53

(b) We find the point estimate of the difference between two population means

Thus,

x -y = 42.5 -22.3

=20.2

Therefore, the annual cost is =$20,200

Note: Kindly find an attached copy of the option c and the complete question stated above.

Answer:

27 and 36

Step-by-step explanation:

Let's call the two numbers x and y.

[tex]3x=4y \\\\x+y=63[/tex]

If you subtract y from both sides of the second equation, you can isolate x and substitute it into the first equation:

[tex]x=63-y \\\\3(63-y)=4y\\\\189-3y=4y\\\\189=7y\\\\y=27\\\\x=63-27=36[/tex]

Hope this helps!

Answer:

A=25000 is the future value. P the value that we need to invest. r= 0.04 represent the interest rate in fraction. n = 12 represent the number of times that the rate is compounded in a year. t = 5 years.

If we solve for the value of P we got:

[tex] P= \frac{A}{(1+ \frac{r}{n})^{nt}}[/tex]

And replacing we got:

[tex] P= \frac{25000}{(1+ \frac{0.04}{12})^{12*5}} =20475.078[/tex]

And rounded to the nesrest penny we need to invest $20475.08 in order to have after 5 years $25000

Step-by-step explanation:

For this case we can use the future value with compound interest given by:

[tex] A = P (1+ \frac{r}{n})^{nt}[/tex]

Where:

A=25000 is the future value. P the value that we need to invest. r= 0.04 represent the interest rate in fraction. n = 12 represent the number of times that the rate is compounded in a year. t = 5 years.

If we solve for the value of P we got:

[tex] P= \frac{A}{(1+ \frac{r}{n})^{nt}}[/tex]

And replacing we got:

[tex] P= \frac{25000}{(1+ \frac{0.04}{12})^{12*5}} =20475.078[/tex]

And rounded to the nesrest penny we need to invest $20475.08 in order to have after 5 years $25000

Answer:

93.6 ml

Step-by-step explanation:

12% of that 780 ml is pure acid:  0.12(780 ml) = 93.6 ml

The amount of pure acid is 93.6 ml.

Proportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are key foundations to understand the various concepts in mathematics as well as in science.

The direct proportion formula says if the quantity y is in direct proportion to quantity x, then we can say y = kx, for a constant k. y = kx is also the general form of the direct proportion equation.

Given:

You have 780 ml of a 12% solution

So,

780 ml represents 100%,

x ml represents 12%.

Using proportion:

780/x= 100/12

780*12/100=x

93.6 ml = x

Learn more about this concept here:

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Answer

51

Explanation

85/15=y/9

765=15y

51

Answer:

y = 51

Step-by-step explanation:

These triangles are similar, so you can set up a proportion to solve for y:

[tex]\frac{85}{15} =\frac{y}{9}[/tex]

Cross multiply:

[tex]\frac{765}{15y}[/tex]

Divide 765 by 15:

y = 51

Answer:

The sequence is of the form

9 ,   13 , 17 , 21 , 25 ,29

Step-by-step explanation:

Explanation:-

Step(i):-

Given sequence   , ___, __17_ ,___,___ 29

The third term = 17

          a + (3-1)d = 17

          a + 2 d = 17 ...(i)

The sixth term = 29

      a + (6-1)d =29

      a + 5 d  = 29 ...(ii)

solving (i) and (ii) equations

Subtracting (i) and (ii) equations , we get

 a + 2 d -a -5 d = 17 -29

   - 3 d = - 12

       d =4

Substitute 'd' =4 in equation (i)

   a + 2 d = 17

  a + 2(4) =17

  a = 17 -8 = 9

Step(ii):-

The arithmetic sequence

            a ,   a+d ,   a+2 d  ,  a+ 3 d , a+ 4 d , a+5 d

            9  , 9 + 4, 9 +2 (4) , 9+3(4) , 9 +4(4) , 9+5(4)

             9 ,   13 , 17 , 21 , 25 ,29

Conclusion:-

The sequence is of the form

9 ,   13 , 17 , 21 , 25 ,29

9, 13, 17, 21, 25, 29

Answer:

4

Step-by-step explanation:

because r2=16 so you have to find the square root of 16 to get r

Answer:1. Dependent

2.Qualitative Variable

Step-by-step explanation:

Step 1--- Dependent

Reason-- The researcher considers a couple as a whole and The sampling is dependent because a spouce selected for one sample dictates or determines which individual to be in the second sample.

Step 2----Qualitative variable

Reason--- it classifies the individual spouce mental health based on mental health inventory of the couple

Because Qualitative variables are variables which can be placed according to characteristic or attribute, here the characteristics is mental health.

Answer:

1) Dependent. It is becasue one sample indicates the individual to be used in another sample.

2) Quantitative. Attribute classification is numerical measure

Step-by-step explanation:

Mental health of Married lawyer and their spouses are to be compared. A married lawyers mental health is to be compared with his/her spouse only

Here attribute is mental health inventory which is quantitative.

Answer:

11

4

Step-by-step explanation:

3 hrs to travel 45 miles downstream

4 hrs to travel 28 miles upstream

speed of boat in still water= s

speed of the current= c

added up the 2 equations, we get:

Answer:

70%

Step-by-step explanation:

Answer:

The probability of rolling a number greater than 2 two times in a row is arond 0.44

Step-by-step explanation:

Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring. In the case of rolling a 3 on a die, the number of events is 1 (there's only a single 3 on each die), and the number of outcomes is 6.

Probability formula is the ratio of number of favorable outcomes to the total number of possible outcomes. Measures the likelihood of an event in the following way: - If P(A) > P(B) then event A is more likely to occur than event B. - If P(A) = P(B) then events A and B are equally likely to occur.

Answer:

The number of cases in the year 2010 is 266.

Step-by-step explanation:

An exponential function is one that the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)=aˣ

being a positive real, a> 0, and different from 1, a ≠ 1.

In this case:

[tex]r(t) = 207*e^{0.005*t}[/tex]

where t is the number of years since 1960 and   e is an irrational number of which it is not possible to know its exact value because it has infinite decimal places. The first figures are 2,7182818284590452353602874713527 and is often called the Euler's number. e is the base of natural logarithms.

In this case, you want to know the number of cases r (t) in 2010. So, to know t you must know how many years have passed since 1960. For that, you can simply do the following subtraction: 2010-1960 and you get as a result : 50.

Replacing in the exponential expression r (t):

[tex]r(t) = 207*e^{0.005*50}[/tex]

Solving:

r(t)=265.79 ≅ 266

The number of cases in the year 2010 is 266.

Answer:

Ivan gets £90 more than Tanya.

Step-by-step explanation:

£150÷5=£30

Every 1 part of the ratio is £30

Ivan : Tanya

£120:   £30

Ivan gets £90 more than Tanya.

Answer:

  see below for the tables

Step-by-step explanation:

The differential equation is separable, so the solution is ...

  [tex]\displaystyle\dfrac{dy}{dx}=2xy\\\\\int{\dfrac{dy}{y}}=\int{2x}\,dx\\\\\ln{y}=x^2+C\\\\\text{Considering the initial condition, $C=-1$}\\\\\boxed{y=e^{x^2-1}}[/tex]

__

The values for yn are y+y'·h = y+2xyh. We take the "absolute error" to be the (signed) difference between the calculated yn and the actual value y(x).

Answer:

The answer would be, 0.454

Step-by-step explanation:

1 pound= 0.454 kilogram

Answer:

1kg = 2.20462262 rounded 2.20

Answer:

We want to test if the  if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 (alternative hypothesis) , then the system of hypothesis are:

Null hypothesis: [tex]p_1 = p_2[/tex]

Alternative hypothesis: [tex] p_1 = p_2[/tex]

And the best option would be:

b. H0:P1=P2; Ha：P1≠P2

Step-by-step explanation:

For this case we have the following info given:

[tex]X_1 = 228 [/tex] the myopia cases in 2019

[tex] n_1= 600[/tex] the sample size in 2019

[tex] \hat p_1= \frac{228}{600}= 0.38[/tex] estimated proportion of myopia cases in 2019

[tex]X_2 = 123 [/tex] the myopia cases in 2010

[tex] n_2= 400[/tex] the sample size in 2010

[tex] \hat p_2= \frac{123}{400}= 0.3075[/tex] estimated proportion of myopia cases in 2010

And we want to test if the  if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 (alternative hypothesis) , then the system of hypothesis are:

Null hypothesis: [tex]p_1 = p_2[/tex]

Alternative hypothesis: [tex] p_1 = p_2[/tex]

And the best option would be:

b. H0:P1=P2; Ha：P1≠P2

And we can conduct a two sample z proportion test in order to verify the hypothesis.

Answer:

Answer:

Mr.Lim had 19610 dollars, and Mr.Tay had 11480 dollars at first.

Step-by-step explanation:

Mr. Lim had 19610 dollars at first.

Given:

Mr. Lim and Mr. Tay had $31 090 at first.

Mr. Lim donated $2390 of his money and

Mr. Tay spent half of his money on a holiday trip.

Mr. Lim had 3 times as much money as Mr. Tay.

Step 1:

Let Mr. Tay had x

Let Mr. Lim had y

x + y=31090………..(1)

Step 2:

Mr. Tay spent on holiday = x + 2390/2

Money left with Mr. Lim = y - 2390

Given,

y - 2390 = 3(x + 2390/2) .............(2)

Step 3:

Equating equation (1) and (2)

we get,

x = 11480

y = 19610

Hence, Mr. Lim has $19610, and Mr. Tay had $11480 dollars at first.

To learn how to calculate the amount spent, refer,

#SPJ2

Answer:

-2, -1

Step-by-step explanation:

the x same cause if you reflect across the x-axis so you move on the y-axis. and reflect means the same distance from the point you reflect (that it was 1 cause it was 1 point above the x-axis) just negative so -1 now. if the original point was -2,-1 so the answer was -2,1.

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Formula for area: [tex]A = \frac{1}{2}(^{b}1 + ^{b}2)(h)[/tex]

In this formula, the bases are the parallel sides.

Now plug the information into the formula.

[tex]A = \frac{1}{2} (3 + 5)(9)[/tex].

Follow your order of operations, simplify inside the parentheses first.

[tex]A = \frac{1}{2}(8)(9)[/tex].

(1/2)(8) is 4 so we have (4)(9) which is 36.

So the area of the trapezoid is 36.

Answer:

5

Step-by-step explanation:

Additive inverses are two numbers that add to 0.

Since -5 + 5 = 0, then the additive inverse of -5 is 5.

Answer: 5

Answer:

It would just be the opposite -5 the inverse is 5.

Step-by-step explanation:

Hope my answer has helped you in anyway and if not I am sorry.