A right triangle has sides of integer lengths a, 40, and 41. Find a.
b) 9
c) 141-140
d) -9
a) 1
e) none of these.

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 :)

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:

(0,1)

(-2,0)

(2,2)

Step-by-step explanation:

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:

x=-14

Step-by-step explanation:

The 2 angles are opposite of each other. This means that they are vertical angles, are they are congruent.

Since they are congruent, we can set them equal to each and solve for x.

9x+184=7x+156

To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

First, subtract 7x from both sides.

9x-7x+184=7x-7x+156

9x-7x+184=156

2x+184=156

Next, subtract 184 from both sides.

2x+184-184=156-184

2x=156-184

2x=-28

Finally, divide both sides by 2.

2x/2= -28/2

x=-28/2

x= -14

The value of X is -14.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

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:

Liability

Step-by-step explanation:

Ap3x

Answer:

a) H0: p1 - p2 = 0

H1: p1 - p2 ≠ 0

b) z=-0.58

c) p-value = 0.562

Step-by-step explanation:

We need to determine whether p1 is not equals p2, so the null and alternative hypothesis are:

H0: p1 - p2 = 0

H1: p1 - p2 ≠ 0

Where p1 and p2 are the proportions of the population. Additionally, the proportions of the sample p1' and p2' are calculated as:

[tex]p1'=\frac{x1}{n1}=\frac{28}{254}=0.1102\\p2'=\frac{x2}{n2}=\frac{38}{301}=0.1262[/tex]

Then, the test statistic is calculated using the following equation:

[tex]z=\frac{(p1'-p2')-(p1-p2)}{\sqrt{p'(1-p')(\frac{1}{n1}+\frac{1}{n2})} }[/tex]

Where p' is calculated as:

[tex]p'=\frac{x1+x2}{n1+n2}=\frac{28+38}{254+301}=0.1189[/tex]

So, replacing the values, we get that the test statistic is:

[tex]z=\frac{(0.1102-0.1262)-(0)}{\sqrt{0.1189(1-0.1189)(\frac{1}{254}+\frac{1}{301})}}=-0.58[/tex]

Finally, using the standard normal table, the p-value is equal to:

[tex]p-value=2*P(z<-0.58)=2*0.281=0.562[/tex]

The p-value is greater that the value of alpha 0.1, so we can't reject the null hypothesis and there is evidence to said that p1 and p2 are equals.

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:

-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.

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Tangents that meet at a point are equal in length so JL and LM are equal

Let's form an equation:

3x + 10 = 7x - 6

+6 to both sides

3x + 16 = 7x

-3x from both sides

16 = 4x

/4 on both sides

x = 4

Now, we can sub this value into the equation:

7(4) - 6 = 22

Thus, your answer is option B. 22

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Answer:

2ND OPTION  

Step-by-step explanation:

in a circle , tangents drawn from an external point to the circle are equal.

ie JL = LM

3x+10 = 7x-6

10 + 6 = 7x- 3x

16 = 4x

x = 16/4

x=4

therefore LM = 7x -6 = 7*4 - 6

LM = 28 - 6 =22

therefore LM =22

HOPE IT HELPS. PLEASE MARK ME AS THE BRAINLIEST....

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.

Subtract 20 from the total weight and divide by 4:

200 - 20 = 180

180/4 = 45

Each other crate weighs 45 pounds each.

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:

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:

  A.  P = 14x+6

  B.  A = 12x^2 +9x

  C.  P = 118; A = 840

Step-by-step explanation:

A. The perimeter is twice the sum of length and width:

  P = 2(L +W) = 2((4x+3) +(3x)) = 2(7x +3)

  P = 14x +6 . . . . the perimeter of the rectangle

__

B. The area is the product of length and width:

  A = LW = (4x +3)(3x)

  A = 12x^2 +9x . . . . . the area of the rectangle

__

C. When x = 8, these values are ...

  P = 14·8 +6 = 118 . . . . . perimeter in units

  A = 12·8^2 +9·8 = 768 +72 = 840 . . . . . area in square units

Answer:

a) [tex] P = 2(4x+3) +2(3x) =8x +6 +6x = 14x +6[/tex]

b) [tex] A= 12x^2 +9x[/tex]

c) [tex] P = 14*8 +6 = 112+6 = 118[/tex]

[tex] A= 12(8)^2 +9*8 = 840[/tex]

Step-by-step explanation:

We know that the length is 4x+3 and the width is of 3x

Part a

For this case the perimeter is given by:

[tex] P = 2(4x+3) +2(3x) =8x +6 +6x = 14x +6[/tex]

Part b

The area is given by:

[tex] A= (4x+3) (3x)[/tex]

And after multiply we got:

[tex] A= 12x^2 +9x[/tex]

Part c

For this case replacing the value of x =8 we got:

[tex] P = 14*8 +6 = 112+6 = 118[/tex]

[tex] A= 12(8)^2 +9*8 = 840[/tex]

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:

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:

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:

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:

The correct answer is m=8

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: 1.5(b)+ 2.25(s) = 10.05

Step-by-step explanation:

Answer:

B & S

Step-by-step explanation:

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:

The answer would be, 0.454

Step-by-step explanation:

1 pound= 0.454 kilogram

Answer:

1kg = 2.20462262 rounded 2.20

Answer:

c = h/(m+w)

Step-by-step explanation:

m=(h/c)-w

Add w to each side

m+w=h/c-w+w

m+w = h/c

Multiply each side by c

c(m+w) = h/c*c

c(m+w) = h

Divide each side by (m+w)

c(m+w)/(m+w) = h/(m+w)

c = h/(m+w)

Answer:

Area of the figure is 60.75 m²

Step-by-step explanation:

If we divide the given figure in three parts,

Area of the figure = Area of rectangle (1) + Area of rectangle (2) + Area of triangle (3)

Area of rectangle (1) = (Length × width)

                                  = 3 × 4.5

                                  = 13.5 m²

Area of rectangle (2) = (12 × 3)

                                  = 36 m²

Area of triangle (3) = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                               = [tex]\frac{1}{2}(7.5)(3)[/tex]

                               = 11.25 m²

Area of the complete figure = 13.5 + 36 + 11.25

                                              = 60.75 m²

Therefore, area of the figure is 60.75 m²

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: