Answer:
32 Bags.
Step-by-step explanation:
Evaluate the integral. (Use C for the constant of integration.) 7x3 5x2 49x 5 (x2 1)(x2 7) dx
Answer:
[tex]\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
Step-by-step explanation:
Perform the partial fraction decomposition
[tex]\int{\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)} } \, dx\\ \\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\ \\7x^3+5x^2+49x+5=(x^2+7)(Ax+B)+(x^2+1)(Cx+D)\\\\7x^3+5x^2+49x+5=Ax^3+Bx^2+7Ax+7B+Cx^3+Dx^2+Cx+D\\\\7x^3+5x^2+49x+5=Ax^3+Cx^3+Bx^2+Dx^2+7Ax+Cx+7B+D\\\\7x^3+5x^2+49x+5=x^3(A+C)+x^2(B+D)+x(7A+C)+7B+D[/tex]
Set up a system of equations and solve for each constant
[tex]\begin{cases} A + C = 7\\B + D = 5\\7 A + C = 49\\7 B + D = 5 \end{cases}[/tex]
[tex]A+C=7\\A=7-C[/tex]
[tex]7A+C=49\\7(7-C)+C=49\\49-7C+C=49\\49-6C=49\\-6C=0\\C=0[/tex]
[tex]A=7-C\\A=7-0\\A=7[/tex]
[tex]B+D=5\\B=5-D[/tex]
[tex]7B+D=5\\7(5-D)+D=5\\35-7D+D=5\\35-6D=5\\-6D=-30\\D=5[/tex]
[tex]B=5-D\\B=5-5\\B=0[/tex]
Plug solved constants in and evaluate
[tex]\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x+0}{x^2+1}+\frac{0x+5}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x}{x^2+1}+\frac{5}{x^2+7}[/tex]
Break up integral
[tex]\int {\bigr(\frac{7x}{x^2+1}+\frac{5}{x^2+7}\bigr) } \, dx[/tex]
[tex]\int {\frac{7x}{x^2+1} } \, dx +\int {\frac{5}{x^2+7}} \, dx\\\\\int {\frac{7x}{x^2+1} } \, dx +5\int {\frac{1}{x^2+7}} \, dx[/tex]
Solve first integral
Let [tex]u=x^2+1[/tex] and [tex]du=2xdx[/tex] for the first integral. Thus, [tex]\frac{7}{2}du=7xdx[/tex]:
[tex]\frac{7}{2}\int {\frac{du}{u}}\\\\\frac{7}{2}ln(|u|)+C\\ \\\frac{7}{2}ln(|x^2+1|)+C[/tex]
Solve second integral
Since [tex]5\int {\frac{1}{x^2+7} } \, dx[/tex] is in the form of [tex]\int{\frac{1}{x^2+a^2} } \, dx[/tex], its formula is [tex]\frac{1}{a}arctan(\frac{x}{a})+C[/tex]:
[tex]5\int {\frac{1}{x^2+7} } \, dx\\\\5\bigr(\frac{1}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\bigr)\\\\\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
Combine integrals
[tex]\biggr[\frac{7}{2}ln(|x^2+1|)+C\biggr]+\biggr[\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\biggr]\\ \\\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]
helpp
helpp i need helpw tih thies
Answer:
20
Step-by-step explanation:
9/g+2h+5
g=3
h=6
=9/3+2(6)+5
=3+12+5
=20
hope dis helps.
pls brainliest!!!!!
work out the size of angles x, y and z.
Answer:
x = 41° , y = z = 74°
Step-by-step explanation:
x and 41 are alternate angles and are congruent , then
x = 41°
the 2 sides of the triangle with vertex = 32° are congruent so the triangle is isosceles with base angles being congruent , then
y = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74°
y and z are vertically opposite angles and are congruent so
z = 74°
What is 2 5/7 ·48+2 2/7 ·48? Please help!!!
9514 1404 393
Answer:
240
Step-by-step explanation:
Your calculator can tell you the answer.
__
If you're doing this by hand, it can be convenient to combine the multipliers of 48:
(2 5/7)·48 +(2 2/7)·48 = (2 5/7 +2 2/7)·48 = ((2+2) +(5/7+2/7))·48
= (4 +7/7)·48 = 5·48 = 240
find 3 ratios
s that are equivalent to the given ratio 9 to 15
Answer:
3:5 & 18:30
Step-by-step explanation:
To find an equivalent ratio, just multiply or divide both terms by the same number. For the two I did, I divided by 3 for one, and multiplied by 2 for the other, but there are infinite possibilities. Hope this helped!
Use the estimates to help you choose each correct answer. 14.8(20.7) = Estimate: 15(20) = 300 1.1(9.8) = Estimate: 1(10) = 10 72.5(4.9) = Estimate: 70(5) = 350
Answer:
1st 306.36 2nd 10.78 3rd 355.25
Step-by-step explanation:
bc i just skipped and it showed me the answers
The angles in a triangle are such that the measure of one angle is twice the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles, in degrees.
Answer:
the smallest angle are 30 degree
Step-by-step explanation:
let x is the angle of triangle
x+2x+3x=180
6x=180
6x/6=180/6
x=30 degree
2x=60 degree
3x=90degree
A bird sits on the branch of a tree, then starts to fly. The height of the bird is described by the function. y=0.6sin(pix/12)+35 where y represents the height of the bird measured in meters, and x represents the number of seconds since the bird left the branch.
Which function expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters?
Answer:
The answer is letter A
Step-by-step explanation:
Use the image above to solve for the
missing angle
3)
106
A) 140°
B) 106
C) 130
D) 85
Sal Boxer decided to divide a gift of $7000 into two different accounts. He placed $1000 in an account that earns an annual simple interest rate of 7.5%. The remaining money was placed in an account that earns an annual simple interest rate of 7.75%. How much interest will Sal earn from the two accounts after one year?
Answer:
Total yearly interest for the two accounts is: $570
Step-by-step explanation:
0.075*1000+0.0825*6000=570
75.0+495.0=570
It’s timed please help
3.2b-4.7b=3b-3.3
What dose b equal
Answer:
b=0.7(3) The 3 in the parentheses means the 3 repeats forever
Step-by-step explanation:
If you simplify the sides, it will equal -1.5b=3b-3.3. This means that 4.5b=3.3. This means that b=0.7(3). The 3 will repeat forever.
Hopefully the explanation and the answer helps you!
Suppose that you have a data set of starting salaries and you find an average starting salary of $47,222 with a standard deviation of $6,528. There are 33 observations. What is the (estimated) standard error? Do not include a dollar sign and answer to two decimal places.
Tim purchases 3,000 shares in company X at $2.49 per share. The company subsequently announces a profit warning, and the share price drops to $2.24 per share. Wishing to minimise his losses, Tim decides to sell his shares. How much of a loss does Tim make? Give your answer in dollars to the nearest dollar
Answer:
$750
Step-by-step explanation:
Tim's share price changes by $2.24 -2.49 = -0.25, so the change in the value of his investment is ...
(3000 shares)(-0.25/share) = -$750
Tim takes a loss of $750 when he sells.
Answer:
Step-by-step explanation:
$\$1170$
Bob's initial investment is given by
Initial Investment =3,000×$1.25=$3,750.
When Bob sells the shares, he sells them for
Sold for price=3,000×$0.86=$2,580.
Therefore Bob's total LOSS is given by
Loss =$3,750−$2,580=$1,170.
can someone please help me on my math please
Answer:
The answer is 112
Step-by-step explanation:
Area= base + base divided by 2 times height.
So 12+16 divided by 2 times 8.
Question 5
An investment of $45 earns 20% interest compounded annually for 3 years. How much is to worth?
O $90.90
O $77.76
O $9.83
O $113.73
Answer:
$77.76
Step-by-step explanation:
The future value formula is useful:
FV = P(1 +r)^t
FV = $45(1.20^3) = $45·1.728 = $77.76
One day in the afternoon 3 groups of 8 students got 5 bags filled with pieces of candy.
they ate a certain amount of candy.
how much candy did each student eat?
Please show work
a. How many quarter-mile laps should Jim run to run 1 mile?
b. How many quarter-mile laps should Jim run to run 5 miles?
Group of answer choices
a. 5, b. 25
a. 3, b. 15
a. 4, b. 20
Answer:
a. 4, b.20
Step-by-step explanation:
There are 4 quarter mile laps in 1 mile, so you multiply the miles covered by 4 to find out the quarter mile laps.
a. 1x4=4
b. 5x4=20
Answer:
a. 4, b. 20
Step-by-step explanation:
A quarter mile is 1/4 a mile is 4/4 so if Jim runs 4 quarter miles he will run a mile so 4 is your answer. Since we know that a quarter mile is 1/4 and a mile is 4/4 we multiply 4*5 and get 20.
Out of all fan items sent for refurbishing, 40% had mechanical defects, 50% had electrical defects and 25% had both. Denote A="fan item has a mechanical defect" and B="fan item has an electrical defect". Determine the probability that a fan item selected at random will have at least one defect.
Using Venn probabilities, it is found that there is a 0.65 = 65% probability that a fan item selected at random will have at least one defect.
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In this problem, the given probabilities are [tex]P(A) = 0.4, P(B) = 0.5, P(A \cap B) = 0.25[/tex], hence, the "or probability", also called the "at least one" probability, is given by:
[tex]P(A \cup B) = 0.4 + 0.5 - 0.25 = 0.65[/tex]
0.65 = 65% probability that a fan item selected at random will have at least one defect.
More can be learned about Venn probabilities at https://brainly.com/question/25698611
Photos and videos have become an important part of the online social experience, with more than half of Internet users posting photos or videos online that they have taken themselves. Let A be the event an Internet user posts photos that they have taken themselves, and B be the event an Internet user posts videos that they have taken themselves. A research center finds that P(A) = 0.44, P(B) = 0.26, and P(A or B) = 0.50.
Required:
Make a Venn diagram showing the events {A and B}, {A and not B}, {B and not A}, and {neither A nor B}.
Answer:
{A and B} = 0.20
{A and not B} = 0.24
{B and not A} = 0.06
{neither A nor B} = 0.50
Step-by-step explanation:
Given the following :
P(A) = 0.44
P(B) = 0.26
P(A or B) = 0.50.
{A and B} = 0.20
{A and not B} = 0.24
{B and not A} = 0.06
{neither A nor B} = 0.50
Kindly check attached picture for detailed explanation
Jane has a pile of 6 books. Together, the books weigh 4 pounds. If the books are
similar in weight, about how much does each book weigh?
Btw the answers not 2 lbs bc 2lb x 6 = 10 lbs and it needs to equal 4 lbs.
Answer:
[tex]\frac{2}{3}[/tex] lbs per book
Step-by-step explanation:
We can divide 4 pounds by the total number of books, 6, to find out how much each book weighs.
4 lbs / 6 books = [tex]\frac{4/2}{6/2}=\frac{2}{3}[/tex] lbs
Each book weighs [tex]\frac{2}{3}[/tex] lbs
2/3 is equal to about 0.667
Another thing I wanted to note, 2 lbs * 6 = 12 lbs, not 10 lbs.
What is the volume of the solid figure?
The solid shape is made up of two rectangular prisms. The first rectangular prism has a height of 10 inches, length of 5 inches, width of 5 inches and with connecting to the second rectangular prism, has a smaller height of 5 inches. The second rectangular prism has a length of 15 inches, height of 5 inches, width of 5 inches. The total length of the solid is 20 inches.
A.
625 in3
B.
750 in3
C.
800 in3
D.
1,250 in3
Answer:
A:
625 in3 I think
ok so I think coz I'm in 4rth
There are 76 milligrams of cholesterol in a 3.1 ounce serving of lobster. How much cholesterol is in 5 ounces of lobster
Answer:
123 milligrams
Step-by-step explanation:
76 : 3.1 = x : 5
76 * 5 = 3.1x
x = 76*5/3.1 = 123 milligrams
If y varies inversely as x and y = 12. When x=20. What is y when x is 15?
Pls help
Answer:
[tex]y = 0.04[/tex]
Step-by-step explanation:
[tex]y[/tex] ∝ [tex]\frac{k}{x}[/tex] (k is a constant we need)
[tex]12 = \frac{k}{20}[/tex]
[tex]k = 0.6[/tex]
[tex]y = \frac{0.6}{15}[/tex]
[tex]y=0.04[/tex]
Translate the sentence into an equation:
three is 5 more than a number
Answer:
3=x+5
Step-by-step explanation:
Answer:
x + 5 = 3
Step-by-step explanation:
"Three is 5 more than a number."
The word is indicates that 3 is the final number, or rather, what the equation equals.
Then, 5 more than a number, shows the rest of your equation. A number is just your variable, so any letter. We'll use X. Then, it says that the answer (3) is 5 more than x. So, your equation is:
x + 5 = 3
Please help
( I will mark brainliest )
Answer:
umm i think A C D E ?
Step-by-step explanation:
because theyre all the same. some is just distribution. you should wait for another opinion though because im too lazy to check for B
13% VAT is levied on the service provided by a company. If the VAT amount is Rs. 260, find the service charge without VAT.
(Ans: Rs. 2,000)
please solve my problems.
The service charge without the VAT is Rs. 2000.
What is the service charge?VAT means value added tax. It is a form of tax levied on goods and services. Taxes are compulsory amounts or percentages that is levied on certain goods and services. Taxes increase the price of products.
Service charge = VAT / percentage VAT
260 / 13%
260 / 0.13 = Rs. 2000
To learn more about taxes, please check: https://brainly.com/question/25311567
Given the information in the diagram below, what is the measure of LBEC?
Answer: angle BEC = 43 degrees
Step-by-step explanation:
Straight angle = 180 degrees
75 + 62 = 137
180 - 137 = 43
A right cylinder has radius of 5 cm and a height of 3 cm
Answer the following questions and make sure to show all your work
(a) Find the surface Area of cylinder.
Answer:
251.33cm³
Step-by-step explanation:
take pie as 22/7
surface area = 2π r h + 2π r²
2×22/7×5×3 + 2×22/7×5²
44/7×15 + 44/7×25
660/7 + 1100/7
660 + 1100 all over 7
= 1760/7
251.33cm³ Or 251.43cm³
Solve by factoring the quadratic equation 2x2 + 13x
=
-21.
Answer:
x = - [tex]\frac{7}{2}[/tex], x = - 3
Step-by-step explanation:
Given
2x² + 13x = - 21 ( add 21 to both sides )
2x² + 13x + 21 = 0 ← in standard form
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 21 = 42 and sum = + 13
The factors are + 6 and + 7
Use these factors to split the x- term
2x² + 6x + 7x + 21 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) + 7(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x + 7) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = - [tex]\frac{7}{2}[/tex]
The population of a certain bacteria colony can be modeled by the functionf(x)=x^2 , where x is the number of hours after the colony started. What will the population of the bacteria colony be after 12 hours?
Answer:
The answer is 24
Step-by-step explanation:
Since the population after x hours is 2x, then after 12 hours, we'll substitute x = 12 into the function.
The population becomes 2 x 12 = 24