Answer:
[tex]A = [\frac{32}{3}][/tex]
Step-by-step explanation:
Given
[tex]y_1 = 2x - x^2[/tex]
[tex]y_2 = 2x - 4[/tex]
Required
Determine the area bounded by the curves
First, we need to determine their points of intersection
[tex]2x - x^2 = 2x - 4[/tex]
Subtract 2x from both sides
[tex]-x^2 = -4[/tex]
Multiply through by -1
[tex]x^2 = 4[/tex]
Take square root of both sides
[tex]x = 2[/tex] or [tex]x = -2[/tex]
This Area is then calculated as thus
[tex]A = \int\limits^a_b {[y_1 - y_2]} \, dx[/tex]
Where a = 2 and b = -2
Substitute values for [tex]y_1[/tex] and [tex]y_2[/tex]
[tex]A = \int\limits^a_b {(2x - x^2) - (2x - 4)} \, dx[/tex]
Open Brackets
[tex]A = \int\limits^a_b {2x - x^2 - 2x + 4} \, dx[/tex]
Collect Like Terms
[tex]A = \int\limits^a_b {2x - 2x- x^2 + 4} \, dx[/tex]
[tex]A = \int\limits^a_b {- x^2 + 4} \, dx[/tex]
Integrate
[tex]A = [-\frac{x^{3}}{3} +4x](2,-2)[/tex]
[tex]A = [-\frac{2^{3}}{3} +4(2)] - [-\frac{-2^{3}}{3} +4(-2)][/tex]
[tex]A = [-\frac{8}{3} +8] - [-\frac{-8}{3} -8][/tex]
[tex]A = [\frac{-8+ 24}{3}] - [\frac{8}{3} -8][/tex]
[tex]A = [\frac{-8+ 24}{3}] - [\frac{8-24}{3}][/tex]
[tex]A = [\frac{16}{3}] - [\frac{-16}{3}][/tex]
[tex]A = [\frac{16}{3}] + [\frac{16}{3}][/tex]
[tex]A = [\frac{16 + 16}{3}][/tex]
[tex]A = [\frac{32}{3}][/tex]
Hence, the Area is:
[tex]A = [\frac{32}{3}][/tex]
Melanie is reading a book that has 335pages. She has already read 111pages of the book and will read an additional 16 pages
per night. Find how many more nights it will take Melanie to finish the book.
Find the sample standard deviation:
2 6 15 9 11 22 1 4 8 19
A) 6.3.
B) 7.1.
C) 6.8.
D) 2.1
Answer:
B. 7.1Step-by-step explanation:
Given the sample data 2 6 15 9 11 22 1 4 8 19, before we can get the standard deviation, we need to first calculate the mean.
mean = 2 +6 +15 +9 +11 +22 +1 +4 +8 +19/10
mean = 97/10
mean = 9.7
Standard deviation for ungrouped data is expressed using the formula;
[tex]S = \sqrt{ \dfrac{\sum(x-\overline x)^2}{n-1} }[/tex]
[tex]\overline x \ is\ the \ mean\\n \ is \ sample \ size[/tex]
[tex]S = \sqrt{\frac{(2-9.7)^2+(6-9.7)^2+(15-9.7)^2+(9-9.7)^2+(11-9.7)^2+(22-9.7)^2+(1-9.7)^2+(4-9.7)^2+(8-9.7)^2+(19-9.7)^2}{10-1} }\\ S = \sqrt{\frac{(-7.7)^2+(-3.7)^2+(5.3)^2+(-0.7)^2+(1.3)^2+(12.3)^2+(-8.7)^2+(-5.7)^2+(-1.7)^2+(9.3)^2}{10-1} }\\\\S = \sqrt{\dfrac{59.29+13.69+28.09+0.49+1.69+151.29+75.69+32.49+2.89+86.49}{10-1} }\\\\\\S = \sqrt{\dfrac{452.1}{9} }\\\\S = \sqrt{50.23}\\ \\S = 7.08\\\\S \approx 7.1[/tex]
Hence the standard deviation of the sample data is 7.1
the sum of the recipocal of two consecutive even number is 7/24.one number is 6.the other number will be
Answer:
8
Step-by-step explanation:
The numbers are 6 and 2x, then:
1/6 + 1/(2x) = 7/241/3 + 1/x = 7/12(x+3)/(3x) = 7/1212(x+3) = 7*3x12x + 36 = 21x21x - 12x = 369x = 36x = 4The other number is 2*4 = 8
HELP DUE TODAY!!!
ILL GIVE BRANLIST!!
Answer: a. 1) we can scale a rate by the reciprocal of its 2nd term to find the unit rate..This makes sense as we know with rates we can divide and that dividing is equivalent to multiplying by the reciprocal.
b. 2) To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate.
a. 2) what we need to know to solve the problem is first the given fractions 3/4 and 1/5 and 2/3 and 1/6. and we need to find what we need to do to those which is division.
Step-by-step explanation:
THE WORKING PART.....
Jaylon... 3/4 ÷ 1/5 = 3/4 × 5/1 is equal to 15/4 or 3 /34
Rene... 2/3 ÷ 1/6 = 2/3 6/1 is equal to 4 (A whole number
I REALLLYYY HOPEE THIS HOPES THIS HELPS. and feel free to brainliest. and friend me if you wanna
Abbys aunt is having a baby. Abby buys ribbon at the craft store to decorate a baby blanket. She buys 12.5 feet of green ribbon and 13.5 feet of polkadot ribbon. the green ribbon cost $.70 per foot in the polkadot ribbon cost $1.10 per foot. How much money does Abby spend on ribbon in all?
Answer:
$23.60
Explanation:
you can make an equation out of the information provided! it will look something like:
12.5(.7)+13.5(1.1)
(12.5 is the amount of green ribbon and .7 is the cost per foot, so you would multiply them to find the total cost of the ribbon. do the same thing for the polka dot ribbon; 13.5 feet times 1.1, the cost per foot, will give u the total cost of polka dot ribbon. then, add them together for the total cost of both ribbons!!)
12.5×.7=8.75
13.5×1.1=14.85
8.75+11.85=23.6, or $23.60!!
Pleeeeeezzzzzzzz answer this
Answer:49 degrees
Step-by-step explanation: because all the opposite angles are same and alternative angles makes it same too plz mark me brainiest
2. Lets be the annual iPad sales (in millions). The value of s is 70 for 2013 (Source: Apple). What does s = 70 mean in this situation?
Answer: 70 million annual iPad sales
Step-by-step explanation:
70 x 1,000,000 = 70,000,000
Helpppp I’m desperate I’ll give brainliest to the first one
Answer:
1(-4)
Step-by-step explanation:
I think it's 1(-4)
since it's moving 1 number over, four times. and if you multiply, the answer -4.
I'm pretty sure this is the answer.
Plane RTX and plane TUX intersect at what figure
Answer:
Line TX or XT
Step-by-step explanation:
Planes always intersect in a line.
x-9=y+2
is it linear or nonlinear
Answer:
x - 9 = y +2 => y = x - 11
It is linear because the exponent of x number is equal to 1.
Hank is a salaried plus commission employee. Hank has a monthly salary of $2,500 and earns 5.5% commission on all
sales. Which of the following expressions represents Hank's total earnings in one month if he has $6,300 in sales?
a. 2,500 + (0.055)(6,300)
b. 2,500 + (5.5)(6,300)
C. (2,500) (5.5) + 6,300
d. (2,500) (0.055) + 6,300
Please select the best answer from the choices provided
B
ОООО
Save and Exit
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Submit
Mark this and retum
Answer:
the answer is A.
Step-by-step explanation:
I just took the test
Set A= {0,3,8}
Set A is not a subset of which set of numbers?
Rational numbers
Integers
Whole numbers
Counting numbers
Set A is not a subset of which set of numbers rational numbers option (A) Rational numbers are correct.
What is set?A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.
It is given that set A:
A ={0, 3, 8}
A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
As we know,
The set of an Integers number = {-∞, ∞}
The set of a whole number = {0, ∞}
The set of a counting number = {-∞, ∞}; all are integer values
Set A is the subset of all the sets shown above.
Thus, set A is not a subset of which set of numbers rational numbers option (A) Rational numbers are correct.
Learn more about the set here:
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The ratio of boys to girls in the 10th grade at Hazlehurst High School is 5:7. If there are 600 students
in the 10th grade, how many are girls?
Answer:
350
Step-by-step explanation:
Total ratio: 12
600/12
each ratio has 50 students
that means the boys are 5 * 50= 250
the girls are 7 * 50 =350
10 x 3 ten thousands = thousands =
fill the answer _+342=675
Answer:
333
Step-by-step explanation:
333+342=675
Answer:
333
Step-by-step explanation:
675 - 342 equals 333
hope this helps you :)
pls mark me brainlest ;)
Lila owes $33,000 in student loans. If her loan is to be repaid in 6.5 years and the interest rate is charged 6.75 percent, how much will she pay all together?
Answer: $ 47,478.75
Step-by-step explanation:
Formula: Interest = Principal x rate x time.
As per given: Principal amount = $33,000
Rate of interest = 6.75 percent = 0.0675 [To convert in decimal divide it by 100]
Time = 6.5 years
∴ Interest = (33000)× (0.0675)×(6.5)
=$ 14,478.75
Total amount need to pay = Principal+ Interest
= $ ( 33,000 +14,478.75)
= $ 47,478.75
∴ She will pay all together = $ 47,478.75
1/5 + 3/15
Answers should be in format for example 5/2 or 2/5. No decimals or mixed numbers
Work Shown:
1/5 = 3/15 after multiplying top and bottom by 3
1/5 + 3/15 = 3/15 + 3/15 = (3+3)/15 = 6/15
Reduce that result to get
6/15 = (2*3)/(5*3) = 2/5
So 6/15 reduces to 2/5
Overall,
1/5 + 3/15 = 2/5
find two consecutive odd integers whose sum is 16
Answer:
7, 9
Step-by-step explanation:
The average of the two is the even integer between them:
average = sum/2 = 16/2 = 8
The two odd integers are 7 and 9.
_____
In this case, the divisor for the average is 2, because there are 2 integers in the sum.
how can i tell when a number is undefined?
Answer: You can tell when a number is undefined when the number is being divided by zero.
Step-by-step explanation:
Diving a number by zero does make a real situation . You can't divide something by nothing.
2/0 = is undefined
3/0 is undefined
what does 2/5y-4+7-9/10y=
Find the missing length.
Answer:
4.8
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relation between angles and sides of a right triangle is ...
Tan = Opposite/Adjacent
tan(75°) = 18/x
Solving for x gives ...
x = 18/tan(75°)
x ≈ 4.8
What is 3/10 in two other forms? Write each fraction in its simplest form.
Group of answer choices
3/10
Decimal: 0.3
Percentage: 30%
What are the solutions to (x + 7)2 = 81?
O A. -74 and 88
O B-2 and 16
O C. -88 and 74
O D. -16 and 2
Please answer as fast as possibleee !!
Think of the binomial squared as its own squared term.
Since the squared term is isolated, we can take the square root of both sides.
On the left, the square root removes the square and we have x + 7.
On the right, the square root of 81 is ± 9.
*Always use plus or minus when taking square root of both sides*
So we have x + 7 = ± 9.
Now, split things up into two separate equations.
Solving each equation from here, we find that x = -2 or x = 16.
We can write this as {-2, 16}.
The solutions to the equation [tex](x + 7)^2 = 81[/tex] are x = 2 and x = -16.
The correct option is D.
To find the solutions to the equation [tex](x + 7)^2 = 81[/tex] , we can start by taking the square root of both sides of the equation. However, since we have a squared term, we need to consider both the positive and negative square roots.
Taking the square root of both sides, we have:
[tex]x + 7 = \pm \sqrt{81}[/tex]
Simplifying the right side, we get:
x + 7 = ±9
Now, we can solve for x by subtracting 7 from both sides:
x = -7 ± 9
This gives us two possible solutions:
x = -7 + 9 = 2
x = -7 - 9 = -16
Hence, the correct answer is option D: -16 and 2.
To learn more about the quadratic equation;
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PLZ HELP PIC INCLUDED
x = # of days
y = total calories
Simba = 1000 + 140x = y
Cuddles = 2650 - 190x = y
Let's set both of these equations equal to each other
1000 + 140x = 2650 - 190x
Add 190x to both sides and subtract 1000 from both sides.
330x = 1650
Divide each side by 330
x = 5
After 5 days, they will be consuming the same amount of calories.
To find out how many calories they will be consuming, let's plug 5 into our Simba equation.
1000 + 140(5) = y
Multiply 140 by 5
1000 + 700 = y
Simplify
1700 = y
They will be consuming 1,700 calories each day.
What value should go in the empty boxes to complete the calculation for finding the product of 0.37 * 0.42
Answer:
0.1554
Step-by-step explanation:
.37x.42=.1554
Abdul invests $5,000 at an interest rate of 4%, compounded quarterly. How much is the investment worth at the end of 3 years?
O A. $624.32
O B. $5624.32
C. $634.13
O D. $5634.13
is 0.085 greater or lesser than 85 thousandths
Answer: they are they same
Step-by-step explanation:
{(-1,1),(7,4),(3,0),(-5,-1)}
Is this a relation or a function
Any one pls...............
Answer:
151.9 or 15.2
Step-by-step explanation:
A. 526 X 10 D. 526 X 0.1 B. 526 X 100 E. 526 X 0.01 C. 526 X 1000 F. 526 X 0.001
Answer:
what?
Step-by-step explanation:
what is the question to this?
Answer:
A. 526 X 10
Step-by-step explanation:
526 X 10 = 5,260
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