Answer:
Step-by-step explanation:
1.) we need to find the bounds of integration which is just the points of intersection
here is it (-2,0) and (2,0)
which means we will integrate from -2 to 2
next, we take the upper equation and subtract that from the lower one
kind of confusing but it would look like (sketch it out if you're not sure)
(4-x²)-0= 4-x²
then we can integrate
[tex]\int\limits^2_{-2} {4-x^2} \, dx =4x-\frac{x^3}{3}|_{-2}^{2}=(4*(2)-\frac{2^3}{3})-(4(-2)-\frac{-2^3}{3})=5.333333-(-5.3333333)= 10.666666667=\frac{32}{3}[/tex]
There are 750 identical plastic chips numbered 1 through 750 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Answer:
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
There are 750 identical plastic chips numbered 1 through 750 in a box
This means that [tex]a = 1, b = 750[/tex]
What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?
[tex]P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358[/tex]
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
This are diferente question help me please
Step-by-step
28.26 in84.9 m5024 cm277.45 mi 452.16 in1.36 mi44.15 m3.14 cmI hope it helps you
evaluate g(x)=x/x-3, if g(1/2)
Answer:
-1/5
Step-by-step explanation:
g(x) = x/(x-3)
Substituting x = 1/2 in g(x),
g(1/2) = 1/2/(1/2-3)
= 1/2/(1/2-6/2)
= 1/2/(-5/2)
= 1/2 ÷ - 5/2
= 1/2 x -2/5
= - 1/5
Step-by-step explanation:
here is your answer
here is your answer
Simplify -4 + (-3) + 6.
Answer:3/6 in simplest fraction form is 1/2.
Step-by-step explanation:EASY and my chanel is FireFlameZero if u can check dat out
The radius of a plant pot is 4.5 cm, and its height is 6 cm. What is the volume of the pot?
Use the value 3.14 for , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
381 cm³
Step-by-step explanation:
Volume of the pot = volume of a cylinder
Volume of the pot = πr²h
Where,
π = 3.14
radius (r) = 4.5 cm
h = 6 cm
Substitute
Volume of the pot = 3.14*4.5²*6
Volume of the pot = 381.51 ≈ 381 cm³ (nearest whole number)
WILL MARK YOU JF YOU HELP PLEASE HELP ME!!
I need help please I dont understand
Question 11 of 45
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
12
6 R
X 2 z
O A. Similarity cannot be determined,
B. SSS theorem
O C. AA postulate
D. SAS theorem
Answer:
You are only given a Side, an Angle, and then a side. So that is what I would choose. It can't be AA because you weren't given two angles. It can't be SSS because you weren't given 3 sides.
Step-by-step explanation:
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Option B is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
Similar triangles are triangles that have the same shape but may have different sizes.
Two triangles are similar if their corresponding angles are equal, and their corresponding sides are proportional.
When two triangles are similar, they have the same shape, but one may be larger or smaller than the other.
Now,
ΔPQR and ΔXYZ
PQ/XY = 12/4 = 3
PR/XZ = 6/2 = 3
Since the two sides are proportional,
QR/YZ will be proportional.
Now,
PQ/XY = PR/XZ = QR/YZ
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Thus,
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Learn more about triangle congruency here:
https://brainly.com/question/12413243
#SPJ7
anyone help me, let's prove
Answer:
In my opinion the limit is equal to 1 not 0, sorry.
Step-by-step explanation: 6 25 13 43
lim n ⇒∞ ((2n - 1)/2n)
lim n ⇒∞ (2n/2n) - 1)/2n) 2n/2n = 1 1/∞ = 0
= 1 - 0
= 1
when I graphed the function I also got 1
Find the measure of WX and show work
Ans : the measure of WX = 8
add negative 4 plus negative 6
-10
thats it, thats what i know
HI CAN SOMEONE THAT REALLY KNOWS ABOUT THIS HELP ME WITH FINAL EXAM...
The data represented by the following stem-and-leaf plot range from
to
489
5147
6235
769
A. 49; 79
B. 48; 79
C. 48; 76
D. 49; 76
A square-based tent covers an area of 64 square feet. What is the length of one side of the tent?
Answer:
8 feet
Step-by-step explanation:
A square's area can be expressed as l², with l representing one side of the tent. Therefore, as our area is 64, we can say that 64 = l². Taking the square root of both sides, we get that √64 = l, and l = 8 feet
There are 200 students in a particular graduate program at a state university. Of them, 110 are female and 125 are out-of-state students. Of the 110 females, 70 are out-of-state students. If two of these 200 students are selected at random, what is the probability that both of them are out-of-state students?
If F(x)= 3x-2 and G(x)= x^2+8, what is G(F(x))?
Answer:
(3x-2)^2+8= 9x^2-12x+12
Segment [tex]$s_1$[/tex] has endpoints at [tex]$(3+\sqrt{2},5)$[/tex] and[tex]$(4,7)$[/tex]. Segment [tex]$s_2$[/tex] has endpoints at [tex]$(6-\sqrt{2},3)$[/tex] and[tex]$(3,5)$[/tex]. Find the midpoint of the segment with endpoints at the midpoints of [tex]$s_1$[/tex] and [tex]$s_2$[/tex]. Express your answer as [tex]$(a,b)$[/tex].
Answer:
The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).
Step-by-step explanation:
Midpoint of a segment:
The coordinates of the midpoint of a segment are the mean of the coordinates of the endpoints of the segment.
Midpoint of s1:
Using the endpoints given in the exercise.
[tex]x = \frac{3 + \sqrt{2} + 4}{2} = \frac{7 + \sqrt{2}}{2}[/tex]
[tex]y = \frac{5 + 7}{2} = \frac{12}{2} = 6[/tex]
Thus:
[tex]M_{s1} = (\frac{7 + \sqrt{2}}{2},6)[/tex]
Midpoint of s2:
[tex]x = \frac{6 - \sqrt{2} + 3}{2} = \frac{9 - \sqrt{2}}{2}[/tex]
[tex]y = \frac{3 + 5}{2} = \frac{8}{2} = 4[/tex]
Thus:
[tex]M_{s2} = (\frac{9 - \sqrt{2}}{2}, 4)[/tex]
Find the midpoint of the segment with endpoints at the midpoints of s1 and s2.
Now the midpoint of the segment with endpoints [tex]M_{s1}[/tex] and [tex]M_{s2}[/tex]. So
[tex]x = \frac{\frac{7 + \sqrt{2}}{2} + \frac{9 - \sqrt{2}}{2}}{2} = \frac{16}{4} = 4[/tex]
[tex]y = \frac{6 + 4}{2} = \frac{10}{2} = 5[/tex]
The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).
Translate the phrase into an algebraic expression.
3 more than b
Answer:
b+3 or 3+b
Step-by-step explanation:
if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line
Answer:
The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation the equation of the straight line will be.
Step-by-step explanation:
Can someone help me with this question please.
Answer:
40
Step-by-step explanation:
As the lawn size increases by 4 the weight increases by 8
Alla and Balla together drink 750 milliliters (ml) of water. If Alla drinks 50% more than
Balla, how much does Alla drink?
Answer:
Step-by-step explanation:
A + B = 750
A = 1.5 B
~~~~~~~~~~~~~~
750-B = 1.5 B
750 = 1.5 B + B
750 = B(1.5 +1)
750 = B (2.5)
B = 300
A = 450
Find the value of y and show work
Answer:
75
Step-by-step explanation:
∠K and ∠ R are congruent (equal)
Triangle Sum Theory - angles of all triangles add to 180
180 - 79 - 26 = 75
When comparing two box-plots that show the same type of information, what determines agreement within the data?
A.the range of the quartiles in each data set
B.the median of each data set
C.the mean of each data set
D.the number of values in each data set
Answer:
c.the mean of each data set
Answer:
A
Step-by-step explanation:
I need help with this.
9514 1404 393
Answer:
$400
Step-by-step explanation:
The word "per" in math often means "divided by". To find price per square foot, find price divided by square feet.
$700,000/(1750 ft²) = $400 /ft²
The price per square foot of House 4 was $400.
Yam
190
Groundnuts
90
Vegetables
30. What is the ratio of the land used
for groundnuts to the land for
vegetables
Answer:
3:1
Step-by-step explanation:
90:30 simplified is 3:1
Select the correct answer.
What is the solution to this equation?
log3 (4x) – 2log3x =2
A. 36
B. 9/4
C. 4/9
D. 1/36
9514 1404 393
Answer:
C. 4/9
Step-by-step explanation:
There are a couple of ways you can do this.
[tex]\log_3{4x}-2\log_3{x}=2\\\\\log_3{4}+\log_3{x}-2\log_3{x}=2\\\\\log_3{4}-2=\log_3{x}\\\\4\cdot3^{-2}=x\qquad\text{take antilogs}\\\\\boxed{x=\dfrac{4}{9}}\\\\\textsf{or}\\\\\dfrac{4x}{x^2}=3^2\qquad\text{take antilogs}\\\\\dfrac{4}{9}=x\qquad\text{cancel $x$, multiply by $\dfrac{x}{9}$}[/tex]
Alix is 10 years older than tamia. Alanna is twice as old as tamia. If the sum of their ages is 74, how old is alanna
Answer:
Alanna is 32 years old
Step-by-step explanation:
Hi there!
We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.
Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x
Alix is 10 years older than Tamia, so Alix must be x+10 years old
Alanna is twice as old as Tamia, so she must be 2x years old
We're also given that Alix+Alanna+Tamia=74
When we substitute it with the expressions we have, it becomes:
x+x+10+2x=74
now combine like terms
4x+10=74
subtract 10 from both sides
4x=64
divide both sides by 4
x=16
We found the value of x (Tamia's age)
However, the problem asks for Alanna's age, which we have set as 2x
So Alanna is 2*16, or 32 years old
Hope this helps! :)
Answer:
32 years
Step-by-step explanation:
that is the procedure above
A box with a square base and open top must have a volume of 256000 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base.
Answer:
Follows are the response to the given question:
Step-by-step explanation:
The volume of the box:
[tex]V = x\times x \times h = 256000 \ cm^3\\\\\to x^2 \times h = 256000\\\\\to h = \frac{256000}{x^2}[/tex]
The surface area of the open box is:
[tex]A(x) = x \times x + 2 \times (x \times h +x \times h)\\\\A(x) = x^2 + 4 \times x \times h\\\\A(x) = x^2 + \frac{1024000}{x}\\\\\frac{d(x^n)}{dx} = n \times x^{(n - 1)}\\\\[/tex]
Use above formula
[tex]A'(x) = 2 \times x - \frac{1024000}{x^2}\\\\[/tex]
[tex]A'(x) = 0\\\\2\times x - \frac{1024000}{x^2} = 0\\\\2x = \frac{1024000}{x^2}\\\\x^3 = 512000\\\\x = (512000)^{(\frac{1}{3})} = 80\ cm\\\\[/tex]
Now
[tex]A''(x) = 2\times 1 + 2\times \frac{1024000}{x^3}\\\\A''(x) = 2 + \frac{2048000}{x^3}\\\\x = 80 \ cm\\\\A''(80) = 2 + \frac{2048000}{80^3} = 6\\\\[/tex]
therefore [tex]A"(x) > 0,[/tex] x amount of material used in minimum.
[tex]h = \frac{256000}{80^2} = 40\ cm[/tex]
Q2 find the degree of the polynomial
x4(4x+1)
Step-by-step explanation:
x⁴(4x+1)
4x⁵+x⁴
degree is 5
What are the rational roots of f(d) = 5d - 6 + d-8?
Write the equation of the circle with center C(-5,8) and radius = 7
Answer:
( h + 5 )^2 + ( y - 8 ) ^2 = 49
Step-by-step explanation:
Equation of a circle:
( x - h )^2 + ( y - k )^2 = r^2
Where ( h , k ) = center and r = radius
We are given that the circle has a center at ( -5 , 8 ) meaning that h = -5 and k = 8
We are also given that the circle has a radius of 7 meaning that r = 7
Now that we have identified each variable we plug the values into the equation
( h - (-5)^2 + ( y - 8 )^2 = 7^2
Our final step is to simplify
we get that the equation of the circle is
( h + 5 )^2 + ( y - 8 ) ^2 = 49
By the way ^ means exponent
