Answer:
a) P(0 < X) = 0.5
b) P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5) = 0.125
d) P(X< -2) = 0
e) P(X < 0 or X>-0.5) = 1
f) value of x is -0.9654
Step-by-step explanation:
Given that;
f(x) = 1.5x²
Now. the probabilities would be the integral of the given function from (-1 to 1)
a) P(0 < X)
P(X > 0)
⇒ Integral from 0 to 1 of f(x)
= (1/2)x³
= 1/2 - 0
= 0.5
Therefore; P(0 < X) = 0.5
b) P(0.5 < X)
P(X > 0.5)
this will also be done in the same way except that, the limits changes to { 0.5 to 1]
= (1)³/2 - (0.5)³ /2
= 0.4375
Therefore; P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5)
The limits become [-0.5 , 0.5]
= (0.5)³/2 - (-0.5)³/2
= 0.125
Therefore; P(-0.5 = X = 0.5) = 0.125
d) P(X<-2)
since value of f(x) = 0 in that region
Therefore P(X< -2) = 0
e) P(X < 0 or X>-0.5)
= P(X < 0) + P(X > -0.5) - P( -0.5 < X < 0 )
= 0.5 + 0.5625 - 0.0625
= 1
Therefore; P(X < 0 or X>-0.5) = 1
f) Determine x such that P(x < X) = 0.05.
Let the value be 'a'
Then, integral from -1 to a will = 0.05
a³ - (-1)³ = 0.05 × 2
a³ + 1 = 0.10
a³ = 0.10 - 1
a³ = -0.9
a = ∛-0.9
a = -0.9654
Therefore, value of x is -0.9654
a) P(0 < X) = 0.5
b) P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5) = 0.125
d) P(X< -2) = 0
e) P(X < 0 or X>-0.5) = 1
f) value of x is -0.9654
Determine the following probabilities:a) P(0 < X)
P(X > 0)
⇒ Integral from 0 to 1 of f(x)
[tex]= (1\div 2)x^3\\\\= 1\div2 - 0[/tex]
= 0.5
So; P(0 < X) = 0.5
b) P(0.5 < X)
P(X > 0.5)
Now
[tex]= (1)^3\div 2 - (0.5)^3 \div2[/tex]
= 0.4375
Therefore; P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5)
The limits become [-0.5 , 0.5]
[tex]= (0.5)^3\div 2 - (-0.5)^3\div 2[/tex]
= 0.125
Therefore; P(-0.5 = X = 0.5) = 0.125
d) P(X<-2)
since value of f(x) = 0 in that region
Therefore P(X< -2) = 0
e) P(X < 0 or X>-0.5)
= P(X < 0) + P(X > -0.5) - P( -0.5 < X < 0 )
= 0.5 + 0.5625 - 0.0625
= 1
Therefore; P(X < 0 or X>-0.5) = 1
f) Determine x such that P(x < X) = 0.05.
Let us assume the value be 'a'
So, integral from -1 to a will = 0.05
[tex]a^3 - (-1)^3 = 0.05 \times 2\\\\a^3 + 1 = 0.10\\\\a^3 = 0.10 - 1\\\\a^3 = -0.9\\\\a = \sqrt[3]{-0.9}[/tex]
a = -0.9654
Therefore, the value of x is -0.9654
Learn more about the probabilities here: https://brainly.com/question/24710931
The expression (2x + 6) + x represents the perimeter of an isosceles triangle. If x represents the length of one side of the triangle, explain how you can use Distributive Property to find the length of each of the two equivalent sides?
Answer:
x+3
Step-by-step explanation:
x= one side of the triangle
(2x+6)=two sides of the isosceles triangle
Factor (2x+6) which is 2(x+3)
So, the length of each side is x+3.
Find 7/12 of 36
I want a good answer!!!
Answer:
option a 21 is the right answer
Step-by-step explanation:
7/12.36
12 into 3 is 36
so 12 1's are and 12 3's are
now it'll become 7 into 3
which is 21
therefore 21 is the answer
The function d = 16t2 models the distance d, in feet, that an object falls in t seconds. Find the inverse function and use the inverse function
o estimate the time it takes an object to fall 100 feet. (1 point)
Answer:
[tex]t = \frac{1}{4}\sqrt d[/tex]
Time to reach 100ft is 2.5 seconds
Step-by-step explanation:
Given
[tex]d = 16t^2[/tex]
Solving (a): Determine the inverse function
[tex]d = 16t^2[/tex]
Swap the positions of d and t
[tex]t = 16d^2[/tex]
Make d the subject
[tex]\frac{t}{16} = d^2[/tex]
Take positive square root of both sides
[tex]\sqrt{\frac{t}{16}} = d[/tex]
[tex]d = \sqrt{\frac{t}{16}}[/tex]
[tex]d = \frac{1}{4}\sqrt t[/tex]
Swap the positions of d and t
[tex]t = \frac{1}{4}\sqrt d[/tex] --- The inverse function
Solving (b): Find t when d =100
Substitute 100 for d in [tex]t = \frac{1}{4}\sqrt d[/tex]
[tex]t = \frac{1}{4}\sqrt {100[/tex]
[tex]t = \frac{1}{4}* 10[/tex]
[tex]t = \frac{1* 10}{4}[/tex]
[tex]t = \frac{10}{4}[/tex]
[tex]t = 2.5[/tex]
Kevin is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 1.75 gallons of gas. How much gas would be in the tank after driving for 5 hours? How much gas would be left after t hours?
Answer:
He would have 2.75 gallons left after 5 hours.
Step-by-step explanation:
What procedure can be used to solve the equation StartFraction x Over 19.3 EndFraction = 38.6, and what is the solution?
Answer: it’s number D I think let me know if I’m wrong
Step-by-step explanation:
Answer:
the answer is d.Multiply both sides by 19.3; the solution is 744.98.
Step-by-step explanation:
got it right on edge.
carmen is taller than ramon but shorter than ricardo. carmen is shorter than ryan who is taller than ricardo. who is the tallest? who is the shortest?
Answer:
ramon is the shortest
ryan is the tallest
carmen is taller than ramon
carmen is shorter than ricardo
carmen is shorter than ryan
ryan is taller than ricardo
How can this expression be written another way?
60x - 24
Factor using the distributive property and the greatest common factor to write an equivalent expression
Enter your answer by filling in the boxes.
Answer:
factor using 12 (gcf)
12(5x-2)
Match each expression with the equivalent expanded expression
Which subject is used most heavily in game design?
a.
Science
c.
Social studies
b.
Language arts
d.
Math
Answer:
nose
Step-by-step explanation:
perdno
Answer:
Language arts
Step-by-step explanation:
find the following (a) 20% of 1 kg in grams
Answer:
20% of 1kg.(1000g)
20/100×1000g
200g
Sam invested $7500, some at 7% interest and the rest at 10%. How much did he invest at each rate if he received $570.00 in interest in one year?
Answer:
.
Step-by-step explanation:
Y is directly proportional to x squared if y=20 when x=2 find y when x= 5
Answer:
y = 125
Step-by-step explanation:
Given that,
y is directly proportional to x² i.e.
[tex]y=kx^2[/tex]
k is a constant of proportionality
Put y = 20 and x = 2 in the given equation to find k.
[tex]k=\dfrac{y}{x^2}\\\\k=\dfrac{20}{(2)^2}\\\\k=5[/tex]
Now put k = 5 and x = 5 in the given equation to find y.
[tex]y=5\times (5)^2\\\\y=125[/tex]
So, the value of y is equal to 125.
Hello! I'm having a problem figuring out this problem: 6c-9d=111 5c-9d=103
I've been looking at different ways to solve it, but I'm not sure how to do it. Please, help give me a step-by-step instruction on how to figure it out. (I'll make you the most Brainliest answer.) (And, you'll get a good amount of points.)
Answer:
C=8
Step-by-step explanation:
6c-9d=111
-) 5c-9d=103
6c-5c=c
-9c+9c=0
111-103=8
(Negative+Negative=Positive)
C=8
I need Brainliest!
Ellen is playing a video game in which she captures butterflies. There are 6 butterflies onscreen, but the number of butterflies doubles every minute. After 4 minutes, she was able to capture 8 of the butterflies.
Part 1 out of 2
Enter an expression for the number of butterflies after 4 minutes. Use a power of 2 in your answer.
Answer:
(2 x 4) - 8
Step-by-step explanation:
4(2x - y) - 3x + 2y
Answer:
5x - 2y
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
4(2x - y) - 3x + 2y
Step 2: Simplify
Distribute 4: 8x - 4y - 3x + 2yCombine like terms (x): 5x - 4y + 2yCombine like terms (y): 5x - 2yWorking together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in 12 hours. Beatrice and Charlie can build the ant hill in 15 hours. How long, in hours, will it take to build the ant hill if Aran, Beatrice, and Charlie work together?
Answer:
They complete the hill in 8 hours
Step-by-step explanation:
Equations:
Let's call the variables:
Aran can make build the ant hill in A hours
Beatrice can make build the ant hill in B hours
Charlie can make build the ant hill in C hours
In one hour, Aran makes 1/A of the ant hill.
In one hour, Beatrice makes 1/B of the ant hill.
In one hour, Charlie makes 1/C of the ant hill.
Aran and Beatrice build it in 10 hours, thus:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}=\frac{1}{10}\qquad\qquad[1][/tex]
Similarly:
[tex]\displaystyle \frac{1}{A}+\frac{1}{C}=\frac{1}{12}\qquad\qquad[2][/tex]
[tex]\displaystyle \frac{1}{B}+\frac{1}{C}=\frac{1}{15}\qquad\qquad[3][/tex]
We need to find the time taken for the three ants to build the anthill:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=[/tex]
Adding [1], [2], and [3]:
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}[/tex]
Adding the fractions (LCM=60):
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6}{60}+\frac{5}{60}+\frac{4}{60}[/tex]
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6+5+4}{60}=\frac{15}{60}=\frac{1}{4}[/tex]
Dividing by 2:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{8}[/tex]
All ants together make 1/8 of the hill, thus they complete the hill in 8 hours
1over 4 power negative 5
Answer:
4 to the 5th power (4^5)
PLEASE HELP, multiple choice! Will give brainliest!!
9514 1404 393
Answer:
(d) x = 3
Step-by-step explanation:
The "vertex form" of the equation of a parabola is ...
y = a(x -h)² +k
In this form, the vertex has coordinates (h, k).
Comparing the form to your equation, you see that h=3, k=4, so the vertex is (h, k) = (3, 4).
The line of symmetry is a vertical line through the vertex. It will have the same x-value as the x-coordinate of the vertex:
x = 3
_____
In short, the equation of the line of symmetry has its constant equal to the opposite of the value added to x. Here, the added constant is -3, so the line of symmetry is x=3.
The values h and k in the vertex-form equation represent the amount of translation right and up from the parent function graph. When the graph is translated 3 units to the right, the line of symmetry moves from x=0 to x=3.
Make P the subject of the formula
pliz pliz ans this
A= P(1+(r/100))^t
Answer:
P = A / (1 + r/100)ᵗ
Step-by-step explanation:
A = P(1 + r/100)ᵗ
We can make P the subject of the above expression as follow:
A = P(1 + r/100)ᵗ
Divide both side by (1 + r/100)ᵗ
P = A / (1 + r/100)ᵗ
Therefore, making P the subject of
A = P(1 + r/100)ᵗ, we have
P = A / (1 + r/100)ᵗ
Mariana jogged 1/2 of a mile to get from school to the park. Then she jogged 3/10 of of mile to get to the store.
What is the total number of miles Mariana jogged
Answer:
Okay, I think the easiest way to approach this problem is to first convert the mixed fractions to irregular fractions:
8
1
8
=
8
⋅
8
+
1
8
=
65
8
7
2
5
=
7
⋅
5
+
2
5
=
37
5
We want the total number of miles, so our equation is:
distance=
65
8
+
37
5
The LCD of 5 and 8 is 5*8=40, so:
distance=
325
40
+
296
40
distance=
621
40
=
15
21
40
miles.
Hope this helps!
Step-by-step explanation:
find the graph below, find the slope of the line. Write your answer as a decimal.
Please help with explanation
1/3 of Cheryl’s savings was the same as 3/4 of Hilda’s savings.Cheryl saved $36.
(a) Find the ratio of Cheryl’s savings to Hilda’s savings.
(b) How much did Hilda save?
Answer:
a) the ratio is 9:4
b) Hilda did save $16.
Step-by-step explanation:
Let's define the variables:
C = Cheryl's savings.
H = Hilda's savings.
We know that:
(1/3)*C = (3/4)*H
We also know that Cheryl saved $36, then we have:
C = $36
Now we can replace that in the above equation to get:
(1/3)*$36 = (3/4)*H
$12 = (3/4)*H
$12*(4/3) = H = $16
Then Hilda did save $16.
And the ratio between of Cheryl's savings to Hilda's savings is:
36 : 16
We can simplify this if we divide both by 2.
(36/2) : 16/2
18 : 8
Again, we can divide both by 2:
(18/2) : (8/2)
9 : 4
Then the ratio is 9 : 4
8x + 3 – 13
31 - 21 - 11
Answer: 8x+10
-1
Step-by-step explanation:
what is 1+1?
(serious question)
Answer:
2
Step-by-step explanation:
If the root of x2-7x+k=0, m=1, find the value of the constant k
Answer:
hfrhghubifhvfuovhtjopugjob
Step-by-step explanation:
A strawberry farmer will receive 37 per bushel of strawberries during the first week of harvesting each week after that the value will drop 0.8 per bushel the farmer estimates that there are approxiamately 129 of strawberries int he fieldsand that the crop is increasing at a rate of four bushels per week when should the farmer harvest the strawberries to maximize their value? (Assume that "during the first week of harvesting" here means week 1. How many bushels of strawberries will yield the maximum value? (Round your answer to the nearest integer.)
bushels
2. What is the maximum value of the strawberries? (Round your answer to two decimal places.)
$
Answer:
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
b.)
Revenue = bx = (157)(31.4) = $ 4929.8
Step-by-step explanation:
Let number of bushes = b
The price of the bushes = x
The time to harvest = t
The revenue = y
Now given,
Price = x = 37 - (0.8)t
and
Number of bushes = b = 129 + 4t
Also,
The revenue = (Number of bushes)(Price of the bushes)
= bx
= (129 + 4t)[37 - (0.8)t]
= 129×37 - 129× (0.8)t + 4×37t - 4×0.8t²
= 4773 - 103.2t + 148t - 3.2t²
= 4773 + 44.8t - 3.2t²
⇒ y = 4773 + 44.8t - 3.2t²
Now,
[tex]\frac{dy}{dt}[/tex] = 0 + 44.8 - 6.4t
Now,
[tex]\frac{dy}{dt}[/tex] = 0
⇒ 44.8 - 6.4t = 0
⇒ - 6.4t = -44.8
⇒ 6.4t = 44.8
⇒t = [tex]\frac{44.8}{6.4} = 7[/tex]
Now,
[tex]\frac{d^{2}y }{dt^{2} }[/tex] = -6.4
As [tex]\frac{d^{2}y }{dt^{2} }[/tex] < 0 ,
It means at time t = 7 , the revenue is maximum
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
Price = x = 37 - (0.8)(7) = 37 - 5.6 = 31.4
b.)
Revenue = bx = (157)(31.4) = 4929.8
Find the volume of the conical paper cup.
3 cm
7 cm
O A. 49 pi cm ^3
B. 7 pi cm^3
C. 21 pi cm ^3
O D. 63 pi cm^3
Answer:
C. 21π cm³
Step-by-step explanation:
Use volume formula for cone
[tex]V = \pi r^{2} \frac{h}{3}[/tex]
r = 3cm
h = 7cm
[tex]V = \pi (3)^{2} * \frac{7}{3}[/tex]
[tex]V = \pi 9 * \frac{7}{3}[/tex]
[tex]V = \pi \frac{63}{3}[/tex]
[tex]V = 21 \pi[/tex]
Answer:
C
Step-by-step explanation:
credit goes to the person up top
What is the equation of the line going through the points (2, 4) and (4, 12)
Answer:
m= 4
b= -12
( 4, -12)
Step-by-step explanation:
m= y2- y1/ x2-x1
m= 12 - 4/ 4 - 2
m= 8/ 2
m= 4
y= 4x + b
(2,4)
4= 4(4) + b
4= 16 + b
-16+4= b
-12= b
b= -12
Find the radius of the circle. The center of the circle is (2, -3) and a point that lies on the circle is (-1, -2).
Answer:
[tex]\displaystyle r = \sqrt{10}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Geometry
Definition of a radius - the center of a circle to any point to the circumferenceAlgebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Center (2, -3) → x₁ = 2, y₁ = -3
Circumference point (-1, -2) → x₂ = -1, y₂ = -2
In this case, the distance d from the center to the circumference point would be the radius r of the circle.
Step 2: Find Radius r
[Distance Formula] Define equation [Radius]: [tex]\displaystyle r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute in points [Radius]: [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2--3)^2}[/tex][Radius] [√Radical] (Parenthesis) Simplify: [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2+3)^2}[/tex][Radius] [√Radical] (Parenthesis) Subtract/Add: [tex]\displaystyle r = \sqrt{(-3)^2+(1)^2}[/tex][Radius] [√Radical] Evaluate exponents: [tex]\displaystyle r = \sqrt{9+1}[/tex][Radius] [√Radical] Add: [tex]\displaystyle r = \sqrt{10}[/tex]The shape below is a horizontal cross section of a figure. Select all the possible figures that could have this shape as a cross section. A Sphere B Rectangular Prism C Triangular pyramid D Rectangular pyramid
Answer:
D. Rectangular prism
Step-by-step explanation:
I believe the answer is D. Rectangular prism
A rectangular prism is also called a cuboid. Like cuboid, it also has three dimensions, i.e., length, width and height. So here the horizontal cross section of the figure is rectangular prism. The correct option is B.
What is a rectangular prism?A rectangular prism is defined as a three dimensional shape which has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. A geometrical box, notebooks, rooms, etc. are in the shape of a rectangular prism.
A rectangular prism has 6 faces, 12 edges and has 8 vertices. For a rectangular prism the pairs of opposite faces are identical or congruent. A prism with six faces that are rectangles and all angles are right angles is a right rectangular prism.
Thus the correct option is B.
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