The formula for the volume of this rectangular prism is:
V = x 3 + 5x 2 - 4x - 20
The length is x+5; the width is x+2; the height is unknown. Find an expression for the height.
Show all steps of your work for full credit.
Answer:
Step-by-step explanation: Explanation:
If
L
,
H
and
W
represent the length, height and width of the prism, then the volume of the rectangular prism is :
V
=
L
.
H
.
W
............. (1)
Given :
V
=
x
3
+
11
x
2
+
20
x
−
32
;
............... (2)
W
=
(
x
−
1
)
;
H
=
(
x
+
8
)
.
Let
L
=
(
x
+
l
0
)
be the expression for the length, then the RHS of equation (1) becomes
L
.
H
.
W
=
(
x
−
l
0
)
(
x
+
8
)
(
x
−
1
)
,
=
(
x
+
l
0
)
(
x
2
+
7
x
−
8
)
=
(
x
+
l
0
)
(
x
2
+
7
x
−
8
)
=
x
3
+
(
7
+
l
0
)
x
2
+
(
7
l
0
−
8
)
x
−
8
l
0
..... (3)
Comparing this to the LHS of equation (1), we get the following set of equations to solve for
l
0
,
7
+
l
0
=
11
;
7
l
0
−
8
=
20
;
8
l
0
=
32
;
l
0
=
4
Therefore
L
=
(
x
+
4
)
What is 162,810.75 rounded to the nearest whole number?
Answer:
162,811
Step-by-step explanation:
Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The tables shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit
Complete question :
A college football coach wants to know if the is a correlation between his players' leg strength and the time it takes for them to sprint 40 yards. he sets up the following test and records the data:
Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The tables shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit? How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions?
Leg Press (reps)|40-yard Dash (s)
15 |5.2
18 |6.3
8 |6.8
30 |8.2
26 |8.0
12 |5.3
21 |5.9
Answer:
ŷ = 0.1073X + 4.5365
6.9
Step-by-step explanation:
Leg Press (reps)X:
15
18
8
30
26
12
21
Y:
5.2
6.3
6.8
8.2
8.0
5.3
5.9
Using a regression calculator :
The equation of line of best fit is :
ŷ = 0.1073X + 4.5365
Slope or gradient = 0.1073
Intercept = 4.5365
X = independent or predictor variable (leg press)
Y = predicted variable (40 yard dash)
B)
X = 22
Y = 0.1073(22) + 4.5365
Y = 6.8971
Y = 6.9
Suppose that there were 226977 visitors to your website over a period of a week, and of those 56330 clicked on the button to get more information about your product. If you wanted to model the probability distribution of the number of visitors who clicked the button, you would typically estimate the mean of the distribution to be equal to the observed number of visitors who clicked, that is the sample mean: 56330.
Required:
Under this setup, what is the variance of this distribution?
Answer:
The variance of this distribution is 42353.2
Step-by-step explanation:
For each visitor, there are only two possible outcomes. Either they clicked on the button, or they did not. Visitors are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
In this question:
226977 visitors, so [tex]n = 226977[/tex]
56330 clicked, so [tex]p = \frac{56330}{226977} = 0.2482[/tex]
Then
[tex]V(X) = 226977*0.2482*(1 - 0.2482) = 42353.2[/tex]
The variance of this distribution is 42353.2
which property is illustrated, 1n = n
1n=n Answer:
Step-by-step explanation:
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee which property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = nwhich property is illustrated, 1n = n
pls help math!!!!!!!!!!!!
Answer:
A) 1000/1 = x/2500 is the answer
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x^2 16y^2
Answer:
The answer is below
Step-by-step explanation:
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16
Solution:
Given that the ellipse has the equation: 4x² + 16y² = 16
let us make x the subject of the formula, hence:
4x² + 16y² = 16
4x² = 16 - 16y²
Dividing through by 4:
x² = (16 - 16y²)/4
x² = 4 - 4y²
Taking square root of both sides:
[tex]x=\sqrt{4-4y^2 }\\[/tex]
The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.
The area of a rectangle inscribed inside an ellipse is given by:
Area (A) = 4xy
A = 4xy
[tex]A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4} \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\ \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}[/tex]
Therefore the length = 2x = 2√2, the width = 2y = 2/√2
Please help me with these math problems! I have had so much going on lately and haven't had time to do them
Will give lots of points and make brainliest please help
Sue cut 3 pieces of ribbon. Each piece was
ot a foot long. How many feet of ribbon does she have in all? Express your answer as the sum of a whole number and the remaining fractional units. Plz help
The functions f(x),8(x), and h(x) are defined below.
f(x)=32
g(x)= 10x+4
h(x)= x - *
Calculate the indicated function values. Simplify your answers,
13. f(7)
14. f(-9)
15. f(s)
16. f(s – t)
17. g(7)
18. g(-9)
19. g(s)
20. g(s - t)
Answer:
Step-by-step explanation:
f(7) = 32
f(-9) = 32
f(s) = 32
f(s-t) = 32
g(7) = 10·7+4 = 74
g(-9) = 10(-9)+4 = -86
Martha went to a restaurant with some friends. The three of them split a large pizza. Martha then ordered a large soda for $5. Martha spent a total of $11. How much was the large pizza? (pls!!!!)
Answer:
$6
Step-by-step explanation:
there was 11 total and 5 went into the soda and 6 went into the pizza so it's 6.
HELP QUICK
A rectangle has a width of 4 meters and a length of 6 meters. A similar rectangle has a width of 12 meters. Find the area of the similar rectangle after finding its length.
Answer:
216 m
Step-by-step explanation:
12/4= x/6
3=x/6
x=3x6
length= 18
area=length x width
12x18=216
Which value of the variable is a solution of the inequality t > -5
Answer:
-4 and any number above.
Which triangle is a translation of the gray triangle?
O ΔDEF
Ο ΔABC
O Neither
Answer:
abc
Step-by-step explanation:
There are 7 girls and 10 boys taking lifeguard lessons. Write the ratio that compares the number of girls taking lifeguard lessons to the total number of students taking lifeguard lessons
Answer:
7 to 10 or 70%
Step-by-step explanation:
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is y 0 1 2 3 4 p(y) 0.50 0.20 0.15 0.10 0.05 Suppose an individual with Y violations incurs a surcharge of 100Y 2 . Calculate the expected amount of the surcharge
Answer:
1) The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1
2) The expected amount of surcharges is $250
Step-by-step explanation:
Given that;
Y 0 1 2 3 4
p(y) 0.50 0.20 0.15 0.10 0.05
1)
Value of E(Y)
E(Y) = (0×0.50) + ( 1×0.20) + ( 2×0.15) + (3×0.10) + (4×0.05)
= 0 + 0.20 + 0.3 + 0.3 + 0.2
E(Y) = 1
Therefore, The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1
b)
Suppose an individual with Y violations incurs a surcharge of $100Y² , the expected amount of the surcharge is given by,
E($100Y²) = 100E(Y)²
= 100∑Y²P(y)
= 100(0²×0.50) + ( 1²×0.20) + ( 2²×0.15) + (3²×0.10) + (4²×0.05)
= 100( 0 + 0.2 + 0.6 + 0.9 + 0.8 )
= 100(2.5)
= $250
Therefore; The expected amount of surcharges is $250
2(x+1)^2=32
Help pls
Answer:
2x+2x2=32
2x+4=32
Step-by-step explanation:
What is the value of p2 + r3, when p = 2 & r = 3?
answer is 13
I hope it helpful
Answer:
The value of p² + r³, when p = 2 & r = 3
(2)²+(3)³=4+27=31
31 is the right answer.The table below represents some points on the graph of a linear function. Which function represents the same relationship?
Answer:
3rd is the answer
Step-by-step explanation:
caculator duhhhhhhhhhh
What is 33x44=? Give brainleist
1452 is 33x44’s sum
33
x 44
____
132
1320
1452
Answer:
1452
Step-by-step explanation:
33 * 44 = 1452
Help on 6 and 7 plz.....
A. 100 degrees
B. 150 degrees
C. 33 degrees
D. 107 degrees
I need help with my exam
Find the volume of the solid generated by revolving the region bounded by the lines and curves about the x-axis. y = x, y =1, x = 0
Answer:
The volume is: [tex]V = \frac{\pi}{3}[/tex] cubic units
Step-by-step explanation:
Volume of a solid:
The volume of a solid, given by the function f(x), over an interval between a and b, is given by:
[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]
y = x, y =1, x = 0
This means that the upper function is y = 1, and the lower function is y = x. So
[tex]f(x) = (1 - x)[/tex]
The lower limit of integration is x = 0.
The upper limit is y = x when y = 1, so x = 1.
Then
[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]
[tex]V = \pi \int_{0}^{1} (1-x)^2 dx[/tex]
[tex]V = \pi \int_{0}^{1} (1-2x+x^2) dx[/tex]
[tex]V = \pi (x-x^2+\frac{x^3}{3})|_{0}^{1} dx[/tex]
[tex]V = \pi(1 - (1^2) + \frac{1^3}{3})[/tex]
[tex]V = \frac{\pi}{3}[/tex]
plz help me i need help w this algebra
Answer:
I think it's the 3 one if in wrong I'm sorry
What is 1/9 as whole number
Answer:
4/3
Step-by-step explanation:
because it is just that
Answer:
0.11111111111
Step-by-step explanation:
A week have five school days and two weekend days. Write as ratio
Answer:
5:2
Step-by-step explanation:
△RST is shown below. XU = –2y + 15 and XW = 3y + 5.
PLEASE HELP ME
The required measure of the radius inscribed in the triangle RST is 11.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
The incenter of the triangle will be the center of the circle inscribed in the triangle. and radius will be the perpendicular distance from the incenter to the sides.
So,
XU = XW,
-2y + 15 = 3y +5
5y = 10
y = 2
Now,
Radius = XU
= -2(2) + 15
= 11
Thus, the required measure of the radius inscribed in the triangle RST is 11.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ2
Circle O has a center at (-2, -2) and a diameter of 10 units. Which point lies on circle O ?
Answer:
Step-by-step explanation:
Many points lie circle O
The points with a distance of 10 units will be on the circle
eg. (8,-2) or (4,6) both lie on the circle as they have a distance of 10 units from the center.
Asap!!
X=
12
9
6 2/3
Answer:
12
Step-by-step explanation:
Complex Numbers I need help
Answer:
Answer is (4+3i)+(5-6i)=(9-3i)
Step-by-step explanation:
I hope it's helpful!
==============================================
Work Shown:
(4+3i) + (5-6i)
4+3i + 5-6i
(4+5) + (3i-6i)
9 + (3-6)i
9 + (-3)i
9 - 3i
As the steps above show, we treat the 'i' as a variable. So we could think of the expression as (4+3x)+(5-6x) and simplify to get 9-3x. Though we use ''i' instead of x.