Answer:
[tex]1.91\ \text{in}[/tex]
[tex]3.84\ \text{in}[/tex]
Step-by-step explanation:
V = Volume of cylinder = [tex]44\ \text{in}^3[/tex]
h = Height of cylinder
r = Radius of cylinder
Volume of cylinder is given by
[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{44}{\pi r^2}[/tex]
Total surface area of a cylinder is given by
[tex]S=2\pi r^2+2\pi rh\\\Rightarrow S=2\pi r^2+2\pi r\times\dfrac{44}{\pi r^2}\\\Rightarrow S=2\pi r^2+\dfrac{88}{r}[/tex]
Differentiating with respect to radius
[tex]\dfrac{dS}{dr}=4\pi r-\dfrac{88}{r^2}[/tex]
Equating with zero
[tex]4\pi r-\dfrac{88}{r^2}=0\\\Rightarrow 4\pi r=\dfrac{88}{r^2}\\\Rightarrow r^3=\dfrac{88}{4\pi}\\\Rightarrow r=(\dfrac{22}{\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.91\ \text{in}[/tex]
Double derivative of S
[tex]\dfrac{d^2S}{dr^2}=4\pi+176>0[/tex]
So [tex]r[/tex] is minimum at [tex]\dfrac{dS}{dr}=0[/tex]
[tex]h=\dfrac{44}{\pi r^2}=\dfrac{44}{\pi 1.91^2}\\\Rightarrow h=3.84\ \text{in}[/tex]
So the radius and height of the cylinder is [tex]1.91\ \text{in}[/tex] and [tex]3.84\ \text{in}[/tex] respectively such that the least amount of metal is used.
Josie bikes 40 miles each month for five months she multiplies 40×5 what unit should she use for the product miles or months?
Answer:40x5 are the factors of every miles times each month so the units she should use is months
Step-by-step explanation: 40= (miles)
5=(months)
If 4% of a number is 8, find 1% of that number.
How do I solve this problem?
Answer:
2
Step-by-step explanation:
First, find the number by dividing 8 by 0.04
8/0.04
= 200
Then, find 1% of 200 by multiplying it by 0.01:
200(0.01)
= 2
So, 1% of the number is 2.
Answer:
The answer is 2
Step-by-step explanation:
4%x5=20% and 8x5=40, 20%x5=100% and 40x5=200 and 1% means you move the decimal to the left twice so it is 2, my explanation might be wrong but I know my answer is correct:
)
Calculate the present value PV of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time. 7 years, at 3% per year, compounded annually.
Answer:
PV= $813.09
Step-by-step explanation:
Giving the following information:
Future Value (FV)= $1,000
Number of periods (n)= 7 years
Interest rate (i)= 3% compounded annually
To calculate the present value (PV), we need to use the following formula:
PV= FV/(1+i)^n
PV= 1,000 / (1.03^7)
PV= $813.09
This is how many classes students at Bronx College take this semester with the probabilities courses1 2 3 4 5 probability (distribution) of taking that many courses.1.1.6.1.1 The variance for this distribution is approximately.
Answer:
1
Step-by-step explanation:
Given the question above :
The probability distribution :
X : ___ 1 ___ 2 ___ 3 ___ 4 ____ 5
P(x): _ 0.1 __ 0.1 __ 0.6 _ 0.1 __ 0.1
The Variance : Var(X) = (Σx²*p(x)) - μ²
μ = E(X) = Σ(X * p(x)) :
Σ(X * p(x)) = (1*0.1)+(2*0.1)+(3*0.6)+(4*0.1)+(5*0.1)
μ = 3
Var(X): [(1^2*0.1)+(2^2*0.1)+(3^2*0.6)+(4^2*0.1)+(5^2*0.1)] - 3²
= 10 - 9
= 1
Hence. Variance = 1
Which of the following shows only multiples of 12
Answer:
there is no following
Step-by-step explanation:
Answer: 12,24,36,48,60,72,84,96,108,120,132,144
Step-by-step explanation:
Hope this helps. Could not see the image attached.
True or false: The mapping notation for reflecting point (x,y) about the x-axis is (−x,y).(1 point) This statement is true. This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (x,−y). This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (y,x). This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (−x,−y).
Answer:
This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (x,-y)
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
cos 60 degrees=1/2 and sin 60 degrees = square root 3/2 true or false
Answer:
cos 60 degrees=1/2 and sin 60 degrees = square root 3/2
The answer it's true.
Write 0.45 as a fraction.
Answer:
9/20
Step-by-step explanation:
0.45 = 45/100
45/100=9/20 (divide numerator and denominator by 5)
If i had 127 tables and each table could fit 4 people how many people could i seat?
The perimeter of the rectangle is 2,500 cm. Find the unknown side length. the other side is 750
Answer:
500 cmStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
From the question we have
[tex]2500 = 2l + 2(750) \\ 2500 = 2l + 1500 \\ 2l = 2500 - 1500 \\ 2l = 1000 \\ \frac{2l}{2} = \frac{1000}{2} \\ l = \frac{1000}{2} \\ l = 500[/tex]
We have the final answer as
500 cmHope this helps you
please help
what is the solution to the equation below?
34x + 95 = 3 (14x + 9)
Answer:
x=8+1/2
Step-by-step explanation:
Hope this helps, good luck!
Answer:
x=7/2=8.500
Step-by-step explanation:
A city bus compny sold 35 one-way tickets and 20 round trip tickets from west elmwood to east elmwood. One way tickets cost $14. Round trip tickets cost $27. How much money did the bus company collect?
Answer:
$1,030
Step-by-step explanation:
Step 1- Multiply One way tickets by How much the tickets cost:
35 x 14= 490
Step 2- Multiply Round trip tickets by how much the tickets cost:
20 x 27= 540
Step 3- Add both sums together:
490 + 540= 1,030
Therefore, the answer is $1,030
can somebody help
me
Answer: answer 2
Step-by-step explanation:
The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. There are six appetizers, two soups, four main courses, and six desserts. Your diet restricts you to choosing between a dessert and an appetizer. (You cannot have both.) Given this restriction, how many three-course meals are possible?
Answer: 96
Step-by-step explanation:
According to the fundamental principle of counting:
Total number of meals possible = (Choices for appetizers) x (Choices for soups) x (Choices for main courses) x (Choices for desserts)
If there is a restriction to choose between appetizer and dessert.
Then, Total number of meals possible = (Choices for appetizers) x (Choices for soups) x (Choices for main courses) + (Choices for soups) x (Choices for main courses) x (Choices for desserts)
= 6 x 2 x 4 + 2 x 4 X 6
= 48+48
= 96
Hence, the number of three-course meals are possible= 96
Answer:
96?
Step-by-step explanation:
if R is the midpoint of QS, RS = 2x-4, ST = tx-1, and RT = 8x-43
The question is incomplete. Here is the complete question.
If R is the midpoint of QS, [tex]RS=2x-4[/tex], ST = [tex]4x-1[/tex] and RT = [tex]8x-43[/tex], find QS.
Answer: QS = 68 units
Step-by-step explanation: The figure below shows a line segment QT.
To determine QS, first, determine value of x:
RT = RS + ST
[tex]8x-43=2x-4+4x-1[/tex]
[tex]8x-43=6x-5[/tex]
2x = 38
x = 19
Now, we determine QS:
Midpoint is a point dividing a line segment in two equal parts.
Then, QR = RS.
QS = QR + RS
QS = 2RS
[tex]QS=2(2x-4)[/tex]
[tex]QS=4x-8[/tex]
Substituting x = 19:
[tex]QS=4.19-8[/tex]
QS = 68
The segment QS is 68 units.
Answer: x = 1
Step-by-step explanation:
I have no idea what the actual answer is, as you didn't ask a question. So i'm assuming that you want the value of x.
Step 1: Draw a line containing all the points
R is in between point Q and point S, while T is last, based on alphabetical order.
Illustration:
2x - 4 Tx - 1
Q R S T
8x - 43
Step 2: Find T's value
To find t, create the substitution equation RS + ST = RT
2x - 4 + tx - 1 = 8x - 43
-2x -2x
-4 + tx - 1 = 6x - 43
tx - 5 = 6x - 43
tx = 6x - 38
tx/x = 6x/x - 38
t = 6 - 38
t = -32
This is the value of t
By the way, there is no correlation between point T and the variable t.
Step 3: Find x's value
Now that we know what t is, we can solve for x
2x - 4 -32x - 1 = 8x - 43
-30x - 5 = 8x - 43
+30x +30x
-5 = 38x - 43
+43 +43
38 = 38x
38/38 = 38x/38
1 = x
This is the value of x
What is the equation of the line that passes through the point (-1,7) and has a slope of -2?
Please help im stuck
Answer:
B
Step-by-step explanation:
substitution because
if m∠3=m∠7, and m∠7=m∠6 you can substitute
m∠7 to m∠3 and get m∠3=m∠6
how many times greateri is the value of the digit 9 in 90,000 than the value of the digit 9 in 9,000
Answer:
It is 10 times greater.
Step-by-step explanation:
The place value of 9 in 90,000 is in the 10,000th place.
The place value of 9 in 9,000 is in the 1,000th place.
10,000 divided by 1,000 = 10.
In conclusion, the place value of 9 in 90,000 is 10 times greater than the palce value of 9 in 9,000.
the pic the pic this is it
Answer:
yes I agree with you
Step-by-step explanation:
thanks for the free question
Answer: mmmmmm Otae?
Step-by-step explanation:
The equation of line j is y= -6/7x +7.Line k is perpendicular to j.What is the slope of line k?
Simplify your answer and write it as a proper fraction,improper fraction,or integer.
Answer:
y=7/6x
Step-by-step explanation:
When given an equation and asked to find the equation of a perpendicular line that intersects it, you know that the slope is the slope of the equation is the negative recipricoal of the given equation. i.e. y=2x+2 and y=-1/2x+2. The y-intercept does not matter.
I hope you understood and that this helps!
A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of Xis given (in units of months) byf(x) ={cxe -x/2 x>0 0 x<0 What is the probability that the system functions for at least 5 months?
Answer:
0.2397
Step-by-step explanation:
Given data:
fX(x) = Cxe^(−x/2) if x >0 0 otherwise, where C > 0 is some constant.
The probability that the system functions for at least 5 months
= 0.2397
attached below is a detailed solution
Estimate the area of the inregular shape. Explain your method and show your work.
Please help 100 points and brainliest
Answer:
30
Step-by-step explanation:
Since we are estimating. We know that it is about 5 units on top and about 6 units on the side. Therefore, you would multiply them
5*6=30
That is why the area of this irregular shape is 30 units.
:∫ PLZZ help ;⊃ plz no playing around I need actual answer
Answer:
d.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
15/10 goes down to 3/2 divide 15 by 5
21/14 goes down to 3/2 divide 21 by 7
The amount of mustard dispensed from a standard dispenser is normally distributed with a mean of 0.9oz and a variance of 0.01oz. If a family of six buys ten hotdogs total and dispenses mustard onto each one using the standard dispenser, what is the probability that more than 3 of them will have more than one ounce of mustard?
Answer:
the probability that more than 3 of them will have more than one ounce of mustard is 0.05975
Step-by-step explanation:
Given te data in the question;
let x rep the quantity of mustard on a hotdog ( in oz)
so
X → N ( u = 0.9, α² = 0.01 )
now P( more than one ounces of mustard on a hotdog) will be
P( X>1 ) = P( Z > ((1-0.9)/(√0.01)) ) = P( Z > 1 ) = 1 - P( Z < 1 )
= 1 - 0.84134 = 0.15866
Also let Y rep the number of hotdogs that have more than one ounces of mustard, so
Y → Bin( n = 10, p = 0.15866 )
P( y = y ) = (¹⁰ _y) ( 0.15855)⁰ ( 1 - 0.15866 )^10-y, y = 0,1,2,3......, 10
so required probability = P(Y > 3) = 1 - P(Y ≤ 3)
= 1 - P(Y=0) - P(Y=1) - P(Y=2) - P(Y=3)
=1 - (¹⁰ ₀) ( 0.15855)⁰ (1 - 0.15855)¹⁰⁻⁰ - (¹⁰ ₁) ( 0.15855)¹ (1 - 0.15855)¹⁰⁻¹ - (¹⁰ ₂) ( 0.15855)² (1 - 0.15855)¹⁰⁻² - (¹⁰ ₃) ( 0.15855)³ (1 - 0.15855)¹⁰⁻³
= 0.05975
Therefore the probability that more than 3 of them will have more than one ounce of mustard is 0.05975
Compare. Select <, >, or=.
6.61? 6.610
The awnser is 6.610
Answer:
6.61=6.610
Step-by-step explanation:
6.61=6.610
After point we can increase no. Of zero.
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
Answer:
man the answers are 40 10 30
Step-by-step explanation:
Colin, Sara and Gordon share some sweets in the ratio 2:5:3. Colin gets 26 sweets. How many sweets are there altogether?
Answer:
130
Step-by-step explanation:
Ratio is 2:5:3. Colin get 2/10 of the sweets so 26/x=2/10. Use the butterfly method to get 260=2x. Divide both sides by 2 and get x=130/
A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 5.3 days. Its average brightness is 2.9 and the brightness changes by /- 0.35. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days:______.B(t)=4.2 +0.45sin(2pit/4.4)
(a) Find the rate of change of the brightness after t days.
(b) Find the rate of increase after one day.
Answer:
[tex]\dfrac{0.7\pi}{5.3}\cos(\dfrac{2\pi t}{5.3})[/tex]
0.16
Step-by-step explanation:
According to the question the mathematical model should be
[tex]B(t)=2.9+0.35\sin(\dfrac{2\pi t}{5.3})[/tex]
Differentiating with respect to time we get
[tex]B'(t)=0.35\cos(\dfrac{2\pi t}{5.3})\times(\dfrac{2\pi}{5.3})\\\Rightarrow B'(t)=\dfrac{0.7\pi}{5.3}\cos(\dfrac{2\pi t}{5.3})[/tex]
So, the rate of change of brightness after t days is [tex]\dfrac{0.7\pi}{5.3}\cos(\dfrac{2\pi t}{5.3})[/tex]
After 1 day means [tex]t=1[/tex]
[tex]B'(1)=\dfrac{0.7\pi}{5.3}\cos(\dfrac{2\pi\times 1}{5.3})\\\Rightarrow B'(1)=0.16[/tex]
The rate of increase after one day is 0.16.
Part D
You now have an equation to model the finances of the car wash. What is the value of the profit when the baseball team washes 0 cars? What point represents the value? What does the y-value of this point mean in terms of the problem?
Answer:
The equation for the profit made on the car wash is y = 5x – 75. Here, y is the profit made and x is the number of cars washed. So if the team washes 0 cars, x will be 0.
y = 5(0) – 75
y = -75
The point that represents this is (0, -75). Here, the value of the y-coordinate of the point is -75. Since it has a negative sign, it means that instead of making a profit, the team suffers a loss. So, if the baseball team washed no cars, it would lose $75.
Step-by-step explanation:
Just select yes and no for all three pls help
.....*+*Kill me*+*.....
*+*.......................*+*
*+*.......................*+*
Answer:
1. Yes 2. No 3. No
Step-by-step explanation: