Answer:
3.3912cm³/minStep-by-step explanation:
Area of the circular plate = πr² where r is the radius of the plate.
dA/dt is the rate at which the plate is increasing
since dA/dr = 2πr and dr/dt = 0.01cm/min
dA/dt = dA/dr * dr/dt
dA/dt = 2πr dr/dt
dA/dt = 2π(54)(0.01)
dA/dt = 2π(0.54)
dA/dt = 3.3912cm³/min
Hence the rate at which the plates area is increasing when the radius is 54cm is 3.3912cm³/min
what does the graph of f(x)=-2/3x+490 represent
Answer:
search that question up on brainly it got the answer bruu
Step-by-step explanation:
7. Find the value of x and y:
x=
y=
(10x - 61)
(18y + 5)º
(x + 10)
Answer:
y = 8º
y = 8º
Step-by-step explanation:
Given:
(10x - 61)º
(18y + 5)º
(x + 10)º
Find:
x and y
Computation:
(10x - 61) + (x + 10) = 180
11x - 51 = 180
11x = 231
x = 21º
(10x - 61)º = (18y + 5)º [Vertical opposite angle]
10x - 61 = 18y + 5
10x - 18y = 66
5(21) - 9y = 33
y = 8º
Help please!! Inverse of Matrix problem!!
Number 8 please!!
Step-by-step explanation:
Inverse of p matrix is in picture
i wish it will make u easy to do♥️✌️
You have asked to design a rectangle box with a square base and an open top. The volume of the box must be620 cm to the 3rd power. the cost of the material for the base is $0.40 per square cm and the cost of the material for the side is $0.10 per square cm.How to determine the dimension of the box that will minimize the cost of manufacturing. What is the minimum cost? in dollars and rounded to the nearest cent.
Answer:
$69.21
Step-by-step explanation:
Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]
Let h be the height of the box
V = Volume of the box = [tex]620\ \text{cm}^3[/tex]
[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]
Now surface area of the box with an open top is given
[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]
Differentiating with respect to x we get
[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]
Equating with zero
[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]
Double derivative of the function
[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]
So, x at 10.74 is the minimum value of the function.
[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]
So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.
The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]
The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]
Cost of the base is $0.40 per square cm
Cost of the side is $0.10 per square cm
Minimum cost would be
[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]
The minimum cost of the box is 69.21 dollars.
Allison traveled a distance of 130 miles in 2
1
hours. What was Allison's average driving
speed, in miles per hour?
Allison's average driving speed in miles per hour is 65.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
130 miles = 2 hours
Divide 2 on both sides.
130/2 miles = 1 hour
65 miles = 1 hour
Thus,
The average speed is 65 miles per hour.
Learn more about speed here:
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Helen has to buy all the butter she needs to make 60 biscuits.
She buys the butter in 250 g packs.
b) (i) What is the exact amount of butter she needs?
g
(1)
Answer:
100 x 2 x10x5
Step-by-step explanation:
I'll braintlist!!!
Find the value of each expression in lowest terms:
1/6 X 11/4
11/5 X 1/3
14/3 X 1/5
5/3 X 2/5
3/4 X 8/9
5/2 X 2/7
Glen got 48 out of 64 correct in his test.
What fraction of the marks did he get wrong?
Give your answer in its simplest form.
Answer:
He got 16 incorrect
Step-by-step explanation:
Answer:
fraction: 3/4
percent: 75%
Step-by-step explanation:
What is the reciprocal of 8 5/6
Answer:
6/53
Step-by-step explanation:
The data below shows the duration of eruption (in seconds) of a geyser in a national park and the height (in feet) of the eruptions for a typical day. Use Excel to find the best fit linear regression equation, where duration of eruption is the explanatory variable. Round the slope and intercept to one decimal place.Duration Height240 140237 154122 140267 140113 160258 140232 150105 150186 160248 155243 125241 136214 140114 155272 130227 125237 125238 139203 125270 140218 140226 135250 141245 140120 139267 110103 140270 135241 140239 135Provide your answer below:y = _x + _
Answer:
ŷ = -0.08522X + 157.7779
The slope = - 0.1
Intercept = 157.8
Step-by-step explanation:
Given the data :
Duration __ Height
240 140
237 154
122 140
267 140
113 160
258 140
232 150
105 150
186 160
248 155
243 125
241 136
214 140
114 155
272 130
227 125
237 125
238 139
203 125
270 140
218 140
226 135
250 141
245 140
120 139
267 110
103 140
270 135
241 140
239 135
General regression equation :
y = mx + c
Where
y = predicted variable
x = predictor / explanatory variable
m = slope or gradient
c = Intercept
The regression equation obtained ;
ŷ = -0.08522X + 157.7779
To one decimal place :
ŷ = -0.1X + 157.8
The slope = - 0.1
Intercept = 157.8
One number is 4 more than 3 times another. Their sum is 16. Find the two numbers.
Give the slope between the points
(-2,3) (-5, -9)
A company order two types of games, board and electronic. A shipment
containing 4 board games and 5 electronic games costs $103. A second
shipment containing 5 board games and 3 electronic games costs $80. Find the
cost of the board games and the cost of the electronic games.
Answer:
C
Step-by-step explanation:
i lied :)
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The slipe of the line passing through the points (7, 5) and (21, 15) is
Answer:
5/7
Step-by-step explanation:
You find a slope by using the equation y2-y1/x2-x1.
In this case: 15-5/21-7
10/14
5/7
Convert 0.49494949 into a fraction. Show all work.
Answer:
0.49 49
=
49 this is a fraction
99
Step-by-step explanation:
Let
XXX
x
=
0.49
¯¯¯¯
49
then
XXX
100
x
=
49.49
¯¯¯¯
49
and
XXX
99
x
=
100
x
−
x
=
49
XXX
x
=
49
99
Why should a combination lock” actually be called a “ permutation lock”? Provide some examples of combinations and permutations that you use to remember which is which
Step-by-step explanation:
Well irs a pertuation lock because you are making a unique combination that only you know and an example of this is like 12395 or 9583644 those two are combinations and there are aproximately 64,000e12 combinations
Jacob has a piece of paper in the shape of a Decagon, how many sides would be there for the
paper.
A) 7
B) 8
C) 9
D) 10
Answer:
10
Step-by-step explanation:
A decagon is a polygon that has 10 sides !
Describe how to round 3.987 to the nearest tenth.
Answer:
4
Step-by-step explanation:
You see the hunderth digit has a 8, so you round up. 0.9+0.1=1 so you add 1 to 3, so 3.987 rounded is 4
1. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. Calculate the Z score associated with 3 siblings. Your answer should be rounded to two decimal places, like 5.43 or 1.30.
2. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. Using the standard normal table, calculate the proportion of respondents who had more than 2 siblings. Your answer should be rounded to two decimal places, like 0.43 or 0.30.
Answer:
-0.24 ; 0.71
Step-by-step explanation:
Given that :
Mean number of siblings (m) = 3.76
Standard deviation (s) = 3.18
Z score associated with 3 siblings
x = 3
Using the relation :
Zscore = (x - m) / s
Zscore = (3 - 3.76) / 3.18
Zscore = - 0.76 / 3.18
Zscore = −0.238993
Zscore = - 0.24
2.) proportion of respondents with more than 2 siblings
Using the z probability calculator :
X > 2
Obtain the standardized score :
Zscore = (x - m) / s
Zscore = (2 - 3.76) / 3.18
Zscore = - 1.76 / 3.18
Zscore = −0.5534591
Zscore = - 0.55
Using the z table :
P(Z ≥ - 0.55) = 1 - p(Z ≤ - 0.55) ; p(Z ≤ - 0.55) = 0.2912
1 - p(Z ≤ - 0.55) = 1 - 0.2912 = 0.7088 = 0.71
A device runs until either of two comonents fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is f(x,y) = x + y/8 for 0 < x < 2 and 0 < y < 2Calculate the probability that the device fails during its first hour of operation.
Answer:
The probability that the device fails during its first hour of operation is 0.625.
Step-by-step explanation:
The joint density function of the lifetimes of the two components, both measured in hours, is:
[tex]f(x,y)=\frac{x+y}{8};\ 0<x<2,\ 0<y<2[/tex]
Compute the probability that the device fails during its first hour of operation as follows:
[tex]P[(X<1)\cup (Y<1)]=1-\int\limits^{2}_{1} {\int\limits^{2}_{1} {\frac{x+y}{8}} \, dx } \, dy[/tex]
[tex]=1-\int\limits^{2}_{1} {\frac{x^{2}+2xy}{16}}|^{2}_{1} \, dy\\\\=1- \int\limits^{2}_{1}[{\frac{4+4y}{16}-\frac{1+2y}{16}}] \, dy\\\\=1-\int\limits^{2}_{1}{\frac{3+2y}{16}}\, dy\\\\=1-[\frac{3y+y^{2}}{16}]^{2}_{1}\\\\=1-0.375\\\\=0.625[/tex]
Thus, the probability that the device fails during its first hour of operation is 0.625.
The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean μ = $633 and standard deviation σ = $45.
Required:
a. If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount?
b. How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16? (Round your answer to the nearest dollar.)
Answer:
a) 0.4121
b) $588
Step-by-step explanation:
Mean μ = $633
Standard deviation σ = $45.
Required:
a. If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount?
We solve using z score formula
= z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
For x = $646
z = 646 - 633/45
z = 0.22222
Probability value from Z-Table:
P(x<646) = 0.58793
P(x>646) = 1 - P(x<646) = 0.41207
≈ 0.4121
b. How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16? (Round your answer to the nearest dollar.)
Converting 0.16 to percentage = 0.16 × 100% = 16%
The z score of 16%
= -0.994
We are to find x
Using z score formula
z = (x-μ)/σ
-0.994 = x - 633/45
Cross Multiply
-0.994 × 45 = x - 633
-44.73 = x - 633
x = -44.73 + 633
x = $588.27
Approximately to the nearest dollar, the amount should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16
is $588
19. Theodore purchased a vintage painting from an art dealer worth $480. The dealer noted that the value of the painting will increase by 12 percent per year. What is the growth factor of the
painting?
All changes
12
480
0.12
1.12
The growth factor of the painting is 0.12
What is percent?"It is a ratio that can be expressed as a fraction of 100."
For given question,
The value of the painting will increase by 12 percent per year.
The 12% in decimal form,
[tex]=12\times \frac{1}{100}\\\\ =0.12[/tex]
So the growth factor of the painting is 0.12
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The marked price of a sweater at the clothing store was $24.
During a sale, a discount of 25% was given. A further 15%
discount was given to the customers who have the store's
credit card. How much would a member customer need to
pay for the sweater during the sale if the customer paid with
the store's credit card? Round your answer to the nearest
cent.
Enter the answer
About how many centimeters larger is it ? Round to the nearest hundretdth
Answer: what is there a picture of it?
Step-by-step explanation:
Help :( I need this :)
Answer:
you can put in any of the numbers that are already listed in the x values. You can put 5, 14, -1, and 23 because something can't be a function if x values repeat.
What is the slope of the line whose equation is y-6=2(x+3)?
Answer:
2
Step-by-step explanation:
y=mx+n m is slope
y-6=2(x+3) so y=2x+12 m=2 is slope.
OBX Cart Rentals has created a website for customer access. They are trying to determine a reasonably secure number of available passwords. They have decided to allow upper case letters, lower case letters, digits (0 â 9), and the three special characters: $, ! ?. Find the number of possible 6 character passwords given each of the conditions (Note: you MUST simplify completely.)
a. The password must begin with a letter (either upper or lower case)
i. repetitions permitted
ii. repetitions not permitted
b. The password must begin with a letter and end with a special character ($, !, ?):
i. repetitions permitted
ii. repetitions not permitted
Answer:
A)
i) for repetitions
there will be : 52 * 65 * 65 * 65 * 65 * 65 = 60335112500 number of passwords
ii) for Non - repetitions
there will be : 52 * 64 * 63 * 62 * 61 * 60 = 47576954880
B)
i) for repetitions
there will be : 52 * ( 65 )^4 * 3 = 2784697500
ii) for Non-repetitions
there will be : 52 * 63 * 62 * 61 * 60 * 3 = 2230169760
Step-by-step explanation:
Total Number of letters = 52
Number of upper case letters = 26
Number of lower case letters = 26
Number of digits ( 0 - 9 ) = 10
special characters = 3
password = 6 characters
Therefore the total number of choices = 52 + 3 + 10 = 65
A) The password must begin with a letter (either upper or lower case)
i) for repetitions
there will be : 52 * 65 * 65 * 65 * 65 * 65 = 60335112500 number of passwords
ii) for Non - repetitions
there will be : 52 * 64 * 63 * 62 * 61 * 60 = 47576954880
B) The password must begin with a letter and end with a special character ($, !, ?):
i) for repetitions
there will be : 52 * ( 65 )^4 * 3 = 2784697500
ii) for Non-repetitions
there will be : 52 * 63 * 62 * 61 * 60 * 3 = 2230169760
Find the measure of each angle
Answer:
All the work and answer is on the screenshot I have attached.
Step-by-step explanation:
Please help me really need help please please will mark brainiest it’s due today at 3:30pm please help me please
Answer:
8 Hours.
Step-by-step explanation:
write 3 numbers that make this inequality true: x>4
Answer:
8, 10, 24
(Basically every number above 4)
Answer:
5,6 and 7
> means more than or greater than.
In this situation, its asking for numbers greater than 5.
Hope this helps. ;)