the city of Picayune has set aside $900,000 to build a new water tower in the shape of a cylinder. If the price per cubic foot is $10.50, what is the largest measure for the radius and height of the cylinder in order to not exceed the budget?
Answers
Answer:
So as not to exceed the budget, where π = 22/7, we have;
The radius = 10 ft and the height = 3/11 ft
For standard 40 ft. height, the radius is approximately 0.8259 ft
Step-by-step explanation:
The amount set aside for the water tower = $900,000
The price (amount) per cubic foot = $10.50
Therefore, we have;
[tex]The \ volume \ of \ the \ water \ tower \ to \ be \ built = \dfrac{The \ amount \ set aside \ for \ the \ water \ tower}{The \ price \ (amount) \ per \ cubic \ foot }[/tex]
[tex]\therefore The \ volume \ of \ the \ water \ tower \ to \ be \ built = \dfrac{\$ 900,000}{\$10.50/ft\\ ^3} = \dfrac{600}{7} ft.^3 = 85 \frac{5}{7} ft^3[/tex]
Whereby the height of a standard water tower = 40 ft., we have;
The shape of the water tower = The shape of the water tower
∴ The volume of the water tower V = π × r² × h
Where;
r = The radius of the water tower
h = The height of the water tower
Taking π = 22/7
600/7 = 22/7 × r² × h
r² × h = 600/7/(22/7) ≈ 300/11 = 100 × 3/11
Solving to get exact dimensions so as to not exceed the budget, we have;
r² × h = 100 × 3/11 = 10 × 10 × 3/11
Therefore, the radius can be 10 ft. and the height = 3/11 ft.
Or for standard 40 ft. height, we have;
r² = 600/7/(π × 40)
r ≈ 0.8259 ft.
Related Questions
If the relative frequencies are 0.48 and 0.52, which
conclusion is most likely supported by the data?
O There is likely an association between the
categorical variables because the relative
frequencies are similar in value.
O An association cannot be determined between the
categorical variables because the relative
frequencies are similar in value.
O An association cannot be determined between the
categorical variables because the relative
frequencies are not similar in value.
O There is likely an association between the
categorical variables because the relative
frequencies are both close to 0.50.
Answers
Answer:The Last One
Step-by-step explanation:
Option (B) an association cannot be determined between the categorical variables because the relative frequencies are similar in value is the correct answer.
What is relative frequency?The relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided by the total number of trials conducted. The sum of all relative frequencies will be one.
For the given situation,
The relative frequencies are 0.48 and 0.52.
A two-way frequency table can be used to show, analyze, and examine the relationships that exists between two categorical variables.
The two relative frequencies have the values that are similar to (close to) each other. So, there will be no association between the categorical values.
Hence we can conclude that option (B) an association cannot be determined between the categorical variables because the relative frequencies are similar in value is the correct answer.
Learn more about relative frequencies here
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An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c. Consider the trinomial 6x2 + 13x + 6. The value of ac is . The value of b is . The two numbers that have a product of ac and a sum of b are 4 and .
Answers
Answer:
1. ac = 36
2. b = 13
3. 4 and 9
Step-by-step explanation:
Given
6x² + 13x + 6
Required
Fill in the gaps
Solving (1): The value of AC
The general form of an equation is:
ax² + bx + c
By comparison:
a = 6
b = 13
c = 6
So,
ac = a * c
ac = 6 * 6
ac = 36
Solving (2): The value of b
In (1) above, we showed that
b = 13
Solving (3): Two numbers that satisfy product ac and sum b
We have that.
ac = 36
If one of the numbers is 4, then the other number is
Other number = 36/4
Other number = 9
Alternatively, we have that.
b = 13
If one of the numbers is 4, then the other number would be:
Other number = 13 - 4
Other number = 9
Answer:
ac = 36
b = 13
The two numbers that have a product of ac and a sum of b are 4 and 9
Step-by-step explanation:
4 • 7 – 6 2 ÷ 3 also show your work
Answers
Answer:
7 1/3
Step-by-step explanation:
Lets do this in steps ok? K!
Important!!!: Look what operation is first in order of operation no parentheses or exponents so division and multiplication is first!
Step 1-- 4 x 7=28
Step 2-- 62 divided by 3 = 20 2/3
Step 3-- 28- 20 2/3
Step 4-- 27 3/3 - 20 2/3= 7 1/3
Hope this helps ∞<3
Answer:
[tex]-11.3333333333[/tex] [tex]or[/tex] [tex]-\frac{34}{3}[/tex] [tex]or[/tex] [tex]7\ \frac{1}{3}[/tex]
Step-by-step explanation:
[tex]--------------------------------------------[/tex]
[tex]\frac{4\cdot7-62}{3}[/tex] = [tex]?[/tex]
[tex]4\cdot7[/tex] = [tex]28[/tex]
[tex]\frac{28-62}{3}[/tex] = [tex]?[/tex]
[tex]28-62[/tex] = [tex]-34[/tex]
[tex]\frac{-34}{3}[/tex] = [tex]?[/tex]
[tex]\frac{-34}{3}[/tex] = [tex]-11.3333333333[/tex] = [tex]7\ \frac{1}{3}[/tex]
[tex]--------------------------------------------[/tex]
Hope this helps! <3
[tex]--------------------------------------------[/tex]
Evaluate g(x)=4 -3x when x=-3,0, and 5
Answers
Answer:
-11
Step-by-step explanation:
help a girl outt!! pleasseee answer asapppp:)) will mark brainliest
Answers
Answer:
ok
Step-by-step explanation:
If x = 4 and y = -2, the value of 3 xy?
Answers
Answer:
-24
Step-by-step explanation:
Answer: -24
Step-by-step explanation:
3xy
3(4)(-2)
12(-2)
-24
16
Jamar skis down Mount Spalding at a constant rate. After skiing for two minutes, Jamar is at an elevation of 2,100 feet. After skiing for 5 minutes, Jamar is at an
elevation of 150 feet. What is the rate of change, in feet per minute, of Jamar's elevation?
A-700
B
-650
С
650
D 700
Answers
please help thanks in advance also best answer get's brainlest
Answers
Answer:
angle t is 55 degrees
Step-by-step explanation:
Here's my work:
Isoscelese means two of the same length sides. A triangle is 180 degrees. 180-70=110
110/2=55 (two because those are the two angles associated with the equal sides)
HELP HELP PLEASE IMPORTANT
Answers
Answer:
2010
Step-by-step explanation:
1/2(24)(20)=240
50*45=2250
2250-240=2010
Rudolfo has 15 toys in his toy box, and he adds 2 new toys every month. Based on this
information, which representation best shows this relationship between the number of toys
Rudolfo has in his toy box, y, and the number of months that have passed, x?
Answers
Answer:
G
Step-by-step explanation:
(x)0 months: (y)15 toys, 1:17, 2:19, 3:21, 4:23, 5:25, 6:27, 7:29, 8:31, etc.
The equation that represents best shows this relationship between the number of toys Rudolfo has will be y = 2x + 15. Then the correct option is G.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Rudolfo has 15 toys in his toy box, and he adds 2 new toys every month.
Let x be the number of months and y be the total number of toys. Then the equation is given as,
y = 2x + 15
The equation that represents best shows this relationship between the number of toys Rudolfo has will be y = 2x + 15. Then the correct option is G.
More about the linear equation link is given below.
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Geometry help I need the statements and reasons
Answers
(3x + 3x²) + (2x² + 2x)?
Answers
Answer:
=5x2+5x
Step-by-step explanation:
Let's simplify step-by-step.
3x+3x2+2x2+2x
help me please I'll mark first answer Brainliest
Answers
Answer:
a. True
b. True
c. True
d. False
e. False
I hope this helped! Thank You!
Answer:
a. False
b. True
c. True
d. False
e. False
6th grade math i mark as brainliest
Answers
9514 1404 393
Answer:
8, 9. Correct
10. 6.1×t
Step-by-step explanation:
8, 9. The answers shown are correct.
__
10. The only product in the given expression is 6.1t, which can be written as ...
6.1×t
when a symbol is used to represent multiplication.
The parts of the product are the multiplicand and the multiplier. Those parts are also called factors.
A man buys a TV. The total cost is $2,500, and the sales commission is 8%. How much should the salesperson get as commission for this sale?
Also please show me how you got the answer cause i have to show my work!!!
Answers
Answer:
$200
Step-by-step explanation:
First Change the percent to a decimal
In this case the percent was %8, change it into a decimal; 8%=.08
Next multiply 2,500 x .08 which gives you 200
The answer is $200! Hope this helps!.
5
The ink page yield for a printer cartridge indicates how many pages a cartridge
should print. A cartridge rated at 550 pages is 66% full.
How many pages should be left to print?
[2]
How many pages have already been printed?
Total
0
11
Ma
Answers
2. 363 pages have been printed
PLEASE I WILL GIVE BRAINLIEST
Write the SLOPE INTERCEPT form of a line that passes through point A at (4,-3) and point B at (2,1)
Answers
Answer:
y = -2x + 5
Step-by-step explanation:
A(4, -3) ; B(2, 1)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{1-[-3]}{2-4}\\\\= \frac{1+3}{2-4}\\\\= \frac{4}{-2}\\\\= -2[/tex]
m = -2 ; A(4,-3)
[tex]y - y_{1}=m(x-x_{1})\\\\y -[-3] = (-2)(x - 4)\\\\y + 3 = -2*x -4 *(-2)\\\\y + 3 = -2x + 8\\\\ y = -2x + 8 - 3 \\\\ y = -2x + 5[/tex]
A line has a slope of 3, is increasing, and passes through the point (2,7). What is its y-intercept?
Answers
First, we need to put this into point slope form which is y-7=3(x-2)
Next, multiply using the distributive property. y-7=3x-6
Lastly, we want to get y by itself so add 7 on both sides. y=3x+1.
Using the slope intercept form, y=mx+b where b is the y-intercept, we can see that the line will cross the y-axis at 1.
Hope this helps✨❤️
The y-intercept of the line is 1
Using the slope - intercept relation :
y = bx + cc = Intercept; b = slope point (2,7)Substituting the values into the relation :
7 = 3(2) + c
7 = 6 + c
c = 7 - 6
c = 1
Therefore, the y-intercept of the line is 1.
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The sum of the first (n) terms of the sequence is given by the formula (given below) . If this sequence is a geometric progression, find q. If this sequence is an Arithmetic progression, find d
Answers
Answer:Example 1:
Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.
S8=1(1−28)1−2=255
Example 2:
Find S10 of the geometric sequence 24,12,6,⋯.
First, find r.
r=r2r1=1224=12
Now, find the sum:
S10=24(1−(12)10)1−12=306964
Example 3:
Evaluate.
∑n=1103(−2)n−1
(You are finding S10 for the series 3−6+12−24+⋯, whose common ratio is −2.)
Sn=a1(1−rn)1−rS10=3[1−(−2)10]1−(−2)=3(1−1024)3=−1023
In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1. Then as n increases, rn gets closer and closer to 0. To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.
Example 4:
Find the sum of the infinite geometric sequence
27,18,12,8,⋯.
First find r:
r=a2a1=1827=23
Then find the sum:
S=a11−r
S=271−23=81
Example 5:
Find the sum of the infinite geometric sequence
8,12,18,27,⋯ if it exists.
First find r:
r=a2a1=128=32
Since r=32 is not less than one the series has no sum.
Step-by-step explanation:
8 = r³
r = ?
Please......
Answers
Explanation:
2 x 2 x 2 = 8
Therefore r = 2
Final Answer: [tex]r = 2[/tex]
Steps/Reasons/Explanation:
Question: [tex]8 = r^{3}[/tex]. [tex]r[/tex] = ?
Step 1: Take the cube root of both sides.
[tex]\sqrt[3]{8} = r[/tex]
Step 2: Calculate using a calculator.
[tex]2 = r[/tex]
Step 3: Switch sides.
[tex]r = 2[/tex]
~I hope I helped you :)~
The area of a rectangle is twice the area of a square. If the rectangle is 6 inches long, and the width of the rectangle is the same as the length of a side of the square, find the dimensions of both the rectangle and the square.
Answers
Answer:
Dimension of rectangle = 6 inches by 3 inches
Dimension of square = 3 inches by 3 inches
Step-by-step explanation:
Given information:
- Length of rectangle = [tex]6[/tex] inches.
- Width of rectangle is the same as the side length of square.
- Area of rectangle is twice the area of square
Variable to define:
Let [tex]s[/tex] = side length of the square and the width of the rectangle
Finding dimensions of rectangle and square:
From the information given, we can write the equation:
[tex]6s=2s^2[/tex] (Area of rectangle is twice the area of square)
[tex]6=2s[/tex] (Divide [tex]s[/tex] on both sides)
[tex]s = 3[/tex] inches
Dimension of rectangle = length by width
= 6 inches by 3 inches
Dimension of square = side by side
= 3 inches by 3 inches
Hope this helps :)
Select three ratios that are equivalent to 7: 6.
Answers
Answer:
ratio number 1- 14:12
ratio number 2- 21:18
ratio number 3- 28:24
Plz help fast answer
Answers
Coastal
Graphic
Heroic
Dramatic
Angelic
Betrayal
Bacterial
Answer:
1: Patriotic
2: Global
3: Graphic
4:heroic
5: betrayel
6:angelic
7: dramatic
8: bacterial
Step-by-step explanation:
I think this is it
pleaseee help I will make you the brainiest.
Answers
please give me correct answer this is major
Answers
Answer:
d
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Please help!!!!! will mark brainliest
Answers
Answer:
It should be B- an=3n+1 because it seems to be adding one every time
Step-by-step explanation:
Answer:
We will count number of squares
first term is 4
so,
second term is 7
so,
third term is 10
so,
We can see that this sequence is in arithematic sequence
we can use nth term formula
where
an is nth terms
a1 is first term
d is common difference
n is total number of terms
now, we can plug values
and we get
b 3n+1
Step-by-step explanation:
Determine the amount of the semi-annual coupon for a bond with a face value of ₱ 300,000 that pays 10%, payable semi-annually for its coupons.
Answers
Answer:
Copuon= $15,000
Step-by-step explanation:
Giving the following information:
Face value= $300,000
Coupon rate= 10%
First, we need to determine the semiannual coupon rate:
Semiannual coupon rate= 0.1/2= 0.05
Now, the coupon using the following formula:
Copuon= face value*coupon rate
Copuon= 300,000*0.05
Copuon= $15,000
Original Tv cost 700 Current Tv cost 500 find the percent of decrease
Answers
Answer:
200 is the decrease ............
Answer:
the percent of decrease=28.57%
Step-by-step explanation:
(Old Price - New Price)/Old Price (and multiply that number by 100)
[(700-500)/700]*100=28.57%
A student worked out at a gym continuously for 50 minutes. The graph shows the remaining percentage of the workout as a linear function of x , the time in minutes.
Which answer choice best describes the domain and range of the function for this situation?
Answers
Answer:
Step-by-step explanation: the answer is c
Evaluate [(30 + 6) -3^2] /9.2
Answers
It's 6 srry that guy above just stole free points