Answers
Answer:
V = 904.32 ft^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The radius is 6 and pi = 3.14
V = 4/3 ( 3.14) (6)^3
V = 904.31999 ft^3
Rounding to the hundredths place
V = 904.32 ft^3
[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: of \: sphere \: = \: \frac{4}{3} \: \pi \: {r}^{3} }}}}}\end{gathered}[/tex]
r = 6 ft[tex] \bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{3} \: \times \: 3.14 \: \times \: {6}^{3} \\ [/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{3} \: \times \: 3.14 \: \times \:216[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: \frac{4}{ \cancel3} \: \times \: 3.14 \: \times \: \cancel{216 \: {ft}^{3} } \: \: \: ^{72 \: {ft}^{3} } [/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 4 \: \times \: 3.14 \: \times \: 72 \: {ft}^{3} [/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 12.56 \: \times \: 72 \: {ft}^{3} [/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: Volume \: of \: sphere \: = \: 904.32 \: {ft}^{3} [/tex]
Related Questions
if fog(x)=((2x-1)/x) and g(x)=5x+2. find f(x)
Answers
9514 1404 393
Answer:
f(x) = (2x -9)/(x -2)
Step-by-step explanation:
We can use the fact that g(g^-1(x)) = x.
[tex](f\circ g)(x) = f(g(x))\\\\(f\circ g)(g^{-1}(x))=f(g(g^{-1}(x)))=f(x)[/tex]
So, we need to know the inverse of g(x):
x = g(y)
x = 5y +2
x -2 = 5y
y = (x -2)/5 . . . . inverse of g(x)
Then we have ...
[tex]f(x)=(f\circ g)(g^{-1}(x))=(f\circ g)\left(\dfrac{x-2}{5}\right)\\\\f(x)=\dfrac{2\left(\dfrac{x-2}{5}\right)-1}{\left(\dfrac{x-2}{5}\right)}=\dfrac{2x-4-5}{x-2}\\\\\boxed{f(x)=\dfrac{2x-9}{x-2}}[/tex]
Taylor wants to find the perimeter of a rectangular playground. The lenght of the playground measures (3x-20) metres. The width of the playground measures (2x+4) metres. What is the perimeter of the playground?
Answers
Answer:
Step-by-step explanation:
P = 2(3x-20) + 2(2x+4) = (6x-40) + (4x+8) = 10x-32
The required perimeter of the playground is 10x-32.
The length of the playground measures (3x-20) metres.
The width of the playground measures (2x+4) metres.
What is the perimeter?
Perimeter, is the measure of the figure on its circumference.
The Required perimeter is for the playground is given by
= 2(3x-20) + 2(2x+4)
= 10x-32
Thus the required perimeter of the playground is 10x-32.
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If car eyelashes sold for $13.99. If you bud double that, how much would you have paid for them? (Hint if needed: if they had been exactly $14, how different would your answer be?)
Answers
Answer:
13.99 x 2 = 27.98 dollars
now if they were 14 dollars exactly and you doubled that it would be 28 dollars so the difference would be 0.02 cents
Step-by-step explanation:
Put the shapes in the venn diagram. Is this right? if wrong tell me please.
Answers
Answer:
I'm not sure if the kite outside has at least a pair of equal sides. The rest I think are right though? Correct me if I'm wrong.
The probability of winning a raffle is 2/5. What is the probability of not winning the raffle?
0
3/5
2/5
Answers
Answer:
3/5
Step-by-step explanation:
um 3/5+2/5 = 1
plzzz help me i need help picture below
A local bakery buys their flour in bulk. The relationship between the cost of the flour and its weight is shown in the graph below.
Is the relationship shown a direct variation? Explain your reasoning using complete sentences.
The point (1, 0.50) is on this graph. What does this ordered pair represent?
Approximately how much does the bakery pay for 40 pounds of flour?
Answers
Answer:
It is a direct variation...
The price of flour does not increase or decrease the
more that you purchase (no discount for large purchases)
(1,0.5) means that a pound of flour costs 50
40 pounds would cost $20
Step-by-step explanation:
An economics professor conducts an experiment to determine if viewing his online video reviews improve the performance of his students on exams. He uses only economics students enrolled in his classes. The treatment group will watch the videos prior to the first exam, and the control group will not watch the videos. Then the scores of the first exam will be compared.
Which of the following variables’ effects could be mitigated by the random assignments? Check all that apply.
Intelligence
Study habits
Professor
Course textbook
Work schedule
Answers
Answer:
1,2,5
A,B,E
Intelligence
Study habits
Work schedule
ED2021
Intelligence and study habits could be mitigated by random assignments.
Options A and B are the correct answer.
What is a random assignment?Random assignment refers to the process of randomly assigning participants to either the treatment or control group in an experiment.
We have,
Random assignment is done to minimize the effect of extraneous variables, such as intelligence and study habits, that could potentially affect the results of the experiment.
By randomly assigning participants to either the treatment or control group, the differences between the two groups are assumed to be due to chance alone.
Variables such as the professor, course textbook, and work schedule are not affected by random assignments.
These variables are considered to be controlled variables that are held constant across both the treatment and control groups.
Thus,
Intelligence and study habits could be mitigated by random assignments.
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Simplify i^38 ????????
Answers
Answer:
i is defined as the square root of -1.
i^2 = -1
i^3 = -i
i^4 = 1
Following the pattern, we see that i^40 = 1, so i^38 is two above, or equal to -1.
So, i^38 = -1.
Let me know if this helps!
Least you greatest (help please but don’t give wrong answer pls)
Answers
Answer:
84.16, 84.31, 675/8, 423/5
Step-by-step explanation:
evaluate -7x^2 -5 + y^2- forx = -2, y=4
Answers
Answer:
The (y^2 ) or (y^–2) It is not clear, I solved it in both ways (y^2) and (y^-2) .^_^
[tex] - 7 {x }^{2} - 5 + {y}^{2} \\ - 7( { - 2}^{2} ) - 5 + {4}^{2} \\ - 7( - 4) - 5 + 16 \\ 28 - 5 + 16 \\ = 39[/tex]
_______o_____o_______
[tex] - 7 {x }^{2} - 5 + {y}^{ - 2} \\ - 7( { - 2}^{2} ) - 5 + {4}^{ - 2} \\ - 7( - 4) - 5 + \frac{1}{16} \\ 28 - 5 + \frac{1}{16} \\ = 23.06[/tex]
I hope I helped you^_^
The probability that a graduate of the Faculty of Finance will defend the diploma “excellent” is 0.6. The probability that he will defend his diploma “perfectly” and receive an invitation to work at the bank is 0.4. Suppose a student defends a diploma. Find the probability that he will receive an invitation to work in a bank?
Answers
The probability that he receives an invitation to work in a bank given that he defends his diploma excellently is [tex]\mathbf{0. \overline 6}[/tex]
The reason for the above probability value is as follows;
The known parameters are;
The probability that a graduate of the Faculty of Finance will defend the diploma excellently, P(A) = 0.6
The probability that he will defend perfectly and receive an invitation to work at a bank, P(A∩B) = 0.4
The unknown parameter is;
The probability that the student will receive an invitation from the bank given that the student defend the diploma excellent, [tex]\mathbf {P(B \ | \ A)}[/tex]
The process;
[tex]\mathbf{ P(B \ | \ A)}[/tex] is found using the conditional probability formula as follows;
[tex]\mathbf {P(B \ | \ A) = \dfrac{P(A \cap B) }{P(A)}}[/tex]
Plugging in the values, we get;
[tex]P(B \ | \ A) = \dfrac{0.4 }{0.6} = \dfrac{2}{3} = 0. \overline 6[/tex]
The probability that the student will receive an invitation from the bank given that the student defend the diploma excellent, [tex]P(B \ | \ A)[/tex] = [tex]\mathbf {0. \overline 6}[/tex]
Learn more about conditional probability here;
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I need help with this question
Answers
A student records the temperature at noon every day for 365 days and displays the results in the following bar graph. Does the bar graph depict the data fairly?
Answers
Answer: no, the vertical scale does not start at zero.
Step-by-step explanation:
Find f(-1) given f(x) = –2x^3 + 3x^2 – 22
Answers
[tex]\\ \sf\longmapsto f(-1)[/tex]
[tex]\\ \sf\longmapsto -2x^3+3x^2-22[/tex]
[tex]\\ \sf\longmapsto -2(-1)^3+3(-1)^2-22[/tex]
[tex]\\ \sf\longmapsto -2(-1)+3(1)-22[/tex]
[tex]\\ \sf\longmapsto 2+3-22[/tex]
[tex]\\ \sf\longmapsto 5-22[/tex]
[tex]\\ \sf\longmapsto -17[/tex]
Differentiate 4x^2+y^2=36 with respect to x. Hence find the turning points of the curve.
Answers
If y = y(x), then the derivative with respect to x is dy/dx. Differentiating both sides of the given equation gives
d/dx [4x ² + y ²] = d/dx [36]
8x + 2y dy/dx = 0
2y dy/dx = -8x
dy/dx = -4x/y
The turning points of the curve, taken as a function of x, are those points where the derivative vanishes.
-4x/y = 0 ===> x = 0
This value of x corresponds to two points on the curve,
4×0² + y ² = 36 ===> y ² = 36 ===> y = ±6
So there are two turning points, (0, -6) and (0, 6).
Janet invests a sum of EUR in an account that offers 3.5% simple interest. After ten years her investment is worth 7425 EUR. How much did she invest?
Answers
We need to find the amount of money Janet invested in 10 years to yield 7425 EUR
She invested EUR 21,214.29
Simple interest = P × R × T
Where,
P = principal = ?
R = interest rate = 3.5% = 0.035
T = Time = 10 years
Simple interest = 7425 EUR
Simple interest = P × R × T
7425 = p × 0.035 × 10
7425 = p × 0.35
7425 = 0.35p
Divide both sides by 0.35
P = 7425 / 0.35
= 21,214.285714285
Approximately,
P = EUR 21,214.29
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The number of bacteria in a certain culture grows exponentially at a rate of 1% per hour. Assuming that 5,000 bacteria are present initially, find the time required for the bacteria population to reach 45,000. (Round your answer to the nearest hour.)
Answers
9514 1404 393
Answer:
221 hours
Step-by-step explanation:
The population is given by the exponential equation ...
population = (initial value) × (1 +growth rate)^t
where the units of t are the same as the units of growth rate.
This lets us write ...
p(t) = 5000×1.01^t
We want this to be 45000, so ...
45000 = 5000×1.01^t
9 = 1.01^t . . . . . . . . . . . . divide by 5000
log(9) = t×log(1.01) . . . . take logs
t = log(9)/log(1.01) ≈ 220.8
It will take about 221 hours for the population to reach 45000.
What are the divisible number(s) for 430?
Answers
Answer:
The numbers that 430 is divisible by are 1, 2, 5, 10, 43, 86, 215, and 430.
What was the average speed if I drove 60 miles per hour to get to my grandmas house and 30 miles per hour to get home. Represent this in two different ways and explain your reasoning.
Answers
Answer:
40 mph.
Step-by-step explanation:
Suppose grandma's house is 30 miles away (any distance would do but 30 is convenient).
Speed = distance / time
time = distance / speed
Time to get there = 30/60 = 1/2 hour.
Time to get back = 30/30 = 1 hour
Average speed = total distance/ total time
= (30 + 30) / ( 1 + 1/2)
= 60 / 1.5
= 40 miles per hour.
You cannot take the average of the speeds directly
(60+ 30)/2 = 45 is not correct as you cannot average ratios ( speed is a ratio).
The length of a rectangle is five times the width if the area of the rectangle is 180 in.² then find the length and the width
Answers
Let breadth be x
Length=5x
ATQ
[tex]\\ \sf \longmapsto Area=Length\times breadth[/tex]
[tex]\\ \sf \longmapsto 5x(x)=180[/tex]
[tex]\\ \sf \longmapsto 5x^2=180[/tex]
[tex]\\ \sf \longmapsto x^2=\dfrac{180}{5}[/tex]
[tex]\\ \sf \longmapsto x^2=36[/tex]
[tex]\\ \sf \longmapsto x=\sqrt{36}[/tex]
[tex]\\ \sf \longmapsto x=6in[/tex]
Width=6inLength=6×5=30inRead image for instructions
Answers
The last part answers the first part for you, just look at the y-values.
In other words:
A' (-8, 2)
B' (-4, 3)
C' (-2, 8)
D' (-10, 6)
Explanation:
When you reflect any point over the x-axis, the y-value of the ordered pair is going to change.
This makes sense especially considering that the x-axis is horizontal, so the only way you could cross is to move up or down. If you were to move left or right, you'd only be able to cross the y-axis, since it's vertical.
Now for the last part, as I mentioned above, if you are reflecting across the y-axis, the x-values of the ordered pair is going to change.
A'' (8, 2)
B'' (4, 3)
C'' (2, 8)
D'' (10, 6)
Take note that the only thing that changes for the respective value is its sign, while the number itself stays the same.
What is log10^6, considering log10^2=a and log10^3=b?
Answers
The answer is simply just a+b.
Solution:
log10^6=log10^2+log10^3
Since log10^2=a and log10^3=b,
The answer is a+b.
I think that the answer is a+b.
Pat bought a new anchor for her boat. She needed to buy rope for the anchor At the
Rope
-N-S store, rope it sold in 4 1/2meter segments. Pat bought 190 segment
for the anchor. Just in case she needed mere.che bought an extra 27 sements. In all,
how many meters of rope did Pat buy?
A.4342
meters
B.976 1/2meters
C.217 meters
D.868 1/2 meters
Answers
Answer:
B
Step-by-step explanation:
Total segment bought=190+27=217 segments
Total length of the whole anchor=217*9/2=1953/2=976 1/2 meters
find the surface area of the cylinder
Answers
Answer
50.24
Step-by-step explanation:
help me plzzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
[2＋(－6)]÷2＝－2
The midpoint is (3, －2)
Hope my answer helped u :)
construct a rectangle PQRS, In which AB= 8cm and diagonal AC= 10cm
Answers
A rectangle can be constructed using a straightedge, and a setsquare or compass
Please find attached the drawing of rectangle ABCD
The steps to construct the rectangle ABCD are as follows:
Question:
The missing part of the question is the name of the rectangle = ABCD
The given parameters are;
The length of the side AB = 8 cm
The length of the diagonal of the rectangle ABCD = AC = 10 cm
The steps to construct a rectangle are;
Draw the segment [tex]\overline{AB}[/tex] = 8 cm on a planeDraw perpendicular lines at points A and B with length h given by Pythagoras's theorem as followsh² = [tex]\overline{AC}[/tex]² - [tex]\overline{AB}[/tex]²
∴ h² = 10² - 8² = 36
h = √36 = 6
h = 6 cm = The length of the sides [tex]\mathbf{\overline{AD}}[/tex] and [tex]\mathbf{\overline{CB}}[/tex]
Draw arcs with radius 6 cm from points A and B to intersect the perpendicular lines drawn from points A and B on the same side of the line [tex]\overline{AB}[/tex] at points D and CJoint point C to D with a straight line which is segment [tex]\overline{CD}[/tex] and which completes the rectangle ABCDLearn more about the construction of basic shapes here;
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Using the formula D = s:t where D equals distance traveled, r equals the average rate of
speed, and t equals the time traveled, choose the expression or equation that correctly
represents this information.
Mary drove 150 miles in three hours. What was her average rate of speed?
=
150 = 3
r = 3 = 150
O p + 150 · 3
Answers
Answer: r = 50 miles/h
Step-by-step explanation:
Let r be the rate of average speed.
Then
r = D/t
r = 150/3
r = 50 miles/h
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Convert 4.206 m into mm
Answers
Answer:
4206 is the answer of this question
Answer:
I think it will help you a lot.
The perimeter of the rectangle below is 124 units. Find the length of side cd
Answers
Answer:
CD = 38
Step-by-step explanation:
Since AB = 3x + 2, CD = 3x + 2
To solve for the length of CD, we'll need to solve for x first by using the perimeter formula
Solving for x...
[tex](3x+2)+(3x+2)+2x+2x=124[/tex]
[tex]3x + 3x + 2x + 2x = 120[/tex]
[tex]10x=120[/tex]
[tex]x=\frac{120}{10}[/tex]
[tex]x=12[/tex]
Now that we know what x equals, plug in x into the expression of side CD
CD = 3x + 2
CD = 3(12) + 2
CD = 36 + 2
CD = 38
Therefore, the length of side CD = 38
-------------------------------------------------------
Check:
AB = CD | BC = DA
38 + 38 for AB and CD
BC + DA = 2x + 2x
BC + DA = 2(12) + 2(12)
BC + DA = 24 + 24
BC + DA = 48
38 + 38 + 48 = perimeter
perimeter = 124
I need to find the distance B in the special counter sink shown
Answers
Answer:
Step-by-step explanation:
87°32' = 86°92'
(86°92')/2 = 43°46'
B = 13/(16cos(43°46')) = 1.125
Answer:
Step-by-step explanation:
