Rosalinda has a circular serving platter in the middle of her circular table.
The radius of the platter is 15 inches less than the radius of the table
The diameter of the table is 4 feet. What is the difference between the
area of the table and the area of the platter? Use 3.14 for 17, and write your
answer in decimal form. 7.G.4
Answers
diameter=4ft=12(4)=48in
Radius of table=48/2=24inRadius of platter=24-15=9inSo
Area of table:-
π(24)^2576πin²Area of platter:-
9²π81π in²Difference:-
576π-81π495π1554.3in²Answer:
1554.3 in²
Step-by-step explanation:
Given information:
The radius of the platter is 15 inches less than the radius of the tableThe diameter of the table is 4 feetπ = 3.141 foot = 12 inches
⇒ 4 ft = 4 × 12 = 48 in
Radius = ¹/₂ diameter
⇒ Radius of table = ¹/₂ × 48 in = 24 in
⇒ Radius of platter = 24 in - 15 in = 9 in
Area of a circle = πr²
⇒ Area of table = 3.14 × 24² = 1808.64 in²
⇒ Area of platter = 3.14 × 9² = 254.34 in²
Difference = area of table - area of platter
= 1808.64 - 254.34
= 1554.3 in²
Related Questions
The revenue generated by a company manufacturing lawn mowers is
R=−0.9x2+90.2x , where x represents the number of mowers produced. The cost to produce the mowers is C=29x+500 , where x is the number of mowers produced.
Answers
The profit generated in terms of x is −0.9x²+61.2x - 500
How to calculate profit functionsGiven the following parameters
Revenue generated by a company = R=−0.9x²+90.2x
The cost to produce the mowers C(x) = 29x + 500
Determine the profit function
p(x) = R(x) - C(x)
P(x) = −0.9x²+90.2x - (29x + 500)
P(x) = −0.9x²+90.2x - 29x - 500
P(x) = −0.9x²+61.2x - 500
Hence the profit generated in terms of x is −0.9x²+61.2x - 500
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The hanger image below represents a balanced equation, write an equation to represent the image.
Answers
The function f(t) = 3 cos(pi over 6t) + 5 represents the tide in Blastic Sea. It has a maximum of 8 feet when time (t) is 0 and a minimum of 2 feet. The sea repeats this cycle every 12 hours. After nine hours, how high is the tide? 12 feet 5 feet 4.5 feet 2.5 feet
Answers
Answer:
5 feet
Step-by-step explanation:
[tex]f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}[/tex]
How to solve this 2 question?
Answers
8. For brevity, let U = unemployed, E = employed, M = male, F = female. We're given that
P(M) = P(F) = 50/100 = 1/2
P(U) = 60/100 = 3/5
P(M | U) = 2/3
P(E) = 40/100 = 2/5
P(F | E) = 3/4
8a. This follows immediately from the given information. Specifically,
P(E) = 1 - P(U) = 1 - 3/5 = 2/5
8b. By definition of conditional probability,
P(A | B) = P(A and B) / P(B) ⇒ P(A and B) = P(A | B) P(B)
It follows that
P(M and U) = P(M | U) P(U) = 2/3 • 3/5 = 2/5
8c. Using Bayes' rule/the definition of conditional probability,
P(U | F) = P(U and F) / P(F) = P(F | U) P(U) / P(F)
Since F and M are mutually exclusive,
P(F | U) = 1 - P(M | U)
and so
P(U | F) = (1 - 2/3) • 3/5 / [(1 - 2/3) • 3/5 + 3/4 • 2/5] = 2/5
8d. Here we assume gender and employment status are independent, so for instance
P(F and E) = P(F) P(E)
We then have by the inclusion/exclusion principle that
P(F or U) = P(F) + P(U) - P(F and U) = P(F) + P(U) - P(F) P(U)
We also have by the law of total probability
P(F) = P(F and U) + P(F and E)
so
P(F or U) = P(F and U) + P(F and E) + P(U) - P(F) P(U)
By the assumed independence,
P(F or U) = P(F) P(U) + P(F) P(E) + P(U) - P(F) P(U)
P(F or U) = P(F) P(E) + P(U)
P(F or U) = 1/2 • 2/5 + 3/5 = 4/5
9.
a. This is mostly a matter of counting the ways a given type of stamp can fall out.
[tex]P(A) = \dfrac{\dbinom{20}3}{\dbinom{24}3} = \dfrac{285}{506}[/tex]
since there are 20 non-green stamps.
[tex]P(B) = \dfrac{\dbinom21 \dbinom{22}2}{\dbinom{24}3} = \dfrac{21}{92}[/tex]
since there are 2 red and unused stamps, 1 of which we want; the other 2 stamps come from the remaining 22 non-red-and-unused stamps.
[tex]P(A \cap B) = \dfrac{\dbinom21 \dbinom{18}2}{\dbinom{24}3} = \dfrac{153}{1012}[/tex]
since exactly 1 of the stamps must be red and unused, and the other 2 stamps that fall out can be neither green nor red and unused.
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = \dfrac{162}{253}[/tex]
which follows from the inclusion/exclusion principle.
b. There is a total of 10 used stamps, so the probability of at least 1 going missing is
[tex]P(C) = \dfrac{\dbinom{10}1\dbinom{14}2 + \dbinom{10}2\dbinom{14}1 + \dbinom{10}3}{\dbinom{24}3} = \dfrac{415}{506}[/tex]
By definition of conditional probability,
[tex]P(C \mid A) = \dfrac{P(C \cap A)}{P(A)}[/tex]
However, there are no used green stamps; any used stamp that goes missing must be red, blue or yellow. So the event A ∩ C is really just the event C, and
[tex]P(C \mid A) = P(C) = \dfrac{415}{506}[/tex]
c. A and C are independent if and only if
[tex]P(A \cap C) = P(A) P(C)[/tex]
We know
[tex]P(C \cap A) = P(C)[/tex]
so if A and C are independent, then
[tex]P(C) = P(A) P(C)[/tex]
but this would imply P(A) = 1, which is clearly not the case as we found in 9.a. So A and C are not independent.
What is the equation of the trend line in the scatter plot?
Answers
Answer:
y=(x-1)
Step-by-step explanation:
PLS HELP MARK AS BRAINLIEST
Suppose that the relation S is defined as follows.
S= {(4, p), (p, 0), (3, 3), (7, m)}
Give the domain and range of S.
Write your answers using set notation.
Answers
Answer:
Domain= {4,p,3,7}
Range= {p,0,3,m}
Step-by-step explanation:
⇒Domain: is the set of the first number in every pair.
⇒Range: is the set of the second number in every pair
TO FIND THE DOMAIN: S= {(4,p),(p,0),(3,3),(7,m)}
so Domain= {4,p,3,7}
TO FIND THE RANGE: S= {(4,p),(p,0),(3,3),(7,m)}
so Range= {p,0,3,m}
Hope this helps :)
Using the illustrations below, determine the relationship between the volumes of
the two given solid figures. Put a check ( / ) on the blank if the sentence states
the correct relationship
Answers
Answer:
I don't see the illustrations
I need extra help. Someone
Answers
Answer:
C. tanS = 5/12, tanT = 12/5
Step-by-step explanation:
Tangent has NOTHING to do with hypotenuse, do we can easily eliminate answer choices involving 13, the hypotenuse. For angle S, the opposite side measures 5 and the adjacent side measures 12. For angle T, the opposite side measures 12 and the adjacent side measures 5. See this below algebraically
tanθ = opp/adj
tanS = 5/12
tanT = 12/5
I hope this helps!
if the scale of a map is 1 in = 62.5 mi, how long is the distance on the map if the actual distance between the two cities is 218.75 miles
Answers
Answer:
3.5in
Step-by-step explanation:
so what i would do is i would divide 218.75 by 62.5
218.75/62.5= 3.5
3.5 in= 218.75 mi
hope that hepls :)
The table below lists four potential investments. The time for all of the investments is 5 years, and compound interest is compounded annually.
Which investment produces the most interest?
Answers
Answer:
Investement P
Step-by-step explanation:
find the mean, variance, and standard deviation of sampling distribution of the sample population p=.2 and n=107
Answers
Answer:
2923 is your p is equal to 2 and n
Samantha collected 352 books to give to her students. If she gives 4 books to her students each day, how many days will it take her to give all of her books away?
Answers
Answer: 88
Step-by-step explanation:since we know 4 books are given each day and the total is 352 . 352 divided by 4 is 88
Answer:
the answer is 88
Step-by-step explanation:
352÷4=88
If the odds against an event are 5:8, then the probability that the event will fail to occur is
Answers
Answer:
Step-by-step explanation:
5/8
Odds against event are 5:8
Means ration of not happening of work =
5/8
Sample space has 8+5=13 possibilities
Probability it being to work=
8/13
Write an equation of the line with a slope of 0 and y -intercept of 5 .
y=
Answers
Answer:
y=-5
Step-by-step explanation:
Find the quotient of 3/5 and 2/3
Give your answer as a fraction in its simplest form.
Answers
Among all rectangles that have a perimeter of 172, find the dimensions of the one whose area is largest. Write your answers as fractions reduced lowest terms.
Answers
Answer:
43 x 43 units 1849 units^2
Step-by-step explanation:
The largest area will be a square (equla sides)
172 / 4 = 43
a square IS a rectangle
43 x 43
Number of Handshakes If eight people greet each other at a meeting by shaking hands with one another, how many handshakes take place?
Answers
The number of handshake that took place is 28.
In any situation where order of an outcome does not matter, mathematical combination (C) are use calculate the total outcomes of an event.
8 people are to shake each other once. The concept to be use to derive the number of hands that took place is Combination.
The formulae of Combination for this Scenario is n(n-1)/2n(n−1)/2 .
The number of people (n) is 8.
\begin{gathered}Total handshake = n(n-1)/2\\Total handshake = 8 * (8-1)/2\\Total handshake = 8 * 7/2\\Total handshake = 56/2\\Total handshake = 28\end{gathered}Totalhandshake=n(n−1)/2Totalhandshake=8∗(8−1)/2Totalhandshake=8∗7/2Totalhandshake=56/2Totalhandshake=28
In conclusion, the number of handshake that took place is 28.
Answer:
28
Step-by-step explanation:
3 people
A B C
AB
AC
BC
3 total
4 people
A B C D
AB
AC
AD
BC
BD
CD
6 total
this can be modeled with
n*(n - 1)/2
8*(8 - 1)/2
8*3.5
28
You estimate that a passive portfolio, that is, one invested in a risky portfolio that mimics the S&P500 stock index that represents the stock market, yields an expected rate of return of 13% with a standard deviation of 25%. You manage an active portfolio with expected return 18% and standard deviation 28%. The risk-free rate is 8%.
a. Draw the CML (Capital Market Line) and your funds’ CAL (Capital Allocation Line) on an expected return-standard deviation diagram. Indicate their slopes.
b. Suppose your client ponders whether to switch the 70% that is invested in your fund to the passive portfolio. Explain to your client the disadvantage of the switch.
c.In the context of part b, Show him the maximum fee you could charge (as a percentage of the investment in your fund, deducted at the end of the year) that would leave him at least as well of investing in your fund as in the passive one.)
(Hint: The fee will lower the slope of his CAL by reducing the expected return net of the fee.)
Answers
The capital market line with fee will be 0.3771 and the capital allocation line will be 0.24.
How to calculate the slope?The slope of the capital market line will be:
= (17% - 7% - f)/27
= (10% - f)/27
f = 0.3771
The slope of the capital allocation line will be:
= (13% - 7%) / 25%
= 0.24
The reward to variability ratio will be:
= (17 -7)/27
= 0.3771
The client's reward to variability ratio will be:
= (13 - 7)/25
= 0.25
This shows that the client will be disadvantaged of the switch since it's lower.
Learn more about capital on:
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convert [tex]\sqrt3 + i[/tex] to polar form
Answers
[tex]a~~\pm~~bi\implies r[\cos(\theta ) \pm i\sin(\theta )] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt{3}~~ + ~~i\implies \stackrel{x}{\sqrt{3}}~~ + ~~\stackrel{y}{1} i\qquad \qquad \begin{cases} r=\sqrt{x^2+y^2}\\\\ \theta =\tan^{-1}\left( \frac{y}{x} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]r=\sqrt{(\sqrt{3})^2+(1)^2}\implies r=\sqrt{3+1}\implies r=2 \\\\\\ \theta =\tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies \theta =\cfrac{\pi }{6} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 2\left[\cos\left( \frac{\pi }{6} \right)~~ + ~~i\sin\left( \frac{\pi }{6} \right) \right]~\hfill[/tex]
Check the picture below.
A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from but only 8 flags will be flown. Find the number of different signals consisting of 8, if the first flag must be blue.
If the first flag is blue then the number of different signals consisting of 8 flags is ??
Answers
Using the permutation formula, it is found that there are 17,297,280 different signals consisting of 8 flags.
In this problem, the order in which the flags are visited is important, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
The first flag is blue, then the remaining 7 are taken from a set of 14, hence:
[tex]P_{(14,7)} = \frac{14!}{7!} = 17,297,280[/tex]
There are 17,297,280 different signals consisting of 8 flags.
More can be learned about the permutation formula at https://brainly.com/question/25925367
HELP ME PLEASE 30 points, HELP
Answers
Answer:A
Step-by-step explanation:
When you translate you are simply moving the shape up, down, left right. You are not rotating it or chanding it's orientation.
Answer: the answer is B
Step-by-step explanation: B because it would’ve reflected off of the 1st quadrant on a grid so it would be facing the opposite direction.
what is 70-(5x2)+18 with explanation and step please
Answers
Step-by-step explanation:
Please Mark me brainliestAnswer:
78
Step-by-step explanation:
70 - (5 x 2) + 18We should solve according to the order of operations, PEMDAS.
P = ParenthesesE = ExponentsM = MultiplicationD = DivisionA = AdditionS = Subtraction#1) Parentheses
70 - (5 x 2) + 1870 - 10 + 18#2) Subtraction
70 - 10 + 1860 + 18#3) Addition
60 + 18784. Jorge has a mass of 45 kilograms and
is skateboarding with a velocity of
3 meters/second north. What is Jorge's
momentum? The units for momentum are
kg-m/s north.
Answers
Jorge's momentum given his mass and the velocity while skateboarding is 135kg-m/s north.
What is momentum?Momentum can be described as the impetus that is gained by an object that is motion. Momentum is velocity multiplied by mass. When put simply, momentum can be described as mass in motion. Thus, when an object is moving, it has momentum.
Momentum velocity x mass
45 x 3 = 135kg-m/s north.
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Find the area of
the parallelogram.
yd
15 yd
The area of the parallelogram is
yd?.
(Type an integer or a decimal.)
Answers
225
Step-by-step explanation:[tex]15\times 15[/tex]
__________________________________________________
Calculate
[tex]15\times 15[/tex]
__________________________________________________
Calculate the product or quotient
[tex]225[/tex]
I hope this helps you
:)
If f (x)=
(3 + x)/
(x-3)
what is f(a + 2)?
Answers
[tex]f(x) = \frac{3 + x}{x - 3} [/tex]
[tex]f(a + 2) = \frac{3 + a + 2}{a + 2 - 3} = \frac{a + 5}{a - 1} [/tex]
exg(x), where g(0) = 6 and g'(0) = 1, find f '(0).
Answers
Evaluate the triple integral
Answers
Answer:
Wow thats hard
Step-by-step explanation:
though luck
find the term to term rule for the following sequence 2,6,18, 54, 162
Answers
:)
Answer:
multiply 3 or *3 that is 2*3=6
Josh wants to spend less than $80 to buy
4 shirts and a pair of pants. The pants cost $24.
The shirts he wants all cost the same.
2. Which inequality can be used to find how
much Josh will spend on each shirt?
A. 4s + 24 > 80
B. 4s + 24 < 80
C. 4s + 24 = 80
D. 4s + 24 = 80
Answers
Answer:
B
Step-by-step explanation:
b because everything must cost less than 80 and
< 80 means the unknown number will be less than 80.
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
How to sketch this graph?
Answers
Answer:
get a book from shop and draw with ruler and write the numbers too
