Can y'all please help me with this? Thanks.
Answer:
j : 7327
Step-by-step explanation:
Split the figure into three parts 1 cylinder and hemispheres.
find the volume of each part and then in the end add them
Vol of cylinder =
[tex]\pi \times r {}^{2} \times h \\ 3.14 \times 10 \times 10 \times 10 \\ = 3140 \\ [/tex]
Find the volume of one hemisphere=
[tex] = \frac{2}{3} \pi \times r {}^{3} \\ 2093.33[/tex]
Vol of 2 hemispheres = 2×2093.33
= 4186.66667
Total volume= 3140 + 4186.6667 = 7326.66
= 7327
It is said that once a Chinese emperor decided to divide a number of horses among his generals such that
(a) if they are divided equally among 3 of his generals, 2 horses will remain;
(b) if they are divided equally among 5 of his generals, 1 horse will remain;
(c) and if they are divided equally among 7 of his generals, 6 horses will remain.
I. Find the smallest number of horses that satisfies this condition.
II. Write an explicit rule for each of part (a), (b) and (c).
III. Write an explicit rule for the number of horses that can be divided in such a way.
IV. Write a recursive rule for the explicit rule found in part III.
Using the three conditions, the smallest number of horses that can be shared among the generals is 41
The smallest number of horsesThe conditions are given as:
A remainder of 2, if divided among 3 generalsA remainder of 1, if divided among 5 generalsA remainder of 6, if divided among 7 generalsThe numbers that can divide 5 and leave a remainder of 1 are:
11, 16, 21, 26, 31, 36, 41, 56, 61, 66, 71......
Of all these numbers, the smallest number that satisfy the three conditions is: 41
i.e.
41/3 = 13 R 2
41/5 = 8 R 1
41/7 = 5 R 6
Hence, the smallest number of horses is 41
The explicit rule for each conditionLet the number of horses a general gets be x.
The explicit rule for each condition can be represented as:
Condition (a): Total = 3x + 2Condition (b): Total = 5x + 1Condition (c): Total = 7x + 6The explicit and the recursive ruleUsing the condition (b), we have:
Total = 5x + 1
Rewrite as a function
f(x) = 5x + 1
When x = 0, we have:
f(0) = 1
For other values of x, we have:
f(1) = 6
f(2) = 11
f(3) = 16
Rewrite as:
f(0) = 1
f(1) = 5 + 1 = 5 +f(0)
f(2) = 5 + 6 = 5 + f(1)
f(3) = 5 + 11 = 5 + f(2)
Express 2 as 3 - 1
f(3) = 5 + f(3 - 1)
Express 3 as x
f(x) = 5 + f(x - 1)
Hence, the recursive function is f(x) = 5 + f(x - 1) where f(0) = 1
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Help asap pleaseeeeeeeee
Answer:
√5
Step-by-step explanation:
Given:
[tex]\displaystyle \large{5\div \sqrt{5}}[/tex]
Which can be rewritten as:
[tex]\displaystyle \large{\dfrac{5}{\sqrt{5}}}[/tex]
To find:
Simplified formTo find simplified form of the expression, keep in mind that surds should not remain as denominators. Therefore, what we have to do is to multiply both numerator & denominator by the surd itself so the denominator will be cleared as rational number.
[tex]\displaystyle \large{\dfrac{5\cdot \sqrt{5}}{\sqrt{5}\cdot \sqrt{5}}}[/tex]
We know that if same surds multiply each other, the surd will be canceled and remains only the insides. To express it in math, it can be as:
[tex]\displaystyle \large{\sqrt{a}\cdot \sqrt{a} = \left(\sqrt{a}\right )^2 =a}[/tex]
Therefore:
[tex]\displaystyle \large{\dfrac{5\sqrt{5}}{5}}[/tex]
Cancel 5:
[tex]\displaystyle \large{\sqrt{5}}[/tex]
Henceforth, the simplified expression is √5
helppppppppppppppppppppppppppppppppppppppppppppp
Calculate the amount of work done when moving a 567 N crate a distance of 20 meters
Answer:
W = 11340 J
Step-by-step explanation:
Given,
Force ( F ) = 567 N
Distance ( s ) = 20 N
To find : Work done ( W )
Formula : -
W = Fs
W = 567 x 20
W = 11340 J
Hence,
the amount of work done is 11340 J.
The HCF of 12, 8 ,32 is?
Answer:
4
Step-by-step explanation:
Prime factorizing all terms :
12 = 2² x 38 = 2³32 = 2⁵The highest common factor (HCF) shared by the 3 numbers is :
2²4Hence, HCF (12, 8, 32) = 4
Students at a school will sell hats to raise money. There are some hats left over from last year, and 20 boxes of hats will be ordered this year. When the order arrives, the total number of hats the student will have can be determined using the function f(x) = 48x + 37, where x represents the number of boxes ordered. If the number of hats per box changes so that the situation is modeled by the function h(x) = 24x + 37, then how many fewer hats will the students have available to sell if they still order 20 boxes?
A)517
B)480
C)997
D)365
Answer: A) 480
Step-by-step explanation:
x=20 substitute in the two equations
48(20)+37
24(20)+37
since the question said fewer , then you should subtract
48(20)+37 - 24(20)+37 = (960+37) - (480+37)
=923 - 443= 480
Students will have 517 hats to sell, that is 480 fewer than determined.
The correct option is B.
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
Given,
Total hats = Left hats of last year + 20 boxes of hats newly ordered
Total hats
f(x) = 48x + 37
where x is number of boxes
But number of hats per box changes,
h(x) = 24x + 37
fewer no. of hats than determined
f(x) - h(x) = 48x + 37 - 24x - 37
f(x) - h(x) = 24x
No. of boxes = 20
No. of hats fewer than determined = 24 × 20 = 480
And no. of hats available
h(20) = 480 + 37
h(20) = 517
No. of hats available to sell = 517
Hence, 517 hats are available to sell that is 480 fewer hats than determined
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Jackie has 3 brothers. Maria has 2 brothers. Keri has 1 brother. Harriet has 2 brothers. Between the four girls, what is the mean number of brothers? Median? Mode?
Answer:
mean is 2 brothers.
mean, means average
Give the value of x .
A. 60 degrees
B. 180 degrees
C. 120 degrees
D. 45 degrees
Answer:
x=120°
Step-by-step explanation:
sum of all angles in a triangle is equal to 180
let the unknown angle be
[tex] \alpha [/tex]
[tex]60 + 60 + \alpha = 180 \\ \alpha = 180 - 60 - 60 \\ \alpha = 60 \\ [/tex]
[tex] \alpha + x = 180 \\ x = 180 - \alpha \\ x = 180 - 60 \\ x = 120[/tex]
Write an equation of the line that passes through the point (6,-9) with the given slope m= 3
Answer:
y=3x-27
Step-by-step explanation:
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Write an equation of the line passing through (6, -9) and has a slope of -3.
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
First, we need to write the equation in point-slope form:-
[tex]\hookrightarrow\sf{y-y_1=m(x-x_1)}[/tex]
Replace y₁ with -9, m with 3, and x₁ with 6:-[tex]\hookrightarrow\sf{y-(-9)=3(x-6)}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\hookrightarrow\sf{y+9=3(x-6)}[/tex]
[tex]\bigstar[/tex] On further simplification,
[tex]\hookrightarrow\sf{y+9=3x-18}[/tex]
[tex]\star[/tex] Subtract 9 from both sides, which results in:-
[tex]\hookrightarrow\sf{y=3x-27}[/tex]
So we conclude that Option B is correct.
Good luck with your studies.
[tex]\rule{300}{1}[/tex]
Solve the problem.
A recipe calls for 6 ounces of unsweetened chocolate for 20 brownies. How much of unsweetened chocolate is needed to make 30 brownies?
Write out the sample space for the given experiment. Use the letter R to indicate red, G to indicate green, and B to indicate blue. A die shows 3 different colors on it. Give the sample space for the next 2 rolls. separate your answers using commas
Answer:
{RR,RG,RB,BR.BB BG,GR,GB,GG}
Step-by-step explanation:
It can be calculated by,
[tex]n^2=3^2=9[/tex]
{RR,RG,RB,BR.BB BG,GR,GB,GG}
A concession stand owner bought some bottles of water for $0.75 each and began selling them for $1.25 each. When he made back all the money he spent, he still had 20 bottles left to sell. What equation can be written to determine the amount of money the owner spent?
Annie bought a package of 100 pens for $167.00. How much did each
pen cost?
Answer:
Step-by-step explanation:
167.00 / 100 = $1.67
Find x. Round to the nearest tenth:
PJ is Decorating Pupcakes for Rocky´s Birthday Party. Her Color Scheme is Black, Purple, and Green. She Will use This Spinner to Determine the Color of Spinkles on each Pupcake. if Pj decorates 60 pupcakes, about how many can she expect to be purple?
A:15 pupcakes
B: 30 pupcakes
C: 20 pupcakes
D: 25 pupcakes
If there is no picture for the spinner and we assume that it is completely fair, meaning that you have an equal chance of landing on any spot: You will expect to get a certain color every 3 spins because you have 3 different colors. In this case the answer would be 20 pupcakes.
What value is an irrational number
Answer: Choice A
Explanation:
The number [tex]\sqrt{8}[/tex] is irrational. We cannot write it as a ratio or fraction of two integers. This is because 8 isn't a perfect square.
Multiplying any irrational number with a rational one leads to an irrational product.
In short:
irrational*rational = irrational
Therefore, the perimeter [tex]4\sqrt{8}[/tex] is also irrational.
BOOM Creations has offered to sell its balloon
bouquets for a fixed down payment of $65 and an
additional charge of $2.75 per bouquet.
Answer:
y intercept: 65
rate of change: $2.75
Step-by-step explanation:
Really quite simple lad. Your equation is y=2.75x+65. 65 is your y-intercept, and you have a rate of change of 2.75 per bouquet.
IMPORTANT!!!! PLS ANSWER FAST!!
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
y=-16x^2+198x+148
Answer:
yes i think
Step-by-step explanation:
In June Gemma paid £68 for her electricity.
In July she will pay 5% more for her electricity.
Work out how much Gemma will pay for her electricity in July.
Blake was born in Minnesota, but now he lives in lowa, close to where lowa,
Wisconsin, and Illinois meet. He works in Illinois, but he buys all of his clothes
at a store in Wisconsin. If the sales tax rates for the four states are as shown
in the following table, which sales tax rate does Blake pay on the clothes he
buys?
The sales tax rate that Blake pay on the clothes he buys is correctly given by: Option D: 5%
What is sales tax rate?The sales tax rate is the rate at which the sales tax is applied.
Total payable amount = Original amount + sales tax on that amount.
We are given that:
He(Blake) works in Illinois, but he buys all of his clothes at a store in Wisconsin.
So, the sales tax rate will be applied according to the rate of Wisconsin.
From the table, we see that the sales tax rate of Wisconsin is 5%.
Thus, the sales tax rate that Blake pay on the clothes he buys is correctly given by: Option D: 5%
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Answer:
5%
Step-by-step explanation:
Jessie finishes 2/5
of the problems on her homework before dinner. She finishes
another 3/10
of the problems on her homework after dinner. What fraction of the
problems on her homework does Jessie still have left to do?
Answer: Jessie still has 3/10 left.
Step-by-step explanation:
Convert 2/5 into tenths by multiplying by 2.
2/5 x 2 = 4/10
3/10 + 4/10 = 7/10
The entirety of her homework is 10/10 so do
10/10 - 7/10 = 3/10
She has 3/10 left.
I have to choose 2 tools
Answer:
scale
Step-by-step explanation:
it would be used to measure
Use the t-distribution to find a confidence interval for a difference in means μ1−μ2 given the relevant sample results. Give the best estimate for μ1−μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.
A 99% confidence interval for μ1−μ2 using the sample results x⎯⎯1=535, s1=103, n1=380 and x⎯⎯2=465, s2=86, n2=200
Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places.
The best estimate and the degree of freedom when the t-distribution is used to find a confidence interval is 7 and 56 respectively.
How to illustrate the research?The best estimate from the information given in the research will be:
= X1 - X2
= 53.5 - 46.5
= 7
The degree of freedom will be:
= 38 + 20 - 2
= 56
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The population of a city decreases by 4.4% per year. If this year's population is
135,000, what will next year's population be, to the nearest individual?
Answer:
129060
Step-by-step explanation:
135 000 - .044(135000) = 129 060
what plus what equals -20
A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 9 hours. Paulo can paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.
A. [tex]\frac{x}{9} + \frac{x}{8} = 1[/tex]; 2.18 hours
B. [tex]\frac{1}{9} + \frac{1}{8} = \frac{1}{x}[/tex]; 3.73 hours
C. [tex]\frac{9}{x} + \frac{8}{x} = 1[/tex]; 8.5 hours
D. [tex]\frac{x}{9} + \frac{x}{8} = 1[/tex]; 4.24 hours
Answer:
D 4.24
Step-by-step explanation:
Assume the area of room be A
Irina painting speed be x, 8x = A
Paulo painting speed be y, 9y = A
Together painting speed = x + y = A/8 + A/9
Assume together painting time = t
(A/8 + A/9) t = A
(1/8 + 1/9)t = 1
17t = 72
t = 4.24
To graph the inequality x > -3, draw an open circle on -3 and shade to the left.
TrueFalse
A pet store has three fish tanks each holding a different volume of water in a different number of fish to a holds 4 L and five fish tank bee holds 100 L in office tanks tea or 108 L and 23 fish. order the tanks by volume per fish from least to greatest.
What are the values of a, and r of the geometric series?
2-2 + 2-2 +2
-
O a = 2 and r=-2
a
O a = -2 and r= 2
O a = -1 and r= 2
O a = 2 and r=-1
The values of a and r is 2 and -1 respectively in the geometric series.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given geometric series is 2-2 + 2-2 +2-
A geometric series is a series for which the ratio of each two consecutive terms is a constant function of the summation index.
In the given series the first term is a and common ration is r
The common ratio is the number you multiply or divide by at each stage of the sequence.
r=-2/2 = -1
a , first term is 2
Hence, the values of a and r is 2 and -1 respectively in the given geometric series.
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