geumath malah 17.pdf
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* 16 The diagram shows a swimming pool in the shape of a prism.
10 m
Sm
Diagram NOT
accurately drawn
וו 1
2 m
4m
DO NOT WRITE IN THIS AREA
2 m
The swimming pool is empty.
Water from 3 water tankers is going to be put into the pool.
There are 20000 litres of water in each water tanker.
Sam thinks that the surface of the water in the pool will be 10 cm below the top of the pool.
Is Sam correct?
You must show how you get your answer.
(lm - 1000 litres)
TE IN THIS AREA
Answers
Answer:
He is wrong.
In my answer I found the complete volume of the pool and then what the volume would be 10 cm empty. You probably only need to find the 10 cm emptied to answer, just a heads up. if you have any questions though let me know.
Step-by-step explanation:
To most easily figure out the volume of the empty pool I think it is easiest to break it up into four parts..
First break off that skinny end bit so it will have 1 m in height, 4 m in length and 5m in width. Width is never going to shange because of how we are breaking this up, and the width is the distance from you into the paper, if that makes sense. Basically not up and down or left and right.
Next another rectangular prism from the right side with 2 height, 2m length and again 5m width.
Now you have a trapezoidal prism with one base of length 1m, another of base 2m and a height of length 4m.
To fond the volume of prisms you want to find the area of their bases then multiply it by their heights. In this instance height is going to be the width again, and the bases are th parts facing us on the picture.
For a rectangular prism area of the base is easy, just multiply length by height. a trapezoid is taking the two bases (b1 and b2) ading them together and dividing that sum by 2, THEN taking this new number and multiplying it by what would be the height of the trapezoid. the trapezoid has its bases as two heights, and its height then would be the horizontal length of the pool. Sorry if that is confusing. Here are the three volumes though.
Rectangular 1: 4*1*5 = 20 m^3
Rectangular 2" 2*2*5 = 20m^3
Trapezoidal: = ([1+2]/2)*4*5 = 30 m^3
So total it is 70 m^3
The question then says each cubic meter can contain 1,000 liters of water. 70 m^3 then is 70,000 liters
The question also says there are three barrels of 20,000 liters each, so combined that's 60,000 liters.
Finally it wants to know if Sam is right saying if you dump all of the 60,000 liters into the pool the surface of the water will not reach the top of the pool by 10 cm. 60,000 is less than 70,000, but we don't know how much lower it is in cm.
The trick here is to know that we are lowering a specific dimension of each prism to a certain amount to be lower by 10cm
In the 4x1x5 rectangular prism the 1m side is lowering.
In the 2x2x5 rectangular prism the 2m side representing the vertical length is getting some amount taken away.
int he trapezoidal prism both of the "bases" are getting an amount taken.
So the trick here is to set up the math again, except this time with 10 cm less being subtracted from each part, then solving t and see if it gets us the 60,000 liters or 60 m^3. Since we are measurng in meters, 10 cm less is the same a subtracting .1, or if you prefer subtracting a decimeter.
4*1*5 becomes 4(.9)5 = 18
2*2*5 becomes 2(1.9)5 = 19
Trapezoidal: = ([1+2]/2)*4*5 becomes ([(.9)+(1.9)]/2)*4*5 = 28
Adding this all together gets us 65 or 65,000 liters. This means that if the pool is filled 10 cm from the top the volume would be 65,000 liters, still more than if the three tankers are emptied completely into it.
You could have probably just done the second part, where we sbtracted 10 cm from each of the dimensions, but I am going to leave it all since I wrote it.
9514 1404 393
Answer:
Sam is not correct.
Step-by-step explanation:
As shown in the attachment, the "base" (front face) of this prism can be divided into a rectangle and a trapezoid. The relevant area formulas are ...
A = LW . . . . area of a rectangle of length L and width W
A = 1/2(b1 +b2)h . . . . area with parallel bases b1 and b2 and height h
__
The rectangle portion of the "base" of the pool has area ...
A = (10 m)(1 m) = 10 m²
The trapezoid portion of the "base" of the pool has area ...
A = 1/2(6 m +2 m)(1 m) = 4 m²
Then the "base" area is ...
B = 10 m² +4 m² = 14 m²
__
The volume of the prism is given by ...
V = Bh . . . . where B is the base area and h is the distance between bases
V = (14 m²)(5 m) = 70 m³
We are told that 1 m³ = 1000 L and that 3 tankers of 20,000 L each are emptied into the pool. That leaves an unfilled volume of ...
70 m³ -3×(20 m³) = 10 m³ . . . . unfilled volume
__
The surface area of the pool is ...
A = LW = (10 m)(5 m) = 50 m²
So the unfilled volume has a height of ...
V = Bh
10 m³ = (50 m²)h
h = (10/50) m = 20/100 m = 20 cm . . . . . the height of the unfilled space
The water in the pool will be 20 cm below the top, not 10 cm. Sam is not correct.
Related Questions
A researcher has obtained the number of hours worked per week during the summer for a sample of 15 students. 40 25 35 30 20 40 30 20 40 10 30 20 10 5 20 Using this data set, compute the following: a. Median b. Mean c. Mode d. 40th percentile e. Range f. Sample variance g. Standard deviation
Answers
Answer:
Mean = 25
Median = 25
Mode = 6
Step-by-step explanation:
Given the data :
Using calculator :
Mode = highest occurring data point
Range = max - min = 40 - 5 = 35
Sample variance = 128.57 (calculator)
Sample standard deviation = sqrt(variance) = 11.34
5. Simplify: 2(4X+3)-(7X+6)
6. Find the perimeter of the metallic sheet
below
n
6
3n
3n
5
7. Write an expression for the sum of on-
sixth of m and one-seventh of n, minus 7
8. Simplify 5-³ x 5⁴ x 2²
9. Find the L.C.M of 2x3², 2x3x7 and 2x3²x5
10. What is the place value of 4 in the number
2043507?
11. Find the G.C.F OF 18,42 and 90
Answers
Answer:
hshdjdjdjffhdiosekskskdkcjfiririrotr8tti5tittttit4i5i6i6832wy
Name the
alternate
interior angle
with angle 5.
HELPP PLEASEEE
Answers
Answer:
angle 4 isthe correct answer
Consider the terms pyramid, line, square, and triangle. The term
is not defined in Euclidean geometry.
Answers
The term line is not defined in Euclidean geometry. ... These words are point, plane and line and are referred to as the "three undefined terms of geometry".
Answer:
LINE is not defined by Euclidian geometry
Step-by-step explanation:
In Euclidean geometry, there are 3 terms that are considered "undefined" they are; point, line and plane. I think it is because considered undefined because they are described, but not every formally defined.
As in a shape I mean I hope I am right,
log (3x+5)=log (2x-7)
Answers
Answer:
x=-12 (BUT IS EXTRENUS)
Step-by-step explanation:
If u dont know what extraneous is, dont worry about it...
Sonia took a loan of $10 000 from ABC bank tob pay for a renovation at home. The bank offered her a period of 30 months at a rate of 10.5%. to repay the loan:
a) Calculate the Simple Interest she would pay in 30 months.
b) Calculate the Total amount Sonia would have to repay the bank.
Answers
Answer:
a. Simple interest, S.I = $2,625
b. Total amount = $12,625
Step-by-step explanation:
Given the following data;
Principal = $10,000
Interest rate = 10.5%
Time = 30 months to years = 2.5 years
a. To find the simple interest;
Mathematically, simple interest is calculated using this formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is simple interest. P is the principal. R is the interest rate. T is the time.Substituting into the formula, we have;
[tex] S.I = \frac {10000*10.5*2.5}{100} [/tex]
[tex] S.I = \frac {262500}{100} [/tex]
Simple interest, S.I = $2,625
b. To calculate the total amount Sonia would have to repay the bank;
Total amount = simple interest + principal
Total amount = 2625 + 10000
Total amount = $12,625
If paper was £1.99 a pack and is now £3.98 a pack, what is the percentage increase in the price of the product?
Answers
Answer:
100%
Step-by-step explanation:
The initial price of the paper = 1.99
The final price of the pack of paper = 3.98
We need to find the percentage increase in the price of the product. It can be solved as follows :
[tex]\%=\dfrac{3.98-1.99}{1.99}\times 100\\\\=100\%[/tex]
So, the percentage increase in the price of the product is 100%.
The cost of making 6 chairs is $410. The cost of making 22 chairs is $570.
What is the cost per chair?
What is the fixed cost (or startup cost) that you need to spend before making the first chair?
Write a linear equation that tells you the total cost, C. of making x chairs.
CE
What is the total cost of making 17 chairs? $
If your total cost is $820, how many chairs did you make?
Answers
Answer:
if it cost 410 dollars to make 6 chairs we can divide 410 by 6 which is 68.3333333333 or 68 1/3
now for the other set of chairs we can divide 570 by 22 which is
25.9090909091 or 25.9
and for the rest it doesn't make any sense to me sorry
Please someone simplify this and please show the workout
Answers
Step-by-step explanation:
(a) 3pq / 4r² × 2rs / 6q²......first start by expanding the expression
It will be ;
3 × p × q / 4 × r × r X 2 × r × s / 6 × q × q
so now ,cancel out like terms. The q on top can cancel out with the q down same thing happens to r
so you'll get something like ;
3 × q / 4 × r X 2 × s / 6 × q ......so now divide , like 3 into 6 and 2 into 4 ,then you'll get something like;
qs / 4q
that's the answer
(b)15 ab² / 8 c²d ÷ 3ab / 4cd.......start by changing the sign from ÷ to × and then 3ab and 4cd will switch places
15ab² / 8c² d × 4cd / 3ab.....expand the expression
15 ×a×b×b / 8×c×c×d X 4×c×d / 3×a×b
then cancel like terms and you'll get;
15b / 8c X 4/3.....then divide 3 into 15 and 4 into 8
5b / 2c
hope this helps
In order for the data in the table to represent a linear
function with a rate of change of +5, what must be the
value of a?
Answers
Answer:
Step-by-step explanation:
Answer: C) a=18
Step-by-step explanation: Hope i helped :)
You recently invested $400,000 of your savings in a security issued by a large company. The security agreement pays you 12% per year and has a maturity of five year from the day you purchased it. What is the total cash flow you expect to receive from this investment, if compounded quarterly, separated into the return on your investment?
Answers
Answer:
$722444.49386776
Step-by-step explanation:
Use Compound Intrest Formula
[tex]a = p(1 + \frac{r}{n} ) {}^{nt} [/tex]
where p is the original amount.R is the amount of percentage compoundedN is amount of times compounded per year.T is how long the interest last.P is 400,00p
T is 12% or 0.12
N is 4 since it is compounded quarterly
T is 5.
Plug the values in
[tex]400000(1 + \frac{0.12}{4} ) {}^{20} [/tex]
Ypu get
$722444.49386776
In a binomial experiment :________
a. the probability does not change from trial to trial
b. the probability does change from trial to trial
c. the probability could change from trial to trial, depending on the situation under consideration
d. None of these alternatives is correct.
Answers
Answer:
Hence the correct option is Option (a).
Step-by-step explanation:
Option (a) is correct.
The probability does not change from trial to trial.
p = Probability of sucess.
The radius of a circle is 12.4 cm. Find the circumference to the nearest tenth.
Answers
PLS HELP ME!!!! use the properties of exponents to simplify the expression
Answers
Answer: 3
(27^1/2)2/3
So this means you multiply the exponents.
27^2/6
Simplify that 27^1/3
So cubed root of 27 is three.
Answer:
According to Indices
(a⁴)²... The exponents will multiply each other to give (a⁶)
Using this here
The two Index would Multiply to give
½ x ⅔ = ⅓
= (27)⅓
Any Number to the Index of ½ simply means its Square root
so also...
Any Number to the index of ⅓ means its cube root...
Cube root of 27 = 3.
So
Option B is your answer.
Use the formula below to find the relative pressure inside the can in psi
Answers
Answer:
b
Step-by-step explanation:
you have to have psi to have p-e-n-i-s sand you get a jack hammer
What percentage of total hours was spent playing football
Answers
Explanation:
10 hours was spent playing football, out of 50 total
10/50 = 1/5 = 0.20 = 20%
What is the monthly payment on a 15-year loan of $57,900 if the annual interest rate is 12%?
Answers
help pls i'll mark brainliest.. state the length of the line segment shown.
Answers
Answer:
i believe its 3 but i could be wrong
Step-by-step explanation:
sorry if i am..
What is the common denominator of
Please ignore my choice I had to click one of them
Answers
Answer:
Your choice is correct. GOOD JOB!!
Step-by-step explanation:
The Hernandez family is evenly splitting 777 liters of gasoline between their 444 cars.
How many liters of gasoline should each car get?
Answers
Answer:
1.75 liters per car
Step-by-step explanation:
777liters /444 cars=1.75 liters per car
Please help me with this problem
Answers
Answer:
x = 19
Step-by-step explanation:
2x + 3 = 90 - 49
2x + 3 = 41
2x = 38
x = 19
please help with the steps thx:)
Answers
Answer:
The answer for the first is $350,325.378, I think
Step-by-step explanation:
I hope this helps, if im wrong im sorry
Answer:
interest: 945, FV: 6345
FV= 323711.4, Interest: 226211.4
25.21 years
Step-by-step explanation:
question 1:
simple interest formula
PV(1+it)
30 months is equal to 30/12 years or 2.5 (so t= 2.5)
5400(1+.07*2.5)= 6345
This is the future value, to find the interst subtract the present value
6345-5400= 945
2.)
future value of continously compounding interst:
PV(e^(it))
97500*e^(.06*20)= 323711.4
finding the interest is the same as the last one
323711.4-97500=226211.4
3.)
same formula
let x= time in years
[tex]30000=7500e^{.055x}\\4=e^{.055x}\\\ln(4)=.055x\\x=25.20535202[/tex]
i guess we can round this to 25.21
HELP ME PLEASE!!!
GIVEN sin0= √23/12
tan0= √23/11
Find cos0
Answers
Answer:
[tex]cos \theta = \frac{11}{12}[/tex]
Step-by-step explanation:
[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]
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Question 12
Mr Espent 65% of his salary on household expenses, and 15% of the remainder on travelling expenses and was finally left with R9 500. How much was his salary?
Answers
Answer:
rs.1680.67
Step-by-step explanation:
His salary = x
remaining % = 100 - 65 = 35%
= 100 - 15 = 85%
x × 35/100 × 85/100 = 500
x = 1680.67
for f(x)=4x+1 and g(x)=x^2-5, find (f-g) (x) need help guys!
Answers
Answer:
-x^2 +4x +6
Step-by-step explanation:
f(x)=4x+1
g(x)=x^2-5
(f-g)(x) = 4x+1 - (x^2-5)
Distribute the minus sign
= 4x+1 - x^2 +5
= -x^2 +4x +6
A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:
a. Let F = the event of getting the white ball twice.
b. Let G = the event of getting two balls of different colors.
c. Let H = the event of getting white on the first pick.
d. Are F and G mutually exclusive?
e. Are G and H mutually exclusive?
Answers
Answer:
See explanation
Step-by-step explanation:
Given
Represent the balls with the first letters
[tex]W =1[/tex]
[tex]R =1[/tex]
Solving (a): P(F) --- White balls twice
The event of F is:
[tex]F = \{(W,W)\}[/tex]
So:
[tex]P(F) = P(W) * P(W)[/tex]
[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(F) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(F) = \frac{1}{4}[/tex]
Solving (b): P(G) --- two different colors
The event of G is:
[tex]G = \{(W,R),(R,W)\}[/tex]
So:
[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]
[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(G) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(G) = \frac{1}{4} + \frac{1}{4}[/tex]
[tex]P(G) = \frac{1}{2}[/tex]
Solving (c): P(H) --- White picked first
The event of H is:
[tex]H = \{(W,R),(W,W)\}[/tex]
So:
[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]
[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(H) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(H) = \frac{1}{4} + \frac{1}{4}[/tex]
[tex]P(H) = \frac{1}{2}[/tex]
Solving (d): F and G, mutually exclusive?
We have:
[tex]F = \{(W,W)\}[/tex]
[tex]G = \{(W,R),(R,W)\}[/tex]
Check for common elements
[tex]n(F\ n\ G) = 0[/tex]
Hence, F and G are mutually exclusive
Solving (e): G and G, mutually exclusive?
We have:
[tex]G = \{(W,R),(R,W)\}[/tex]
[tex]H = \{(W,R),(W,W)\}[/tex]
Check for common elements
[tex]n(G\ n\ H) = 1[/tex]
Hence, F and G are not mutually exclusive
A man is changing the oil in his car. The instruction manual indicates that the car hold pints of oil. The man only has a cup measure. How many cups equal three pints?
Answers
The volume contained in a cup of oil is a fraction of the volume
contained in a pint of oil.
Correct response:
6 cupsMethod used for the above unit conversionThe measure of the volume of oil the car holds = Pints of oil
The measurement the man has for use = Cups of oil
Required:
The number of cups equal to three pints.
Solution;
1 pint of oil = 2 cups of oil
Therefore;
3 pints of oil = 3 × 2 cups of oil = 6 cups of oil
The number of cups of oil equal to 3 pints of oil is 6 cups of oilLearn more about units conversion here:
https://brainly.com/question/4845674
Without using a calculator, compute the sine, cosine, and tangent of
330∘ by using the reference angle.
Answers
Answer:
sin(330)=-0.5
cos(330)=0.86
tan(330)=-0.57
How to learn tables 11 to 15
For 12 years old easyliy please tell guys
Answers
Answer:
For eleven, it had the same two numbers. For twelve, it continues up by even numbers. For thirteen, it's the same as twelve but by odd numbers. For fourteen, it's a little difficult but they have a pattern for every five multiples of fourteen. For fifteen, the numbers add by five but also counting up.
Step-by-step explanation:
Examples for the table of eleven would be: 11 × 3 = 33 or 11 × 6 = 66.
Table twelve would be (as examples): 12 × 2 = 24 and 12 × 3 = 36.
Table thirteen have numbers/answers like: 13 × 7 = 91 and 13 × 8 = 104.
Table fourteen as examples: 14 × 3 = 42 or 14 × 4 = 56.
Table fifteen would be like: 15 × 6 = 90 and 15 × 7 = 105.
Find the volume of the cone
Answers
Volume= 37. 7
V=π r² h/3 = π · 22 · 9/3 ≈37.69911
I hope this helps!