Answer:
(i) 512,000 cubic cm
(ii) 512,000 cubic cm
(iii) The tank holds 512 liters of water
Step-by-step explanation:
Capacity and Volume
Volume is the amount of space a container or object occupies. Capacity is the amount of matter required to fill the container.
(i)
The cubic tank has a side length of a=80 cm. The volume of a cube is:
[tex]V=a^3[/tex]
[tex]V=80^3[/tex]
[tex]C=512,000\ cm^3[/tex]
(ii)
The tank holds 512,000 cubic cm of water
(iii)
Since 1 liter = 1,000 cubic cm, the tank holds 512,000/1,000 = 512 liters of water.
Twice a number is 42 less than five times a number. What is the number?
Answer:
21
Step-by-step explanation:
I am 90% sure but tell me if i'm wrong
Rectangle LMNO is reflected over the x-axis to create rectangle L'M'N'O'. If a line segment is drawn from point M to point M', which statement would best describe the relationship between segment M M prime and the x-axis? They are diameters of concentric circles. They share the same midpoints. They are perpendicular to each other. They share the same endpoints.
Answer:I am pretty sure the answer is
C. "They are perpendicular to each other."
Step-by-step explanation:
For a shape to be reflected, it must be reflected across a line.
The true statement about the relationship between segments M, M' and the x-axis is that (c) they are perpendicular to each other
Given that:
Shape: rectangle LMNOReflection line: x-axisWhen the shape is reflected across the x-axis, we have the following perpendicular and congruent lines
L x-axis and L' x-axis M x-axis and M' x-axis N x-axis and N' x-axis O x-axis and O' x-axisHence, the relationship between segments M, M' and the x-axis is that (c) they are perpendicular to each other
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The mean number of typhoon hitting US follows a Poisson distribution with
variance 0.5 per month. Find the probability that
(a) 4 typhoons will hit US in a year.
(b) at least 2 typhoons will hit US in a given half-year.
Answer:
A) 0.1339
B) 0.8078
Step-by-step explanation:
The Poisson Distribution formula is given by;
P(x; μ) = (e^(-μ) × (μ^(x))/x!
We are given;
Variance = 0.5 per month
Now, in Poisson distribution, variance = mean.. Thus, mean μ = 0.5 per month
A) We want to find the probability that 4 typhoons will hit US in a year.
Thus, x = 4
But since it's for a year, then μ = 0.5 × 12 = 6
So;
P(x = 4) = (e^(-6) × (6^(4))/4!
P(x = 4) = 0.00247875 × 1296/24
P(X = 4) = 0.1339
B) probability that at least 2 typhoons will hit US in a given half-year is;
P(X ≥ 2) = 1 - P(X < 2)
P(X < 2) = P(X = 0) + P(X = 1)
In a half given year, μ = 0.5 × 6 = 3
P(X = 0) = (e^(-3) × (6^(0))/0!
P(X = 0) = 0.0498
P(X = 1) = (e^(-3) × (6^(1))/1!
P(X = 1) = 0.1494
P(X < 2) = 0.0498 + 0.1494
P(X < 2) = 0.1922
P(X ≥ 2) = 1 - 0.1922
P(X ≥ 2) = 0.8078
Automobiles arrive at the drive-through window at a post office at the rate of 7 every 10 minutes. The average service time is 7 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. (Note: the given equations are NOT necessarily in the correct order.) What is the average time a car is in the system?Formulas for 13.17 What is the average number of cars in the system? What is the average time cars spend waiting to receive service? What is the average number of cars in line behind the customer receiving service? What is the probability that there are no cars at the window? What percentage of the time is the postal clerk busy? What is the probability that there are exactly two cars in the system?
Answer:
1) the average time a car is in the system is 0.1587 min
2) the average number of cars in the system 0.1111
3) the average time cars spend waiting to receive service is 0.01587 min
4) the average number of cars in line behind the customer receiving service is 0.01111
5) the probability that there are no cars at the window is 0.9
6) the percentage of time that the postal clerk is busy is 10%
7) the probability that there are exactly two cars in the system is 0.1217
Step-by-step explanation:
Given that;
Arrival rate λ = the rate of 7 every 10 minutes = 7/10 = 0.7
Average service time μ = 7 minutes
The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.
1) What is the average time a car is in the system?
Average in the system W = 1 / (μ - λ)
= 1 / (7 - 0.7) = 1 / 6.3 = 0.1587 min
therefore the average time a car is in the system is 0.1587 min
2) What is the average number of cars in the system?
Average number of cars L = λ / (μ - λ)
= 0.7 / (7 - 0.7) = 0.7/6.3 = 0.1111
Therefore the average number of cars in the system 0.1111
3) What is the average time cars spend waiting to receive service?
Average time spend waiting for services Wq = λ / μ(μ - λ)
= 0.7 / 7(7 - 0.7) = 0.7/44.1 = 0.01587 min
Therefore the average time cars spend waiting to receive service is 0.01587 min
4) What is the average number of cars in line behind the customer receiving service?
average number of cars in line behind the customer receiving service
Lq = λ² / μ(μ - λ) = (0.7)² / 7(7 - 0.7) = 0.49 / 44.1 = 0.01111
Therefore the average number of cars in line behind the customer receiving service is 0.01111
5) What is the probability that there are no cars at the window?
probability that there are no cars at the window = 1 - (λ / μ)
= 1 - (0.7 / 7) = 1 - 0.1 = 0.9
Therefore the probability that there are no cars at the window is 0.9
6) What percentage of the time is the postal clerk busy?
percentage of the time is the postal clerk busy = (λ / μ)
= (0.7 / 7) = 0.1 ≈ 10%
Therefore the percentage of time that the postal clerk is busy is 10%
7) What is the probability that there are exactly two cars in the system?
the probability that there are exactly two cars in the system = (λ²e^-λ) / 2!
= (0.7²e^-0.7) / 2! = 0.2433 / 2 = 0.1217
Therefore the probability that there are exactly two cars in the system is 0.1217
The radius of a cylindrical tank is 3' and the height is 8'what is the volume
Answer:
226 cubed foot (rounded to 3 s.f.)
Step-by-step explanation:
Volume of cyclinder: [tex]\pi[/tex] × r² × h
Volume of cylindrical tank = [tex]\pi[/tex] × 3² × 8
= 72[tex]\pi[/tex]
= 226 cubed foot (rounded to 3 s.f.)
From A to Z BU
9 Love From A to Z
9 Love From A to Z
20
The
equation d = n²-12n + 43
models the number of defective
items d
produced in a manufacturing process where there
workers in a restricted
are n
area
a) solve for
When
do 30
I
b) solve for n
when
d=20
Answer:
a) we get value of n: n=10.7 or n=1.2 when d=30
b) we get value of n: n=9.6 or n=2.3 when d=20
Step-by-step explanation:
a) solve for n When do= 30
Put d= 30 in the given equation:
[tex]d = n^2-12n + 43[/tex]
[tex]30=n^2-12n+43\\n^2-12n+43-30=0\\n^2-12n+13=0\\[/tex]
Now, we will find value of n by using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a=1, b=-12 and c=13
[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(13)}}{2(1)}\\n=\frac{12\pm\sqrt{144-52}}{2}\\n=\frac{12\pm\sqrt{92}}{2}\\n=\frac{12\pm9.59}{2}\\n=\frac{12+9.59}{2} , n=\frac{12-9.59}{2}\\n=10.7 , n=1.2\\[/tex]
So, we get value of n: n=10.7 or n=1.2
b) solve for n when d=20
[tex]d=n^2-12n+43\\20=n^2-12n+43\\n^2-12n+43-20=0\\n^2-12n+23=0\\[/tex]
Now, we will find value of n by using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a=1, b=-12 and c=23
[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(23)}}{2(1)}\\n=\frac{12\pm\sqrt{144-92}}{2}\\n=\frac{12\pm\sqrt{52}}{2}\\n=\frac{12\pm7.21}{2}\\n=\frac{12+7.21}{2} , n=\frac{12-7.21}{2}\\n=9.6 , n=2.3\\[/tex]
So, we get value of n: n=9.6 or n=2.3
Complete the congruence statement by naming the corresponding angle or side.
50 points
Step-by-step explanation:
Triangles RQP and RBC are congruent.
Letters R and P are the 1st and 3rd letters in RQP.
Letters R and C are the 1st and 3rd letters in RBC.
Hence line RP = line RC = line CR (D).
D) CR
ΔRQP ≅ ΔRBC
They are congruent so if you highlight the line PR and find the similar one,
ΔRQP ≅ ΔRBC
The line would be line CR.
This year Rachel watched 65 movies she thought that 26 of them were very good of the movies she watched what percentage did she think we’re very good
Answer:
40%
Step-by-step explanation:
26×100=2600÷65=40
40%×65=26
Which of the following is equal to 16.4 ?
O A. 32
O B. V16.4
O c.
D. 64
Answer:
b?
Step-by-step explanation:
b= v16.4
pleaseee helppp meeee
helppp meee
Answer: Slope = -1.000/2.000 = -0.500
x-intercept = 0/1 = 0.00000
y-intercept = 0/2 = 0.00000
Step-by-step explanation:
Plzzzz help!
What is the equation of the line that passes through the point (2,-6) and has a
slope of -12
Write the equation 8x - 5y = 20 in
slope intercept form.
Answer:
The equation in slope-intercept form is y = 8/5x-4.
I hope this helps! Have a nice day!!
Sara and Harry are putting together a puzzle. Sara put together 7/12 of the puzzle pieces. Harry put together 7/24 of the puzzle pieces. What fraction of the total number of puzzle pieces has NOT been used? Enter your answer as a fraction, in simplest form, in the box provided.
Answer:
1/8
Step-by-step explanation:
7/12= 14/24 14/24 + 7/24= 21/24
21/24= 7/8 1-7/8= 1/8
The fraction of the total number of puzzle pieces has not been used is 1/8.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Sara and Harry are putting together a puzzle. Sara put together 7/12 of the puzzle pieces. Harry put together 7/24 of the puzzle pieces.
The fraction of the total number of puzzle pieces has not been used is calculated as,
7/12= 14/24
21/24= 7/8
1-7/8= 1/8
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x/x+2 -4/x-2=1 solve the equation
i will mark the brainliest plz help
Answer: x = -2/3
[tex]\frac{x}{x+2}- \frac{4}{x-2}=1\\\\<=>\frac{x(x-2)}{(x+2)(x-2)}-\frac{4(x+2)}{(x+2)(x-2)}=1\\\\\\<=>\frac{x(x-2)-4(x+2)}{(x-2)(x+2)}=1\\\\\\=>x(x-2)-4(x+2)=(x-2)(x+2)\\\\\\<=> x^{2} -2x-4x-8=x^{2} -4\\\\\\<=>-6x-8=-4\\\\\\<=>-6x=8-4\\\\\\<=>-6x=4\\\\\\<=>x=-4/6=-2/3[/tex]
Step-by-step explanation:
Evaluate if a = 6, b = 2, c = 9, & d = 3
Answer:
12
Step-by-step explanation:
a2 b
( )2 ( )
(–2)2 (3)
(4)(3)
find the number of permutations of the letters in twelve
Answer:
360
Step-by-step explanation:
Six letters in twelve with a repeated e would be 6! ÷ 2
You run around the perimeter of a baseball field at a rate of at most 12 feet per second. Which of the following are possible amounts of time that it takes you to run around the baseball field?
Answer: 79 seconds.
Step-by-step explanation:1) we have to calculate the lenght of the baseball field.
perimeter of the baseball field=2(radius)+lenght of a semicircle.
2(radius)=2(175 ft)=350 ft
lenght of a semicircle=40% of a circumference=(40/100)(2πr)
Perimeter of the baseball field=2(175 ft) + (40/100)(2π175 ft)=
=350 ft + 140π ft=350 ft + 439.82 ft=789.82 ft,
2)Now, we calculate the amounts of time that it takes you to ruan arount the baseball field.
10 ft------------------------1 second
789,82 ft----------------- x
x=(789.82 ft * 1 second) / 10 ft=78.98 s≈79 s
Plot -7 in the complex plane.
Answer:
the phone with me and I will be in the future of our games in call of duty Black ops game clip is not available for remote playback of the phone with me know if I can be used for
Step-by-step explanation:
explain the IF
poem in 5 linesexplain the IF
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explain the IF
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poem in 5 linesexplain the IF
poem in 5 lines
The lines represented by the equations 2y + 5x = –2 and y
- x + 3 are
parallel
Submit Answer
neither parallel nor perpendicular
perpendicular
the same line
Answer:
you should use desmos graphing. When you get there in the top left corner there are 3 lines. press that and scroll down. when you see sarcastic linear regression press that and put the coordinates points I hope this helped :))
WHAT IS 5/6 TIMES 15
Answer:
12.5
Step-by-step explanation:
it's the awnser. I need to explain why
A parallelogram is a:
rectangle
square
quadrilateral
rhombus
Answer:
quadrilateral
Step-by-step explanation:
A quadrilateral that has two pairs of parallel sides.
Need help with this ASAP it’s due in 10 minutes
Answer:
Step-by-step explanation:
Formula to be used,
A = [tex]P(1+\frac{r}{n})^{nt}[/tex]
Here, A = Final amount
P = Principal amount
r = rate of interest
n = Number of compounding (In a year)
t = Duration of investment (In years)
Question (5)
P = $4250
r = 0.015
n = 4
t = 3 years
A = [tex]4250(1+\frac{0.015}{4})^{4\times 3}[/tex]
A = [tex]4250(1.00375)^{12}[/tex]
A = $4445.24
Part (C)
1). P = $6000
r = 0.03
n = 2
t = 10 years
A = [tex]6000(1+\frac{0.03}{2})^{2\times 10}[/tex]
= [tex]6000(1.015)^{20}[/tex]
= $8081.13
2). P = $9000
r = 0.05
n = 2
t = 8 years
A = [tex]9000(1+\frac{0.05}{2})^{2\times 8}[/tex]
= [tex]9000(1.025)^{16}[/tex]
= $13360.55
PLEASE TAKE A PIC OF YOU WORK ON A PECIE OF PAPER WITH THE AWNSER ON IT!!!! Hey! I need help with this! I’m bad at math and have a 55% in it rn it would mean a lot if you could take this seriously. Only 5 questions.
Answer:
Step-by-step explanation:
Hey if you give me your email i ca email you the aswer it wot let me link a photo lol
Find the measure of angle A.
Answer:
I had this question and i got it right it is the measure is four
Step-by-step explanation:
The Student Council sold the following items at the home football game. A B с D E F G H
Item Price Income Cost Per Expenses Profit Number Sold Item 2 lollipops 85 $21.25 $0.12 $10.20 $11.05 $8.16 3 Gummies 48 $16.80 $0.18 $0.25 $0.35 $0.45 $0.55 4 Bubble Gum 79 $35.55 $8.64 $17.38 $11.96 $0.22 $0.26 $18.17 5 Combos 46 $25.30 $13.34 $50.72 6 TOTAL: $50.72
i stands for income and e stands for expenses, what is the formula for p, profits?
A: p = i/e
B: p = e/i
C: p = e-i
D: p = i-e
Answer:
[tex]p = i - e[/tex]
Step-by-step explanation:
Given
[tex]i = income[/tex]
[tex]e = expenses[/tex]
Required
Determine the profit (p)
Profit (p) is the difference between income (i) and expenses (e)
.
Mathematically:
[tex]Profit = Income - Expenses[/tex]
i.e.
[tex]p = i -e[/tex]
Option D is correct.
Answer:
d
Step-by-step explanation:
Joselyn saw an alligator that was 5 feet long. How many inches is 5 feet.
Answer:
The alligator is 60 Inches long.
Step-by-step explanation:
5 feet is 60 inches.
hope it helps!
Answer:
60 inches
Step-by-step explanation:
There are 12 inches in 1 foot, therefore the ratio of inches to feet is 12:1.
If the alligator is 5 feet than the amount of inches increase.
In order to find how long the alligator is in inches, multiply 5 by 12
5 x 12 = 60
the following formula gives the area of a circle, A, dependent on its radius, r.
A = πr²
solve the equation for the variable r.
Answer:
sqrt(A/pi), -sqrt(A/pi)
Step-by-step explanation:
A=pi*r^2
r^2=A/pi
r=sqrt(A/pi), -sqrt(A/pi)
The following list gives the number of siblings for each of 11 students. 0, 8, 9, 6, 5, 7, 2, 4, 3, 1, 11 Find the modes of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."
Answer:
[tex]0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11[/tex]
Step-by-step explanation:
Given
[tex]0, 8, 9, 6, 5, 7, 2, 4, 3, 1, 11[/tex]
Required
Determine the mode
Though, not necessary; it is a good practice to order the given data either in ascending or descending order.
In ascending order, the ordered data are:
[tex]0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11[/tex]
Mode implies that: the data that has the highest number of occurrence.
In the given data, each data has a frequency of 1.
Hence, the mode is:
[tex]0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11[/tex]
I also need help with this question I’m confused
Answer:
x = 4Step-by-step explanation:
From the diagram, we can se that line l is parallel to m. This means that according to geometry, m<7 and m<9 are located on the same position on line n. Hence m<7 = m<9 (corresponding angle)
Given
m<7 = 9x+ 5
m<9 = x+37
Equaling both
9x + 5 = x+ 37
9x - x = 37-5
8x = 32
x = 32/8
x = 4
Hence the value of x is 4
The length of a rectangular piece of cardboard is 2 cm greater than its width. If the length and the width were each decreased by 1 cm, the area of the cardboard would be decreased by 27 cm². What are the dimensions of the original piece of cardboard?
Write and solve an equation to represent the problem.
9514 1404 393
Answer:
13 cm wide; 15 cm long
Step-by-step explanation:
Let w represent the original width. Then the original length is (w+2) and the original area is w(w+2). After the decrease, the width is (w-1) and the length is (w+1). The decreased area is (w-1)(w+1). The difference between these areas is 27, so we have ...
w(w+2) -(w-1)(w+1) = 27
w^2 +2w -(w^2 -1) = 27
2w +1 = 27
w = (27-1)/2 = 13
The original piece of cardboard was 13 cm wide and 15 cm long.