A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the water changing when the height is 3m?
Answer:
[tex]\dfrac{1}{\pi}$ m/s[/tex]
Step-by-step explanation:
Volume of a cylinder, [tex]V=\pi r^2h[/tex]
When the water is leaking, the radius of the cylinder remains constant while the height changes with respect to time.
Therefore, the rate of change of the volume,
[tex]\dfrac{dV}{dt}=\pi r^2 \dfrac{dh}{dt}[/tex]
[tex]4=\pi \times 2^2 \times \dfrac{dh}{dt}\\\\\dfrac{dh}{dt}=\dfrac{4}{4\pi}\\\\\dfrac{dh}{dt}=\dfrac{1}{\pi}$ m/s[/tex]
e^2x -2e^x -24=0 please answer fast
Answer:
x = ln6
Step-by-step explanation:
e^2x - 2e^x - 24 = 0
a = e^x
=> a^2 - 2a - 24 = 0
=> (a + 4)(a - 6) = 0
=> a = -4 => e^x = -4 (invalid because e^x > 0)
=> a = 6 => e^x = 6 => x = ln6
What is the greatest common factor of the polynomial below?
20x^3 - 14x
Answer:
the correct answer is 2x
Answer:
D. 2x
Step-by-step explanation:
20x² : 1, 2, 4, 5, 10, 20, x
14x : 1, 2, 7, 14, x
The greatest common factor of the polynomial is 2x.
2x(10x² - 7)
Ann spent 1/3 of her money on transport, 2/5 on food, 1/6 on clothing and saved $80.00. How much money did she have to begin with?
Answer:
Her initial money she started with us $800.00
Step-by-step explanation:
Let the initial money Ann began with be x.
So she spent 1/3 of x on transport,
2/5 of x on food
1/6 of x on clothing
And the remaining is $80.00.
Let's find the value of x
X(1/3) +x(2/5) + x(1/6) +80 = x
X(1/3) +x(2/5) + x(1/6) -x = -80
Taken 30 as the lowest common multiple of the factors gives
(10x + 12x + 5x -30x)/30 = -80
(10x + 12x + 5x -30x)= -2400
-3x = -2400
X = -2400/-3
X= 800
AT&T would like to test the hypothesis that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans. A random sample of 200 18- to 34-year-old Americans found that 126 owned a smartphone. A random sample of 175 35- to 49-year-old Americans found that 119 owned a smartphone. If Population 1 is defined as 18- to 34-year-old Americans and Population 2 is defined as 35- to 49-year-old Americans, the correct hypothesis statement for this hypothesis test would be
Answer:
The null and alternative hypothesis can be written as:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.
This claim will be reflected in the alternnative hypothesis, that will state that the population proportion 1 (18 to 34) is significantly smaller than the population proportion 2 (35 to 49).
On the contrary, the null hypothesis will state that the population proportion 1 is ot significantly smaller than the population proportion 2.
Then, the null and alternative hypothesis can be written as:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
The significance level is assumed to be 0.05.
The sample 1, of size n1=200 has a proportion of p1=0.63.
[tex]p_1=X_1/n_1=126/200=0.63[/tex]
The sample 2, of size n2=175 has a proportion of p2=0.68.
[tex]p_2=X_2/n_2=119/175=0.68[/tex]
The difference between proportions is (p1-p2)=-0.05.
[tex]p_d=p_1-p_2=0.63-0.68=-0.05[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{126+119}{200+175}=\dfrac{245}{375}=0.653[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.653*0.347}{200}+\dfrac{0.653*0.347}{175}}\\\\\\s_{p1-p2}=\sqrt{0.001132+0.001294}=\sqrt{0.002427}=0.049[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.05-0}{0.049}=\dfrac{-0.05}{0.049}=-1.01[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=P(z<-1.01)=0.1554[/tex]
As the P-value (0.1554) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.
HELP!!
Which Platonic solid has four faces that are equilateral triangles?
A. Hexahedron
B. Dodecahedron
C. Tetrahedron
D. Icosahedron
Answer:
C. Tetrahedron
Step-by-step explanation:
In figure
The Platonic solid that has four faces that are equilateral triangles is the Tetrahedron. The correct option is C.
What is Tetrahedron?A Tetrahedron is a three-dimensional shape made up of four equilateral triangles. It is one of the five Platonic solids, which are regular, convex polyhedra with identical vertices and faces.
Each vertex in a Tetrahedron is connected to the other three vertices by an edge, resulting in a pyramid-like structure.
The Tetrahedron is a unique shape with numerous applications in mathematics, engineering, and chemistry.
The Tetrahedron is a Platonic solid with four equilateral triangle faces. It has four faces, four vertices, and six edges in total. It is the most basic of the Platonic solids and the only one with no parallel faces.
Thus, the correct option is C.
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Carleen has 104 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 8 kids on her block. Write an equation to show how many pieces of candy each kid will receive.
Answer:
8x = 104
x = 13
Step-by-step explanation:
Since we are trying to distribute it evenly, we divide 104 by 8 to get 13 pieces of candy per child.
The equation is saying 8 kids times x amount of candy per kid is equal to a total amount of 104 pieces of candy.
Answer:
Each kid will get 13 pieces of candy.
Step-by-step explanation:
If Carleen has 104 pieces of candy leftover from Halloween, and she splits the candy with 8 of the kids on her block, each kid gets 13 pieces. I know this because you divide:
104 divided by 8 equals 13
What is the value of 500$ invested at 4% interest compounded annually for 7 years
Answer:
657.96
Step-by-step explanation:
use formula A=P(1+r/n)^nt
A=500(1+.04/1)^1*7
A=500(1.04)^7
A=500(1.3159~)
A= 657.96~
Jasmine compared the two graphs below. Graph A Daily High Temperatures and Bottled Water Sales Graph A has temperature (degrees Fahrenheit) on the x-axis and Number of bottles sold on the y-axis. Points are grouped together in a line with positive slope. Graph B Daily High Temperatures and Bottled Water Sales Graph A has temperature (degrees Fahrenheit) on the x-axis and Number of bottles sold on the y-axis. Points are grouped together and increase. A few points are outside of the group. She decide to use graph A to predict the number of bottles of water that would be sold when the temperature is 100 degrees Fahrenheit. Which is likely Jasmine’s reasoning? Graph A has a stronger correlation, so it is more likely to provide an accurate prediction. Graph A has a temperature reading of 90 degrees, which is closer to 100 degrees. Graph B has a negative correlation, so it would not be suitable. Graph B has a strong correlation, but it has an outlier.
Answer:
i think it is a
Step-by-step explanation:
Answer:
a) Graph A has a stronger correlation, so it is more likely to provide an accurate prediction.
Step-by-step explanation:
Solve 2x² - 11x + 5 = 0.
Answer:
x=1/2, x=5
Step-by-step explanation:
2x^2-11x+5=0
Factor them
(x-0.5)(x-5)
x=0.5 or 1/2
x=5
HELP HELP PLEASE the height of the triangle is 16 cm, and fe=10 cm. What is the area of the triangle? A. 50 CM^2 B. 80 CM^2 C.160 CM^2 D.192 CM^2
Answer:
B. 80 cm^2
Step-by-step explanation:
A = bh/2
A = (FE)(16 cm)/2
A = (10 cm)(16 cm)/2
A = 80 cm^2
Please help me find the end behavior!:(
Answer:
D
Step-by-step explanation:
This is an odd degree polynomial (the highest degee is an odd number) so both ends will be in different directions, one will be up the other will be down. So rule out any option that has p(x) pointing in the same direction (A & C)
Now we are between B & D. Look at the leading coefficient 6 which is positive so we know that the left end goes down and the right end goes up. If the lc was negative the opposite would be true. So
D is the right answer
Karri tests the charges of a random sample of 64 batteries from a large production run. The mean charge was 8.93 volts, and the process typically has a standard deviation of 0.2 volts. To see if the batch has a significantly different mean voltage from 9 volts, the value of the z-test statistic would be ___________.
Answer:
The Z-statistic value is
Z = -2.33
Step-by-step explanation:
Step(i):-
Random sample size 'n' = 64
mean of the sample 'x⁻ ' = 8.93 volts
standard deviation of the sample = 0.2 volts
mean of the Population"μ" = 9 volts
Step(ii):-
Z -statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{8.93 -9}{\frac{0.2}{\sqrt{64} } } = -2.33[/tex]
Conclusion:-
The Z-statistic value is = -2.33
Thompson's hardware spent $66,170 this year on general insurance alone. if total sales were $713,200, what percent total sales was spent on general insurance? round to the nearest tenth of a percent, if necessary.
Answer:
We have our answer as approximately 10 %
Step-by-step explanation:
We are simply expected to express the sum of money spent on insurance as a percentage of the total sales in this question.
The first step is to set up a fraction, having the sum spent on insurance as the numerator, and the total sales as the denominator. This is shown below
[tex]\frac{66,170}{713,200}[/tex]
To convert this fraction to a percentage, we will have to multiply it by 100 and reduce it to its lowest term.
Here we have
[tex]\frac{66,170}{713,200} \times 100= 9.28 percent[/tex]
Rounding of to the nearest tenth, we have our answer as approximately 10 %
There are (7^13)^3 x 7^0 strawberries in a field . What is the total number of strawberries in the field
Answer:
Step-by-step explanation:
[tex]7^{0}=1[/tex]
[tex](7^{13})^{3}*7^{0}=7^{13*3}*1\\\\=7^{39}[/tex]
The quotient of y and 3
Answer:
[tex]\frac{y}{3}[/tex]
Step-by-step explanation:
Well the quotient is the answer if y divided by 3.
So y divided by 3 is y over 3 y/3.
Abox in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12
cubes measuring 6 inches on each side.
If the length and width of the base are doubled, how many cubes could the new box hold?
18
0 24
48
o 96
Answer:
48
Step-by-step explanation:
You are doubling 2 dimensions, so you just multiply the volume by 2 each time. Since you are doing it twice, you multiply the volume by 4. 12*4=48. You could also brute force it and just do 24*36*12/216(the volume of the 6 inch cube).
Given that, a box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.
We need to find that how many cubes it holds if the length and width of the base are doubled,
We know that,
Volume of a rectangular prism = length × width × height
Volume of the new rectangular prism, = 2length × 2width × height
= 4(length × width × height)
= 4(12·12·18)
= 4×2592
= 10,368
Volume of the cube = side³
= 6³ = 216
The number of cube that the new rectangular prism can hold = Volume of the rectangular prism / Volume of the cube
= 10,368 / 216
= 48
Hence, the new rectangular prism, can hold 48 cubes.
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Jacqueline and Maria set up bug barns to catch lady bugs. Jacqueline caught ten more than three times the number of lady bugs that Maria caught. If c represents the number of lady bugs Maria caught, write an expression for the number of lady bugs that Jacqueline caught.
Answer:
(CX3)+10
Step-by-step explanation:
Answer:
c×3+10= j
Step-by-step explanation:
18 is divisible by both 2 and 3 it is also divisible by 2 into 36 similarly a number is divisible by both 4 and 6 can we say that the number must also be divided by 4 and 2 6 24 if not give an example to justify your answer
Answer:
no; 12
Step-by-step explanation:
A number divisible by 4 and 6 will be divisible by their least common multiple, 12. If it is an odd multiple of 12, it will not be divisible by 24.
Examples:
12÷4 = 3; 12÷6 = 2; 12 is not divisible by 24
24÷4 = 6; 24÷6 = 4; 24 is divisible by 24
36÷4 = 9; 36÷6 = 6; 36 is not divisible by 24
WILL GIVE BRAINLIEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter. plz help me
Answer:
P ≈ 317.08 m
Step-by-step explanation:
Circumference: C = πd
Step 1: Find circumference of both domes
C = π(50)
Since it's a dome, we divide by 2
50π/2 = 25π
Since we have 2 domes, we simply multiply by 2 again
25π(2) = 50π
Step 2: Find perimeter of track
50π + 80(2)
P = 50π + 160
P = 317.08 m
Estimate the volume of material in a cylindrical shell with height 32 in., radius 7 in. comma and shell thickness 0.5 in. Round to one decimal place. (Use 3.14 for pi.)
Answer:
703.36 in ^ 3
Step-by-step explanation:
We have the following information:
Height (h) = 32 in
Radius (r) = 7 in
Thickness (dr) = 0.5 in
Now the volume of a cylinder is:
V π (r ^ 2) * h
if we derive with respect to the radius we are left with:
dV / dr = 2 * π * r * h
then solved for dV, we would have:
dV = 2 * π * r * h * dr
we know all these values so we replace:
dV = 2 * π * 7 * 32 * 0.5
dV = 224 * π
if we say that π is approximately 3.14
V = 703.36
Therefore the estimate of the volume of that cylinder is 703.36 in ^ 3
I NEED HELP PLEASE, THANKS! :)
Answer:
Option C
Step-by-step explanation:
Our input is function f( x ), but to find the derivative of this function, you must convert this f ( x ) into a " [tex]d / dx[ f( x )] / f'x[/tex] " format. In this case it can be done multiplying the numerator by 7, and squaring the denominator. We would have to separate this into two fractions, as the following -
[tex]\frac{4}{7x-18}-\frac{28x}{\left(7x-18\right)^2}[/tex]
Now all that has to be done is to simplify this expression! The least common multiple of 7x - 18, ( 7x - 18 )^2 is ( 7x - 18 )^2. That, respectively makes it our denominator. Based on the LCM we would receive the following -
[tex]\frac{4\left(7x-18\right)}{\left(7x-18\right)^2}-\frac{28x}{\left(7x-18\right)^2}[/tex]
Now the denominators are equal, so we can combine the two fractions and simplify -
[tex]\frac{4\left(7x-18\right)-28x}{\left(7x-18\right)^2} - ( Simplify ),\\\\-\frac{72}{\left(7x-18\right)^2}[/tex]
Hence, the solution is option c. Hope that helps!
Will give brainliest answer
Answer: 49π square units
Step-by-step explanation:
Area of a circle = πr^2
Area = π x 7^2
Area = 49π
Answer:
9.8646 or I think 14 units 2
the length of a rectangular sheet of metal is 9.96m and it's breadth is 5.08m. Find the area of the metal.Correct the answer to 2 significant figures and then correct the answer to 0.1 meter square
Answer:
The area of the sheet is approximately 50.59 m² or 50.6 m²
Step-by-step explanation:
The area of a rectangle is given by the following expression:
[tex]area = width*height[/tex]
Since breadth is the same as the width of the sheet, we can calculate its area as shown below:
[tex]area = 9.96*5.08 = 50.59[/tex]
The area of the sheet is approximately 50.59 m² or 50.6 m²
Here is a list of numbers 83,73,76,72,75,85,79,76 work out the median from the numbers from the list
Answer:
552.5
Step-by-step explanation:
Answer:
76Step-by-step explanation:
Median means the middle or central value.
Given data : 83 , 73 , 76 , 72 , 75 , 85 , 79 , 76
Arranging the data in ascending order:
72 , 73 , 75 , 76 , 76 , 79 , 83 , 85
N ( total number of items ) = 8
Here, as there are 8 terms , we cannot find the one central value within the set.
The median will be average of the two central terms, 76 and 76
Now, to find the median, we have to divide the sum of two central terms ( 76 and 76) by 2
Median :[tex] \frac{76 + 76}{2} [/tex]
Calculate the sum:
[tex] \frac{152}{2} [/tex]
Divide:
[tex]76[/tex]
Hope this helps..
Best regards!
which linear function is represented by the graph below?
A) f(x) = -2x + 1
B) f(x) = -1/2x + 1
C) f(x) = 1/2x + 1
D) f(x) = 2x + 1
Answer:
The answer is answer choice b.
Step-by-step explanation:
b/c its a negative line
Which data set is accurate and precise based on a correct value of 30?
Set 1: 30, 35, 32, 30, 29
Set 2: 15, 16, 12, 15, 14
Set 3: 19, 30, 78, 43, 30
Set 4: 30, 30, 67, 12, 90
Answer:
Set 1: 30, 35, 32, 30, 29
Step-by-step explanation:
Let's first clarify what is accurate and precise:
Precise is based on how close two or more measured values are to each other. While something is said to be accurate, when the standard value values are close, which in our case is 30.
Therefore, we analyze each set:
Set 1: 30, 35, 32, 30, 29
This set is precise and accurate, since 2 values are 30 and all their values are close to each other.
Set 2: 15, 16, 12, 15, 14
This set is precise, because all of its values are close but not accurate.
Set 3: 19, 30, 78, 43, 30
This set is somewhat accurate because there are 2 values of 30, but it is not precise because its values are separate.
Set 4: 30, 30, 67, 12, 90
It is the same case of Set 3.
Therefore the answer is Set 1.
Answer:
Set 1: 30, 35, 32, 30, 29
Step-by-step explanation:
A travel agent is booking trips for tourists who travel from New York to Chicago. Tourists have three choices for how to travel from New York to Chicago. They can take an airplane for $350, a bus for $150, or a train for $225. Once they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. If each option is equally likely to occur, what is the probability that a tourist will spend more than $275 on these 2 legs of the trip?
Answer:
P = 1/2
Step-by-step explanation:
If the tourist spends more than 275$, they must not arrive in Chicago by bus.
( 150 + 60 < 275, 150 + 40 < 275)
The total options the tourist can make:
3 x 2 = 6
(1st leg: 3 possible options, 2nd leg: 2 possible options)
The number of options the tourist can make after excluding bus option:
2 x 2 = 4
(1st leg: 2 remaining possible options, 2nd leg: 2 possible options)
The number of options the tourist can make after excluding the bus option and spend more than 275$:
4 - 1 = 3
(excluding the case of selecting train and cab, because 225 + 40 < 275)
=> The probability that the tourist will spend more than 275$ on these 2 legs of the trip:
P = 3/6 = 1/2
Probability helps us to know the chances of an event occurring. The probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that Tourists have three choices for how to travel from New York to Chicago. They can take an aeroplane for $350, a bus for $150, or a train for $225. Also, when they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. Therefore, the cost of different routes is,
Aeroplane($350) + Van($60) = $410Aeroplane($350) + Cab($40) = $390Bus($150) + Van($60) = $210Bus($150) + Cab($40) = $190Train($225) + Van($60) = $285Train($225) + Cab($40) = $265As it can be seen that there are 3 cases where a tourist will spend more than $275, while the total number of cases is 6. Therefore, the probability that a tourist will spend more than $275 on these 2 legs of the trip is,
Probability = 3/6 = 1/2 =0.5z
Hence, the probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.
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How do you write 89,700,000,000 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]89.7 \times {10}^{9} [/tex]
Or
[tex]8.97 \times {10}^{10} [/tex]
Hope this helps you
Answer:
8.97 * 10 ^10
Step-by-step explanation:
We want one nonzero digit to the left of the decimal
8.97
We moved the decimal 10 places to the left
The exponent is positive 10 since we moved 10 places to the left
8.97 * 10 ^10
Calculate the average of the following numbers (round to the nearest 10 th): 34, 43, 45, 35
Answer:
40
Step-by-step explanation:
(34 + 43 + 45 + 35)/4 = 39.25
To the nearest 10th = 40
Find the slope-intercept form of the line with slope 6 that passes through the point (3,5).
Answer:
y=6x-13
Step-by-step explanation:
Since we are given a point and a slope, we can use the slope intercept formula.
[tex]y-y_{1} = m(x-x_{1} )[/tex]
where (x1, y1) is a point and m is the slope.
We know that the slope is 6 and the point is (3,5). Therefore,
x1= 3
y1= 5
m=6
Substitute these into the formula.
[tex]y-5 = 6(x-3 )[/tex]
Distribute the 6. Multiply each term inside the parentheses by the number outside the parentheses.
[tex]y-5= (6*x) + (6*-3)[/tex]
[tex]y-5=6x-18[/tex]
We want to find the slope-intercept form, or y=mx+b. Therefore, we must get y by itself.
5 is being subtracted from y. The inverse of subtraction is addition. Add 5 to both sides.
[tex]y-5+5=6x-18+5[/tex]
[tex]y= 6x-18+5[/tex]
[tex]y= 6x -13[/tex]