Answer:
Step-by-step explanation:
Work done is given as the product of force and distance.
The liquid in the cylindrical tank weighs 62.4 lb/ft^3.
This means that each ft^3 of the tank has 62.4 lb of the liquid.
To find the wight of the liquid in the entire tank, we multiply 62.4 by the volume of the cylindrical tank.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r is its radius and h is its height
The radius of the tank is 6 ft (since its diameter is 12 ft) and its height is 20 ft.
Therefore, the weight of the liquid in the tank is given as:
[tex]V = \pi * 6^2 * 20 = 2261.95 lb[/tex]
This weight is a force.
The height of the tank is 20 ft.
Therefore, the work done in pumping the liquid to the top of the tank is:
W = 2261.95 * 20 = 45239 ft.lb
A car with 15 gallons of gasoline drives 420 miles until the tank is empty. Write a linear equation that describes the amount of gas left in the car, y, after driving x miles.
Answer:
[tex] y = -\dfrac{1}{28}x + 15 [/tex]
Step-by-step explanation:
The car uses 15 gallons of gasoline to drive 420 miles.
(15 gal)/(420 mi) = 1/28 gal/mi
The car uses 1/28 gallon of gasoline per mile.
y = mx + b
When x = 0, at the start of the drive, the car has 15 gallons of gasoline.
y = mx + 15
Then for every mile it travels, the amount of gasoline goes down by 1/28 gal. For x miles of travel, it uses 1/28 * x gallons of gasoline.
[tex] y = -\dfrac{1}{28}x + 15 [/tex]
FIND THE SMALLEST ANGLE IN THE TRIANGLE! PLEASE HELP!! 25 POINTS!!
From the side/angle inequality, we see that the smallest angle of a triangle must be opposite its shortest side. In this case, that angle is opposite the shortest side [tex]\overline{AC},[/tex] so our answer is [tex]\boxed{\angle B}.[/tex]
As for finding its measure (which I'm aware the question probably didn't ask for), we can use the law of cosines:
[tex]5^2=6^2+7^2-2(6)(7)\cos B[/tex]
[tex]\cos B=\frac{5}{7}\implies\angle B\approx\boxed{44.4^\circ}.[/tex]
Answer:
Smallest Angle in the triangle is angle c.
Students at an agricultural station conducted a study to compare geneticallymodified (GM) corn with regular corn. Each of 33 plots of land was divided intotwo half-plots; one half-plot was randomly selected to be planted with the GMcorn, and the other half-plot was planted with the regular corn.The table shows summary statistics for the yields, in bushels per acre, and thedifference in yield (GM minus regular) for each plot.MeanStandardDeviation n Minimum Q1 Median Q3 MaximumGM 125.018 13.623 33 107.4 111.9 127.5 138.0 144.0Regular 120.482 10.321 33 102.9 111.0 119.4 129.0 133.5Difference 4.536 6.444 33 –2.1 –0.9 3.0 6.0 20.1(a) Explain why the yields from one type of corn are not independent of the yields from the other type of corn.(b) Based on the summary statistics, would it be more likely to obtain a yield of 123 or more bushels per acre from a plot of GM corn or a plot of regular corn? Justify your answer.
Answer:
Step-by-step explanation:
The given data is represented in the attachment.
a) Explain why yields from one type of corn are not independent of the yields from the other type of corn.
Yields from one type of corn are not independent of the yields from the other type of corn because, as the corns are planted in two similar plots, they could compete during watering process, even the amount of nutrients shared and the type of air. This means one corn may get more nutrients than the other. Therefore, they are not independent (they are dependent).
b) Based on the summary statistics, GM is expected to more likely obtain yield greater than 123, because 123 is greater than mean for regular corn but less than mean for GM corn.
Thus,
P(yield>123|GM)>0.5; and P(yield>123|Regular)<0.5
There were 500 goats and geese on a farm. If I see 1,468 legs, how many of each are on the farm? Pls help now
Answer:
734
Step-by-step explanation:
divide 1468 by 2
Answer:
234 goats266 geeseStep-by-step explanation:
Let x represent the number of goats. The 500-x is the number of geese. The total number of legs is ...
4x +2(500 -x) = 1468
2x +1000 = 1468 . . . . . . . eliminate parentheses
2x = 468 . . . . . . . . . . .subtract 1000
x = 234 . . . . . . . . .number of goats
(500 -x) = 266 . . number of geese
1. Determine a rule that could be used to explain how the volume of a
Cylinder or cone is affected when the radius is multiplied by a positive
number.
Answer:
See explanation
Step-by-step explanation:
Solution:-
- We will use the basic formulas for calculating the volumes of two solid bodies.
- The volume of a cylinder ( V_l ) is represented by:
[tex]V_c = \pi *r^2*h[/tex]
- Similarly, the volume of cone ( V_c ) is represented by:
[tex]V_c = \frac{1}{3}*\pi *r^2 * h[/tex]
Where,
r : The radius of cylinder / radius of circular base of the cone
h : The height of the cylinder / cone
- We will investigate the correlation between the volume of each of the two bodies wit the radius ( r ). We will assume that the height of cylinder/cone as a constant.
- We will represent a proportionality of Volume ( V ) with respect to ( r ):
[tex]V = C*r^2[/tex]
Where,
C: The constant of proportionality
- Hence the proportional relation is expressed as:
V∝ r^2
- The volume ( V ) is proportional to the square of the radius. Now we will see the effect of multiplying the radius ( r ) with a positive number ( a ) on the volume of either of the two bodies:
[tex]V = C*(a*r)^2\\\\V = C*a^2*r^2[/tex]
- Hence, we see a general rule frm above relation that multiplying the result by square of the multiple ( a^2 ) will give us the equivalent result as multiplying a multiple ( a ) with radius ( r ).
- Hence, the relations for each of the two bodies becomes:
[tex]V = (\frac{1}{3} \pi *r^2*h)*a^2[/tex]
&
[tex]V = ( \pi *r^2*h)*a^2[/tex]
(2k2 - 8k + k4) - (7k+8k^2-5k^4) simplify each difference. write the final answer in standard form. identify the leading coefficient and the constant. show all work
Answer:
-7k-8k^2+5k^4
Step-by-step explanation:
Suppose that each customer asks to sample a food item with probability 1/4, independently of all other customers. The service time for a customer who samples a food item is an exponential random variable with parameter 1/5. i. What is the expected number of minutes until you reach the front of the line
Answer:
An approximately 2 minutes is expected to reach the front of the line
Step-by-step explanation:
Expected value of minutes =
(1/4)^(1/5) + (1 - 1/4)^(1/5)
= (1/4)^0.2 + (3/4)^0.2
= 0.7579 + 0.9441
= 1.702.
≈ 2 minutes
10+10+10-10+10+10+10
Answer:
60
Step-by-step explanation:
=> 10+10+10-10+10+10+10+10
=> 30-10+40
=> 20+40
=> 60
Answer:
60
Step-by-step explanation:
10+10+10-10+10+10+10
If the angles are represented in degrees, find both angles: \cos(3x+13)=\sin(2x+42) cos(3x+13)=sin(2x+42)
Answer:
cos34°
sin56°
Step-by-step explanation:
Sin(2x+42)= sin90-(3x+13)
Sin(2x+42) = sin(90-13-3x)
Sin(2x+42) = sin(77-3x)
2x + 42 = 77-3x
5x. = 35
X = 7
If x = 7
cos(3x+13) = cos((3*7)+13)
cos(3x+13) = cos(21+13)
cos(3x+13)= cos34
And
sin(2x+42) = sin((2*7)+42)
sin(2x+42)= sin (14+42)
sin(2x+42) = sin56
Express the following number in scientific notation. 46,000,000 = _____ 4.6000 x 10 7 4.6 x 10 7 4.600 x 10 7 0.460 x 10 6
Answer:
4.6 x 10^7
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Solve the equation.
6.35 + b = 9.89
Answer:
b=3.54
Step-by-step explanation:
9.89-6.35=3.54
Answer: b=3.54
Step-by-step explanation:
Subtract 6.35 from both sides and you will get that b=9.89-6.35 solve that and you will get that b= 3.54.
Based on the family the graph below belongs to, which equation could represent the graph? image below.
Answer:
y = 1/x+2 + 3
Step-by-step explanation:
x = -2
y = 3
What is the scale factor of the dilation?
1/8.... 1/4..... 4.... 8...?
Answer:
4
Step-by-step explanation:
When parallelogram FGHJ is dilated and translated to similar parallelogram F'G'H'J', the scale factor of dilation is 4.
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape.
As visible,
FG = GH = JH = FJ = 2 units
F'G' = G'H' = J'H' = F'J' = 8 units
Scale factor of Dilation = 8/2 = 4 units
Learn more about dilation here
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Write this number in expanded notation 2,930,365
Answer:
2,000,000+900,000+30,000+300+60+5
Step-by-step explanation:
hope this helps and Please Rate brainliest!!!
Find the five-number summary for the data.
{238, 213, 223, 212, 225, 233, 230, 239, 223, 207, 219,
217, 234, 204, 212, 242}
A. 204, 212.5, 223, 233.5, 242
B. 204, 212, 223, 233, 239
OC. 204, 212, 219, 233, 242
OD. 207, 212, 223, 234, 239
Answer:
The correct option is A. 204, 212.5, 223, 233.5, 242.
Step-by-step explanation:
The five number summary of a data set is:
Minimum First Quartile Median Third Quartile Maximum.The data provided, in ascending order is:
S = {204 , 207 , 212 , 212 , 213 , 217 , 219 , 223 , 223 , 225 , 230 , 233 , 234 , 238 , 239 , 242}
There are a total of 16 values in the data set.
The minimum value is,
Minimum = 204
The first quartile is the median value of the first half of the data.
The first half of the data is:
S₁ = {204 , 207 , 212 , 212 , 213 , 217 , 219 , 223 }
The median for even number of observations is the mean of the middle two values.
[tex]\text{Q}_{1}=\frac{4^{th}+5^{th}}{2}=\frac{212+213}{2}=212.5[/tex]
The first quartile is 212.5.
The median for even number of observations is the mean of the middle two values.
[tex]\text{Median}=\frac{8^{th}+9^{th}}{2}=\frac{223+223}{2}=223[/tex]
The median of the data is 223.
The third quartile is the median value of the second half of the data.
The first half of the data is:
S₂ = {223 , 225 , 230 , 233 , 234 , 238 , 239 , 242}
The median for even number of observations is the mean of the middle two values.
[tex]\text{Q}_{3}=\frac{12^{th}+13^{th}}{2}=\frac{233+234}{2}=233.5[/tex]
The third quartile is 233.5.
The maximum value is,
Maximum = 242
Tiffany needs to rent a car while on vacation. The rental company charges $18.95, plus 17 cents for each mile driven. If Tiffany only has $50 to spend on the car rental, what is the maximum number of miles she can drive?
Answer: 182 miles.
Step-by-step explanation:
0.17x + 18.95 ≥ 50
- 18.95 -18.95
0.17x = 31.05
x= 182
Complete the square to make a perfect square trinomial. Write the result as a binomial square. q2−23q
Answer:
[tex]\left(q-\dfrac{23}{2}\right)^2[/tex]
Step-by-step explanation:
Given the expression: [tex]q^2-23q[/tex]
To complete the square, we follow these steps:
Step 1: Identify the coefficient of q
Coefficient of q=-23
Step 2: Divide the coefficient of q by 2
[tex]=-\dfrac{23}{2}[/tex]
Step 3: Square your result from step 2 and add it to the equation
This gives us: [tex]q^2-23q+\left(-\dfrac{23}{2}\right)^2[/tex]
We have now completed the square.
Step 4: Write the result as a binomial square.
To write it as a binomial square, pick the variable and add the term in the bracket.
Therefore:
[tex]q^2-23q+\left(-\dfrac{23}{2}\right)^2=\left(q-\dfrac{23}{2}\right)^2[/tex]
The perfect square form of the given expression will be [tex](q-\dfrac{23}{2})^2[/tex].
The given expression is [tex]q^2-23q[/tex].
It is required to write the given expression as a perfect square polynomial or trinomial.
We will use the identity [tex](a+b)^2=a^2+2ab+b^2[/tex].
So, the first term from the given expression will be [tex]a=q[/tex].
To find the second term b, divide the 2nd term of the given expression by 2,
[tex]b=\dfrac{-23}{2}[/tex]
So, the given expression can be written in the perfect square form as,
[tex]a^2+2ab+b^2=q^2-23q+(\dfrac{-23}{2})^2\\=(q-\dfrac{23}{2})(q-\dfrac{23}{2})\\=(q-\dfrac{23}{2})^2[/tex]
Therefore, the perfect square form of the given expression will be [tex](q-\dfrac{23}{2})^2[/tex].
For more details, refer to the link:
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Which is the graph of y = ⌊x⌋ – 2? On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 5, negative 5) to (negative 4, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 4) to (5, 4). On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 5, negative 5) to (negative 4, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 4) to (5, 4). On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 3, negative 5) to (negative 2, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 2) to (5, 2). On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 4, negative 5) to (negative 3, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 3) to (5, 3).
Answer:
On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 3, negative 5) to (negative 2, negative 5). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, 2) to (5, 2).
Step-by-step explanation:
The floor function graphs as horizontal segments 1 unit long, each 1 unit up from the segment to its left. It will have a closed circle at the left end of the segment, and an open circle at the right end.
Since 2 is subtracted from the floor of the x-value, the closed circle at the left end of the segment will have coordinates (x, x-2). The only offered choice meeting that condition is the 3rd choice listed here.
Answer:
c on edge
Step-by-step explanation:
I js did it tbh
Which are perfect cubes? Check all that apply. 64 x16 8x3 27x4 81x6 125x9
Answer:
A,C,F
Step-by-step explanation: I took the test :)
The expression 64 is perfect cube of 3.
The expression [tex]8x^{3][/tex] is the perfect cube of [tex](2x)^{3}[/tex].
The expression [tex]12x^{9}[/tex] is perfect square of [tex](5x^{3})^{3}[/tex]
We have to determine, which to the following is perfect cube.
According to the question,
A perfect cube is an integer that is equal to some other integer raised to the third power.
To obtain the perfect cubes of the expression, it can be determined in following steps.
The given expression is 64.
To convert it into perfect square written in small factor parts.
Therefore, 64 written as,
[tex]= 64\\\\= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\\\= (2)^{3} \times (2)^{3}\\\\= (2\times 2)^{3}\\\\=( 4)^{3}[/tex]
The expression 64 is perfect cube of 3.
The given expression is 16x.
To convert it into perfect square written in small factor parts.
Then,
16x can be written as,
[tex]= 16x \\\\= 2\times 2\times 2\times 2\times x\\\\= 2x.(2)^{3}\\[/tex]
The expression 16x is not perfect cube.
The given expression is [tex]8x^{3][/tex].
To convert it into perfect square written in small factor parts.
Then,
[tex]8x^{3}[/tex] can be written as,
[tex]= 8x^{3}\\\\= 2 \times 2 \times 2 \times x^{3}\\\\= (2)^3 \times {x^{3}}\\\\= (2x)^{3}[/tex]
The expression [tex]8x^{3][/tex] is the perfect cube of [tex](2x)^{3}[/tex].
The given expression is [tex]27x^{4}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]27x^{4}[/tex] can be written as,
[tex]= 27x^{4}\\\\= 3 \times3 \times3 \times x^{4}\\\\= (3)^{3} \times x \times x^{3}\\\\= x \times (3x)^3[/tex]
The expression [tex]27x^{4}[/tex] is not a perfect cube.
The given expression is [tex]81x^{6}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]81x^6[/tex] can be written as,
[tex]= 81x^{6}\\\\= 3 \times3 \times3 \times3 \times x^{6}\\\\= 3.(3)^{3} \times x^{3} \times x^{3}\\\\= 3 \times ( 3x^{2}) ^{3}[/tex]
The expression [tex]81x^{6}[/tex] is not a perfect cube.
The given expression is [tex]81x^{6}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]125x^{9}[/tex] can be written as,
[tex]=125x^{9}\\\\= 5 \times 5 \times 5 \times x^{3} \times x^{3} \times x^{3}\\\\= (5x^{3})^{3}[/tex]
The expression [tex]12x^{9}[/tex] is perfect square of [tex](5x^{3})^{3}[/tex]
To know more about perfect square click the link given below.
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A particle moves on a straight line and has acceleration a(t)=24t+2. Its position at time t=0 is s(0)=3 and its velocity at time t=0 is v(0)=13. What is its position at time t=5?
Answer:
It's position at time t = 5 is 593.
Step-by-step explanation:
The velocity v(t) is the integral of the acceleration a(t)
The position s(t) is the integral of the velocity v(t)
We have that:
The acceleration is:
[tex]a(t) = 24t + 2[/tex]
Velocity:
[tex]v(t) = \int {a(t)} \, dt = \int {24t + 2} \, dt = 12t^{2} + 2t + K[/tex]
K is the initial velocity, that is v(0). Since V(0) = 13, K = 13
Then
[tex]v(t) = 12t^{2} + 2t + 13[/tex]
Position:
[tex]s(t) = \int {s(t)} \, dt = \int {12t^{2} + 2t + 13} \, dt = 4t^{3} + t^{2} + 13t + K[/tex]
Since s(0) = 3
[tex]s(t) = 4t^{3} + t^{2} + 13t + 3[/tex]
What is its position at time t=5?
This is s(5).
[tex]s(t) = 4t^{3} + t^{2} + 13t + 3[/tex]
[tex]s(5) = 4*5^{3} + 5^{2} + 13*5 + 3[/tex]
[tex]s(5) = 593[/tex]
It's position at time t = 5 is 593.
What is the measure of angle 1 in the diagram below?*
D
18°
A
B
120°
E
Answer:
123
Step-by-step explanation:
A farmer plants corn in of his field. He plants white corn in of the corn
section of his field. This situation is shown in the model. What fraction of the
whole field is planted with white corn?
Answer:
3/20
Question:
A farmer plants corn in 1/4 of his field. He plants white corn in 3/5 of the corn
section of his field. This situation is shown in the model. What fraction of the whole field is planted with white corn
Step-by-step explanation:
Portion of the field planted with corn = 1/4
Total corn planted = 1/4 of field
Portion of the corn section planted with white corn = 3/5
Total white corn planted = 3/5 of corn section
We need to find the portion of the total field planted with white corn
The fraction of the whole field planted with white corn would be the product of the fraction of Total corn planted and fraction of Total white corn planted
= 1/4 × 3/5
= 3/20
The fraction of the whole field planted with white corn = 3/20
simplify the following algebraic expression. 3/4(1/2x-12)+4/5
Answer:
Step-by-step explanation:
(3/8)x - 9 + 4/5
40(3/8x - 9 + 4/5)
15x - 360 + 32
15x - 328
Answer:
3/8 x - 7 1/5
Step-by-step explanation:
3/4 (1/2 x - 12) + 4/5
3/8 x - 8 + 4/5
15/40 x - 8 x 32/40
15/40 x - 7 8/40
15/40 x - 7 1/5
3/8 x - 7 1/5
is it possible for a triangle to have the side lengths of 3, 8, and 13
Answer:
No
Step-by-step explanation:
The longest side of a triangle must be less than the sum of the shorter two sides.
3 + 8 = 11. 13 is not less than 11. So it is not possible for a triangle to have these sides.
I need this quick because I am on Khan 2(3-8y)= ? Plz help
-her daughter
Answer:
6-16y
Step-by-step explanation:
Distribute, 2 x 3 and 2 x 8
6-16y
what is the probability of choosing an even number from the set of numbers 1,2,3,4,5,6,7,8,9,10
Answer:
the probability of getting an even numbers out of this set is 1/2
Step-by-step explanation:
The set of numbers are: 10
1,2,3,4,5,6,7,8,9,10
Even Numbers: 5
2,4,6,8,10
Probability = [tex]\frac{NumberOfFavourableOutcomes}{TotalNumberOfOutcomes}[/tex]
P = [tex]\frac{Even Numbers}{Total Numbers}[/tex]
P = [tex]\frac{5}{10}[/tex]
P = [tex]\frac{1}{2}[/tex]
So, the probability of getting an even numbers out of this set is 1/2
Answer:
The probability of this set of numbers is 1/2.
Step-by-step explanation:
Probability is the odds of an event happening. It is expressed by writing it as a fraction, decimal, or a percent.
The formula for probability is the number of favorable outcomes divided by the total number of outcomes. In this case, we have odd and even numbers. The even numbers in this set are 2, 4, 6, 8, and 10.
These are the favorable outcomes.
Since there are 5 even numbers, there are 5 favorable outcomes.
There are total of 10 outcomes. Therefore P(Even number)= 5/10.
Don't forget to always simplify. You can divide the numerator and denominator by 5. 5 divided 5 is 1 and 10 divided by 5 is 2.
Therefore, the probability of choosing an even number from this set of numbers is 1/2.
I hope this helps, and I hope you enjoy the rest of your day!
Which is the area of a square with one side that measures 1 foot?
A) 1 square inch
B) 100 square inches
C) 144 square inches
D) none of the above
what is the answer to he equation to of x+3 x 4x-7
Answer:
4x^2 +5x -21
Step-by-step explanation:
(x+3) * (4x-7)
FOIL
first : x*4x = 4x^2
outer: -7x
inner: 3*4x =12x
last: -7*3 = -21
Add them together : 4x^2 -7x+12x -21
Combine like terms : 4x^2 +5x -21
What is 10 times larger than the 7 in this number 16372
Answer:
700
Step-by-step explanation:
I am slightly confused by your wording, but Im assuming you mean the expanded form.
In the base ten system, the second to last digit is the tens place. Therefore, the 7 represents 7*10 = 70
10 times larger than 70 is 700
The outside temperature at 6:00 was 75º F. The temperature dropped 0.8ºF for the next 4 hours.What was the outside temperature after 4 hours?
Answer:
71.8° F
Step-by-step explanation:
Given 75° and 4 times 0.8° drop = 3.2°, so the temperature is 75° - 3.2°
= 71.8° F