Final answer:
To determine the radius and height of the cylindrical tank with a given volume of 15.71 cubic meters, where height is 4 meters greater than the radius, we use the volume formula for a cylinder, resulting in a cubic equation that must be solved.
Explanation:
The question asks for the radius of the top and the height of a cylindrical tank with a volume of 15.71 cubic meters, where the height is 4 meters greater than the radius. The formula for the volume of a cylinder is V = πr²h, where V is volume, r is radius, and h is height. Since h = r + 4, we can write the equation in terms of r as V = πr²(r + 4).
To find the radius, we substitute the given volume, 15.71 m³, into the equation:
15.71 = πr²(r + 4)
This results in a cubic equation which we need to solve to find the value of r. After solving (which may require numerical methods or approximations due to the complexity of cubic equations), we find the value of the radius and can then determine the height by adding 4 meters to the radius.
Philip has 2,000 and spends $23.75 on supplies.he divides the remaining amount equally among his 8 employees how much does each employee receive?
for every five baseball cards that Mickey has Mike has 3 baseball cards if Mike has 72 baseball cards how many cards does Mickey have?
Mickey has 3 cards.
Explanation:To determine how many cards Mickey has, we can set up a proportion using the information given. We know that for every five cards Mickey has, Mike has 3 cards. So the proportion would be: (Mickey's cards) / 5 = 3 / (Mike's cards).
Given that Mike has 72 cards, we can plug that into the proportion: (Mickey's cards) / 5 = 3 / 72.
To solve for Mickey's cards, we can cross multiply: (Mickey's cards) = (3 / 72) * 5.
After simplifying, we find that Mickey has 3.125 cards. However, since we can't have a fraction of a card, we know that Mickey has 3 cards.
Ana is driving from her home in Miami to her grandmothers house in New York. On the first day she will travel 240 miles to Orlando Florida to pick up her cousin. Then they will travel 350 miles each day write an equation for the total number of miles m that Ana has traveled after d days
The equation for the total number of miles m that Ana has traveled after d days is m = 240 + 350d.
What is an equation?
An equation is an equality relationship between two expressions written on both sides of the equal to sign.
Ana travels 240 miles on the first day.
Her cousin and she travel 350 miles everyday.
If d is the number of days, then to find the equation for the total number of miles covered m,
m = 240 + 350d miles in d days.
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The spelling contest awards four prizes Tim,Sam,Jen, and Kate all made it to the final round. In how many ways can first, second, third, and fourth place be assigned
In 24 ways the first, second, third, and fourth place be assigned
What is Permutation?A permutation is an arrangement of objects in a definite order. .
Given that, for a spelling contest awards four prizes Tim, Sam, Jen, and Kate all made it to the final round.
We need to find in how many ways can first, second, third, and fourth place be assigned.
This can be arranged in 4! ways.
4!=4×3×2×1
4!=24
Hence in 24 ways the first, second, third, and fourth place be assigned.
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A board is 4.6 feet long. How many meters long is the board?
How do I find the value of the variable?
the three inside angels need to equal 180, so first find the missing inside angle:
86.5 + 41.4 = 127.9
180-127.9 = 52.1
now that angle and y need to equal 180 degrees
so 180 - 52.1 = 127.9
y = 127.9 degrees
Find JL if JK = 17 - x, KL = 2x - 7, and K is the midpoint of JL
Final answer:
By setting up an equation where JK equals KL since K is the midpoint, solving for x, and substituting back to find the length of JL, we find that JL is 18 units long.
Explanation:
To find the length of JL when given that JK = 17 - x and KL = 2x - 7, and knowing that K is the midpoint of JL, we can form an equation recognizing that JL is the sum of JK and KL. Because K is the midpoint, we know that JK and KL are actually equal in length, so we can set them equal to each other and solve for x:
17 - x = 2x - 7
Combining like terms by adding x to both sides and adding 7 to both sides gives us:
24 = 3x
Dividing both sides by 3:
x = 8
Since JK and KL are equal and K is the midpoint, JL will be twice the length of either segment. Substituting x into either expression, JK or KL:
JL = 2 * JK = 2 * (17 - x) = 2 * (17 - 8) = 2 * 9 = 18
or
JL = 2 * KL = 2 * (2x - 7) = 2 * (2*8 - 7) = 2 * (16 - 7) = 2 * 9 = 18
Therefore, JL = 18.
Write the point-slope form of the equation of the line that passes through the origin and has a slope of 2. include your work in your final answer. type your answer in the box provided or use the upload option to submit your solution.
What is the simplified form of each expression? (1 point)
1.) -(10)^-1
-1/10
-1/1^10
1/10
10
2.) 1/c^-5 (1 point)
c^5
5c
-c^5
-5/c
3.) What is the value of y^-5/x^-3 for x = 2 and y = -4? (1 point)
10/3
128
-1/128
-128
4.) Is the number written in scientific notation if not, explain. 5.1 x 10^8 (1 point)
Yes; the number is written in scientific notation.
No; the first factor is not a number between 1 and 10.
No; it is not written as a number times a power of 10.
5.) What is the number written in a standard notation? (1 point)
5.71 x 10^-3
-171.3
0.0571
0.000571
0.00571
6.) Suppose that the diameters of different types of hairs are 1.7 x 10^-4 cm, 1.4 x 10^-3 cm, 1.2 x 10^-5 cm, and 1.9 x 10^-4 cm? what is the order of the hairs from least to greatest diameter? (1 point)
Who ever is good at math please ''Try'' to help me out here?! :D And Thank you so much if ya do! :P
Answer:
a
b
a
d
a
a
Step-by-step explanation:
Please help me with these questions thank you.
Answer:
CPCTC; JP≅MI; SAS
Step-by-step explanation:
For the first question, we use the congruence statement. When we are using the congruence statement to match corresponding pieces, the justification is that Congruent Parts of Congruent Triangles are Congruent, or CPCTC.
For the second question, we again use CPCTC and the congruence statement. P matches T and B matches I, so PB = TI and B = I. J matches M also, so BJP = IMT. However, P does not match I, so JP does not equal MI.
For the third question, we have two sides (AM matching ZD and BD matching itself) and an included angle (AMD and ZDM). This is Side-Angle-Side, or SAS.
What is
Write
52 over 6
as a mixed number.
Give your answer in its simplest form.
What is the best first step in solving the equation 3 + = 5? Subtract 3 from both sides. Find the cube of . Cube both sides of the equation. Subtract 5 from both sides.
If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
The area of the front cover of the square notebook is A = 400 cm²
What is the area of a square?A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the area of the square be represented as A
Now , the side length of the notebook a = 20 cm
And , the area of the front cover of the notebook = area of square
On simplifying , we get
The area of front cover A = a²
The area of the front cover of the notebook A = 20 x 20
The area of the front cover of the notebook A = 400 cm²
Hence , the area of the square notebook is 400 cm²
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The length of each edge of a cube is 22 inches. The area of each face of the cube is square inches. The surface area of the cube is square inches.
Answer: Each face would have an area of 22 * 22 = 484 square inches.
Since a cube has 6 faces, then the total area = 6 * 484 = 2,904 square inches.
Step-by-step explanation:
If the typical balance on Lucy's credit card is $750 and the interest rate (APR) on her credit card is 16%, how much in interest would you expect Lucy to be charged in a typical month?
Marcello is constructing the perpendicular bisector of AB¯¯¯¯¯. He has already constructed arcs as shown.
What should Marcello do for his next step?
a) Place the point of the compass on point X and draw an arc, using AY as the width for the opening of the compass.
b) Use the straightedge to draw a line through points X and Y.
c) Use the straightedge to draw AX←→ and AY←→.
d) Place the point of the compass on point X and draw an arc, using AX as the width for the opening of the compass.
Answer: "Use the straightedge to draw a line through points X and Y." is the right answer.
Step-by-step explanation:
To perpendicular bisector of line segment AB. There are following steps:
1) Draw arcs from points A and B on the both sides of AB.
2) Name the intersection points as X and Y.
3) Use the straightedge to draw a line through points X and Y.
4) Name the point as O
hence we have construct perpendicular bisector XY of AB which bisects at O.
Use the distributive property of multiplication to find the missing number.use the distributive property of multiplication to find the missing number.
The distributive property of multiplication involves multiplying a number with each term inside a bracket, then adding or subtracting the results. To find a missing number, set up an equation based on the distributed multiplication and solve for the unknown.
Explanation:The distributive property of multiplication can be simply defined as a(b + c) = ab + ac. In this equation, 'a' is distributed over 'b' and 'c', which means we multiply 'a' individually with 'b' and 'c', and then add the results.
Let's consider an example: 2(3 + 4) = ? Here, applying the distributive property, we multiply 2 with 3 and 2 with 4 separately. Hence, 2*3 + 2*4 = 6 + 8 = 14. So, the result is 14.
To solve distribution problems with a missing number, you would set up the equation and solve for the unknown. For example, if we have 3(x+5) = 21, we can first distribute the 3 to get 3x + 15 = 21. Then, you'd subtract 15 from both sides to isolate the 'x'. So, 3x = 21 - 15, which simplifies to 3x = 6. Finally, dividing both sides by 3 gives x = 2. So, the missing number is 2.
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Complete the point-slope equation of the line through (1,3) and (5,1)
The point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1), where the slope m= -0.5 was calculated using the formula m = (y2 - y1) / (x2 - x1).
Explanation:To complete the point-slope equation of the line through points (1,3) and (5,1), we first need to find the slope of the line, which can be calculated using the formula: m = (y2 - y1) / (x2 - x1), here (x1,y1) and (x2,y2) are the coordinates of two points on the line.
Substituting in the given coordinate values gives us m = (1 - 3) / (5 - 1), which simplifies to m = -0.5, indicating a downward slope.
The point-slope form of the equation of a line is y - y1 = m(x - x1). So, substituting one of the given points (1, 3) and the calculated slope into the point-slope form gives us y - 3 = -0.5(x - 1).
Therefore, the point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1).
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Find the slope write into slope intercept form (19,-16),(-7,-15)
Answer: [tex]m= -\frac{1}{26}[/tex]
(19,-16) = (x1,y1)
(-7-15) = (x2,y2)
Slope= [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{-15-(-16)}{-7-19}[/tex]
= [tex]\frac{-15+16}{-7-19}[/tex]
= [tex]\frac{-15+16}{-26}[/tex]
= [tex]-\frac{1}{26}[/tex]
I need to skip count by ten from 350 to 240
Skip counting by ten from 350 to 240 involves starting at 350 and counting backwards by subtracting ten each time until you reach 240. The sequence would look as follows: 350, 340, 330, 320, 310, 300, 290, 280, 270, 260, 250, 240.
Explanation:In Mathematics, when asked to 'skip count' it means that you are counting up or down by a specified number, in this case, by ten. However, the student's question asks to skip count by ten from 350 to 240, which would require counting backwards or decreasing the count by ten each time.
To skip count by ten from 350 to 240, you would start at 350 and then subtract 10 each time, like this: 350, 340, 330, 320, 310, 300, 290, 280, 270, 260, 250, 240. Note: 240 is included in the sequence as it is the final number we're skip counting down to.
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A birthday cake was cut into equal pieces, and five pieces were eaten. The fraction 2/7 shows how many pieces are left. According to the fraction, how many pieces were not eaten
A.2
B.7
C.12
D.5
What is (0.3 x 2.8)2
Suppose a random sample of 36 is selected from a population with a standard deviation of 12. if the sample mean is 98, the 95% confidence interval for the population mean is ______________.
Answer:
36%
Step-by-step explanation:
Kelly reads x hours a week. tim reads two times more than kelly and jim reads five hours more than tim. which expression represents the amount of time jim reads?
Answer:
2x+ 5 expression represents the amount of time jim reads
Step-by-step explanation:
As per the statement:
Kelly reads x hours a week.
⇒Kelly read in a week = x hours
Also, tim reads two times more than kelly
⇒tim read in a week= 2x
It is also given that:
jim reads five hours more than tim.
⇒Jim = tim read + 5
⇒Jim read in a week = 2x +5
Therefore, expression represents the amount of time jim reads is, 2x+ 5
Hey I need geometry help asap (please Help) and you get some points
the answer is A x=15 and y =12
A 2005 study by the fisheries research services in aberdeen, scotland, suggests that the average length of the species clupea harengus (atlantic herring) as a function of age t (in years) can be modeled by l(t) = 32(1 − e−0.37t) cm for 0 ≤ t ≤ 13. how fast is the length changing at age t = 7 years?
The rate of change of length of the Clupea harengus (Atlantic herring) at t = 7 years is approximately 2.8 cm per year.
Explanation:To determine how fast the length of Clupea harengus (Atlantic herring) is changing at age t = 7 years, you need to calculate the derivative of the given function, l(t) = 32(1 − e−0.37t), with respect to time. The derivative measures the rate of change of a function, which in this case corresponds to the speed of growth of the herring.
The derivative of l(t) with respect to t is given by: l'(t) = 32 * 0.37e^(-0.37t).
Substitute t = 7 into this derivative function to get: l'(7) = 32 * 0.37e^(-0.37*7) ≈ 2.8 cm/year.
So, the length of the Atlantic herring is increasing at approximately 2.8 cm per year when the herring is 7 years old.
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To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to take the derivative of the length function and evaluate it at t = 7.
Explanation:To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to find the derivative of the length function with respect to time. The function l(t) = 32(1 − e−0.37t) represents the average length of the herring at age t. Taking the derivative of this function gives us:
l'(t) = 32 * (-0.37) * e−0.37t
Now, we can substitute t = 7 into the derivative to find the rate of change at that age:
l'(7) = 32 * (-0.37) * e−0.37(7)
This expression can be simplified further to find the exact value of the rate of change.
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A rectangular prism is 3 feet long, 8 feet wide, and has a height of 6 feet. what is its volume?
What is the midpoint of the line segment whose endpoints are (-8, 12) and (-13, -2)?
(-10.5, 5)
(-10.5, 7)
(-2.5, 7)
The midpoint of the line segment is [tex](\frac{-21}{2} ,5)[/tex].
What is midpoint of a line segment?
Midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Formula for finding the midpoints of a line segment[tex](x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2} )[/tex]
Where,
[tex](x, y)[/tex] is the midpoint of the line segment.
[tex](x_{1},y_{1}) and (x_{2} ,y_{2} )[/tex] are the endpoints of the line segment.
Let (x, y) be the midpoint of the line segment.
According to the given question
We have
(-8, 12) and (-13, -2) are the endpoints of the line segment.
Therefore, the midpoint of the line segment is given by
[tex](x,y)=(\frac{-8-13}{2} ,\frac{12-2}{2} )[/tex]
⇒[tex](x, y) = (\frac{-21}{2} ,\frac{10}{2})[/tex]
⇒[tex](x,y)=(\frac{-21}{2} ,5)[/tex]
Hence, the midpoint of the line segment is [tex](\frac{-21}{2} ,5)[/tex].
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Find the area under the standard normal distribution curve for each.
a. between z 0 and z 1.95
b. between z 0 and z 0.37
c. between z 1.32 and z 1.82
d. between z 1.05 and z 2.05
e. between z 0.03 and z 0.53 2. find
To find the area under the normal distribution curve for a range of z-values, you refer to a z-table and possibly subtract two areas to find the area between two z-values. The areas above were calculated as examples.
Explanation:The subject in question involves finding the area under the standard normal distribution curve for various z-values. This is a concept in statistics that evaluates the probability which a particular range of values under the normal distribution curve might occur.
For z between 0 and 1.95, we refer to the z-table and find the area under the curve as 0.975.For z between 0 and 0.37, using the z-table, the area under the curve is 0.644.For z between 1.32 and 1.82, we find the areas corresponding to each value on the z-table and subtract them. This is 0.9664 - 0.9066 = 0.0598.For z between 1.05 and 2.05, again we find the areas corresponding to each value and subtract them, which gives us 0.975 - 0.8543 = 0.1207.For z between 0.03 and 0.53, we find the corresponding areas and subtract, resulting in 0.7054 - 0.5120 = 0.1934.Learn more about standard normal distribution here:https://brainly.com/question/29509087
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Is the sum of two angles sometimes , always , or never an obtuse angle ?