Scientists are drilling a hole in the ocean floor to learn more about the Earth's history. Currently, the hole is in the shape of a cylinder whose volume is approximately 3500 cubic feet and whose height is 2.9 miles. Find the radius of the hole to the nearest hundredth of a foot. (Hint: Make sure the same units of measurement are used.)
The radius of the hole is 0.07 feet.
What is the radius?A cylinder is a three-dimensional object that is made up of a prism and a circular base.
Volume of a cylinder = πr²h
Radius = √volume / (π x h)
Where:
π = pi = 22/7r = radiush = heightThe volume of the hole and the height of the hole are in different dimensions. Thus, the height of the hole has to be converted to feet.
1 mile = 5280 feet
5280 x 2.9 = 15,312 feet
3500 / (22/7 x 15,312) = 0.07 feet
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Question 1: Factor −6x^2 + 18x.
Question 2: Rewrite 6x + 36 using a common factor.
[tex] \phi = - 6x {}^{2} + 18x \\ \phi = - 6x(x - 3)[/tex]
Question 2:[tex] \psi = 6x + 36 \\ \psi = 6(x + 6)[/tex]
Answer:
Step-by-step explanation:
Answer:
Question 1 = -6x(x-3)
Question 2 = 6(x+6)
Step-by-step explanation:
Hope this helps
what is the distance between the points (5, 14) and (18, 3)?
Answer:
14.87
Step-by-step explanation:
a - 15 = 22
———
83 = y - 17
could someone please give me the step-by-step answer for these?
I’m really confused
Answer:
a = 37 y = 100
Step-by-step explanation:
Think of the inverse operation of addition which is subtraction. Then you can guess and check and see what fits where. The letters are just placeholders so I took the given number and added it to the answer to get the answers for the blanks.
Cheers!
Two splice plates are cut from a piece of sheet steel that has an overall length of 19 3/8 in. The plates are 9 1/4 in. and 6 15/16 in. long. How much material remains from the original piece if each saw cut removes 1/16 in.?
The material that remains from the original price is 3 1/16 inches.
How much material remains?A fraction is a non-integer that consists of a numerator and a denominator. A mixed fraction is made up of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is less than the denominator.
Material left = initial length - length of the first plate - length of the second plate - (2 x 1/16)
[tex]19\frac{3}{8} - 9\frac{1}{4} - 6\frac{15}{16} - \frac{2}{16}[/tex]
[tex]4\frac{6 - 4 - 15 - 2}{16}[/tex]
4[tex]\frac{-15}{16}[/tex]= 3 1/16 inches
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WILL GIVE BRAINLIST
Write an equation for the line, in point-slope form, that passes through the following points. (2,-1) (5,-7)
Answer: y + 1 = -6(x-2)
Step-by-step explanation:
First find the slop with m = y2 - y1 / x2 - x1
-7 - (-1)/ 5 - 2 = -6
-7 + 1 / 5 -2 = -6
m = -6
Then use the point slope form y - y1 = m(x - x1) with coordinates (2, -1)
y - (-1) = -6(x - 2)
y + 1 = -6(x-2)
Joey walked 10 laps around the school's track. He walked a total distance of 6.74 miles. Monica walked 30 laps around the same track. What is the total distance Monica walked?
Answer:
20.22 miles
Step-by-step explanation:
If 10 laps is 6.74 then 30 laps is 3*6.74 which is 20.22
Describe the similarities and differences between finding the slope of a linear equation from a graph that has x and y scales that are 1:1, and from a graph that has x and y scales that are not 1:1 (say your x and y scales are 2, 4, 6).
Using linear function concepts, we have that:
For a graph in a 1:1 scale, we can look at two consecutive values, y when x = a and y* when x = a + 1, and subtract y* by y. For a graph in another scale, we also do the same thing, but since the scale is not 1:1, we have to divide the subtraction of y* by y by the scale.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Given two points in a graph, the slope is given by change in y divided by change in x, hence:
For a graph in a 1:1 scale, we can look at two consecutive values, y when x = a and y* when x = a + 1, and subtract y* by y. For a graph in another scale, we also do the same thing, but since the scale is not 1:1, we have to divide the subtraction of y* by y by the scale.More can be learned about linear function concepts at https://brainly.com/question/24808124
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Question
Ray invested $1700 in an account with continuously compounded interest at a rate of 2.8%. After 3 years, how much
money did he have in the account? Round your answer to the nearest dollar.
The amount of money in Ray account after investing for three years was $1846.84
What is an equation?An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.
Let y represent the total money after x years, hence:
y = 1700(1.028)ˣ
After 3 years:
y = 1700(1.028)³ = $1846.84
The amount of money in Ray account after investing for three years was $1846.84
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Answer:
$1849
Step-by-step explanation:
Use the formula for calculating compound interest A=P0ert where r=0.028, P0=1700, and t=3. Substitute the values into the formula and simplify.
A=1700e0.028⋅3
A=1700e0.084
A=1700(1.087...)
A=1848.97
To the nearest dollar, the amount in the account after three years is A≈1849.
A cone-shaped pile of sawdust has a base diameter of 40feet, and is 17feet tall. Find the volume of the pile.
Answer:
7120.94 cubic feet
Step-by-step explanation:
volume of a cone =
pi times radius squared times (height ÷ 3)
pi times 20 squared times (17 ÷ 3)
HELP ASAPPP PLEASE!!!!
Answer:
4, -8
Step-by-step explanation:
A={x|x is an even number more than 0 but less than 5}
Answer:
A = {2, 4}
Step-by-step explanation:
This can be written as
A = {2, 4}
Rewrite 42= 6x7 using commutative law of multiplication
we get 6 = 6 , in 42= 6x7 using commutative law of multiplication.
What do associative law and commutative law mean?
The order of some mathematical operations is addressed by the commutative property. We can write the binary operation as a + b = b + a. The associative attribute, on the other hand, deals with the grouping of numbers in an operation. For instance, we could write it as (a + b) + (a + b + c).This law states that no matter how the numbers are arranged, the outcome of multiplying two integers remains the same. So A.B = B.A. Examples include: 1 + 2 + 1 + 2 + 4 + 5 + 4 + 20.using the Commutative Law of Multiplication.
42 = 6 x 7
42 / 7 = 6
6 = 6
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how do you find the nth term of 70, 110, 150, ….
Answer: an=40(n-1)+70
Step-by-step explanation:
70, 110, 150, ….
Notice the terms get bigger by 40 as the sequence progresses. Hence, we can model this sequence with a linear equation. y=40(x-1)+70 where y=term value, x=term number and 70 is the first term.
y=40(x-1)+70
an=40(n-1)+70 ==> an=term value/nth term. n=term number
Determine which answer in the solution set will make the equation true.
4p + 5 = 6p − 15
S: {−10, 0, 10, 20}
A: 0
B: −10
C: 20
D: 10
Answer:
d) 10
Step-by-step explanation:
Let's solve the problem,
→ 4p + 5 = 6p - 15
→ 6p - 4p = 5 + 15
→ 2p = 20
→ p = 20/2
→ [ p = 10 ]
Hence, option (d) is correct.
In which situation would the result be 0?
Answer:
C, adding -1 1/5 to the coordinate of point J
Step-by-step explanation:
J= 1 1/5
1 1/5+(-1 1/5)
- use the distributive property
- positive x negative # = negative #
1 1/5 - 1 1/5
= 0
Which shows the equation below written in the form ax² + bx + c = 0?
x+ 9 = 2(x-1)²
Answer:
[tex]2x^2 -5x - 7 =0[/tex]
Step-by-step explanation:
We have the equation
[tex]x + 9 = 2(x-1)^2[/tex]
[tex](x-1)^2 = x^2-2x+1[/tex] using the formula [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]
[tex]x + 9 = 2(x^2-2x\cdot \:1+1^2)[/tex] = [tex]2x^2-4x+2[/tex]
Switch sides
[tex]2x^2-4x+2=x+9[/tex]
Subtract 9 from both sides
[tex]2x^2-4x+2 - 9=x+9-9[/tex]
[tex]2x^2 -4x -7 = x[/tex]
Subtract x on both sides
[tex]2x^2 - 4x -7 -x = 0[/tex]
[tex]2x^2 - 4x - x -7 = 0[/tex]
[tex]2x^2 -5x - 7 =0[/tex]
where
[tex]a = 2, b = -5, c = -7[/tex]
Answer: I hope this helps.
Step-by-step explanation:
A sample of n = 5 scores has a mean of M= 10. One new score is added to the sample, and the new mean is calculated to be M = 9. What is the value of the new score?
A) X=5 B X=55 C) X=4.5 D X=4 E)
The value of the new score in discuss according to the task content is; Choice D; X= 4.
What is the value of the new score?According to the task content, it follows that the mean of the initial 5 scores was; M = 10.
Hence, the sum of all 5 scores is; 5 × 10 = 50.
Hence, upon addition of the sixth score, x the new mean is; M = 9.
Hence, the value of the new score can be determined as follows;
(50+x)/6 = 9
50 + x = 54
x = 54-50
x = 4.
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Find the value of m: −3(m − 4) = −6
m = −6
m = −2
m = 2
m = 6
Answer:
m=6
Step-by-step explanation:
-3m+12=-6
3m=12+6
3m=18
m=6
m = 6.
Step-by-step explanation:
[tex]{ \green{ \tt{ - 3}}}({ \green{ \tt{m - 4}}}) = { \green{ \tt{ - 6}}}[/tex]
[tex]{ \green{ \tt{ - 3m + 12}}} = { \green{ \tt{ - 6}}}[/tex]
[tex]{ \green{ \tt{3m}}} = { \green{ \tt{12}}} \: + \: { \green{ \tt{6}}}[/tex]
[tex]{ \green{ \tt{3m}}} = { \green{ \tt{18}}}[/tex]
[tex]{ \green{ \tt{m}}} = \frac{ \green{ \tt{18}}}{ \green{ \tt{3}}} [/tex]
[tex]{ \green{ \tt{m}}} = { \red{ \mathfrak{6}}}[/tex]
2. There are 30 students in Mrs. Woodward’s class and 1/5 of the class has their own cell phone. Of this group of students, 1/2 of them are allowed to use social media. How many of the students have a cell phone and can use social media?
Answer:
Step-by-step explanation:
Im guessing but i did 5*___= 30 which is 6 so 6 of his student have their own cell phone, and then the half is 3
For a sporting event 6,000 tickets were sold, and the proceeds were $78,000. Tickets for children 16 and younger, were $8, adults were $16, and seniors 60 and older were $12. There were 2 times more adults than children at the sporting event.
What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the sporting event?
Responses
c+a+s=6,000
8c+12a+16s=78,000
2a=c
c+a+s=6,000
8c+16a+12s=78,000
a=2c
c+a+s=6,000
8c+12a+16s=78,000
a=2c
c+a+s=6,000
8c+16a+12s=78,000
2a=c
Option 2 is the answer.
No. on tickets sold = 6000
Proceedings of the tickets sold = $78,000
Cost of tickets for children = $8
Cost of tickets for adults = $16
Cost of tickets for seniors = $12
2 times more adults were present than the children.
Let the number of children be 'c.'
Let the number of adults be 'a.'
Let the number of seniors be 's.'
Since 2 times more adults were present than the children, we get the equation,
a = 2c
No. of tickets sold will be equal to the total no, of people.
∴ c + a + s = 6000
The proceedings will be equal to the sum of the amounts and number of people who bought tickets with that amount,
∴ 8c + 16a + 12s = $78,000
Thus, we have the three equations,
c + a + s = 6000
8c + 16a + 12s = $78,000
a = 2c
This series of equations are given in option 2 Thus, option 2 is the answer.
Answer) Option 2.
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Select all of the following tables which represent y as a function of x
.
The ordered pairs that represents a function y in terms of x are {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}
Linear functionsA set of ordered equation represents a linear function if the domain of the coordinates are not repeated.
For instance, the ordered pairs that is a function are the coordinates that do not have any repeated y-coordinates.
From the given linear functions, the ordered pairs that represents a function y in terms of x are {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}
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11.4.3 Quiz: Computing Slope
Question 2 of 10
Rise is the change between the y-coordinates of any two points along a line in
the xy-plane.
A. True
B. False
Answer:
It is very very rue
. Verify the concepts you havelearned about the Law of Acceleration in doing some problem – solving exercises.1.The rising concern among athletic trainers regarding concussions among football playershas prompted numerous studies of the effectiveness of protective head gears.
1.One study suggests that concussions may result from impacts rated at 740 m/s2. If a player’s head mass (with helmet) is 6 kg and considered to be a free body, then what net force would be required to produce an acceleration of 740 m/s2?2.Captain John Stapp of the U.S. Air Force tested the human limits of acceleration by riding on a rocket sled of his own design.
2.His rocket sled, known as the Gee Whiz, had a mass of about 82 kg. What net force would be required to accelerate Gee Whiz and 82 kg Stapp at 450 m/s2 (the highest acceleration tested by Stapp)?3.Space Shuttle Max is one of the extreme rides in Enchanted Kingdom.
3.The first of its kindin the country, the roller coaster ride inverts its riders six times. If during one of its operations, a 53 kg boy experiences a net force of 1800 N at the bottom of its roller coaster loop, how fast would he be accelerating at this location
Answer: 1. f = 444N
2. f = 36900N
3. a=34 m/s2
Step-by-step explanation:
f=net force. a=acceleration. m=mass.
f = m*a
1. f = m*a
f = 6 * 740
f = 444N
2. f = 82 * 450
f = 36900N
3. f = m*a
1800=53*a
a=1800/53
a=34 m/s2
Answer:
1) 4440 N
2) 36900 N
3) 34.0 m/s² (nearest tenth)
Step-by-step explanation:
Newton's Second Law of Motion
The overall resultant force acting on a body is equal to the mass of the body multiplied by the body's acceleration.
[tex]\large\boxed{F_{net}=ma}[/tex]
F = force measured in N (Newtons).m = mass measured in kg (kilograms).a = acceleration measured in m/s² (meters per second squared).Question 1Given:
m = 6 kga = 740 m/s²Substitute the given values into the formula:
[tex]\begin{aligned}F_{net} & =ma\\\implies F_{net} & =6 \cdot 740\\& =4440\:\sf N\end{aligned}[/tex]
Question 2Given:
m = 82 kga = 450 m/s²Substitute the given values into the formula:
[tex]\begin{aligned}F_{net} & =ma\\\implies F_{net} & =82 \cdot 450\\& =36900\:\sf N\end{aligned}[/tex]
Question 3Given:
m = 53 kgF = 1800 NSubstitute the given values into the formula:
[tex]\begin{aligned}F_{net} & =ma\\\implies 1800& =53a\\a & = \dfrac{1800}{53}\\ a& =33.96226415...\\ & = 34.0\:\sf m/s^2 \:\:(nearest\:tenth)\end{aligned}[/tex]
help fast please math!!!!!!!!
Answer:
I am thinking 180
Step-by-step explanation:
The reason why I say this is because 180 over 12 equals to 15
. Communicate and Justify Rafael's
mom buys 6 packages of water balloons
for a party Each package has 24 water
balloons Rafael says that there are 204
water balloons in all. Do you agree with
Rafael? Why or why not?PLEASE HELP:(
I disagree with Rafael's as 204 is incorrect, the correct number of balloons is 144 balloons
How to calculate the number of balloons ?Water ballon is a type of ballon that is filled up with water. It is used by children during different outdoor and relaxation activities.
Rafael's mum buys 6 packages of water balloons for a party
Each package has 24 water balloons
Therefore the total number of balloons can be calculated by multiplying the number of packages which is 6 by the number of balloons which is 24
= 24 × 6
= 144
Hence the are 144 water balloons
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A rotation is turning a point in a ____________ motion around a _____________ point.
a A clockwise B. fixed
b A. counterclockwise B. reflected
c A. circular B. fixed
d A. rectangular B. reflected
Find domain of the following functions
The domain of the function g (x) = (x² - 2 x - 15) / (x² + x - 6) is R - {-3, 2}.
We are given a function:
g (x) = (x² - 2 x - 15) / (x² + x - 6)
We need to find the domain of the function.
We know that a function becomes not defined when the denominator becomes 0.
Put x² + x - 6 = 0
x² + 3 x - 2 x - 6 = 0
x (x + 3) - 2( x + 3) = 0
( x + 3 ) ( x - 2 ) = 0
We get x = - 3 and x = 2.
So, these cannot be the values of x
So, the domain is
Domain = R - {-3, 2}
Therefore, the domain of the function g (x) = (x² - 2 x - 15) / (x² + x - 6) is R - {-3, 2}.
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how many fix points are there for the function f (x) =x^3
The fix points of the function f (x) = x³ are,
⇒ x = 0, x = 1 and x = -1
What is fixed point of a function?
The fixed point of a function is determine by solving the function
f (x) = x.
The function is given as;
⇒ f (x) = x³
Since, The fix point of a function is determine by solving the function
f (x) = x
Hence, we can solve as;
f (x) = x
x³ = x
x³ - x = 0
x ( x² - 1 ) = 0
x ( x² - 1² ) = 0
x ( x - 1 ) ( x + 1 ) = 0
Equate each term to zero,
x = 0
x - 1 = 0 ⇒ x = 1
x + 1 = 0 ⇒ x = -1
Therefore, The fix points of the function f (x) = x³ are,
⇒ x = 0, x = 1 and x = -1
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Write the equation of the line that is parallel to the given line and passes through the given point
The slope of parallel lines is the same, which is y = 5x - 12.
Parallel lines have the same slope in two dimensions. If we are aware of a point on the line and the equation of the supplied line, we can construct the equation of a line that is parallel to the given line.
Given: a line or point with a slope of m (x - x1), where m is the slope, and (x1,y1) is a point on the line, we obtain
y - (-1) = m (x - 2), and now the line is parallel to the one that was supplied. The slope is the SAME for parallel lines.
y + 2 = 5 (x - 2)
A line with a slope of y + 2 = 5x - 10 points...
Y = 5x – 12 – 2 – Subtract 2 from both sides.
Hence, the equation of the line that is perpendicular to the provided line and passes through has the form y = 5x – 12.
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