The change in the amount of water in the pool is the difference between the amount of water that enters and leaves the pool
Change in volume of water in the pool after 112 minutes is [tex]\underline{-117\frac{1}{3}}[/tex] gallons
Reason:
The given parameters are;
The volume volume of entering the pool = 10 3/4 gallons per minute
The volume of water leaving the pool = 12 1/3 gallons per minute
Required:
The change in the amount of water in the pool after 112 minute
Solution:
The volume of water, V₁, that enters the pool in 112 minute is given as follows;
V₁ = 10 3/4 × 112 = 1,204The volume of water, that enters the pool, V₁ = 1,204 gallons
The volume of water, V₂, that leaves the pool in 112 minute is given as follows;
V₂ = 12 1/3 × 112 = 1,381[tex].\overline 3[/tex]The volume of water, that that leaves the pool, V₂ = 1,381[tex].\overline 3[/tex] gallons
The change in the amount of water in the pool after 112 minutes, ΔV, is given as follows;
ΔV = V₁ - V₂
ΔV = 1,204 - 1,381[tex].\overline 3[/tex] = -177[tex].\overline 3[/tex] = -(117 1/3)Change in volume of water in the pool after 112 minutes, ΔV = [tex]\underline{-117\frac{1}{3}}[/tex] gallons
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what type of mathematical law is this (6+4)+100=6+(4+100)
Answer:
Associative Property of Addition
Step-by-step explanation:
According to the Associative Property of Addition: when three real numbers are added, it makes no difference which two are added first.
a + (b + c) = (a + b) + c
Therefore, in the given equality statement: (6 + 4) + 100 = 6 + (4 + 100), the sum of the numbers on either side of the equation will have the same results.
(6 + 4) + 100 = 6 + (4 + 100)
(10) + 100 = 6 + (104)
110 = 110
Please mark my answers as the Brainliest, if you find this explanation helpful :)
Please help me with the explanation! I need to remember how to do this
Answer:
like what do you want to remember.
1. Find three consecutive interferes whose sum is -30. (Answer choices) A.)-8, -10, -12 B). -11, -12, -13 C.) 11, -10, -9 D.) -8, -9, -10
Find three consecutive even internet’s whose sum is 120
A.) 38, 39, 40
B.) 39, 40, 41
C.) 36, 38, 40
D.) 38, 40 , 42
HELP ASAP
Answer:
] The three consecutive even numbers are 38, 40 and 42. The smallest of the three is clearly 38. Step-by-step explanation:Even numbers are of the form [math]2k[/math], [math] k \in \mathbb{Z}[/math]. Three consecutive even numbers are of the form [math]2k[/math], [math]2(k+1)[/math], [math]2(k+2)[/math]. We have that their sum is 120 therefore [math]\\2k + 2(k+1) + 2(k+2) = 120 \Leftrightarrow k+(k+1)+(k+2) = 60 \Leftrightarrow 3(k+1) = 60 \\ \Leftrightarrow k+1=20 \Leftrightarrow \boxed{k=19}.[/math
What is the solution to 8x minus 3(2x minus 4) = 3(x minus 6)
Answer:
x = 30.
Step-by-step explanation:
8x - 3(2x - 4) = 3(x - 6)
8x - 3*2x + - 3*-4 = 3*x + 3 * -6
8x - 6x + 12 = 3x - 18
2x + 12 = 3x - 18
2x - 3x + 12 = 3x - 3x - 18
-x + 12 = -18
-x + 12 - 12 = -18 - 12
-x = -33
-x/-1 = -30/-1
x = 30.
Answer:
[tex]x=30[/tex]
Step-by-step explanation:
[tex]8x-3\left(2x-4\right)=3\left(x-6\right)[/tex]
First, we will expand [tex]-3\left(2x-4\right)[/tex] by applying the distributive property:
[tex]-3\times \:2x-\left(-3\right)\times \:4[/tex]
** [tex]-\left(-a\right)=a[/tex]
[tex]-6x+12[/tex]
[tex]8x-6x+12=3\left(x-6\right)[/tex]
Expand, [tex]3\left(x-6\right):[/tex]
[tex]3x-3\times \:6[/tex]
[tex]3x-18[/tex]
[tex]2x+12=3x-18[/tex]
Subtract 12 from both sides:
[tex]2x+12-12=3x-18-12[/tex]
[tex]2x=3x-30[/tex]
Subtract 3x from both sides:
[tex]2x-3x=3x-30-3x[/tex]
[tex]-x=-30[/tex]
Divide both sides by -1:
[tex]\frac{-x}{-1}=\frac{-30}{-1}[/tex]
[tex]x=30[/tex]
________________________
4. Each morning you do a combination of aerobics, which burns about 12 calories per
minute, and stretching, which burns about 4 calories per minute. Your goal is to burn
416 calories during a 60-minute workout. How long should you spend on each type of
exercise to burn the 416 calories?
22 minutes is spent doing aerobics and 38 minutes doing stretching
Let x represent the amount of time spent doing aerobics, Let y represent the amount of time spent doing stretching.
Since the goal is to do a 60-minute workout, hence:
x + y = 60 (1)
Also, 416 calories needs to be burnt hence:
12x + 4y = 416 (2)
We need to solve equation 1 and 2 simultaneously; multiply equation 1 by 4 and subtract the result from equation 2, hence:
8x = 176
x = 22 minutes
Put x = 22 in (1)
22 + y = 60
y = 38 minutes
Therefore 22 minutes is spent doing aerobics and 38 minutes doing stretching.
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help me please
in a sale, the normal price of a hat is reduced by 15%
The sale price of the hat is 20.40 euros.
Work out the normal price of the hat.
Answer:
The correct answer is 24
Step-by-step explanation:
To solve this math problem, you will need to divide 20.40 with 1 (1 is 100% as a decimal) and 0.15 (0.15 is 15% as a decimal).
--
[tex]20.40[/tex] ÷ [tex](1-0.15)[/tex]
--
First, subtract 1 and 0.15
[tex]1-0.15=0.85[/tex]
Next, divide 20.40 and 0.85
[tex]20.40[/tex] ÷ [tex]0.85 = 24[/tex]
--
Therefore, the final product of this math problem is 24
A convenience store has two separate locations where customers can be checked out as they leave. These locations each have two cash registers and two employees who check out customers. Let X be the number of cash registers being used at a particular time for location 1 and Y the number being used at the same time for location 2. The joint probability function is given by y x 012 0 0.12 0.04 0.04 1 0.08 0.19 0.05 2 0.06 0.12 0.30 (a) Give the marginal density of both X and Y as well as the probability distribution of X given Y
Hardest questions please help
Please
Answer:
17. landmark
18. BANALITIES
Step-by-step explanation:
The price of a dress was reduced from $40 to $30. By what percentage was the price of the dress reduced?
Answer:
The price of the dress was reduced by 25%
Step-by-step explanation:
Answer:
The price for the dress was reduced by 25%.
Step-by-step explanation:
25% of 40 is 10.
40 - 10 = 30, explaining the dress' price reduction from 40 to 30.
Hope this helps!
prove that 5^(2n - 1) is divisible by 8
Answer:
Step-by-step explanation:
Prove that 52n − 1 is divisible by 8 for all n ∈ N.
Solution
To prove by induction, we must
1. Show it is true for n = 1
2. Assume true for n and prove it is true for n + 1.
Let P(n) be the statement 52n − 1 is divisible by 8.
When n = 1, 52 − 1 = 24, which is divisible by 8.
This proves P(1).
Suppose that P(n) is true, i.e., 52n − 1 is divisible by 8.
Then 52(n+1) − 1 = 52
· 5
2n − 1 = 52
(52n − 1) + (52 − 1).
Note that 52n −1 is divisible by 8 using P(n) and also 52 −1 = 24 is divisible
by 8. Thus we have proved that P(n + 1) is true.
We conclude that P(n) is true for all n ∈ N.
find the measure of the angle indicated
Answer: 35
Triangle sum theory tells us the internal angles of any triangle add up to 180. This means we can take each given angle from 180 to find the remaining angle.
In Livingston, the library is 9 miles south of the courthouse and 2 miles west of the community swimming pool. If a bird flew directly from the courthouse to the library, then from the library to the swimming pool, and then from the swimming pool back to the courthouse, what would be the total distance flown? If necessary, round to the nearest tenth.
Answer:
i think it's 18 but im not sure
Step-by-step explanation:
and y represents the number of tiles), which figure number has 40 tiles in it?
For a tile pattern with the rule y = 6x+4 (where x represents the figure number
How do you know?
Donna bought 5 bags of dog treats for $10.90. What is the cost per bag of dog treats? A. $0.46 B. $2.73 C. $15.90 D. $2.18
Answer: $2.18
Step-by-step explanation:
You are trying to solve for the cost of one bag or unit cost. Take
the amount of money spent and divide it by the number of bags
purchased.
10.90 ÷ 5 = 2.18
Please explain why if you no the answer
Answer:
No, she isn't
Step-by-step explanation:
(-2)² is basically -2 x -2, which we know is 4.
-2² is slightly different. In this case, you don't consider it as the square of -2, but you do the square ignoring the negative sign, and then add it at the end.
So think about it like this,
We do 2² first, and then add the minus, so it becomes -4 instead of positive 4. Does that make sense?
Answer: Incorrect
Step-by-step explanation:
Rule :
[tex](-10)^2=| -10|^2 =100 \\\\ -10^2=-(10)^2=-|10|^2=100[/tex]
Then :
[tex]\rm -2^2=-|2|^2=-4 \\\\ (-2)^2= |-2|^2=4 \\\\ Then : \\\\ -2^2 =(-2)^2 \\\\ -4 \neq 4[/tex]
If EF=2x−12, FG=3x−15, and EG=23, find the value of FG
Answer:
FG= 15
Step-by-step explanation:
2x-12+3x-15=23
5x-27=23
-27+27 23+27
5x=50
5x/5=50/5
x=10
FG= 3x-15
3(10)-15
30-15
FG=15
What type of dilation is formed when the scale factor K is greater than one
Answer:
Enlargement
Step-by-step explanation:
When k > 1, the dilation is an enlargement. When k > 0 and k < 1, the dilation is a reduction. In a dilation, the original figure and its image are similar. The ratio of the side lengths of the image to the corresponding side lengths of the original figure is the scale factor of the dilation.
Which set of ratios is equivalent to 4:4
A. 8 to 10, 10/15 B, 8 to 10, 16/20
C. 15/20, 20:25 D. 40/50, 24;36
Answer:
B
Step-by-step explanation:
both simplify into 4:5
Fill in the missing statements and reasons in this proof. Number your reasons 1 through 5 as they would be shown in the chart below.
Given: m∠LOM = m∠JKI;
m∠MON = m∠IKH
Prove: m∠LON = m∠HKJ
The missing statements and their reason are shown below.
What is angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
1. m∠LOM = m∠JKI and m∠MON = m∠IKH
Reason : Given
2. m∠LOM + m∠MON = m∠JKI +m∠MON
Reason :equals are added to another remains equal.
3. m∠LOM + m∠MON = m∠JKI +m∠JKH
Reason :m∠MON = m∠IKH.
4. m∠LOM + m∠MON = m∠LON
m∠JKI +m∠JKH = m∠HKJ
Reason: parts are equal to whole.
5. m∠LON = m∠HKJ
Reason: from point 3 and 4
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In the following diagram lines m are n parallel the measures of AEB, BAE and CED are shown what is the measure of EBF
Answer:
∠ EBF = 98°
Step-by-step explanation:
(3x - 15) and (2x + 10) are vertically opposite angles and are congruent, then
3x - 15 = 2x + 10 ( subtract 2x from both sides )
x - 15 = 10 ( add 15 to both sides )
x = 25
3x - 15 = 3(25) - 15 = 75 - 15 = 60°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ EBF is an exterior angle of the triangle , then
∠ EBF = 60° + 38° = 98°
What would be the range of possible whole number values (x) for a 3rd side of the triangle with two sides of 5 in. and 8 in.?
& Name one possible value for a third side?
Correct Answer Only
Answer:
Range of the third side of a triangle
Step-by-step explanation:
Any one side of a triangle must be shorter than the sum of the other two sides. Therefore, the third side length x must be between 5 and 35, not including those endpoints: 5 < x < 35. All whole numbers satisfying this range would form a triangle.
20 is a possible value for a third side
Ksjdjfnfkdkdklddkdkfjfnfnfnnffk
Answer: X = 20
Step-by-step explanation:
Answer: X = 20
Step-by-step explanation:
To get this
3 * 20 + 12 = 20
3*20=60
60+12=72
72
If one of the 9 players
on a team catches a
ball, what is the
probability that it was
one of the 4 infielders
who caught it?
19/24 nearest hundred
Answer:
0.79
Step-by-step explanation:
Answer:
if speaking in decimal terms, your answer would be 0.79/ 0.7916/ 0.79167
Step-by-step explanation:
What is m∠JNM? Line J L and line M K slightly inclined with horizontal intersects at N. The upward and downward angles of the intersecting lines are obtuse. The left and right angles of the intersecting lines are acute. The measure of angle J N M is labeled as left parenthesis 4 x plus 6 right parenthesis degrees. The measure of angle L N K is labeled as left parenthesis 7 x minus 21 right parenthesis degrees.
Answer:
JNM=42
Step-by-step explanation:
JNM is equal to LNK so you can set the equations equal to each other.
7x-21=4x+6, subtract 4x from both sides
3x-21=6, add 21 to both sides
3x=27, divide by 3
x=9, then you plug it into an equation
4 times 9 + 6
36+6
42
<JNM = [tex]42[/tex] degrees.
What is horizontal angle?The angle made by two ground lines is measured horizontally , and is called a horizontal angle.
According to the question
Line J L and line M K slightly inclined with horizontal intersects at N.
<JNM = <LNK
[tex]4x + 6 = 7x - 21[/tex]
Subtract 4x from both sides
[tex]6 = 3x -21[/tex]
[tex]3x=27[/tex]
Divide by 3
[tex]x=\frac{27}{3}[/tex]
[tex]x =9[/tex]
<JNM = [tex]4x+6[/tex]
<JNM = [tex]4(9)+6[/tex]
<JNM = [tex]42[/tex] degrees
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What is an equation of the line with slope 3 that goes through point ( -1/2 , 5/2)
Oy = 4x + 3
Oy=-3x + 4
Oy=4x - 3
Oy = 3x + 4
Pls no links helppppp
Step-by-step explanation:
The only equation that has 3 as the coefficient of x (a slope of 3) is ...
... d.) y = 3x+4
Happily, it also goes through the given point.
... 5/2 = 3(-1/2) +4
... 5/2 = -3/2 + 8/2 i hope this works
Selena has been hired as a sales associate at Better Rooms furniture store. She has two salary options. She can choose to receive either a fixed salary of $850 per week or a salary of $400 per week plus a 6% commission of her weekly sales. Which solution set below represents the dollar amount of sales that she must generate each week in order for the option with commission to be the better choice? Let s represent the sales for the week
Answer:
Sales have to be more than $7,500.
Step-by-step explanation:
850 > 400 + 0.06s
850 - 400 < 0.06s
450/0.06 < s
7500 < s
A basketball player spent 6 hr
watching game films, practic-
ing free throws, and lifting
weights. He spent twice as
much time lifting weights as
practicing free throws and
2 hr longer watching game
films than practicing free
throws. How many hours did
he spend on each task?
Answer:
watching game= 3 hours
practicing free throw= 2 hours
lifting weight=1 hour
A company rents out 19 food booths and 20 game booths at the county fair. The fee for a food booth is $200 plus $7 per day. The fee for a game booth is $65 plus $5 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
Answer:
$2715
Step-by-step explanation:
Given that 15 food booths were rented out for ‘d’ days at $100 plus $5 per day. On the food booths only, the company will earn 15($100+$5d) = $1500 + $75d Given that 20 game booths were rented out for ‘d’ days at $50 plus $7 per day. On the game booths only, the company will earn 20($50 + $7d) = $1000 + $140d
The total amount that the company is paid is therefore, $1500 + $75d + $1000 + $140d = $2500 + $215d
x to the second power plus 24 to the second power equals 30 to the second power .
Answer:
x = 18 or -18
Step-by-step explanation:
x^2 + 24^2 = 30^2
simplify
x^2 + 576 = 900
subtract 576 from both sides
x^2 = 324
Take square root of 324
+/- √324
x = 18 x = -18
18 or -18 is the answer
