Our water faucet leaked 3 2/6 liters of water every 3/5 of a hour.
We are to find the rate in liter per hour at which the water faucet leaked.
First, use the number of liters the water faucet leaked in 3/5 of a hour.
This is 3 2/6 = 20/6
Therefore, the number of liters of water faucet leaked in 1 hour is
(20/6) / (3/5)
Before we solve this, we should simplify,
20/6 can be simplified to 10/3
3/5 cannot be simplified
Then, we should modify our problem to use reciprocation instead of a complex fraction,
(10 • 5) / (3 • 3)
This equals 50/9
Now, solve 50/9 for 5.555555555556
This rounds to 5.6
Thus, the required rate at which the water faucet leaked is 5.6 liters per hour.
PLEASE HELP MEEE.....
im not sure sry man....... delete this answer bc im not sure how to
The formula V=1/3 pi r to the second power h is the formula for the volume of a cylinder. To the nearest tenth, what is the height of a cylinder with volume 100 cm to the third power and radius 2 cm?
8 cm is the height of the cylinder.
What is a cylinder?Traditionally, a cylinder was a three-dimensional solid, one of the most fundamental curvilinear geometric shapes. It has been described geometrically as a prism with a circle as its base.This traditional viewpoint is still used in elementary geometry treatments, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface, which is now how a cylinder is defined in various modern branches of geometry and topology.The formula of Height for cylinder: h = V/πr²
Put the values in the formulas as:
h = V/πr²h = 100/π2²h = 7.95775Rounding off to the nearest tenth it's 8 cm.
Therefore, the height of the cylinder is 8 cm.
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(0,0) and (-10, 6), then the midpoint is located at
Answer:
(-5,3)
Step-by-step explanation:
x: (-10-0)/2=-5
y: (6-0)/2=3
The best-selling fruits at Joy's Fruit Shack are
peaches and bananas. During one month Joy
sold 398 peaches and 410 bananas.
$0.20
0.25
The total cost for both the fruits is $182.1
The shopkeeper is selling the peaches and bananas.
the cost for both is as follows:
For peaches it is $0.20
and, for bananas it is $0.25
Peaches = 398×0.20$
= $79.6
Bananas = 410×$0.25
= $102.5
The total cost is
= $79.6 + $102.5
= $ 182.1
The variable and fixed expenses of delivering commodities are combined to get a total using the total cost formula. Total cost is calculated as follows: (Average Fixed Cost x Average Variable Cost) x Units Produced.
Your cost function may like this, for example, if your variable costs for labor are fixed regardless of quantity but your variable costs for supplies vary based on the amount of each item: Total costs are calculated as fixed costs plus labor costs plus (unit count * material variable costs).
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Suppose each side of
the inequality a − b < 0 is multiplied by c.
a. If c < 0 and c(a − b) > 0, write an inequality to
represent the relationship between a and b.
b. If c < 0, is c(a − b) always greater than 0?
Explain your reasoning.
The required solution is ca is less than cb.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
Suppose each side of the inequality a − b < 0 is multiplied by c.
According to given question we have
a. If c < 0
Each side of the inequality a − b < 0 is multiplied by c.
=c(a-b)<0
=ca-cb<0
=ca<cb
It should be clear that number that ca is less than cb.
Therefore, the required solution is ca is less than cb.
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m to the second power equals 14
Answer:
bro whut are u doing here? -.-
What are the correct answers? 3 are correct
Adam and Kevin are roommates. Adam can clean their apartment in 45 minutes. Kevin can clean it in 60 minutes. Rounded to the nearest minute, how much time will it take if they work together?
Which equations are in standard form? Check all that apply y = 2x + 5 2x + 3y = –6 –4x + 3y = 12 y = x – 9 x + 3 = 6 x – y = 5 5x + 3y =
The equations which are in standard form include the following:
2x + 3y = -6.5x + 3y = 1/2.What is a linear equation?A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
This ultimately implies that, the variables in all linear equations share a direct relationship and as such they are directly proportional to one another.
In Mathematics, the standard form of a linear equation is given by the following:
Ax + By = C.
In this context, we can reasonably infer and logically deduce that the equations which are in standard form include the following:
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How many solutions does this equation have? 3x + 1 = 3( x - 1) + 4
Answer:
infinite number
Step-by-step explanation:
3x + 1 = 3(x - 1) + 4
3x + 1 = 3x - 3 + 4
3x + 1 = 3x + 1
3x = 3x
x = x
x = x is true for every value of x, so the equation has an infinite number of solutions.
Can someone help with this question?✨
The measure of the angle is 11. 5°
What are trigonometric identities?
Trigonometric Identities are defined as the identifiers involving trigonometry functions and holding true for all the values of variables given in the equation.
The types of trigonometric identities include;
SineCosineTangentCosecantSecantFrom the diagram shown, we can see that;
The opposite side of the angle is 2
The hypotenuse side of the angle is 10
The trigonometric identity in this case is sine
sin θ = opposite/ hypotenuse
Substitute the values
sin θ = 2/ 10
sin θ = 0. 2
Take the sine inverse of the value
θ = [tex]sin^-^1(0. 2)[/tex]
θ = 11. 5°
Thus, the measure of the angle is 11. 5°
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Evaluate the expression when a = 2 and x = - 6
6a -x
Answer:
18
Step-by-step explanation:
6(2) - (-6)
12 +6
18
The ratio of soccer balls to basketball is 12 to 15 If there are 48 soccer balls how many basketball are there
Answer:
60Step-by-step explanation:
The ratio of soccer balls to basketball is 12 to 15 If there are 48 soccer balls how many basketball are there
we can solve with a proportion
12 : 15 = 48 : x
x = 15 * 48 : 12
x = 60
Can someone help me it geometry
How is this not right???????
Absolute Max and min
Answer:
I honestly have no clue why you hot that wrong that is correct
Answer:
[tex]\textsf{(a)} \quad \textsf{Interval}=[-10,0].\\\textsf{1.} \quad \textsf{Absolute maximum}=\boxed{497}\\\textsf{2.} \quad \textsf{Absolute maximum}=\boxed{11}[/tex]
[tex]\textsf{(b)} \quad \textsf{Interval}= [-7, 2].\\\textsf{1.} \quad \textsf{Absolute maximum}=\boxed{445}\\\textsf{2.} \quad \textsf{Absolute maximum}=\boxed{-3}[/tex]
[tex]\textsf{(c)} \quad \textsf{Interval}=[-10, 2].\\\textsf{1.} \quad \textsf{Absolute maximum}=\boxed{497}\\\textsf{2.} \quad \textsf{Absolute maximum}=\boxed{-3}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^3+12x^2-27x+11[/tex]
Differentiate the function:
[tex]\implies f'(x)=3 \cdot x^{3-1}+2 \cdot 12x^{2-1}-27x^{1-1}+0[/tex]
[tex]\implies f'(x)=3x^2+24x-27[/tex]
Find the critical points of the function by setting the derivative to zero and solving for x:
[tex]\implies f'(x)=0[/tex]
[tex]\implies 3x^2+24x-27=0[/tex]
[tex]\implies 3(x^2+8x-9)=0[/tex]
[tex]\implies x^2+8x-9=0[/tex]
[tex]\implies x^2+9x-x-9=0[/tex]
[tex]\implies x(x+9)-1(x+9)=0[/tex]
[tex]\implies (x-1)(x+9)=0[/tex]
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies x+9=0 \implies x=-9[/tex]
Therefore, the critical points are x = 1 and x = -9.
Evaluate the function at the endpoints of each interval as well as the critical points if the critical points fall within the given interval. The largest and smallest values of the function are the absolute extrema.
Part (a)
Given interval = [-10, 0].
One of the critical points is included in the interval.
Evaluate the function at the endpoints and critical point:
[tex]f(-10)=(-10)^3+12(-10)^2-27(-10)+11=481[/tex]
[tex]f(0)=(0)^3+12(0)^2-27(0)+11=11[/tex]
[tex]f(-9)=(-9)^3+12(-9)^2-27(-9)+11=497[/tex]
Therefore:
The absolute maximum of f(x) is 497 which occurs at x = -9.The absolute minimum of f(x) is 11 which occurs at x = 0.Part (b)
Given interval = [-7, 2].
One of the critical points is included in the interval.
Evaluate the function at the endpoints and critical point:
[tex]f(-7)=(-7)^3+12(-7)^2-27(-7)+11=445[/tex]
[tex]f(2)=(2)^3+12(2)^2-27(2)+11=13[/tex]
[tex]f(1)=(1)^3+12(1)^2-27(1)+11=-3[/tex]
Therefore:
The absolute maximum of f(x) is 445 which occurs at x = -7.The absolute minimum of f(x) is -3 which occurs at x = 1.Part (c)
Given interval = [-10, 2].
Both of the critical points are included in the interval.
Evaluate the function at the endpoints and critical points:
[tex]f(-10)=(-10)^3+12(-10)^2-27(-10)+11=481[/tex]
[tex]f(2)=(2)^3+12(2)^2-27(2)+11=13[/tex]
[tex]f(-9)=(-9)^3+12(-9)^2-27(-9)+11=497[/tex]
[tex]f(1)=(1)^3+12(1)^2-27(1)+11=-3[/tex]
Therefore:
The absolute maximum of f(x) is 497 which occurs at x = -9.The absolute minimum of f(x) is -3 which occurs at x = 1.how do u solve -3|4x-9|=24
Answer:
No solution
Step-by-step explanation:
An absolute value expression being multiplied by a negative number will never have a positive y-value output like 24. You can see this when the equation is graphed.
2x - 3y less than or equal to 27?
Answer:less
Step-by-step explanation:
Answer:
Less Than
Step-by-step explanation:
Solve for yy. y=2x3y=2x3 Rewrite in slope-intercept form.y=23xy=23xUse the slope-intercept form to find the slope and y-intercept.Slope: 2323y-intercept: (0,0)(0,0)Any line can be graphed using two points. Select two xx values, and plug them into the equation to find the corresponding yyvalues.xy0032xy0032Graph the line using the slope and the y-intercept, or the points.
I NEED HELP ASAP!!!
See attached file.
20 Points!! First one gets brainlist!
Answer:
$75
Step-by-step explanation:
2x+2.49= 27.5+124.99
2x=159
x=75
The equation of line c is y=1/8x+10. Line d is perpendicular to line c and passes through (–1,1). What is the equation of line d?
The equation of line d is y = -8x + 9
What is an equation of a line?The general form of the equation of a line with a slope m and passing through the point (a, b) is given by:
y - b = m ( x - a )
We have,
Equation of line c:
y = (1/8)x + 10
Line d is perpendicular to line c.
Since line d and line c is perpendicular their slope is given by:
[tex]m_{1} m_{2} = -1[/tex]
Where [tex]m_{1}~and ~m_{2}[/tex] is the slope of line c and line d.
Now,
[tex]m_{1}[/tex] = 1/8
And,
[tex]m_{2}[/tex] = -1 / (1/8) = -8
The equation of line d passes through (-1, 1) so the equation of line d can be written as:
y - 1 = -8 ( x - 1 )
y - 1 = -8x + 8
y = -8x + 8 + 1
y = -8x + 9
Therefore the equation of line d is y = -8x + 9
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Use the linear regression feature on a graphing calculator to find an equation of the line of best fit for the data. Round each value in your equation to the nearest tenth.
The equation of line for the given data is y = 5x -1.
According to the given question.
We have a data of points for a equaton of line.
As we know that the standard equation of line is y = mx + b.
Where, m is the slope of line and b is the y intercept.
Since, the points which are given in the data must satisfy y = mx + b.
Therefore,
Lets take the points (1, 4) and (2, 9) and substitute it in y = mx + b to find the value of m and b.
At x = 1 and y = 4
4 = m + b ..(i)
And at x = 2 and y = 9
9 = 2m + b ..(ii)
From equation i and ii
m = 5
So, b = -5 + 4 = -1
Hence, the equation of line for the given data is y = 5x -1.
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What is standard deviation of 134.37
Answer:
If its 134, 37 its 48.5
Step-by-step explanation:
a grapefruit weight 3/4 of a kilogram. what is its weight in grams
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Explanation below. Enjoy!
- - - - - - - - - - - - - - - - - - - - - - - -
Personally, I think grapefruit is great. But that's unrelated. :)
You have to start with the values of kilograms and grams. So, here they are:
1 Kilogram = 1000 Grams
(For the record, the root kilo means 1000 in math.)
3/4 should be converted to decimals, so 0.75 is our number now.
0.75 kilograms = 750 grams
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Have a wonderful day/night!
(Please consider leaving a Brainly, it would help me greatly!)
~pinetreee
At the annual book fair, the students at water middle school found that they had $1,4888.80 in the cash register. Their teacher had given them a loan of 92.89 to buy supplies for the fair. What is the best estimate of the amount of money they had after they paid the money back to the teacher
Answer:
1395.91
Step-by-step explanation:
Subtract 1,488.80-92.89
If you want to round it up to a whole number then it would be 93.
If you want to round it up to the tenth then it would be 92.9.
Which ordered pair is a solution to the inequality 4x - 3y < 16?
The ordered pair (3, -1) that is a solution is the one which makes the inequality TRUE when the value of the ordered pairs are substitute into the inequality 4x - 3y < 16
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
WE have been given an inequality as 4x - 3y < 16.
Here, we need to get the ordered pair solution to the system of linear equations.
Then Substitute x = 3 and y = -1 into 4x - 3y < 16
4(3) - 3(-1) < 16
12 + 3 < 16
15 < 16
(TRUE)
Therefore, the ordered pair, (3, -1) is the solution because it is the only given ordered pair which makes the inequality true.
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Which pairs of events are independent?
(a) P(A) = 0.46, P(B) = 0.57, P(A∩B) = 0.25.
P(A) and P(B) are not independent events.
Event A is said to be independent of event B if the probability of occurrence of one of them is not affected by the occurrence of the other.
P(A∩B) = P(A)*P(B) for independent events, which is given 0.25 but P(A∩B) = P(A)*P(B) = 0.46*0.57 = 0.26, data does not match.
P(A) = 0.46 and P(B) = 0.57
For A and B to be independent
P (A and B) = 0.46*0.57 = 0.26 [ does not match with given data that is 0.25]
P (A, not B) =0.46*(1-0.57) = 0.19
P (B, not B) =0.57*(1-0.46) = 0.30
P (not A, not B) = (1-0.46) *(1-0.57) = 0.23
To check if they are independent, sum of all values should be equal to 1
0.57+0.19+0.30+0.23 = 0.98 which is not equal to one.
Therefore P(A) and P(B) are not independent events.
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You have a canteen that holds 32 fluid ounces and weighs 0.25 pounds when empty. Water weighs 0.065 pound per fluid ounce. You begin a hike with a full canteen of water. Write and simplify an expression for the weight of the canteen and water after you drink x fluid ounces.
The simplification of the expression for the weight of the canteen after drinking is 2.33 lbs
How to write the expressionThe total weight can be gotten as:
weight of empty canteen + ( 32 - x ) of the water x weight of water
This would be represented by
total weight = 0.25 + 0.065 * (32-x)
We have to open up the expression
weight = 0.25 + 2.08 - 0.065x
When the weight is 0 we would have
0.25 + 2.08 - 0.065x0
= 2.33 lbs
Hence the simplification of the expression for the weight of the canteen after drinking is 2.33 lbs
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Solve 2x-5=7
Please help
Free Cash Flow 100 Growth rate 2% Tax Rate 1% Cost of Capital 5% Debt-to-total value 50% Given the data in the above table, what is the terminal value of the business (using the growing perpetuity formula)? Review Later 3400 3000 3366 3600
The terminal value of the business, using the growing perpetuity formula is 3,400
What is terminal value of the company?
The terminal value of the company refers to the cash flows attributable to the company's long-term growth period whose growth rate is 2%, in an investment appraisal context, it is the value of all cash flows beyond the horizon considered in the analysis
terminal value=Free Cash Flow*(1+terminal growth rate)/(cost of capital-terminal growth rate)
Free cash flow=100
terminal growth rate=2%
cost of capital=5%
terminal value=100*(1+2%)/(5%-2%)
terminal value=100*1.02/0.03
terminal value=3,400
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1,058 written in expanded notation
Answer:
1,000+50+8
Step-by-step explanation:
Each place value is divided up into their separate values.
Find the formula for the nth term of the following sequence:
648, 108, 18, 3...
Include "n=" in your answer, and do not use any spaces.
The nth term of the sequence is Tn = 3888^n - 1
What is a geometric sequence?A geometric sequence can be defined as a sequence in which each term is determined by multiplying the preceding term in the sequence by the same value.
The formula for the nth term of a geometric sequence is expressed as;
Tn = ar^n - 1
Where;
Tn is the nth terma is the first termr is the common ratioFrom the given sequence, we have that;
a = 648
r = 6
Substitute into the formula
Tn = 648 × 6^n - 1
Tn = 3888^n - 1
Thus, the nth term of the sequence is Tn = 3888^n - 1
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