Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.

Answer:

40

Step-by-step explanation:

another answer to something elsse it might help Solve for x x-4=10. x − 4 = 10 x - 4 = 10. Add 4 4 to both sides of the equation. x = 10+ 4 x = 10 + 4. Add 10 10 and 4 4. x = 14 x = 14.

Answer:X=40

Step-by-step explanation:

Answer:13

Step-by-step explanation:(2)²+3(3)=4+9=13

Answer:

2a^n+ 3b

Differentiate w.r.t a

2na^n - 1

= 13

Given that the between 16 and 20 minutes driving times to the campus is uniformly distributed, the mean driving time is 18 minutes

The correct option is therefore;

The time it takes to drive from the apartment to the campus = Between 16 and 20 minutes

The mean of a continuous uniform distribution between two boundaries, a and b is given by the formula;

[tex] \mu = \frac{a+b}{2} [/tex]

The mean amount of time it takes to drive to campus is therefore;

[tex] \mu = \mathbf{\frac{16+20}{2}} = 18 [/tex]

The correct mean driving time is the option;

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Answer:

yes it is 604892÷4=151,223

Answer:

x-7

Step-by-step explanation:

Whatever her current age is, she was 7 years younger 7 years ago. Because her current age is undefined, it must remain an equation.

A coordinate system is geometry is a system that employs one or more integers, or coordinates, to define the position of points. The rules that maps the other vertices of the figure to their images is T<-2, -7> (x,y).

What are coordinates?

A coordinate system is geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Given that Sanjay determined that one vertex of a figure was mapped to its image by translating the point 2 units left and 7 units down.

In order to translate coordinates, 2 units left we need to subtract 2 units from the x-coordinate of the point, while to translate the point 7 units down we need to subtract 7 from the y-coordinate of the point.

Therefore, the rule that maps the other vertices of the figure to their images is, (x¹,y¹)=(x-2,y-7), or it can bse written as T<-2,-7> (x, y),

where x¹ and y¹ are the coordinates of the points after transliteration.

Hence, the rule that maps the other vertices of the figure to their images is T<-2,-7> (x, y,).

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∑ Hey, shadowwolf9764 ⊃

Answer:

1.52545155993

Round if needed: 1.53

Step-by-step explanation:

Given:

[tex]\frac{0.128\div 3.2+0.86}{\frac{5}{6}\cdot 1.2+0.8}+\frac{\left(1\:\frac{32}{63}-\frac{13}{21}\cdot 3.6\right)}{0.505\cdot \frac{2}{5}-0.002}[/tex]

Solution:

Convert Mixed Number to a improper fraction:

[tex]1\frac{32}{63}=\frac{95}{63}[/tex]

Now we have;

[tex]=\frac{\frac{0.128}{3.2+0.86}}{\frac{5}{6}\cdot \:1.2+0.8}+\frac{95}{63}[/tex]

Solving the first part:

[tex]\frac{\frac{0.128}{3.2+0.86}}{\frac{5}{6}\cdot \:1.2+0.8}=\frac{0.128}{7.308}[/tex]

Then we have;

[tex]=\frac{0.128}{7.308}+\frac{95}{63}[/tex]

Least common factor: 460.404

[tex]=\frac{8.064}{460.404}+\frac{694.26}{460.404}[/tex]

Now using this formula: [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]

[tex]=\frac{8.064+694.26}{460.404}[/tex]

Adding the numbers:

[tex]=\frac{702.324}{460.404}[/tex]

Next divide the numbers:

[tex]1.52545155993[/tex]

Hence, the answer is:

[tex]1.52545155993[/tex]

Round if needed:

[tex]1.53[/tex]

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The expression of [tex] \mathbf{sec( \theta)}[/tex] in terms of [tex]tan( \theta)[/tex] in Quadrant IV is presented as follows;

[tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]

The given trigonometric functions are;

[tex]sec( \theta)[/tex]

[tex]tan( \theta)[/tex]

[tex] {sec( \theta)}^{2} = {tan( \theta)}^{2} + 1[/tex]

In Quadrant IV, the tangent of an angle is -ve, while the secant is +ve

However, the square of -ve is positive;

Therefore;

[tex] \left({tan( \theta)}^{2} + 1 \right) \: is \: positive[/tex]

Which gives;

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(A) The expression to represent the elevation level of city D, in feet will be :  [tex]D = \frac{1}{4} * [C][/tex]    
(B) The elevation of city D will be -6 feet. The negative here shows that city D is below sea level.

In the question, it is given that city A is 96 feet below sea level, city C is 24 feet below sea level, and the elevation of city D is 1 over 4th of the elevation of C. Since, City A & C are both below sea level their elevation will be negative. So, by these we get elevations:

For City A,  A = -96

      City C,  C = -24

      City D,  [tex]D = \frac{1}{4} *[C][/tex]      ----> Equation (1)

By Equation (1) we get the representation of elevation for City D.

Now, Calculating the elevation of city D, we will put the value of city C in equation (1).

        =>   [tex]D = \frac{1}{4} *[-24][/tex]

        =>   [tex]D = -6\\[/tex]

The negative sign here shows that the elevation is below sea level for city D.

Hence, the expression representing the elevation of city D will be [tex]D = \frac{1}{4} * [C][/tex] and, the elevation of city D will be -6.

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The equation of a line is y = [tex]\frac{-x}{5}[/tex] ± √2.

Given Line : 5x - y = 1

slope of line = [tex]\frac{-5}{-1}[/tex] = 5

product of slopes of two perpendicular lines is - 1.

m₁ × 5 = -1

slope of required line m₁ = [tex]\frac{-1}{5}[/tex]

Let the equation of the required line be

y = mx + c where m is slope

y = [tex]\frac{-x}{5}[/tex] + c

Area of the triangle formed by a line with intercepts a,b = [tex]\frac{1}{2} ab[/tex]

Here, x-intercept = 5c

y-intercept = c

Area of triangle = [tex]\frac{1}{2} (5c)(c)[/tex]

                          =[tex]\frac{5c^{2} }{2}[/tex]

Given area = 5

⇒ [tex]\frac{5c^{2} }{2}[/tex] = 5

⇒ c² = 2

⇒ c = ±√2

Hence, The equation of a line is y = [tex]\frac{-x}{5}[/tex] ± √2.

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The length of the arc is calculated for the given semicircle as 15.7 units.

For, the given question.

The radius of the semicircle is 5 units.

The length of the arc of semicircle is equal to the perimeter of the semicircle.

The formula for perimeter;

P = πr

where, r is the radius and π = 3.14.

Put the values in the formula.

Perimeter = 3.14×5

Perimeter = 15.7 units.

Therefore, the length of the arc of the semicircle is 15.7 units.

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she could have scored the 10 points in 302400 ways.

The given parameters are

n= total points =10

r1 =one-point free throw = 1

r2 = two-point field goals = 2

r3 =  three-point field goals = 3

The number of ways (k) she could have scored the points is:

k=(n!)/(r1!×r2!×r3!)

The factorial function is a mathematical formula represented by an exclamation mark "!".

k= 10!/(1!×2!×3!)

k= 3628800/(1×2×6)

k= 302400

so.. she could have scored the 10 points in 302400 ways.

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The solution set of the given inequality i.e.{x ; 2<x≤7} is (2,7].

Given that a inequality y={x ; 2<x≤7} and asked to find the solution set for the given inequality and plot graph according to that

⇒ y={x ; 2<x≤7} i.e domain=(2,7].

⇒y=x ∀ x ∈ (2,7]

The solution of the given inequality is x ∈ (2,7].

Therefore,The solution set of the given inequality i.e.{x ; 2<x≤7} is (2,7].

Graph: image attached

y=x  ∀ x ∈ (2,7] is plotted {open at (2,0) and close at (7,0)}              

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The solution to the inequality is x ≥ 3

Given the inequality;

– 7x + 3 ≥ – 18

To determine the solution , we take the following steps;

collect like terms

-7x ≥ - 18 - 3

Find the difference

- 7x ≥ - 21

Make 'x' the subject of the formula by dividing both sides by its coefficient, - 7

We have;

-7x / -7 ≥ - 21/ -7

x ≥ 3

Thus, the solution to the inequality is x ≥ 3

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The solution to each division problem is;

1) 4

2) 2

3) 3

4) 3

5) 3

1) We are given the expression;

(5 * 3) * ___ = 60

To get the blank answer, we will divide both sides by (5 * 3) to get;

60/(5 * 3) = 4

2) We are given the expression;

4 *( ___ * 9) = 72

To get the blank answer, we will divide both sides by (4 * 9) to get;

72/(4 * 9) = 2

3) We are given the expression;

7 * (2 * ___) = 42

To get the blank answer, we will divide both sides by (7 * 2) to get;

42/(7 * 2) = 3

4) We are given the expression;

(___ * 5) * 5 = 75

To get the blank answer, we will divide both sides by (5 * 5) to get;

75/(5 * 5) = 3

5) We are given the expression;

(3 * 3) * ___ = 27

To get the blank answer, we will divide both sides by (3 * 3) to get;

27/(3 * 3) = 3

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Answer:

Step-by-step explanation:

400,000

The rate of discharge is 1,54,550 cubic meter/sec.

This is the problem related to conversion of units. We need to convert cubic feet into cubic meter here.

Also we know that 1 foot = 0.305 meter.

The rate of discharge of water is given as 5,500,000 cubic feet per second.

So, now to convert to cubic meter we need to divide the given rate by cube of 0.305.

Now discharge in cubic meter per second = [tex]5,500,000*(0.305)^{3}[/tex]

                                                                  = [tex]5,500,000*0.028[/tex]

                                                                  = 1,54,550 cubic meter/sec

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The area of the figure is 22.785 square yards

The figure is a triangle, and it has the following properties

Base = 9.3 yards

Height = 4.9 yards

The area of the figure is calculated as

Area  = 0.5 * Base * Height

So, we have

Area = 0.5 * 9.3 * 4.9

Evaluate

Area = 22.785

Hence, the area of the figure is 22.785 square yards

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Answer: 24/25

The answer to the question is 0.96, 0.96 in simplest form is 24/25

Answer:

k = -0.1

Step-by-step explanation:

An ordered pair is in the form (x,y)  We can use the x and y from the point (-30,3) to find k

y = kx  We will replace x with -30 and y with 3

3 = (-30)k  divide both sides by -30

-0.1 = k  or [tex]\frac{-1}{10}[/tex] in the fraction form

Answer:

Step-by-step explanation:

100 more than 365 is equal to 65more then

we can solve with an equation

100 + 365 = 65 + x

100 + 365 - 65 = x

465 - 65 = x

400 = x

------------

check

100 + 365 = 65 + 400

465 = 465

the answer is good

Joe could arrange the eraser in an array by placing 5 rows of 3 erasers each. The multiplication fact for this representation in an array is given by 5 × 3 .

A group of numbers or objects that will follow a predetermined pattern are referred to as an array in mathematics.

Here Joe has 15 eraser and he placed them on his rectangular bench.

Assuming that the erasers are all uniform , Joe placed them on the bench in an array of 5 rows each containing 3 erasers.

The multiplication fact for this representation in an array is given by

5 × 3 .

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The percentage increase is the ratio of value increased to the original value and multiplied by 100.

The percentage increase in his hourly wage between year 1 and year 2 is 15.61%.

Option A is the correct answer.

The percentage increase is the ratio of value increased to the original value and multiplied by 100.

It is expressed in percentage.

If there is an increase in the value of anything, then there is an increase in percentage.

We have,

Wage in the first year per hour = $8.65

Wage in the second year per hour = $10

The percentage increase in hourly wage:

= [ (10 - 8.65) / 8.65 ] x 100

= ( 1.35 / 8.65 ) x 100

= 15.6069 %

= 15.61 %

Thus the percentage increase in his hourly wage between year 1 and year 2 is 15.61%.

Option A is the correct answer.

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Answer:

m will be the right answer

The scale used on the map is 1 centimeter to 12.5 kilometers.

When we do a scale drawing of something in scale (like a map, that represents a given location) the dimensions suffer a change of scale.

This means that each unit on the scale drawing not represents the same unit on the original thing.

On this case we have a map where a actual distance of 50 kilometers is represented by a distance of 4cm (this means that each 4cm in the map are equivalent to 50 kilometers in the actual place).

Then the scale will be in cm to km, and to get the scale we can write:

4cm = 50km

Dividing both sides by 4 we get:

1cm = 50km/4 = 12.5 km

Then we conclude that the scale used for the map is 1 centimeter to 12.5 kilometers.

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Answer:

1 : 5

Step-by-step explanation:

Circles + Triangles = Total shapes

8 + 2 = 10

Number of triangles : Total shapes

2 : 10

Both can be divided(simplified) by 2

= 1 : 5

Hope this helped! ^^

Answer: the ratio is 1.13

Step-by-step explanation:

The ratio of non-black sedans to black sedans is 40/31, as of the given condition.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,

The total number of sedans in the parking lot is,
496 black sedans + 640 non-black sedans = 1136 sedans.

The ratio of non-black sedans to black sedans can be found by dividing the number of non-black sedans by the number of black sedans:

Ratio = 640 non-black sedans / 496 black sedans
Ratio  = 640/496
Ratio = 40/31

So, the ratio of non-black sedans to black sedans is 40/31.

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A scalar quantity, speed is defined as the size of the change in an object's or particle's location over time or the size of the change in an object's position per unit of time.

In statistics, a percentile (or centile) is a metric that expresses the value at or below which a specified percentage of observations in a collection of observations fall. The value (or score) below which 20% of the observations may be found is called the 20th percentile, for instance.

A higher percentile for speed is preferable for runners in a race. A high percentile indicates a faster, greater speed.

40% of athletes completed their runs at 7.5 mph or less (slower). 60% of athletes covered at least 7.5 miles per hour (faster).

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