Sam is filling up his pool. The water hose filled the 288 gallon pool in 48 minutes. At what rate did the hose fill the pool in gallons per minute?

Particular solution of the differential equation that satisfies the initial condition f'(s) = 10s - 4s³ , f(3) = 5 is f(s) =  5s² - s⁴ + 41.

We determine the particular solution to the differential equation. We do this by integrating the given differential equation and then applying the given initial condition. The power rule should be used for the given expression.

[tex]\int\ {x^{a} } \, dx[/tex] = [tex]\frac{x^{a+1} }{a+1} }[/tex]

we have given that,

f'(s) = 10s - 4s³

f(s) = ∫ f'(s)ds

     = ∫(10s - 4s³)ds

    = [tex]\frac{10s^{2} }{2} - \frac{4s^{2} }{4}+ C[/tex]

f(s) = 5s² - s⁴ + C

Now we will apply the initial condition,

f(3) = 5

⇒5(3)² - (3)⁴ + C =5

             -36 + C = 5

                       C =41

Therefore the solution is expressed as,

f(s) = 5s² - s⁴ + 41

This is the particular solution.

Given question is incomplete. Complete question is given as:

find the particular solution of the differential equation that satisfies the initial condition(s). f '(s) = 10s - 4s³, f(3) = 5.

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The amount of carbon dioxide does a person exhale each minute is, 0.625 x 10^-2 kilogram.

What is kilogram?

With the unit symbol kg, the kilogram serves as the International System of Units' unit of mass. The term "kilo" is frequently used in colloquial speech and is a unit of measurement that is widely used in science, engineering, and commerce worldwide. It denotes "a thousand grams."

Given:

A person exhales about 1.25 x 10^-5 kilogram of carbon dioxide in 2 x 10^-2 minute.

We have to find the amount of kilograms of carbon dioxide does a person exhale each minute.

The amount of carbon dioxide for each minute is,

[tex]\frac{1.25*10^_^5}{2*10^-^2} =\frac{1.25}{2}*10^-^5^+^3 = 0.625*10^-^2[/tex]

Hence, the amount of carbon dioxide does a person exhale each minute is, 0.625 x 10^-2 kilogram.

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Answer:

4.75

Step-by-step explanation:

Answer:

NONE

;)

Step-by-step explanation:

Answer: A

Step-by-step explanation: Because when your weighing a box there can sometimes be decimals in the weight

Answer:

Step-by-step explanation:

248miles ÷ 4hrs = 62mph

62mph × 6 hrs = 372miles

Mr. Chung will have driven 372 miles in 6 hours

Answer: Mr. Chung will have driven 372 miles in 6 hours

Step-by-step explanation:

The graph f(x) of  y = 1/2 f(x).

The graph demonstrates that regardless of its value, y is always positive. From the question figure, the following conclusions can be made.

Whenever x is 0, y also equals 0.

If x is 1, then y is 2.

when x is two, y is four.

Y is two when x is -1.

If x is -2, then y is 4.

It implies that the modulus function (|x|) is a function of f(x).

Here is a definition of the modulus function:

g(x)

g(x) = |x| = {x,i∫x≥0

               {-x,i∫x<0

As we can see, it is twice as large as |x|, therefore the graph in the question figure

y = f(x) = 2|x |{ -2 ≤ x ≤2}

Therefore, we must create a graph y = 1/2 f(x)

y = |x | {-2 ≤ x ≤ 2}

Please see the graphic in the attachment for the graph of  y = 1/2 f(x).

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The correct answer to this Question based on Frequency Tables is B

What are frequency Tables?

These are a form of storing data that is easy to manipulate and use it for required purposes

This is an easy way to store and use data than other storing Methods

Solution:

As we can clearly see that 13 students who have completed the review sheet have passed the exam whereas 4 students who havent Completed the review sheet have also passed the exam according to given frequency table

Means we can say that reviw sheet must have some important problems that are similar to problems asked in exam hence chances are more that if a student solves and completed review sheet he will get passed in the exam acc to given frequency table Hence Option B is correct answer

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You see from the graph that when x = 0, y = 2 so the y-intercept is ( 0 , 2).

you are given points (-5 , 6) and (5 , -2). Find slope:

slope = change in y / change in x

slope = (6 - (-2)) / (-5 - 5)

slope = (6 +2) / (-5 - 5)

slope = 8/-10

slope = -4/5

slope-intercept form: y = mx + b where m = slope and b = y intercept.

y = -4/5x + 2

Answer:

x= 5/2 and y=0

Step-by-step explanation:

i'm not sure if this is right but ill have a go at it.  I did this last year so you may have to wait for another person.

Answer:

x=0 y=1.6

Step-by-step explanation:

y=5/3 or 1.6

x=0

Hence, the total gallons of water made use of in the park after the new ride is installed is 9.51*10⁵ gallons

The form of the container the water is contained in affects how much water is contained inside. You must know the length, breadth, and depth of a square or rectangular vessel in order to calculate its volume using the volume equation V=L*W*D, where L stands for length, W for width, and D for depth. The volume equation in this case reads: V= (r²)Dπ, where r stands for the radius, D for depth, and, or pi, is a constant value that is typically rounded to 3.14. To perform the same volume calculation for a circular vessel, you must know the vessel's depth and diameter or radius.

Given, the water park has water which is 8.6*10⁵ gallons.

We know that 10⁵ = 100000

Thus, 8.6*10⁵ = 860000

The new ride would use an additional 9.1*10⁴ gallons.

Again, 10⁴ = 10000

Thus, 9.1*10⁴ = 91000

Total water that would be required now is equal to the sum of the original water volume and the volume required by the new ride

= (860000+91000) gallons

= 951000 gallons

= 9.51*10⁵ gallons

Hence, the total gallons of water made use of in the park after the new ride is installed is 9.51*10⁵ gallons

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Probability of getting a particular number on ticket = 1/7320300

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.

The following values of x: 100000, 1000, 500, 100, 75, 50, 20, 15, 10, 5

Their corresponding values of p(x) are 1/7320300, 1/7320300, 1/7320300, 1/7320300, 1/7320300, 1/7320300, 1/7320300, 1/7320300,

Expected Each lottery ticket's winnings are calculated as follows: (100000+1000+500+100+75+50+20+15+10+5)(1/7320300) = 101775/7320300 = 0.014 $.

But he does purchase a $5 ticket.

In other words, the Net Expected Value of Money is equal to 0.014 - 5 = -4.986 $.

due to the negative anticipation. There are therefore greater chances for failure. The predicted loss is $4.986.

Probability of getting a particular number on ticket = 1/7320300

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Answer:

v=50

Step-by-step explanation:

since the angle next to x+50 if you add them the rule is they will equal 180 degrees and that the entire triangle equals 180 degrees then the 2 other angles will equal v+50

v+v=v+50

 -v.  -v

v=50

hopes this helps

Correct representations of the inequality -3(2x - 5) 5 are - 6x + 15 10 - 5x (2 – x)

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1]

The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities[1]. Equivalence is not considered.

There are two form of inequality relations that are not strict, in contrast to strict inequalities:

The indication of an or b denotes that.

According to our question-

The fourth response is shown by an open circle at 5, and a bold line that begins at 5 and points to the right (attached figure)

Detailed explanation

The difference is 5 (-3(2x - 5)). (2 - x)

First, make each side simpler.

∵ -3(2x - 5) = -3(2x) + -3(-5) (-5)

Recall that (+)=(-)

∴ -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x) (-x)

Recall that (+)(-) = (-)

∴ 5(2 - x) = 10 - 5x

∴ - 6x + 15 < 10 - 5x

Take 15 away from both sides.

∴ - 6x < -5 - 5x

5 times on both sides

∴ - x < - 5

Because the coefficient of x is negate, you must change the inequality's sign when you divide both sides by it.

The x coefficient is -1.

∴ Add -1 to both sides.

∴ x > 5

The appropriate answers are:

- 6x + 15 < 10 - 5x

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Answer:

A y = -3x + 1

Step-by-step explanation:

y = mx + b  When need to know the m (slope) and the b (y-intercept

The b is where the line crosses the y axis.  It crosses the y axis at 1.  The slope tells us the steepness of the line.  

If you start at the point (0,1) and move three units down and I unit to the right, you will be back on the line.  The slope is -3/1 which simplifies to -3

Answer:

y = -1/2x - 7

Step-by-step explanation:

First, let's get the line in slope-intercept form. This is of the form y = mx + b. This helpful because we will be able to tell what the slope is, which is important because the parallel line will have the same slope. To do this, we need to isolate y. Subtract x from both sides. This gives us [tex]2y = 8-x[/tex]. Now divide both sides by 2 to completely isolate y. This gives us [tex]y = (8-x)/2[/tex], or [tex]y = -x/2 + 4[/tex]. From this we can tell that the slope is -1/2, because that is the coefficient of x.

This is the same slope we need for the parallel line! Let's put the line in slope-intercept form. We have our slope(-1/2), so we need to solve for b, which is the y-intercept. To do this, we will plug in the point on the graph to the equation for x an y. This gives us [tex]-6 = -1/2*-2 + b[/tex], or [tex]-6 = 1 + b[/tex]. Subtracting 1 from both sides tells us that which tells us b = -7. This is the y-intercept! Now we can plug this and the slope into our equation to get our answer: y = -1/2x - 6

I hope this helps!

Answer:

x= -6/5

Step-by-step explanation:

[tex]\dfrac{1}{3} x=-\dfrac{2}{5}[/tex]

Multiply both sides by 3:

[tex]3\times(\dfrac{1}{3} x)=3\times(-\dfrac{2}{5} )[/tex]

[tex]\fbox{x = -$\dfrac{6}{5} $}[/tex]

The break even point is x = 4  for cost C = 24x + 80 and Revenue R = 44x.

Cost is the amount of money spent by a business to produce or provide goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a thing or product, as seen from the seller's perspective.

Cost is defined as the total of real input costs and imputed costs associated with owner-supplied inputs.

The entire money derived from the sale of products or services pertaining to a business's core operations is referred to as revenue. Because it appears at the top of the income statement, revenue, which is also known as gross sales, is sometimes referred to as the "top line." A company's overall profits or profit are referred to as income, or net income.

The break-even threshold is reached when overall costs and total revenues are equal, leaving your small firm with no net benefit or loss. In other words, you've achieved the point in manufacturing when the income from a product matches the cost of manufacture.

At break even point cost equals revenue,

Therefore,

Cost = Revenue

⇒ 24x +80 = 44x

⇒ 20x = 80

⇒ x = 4.

The break even point is x = 4 .

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The monthly payment is given as 11.95 0f the loan amount.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The given problem can be solved by the loan formula as follows,

The expression for the loan formula is given as,

PM = A(r(1 + r)ⁿ)/((1 + r)ⁿ- 1)

Where A is the loan amount, r is the rate of interest and n is the time interval.

The corresponding values of r and n as per the question are 6% = 0.06 and 12 respectively.

Substitute these values in the above expression to get,

PM = A(0.06(1 + 0.06)ⁿ)/((1 + 0.06)ⁿ- 1)

     = 0.119A

Which can be written in the form of percentage as,

PM = 0.119 × 100% of A

      = 11.9% of A

Hence, the per month payment of the loan will be 11.9% of the loan amount.

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Answer:

  (b)  60.2°

Step-by-step explanation:

You want the measure of angle W if angles W and X are complementary and X = 29.8°.

Complementary angles total 90°:

  X + W = 90° . . . . . . . . . complementary relation

  29.8° +W = 90° . . . . . . use given value

  W = 90° -29.8° . . . . . . subtract 29.8°

  W = 60.2°

The following expression represents a 2-scale factor vertical stretch, a transformation of 4 units left, and a transformation of 1 unit down:

g(x) = 2f(x + 4) - 1

A vertical stretch of scale factor K is expressed as follows for the general function f(x):

g(x) = Kf(x).

Horizontal translation:

A horizontal translation of N units for a general function f(x) is written as:

g(x) = f(x + N).

The shift is to the left if N is positive and the shift is to the right if N is negative.

Vertical translation:

A vertical translation of N units for a generic function f(x) is expressed as follows:

g(x) = f(x) + N.

When N is positive, there is an upward movement and N shifts downward if it is negative.

So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:

g(x) = 2f(x)

Then we translate it into 4 units left:

g(x) = 2f(x + 4)

Then we translate 1 unit down:

g(x) = 2f(x + 4) - 1

This is the equation for the transformation.

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Answer:

a < -7

Step-by-step explanation:

The ratio of false positives to true positives is 3/49.

So, option B is correct.

A percentage is an expression that converts two ratios into an equal value. For instance, you may write the ratio as 1: 3 if there is 1 man and 3 women, meaning that 40% of the population is female and 14% is male. For any two numbers, the ratio formula is stated as a: b a/b. The percentage formula, on the other hand, is represented as a:b::c:da:b::c:da:b=cd. In mathematics, a ratio shows how many times one number is represented by another. For instance, if there are eight oranges and six lemons in a dish of fruit, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

The percentage of false positives=3%

The percentage of true positives=49%

Ratio=3/49

Therefore, the ratio of false positives to true positives is 3/49.

So, option B is correct.

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Answer:

Step-by-step explanation:

1. 2310/35805 -> 3/10

2. 480/720 -> 2/3

3. 120/600 -> 1/5

4. 315/1680 -> 3/16

5. 126/840 -> 3/20

6. 1848/252​ -> 22/3

Answer: $336.77

Step-by-step explanation:

So, the fencing is technically the perimeter, so we have to find the perimeter of the semicircle.

Perimeter of a semicircle = 2(pi)(r)/2

So, divide 26 by 2 to get the radius, which is 13.

(We will use 3.14 for pi)

Then fill in the variables 2 x (3.14) x (13) / 2

So, when you multiply all the numbers you will get 81.64/2.

81.64/2 = 40.82 ft.

Now that you have found how much feet the fencing will be, multiply it by the cost.

40.82 x 8.25 = 336.765.

Round your final answer by the nearest hundredth which is 336.77.

Answer: $336.77

The original price of the table is $440.

What is the selling price?

The selling price of a good or service is the final cost to the seller, or what the buyer actually pays. A commodity or service in a specific amount, weight, or measurement can be exchanged.

Given, the selling price of the table = $127.60 which is 29% of the original price

Let x be the original price of the table, then

29% of x = 127.6

or, 0.29x = 127.6

or, x = 127.6/0.29 = 440

Hence,  the original price of the table is $440.

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You should spend 30 minutes on machine 1 and 10 minutes on machine 2.

Given,

In the question:

You have 40 minute to exercise at the gym, and you want to burn a total of 300 hundred calorie using both machine.

Now, According to the question;

300 calories in 40 minutes can be set up as a ratio to find out how many calories per hour or calories per minute you are trying for:

300 calories /40 minutes = x calories/60 minutes for calories per hour (you are aiming for 450 calories burned per hour)

300 calories / 40 minutes = 7.5 calories per minute if you want to look at it that way instead.

One version of this problem that I found online completes the setup this way:

This allows us to set up a system of equations. The first equation will be for calories burned:

8x + 6y = 300

x is minutes on the 8 calorie per minute machine; y is minutes on the 6 calories per minute machine.

A second equation simply shows that the total minutes add up to 40:

x + y = 40

Now you can use substitution, elimination, or linear combinations to solve the system. I'll use substitution to rewrite the second equation:

x = 40 - y....(1)

Now substituting into the first equation:

8(40 - y) + 6y = 300

320 - 8y + 6y = 300

2y = 20

y = 10

Put the value of y in eq.(1)

Then, x gives the 30

Hence, You should spend 30 minutes on machine 1 and 10 minutes on machine 2.

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The values of the expressions are,

a)3⁻² = 1 / 9

b)4⁻³ = 1 / 64

c)2⁻⁶ = 1 / 64

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expressions will be calculated by solving the powers and writing in the fractions,

a)3⁻² = 1 / 9

b)4⁻³ = 1 / 64

c)2⁻⁶ = 1 / 64

Therefore, the values are 1 / 9, 1 / 64, and 1 / 64.

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Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?

Step-by-step explanation:

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