Marty swans 36 yards in 42 seconds. If he continues to swim at the same rate, how long will it take him to swim 500 yards

let's firstly convert the mixed fractions to improper fractions.

\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{11}{3}-\left( \cfrac{9}{4} \right)\implies -\cfrac{11}{3}+\cfrac{9}{4}\implies \cfrac{-(4)11~~ + ~~(3)9}{\underset{\textit{using this LCD}}{12}} \\\\\\ \cfrac{-44+27}{12}\implies \cfrac{-17}{12}\implies {\Large \begin{array}{llll} -1\frac{5}{12} \end{array}}\)

Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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The equation is: (2x + 8) / 4 - 3 = x - 7

The solution is x = 12

Let x be the number you thought of at the beginning. Following the steps:

Multiply by 2: 2x

Add 8: 2x + 8

Divide by 4: (2x + 8) / 4

Subtract 3: (2x + 8) / 4 - 3

The final answer is seven less than the number you thought of at the beginning: (2x + 8) / 4 - 3 = x - 7

The equation is: (2x + 8) / 4 - 3 = x - 7

2. (2x + 8) / 4 - 3 = x - 7

(1/2)x + 2 - 3 = x - 7

(1/2)x - 1 = x - 7

Now add 1 to both sides:

(1/2)x = x - 6

Subtract (1/2)x from both sides:

-1/2x = -6

Now multiply both sides by -2:

x = 12

3. Properties used to solve the puzzle

Addition Property of Equality

Multiplication Property of Equality

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The length of 2 sides and an angle between them is given A = ½ × b × c × sin(α) If two angles and the length between them is given A = For an isosceles right triangle A = ½ × a.

If the height (i.e. the altitude) and base of an isosceles triangle are known, the area can be easily calculated. The area of the isosceles triangle is calculated by multiplying the height by the base and dividing by two. As a result, an isosceles triangle has two equal sides and two equal angles. The name is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

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Answer:

how to get a mean of the data in the morning and after some time

Answer:

\( y = \frac{z^2 - x}{2} \)

Step-by-step explanation:

Given:

\( \sqrt{x + 2y} = z \)

Required:

Solve for y (make y the subject of the formula)

SOLUTION:

\( \sqrt{x + 2y} = z \)

Square both sides

\( (\sqrt{x + 2y})^2 = z^2 \)

\( x + 2y = z^2 \)

Subtract both sides by x

\( 2y = z^2 - x \)

Divide both sides by 2

\( y = \frac{z^2 - x}{2} \)

The proportionality constant is 3.5.

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

Given:

x          y

2         7

7        24.5

9        31.5

Now, using proportionality constant

y= kx

y/x= k

where if is proportionality constant

So, k= 7/2

k= 3.5

again, k = 24.5/7

K=3.5

Hence, the proportionality constant is 3.5.

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Answer: it was be cos4

Step-by-step explanation: 1/2 divided by 3/4 = cos4

Step-by-step explanation:

h more than 172 is the same as 32

Answer:

$ 148.75

Step-by-step explanation:

       Principle = $ 425

         Rate = 7%

       Time = 5 yeats

\(\sf \boxed{Simple \ Interest = \dfrac{Principle*rate*time}{100}}\)

                           \(= \dfrac{425*7*5}{100}\\\\=\dfrac{17*7*5}{4}\\\\\\=\dfrac{595}{4}\\\\=148.75\)

Answer:

Step-by-step explanation:

The compound interest formula is expressed as;

A = P(1+r/n)^nt

r is the rate

n is the time of compounding

t is the time in years

Given

P = 20,000

r = 6.5% = 0.065

t = 4

n = 1/12

Substitute

A = 20000(1+0.065(12))^40(1/12)

A = 2000(1+0.78)^3.33

A = 20000(1.78)^3.33

A = 20000(6.8218)

A = 136,435.88

Hence $he will have approximately  136,436 in his account after 40years compounded monthly

Answer: y=-3x-4

Step-by-step explanation:

Since we know slope, we can plug it into slope-intercept form to find the y-intercept by using the given points,

y=-3x+b

8=-3(-4)+b

8=12+b

b=-4

Now that we know the y-intercept, we can complete the slope-intercept form.

y=-3x-4

Answer: 1672

explanation:              add 3% from each previous year to get to the 6th year            

Answer:

16717

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

The total number of points in PS is a sum of the number of points in :

PQ + QR + RS ;

PQ = 7 ; QR = 13 ; RS = 5

PS = (7 + 13 + 5) = 25

Probability that point selected at random is in RS ;

Required outcome = point in RS

Total possible outcomes = points in PS

Probability = RS / PS = 5 / 25 = 0.2

The experimental probability of choosing a student who walks to school is given by 0.15625 or 15.625%.

Given data ,

The experimental probability of choosing a student who walks to school can be calculated by dividing the number of students who walk to school by the total number of students in Joe's class.

Number of students who walk to school = 5

Total number of students in the class = 32

Experimental probability = Number of students who walk to school / Total number of students

= 5 / 32

P = 0.15625

Hence , the experimental probability of choosing a student who walks is 0.15625 or 15.625%.

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Answer:

$103

Step-by-step explanation:

Answer:

Width = 8 ft

Length = 53 ft

Height = 9 ft

Step-by-step explanation:

Let width be x

Length will be 8x-11

Height will be x + 1

Volume = width x height x length

=

x * (8x-11) * (x+1) = 3816

(8x^2 - 11x) * (x+1) = 3816

8x^3 + 8x^2 - 11x^2 - 11x = 3816

8x^3 -3x^2 - 11x = 3816

8x^3+64x^2-61x^2-488x +477x-3816= 0

8x^2 (x-8)+61x(x-8)+488(x-8)

(x-8)(8x^2 + 61x + 477) = 0

x-8

8x^2 + 61x + 477 = 0

Solve the equations:

x = 8

Length = 8x -11 = 64-11 = 53

Height = 8+1 = 9

Answer:

8w^3-3w^2-11w=3816

Step-by-step explanation:

Find the equation, in terms of w, that could be used to find the dimensions of the trailer in feet. Your answer should be in the form of a polynomial equals a constant.

Answer:

As per the given information there are 4 different price intervals.

Let x be the age and y be the admission price, then we have following equations;

Answer:

north wind traders,fifth cofffe, margies coffe

Step-by-step explanation:

anwsers from khan.

As per given by the question,

There are given that angle XBY is 70 degree and ray BA bisects.

Now,

According to the properties of the bisect,

A line that splits an angle into two angles.

Then the bisects means to divide into equal part.

Then,

Angle XBY is given that 70 degree.

So,

The angle XBA is equal to the half of the angle XBY, that means half of bisects angle.

The angle XBA is 35 degree.

Hence, the option B is correct.

Answer:

i dont know anything so help me

Step-by-step explanation:

Answer: 25%

Step-by-step explanation:

First week of July = 1040 people

Fourth week of July = 1040- 100 + 130 - 290 = 780

The number of people that went to the swimming pool in 1st week was 1040 while the 4th week had 780. The percentage decrease will be:

= (1040 - 780) / 1040 × 100

= (260 / 1040) × 100

= 0.25 × 100

= 25%

The numeric value of the expression ((2.1)² + 5.2 - 7.2) x 7.1 is given as follows:

17.1.

The expression for this problem is defined as follows:

((2.1)² + 5.2 - 7.2) x 7.1

The precedence of operators follows the PEMDAS acronym, as follows:

Hence the parenthesis takes precedence, thus:

(2.1)² + 5.2 - 7.2.

Then the power takes precedence, thus:

(2.1)² + 5.2 - 7.2 = 4.41 + 5.2 - 7.2

Addition and subtraction can be done in any order, hence:

4.41 + 5.2 - 7.2 = 2.41.

Then the multiplication is given as follows:

2.41 x 7.1 = 17.1.

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Answer

The amount that Diana's sister would buy the remaining 720 square inches piece of cloth = $5

Step-by-step Explanation

We are told that Diana bought a piece of cloth that was 48 inches wide and 1 yard long for $12.

Then, she had different parts of the cloth taken to do different stuff until the remaining piece of the cloth was to be bought by her sister at the same rate that she bought the original full piece of cloth.

Before we proceed, we need to establish and find the initial rate of the cloth, that is, how much is 1 unit of area.

Area of a rectangular figure (the cloth) = Length × Breadth

Length of the cloth = 1 yard = 36 inches

Breadth of the cloth = 48 inches

Area of the cloth = 36 × 48 = 1728 square inches.

1728 square inches of the cloth = $12

1 square inch of the cloth = (12/1728) = (1/144) dollars

So, now, we can now find how much of the cloth is removed.

- She cut off one-fourth of the cloth to make a tablecloth.

One-fourth of the 1728 square inches piec of cloth = (1/4) × 1728 = 432 square inches

- She used a piece that was 12 inches wide and 12 inches long to make a scarf.

Area of the piece she used to make a scarf = 12 × 12 = 144 square inches

- She used a piece that was 1.5 feet by 2 feet to make a cover for a pillow.

To find the area of this piece, we need to convert the dimensions into inches.

1 feet = 12 inches

So,

1.5 feet = 18 inches

2 feet = 24 inches

Area of this piece of cloth = 18 × 24 = 432 square inches

So, her sister now wants to buy the remaining piece of cloth from Diana.

Originally, the piece of cloth was 1728 square inches.

The total area removed from the original piece of cloth sum up to

432 + 144 + 432 = 1008 square inches.

The remaining piece of cloth will now have an area calculated by subtracting the area of pieces removed from the original area of the piece of cloth.

The area of the remaining piece of cloth = 1728 - 1008 = 720 square inches

Recall that the Diana's sister wants to but the remaining piece of cloth at the rate that Diana bought the original piece of cloth.

We have calculated this rate at which Diana bough the original piece of clothing to be (1/144) dollars for 1 square inch. So, we can then use this rate to calculate the amount Diana's sister will pay for the remaining piece of cloth

Area of the remaining piece of cloth = 720 square inch

1 square inch costs (1/144) dollars.

Let the cost of 720 square inches be x.

1 square inch = (1/144) dollars

720 square inches = x dollars

We can from a mathematical relationship simply by cross multiplying

1 × x = 720 × (1/144)

x = 5 dollars.

Hence, the amount that Diana's sister would buy the remaining 720 square inches piece of cloth = $5

Hope this Helps!!!

For the guess and check method, we would still need to first find the cost of 1 square inch of material which we obtained to be (1/144) dollars per square inch of cloth.

We would also still need to calculate the total area removed from the cloth, which we calculated to be 1008 square inches.

But now, we will now use the cost of 1 square inch, to calculate the cost of the pieces that have been removed from the cloth.

1008 × (1/144) = 7 dollars.

We can now guess how many dollars will top up the 7 dollars so that it gives the original 12 dollars that the cloth was bought.

After a series of guess, we will end up to get that it is (7 + 5) that is equal to 12 dollars.

So, guess and check would give us 5 dollars too as the answer.

Given statement solution is :- The correct answer is: The frequency is 3 more than expected.

To determine the expected frequency of landing on an even number when rolling a fair six-sided number cube, we need to calculate the probability of landing on an even number and multiply it by the total number of rolls.

The number cube has six possible outcomes: 1, 2, 3, 4, 5, and 6. Of these, three are even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2 or 0.5.

The expected frequency can be found by multiplying the probability by the total number of rolls:

Expected frequency = Probability of landing on an even number × Total number of rolls

Expected frequency = 0.5 × 30 = 15

Now, we can compare the expected frequency (15) to the actual frequency (18) given in the problem statement.

The actual frequency is 18, and it is 3 more than the expected frequency (18 - 15 = 3).

Therefore, the correct answer is: The frequency is 3 more than expected.

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Answer:

Step-by-step explanation:

45