The length of a swimming pool is triple the width. The area of the pool is 6627 ft2. Find the length and width of the pool.

The Maximum height of the object is 2888.9 feet which is at 23.06 seconds

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let h represent the height of an object after t seconds. Given that:

h(t) = -4.9t² + 226t + 283

The maximum height is at h'(t) = 0, hence:

h'(t) = -9.8t + 226

-9.8t + 226 = 0

9.8t = 226

t = 23.06 s

h(23.06) = -4.9(23.06)² + 226(23.06) + 283 = 2888.9

Maximum height is 2888.9 ft

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Using a system of equations, it is found that 4 tangerines will balance one apple.

The equations are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

For this problem, the variables are given as follows, considering the situation described:

For the first picture, one apple and one tangerine balance one grapefruit, hence:

a + t = g.

For the second picture, one banana and one tangerine balance one apple, hence:

b + t = a.

For the third picture, two grapefruits balance three bananas, hence:

2g = 3b.

g = 1.5b.

Replacing on the first equation, we have that:

a + t = 1.5b.

From the second equation, we have that:

b = a - t.

Hence, replacing on the first:

a + t = 1.5(a - t)

1.5a - 1.5t = a + t

0.5a = 2t

a = 4t

Hence 4 tangerines will balance one apple.

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Apply right triangle proportions:

20 (16) = x (x)

320 = x^2

√320 = x

x = 8√5

[tex] \frac{1}{2} = {2}^{x} \\ {2}^{ - 1} = {2}^{x} \\ x = - 1[/tex]

ATTACHED IS THE SOLUTION

Answer: The median and mean of height of students is not equal, the median is greater.

Step-by-step explanation:

Definition of Median:

Median is the middle value in the picture. To find the median, order the numbers and see which one is in the middle value of the list.

in this picture, first, we order the numbers in numerical order:

1,1,1,2,2,3,3,5,6,6

Find the middle number:

1,1,1,2,2,3,3,5,6,6

As above, 3 is the middle number, then we find which bar represents the median of height of students:

1+1+1+2+2+3 = 10 students

Referring back to the chart, if we add the first 2 bars together, we will get 6+2 = 8 students, but the median number is 10 students, that means the median will be at the third bar, median of height of students = 62-64.

Definition of Mean:

Mean is the sum of the numbers divided by the number of numbers.

In this picture, the Mean will be

(2+6+5+6+3+3+2+1+1+1) / 10

= 3 students

which means the mean height of students = 60-62.

Given model is

Substitute A=12981 to find the value of t, we get

Subtracting 8000 from both sides, we get

Multiplying 8000 and 0.045, we get

Dividing both sides by 360, we get

Round off nearest tenth, we get

Hence it would take 13. 8 years for the loan amount to $ 12981.

The following rational fractions is graphed below?

f(x) = 1/ is the rational function seen in the given graph (x - 4)

How Are Graphs of Asymptotes Functions Interpreted?

The vertical asymptote of the graph is located at x = 4.

Let's determine each function's vertical asymptote.

We set the denominator equal to 0 to determine the vertical asymptote.

A) x + 4 = 0\sx = -4

That's incorrect

B) 4x = 0 x = 0 Invalid

C) The denominator is erroneous since it lacks a variable.

D) x - 4 = 0\sx = 4

So, this is true.

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Answer

Option C is correct.

The equation has infinitely many solutions.

Explanation

To know the nature of the solutions, we need to solve the given equation

3 (4g + 6) = 2 (6g + 9)

12g + 18 = 12g + 18

12g - 12g = 18 - 18

0 = 0

Any equation that results in 0 = 0, is known to have infinitely many solutions because any number will fit in for g and still work for the given equation.

Hope this Helps!!!

Answer:

u did not addd the pic

Step-by-step explanation:

Answer: 1.3660254037844

-0.36602540378444

Step-by-step explanation:

Answer:

g(7) = 21

Explanation:

To calculated g(7), we need to replace x by 7 in g(x) as:

Therefore, g(7) is equal to 21

From the statement, we know that:

0. the company sells 1000 packs of cards per day for $5 per pack,

1. with every $0.02 reduction in price, 10 more packs a day are sold.

To solve this problem, we define the following variables and functions:

• r = # of price reductions,

• n(r) = # of packs sold by the company as a function of r,

• p(r) = price per pack (in $) as a function of the # of price reductions,

• I(r) = income (in $) as a function of the # of price reductions.

Using points 1 and 2, we write the following functions: function of # of packs sold n(r) as:

• the i

• the function of the price per pack p(r):

• the function for the income I(r) is given by the product of the # of packs sold n(r) and the price per pack p(r):

(1) To find the maximum income, we must maximize the function I(r) for r. To do that, we compute and make equal to zero its first derivative:

Solving for r, we get:

We have found that the maximum income is achieved when the # of price reductions is equal to r = 75.

(2) s

We have found that the maximum possible income per day is $6125.

(3) s

We have found that the price per pack that maximizes the income is $3.5.

(4) s

With this new price structure, the company wins $6125 s

• The maximum possible income per day is $6125.

• The price per pack that maximizes the income is $3.5.

• The company makes $1125 extra with this new price structure.

Answer:

x= 12

Step-by-step explanation:

8/4 = 2

2x6 = 12

Answer:

A

Step-by-step explanation:

if you feel cold your body will tell your brain or give feedback to make you think or say its cold

Answer:

10+5y

Step-by-step explanation:

5(2+y)

distribute

=5(2)+5(y)

simplify

=10+5y

Answer:

[tex]y+1=\frac{1}{3}(x-3)[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we want to find is 1/3.

Using point-slope form, the equation is

[tex]y+1=\frac{1}{3}(x-3)[/tex]

1. Using estimation shows that Stephen's answer is incorrect because when the whole number 3 is subtracted from 154, it gives 151 and not 119.  The actual result should be between 150 and 151.

2. The strategy that Stephen could use to solve this subtraction problem is an approximation. Approximately, 3.48 is 3.5, but for a quick estimation, the decimals are eliminated or appropriated.

Estimation means a rough calculation or an approximation.

Estimation provides a quick means of arriving at number solutions without going into detailed calculations.

Estimates are used for decision-making when complete information is not required or available.

The minuend = 154.2

The subtrahend = 3.48

The estimated value of the minuend reduces it to 154.

The estimated value of the subtrahend reduces it to 3.

Using estimation, the difference = 151 (154 - 3)

Actual difference = 150.72 (154.2 - 3.48)

The actual difference can be approximated to 151.

Thus, using appropriate estimation, Stephen can easily solve this subtraction problem without difficulty.

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By using conversion factor, if Lorraine prepared a 2.5 gallon pot filled with tomatoes to be canned in jars and each jar will hold 1.25 quarts of tomatoes, then Lorraine can fill 8 jars  

The quantity of tomatoes prepared by Lorraine = 2.5 gallon

The quantity of tomatoes can be filled in one jar = 1.25 quarts

We know

1 gallon = 4 quarts

First convert the quantity of tomatoes prepared by Lorraine from gallon to quarts

2.5 gallon =  2.5×4 = 10 quarts

How many jars can Lorraine fill = The quantity of tomatoes prepared by Lorraine/The quantity of tomatoes can be filled in one jar

we have to use division

= 10/1.25

= 8 jars

Hence, if Lorraine prepared a 2.5 gallon pot filled with tomatoes to be canned in jars and each jar will hold 1.25 quarts of tomatoes, then Lorraine can fill 8 jars

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The volume of this triangular prism 7yd x 7yd x 8yd is calculated as 196 [tex]yd^3\\[/tex] as per answered with the correct unit.

A prism is a kind of a polyhedron in geometry that has n number of parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the present first base, and the n faces.

The bases are all translated into all cross-sections that are parallel to them.

The volume of this prism can be found by applying the formula

1/2 Area x Height

= 1/2 x 7 x 7 x 8

= 196 [tex]yd^3\\[/tex]

V=Bh

V=Bh, where B can be said as the base area and h as the height, is the formula for a prism’s volume. The prism has a rectangular base.

The total area that any kind of prism takes up in three dimensions is known as its volume. It is defined in mathematically as the result of the base’s area and length.

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I hope this is clear enough , although I did not arrive at the same answer using x in both equation .

Answer:

(4,8) x=4/y=8

Step-by-step explanation:

the four is the x line  and the 8 the y line.

4 laying down line to the right (positive four)

8 straight up line top(positive 8)

With the aid of subjective judgment, we can describe the number of girls as; A. The number of girls is significantly low.

Subjective judgement is simply defined as something that is subjective is based on personal opinions and feelings rather than on facts.

Now, we are told to assume that 600 births are randomly selected and 26 of the births are girls.

Now, we see that the total number of births are assumed as 600.

Now, since only 26 of that size are seen to be girls, then it means that;

Percentage that are girls = (26/600) * 100 = 4.33%

Thus, using subjective judgement we see that the percentage that are girls is so low that it is even lower than 5%. Thus, we can say that The number of girls is significantly low.

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Using an exponential function, it is found that it would take 80.12 minutes for the element to decay to 6 grams.

An exponential function is defined according to the following rule:

[tex]y = a(b)^{\frac{t}{n}}[/tex]

In which:

Considering the half life of the substance, and the initial amount of 430 grams, the parameters are given as follows:

a = 430, b = 0.5, n = 13.

Then the amount of the substance after t minutes is given by:

[tex]y = 430(0.5)^{\frac{t}{13}}[/tex]

The time it will take for the element to 6 grams is t when y = 6, hence:

[tex]6 = 430(0.5)^{\frac{t}{13}}[/tex]

[tex](0.5)^{\frac{t}{13}} = \frac{6}{430}[/tex]

[tex]\log{((0.5)^{\frac{t}{13}})} = \log{\left(\frac{6}{430\right)}[/tex]

[tex]\frac{t}{13}\log{0.5} = \log{\left(\frac{6}{430\right)}[/tex]

[tex]t = 13\frac{\log{\left(\frac{6}{430}\right)}}{\log{0.5}}[/tex]

t = 80.12 minutes.

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The value of k = -10 in f(x).

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

The amount "left over" after a calculation is the remainder. The integer that remains after multiplying one integer by another to create an integer quotient is known as the remnant in mathematics.

Given that,

f(x) = x³ + kx + 13

The remainder when f(x) is divided by x + 1 is 22,

Here, the f(x) is divided by x+1

Hence, x = -1

Substitute x = -1 in f(x)

22 = f(x) = x³ + kx + 13

22 = f(-1) = (-1)³ + k(-1) + 13

22 = -1 –k +13

22 = -k +12

K = -10

Therefore, the value of k = -10 in f(x).

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This just means that the y coordinate will  always be 3 for all coordinates of x that means that the y coordinate of the point ( -7,1) will change to

(-7,3)

Using it's concept, the probabilities are given as follows:

a) Type A die and orange: 1/10 = 0.1.

b) Blue: 23/30

c) Type B, if blue: 8/23.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

For item a, the probability that a type A dice is chosen is:

3/5.

As there are 5 dices, 3 of type A and 2 of type B.

The probability that a type A dice comes up orange is:

1/6.

As it has six faces, one of which is orange.

Then the probability of an orange type A dice being chosen is:

3/5 x 1/6 = 1/10 = 0.1.

For item b, the probability of blue is divided as follows:

Hence the probability of a blue dice is:

p = 5/6 x 3/5 + 4/6 x 2/5 = 23/30

For item c, we apply the conditional probability, hence the probability is given as follows:

p = (4/6 x 2/5)/(23/30) = (8/30)/(23/30) = 8/23.

Dividing the probabilities of type B and blue by the probability of blue.

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By using the method of addition, the equation is 12x + 1.

Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The sum is the entire value, and the addends are the integers that are being added. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum.

Given that,

5x - 4 > 12 adding 4 to both sides;

5x - 4+ 4 > 12 + 4

5x > 16 dividing both sides by 5;

x > 16/5

12x + 5-4

12x + 1

Therefore, the equation is 12x + 1.

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Answer:

  A: y = 10

  B: ∠A = 42; ∠C = ∠D = 138

Step-by-step explanation:

Given vertical angles A and B, with A marked 5y-8 and B marked 42, you want to know the value of y and the measures of supplementary angles C and D.

Vertical angles A and B are congruent, so we have ...

  ∠A = ∠B

  5y -8 = 42

  5y = 50 . . . . . . . add 8

  y = 10 . . . . . . . divide by 5

As we noted above, angle A has the same measure as vertical angle B:

  ∠A = 42

Angle C forms a linear pair with angle B, so is supplementary:

  ∠C = 180 -∠B = 180 -42

  ∠C = 138

Angle D is a vertical angle to angle C (and is also supplementary to angle B).

  ∠D = 138

Answer:

True

Step-by-step explanation: