The perimeter of a pool is 116 feet. If the length of the pool is 3 times its width,
what is the width of the pool?
(Show work)

TO KNOW HOW MANY WHOLE NUMBERS THERE ARE BETWEEN 121 AMD 176 WE CAN SIMPLY GET THEIR DIFFERENCE.

THE DIFFERENCE IS THE NUMBER OF WHOLE NUMBERS INBETWEEN 121 AND 176.

[tex] = 176 - 121 \\ = 55[/tex]

THERE ARE 55 WHOLE NUMBERS BETWEEN 121 AND 176.

Answer:

54

Step-by-step explanation:

Whole numbers are 0,1,2,3,...  Following that pattern forever.

Take a simpler example.  How many whole numbers between 2 and 5?  It would be just 3 numbers; 3 and 4.  

We could subtract 5-2 to get 3 and then subtract 1 more to get the answer of 3

What if I wanted to know the number of whole numbers between 3 and 7?

The numbers would be 4,5,6.

7-3 = 4 and then subtract 1 more to get the answer that there are 3 whole numbers between 3 and 7.

176 - 121 = 55 take one more away to get 54

The relationship between the distance that Justin runs, in kilometers, and the running time, in hours, is equal to d = (17 / 2) · t.

In this problem we find that the distance that Justin runs (d), in kilometers, is directly proportional to the running time (t), in hours. That is:

d ∝ t

d = k · t

Where:

If we know that d = 17 km and t = 2 h, then the relationship between distance and time is described below:

k = 17 km / 2 h

k = 17 / 2 km / h

d = (17 / 2) · t

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The distance from Durham to Cary on the second map is 75 km

The scale of the first map:

1 cm = 2 km

The scale of the second map:

1 cm = 5 km

Map scale: A distance on a map and its corresponding distance on the planet are related by a scale. The equivalent of a map scale can be expressed, typically using different units. or visually, using a bar scale.

Distance from Durham to Cary = 15 cm

Distance from Durham to Cary on the second map = Scale of the second map * Distance from Durham to Cary

= 5*15

= 75 km

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The equation of the straight line is 3y + 2x = 15

The generic form of a straight line, Ax + By = C, is also the typical form for two-variable linear equations.

Standard form is used, for instance, in the linear equation 4x+7y= 1. This method makes it easy to find the two intercepts (x and y) of an equation.

Y = mx + c is the cartesian equation for a straight line, where m denotes the gradient or slope of the line and c denotes the location of its y-axis intersection.

Two geometrical objects are perpendicular if they cross at a right angle.

We are aware that the product of the slopes of two lines when they are perpendicular equals -1.

The given straight line is of the form  y =3/2 x - 1 .

Slope of the straight line = 3/2

Slope of the perpendicular(90°) line (m) = -2/3

The equation of a line is formulated by :

y -y₁ = m (x - x₁ )

The straight line passes through  (-3 , 7)

∴y - 7 = -(2/3) (x + 3 )

or,  -2x - 6 = 3y - 21

or, 3y + 2x = 15

Therefore the equation of the straight line is 3y + 2x = 15 .

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Answer:

1. acute angle (less than <90)

2. right angle (approximately <90)

3. obtuse angle (more than <90)

4. acute angle (less than <90)

The relationship is that number sense can be used to solve area models or partial products.

Number sense refers to a set of important numerical skills. It includes the capacity to comprehend numbers and concepts such as more and less. Some people have a better sense of numbers than others.

Number sense is a set of abilities that enable humans to work with numbers. These abilities are essential for performing math as well as many other jobs.

In this case, partial products model of multiplication. This is a model which breaks numbers down into their factors. or place values in order to make multiplication easier. This depicts number sense.

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Answer:

cost per day = 2.99(c)+20
sam's lessons cost $30.47 per day

Step-by-step explanation:

2.99 (price of clay used per pound) * c (pounds of clay used) + 20 (cost of lesson)
2.99(c)+20
since sam uses 3.5 pounds of clay per lesson that's 2.99(3.5)+20, which is equal to 30.47

The given graph represents a non-linear function.

Take two points in the graph and calculate the slope:

Slope of (-2,1) and (0,2) = (2-1)/(0-(-2) = 1/2

Slope of (2,1) and (0,2) = (2-1)/(0-2) = 1/(-2)

As the slope of the given graph is variable, it is a non-linear function.

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Answer:

20

Step-by-step explanation:

Simplify the following:

(2 sqrt(5))^2

Multiply each exponent in 2 sqrt(5) by 2:

2^2×5^(2/2)

2/2 = 1:

2^2×5

2^2 = 4:

4×5

4×5 = 20:

Answer:  20

the probability that at least 5 will do their homework on time in a class of 50 students is 0.1

How do you calculate probability?

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.

the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06.

each student does homework independently.

in a statistics class of 50 students, what is the probability that at least 5 will do their homework on time?

probability = event occur/ total number of outcomes

                 = 5/50= 1/10=0.1

thus the probability becomes 0.1

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Answer:

A- 2/4

simplified-1/2

B- 3/5

C- 4/9

D-3/3 which=1

so basically D is 1

hope this helped

please mark as brainliest and have a good day!

Step-by-step explanation:

The property used is Distributive property

What is Distributive property ?

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Given, equation

5x+9+5x+12

Step 1 =(5x+9)+(5x+12)

Step 2 = 5x+(9 +5x)+12

Step 3 = 5x+(5x+9)+12

Step 4 =(5x+5x)+(9+12)

Step 5 = (5 + 5)x+ (9 + 12)

Step 6 = 10x + 21

The property used in this equation is called Distributive property

Hence, the property use in here Distributive property

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Answer:

Step-by-step explanation:

(1,0),(2,6). Explanation: express the equation, giving y in terms of x. ⇒y=6x−6. now choose any value for x , substitute into the equation

Step-by-step explanation:

the approach of the other answer is basically correct, but we need to use the correct numbers.

so, I assume that the 33% of the first solution is correct, and not the 23% mentioned later.

x = liters of the 33% solution.

y = liters of the 17% solution.

we know that

x + y = 1.8

and therefore

x = 1.8 - y

and then we want to enforce the desired result (ab% are simply 0.ab)

0.33x + 0.17y = 0.22×1.8

we use the identity from above in this equation :

0.33(1.8 - y) + 0.17y = 0.396

0.594 - 0.33y + 0.17y = 0.396

0.198 - 0.16y = 0

0.198 = 0.16y

y = 1.2375 liters

x = 1.8 - y = 1.8 - 1.2375 = 0.5625 liters

if the first solution is truly only 23%, then we only need to change the number :

0.23(1.8 - y) + 0.17y = 0.396

0.414 - 0.23y + 0.17y = 0.396

0.018 - 0.06y = 0

0.018 = 0.06y

y = 0.3 liters

x = 1.8 - y = 1.8 - 0.3 = 1.5 liters

Answer:

Commutative Property for Multiplication

Answer:

Commutative Property for Multiplication

Step-by-step explanation:

Answer:

105 cause you will divide to get the total

The Inverse Function Line Test

A given graph represents a function only if for every value of x there is only one corresponding value of y.

This can be checked by using a vertical line and moving it through the x-axis. If that line intersects the graph more than once, then the graph does not correspond to a function.

The image shows a graph and if we move our imaginary vertical line from x=-2 to x=7 that line would intersect the graph only once. This means that the graph corresponds to a function in the domain [-2,7].

For the inverse function to exist, the horizontal line test must be passed.

Imagine a horizontal line moving through the y-axis. It would intersect the graph only once from y=0 to y=6.

We can conclude this graph corresponds to a function and it has an inverse function because it passed the horizontal line test.

Answer: D.

For the linear function y = 9 - 5x, it is found that:

A linear function, in slope-intercept format, is modeled according to the following rule below:

y = mx + b

In which:

In the context of this problem, the linear function is modeled as follows:

y = 9 - 5x.

In standard format, with the slope in front, we have that:

y = -5x + 9.

Meaning that the coefficients are given as follows:

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Answer: 2:7

Step-by-step explanation:

[tex]\displaystyle\\\frac{6}{15+6} =\\\\\frac{6}{21} =\\\\\frac{2(3)}{7(3)} =\\\\\frac{2}{7} =\\\\2:7[/tex]

The ratio of triangles to total shapes in simplest form is 2 : 7.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, There are 15 squares and 6 triangles.

Therefore, The total number of shapes is (15 + 6) = 21.

So, The ratio of triangles to total shapes is,

triangle/total shapes = 5/15 + 6.

triangles/total shapes = 6/21.

triangles : total shapes = 6 : 21 = 2 : 7

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120% is considered an enlargement since the scale factor is greater than one.

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.

It is considered a reduction of the scale factor is less than one, and an enlargement if the scale factor is greater than one.

120% = 1.2 > 1, hence an enlargement.

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The solution to the given system of linear equations is x = 3, y = -3. That is, (3, -3)

The graph of the system of equations is shown below

From the question, we are to determine the apparent solution to the given system of linear equations

The given system of equations is

y = -2x + 3

y = 1/3x - 4

Set the two equations equal

That is,

-2x + 3 = 1/3x - 4

Multiply through by 3

-6x + 9 = x - 12

Add 6x to both sides of the equation

-6x + 6x + 9 = x + 6x - 12

9 = 7x - 12

Add 12 to both sides of the equation

9 + 12 = 7x - 12 + 12

21 = 7x

x = 21/7

x = 3

Substitute the value of x into the first equation

y = -2x + 3

y = -2(3) + 3

y = - 6 + 3

y = - 3

The solution is (3, -3)

The graph is shown below

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7x + 49 rewritten using common factor is 7(x + 7)

A common factor is a whole number which is a factor of two or more numbers.

In other words, common factors of two or more numbers are a number which divides each of the given numbers exactly.

For example the common factor of 24 and 36 are 1, 2, 3, 4, 6 and 12.

Therefore,

rewriting 7x + 49 using common factors is as follows:

7x + 49 = 7(x + 7 )

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The measure of ∡KJR is 69°.

What is the sum of two supplementary angles?
Two angles are referred to as supplementary angles if their combined value is 180°. A straight angle is created when supplementary angles are combined (180°).
In other words, ∡A and ∡B are supplementary if ∡A plus ∡B equals 180°. Angles A and B are described as "supplements" of one another in this context.
In math, A° + B° = 180°.

Given, m∡RJI = 12x - 3, m∡KJR = 6x - 5, m∡KJI = 172°
As seen from diagram, m∡RJI + m∡KJR = m∡KJI
⇒ (12x-3)+(6x-50) = 172° ⇒ 18x - 53 = 172° ⇒ x = ([172 + 53]/18)° = 12.5°
Therefore, the value of x = 12.5°
Thus, m∡KJR = 6x - 5 = (6*12.5) - 5 = 69°

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Answer:

267 times 6

Step-by-step explanation:

See below for the pseudocode and the flowchart is added as an attachment

Flowcharts and pseudocodes are used as prototypes of actual programs.

Area of circle

The pseudocode is as follows:

Perimeter of rectangle

The pseudocode is as follows:

Perimeter of square

The pseudocode is as follows:

See attachment for the flowcharts

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Using an exponential function, it is found that:

An exponential function is modeled according to the following rule:

[tex]y = ab^{\frac{x}{n}}[/tex]

In which:

Considering that the pool has 1500 gallons, and drains 3% every 5 minutes, the parameters of the function are given as follows:

a = 1500, b = 1 - 0.03 = 0.97, n = 5.

Hence the amount of water in the poll after x minutes is given by:

[tex]y = 1500(0.97)^{\frac{x}{5}}[/tex]

After 50 minutes, the amount of water in the pool is:

[tex]y = 1500(0.97)^{\frac{50}{5}} = 1500(0.97)^{10} = 1106[/tex]

1106 gallons.

The poll will have less than 1000 gallons when:

y = 1000 (we can use it because the function decreases continuously).

Hence:

[tex]1500(0.97)^{\frac{x}{5}} = 1000[/tex]

[tex](0.97)^{\frac{x}{5}} = \frac{1000}{1500}[/tex]

[tex](0.97)^{\frac{x}{5}} = \frac{2}{3}[/tex]

[tex]\log{(0.97)^{\frac{x}{5}}} = \log{\left(\frac{2}{3}\right)}[/tex]

[tex]\frac{x}{5}\log{0.97} = \log{\left(\frac{2}{3}\right)}[/tex]

[tex]x = 5\frac{\log{\left(\frac{2}{3}\right)}}{\log{(0.97)}}[/tex]

x = 66.6 minutes.

The capacity of the pool is missing, and it is of 1500 gallons.

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The statement that cannot be assumed based on the diagram is ∠DBC is vertical to ∠FDE.

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