12 foot by 15 foot swimming pool has a 3 ft wide no slip surface around it what is the outer perimeter of the no slip surface

Let

p--------> number of additional people who can enter the pool

we know that

the maximum capacity of the pool is [tex]600\ people[/tex]

so

the inequality is

[tex]430+p \leq 600[/tex]

[tex]p \leq 600-430[/tex]

[tex]p \leq 170[/tex]

the solution is the interval ----------> (-∞,170]

but remember that the number of people can't be a negative number

so

the solution is the interval -------> [0,170]

therefore

the answer is

The inequality is equal to [tex]430+p \leq 600[/tex]

By solving a system of linear equations, the set fee for renting a bike is determined to be $6 and the hourly rate is $4.50. Hence, the cost to rent the bike for 3 hours is $19.50.

The question involves creating linear equations based on the given information to find the cost of renting a bike for a certain number of hours. We are told that renting a bike for 4 hours costs $24 and renting for 7 hours costs $37.50. We can express this situation with two equations, where x represents the set fee and y represents the hourly rate:

We solve this system of equations to find the values of x and y. Subtracting the first equation from the second gives us 3y = 13.5, hence y = 13.5 / 3 = $4.50 per hour. We can then substitute y back into the first equation: 4(4.50) + x = 24, which simplifies to 18 + x = 24, hence x = $6.

To rent the bike for 3 hours, the cost would be 3(4.50) + 6 = $13.50 + $6 = $19.50.

NMO = LMO = x+34

LMO = 1/2 of LMN

so 2(x+34) = 6x-28

2x+68 = 6x-28

2x +96 = 6x

96 = 4x

x =96/4 = 24

x = 24

 LMO = x+34 = 24+34 = 58

 since NMO = LMO, NMO = 58

Answer:  -2 is the correct answer

Explanation:

This is the graph for greatest integer function  by looking at the graph we can clearly conclude that  f at zero is giving the value -2

Greatest integer function gives the value that is less than or equal to the value taken inside the function

For example if we have 2.09  and is operating under greatest integer function the value comes out to be 2  because it will convert the decimal value in integer

denoted as [2.09]=2

Answer:  [tex]\dfrac{15}{28}[/tex]

Step-by-step explanation:

The given word : geometry

Total letters in the above word = 8

Number of vowels (a e i o u) in word  =3

Number of consonants = 5

Number of ways to choose two consonant and one vowel is given by :-

[tex]F=^5C_2\times^3C_1\\\\=\dfrac{5!}{2!(5-2)!}\times (3)\ [ \because ^nC_1=n]\\\\=5\times2\times3=30[/tex]

Number of ways to choose any three letters from the 8 alphabets:-

[tex]T=^8C_{3}=\dfrac{8!}{3!(8-3)!}=8\times7=56[/tex]

Now, the probability that two consonants and one vowel are chosen :-

[tex]=\dfrac{F}{T}\\\\=\dfrac{30}{56}=\dfrac{15}{28}[/tex]

Hence, the required probability = [tex]\dfrac{15}{28}[/tex]

The response explains which statements are substantiated facts and why. It clarifies the concept by using examples from the question.

Substantiated facts are statements supported by evidence or proof. In the given examples:

Answer:

The owner of a business sometimes withdraw assets other than cash because cash is more liquid and can be used in transactions easily, whereas the assets after a period of times becomes liable of depreciation.

The depreciation on assets decreases the amount of the assets based on the time and wear and tear of the tangible assets.

Therefore, to retain some liquid assets in hand the tangible or intangible assets are used first.

Hence, the businessman here did the right thing.

The result of evaluating the expression 4(2m-n)-3(2m-n) with respect to m=-15 and n=-18 is -12.

To evaluate the expression 4(2m-n)-3(2m-n) for m=-15 and n=-18, we first substitute these given values into the expression.

Therefore, our expression becomes 4(2*(-15) - (-18)) - 3(2*(-15) - (-18)). Simplify the expression in the parentheses first according to the order of operations (also known as BEDMAS or PEMDAS) which stands for Brackets/parentheses, Exponents/Orders, Division/Multiplication, Addition/Subtraction.

4(2*-15 - (-18)) - 3(2*-15 - (-18)) simplifies to: 4(-30 +18) - 3(-30 + 18). Further simplify to: 4*-12 - 3*-12.

Then, doing the multiplication gets: -48 - (-36), which simplifies to: -48 + 36. Therefore, the value of the expression is -12.

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Inga lives 2b + 3 miles from school, where b is the distance Brent lives from school in miles.

Therefore, the distance that Inga lives from school, in terms of b, is 2b + 3 miles.

The problem states that Inga lives 3 miles more than twice the distance that Brent lives from school. If the distance Brent lives from school is b miles, this can be expressed algebraically as 2*b (twice the distance of Brent) + 3 (the extra 3 miles that Inga lives). Therefore, the distance that Inga lives from school, in terms of b, is 2b + 3 miles.

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The expression f - 2g evaluates to -60, considering f = 4 and g = 32. The answer is not listed in the given multiple-choice options, suggesting a potential error in the question or options.

The expression to evaluate is f - 2g. With the given values for f and g, f = 4 and g = 32, we can substitute these into the expression. The calculation will be:

Therefore, the value of f - 2g is -60. This answer is not given in the multiple choice options, indicating a possible discrepancy between the question and the provided options. The correct evaluation should be confirmed.

The probability of the event E = {b, f, h} with the sample space S = {a, b, c, d, e, f, g, h} is 3/8 or 0.375.

The student has asked to find the probability of the event E = {b, f, h} given the sample space S = {a, b, c, d, e, f, g, h} where all outcomes are equally likely. To calculate the probability, we need to use the formula for theoretical probability, which is the number of favorable outcomes divided by the total number of possible outcomes in the sample space.

We see that the event E has 3 outcomes (b, f, h) and the sample space S has 8 outcomes. So the probability of event E is given by:

P(E) = Number of outcomes in E / Number of outcomes in S = 3 / 8 = 0.375

Answer:

The answer is 2

Step-by-step explanation:

Answer: The expression shows the number of dollars he will have saved by the end of the year is given by [tex]35(7)+40(5)=\$445[/tex]

Step-by-step explanation:

Since we have given that

Amount he saved per month over the first 7 months = $35

Amount he saved per month over the next 5 months = $40

So, total saving by the end of the year is given by

[tex]35\times 7+40\times 5\\\\=\$245+\$200\\\\=\$445[/tex]

Hence, the expression shows the number of dollars he will have saved by the end of the year is given by

[tex]35(7)+40(5)=\$445[/tex]

Answer:

33.56 miles per hour.

Step-by-step explanation:

First we will see how many meters the hummingbird can travel in an hour (in meters)

it can travel up to 15 meters per second, but we know that one hour has 3600 seconds ( because an hour has 60 minutes of 60 seconds each one ( 60 x 60 = 3600)

So the hummingbird can travel 3600 x 15 = 54,000 meters in one hour.

Now, we know that 1 mile = 1609 meters, so in order to convert the 54,000 meters in miles per hour we're going to use a rule of three.

1 mile ----------- 1609 meters

x miles ---------- 54,000 meters

x miles = 54,000/1,609 = 33.56

Therefore, the hummingbird speed is 33.56 miles per hour.

The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore, a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

B(a) = a/6 - 9

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s - 2 ≤ 7

  +2   +2

s ≤ 9

s ≤ 9

Thye given Quadrilateral WILD is inscribed in circle O. The measure of angle D is 135 degrees.

Since the quadrilateral is inscribed inside the circle,

Where the four vertices are on the circle itself,

The opposite angle addition is 180 degrees.

Angle I and Angle D are opposite angles.

They add to 180 degrees

(angle I) + (angle D) = 180

(45 degrees) + (angle D) = 180

(angle D) + 45 = 180

(angle D) + 45 - 45 = 180 - 45 ... subtract 45 from both sides.

angle D = 135

The measure of angle D is 135 degrees.

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