Mathematics High School

There 430 people in wave pool. Write an inequality that represents how many more people p can enter the pool.

Answers

Answer 1

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]

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

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

therefore

the answer is

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

Related Questions

Find three solutions of the equation (x^2-9)(x^3-8)=0

Answers

(x^2-9)(x^3-8)=0

as you can see that (x^2-9) is in the form of a^2 - b^2 which equals (a+b)(a-b)

x^2 - 9
= (x)^2 -(3)^2
= (x+3)(x-3)

now, the equation becomes
(x+3)(x-3)(x^3-8)=0

(x+3) =0
x = -3

(x-3) = 0
x = 3

x^3 -8 = 0
x^3 = 8
x = cube rt. 8
= 2

so, the three solutions are -3, 3 and 2.

A box contains 5 blue marbles 3 red marbles and 6 white marbles. if three marbles are drawn, without replacement, what is the probability that all three are blue?

Answers

The probability that all three are blue it's 3:14

Chan Hee bought 3.4 pounds of coffee that cost $6.95 per pound. How much money did he spend on coffee?

Answers

That would be 3.4 * 6.95 = $23.63 answer

Prove that the cube root of 2 is irrational.

Answers

The cube root of 2 is irrational. The proof that the square root of 2 is irrational may be used, with only slight modification. Assume the cube root of 2 is rational. Then, it may be written as a/b, where a and b are integers with no common factors. (This is possible for all nonzero rational numbers). Since a/b is the cube root of 2, its cube must equal 2. That is, (a/b)3 = 2 a3/b3 = 2 a3 = 2b3. The right side is even, so the left side must be even also, thatis, a3 is even. Since a3 is even, a is also even (because the cube of an odd number is always odd). Since a is even, there exists an integer c such that a = 2c. Now, (2c)3 = 2b3 8c3 = 2b3 4c3 = b3. The left side is now even, so the right side must be even too. The product of two odd numbers is always odd, so b3 cannot be odd; it must be even. Therefore b is even as well. Since a and b are both even, the fraction a/b is not in lowest terms, thus contradicting our initial assumption. Since the initial assumption cannot have been true, it must be false, and the cube root of 2 is irrational.

Solve the proportion. 2/8 = -30/x

Answers

To solve a proportion set it up like
[tex]\frac{2}{8} = -\frac{30}{x} [/tex]

Now cross multiply the -30 and the 8 so -30 x 8 = -240
Now take the -240 and divide it by 2
[tex] \frac{-240}{2} = -120[/tex]
So x = -120

Answer = 120

The solution to the proportion 2/8 = -30/x is x = -120, found by cross multiplying and simplifying the resulting equation.

To solve the proportion 2/8 = -30/x, we will cross multiply to find the value of x. After cross multiplying, we obtain 2x = -30 imes 8. Simplifying this gives us 2x = -240, and dividing both sides by 2 yields x = -120. So the solution to the proportion is x = -120.

What are the steps to find x

Answers

6 - 3(x +2) = 15
First you would want to distribute
6 - 3x - 6 = 15
Then combine like terms
-3x = 15
Then divide
x = -5

6-3(x+2)=15 (problem)
6-3x-6=15 ( distributive property)
-3x=15 ( combine like terms)
x=-5 ( divide both sides by -3)

Scott and Teri read mystery novels. Teri has read 3 less than 5 times as many as Scott. She has read 17. How many has Scott read?

Answers

Scott read 4. Put it this way: x=4. If = 4, then put it into an equation. 5x-3= 17. So, you add three to both sides, then it comes out as this: 5x= 20. Divide by five, and you get x= 4.

Setup an equations:
S = # Scott has read
T = # Teri has read

T = 5S - 3 (3 less than means subtraction but switch term order)
17 = 5S - 3 ( substitute 17 for T because Teri read 17)
4 = S (when you solve the equation)
Therefore, Scott read 4 books.

In the diagram, AB = 10 and AC = 2√10. What is the perimeter of △ABC?

A. 10 units
B. 10 + 2√10 units
C. 20 units
D. 20 + 2√10 units

Answers

Answer:

D. 20 + 2√10 units

Step-by-step explanation:

Perimeter is the distance all round a figure.

AB = 10. This is given in the question

AC = √((3-5)²+(4--2)²

= √(4+36)

=√40 = 6.32 units

BC = 5 - -5 = 10 units

Perimeter = AB+AC+BC

= 10+6.32+10

= 26.32 units

Plzzzz Help mee with the one that isnt answered look at the pic i took

Answers

Well all you have to do is multiply 5 by 500 giving you your answer so...

500×5=25000

So she defends 25000 feet.

___ L = 240 kL ?

A. 24,000
B. 240,000
C. 0.240
D. 2.4

Answers

Answer: B.240,000
240 Kiloliter =240,000 Liter

The formula for the perimeter of a rectangle is P=2(L+W) solve for W.
A. W=p/2-l
B. W=2p-l
C. W=p-2/+l
D. W=P/2+L

Answers

cccccccccccccccc because u would want to get w by it self

Answer:

Option A - [tex]W=\frac{P}{2}-L[/tex]

Step-by-step explanation:

Given : The formula for the perimeter of a rectangle is P=2(L+W).

To find : Solve for W ?

Solution :

The formula for the perimeter of a rectangle is

[tex]P=2(L+W)[/tex]

Multiply,

[tex]P=2L+2W[/tex]

Subtract 2L both side,

[tex]P-2L=2W[/tex]

Divide by 2 both side,

[tex]W=\frac{P-2L}{2}[/tex]

or [tex]W=\frac{P}{2}-L[/tex]

Therefore, Option A is correct.

A used-boat dealership buys a boat for $2600 and then sells it for $3800. What is the percent increase?

the % increase is about ?%

Answers

46% Find the difference of 2600 and 3800= 1200. Now divide 1200 into 2600. If you round the number it will be 0.46= 46%

474: the 4 in the ones place is _____ the value of the 4 in the hundreds place.

Answers

Final answer:

In the number 474, the 4 in the ones place is less than the value of the 4 in the hundreds place by a factor of 100 because each position to the left in the place value system is worth ten times more than the one to its right.

Explanation:

The question deals with the concept of place value in mathematics. Specifically, it requires understanding how the value of a digit changes based on its position within a number. In the number 474, the 4 in the ones place has a value of 4, whereas the 4 in the hundreds place has a value that is 100 times greater, since each move to the left in place value represents a multiplication by 10. Therefore, the 4 in the ones place is less than the value of the 4 in the hundreds place. Here's a simple breakdown of the place values in the given number 474:

The first 4 (from left to right) is in the hundreds place, so its value is 4 x 100 = 400.The second 4 is in the ones place, so its value is 4 x 1 = 4.

Since 1 is less than 100, the 4 in the ones place is worth less than the 4 in the hundreds place by a factor of 100.

Final answer:

The value of the 4 in the ones place is 10 times the value of the 4 in the hundreds place.

Explanation:

The 4 in the ones place is 10 times the value of the 4 in the hundreds place.

Solve each system by elimation 2x-3y=6 and 6x-9y=9

Answers

6x - 9y = 9....divide everything by 3
2x - 3y = 3
-3y = -2x + 3
y = 2/3x - 1....slope is 2/3, y int is -1

2x - 3y = 6
-3y = -2x + 6
y = 2/3x - 2...slope is 2/3, y int is -2

same slope, different y int means parallel lines means no solutions

PLEASE HELP!

Solve for x.

x/3≤−6

A) x≤−18

B) x≤−2

C) x≥−2

D) x≥−18

Answers

The answer is A) x≤−18

Mark has a container in the shape of a cube. He uses 64 cubes with side lengths of 1 inch to completely fill the container. What is the edge length of the container?

Answers

This means the area is 64 inches^2:

x * x = 64
x = 8

Hope this helps!

Answer:

4 inches is the edge length of the container.

Step-by-step explanation:

Length of the small cubes = a = 1 inch

Volume occupied each small cube = v = [tex]a^3=(1 inch )^3= 1 inches^3[/tex]

Length of the big cube = A

Volume of the big cube = V

[tex]V=A^3[/tex]

He uses 64 cubes with side lengths of 1 inch to completely fill the container.

[tex]V=64\times v=64\times 1 inches^3[/tex]

[tex]A^3=64\times 1 inch^3[/tex]

A = 4 inch

4 inches is the edge length of the container.

The running aces card team won $548 playing in poker tournaments last year. the winnings were split evenly among the p players. how much of money did each player receive?

Answers

Each player received 548/p dollars. To find this, simply consider the total amount of money the card team won, which is given as $548. Then consider that that the winnings are being distributed evenly, so each person gets an equal share. Since we are told that there are p players on the team, but not given a specific value for p, all we can do is give the general form of the expression for dividing $548 dollars among p players.

Answer:

Each player received 548/p dollars.

I need to find the answer to 2/3 - 1/5. What is it?

Answers

2/3 - 1/5

make a common denominator

10/15 - 3/15

simplify

7/15 is your answer

hope this helps

Angles A and B are the acute angles of a right triangle. If the tangent of A is 2.1445, then angle B measures

25
64
65

Answers

tan A = 2.1445
A = tan^(-1) 2.1445 = 64.999 ≈ 65°
In a right triangle:
A + B = 90°
65° + B = 90°
B = 90° - 65° = 25°
Answer:
A ) 25° (or your first option)

The requried measure of angle B is 25 degrees. Option A is correct.

What is the triangle?

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Let A be one of the acute angles of the right triangle. Then, we have:

tan(A) = opposite/adjacent

Given that the tangent of angle A is 2.1445, we can write:

2.1445 = opposite/adjacent

Since angle B is also an acute angle of the same right triangle, we have:

tan(B) = opposite/adjacent

But since the sum of the angles of any triangle is 180 degrees, and one of the angles in this triangle is a right angle (90 degrees), we have:

A + B + 90 = 180

B = 90 - A

Substituting the expression for B into the equation for the tangent of angle B, we get:

tan(90 - A) = opposite/adjacent

tan(90 - A) = (1/tan(A)) x adjacent/opposite

tan(90 - A) = (1/2.1445) x adjacent/opposite

tan(90 - A) = 0.466

Taking the inverse tangent of both sides, we get:

90 - A = tan⁻¹0.466)

90 - A = 25.38

A = 90 - 25.38

A = 64.62

Therefore, the measure of angle B is,
B = 90 - A
= 90 - 64.62 = 25.38 degrees

Thus, the requried measure of angle B is 25 degrees.

Learn more about triangles here:
https://brainly.com/question/2773823

#SPJ2

how do you work out px+py=a?

Answers

[tex]\bf px+py=a\implies \stackrel{\textit{common factor}}{p}(x+y)=a\implies p=\cfrac{a}{x+y}[/tex]

what is the measure of

Answers

Since opposite angles are equal, 8x+12=5x+57. Subtracting 5x as well as 12 from both sides, we get 3x=45. . Dividing both sides by 3, we get x=15. Plugging x=15 into 5x+57, we get 5*15+57=75+57=132

What happens to light energy from the Sun when it reaches the surface of Earth?

A.
The light energy is multiplied when it reaches the plants on Earth.

B.
The light energy is destroyed when plants are eaten by herbivores.

C.
The light energy is transformed to chemical energy by photosynthesis.

D.
The light energy is converted to potential energy by cellular respiration.

Answers

you're answer is C hope that helps

The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.

Answers

a + b = 90
a = 2b - 15

2b - 15 + b = 90
3b - 15 = 90
3b = 90 + 15
3b = 105
b = 105/3
b = 35 <== second angle

a = 2b - 15
a = 2(35) - 15
a = 70 - 15
a = 55 <== first angle

Answer: The measure of angle a is 90-25=65° and the measure of angle be is 25°.

Step-by-step explanation:

Let the two complementary angles be 'a' and 'b'.

So, the sum of two complementary angles is 90°.

So, it becomes,

[tex]a+b=90^\circ---------------(1)[/tex]

First angle is 15 less than twice the measure of the second angle.

So, it becomes,

[tex]a=2b-15-------------(2)[/tex]

Put the equation (2) in equation (1), we get

[tex]a+b=90^\circ\\\\2b-15+b=90^\circ\\\\3b+15=90^\circ\\\\b=90-15\\\\3b=75^\circ\\\\b=\dfrac{75}{3}\\\\b=25^\circ[/tex]

Hence, the measure of angle a is 90-25=65° and the measure of angle be is 25°

please help fast and show all work thanks

Answers

(-1-16^)^2+(14-16)^2
(-7)^2+(-2)^2
49+4
53= 7.3
So 7.3 is your answer

A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 66 feet per second. The elevator for the miners descends 1616 feet per second. One day, the equipment elevator begins to descend. After 2323 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 1616 seconds? At that time, which elevator is deeper? The position of the equipment elevator relative to the surface is negative 234−234 feet. The position of the elevator for the miners relative to the surface is nothing feet.

Answers

Given that the equipment elevator descends at 6 feet per second.

The total number of seconds travelled by the equipment elevator is 23 + 16 = 39 seconds.

Thus the position of the equipment elevator relative to the surface is given by -(6 x 39) = -234 feet.

Given that the miners elevator descends at 16 feet per second.

The total number of seconds travelled by the miners elevator is 16 seconds.

Thus, the position of the miners elevator relative to the surface is given by -(16 x 16) = -256 feet.

At that time the miners' elevator is deeper.

Write the slope-intercept form of the equation for the line

Answers

y= 2x -1. I hope this helps love! :)

Ray divides ∠COA into two angles of what measure?
20
30
40
35

Answers

The answer to ur question is 20 degree angles cause each dot is 5 degrees so that would equal 20 after you split them up

Answer:

Step-by-step explanation:

plz help me with number 9

and show work so i can understand thx

Answers

The answer is A, and there's no work needed, because the unit of millimeters is the most precise.

I think the answer is C, since it is measured to 2 decimal places

A fair coin is tossed 10000 times the odds of getting exactly 5000 heads is closest to

Answers

Both heads and tails because there are only 2 choices

Answer:

5000 tails there are only two sides on coin

Step-by-step explanation:

Find the approximate side length of a square game board with an area of 192 in2.

Answers

Squares have 4 equal sides, thus, the answer is 48 in^2.

look it's a square therefor it will have 4 sides hence the answer will be 48 /2 which is 16

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