how many cubic feet of water can the following in ground swimming pool hold
a) 42ft4
b)144 ft3
c)303 ft3
d) 528 ft3

Answer:

X = -1   Y = 4

Step-by-step explanation:

Put the 7y over so it is 27-7y

after that you fill in the x on the top formula with (27-7y)

From there you solve like normal for Y, which ends out being 4.

Once you have that you can plug 4 into the Y spot in the bottom formula and just solve for X

:3

Answer:[tex]4.71\ in.[/tex]

Step-by-step explanation:

Given

diameter of pie is [tex]d=9\ inch[/tex]

radius [tex]r=\frac{9}{2}=4.5\ inch[/tex]

If child divides pie into 12 equal parts then each part subtends an angle of

[tex]=\frac{360^{\circ}}{12}=30^{\circ}[/tex] at the center

and crust length of single piece is

[tex]=\frac{30}{360}\times 2\pi r[/tex]

[tex]=\frac{1}{12}\times 2\times \pi \times 4.5[/tex]

[tex]=2.35\ in.[/tex]

For two slice length is [tex]2\times 2.35=4.71\ in.[/tex]

Thus the total length of crust eaten is [tex]=4.71\ in.[/tex]

Answer:

15%

30 percent passed BOTH tests.....Only 15% passed ONLY first test

30/(30+15) = 67% of those who passed the first test ALSO passed the second test.

Answer:

y = (4/5)x - 3

Step-by-step explanation:

slope intercept form: y = mx + b

Note the equal sign, what you do to one side, you do to the other. First, subtract 4x from both sides:

4x - 5y = 15

4x (-4x) - 5y = 15 (-4x)

-5y = -4x + 15

Next, divide -5 from both sides:

(-5y)/-5 = (-4x + 15)/-5

y = (-4x + 15)/-5

Simplify Divide -5 from all terms within the parenthesis:

y = (4/5)x - 3

y = (4/5)x - 3 is your answer.

~

Answer:

Step-by-step explanation:

Answer:

x = 5/7

Step-by-step explanation:

We find x by watching organic tutor

Answer:

point B

Step-by-step explanation:

The coordinates (4,0) is has the numbers 4 and 0.

4 is positive and  can be represented as moving right on the origin. Since, there is no rise it stays.

The system of equations 5x+5y=20 and 2x+2y=8 is dependent with infinitely many solutions, meaning there is more than one solution

To solve the system of linear equations:

First, notice that both equations are multiples of the other. If you divide the first equation by 5 and the second equation by 2, you get the same equation:

x + y = 4

Since both equations are effectively the same, every solution to one is a solution to the other, which means that there are infinitely many solutions. This sort of system is called dependent, meaning one equation can be derived from the other.

So, using a matrix solver on a calculator will indicate that the system does not have a unique solution. The correct answer is:

Answer: The 4 correct answers are A,C,D, and E.

Answer:

3

Step-by-step explanation:

gradient = (7-1)/(3-1) = 6/2=3

Answer:

Slope is 3

Step-by-step explanation:

m = Δy/Δx

m = (7-1)/(3-1)

m = 6/2

m=3

Hope this helps :)

Answer:

16x + 96

Step-by-step explanation:

You can add 88 + 8 for and get the same answer

Answer: 16x+8+88

Step-by-step explanation:

All you need to do is move around the numbers and then you get the answer

Answer:

It would be 5

Step-by-step explanation:

SO the additive inverse would basically just be the opposite of the number, for example lets say you had 12, the additive inverse would be -12. You're just changing the sign of the number! From what i know i believe that's it. Have a nice day! :D

Answer:

C. Less than or equal to

Step-by-step explanation:

The floor function is a function used to return an integer value that is great than the input number.

More often than not, the input number is a real number.

Take for instance.

Floor(3.2).

Going by the explanation above, the result of this will be 3

How about floor(-3.2)

The result of this will be -4.

This is so because -4 is less than or equal to -3.2.

The floor function maps any number to the greatest integer that is C.) less than or equal to the number.

The floor function maps any number to the greatest integer that is less than or equal to the number. This means that for any real number \( x \), the floor function, denoted as [tex]\( \lfloor x \rfloor \),[/tex] will produce the largest integer that does not exceed \( x \). For example, \( \lfloor 3.7 \rfloor = 3 \) and \( \lfloor -2.3 \rfloor = -3 \).

The floor function is widely used in mathematics and computer science for rounding down numbers to the nearest integer. It is especially useful in discrete mathematics, algorithms, and number theory. When working with the floor function, it is essential to understand that it always rounds down towards negative infinity, not necessarily towards zero. Thus, for any real number \( x \), \( \lfloor x \rfloor \leq x \).

Therefore, the correct phrase to complete the statement about the floor function is:

C.) less than or equal to.

[tex]( {y}^{8} )( - 2 {y}^{2} ) = - 2 {y}^{10} [/tex]

To multiply the monomials (Y⁸)(-2y²), add the exponents and multiply the coefficients resulting in -2y¹⁰.

To multiply the given monomials (Y⁸)(-2y²), we use the laws of exponents which state that when multiplying like bases, we add the exponents. The coefficient -2 multiplies by 1 (the implied coefficient of Y⁸) to remain -2. The new exponent for 'y' is the sum of 8 and 2, which is 10. So, the product in standard form is -2y¹⁰.

Step by step solution:

Answer:

Circle

Octagon

Step-by-step explanation:

There are no curves in a cube to make a circular cross section, and there aren't enough edges to make an octagon (just visualize)

Answer:

A circle is not possible. Neither is a square or a rectangle.

Step-by-step explanation:

Answer:

M + $13.72 = $58.22

Step-by-step explanation:

Manny and Sam combined (+) have a total (=) of $58.22

M + S = $58.22

M + $13.72 = $58.22

Answer:

m + $13.72 = $58.22

Step-by-step explanation:

Together they have $58.22.

We know one of them has $13.72, so if we add that to (m) we should get $58.22.

Answer is <

Step-by-step explanation:

To compare the square root of 7 and 14 over 5, we find their approximate values. Since 2.65 (root 7) is less than 2.8 (14/5), the correct mathematical symbol to use is <.

The question asks us to compare two real numbers: the square root of 7 and 14 over 5. First, we need to estimate these numbers. The square root of 7 is approximately 2.65. 14 divided by 5 equals 2.8. Therefore, we can say that 2.65 is less than 2.8. As such, the mathematical symbol that should be used is < which means 'less than'.

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When adding polynomial expressions, add the monomials with the same degree:

[tex]3g^2 + 3g^2[/tex]

[tex]-g - 8g[/tex]

[tex]4[/tex]

=

[tex]6g^2 -9g + 4[/tex]

Answer:

Letter B is the answer.

Answer:

The expected value of playing the game is -$7.

Bill should not play this game.

Step-by-step explanation:

The probability distribution of gain and loss is as follows:

  X         P (X)

-$20       0.30

-$40       0.20

$50        0.10

  $5        0.40

Total        1.00

The expected value of a probability distribution is given by:

[tex]E(X)=\sum {X\times P(X)}[/tex]

Compute the expected value of playing the game of chance as follows:

[tex]E(X)=\sum {X\times P(X)}[/tex]

         [tex]=(-\$20\times 0.30)+(-\$40\times 0.20)+(\$50\times 0.10)+($5\times 0.40)\\\\=-\$6-\$8+\$5+\$2\\\\=-\$7[/tex]

The expected value of playing the game is -$7.

The expected value of the game suggests that Bill will incur a loss of $7 if he plays.

So, it is safe not to play the game.

The coordinates of the midpoint would be (5/2, -3/2) of line segment AB.

A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.

Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,

M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Coordinates of A are (-2,-7),

Coordinates of B are (7, 4),

M is the midpoint of AB which is given in the question

So the coordinates of M as:

⇒ M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Substitute the values, and we get

⇒ M = ((-2 + 7)/2, ( -7 + 4)/2)

⇒ M = ((5)/2, ( -3)/2)

⇒ M = (5/2, -3/2)

Therefore, the coordinates of the midpoint would be (5/2, -3/2) of line segment AB.

Learn more about the midpoint here :

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Answer:

The number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively

Step-by-step explanation:

This is a question that deals with consecutive numbers.

Let x represent the number of seashells collected on her first day.

Given that she collected 3 more each day, then

On day 2, she collected x + 3

On day 3, she collected x + 6

On day 4, she collected x + 9

On day 5, she collected x + 12

Adding up the above will give the number of sea shells collected on day 1;

i.e.

x + x + 3 + x + 6 + x + 9 + x + 12 = 50

Collect like terms

x + x + x + x + x + 3 + 6 + 9 + 12 = 50

5x + 30 = 50

5x = 50 - 30

5x = 20

Multiply ⅕ to both sides

⅕ * 5x = ⅕ * 20

x = 4.

This mean that she found 4 seashells on day 1;

Recall that day 2 = x + 3

So, day 2 = 4 + 3 = 7 seashells

day 3 = x + 6

day 3 = 4 + 6 = 10 seashells

day 4 = x + 9

day 4 = 4 + 9 = 13 seashells

day 5 = x + 12

day 5 = 4 + 13 = 16 seashells

Hence, the number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively

We have been given that ∠Q is an acute angle such that [tex]\text{tan}(Q)=0.04[/tex]. We are asked to find the measure of angle Q to nearest tenth of a degree.

We will use arctan to solve for measure of angle Q as:

[tex]Q=\text{tan}^{-1}(0.04)[/tex]

Now we will use calculator to solve for Q as:

[tex]Q=2.290610042639^{\circ}[/tex]

Upon rounding to nearest tenth of degree, we will get:

[tex]Q=2.3^{\circ}[/tex]

Therefore, measure of angle Q is approximately 2.3 degrees.

The measure of angle Q, rounded to the nearest tenth of a degree, is approximately 131.4 degrees.

To approximate the measure of angle [tex]\( \angle Q \)[/tex] given [tex]\( \tan Q = 0.04 \)[/tex], follow these steps manually:

1. Use the inverse tangent function : Use the inverse tangent function [tex](arctangent or \( \tan^{-1} \)) to find \( Q \)[/tex].

2. Calculate [tex]\( Q \)[/tex] : Calculate [tex]\( Q = \tan^{-1}(0.04) \)[/tex].

3. Convert to degrees : The result of [tex]\( \tan^{-1}(0.04) \)[/tex] will give you [tex]\( Q \)[/tex] in radians. To convert radians to degrees, multiply by [tex]\( \frac{180}{\pi} \)[/tex].

- [tex]\( Q = \tan^{-1}(0.04) \)[/tex]

- Suppose [tex]\( \tan^{-1}(0.04) \approx 2.29161 \)[/tex] radians.

- Convert radians to degrees: [tex]\( Q \approx 2.29161 \times \frac{180}{\pi} \)[/tex]

- [tex]\( Q \approx 2.29161 \times 57.2958 \)[/tex]

- [tex]\( Q \approx 131.384 \)[/tex] degrees (this is the exact calculated value).

4. Round to the nearest tenth :

Since we need to round to the nearest tenth of a degree,

- [tex]\( Q \approx 131.4^\circ \)[/tex].

Therefore, the measure of [tex]\( \angle Q \)[/tex], rounded to the nearest tenth of a degree, is approximately [tex]\( 131.4^\circ \)[/tex].

Answer:

i did the math and it should be B. 7 hours

Step-by-step explanation:

Answer: [tex]1272cm^3[/tex]

Step-by-step explanation:

[tex]V=\pi r^2\frac{h}{3}\\ V=(3.14)(9)^2(\frac{15}{3} )\\V=(3.14)(81)(5)\\V=1271.70cm^3\\V=1272cm^3[/tex]

Answer:

The answer is 3 * 5 * 4

Step-by-step explanation: It's because volume is length times width times height so you would have to multiply all three numbers.

Answer:

6,000,000 + 20,000 + 300

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The Fundamental theorem of algebra states that a polynomial of degree n has n roots. These can be real or complex.

A quadratic is of degree 2 and has 2 roots.