Safety standards require a pool to add 333 chlorine tablets to every 2,0002,0002, comma, 000 liters of water. Today, the lifeguards at Park Pool added 888 chlorine tablets to their pool's10,00010,00010, comma, 000 liters of water.How does Park Pool's chlorine compare to the safety standards?

The given function of the height of the diver is

h is the height in feet

t is the time in seconds

To find the time for the whole motion equate h by 0, as when the diver inter the water his jumper height will be zero. (The surface of the water is the initial position)

Switch the 2 sides and change all signs to opposite

Now, we have a quadratic equation, then we will use the calculator to find the values of t

Since time can NOT be a negative value, then we will ignore the 2nd value of t

The answer should be about 15.44 seconds to the nearest 2 decimal place

to do a perfect-square trinomial the third term must be the square of the half of the second term

the sencond term is 7,so

so the expresion is

and the factor

An example

the third term is

so the percet-square is

Answer:

9.53

Step-by-step explanation:

Estimate of trees: 99,300
Estimate of branches: 60

Estimate of leaves: 1600

All of the numbers multiplied togethered: 99,300 x 60 x 1600 = 9,532,800,000

9,532,800,000 to the billions is 9.53b

Note: i do not know if this will be accepted since you didn't put any answer choices so yeah

Answer: B

Step-by-step explanation:

[tex]\tan \theta=10 \implies \sin \theta=\frac{10}{\sqrt{101}}, \cos \theta=\frac{1}{\sqrt{101}}[/tex]

[tex]\sin 2\theta=2\sin \theta \cos \theta=2 \left(\frac{10}{\sqrt{101}} \right)\left(\frac{1}{\sqrt{101}} \right)=\frac{20}{101}[/tex]

[tex]\cos 2\theta=2\cos^2 \theta-1=2 \left(\frac{1}{\sqrt{101}} \right)^2 -1=-\frac{99}{101}[/tex]

[tex]\therefore \sin 2\theta+\cos 2\theta=\frac{20}[101}-\frac{99}{101}=-\frac{79}{101}[/tex]

Answer:

6. C

7. 105 ft²

Explanation:

The square pyramid has a square base with a side's length equal to 5 ft and a slant height equal to 8 ft.

Now, the only option that shows a square with a side length equal to 5 is C. So, the right net is C.

Then, the amount of fabric depends on the area of the net. The area of the net is equal to the area of the square added to the area of the triangles.

The area of the square is:

Area = side x side = 5 x 5 = 25 ft²

The area of the triangles is:

Area = 1/2 x base x height = 1/2 x 5 x 8 = 20 ft²

Then, the total area of the net is:

Total Area = 25 ft² + 4( 20 ft²)

Total Area = 25 ft² + 80 ft²

Total Area = 105 ft²

So, Frank needs 105 ft² of fabric to make the fort.

In this case, the answer is very simple.

Defines substitution.

The answer is:

The substitution method for solving systems of linear equations, consists of solving or isolating one of the unknowns (for example, x) and substitute its expression in the other equation.

In this way, we will obtain a first degree equation with the other unknown (y), and once solved ''y'', we calculate the value of ''x'' substituting the value of ''y'', that we already know.

Main Answer: The probability that a randomly selected passenger has a waiting time greater than 3.25 minutes is 0.59375.

Explaination:

Calculation of the probability:

Since The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes.

So, here the probability is

= 0.59375

Hence, The probability that a randomly selected passenger has a waiting time greater than 3.25 minutes is 0.59375

Answer:

Let flour, sugar, raisins be 3x, 1.5x, x grams respectively.

Total Mass = 550g 3x+1.5x + x = 550g

5.5x = 550 x = 100g

Flour = 3x= 3 x 100 = 300g

Hence, flour in mixture is 300g

The midpoint formula   [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex] and the length of coordinates can be determined from the formula [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].

What are coordinates?

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane.

The x-axis & y-axis are the two axes that make up a coordinate plane (vertical).

The coordinates of the origin, which is the location where the two axes connect, are (0, 0).

The following formula is used to determine the separation between two coordinates :

The midpoint formula   [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex] and the length of coordinates can be determined from the formula [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].

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two thousand people attend the theater during the week of a movie's release (option A)

The equation:

y = -50x + 2000

y = number of people in the theater

x = number of weeks since the movie release

2000 will be the number of people in the theater at the begining of the movie release

y-intercept of an equation represent the value of y when x is zero

The 2000 is the number of people in the theater at week zero.

Hence, y-intercept indicate two thousand people attend the theater during the week of a movie's release (option A)

Point of B is ( -10 , 0) is midpoint of AB .

What is midpoint of a segment?

The midpoint of AB =  ( – 5, 4) = ( x ,y)

A = (0, – 9) ⇒ ( x₁ , y₁)

Let B = ( x₂, y₂ )

midpoint of AB ⇒ x =  x₁ + x₂/2 ,  y = y₁ + y₂/2

                              -5 = 0 + x₂/2  , -9 = -9 + y₂/2

                              x₂ = -10  , y₂ = 0

point of B is ( -10 , 0)

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Multiply the full number by the denominator to convert a mixed number to an improper fraction. If the value be 3 11 / 16 then simplifying the value 59 / 16.

Multiply the full number by the denominator to convert a mixed number to an improper fraction. Include it in the numerator. Add that total to the denominator from the beginning.

To make a mixed number from an improper fraction, divide the numerator by the denominator. After division, the mixed number is produced in such a way that the obtained quotient becomes the entire number, the remainder becomes the new numerator, and the denominator remains constant.

Let the value be 3 11 / 16

Convert mixed numbers to improper fraction: [tex]$a \frac{b}{c}=\frac{a \cdot c+b}{c}$[/tex]

[tex]$&3 \frac{11}{16}=\frac{3 \cdot 16+11}{16}=\frac{59}{16} \\[/tex]

= 59 / 16

Therefore, the correct answer is 59 / 16.

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For a initial amount invested P at a annual interest rate r, the total amount after n years is given by:

For P = $83927, r = 0.07 and n = 7, we have:

Then, the amount of interest Tiana will earn on this investment is given by:

Recall that the symbols ≤ and ≥ in interval notation are represented by ] and [ respectively.

Also, the symbols < and > in interval notation are represented by ) and ( respectively.

Therefore:

a)

in interval notation is:

b)

Answer:

a)

b)

Answer: 6.33

Step-by-step explanation:

[tex]x^2 =36 \implies x=\pm 6\\\\x^3 =125 \implies x=5\\\\x^2=81 \implies x=\pm 9\\\\x^3 =512 \implies x=8\\\\x^2 =100 \implies x=\pm 10\\\\x^2 =121 \implies x=\pm 11\\\\x^2 =49 \implies x=\pm 7\\\\x^3 =64 \implies x=4\\\\x^3 =8 \implies x=2\\\\[/tex]

So, the correct answers are 5, 10, and 4, and thus the mean is 19/3, or about 6.33.

the amount paid for gatuities which 5 percent of the cost of banquet is  

A percentage refers to a specific number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%.". The cost of gratuities is 1/20 or 5 percent of the amount paid for banquet. let us assume that x is the amount paid for banquet so

2457 is 120 percent of x

or 2457= [tex]\frac{120}{100}[/tex]×x

which implies x=2457×[tex]\frac{100}{120}[/tex]

     x=2047.5$

this is the amount of banquet. to get the cost of gratuities we subtract this amount from the total cost.

amount paid for gratuities is 2457-2047.5=409.5$

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What is the solution to the given equation?

x= 20

How is the equation in the bar diagram solved?

3.5x + 12.5x =320

16x = 320

x = 20

What is a bar diagram?

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The equation of the parabola with a vertex at the origin and a directrix at; y = 5 as described in the task content is; x² = -20y.

It follows from the task content that the vertex of the parabola is at the origin while it's directrix is the line; y = 5.

Therefore, it follows that the focus of the parabola is; f = -5, since; (f - k) = (k - 5) where, k = 0.

Ultimately, a = 1/4(f-k).

a = 1/4(-5-0) = -1/20.

Recall, the vertex form equation of a parabola takes the form;

y = a(x - h)² + k; where (h, k) is the vertex.

Therefore, since the vertex is at the origin; we have;

y = (-1/20) (x -0)² + 0

y = -x²/20

20y = -x²

Ultimately, the required equation of the parabola is;

x² = -20y.

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Answer:

[tex]y = -\frac{1}{20} x^{2}[/tex]

Step-by-step explanation:

[tex]y = \frac{1}{4(f-k)}(x - h)^{2} + k[/tex] Use the equation of the parabola. The vertex is at the origin, then (h, k) is (0, 0). Substitute 0 for h and k in the equation.

[tex]y = \frac{1}{4(f-0)} (x-0)^{2} + 0[/tex] Simplify.

[tex]y = \frac{1}{4f} x^{2}[/tex]

The directrix is given [tex]y = 5[/tex]. The distance from the focus to the vertex equals the distance from the vertex to the directrix, so

[tex]f - k = k - 5\\f = -5[/tex] Substitute -5 for f  in the equation of the parabola above.

[tex]y = \frac{1}{4 * - 5} x^{2}[/tex] Simplify.

[tex]y = - \frac{1}{20} x^{2}[/tex]

The product of two expressions can be calculated using distributive property as,

(Distributive property (A+B)C=AC+BC) )

Therefore, the product of the expressions is,

The value of x = - 12°

The triangle which has two equal sides or two equal sides is called an Isosceles triangle. In a Isosceles triangle the angles made by equal sides with 3rd side will be equal

Here from given question we have,

Measure of ∠2 = x + 85

And the measure of another angle = 73

From given picture,

Two sides of triangle are equal then the given triangle will be an Isosceles triangle

As we know in a Isosceles triangle the angles made by the two equal sides with 3rd side will be equal  

=> ∠2 = 73

=> x + 85 = 73

=> x = - 85 +73

=> x = -12°

Therefore,

The value of x = -12°

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The number of miles you hike each day is 7.4 miles.

The unitary approach, to put it simply, is used to determine the value of a single unit from a specified multiple. How to determine the worth of a single pen, for instance, if 40 pens cost Rs. 400. The unitary approach can be utilized. Additionally, after determining the value of a single unit, we can multiply it to determine the value of the other units. Most ratio and proportion concepts are addressed using this methodology. To compute the value of other units using the unitary approach, the value of a unit quantity must first be determined. This can be varied in two different ways.

3 days = 22 miles

1 day = x

x = 7.4 miles

Still 12 miles are left so I will need half a day more approximately.

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hope you understand from the image...

:-)

a. Since GC bisects FGH and the angle FGH = 122°, we know that the angle FGC = 122/2 = 61°

b. Since GC bisects FGH and the angle CGH = 42°, we know that the angle FGH = 2*42 = 84°

Answer:

Explanation:

We are given absolute value function:

It has been stretched horizontally by a factor of 3, we need to find a new function that shows the stretched functions:

Stretch-Compress-along x:

Stretch if:

Since our function is Stretched by a factor of 3, therefore our function g(x) is:

This is a new function.

Answer:

Step-by-step explanation:

g(x) = |1/3x|

Solve for y in the equation in standard form

everything u need id in the picture

Explanation

to plot this, you need to count the numbers of weigth for that number, for example

for 18

count in the table all the 18

you will get 18 is 2 times in the table (2)

now, for 19

count the number of 19's in the table 3

and so on

Step 1

then, for 24

total = 0

so, as we have not 24 as a data, there is not need to plot it

I hope this helps you

From the graph

the curve start from a point close to 40

Hence at the beginning of the year January, the teperature was 38 degree

The trigonometric functions tangent, sine and cosine are related by the following equation:

In this case, the angle is y°, so:

Since we want the cosine, we can solve for it ans substitute the given tangent and sine:

This corresponds to the third alternative.

The true statement is b.