there are about 6*10^24 molecules in a litre of water. it is estimated that a person drinks about 2.2 *10^3 litres of water a year. how many molecules of water does a person drink in a year?

Given the regular price is $43.

S.P= 35% off on regular price i.e.

Hence, after 35% off, the price is $27.95

Let

x -----> the number of milliliters of the 3.5% solution

y ----> the number of milliliters of the 6% solution

we have that

3.5%=3.5/100=0.035

6%=6/100=0.06

5%=5/100=0.05

so

0.035x+0.06y=0.05(500) -------> equation A

and

x+y=500 -----> x=500-y ------> equation B

solve the system of equations

substitute equation B in equation A

0.035(500-y)+0.06y=0.05(500)

solve for y

17.5-0.035y+0.06y=25

0.025y=25-17.5

0.025y=7.5

y=300

Find out the value of x

x=500-300=200

therefore

Answer:

  y = -7/8x -2

Step-by-step explanation:

You want the slope-intercept equation of the line through the points (8, -9) and (0, -2).

The slope of the line through points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope of the line is ...

  m = (-2 -(-9))/(0 -8) = -7/8

The y-intercept of the line is the y-value when x = 0. The point (0, -2) tells you the y-intercept is -2.

The slope-intercept equation is ...

  y = mx +b . . . . . . where m is the slope, and b is the y-intercept

For a slope of -7/8 and a y-intercept of -2, the equation is ...

  y = -7/8x -2

Answer: 80

Step-by-step explanation:

You do 2 times= 8 and multiply 8 to the 5 white and black tiles which equals 40+40=80.

The total area for the parallelogram shaped tiles Felix needs to buy is 80cm² at the price of $40.

In calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.

Given that, the base of one parallelogram shaped tile is 4cm with height as 2cm.

Area of one parallelogram shaped tile = 4cm × 2cm

Area of one parallelogram shaped tile = 8cm²

Total area for the 5black and 5white tiles = 10 × 8cm²

Total area for the 5black and 5white tiles = 80cm²

Therefore, Felix needs to buy a total of 80cm² of 10 parallelogram shaped tiles.

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ANSWER

A. x ≥ -5 and x < 4

EXPLANATION

We have the two inequalities:

- 4x + 1 ≤ 21 and 5x + 2 < 22

Let us solve them separately:

FIRST ONE

-4x + 1 ≤ 21

Collect like terms:

-4x ≤ 21 - 1

-4x ≤ 20

Divide through by -4, the sign changes:

SECOND ONE

5x + 2 < 22

Collect like terms:

5x < 22 - 2

5x < 20

Divide through by 5:

x < 20 / 5

x < 4

The answer is Option A.

Answer:

No

Step-by-step explanation:

In order to solve this, we plug in the values for x and y. Remember that x = -1 and y = -9

-9 = 7 - 2(-1)

-9 = 7 + 2

-9 ≠ 9

We need to examine each expression at a time.

(A) x^2 + x - 6

notice the -6 has factors 3 and -2 which could be used to reverse the FOIL method:

x^2 + x - 6 = x^2 + 3 x - 2 x - 6 = x( x + 3) - 2 (x + 3) = (x+ 3) (x - 2)

(B) In this cubic expression we cannot use the reverse FOIL to extract factors.

(C) 4 x^2 - 2 x + 1 We cannot reverse the FOIL property either.

(D) x^2 + 8 x + 12

We notice that 12 has factors 2 and 6 which can be used to factor out this expression as shown below:

x^2 + 2 x + 6 x + 12 = x (x + 2) + 6 (x + 2) = (x + 2) (x + 6)

Therefore we were able to use the reverse of the FOIL property in expressions (A) and (D).

Answer:

5/3

Step-by-step explanation:

rise over run

(8-3)/(3-0)

To reflect the figure, we have to draw the new vertex at the same distance from the line x = -4, the image below shows this reflection.

Notice that the new figure has the same distance from x = -4 as the pre-image.

SOLUTION

In a photograph, a skyscraper measures 5.8 in, tall

The scale of the photo to the actual skyscraper is 1 : 245

That is 1 : 245 = 1 / 245 = 5. 8 / x

Cross- multiply we have:

1 X x = 5 . 8 X 245

x = 1421 inches in feet = 118.4167 feet

hello

to solve this question, we need to plot the graph of this equation

The rate at which the area of this square increases when the area of the square is 9 cm is 24 cm²/s.

The rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Mathematically, the area of a square can be calculated by using this formula;

A = s²

Where:

Next, we would determine the side length of a square by making s the subject of formula as follows:

A = s²

s = √A

s = √9

s = 3 cm.

By applying chain rule of differentiation, the rate of change (da/dt) in area of this square with respect to time is given by:

dA/dt = 2 × s(t) × ds/dt

dA/dt = 2 × 3 × 4

dA/dt = 24 cm²/s.

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Given the following question:

The principal wants to estimate the percentage of students in the school who play video games, which is a good number of students. Selecting 30 random students and asking them if they play video games can represent the entire school. Asking 30 random students keeps it from being biased for example option B, asking 30 students who take coding classes is biased because they are in one specific class, they do not represent the majority of the school unless the school is a coding school.

The answer is the first option because it is a random sample of people to represent a population of people. This keeps the results from being biased so asking 30 random students is the way to go.

Answer:

Please see the enclosed screenshot.

Step-by-step explanation:

Please see the enclosed screenshot.

IN THE PLACE OF x PLYG IN 4 AND SOLVE.

[tex]f(4) = - (4)^{2} - 8 \\ f(4) = - (16) - 8 \\ f(4) = - 16 - 8 \\ f(4) = - 24[/tex]

HOPE THIS HELPS

The number of bookshelves needed if each bookshelves contain 5 books is 10.

She has 47 books. . She wants to put them all on bookshelves.

Therefore, the number of bookshelves she will need if each shelf holds 5 books can be calculated as follows:

The total number of books she has in her possession is 47 books.

All the books must have a place in the bookshelves.

Each bookshelves can only contain 5 books.

Hence,

let

x = number of bookshelves

Therefore,  the equation to find the number of bookshelves is as follows:

5x = 47

divide both sides by 5

x = 47 / 5

x = 9.4

Therefore, Shiloh will require 10 book shelves.

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To find the slope of the line that passes through (9, 10) and (6, 12)

We will use the formula;

From the points given;

x₁ = 9 y₁=10

x₂ = 6 y₂=12

Substitute the values into the formula;

Evaluate;

Answer:

Solutions below.

Step-by-step explanation:

This question tests on the concept of graph reading.

To find the slope of a line, we have to use the following formula:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

Now, we can pick 2 random points on the line to substitute the values in to find the slope.

We will pick

(0, 3) as (x1, y1)

and

(2,0) as (x2, y2)

Therefore the slope will be:

[tex] \frac{0 - 3}{2 - 0} \\ = \frac{ - 3}{2} \\ = - \frac{3}{2} [/tex]

Now to find the y-intercept, as the name suggests, it is the point where the line intercepts the y-axis (vertical axis) , in this case, it is 3.

The point of this intercept is (0,3).

Answer:

Step-by-step explanation:

You want the slope and the y-intercept of the line shown in the graph.

The slope is the ratio of "rise" to "run". It is best found by identifying points on the graph where the line crosses grid intersections. The attachment shows two of those: (0, 3), (3, -2).

You can count grid squares or use the slope formula to find the slope.

  slope = rise/run = (y2 -y1)/(x2 -x1)

  slope = (-2 -3)/(3 -0)

  slope = -5/3

The y-intercept is the y-value of the point where the line crosses the y-axis. We have already found that to be 3, at one of the points used to find the slope.

  y-intercept = 3 . . . . point (0, 3)

__

Additional comment

The slope-intercept form equation for the line would be ...

  y = -5/3x +3

The standard-form equation would be ...

  5x +3y = 9

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Given:

A figure is given.

Required:

To find the area of the given figure.

Explanation:

The given figure is made up of three figures. So we will find the area of the three figures.

Area of square

Area of the triangle

Answer:

====================

Solve by substitution

Answer:7719

Step-by-step explanation:

The measure of angle TRS would be of 37º.

The vertices of the triangle can be attributed freely, hence we attribute as is in the drawing.

The altitude RT bisects the triangle forming a right angle, with R and T, hence the internal angles of the triangle TRS are as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle TSR can be found as follows:

43 + 90 + x = 180

133 + x = 180

x = 180 - 133

x = 47º -> m<TSR = 47º.

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Answer:

what is the problem text me

I can probably

Step-by-step explanation:

Basketball 12 votes; Soccer 24 votes; Football 24 votes

Here, we want to select the options that could represent the percentage

From what we have, soccer and football are same value and basketball is half of these

So the option where we have the given outline is the correct answer

Looking at the options, the only place we have the outline is;

Basketball 12 votes; Soccer 24 votes; Football 24 votes

⇒First step is to find the gradient

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} } \\m=\frac{8-(-3)}{-5-2} \\m=\frac{8+3}{-7} \\m=-\frac{11}{7}[/tex]

In the general equation y=mx+c let us find the value of c by plugging in the known values

I will use the point (-5,8) Note you can use any .You will get the same value of c.

[tex]8=-\frac{11}{7} (-5)+c\\8=\frac{55}{7} +c\\c=8-\frac{55}{7} \\c=\frac{1}{7}[/tex]

The equation now is:

[tex]y=-\frac{11}{7} x+\frac{1}{7}[/tex]

Problem

Which of the following equations represents a line that passes through the

points (-3, -14) and (0, –2)?

Solution

For this case we want to create an equation with this general form:

y= mx+b

We can calculate the slope with this operation:

And the intercept can be founded with the second point:

-2= 4(0)+b

b= -2

And the equation would be:

y= 4x -2

If we analyze the second option given we can see that we can write like this:

y-6 = 4(x-2)

y-6= 4x-8

y-6+8 =4x

y+2= 4x

y= 4x-2

So then the best option would be:

II. y-6 = 4(x-2)

The value of g(x) will be expressed as g(x) = (x + 5)

A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called as independent variable and output variable is called dependent variable. Composite functions are the functions which are written as combination of two functions. A function f(x) may be defined as composite function of another function g(x) when it can be written as either f(g(x)) or g(f(x)). We know that f(x) = x⁹ and the composite function H(x) = f(g(x)) = (x + 5)⁹. So, from this we can say that the function g(x) will be given as (x + 50 as we put (x + 5) as x in the function H(x).

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We have the function f(t) defined as:

We have to find f'(x).

We can solve this integral as:

If we derive this expression for f(x) we obtain:

NOTE: This expression could have been derived from the function inside the integral.

We can now find f'(3) as:

Answer:

f'(x) = x^4

f'(3) = 81

The distances that the footballs travel before hitting the ground is 50 yards.

For the given question;

The football is kicked by the player.

The second kick is modeled by f(x) = -0.051x(x - 50).

Where, f is the height (in yards) and x is the horizontal distance (in yards).

For calculating the distances that the footballs travel before hitting the ground, Put f(x) = 0.

As, the ball will reach the ground the height of ball above ground will be zero, thus f(x) = 0.

f(x) = -0.051x(x - 50) = 0

Simplifying;

-0.051x² + 2.25x = 0

Or, divide wole equation by x.

0.051x = 2.25

x = 50 yards.

Thus, the distances that the footballs travel before hitting the ground is 50 yards.

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The domain is

and the range

Then, the answer is d)