In 2003, a school population was 1219. By 2009 the population had grown to 1987.
1) How much did the population grow between the year 2003 and 2009?
students
2) How long did it take the population to grow from 1219 students to 1987 students?
years
3) What is the average population growth per year?
P =
students/year
4) What was the population in the year 2000?
students
5) Find an equation for the population, P, of the school t years after 2000.
:
6) Using your equation, predict the population of the school in 2012.
students

Answer:

2nd answer option

Step-by-step explanation:

the domain is the interval or set of valid x values. the range is the same for valid y values.

so, what is the smallest x value we see in the functional graph ?

x = 0

there is no functional value for any x smaller than that.

and then the function goes on and on to the right in all eternity. that means it goes to infinity.

so, domain = [0, infinity)

please consider the round bracket at the end, because "infinity" is not a number.

now for the range and the y values.

in this case I start to ask for the largest y value.

y = 4

for no x value do we get a larger y value.

but it goes down and down in all eternity, going also to infinity, but -infinity (down is negative for y).

so, the range = (-infinity, 4]

"-infinity" is also not a number and therefore not included (hence the round bracket).

Answer:

  H.  99 ft²

Step-by-step explanation:

Area is proportional to the number of tiles.

The total area of the bathroom is 6×9 = 54 tiles. Of these, 12 are shaded. The proportion can be written as ...

  total area / shaded area = total tiles / shaded tiles

  total area / (22 ft²) = 54/12 . . . . . use given numbers

  total area = (22 ft²)×(54/12) = 99 ft² . . . . . multiply by 22 ft²

The total floor area of the bathroom is 99 square feet.

Answer:

134217728

Step-by-step explanation:

The geometric sequence formula is:

[tex]\displaystyle{a_n = a_1r^{n-1}}[/tex]

We know that [tex]\displaystyle{a_1=8}[/tex] and [tex]\displaystyle{r=2}[/tex], we also want to find the 25th term, substitute n = 25:

[tex]\displaystyle{a_{25}=8\cdot 2^{25-1}}\\\\\displaystyle{a_{25}=8\cdot 2^{24}}\\\\\displaystyle{a_{25}=134217728}[/tex]

Therefore, the 25th term of sequence is 134217728

Answer:

2/3 x - 5 < 11

2/3 x < 16 (add 5 to both sides)

x < 16 * 3/2 (multiply both sides by 3/2)

x < 24

Step-by-step explanation:

Answer:

it's

answer

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32.36

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Answer:

y-x-1 < 0

Step-by-step explanation:

according to the graph (0,1) and (-1,0) lies on the doted line,

equation of the dotted line is y-x-1=0

shaded region = y-x-1 < 0

Answer:

z=2

Step-by-step explanation:

We are given that a line has a slope of 3.

The line passes through the points (-10, z) and (-8, 8)

We want to find the value of z.

To do that, we can calculate the slope.

The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

Even though we already have 2 points, let's label their values to avoid any confusion.

[tex]x_1=-10\\y_1=z\\x_2=-8\\y_2=8[/tex]

Now substitute those values into the formula, and set it equal to 3. Remember that the formula uses subtraction.

[tex]\frac{8-z}{-8--10}[/tex] = 3

We can simplify this first.

[tex]\frac{8-z}{-8+10}[/tex] = 3

[tex]\frac{8-z}{2}[/tex] = 3

We can multiply both sides by 2 to clear the fraction and make it easier to calculate.

2([tex]\frac{8-z}{2}[/tex])  = 2(3)

Multiply.

8 - z = 6

Subtract 8 from both sides

-z = - 2

Multiply both sides by -1.

-1(-z) = -1(-2)

Multiply.

z = 2

The number of people that studied only one subject is 108.

A set is a collection of well-defined objects.

Objects in a set are called elements or members of a set.

Set notation or the use of Venn diagrams are the methods used to solve set problems.

Analysis:

let P = physics

C = chemistry

M = mathematics

n(P) = 70

n(C) = 46

n(M) = 100

n(M n P n C) = 18

n(M n P) = 30

n(M n P n C') = 30 - 18 = 12

n(M n C) = 28

n(M n C n P') = 28 - 18 = 10

n(P n C ) = 23

n(P n C n M') = 23 - 18 = 5

n(P n C' n M') = 70-(12+18+5) = 70 - 35 = 35

n(P' n C n M') = 46-(18+5+10) = 46-23 = 13

n(P' n C' n M) = 100 - (10+18+12) = 100 - 40 = 60

people that studied only one subject are = 35 + 13 + 60 = 108

In conclusion 108 students studied only one type of subject.

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By solving a system of equations we will see that the two-digit number is 84.

"The tens digit of a number is twice the ones digit"

"The sum of the digits is 12".

A two-digit number can be written as:

a*10 + b

Where a is the tens digit and b is the ones digit.

The word problem can then be written as:

a = 2*b

a + b = 12

So we have a system of equations.

To find the number we need to solve these, if we replace the first equation into the second one:

a + b = 12

(2b) + b = 12

3b = 12

b = 12/3 = 4

Then:

a = 2b = 2*4 = 8

So the two-digit number is 84.

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The true statements are:

The marked up price of chicken before 10pm is $6

The 50% mark down is taken off the marked up price

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Price after the mark up= (1 + mark up) x initial price

1.50 x 4 = $6

Price after the mark down = (1 - percentage mark down) x price after mark up

0.50 x $6 = $3

Here are the options:

The marked up price of chicken before 10pm is 6

The 50% mark down is taken off the marked up price

The chickens sell for $4 after 10pm

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[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]

[tex] \bold{ \blue{Answer:} \sf{x = \sqrt{2} - 3, - \sqrt{2 } - 3 }}[/tex]

[tex]\bold{Step \: \: by \: \: step \: \: explanation }[/tex]

1: The expression x² + 6x + 7 fits the form a x²+ bx + c Let's complete the square, where:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{a = 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf{ b = 6} \\ \sf{c = 7}[/tex]

2: Enter the constant k, which is 9 in our case.

[tex] \sf{x {}^{2} + 6x {}^{} + 9 - 9 + 7}[/tex]

3: Use Sum Square (a + b) ² = a² + 2ab + b².

[tex] \sf{(x + 3) {}^{2} - 9 + 7}[/tex]

4: Simplify

[tex] \sf{(x + 3) { }^{2} - 2}[/tex]

5: Substitute the above back into the original equation.

[tex] \sf{( x + 3) {}^{2} - 2 = 0}[/tex]

6: Add 22 to both sides.

[tex] \sf{(x + 3) {}^{2} = 2}[/tex]

7: Take the square root of both sides.

[tex] \sf{x + 3 = ± \sqrt{2}} [/tex]

8: Divide the problem into these 2 equations.

[tex]\sf{x + 3 = \sqrt{2} } \\ \: \: \: \: \: \sf{x + 3 = - \sqrt{2} }[/tex]

9: Solve the 1st equation:

[tex] \sf{ x + 3 = \sqrt{2} } \\ \sf{x = \sqrt{2} - 3 }[/tex]

10: Solve the 2nd equation.

[tex] \sf{ x + 3 = - \sqrt{2} } \\ \sf{x = - \sqrt{2} - 3 } [/tex]

11: Collect all the solutions.

[tex] \sf{x = \sqrt{2} - 3, - \sqrt{2} - 3 }[/tex]

I hope I've helped : )

Answer + Step-by-step explanation:

-2|x| = -6

⇔ 2|x| = 6

⇔ |x| = 3

⇔ x = 3  or  x = -3

The two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals

The conjugate of a radical is the value which when multiplied with the radical expression clears the radical. Conjugates have the same numbers but the opposite sign in the middle.

The given roots are

[tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex]

They have the same numbers but opposite signs in the middle.

Hence, the two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals

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Answer: Sorry If I'm wrong but if you are asking for the missing angle on the bottom, I think it is 30 degrees.

Step-by-step explanation: All the angles in a triangle add up to 180 degrees. we already know that one is 50 degrees. The 2nd angle is a bit wider than a 90 degree angle, and the third angle is 30 degrees, so 50 degrees + 100 degrees + 30 degrees add up to 180. So, I think your answer would be 30 degrees.

Answer:

x = 25

Step-by-step explanation:

I added a drawing down below to guide you through!

First, we should remember, that if a line crosses two parallel lines, then the adjacent angles will have the same value. Since Line D and Line E are parallel and line BC is crossing it, angles ABC and 105 will be the same.

Now that we know one of the missing angles, we can find x easily!

All angles in a triangle add up to 180, so in this case, the equation will be: 50 + 105 + x = 180.

155 + x = 180

x = 25.

So x will equal to 25 degrees!

The fraction of pizza each of her friends get if they split it evenly is 1/8

Number of pizza each friend gets = Quantity of pizza Elaine has ÷ Number of Elaine friends

= 5/8 ÷ 5

= 5/8 × 1/5

= (5 × 1) / (8 × 5)

= 5/40

= 1/8

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The mean is 87 and median is 86.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered from smallest to largest.

Given:

79, 91, 93, 85, 86, and 88

So,

79+85+86+88+91+93/6 = 87

and, the median

79, 85, 86, 88, 91, 93

median = 86

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Answer:

Step-by-step explanation:

can you show part a nd b for a better understanding of the question

Answer:

30 pupils

Step-by-step explanation:

first you divide 75 and 2.5 to get 30.

Answer:

30 prefer red

Step-by-step explanation:

Multiply the fraction by the number of students:

[tex]75(\frac{2}{5})=\frac{(75)(2)}{5} =\frac{150}{5} =30[/tex]

Hope this helps

Using proportions, it is found that the new minimum price you need to set for the remaining watercolor paintings in order to pay for the materials is of $2.89.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

To pay for the materials, you need to sell 18 paintings at $2.25 each, hence the total is:

T = 18 x 2.25 = $40.5.

If you lose four paintings, you will sell 14, and still need to make $40.5, hence the price will be of:

P = $40.5/14 = $2.89.

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Answer:

-2

Step-by-step explanation:

you will group the like terms and add and subtract the remaining digits

Using it's concept, it is found that the period of the function is of 20 units.

The period of a function is given by the distance between it's repetitions.

Looking at the graph, the distance between the repetitions is of 20 units, which is the period of the function.

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Answer:

D

Step-by-step explanation:

Let's start by crossing everything out!

12/3 can be crossed out to 4.

a^3/a^2 can be crossed out to a.

b^6/b^4 can be crossed out into b^2.

c^5/c^5 is just 1.

So which the results we got, we can multiply them, so that it is 4ab^2.

4ab^2 is our final answer!

Answer:

(z+2)(z+3)(x-8)

Step-by-step explanation:

z² + 5z + 6 can be factored into (z+3)(z+2)

zx + 2x − 8z-16 can be factored into (x-8)(z+2)

the LCM would be (z+2)(z+3)(x-8)

if you were to multiply the two expressions together, you would multiply (z+2)^2, which is not necessary for LCM, which is why you factor them first

Answer:

523.6

Step-by-step explanation:

Volume of sphere= 4/3πr^3

V=4/3π(5^3)

V=523.6 (correct to 1 dp)

Considering the volume of the rectangular prism, you will need 2240 bags will be needed for the patio.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, the dimensions are:

l = 14 ft, w = 12 ft, h = 8 ft.

Hence the volume is:

V = 14 x 12 x 8 = 1344 ft³

Each bag yields 0.6 ft³, hence the number of bags is:

n = 1344/0.6 = 2240 bags.

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A. The exponential growth function that models the data is: [tex]A(t) = 5.89{0.0106t}[/tex]

B. Using the function, the population will be 11 million by 2059.

The function is given by:

[tex]A(t) = A(0)e^{kt}[/tex]

In which:

Item a:

We have that:

A(0) = 5.89, A(50) = 10.

We use this to find k, hence:

[tex]A(t) = A(0)e^{kt}[/tex]

[tex]10 = 5.89e^{50k}[/tex]

[tex]e^{50k} = \frac{10}{5.89}[/tex]

[tex]\ln{e^{50k}} = \ln{\frac{10}{5.89}}[/tex]

[tex]50k = \ln{\frac{10}{5.89}}[/tex]

[tex]k = \frac{\ln{\frac{10}{5.89}}}{50}[/tex]

k = 0.0106.

Hence the equation is:

[tex]A(t) = 5.89{0.0106t}[/tex]

Item b:

We have to solve for t when A(t) = 11, hence:

[tex]A(t) = A(0)e^{kt}[/tex]

[tex]11 = 5.89e^{0.0106t}[/tex]

[tex]e^{0.0106t} = \frac{11}{5.89}[/tex]

[tex]\ln{e^{0.0106t}} = \ln{\frac{11}{5.89}}[/tex]

[tex]0.0106t = \ln{\frac{11}{5.89}}[/tex]

[tex]t = \frac{\ln{\frac{11}{5.89}}}{0.0106}[/tex]

t = 58.9

Rounding up, the population will be of 11 million in 2059.

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