When a new charter school opened in 2005, there were 350 students enrolled. Since then, the student population has
decreased by 100 students every two years.
Choose the formula below which gives the function N(t) representing the number of students attending the charter school
t years after 2005.
Select the correct answer below:
ON(t) = 100t + 350
ON(t)=-100t + 350
ON(t) = 50t + 350
ON(t) = -50t + 350
ON(t) = 350t + 100
ON(t) = -350t + 100

Answer:

Step-by-step explanation:

From the figure attached,

ΔABC has been dilated to form another triangle ΔA'B'C'.

Therefore, ΔA'B'C' is the image triangle of preimage ΔABC.

Coordinates of preimage ΔABC are,

A(3, 3), B(2, 0) and C(5, 2)

Coordinates of ΔA'B'C',

A'(6, 6), B'(0, 4) and C'(10, 4)

Since, dilation of a triangle is a similarity transformation which produces the  similar image of the preimage.

Rule for the dilation is,

(x, y) → (kx, ky)

Here, k = scale factor of dilation

By this rule,

A(3, 3) → A'(6, 6)

          → A'(2×3, 2×3)

Scale factor = 2

Therefore, "Triangle (ABC) is dilated by a scale factor 2 about the origin to form triangle (A'B'C') ".

Answer:

40

Step-by-step explanation:

Emma age: yE = 10 + x   (x is timeline)

Father age: yF = A + x (x is timeline, A is Father age today)

in time x1: Emma will be A years old, and Father will be 70 years old.

yE (x1) = 10 + x1 = A

yF (x1) = A + x1 = 70

System of equations with unknown values: x1 and A.

substract equation 1 - equation 2:

10 - A = A - 70 ⇒ 80 = 2A ⇒ A = 40

So, father is 40 years old now

Emma's father is 40 years old

Let the age of Emma father be y

Age of emma = 10 years

In x years time;

If in x1 years time, Emma will be y years old and his father will be 70 years old

Emma age: yE = 10 + x   (x is timeline)

Solving both equations simultaneously;

10 - y = y - 70

10+70 = y + y

80 = 2y

2y = 80

y = 80/2

y = 40 years

Hence Emma's father is 40 years old

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The family size has the lowest price compared to the family price per ounce which the amount is $0.21 / ounce.

To compare the box of cereal price we need to know the price per ounce first. It can be written as

Price per ounce = price /  total ounces

From the text above, we know that :

large size price = $3.34

large size ounces = 15

family size price = $5.14

family size ounces = 24

By substituting the parameter we can get the price per ounce of large size and family size

Large size

Price per ounce = price /  total ounces

Price per ounce = 3.34 / 15

Price per ounce = $0.22 / ounce

Family size

Price per ounce = price /  total ounces

Price per ounce = 5.14 / 24

Price per ounce = $0.21 / ounce

Hence, the family size has the lowest price compared to the family price per ounce which the amount is $0.21 / ounce.

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Answer:

Step-by-step explanation:

There are three 0s so it is 3

3.82 × 10^-3

The value of expression in scientific notation is,

⇒ 3.82 × 10⁻³

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The number is,

⇒ 0.00382

Now, We can write the number in scientific notation as;

⇒ 0.00382

⇒ 3.82 × 10⁻³

Thus, The value of expression in scientific notation is,

⇒ 3.82 × 10⁻³

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Answer: The Y intercept is 50 and it represents where the temperature starts.

Step-by-step explanation: The Y intercept is basically where the line is touching on the y line.

The length of the curve is:

\(=\frac{(68)^\frac{3}{2}-8 }{3}\)

Using the arc length formula in terms of polar coordinates \(\int\limits\sqrt{r^2+(\frac{dr}{d\theta})^2 }\)

To find the length of the curve we will use the formula:

\(\int\limits\sqrt{r^2+(\frac{dr}{d\theta})^2 }\)

Now, Let us put it in the expression:

\(r = \theta^2\\\\\frac{dr}{d\thera} =2\theta\)

Now the integral becomes:

\(=\int\limits^8_0 \sqrt{(\theta)^4+(2\theta)^2} \, d\theta\\ \\=\int\limits^8_0\theta \sqrt{(\theta)^2+4} \, d\theta\\\)

Now using the substitution method:

\(\theta^2+4=t\\\\2\thetad\theta=dt\\\\=\int\limits\frac{\sqrt{t}dt }{2}\\ \\=\frac{t^\frac{3}{2} }{3}\\ \\=\frac{(\theta^2+4)^\frac{3}{2} }{3}\)

Now, Let us plug in the values:

\(=\frac{(68)^\frac{3}{2}-8 }{3}\)

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The smallest value of 'n' that can be obtained by adding three consecutive numbers is 48.

By using Monte-Carlo simulations,

A large class of computational techniques known as "Monte Carlo procedures" or "Monte Carlo experiments" rely on repeated random sampling to get numerical results. The core idea is to leverage randomness to find solutions to issues that, in theory, may be deterministic.

16    22    10     7    28    13     1    19    25     4

7    10    25    13     4    28    16     1    19    22

16    10    22     7    13    28     1    19    25    4

(remember that the numbers are arranged in a circle, rather than the straight line shown here)

The underline number represent the smallest value for n that can be obtained by the summation of three consecutive numbers.

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The corporation should deposit $4,298.46 at the end of each month into the sinking fund.

The amount of interest earned over the life of the account is: $47,616.64.

The value of the fund after 2, 4, 6 are $56,243.62, $115,263.54, $178,155.28 respectively.

The interest earned during the second month of the 7th year is $317.13

To determine the amount that should be placed in the sinking fund at the end of each month, we can use the formula for present value of an annuity:

PV = R[(1-(1+i)^(-n))/i]

where:

PV = present value of the sinking fund

R = monthly deposit

i = monthly interest rate

n = number of months

We know that the sinking fund needs to have a future value of $460,000 in 8 years. If we assume monthly deposits and monthly compounding, we have:

PV = 0

FV = $460,000

i = 6.5%/12 = 0.00541667

n = 8 years * 12 months/year = 96 months

Using the formula, we can solve for R:

R = (FV*i)/((1+i)^n - 1) = ($460,000 * 0.00541667)/((1+0.00541667)^96 - 1) = $4,298.46

Therefore, the corporation should deposit $4,298.46 at the end of each month into the sinking fund.

To determine the amount of interest earned over the life of the account, we can subtract the total amount deposited from the total amount in the sinking fund at the end of 8 years:

Total amount deposited = $4,298.46/month * 96 months = $412,383.36

Total amount in sinking fund after 8 years = $460,000

Interest earned = $460,000 - $412,383.36 = $47,616.64

To determine the value of the fund after 2, 4, and 6 years, we can use the formula for future value of an annuity:

FV = R[((1+i)^n - 1)/i]

where:

FV = future value of the sinking fund

R = monthly deposit

i = monthly interest rate

n = number of months

After 2 years, we have:

FV = $4,298.46[((1+0.00541667)^(2*12)) - 1]/0.00541667 = $56,243.62

After 4 years, we have:

FV = $4,298.46[((1+0.00541667)^(4*12)) - 1]/0.00541667 = $115,263.54

After 6 years, we have:

FV = $4,298.46[((1+0.00541667)^(6*12)) - 1]/0.00541667 = $178,155.28

To determine the interest earned during the second month of the 7th year, we can first calculate the total amount in the sinking fund at the beginning of the 7th year:

FV = $4,298.46[((1+0.00541667)^(6*12)) - 1]/0.00541667 = $178,155.28

Then, we can calculate the amount of interest earned during the first month of the 7th year:

Interest earned = $178,155.28 * 0.00541667 = $964.11

Finally, we can calculate the amount of interest earned during the second month of the 7th year by subtracting the interest earned during the first month from the total interest earned during the 7th year:

Interest earned during second month = $47,616.64 * (0.065/12) - $964.11 = $317.13

Therefore, the interest earned during the second month of the 7th year is $317.13

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The measures of the smallest and the largest possible integral lengths of the third side of the triangle is 21 and 1 respectively

What is Triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

A side of a triangle must be always less than or equal to the sum of other two sides and greater than the difference of other two sides.

Say the required side is x.

So x<9+11 and x>9-11

So 20<x<2

So the smallest integer is 21 and the largest integer is 1

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The measures of the smallest and the largest possible integral lengths of the third side of the triangle is 21 and 1 respectively

What is Triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

A side of a triangle must be always less than or equal to the sum of other two sides and greater than the difference between the other two sides.

Say the required side is x.

So x<9+11 and x>9-11

So 20<x<2

So the smallest integer is 21 and the largest integer is 1

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Answer:

289π cm²

Step-by-step explanation:

Area = πr²

= π x (17)²

= 289π cm²

There will be  2850 of the 3000 random samples will contain the population mean.

If 95% confidence intervals are computed for each sample, it means that we expect approximately 95% of the intervals to contain the population mean.

In the case of 3000 random samples, we can estimate the number of intervals that will contain the population mean by multiplying 3000 by the percentage of intervals that are expected to contain the mean.

Approximately, 95% of the 3000 random samples will contain the population mean. So, the estimated number of intervals that will contain the population mean is:

Estimated number = 0.95 * 3000 = 2850

Therefore, approximately 2850 of the 3000 random samples will contain the population mean.

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Answer:

4.75 hours

Step-by-step explanation:

First you need to find the median of the two numbers. The fastest way to do it is to add 9.3 and 9.7 and divide by 2, which will give you 9.5. Since there's going to be two of them working, divide 9.5 by 2, and you get 4.75.

1/9.3 + 1/9.7 = 1/x

x=4.74789

If simplicity is to be applied,

rounded to tens: 0

rounded to ones: 5

rounded to tenths:4.7

rounded to hundreths:4.75

rounded to thosandths:4.748

Answer:

\(x=\frac{5\±i√203}{6}\)(the lanky a is a square root)

Step-by-step explanation:

I suppose the equation is \(3x^2-5x+19=0\)?

A good old quadratic equation! Back to the good old days when we are memorizing the formula...

\(x=\frac{-b\±√(b^2-4ac)}{2a}\)

(Yes that little lanky a is a square root)

\(x=\frac{-(-5)\±√((-5)^2-4(3)(19))}{2(3)} \\x=\frac{5\±√(25-228)}{6}\\x=\frac{5\±√-203}{6} \\x=\frac{5\±i√203}{6}\)

Since the discriminant is negative, there are no real solutions, but instead, we have complex solutions shown above.

Answer:

-11, -1, 0, 6/5, 1.25

Step-by-step explanation:

Answer:

we start from the lowest to the highest

-11, -1, 0, 6/5, 1.25

the slope is m equals 2/5.

the y intercept is (0,-4), the x intercept is (10,0).

the equation is linear.

the equation I believe is y= 2/5x - 4

Answer:

this is very easy.

Step-by-step explanation:

if he started at a temperature of 12, then added 8 and added 13 onto that? the sum of those numbers would be 33. so 33 degrees Celsius

Answer:

x = 3

Step-by-step explanation:

if the triangles are similar then the side lengths must be proportional:

8/6 = 4/x cross multiply expressions

8x = 24 divide both sides by 8

x = 3

The slope of the line containing BC is \(\frac{-1}{2}\).

Trapezium or Trapezoid is defined as a quadrilateral that have two parallel sides and two non-parallel sides.

Slope of a line is defined as tan(α) where α is the angle that line makes with positive x axis.

Two parallel lines have same slope.

In the given figure

right trapezoid ABCD , the lines BC and AD are parallel,

Hence they will have same slope.

Given line AD

\(y=\frac{-1}{2} x+10\)...…..(1)

On comparing (1) with the slope intercept form of the line

y=mx+c , where m = slope and c =y-intercept (where the graph crosses the y-axis)

we get \(m=\frac{-1}{2}\)

The slope of the line AD= -1/2  and since the line's AD and BC are parallel,

the slope of BC is also \(\frac{-1}{2}\).

Therefore , the slope of the line containing bc is  \(\frac{-1}{2}\).

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

16675514 Frog

Step-by-step explanation:

\(g(25)=14(1.75)^{25} =16675514\)

The question is not complete because it is not written correctly

Complete Question:

The drama club is holding auditions for five different parts in a one act play. If 9 people audition, how many ways can the roles be assigned?

a. 362,880

b. 15,120

c. 126

d. 120

Answer:

b. 15,120

Step-by-step explanation:

In other to solve the question above, we would use the formula for permutation.

This is because when assigning 5 DIFFERENT roles to 9 people, the order of assigning the roles is important. The formula for permutation, is used when order is involved.

Permutation (n, r) = nPr = n!/(n - r)!

In the above question,

n = 9 people

r = 5 different parts

9P5 = 9!/(9 - 5)!

= 9!/4! = 9×8×7×6×5×4×3×2×1/ 4×3×2×1

= 362880/ 24

= 15,120

Therefore, the number of ways that the roles can be assigned is 15,120 ways

Answer:

Table A

Step-by-step explanation:

If you do delta method (Change in y and x)

For example, 120-24

______ = 96/8

10-2

Then you divide both the numerator and denominator by the denominator (which is 8) and that gets us to 12 as our answer. Do the same method for all of the numbers in table A.

Ps: I hope that I was helpful, and you are welcome.

Given:  The given function is

\(f(x,y)=c(x-y)\)

To find: Here we need to find the value of c for which f(x,y) will be a joint

discrete probability density function.

Solution:

Now, to find c we have,

\(\int\limits^3_{-2} \,\int\limits^2_0 {f(x,y)} \, dx dy\\=\int\limits^3_{-2} \,\int\limits^2_0 {c(x-y)} \, dx dy\\\\=\int\limits^3_{-2} \,[2c-2cy]dy\\=10c-5c\\=5c\\The integral should be1.\\So, 5c=1\\\)

∴\(c=\frac{1}{5}\)

Therefore, the required value of c is 1/5.

Answer:

My awnser isss

Step-by-step explanation:

32% my homie

Answer:30%

Step-by-step explanation:

Discount = Original Price (X) discount (X) %/100

Discount = 310 × (30)/100

Discount = 310 x 0.3

You save = $93.00

The confidence interval for the mean usage of water is (18.7,20.5).

Given population standard deviation of 2.4, mean of 19.5 gallons per day and confidence interval of 98%.

We have to find the confidence interval for the mean usage of water.

To find out the confidence interval we have to first find margin of error.

μ=19.5

σ=2.4

α=0.98

α/2=0.49

We have to find the z value for the p value 0.49 which is z=2.33

Margin of error=z*μ/\(\sqrt{n}\)

=2.33*19.5/\(\sqrt{3034}\)

=0.82

lower level=mean -m

=19.5-0.82

=18.68

after rounding upto 1 decimal

=18.7

upper mean = mean+m

=19.5+0.82

=20.52

Hence the confidence interval for the usage of water is (18.7,20.52).

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The equation of the line that passes through the points (0,-2) and (3,2) is  4x-3y-6 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

In the given graph,

The points are (0,-2) and (3,2)

To find the equation of the line,

Find slope by using formula  m = (y₂-y₁)/(x₂-x₁)

m = (2-(-2))/(3-0)

m = 4/3

The equation of line is,

y-y₁ = m (x-x₁)

y-(-2) = 4/3(x-0)

y+2 = 4/3x

3y+6 = 4x

4x-3y-6 = 0

The required equation of line is 4x-3y-6 = 0.

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In British Columbia, Canada, the number y of purple martin nesting pairs x years since 2000 can be modeled by the equation y = 0.63x² +51.8x + 144 there were about 1000 nesting pairs around the time of year 2011.5.

To find when there were about 1000 nesting pairs, we need to solve the given equation for x.

y = 0.63x² +51.8x + 144

We substitute y = 1000 and solve for x:

1000 = 0.63x² +51.8x + 144

0.63x² + 51.8x - 856 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 0.63, b = 51.8, and c = -856.

x = (-51.8 ± sqrt(51.8² - 4(0.63)(-856))) / 2(0.63)

x ≈ -86.3 or x ≈ 11.5

Since we are interested in the time after 2000, we discard the negative solution and get:

x ≈ 11.5

This means that there were about 1000 nesting pairs approximately 11.5 years after 2000. To find the actual year, we add 11.5 to 2000:

2000 + 11.5 = 2011.5

Therefore, there were about 1000 nesting pairs around the time of  year 2011.5.

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