A sample of 500 high schools in a state results in an average number of students per grade level of 178.6 students, with a margin of error of ±45.2. If there are 3250 high schools in the state, what is the estimated number of students per grade level?

between
and
students

Answer:

Step-by-step explanation:

V = πr²h

h = V/(πr²)

V = 42 gal

42 gal x 3.7854 l/gal = 158.987 l

158.987 l = 158,987 ml = 158,987 cm³

r = 18/2 = 9 in

9 in x 2.54 cm/in = 22.86 cm

h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm

depending on how you round, the more precise answer is 96.8285 ≈ 96.83

a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.

(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.

To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.

Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:

19 = 0.693 / k

k = 0.693 / 19

So the formula relating y to t is:

y = 45.1 * e^(-0.693/19 * t)

(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):

y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg

So, there will be approximately 30.1 mg of the substance present after 9 minutes.

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Answer:Therefore, f(-x) = -x^3 - 3x^2 - 2x + 2.

Step-by-step explanation:o find f(-x), we replace every instance of x in the function f(x) with -x:

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

Simplifying, we get:

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

[tex]f(2) = g(2) = 4[/tex], which means that the graphs of the two functions intersect at x = 2.

To show that the graphs of the functions   [tex]f(x) = 2^x[/tex] and [tex]g(x) = \sqrt(4x + 1) + 1[/tex]  intersect at the abscissa point x = 2, we need to show that both functions have the same value at  [tex]x = 2.[/tex]

First, we evaluate f(2):

[tex]f(2) = 2^2 = 4[/tex]

Next, we evaluate g(2):

[tex]g(2) = \sqrt(4(2) + 1) + 1 = \sqrt9 + 1 = 4[/tex]

Therefore,  [tex]f(2) = g(2) = 4[/tex] , which means that the graphs of the two functions intersect at [tex]x = 2[/tex] .

To visualize this, we can plot the two functions on the same set of axes:

As we can see from the graph, the two curves intersect at the point (2, 4).

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The complete question is: How can you show that the graphs of the functions f(x) = [tex]2^x[/tex] and g(x) = √(4x + 1) + 1 intersect?

Answer: w(t) = 60 * 4^(t-1).

Step-by-step explanation:

The given ordered pairs model an exponential function of the form w(t) = ab^t, where w is the function name, t is the input variable, a is the initial value, and b is the growth factor.

From the first ordered pair (1, 60), we can see that the initial value a is 60. From the second and third ordered pairs (2, 240) and (3, 960), we can see that the output value is multiplied by 4 when the input value increases by 1. This means that the growth factor b is 4.

So, the function equation in sequence notation is w(t) = 60 * 4^(t-1).

The inequality can be solved to get x < 2, the graph is on the image at the end.

Here we have the inequality.

x + 5 < 7

To solve this, we need to isolate the variable, subtracting 5 in both sides we will get.

x < 7 - 5

x < 2

The graph of this inequality will be a number line with an open circle at x = 2, and an arrow that extends to the left side (because x is smaller than 2)

Then we will get the graph that you can see in the image at the end.

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Answer:

-4x+19

Step-by-step explanation:

Otherwise known as option B :D

Answer:

x=28

Step-by-step explanation:

solve for x by simplifying both sides of the equation, then isolating the variable.

have a good day :)

Answer

x=3 1/9

Step-by-step explanation:

a) over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.

b) the average temperature of the water in the system is 1527.

c) over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.

a) g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt

g'(-3) = -2

b) The absolute maximum value of g on the closed interval [-5, 5]=

10 + 2√7.

c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.

What is right Riemann sum formula?

The right Riemann sum formula uses the right-most value of each interval as the value of the function over that interval.

a) g(5) = 2(5) + [tex]\int\limits^5_0[/tex] ƒ(t) dt

= 10 + 2√7

g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt

g'(-3) = 2 + [tex]\int\limits^3_0[/tex]ƒ'(t) dt

= 2 - (4 + 0)

= -2

b) The absolute maximum value of g on the closed interval [-5, 5]=

10 + 2√7.

This is because the highest value of ƒ(t) dt on the interval= 4√7, which occurs at x = 2.

The highest value of g is thus given by 10 + 2√7.

c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.

This is because ƒ'(t) dt is undefined at these points, so the second derivative of g is also undefined.

a) To evaluate the  S'(t) dt, we need to calculate the area under the curve of the temperature data given in the table. To do this, we use the trapezoidal rule. This gives us the following:

[tex]\int\limits^10_0[/tex] S'(t) dt = [(142 + 210 + 254 + 280 + 274 + 268)/2] × 8

= 17,088

This means that over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.

This can be interpreted in the context of the problem as the average rate at which the temperature of the water in the solar steam power system is changing over the given time interval.

b) To approximate the average temperature of the water in the system using a right Riemann approximation, we need to calculate the area under the curve of the temperature data given in the table. We can do this using the right Riemann sum formula, which gives us the following:

Right Riemann Approximation = [(210 + 254 + 280 + 274)/4] × 6 = 1527

In this case, the right-most value of each interval is lower than the true average over that interval, so the approximation will be lower than the true average.

c) To determine the total change in the temperature of the system for the interval 10≤t≤20, we need to calculate the area under the curve of the equation S'(t)=-√2xe (√x²-100)/x.

This can be done using the definite integral of the equation, which gives us the following:

Total Change = ∫1020-√2xe (√x²-100)/x dx

= -14,351

This means that over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.

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Answer:

A = 5

B = 4

C = 8

D = 3

Step-by-step explanation:

This is more of a visual calculation so I can't really explain much about it other than that you match up the side in the prism with the side in the net

Answer: 108

Step-by-step explanation:

If you turn the shape, where the pointy side of the ramp is facing you and you flipped it open and laid out the sides,  that's the "net" image on right

A =  5   the long side of that triangle is also the short side of that rectangle

B = 3    it's the short side of the triangle

C = 8    long part of the rectangle

D =  4  long side of triangle

To find surface area.  Find the area of each of the shapes and add it all up

Top Rectangle:

A=Lw=C*A = 5*8 = 40

Middle Rectangle:

A=Lw = B*C =  3*8 = 24

Bottom Rectangle:

A=LW = 4*C = 4*8=32

Triangles are same

A=1/2 bh = 1/2 D*B = 1/2 * 4* 3 =6

But there are 2 of them so A=12

Now add all the shapes together

A(total)=40+24+32+12=108

Answer: 6s + 10n less than or equal to 90

The graph of the function g(x) has an equation of g(x) = 6√(x - 3)

From the question, we have the following parameters that can be used in our computation:

f(x) = 3√x

The transformed function g(x) is given as

g(x) = 2f (x − 3)

In f(x) = 3√x , we have

f(x - 3) = 3√(x - 3)

Multiply both sides by 2

So, we have

2f(x - 3) = 2 * 3√(x - 3)

Evaluate the products

2f(x - 3) = 6√(x - 3)

Recall that

g(x) = 2f (x − 3)

So, we have

g(x) = 6√(x - 3)

This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)

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Answer: I believe the only option would be Length.

The length determines the distance between the two endpoints.

I can't think of a reason why you'd need to use height or width when measuring a line on a graph. Besides if it were height, it'll just be the length of the line when vertical. And all generated graphed lines have the same width. You wouldn't need to measure it.

Hopefully it's correct.

The measure of angle JKM is 26°

The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the opposite angles in the triangle.

Also the sum of angle in a triangle is 180°

Therefore ;

3x+64 = 5x+4

collecting like terms

5x -3x = 64-4

2x = 60

x = 60/2

x = 30

since x = 30

value of the exterior angle = 5x+4

= 5×30+4

= 150+4 = 154

therefore angle JKM = 180-( 154)

= 26°

Therefore the measure of angle JKM is 26°

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Note that adding one pair does not make the table a function. This is why it is trickly. For the table to be a function, each value of x must be related to only one unique value of y and vice versa.

For the table to become a function, we must eliminate any repeated ordered pairs such as (3, 8) and (7, 8)

For example, we can say (3, 6) and (7, 8) then pick the last to be (5, 10)

So the table becomes a function when you have:

X    Y

6     0

3     6

9     12

7     8
5     10

The word linear function in mathematics refers to two separate but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

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The recursive formula for the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The first term of the sequence is given as follows:

[tex]a_1 = -\frac{1}{8}[/tex]

Each term is the previous term multiplied by two, hence the common ratio is given as follows:

q = 2.

Then each term is the previous term multiplied by two, and the recursive rule is given as follows:

[tex]a_n = 2a_{n - 1}[/tex]

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The perimeter of the composite figure is 46 metres.

The perimeter of a figure is the sum of the whole sides of the 2 dimensional figure. Therefore, the perimeter of the composite figure is the sum of the whole sides.

Therefore, the perimeter of the figure can be found as follows:

perimeter of the shape = 5 + 6 + 9 + 11 + 3 + 12

perimeter of the shape = 11 + 9 + 11 + 15

perimeter of the shape =20 + 11 + 15

perimeter of the shape = 31 + 15

perimeter of the shape = 46 metres

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Answer:

A trainee requires 3 days of training before they can assemble 9 heaters.

Step-by-step explanation:

We are given the formula for the number of water heaters h that a trainee can assemble per 8-hour shift as:

h = 2.1 0.9t + 4

where t is the number of days of training the trainee has received. We need to find out how many training days are required before a trainee can assemble 9 heaters. So we set h to 9 and solve for t:

9 = 2.1 0.9t + 4

Subtracting 4 from both sides, we get:

5 = 2.1 0.9t

Dividing both sides by 2.1 0.9, we get:

t = (5 / (2.1 0.9))

Using a calculator, we get:

t ≈ 2.49

Rounding up to the nearest day, we get:

t = 3

Therefore, a trainee requires 3 days of training before they can assemble 9 heaters.

The value of the matrix 4G + 2F is [tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]

Matrices are an essential tool in mathematics and can be used to solve a variety of problems. In this case, we are given two matrices G and F, and we are asked to find the value of 4G + 2F.

To understand how to calculate the value of 4G + 2F, we first need to understand what it means to multiply a matrix by a scalar. When we multiply a matrix by a scalar, we simply multiply every element in the matrix by that scalar.

Now that we understand scalar multiplication, we can use it to find the value of 4G + 2F. We simply need to multiply each matrix by its respective scalar and then add the results element-wise.

[tex]4G = 4\begin{bmatrix}8 &-5 &8 &-2 &10 \\-6& -7&1 & 9& 2\\4&6 &3 &7 &5 \\-4 & -3& 0& -10& -9\end{bmatrix}= \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix}[/tex]

Now we have to find the value of 2[F]. that can be calculated as follows

[tex]2F = 2\begin{bmatrix}1 &8 &-2 &-5 &9 \\-9& 10&6 &-3&0\\4&5 &-4 &3 &7 \\2 &-10&-6 & -1& -8\end{bmatrix}= \begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]

Now we can add the two matrices element-wise to get the final result:

[tex]4G + 2F = \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix} +\begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]

[tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]

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To the nearest mile, the distance that Marcus ran is 6 miles.

To calculate the total distance that Marcus ran in the morning, we will sum up the distance for all the routes that he ran.

From the map, the distances that Marcus ran are as follows:

1 inches + 3 inches + 2 inches + 3 inches

= 8.3 inches

The scale then shows that 4 inches equal 3 miles. Now, we convert 8.3 inches to miles and this gives us:

8.3 inches × 3 miles/4 inches

= 6.225

To the nearest miles, this is 6 miles.

Complete Question:

Marcus looked up the path that he had taken on his run this morning on the map shown below.

To the nearest mile, what is the total distance that he ran?

6 miles

8 miles

11 miles

25 miles

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The value of the product of -4  row one and row 3 is [90    -9     -1]

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or expression.

The given matrix is

[tex]\left[\begin{array}{ccc}1&2&1\\0&4&-2\\4&-1&6\end{array}\right] \left[\begin{array}{ccc}-5&\\3\\-8&\end{array}\right][/tex]

the product is given as

-4[1    2    1]  + [4    -1     3]

= [ -4 -8   -4]   +  [  4   -1    3]

= [90    -9     -1]

The sum of the product is [90    -9     -1]

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Answer:

Triangle P has been rotated clockwise by 90° about the point (0,0).

PLEASE MARK IT THE BRAINLIEST!!!!

Answer:   is d

Step-by-step explanation:

well it is just     3 times 3 times 3 times 3

Answer:

30%

Step-by-step explanation:

Answer: According to the problem, N Heracio used the computer for 40 hours last week. We are asked to find the difference between the time spent on shopping online and doing homework.

To do this, we first need to find the amount of time spent on each activity. We can do this by multiplying the total computer time by the percentage of time spent on each activity:

Time spent on videos = 10% of 40 hours = 4 hours

Time spent on homework = 15% of 40 hours = 6 hours

Time spent on games = 20% of 40 hours = 8 hours

Time spent on social media = 25% of 40 hours = 10 hours

Time spent on shopping online = 20% of 40 hours = 8 hours

Therefore, Heracio spent 6 hours on homework and 8 hours on shopping online.

The difference between these two amounts is:

6 hours - 8 hours = -2 hours

This means that Heracio spent 2 hours more on shopping online than on doing homework.

Step-by-step explanation:

Answer: 16 pounds

Step-by-step explanation:

12/3=4 and 4x4=16

The solution to the system of equations y=-3x+5 and 2x+y=6 is (x,y) = (-1,8).

To solve the system of equations using substitution, we can substitute the expression for y in the second equation with the expression for y in the first equation:

2x + y = 6

2x + (-3x + 5) = 6 (substitute y = -3x + 5)

2x - 3x + 5 = 6

-x + 5 = 6

-x = 1

x = -1

Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y:

y = -3x + 5

y = -3(-1) + 5

y = 8

We can check our solution by verifying that it satisfies both equations:

y = -3x + 5 => 8 = -3(-1) + 5 => 8 = 8 (true)

2x + y = 6 => 2(-1) + 8 = 6 => 6 = 6 (true)

Thus, our solution is correct.

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