There are 5 fourth-grade classes at Lincoln School. The table below shows the number of students in each class. Which is the median number of students per class?
23
24
25
26

Steph, let's recall that composite function is a function that depends on another function. A composite function is created when one function is substituted into another function.

Given f(x) = x +3, g(x) = x - 3

• f (g(x)) = f (x - 3)

• (x - 3) + 3

• x - 3 + 3

• x

• g (f(x)) = g (x + 3)

• (x + 3) - 3

• x + 3 - 3

• x

For the given functions, f (g(x)) = g (f(x))

Student became unresponsive, no final interaction

the probability of y1 being less than 1 is 1, regardless of the actual value of y1. P(y1 < 1) = 1

Since y1 and y2 are both uniformly distributed on the interval (0,1), this means that all possible values of y1 and y2 are equally likely. Therefore, the probability of y1 being less than 1 is 1, since any value of y1 between 0 and 1 has the same probability of occurring. This means that the probability of y1 being less than 1 is 1.

Since y1 and y2 are both uniformly distributed on the interval (0,1), this means that all possible values of y1 and y2 between 0 and 1 are equally likely to occur. This means that the probability of y1 being less than 1 is the same as the probability of y1 being equal to any value between 0 and 1. Since this probability is the same for all possible values of y1, the probability of y1 being less than 1 is 1, regardless of the actual value of y1. This is because any value of y1 between 0 and 1 has the same probability of occurring, meaning that the probability of y1 being less than 1 is 1.

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Answer:

No.

Step-by-step explanation:

7=8-(-3)

7=8+3

7≠11

Answer:

The answer is 1/2

Step-by-step explanation:

3 and 6 are the known sides of the triangle as you can see three is half of six making it a 1/2 dilation

\(\dfrac{6}{3} = 2\)

the scale factor is

1 : 2

Answer:

$400

Step-by-step explanation:

Saturday: $1600, 4 times the amount of Friday

Friday: 1/4 the amount of Saturday

Friday: 1/4 * $1600 = $400

a) Positive correlation. b) Slope = 0.02, Intercept = 3.17; rate increases ~2%/yr, starting at 3.17%. c) Predicts interest rate of 5.17% in 2000.

a) The correlation between rate and year can be determined by constructing a scatter plot. From the given plot, we can see that there is a positive correlation between the two variables, meaning that as the year increases, the rate increases as well.

b) The regression model fit to the data provides the slope and intercept of the line of best fit. The slope is 0.02, which means that the rate is increasing by 0.02% per year. The intercept is 3.17, which means that the interest rate starts at 3.17% in 1950.

c) The model predicts that the interest rate in the year 2000 will be 5.17%. This can be calculated by plugging in 2000 for the year in the model equation (Rate = 0.02*Year + 3.17).

d) In summary, the regression model fit to the data shows that on average, interest rates during this period increased by about 0.02% per year, starting from an interest rate of about 3.17% in 1950. The model predicts that the interest rate in the year 2000 will be 5.17%.

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Answer:

x = -2

Step-by-step explanation:

The line passing through the points (-2, -10) and (-2, -5) is a vertical line because both points have the same x-coordinate (-2).

Therefore, the equation of the line is simple:

x = -2

This means that for any value of y, the corresponding value of x is always -2. Visually, this line looks like a straight vertical line passing through the point (-2, -10) and (-2, -5) on the coordinate plane.

Answer:

Step-by-step explanation:

Answer: 0.25

Step-by-step explanation:

The relative frequency of the customers that buy computers is equal to the number of customers that bought a computer divided the total number of customers that entered the shop.

p = 25/100 = 0.25

If we take this as the probability, then the probability that the next customer that enters the shop buys a computer is 0.25 or 25%

Answer:

Step-by-step explanation:

The top is rectangular pyramid

The second a sphere

The third is a cube

Triangular pyramid is the last

The required number of nickels and dimes is given as 12 and 9 respectively.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given a system of the equation,
n + d = 21
n = 21 - d - - - - - (1)
0.05n + 0.10d = 1.50 -----(2)
Substitute n in the above equation,
0.05[21 - d] + 0.10d = 1.50
1.05 - 0.05d + 0.10 d = 1.50
0.05d = 0.45
d = 0.45/0.05
d = 9
Now, put d in equation 1,
n = 21 - 9
n = 12

Thus, the required number of nickels and dimes is given as 12 and 9 respectively.

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Answer:25.45

Step-by-step explanation:

52936/1 year x 1 year/52 weeks x 1 week/40hours

It could be 1:1 or 2:1 if you dont give them more than 1 apple and save some

Step-by-step explanation:

Answer: -4x^2 + 8xy - 20y^2 + 12

Step-by-step explanation:

-4 (x2 - 2xy + 5y2 - 3)

-4(x^2) = -4x^2

-4(-2xy) = 8xy

-4(5y^2) = -20y^2

-4(-3) = 12

Answer:

Step-by-step explanation:

20/2 + 5/2 = 25/2 = 12 1/2

Answer:

A: 3/5 + 2/5 = 5/5

A: 3/5 + 1/5 = 4/5

B: 3/5 - 2/5 = 1/5

B: 3/5 - 1/5 = 2/5

C: 3/5 x 2/5 = 6/25

C: 3/5 x 1/5 = 3/25

C: 2/5 x 1/5 = 2/25

D: 1/2 + 1/4 = 3/4

D: 4/5 + 4/10 = 6/5

E: 4/6 ÷ 2/6 = 2

E: 1/6 ÷ 1/6 = 1

Step-by-step explanation:

Answer:

\(\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}\)

Step-by-step explanation:

We need to find 9 rational number between \(\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}\)

We make the denominators of both fractions same. So,

\(\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}\)

and

\(\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}\)

The rational number are:

\(\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}\)

Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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JB is a median

CI is a median

JW=6x+2

JB=10x+1

If W is the centeroidof the triangle, determined by medians JB, CI and KA, it means that it cuts both line segments following the ratio 2:1 → meaning that the segment JW is 2/3 of the segment JB while the segment WB is 1/3 of JB.

This means that the ratio between segments JW and JB is as follows:

Replece it with the given expressions:

Use cross multiplication between both fractions:

And finally solve for x

The unknown value is x=2

Now you can calculate the length of segment JW as:

The length of segment JW is 14 units.

Answer:

They are equal

Step-by-step explanation:

12 inches is equal to 1 foot. 7 feet is equal to 12x7 which is equal to 84. Therefore, they are the same.

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Both numbers 7 feet or 84 inches are equal.

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

Two numbers are,

⇒ 7 feet and 84 inches

We know that;

⇒ 1 feet = 12 inches

Hence, We get;

7 feet = 12 × 7 inches

         = 84 inches

Therefore, Both numbers 7 feet or 84 inches are equal.

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Answer:

C. Your time will increase

Step-by-step explanation:

Since r= d/t, then if you increase d, t will decrease since r is staying the same

Answer:

Profit =  $6,922.1

Step-by-step explanation:

Total weight of pecans = 950 kg

1 kg = 1000g

Total weight of pecans in gram = 950 *1000 g = 950,000 g

Note : we have calculated weight in gram as later in question weight of pecans in bag is given in gram so to make uniformity in unit of weight)

Given quantity one bag can store = 250 g

let there be x bag to store 950,000 g of pecan

weight of x bag = quantity one bag can store*x  = 250x (this will be equal to total weight of pecan as given)

250 x= 950,000 g

=> x = 950000/250 = 950*4 = 3800

Thus, there are 3800 bags.

Selling price for 1 bag = $1.90

Selling price for  3800 bag = $1.90*3800 = $7,220

we know profit = selling price - cost price

given cost price of 950 kg pecan = $297.90

Profit = $7,220 - $297.90 = $6,922.1 (answer)

The equation of a tangent line to the circle is, \(x^{2} +y^{2}\) = 34

Given that,

The equation of a tangent line to the circle with center = (3,6)

The line contains point = (-2,3)

For a circle or curve, the tangent is a line or line segment that touches the circle at one point only. For a circle, the tangent will be perpendicular to a radius drawn to the tangent point.

A tangent to a circle at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c

The equation of circle of radius r and center (h , k) is given by

\((x-h)^{2}\) + \((y-k)^{2}\) = \(r^{2}\)         (Equation-1)

And it is given that the center is (3,6) and it passes through (-2,3).

So values of h and k are (3,6) each and values of x and y are 2 and respectively .

Substituting these values in the equation, we will get

(h , k) = (3,6)

We can substitute h , k values in equation-1,

\((x-h)^{2}\) + \((y-k)^{2}\) = \(r^{2}\)  

\((x-3)^{2}\) + \((y-6)^{2}\) = \(r^{2}\)

Then we can substitute x , y values,

So,

We can write,

( x , y ) = (-2 , 3)

\((-2-3)^{2}\) + \((3-6)^{2}\) = \(r^{2}\)

\((-5)^{2}\) + \((-3)^{2}\) = \(r^{2}\)

25 + 9 = \(r^{2}\)

34 = \(r^{2}\)

Substituting the values of h, k and r, we will get

\(x^{2} +y^{2}\) = 34

Therefore,

The equation of a tangent line to the circle is, \(x^{2} +y^{2}\) = 34

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Answer:

3/6

Step-by-step explanation:

Answer:

0.31 if you get exactly 3 heads or 0.66 probability if you get at least 3 heads, or 50%

Step-by-step explanation:

0.31 is the probability of getting exactly 3 Heads in 6 tossed

0.66 is the probability of getting at least 3 heads

Answer: sure, with what though?

Step-by-step explanation:

The vertices of the feasible region are (0 , 15/2) , (21/11 , 19/11) and (6 , 0)

Given, the constraints of a problem

2x+3y≥12

5x+2y≥15

x ≥ 0

y ≥ 0​

On solving the equations, we get

( 2x + 3y ≥ 12 ) × 2

( 5x + 2y ≥ 15 ) × 3

4x + 6y ≥ 24

15x + 6y ≥ 45

On subtracting, we get

11x ≥ 21

x ≥ 21/11

x = 21/11

On putting the value of x, we get

42/11 + 3y = 12

y = 19/11

Hence, the vertices of the feasible region are (0 , 15/2) , (21/11 , 19/11) and (6 , 0)

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Answer:

First term = 64

Step-by-step explanation:

We are given the formula for the nth term of a geometric series to be;

S_n = (a1(1 - rⁿ))/(1 - r)

Where:

S_n is the sum of n terms

A1 is first term

r is common ratio

We are given;

S_112 = 256

r = ¾

Thus;

256 = a1(1 - ¾^(112))/(1 - ¾)

256 = a1(4)

a1 = 256/4

a1 = 64

Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

Answer:

(-5, 9)

Step-by-step explanation:

(-3-2, 2+7)= (-5,9)