2.) The amount of sleep that elementary school children get per night follows a Normal distribution with a
mean of 9.5 hours and a standard deviation of 0.55 hours.
a.) Find the proportion of elementary school children who get between 9 and 10 hours of sleep per
night. Sketch the Normal curve and shade the area under the curve that is the answer to the
question.

The answers to both the subparts using the binomial theorem are shown:

Probability:

(A) Summation notations:

(B) Simplified terms of the expansion:

Therefore, the answers to both the subparts using the binomial theorem are shown:

To learn more about binomial theorem visit:

brainly.com/question/13672615

#SPJ13

Answer: x = 77 - 2y    y = -x/2 + (77/2)

Step-by-step explanation:

Step-by-step explanation:

slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

we have

2x + 3y = 15

3y = 15 - 2x

y = (-2/3)×x + 5

The linear function equation exists the slope-intercept form. A linear equation exists represented as: h(x) = mx + b  then [tex]$\mathbf{h}(\mathrm{x})=-\frac{1}{5} \mathrm{x}+3$\\[/tex].

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let the independent variable be x.

The value of the function at 0 is 3.

If h(0) = 3

When the independent variable decreases by 5, the independent variable increases by 1.

So, the slope (m) exists -1/5.

Where, m = -1/5 the slope

b = 3 - the y-intercept

A linear equation exists represented as: h(x) = mx + b then [tex]$\mathbf{h}(\mathrm{x})=-\frac{1}{5} \mathrm{x}+3$\\[/tex].

To learn more about linear functions refer to:

brainly.com/question/20286983

#SPJ13

After reflection across the line x = -2, point L(-6,2), M(-6,0), K(-1,3) and J(3,0) becomes L'(1,2), M'(1,0), K'(-3,3) and J'(-1,0)

The line x = -2 will be parallel to y-axis. Let us say that there is a general point A(a,b). If this point is reflected across the line x = -2 then the y coordinates should remain same for the reflected point but x coordinate will change.

The new x coordinate will be parallelly opposite to the initial point and also at the same distance from the line as the initial point

From the Figure, we can see,

The coordinates of,

The point L is (-6,2),            

The point M is (-6,0),

The point K is (-1,3) and,

The point J is (3,0).

After reflection across the line x = -2, the coordinates of,

The point L' is (1,2),      

The point M' is (1,0),

The point K' is (-3,3),    

The point J' is (-1,0)

To know more about Reflection across line, visit,

https://brainly.com/question/26642069

#SPJ1

Equivalent or not equivalent result for each pair of given expressions are as follow:

a.5x-7+3x and 3x-7 +5x is equivalent.

b. 4y +9 +3y and 3y + 9 + 4y is equivalent.

c. 6z -2z +4 and 4 +2z-6z is not equivalent.

As given in the question,

Each pair of given expressions are equivalent or not equivalent :

a. 5x-7+3x and 3x-7 +5x

5x-7+3x

=(5x +3x) -7

= 8x -7

3x-7 +5x

= (3x +5x) -7

= 8x -7

This pair is equivalent.

b. 4y +9 +3y and 3y + 9 + 4y

4y +9 +3y

=(4y+3y)+9

= 7y +9

3y + 9 + 4y

=(3y +4y) +9

= 7y +9

This pair is equivalent.

c. 6z -2z +4 and 4 +2z-6z

6z -2z +4

=4z + 4

4 +2z-6z

= 4 -4z

This pair is not equivalent.

Therefore, equivalent or not equivalent result for each pair of given expressions are as follow:

a.5x-7+3x and 3x-7 +5x is equivalent.

b. 4y +9 +3y and 3y + 9 + 4y is equivalent.

c. 6z -2z +4 and 4 +2z-6z is not equivalent.

Learn more about equivalent here

brainly.com/question/14672772

#SPJ1

a. Inadequate chlorine levels cause cloudy or creamy swimming pool water.

b. Even though water represents the most ample substance on the planet, it is rarely encountered in its pure form in nature.

Part a: Cloudy or milky pool water is ended up causing by seven major issues: insufficient chlorine, an imbalanced pH and alkalinity, extremely high calcium hardness (CH), a faulty or clogged filter, and the initial phases of algae, ammonia, as well as debris.

Methods for Cleaning Cloudy Pool Water

Part b: A swimming pool mixture of water as well as chlorine is made reference to as a homogenous mixture even though water and chlorine cannot be separated back to one‘s distinct materials once mixed together.

Because chlorine as well as water diffuse between each other, they cannot be kept separate into their pure forms again.

To know more about mixture, here

https://brainly.com/question/2331419

#SPJ13

Answer:

number is 3

Step-by-step explanation:

let n be the number , then 3 more than the number is n + 3 and six less than 4 times the number is 4n - 6 , so

4n - 6 = n + 3 ( subtract n from both sides )

3n - 6 = 3 ( add 6 to both sides )

3n = 9 ( divide both sides by 3 )

n = 3

the number is 3

If T = 1, then the number T2580 represents 2580 as the right answer. This is the basic rules of linear equation.

The first order of equations are linear equations. For lines in the coordinate system, linear equations are defined. It is referred to as a linear equation in one variable when the equation contains a homogeneous variable of degree 1 (i.e., only one variable).

There may be multiple variables in a linear equation. Linear equations in two variables, and so forth, are what the equation is known as if it contains two variables. 2x-3=0, 2y=8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are a few examples of linear equations.

The three forms of linear equations are

Learn more about linear equation

https://brainly.com/question/12788590

#SPJ9

Answer:

Step-by-step explanation:

Brandon takes 1/4 of a 24-hour period to read 1/3 of his book. At this rate, how many hours will it take Brandon to complete the book?

1/4 of 24 hours = 0.25 × 24 = 6 hours

so:

Brandon takes 6 hours to read 1/3 of his book. To read the full book, going at the same reading rate:

6 × 3 = 18

It takes Brandon 18 hours to read the book.

The slope-intercept form for this linear function is y = 8x + 47.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

From the linear function, we have:

Points on x-axis = (-3, 2).

Points on y-axis = (23, -17).

Substituting the given points into the formula, we have;

Slope, m = (-17 - 23)/(2 + 3)

Slope, m = -40/5

Slope, m = -8

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + c

Where:

At point (-3, 23), we have:

y = mx + c

23 = 8(-3) + c

23 = -24 + c

c = 23 + 24

c = 47

Therefore, the slope-intercept form is as follows:

y = mx + c

y = 8x + 47

Read more on slope-intercept form here: brainly.com/question/1884491

#SPJ1

Unit rate for the given expression 625 ft² in 2/3 hours is equal to

975ft² /hour.

As given in the question,

Given expression :

650 ft² in 2/3 hours

Unit rate for the given expression 625 ft² in 2/3 hours is equal to

In 2 /3 hours  = 650 ft²

Simplify the given expression for the unit rate

  1 hour = 650 / 2 / 3 ft² / hour

Multiply 650 to 3 and divide it by 2 we get,

   1 hour = ( 650× 3 ) / 2 ft² / hour

⇒ 1 hour = 1950 / 2 ft² / hour

⇒  1 hour = 975 ft²/hour

Therefore, unit rate for the given expression 625 ft² in 2/3 hours is equal to 975ft² /hour.

Learn more about unit rate here

brainly.com/question/11258929

#SPJ1

5 is in hundreds place and its place value is 500, 4 is in tens place and its place value is 40, 8 is in ones place and its place value is 8.

I hope this helps :)

The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12.

The number system is a way to represent or express numbers.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given sum of the mixed number,

1 1/4 + 4 2/3

⇒ 1 + 1/4 + 4 + 2/3

⇒ 1 + 4 + 1/4 + 2/3

⇒ 5 + 1/4 + 2/3

Take LCM of 1/4 and 2/3 as 12.

⇒ 5 + (3 + 8)/12

⇒ 5 + 11/12 = 5 11/12

Hence "The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12".

For more about the number system,

https://brainly.com/question/22046046

#SPJ1

A variable is a symbol and a stand-in for any mathematical object in mathematics.  A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable. Independent, dependent, and controlled variables are typically found in experiments. A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

The ladder's position would serve as an illustration.

Both 4x-2y=12 and -4x-9=54 are supplied to you. You are required to determine the ladder's order. But you didn't say which variable stands in for the ladder. I'll simply solve for both variables. I'll use the substitute strategy.

Let equations one and two be equivalent to 4x-2y=12 and -4x-9=54, respectively.

4x-2y=12

4x=12+2y

x=3+1/2y

Put this x in place of it in equation 2.

-4x-9y=54

-4(3+1/2y )-9y=54

Y=-6

X=3+1/2y = 3+1/2(-6) = 3+(-3) = 0 \s.

To learn more about variables refer to:

https://brainly.com/question/25223322

#SPJ13

For any function f(x), the average rate of change on the interval [x1,x2] is given by [f(x2) - f(x1)]/(x2-x1)

For f(-1) = 2.5 and f(3) = 40, the average rate of change on the interval [-1,3] is given by:

step 1 - (40 - 2.5)/[3-(-1)] = 37.5/4 = 9.375

step 2 - (37.5)/4

step 3 - Solving the fraction we find that the average rate of change is 9.375 (or 75/8)

Answer:

M = 7p - 147

Step-by-step explanation:

Nicole is selling wing plates to fund raise. She's selling the plates for $7 each. She spent $147 on the ingredients and package for the plates. Which equation represents M, her profit of money, after selling p plates of wings?​

profit - sales - cost of goods sold

where p = number of plates sold

M = 7p - 147

It took me 120 minutes to answer 25 questions. How long did each question take?

120/25 = 4.8 minutes per question

There are two more quarters than dimes and as many nickels as dimes and quarters together. The total amount of money is 3. 75 dollars, then nickels dimes and quarters are there each, D =7 dimes , Q =  9 quarters, and N  =  16 nickels

tart by defining the variables for this problem :

Q : number of quarters

D : number of dimes

N : number of nickels

There are two more quarters than dimes so the equation :

Q = D+2

And as many nickels, as quarters and dimes together so the equation :

N = Q+ D

The total amount of money is $3.75  so the equation :

0.25Q + 0.10D + 0.05N =3.75

Solve the following system :

Q = D + 2 (I)

N = Q + D (II)

0.25Q + 0.10D + 0.05N =3.75(III)

In the equation (II)  find Q in terms of N and D :

N = Q + D (II)

Q = N - D (IV)

If  use (I) in (IV) :

Q = N - D

D + 2 = N - D

2D = N - 2

N = 2D + 2 (V)

If use (I) and (V) in (III)

0.25Q + 0.10D + 0.05N =3.75

(0.25) . (D + 2) + 0.10D + (0.05) . (2D + 2) = 3.75

0.25D +0.50 + 0.10D + 0.1D + 0.1 = 3.75

0.45D = 3.75

D = 3.75/ 0.45

D = 7

if D = 7 -----------replacing in (I)

Q = D + 2

Q = 7 + 2

Q   = 9

If  replace this values in (II)

N = Q + D

N = 9 + 7

N = 16

there are D =7 dimes,

                 Q =  9 quarters

                  N  =  16 nickels

To learn more about Dollars visit:

brainly.com/question/28547396

#SPJ4

Answer: Hi this is neither.

The solutions for the inequalities are:

z < -6 or z > 3 and -9 ≤ x ≤9

We are asked to solve the inequalities given.

For the inequality 4z−5<−29 or 4z+3>15, we have to solve for z. i.e., find the value for z.

4z−5<−29 or 4z+3>15

⇒ 4z < -29 + 5 or 4z > 15 -3

⇒ 4z < -24 or 4z > 12

⇒ z < -24/4 or z > 12/4

⇒ z < -6 or z > 3

The solution for z are the values above 3 and less than -6.

For 8x+8 ≥ −64 and −7−8x ≥ −79, we need to solve for x.

8x+8 ≥ −64 and −7−8x ≥ −79

⇒ 8x ≥ -64 -8 and -8x ≥ -79 + 7

⇒ 8x ≥ -72 and -8x ≥ -72

⇒ x ≥ -72/8 and -x ≥ -72/8

⇒ x ≥ -9 and x ≤ 9

⇒ -9 ≤ x ≤9

The solution for x are between -9 and 9.

The question is not complete. The complete question is given below:

Solve the system of inequalities.

4z−5<−29 or 4z+3>15

8x+8≥−64 and −7−8x≥−79.

Learn more about solving inequalities at https://brainly.com/question/24372553

#SPJ1

Answer: [tex]-\frac{x^2}{4}[/tex]

Step-by-step explanation:

The graph of g(x) is the graph of f(x) reflected over the x-axis and horizontally stretched by a factor of 2.

So, the equation is [tex]g(x)=-(x/2)^2 =-\frac{x^2}{4}[/tex]

Answer:

53.998x

Step-by-step explanation:

9.31x  · 5.8

9.31 · 5.8x

=53.999x

We are trying to find the Least Common Multiple. This is a number that both 4 and 8 can be multiplied by a whole number to achieve, more specifically, the minimum of that list of numbers. This one is really simple. Since 8 is a multiple of 4 (4 x 2 = 8), the LCM is 8! (8 is also a multiple of 8 because 8 x 1 = 8).

So the answer is 8.

Answer:

Ages are as follows:
Father: 40

Mother: 37

Son: 11

Each twin daughter: 6

Step-by-step explanation:

Interesting puzzle!

Let

F denote the age of the father

M the age of the mother

S the age of the son

D the age of each of the twin daughters

Total of all ages is

F + M + S + 2D = 100  [1]

We also have

F + S = 51   ==>  S = 51- F    [2]

F - M = 3    ==>  M = F - 3    [3]

S - D = 5 ==> D = S -5  [4]

==> D = (51-F) -5  

==> D = 46 - F         [5]

Substitute this in equation [1] to get

We now have everyone's age in terms of the father's age F

Substituting each of equations [2], [3]  and [5] into [1] we get one equation in terms of F

F + (F-3) + (51-F) + 2(46-F) = 100

(F + F - F -2F ) + (-3 + 51 + 92) = 100

-F + 140 = 100

- F = 100 - 140

-F = -40

or

F = 40

From [3]

M = F - 3 = 40 - 3 = 37

From [2]

S = 51 - F = 51 - 40 = 11

From [4]

D = S - 5  = 11 - 5 = 6

Verify:

F + M + S + 2D = 40 + 37 + 11 + 2 x6 = 100

Step-by-step explanation:

a = father age

b = mother age

c = son age

d = daughters age

1. a + b + c + 2d = 100 (don't forget : twin-daughters)

2. a + c = 51

3. a = b + 3

4. d = c - 5

we need to transform the equations 2-4 to express 3 variables by the 4th, and then put that into the first equation and solve for that one variable.

once we have that, we can use again the equations 2-4 to solve for the other variables.

2. tells us that

c = 51 - a

3. tells us that

b = a - 3

4. and 2. tells us that

d = c - 5 = (51 - a) - 5 = 46 - a

with that we get in 1.

a + (a - 3) + (51 - a) + 2(46 - a) = 100

a + a - 3 + 51 - a + 92 - 2a = 100

2a - 3a + 48 + 92 = 100

-a + 140 = 100

-a = -40

a = 40

b = a - 3 = 40 - 3 = 37

c = 51 - a = 51 - 40 = 11

d = c - 5 = 11 - 5 = 6

so, the father is 40 years old

the mother is 37 years old

the son is 11 years old

both of the twin daughters are 6 years old.

Answer: $63

Step-by-step explanation:

If the electrician gains $18 an hour and works for 3 and a half hours, once you add the money for the total time up you will get $63.

$9 (for the 30 minutes) + $18 x 3 (for the 12-2 full working hours).

Hope this helps^^

[7th Grader]

Answer:

a = h/2 would be the answer.

Step;-

Find slope:-

m = rise/run = (16-8)/(8-4) = 8/4 = 2

Now,

y = mx + b

or, 8 = 2(4) + b

so, b = 0

So,

y = mx + b

or, h = 2a + 0

so, h = 2a

hence,a = h/2.

The sea sponges's height grows 2cm every 1 year, so you can write an equation to find the height at any age [tex]a = \frac{h}{2}[/tex]

Answer:

Part A: C. 3c - 2 = c + 22

Part B: The cat weighs 12 pounds, and the dog weighs 34 pounds.

Step-by-step explanation:

Create a system of equations:

d = 3c - 2, d = 22 + c

And substitute to get the answer to part A:

22 + c = 3c - 2

If you solve the system, you get d = 34 and c = 12 as the answer to part B.

The cat weighs 12 pounds, and the dog weighs 34 pounds.

Answer: The weight of the dog is 34 pounds and The weight of the cat is 12 pounds The answer should be B I think that's the answer

Step-by-step explanation:

Answer: y = x -7

Step-by-step explanation: -x + y = 5

y = x + 5

y = x + a

-5 = 2 + a

a = -7

y = x - 7