your company is producing special battery packs for the most popular toy during the holiday season. the life span of the battery pack is known to be normally distributed with a mean of 250 hours and a standard deviation of 20 hours. what is the probability that a randomly chosen battery pack lasts longer than 260 hours?

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)

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Step-by-step explanation:

(2x² + 3x+8) (x²-x-4)

= (2x² + 3x+8) (x² +-x²+-4)

= (2x²) (x²) + (2x²) (-x) + (2x²) (-4) +(3x) (x²) + (3x) (-x) + (3x) (-4) + (8) (x²) + (8) (-x) + (8) (-4)

= 2x⁴ - 2x³ -8x² + 3x³ -3x² - 12x + 8x² - 8x - 32

=2x⁴ + x³ - 3x² - 20x - 32

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

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

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

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.

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

120/25 = 4.8 minutes per question

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.

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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

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]

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].

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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

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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:

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:

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Answer: Hi this is neither.

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.

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 probability of selecting two students has 10 ways

Total number of students = 5

Only two students can be selected for the conference who are equally qualified.

The probability that the first two students selected alphabetically is derived from the combinations.

Therefore, the final probability for selecting the students randomly is,

x = ⁵C₂

x = [tex]\frac{5!}{2!*(5 - 2)!}[/tex]

x = 10

Hence, the probability of selecting two students has 10 ways.

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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: $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]

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.

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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 :)

Answer:

The items can be equally shared between 45 students.

Each student will get 3 pens, 5 books and 7 copies.

Step-by-step explanation:

We have to find the GCF (Greatest common factor) of 135 , 225 and 315.

          135 = 5 * 3 * 3 * 3 = 45 * 3

          225 =  5 * 5 * 3 * 3 = 45 * 5

          315 =  5 * 3 * 3 * 7 =  45 * 7

GCF = 5 * 9 = 45

The items can be equally shared between 45 students.

Each student will get 3 pens, 5 books and 7 copies.

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".

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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.

The total distance from his highest point to his lowest point is 21.8 feet.

Height H climbed by Zack and Zane is 14.6 feet.

The depth D underwater that Zack got down to is 6.8 feet.

The distance between the highest and the lowest point can be found by assuming the coordinates axis.

Let us assume the origin is on the water surface,

So, going by this logic, highest point is at +14.6 feet.

The lowest point is at -6.8 feet.

The distance L between lowest and highest point is,

L = H - D

L = 14.6 -(-6.8) feet

L = (14.6 + 6.8) feet

L = 21.8 feet

So the distance L is 21.8 feets.

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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.

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