Find the mean and population standar deviation for each data set.

Hours slept

The initial amount that was deposited by Clare is $725.

The equation for the amount of money in Clare's bank account after x months will be 725 + 175x

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let the amount deposited initially be x.

Based on the information, this will be illustrated as:

x + 175(10) = 2475

x + 1750 = 2475

Collect like terms

x = 2475 - 1750

x = 725

The initial amount is $725.

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The empty boxes of the numerators for the given rational expression is to be filled with 4x and 2 respectively.

Rational expression is a division of two polynomials. Which implies that the numerator and denominator of the fraction consists of polynomials.

To solve this, we will first factorise the expression of the denominator as follows;

x² - 9x + 8 = x² - 8x - x + 8

x² - 9x + 8 = x(x - 8) -1(x - 8)

x² - 9x + 8 = (x - 1)(x - 8)

Hence, we can rewrite the rational expression as:

(4x + 2)/[(x - 1)(x - 8)]

we can break the expression further by dividing each term of the numerator with the expression (x - 1)(x - 8) as follows;

(4x + 2)/[(x - 1)(x - 8] = [4x/(x - 1)(x - 8)] + [2/(x - 1)(x - 8)]

Therefore, 4x and 2 will be the appropriate values to be filled in the empty boxes equated to the rational expression.

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Based on the information provided about Arthur, we have the following:

In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate).

Distance simply refers to the amount of ground that is covered or travelled by a physical object (body) over a particular period of time and speed, irrespective of the physical object's direction, starting point, or ending point.

In conclusion, the distance covered by a physical object (body) over a particular period of time can be plotted by using a position-time graph as shown in the image attached below.

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Answer:

. The horizontal distance

Step-by-step explanation:

The vertical distance is

. The horizontal distance is

. So the slope can be represented by the ratio

. The ordered pair for the red point on the line is

. If we substitute the numbers from the ordered pair in for x and y in the ratio, it will equal

please help ill give brainly

.

Answer: 3x-4

Step-by-step explanation: First Simplify, add the numbers 2x-9+x+5=2x-4+x Then combine like terms, 2x-4+x= 3x-4

The inequality representing d, the total number of days is 76.5d + 24 ≤ 330

From the question, the given parameters are:

Charges per day = $76.50

Charges per mile = $0.06

This means that the equation that represents the total charges for d days is

Total = Charges per day x Number of days + Charges per mile x Number of miles

So, we have

Total = 76.5 x d + 0.06 x m

Where m represents the number of miles

From the question, we have

This means that

m = 400 and Total ≤ 330

So, we have

76.5 x d + 0.06 x 400 ≤ 330

Solve

76.5 x d + 24 ≤ 330

This gives

76.5d + 24 ≤ 330

Hence, the inequality that represents the scenario is 76.5d + 24 ≤ 330

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Answer:

17. s = 9

18. x = 8x^(½)

Step-by-step explanation:

s² - 7 = 74?

s² = 74 + 7

s² = 81

√(s²) = √(81)

s = 9

x² - 8x = 0

x² = 0 + 8x

x² = 8x

√(x²) = √(8x)

x = 8x^(½)

OR by factoring

x²−8x=0

x(x−8)=0

x=0 or x−8=0

x=0 or x=8

Given:

There is a density curve given in the question

Required:

We need to find for

Explanation:

Part a

We want to find P(X<1.6)

For this we just need to find the area below the curve until x=1.6, since we have a triangle we can do this:

Part b

For this case we want to find this probability:

P(X>4.8)

and we can complement rule and we got

Final answer:

0.04

0.64

Answer:

1 answer

Step-by-step explanation:

when the terms are collected

[tex]4k = 0[/tex]

[tex]k = 0[/tex]

The minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.

Speed can be calculated as the ratio of distance traveled to the time taken.

Speed = distance /time

Also, Time = distance/ speed

In this case, the distance is 4 laps of 400 meters, so;

4 x 400=1600 meters

Speed = 250 per minute

Now,

Time =1600 meters /250 meter per minute

= 6,40 minutes is the same 6 minutes 24 seconds

Hence, the minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.

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The equation that has the same solution as x = 5 are as follows:

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

In other words, an equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The equation can be solved as follows:

The equation will have the same solution as x = 5.

Therefore,

25 / x + 4 = 9

subtract 4 from both sides of the equation

25 / x + 4 = 9

25 / x + 4 - 4 = 9 - 4

25 / x  = 5

cross multiply

5x = 25

divide both sides by 5

x = 25 / 5

x = 5

x / 5 +  5 = 6

x / 5 = 6 - 5

x / 5 = 1

cross multiply

x = 5

32 - 4x = 12

- 4x = 12 - 32

- 4x = - 20

divide both sides of the equations by - 4

x = -20 / - 4

x = 5

Therefore, the equation with same solution are 25 / x + 4 = 9, x / 5 +  5 = 6 and  32 - 4x = 12

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The expression to show the number of cookies that Cindy receive is 96/8 - c.

An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, 96 cookies were shared among 8 people and Cindy has c fewer cookies. This will be:

= 96/8 - c

This illustrates the concept of expression.

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Answer: x=2

Step-by-step explanation:

1. Distribute

2. Subtract 9 from both sides

3. Simplify

4. Subtract x from both sides

5. Simplify

6. Divide both sides by the same factor

7. Simplify

The Points are in the form (x,y), and they are A(-3,8) and B(5,-4).

The length between two points is:

In this case:

The correct anser is:

The least polynomial that contains the roots - 1 and 3 - i is x³ - 5 · x² + 4 · x + 10.

In this case we need to find a polynomial that contains a set of roots, a real root and a complex root. In accordace to the quadratic formula, the root 3 - i must be accompanied by its conjugate, that is, 3 + i to guarantee that all coefficients of the polynomial are real.

Then, the factor form of the cubic equation is:

f(x) = (x + 1) · (x - 3 + i) · (x - 3 - i)

f(x) = (x + 1) · [x² - (3 - i) · x - (3 + i) · x + (3 - i) · (3 + i)

f(x) = (x + 1) · (x² - 3 · x + i x - 3 · x - i x + 9 - i²)

f(x) = (x +1) · (x² - 6 · x + 10)

f(x) = x³ - 6 · x² + 10 · x + x² - 6 · x + 10

f(x) = x³ - 5 · x² + 4 · x + 10

The least polynomial is x³ - 5 · x² + 4 · x + 10.

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(1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375  and x+y ≤ 500 .

(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .

In the question ,

Part(1)

let the number of chocolates be "x" .

let the number of chocolates with covered almonds be "y"

price of each chocolate bar = $1.25

price of each chocolate covered almonds = $2

Beta club needs more than $375

So , according to the question

1.25x + 2y > 375

and also the students can sell up to 500 bars and covered almonds altogether.

So , x+y ≤ 500 .

Part(2)

Given , the club sells 100 chocolate bars.

substituting x= 100 in the inequality 1.25x + 2y > 375  , we get

1.25(100) + 2y > 375

125 + 2y > 375

2y > 375-125

2y > 250

y > 125

least number of chocolate covered almonds to be sold is 126 .

Therefore , (1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375  and x+y ≤ 500 .

(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .

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Answer:

9(x-4)-5x=

open brackets

9x-36-5x=0

relate with similar expressions

note,when negative crosses the equal sign,it becomes positive

9x-5x=36

4x=36

x=9

The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.

A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.

Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.

The answer is that point  is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.

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The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)

a) the independent variable is the: Number of month after the first year

b) the dependent variable is the: Amount remaining on the card

To solve this problem, we have to state the equation using the information of the problem.

Information about the problem:

Writing the equation according to the information gave, we have:

y = 25 - (2.50x)

Where:

The relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.

The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer:

Rewrite using the commutative property of multiplication.

2

(

2

x

0

y

2

)

−

3

y

x

3

Anything raised to

0

is

1

.

2

(

2

⋅

1

y

2

)

−

3

y

x

3

Multiply

2

by

1

.

2

(

2

y

2

)

−

3

y

x

3

Rewrite the expression using the negative exponent rule

b

−

n

=

1

b

n

.

2

1

(

2

y

2

)

3

y

x

3

Simplify the denominator.

Tap for more steps...

2

1

8

y

6

y

x

3

Simplify terms.

x

3

4

y

5

The equation of line is 11y + 3x + 37 = 0

What is Equation of Line ?

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

The given points are, (5, -6) and (-5, -2)

To find slope we have formula ,

m = (y2 - y1 ) / (x2 - x1)

where,

(x1, x2) = (5, -6) and,

(y1, y2) = (-5, -2)

Put the values in given formula of slope,

m = (-2 - (-5) ) / (-6 - 5)

m = (-2 + 5) / (-11)

m = - (3/11)

we get the slope, now to find the equation of line.

We know, the equation of the line with slope intercept is

y = mx + b

Now, for x and y value take any point and put it into this equation and find 'b'

let's take (-5, -2)

-2 = -(3/11) * -5 + b

-2 = 15/11 + b

-2 = (15 + 11b) / 11

-22 = 15 + 11b

-22 - 15 = 11b

-37 = 11b

b = -37/11

We got m = - 3/11 and b = -37/11

Now put these value in equation of line and form the equation

y = mx + b

y = -3/11 x - 37/11

11y = -3x - 37

3x + 11y + 37 = 0

Hence, the equation of line is 11y + 3x + 37 = 0

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When the mass is 500 grams and the volume is 40 cubic centimeters then density is 12.5 gm per cc.

When the mass is 125 grams and the volume is 1.4 cubic centimeters then density is 89.28 gm per cc.

The amount per unit of length, area, or volume as. a: a substance's mass per unit volume. b: the distribution of an amount (such as mass, electricity, or energy) per unit, typically of space.

D = M/V

a) M = 500 gms

V = 40 cubic cm

D = 500/40

D = 12.5 gm per cc

b) M = 125 gms

V = 1.4 cubic cm

D = 125/1.4

D =89.28 gm per cc

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Answer:

Step-by-step explanation:

Let's illustrate the situation in a diagram to understand.

In a right triangle if the altitude drawn divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.

Therefore,

The given expression is 3 x (5-2)-1

From the options

If Orlando has 5 actions figures.

He decides to give 2 of them to his younger brother, then he will have (5-2) action figures left

His parents were happy with him and tripled what he had left

3 x ( 5 -2 ) action figures.

If he had so many actions figures after that and he gave his brother 1 more action figure then he will have

3 x ( 5-2) - 1 action figures left.

The right answer is therefore option B

Let the smaller angle be

The larger angle is 4 times bigger than the smaller angle means

Concept:

The sum of two or more angles on a straight line is always 180°

Therefore,

By substituting the value of y=4x in the equation above, we will have

substitute the value of x= 36° in y=4x to find the value of the bigger angle

Hence,

The larger angle is =144 °

OPTION D IS THE CORRECT ANSWER

The distance between C and D is 17.26 units

What is meant by distance?

Distance is a numerical or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other factors in physics or common use (e.g. "two counties over"). Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between text strings) or a degree of separation (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such conceptions of measurement, both real and metaphorical.

Distance CD = √{(-9-8)² + (-6+3)²}

                      = √{(-17)² + (-3)²}

                      = √{289 + 9}

                      = √298

                      = 17.26 units

Hence, the distance between C and D is 17.26 units

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Answer: 17.3

Step-by-step explanation:

Answer:

1) 64 and 81

2) a(n) = (n + 2)^2, where n = 1, 2, 3, ...

3) a(25) = (25 + 2)^2 = 27^2 = 729

√2 and -√3 belong to the set of Irrational Numbers.

1 belong to the following sets:

• Rational

• Whole

• Natural

• Integers

0 belongs to the following sets:

• Rational

• Whole

• Integers

The age of Evelyn is 10.5 years finding by the properties of linear equation.

What is linear equation?

A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.

Let the age of James is x years.

The age of Evelyn is x - 2.5 years

Sum of age of Evelyn and James are x + x - 2.5 = 2x - 2.5

According to question,

2 x (2x - 2.5) = 57

=> 4x - 5 = 57

=> 4x = 57 - 5

=> 4x = 52

=> x = 52/4

=> x = 13

Age of James is 13 years and the age of Evelyn is 13 - 2.5 = 10.5 years.

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pls provide the picture below, because of that its an incomplete answer