Evaluate. Write your answer as a whole number or as a simplified fraction.

Answer:

The range is 28

The variance is 90.855

The mean is 56.36

The median is 53

The sample standard deviation is 9.532

Step-by-step explanation:

Answer:

30.24%

Step-by-step explanation:

Each time you lose x%, you end up with 1 - 0.01x.

For example, if you lose 10% of an amount, you end up with 1 - 0.01(10), or 0.9 times the original amount.

Let's say you started with x.

You lost 10%. Now you have 0.9x.

Then you lost 20% of the remaining amount. Now you have 0.8(0.9x).

Then you lost 30% of the remaining amount. Now you have 0.7(0.8)(0.9x).

Finally you lost 40% of the remaining amount. Now you have 0.6(0.7)(0.8)(0.9x).

The final amount you have is

0.6(0.7)(0.8)(0.9x) = 0.3024x = 30.24% of x

Answer: 30.24%

In serving punch to guests at the party, Vinny can fill 9 guests' cups to the top based on this unit rate.

The unit rate is the ratio of a variable to another.

The whole number here is the total gallons of punch available to serve the guests.

The unit rate is the volume that each guest's cup can hold or contain.

This implies that the ratio is 5/64: 3/4

The total number of gallons of punch = 3/4 or 0.75 gallons.

The volume or capacity of each guest's cup = 5/64 gallons or 0.078125.

The number of guests' cups to fill to the brim = 9.6 cups (0.75/0.078125)

= 9 guests' cups.

Thus, Vinny can fill 9 guests' cups to the brim, using the given ratio or unit rate.

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Answer:

77.5

Step-by-step explanation:

180-25=155

155/2=77.5

Answer:

Answer down below!

Step-by-step explanation:

The set (1, 2, 3) would have 8 sets in total

The indicated numeric values for the composite functions are given as follows:

1. f(g(-3)) = -25.

2. g(f(2)) = -64.

3. h(f(-5)) = -3.

4. g(g(-3)) = -81.

The composite function of f(x) and g(x) is according to the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function. Hence, to calculate f(g(-3)), for example, we calculate g(-3), then we calculate the numeric value of function f(x) at x = g(-3).

For this problem, the functions are given as follows:

For item 1, the numeric values are found as follows:

For item 2, the numeric values are found as follows:

For item 3, the numeric values are found as follows:

For item 4, the numeric values are found as follows:

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The range of the function is 1

As seen by the graph in the following figure

As can be seen, x's value falls between

nonetheless, y is equal to 1 for all values of x.

This holds true regardless of x's value.

Consequently, the function's range is 1.

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Answer:

Positive, so the answer would be y=4/2 or 2. y=2x-4

Step-by-step explanation:

Slope formula y=mx+b

The mx is the rise/ over run

The b is the y-intercept

You can check in the end by checking so to see if the rise over the run is correct

Also, you can check the b by looking at the y-intercept, which is -4

Hope this helps!

Answer:

b Adding 4 to the parent function shifts the function up four units.

Step-by-step explanation:

The original function is y(x) = 2^x

Adding four is y(x) = 2^x + 4

We've simply told y to take whatever value is generated for x and add four to it.

So the new value for the same x would have 4 added to y:  (x,y+4),

Point (1,2) would shift to point (1,6).

Adding four to the parent function will shift the entire graph up by 4.  See ate attached graph.

The answer will de 10 bacterias

Answer: 1024

Step-by-step explanation: Since there's only 1 bacteria at first, we can just do 2^x. x being the amount of time divided by the amount of time between each time it doubles. Since the bacteria doubles every 2 seconds, and 20/2 = 10 we get 2^10 which is 1024.

Answer:

$390,000

Explanation

To do this, we will use the compound interest formula;

A = P(1+r)^t

P = 275000

rate r = 6%

Time t = 30years

Substitute

A = 275000(1+0.06)^30

A = 275000(1.06)^30

A = 275000(5.7435)

A = 1,579,460.07

For the rate of 5%

A = 275000(1+0.05)^30

A = 275000(1.05)^30

A = 275000(4.3219)

A = 1,188,534.15

Takeing their difference;

Difference = 1,579,460.07-1,188,534.15

Difference =390,925.92

Hence the approximate difference in his ending balance of the actual rate is 5% instead of six ​is about $390,000

The unknown angles are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.

Therefore,

∠1 = 110 degrees(given)

∠2 = 180 - 110 (sum of angles on a straight line)

∠2 = 70°

∠3 = ∠1 (vertically opposite angles)

Vertically opposite angles are congruent.

Therefore,

∠3 = 110°

∠2 = ∠4 (vertically opposite angles)

∠4 = 70°

∠1 = ∠5 (corresponding angles)

Corresponding angles are congruent

∠5 = 110°

∠6 = ∠4(alternate angles)

Alternate angles are congruent.

∠6 = 70°

∠1 = ∠7 (alternate exterior angles)

∠7 = 110°

∠2 = ∠8(alternate exterior angles)

∠8 = 70°

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Answer:

x = 58°

y = 74°

z = 106°

w = 42°

Step-by-step explanation:

  Finding the value of unknown variables:

  x + 32° = 90°

           x  = 90 - 32

          [tex]\sf \boxed{\bf x = 58^\circ}[/tex]

  x + y + 48 = 180  {Angle sum property of triangle}

 58 + y + 48 = 180

         y + 106 = 180

                  y = 180 - 106

                  [tex]\sf \boxed{\bf y = 74\°}[/tex]

y + z = 180  {Linear pair}

74 + z = 180

       z = 180 - 74

     [tex]\sf \boxed{\bf z = 106\°}[/tex]

32 +z + w = 180 {Angle sum property of triangle}

32 + 106 +w = 180

       138 + w = 180

                w = 180 - 138

              [tex]\sf \boxed{\bf w = 42\°}[/tex]

By using triangles laws, we know that the height of the tree is 8.42 meters.

So, 1.45 m is Joshua's height.

We must ascertain the tree's height.

The right triangles are all alike.

The ratio of the corresponding sides is equal when two triangles are comparable.

Now, put values as follows:

Therefore, by using triangles laws, we know that the height of the tree is 8.42 meters.

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The correct form of the question is given below:

Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away from the tree so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

The scale factor of the dilation = 2.5

The original dimensions of the rectangle:

Length = 32 ft

Width = 8 ft

The dimensions of the rectangle after dilation:

Length = 80 ft

Width = 20 ft

Dilation is a transformation where the dimensions of the figure is enlarged by multiplying with a number. This number multiplied with all dimensions of the original figure is called its scale factor.

So the new dimension of the figure will be scale factor times the original dimensions of the figure.

Thus the scale factor can be defined as the ratio of larger dimension to the smaller dimension of a figure.

Hence the scale factor used here is the ratio of new length to the original length or the ratio of new width to the original width of the rectangle.

That is, scale factor = 80/32 = 20/8 = 2.5

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The length of the rectangle is 10, the width is 2.5 and the perimeter is 25

Let the width of the rectangle be x

The length of rectangle = 2x + 5

The overall length of the outline determines a rectangle's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter.

Perimeter = 10 times of width

= 10*x

= 10x

The formula for the perimeter of a rectangle is given:

Perimeter = 2(Length+Breadth)

10x = 2(x + 2x+5)

10x = 2(3x+5)

10x = 6x + 10

4x = 10

x=2.5

Length = 10

Width = 2.5

Perimeter = 25

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A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.

A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.

The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A mathematical phrase, rule, or law that establishes the relationship between two variables, one of which is independent and the other dependent (the dependent variable)

The complete question is:

What is a mathematical function? After studying the vending machine examples, write a definition that communicates precisely what it means for a mathematical relationship to be a function.

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The smallest number of packets of buns that Jonathan could buy is  4.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. 

We have,

Buns come in a packet of 6

Sausages come in a pack of 10

Burgers come in a pack of 8.

Sausage = 2 x burgers ____(1)

Buns = Sausages + Burgers _____(2)

The smallest number of packets of buns can be calculated when only one packet of Burgers is bought.

So,

Burgers = 1 pack = 8

From (1) and (2),

Sausage = 2 x 8 = 16

Buns = 16 + 8 = 24

Buns = 24

This can be put in 4 packets.

Thus,

The smallest number of packets of buns that Jonathan could buy is  4.

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Answer:

-40

Step-by-step explanation:

10/1*(-4)    Set up equation

10/1 * -4    Open up parentheses

10/1 =10    Next, divide 10 by 1

10*-4        Now, multiply 10 and -4

-40 Answer

Answer:

-40

Step-by-step explanation:

Given expression

[tex]\dfrac{10}{1} \cdot (-4)[/tex]

When dividing and multiplying, follow the order of operations and work from left to right.

Divide the numbers

When dividing anything by 1, the quotient is the numerator:

[tex]\implies \dfrac{10}{1} \cdot (-4)=10 \cdot (-4)[/tex]

Multiply the numbers

When multiplying a positive number by a negative number, the product is always negative:

[tex]\implies 10 \cdot (-4)=-40[/tex]

Answer:

The larger number is 68 and the small number is 25

Step-by-step explanation:

Large number y

small number is x

y=2x+18

x+y=93

Answer:

y = -3

Step-by-step explanation:

-53 = 8y + 4y - 17

combine y terms on right side:

-53 = 12y - 17

add 17 to both sides:

-53 + 17 = 12y - 17 + 17

-36 = 12y

divide both sides by 12:

-36/12 = 12y/12

y = -3

a) Value of Expression 1 is 29.833.

b) After inserting the parentheses the expression is (5+4) * 2 + 6 -2 * 2 - 1.

The order of operations to solve in expression 1 is:

First parenthesis, then multiplication and division, and then addition and subtraction.

So, the expression is:

6 × 7 - 3 ÷ 2 × 9 + 4 ÷ 3

First, solve division and then multiplication:

= 42 - 1.5 × 9 + 1.34

= 42 - 13.5 + 1.34

= 29.84

b) Because the parenthesis is the initial action, so insert it in 5+4 which provides the following result:

(5 + 4) × 2 + 6 - 2 × 2 - 1

First, calculate the parenthesis, then the multiplication and division, and finally perform addition and subtraction:

= (9) × 2 + 6 - 4 - 1

= 18 + 6 - 4 - 1

= 19

The final value is 19.

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Step-by-step explanation:

any ordered pair is a solution, if we can use its coordinates in the equation, and the equation stays true.

for x - 3y = 6

1. (3, -1)

3 - 3×-1 = 6

3 + 3 = 6

6 = 6

true, this is a solution.

2. (0, 2)

0 - 3×2 = 6

-6 = 6

false, this is not a solution.

3. (3, 1)

3 - 3×1 = 6

3 - 3 = 6

0 = 6

false, this is not a solution.

The score 3 months ago was 4.130.

What is rate of increase?

Rate of increase is defined the change in rate that describes how one quantity changes in relation to another quantity.

Assume the score 3 months ago was x. This means that the above can be expressed as:

Current score = x × ( 1 + rate) ^ number of months

5.20= x(1+8%)^3

5.20 = x(1.259)

x= 5.20/1.259

x= 4.130

therefore, the score was 4.130

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Explanation:

The tenths decimal place is right after the decimal point

7 is in the tenths place

The digit just to the right of 7 is 4

Since the 4 is not 5 or larger, this means we erase everything after the 7 and go with 3.7

If we had something like 3.76, then the 7 bumps up to 8 to get 3.8

The amount of change Maria receives is 100y - np

What is Conversion rate ?

A conversion rate is the ratio between two currencies, most commonly used in foreign exchange markets, which designates how much of one currency is needed to exchange for the equivalent value of another currency.

Given,

The cost of each pencil is = p

Maria buys = n pencils

so, the cost of n pencils is = np

She pays for the n pencils is = $y

Now, in question given that we need to find answer in cents

so, We know 1$ = 100 cents

By that, $y = 100y

Maria received the change is = 100y - np

Therefore,  the amount of change Maria receives is 100y - np

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If the quadratic [tex]3x^2[/tex]+4x-9 =0  has two real roots, then the sum of the square of the these roots is 7.77

The polynomial is  [tex]3x^2[/tex]+4x-9 =0

Here,

a = 3

b = 4

c = -9

Here the quadratic equation

= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

Substitute the values in the quadratic equation

= [tex]\frac{-4+/-\sqrt{4^2-4(3)(-9)} }{2(3)}[/tex]

The result will be

= [tex]\frac{-2+/-\sqrt{31} }{3}[/tex]

Therefore, the roots are

[tex]\frac{-2+\sqrt{31} }{3}[/tex] and [tex]\frac{-2-\sqrt{31} }{3}[/tex]

Square of the first root = [tex](\frac{-2+\sqrt{31} }{3} )^{2}[/tex]

= 1.414

Square of the second root = [tex](\frac{-2-\sqrt{31} }{3} )^2[/tex]

= 6.363

The sum of the square of the roots = 1.414+6.363

= 7.77

Hence, if the quadratic [tex]3x^2[/tex]+4x-9 =0  has two real roots, then the sum of the square of the these roots is 7.77

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When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, yreflection )'s across the x-axis is (x, -y).  A point's reflection over the y axis is shown. The reflection rule over the y axis is (x,y)(x,y).

A coordinate plane is a two-dimensional plane formed by two number lines intersecting. One of these number lines is a horizontal number line known as the x-axis, and the other is a vertical number line known as the y-axis.

1) Determine the absolute value of x1(y2-y3) + x2(y3-y1) + x3(y1-y2).

2) The area of the triangle is calculated by dividing this value by two.

3) Use our area of a triangle with coordinates calculator to confirm this result.

The coordinate plane can be used to draw lines and points. This system allows us to visually describe algebraic relationships, as well as create and interpret algebraic concepts.

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The total area of the figure is; 32 millimeters sq.

The area of a parallelogram is the product of the base and the height of the figure.

The area of a parallelogram = Base x Height

We have been given that a parallelogram has a base is 6 millimeters and a height is 4 millimeters

The area of a parallelogram = Base x Height

= 6 x 4

Area = 24 millimeters sq.

Similarly, The area of the triangle = 1/2 x b x h

= 1/2 x 8 x 2

= 8 millimeters sq.

The total area of the figure is;

Total = area of the triangle + area of a parallelogram

Total = 24 + 8 = 32

Hence, the total area of the figure is; 32 millimeters sq.

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