Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

The domain of g(x)= 3x^2 is Real number and it's range is {y∈R / y≥0}

The domain of h(x)= -3x^2 is Real number and it's range is {y∈R / y ≤0}

The domain of a function f(x) is the set of all values for which the function is defined, and the domain of a function is the set of all values that f takes on. The domain and range are defined for a relation and are the sets of all x-coordinates and all y-coordinates of ordered pairs.

The graph of f(x)= x^2 is given

We need to find the domain and range of g(x)=3x^2 and h(x)= -3x^2

The Graph of 3x^2 is different from x^2 in terms of plotting

When ,

x= -2 g(x)=12

x=-1 g(x)=3

x=0 g(x)=0

x=1 g(x)=3

x=2 g(x)=12

The Graph of -3x^2 is different from x^2 in terms of plotting

When ,

x= -2 g(x)=-12

x=-1 g(x)= -3

x=0 g(x)=0

x=1 g(x)= -3

x=2 g(x)=-12

Domain of g(x) is R and it's range is {y∈R / y≥0}

Domain of h(x) is R and it's range is {y∈R / y ≤0}

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Answer:

the answer is 17y 3y+6y is 9y plus 8y is 17y

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Simplifying it:}[/tex]

[tex]\mathsf{3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathsf{(3y + 6y + 8y)}[/tex]

[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]

[tex]\mathsf{\rightarrow 9y + 8y}[/tex]

[tex]\mathsf{\rightarrow 17y}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{17}\mathsf{y}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The value of the given division operation is 3/7

From the question, we are to determine the quotient of the given division operation

The given division operation is

-3/2÷-7/2

[tex]\frac{-3}{2} \div \frac{-7}{2}[/tex]

[tex]=\frac{-3}{2} \times \frac{2}{-7}[/tex]

[tex]=\frac{-3}{-7}[/tex]

[tex]=\frac{3}{7}[/tex]

Hence, the value of the given division operation is 3/7

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Answer:

Please see the picture below.

Step-by-step explanation:

The probability that a student buys coffee OR a muffin before class is 55%

The given parameters are:

P(Coffee) = 30%

P(Muffin) = 40%

P(Tea) = 20%

P(Coffee and Muffin) = 15%

P(Tea and Muffin) = 10%

The probability that a student buys coffee OR a muffin before class is

P(Coffee or Muffin) = P(Coffee) + P(Muffin) - P(Coffee and Muffin)

This gives

P(Coffee or Muffin) = 30% + 40% - 15%

Evaluate

P(Coffee or Muffin) = 55%

Hence, the probability that a student buys coffee OR a muffin before class is 55%

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The correct values for a and b which models this relationship through an exponential function are 8 and 2 respectively.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = eˣ

Based on the information provided, we can logically deduce that the other copy machine can reduce image dimensions by a different percentage and this is defined by the following exponential function:

f(x) = abˣ

From the graph (see attachment), we have;

When x = 0, y = f(x) = 8. Thus, f(0) = 8

f(x) = abˣ

8 = ab⁰

8 = a × 1

a = 8.

Also, from the graph (see attachment), we have;

When x = 1, y = f(x) = 4

f(x) = abˣ

4 = 8b¹

4 = 8 × b

4 = 8b.

b = 8/4

b = 2.

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The volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex]

The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.

Thus, the volume (V) of a right circular cylinder, using the above formula, is, [tex]V = \pi r^2h[/tex] , where

'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

Given:

Height(h) = 8 x diameter = 16 x radius (r)      (diameter = 2 x radius )

∴ h = 16r.

V= [tex]\pi r^2h[/tex]

Substituting h = 16r in the volume formula we get

V = [tex]\pi r^2(16r)[/tex] =  [tex]16\pi r^3[/tex]

Thus the volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex].

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Answer:

a) is the correct answer

Answer:

x ^ (1/3)

Step-by-step explanation:

solution:

the answer is in the picture I have sent.

I hope this will help you

Answer:  [tex]f^{-1}(\text{x}) = (\text{x}-9)^2+4[/tex] when [tex]\text{x} \ge 9[/tex]

=================================================

Work Shown:

[tex]f(\text{x}) = 9 + \sqrt{\text{x} - 4}\\\\\text{y} = 9 + \sqrt{\text{x} - 4}\\\\\text{x} = 9 + \sqrt{\text{y} - 4}\\\\\text{x}-9 = \sqrt{\text{y} - 4}\\\\(\text{x}-9)^2 = (\sqrt{\text{y} - 4})^2\\\\(\text{x}-9)^2 = \text{y}-4\\\\(\text{x}-9)^2+4 = \text{y}\\\\f^{-1}(x) = (\text{x} - 9)^2+4[/tex]

Explanation:

I replaced f(x) with y. After that I swapped x and y, then solved for y to get the inverse.

The smallest that [tex]\sqrt{\text{x}-4}[/tex] can get is 0, which means the smallest f(x) can get is 9+0 = 9. The range for f(x) is [tex]\text{y} \ge 9[/tex]

Since x and y swap to determine the inverse, the domain and range swap roles. Therefore, the domain of the inverse [tex]f^{-1}(\text{x})[/tex] is [tex]\text{x} \ge 9[/tex]

So we will only consider the right half portion of the parabola.

The graph is below. The red curve mirrors over the black dashed line to get the blue curve, and vice versa.

Answer:

[tex]f^-^1(x)=(x-9)^2+4[/tex]   OR [tex]x^2-18x+85[/tex] if you simplify it

Step-by-step explanation:

to find the inverse function you have to switch x and y with each other and solve for y.

[tex]y=9+\sqrt{x-4}\\x=9+\sqrt{y-4}[/tex]           step 1: switch x and y with each other

[tex]x-9=\sqrt{y-4}[/tex]           step 2: subtract 9 from both sides

[tex](x-9)^2=\sqrt{y-4}^2[/tex]     step 3: square both sides to get rid of the square root

[tex](x-9)^2=y-4\\(x-9)^2+4=y\\[/tex]         step 4: add 4 to both sides

you could leave the answer like this or you can simplify to get [tex]x^2-18x+85[/tex]

The plane is parallel to the base of the cone describes the relationship between the plane and the cone

A circle is a spherical form without boundaries or edges or we can say that A circle is a closed, curved object with two dimensions in geometry.

The produced cross-section is a circle when a plane slices a cone such that the plane is parallel to the base of the cone.

Ellipse is the shape that is produced when a plane cuts a cone at an angle such that it misses the base or the vertex. (As shown in figure)

Hence A circle is formed when a plane slices through a cone and the plane is parallel to the base of the cone

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Answer:

104 miles.

Step-by-step explanation:

5 inches is 2 * 2.5 inches so the distance required is 2*52 = 104 miles.

Answer: A.  2x + 30 = 90

Step-by-step explanation:

You want to choose answer A because you know that together the section of 2x and the section of 30 equal 90 degrees (we know this because the other side shows the right angle which equals 90 degrees).

The equation 2x + 30 = 90 will be used to determine x so option (A) will be correct.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

Given an angle with two participants, one is 2x and another one is 30°.

Now if we look right-hand side angle it is a right-angle i.e. 90°.

Since the complete angle above a straight line is 180°

So,

2x + 30 + 90° = 180°

2x + 30 = 90

Hence "The equation 2x + 30 = 90 will be used to determine x".

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Answer:

see explanation

Step-by-step explanation:

- 3 | 5x + 6 | + 1 ≥ 6

First step : subtract 1 from both sides

- 3 | 5x + 6 | ≥ 5

The linear inequality of the given graph is: D. y < -2x + 3.

First, using two points on the line, (0, 3) and (1.5, 0), find the slope (m).

Slope (m) = change in y / change in x = (3 - 0) / (0 - 1.5)

Slope (m) = 3/-1.5 = -2.

Next, substitute (x, y) = (0, 3) and m = -2 into y = mx + b to find the value of b.

3 = -2(0) + b

3 = 0 + b

b = 3

Substitute m = -2 and b = 3 into y < mx + b (the shaded part is at the left, so we use the "<" sign)

y < -2x + 3

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Laura's walking speed is 4.50 feet per second.

Speed is the total distance travelled per time. Speed can be determined by dividing the distance walked by Laura by the time.

Average speed = total distance / total time

54 / 12 = 4.50 feet per second

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Answer:

1/16

Step-by-step explanation:

This means 1/2x2x2x2  = 1/16

Answer:

Step-by-step explanation:

Formula

Area = 1/2 b* h

Givens

b = 25

h = 9

Solution

Area = 1/2 * 25 *  9     Substitute givens into formula

Area = 1/2 * 225         Combine

Answer

Area = 112.5 ft^2

Answer 1: A and C

Step-by-step explanation:

Use distribution law to see which answer match the equation at the top.

Answer 2: 16q + 4

10q and 6q are like terms

10q + 6q = 16q

+

5 - 1

Answer:

Hello,

Step-by-step explanation:

page 1:

60-36j=12(5-3j) answer C
=6(10-6j) answer A

page 2:

10q+5+6q-1=16q+4=4(4q+1)

page 3:

24j-16=8(3j-2)

page 4:

10h+30+50j=10*(h+3+5j) answer B
=2*(5h+15+25j) answer C

=5(2h+6+10j) not A  nor D

1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)

2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)

3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)

4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)

Outliers are sample values that lie very far away from the majority of the other sample values.

We know that, an outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

It differs significantly from other observations in a sample values.

Outlier is a value that is distant from the majority of the values in a data set.

For a scatter plot, an outlier is the point or points that are farthest from the regression line.

For example in the record of marks 25, 29, 7, 32, 85, 33, 27, 28 both 7 and 85 are outliers.

Therefore, outliers are sample values that lie very far away from the majority of the other sample values.

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Answer:

b = 3.5

a = 7

Step-by-step explanation:

Hello!

This triangle is a 30°-60°-90° triangle, as the missing angle is 30° and the other two angles are 60° and 90°.

There are some important Rules:

We can first solve for the leg that is opposite to the 30° angle.

Since [tex]\frac{7\sqrt3}{2}[/tex] is [tex]b\sqrt3[/tex]:

The length of b is 3.5.

We can multiply 3.5 by 2 to find the length of a.

The length of a is 7.

Answer:

306 square meters

Step-by-step explanation:

The maximum area is when the length and width are the closest together.

70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle

35/2=17.5, find the 2 closest integers, they are 17 and 18

17*18=306

The statement which is true is the slopes are all positive in quadrant I.

Given the differential equation is dy/dx=2x-2y

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

Given dy/dx=2x-2y

now slope=2x-2y

Along x-axis, y=0.

So, slope=2x≠0.

Since it depends upon x hence the slope along the y-axis are not horizontal.

Along y-axis, x=0.

So, slope=-2y≠0.

Since the slope along the x-axis are also not horizontal.

In quadrant I

x,y≥0

So, dy/dx≥0

Hence the slopes are all positive in quadrant I.

In quadrant IV,

x≥0,y≤0

so, dy/dx is  not always positive.

This, the slope are not all positive in quadrant IV.

Hence, the slope are all positive in quadrant I for the differential equation dy/dx=2x-2y.

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98.3, 94.1, 89.9, 85.7 (Arithmetic)

1, 0, -1, 0 (Neither)

1.75, 3.5, 7, 14 (Geometric)

-1, 1, -1, 1..... (Geometric)

An arithmetic sequence has a common difference

A geometric sequence has a common ratio

Considering the given sequences one after the other:

For 98.3, 94.1, 89.9, 85.7,..........

The common difference, d = 94.1 - 98.3 = -4.2

Therefore, 98.3, 94.1, 89.9, 85.7 is an arithmetic sequence

For 1, 0, -1, 0......

The sequence does not have a common difference or a common ratio. Therefore, it is neither an arithmetic nor geometric sequence

For 1.75, 3.5, 7, 14,.....

The common ratio = 3/1.75 = 2

Therefore, it is a geometric sequnec

For -1, 1, -1, 1.....

The common ratio = 1/-1 = -1

It is a geometric sequence

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The different ratios are 2 : 7, 2 : 9 and 7 : 9

The statement is given as:

8 out of 36 squares unfilled

This means that:

The part-to-part ratio is represented as:

Ratio = Unfilled : Filled

This gives

Unfilled : Filled = 8 : 28

Simplify

Unfilled : Filled = 2 : 7

The part-to-whole ratios are represented as:

Ratio = Unfilled : Total

Ratio = Filled : Total

So, we have:

Unfilled : Total = 8 : 36

Filled : Total = 28 : 36

Simplify

Unfilled : Total = 2 : 9

Filled : Total = 7 : 9

Hence, the different ratios are 2 : 7, 2 : 9 and 7 : 9

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It is important to be able to express a clear and coherent argument visually or in writing because without establishing coherence, your reader will not be able to know or understand the key points that you are trying to express or show.

Coherence is known to be a key quality for kind of good academic write up.

Note that in the area of academic writing, the ways that ideas flows is very important and as such, it need to be smooth and logical.

Therefore  without coherent argument , the reader cannot understand the key points that a person is trying to show and thus hinders the readability of your work.

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It is necessary to imagine the sum of the areas between each z-score and the average.

Given as the ratio of the area under the normal curve between two z-scores, both above average.

The  Z score accurately measures the number of standard deviations above or below the mean of the data points.

The formula for calculating the z-score is

z = (data points – mean) / (standard deviation).

It is also expressed as z = (x-μ) / σ.

Therefore, to find the percentage of the area under the normal curve between two z-scores, both above the mean, you need to look at the sum of the areas between the z-score and the mean.

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Question :

Solution :

⇒ 3 [-x + 2x + 1] = x - 1

⇒ 3 [x + 1] = x - 1

⇒ 3 × [x + 1] = x - 1

⇒ 3x + 3 = x - 1

⇒ 3x - x + 3 = -1

⇒ 2x + 3 = -1

⇒ 2x = -1 - 3

⇒ 2x = -4

⇒ x = -4 / 2

⇒ x = -2

Simplifying

3[-1x + (2x + 1)] = x + -1

Reorder the terms:

Remove parentheses around (1 + 2x)

Reorder the terms:

Combine like terms: -1x + 2x = 1x

Reorder the terms:

Solving

Solving for the variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

Combine like terms: 3x + -1x = 2x

Combine like terms: x + -1x = 0

Add '-3' to each side of the equation.

3 + -3 + 2x = -1 + -3

Combine like terms: 3 + -3 = 0

Combine like terms: -1 + -3 = -4

Divide each side by '2'.

Simplifying

Answer: x = 3

Step-by-step explanation:

The equation of the line perpendicular to a horizontal line is a vertical line, which has an equation of the form x=c.