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The probability of P(B and C) is 1/6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. It is more likely that an event will occur if its probability is higher.

For e.g., A straightforward illustration is tossing a fair (impartial) coin.

Given that, the probabilities, P(A) = 1/8, P(C) = 1/4, and P(A and B) = 1/12

P(A and B) = P(A)×P(B)

Therefore,

1/12 = 1/8 × P(B)

P(B) = 8/12 = 2/3

Now,

P(B and C) = P(C)×P(B)

P(B and C) = 1/4×2/3

P(B and C) = 1/6

Hence, P(B and C) = 1/6

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The essays that she can review in 1 hour would be; 2 2/3.

A fraction represents a part of a number or any number of equal parts.

We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.

Thus, Fraction of the essay reviewed = 2/3

Amount of time used = 1/4

Therefore, the fraction of essay for an hour can be calculated as;

= Fraction of the essay reviewed / Amount of time used

= 2/3 ÷ 1/4

= 2/3 × 4

= 8/3

= 2 2/3

Hence, She will review 2 2/3 essay.

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When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

area of the polygon ( triangle ) = 1/2 * b * h

= 1/2 * 4 * 4

= 8 units

so When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)

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Answer:

1.8 meters

Step-by-step explanation:

Multiply 12 by 0.15 to get your answer. You multiply because the question says "15% of 12 meters" which means you need to multiply.

Answer: 1.8

Step-by-step explanation:

Multiply 12 by .15 (15% as a decimal), and you'll get 1.8 meters. You multiply, because it says 15% of 12 meters.

The points to be graphed are (6, 0) and (0, 3). The graph of the equation is shown in the attached image

y = - 1/2x + 3

In order to graph the equation of the line:

First, find the value of x when y = 0:

y = - 1/2x + 3 , when y = 0:

0 = - 1/2x + 3

1/2x = 3

x = 3 × 2

x = 6

Also, find the value of y when x = 0:

y = - 1/2x + 3, when x = 0:

y = - 1/2(0) + 3

y = 3

Therefore,  the values to be plotted on our graph are (6, 0) and (0, 3). The image of the graph is attached

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Answer:

going to have to to get the house ready

Dirk will make 70 pars or better.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.

Out of 90 holes, Dirk made par or better on 42 holes.

At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.

Then, Out of 150 holes, Dirk will make par or better on -

(42/90 x 150) holes

(42/90 x 150)

70

Therefore, Dirk will make 70 pars or better.

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Answer:

4

Step-by-step explanation:

The coefficient is 4 because it is the amount placed before a variable. The variable is the x, therefore, the coefficient is the 4, the amount placed before the x.

Hope this helps! :)

Answer:

(3,18)

Step-by-step explanation:

You do not give the center of dilation, so I am using the origin (0,0)

You multiply the x and y by 3

(1,6)

1 x 3 = 3

(1,6)

6 x 3 = 18

(3,18)

Using the Algebraic tile method we get x=2 solution for equation model

The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.

In the question, we have 3 kinds of tile

Equation will be :

⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1

⇒ 3x - 2 = 4

⇒ 3x = 6

⇒ x = 2

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The profits last year were $2041.66

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here, profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, then let the profit last year be x then we have 2.4x=4900

                            x=4900/2.4

                            x=2041.66

Hence, The profits last year were $2041.66

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If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

First step:-

Right triangular prism=1⁵/₆ inches= 11/6 inches

Height of the base=8²/₃ inches = 26/3 inches

Second step:-

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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The function's general shape is a downward-opening parabola.

From the question, we have the following parameters that can be used in our computation:

f(x)=-x^4+8x^3+8x^2-96x-144

Express properly

So, we have

f(x) = -x⁴ + 8x³ +8x² - 96x - 144

Next, we plot the graph (see attachment)

From the attached graph, we can see that the function opens down

This means that the general shape is a downward-opening parabola.

The function faces down (as shown on the graph)

Here, we set x = 0

So, we have

f(0) = -(0)⁴ + 8(0)³ + 8(0)² - 96(0) - 144

Evaluate

f(0) = -144

So, the y-intercept is -144

We start by setting the factor to 0

So, we have

x - 6 = 0

Solve for x

x = 6

From the graph;

When x = 6, y = 0

This means that x - 6 is a factor

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Answer: atleast alot

Step-by-step explanation:

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.

Here,

A cylinder has a volume of V = r2h.

As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.

The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.

Thus, you would receive one-third of the initial mass.

What would occur if you increased the radius by 1/3 in contrast to this?

Next, you would have

=> V = π[(1/3)r]2h

=> V = π(1/9)r2h

=> V = (1/9)πr2h

You would then possess 1/9 of the volume.

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

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Answer:

78

Step-by-step explanation:

a + 8b = 6 + 8 x 9 = 6 + 72 = 78

Answer: 78

Step-by-step explanation:

value of a=6

value of b=9

a+8b= 6+8*9

as the 8 will be multiplied by 9

6+8*9= 6+72

6+72 = 78

The closest to the number of yards of ribbon Mario had altogether will be ;

⇒ 11 yards

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

Mario had 8 1/5 yards of ribbon for a project.

And, Sue gave him 2 3/4 more yards of ribbon.

Now,

Since, Mario had 8 1/5 yards of ribbon for a project.

And, Sue gave him 2 3/4 more yards of ribbon.

Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards

                                                                        = 41/5 + 11/4

                                                                        = (164 + 55) / 20

                                                                         = 219 / 20 yards

                                                                         = 10.95 yards

                                                                         ≈ 11 yards

Thus, Total ribbon for the project Mario have = 11 yards

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Answer: 0.155

Step-by-step explanation:

To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:

P(k) = (μ^k * e^(-μ)) / k!

Where:

Plugging in the given values, we get:

P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550

So the probability of the event occurring 5 times is approximately 15.5%.

Answer: -2, -3, and -4.

Step-by-step explanation:

The range is all the Y Values the graph uses, and the Y values range from -0.5 to -5.5, making every number in between those included.

The total amount that Latoya ended up paying for the machinery, was $ 13, 080 .96

The amount of interest that Latoya paid was $ 980.96

The total amount paid by Latoya for the machinery can be found as :

= Down payment of the machinery + ( Monthly payments x Number of months per year x Number of years )

= 1, 800 + ( 313. 36 x 12 x 3 )

= $ 13, 080 .96

The total interest paid on the loan was :

= ( Monthly payments x Number of months per year x Number of years ) - Worth of the machine - down payment

= ( 313. 36 x 12 x 3 ) - 12, 100 - 1, 800

= $ 980.96

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2 copies of 1/10 can be written as 2/10

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here 2 copies of 1/10 thus 2×1/10=2/10

                                                                =1/5

Hence, 2 copies of 1/10 can be written as 2/10

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The required temperature in Beijing China is -7°C on Tuesday.

As mentioned in the numeral,

On Monday in December
The temperature in Harbin China is  -8°C,

Now,
The Temperature in Beijing china is -2°C
According to the condition, the temperature on the next day in Beijing is 5° degrees colder than it was yesterday since the temperature is becoming colder implying that the temperature is getting decreased by -5°C.

The temperature on Tuesday is given as,
T = -2°C - 5°C  [subtracting -5 because the temperature is decreased]
T = - 7°C

Thus, the required temperature in Beijing China is -7°C on Tuesday.

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Dilation is a type of transformation that enlarges or shrinks shapes (called archetypes) to create new shapes (called images). Archetype area is 5050 [tex]unit^2[/tex] * 3 = 15,150 [tex]unit^2[/tex]

Add the square of the scaling factor s to the area of ​​the figure before stretching Ap. In other words, the equation Ad = s2Ap gives the area of ​​the figure after dilation Ad. a d = s2a p .

To find the archetype area, we need to undo the applied stretch. Since the stretch factor was 1/3, we can undo it by multiplying the image area by the inverse of the scale factor (1/1/3 = 3). So the area of ​​the archetype is 5050 [tex]unit^2[/tex] * 3 = 15,150.[tex]unit^2[/tex]

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h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.

Here,

We can draw the graph as

h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)

h(x) = f(x) + 5

The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.

Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

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Answer:

(2,-2)

Step-by-step explanation:

The answer is the intercept point of both lines, so we need to find the point when both the line touches, with out graphing we can see by the table that point (2, -2) intercepts with the line on the graph.

hope this helps :)

Answer:

--------------------------

From the table we see each y-coordinate is the negative of the corresponding x-coordinate. It gives us the second line:

The first line is given y = 1/2x - 3, equate both to get:

Then the value of y:

The solution is (2, - 2).

Answer: x = -5, y = 4

Step-by-step explanation:

Align the two equations according to their terms:

[tex]\left \{ {{-3x-3y = 3} \atop {3x+6y = 9}} \right.[/tex]

Add the two equations. Because -3x and 3x equals zero, they can be eliminated from the equation. This results in:

[tex]3y = 12\\y = 4[/tex]

Plug in y = 4 into the first equation:

[tex]-3x - 3(4) = 3\\[/tex]

Solve for x:

[tex]-3x-12 = 3\\-3x = 15\\x = -5[/tex]

Check by plugging in both x and y:

[tex]-3(-5) - 3(4) = 3\\15 - 12 = 3\\3 = 3[/tex]

So, x = -5 and y = 4

Answer:

D

Step-by-step explanation:

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{3}{4}[/tex]  Use the common denominator of 8 Multiply [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{2}[/tex]

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{6}{8}[/tex]

7[tex]\frac{9}{8}[/tex]

7 + [tex]\frac{8}{8}[/tex] + [tex]\frac{1}{8}[/tex]  Another name for [tex]\frac{8}{8}[/tex] is 1

7 + 1 + [tex]\frac{1}{8}[/tex]

8[tex]\frac{1}{8}[/tex]

The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.

What does rate of change mean?

An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then the rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.

Surafce area of a prism is equal to

2(Area of base) + (perimeter of base)(height)

2b^2+4bh

[tex]S=2b^2+4bh[/tex]

[tex]\frac{ds}{dt}=4b\frac{db}{dt} + 4b\frac{db}{dt} + 4h\frac{db}{dt} \\[/tex]

It is given that db/dt= -7 and dh/dt -=10.

At a particular instant b= 4km, h=9 km.

Now we will substitute the values in this formula:

[tex]\frac{ds}{dt}=-4*4*7-4*4*7+ 4*9*10\\\frac{ds}{dt}=136[/tex]

The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.

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The value of x is 10°.

What is a measure of an angle?

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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The value of x is 10°.

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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