1. Mr. McClellan has a board game that requires the use of two 4-sided dice. According to his rules, you can only start the game if you roll a 2 on at least one of the dice.
(a) Make a list of all the different possible outcomes when two 4-sided dice are rolled.
(b) What is the probability of a favorable outcome
(c) Suppose you rolled the two 4-sided dice 100 times, would you expect at least one 2 more or less than 28 times? Explain.

Answer:

[tex]y=-0.10x+60[/tex]

Step-by-step explanation:

Let

y -----> gallons of water remaining in the barrel

x-----> number of minutes elapsed

we know that

Water leaks out of the barrel at a rate of 1 gallon every 10 minutes

so

[tex]1/10=0.10\frac{gal}{min}[/tex]

The linear equation that represent this situation is  

[tex]y=-0.10x+60[/tex]

The graph in the attached figure

Answer:

68°

Step-by-step explanation:

To find the angles represented by the percentages , you should have in mind that the total sum of all angles in the pie-chart equals 360°

The percentages given are;

The total percentages for the items

[tex]=34+8+11+12+15+20=100[/tex]

To get the angles represented by each percentage

Angle x=item/100 ×360°

Where x is the angle of an item in the circle graph

Calculating angles for carrot and potatoes

[tex]C=\frac{11}{100} *360=39.6\\\\\\P=\frac{8}{100} *360=28.8\\\\\\P+C=39.6+28.8=68.4[/tex]

The combined angle will be 68.4°

Answer:

B

Step-by-step explanation:

It is a function because it passes the vertical line test... (There is no vertical line you can draw that will go through 2 or more than 2 points.)

For this case we must simplify the following expression:

[tex]\frac {\frac {4t ^ 2-16} {8}} {\frac {t-2} {6}} =[/tex]

Applying double C we have:

[tex]\frac {6 (4t ^ 2-16)} {8 (t-2)} =[/tex]

Simplifying:

[tex]\frac {3 (4t ^ 2-16)} {4 (t-2)} =[/tex]

We take common factor 4 from the parentheses of the numerator:

[tex]\frac {3 * 4 (t ^ 2-4)} {4 (t-2)} =[/tex]

We simplify:

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

We factor the numerator:

[tex]t ^ 2-4 = (t + 2) (t-2)[/tex]

We rewrite the expression:

[tex]\frac {3 (t + 2) (t-2)} {(t-2)} =[/tex]

We simplify:

[tex]3 (t + 2) =\\3t + 6[/tex]

Answer:

[tex]3t + 6[/tex]

Answer:

The resulting vector b - a is <-5 , 7>

The resulting vector 2a - b is <8 , -9>

Step-by-step explanation:

* Use the graph to solve the problem

- The vector a is <3 , -2>

- The vector b is <-2 , 5>

* We can add and subtract the vectors

∵ a = <3 , -2>

∵ b = <-2 , 5>

- To find b - a subtract a from b

∴ b - a = <-2 , 5> - <3 , -2> = <(-2 - 3) , (5 - -2)> = <(-5) , (7)>

∴ The resulting vector b - a is <-5 , 7>

* 2a means multiply vector a by 2

∵ a = <3 , -2>

∴ 2a = <(2 × 3) , (2 × -2) = <6 , -4>

* Now lets find the resulting vector 2a - b

- Subtract b from 2a

∵ 2a = <6 , -4>

∵ b = <-2 , 5>

∴ 2a - b = <6 , -4> - <-2 , 5> = <(6 - -2) , (-4 - 5> = <(8) , (-9)> = <8 , -9>

∴ The resulting vector 2a - b is <8 , -9>

Answer:

it would be 7x+12y=140

The required system of equation is that can be used to find number of 7-inch plates and 12-inch plates is:

        [tex]x+y=15\\7x+12y=140[/tex]

Given information:

The plates in a kitchen cabinet = 15

The diameter of each plates is either 7 inch or 12 inch.

The diameter of all 12[tex]x+y=15[/tex] plates combined is 140 inches.

Now, for the system of equation:

According to the question:

The number of 7 inches plates is [tex]x[/tex]

The number of 12 inches plates is [tex]y[/tex]

So, by the information given in the question:

[tex]x+y=15[/tex]

Because, there are 15 plates in the cabinet we can write the above equation.

Now, the sum of diameters of all plates is 140, that is also given in the question.

Hence, we can write the second equation as:

[tex]7x+12y=140[/tex]

Hence, The required system of equation is that can be used to find number of 7-inch plates and 12-inch plates is:

[tex]x+y=15\\7x+12y=140[/tex]

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Answer:

-8

Step-by-step explanation:

Answer:

x = 98

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠x is an exterior angle and

∠GFH and ∠FHG are the 2 opposite interior angles, hence

x = 53 + 45 = 98

The value of x is 98 degree.

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠GFH and ∠FHG are the 2 opposite interior angles to exterior angle 'x',

x = 53 + 45

x = 98

Hence, the value of x is 98 degree.

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Answer:

-8

Step-by-step explanation:

All you have to do is divide 56/7 and you get -8.

Hope this helps!

Feel free to ask if you have any questions!

When you divide 56 by -7, the result is -8. This means that -8 is the quotient or simplified expression obtained when dividing 56 by -7.

A simplified expression is a mathematical expression that has been reduced or simplified to its most concise or straightforward form. It typically involves combining like terms, applying rules of arithmetic, or simplifying fractions or radicals. Simplifying an expression helps to make it easier to understand and work with.

To simplify the expression 56 ÷ (-7) step by step, you can follow these steps:

Divide 56 by -7:

56 ÷ (-7) = -8

Therefore, the simplified expression is -8.

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Answer:

[tex]\large\boxed{x<\dfrac{6}{7}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7x}{3}<2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{7x}{3\!\!\!\!\diagup_1}<(3)(2)\\\\7x<6\qquad\text{divide both sides by 7}\\\\x<\dfrac{6}{7}[/tex]

Answer:

x<6/7

Step-by-step explanation:

Multiply by 3 from both sides of equation.

3*7x/3<2*3

Simplify.

7x<6

Divide by 7 from both sides of equation.

7x/7<6/7

Simplify, to find the answer.

x<6/7 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

The plant increased a total of 4 inches. Week 3 the plant increased 8 inches and week 4 the plant was 12 in, now subtract 12-8= 4

Answer:

The plant increased a total of 4 inches.  

Week 3, the plant was 8in and week 4, the plant was 12in.

To find our solution, subtract 8 from 12

12-8=4

Step-by-step explanation:

[tex]\left(\dfrac{g}{f}\right)(x)=\dfrac{x^2-6}{3x+1}[/tex]

Answer:

15/2 or 7.5

Step-by-step explanation:

cos(60)=1/2

so 15(1/2)=15/2 or 7.5

For this case we must evaluate the following expression:

[tex]15 * cos (60)[/tex]

By definition we have that the cosine of 60 degrees is [tex]\frac {1} {2}.[/tex] Then, substituting in the expression we have:

[tex]15 * \frac {1} {2} = \frac {15} {2} = 7.5[/tex]

So, we have:

[tex]15 * cos (60) = 7.5[/tex]

Answer:

[tex]15 * cos (60) = 7.5[/tex]

Answer:

Acute, Equilateral

Step-by-step explanation:

Acute because all angles (which are 60 degrees) are less than 90 degrees.

Equilateral because all sides are equal.

Please mark for brainliest!! :D Thanks!

For any more questions or explanation / information, please comment below and I'll respond ASAP :)

Answer:

The correct options are

A.  Acute

E. Isosceles

F. Equilateral

Step-by-step explanation:

From the figure we can see a triangle.

To find the correct options

1). From figure we get  all the angles are equal.

Each angle is equal to 60°

60 < 90

Option A. Acute is TRUE

2). Also all the sides of the triangles are equal,

Therefore the given triangle is equilateral triangle.

Option F. Equilateral is TRUE

Every equilateral triangle is Isosceles triangle.

Therefore option D. is also true

Answer:

112

Step-by-step explanation:

Monday=14

Tuesday=2x14=28

Wednesday= 2x28=56

Thursday= 2x56=112

Answer:

Option C.

[tex]x=2\sqrt{2}[/tex]

[tex]y=2\sqrt{6}[/tex]

Step-by-step explanation:

step 1

Find the value of x

In the right triangle of the figure

[tex]sin(30\°)=\frac{x}{4\sqrt{2}}[/tex] -----> opposite side angle of 30 degrees divided by the hypotenuse

Remember that

[tex]sin(30\°)=\frac{1}{2}[/tex]

so

[tex]\frac{1}{2}=\frac{x}{4\sqrt{2}}[/tex]

[tex]x=\frac{4\sqrt{2}}{2}[/tex]

[tex]x=2\sqrt{2}[/tex]

step 2

Find the value of y

In the right triangle of the figure

[tex]cos(30\°)=\frac{y}{4\sqrt{2}}[/tex] -----> adjacent side angle of 30 degrees divided by the hypotenuse

Remember that

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{\sqrt{3}}{2}=\frac{y}{4\sqrt{2}}[/tex]

[tex]y=\frac{4\sqrt{6}}{2}[/tex]

[tex]y=2\sqrt{6}[/tex]

Answer:

[tex]\frac { 4 } { 5 } [/tex]

Step-by-step explanation:

We are given the following two points and we are to find the slope of the line which passes through these points:

[tex](3.-1)[/tex] and [tex](-2,-5)[/tex]

The formula of the slope is given by:

Slope = [tex] \frac { y _ 2 - y _ 1 } { x _ 2 - x _ 1 } [/tex]

Substituting the given coordinates in the above formula:

Slope = [tex] \frac { - 5 - ( - 1 ) } { - 2 - 3 } = \frac { 4 } { 5 } [/tex]

Answer:

Number of candy received by each kid, [tex]x=\frac{104}{8}=23[/tex]

Step-by-step explanation:

Let x be the pieces of candy each  kid will receive.

Total number of candy left with Carleen = 104

Number of kids for which she is distributing = 8

Number of candy received by each kid, [tex]x=\frac{104}{8}=23[/tex]

23 pieces of candy each kid will receive.​

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

According to the question,

The pieces of candy each  kid will receive will be x

Total number of candy left with Carleen = 104

The number of kids for which she is distributing = 8

The equation will be

[tex]x =\frac{104}{8}[/tex]

[tex]x = 23[/tex]

Here , the number of candies receive by each kid will be 23.

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Answer:

(-3,4)

Step-by-step explanation:

That means to reflect the point across the y-axis... If you draw (3,4) on the coordinate plane you should see (-3,4) is the reflection across the y-axis from that point.

Answer:

P' = (- 3, 4 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ), hence

P(3, 4 ) → P'(- 3, 4 )

Answer:

x^2-3x+6/x^2-2x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]\large\boxed{V=\dfrac{4}{3}\pi R^3=\dfrac{D^3}{6}\pi}\\\\\boxed{V=\dfrac{500\pi}{3}\ in^3\approx523.33\ in^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=\dfrac{D}{2}.\\\\\text{Therefore}\\\\V=\dfrac{4}{3}\pi\left(\dfrac{D}{2}\right)^3=\dfrac{4}{3}\pi\left(\dfrac{D^3}{8}\right)=\dfrac{D^3}{6}\pi[/tex]

[tex]\text{We have the dimater}\ D=10in.\ \text{Substitute:}\\\\V=\dfrac{10^3}{6}\pi=\dfrac{1000}{6}\pi=\dfrac{500\pi}{3}\ in^3[/tex]

For this case we have that by definition, the volume of a sphere is given by:

[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]

Where:

r: It is the radius of the sphere

We are told as data that the diameter of the sphere is 10in, so the radius is 5in:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi\\V = 523.33in ^ 3[/tex]

Answer:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi[/tex]

Any of the three given expressions can be used to find the volume of the sphere.

Answer:

OE. (2,0)

Step-by-step explanation:

Since x is by itself x equals 1 so the x value would be 1/1. The y intercept is 2 which means you began on the y axis 2 and x axis 0 and then you move 1/1 from that spot because of your x value or slope.

Answer: agree

Step-by-step explanation:

5(2)=10•2=20

Answer:

disagree

Step-by-step explanation:

Given

5x² = 20 ( divide both sides by 5 )

x² = 4 ( take the square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2

x = 2 or x = - 2 are the solutions to the equation

Answer:

180°

Step-by-step explanation:

(8y+17)°=(6x-7)°

(3x-29)°+(8y+17)°=180°

so,

(3x-29)°+(6x-7)°=180°

To solve the expression (6x-7)+(3x-29), we combine like terms. The 'x' terms (6x + 3x) sum up to 9x and the constants (-7 and -29) sum up to -36. Therefore, the simplified expression is 9x - 36.

The student wants to solve the expression (6x-7)+(3x-29). To do this,  you should combine like terms, which means you should add together the terms that have the same variable.

Step 1: Add the 'x' terms together. This would give us 6x + 3x which equals 9x.

Step 2: Then add the constants together, in this case -7 and -29, you get -36.

So, the simplified result of the expression (6x-7)+(3x-29) is 9x - 36.

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Answer:

C

Step-by-step explanation:

A major arc is an arc that is greater than 180 degrees.

A minor arc is an arc less than 180 degrees.

An acute angle is an angle less than 90 degrees.

A central angle is the angle created in the center of a circle with 2 sides being the radius.

Thus, we can see in the figure that we are talking about the angle so we can eliminate major arc and minor arc.

Now, we clearly see that the angle is greater than 90 degree so it cannot be acute angle.

The correct answer is central angle as it goes with the definition.

Final answer:

AOR or Adjusted Odds Ratio is used in medicine as a measure of association between exposures and outcomes, and it tends to overestimate the RR for common diseases.

Explanation:

The term AOR refers to the Adjusted Odds Ratio, which is a statistical measure used to describe the strength of association or non-independence between two binary data values in epidemiology and other fields. In comparison to the Relative Risk (RR), the AOR is a more complex measure that takes into account additional variables that may affect the outcome. In the context of disease prevalence, when a disease is uncommon (around 5% prevalence or less), the AOR can closely approximate the RR. However, for more common diseases (for example, with a 40% prevalence of hypertension), the odds ratio tends to overestimate the risk compared to the RR, diverging more as the prevalence increases.

Answer:

4 cm.

Step-by-step explanation:

Area of the shape =

136 =  6 * 14 + (h/2)(12 + 14)      where the last part is the area of the trapezoid.

84 +  13h = 136

13h = 138 - 84 = 52

h = 4 (answer).

Answer:

Possible values of dimensions are (24,16,2) or (24,8,4)

Step-by-step explanation:

We are given the volume of the Cuboid and length . We are required to find the possible values of width and height from this information.

Let us say that the width is x and height is y

Length = 24

Volume of a cuboid = length * width * height

Volume = 768

768=24*x*y

[tex]xy=\frac{768}{24}\\xy=32\\[/tex]

xy=32

Now the possible factors of 32

32=1*32 ( Which shall not be taken into consideration as length is already given as 24 and width or height can  not be more length)

32=2*16

32=4*8

Hence the possible values width are 8, 16 and that of height 4 and 2

Hence the possible values of dimensions are (24,16,2) or (24,8,4)