There is a game at the carnival that costs $20 to play. There are two outcomes: either you win $100 , or you lose.

To play you roll a die. If a six appears you win; all other rolls you lose. What is the mean (or the expected value) of the game?

A. -$1.66
B. -$3.33
C. $1.66
D. $3.33

Answer:

2.  Circumcenter is (-2, 1)

4.  Orthocenter is (5, 0)

6. II ∠DOS and ∠CAT are vertical and III ∠DOS and ∠CAT are adjacent

8.  m∠PBC = 30°

10.  KV, VM, KM

12.  DC is greater

14.  x = 12

Step-by-step explanation:

2.  Equation of the perpendicular bisector of AB is x = -2 and the equation of the perpendicular bisector of BC is y = 1.

Circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle.

Hence, circumcentre is (-2, 1).

4.  Orthocenter is the point of intersection of the altitudes. Here, AB and BC are two altitudes and B is their point of intersection.

Hence, the orthocenter is (5, 0).

6.  Adjacent angles are angles separated by a line and vertical angles are angles vertically opposite to each other.

Hence, statements II and III contradict to each other.

8.  If P is equidistant from all the three sides, then P is the center of the in-circle and hence it is the incenter of the triangle.

If P is the incentre, then PB is the internal bisector.

Therefore, ∠PBC = [tex]\frac{1}{2}[/tex] ∠ABC = 30°

10.  From the triangle sum property, ∠ M = 180 - (110 + 40) = 30.

Since, the side opposite to the smallest is the shortest, the correct order is:

KV, VM, KM

12.  Clearly, ∠ ABD is acute. Therefore, ∠ DBC > ∠ ABD.

Since, side opposite to larger angle is greater, DC is greater.

14.  Let the sides of the top triangle be p and q. So, two sides of whole triangle are 2p and 2q.

Now, if we compare the top small triangle and the whole triangle, they are similar by SAS similarity since,

the top angle is common and [tex]\frac{p}{2p}=\frac{q}{2q}=\frac{1}{2}[/tex].

Since, corresponding parts of similar triangles are proportionate,

[tex]\frac{3x}{5x+12} =\frac{1}{2}[/tex]

6x = 5x + 12

6x - 5x = 12

x = 12

Answer:

2.  Circumcenter is (-2, 1)

4.  Orthocenter is (5, 0)

6. II ∠DOS and ∠CAT are vertical and III ∠DOS and ∠CAT are adjacent

8.  m∠PBC = 30°

10.  KV, VM, KM

12.  DC is greater

14.  x = 12

Step-by-step explanation:

Put the value of x = 4 to the expression 3x + 2.

(3)(4) + 2

first multiplication and next addition

= 12 + 2 = 14

Answer:

Correct choice is D

Step-by-step explanation:

The graph of the function shows that the function is not continuous at point x=3.

When moving to the point x=3 from the left side, you can see that y approaches to -1. When moving to the point x=3 from the right side, then y approaches to -3 and at x=3, y=7. This gives you that the limit doesn't exist.

Answer:

The slope is  -14/11

Step-by-step explanation:

To find the slope, use the formula

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

   = (8--6)/ (-1-10)

   = (8+6)/(-1-10)

   = 14/-11

  = -14/11

The square root of 101 lies between 10 and 11, as 101 falls between the perfect squares of these two numbers (100 and 121, respectively).

The square root of 101 is a value which, when multiplied by itself, results in 101. In order to find which two consecutive numbers this square root lies between, we need to consider which two perfect squares it falls between. The perfect squares closest to 101 are 100 (which is 10^2) and 121 (which is 11^2). Therefore, the square root of 101 lies between the numbers 10 and 11.

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Question

Find 1/8 of 12. Express your answer in simplest form.

1 1/2

2/3

1/96

12/8

Answer:

Step-by-step explanation:

12 : 8 = 1.5 (1 1/2)

To find 1/8 of 12, multiply 12 by 1/8 and simplify the fraction to its simplest form, which is 3/2.

To find 1/8 of 12, we can multiply 12 by 1/8. Multiplying fractions is done by multiplying the numerators together and multiplying the denominators together. In this case, 12 multiplied by 1 equals 12, and 8 multiplied by 1 equals 8, so the answer is 12/8.

However, 12/8 is not in simplest form because the numerator and denominator have a common factor of 4. To simplify the fraction, we divide both the numerator and denominator by 4. 12 divided by 4 is 3, and 8 divided by 4 is 2. So, the simplest form of 12/8 is 3/2.

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Answer:

the answer would be 28.

Step-by-step explanation:

you're multiplying the top and bottom by 7. 3 *7=21 for the bottom

4*7 = 28 for the top

Hope this helps

-Kayla

Answer:

The answer is A. 28

Step-by-step explanation:

When you divide 21 into 3 you get 7.

So you have to multiply 7 to get 21. Whatever you do to the bottom or top you have to do to the opposite so you have to  multiply 7 by 4 and you get 28.

Hope this helps

Step-by-step explanation:

Let's get an important definition out of the way first. A parallelogram is a quadrilateral with two pairs of parallel sides. We can translate this idea to coordinate geometry by saying that each pair of opposite sides must have the same slope.

Slope, as you might remember, is a measure of change. Specifically, it's the change in a line's y value (Δy) divided by the corresponding change in its x value (Δx). This means that if we can prove that:

We'll have proved our figure is a quadrilateral. Let's prove those cases, then. For KA and IT:

[tex]slope_{KA}\stackrel{?}{=}slope_{IT}[/tex]

To find the slope of any line segment, we can find the difference between the corresponding coordinates of its endpoints and divide the difference in y-coordinates by the difference in x-coordinates. Since the endpoints of KA are K(0, 0) and A(a, 0), the slope of these points is

[tex]slope_{KA}=\frac{0-0}{a-0} =\frac{0}{a} =0[/tex]

We can do this same for IT using its endpoints I(a + b, c) and T(b, c):

[tex]slope_{IT}=\frac{c-c}{b-(a+b)} =\frac{0}{-a}=0[/tex]

Since 0 = 0, we can say that [tex]slope_{KA}=slope_{IT}[/tex], and we've proven our first condition. Now we just need to prove that [tex]slope_{KT}=slope_{AI}[/tex]:

[tex]slope_{KT}\stackrel{?}{=}slope_{AI}[/tex]

Using K(0, 0) and T(b, c), [tex]slope_{KT}=\frac{c-0}{b-0}=\frac{c}{b}[/tex], and using A(a, 0) and I(a + b, c), [tex]slope_{AI}=\frac{c-0}{(a+b)-a}=\frac{c}{b}[/tex], proving that [tex]slope_{KT}=slope_{AI}[/tex].

Since we've proven that [tex]slope_{KA}=slope_{IT}[/tex] and [tex]slope_{KT}=slope_{AI}[/tex], we've proven that the quadrilateral KAIT is, by definition, a parallelogram.

To find the height of the ramp at its highest point, we can use trigonometry and the sine function.

To find the height of the ramp at its highest point, we need to determine the vertical component of the ramp. We can use trigonometry to do this. Assuming the ramp forms a right triangle with the ground, we can use the sine function to calculate the height:

height = ramp length * sin(angle)

Given that the ramp length is 24.5 feet and the angle is not provided, we cannot calculate the exact height without that information. Please provide the angle, and I'll be happy to help you find the height.

Answer:

7/11 = 0.6363... and so on.

Step-by-step explanation:

How I did it: 7/11  =      11   so over the 7 you put a 0 and . over the 0s you put 636363 under the 7 you put a 6 and under the 0 next from the 7 you put a 6 also under the 6. then you put a line under the 66. under the 6 from the right you put a 4 next to the four you put a 0 then you make 33 under the 40 and make a line. on the 3 of the right side you put a 7 under and take a 0 again you put 66 under the 70 and make a line, underthe line you put 40 again but you put the 4 under the 6 on the right side and then put 33 under 40 make a line and put 7 on the right side of the 33 and the 0: 70. thats it I hope you understood! and it helped.

Goodluck!

^.^

nth term in an Arithmetic Sequence is given by :

✿  [tex]\mathsf{T_n = a + (n - 1)d}[/tex]

Where : a is the First term and d is the Common Difference

Given : First term (a) = 1 and Common Difference (d) = 5

[tex]\mathsf{\implies T_2_3 = 1 + (23 - 1)5}[/tex]

[tex]\mathsf{\implies T_2_3 = 1 + (22)5}[/tex]

[tex]\mathsf{\implies T_2_3 = 1 + 110}[/tex]

[tex]\mathsf{\implies T_2_3 = 111}[/tex]

So, The 23rd Term of the Arithmetic Sequence is 111

The 23rd term of the arithmetic sequence will be 111.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the 23 rd term of the arithmetic sequence whose common difference is d=5 and whose first term is a1=1

The 23rd term will be calculated as,

T₂₃ = a₁ + d(n-1)

T₂₃ = 1 + 5(23-1)

T₂₃ = 111

Therefore, the 23rd term of the arithmetic sequence will be 111.

To know more about arithmetic progression follow

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Answer:

The area of the box is equal to 9^3 = 729 in^3

729<1000  

Step-by-step explanation:

No since the volume of the box is less than the total volume of the cubes

Answer:

b) 8.5 feet

Step-by-step explanation:

Answer:

Answer is 9.6

Step-by-step explanation:

From the illustration above. See attachment for interpretation of this illustration.

To find the part label a in the attachment which is the length of the foot of the guide wire from the ground to the palm tree, we apply the sine rule, which says

a/sineA = b/sineB

In this case

a = ? , A = 58° , b = 6ft, B = 32°

So

a/sine58 = 6/sine32

a/0.848 = 6/0.5299

a = 6*0.848/0.5299

a = 5.088/0.5299

a = 9.601 ~ 9.6

Answer:

12) -60/1 =60

14) 110

16)45

18) 7

32) -18

Step-by-step explanation:

Answer:

Distributive Property

Step-by-step explanation:

They distributed the -3 to x and 4. In this case, to distribute the -3, you multiply it to each term.

-3 × x = -3x.

-3 × 4 = -12.

-3x - 12

Answer:

Do you have the rest of the answers for the test??? I'm taking it right now

Step-by-step explanation:

Answer:

The answer is one mile from town.

Step-by-step explanation:

First you would change 2/3 to 4/6

Ignore the part where he took a break. This isn't about time its distance.

Then you would add 4/6 and 5/6 and end with 1  1/2

Last you subtract 1/2 from 1  1/2 and you get the answer of 1

Answer:

x=3

Step-by-step explanation:

3(x+1)-8=14-2(3x-4)

3x+3-8 = 14 -6x+8

3x+3-8-14+6x-6=0

9x-27 = 0

9(x-3) = 0

x-3=0

x=3

The solution to the equation is x=3.

To solve the equation 3(x+1)−8=14−2(3x−4), you can follow these steps:

Distribute the constants and variables on both sides of the equation.

Combine like terms.

Isolate the variable on one side of the equation.

Solve for the variable.

[tex]\text{Starting equation: } & 3(x+1) - 8 = 14 - 2(3x-4) \\\text{Distribute terms: } & 3x + 3 - 8 = 14 - 6x + 8 \\\text{Combine like terms: } & 3x - 5 = -6x + 22 \\\text{Rearrange terms: } & 3x + 6x = 22 + 5 \\\text{Simplify: } & 9x = 27 \\\text{Solve for } x: & x = \frac{27}{9} = 3[/tex]

complete question;

The given equation is:

[tex]$$3(x+1) - 8 = 14 - 2(3x-4)$$[/tex]

The answer is 12

i hope this helps

Answer:

the answer is 12 units squared

Step-by-step explanation:

count the boxes and add the halves together.

Hope this helps :)

Answer:

see explanation

Step-by-step explanation:

to find the intercepts, that is where the line crosses the x and y axes

• let x = 0, in the equation for the y-intercept

• let y = 0, in the equation for x-intercept

x = 0

⇒ - 5 = 4y ( divide both sides by 4 )

y = - [tex]\frac{5}{4}[/tex] ← y- intercept

y = 0

7x - 5 = - 6x ( add 6x to both sides )

13x - 5 = 0 ( add 5 to both sides )

13x = 5 ( divide both sides by 13 )

x = [tex]\frac{5}{13}[/tex] ← x- intercept

Answer:

770

Step-by-step explanation:

3.5 x 220 = 770

770/3.5 = 220

770/220 = 3.5

To find what 3.5 multiplied by 220 is, you simply multiply the two numbers together to get 770. This can be related to weight calculations in personal training contexts.

This question demands basic understanding of mathematical operations (addition, subtraction, multiplication, division) in general and about multiplication in particular.

The question What's 3.5 x 220? is asking for the product of the two numbers, 3.5 and 220, which is a mathematics calculation. To find the answer, you multiply 3.5 by 220, which equals 770.

Another way is to find 350% of 220 which means 350/100 * 220 = 770

This calculation is relevant for the student's personal training classes, potentially relating to the amount of weight lifted or the calculation of potential energy.

Therefore, as per the above explaination, the correct answer is 770.

Answer:

x = 2.5 inches. Or

x = 5/2

Step-by-step explanation:

Length: 7 + 2x

Width: 5 + 2x

Note that you have to add x at each end of the picture and onto each part of the width.

The entire area is 120 square inches.

Formula

L*W = Area

(2x + 7)(2x + 5) = 120

Solution

4x^2 + 10x + 14x + 35 = 120                Subtract 120 from both sides. Add xs

4x^2 + 24x + 35 - 120 = 0

4x^2 + 24x - 85 = 0                             Factor

(2x + 17)(2x - 5)

2x + 17 has no meaning. It will give -  8.5 which is not possible.

2x - 5 =0

2x = 5                                                  Divide by 2

x = 5/2

x = 2.5

Note: I don't know which one the computer is looking for.

Answer:

The right option is A) 0.72%

Step-by-step explanation:

We have given,

Number of shares = $100

Park stock per share = $52.89

Total parks stock = 100×52.89 = $5289

Since company paid annual dividends of $0.38 per share.

Total annual dividend company paid = 100×0.38 =$38

Total annual yield in % = [tex]\frac{38}{5289} *100[/tex] = 0.718 % ≈0.72%

Hence the right option is A) 0.72%

A.72% I took the test at k12

Answer:

3 miles per hour

Step-by-step explanation:

We need to subtract the two numbers to find the difference in speeds

4/5 - 3/4

We need to get a common denominator of 20

4/5 *4/4 - 3/4 *5/5

16/20 - 15/20

1/20  

The car going 4/5 miles per minute is going 1/20 miles per minute faster than the car going 3/4 miles per minute.

The question asks for miles per hour, not miles per minute.  We know  that there are 60 minutes per hour.

1/20 miles per minute * 60 minutes / hour

60/20 miles/hour

3 miles/ hour

The car going 4/5 miles per minute is going 3 miles per hour faster than the car going 3/4 miles per minute.

Let the smaller number = X

Then the larger number is 3x+4 ( four more than 3 times the smaller number)

The sum of both numbers = 80

so you have X + 3X+4 = 80

Simplify the left side:

4x+4 = 80

Subtract 4 from each side:

4x = 76

Divide both sides by 4:

X = 76/4

X = 19

The smallest number is 19

The largest number is 80 - 19 = 61 ( check: 3*19 = 57+4 = 61)

The two numbers are 19 and 61

Answer:

B. If x isn’t divisible by 4, then x isn’t divisible by 2.

Step-by-step explanation:

contra positive statement is obtained by interchanging the hypotheses and conclusion of the inverse statement.

Here given that statement p is

If x is divisible by 4, then x is divisible by 2.

To write contrapositive of p, first we interchange the hypothesis.

Then it would look like

If x is divisible by 2, then x is divisible by 4.

Now we make conclusion as negative. i.e.

If x is not divisible by 4, then x is not divisible by 2.

This is the contra positive statement of p

Hence option B is right.

Answer:

C. If x isn’t divisible by 2, then x isn’t divisible by 4.

Step-by-step explanation:

I just took a test with this question and this was the right answer

~Please mark me as brainliest : )