in a game, you have 1/42 a probability of winning $67 and a 41/42 probability of losing $7. what is your expected value?

The sum of the interior angles of the polygon is 540° by the Sum of angles property of pentagon.

We know that the diagram is a plane figure with five sides, which means it is a Pentagon (Five-sided polygon), when from one vertex a line was drawn to the non-consecutive vertices, we need to find the sum of the interior angles of the polygon:

The total of interior angles in a polygon can be found by multiplying the quantity of triangles by 180°. It is noticeable that the number of triangles is consistently two less than the number of sides.

As a result, we can conclude that the formula for determining the sum of interior angles in a convex polygon with n sides is:

S = (n - 2) × 180°

This formula provides the sum of interior angles for any polygon.

Solution: A pentagon has five sides.

Therefore, by the angle sum formula we know that:

S = (n − 2) × 180°

Here we know that n = 5 as pentagon has 5 sides,

Hence, by the Sum of angles of pentagon = (5 − 2) × 180°

S = 3 × 180°

S = 540°

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Answer:

540°

Step-by-step explanation:

The Garden B has 76.47% more data than Garden A.

Percentage is a way of expressing a number as a fraction of 100. It is a commonly used method to represent proportions, rates, and percentages in various fields such as finance, economics, and statistics.

Let's first find the actual values of Garden A's and Garden B's data:

For Garden A, we know that 75% of its data is equal to 12.75. We can use this information to set up an equation:

0.75x = 12.75

Solving for x, we get:

x = 12.75 / 0.75 = 17

Therefore, Garden A's total data is 17.

For Garden B, we know that 50% of its data is equal to 15. We can use this information to set up an equation:

0.5x = 15

Solving for x, we get:

x = 15 / 0.5 = 30

Therefore, Garden B's total data is 30.

Now, to find how much more percent Garden B has than Garden A, we can use the formula:

percent difference = |(Garden B - Garden A) / Garden A| * 100

Plugging in the values, we get:

percent difference = |(30 - 17) / 17| * 100 = 76.47%

Therefore, Garden B has 76.47% more data than Garden A.

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Answer:

x =107+88 =195, 360 -195 =165

Answer:

73°

Step-by-step explanation:

In an inscribed quadrilateral opposite angles are supplementary( they add up to 180) so angle x and its opposite angle( which is 107°) are equal to 180.

x + 107 = 180

Subtract 107 from both sides to isolate the x

x = 73

First, we need to calculate the percentage of citizens who chose either Snakes or Dogs.

The percentage of citizens who chose Dogs is 26%, which is equivalent to 0.26 as a decimal.

The percentage of citizens who chose Snakes is 10%, which is equivalent to 0.10 as a decimal.

To find the number of citizens who chose either Snakes or Dogs, we need to multiply the total number of citizens by the combined percentage of Snakes and Dogs:

0.26 + 0.10 = 0.36

So the combined percentage of Snakes and Dogs is 36%.

To find the number of citizens who chose Snakes or Dogs, we can multiply the total number of citizens by this percentage:

0.36 x 95,000 = 34,200

Answer:  [tex]a_n = 2n+11[/tex]

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

Explanation:

The gap between adjacent terms is 2.

We add 2 to each term to get the next. Therefore, d = 2 is the common difference.

The first term is [tex]a_1 = 13[/tex]

Use that and the value of d to determine the nth term formula of this arithmetic sequence.

[tex]a_n = a_1 + d(n-1)\\\\a_n = 13 + 2(n-1)\\\\a_n = 13 + 2n-2\\\\a_n = 2n+11 \textbf{ is the final answer}\\\\[/tex]

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

Check:

Plug in n = 1

[tex]a_n = 2n+11\\\\a_1 = 2*1+11\\\\a_1 = 2+11\\\\a_1 = 13\\\\[/tex]

That confirms 13 being the 1st term.

Now use n = 2

[tex]a_n = 2n+11\\\\a_2 = 2*2+11\\\\a_2 = 4+11\\\\a_2 = 15\\\\[/tex]

That matches with the fact 15 is the 2nd term.

I'll let you check the third term.

It is unlikely that carrying more or fewer pencils in one's backpack would have a direct impact on GPA.

To determine if there is a relationship between a student's GPA and the number of pencils in their backpack, Jordynn and Angie would need to conduct the following steps:

If a correlation is found, then it suggests that there may be a relationship between the students' GPA and the number of pencils in their backpack. However, in this case, it is unlikely that carrying more or fewer pencils in one's backpack would have a direct impact on GPA.

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Will is therefore more likely to choose a blue tile before choosing a yellow tile.

The likelihood or possibility of an event happening is measured by probability. It is represented by a number in 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. By dividing total number of favourable possibilities by the total number of potential outcomes, one can determine the probability of an occurring. In other respects, it is the proportion between the amount of alternative outcomes to the number of possible ways the event could happen. In many fields, including statistics, mathematics, physics, economics, and the social sciences, probability is used to create predictions and well-informed judgements based on the likelihood that events will occur.

given

We must take into account the likelihood of each event and then combine them together in order to get the probability of choosing a blue tile first, followed by a yellow tile.

Will picks blue first, then yellow, therefore P(Will) = (6/15) * (5/15) = 2/15

The likelihood that Joan will first choose a blue tile is the same as before: 6/15.

Joan picking a yellow tile on her second pick thus has a 5/14 chance of doing so. Hence, the likelihood that Joan will choose a blue tile first, followed by a yellow tile, is:

P(Joan chooses yellow first, then blue) = (6/15) * (5/14) = 3/35

Will is therefore more likely to choose a blue tile before choosing a yellow tile.

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Matthew's family cannot drive for 25 days without the warning light coming on, and they will need to refill the tank before that point.

If the car uses 0.6 gallons of fuel per day, then in 25 days, it will use:

= 0.6 gallons/day × 25 days

= 15 gallons

This means that if Matthew's family starts with a full tank of 14 gallons, they will not be able to drive for 25 days without running out of fuel.

The question asks if they can drive for 25 days without the warning light coming on. If the warning light comes on when there is 1.5 gallons or less of fuel remaining, then Matthew's family can drive for:

= 14 gallons - 1.5 gallons

= 12.5 gallons before the warning light comes on.

Since they use 0.6 gallons of fuel per day, they can drive for:

= 12.5 gallons / 0.6 gallons/day

≈ 20.8 days without the warning light coming on.

Therefore, they cannot drive for 25 days without the warning light coming on, and they will need to refill the tank before that point.

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Part A: compound inequality for the speed Shala's car: | x - 65 | ≤ 2.5

Part B: 67 mph < 67.5 (maximum value) Thus, she will not get the ticket.

Two or more inequalities are connected together with or or and to form a compound inequality (also described as a combined inequality). A value must only make one aspect of an inequality true in order to be the solution to an or inequality. An inequality's solution must make both portions true in order to succeed.

Speed limit set by car's cruise control function = 2.5 mph.

Speed limit set by Shala = 65 mph.

Thus,

Maximum speed of car = 65 + 2.5

Minimum speed of car = 65 - 2.5

Let x represents the current speed of car,

x ≤ 65 + 2.5 or x ≥ 65 - 2.5

x - 65 ≤ 2.5 or x - 65 ≥ - 2.5

x - 65 ≤ 2.5 or - (x-65) ≤ 2.5

| x - 65 | ≤ 2.5 ( required compound inequality)

Now,

65 - 2.5 ≤ x ≤ 65 + 2.5

62.5 ≤ x ≤ 67.5

In interval notation; [62.5, 67.5]

The inequality on the number is drawn.

If Shala goes with 7 mph over the speed limit.

60 + 7 = 67 mph < 67.5 (maximum value)

Thus, she will not get the ticket.

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The ratios of[tex]4[/tex]:[tex]5[/tex] and [tex]40[/tex]:[tex]3[/tex] are not equal, the initial ratios of [tex]12[/tex]:[tex]15[/tex] and [tex]200:15[/tex]are not proportionate.

When two or more numbers or values are compared, the outcome is the ratio, which is expressed as a fraction or a colon. It is used to describe how the relative magnitudes of two or more objects correlate. Ratios can be used to evaluate quantities of the same unit or of different units.

For instance, a ratio of [tex]3:1[/tex] is used to compare three units to four, while a ratio of [tex]2:1[/tex] is used to compare two units to one. Ratios can be expressed or simplified in a variety of methods.

The ratio [tex]6:9[/tex] will become[tex]2:3[/tex] if both parts are multiplied by[tex]3[/tex]. Ratios can also take the shape of decimals or percentages.

[tex]12:15 =200:15[/tex]

multiplying both the left side  by[tex]3[/tex] and right side by [tex]5[/tex] we get

[tex]4:5= 40:3[/tex]

Hence it shows that they are not equal so they are not proportionate

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Answer:

sin A = cos B = a/h

A and B are complements of each other, so A + B = 90°. It follows that B = 90° - A, meaning sin A = cos(90° - A).

Thus, the measure of the minor arc CG for the given chord for the circle is found as: arc CG = 30°.

The shortest arc that connects two points on a circle is called a minor arc.

For the given figure:

Using the intersecting chord theorem:

m∠FED = 1/2(arc CG - arcFD)

39 = 1/2(arc CG - 48)

arc CG - 48 = 39*2

arc CG = 78 -  48

arc CG = 30°

Thus, the measure of the minor arc CG for the given chord for the circle is found as: arc CG = 30°.

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Complete question:

Find the measure of minor arc CG for the attached figure.

Answer:

Step-by-step explanation:4(3x+y)+2(x-5y)+x²=12x+4y+2x-10y+x²

=14x-6y+x²

=x²+14x-6y

Answer:

Step-by-step explanation:

Step 1:

Butterflies is greater than Snails

More=addition

GP: 28+9=B

Step 2:

28+2=30

30+7=37

Answer: 37 Butterflies

Hope this helps!

Given that,

Total butterflies = 28

Total snails = 9

More butterflies than snails are = butterflies + snails

[tex]\implies28+9[/tex]

[tex]\implies 37[/tex]

Therefore, there are 37 butterflies.

There is no significant difference in the average scores of two groups of SOC 390 students who took Exam 1 in the spring and fall semesters, respectively, as per the two-sample t-test with a p-value of 0.388.

The average score of the spring group of 50 students in SOC 390 on Exam 1 was 80, with a standard deviation of 12, while the average score of the fall group of 52 students was 81, with a standard deviation of 6. To determine if the difference in the means of the two groups is statistically significant, we can use a two-sample t-test.

Assuming unequal variances, the t-value for the two groups is 0.87, with a corresponding p-value of 0.388. Since the p-value is greater than the standard alpha level of 0.05, we fail to reject the null hypothesis that the two groups have equal means.

Therefore, we can conclude that there is no significant difference in the average scores of the two groups of SOC 390 students who took Exam 1 in the spring and fall semesters, respectively.

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The complete question is :

What is the difference between the average scores of two groups of students who took Exam 1 in SOC 390 in the spring and fall semesters, respectively, given that the spring group consisted of 50 students who scored an average of 80 with a standard deviation of 12, and the fall group consisted of 52 students who scored an average of 81 with a standard deviation of 6?

Answer:If 104° is a measure of one of the vertical angles formed by the intersection of two straight lines, then the measure of the other vertical angle would also be 104°. This is because vertical angles are always congruent, which means they have the same measure.

Step-by-step explanation:

Answer:

1/15 or approximately 0.067 or 6.7%.

Step-by-step explanation:

The total number of marbles in the bag is 3+2+4+1=10.

The probability of pulling a red marble on the first draw is 3/10, since there are 3 red marbles out of 10 total marbles.

Since we are not replacing the marble after each draw, the probability of pulling another red marble on the second draw decreases slightly. After one red marble has been drawn, there are only 2 red marbles left out of 9 total marbles. So the probability of pulling a second red marble is 2/9.

Therefore, the theoretical probability of pulling two red marbles without replacement is:

P(Red, Red) = P(Red on first draw) x P(Red on second draw, given that the first marble was red)

= 3/10 x 2/9

= 1/15

So the theoretical probability of pulling a red marble without replacement is 1/15 or approximately 0.067 or 6.7%.

The value of the theoretical probability of pulling a red marble without replacement is,

= 3/10

= 0.3

= 30%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A bag has 3 red marbles, 2 blue, 4 green and 1 yellow.

Hence, Total marbles = 3 + 2 + 4 + 1 = 10

Thus, The value of the theoretical probability of pulling a red marble without replacement is,

P = Desired Outcomes / Total number of outcomes.

P = 3 / 10

P = 0.3

P = 30%

Thus, The value of the theoretical probability of pulling a red marble without replacement is,

= 3/10

= 0.3

= 30%

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The area of the triangle is approximately 11.524 km²

What is an area?

We can find the area of the triangle using the formula:

Area = (1/2) * a * b * sin(C)

where a and b are the lengths of the two sides and C is the angle between them.

In this case, a = 5 km, b = 7 km, and C = 143°. However, before we can use this formula, we need to convert the angle to radians. We can do this by multiplying by pi/180:

C = 143 * pi/180

C ≈ 2.495 radians

Now we can substitute the values into the formula and calculate the area:

Area = (1/2) * 5 km * 7 km * sin(2.495)

Area ≈ 11.524 km²

Therefore, the area of the triangle is approximately 11.524 km².

What is triangle?

A triangle is a 2-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and is used in various fields such as mathematics, engineering, architecture, and art. Triangles can be classified into different types based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. The area of a triangle is calculated by using the formula A = 1/2 * base * height, where the base is the length of one of its sides and the height is the perpendicular distance between the base and the opposite vertex.

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Complete question is: The area of the triangle is approximately 11.524 km²

Answer:

To find the center and radius of the circle, we need to rewrite the equation in standard form, which is: (x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center of the circle and r is the radius. To rewrite the given equation in standard form, we need to complete the square for both x and y terms. Let's start with the x terms: x^2 - 12x = -(y^2 - 2y + 33) To complete the square for x, we need to add and subtract (12/2)^2 = 36: x^2 - 12x + 36 - 36 = -(y^2 - 2y + 33) (x - 6)^2 - 36 = -(y^2 - 2y + 33) Now

To find the center and radius of the circle given by the equation:

x^2 + y^2 -12x + 2y + 33 = 0

We need to rewrite the equation in standard form, which is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

To do this, we need to complete the square for both x and y terms by adding and subtracting appropriate terms inside the parentheses.

(x^2 - 12x) + (y^2 + 2y) + 33 = 0

To complete the square for x terms, we need to add (12/2)^2 = 36 inside the first set of parentheses and subtract it from the equation:

(x^2 - 12x + 36) + (y^2 + 2y) + 33 - 36 = 0

(x - 6)^2 + (y^2 + 2y) - 3 = 0

To complete the square for y terms, we need to add (2/2)^2 = 1 inside the second set of parentheses and subtract it from the equation:

(x - 6)^2 + (y^2 + 2y + 1) - 4 = 0

(x - 6)^2 + (y + 1)^2 = 4

Now we can see that the equation is in standard form, where (h, k) = (6, -1) is the center of the circle, and r^2 = 4, so the radius is r = 2.

Therefore, the center of the circle is (6, -1) and the radius is 2.

At Arcade Palace, each video game token costs 0.25.

At Arcade Palace, a child can buy 16 video game tokens for 4.

The total number or cost of something is the number or cost that you get when you add together or count all the parts

in it.

A number is a mathematical value used for counting or measuring or labeling objects. Numbers are used to performing

arithmetic calculations.

To find the cost per token, follow these steps:

Determine the total number of tokens (16) and the total cost (4).

Divide the total cost by the total number of tokens to find the cost per token.

In this case, 4 ÷ 16 tokens = 0.25 per token.

Therefore, at Arcade Palace, each video game token costs 0.25.

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Using the alternate angles theorem,

(a) The measure of angle ABQ is 54°

(b) The measure of angle CDE is 128°

From the question, we are to determine the measure of the unknown angles

First, let us produce line BCD to Z

Then,

m ∠FDZ = m ∠BCP

From the given diagram

m ∠BCP + 148° = 180° (Sum of angles on a straight line)

m ∠BCP = 180° - 148°

m ∠BCP = 32°

Therefore,

m ∠FDZ = 32°

Also,

m ∠EDZ = 84° - m ∠FDZ

m ∠EDZ = 84° - 32°

m ∠EDZ = 52°

m ∠CDE + m ∠EDZ = 180° (Sum of angles on a straight line)

m ∠CDE + 52° = 180°

m ∠CDE = 180° - 52°

m ∠CDE = 128°

m ∠ABQ + m ∠QBD = m ∠CDE (Alternate interior angles)

m ∠ABQ + 74° = 128°

m ∠ABQ = 128° - 74°

m ∠ABQ = 54°

Hence,

m ∠ABQ is 54°

and

m ∠CDE is 128°

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(6) / (4.5) = 4 / 3  =  1.333...

The level increased by 33-1/3 % .

The old level was  75%  of the new level.

The amount of water in the pool also had to

increase  33-1/3 % .  If you didn't have that

much water to put in the pool, you couldn't

change the surface level from  4.5ft  to  6ft .

An error made by Mariya resulted in incorrect graph and answer. The open circle at 208 should have been coloured to the left rather than to the right in the proper graph.

Mariya made a mistake in Step 1 of her work.

Step 1:

StartFraction a over negative 13 End Fraction less-than-or-equal-to negative 16

(Negative 13) StartFraction a over negative 13 End Fraction less-than-or-equal-to negative 16 (negative 13)

Mariya multiplied both sides of the inequality by -13, which would require her to flip the direction of the inequality symbol from "less than or equal to" to "greater than or equal to". However, she did not do so and continued to work with the original direction of the inequality.

The correct approach to solve the inequality would have been to multiply both sides by -13 and then flip the direction of the inequality as follows:

Step 1:

StartFraction a over negative 13 EndFraction less-than-or-equal-to negative 16

(-13) StartFraction a over negative 13 EndFraction greater-than-or-equal-to (-13) (16)

Step 2:

a greater-than-or-equal-to 208

Step 3:

A number line going from 205 to 211. An open circle is at 208. Everything to the right of the circle is shaded.

Therefore, Mariya's error in Step 1 led to an incorrect solution and an incorrect graph. The correct graph would have shaded everything to the left of the open circle at 208, instead of everything to the right.

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Answer: 3.45

Step-by-step explanation:

Answer:

aswer will be 11.25 hope this helps

The probability that a uniformly distributed random variable between 12 and 41 is between 22 and 35 is 41.7%.

Since the random variable is uniformly distributed between 12 and 41, the probability density function (PDF) of the random variable is constant within that interval and zero outside of it. Let X be the random variable between 12 and 41. Then,

f(x) = 1/(41-12) = 1/29, for 12 ≤ x ≤ 41

The probability that the random variable is between 22 and 35 can be found by integrating the PDF over the interval [22, 35]:

P(22 ≤ X ≤ 35) = ∫(22 to 35) f(x) dx = ∫(22 to 35) 1/29 dx

Using the definite integral, we get:

P(22 ≤ X ≤ 35) = [x/29] from 22 to 35

P(22 ≤ X ≤ 35) = (35/29 - 22/29) = 13/29

So, the probability that the random variable is between 22 and 35 is 13/29, which is approximately 0.4483 or 44.8% when expressed as a percentage rounded to one decimal place.

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The probability that the proportion of airborne virus in the sample of 553 viruses is greater than 5% is 0.1151.

According to the central limit theorem, if a large sample of n > 30 is selected from an unknown population and the sample proportion of each sample is calculated, the sampling distribution of the sample proportion obeys the normal distribution.

The mean of the sampling distribution (U) for this sample proportion is:

U = p

The standard deviation (p) of the sampling distribution for this sample proportion is:

U = √ ((p(1 - p)) /n )

The sample size is, n = 553 > 30 so the central limit theorem applies in this case.

Up = √((p(1 - p))/n) = √((0.04 * 0.96)/553) = 0.0083

Calculate the probability that the proportion of virus in the air in 553 virus samples is greater than 3% as follows:

P(p >0.03)

= P (p - Up > (0.

= 0.11507

≈ ≈ 0.1151

Therefore, the probability that the proportion of airborne virus in a sample of 553 viruses is greater than 3% is 0.1151.

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Answer:

- 40

Hope this helps!

Step-by-step explanation:

( 4d - 6 )( 4d - 4 )  :  Cross Multiply

( 4d × 4d ) + ( 4d × (-4)) + ((-6) × 4d ) + ((-6) × (-4))

[tex]16d^{2}[/tex] - 16d - 24d + 24  :  ( Combine like terms )

[tex]16d^{2}[/tex] - 40d + 24

There is No statisti-cally signi-ficant evidence against the teacher's-claim that Charlie is just guessing because the probability is very low.

The total number of True-false questions are = n = 201.

The probability of getting a correct answer by guessing is = p = 0.5,

Charlie answered 53.7% = 0.537 of the questions correctly,

So, P(p' ≥ 0.537)

⇒ P(z ≥ (0.537 - 0.5)/√(0.5×0.5)/201,

⇒ P(z ≥ 1.05) = 1 - P(z < 1.05)

⇒ 0.1469

Since, the probability is very low,

Therefore, there is not any significant evidence against the teachers claim.

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Step-by-step explanation:

This is an ordinary annuity  type of question :

FV = C [  ((1+i)^n) -1 )/i ]   plug in the numbers

 FV = 25 000 [ (1+.08)^9 -1 ]/ .08  = ~ $ 312 189