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The total number of possible outcomes when flipping a coin 8 times is 2^8 = 256.

a. To get exactly 6 heads, we need to choose 6 out of the 8 flips to be heads, and the remaining 2 flips to be tails. The number of ways to choose 6 out of 8 is given by the binomial coefficient (8 choose 6) = 28. Therefore, there are 28 possible outcomes with exactly 6 heads.

b. To get at least 3 heads, we need to count the number of outcomes with 3, 4, 5, 6, 7, or 8 heads. Using the same logic as part (a), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at least 3 heads.

Number of outcomes with 3 heads: (8 choose 3) = 56

Number of outcomes with 4 heads: (8 choose 4) = 70

Number of outcomes with 5 heads: (8 choose 5) = 56

Number of outcomes with 6 heads: (8 choose 6) = 28

Number of outcomes with 7 heads: (8 choose 7) = 8

Number of outcomes with 8 heads: (8 choose 8) = 1

Total number of outcomes with at least 3 heads = 56 + 70 + 56 + 28 + 8 + 1 = 219.

c. To get at most 6 heads, we need to count the number of outcomes with 0, 1, 2, 3, 4, 5, or 6 heads. Using the same logic as part (b), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 6 heads.

Number of outcomes with 0 heads: (8 choose 0) = 1

Number of outcomes with 1 head: (8 choose 1) = 8

Number of outcomes with 2 heads: (8 choose 2) = 28

Number of outcomes with 3 heads: (8 choose 3) = 56

Number of outcomes with 4 heads: (8 choose 4) = 70

Number of outcomes with 5 heads: (8 choose 5) = 56

Number of outcomes with 6 heads: (8 choose 6) = 28

Total number of outcomes with at most 6 heads = 1 + 8 + 28 + 56 + 70 + 56 + 28 = 247.

d. To get at most 2 heads, we need to count the number of outcomes with 0, 1, or 2 heads. Using the same logic as parts (b) and (c), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 2 heads.

Number of outcomes with 0 heads: (8 choose 0) = 1

Number of outcomes with 1 head: (8 choose 1) = 8

Number of outcomes with 2 heads: (8 choose 2) = 28

Total number of outcomes with at most 2 heads = 1 + 8 + 28 = 37.

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You can take a look at this, the image that I attached might help.

For example, the first one shifts left because the h value is positive 3. -(3) = -3.

The solution to the system by elimination is (-2, 4).

To solve the system using elimination, we need to eliminate one of the variables by multiplying one or both of the equations by a constant.

-6X = 18 - Y

9 = -3X - 8Y

Rewrite as

-6X = 18 - Y

3X = 9 - 8Y

So, we have

-6X = 18 - Y

6X = 18 - 8Y

Now we can add this equations to the second equation to eliminate x:

0 = 36 - 9Y

This gives

9Y = 36

So, we have

Y = 4

Recall that

-6X = 18 - Y

So, we have

-6X = 18 - 4

So, we have

-6X = 12

Divide by 2

X = -2

Therefore, the solution to the system is (-2, 4).

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Answer:

[tex]2\sqrt{65}[/tex] cm, decimal form is about 16.1 cm

Step-by-step explanation:

Use the pythagorean theorem:

A^2 + B^2 = C^2

A and B are legs, c is hypotenuse

First leg is 16, second leg is 2

Plug it in:

16^2 + 2^2 = hypotenuse^2

256 + 4 = hypotenuse ^2

260 = h^2

[tex]\sqrt[2]{260}[/tex] = h

To simplify the square root of 260, we can factor 260 into its prime factors:

260 = 2 x 2 x 5 x 13

Then, we can take out the pairs of identical factors from under the square root symbol:

sqrt(260) = sqrt(2 x 2 x 5 x 13)

= sqrt(2 x 2) x sqrt(5) x sqrt(13)

= 2sqrt(65)

[tex]2\sqrt{65}[/tex]

Answer:

16.2 or 16.00

Step-by-step explanation:

Leg #1 --->16

Leg #2 --->2

C ---> hypotenuse

16.12452---->16.12

16.12 rounded to the nearest tenth is 16.00

Required value of cosy is 12/13.

What is Complementary angle?

Two angles are said to be complementary if their addition is 90°.Let if one angle is x then the other angle will be 90° – x. Hence, we use these complementary angles for trigonometry ratios, where one ratio is complementary to another ratio by 90 degrees such as,

[tex]sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)[/tex]

Given, here x and y are complementary.

So, we can say that

[tex]x + y = {90}^{o} \\ y = {90}^{o} - x[/tex]

So,

[tex] \sin( x) = \frac{12}{13} \\ \sin( {90}^{o} - y) = \frac{12}{13} \\ \cos(y) = \frac{12}{13} [/tex]

Therefore, required value of cosy is 12/13.

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Answer: brainliest ?

-3 and -7

Step-by-step explanation:

As a result, they would pay: 5/6 x $36 = $30 as Kendie's family would shell out 1/6 less than the standard admission price.

In mathematics, the linear approach is a way when resolving issues with direct or negative proportion. It entails figuring out the value of one unit of a quantity and utilising that value to figure out the value of any given quantity divided by that number of units. For instance, using the unitary technique, if we know that 5 oranges cost $10, we may calculate the price of 10 apples by first dividing $5 by 5 to get $2 per apple, multiplying $two by 10 to get $20 for 10 apples, and then using the result to get the price of 5 apples. In industries where proportional correlations are regularly found, like banking, business, and science, the unitary technique is frequently employed.

given

On Sunday, Kendie's family would shell out 1/6 less than the standard admission price, or 5/6 of the standard admission price.

As a result, they would pay: 5/6 x $36 = $30 as Kendie's family would shell out 1/6 less than the standard admission price.

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Answer: 41/56

Step-by-step explanation:

first you would try to find a common denominator (or LCM) in this case, its 56 so the revised question is 48/56+7/56 because you have to change the numerator as well. if you subtract the numerators it is 41. so its 41/56. 41/56 is already in its simplest form, so the answer is 41/56

Answer:

there is no Modal number because all the numbers appears only once

Answer:

7x + 13

Step-by-step explanation:

because the correct answer is 7x+13

Answer:

[tex] {10}^{32} {10}^{6} = {10}^{38} [/tex]

Answer:

A. They have different y-intercepts but the same end behavior.

Step-by-step explanation:

From the shape of f we see that its a descending exponential  fnction, so the  factor taken to the power x will be a fraction,  and from the points the eqation is

f(x) = 2(1/4)^x + 2

and the y-intercept is 4

g(x) has y-intercept of 4(1/4)^0 + 2 = 6  so they are different.

As x approaches infinity  both  f and g approach 2 so the end behavior s the same.

Step-by-step explanation:

Radius simply means half of the diameter. In other words radius is the distance between the center of the circle to the outside of the circle

Answer:

To write the equation of the line that represents Calvin’s spending on candy, we need to first find the slope and the y-intercept of the line.

We can use the two points given in the problem: (4, 28) and (10, 25)

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

= (25 - 28) / (10 - 4)

= -3/6

= -1/2

The slope represents the rate at which Calvin is spending money on candy.

Now, we can use the point-slope form of the equation of a line to find the equation of the line.

y - y1 = m(x - x1)

y - 28 = (-1/2)(x - 4)

y - 28 = (-1/2)x + 2

y = (-1/2)x + 30

Therefore, the equation of the line that represents Calvin’s spending on candy is y = (-1/2)x + 30.

Answer: Equation that represents his spending on candy- y = (³⁄₁₀) x

X = number of candy

Step-by-step explanation:

y = money spend            x = number of candy

y = (m)x

cost for 10 pieces of candy = $(28 - 25) = $3

⇛ 3 = (m)x10 (x = 10 & y = 3)

⇛m=(³⁄₁₀)

Therefore the equation representing his spending on candy is

⇛ y = (³⁄₁₀) x

Number of clients who do not play either the piano or the guitar is 22

To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.

Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments

Substituting the given values, we get

|A ∪ B| = 46 + 58 - 17

|A ∪ B| = 87

Therefore, the number of clients who do not play either instrument is:

109 - 87 = 22

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Answer: A.

Step-by-step explanation: It is parallel because of the angles that are the same and if u fill all the angles up angles 2 and 6 will be congruent there fore its parallel

Answer:

A. Yes, because angles 2 and 6 are congruent.

Step-by-step explanation:

The lines arent touching, parallel. Angles 2 and 6 share the same angle, congruent.

The area of the rectangle is 231 square meters.

To find the area of a rectangle, we need to multiply its length by its width.

Given that the length of the rectangle is 21 meters and the width is 11 meters, we can find the area as:

Area = Length x Width

Area = 21 meters x 11 meters

Area = 231 square meters

Therefore, the area of the rectangle is 231 square meters.

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Answer:

Step-by-step explanation:

the triangles are similar, therefore with the measures in proportion

6 : 8 = 2 : x

x = 2 x 8 : 6

x = 16 : 6

x = 2.66 round 2.7

x - 4/3 ≤ 0 is equivalent to x ≥ 4/3, and they both represent the same set of values for x. My friend is correct.

The relationship between two values that are not equal is defined by inequalities.

When we subtract 4/3 from both sides; x ≤ 4/3 can be rewritten as:

x - 4/3 ≤ 0

-6x ≤ -8 can be simplified by dividing both sides by -6 and reversing the inequality which gives:

x ≥ 4/3.

Full question "Your friend says that the inequalities x ≤ 4/3 and -6x ≤ -8 is your friend correct? Explain the reason"

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The equation of the circle is (x + 1)² + (y - 1)² = 16.

option D

The radius of the circle is 4, and the center of the circle is (-1, 1).

The equation of a circle with center (a,b) and radius r is given by:

(x - a)² + (y - b)^2 = r²

In this case, the center of the circle is (-1, 1) and the radius is 4. Plugging these values into the equation, we get:

(x - (-1))² + (y - 1)² = 4²

Simplifying the equation, we get:

(x + 1)² + (y - 1)² = 16

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Answer:

The baseball team won 60% of the games they played.

Step-by-step explanation:

To find the percentage of games the baseball team won, we can use the following formula:

percentage = (wins / total games) x 100

where wins is the number of games won and total games is the total number of games played.

Substituting the given values, we get:

percentage = (9 / 15) x 100

percentage = 0.6 x 100

percentage = 60%

Therefore, the baseball team won 60% of the games they played.

Answer:

60%

Step-by-step explanation:

9 out of 15, written in *fraction form* is 9/15, when reduced down,  9/15 becomes 3/5. When you insert 3/5 into a calculator you get 0.6 . Since percentage is based off a x/100, you move the decimal point of 0.6 over 2 units to the right, you get 60, so it would in final would be 60/100 which equals 60%

* ( Ex.  1 out of 3 = 1/3 )

Happy Mathing <3

   -J

To find a reasonable estimate for the total time of the album, we can add the times of the shortest and longest songs and divide by 2 to find the average time per song, and then multiply by the total number of songs on the album.

The shortest song on the album is 1 minute and 14 seconds, which is equivalent to 74 seconds.

The longest song on the album is 5 minutes and 54 seconds, which is equivalent to 354 seconds.

Therefore, the average time per song is:

(74 + 354) / 2 = 214 seconds

And the total time of the album is approximately:

13 songs x 214 seconds/song = 2,782 seconds

Converting this to minutes and seconds, we get:

2,782 seconds = 46 minutes and 22 seconds

So a reasonable estimate for the total time of the album is about 46 minutes and 22 seconds.

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Answer:

18.62π square inches

Step-by-step explanation:

To find the surface area of the cylinder, we need to find the area of each of its components and add them together. We can use the net of the cylinder to visualize its components and dimensions.

First, let's find the area of the top and bottom circles. We know the diameter of each circle is 3.8 inches, so the radius is half of that, or 1.9 inches. The formula for the area of a circle is A = πr^2, so:

A(top and bottom circles) = 2π(1.9 in)^2

= 2π(3.61 in^2)

= 7.22π in^2

Next, let's find the area of the curved surface of the cylinder. The height of the cylinder is labeled as 3 inches, which is also the height of the rectangle in the net. The length of the rectangle is the circumference of one of the circles, which is πd (where d is the diameter). So:

length of rectangle = π(3.8 in) = 11.96 in

The formula for the area of the curved surface of a cylinder is A = 2πrh, where r is the radius and h is the height. We can use the radius we found earlier and the height of 3 inches to calculate the area of the curved surface:

A(curved surface) = 2π(1.9 in)(3 in)

= 11.4π in^2

Finally, we can add the areas of the top and bottom circles and the curved surface to get the total surface area of the cylinder:

Total surface area = A(top and bottom circles) + A(curved surface)

= 7.22π in^2 + 11.4π in^2

= 18.62π in^2

Therefore, the surface area of the cylinder in terms of π is 18.62π square inches.

The third outer loop execution (i = 3), the loop compares the third element (12) with the remaining elements in the list (13, 14, 15) for a total of 3 comparisons

Assuming the outer loop is a standard loop that iterates through the list from the first to the second-to-last element, the number of comparisons made during the third outer loop execution (i = 3) would be 3.

During the first outer loop execution (i = 1), the loop compares the first element (10) with the rest of the elements in the list (11, 12, 13, 14, 15) for a total of 5 comparisons.

During the second outer loop execution (i = 2), the loop compares the second element (11) with the remaining elements in the list (12, 13, 14, 15) for a total of 4 comparisons.

During the third outer loop execution (i = 3), the loop compares the third element (12) with the remaining elements in the list (13, 14, 15) for a total of 3 comparisons.

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Assuming you are using a standard bubble sort algorithm, during the third outer loop execution (i = 3), there will be 3 comparisons made.

The given list (10, 11, 12, 13, 14, 15) and the number of comparisons made during the third outer loop execution (i = 3):

In the first outer loop iteration (i = 1), there will be 5 comparisons (comparing elements at positions 1-2, 2-3, 3-4, 4-5, and 5-6).

In the second outer loop iteration (i = 2), there will be 4 comparisons (comparing elements at positions 1-2, 2-3, 3-4, and 4-5).

In the third outer loop iteration (i = 3), there will be 3 comparisons (comparing elements at positions 1-2, 2-3, and 3-4).

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using trignometric ratio of sine thee measure of the angle x to the nearest degree is 28 degrees

Trigonometric ratios are ratios of the sides of a right triangle, such as sine, cosine, and tangent, that are used to find missing side lengths or angles.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is typically measured in degrees or radians.

According the given information:

We can use the trigonometric ratio of sine to find the measure of the angle x.

sin(x) = opposite/hypotenuse

In this case, the opposite side is the height of the triangle, which is 13, and the hypotenuse is the length of the diagonal line connecting the base and the top of the triangle. We can use the Pythagorean theorem to find the length of the hypotenuse.

hypotenuse² = base² + height²

hypotenuse² = 22² + 13²

hypotenuse² = 769

hypotenuse ≈ 27.73

Now we can substitute the values into the sine ratio:

sin(x) = 13/27.73

x ≈ 28 degrees

Therefore, the measure of the angle x to the nearest degree is 28 degrees.

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Answer:in your mouth

Step-by-step explanation:

The drive-thru that typically has more wait time is

Burger Quick, because it has a larger median.

Option A is correct.

Because Burger Quick's box plot displays a higher interquartile range (from 9.5 to 24) than Super Fast Food (from 8.5 to 15.5), Burger Quick often has longer wait times.

Additionally, Burger Quick's median (15.5) is greater than Super Fast Food's median (12), demonstrating that Burger Quick's middle value of reported wait times is higher than Super Fast Food's middle value of reported wait times.

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The equation of line passes through the point (2, -2) and is perpendicular to the line represented by y=2/5x+2 is y = -5x/2+3

Given that a line is passing through the point (2, -2) and is perpendicular to the line y = 2x/5+2, we need to find the equation of the line,

The equation of line is, y = mx + c, where m is the slope,

So, we know that the slopes of the perpendicular lines are negative reciprocal of each other,

So, the slope of the required line is -5/2.

Therefore, the equation will be

y = -5x/2 +c

To find c put x = 2, y = -2

-2 = -5(2)/2 + c

-2 = -5 + c

c =3

Hence, the equation is, y = -5x/2+3

Therefore, the equation of line passes through the point (2, -2) and is perpendicular to the line represented by y=2/5x+2 is y = -5x/2+3

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