The probability of a high school basketball team winning any game is 58%. This team is in a six-game tournament,


and the games are played independently of one another. Let X represent the number of games the team might win


in this tournament. What are the mean and standard deviation of X?

The first six terms of the sequence are 1, 1, 2, 3, 5 and 8. The solution has been obtained by using arithmetic progression.

What is arithmetic progression?

In an arithmetic progression (AP) sequence of numbers, there is always the same amount of difference between any two subsequent integers. Arithmetic Sequence is another name for it.

We are given a sequence as a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + a[tex]_{n-2}[/tex] where a₀ = 0 and a₁ = 1.

So, the first term is a₁ = 1

The second term is

a₂ = a₂₋₁ + a₂₋₂

a₂ = a₁ + a₀

a₂ = 1

The third term is

a₃ = a₃₋₁ + a₃₋₂

a₃ = a₂ + a₁

a₃ = 1 + 1

a₃ = 2

The fourth term is

a₄ = a₄₋₁ + a₄₋₂

a₄ = a₃ + a₂

a₄ = 2 + 1

a₄ = 3

The fifth term is

a₅ = a₅₋₁ + a₅₋₂

a₅ = a₄ + a₃

a₅ = 3 + 2

a₅ = 5

The sixth term is

a₆ = a₆₋₁ + a₆₋₂

a₆ = a₅ + a₄

a₆ = 5 + 3

a₆ = 8

Hence, the first six terms of the sequence are 1, 1, 2, 3, 5 and 8.

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Answer:

Hi There! Here's your answer.

Answer:

( 11 )y + ( 1 )z

Step-by-step explanation:

8y + 3y

5z - 4z

The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour. The solution has been obtained by using the concept of slope.

What is a slope?

In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate.

We are given that the graph of the line passes through (0,8) and (3,6) .

So,

Slope of the line = (6 - 8) ÷ (3 - 0) = -2/3

From this, we get the equation of line as

y - 6 = -2/3 (x - 3)

Now, for y-intercept, we need to put x = 0

So, we get

⇒y - 6 = -2/3 (-3)

⇒y - 6 = 2

⇒y = 8

Hence, the slope is negative two thirds, and the y-intercept is 8.

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Answer:

[tex]\mbox{\large \boxed{ 0.98}}[/tex]

Step-by-step explanation:

Cos H = ratio of the base to the length of the hypotenuse

In this triangle, the base = 40, hypotenuse = 41

cos H = 40/41 = 0.9756

To the nearest hundredth this would be 0.98

Using percentages we can conclude that out of 800 people, 20% of the people who attended the football match were teenagers, 160.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.

If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction.

Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

So, we know that:

800 people attended the football game.

20% were teenagers.

Then, the number of teenagers was:

= 800/100*20

= 8*20

= 160

Therefore, using percentages we can conclude that out of 800 people 20% of the people who attended the football, match were teenagers, and 160 were.

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Answer:

-7/8

Step-by-step explanation:

slope = Δy/Δx = (-2 - 5) / (8 - 0) = -7/8

Answer:

To make a frame with an area of 30in², Travis needs to cut out a piece of steel with an area of A = (11+2x)(6+2x)in², where x is the width of the frame. The inside of the frame must be 11in by 6in, so the width of the frame must be x = (30 - 11*6)/4 = 2.25in. The total area of the piece of steel must therefore be A = (11+2*2.25)(6+2*2.25) = 30in².

Step-by-step explanation:

To determine the value of x that will result in a final area of the frame of 30in², we can use the equation for the area of the piece of steel before cutting out the frame:

A = (11 + 2x)(6 + 2x)

We can expand this expression to get:

A = 66 + 44x + 12x^2

Since the inside of the frame has to be 11in by 6in, the area of the frame is 11 * 6 = 66in². So, we want to find the value of x that will result in the area of the piece of steel being equal to the area of the frame plus 30in². This means we want to find the value of x that will satisfy:

66 + 44x + 12x^2 = 96

Expanding the left-hand side of this equation and collecting like terms, we get:

12x^2 + 44x = 30

Dividing both sides of the equation by 12, we get:

x^2 + 3.67x = 2.5

To solve for x, we can use the quadratic formula or factoring. Once we have found the value of x, we can use it to determine the dimensions of the piece of steel before cutting out the frame.

Using permutations and combinations, we know that a total of 60,060 different arrangements of flowers can be made in a row.

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations.

When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination.

Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colors.

Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.

So, we have:

3 yellow, 4 red, and 6 blue flowers.

3 + 4 + 6 = 13

Now, the number of arrangements in the row will be:

= 13!/3!4!6!

= 6,22,70,20,800/6*24*720

= 6,22,70,20,800/1,03,680

= 60,060

Therefore, using permutations and combinations, we know that total of 60,060 different arrangements of flowers can be made in the row.

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So the perimeter of the octagon is approximately 45.25 centimeters (rounded to two decimal places).

In geometry, a shape's perimeter is sometimes referred to as its total length. By adding up the lengths of all of an object's sides and borders, one can determine the circumference of something such as a form. The perimeter of a form can be calculated by adding up all of the edges' lengths. For instance, a rectangular with dimensions of 24 yards long as well as 15 yards wide will have a 78 yard perimeter.

Here,

To find the perimeter of the octagon, we need to determine the length of each side of the octagon.

First, let's find the length of the diagonal of the smaller square. We can use the Pythagorean theorem:

d²=4² + 4²=

d² = 16+16 =32

d = √32

=> d = 4√2

​

This diagonal of the smaller square is also the side length of the overlapping square.

Next, let's find the length of one of the sides of the larger square that overlaps with the smaller square. Since the length of the larger square is 6cm, the side length of the overlapping region (part of the larger square that overlaps with the smaller square) is:

6 - 4√2

Finally, the length of one of the sides of the octagon is the sum of the side lengths of the two squares that overlap, minus the side length of the overlapping square (since this side is counted twice):

=> 6 + 6 - 4√2 - 4√2 - (6 - 4√2)

Therefore, the perimeter of the octagon is:

=>8 (12 - 6√2) = 96 - 48√2

So the perimeter of the octagon is approximately 45.25 centimeters (rounded to two decimal places).

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Answer:

[tex]\textsf{Standard form}: \quad (x+11)^2+(y-15)^2=81[/tex]

[tex]\textsf{Simplified form}: \quad x^2+22x+y^2-30y+265=0[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Equation of a circle in standard form}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Given the center is (-11, 15) and the radius is 9:

Substitute the values of a, b and r into the equation of a circle:

[tex]\implies (x-(-11))^2+(y-15)^2=9^2[/tex]

[tex]\implies (x+11)^2+(y-15)^2=81[/tex]

To write the equation in simplified form, expand the brackets:

[tex]\implies x^2+22x+121+y^2-30y+225=81[/tex]

Collect like terms:

[tex]\implies x^2+22x+y^2-30y+225+121-81=0[/tex]

[tex]\implies x^2+22x+y^2-30y+265=0[/tex]

The probability that x is between 25 and 30 is 0.087.

The cumulative distribution function (CDF) of an exponential distribution with mean 25 is given by:

F(x) = 1 - exp(-x/25)

The probability that x is between 25 and 30 can be found by evaluating the CDF at x = 30 and x = 25 and subtracting the two values:

P(25 < x < 30) = F(30) - F(25) = (1 - exp(-30/25)) - (1 - exp(-25/25))

= (1 - exp(-1.2)) - (1 - exp(-1))

= 0.255 - 0.368

= 0.087

So, the probability that x is between 25 and 30 is 0.087.

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We divided both sides of the equation by (3/8) to get x = (40/3), the number is 40/3.

Let the number be x.

Then one half of three fourths of x can be expressed as [tex](3/4)*(1/2)*x = (3/8)*x[/tex]

Two fifths of x can be expressed as[tex](2/5)*x[/tex]

Therefore, according to the given statement, [tex](3/8)*x = (2/5)*x - 20[/tex]

Solving for x, we get: x = (40/3)

Therefore, the number is 40/3.

To calculate this, we first wrote the given statement in terms of fractions. Then we used algebraic manipulation to solve for x. We multiplied both sides of the equation by the LCD, 40, to get [tex]40*(3/8)*x = 40*(2/5)*x - 20*40[/tex]. Then we combined like terms to get ([tex]3/8)*x + 20*(5/8)*x = 40[/tex]. Then we subtracted [tex]20*(5/8)*x[/tex] from both sides to get [tex](3/8)*x = 40 - 20*(5/8)*x[/tex]. Finally, we divided both sides of the equation by (3/8) to get x = (40/3). Therefore, the number is 40/3.

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Answer:

  x = 6

Step-by-step explanation:

You want the value of x in the geometry where an angle bisector has divided a triangle into sides 42 and (6x-1), and corresponding sides 78 and (10x+5).

The angle bisector divides the sides of the triangle proportionally:

  (6x -1)/42 = (10x +5)/78

  13(6x -1) = 7(10x +5) . . . . . . . . multiply by 546

  78x -13 = 70x +35 . . . . . . . simplify

  8x = 48 . . . . . . . . . . . . . . add 13-70x

  x = 6 . . . . . . . . . . . . . . divide by 8

About $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.

What is a graph ?

A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.

Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.

Since the graph shows the balance for two accounts with the same principal and annual interest rate, we can assume that one account is earning simple interest while the other is earning compound interest.

To estimate the amount of compound interest earned after 35 years, we can look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 35 years is approximately $4,000, while the balance for the compound interest account is approximately $10,000. Therefore, the amount of compound interest earned after 35 years is approximately:

$10,000 - $4,000 = $6,000

To estimate the amount of compound interest earned after 45 years, we can again look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 45 years is approximately $5,500, while the balance for the compound interest account is approximately $18,000. Therefore, the amount of compound interest earned after 45 years is approximately:

$18,000 - $5,500 = $12,500

Therefore,  about $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.

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The solution of the given problem of triangle comes out to be tan ∠A = 0.25.

Triangles are called polygons if they have four quadrants or more. Its form is a simple geometric figure. When put together, the characters ABC create a right-angled triangle. When the boundaries are incompatible, Euclidean geometry generates a new rectangle with square corners. Triangles are regarded as polygons because they have three edges and three corners.

Here,

Since △ABC is a right triangle with m∠C = 90°, we know that m∠A + m∠B = 90°.

Using the fact that tan ∠B = opposite/adjacent, we can set up a ratio using a common factor, x, for the opposite and adjacent sides of ∠B:

tan ∠B = 0.25 = opposite/adjacent = x/4x

Simplifying the right side, we get:

0.25 = x/4x = 1/4

Multiplying both sides by 4x, we get:

x = 4

So the opposite side of ∠B has length x = 4, and the adjacent side has length 4x = 16.

Using the Pythagorean theorem, we can find the length of the hypotenuse of △ABC:

c² = a² + b²

c² = 4²+ 16²

c² = 256

c = √256

c = 16

Now, we can use the fact that tan ∠A = opposite/adjacent to find tan ∠A:

tan ∠A = opposite/hypotenuse = 4/16 = 1/4

Therefore, tan ∠A = 0.25.

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The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

We can use similar triangles to find the distance across the lake (DE). Since triangle CGF is similar to triangle CED, we can use ratios of the sides to find DE.

Let's call DE = x. Then, we have:

CE/FG = x/142.1

Solving for x, we have:

x = (CE * 142.1) / FG

CE = CF + FD = 130 + 60 = 190m

x = (190 * 142.1) / 142.1 = 190m

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

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The complete question is :

To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter.

The solution of the equations y = 9x + 2 and y = - 3x + 12 will be (5/6, 19/2). Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The linear equations are given below.

y = 9x + 2              ...1

y = - 3x + 12          ...2

From equations 1 and 2, then we have

9x + 2 = - 3x + 12

12x = 10

x = 5 / 6

Then the value of 'y' is given as,

y = 9(5/6) + 2

y = 15/2 + 2

y = 19 / 2

The solution of the equations y = 9x + 2 and y = - 3x + 12 will be (5/6, 19/2). Then the correct option is C.

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Answer:

9yd^2

Step-by-step explanation:

A = bh

You are given the height of 2yd and a base of 4.5 yd.

A = (2yd)(4.5yd)

= 9yd^2

Answer:

9yd

Step-by-step explanation:

3½²-2²= √8.25=2.8

4.5-2.87=1.63

½×2.87×2=2.87

½(4.5+1.63)2=6.13

6.13+2.87=9yd

Answer:

Step-by-step explanation:

7x + 19 = cost rent and electricity

2x - 7 = cost of rent only

cost of electricity only = (7x + 19) - (2x - 7) = 5x + 26

5x + 26 < 100

5x < 74

x < 74/5

x < $14.80

Based on the given information, the best estimate for the owl population is 891.

The team of volunteers released 29 owls, and later the researchers counted 902 owls, 11 of which had tags. This means that 891 owls were not tagged, so the total owl population is 891 + 29 = 920. However, the question is asking for an estimate to the nearest whole number, so the best estimate for the owl population is 891.

To further understand the owl population, researchers can look at several factors. These include the types of habitats that owls inhabit, the availability of food in those habitats, the presence of predators or other threats, and the overall health of the owl population.

Researchers can also use various methods to monitor the population and determine if it is increasing or decreasing over time.

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I'll do problem 8 to get you started.

Part (a)

To find the mean, we first add up the values

1.53+1.49+1.60+1.65+1.90+1.43 = 9.6

Then divide over 6 since this is the number of values in the set.

9.6/6 = 1.6

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

Part (b)

The shortest boy is 1.43 meters tall. If he leaves the group, then we have these heights leftover

1.53, 1.49, 1.60, 1.65, 1.90

Adding them up gets us

1.53+1.49+1.60+1.65+1.90 = 8.17

Then divide by 5

8.17/5 = 1.634

Answer:

12

Step-by-step explanation:

i hope this is right I suggest you double check

The required error interval for y(probability of picking two green

apples) is  [1/4, 1/4].

The probability of picking two green apples can be calculated by multiplying the probability of picking a green apple on the first pick by the probability of picking another green apple on the second pick, given that the first pick was a green apple.

Let's call the number of green apples in the crate G, and the number of red apples in the crate R. Based on the given information, the ratio of green to red apples is 2:1, so we have G = 2R.

The probability of picking a green apple on the first pick is G/(G + R), and the probability of picking a green apple on the second pick, given that the first pick was a green apple, is (G-1)/(G + R - 1).

Therefore, the probability of picking two green apples is:

y = (G/(G + R)) * ((G-1)/(G + R - 1)) = (G/(G + R))²

Since we know that G = 2R, we can substitute that into the equation for y to get:

y = (2R/(2R + R))² = (2/(3R + R))² = (2/4R)² = 4/16 = 1/4

So the error interval for y is [1/4, 1/4].

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The value of c for which the limit of the function does not exist is given as follows:

c = -2.

The limit of a function will not exist if a function has different lateral limits, that is, if the to the right of x = c the graph has a different numeric value than to the left of x = c.

For this problem, we look at the graph at x = -2, hence:

This means that the function has different lateral limits, hence the limit of the function does not exist for c = -2.

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True, a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.

What does standard deviation mean ?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                                Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

What does a simple random sample mean?

A subset of participants is randomly chosen from a population by the researcher using simple random sampling, a sort of probability sampling.

                          The probability of being chosen is the same for every person in the population. Then, data are gathered from as much of this randomly selected subgroup as possible.

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Step-by-step explanation:

Volume.

[tex]v = lwh[/tex]

[tex]l = 20 \: w = 18 \: h = 0.5[/tex]

We just multiply these three numbers.

[tex](20)(18)(.5) = 180[/tex]

[tex]180 {ft}^{3} [/tex]

Step-by-step explanation:

x = number of years after 2007.

x = 0 for 2007.

PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).

PC(x) = 0.8x + 52

0 <= x <= 5

in 2007 (x = 0) the average adult ate 52 pounds.

in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.

so, in 2012 (x = 5) the average adult will eat

PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.

The answers for questions G, H, K, and L are the same as questions C, D, K, and L, respectively, because the speed (65mi/h) remains constant.

A. 65 miles in one hour: If a car is traveling at 65 miles per hour (mi/h), then in one hour it will travel 65 miles.

B. 340,800 feet in one hour, 65 miles is equal to 5,280 x 65 = 340,800 feet.

C. 5,680 feet in one minute, 340,800 feet ÷ 60 = 5,680 feet in one minute.

D. 94.67 feet in one second, 5,680 feet ÷ 60 = 94.67 feet in one second.

E. 42 miles in one hour: If a car is traveling at 42 miles per hour, then in one hour it will travel 42 miles.

F. 221,760 feet in one hour, 42 miles is equal to 5,280 x 42 = 221,760 feet.

G. 5,680 feet in one minute.

H. 94.67 feet in one second.

I. x miles in one hour.

J. 5,280 x x feet in one hour:

K. (5,280 x x) ÷ 60 feet in one minute.

L. ((5,280 x x) ÷ 60) ÷ 60 feet in one second.

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There are 5,280 feet in a mile. Round answers to the nearest unit.

A. How many miles does a car traveling at 65mi/h go in one hour?

B. How many feet does a car traveling at 65mi/h go in one hour?

C. How many feet does a car traveling at 65mi/h go in one minute?

D. How many feet does a car traveling at 65mi/h go in one second?

E. How many miles does a car traveling at 42mi/h go in one hour?

F. How many feet does a car traveling at 42mi/h go in one hour?

G. How many feet does a car traveling at 65mi/h go in one minute?

H. How many feet does a car traveling at 65mi/h go in one second?

i. How many miles does a car traveling at x mi/h go in one hour?

J. How many feet does a car traveling at x mi/h go in one hour?

K. How many feet does a car traveling at x mi/h go in one minute?

L. How many feet does a car traveling at x mi/h go in one second?

Step-by-step explanation:

the first one because positive (+) x negative (-) = negative (-), so it give you the negative sign in the middle