What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?

7ab3

6a4b
42a5b4
77a8b7

Answers

Answer 1

7ab3

To find the GCF, find the number(s) that that have the highest multiple factor in common. The first numbers can all be divided by 7, there's 1 a in common, and 3 b's in common. Combine them since you have variables and numerical values to get 7ab3 .

Answer 2

The greatest common factor of 42a⁵b³, 35a³b⁴, and 42ab⁴ is,

⇒ 7ab³

What is Greatest common factors?

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

We have to given that;

The numbers are,

⇒ 42a⁵b³, 35a³b⁴, and 42ab⁴

Now, We can formulate;

⇒ GCD {42, 35, 42 } = 7

⇒ GCD {a⁵, a³, a } = a

⇒ GCD {b³ , b⁴, b⁴} = b³

Thus, The greatest common factor of 42a⁵b³, 35a³b⁴, and 42ab⁴ is,

⇒ 7ab³

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Related Questions

Find the value of the expression given below. 2/3-1/7

Answers

Answer:

the answer is 11/21 or 0.523809524

hope this helped

Step-by-step explanation:

Write an equation with integer solutions of:

x = ±6, y = 0
and
x = 0, y = ±12

A)x2 + y2 + 6 = 0
B)4x2 + y2 + 144 = 0
C)x2 + y2 − 6 = 0
D)4x2 + y2 − 1

Answers

The correct answer is:

D. 4x2 + y2 − 1

[tex]|Huntrw6|[/tex]

Answer:  Option 'D' is correct.

Step-by-step explanation:

Since we have given that

x = ±6, y = 0

and x = 0 and y = ±12

And we need an equation which has above as an integer solutions.

So, it becomes,

Consider [tex]4x^2+y^2-144=0[/tex]

Put x = 0, we get

[tex]0+y^2=144\\\\y^2=144\\\\y=\sqrt{144}\\\\y=\pm 12[/tex]

Similarly,

Put y = 0,

[tex]4x^2+0=144\\\\4x^2=144\\\\x^2=\dfrac{144}{4}\\\\x^2=36\\\\\x=\pm 6[/tex]

Hence, Option 'D' is correct.

chester wanted to find the product of 3840 and 5.he was going to use an area model to help find the product.finish chesters incomplete area model below and find the product​

Answers

Answer:

fghjk²;.

Step-by-step explanation:

Final answer:

To find the product of 3840 and 5 using an area model, we can draw a rectangle with a length of 3840 units and a width of 5 units. Then, we divide the rectangle into smaller squares or rectangles of equal size. The product of 3840 and 5 is 19,200.

Explanation:

To find the product of 3840 and 5 using an area model, we can draw a rectangle with a length of 3840 units and a width of 5 units. Then, we divide the rectangle into smaller squares or rectangles of equal size. For example, we can divide the rectangle into 384 squares of length 10 and width 5, or into 192 squares of length 20 and width 10. After that, we count the total number of squares to find the product. In this case, the product of 3840 and 5 is 19,200.

A store sells a television for $1000. Customers can choose to receive a 10% discount and pay it off with a loan at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years no interest. If the customer plans to pay it off in 3 years, which option is better

Answers

Answer:

Second option

Step-by-step explanation:

Option 1:

1. Original cost: 90% * 1000 = $900

2. Interest: A = P(1 + rt), A = amount, P = original amount, r = rate, t = years

Plug in: A = 900(1 + 0.05*3)

Multiply + add: A = 900(1.15)

Multiply: A = $1035

Option 2: $1000

So, paying full price upfront will save more money if all goes to plan.

Find the missing term. The roots of x2 − ( ) + 34 are 5 ± 3i.

Answers

Answer:

the required equation is:

[tex]x^2 -10 +34[/tex]

Step-by-step explanation:

The equation given is:

[tex]x^2 -()+34[/tex]

Comparing it with standard quadratic equation

[tex]a^2 +bx+c[/tex]

a= 1,

b=?

C= 34

We can find the value of b using Vieta's formulas :

That states that if roots x₁ and x₂ are given then,

x₁ + x₂ = -b/a

We are given roots: 5 ± 3i i.e, x₁= 5 + 3i and x₂= 5 - 3i

solving

5 + 3i + 5 - 3i = -b/1

10 = -b

Since the given equation already gives b as -b so, -b= 10 => b=10

Putting value of b in the missing place the required equation will be:

[tex]x^2 -10 +34[/tex]

To find the missing term in a quadratic equation given complex roots, use the properties of conjugate roots to determine the term.

Since the roots are in the form of a complex number, they are conjugates of each other, which helps in finding the missing term.

Given roots: 5 ± 3i

Using the sum and product of roots formula

Sum: (5 + 3i) + (5 - 3i) = 10. Product: (5 + 3i)*(5 - 3i) = 34

Construct the equation: x2 - (10x) + 34 = 0

At your construction job, you're standing on a ladder at ground level. First, you climb down 7 feet to see the basement. Then you climb up 22 feet to see the second floor. Later, you climb down 9 feet. How high above or below the ground are you?

7 feet below the ground

6 feet below the ground

9 feet above the ground

9 feet below the ground

6 feet above the ground

Answers

Final answer:

After descending 7 feet, ascending 22 feet, and descending 9 feet, the individual is 6 feet above the ground level.

Explanation:

The question involves a sequence of movements by an individual on a ladder at a construction site. To solve this, let's track each movement relative to the initial position at ground level.

The individual climbs down 7 feet to the basement, so they are now 7 feet below ground.Then they climb up 22 feet which brings them 15 feet above ground level (since they were originally 7 feet below).Finally, climbing down 9 feet from the second floor, they are now 6 feet above the ground level.

Therefore, the individual is 6 feet above the ground after these movements.

The equation of a circle is (x + 3)2 + (y – 5)2 = 81. Determine the coordinates of the center of the circle and the length of the radius.

Answers

Answer:

The center of the circle is (-3 , 5) and the length of the radius is 9 units

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- The center-radius form of the circle equation is in the format

 (x – h)² + (y – k)² = r², where the center is the point (h, k) and

 the radius is r.

- This form of the equation is helpful, because you can easily find

  the center and the radius.

* Now lets solve the problem

- The equation is (x + 3)² + (y - 5)² = 81

- By comparing the two equations

∵  (x – h)² + (y – k)² = r² and  (x + 3)² + (y - 5)² = 81

# x - h = x + 3

∴ -h = 3 ⇒ divide both sides by -1

∴ h = -3

# y - k = y - 5

∴ k = 5

# h and k are the coordinates of the center of the circle

∴ The center of the circle is (-3 , 5)

# r² = 81 ⇒ take √ for both sides

∴ r = 9

∴ The length of the radius = 9 units

* The center of the circle is (-3 , 5) and the length of the radius is 9 units

Final answer:

The center of the circle is at (-3, 5), and the radius of the circle is 9, determined by the given equation (x + 3)^2 + (y – 5)^2 = 81.

Explanation:

The student is asking about the equation of a circle and how to determine the coordinates of the center and the length of the radius. The given equation is (x + 3)2 + (y – 5)2 = 81. The general form of a circle's equation is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.

To find the center of the circle, we look at the values h and k in the equation, which are the opposites of the constants added to x and y, respectively. Therefore, the center is at (-3, 5). To find the radius of the circle, we take the square root of the number on the right side of the equation. The square root of 81 is 9, so the radius is 9.

Calculating area and perimeter worksheet works.com answer #4-9

Answers

Step-by-step explanation:

dude i have no idea sorry

The Calculating area and perimeter worksheet from works.com

#4

Area: [tex]360 yd^2[/tex]

Perimeter: 30 yd

#5

Area: [tex]45 yd^2[/tex]

Perimeter: 22 yd

#6

Area: 87 yd^2

Perimeter: 30 yd

#7

Area: 72 ft^2

Perimeter: 24 ft

#8

Area: 150 ft^2

Perimeter: 30 ft

#9

Area: 2128 ft^2

Perimeter: 70 ft.

Area is the amount of space that a two-dimensional shape takes up. It is measured in square units, such as square feet (ft^2), square yards (yd^2), or square meters (m^2).

To calculate the area of a rectangle, multiply the length by the width.

Area of a rectangle = length * width

To calculate the area of a square, multiply the side length by itself.

Area of a square = side length * side length

To calculate the area of a triangle, multiply the base by the height and divide by 2.

Area of a triangle = base * height / 2

Perimeter is the total length of all the sides of a two-dimensional shape. It is measured in linear units, such as feet (ft), yards (yd), or meters (m).

To calculate the perimeter of a shape, add up the lengths of all the sides.

Perimeter of a shape = sum of the lengths of all the sides

Example:

To calculate the area and perimeter of the rectangle in question #4, we would use the following formulas:

Area = length * width = 5 yd * 72 yd = 360 yd^2

Perimeter = sum of the lengths of all the sides = 5 yd + 72 yd + 5 yd + 72 yd = 30 yd

Answers to the remaining questions:

#5:

Area = 45 yd^2

Perimeter = 22 yd

#6:

Area = 87 yd^2

Perimeter = 30 yd

#7:

Area = 72 ft^2

Perimeter = 24 ft

#8:

Area = 150 ft^2

Perimeter = 30 ft

#9:

Area = 2128 ft^2

Perimeter = 70 ft.

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Simplify 5x/(-3+2x+x^2)

Answers

Answer:5x/(x-1)(x+3)

Step-by-step explanation:Factor -3+2x+x^2 by using the AC method hope this helps. Branliest plz

Charles owed 390$ to his friend. On the first day Charles paid his friend 12$. Each following week the amount Charles paid his friend increased by the same amount. After 10 payments, Charles had paid back the full amount. By how much did each payment increase?

Answers

Answer:  Step-by-step explanation: 390-12  378 divided by 9 42!!!!!!!!!!!!!!!

find the value of the trigonometric function sin (t) if sec t = -4/3 and the terminal side of angle t lies in quadrant II

Answers

Answer:

[tex]sin(t) =\frac{\sqrt{7}}{4}[/tex]

Step-by-step explanation:

By definition we know that

[tex]sec(t) = \frac{1}{cos(t)}[/tex]

and

[tex]cos ^ 2(t) = 1-sin ^ 2(t)[/tex]

As [tex]sec(t) = -\frac{4}{3}[/tex]

Then

[tex]sec(t) = -\frac{4}{3}\\\\\frac{1}{cos(t)} =-\frac{4}{3}\\\\cos(t) = -\frac{3}{4}[/tex]

Now square both sides of the equation:

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

[tex]cos^2(t) = \frac{9}{16}\\\\[/tex]

[tex]1-sin^2(t) =\frac{9}{16}\\\\sin^2(t) =1-\frac{9}{16}\\\\sin^2(t) =\frac{7}{16}\\\\sin(t) =\±\sqrt{\frac{7}{16}}[/tex]

In the second quadrant sin (t) is positive. Then we take the positive root

[tex]sin(t) =\sqrt{\frac{7}{16}}[/tex]

[tex]sin(t) =\frac{\sqrt{7}}{4}[/tex]

The value of sin(t) = √7/4 because sine is positive in Quadrant II.

First, recall that sec(t) is the reciprocal of cos(t):

sec(t) = 1/cos(t)

Given: sec(t) = -4/3, so:

cos(t) = -3/4

Since angle t lies in Quadrant II, cosine is negative, and sine is positive. Use the Pythagorean identity:

sin²(t) + cos²(t) = 1

Substitute cos(t):

sin²(t) + (-3/4)² = 1

sin²(t) + 9/16 = 1

Solve for sin²(t):

sin²(t) = 1 - 9/16

sin²(t) = 16/16 - 9/16

sin²(t) = 7/16

Take the square root of both sides:

sin(t) = √(7/16) = √7/4

Since we are in Quadrant II, sine is positive:

sin(t) = √7/4

If a sample proportion is 0.26 which of the following is most likely the range of possible values that best describes an estimate for the population parameter

Answers

Answer: (0.15,0.37)

Step-by-step explanation:

did the quiz

The range of possible values that best describes the estimate for the population parameter is [0.16, 0.38]. Therefore, the correct answer is option D.

Given that, a sample proportion is 0.26.

In statistics, the sample proportion is an estimate for the population parameter. When given a sample proportion, the range of possible values that best describes the estimate for the population parameter is typically the 95% confidence interval for the sample proportion. The 95% confidence interval states that if the same sampling procedure is repeated on many samples, then 95% of the confidence intervals constructed this way will contain the true population parameter.

The 95% confidence interval for a sample proportion is given by [p-1.96√(pq/n), p+ 1.96√(pq/n)], where p is the sample proportion, q is the complement of the sample proportion (q = 1 − p), and n is the sample size.

In this case, the sample proportion given is 0.26, and so p = 0.26, q = 0.74, and the sample size can be assumed to be large (n ≥ 30). Substituting these values into the 95% confidence interval equation yields the range of possible values that best describes the estimate for the population parameter: [0.16, 0.38].

Therefore, the correct answer is option D.

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"Your question is incomplete, probably the complete question/missing part is:"

If a sample proportion is 0.26 which of the following is most likely the range of possible values that best describes an estimate for the population parameter?

A. (0.14, 0.36)

B. (0.17, 0.39)

C. (0.15, 0.37)

D. (0.16, 0.38)

Find the arc length of a partial circle

Answers

Answer is...

23.55

See attached photo

All equilateral triangles are ________ triangles.

10pts this on is easy

Answers

Answer:

isosceles

Step-by-step explanation:

what is the missing reason in the proof

Answers

Answer:

SSS Congruence Theorem

Step-by-step explanation:

sss congruence theorem. you can get this answer by marking all the givens.

What is the value of x?!​

Answers

Answer:

5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value of

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]

Multiply both sides by 10

10 × sin60° = x

10 ×[tex]\frac{\sqrt{3} }{2}[/tex], hence

x = 5[tex]\sqrt{3}[/tex]

Express 2/5% as a fraction and decimal

fraction=

decimal=

HELP ASAP!

Answers

Answer:

Fraction: 1/250

Decimal: 0.004

Step-by-step explanation:

2/5=0.4 0.4%=0.004 0.004=4/1000=2/500=1/250

Mr. Olaffsen opened a sandwich shop and a smoothie stand in his neighborhood. The following table and equation show function f, representing Mr. Olaffsen's profit, in dollars, x months since opening the sandwich shop. x 1 2 3 4 5 6 7 f(x) 12,000 15,500 18,000 19,500 20,000 19,500 18,000 The following table and equation show function g, representing Mr. Olaffsen's profit, in dollars, x months since opening the smoothie stand. x 1 2 3 4 5 6 7 g(x) 9,300 12,000 14,100 15,600 16,500 16,800 16,500 Select the true statement. A. The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,000. B. The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,200. C. The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,500. D. The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700.

Answers

Answer: the difference between the max is 3200.

Step-by-step explanation:

20000-16800= 3200

The difference between the max is 3200.

What is the difference?

Subtract the smaller of the two numbers from the larger of the two numbers to find the difference between them. The difference between the two numbers is the sum's product. For instance, you could calculate the difference between 100 and 45 as follows: 100 - 45 = 55.

Given

20,000 - 16,800 = 3200

therefore, The difference between the max is 3200.

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confused, so can someone pls help

Answers

Answer:

Choice C

Step-by-step explanation:

(f+g)(x) is a composite function which is obtained by adding the two given functions f(x) and g(x)

(f+g)(x) = f(x) + g(x)

            = [tex]3^{x} +10x+4x-2[/tex]

            = [tex]3^{x} +14x-2[/tex]

Emma is 9 and one fourths Year’s old. How many months old is Emma?

Answers

She is 4 years an d3 months old

Answer:

111 months

Step-by-step explanation:

First, look at how many whole years old Emma is. Emma is 9 whole years old. 1 year consists of 12 months. So, multiply 9 [years] by 12 [months] to get 108. The number 108 is how many months are in 9 years. However, Emma is 9 months and 1/4 years old.

To find out how many months 1/4 of a year is, multiply 1/4 [year] by 12 [months] . 12 is the same as 12/1, so multiply the numerators and denominators of 1/4 and 12/1

1 x 12 = 12

4 x 1 = 4

12/4 = 3

Therefore, 1/4 year is 3 months. Now, add 108 months and 3 months to get 111 months. Therefore, Emma is 111 months old.

I hope this helps! :)

What is the answer?

Answers

Answer:

x ≤ - 4

Step-by-step explanation:

Given

3 - x ≥ 2x + 15 ( add x to both sides )

3 ≥ 3x + 15 ( subtract 15 from both sides )

- 12 ≥ 3x ( divide both sides by 3 )

- 4 ≥ x, hence

x ≤ - 4

3 - x is greater than equal to 2 X + 15

3 is greater than equal to 3X + 15

- 12 is greater than equal to 3 x

- 4 is greater than equal to x

hence x b - 4 - 4 is greater than x

the graph shows the amount of money Hachi earns at his job in relation to the number of hours he works.

what is Hachi's pay rent in dollars per hour? record your answer and fill in the bubbles on your answer form. Be sure to use the correct place value.​

Answers

Answer:

(A) - Hachi does not earn any money if he does not work

Step-by-step explanation:

THE FIRST GUY IS WRONG TRUST ME.

If you think about it the graphed point is (0,0), so it is self explanatory that he works 0 hours and OBVIOUSLY he wont earn any money if he doesnt work.

The graph shows the amount of money Hachi earns at his job in relation to the number of hours he works. Hachi does not earn any money if he does not work.

What is a function?

A function is defined as a relation between the set of inputs having exactly one output each.

We can see that the graph linearly increases as the hour he worked and the money he earned will increase.

we know that the graphed point is (0,0),

He earned 10 money per hour of work.

so it is self-explanatory that he works 0 hours and obviously, he won't earn any money if he doesn't work.

Thus, Hachi does not earn any money if he does not work.

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Pablo's is running a special for Cinco de Mayo (fifth of May). All entree's are $5.55. You and your family, a total of six people, eat. The tax is 7%. It was extremely busy that night and the service wasn't good. Mom leaves a 12% tip. How much money did she spend in all? *

Please HELP!

Answers

Answer:

$39.91

Step-by-step explanation:

6*5.55=33.30

33.30*1.07=35.63

35.63*1.12=39.91

Don't know how to delete the incorrect answer that my sister put but I can edit it, so this is what I'm editing it to.

A 50ft. cable is stretched from the top of an antenna to an anchor point on the ground 15 ft. from the base of the antenna. How tall is the antenna? Round the nearest tenth.

Answers

Answer:

h = 47.70 ft

The antenna is 47.70 ft tall.

Step-by-step explanation:

Final answer:

The height of the antenna is approximately 47.4ft when calculated using the Pythagorean theorem: √((50ft)^2 - (15ft)^2).

Explanation:

The question is asking for the height of the antenna. We can solve this problem by using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the hypotenuse is the length of the cable (50 ft), one side is the distance from the base of the antenna to the anchor point (15 ft) and the other side (which we are trying to find), is the height of the antenna.

According to the Pythagorean theorem, the height of the antenna can be calculated as follows: Height = √(Hypotenuse^2 - Base^2), which translates into Height = √((50ft)^2 - (15ft)^2). When you calculate that you get the height of the antenna as approximately 47.4 feet, rounded to the nearest tenth.

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find a9 in the arithmetic sequence with a1 = -2.75 and d = 0.25

Answers

Answer:

The ninth term is -0.75.

Step-by-step explanation:

Let's write the actual formula for this arith. seq.

It will have the general form a(n) = a(1) + (n-1)d, where a(1) is the first term, n is the term counter (1, 2, 3, .... ) and d is the common difference.

Here, a(n) = -2.75 + (n - 1)(0.25)

So the ninth term of this sequence is

a(9) = -2.75 + (9 - 1)(0.25

      = -2.75 + 8(0.25)

      = -2.75 + 2

       = -0.75

The ninth term is -0.75.

Answer:

[tex]a_9=-0.75[/tex]

Step-by-step explanation:

The given sequence has the first term, [tex]a_1=-2.75[/tex] and d=0.25

The general formula for an arithmetic sequence is given by;

[tex]a_n=a_1+d(n-1)[/tex]

Since we want to find [tex]a_9[/tex], it means n=9

We substitute the given values into the formula to obtain;

[tex]a_9=-2.75+0.25(9-1)[/tex]

[tex]a_9=-2.75+0.25(8)=-0.75[/tex]

Hence, the 9th term is

[tex]a_9=-0.75[/tex]

Please help. Brainliest to first answer.

Answers

I think they are complementary angles but i am not sure

Answer:

They form a linear pair.

Step-by-step explanation:

Because both are not 180 so that marks out the last checkbox and the second. Plus, they both don't add up to 90 so it checks off the first.

how do i factor this trinomial?

Answers

[tex]\text{Hey there!}[/tex]

[tex]\text{The answer is: (3g + 2)(g + 2)}[/tex]

[tex]\text{To make sure it comes back to the original problem}\bf{(3g^2+8g+4)}[/tex] [tex]\text{You would have to distribute the answer}[/tex]

[tex]\text{3g(g)=}3g^2\\ \text{3g(2)=6g}\\ \text{2(g)=2g}\\ \text{2(2)=4}[/tex]

[tex]\text{After distributing combine your like terms:}[/tex]

[tex]\text{In this particular answer we have: 1 term with TWO LIKE TERMS}[/tex]

[tex]\text{6g+2g=8g(That's how we got the 8g in the original equation)}[/tex]

[tex]\text{The}\bf{\ 3g^2}\text{ stays the same because there's nothing to go with it}[/tex]

[tex]\text{The 4 also stays the same because nothing goes with it as well}[/tex]

[tex]\boxed{\boxed{\text{Answer:(3x + 2 (x + 2)})}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Estimate the sum 7 1/4 + 2 5/8.

Answers

Answer:

10

Step-by-step explanation:

What is the perimeter of the rectangle shown below?

Answers

Answer:

To find perimeter, you must add length plus length plus width plus width.

(L+L+W+W)

the length is 5, and the width is 8. since there are 4 sides, we must add 5+5+8+8, and that equals 26.

So the perimeter of the rectangle is 26 units.

As we know the formula for finding the perimeter of a rectangle is:

[tex]Perimeter=2(L+B)[/tex]

here, L is the length of the rectangle and B is the breadth of the rectangle.

As the values of the length and breadth are given, we will put in the formula;

[tex]Perimeter=2(8+5)[/tex]

[tex]Perimeter=2(13)[/tex]

[tex]Perimeter=26[/tex]

Hence, the perimeter of the rectangle is 26 units.

What is the perimeter in math?

Perimeter is the distance around the edge of a shape.

What is a perimeter and its formula?

The total length of the boundary of a closed shape is called its perimeter. Hence, the perimeter of that shape is measured as the sum of all the sides. Thus, the perimeter formula is Perimeter(P) = Sum of all the sides.

What is parameter formula?

Any equation expressed in terms of parameters is a parametric equation. The general equation of a straight line in slope-intercept form, y = mx + b, in which m and b are parameters, is an example of a parametric equation.

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What is the probability of getting a vowel (a successes) for the spinner? Compute P(3 successes) for 5 spins of the spinner

Answers

Answer:

What is the probability of getting a vowel (a success) for the spinner shown?

✔ 1/3

Suppose you spin the spinner 5 times.

✔ P(3 successes) means “the probability of getting a vowel on exactly 3 of the spins.”

Step-by-step explanation:

edg 2020

Using the binomial distribution, it is found that:

The probability of a success is of 1/3.P(X = 3) = 0.1646.

For each spin, there are only two possible outcomes, either it is a vowel, or it is not. The result of a spin is independent of any other spin, hence the binomial distribution is used to solve this question.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

In this problem:

The spinner has 3 regions, A, B and C, one of which is a vowel, hence p = 1/3 = 0.3333.There will be 5 spins, hence n = 5.

The probability of 3 successes is given by:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{5,3}.(0.3333)^{3}.(0.6667)^{2} = 0.1646[/tex]

More can be learned about the binomial distribution at https://brainly.com/question/14424710

Other Questions
Read this excerpt from a Wikipedia entry: Man of La Mancha3 and the biography entry for Miguel de Cervantes and answer the question.SynopsisIt is the late sixteenth century. Failed author-soldier-actor and tax collector Miguel de Cervantes has been thrown into a dungeon by the Spanish Inquisition, along with his manservant. They have been charged with foreclosing on a monastery. The two have brought all their possessions with them into the dungeon. There, they are attacked by their fellow prisoners, who instantly set up a mock trial. If Cervantes is found guilty, he will have to hand over all his possessions. Cervantes agrees to do so, except for a precious manuscript which the prisoners are all too eager to burn. He asks to be allowed to offer a defense, and the defense will be a play, acted out by him and all the prisoners. The "judge," a sympathetic criminal called "the Governor," agrees.Cervantes takes out a makeup kit from his trunk, and the manservant helps him get into a costume. In a few short moments, Cervantes has transformed himself into Alonso Quijana, an old gentleman who has read so many books of chivalry and thought so much about injustice that he has lost his mind and now believes that he should go forth as a knight-errant. Quijana renames himself Don Quixote de La Mancha, and sets out to find adventures with his "squire," Sancho Panza. They both sing the title song Man of La Mancha (I, Don Quixote) .SynopsisThe son of a deaf surgeon, Miguel de Cervantes was born near Madrid in 1547. He became a soldier in 1570 and was badly wounded in the Battle of Lepanto. Captured by the Turks in 1575, de Cervantes spent five years in prison. He was freed in 1580 and returned home. De Cervantes finally achieved literary success in his later years, publishing the first part of Don Quixote in 1605. 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By the following year, de Cervantes had put his words aside and, instead, picked up a weapon: He had joined a Spanish military unit in Italy.Known for his bravery, de Cervantes took part in the Battle of Lepanto. Stationed on the ship La Marquesa, he fought against the Ottoman Empire and sustained serious injuries in the conflict: He suffered two chest wounds and his left hand was completely maimed. Despite his disability, de Cervantes continued to serve as a soldier for several more years.In 1575, de Cervantes and his brother, Rodrigo, tried to return to Spain, but they were captured by a group of Turkish ships during their voyage. De Cervantes spent five years as a prisoner and a slave, and made several failed attempts to escape during his imprisonment. He finally went home after a ransom was paid for his release.Don QuixoteDe Cervantes published his first novel, La Galatea, in 1585. This pastoral romance failed to make much of a splash. 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