Driver's Delight is considering building a new track. They have a circular space
with a diameter of 150 feet. Compute the circumference of the circular space.
Use 3.14 for it. Round your answer to the nearest hundredth, if necessary.​

Answers

Answer 1

Answer:

The answer is 471 feet

Step-by-step explanation:

Since the the track is circular

Circumference of a circle = πd

where

d is the diameter

π = 3.14

From the question

diameter = 150 feet

Circumference = 150π

= 150(3.14)

We have the final answer as

Circumference = 471 feet

Hope this helps you

Answer 2

Answer:

471.23 ft

Step-by-step explanation:

The circumference of this space is C = πd = (150 ft)π, or approximately

471.23 ft


Related Questions

1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident​

Answers

Answer:

math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.

The mathematics assessment defines as "the process of gathering evidence about a content performance of capacity to use, as well as comportment away from traditional maths, as well as of making presumptions from that proof for a range of functions". In several inferences could be derived from the information in the Educational section. In order to enhance a program that promotes learning outcomes, assessment involves the use of empirical evidence on student learning. As just a result, students' learning is improved.As per my opinion, the given question is an opinion question and in the education sector some student likes math and some aren't. In this, I will select the "excited and confident" choice because I love maths.

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Reading a Tape Measure
Measure the green bar using the provided image of a tape measure

Answers

Answer:

3 inches

Step-by-step explanation:

The green bar reaches all the way to the 3 on the ruler, and each number represents an inch.

(x+1)(x−1)(x−5)=0 HELP

Answers

Answer:

x³ - 5x² - x + 5

Step-by-step explanation:

(x+1)(x-1)(x-5) = 0

fisrt step:

(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1

then:

(x+1)(x-1)(x-5) = (x²-1)(x-5)

(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5

f(x) = x^2 + 2x + 1, then for what values of x, f(x)=f(x+2) step by step plz​

Answers

Answer:

x = -2

Step-by-step explanation:

given f(x) = x² + 2x + 1

f(x+2) = (x+2)² + 2(x+2) + 1

= x² 4x+4+2x+4+1

= x² + 6x + 9

for f(x) = f(x+2), simply equate the two expressions and solve for x

f(x) = f(x+2)

x² + 2x + 1 = x² + 6x + 9      (x² terms cancel out)

2x + 1 = 6x + 9  (subtract 1 from both sides)

2x  = 6x + 9 - 1

2x  = 6x + 8  (subtract 6x from both sides)

2x - 6x = 8

-4x = 8 (divide both sides by -4)

x = 8 / (-4)

x = -2

The number of weekly hours spent on a smart device varies inversely with the person's age. If a 20-year-old person spends 52 hours on their smart device each week, how many hours does a 50-year-old person spend on their smart device?

Answers

Answer:

20.8 hours

Step-by-step explanation:

Given that hours (h) varies inversely with age (a) then the equation relating them is

h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation

To find k use the condition h = 52 when a = 20, thus

52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )

1040 = k

h = [tex]\frac{1040}{a}[/tex] ← equation of variation

When a = 50, then

h = [tex]\frac{1040}{50}[/tex] = 20.8 hours

Find the values of x which satisfy the following inequation:
x3 – x² <12x​

Answers

Answer:

x< -3 and 0 < x < 4

Step-by-step explanation:

x^3 – x² <12x​

Subtract 12x from each side

x^3 -x^2 - 12x< 0

Factor

x( x^2 -x-12) <0

Factor

x( x-4) ( x+3) < 0

Using the zero product property

x=0   x=4  x=-3

We have to check the signs regions

x < -3

-( -) (-) < 0   True

-3 to 0

-( -) (+) < 0   False

0 to 4

+( -) (+) < 0   True

x>4

+( +) (+) < 0   False

The regions this is valid is

x< -3 and 0 < x < 4

I will rate you brainliest Select the best description of what the LCM of a set of polynomials is. a.It is the quotient of all the factors of the polynomials. b.It is the common numerator of a rational expression. c. It is the product of the prime factors that are either unique to or shared by the polynomials. d. It is all the polynomials in the set.

Answers

Answer:

C. It is the product of the prime factors that are either unique to or shared by the polynomials.

Step-by-step explanation:

LCM of polynomials is:

=> Finding the factors of all the numbers and variable in the expression

=> Next, we multiply the unique numbers and the variable of the expression to find the LCM.

So, C is the correct answer.

The LCM of a set of polynomials  is the product of the prime factors that are either unique to or shared by the polynomials.  

What is LCM of polynomial?

To find the lowest common multiple (L.C.M.) of polynomials, we first find the factors of polynomials by the method of factorization and then adopt the same process of finding L.C.M.

Example : The L.C.M. of 4a2 - 25b2 and 6a2 + 15ab.

Factorizing 4a2 - 25b2 we get,

(2a)2 - (5b)2, by using the identity a2 - b2.

= (2a + 5b) (2a - 5b)

Also, factorizing 6a2 + 15ab by taking the common factor '3a', we get

= 3a(2a + 5b)

L.C.M.  is 3a(2a + 5b) (2a - 5b)

According to the question

The LCM of a set of polynomials is

 is the product of the prime factors that are either unique to or shared by the polynomials.  

(from above example we can see that )

Hence,  It is the product of the prime factors that are either unique to or shared by the polynomials.  

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ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information

Answers

Answer: B. Always

Explanation:

Two points always create a line. The correct answer is option B.

What is a line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, the two points always create a line. The correct answer is option B.

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5. What is the solution of the following linear system?
y= 3x + 1
2y = 6x + 2
O A. (5,-2)
OB. (34)
C. Infinitely many solutions
D. No solution

Answers

Answer:

C. Infinitely many solutions

Step-by-step explanation:

First, simplify the second equation by dividing it by 2

2y = 6x + 2

y = 3x + 1

Now, we can see that both equations are the same, both y = 3x + 1.

Since they are the same line, this means that there are infinitely many solutions.

So, the correct answer is C.

Simplify the following expression.X^1/3 * X^1/5

Answers

Answer:

[tex] X^{\frac{8}{15}} [/tex]

Step-by-step explanation:

[tex] X^\frac{1}{3} \times X^\frac{1}{5} = [/tex]

To multiply two powers with the same base, write the base and add the exponents.

[tex] = X^{\frac{1}{3} + \frac{1}{5}} [/tex]

[tex] = X^{\frac{5}{15} + \frac{3}{15}} [/tex]

[tex] = X^{\frac{8}{15}} [/tex]

PLS HELP:Find the side length, C.
Round to the nearest tenth.

Answers

Answer:

[tex]\huge\boxed{c = 14.9}[/tex]

Step-by-step explanation:

Using Cosine Rule

[tex]c^2 = a^2 + b^2 -2abCosC[/tex]

Where a = 11 , b = 7 and C = 110

[tex]c^2 = (11)^2+(7)^2-2(11)(7)Cos 110[/tex]

[tex]c^2 = 121+49-154 (-0.34)\\c^2 = 170+52.7\\c^2 = 222.7[/tex]

Taking sqrt on both sides

c = 14.9

Please help. I’ll mark you as brainliest if correct!

Answers

Answer: x= -1, z=2, y= -4

Step-by-step explanation:

System of equations:

-5x - 4y - 3z= 15  +

-10x + 4y + 6z= 6

-15x         + 3z = 21  ------>  3 (-5x + z) = 7.3

-5x + z = 7

now,

-10x + 4y + 6z= 6

2(-5x + z) + 4y + 4z = 6

14 + 4y + 4z = 6

7 + 2y + 2z = 3

2y + 2z= -4

y+z=-2

Now we were using the equation: 20x + 4y + 4z = -28

20x + 4(y+z) = 20x -8= - 28

20 x = -20

x= -1

With this we can find y and z

X=-1

-5x + z = 7

z= 2

y+z=-2

y=-4

Finally we have: x= -1, z=2, y= -4

I hope this can help you.

Thank you


[tex]4x - 2x = [/tex]

Answers

Answer:

2x

Step-by-step explanation:

These are like terms so we can combine them

4x-2x

2x

Answer:

2x

Explanation:

Since both terms in this equation are common, we can simply subtract them.

4x - 2x = ?

4x - 2x = 2x

Therefore, the correct answer should be 2x.

Point A is at (2, -8) and point C is at (-4, 7).
Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.

Answers

Answer:

(-2, 2)

Step-by-step explanation:

Given:

Point A is at (2, -8) and point C is at (-4, 7)

Difference of coordinates:

Δx = 2 - (-4) = 6Δy = - 8 - 7 = - 15

The ratio of AB to AC is 2:1. So:

AB = 2*AC/3 and BC = AC/3

Then coordinates of point B should be 2/3 from the point A:

x = 2- 6*2/3 = 2 - 4 = -2y = - 8 - (-15)*2/3 = -8 + 10 = 2

So point B has coordinates of (-2, 2)

Find a vector equation and parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5.

Answers

The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.

Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:

(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)

This is the vector equation; getting the parametric form is just a matter of delineating

x(t) = 1 + t

y(t) = 3t

z(t) = 6 + t

The vector equation for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5 is v =(1+t)i + (3t)j + (6+t)k

The parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5

x(t) = 1+ty(t) = 3tz(t) = 6+t

The parametric equation of a line through the point A(x, y, z) perpendicular to the plane ax+by+cz= d is expressed generally as:

A + vt where:

A = (x, y, z)

v = (a, b, c) (normal vector)

This can then be expressed as:

s = A + vt

s = (x, y, z) + (a, b, c)t

Given the point

(x, y, z) = (1,0,6)

(a, b, c) = (1, 3, 1)

Substitute the given coordinate into the equation above:

s = (1,0,6) + (1, 3, 1)t

s = (1+t) + (0+3t) + (6+t)

The parametric equations from the equation above are:

x(t) = 1+t

y(t) = 3t

z(t) = 6+t

The vector equation will be expressed as v = xi + yj + zk

v =(1+t)i + (3t)j + (6+t)k

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Original price of a soda: $800 tax 7% selling price: $

Answers

Answer:

$856

Step-by-step explanation:

Find 7% of $800 and then add it to $800

A regression analysis between sales (y in $1000) and advertising (x.in dollars) resulted in the following equation: ỹ= 30,000 + 4x
The above equation implies that an:________
a. increase of $l in advertising is associated with an increase of $4 in sales.
b. increase of $4 in advertising is associated with an increase of $4000 in sales.
c. increase of $1 in advertising is associated with an increase of $34,000 in sales.
d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Answers

Answer:

Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Step-by-step explanation:

Given the equation of regression analysis is given as:

[tex]y= 30,000 + 4x[/tex]

where [tex]x[/tex] is the cost on advertising in Dollars.

and [tex]y[/tex] is the sales in Thousand Dollars.

To find:

The correct increase in sales when there is increase in the advertising cost.

Solution:

Suppose there is an increase of [tex]\$1[/tex] in the advertising cost.

Let the initial cost be [tex]x[/tex] then the cost will be [tex](x+1)[/tex].

Initial sales

[tex]y= 30,000 + 4x[/tex] ....... (1)

After increase of $1 in advertising cost, final cost:

[tex]y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)[/tex]

Subtracting (2) from (1) to find the increase in the sales:

[tex]y'-y=30004+4x-30000-4x = 4[/tex]

The units of sales is Thousand Dollars ($1000).

So, increase in sales = [tex]4 \times1000 = \bold{\$4000}[/tex]

So, correct answer is:

d. increase of $1 in advertising is associated with an increase of $4000 in sales.

On a map 1 cm represents 4.5km. What is the actual distance between two towns which are 4cm apart on the map?

Answers

Answer:

18km

Step-by-step explanation:

1cm:4.5km/4cm then get the answer as 18km

1 cm represents [tex]4.5[/tex] km. To find the actual distance between two towns that are 4 cm apart on the map, we can use the scale ratio.

Since 1 cm represents [tex]4.5[/tex] km, we can calculate the actual distance by multiplying the map distance with the scale ratio. Map distance: 4 cm Scale ratio: 1 cm represents [tex]4.5[/tex] km Actual distance = Map distance × Scale ratio Actual distance[tex]= 4 cm × 4.5[/tex] km/cm Actual distance[tex]= 18 km[/tex]

Therefore, the actual distance between the two towns is18 [tex]18[/tex] km. Using the given scale, 1 cm on the map corresponds to[tex]4.5[/tex]km in reality. As the towns are represented as 4 cm apart on the map, the actual distance between them is [tex]18[/tex]km.

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Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find the percentile corresponding to the data speed 4.9 Mbps.

0.2 0.8 2.3 6.4 12.3 0.2 0.8 2.3 6.9 12.7 0.2 0.8 2.6 7.5 12.9 0.3 0.9 2.8 7.9 13.8
0.6 1.5 0.1 0.7 2.2 6.1 12.1 0.6 1.9 5.5 11.9 27.5 0.6 1.7 3.3 8.3 13.8 1.3 3.5 9.8
14.6 10.1 14.7 11.8 14.8

Answers

Answer:

Thus percentile lies between 53.3% and 55.6 %

Step-by-step explanation:

First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N

where n is the ordinal rank of the given value

N is the number of values in ascending order.

The data in ascending order is

0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3

1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5

Number of observation = 45

4.9 lies between 3.3 and 5.5

x*n = 24 observation x*n = 25 observation

x*45= 24 x*45= 25

x= 0.533 x= 0.556

Thus percentile lies between 53.3% and 55.6 %

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (3x2 − 2y2)i + (4xy + 4)j

Answers

In order for F to be conservative, there must be a scalar function f such that the gradient of f is equal to F. This means

[tex]\dfrac{\partial f}{\partial x}=3x^2-2y^2[/tex]

[tex]\dfrac{\partial f}{\partial y}=4xy+4[/tex]

Integrate both sides of the first equation with respect to x :

[tex]f(x,y)=x^3-2xy^2+g(y)[/tex]

Differentiate both sides with respect to y :

[tex]\dfrac{\partial f}{\partial y}=-4xy+\dfrac{\mathrm dg}{\mathrm dy}=4xy+4\implies\dfrac{\mathrm dg}{\mathrm dy}=8xy+4[/tex]

But we assume g is a function of y, which means its derivative can't possibly contain x, so there is no scalar function f whose gradient is F. Therefore F is not conservative.

In this problem, since the condition of equal derivatives does not apply, the vector field is not conservative.

A vector field can be described as:

[tex]F = <P,Q>[/tex]

It is conservative if:

[tex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}[/tex]

In this problem, the field is:

[tex]F = <3x^2 - 2y^2, 4xy + 4>[/tex]

Then:

[tex]P(x,y) = 3x^2 - 2y^2[/tex]

[tex]\frac{\partial P}{\partial y} = -4y[/tex]

[tex]Q(x,y) = 4xy + 4[/tex]

[tex]\frac{\partial Q}{\partial x} = 4y[/tex]

Since [tex]\frac{\partial P}{\partial y} \neq \frac{\partial Q}{\partial x}[/tex], the field is not conservative.

A similar problem is given at https://brainly.com/question/15236009

Can someone please help me?

Answers

Negative Integers are :

Less than zeroTo the left of zero on a number line.

FIND THE VALUE OF NT
PLEASE HELP ASAP :(

Answers

Answer:

NT = 14 units

Step-by-step explanation:

In this question we will apply the theorem of intersecting chords.

Two chords MY and TN are intersecting each other inside a circle at a point H.

Theorem states,

MH × HY = TH × HN

12(x) = 8(x + 2)

12x = 8x + 16

12x - 8x = 16

4x = 16

x = 4

Therefore, measure of chord NT = NH + HT

                                                       = 8 + (x + 2)

                                                       = x + 10

                                                       = 4 + 10

                                                       = 14 units

PLEASE SOLVE THE ABOVE PROBLEM you’ll get 43 POINTS

Answers

heya friend

0.2

0.2**10/10

=2/10

in 2/10 2 and 10 are integers

and 10 is not zero

so it is sacrificed

hope this helps u

Answer:

0.2

0.2**10/10

=2/10

in 2/10 2 and 10 are integers

10 is not 0

Step-by-step explanation:

Michelle is 7 years older than her sister Joan, and Joan is 3 years younger than their brother Ryan. If the sum of their ages is 64, how old is Joan?

16
22
18
19

Answers

Answer:

(C) 18

Step-by-step explanation:

We can create a systems of equations. Assuming [tex]m[/tex] is Michelle's age, [tex]j[/tex] is Joan's age, and [tex]r[/tex] is Ryan's age, the equations are:

[tex]m = j + 7[/tex]

[tex]j = r-3[/tex]

[tex]m+j+r = 64[/tex]

We can use substitution, since we know the "values" of m and j.

[tex](j+7)+(r-3)+r = 64\\(j+7)+(2r-3)=64\\2r + j + 4 = 64\\2r + j = 60\\\\[/tex]

[tex]r = 21, j = 18[/tex]

So we know that Joan is 18 years old.

Hope this helped!

In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question)
a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?

Answers

Answer:

a

  [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

b

  [tex]P( X >0.025 ) = 0.99379[/tex]

Step-by-step explanation:

From the question we are told that

   The  population proportion is  [tex]p = 0.10[/tex]

    The sample size is  [tex]n = 100[/tex]

Generally the standard error is mathematically represented as

       [tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]

=>   [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]

=>   [tex]SE =0.03[/tex]

The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178

   [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]

  Generally  [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]

   [tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]

From the z-table  

      [tex]P(Z < 2.6 ) = 0.99534[/tex]

     [tex]P(Z < 2.4 ) = 0.9918[/tex]

[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]  

 [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as

        [tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]

        [tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]

From the z-table  

        [tex]P (Z > -2.5 ) = 0.99379[/tex]

Thus

      [tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]

If x=64 &y=27 Evaluate x½-y⅓÷y-x⅔​

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

-191/162

▹ Step-by-Step Explanation

Answer:

-191/162

Step-by-step explanation:

Substitute the numbers for the variables:

64 1/2 - 27 1/3 ÷ 27 - 64 2/3

Convert the mixed numbers to improper fractions:

129/2 - 82/3 * 1/27 - 194/3

Multiply the improper fractions:

129/2 - 82/81 - 194/3

= -191/162

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

will rate you brainliest

Answers

Answer:

A

Step-by-step explanation:

f(x)→g(x)

(0, 0) → (3, -4)

Therefore it increases it x-axis from 0 to 3

And decreases in y-axis from 0 to -4

Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42 . Find their ages. Use whole numbers.

Answers

Answer: Jake is 9 and his dad is 33.

Step-by-step explanation: 9x3=27+6=33 9+33=42

Answer:

Jake is 9 and Jake's dad is 33

Step-by-step explanation:

To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake

J+D=42

3J+6=D

Solve by substitution

A person collected ​$700 on a loan of ​$600 they made 5 years ago. If the person charged simple​ interest, what was the rate of​ interest? The interest rate is ​%. ​(Type an integer or decimal rounded to the nearest hundredth as​ needed.)

Answers

Answer:

Rate= 3 1/3%

Or Rate= 3.33%

Step-by-step explanation:

Final amount collected= $700

Initial amount given out= $600

Interest made= Final amount - initial amount

Interest made= $700-$600

Interest made= $100

Type of interest rate = simple

Number of years = 5

PRT/100= interest

R=(100*interest)/(PT)

R= (100*100)/(600*5)

R= 10000/3000

R= 10/3

R= 3 1/3%

Or R= 3.33%

Assume that random guesses are made for ​multiple-choice questions on a test with choices for each​ question, so that there are n ​trials, each with probability of success​ (correct) given by p. Find the probability of no correct answers

Answers

Complete Question

Assume that random guesses are made for 7 ​multiple-choice questions on a test with 5 choices for each​ question, so that there are n=7 ​trials, each with probability of success​ (correct) given by  p=0.20. Find the probability of no correct answers.

Answer:

The  probability is [tex]P(X = 0 ) = 0.210[/tex]

Step-by-step explanation:

From the question we are told that

    The number of trial is  n =  7

    The  probability of  success is  p =  0.20

   

Generally the probability of failure is

       [tex]q = 1- 0.20[/tex]

       [tex]q = 0.80[/tex]

Given that this choices follow a binomial distribution as there is only two probabilities i.e success or failure

Then the probability is mathematically represented as

          [tex]P(X = 0 ) = \left n} \atop {}} \right. C_0 * p^{0} * q^{n- 0}[/tex]    

          [tex]P(X = 0 ) = \left 7} \atop {}} \right. C_0 * (0.2)^{0} * (0.8)^{7- 0}[/tex]

Here   [tex]\left 7} \atop {}} \right. C_0 = 1[/tex]

=>      [tex]P(X = 0 ) = 1 * 1* (0.8)^{7- 0}[/tex]

=>     [tex]P(X = 0 ) = 0.210[/tex]

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