Suppose you roll a fair six-sided die 25 times. What is the probability that you roll 5 or more 6’s on that die?

A. 0.3883

B. 0.5937

C. 0.5

D. 0.4063

Answers

Answer 1

Answer:

D. P(5+ 6's) = 0.4063

Step-by-step explanation:

Binomial distribution.

For the distribution to be applicable, the experiment must

1. Have a know and constant number of trials

2. Probability of success of each trial remains constant (and known if available)

3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.

4. Independence between trials.

Let  

n = number of trials  = 25

p = probability of success of each trial  = 1 / 6

x = number of successes  (0 ≤ x ≤ n)  = 5

C(n,x) = number of combinations of picking x identical objects out of n

Applying binomial distribution

P(x,n) = probability of x successes in an experiment of n trials.

= C(n,x) * p^x * (1-p)^(n-x)

For n = 25 trials with probability of success (roll a 6) = 1/6

and x = 5,6,7,8,...25

It is easier to calculate the complement by

P(5+ 6's) = 1 - P(<5 6's)

= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )

1- (

    P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961

    P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051

     P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532

    P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883

    P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171

)

= 1 - 0.59373

= 0.40626

= 0.4063 (to 4th decimal place)


Related Questions

Dr. Green has to multiply the weight of the team's bug spray bottles, 7 x 90 grams. To solve this, he writes out the equation 7 x 9 x 10. Why does this strategy work?

Answers

Because 9 × 10 equals 90

Then 7×90=7×9×10

How many and of which kind of roots does the equation
f(x) = x5+ 3x4 + 8x3 + 14x2 + 16x + 8 have?
A. 2 real; 3 complex
B.5 real
C. 3 real;2 complex
D.1 real;4 complex

Answers

Answer:

D. 1 real; 4 complex  

Step-by-step explanation:

1. Calculate the total number of roots

The fundamental theorem of algebra states that any polynomial of degree n has n roots.

Your polynomial is fifth degree, so it has five roots.

2. Calculate the number of real roots

We can use Descartes' rule of signs to determine the number of real roots:

The number of positive real roots is the same as the number of changes in the sign of the coefficients of ƒ(x) or less than by an even number.

The number of negative real roots is the same as the number of changes in sign of the coefficients of the terms of f(-x) or less than this by an even number.

(a) Number of positive real roots

The coefficients of ƒ(x) are

+1 +3 +8 +14 +16 + 8  

There are no changes of sign, so there are no positive real roots.

(b) Number of negative real roots

(i) Find f(-x)

f(-x) = -x⁵+ 3x⁴ - 8x³ + 14x² - 16x + 8

(ii) Count the changes of sign

The coefficients of f(-x) are

-1 ∥ +3 ∥ -8 ∥+14 ∥ -16 ∥ +8

There are five changes of sign.

Thus, the number of negative roots is five, three, or one.

So far, we know that we have five roots. None is positive, and there could be one, three, or five negative real roots.

3. Confirm by sketching the graph

The real roots are the points at which the graph crosses or touches the x-axis.

The graph (see below) crosses the x-axis at only one point.

Thus. we have

one real root (negative) four complex roots

 

Can any kind soul help me please



Use the cosine rule​

Answers

Answer:

M = 45°

Step-by-step explanation:

a²=b²+c²-2bc Cos A

m² = n² + p² - 2np cos M

(5.1)² = (7.2)² + (5.3)² - 2(7.2)(5.3) cos M

26.01 = 51.84 + 28.09 - 76.32 cos M

-53.92 = -76.32 cos M

0.7065 = cos M

M = [tex]cos^{-1 }[/tex](0.7065)

M = 45°

If y=26−(3x+2), then x = ?

Answers

Answer:

-1/3y +8 = x

Step-by-step explanation:

y=26−(3x+2)

Distribute

y = 26 -3x-2

Combine like terms

y = 24 -3x

Subtract 24 from each side

y -24 = -3x

Divide each side by -3

y / -3 -24/-3 = -3x/-3

-1/3y +8 = x

write as an expression: a number that is equal to five less than b

Answers

Answer:

[tex]\huge\boxed{a = b-5}[/tex]

Step-by-step explanation:

Let the number be a

So, the given condition is:

a = b-5

Answer:

[tex]\Huge \boxed{a=b-5}[/tex]

Step-by-step explanation:

Let the number be [tex]a[/tex].

[tex]a[/tex] is equal to 5 less than [tex]b[/tex].

5 is subtracted from [tex]b[/tex].

24 is 75% percent of what number?

Answers

Answer:

32

Step-by-step explanation:

We can call the number x. 75% can be expressed as 0.75 so we can write the following equation: 0.75x = 24. Dividing both sides by 0.75 to get rid of the coefficient of x, we get that x = 32.

Answer:

32.

Step-by-step explanation:

Let's say the number we are trying to find is x.

24 = 0.75x

0.75x = 24

x = 24 / 0.75

x = 32

Hope this helps!

A culture of bacterial triples in size every four hours. If the bacteria population is estimated to be three million now, what will it be one day from now?

A. 4,238,000,000
B. 6,561,000,000
C. 243,000,000
D. 2,187,000,000

Answers

Answer:

1 day = 24 hours

we cam divide in 6 periods of 4 hours

if bacteria triples in size every four hours

3 millions at begining

3^7 = 2'187'000'000 bacteria

Espero que te sirva

Answer: Geometric progression

Step-by-step explanation:

0h -> 3x10^6 /4h-> 9x10^6 / 8h-27x10^6 / 12h->81x10^6 / 16h->243x10^6 / 20h-> 729x10^6 / 24h->2187x10^6 = 2.187.000.000.:

Please answer this question now

Answers

Answer:

76 degrees.

Step-by-step explanation:

Let as consider O is the center of the circle . So from the figure it is clear that

[tex]\angle AOB=44^{\circ}[/tex]

[tex]\angle COD=118^{\circ}[/tex]

By central angle theorem, central angle subtended by an arc is twice of inscribed angle of the same arc.

We know that, [tex]\angle BAD=97^{\circ}[/tex] and angle BOD is the central angle subtended by arc BD.

[tex]\angle BOD=2\times \angle BAD[/tex]

[tex]\angle BOD=2\times 97^{\circ}[/tex]

[tex]\angle BOD=194^{\circ}[/tex]

Now,

[tex]\angle BOD=\angle BOC+\angle COD[/tex]

[tex]194^{\circ}=\angle BOC+118^{\circ}[/tex]

[tex]194^{\circ}-118^{\circ}=\angle BOC[/tex]

[tex]76^{\circ}=\angle BOC[/tex]

[tex]m(arc(BC))=76^{\circ}[/tex]

Therefore, the measure of arc BC is 76 degrees.


EXAMPLE 10 Show that the points (a, a),(-a, - a) and (-3a, 3a) are the vertices of an equilateral triangle. Also find its area.​

Answers

Answer:

The triangle is not equilateral.

Step-by-step explanation:

Distance formula:

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

Distance from (a, a) to (-a, -a):

[tex] d_1 = \sqrt{(-a - a)^2 + (-a - a)^2} [/tex]

[tex] d_1 = \sqrt{(-2a)^2 + (-2a)^2} [/tex]

[tex] d_1 = \sqrt{8a^2} [/tex]

Distance from (-a, -a) to (-3a, 3a):

[tex] d_2 = \sqrt{(-3a - (-a))^2 + (3a - (-a))^2} [/tex]

[tex] d_2 = \sqrt{(-2a)^2 + (4a)^2} [/tex]

[tex] d_2 = \sqrt{20a^2} [/tex]

Distance from (-3a, 3a) to (a, a):

[tex]d_3 = \sqrt{(-3a - a)^2 + (3a - a)^2}[/tex]

[tex]d_3 = \sqrt{(-4a)^2 + (2a)^2}[/tex]

[tex]d_3 = \sqrt{20a^2}[/tex]

The three sides do not have the same length, so the triangle is not equilateral.

simplfy given equation using the distributive property 6 - (3x+10) + 4(2 - x) =15

Answers

Answer:

see below

Step-by-step explanation:

6 - (3x+10) + 4(2 - x) =15

Distribute

6 - 3x -10 +8 -4x = 15

Combine like terms

4 -7x = 15

Subtract 4 from each side

4 -7x-4 =15-4

-7x =11

Divide each side by -7

-7x/-7 = 11/-7

x = -11/7

Write an equation in slope-intercept form for the line the road will follow. (The road is the dashed line.)

Answers

Answer:

x=6

Step-by-step explanation:

The crocodile river is y = 4

The road will intersect at ( 6,4)

We have two points on the line

(6,7) and (6,4)

The slope is

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

   = (4-7)/ (6-6)

  = -3/0

The slope is undefined

That means the equation is in the form

x=

Since the x coordinate is 6

x=6

Given the two figures are similar, calculate the value of y

Answers

Answer:

y+1/12.5=2/5

or,5y+5=25

ory=20/5

so, y=4

Step-by-step explanation:

hope it helps you

I need Help please answer :((

Answers

Answer:

Second option is the correct answer

[tex] {3}^{ - 4} [/tex]

Step-by-step explanation:

[tex] {3}^{ - 8} . {3}^{4} = {3}^{ - 8 + 4} = {3}^{ - 4} [/tex]

Answer:

The answer is D because you multiply the exponents so -8 times 4 is -32

Hope this helps and plz mark branliest!

Step-by-step explanation:

please help !!! idk how to do this

Answers

Answer:

C

Step-by-step explanation:

Here, we want to state the interval that has the highest frequency.

What we are asked here is the range of values where we have the the most common salary.

For 0-10, we have 1 ( Estonia)

For 11-20, we have 1 (Israel)

For 21-30 , we have 0

For 31-40, we have 1 ( Greece)

For 41-50, we have 5

For 51-60, we have 3

For 61-70, we have 1 (Luxembourg)

So 41-50 is the class with the highest frequency

use the given information to find the new price

wholesale price: $35
markup: 95%​

Answers

Answer:

i think the answer is either $68.25 or $110

i hope this helped

How to do this question plz answer me step by step plzz plz ​

Answers

Answer:

194.25meters

Step-by-step explanation:

The distance around the running track is calculated as:

Perimeter of the first semi circle + Perimeter of the second circle +50m + 50m

Semi circle has a length or diameter of = 30m

r = 30/2 = 15m

Perimeter of a circle = 2πr

Hence for a semi circle = 2πr/2 = πr

Perimeter of the first semi circle = π × 15

= 47.123889804m

Perimeter of the second semi circle is the same hence,

π × 15 = 47.123889804m

The distance around the running track

= 47.123889804m + 47.123889804m + 50m + 50m

= 194.24777961m

Approximately= 194.25meters.

The length of a rectangle is represented by the function L(x) = 4x. The width of that same rectangle is represented by the function W(x) = 7x2 − 4x + 2. Which of the following shows the area of the rectangle in terms of x? (L + W)(x) = 7x2 + 2 (L + W)(x) = 7x2 − 8x + 2 (L • W)(x) = 28x3 − 16x2 + 8x (L • W)(x) = 28x3 − 4x + 2

Answers

Answer:

(L ⋅ W)(x) = 28x3 − 16x2 + 8x

Step-by-step explanation:

I took the test hope it helps :3

The area of the rectangle is (L · W) (x) = 28x³ - 16x² + 8x. Thus, the correct option is C.

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given the length of the rectangle is L(x)=4x, and the width is W(x)=7x²-4x+2. Therefore, the area of the rectangle in terms of x is,

L(x)×W(x) = 4x × (7x²-4x+2)

(L · W) (x) = 28x³ - 16x² + 8x

Hence, the area of the rectangle is (L · W) (x) = 28x³ - 16x² + 8x. Thus, the correct option is C.

Learn more about the Area:

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reduce to simplest form -7/12+3/8 =_____

Answers

I simplified it and I got -5/24

Answer:

-5/24

Step-by-step explanation:

make the denominators the same!

The distance between two points on a number line can be found by taking the ____A_____ of the ____B_____ of the coordinates. Fill in the blanks in the previous sentence by matching the letter for each blank with the correct answer.

Answers

Answer:

The distance between two points on a number line can be found by taking the absolute value of the difference of the coordinates.

Step-by-step explanation:

Every point can be paired with a number on a number lineThe coordinate is the number associated with a pointTo find the distance between point A and B you subtract the coordinates in any order you like and take the absolute value.

which choice is the solution set for the inequality below

x < 3

Answers

Answer:

B) x < 9

Step-by-step explanation:

√x < 3

(√x)² > 3²

x < 9

7a - 3 = 3 - 2a What does a equal?

Answers

Answer:

2/3

Step-by-step explanation:

1) Move the 7a to the other side

2) Move the 3

3) Combine like terms

4) Divide by 9

5) Answer is 2/3

Answer:

a=2/3

Step-by-step explanation:

All this problem needs is some knowledge of how an = sign and basic equations work

7a-3=3-2a

7a+2a=3+3  (Sign becomes opposite on the other side of the equation)

9a=6

a=2/3

Thank you for your time!

9. You run a business making birdhouses. You spend $600 to start your business, and it costs you $5.00
to make each birdhouse.
# of birdhouses
1
2
3
4
5
6
7
Total cost to build

Answers

Answer:

$635

Step-by-step explanation:

$5x7 birdhouses=$35want

So, $35+$600=$635 total!

I hope this helps you!

Multiplication is the process of multiplying. The cost of building 7 birdhouses will be $635.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The cost of the birdhouse is the sum of the fixed cost, which is the setup cost of the business of $600, and the variable cost is the cost that is needed to make a single house, therefore, $5.

Now, the total cost of making n number of houses will be,

Cost of making n house = Fixed cost + variable cost

                                        = $600 + $5(n)

Further, the table can be filled using the above formula by substituting the value of n for the number of houses. Therefore,

Number of bird houses     Total cost to build

       1                                     $600+$5(1) = $605

       2                                    $600+$5(2) = $610

       3                                    $600+$5(3) = $615

       4                                    $600+$5(4) = $620

       5                                    $600+$5(5) = $625

       6                                    $600+$5(6) = $630

       7                                    $600+$5(7) = $635

Hence, the cost of building 7 birdhouses will be $635.

Learn more about Multiplication here:

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If JK = 28, JL = 20, KL = 13, and ML = 22, calculate NL. Image not set to scale.

Answers

Answer:

NL  = 440 /13  or 33.85 (to two decimals)

Step-by-step explanation:

Consider triangles JKL and NML

angle JLK = angle NLM           vertical angles

angle KJL = angle MNL           given

Therefore triangles JKL and NML are similar

By proportion of corresponding sides of similar triangles,

NL / JL = LM / LK

Substitute given values

NL / 20 = 22 / 13

solve for NL

NL = 20*22 / 13 = 440 /13  or 33.85 (to two decimals)

Answer:

[tex]\huge \boxed{33.85}[/tex]

Step-by-step explanation:

JL is similar to NL. KL is similar to ML.

We can use ratios to solve.

JL/KL = NL/ML

Let the length of NL be x.

20/13 = x/22

Cross multiply.

13 × x = 22 × 20

13x = 440

Divide both sides by 13.

(13x)/13 =440/13

x = 440/13 = 33.846154...

a police car drives a constant speed of 64 mph.how far can it travel in 2 hours​

Answers

ABCDEFGHIJKLMNOPQRSTUVWXYZ

If a square has a side of length 3, then it’s area is 9. This square has a side of length 3, so it’s area is 9. Is it valid or invalid?

Answers

Answer:

Yes it is valid

Step-by-step explanation:

A square is a geometric shape which is also known as a Quadrilateral. This means that it has 4 sides.

For a square, it's 4 sides are equal to one another or we can put it in other words as the length of the 4 sides of a square are congruent to one another.

From the above question, we are asked that:

"If a square has a side length of 3, it's area is 9. Is it valid or invalid?"

The above statement is valid. This is because, the formula for the Area of a Square is given as

L × L = L²

Where L = Side length = 3

Area = 3 × 3 = 3²

Area = 9

Therefore, the statement is valid.

In Isosceles trapezoid ABCD, the longer base, AB, is one and one half times as long as the shorter base, CD. The other two sides, AD and BC, are both 13 cm. long. a. If the perimeter is 76 cm. find the lengths of AB and CD. b. If the height of the trapezoid is 12 cm. find its area. (Hint: Area

Answers

otal perimeter = 76cm = AB + BC + CD + AD

AD & BC = 13cm

AB = 1.5*(CD)

Solution:

Since we know AD & BC are both 13cm long, plug those numbers into the perimeter equation

76cm+=+AB+%2B+BC+%2B+CD+%2B+AD Place 13cm in for AD & BC

 

76cm+=+AB+%2B+13cm+%2B+CD+%2B+13cm Combine like terms

76cm+=+AB+%2B+CD+%2B+26cmSubtract 26cm from both sides

50cm+=+AB+%2B+CD Now it is time to substitute the 1.5*(CD) for AB

50cm+=+1.5%2A%28CD%29+%2B+CD rewrite the equation

50cm+=+2.5%2A%28CD%29 Divide both sides by 2.5

20cm+=+CD

To find AB, plug 20cm in for CD in the equation AB = 1.5*(CD)

AB+=+1.5%2A20cm

AB+=+30cm

I need hellp please its my last chance to become a senior please someone

Answers

Answer:

d= 6

r= 6/2

r=3

V= π. r². h

V= π . 3². 14

V= π. 9 . 14

V= π 126 cm³

V= 126 π cm³ (π not in number)

hope it helps^°^

Answer:if you use the formula it is 126 pi cm cubed

The answer is c

Step-by-step explanation:

what is the answer to x2 = 121.

Answers

Answer:

11 if you mean x^2

Step-by-step explanation:

Since we are solving for x, we need to just get x by its self. The only thing we have to do is get rid of the exponent of (^2). to do this, we have to take teh square root of both sides:

The square root of x^2 is x

The square root of 121 is 11

So the asnwer is x = 11

Step-by-step explanation: A common mistake in this problem would be to say that if x² = 121, x must equal 11.

However, you must set the equation equal to 0 first.

So our first step is to subtract 121 from both sides to get x² - 121 = 0.

Next, factor the left side to get (x + 11)(x - 11) = 0

So either x + 11 = 0 or x - 11 = 0.

Solving each equation from here, we find that x = -11 or x = 11.

So our answer is not just 11, it's {11, -11}.

A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?

Answers

Answer:

y = -x +2

Step-by-step explanation:

y =x  has a slope of 1

Perpendicular lines have slopes that multiply to -1

m* 1 = -1

The slope of the perpendicular line is -1

We have a slope and a point

y = mx+b

y= -1x+b

Substitute the point into the equation

-3 = -1(5) +b

-3 =-5 +b

Add 5 to each side

-3+5 = b

2 =b

y = -x +2

A will states that 4/5 of estate is to be divided among relatives. Of the remaining estate1/4 goes to the American cancer society. What fraction of the estate goes to the American cancer Society

Answers

Answer:

 1/9 of the estate is for American cancer society

Step-by-step explanation:

 

In this problem we are expected to calculate the fraction of a whole that belongs to a part. that is the fraction of the estate the belongs to American cancer society.

let us  state as given that the total estate is 5

and 4 is to be divided among relatives, remaining 1

out of the remaining 1 estate,

1/4 belongs to American cancer society

Therefore the fraction of the 5 estates that belongs to American cancer society is = 1/4 of 1/5= 1/9

Other Questions
Read the sentence.The Canary Islands are a popular vacation spot for people from Finland, a chain of seven islands off the coast of Africa.What is the best way to rewrite the sentence?A-The Canary Islands, a chain of seven islands off the coast of Africa, are a popular vacation spot for people from Finland. B-A popular vacation spot for people from Finland, a chain of seven islands off the coast of Africa are the Canary Islands. C- ***NOT CORRECT**The Canary Islands are a chain of seven islands off the coast of Africa, a popular vacation spot for people from Finland. D-A chain of islands off the coast of Africa, a popular vacation spot for people from Finland, are the Canary Islands. Raw celery has a slight sparkle, a zingy taste that you don't get in cooked celery. When Mrs. Gleason came around with the relish tray, we each took another stalk of celery, except my brother. He took two. "The All-American Slurp," Lensey Namioka What does the word stalk mean in this sentence? HELP! QUICK!What is the equation for the parabola with focus (2,7) and directrix y = -2? Find all points having an x- coordinator of 5 whose distance from the point (-1,-3) is 10. (type an ordered pair. Use a comma to separate answers as needed.) Consider that President Roosevelt delivered the Four Freedoms speech on January 6, 1941. What is the historical context of this speech in relation to World War II A NASDAQ security is bid at $30.25 and offered at $30.75. An over-the-counter trader effects a trade at $30.75 and charges a commission of $.50 to the customer. The price that will show on the tape is: Dave loves a bargain and buys a feather boa whichhas been reduced in price by 70%. If the sale priceis 2.85, what was the original price of the boa? If A = { 10, 30,} B = { 10, 20, 30, 40, 50, 60, 70, 80,90} find A B There are options. Choose one option only: A- { 30 ,10} B- { 90 ,30 ,10} C- { 90 } D- { 80, 70, 60, 50, 40, 20 } Use the rule "add 2" to create a sequence of 5 numbers starting with 8. sin3/54/53/45/4 the length of rectangle is 6/5 of its breath and perimeter is 132 m find area of rectangle How would I solve this? (y-z) z y=-2 and z=4/5 What new technology defined the war and tactics in the pacific? Evaluate the expression you got in part f for d = 5. Which of the following statements is CORRECT? a. Commercial paper can be issued by virtually any firm so long as it is willing to pay the going interest rate. b. Short-term debt is favored by firms because, while it is generally more expensive than long-term debt, it exposes the borrowing firm to less risk than long-term debt. c. Commercial paper is a form of short-term financing that is primarily used by large, strong, financially stable companies. d. Trade credit is provided only to relatively large, strong firms. e. Commercial paper is typically offered at a long-term maturity of at least five years. An agile team used planning poker to estimate user stories. After all team members read a user story, the facilitator asks everyone to choose a card with estimated number of ideal days to complete a user story and then reveal the card. If estimates were widely different, the facilitator would immediately ask for re-estimates until all the estimates converge. What did the facilitator do wrong?A. Participants used ideal days as the unit for the estimates.B. Participants re-estimated immediately after everyone revealed their cards.C. Cards were revealed when the process should have been anonymous.D. The facilitator did nothing wrong and played by the rules. Which areas of the Great Plains were most severely affected by the Dust Bowl? Land and other real estate held as investments by endowments in a government's permanent fund should be reported at Joe has been traveling the country on a road trip for a couple of weeks and is now finally on his way home. He decides to make one more stop at a hotel in State B before he finishes up the drive to his home in State A. While at the hotel, Joe runs into Bill, an old friend and an agent, registered in State B, who solicits the purchase of a security to Joe. Joe agrees to purchase the security and pays for it then and there. Bill informs Joe that he will send the confirmation to Joe's residence in State A and does so. If Bill is properly registered throughout all states of the country, but sold Joe a security that is not registered and is not exempt in any way from registration, which of the following is correct?[A] Every state within which Bill is registered (50 states), may take action against Bill.[B] Only State A and State B can take action against Bill.[C] Only State B can take action against Bill.[D] Only State A can take action against Bill. I have four brothers"This is what type ofobservation?