what is the probability that if 4 letters are typed, no letters are repeated? write your answer in decimal form, rounded to the nearest thousandth. the probability that no letters are repeated is .

Rajiv chose to make a cardboard box of length 7 cm from the given cardboard available.

It is given that the amount of cardboard available is 245 cm.  Therefore, the box's surface area will be less than or equal to 245 cm².

We are given that the box does not have any lid. Hence, the box is made up of 5 squares.

Let the length of one side of the box be x cm.

We know, that the surface of the area of a regular cube is

6a².

That means,

no. of squares X square of the length.

Hence, the surface area of the box is 5x².

Therefore from the given problem, we get that

5x² ≤ 245

or, x² ≤ 245/5

or, x² ≤ 49

49 is a perfect square of 7. Hence assuming Rajiv makes the largest possible box,

the length of the side he chose is 7 cm.

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Answer:

Two points A(x,y) B(x₂,y₂) or One point A(x,y) and gradient(slope).

Step-by-step explanation:

Answer:

(3,2)

Step-by-step explanation:

-5+8=3

6-4=2

(3,2)

Answer:

1/4b

Step-by-step explanation:

The age of Jane based on the information is 10 3/10 years.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

In this case, Dan is 12 4/5 years old, Karina is 1 1/6 years younger than Sarah and Jane is 1 1/3 years younger than Greg

The age of Jane will be:

= 12 4/5 - 1 1/6 - 1 1/3

= 12 24/30 - 1 5/30 - 1 10/30

= 12 24/30 - 2 15/30

= 10 9/30

= 10 3/10

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Mr. Patrick instructs 15 students in math. He discovered that Payton had received a 95 on the test while grading them from average.

There are 15 kids in Mr. Patrick's class. The average score on his most recent exam was 80 for 14 candidates (not including Payton).

I'm going to use x to represent the unknowable sum of the 14 test scores. Average is computed by adding all the numbers in the set (whose average you're trying to get) together, then dividing by the total number of numbers in that set.

This was the total of their scores: x=1120.

Adding Payton's score now (I'll use the letter p to stand in for her score):

1120+p /15=81→ Her test score was included in the fifteen students' average, which was 81 1120+p=1215

P=95.

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The store has 16 board games

What are equivalent ratios?

The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.

Let x = number of legos

Let y =  number of board games

Given ratio: 9:6= 9/6

x/y = 9/6

substitute x=24

24/y=9/6

Do cross multiplication

(6*24)/9=y

16=y

or

y=16

So, the store has 16 board games

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The 99 percent confidence interval for the mean score of all subjects lies greater than 63.464 and less than 78.936.

Given:

No. of samples (n)= 16

df = n-1 = 16 -1 = 15

The mean score is 71.2

The standard deviation = 10.5.

So, from the t-distribution of critical values table through the above-mentioned details. We get the values:

Alpha / 2 = 0.005

z = 99/100 + 0.005 = .99 + .005 = .995

Sample mean = xbar = 76.2

t = 2.947

The formula for standard error = E = value of t (at z, and df) / S.D./sqrt(n)

i.e. E = 2.947 x 10.5 / sqrt 16 = 7.736

I = 71.2 +/- E =  71.2 +/-  7.736

99 percent confidence interval - 71.2 +/- 7.736

Adding both sides 7.736 for range. We get,

63.464 < u < 78.936

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The dimensions x and x+50 are 150 ft by 200 ft. When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them.

When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.

If you draw a diagonal, you have 2 right triangles, each with leg lengths of x and x + 50.

The diagonal is the hypotenuse, h = 250

Using Pythagorean theorem:

X² + (x+50)² = 250²

x² + x²+ 100x + 2500 = 62500

2x²+ 100x - 60000 = 0

All are even, so factor out a 2:

x² + 50x - 30000 = 0

From quadratic equation:  x = [-50±√(50²-4(1)(-30000))]/(2(1))

x = (-50 ± 350)/2

We can disregard the negative so

x = (-50 + 350)/2 = 300/2 = 150 ft

The dimensions x and x+50 are 150 ft by 200 ft

The complete question is: A rectangular parking lot is 50ft longer than it is wide. Determine the dimensions of the parking lot if the diagonal distance from corner to corner of the lot is 250ft.

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Answer:

The vector which has a greater magnitude.

Solution:

We know that, magnitude of a vector represents the length of it.

The first vector that is 2 meters long has a magnitude 2.

The second vector that is 4 meters long has a magnitude 4.

Clearly, 4 is greater that 2, i.e., 4 > 2. So, magnitude of second vector is greater.

Therefore, the vector that is 4 meters long has greater magnitude.

Step-by-step explanation:

The probability of an event {a or b} is 0.7

Probability: It is the branch of mathematics concerning numerical, descriptions of how likely an event is to occur or how likely it is that a proposition is true. the probability of an event is a number between

0 and 1.

if the two events a and b are mutually exclusive then the addition rule of probability is:

P( a or b) = P(a) + P(b) - P(a∩ b)

Given that,

P(a) = 0.6                    P(b) = 0.5

               P(a ∩ b)= 0.4

According to probability methods, if two events are mutually exclusive, then the probability of either occurring is denoted as P (a ∪ b).

Now, we know that,

P( a ∪ b) = P(a) + P(b) - P( a ∩ b)

              = 0.6 + 0.5 - 0.4

              = 0.7

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If Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. The number of  subscribers they must  sample to obtain this interval is: b) 385.

Using this formula to find the number of  subscribers  they must sample to obtain this interval

n≥ (zσ/2 ÷ 2ME)²

Where:

n= Sample =?

zσ = Z-score for 95% confidence interval = 1.96

ME = margin of error = 0.05

Let plug in the formula

n≥ [1.96 / 2(0.05)]²

n≥ [1.96 / 0.1]²

= (19.6)²

= 384.16

=385 (Rounded)

Therefore the correct option is B.

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The complete question is:

Netflix would like to estimate the proportion of their current subscribers who would pay

extra for a premium membership including access to more movies and TV shows. To do

this, they plan to calculate a 95% confidence interval to estimate the proportion. They

would like a margin of error of .05. How many subscribers must they sample to obtain this

interval?

a) 1537

b) 385

c) 192

d) 10

The answer to the question probability of randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.

What is standard deviation?

A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.

The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.

The mean blood pressure for people in china is 128 mmHg.

The standard deviation of 23 mmHg.

For blood pressure of 182.6 mmHg

=p(x> 182.6)

=p(z> 182.6-128/23)

=p(z> 2.37)

=0.0088

Hence the probability of a randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.

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Answer: r = 11.3

Step-by-step explanation:

Standard form : (x-h)2 + (y-k)2 = r2

(h,k) = (5,7)

(x,y) = (-3,-1)

r2 = (-3-5)2 + (-1-7)2

r2 = [tex]-8^{2} + -8^{2} = 64 + 64 = 128\\r = \sqrt{128} = 11.3[/tex]

When coordinates of the center of the circle and a point on the circle are known, Standard form is the one to use.

The measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees

What are isosceles triangles?

Isosceles triangles are triangles that have two sides equal in measurement.

Main Body:

From the given diagram;

∠BAC = 18 degrees

∠BDC = 48 degrees

Required angle  : ∠ABD

From the diagram, ∠DAB = ∠BAC = 18 degrees

Also, ∠ADC + ∠ACD + ∠DAC = 180

Since triangles ACD is isosceles, hence ∠ADC = ∠ACD. The expression above becomes

∠ADC + ∠ADC + ∠DAC = 180

2∠ADC + ∠DAC = 180

2∠ADC  = 180 - 36

2∠ADC = 144

∠ADC = 144/2

∠ADC = 72 degrees

This means that ∠ADB = 72 - ∠BDC

∠ADB = 72 - 48

∠ADB = 24 degrees

Get the required angle ABD

From triangle ADB, ∠ABD + ∠ADB + ∠DAB = 180

∠ABD + 24 + 18 = 180

∠ABD + 42 = 180

∠ABD = 180 - 42

∠ABD = 138 degrees

Hence the measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees.

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Answer: 4

Step-by-step explanation:

100/8 = 12 golf balls in each box

8*12 = 96 golf balls are used

100-96= 4 gold balls left

Answer:

D

Step-by-step explanation:

D   the premium you pay is your bill for insurance

The total distance traveled when Bo fell asleep is 504 miles.

What is the distance traveled?

The path taken by an object to move from a starting point to an ending location in a specified amount of time with a specific velocity is known as the distance traveled.

Given, the total length of distance = 600 miles

           Bo fell asleep = 84%

Let 'x' be the distance traveled.

Then, according to the question

         x = 84% of 600 miles

or,      x = [tex]\frac{84}{100} * 600[/tex]

or,      x = 84*6

or,      x = 504 miles

Hence, the total distance traveled when Bo fell asleep is 504 miles.

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Answer:

343

Step-by-step explanation:

Answer:

v<-1.3

Step-by-step explanation:

Add 3.9 to -5.2

v<-1.3

Hope this helped!

The points on the ellipse 5x² + y² = 5 that are farthest away from (1, 0) are (-0.25, ±√4.6875).

The square of the distance from a point on the ellipse to the point (1, 0) is ...

 d^2 = (x -1)^2 +y^2

Using the equation of the ellipse to write an expression for y^2, we have ...

 d^2 = (x -1)^2 +5 -5x^2

 d^2 = -4x^2 -2x +6

The expression on the right is that of a downward-opening parabola with ...

 a = -4, b = -2, c = 6

The maximum is located at ...

 x = -b/(2a) = -(-2)/(2(-4)) = -1/4

The value of y there is ...

 y^2 = 5 -5(-1/4)^2 = 4 11/16

 y = √4.6875

Hence the points on the ellipse farthest from (1, 0) are (-0.25,±√4.6875).

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The ratio of boys to girls of the junior members of a tennis club is  1 : 3.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, Three-quarters of the junior members of a tennis club are boys.

Assuming the total no. of boys and girls is 1.

∴ 3/4 members are boys and (1 - 3/4) = 1/4 are girls.

So, the ratio of boys to girls is 1/4 : 3/4 which is equal to 1 : 3.

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Answer: A. Yes, their slopes are negative reciprocals

Step-by-step explanation:

x=3 is a vertical line where every y value lands on x=3. (Undefined slope)

y=5 is a horizontal line where every x value lands on y=5 (Zero slope)

Even though the slopes are not numbers they can still be negative reciprocals. The lines are indeed perpendicular and thus the slopes are negative reciprocals. The relationship between undefined slopes and zero slopes is negative reciprocals because 0/1 cannot be inversed because anything divided by 0 is undefined.

Answer:

....

Step-by-step explanation:

....

....

....

....

...

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-3)}}} \implies \cfrac{-7 +2}{1 +3} \implies \cfrac{ -5 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{5 }{ 4 } \end{array}}[/tex]

When  you transform row score into a set of z- score, you are able to compare the score of both distribution. When you compare the scores you can allow one to have a mean of 0 and standard deviation 01. A z- score let us see how many standard deviation away from the mean an element lies.

Z- score: It is a numerical measurement that describes a value's relationship to the mean of a group of values and is measured in terms of standard deviation from mean.

Raw score: A raw score is unaltered measured. For example:- if there is a test in a class and someone for 75 out of 100, 75 would be there raw score.

Transform a set a raw scores into  a set of z score:

Lets understand the importance of transforming  raw scores into  a set of z score with the help of an example.

For admission in PG program students need to appear  in the entrance exam which held in two batches. John appeared in both the exams and he scored 160 out of 200 in paper A and 145 out of 185 on paper B.

Solution: we needs to find the z score corresponding to each paper in order to compare them.

paper A: Score obtained : 160

              Average score: 155

              Standard Deviation: 10

Paper B: Score obtained: 145

               Average obtained: 135

                Standard deviation: 08

Using the Z- score formula:

             Z = (x - μ) /α

Using the above Z score formula to calculate z score for given raw score values:

z score for Paper A =  ( 160-155)÷ 10    

Z score for paper B = ( 145 - 135 ) ÷ 1.25

While Evaluating based on z score, we can say that John performed relatively better in paper B as compared to paper A.

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The compound interest compounded at a rate of 3% quarterly for 5 years is $15,095.39

The compound interest is the interest-based on the initial principal amount and the interest collected over the period of time.  The compound interest formula is given below:

A = P(1 + r/n)^nt

Substituting the values into the equation given;

A = 13000(1 + 0.03/4)^4 * 5

A = 13000(1.0075)^20

A = $15,095.39

The amount at the end of 5 years is $15,095.39

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The equation to represent total amount of money that she receives for the tee shirts in terms of number of machines is  2800*n*(200 - n)  .

In the question ,

it is given that

the cost of 1 tee - shirt = $14

total days required to deliver the tee shirt = 20

number of tee - shirts that a machine can produce = 200 per day

let the number of machines = n

so the number of days require to set up the machines = n

hence all the machine will work for = (20 - n) days  

1  machines will produce 200(200 - n) tee shirts

n machines will produce = 200n(200 - n) tee shirts in the remaining (20 - n) days .

the selling price of 1 tee shirt is = $14

So, the total money M that she will receive is = 14*200*n*(200 - n)

= 2800*n*(200 - n)

Therefore , The equation to represent total amount of money that she receives for the shirts in terms of number of machines is  2800*n*(200 - n)  .

The given question is incomplete , the complete question is

A manufacturer wishes to make tee-shirts for the band dixie chicks. They sell for $14 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money( M ) she will receive for the shirts in terms of the number of machines she decides to set up (assuming she sells all the shirts she makes).

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Answer: A: x=4

Step-by-step explanation:

5(4)-5=15

20-5=15

15=15

There are in total 1.04 x 10^6 bacteria that are growing in the petri dish.

Given that, there are 5.2 x10^4 bacteria in each 20 petri dish, we have to multiply 5.3x10^4 by 20, get the total bacteria in all 20 petri dish.

5.2 x10^4x 20

= 1,040,000

We have to write this in scientific notation.

The goal of scientific notation is to make it simple for scientists to write extremely large or extremely small numbers.

Since it always follows this notation, calculating scientific notation for a positive integer is straightforward:

a x 10^b

1.040000

1 is a, there are 6 digits right to the decimal point.

a=1.04

b=6

The scientific notation for total bacteria in 20 petri dish is 1.04 x 10^6.

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