Evaluate the expression when e=13 and f=16.

4(19+e2)+3f

Enter your answer as a mixed number in simplest form

Using the binomial distribution, it is found that:

a) The possible values of X are between 0 and 20.

b) 0.0596 = 5.96% probability that exactly 3 experience insomnia as a side effect.

c) 0.9842 = 98.42% probability 3 or fewer experience insomnia.

d) 0.639 = 63.9% probability that between 1 and 4 experience insomnia.

e) Since [tex]4 > E(X) + 2.5\sqrt{V(X)}[/tex], it would be unusual to find 4 or more patients experience insomnia as a side effect.

For each patient, there are only two possible outcomes, either they experience insomnia, or they did not. The probability of a patient having experienced insomnia is independent of any other patient, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n trials, with p probability.

[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 expected value is:

[tex]E(X) = np[/tex]

The standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]

If a measure is more than 2.5 standard deviations above the mean, it is considered unusual.

In this problem:

Item a:

The possible values of X are always between 0 and n, thus in this case, it is between 0 and 20.

Item b:

This probability is P(X = 3), thus:

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

[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]

0.0596 = 5.96% probability that exactly 3 experience insomnia as a side effect.

Item c:

This probability is [tex]P(X \leq 3)[/tex], given by:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Then:

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

[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]

[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]

[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]

[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]

0.9842 = 98.42% probability 3 or fewer experience insomnia.

Item d:

This probability is:

[tex]P(1 \leq X \leq 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Then

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

[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]

[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]

[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]

[tex]P(X = 4) = C_{20,4}.(0.05)^{4}.(0.95)^{16} = 0.0133[/tex]

[tex]P(1 \leq X \leq 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.3774 + 0.1887 + 0.0596 + 0.0133 = 0.639[/tex]

0.639 = 63.9% probability that between 1 and 4 experience insomnia.

Item e:

[tex]E(X) = np = 20(0.05) = 1[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.95)} = 0.975[/tex]

[tex]E(X) + 2.5\sqrt{V(X)} = 1 + 2.5(0.975) = 3.44[/tex]

Since [tex]4 > E(X) + 2.5\sqrt{V(X)}[/tex], it would be unusual to find 4 or more patients experience insomnia as a side effect.

A similar problem is given at https://brainly.com/question/24863377

- tan(50) → Choice A

Step-by-step explanation:

tan(-α) = - tan(α)

tan(-50) = - tan(50)

Further more :

tan (-50) = - tan (50) ≈ 0,27

Answer:

$7

Step-by-step explanation:

Wyatt will have $7 more in his account than Sophie.

Compound interest is the interest you earn on interest.

Given that, Sophie invested $170 in an account paying an interest rate of [tex]2\tfrac{3}{4}[/tex]% compounded continuously.

Wyatt invested $170 in an account paying an interest rate of [tex]3\tfrac{1}{8}[/tex]% compounded monthly.

We need to find how much more money would Wyatt have in his account than Sophie after 9 years,

For compounded continuously = [tex]Amount = Principal \times e^{rt[/tex]

Sophie =

[tex]Amount = 170 \times e^{0.0275 \times 9[/tex]

A = $217.74

Therefore, Sophie will have $217.74 in her account after 9 years.

For Wyatt,

So, using the formula of CI,

[tex]Amount = Principal(1+r/n)^{nt[/tex]

So,

[tex]= 170(1.0026)^{108[/tex]

A = $225

Therefore, Wyatt will have $225 in his account after 9 years.

The amount Wyatt have more than Sophie = 225-217.74 = $7.26 ≈ $7.

Hence Wyatt will have $7 more in his account than Sophie.

Learn more about compound interest click;

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#SPJ2

6- (-2) - 3(-5)

= 6- (-2) +15

= 6+ 2 +15

= 8+ 15

=23.

Thus, your answer is 23

Answer:

look at the photo..............

Answer:

The decimal point should be moved 4 places to the right

Step-by-step explanation:

38.75x10000= 387500

Answer:

I would estimate 923

Step-by-step explanation:

Answer:

0.4⎯⎯

Step-by-step explanation:

BRAINLIEST?

Answer:

b

Step-by-step explanation:

The sum of angles 7 and 8 is 180, so to find angle 8 you would subtract angle 7 from 180. So:

180 - 92 = 88  

The answer is B, 88 degrees.

Answer:

88° is your answer......

Answer:22% or A!

Step-by-step explanation: 400 x 9 = 3600 he has ran 792 so far so its about 22.%  

Answer:

54

Step-by-step explanation:

the ladder need to be 54 feet high

9514 1404 393

Answer:

  -2/a^3

Step-by-step explanation:

Anything (except 0) to the 0 power is 1, so b^0 = 1. This immediately simplifies the expression to -2a^-3. If you also want it with positive exponents, this will be ...

  -2/a^3

I believe the given limit is

[tex]\displaystyle \lim_{x\to\infty} \bigg(\sqrt[3]{3x^3+3x^2+x-1} - \sqrt[3]{3x^3-x^2+1}\bigg)[/tex]

Let

[tex]a = 3x^3+3x^2+x-1 \text{ and }b = 3x^3-x^2+1[/tex]

Now rewrite the expression as a difference of cubes:

[tex]a^{1/3}-b^{1/3} = \dfrac{\left(a^{1/3}-b^{1/3}\right)\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)}{\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)} \\\\ = \dfrac{a-b}{a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}}[/tex]

Then

[tex]a-b = (3x^3+3x^2+x-1) - (3x^3-x^2+1) \\\\ = 4x^2+x-2[/tex]

The limit is then equivalent to

[tex]\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}}[/tex]

From each remaining cube root expression, remove the cubic terms:

[tex]a^{2/3} = \left(3x^3+3x^2+x-1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3}[/tex]

[tex](ab)^{1/3} = \left((3x^3+3x^2+x-1)(3x^3-x^2+1)\right)^{1/3} \\\\ = \left(\left(x^3\right)^{1/3}\right)^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1x\right)\left(3-\dfrac1x+\dfrac1{x^3}\right)\right)^{1/3} \\\\ = x^2 \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3}[/tex]

[tex]b^{2/3} = \left(3x^3-x^2+1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}[/tex]

Now that we see each term in the denominator has a factor of x ², we can eliminate it :

[tex]\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}} \\\\ = \lim_{x\to\infty} \frac{4x^2+x-2}{x^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}\right)}[/tex]

[tex]=\displaystyle \lim_{x\to\infty} \frac{4+\dfrac1x-\dfrac2{x^2}}{\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}}[/tex]

As x goes to infinity, each of the 1/x ⁿ terms converge to 0, leaving us with the overall limit,

[tex]\displaystyle \frac{4+0-0}{(3+0+0-0)^{2/3} + (9+0-0+0+0-0)^{1/3} + (3-0+0)^{2/3}} \\\\ = \frac{4}{3^{2/3}+(3^2)^{1/3}+3^{2/3}} \\\\ = \frac{4}{3\cdot 3^{2/3}} = \boxed{\frac{4}{3^{5/3}}}[/tex]

Answer:

Step-by-step explanation:

Just make an example

Answer:

Bro it is simple,see when the 2 numbers are multiplying in 1st number decimal is before 2 digits and in 2nd number decimal is before 1 digit and in product decimal is before 3 digits so to place the decimal you need to + the digits afer decimal of numbers eg. in 0.43 there are 2 digits afer decimal and in 0.2 there is 1 digit after decimal and in answer there are 3 digits after decimal

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer: SEE BELOW

Step-by-step explanation:

Decimals are multiplied as if they were whole numbers, and then the decimal point is placed in the product. To find out where the decimal point should be placed, count the number of decimal places after the decimal point in each factor.

0.43......... 2 decimal place(s) Add your decimal places = 3

0.2......... 1 decimal place(s)

0.086 Place decimal 3 decimal places in answer like so.

hope this helps you! Smile ; )

Answer:

x + 93 = 124

Step-by-step explanation:

4x = x + 93  {Vertically opposite angles are equal}

Subtract 'x' from both sides

4x - x = 93

3x = 93

Divide both sides by 3

x = 93/3

x = 31

x + 93 = 31+ 93 = 124

Answer:

The domain is the set of x-values:

The range is the set of y-values:

This can be a function as each x- value has exactly one corresponding y- value.

Points are

All x values has a unique image in y so it's a function

[tex]\\ \sf\longmapsto D_f=\{-4,-2,1,4,2\}[/tex]

[tex]\\ \sf\longmapsto R_f=\{-1,1,-2,-4,4\}[/tex]

The cauliflower for one portion cost $6.75.

The first step is to convert pounds to ounces. The unit of conversion of pounds to ounces is 1 pound is equivalent to 16 ounces.

1 pound = 16 ounces

Therefore, 16 ounces of cauliflower costs $18.

The cost of one ounce = 18 / 16 = $1.125

The cost of one portion of cauliflower is:

Cost of one ounce x number of ounces in one portion

$1.125 x $6 = $6.75

A similar question was answered here: https://brainly.com/question/4429484?referrer=searchResults

y = -1/4x + 2

yeah

that's it

Answer:

1. 2x + 4= slope: 2 | y intercept: (0,4)

2. 2x + 4= slope: 2 | y intercept: (0,4)

3. -1/4x + 2= slope: -1/4 | y intercept: (0,2)

4. -1/4x + 2= slope: -1/4 | y intercept: (0,2)

Let's say c is the cost of the cantaloupe, and that p is how many pounds the cantaloupe weights.

In that case, $1.19 is the amount of money it will cost per pound of cantaloupe.

If the cantaloupe you buy is 3.5 pounds, it will cost you $4.165, but since money is only two decimal places, and since you can only round up when it's a 5 at the end, it becomes $4.17.

In other words, each pound of cantaluope you buy will cost you $1.19, and a cantaloupe that weighs 3.5 pounds will cost you $4.17.

Answer:

1. f(x)+g(x)=3x−7+x2+5x

2. 5x+x2-7+3x

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Ok, first the formula for this is a^2+b^2=c^2

or leg^2+ leg^2= hypotenuse^2

so (12)^2+(9)^2=hy^2

144+81, 225=hy^2

hy=square root of 225: 15

Answer:

X=6 Because if you multiply 16×3= 48

and If you do it with 2 it is 2×3= 6

Step-by-step explanation:

16×3= 48

2×3=6

The sum of 15 and twice Carlos' age.

The sum would be addition. So;

[tex]15\: +[/tex]

Twice means 2 times Carlos' age. And [tex]c[/tex] is the variable, so;

[tex]15+2c[/tex]

Note that 2 and c together like that is multiplication.

Step-by-step explanation:

y = 5x - 2…Equation 1

3x - 5y = 4…Equation 2

Subtitute value of y to Equation 2 :

3x - 5(5x - 2) = 4

3x - 25x + 10 = 4

-22x + 10 = 4

10 - 4 = 22x

6 = 22x

6/22 = x

3/11 = x

Subtitute value of x to one of Equation :

for example Equation 2…

3x - 5y = 4

3(3/11) - 5y = 4

9/11 - 5y = 4

9/11 - 4 = 5y

(9 - 44)/11 = 5y

(-35)/11 = 5y

(-35)/11 × 1/5 = y

-7/11 = y

Answer:

Q1. 3.14 × 0.8 = 2.512

Q2. 6.28 × 6.8 = 42.704

Q3. 25.5 × 9.3 = 237.15

Q4. 1.3 × 5.7 = 7.41

Q5. 7.41 × 3.7 = 27.417

Answer:

so we're dealing with negative numbers here so after learning negative numbers you have to add negative15 to -182 Wich is negative 197

Answer:

9-22=c

-13=c

The football team lost 13 yards in overall change in field position. Meaning, the team didn't gain any yards, they lost 13.

Answer:

Step-by-step explanation:

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