What is this expression in simplified form?

Answer:

C.[tex]P(7.0039<x<7.8026)=0.1334[/tex]

D.[tex]P(7.0039<\bar{x}<7.8026)\approx 0.2942[/tex]

Step-by-step explanation:

We are given that

n=18

Mean, [tex]\mu=6.75[/tex]

Standard deviation, [tex]\sigma=2.28[/tex]

c.

[tex]P(7.0039<x<7.8026)=P(\frac{7.0039-6.75}{2.28}<\frac{x-\mu}{\sigma}<\frac{7.8026-6.75}{2.28})[/tex]

[tex]P(7.0039<x<7.8026)=P(0.11<Z<0.46)[/tex]

[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]

Using the formula

[tex]P(7.0039<x<7.8026)=P(Z<0.46)-P(Z<0.11)[/tex]

[tex]P(7.0039<x<7.8026)=0.67724-0.54380[/tex]

[tex]P(7.0039<x<7.8026)=0.1334[/tex]

D.[tex]P(7.0039<\bar{x}<7.8026)=P(\frac{7.0039-6.75}{2.28/\sqrt{18}}<\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}})<\frac{7.8026-6.75}{2.28/\sqrt{18}})[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=P(0.47<Z<1.96)[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=P(Z<1.96)-P(Z<0.47)[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=0.97500-0.68082[/tex]

[tex]P(7.0039<\bar{x}<7.8026)=0.29418\approx 0.2942[/tex]

Answer:

The sum is 2275

Step-by-step explanation:

Given

[tex]75,76,77....99,100[/tex]

Required

The sum

Using arithmetic progression, we have:

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where:

[tex]T_1 = 75[/tex] --- first term

[tex]T_n = 100[/tex] --- last term

[tex]n = T_n - T_1 + 1[/tex]

[tex]n = 100 - 75 + 1 = 26[/tex]

So, we have:

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]

[tex]S_n = 13*175[/tex]

[tex]S_n = 2275[/tex]

Answer:

The expected value is of 5 green balls.

Step-by-step explanation:

For each experiment, there are only two possible outcomes. Either it is a green ball, or it is not. Since there is replacement, the probability of a green ball being taken in an experiment is independent of any other experiments, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

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

The expected value of the binomial distribution is:

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

20 experiments

This means that [tex]n = 20[/tex]

There is equal probability of selecting the red, black, green, or blue ball.

This means that 1 in 4 are green, so [tex]p = \frac{1}{4} = 0.25[/tex]

What is the expected value of getting a green ball out of 20 experiments with replacement?

[tex]E(X) = np = 20*0.25 = 5[/tex]

The expected value is of 5 green balls.

The expected value of getting a green ball out of 20 experiments with replacement is 5.

The binomial probability distribution of the number of successes in a sequence of n independent experiments is the binomial distribution with parameters n and p.

As it is given that the probability of all the balls coming out of the bag is equal. Therefore, the probability of a green ball coming can be written as,

[tex]\text{Probability of Green Ball} = 0.25[/tex]

Also, we can write the probability of not getting a green ball can also be written as,

[tex]\rm Probability(\text{Not coming Green Ball}) = P(Red\ ball)+P(Black\ ball)+P(Blue\ ball)[/tex]

                                                         [tex]=0.25+0.25+0.25\\\\=0.75[/tex]

Now, as there are only two outcomes possible, therefore, the distribution of the probability is a binomial distribution. And we know that the expected value of a binomial distribution is given as,

[tex]\rm Expected\ Value, E(x) = np[/tex]

where n is the number of trials while p represents the probability.

Now, substituting the values, we will get the expected value,

[tex]\rm Expected\ Value, E(Green\ ball) = 20 \times 0.25 = 5[/tex]

Hence, the expected value of getting a green ball out of 20 experiments with replacement is 5.

Learn more about Binomial Distribution:

https://brainly.com/question/12734585

Answer:

Option D is answer.

Step-by-step explanation:

Hey there!

Given;

f(x) = 10/9 X + 11

Let f(X) be "y".

y = (10/9) X + 11

Interchange "X" and "y".

x = (10/9) y + 11

or, 9x = 10y + 99

or, y = (9x-99)/10

Therefore, f'(X) = (9x-99)/10.

Hope it helps!

9514 1404 393

Answer:

  B. (x-2)^2=12

Step-by-step explanation:

The constant that completes the square is the square of half the coefficient of the x-term. That value is (-4/2)^2 = 4.

There is already a constant of 2 on the left side of the equal sign, so we need to add 2 to both sides to bring that constant value up to 4.

  x^2 -4x +2 = 10 . . . . . . . given

  x^2 -4x +2 +2 = 10 +2 . . . . complete the square (add 2 to both sides)

  (x -2)^2 = 12 . . . . . . . . . write as a square

Answer:

Rs. 100 and Rs. 150

Step-by-step explanation:

the ratio = 2:3 => the sum = 2+3=5

Sita gets = 2/5 × 250 = 100

Ram gets = 3/5 × 250 = 150

Answer: third from the top

Step-by-step explanation:

The correct answer is third from the top.

Arranging numbers in ascending order:

15 17 17 17 18 18 18 19 19 19 21 21 22 23 24

Let's count how many times each number occurs in this series of numbers.

row of numbers

15 +

16 not

17 + + +

18 + + +

19 + + +

20 not

21 + +

22 +

23 +

24 +

25 not

Answer:

10 pounds of potatoes would cost $15.

Step-by-step explanation:

Set up proportion.

4/6=10/x

simplify 4/6 into 2/3,

2/3=10/x

cross product,

2*x=3*10

2x=30

x=30/2

x=15

lemme just add some to the great reply above,

[tex]\begin{array}{ccll} lbs&\$\\ \cline{1-2} 4&6\\ 10&x \end{array}\implies \cfrac{4}{10}=\cfrac{6}{x}\implies 4x = 60\implies x = \cfrac{60}{4}\implies x = 15[/tex]

Answer:

f(x) = 8x

Explanation:

4 x 2 =8

Answer:

x = -2; y = 1

Step-by-step explanation:

See picture below.

We are told matrices B is the inverse of matrix A.

The product of a matrix and its inverse is the identity matrix.

Answer:

300 + 15x = 500

15x = 200

x = 200/15

x=13.333

14 pair of shoes

Step-by-step explanation:

Answer:

hole at x=-3

Step-by-step explanation:

The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)

The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.

So anyways we have (x+3)/(x^2-9)

= (x+3)/((x-3)(x+3))

Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.

Answer: The first number is 2, the second number is 3 and the third number is -2

Step-by-step explanation:

Let the first number be 'x', the second number be 'y' and the third number be 'z'

The equations according to the question becomes:

⇒ x + y + z = 3              ....(1)

⇒ x - y + z = -3              ....(2)

⇒ x - z = 1 + y              ....(3)

Rearranging equation 3:

⇒ x - y = 1 + z                .....(4)

Putting in equation 2:

⇒ 1 + z + z = -3

⇒ 1 + 2z = -3

⇒ z = -2

Putting this value in equation 4 and equation 1, we get:

⇒ x - y = -1

⇒ x + y = 5

Cancelling 'y' by eliminiation method and equation becomes:

⇒ 2x = 4

⇒ x = 2

Putting value of 'x' and 'z' in equation 1:

⇒ 2 + y - 2 = 3

⇒ y = 3

Hence, the first number is 2, the second number is 3 and the third number is -2

Answer:

b) 6.68%

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean score on the scale is 50. The distribution has a standard deviation of 10.

This means that [tex]\mu = 50, \sigma = 10[/tex]

Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?

The proportion is 1 subtracted by the p-value of Z when X = 65. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{65 - 50}{10}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

1 - 0.9332 = 0.0668

0.0668*100% = 6.68%

So the correct answer is given by option b.

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

Find the probability that the mean life expectancy will be less than years.

The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Step-by-step explanation:

28:20

Once simplified its 7:5

hiiksbsjxbxjsoahwjsissnsks

Answer:

BH/2

Step-by-step explanation:

For the area of the triangle, (BH)/2. B=base and H=height

width = x

length = 3 + x

perimeter = x + x + ( 3 + x ) + (3+x)

18 = x + x + ( 3 + x ) + (3+x)

x + x + ( 3 + x ) + (3+x) = 18

6 + 4x = 18

4x = 12

x = 3

Given that exp(2x) is a solution, we assume another solution of the form

y(x) = v(x) exp(2x) = v exp(2x)

with derivatives

y' = v' exp(2x) + 2v exp(2x)

y'' = v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)

Substitute these into the equation:

(2x + 5) (v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)) - 4 (x + 3) (v' exp(2x) + 2v exp(2x)) + 4v exp(2x) = 0

Each term contains a factor of exp(2x) that can be divided out:

(2x + 5) (v'' + 4v' + 4v) - 4 (x + 3) (v' + 2v) + 4v = 0

Expanding and simplifying eliminates the v term:

(2x + 5) v'' + (4x + 8) v' = 0

Substitute w(x) = v'(x) to reduce the order of the equation, and you're left with a linear ODE:

(2x + 5) w' + (4x + 8) w = 0

w' + (4x + 8)/(2x + 5) w = 0

I'll use the integrating factor method. The IF is

µ(x) = exp( ∫ (4x + 8)/(2x + 5) dx ) = exp(2x - log|2x + 5|) = exp(2x)/(2x + 5)

Multiply through the ODE in w by µ :

µw' + µ (4x + 8)/(2x + 5) w = 0

The left side is the derivative of a product:

[µw]' = 0

Integrate both sides:

∫ [µw]' dx = ∫ 0 dx

µw = C

Replace w with v', then integrate to solve for v :

exp(2x)/(2x + 5) v' = C

v' = C (2x + 5) exp(-2x)

∫ v' dx = ∫ C (2x + 5) exp(-2x) dx

v = C₁ (x + 3) exp(-2x) + C₂

Replace v with y exp(-2x) and solve for y :

y exp(-2x) = C₁ (x + 3) exp(-2x) + C₂

y = C₁ (x + 3) + C₂ exp(2x)

It follows that the second fundamental solution is y = x + 3. (The exp(2x) here is already accounted for as the first solution.)

Answer:

L = 0.16 yd, W = 0.22 yd

Step-by-step explanation:

Dimensions of play ground 23/147 yd x 3/14 yd

reducing factor 2/147

Let the original length is L.

[tex]L - \frac{2L}{147} = \frac{23}{147}\\\\L\frac{143}{147} = \frac{23}{147}\\\\L=\frac{23}{143} yd[/tex]

L = 0.16 yd

Let the width is W.

[tex]W - \frac{2W}{147} = \frac{3}{14}\\\\W\frac{143}{147} = \frac{3}{14}\\\\W=0.22 yd[/tex]

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after t seconds is modeled by the function:

[tex]h(t)=-16t^2+104t+56[/tex]

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -16, b = 104, and c = 56.

Find the x- (or rather t-) coordinate of the vertex. So:

[tex]\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}[/tex]

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

[tex]\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}[/tex]

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:

[tex]0=-16t^2+104t+56[/tex]

We can simplify a bit. Divide both sides by -8:

[tex]0=2t^2-13t-7[/tex]

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

[tex]\displaystyle 0=2t^2-14t+t-7[/tex]

Factor out a 2t from the first two terms and group the last two terms:

[tex]0=2t(t-7)+(t-7)[/tex]

Factor by grouping:

[tex]0=(2t+1)(t-7)[/tex]

Zero Product Property:

[tex]2t+1=0\text{ or } t-7=0[/tex]

Solve for each case:

[tex]\displaystyle t=-0.5\text{ or } t=7[/tex]

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

Answer:

y - 1 =  -1/4(x+5)

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

it is feometeic progression

r=0.5

Answer:

you mean the mean not the meaning right?

The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.

Answer:

(a)[tex]0.15731[/tex]

(b)0.02275

Step-by-step explanation:

We are given that

Mean=0

Standard deviation=0.5 g

True weight of a sample=166 g

Let X denote the normal random variable  with mean =166+0=166

(a)

P(166.5<X<167.5)

=[tex]P(\frac{166.5-166}{0.5}<\frac{X-\mu}{\sigma}<\frac{167.5-166}{0.5})[/tex]

=[tex]P(1<Z<3)[/tex]

=[tex]P(Z<3)-P(Z<1)[/tex]

[tex]=0.99865-0.84134[/tex]

[tex]=0.15731[/tex]

(b)

[tex]P(X>167)=P(Z>\frac{167-166}{0.5})[/tex]

[tex]=P(Z>2)[/tex]

[tex]=1-P(Z<2)[/tex]

[tex]=1-0.97725[/tex]

[tex]=0.02275[/tex]

Answer:

x= -3

Step-by-step explanation:

(2x/3)-2=-4

Add 2 to both sides

2x/3=-2

multiply both sides by 3

2x=-6

divide both sides by 2

x= -3

Answer:

x = -3

Step-by-step explanation:

2x/3 - 2 = -4

Add 2 to both sides.

2x/3 = -2

Multiply both sides by 3/2.

x = -2 * 3/2

x = -3

Answer:

A - $214.40

Step-by-step explanation:

Since b is the number of boxes of cards and n is the number of ink colors, and we're given the number of boxes of cards, and number of ink colors, we plug in:

4= b

and

3 = n

into the given equation to solve for C.

Using the order of operations we start inside our parentheses and work from there:

C= $25.60*4 + $14.00*4(3 - 1)

C= $25.60*4 + $14.00*4(2)

C= $102.40 + $112

C= $214.40

Answer:

262.5 miles

Step-by-step explanation:

Correct me if I am wrong

Answer:

Discount amount = $328.73

Step-by-step explanation:

Below is the calculation for the discount amount:

The marked price of bicycle = 2000

Purchase price = Rs 1921

VAT = 13%

First find the purchase price excluding VAT = 1921  - (13% of 1921) = 1671.27

Discount amount = 2000 - 1671.27

Discount amount = $328.73