Let X1,X2,...,X32 be a random sample from an exponential distribution with a mean of 4. Find an approximate probability that the sample mean is less than 5 (round off to third decimal place).

Answer: 325

Step-by-step explanation:

723 -73 =650 divided by 2

Hope this helps

If the probability that the bug moves to its starting vertex on its tenth move is m/n , then the value of m+n is 683 .

In the question ,

it is given that ,

the bug starts from a vertex of an equilateral triangle , and

in each move , it randomly selects one of  two vertices where it is not currently located .

Let the probability that the bug is at its starting vertex after n moves is Pₙ .

If the bug is on its starting vertex after n moves, then it must be not on its starting vertex after n-1 moves .

At this point it will has (1/2) chance of reaching starting vertex in the next move.

Thus Pₙ =  (1/2)(1 - Pₙ₋₁) . P₀ =1 ,

So , the probabilities in each move can be written as

P₁ = 0 ,  P₂ = 1/2, P₃ = 1/4 , P₄ = 3/8 , P₅ = 5/16, P₆ = 11/32 , P₇ = 21/64 , P₈ = 43/128, P₉ = 85/256, P₁₀ = 171/512 ,

So , the tenth move P₁₀ is given as 171/512 , which is m/n .

So, m + n is = 171 + 512 = 683 .

Therefore , the value of m+n is = 683 .

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In the ellipse, the center is (-3/2,5/2) semi-major axis is 2√3 and the semi-minor axis is 2.

What is ellipse?

In addition to being drawn outside the ellipse, the directrix of the ellipse is parallel to its latus rectum. There are two directions on the ellipse that are parallel to its principal axis. The ratio of distances between any point on an ellipse and its foci, as well as the directrix of the ellipse, is used to define an ellipse's eccentricity, and it is less than 1.

6x^(2)+2y^(2)+18x-10y+2=0

[tex]\frac{\left(x-\left(-\frac{3}{2}\right)\right)^2}{2^2}+\frac{\left(y-\frac{5}{2}\right)^2}{\left(2\sqrt{3}\right)^2}=1[/tex]

[tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{5}{2}\right),\:a=2,\:b=2\sqrt{3}[/tex]

[tex]\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{5}{2}\right),\:\:b=2\sqrt{3},\:\:a=2[/tex]

Hence, In the ellipse, the center is (-3/2,5/2) semi-major axis is 2√3 and the semi-minor axis is 2.

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The area of a trapezoid is 136[tex]cm^{2}[/tex].

we know that the area of a trapezoid is:

Area= 1/2 * (a+b) * h

where a and b are the lengths of the parallel sides of the trapezoid, and h is the height.

Now as per the question,

first parallel side, a = 12cm

second parallel side, b = 22cm

height, h =8cm

Area of a trapezoid = 1/2 * (12+22) *8 [tex]cm^{2}[/tex]

                                 = 136[tex]cm^{2}[/tex]

Therefore, the area of a trapezoid is 136[tex]cm^{2}[/tex].

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The top five percent of the distribution's lowest weight as calculated from the given data  for a bag is 246.

Average population = 240

Standard deviation for the population; 3

Z-score can be calculated as ,

z = (x' - μ)/σ

Now, in order to determine which of the top 5 values in the distribution has the least weight, we will use the significance threshold of 1 - 0.05/2 = 0.025.

Z-score is 1.96 at significance level 0.025.

Thus;

1.96 = (x' - 240)/3

3 × 1.96 = x' - 240

x' = 240 + 5.88

x' = 245.88

Getting close to a whole number results ,

x' = 246

The two z-score tables are as follows:

Positive Z Score Table: The observed value is greater than the average of all values.

An observed value that is below the mean of all values is shown by a negative Z score table.

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Answer:

Assuming that you're trying to multiply each one by five, the mistake is that in the second one, it would be [tex]\frac{-5}{25}[/tex] and not [tex]\frac{5}{25}[/tex]

Answer:

Below

Step-by-step explanation:

35/40    - 1/5 =

35/40 - 8/40 =

27/40

Answer:

5x³ - x - 3

Step-by-step explanation:

(f - g)(x) =

f(x) - g(x) =

5x³-2 - (x+1) =  ==> plug in known values

5x³-2 - x - 1 =   ==> simplify

5x³ - x - 2 - 1 = 5x³ - x - 3

f(x) = 5x³ - 2

g(x) = x + 1

Therefore, (f - g)(x) = (5x³ - 2) - (x + 1) = 5x³ - x - 3

So, (f - g)(x) = 5x³ - x - 3.

As per the given matrix, the stable age distribution vector is 25 and 25

Matrix:

In algebra, matrix means a set of numbers arranged in rows and columns so as to form a rectangular array.

Given,

Here we have the age transition matrix L and the age distribution vector x1 to find the age distribution vectors x2 and X3.

In order to find a stable age distribution vector we need to find an eigenvalue λ and a corresponding eigenvector x such that 

=> Lx=λx.

Here the characteristics polynomial of L is x2−41​ which implies the eigenvalues are 21​ and −21​.

Now, we have to choose the +ve eigenvalue, λ=21​, we need to find the corresponding eigenvector i.e. to find a basis of the solution space (L−21​I2​)x=0.

Then the augmented matrix is

[tex]\begin{bmatrix}200 & 0 \\ 0& 200\end{bmatrix}[/tex]

Then the age transmission is written as 25 and 25.

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No, we do not have enough information to find out the percentage of Americans who either do not follow football or do not follow basketball. We would need to know the percentage of Americans who do follow both sports.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 out of 100 questions correctly on a test, you would have received a 75%.

The percent sign (%), which denotes a division by 100, is used. Therefore, 25% translates to 25/100, or 1/4. Dividing by 100 will change a percentage to a decimal. Therefore, 25% is equal to 25/100, or 0.25. A decimal can be multiplied by 100 to become a percentage (just move the decimal point 2 places to the right)

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The system of equations that describes Tammy and Luke's outcomes is written below

It can be deduced form the question that

x represents the number of points for a catch

y to represent the number of points for a miss

Tammy makes 5 catches and misses 1, ending the game with 23 points

5x - y = 23

Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points

8x - 5y = 30

The system of equations required are

5x - y = 23

8x - 5y = 30

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True, Regardless of the testing point used we arrive at the same answer for the direction of a phase plane.

We were able to sketch the solution, y(t), in the y-t plane for the single differential equation case and observe actual solutions. Due to the fact that our answers are actually vectors, this would be fairly challenging in this situation.

Here, we're going to plot the points that we represent as the system's solutions as points in the x1x2 plane. Our equilibrium solution will line up with the x1x2 plane's origin, which is also known as the phase plane.

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6/11 is the probability that a randomly selected student speaks French, given that the student is male

It is a branch of mathematics that deals with the occurrence of a random event.

There are 11 members who speak french and 5 are females in 11 members

5/11

p(a given b) = p(a and b) / p(b).

6 of the people in the group are men that speak french, then the probability of (a and b) becomes 6/40

probability that a person speaks french is 11/40

p(a given b)=6/40/11/40

=6/40×40/11=6/11

Hence, 6/11 is the probability that a randomly selected student speaks French, given that the student is male.

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Therefore the point P in the coordinate plane comes out to be (2,10)

and the distance between the points is 50.99 units

equation is another name for a declaration of equality between two expressions that contain variables and/or numbers. From solving equations is essentially solving problems, solving equations has been the central goal of mathematics since its inception. There are many distinct types of equations that range in complexity, from simple algebraic equations that merely need addition or multiplication through differential equations, exponential equations that use exponential expressions, and integral equations.

we know that,

the point p on the line y=5x that is closest to the point (52,0) will be on the line perpendicular to the line y=5x and go through the point (52,0)

step 1

the slope m perpendicular to the line y=5x is

m1=5

if two lines are perpendicular

m1*m2=-1

m2=-1/5

step 2

with m=-1/5 and the point (78,0) find the equation of a line

y-y1=m*(x-x1)-----> y-0=(-1/5)*(x-52)----> y=-0.20x+10.4

step 3

resolve the equation systems

y=5x

y=-0.20x+10.4

Thus substituting the values in y of x

=> 5x=-0.20x+10.4

=> 5.20x=10.4

=> x=2

Therefore the point comes out to be

x=2

y=10

The least distance between P(2,10) &(52,0)= 50.99 units

Therefore the point P in the coordinate plane comes out to be (2,10)

and the distance between the points is 50.99 units

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If a sample of 40 teams is selected at random from the population, the expected mean is $750 and the standard deviation is $29.25

The mean of the cost of joining a team = $750

Standard deviation = $185

A sample of 40 teams is selected at random from the population

The expected standard deviation = [tex]\sqrt{\frac{185^2}{40} }[/tex]

= $29.25

Here the cost of joining a team is normally distributed with a mean of $750

Here the distribution of the cost of joining is normal the mean of the sample distribution, so it will be equal to the mean of the population

The mean = $750

Therefore, the standard deviation is $29.25 and the mean is $750

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g is the centroid of triangle abc, the value of x is 2/3.

The length of segment DG is (2/3) * (length of AB) ,The length of segment AG is (1/3) * (length of AB),The length of segment AD is (1/3) * (length of AB).

The centroid of a triangle is the point at which the three medians of the triangle intersect each other. In other words, it is the point of intersection of the three lines which each divide the opposite side of the triangle into two equal parts.

Let us consider a triangle ABC with vertices A (a1, b1), B (a2, b2), and C (a3, b3). The x coordinate of the centroid G (x, y) is given by:

x = (a1 + a2 + a3) / 3

The y coordinate of the centroid G (x, y) is given similarly as x

In your question, the x coordinate of the centroid G is given as x = 2/3. This means that the x coordinate of G is 2/3 of the way between A and B.

Therefore, the length of segment DG is (2/3) * (length of AB).

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The required total cost of all the purchases is $7,930.00. Option C is correct.

Given that,
Al Roy bought five bonds of Jort Co. 11 3/4 at 93.25% and four bonds of Inst. System 12x08 for 81.125%, the commission on the bonds is $2.50 per bond.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Total bond = 4 + 5 = 9

Face value of a bond = $1000
Total cost = $1000 × 0.9325 × 5 + $1000 × 0.81125 × 4 + 2.50 × 9

Total cost = $7,930.00

Thus, The required total cost of all the purchases is $7,930.00. Option C is correct.

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Slope: −34

y-intercept: (0,−14)

[IF ITS WRONG TELL ME]

The time is taken by the substance to decay, if A radioactive substance decays according to [tex]A = A_o \times e^{-0.0037t}[/tex] Where A₀ is the initial amount and t is the time in years. If A0=740 grams is  185.18 years.

Atoms in radioactive materials naturally decay. They are capable of emitting gamma radiation, beta radiation, and alpha radiation. They cannot be turned off, so controlling them is more challenging than controlling X-ray sources.

Given:

The initial amount, A₀ = 740 g,

The final amount, A = 373 g,

Calculate the time by using the formula given below,

[tex]A = A_o \times e^{-0.0037t}[/tex]

373 = 740 [tex]\times e^{-0.0037t}[/tex]

[tex]e^{-0.0037t}[/tex] = 373 / 740

[tex]e^{-0.0037t}[/tex] = 0.504

Taking log on both sides,

㏑ 0.504 - ㏑ 0.0037 = t

t = 185.18

Therefore, the time taken by the substance to decay if A radioactive substance decays according to A=A0e−0.0037t, where A0 is the initial amount and t is the time in years. If A0=740 grams is 185.18 years.

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Question 1

[tex]a=1, r=1/2 \implies S_{\infty}=\frac{1}{1-(1/2)}=\boxed{2}[/tex]

Question 2

[tex]d=10, a_1+5d=52 \implies a_1=2 \\ \\ a_{15}=a_1+14d=2+14(10)=\boxed{142}[/tex]

The answer is A & C

To determine if a set of ordered pairs represents a function, you can check if each input (x value) is associated with only one output (y value).

In set A, input 4 is paired with output 1 and input 8 is paired with output 2. These two inputs are paired with only one output, so the set A can represent a function.

In set B, input -2 is paired with two different outputs.

-1 and 5. This means that -2 has multiple exits, so set B does not represent a function. In set C, input 7 is paired with output 4 and input 8 is paired with output 3. The set C can represent a function because these two inputs are paired with only one output.

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They can be arranged in 2 ways around a circular table.

Permutation in a circle is called circular permutation. The number of ways to arrange distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is. The number is instead of the usual factorial since all cyclic permutations of objects are equivalent because the circle can be rotated.

If we consider a round table and  persons then the number of different sitting arrangement that we can have around the round table is an example of circular permutation.

It is represented as; P = (n -1)!

P = (n -1)!

where n = 3

P = (3-1)!

P = 2!

P = 2 ways.

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Indefinite integral using integration by parts from x2 ln(x) dx is

[tex]\frac{1}{3}[/tex] [tex]X^{3\\}[/tex] (ln(x) - [tex]\frac{1}{3}[/tex]) + C

The given choice of u and dv

∫ [tex]x^{2} ln(x) dx[/tex]

we can use the formula

∫ u dv = uv - ∫ v du

Then split the component

u =  [tex]ln(x)[/tex]     du = [tex]\frac{1}{x}[/tex][tex]dx[/tex]

dv = [tex]x^{2}[/tex]         v = [tex]\frac{1}{3}x^{3}[/tex]

∫ u dv = uv - ∫ v du

∫ [tex]x^{2} ln(x) dx[/tex]   =  ln(x) [tex]\frac{1}{3}x^{3}[/tex] - ∫ [tex]\frac{1}{3}x^{3}[/tex] [tex]\frac{1}{x}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{3}[/tex] [tex]\frac{1}{x}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{3} . x^{-1}[/tex] dx

                    = [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{2}[/tex] dx     ----> ∫ [tex]x^{2}[/tex] dx = [tex]\frac{1}{3} x^{3} + C[/tex]

                    =  [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] [tex]\frac{1}{3} x^{3} + C[/tex]

                    = [tex]\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C[/tex]

Therefore Indefinite integral using integration by parts

∫ [tex]x^{2} ln(x) dx[/tex]  is  [tex]\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C[/tex]

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Answer:

you answer is 7 1/25

Step-by-step explanation:

0.04 ---> 1/25

7 ---> 7

7 + 1/25 = 7 1/25

The probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%, the probability of flipping a coin and it landing heads is 1/2 or, 50%, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%, and the probability of getting heads both times the coin is flipped is 0.25.

There are different situations for us stated as -

(a) What is the probability of a coin landing on heads 4 times in a row?

(b) What is the probability of flipping a coin and it landing heads?

(c) What is the probability that exactly four students toss heads at least 4 times each?

(d)What is the probability of flipping a coin and getting heads both times?

We have to find out the probability of the given situations happening.

(a) It is known to us that a coin is flipped.

We have to determine the probability of this coin landing on heads 4 times in a row.

In order to get 4 heads in a row, the coin should be flipped 4 times.

For n (say) number of heads, the value of n = 0, 1, 2, 3, 4

Total number of possible outcomes = 16

It can be concluded that there is only one possible outcome that will result in the coin landing on 4 heads where each flip ends up as a head.

So, the probability = 1/16

Thus, the probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%.

(b) It is known to us that a coin is flipped.

We have to find out the probability of this flipped coin landing on heads.

When a coin is flipped in the air, there is always 50% chance of the coin landing on heads and a 50% chance of the coin landing on tails.

So, the probability = 1/2

Thus, the probability of flipping a coin and it landing heads is 1/2 or, 50%.

(c) It is known to us that exactly four students toss coins.

We have to determine the probability that exactly four students toss heads at least 4 times each.

As mentioned in the previous part of the question, there is always 50% chance of the coin landing on heads.

So, the probability of getting heads when the coin is flipped first = 1/2

=> the probability of getting two heads in a row = 1/2 * 1/2 = 1/4

=> the probability of getting three heads in a row = 1/2 * 1/4 = 1/8

=> the probability of getting four heads in a row = 1/2 * 1/8 = 1/16

Thus, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%.

(d) It is known to us that a coin is flipped.

We have to find out the probability of getting heads both times.

Since, there is always 50% chance of the coin landing on heads. So, the probability of getting heads both times = 0.5 * 0.5 = 0.25

Thus, the probability of getting heads both times the coin is flipped is 0.25.

Therefore, the probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%, the probability of flipping a coin and it landing heads is 1/2 or, 50%, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%, and the probability of getting heads both times the coin is flipped is 0.25.

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The formula of the volume of the rectangular prism is,

V = l * w * h

The formula of the surface area of the rectangular prism is,

A = 2(lw + wh + lh)

the surface area of a box is 72 sq.ft.

For a rectangular prism with length(l), width(w) and height(h),

The formula of the volume of the rectangular prism is,

V = l * w * h

The formula of the surface area of the rectangular prism is,

A = 2(lw + wh + lh)

For a rectangular box with a length of 6 ft a width of 3 ft and a height of 2 ft,

here, l = 6 ft, w = 3 ft and h = 2 ft

using the formula for the surface area of a rectangular prism, the surface area of box would be,

A = 2(lw + wh + lh)

A = 2(6 * 3 + 3 * 2 + 6 * 2)

A = 2(18 + 6 + 12)

A = 2(36)

A = 72 sq.ft.

Therefore, the surface area of a box is 72 sq.ft.

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Answer:

Samuel's watch is slower than the actual time 10 seconds.

Step-by-step explanation:

30 - 20 = 10 (seconds)

So Samuel's watch is slower than the actual time 10 seconds.

PLEASE GIVE ME BRAINLIEST IF THIS IS THE CORRECT ANSWER! THANKS!

Answer: 240 seconds

Step-by-step explanation:

So, here Samuel's watch gains 20 seconds every hour with respect to the alarm clock.

Also, alarm clock lags by 30 seconds every hour with respect to the actual time.

Therefore, Samuel's watch lags by (30-20) seconds every hour with respect to the actual time.

30-20=10 seconds

In 1 hour Samuel watch deviate by 10 seconds, then in 24 hours, it deviates by 24*10 seconds= 240 seconds..

An odd degree polynomial with a negative leading coefficient would have endpoint behavior of "as x approaches -∞, y approaches ∞ and as x approaches ∞, y approaches -∞.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² - 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The leading coefficient and the degree of the monomial n have an impact on the final behavior.

The function behaves the same at both "ends" when n is even. They both either approach + ∞ or they both approach depending on the sign of the leading coefficient.

The behaviour of the function at both "endpoints" is the reverse when n is odd. Which one is +∞and which one is depends on the sign of the leading coefficient.

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The value of x will make on similar to SRQ by the SSS similarity theorem is 25.

From the figure :

NM = 10

SR = 20

NO = 8

QR = x

SAS Similarity Theorem:

states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

NO/NM = SR/QR

substitute the values

8/10 = 20/x

cross multiplication

8x = 200

dividing both sides by 8

x = 25

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Full question :

What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?What value of will make the triangles similar by the similarity theorem?; How do you find similar triangles in SSS?; How do you find the value of X that makes triangles similar?

The simplest radical representation of square root of 200 is 10√2.

The radical symbol used to denote a number's root is "." The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of 3 is 9, the square root of 9 is 9, and 32 also equals 9.

e that divides into the initial number or pair should be located.

Add the square to the initial number or pair.

Drop the following pair down.

The square's leading digit should be multiplied by two.

Create the following factor equation.

If we are aware of a number's prime factors, we can write the square root of that number in radical form. Thus, 200 can be factored into its primes as 2 ,2 ,2 ,5 ,5. As a result, 10√2. should be the square root of 200 in the simplest radical form.

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Answer:

15√3

Step-by-step explanation:

√ 15 ⋅ √ 45

Because both of them have the same base is the square root of two, we can combine them

√15 ⋅ 45

√675

Next, we factor √675 out and get

√15^2 ⋅ 3

= 15√3

So, the answer is  15√3

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