7. (06.02 MC)
A movie theater made $63 selling 29 tickets. They sell child tickets for $3, adult tickets for $2, and senior tickets for $2. They sold three times as many child tickets as adult tickets. Using c for a child ticket, a for an adult ticket, ands for a
senior ticket what system of equations represents this scenario? (1 point)
c+a+s=63
3c+2a+2s-29
3a = c
c+a+s=29
3c+2a+2s 63
3a=c
c+a+s=29
3c+2a+2=63
a=3c
c+a+s=63
6c+10a+8s-29
a = 3c

The maximum possible area of such a triangle is $\frac{1}{2} \cdot \sqrt{4 + 2\sqrt{3}} = \frac{\sqrt{12 + 6\sqrt{3}}}{2} = 3\sqrt{3} + 3$, and $a + b + c = 3 + 3 + 3 = \boxed{9}$.

Let O and O' be the centers of the circles with radii 1 and 3, respectively, and let P and Q be points on the small and large circles, respectively, such that TPQ is a triangle. ]

Since the radius of the small circle is 1, we have TP = 1. Let R be the midpoint of PQ, so that TR is the altitude of triangle TPQ from T. Let x = TP = 1, y = TQ, and z = TR.  [asy]

unit size(0.6 cm);

pair O, OO, P, Q, R, T;

O = (0,0);

OO = (4,0);

T = (0,3);

P = intersection points(Circle(O,1),Circle(T,2))[1];

Q = intersection points(Circle(OO,3),Circle(T,2))[0];

R = (P + Q)/2;

draw(Circle(O,1));

draw(Circle(OO,3));

draw(T--P--Q--cycle);

draw(T--R);

label("$O$", O, SW);

label("$O'$", OO, SE);

label("$P$", P, NW);

label("$Q$", Q, NE);

label("$R$", R, S);

label("$T$", T, N);

label("$x$", (T + P)/2, W);

label("$y$", (T + Q)/2, E);

label("$z$", (T + R)/2, W);

[/asy]

Then we have TR = z, and by the Pythagorean Theorem in right triangle TPQ we have

\begin{align*}

TQ^2 - 1 &= TR^2 = z^2, \

TQ^2 + 9 &= (TQ + TR)^2 = (TQ + z)^2.

\end{align*}Solving for TQ in the first equation and substituting into the second, we obtain

[(1 + z)^2 + 9 = (1 + z)^2 + 4z^2,]which simplifies to $z^2 - 2z - 2 = 0$. The positive root of this quadratic equation is $z = 1 + \sqrt{3}$, so $TQ = \sqrt{4 + 2\sqrt{3}}$. Then the area of triangle TPQ is

[\frac{1}{2} \cdot TP \cdot TQ = \frac{1}{2} \cdot \sqrt{4 + 2\sqrt{3}}.]Thus the maximum possible area of such a triangle is $\frac{1}{2} \cdot \sqrt{4 + 2\sqrt{3}} = \frac{\sqrt{12 + 6\sqrt{3}}}{2} = 3\sqrt{3} + 3$, and $a + b + c = 3 + 3 + 3 = \boxed{9}$.

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The range of x-values is 1 < x < 21.

According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side.

Given:

We have three sides of Triangle as

PQ = 7x + 13, QR = 10x-2, PR = x + 27.

So, PQ + QR  > PR

(7x + 13) + (10x - 2) > x + 27, which simplifies to x > 1

and, PQ + PR > QR

(7x + 13) + (x + 27) > 10x - 2, which simplifies to x < 21

and, QR + PR > PQ

(10x - 2) + (x + 27) > 7x + 13, which simplifies to x > -3

So, the Range of sides is 1 < x < 21.

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Answer:

Step-by-step explanation:16/17

Answer:

16/17 is the simplest form

Step-by-step explanation:

reflect the shape, will give you:

A = (-1,0)

B= (3, -5)

C= (-6, -7)

D= (-4, -1)

If a point A(x, y) is dilated by a factor P, the new point would be at

A'(Px, Py).

A = -1/2.5 = -0.4             0/2.5= 0

= ( - 0.4, 0)

B = 3/2.5 =  1.2              -5/2.5 = -2

= (1.2, -2)

C = -6/2.5= -2.4       -7/2.5 = -2.8

= ( -2,4, -2.8)

D = -4/2.5 = -1.6.     -1/2.5 = -0.4

= ( -1.6, -0.4)

You're Welcome!

Answer:

Step-by-step explanation:

( -1.6, -0.4)

Both items have different rate of change, m₁ = -2, m₂ = -1/2, Item 1 is steeper.

Correct option is C.

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

m = Δy/Δx

where,m is the slope

Slope of line denotes rate of change and steepness.

Given,

A) a line with y-intercept (0,0) and passes through point (-2 , 4).

slope of the line

= (y₂ - y₁)/(x₂ - x₁)

= (4 - 0)/(-2 - 0)

= 4/-2

m₁ = -2

B) In the graph, line passes through (2, -1) and (-2 , 1 )

slope of the line

= (y₂ - y₁)/(x₂ - x₁)

= (1 - -1)/(-2 - 2)

= 2/-4

m₂ = -1/2

Hence, by the calculation

Items have different rate of change, Item 1 is steeper.

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The adjusting entry for deferred revenue at its year-end of December 31 is $1,150

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

We are given that;

The amount of payment=$3,450
Now,

The adjusting entry for deferred revenue at its year-end of December 31

Debit: Deferred Revenue $1,150 (which is one-third of the total payment received)

Credit: Revenue $1,150 (which represents the portion of the service that has been provided in December)

Therefore, by the given interest answer will be $1,150

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The number of pounds of chocolate costing $8.20 per pound should be mixed with trail mix is; 18 pounds

Let c represent the pounds of chocolate needed.

The weight of the snack mix is c + 23.

Thus, the algebraic expression here is;

8.2c + 3.4(23) = 5.49(c + 23)

8.2c + 78.2 = 5.49c + 126.27

8.2c - 5.49c = 126.27 - 78.2

2.71c = 48.07

c = 48.07/2.71

c ≈ 18 pounds

This value represents the number of pounds of chocolate costing $8.20 per pound should be mixed with trail mix

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The first derivative of the composite function r(x) = √[x + √(x + √x)] is equal to r' (x) = [1 / [2 · √[x + √(x + √x)]]] · [1 + [1 / [2 · √(x + √x)]] · [1 + 1 / (2 · √x)]].

In this problem we find the case of a composite function of the form:

f ° g ° h (x) = f [g [h (x)]]

Whose first derivative must be found by means of the following differentiation rules:

Chain rule

d [f [u (x)]] / dx = (df / du) · (du / dx)

Derivative of a square root

d (√x) / dx = 1 / (2√x)

And the first order derivative of the function r(x) = √[x + √(x + √x)] is:

r' (x) = [1 / [2 · √[x + √(x + √x)]]] · [1 + [1 / [2 · √(x + √x)]] · [1 + 1 / (2 · √x)]]

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The inequality 2x - 3y < 7 represents the given graph, which is the correct option (B).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per option (B), we have

2x - 3y < 7

Subtract 2x from both sides of the inequality:

-3y < 7 - 2x

Divide both sides of the inequality by -3.

y > (7 - 2x) / (-3)

y > (2/3)x - (7/3)

This represents a region in the coordinate plane that is above the line y = (2/3)x - (7/3).

Thus, the inequality 2x - 3y < 7 illustrates the given graph as shown.

Therefore, the correct answer is an option (B) 2x - 3y < 7.

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The median of the randomly selected list of prices of trucks will be 26 thousands dollars.

To find the median , first we need to arrange the list in either ascending form or descending form. Let us arrange the list in ascending form  :

List before sorting : 20,46,19,14,42,26,33

List after sorting it in ascending form : 14,19,20,26,33,42,46

Here, the number of observations is 7 which is odd. So, The formula to find the median term from a given number of "Odd" observations in a set is :

⇒ {(n+1) / 2}th term (where n is the number of observations in a set)

⇒({7+1}/2)

⇒8/2

⇒4th term

Therefore, the 4th term in our list of prices of trucks is the median which is 26 thousand dollars

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Saif's performance was better.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We will compare the run rates of Saif and Anus.

The run rate is the average number of runs scored per over.

Now,

The run rate of Saif.

= 60 / 5

= 12 runs per over

And,

The run rate of Anus

= 72 / 8

= 9 runs per over

Therefore,

Saif's performance was better.

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1. Two lines are MT and UW. 2. Two segments are SX and SY. 3. A pair of congruent angles is ∠QNT and ∠QNM. 4. Four right angles are ∠QNT and ∠QNM. ∠TNY and ∠MNY.

Angles that are both vertical and obtuse are known as obtuse vertical angles. In order to comprehend what obtuse vertical angles are, we must first learn the definitions of each of these kinds of angles.

Angles that cross one other at the junction of two lines are known as vertical angles. There is always an equal amount of vertical angles.

With these definitions, we get that obtuse vertical angles are angles that are in front of one another at the intersection between two lines, and both of which share a comparable measure that is between 90° and 180°.

From the given figure we observe that:

1. Two lines are MT and UW.

2. Two segments are SX and SY.

3. A pair of congruent angles is ∠QNT and ∠QNM.

4. Four right angles are ∠QNT and ∠QNM. ∠TNY and ∠MNY.

5. Two pairs of obtuse vertical angles ∠MSW and ∠UST. ∠VNT and ∠PNM.

6. Two pairs of adjacent supplementary angles are ∠MSW and ∠WST. ∠WNM and WNT.

7. Two pair of complementary angles are ∠TNP and ∠PNY. ∠QNW and ∠WNM.

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Answer:

x=2

Step-by-step explanation:

We will begin by subtracting both sides by 3

3x+2=4x

We will then subtract both sides by 3x since 3x and 4x are like terms

2=x OR x=2

Hope this helps!

The probability the child arranges the blocks in such a way that block f is in either the first position or the last position is found to be 1/3.

The child under observation of the researcher is given 6 unequally labelled block that are number as, a, b, c, d, e and f.

Now, the total number ways in which the child can arrange these block is,

Total possible ways = 6 x 5 x 4 x 3 x 2 x 1

Total possible ways = 720

Now, if the position of the block labelled f is fixed at either 1st or the last position then, total such ways are,

= 2 x 5 x 4 x 3 x 2 x 1

= 240

So, the probability that the child arranges the blocks in such a way that block f is in either the 1st position or the last position,

P = 240/720

P = 1/3

So, the probability is found to be 1/3.

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Answer: 36

Step-by-step explanation:

It must be a multiple of 9 for them to be in rows of 9 at the beginning therefore it can only be one of  18, 27, 36, 45 as it has to be bigger than 10 and smaller than 50 it cant be 9 or 54

It must also be a square number in order to have an equal amount of rows and column.

So it must be 36 as it is both a multiple of 9 and a square number.

Let's call the amount of money Rosa spent on art supplies "x". Since Rosa spent 1/4 of her money on art supplies, we can write the equation:

x = (1/4) * 300

x = 75

So Rosa spent $75 on art supplies.

Now we can find out how much money she had left after spending the $75 on art supplies.

remaining = 300 - 75

remaining = 225

And we can find out how much she spent on the boots.

boots = (2/5) * remaining

boots = (2/5) * 225

boots = 90

So Rosa spent $90 on the boots.

Let's call the amount of money Rosa spent on art supplies "A". Since Rosa spent 1/4 of her original $300 on art supplies, we can write the equation:

A = 1/4 * $300

A = $75

So, Rosa spent $75 on art supplies.

Next, let's find out how much money she had left after buying the art supplies. We can subtract the amount she spent on art supplies from her original $300:

$300 - $75 = $225

Now, let's find out how much she spent on the boots. We know that she spent 2/5 of the remainder on the boots, so we can write the equation:

B = 2/5 * $225

B = $90

So, Rosa spent $90 on the boots.

The area of the bookmark is 72.56 cm².

The area of Rectangle is length times of width.

The width of the rectangle is 4 cm, so the diameter of each semicircle is also 4 cm.

Radius of each semicircle is 2 cm.

The area of the rectangle is length x width

= 15 cm x 4 cm

= 60 cm².

The area of each semicircle is (1/2) x π x radius²

= (1/2) x 3.14 x 2² = 6.28 cm².

The total area of the two semicircles is 2 x 6.28 = 12.56 cm².

The total area is 60 cm² + 12.56 cm² = 72.56 cm²

Therefore, the area of the bookmark is 72.56 cm².

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The probability of carrying the AIDS virus in B1 is 0.5%

Probability is a fundamental concept in understanding the ELISA test results for AIDS diagnosis.

The probability of carrying the AIDS virus (B1) can be calculated by dividing the number of people who carry the virus by the total number of people who were tested.

From the contingency table, we can see that the number of people who carry the virus is 5000. Therefore, the probability of carrying the virus can be expressed as:

=> P(B1) = Number of people who carry the virus / Total number of people tested

=> 5000 / 1000000

=> 0.005 or 0.5%

This means that out of 1 million people who were tested, only 0.5% were found to be carrying the AIDS virus.

In this context, probability helps us understand the likelihood of carrying the virus and the accuracy of the test results. It also allows us to estimate the prevalence of the virus in a population and make informed decisions about public health policies and interventions.

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Complete Question:

A common test for AIDS is called the ELISA(enzyme-linked immunosorbent assay) test. Among 1 million peoplewho are given the ELISA test. we can expect results similar tothose given in the following table:

                     B1: Carry AIDS Virus       B2: Do not Carry AIDS Virus  Totals

A1: Test          4885                                73630                                       78515

Positive

A2: Test         115                                    921370                                   921485

Negative

Totals           5000                                995000                               1000000

If one of these 1 million people is selected randomly, find the value of P(B1).

Approximately 7.11 fluid ounces of shampoo to fill a one-gallon container.

One gallon is equal to 128 fluid ounces.

The ratio of shampoo to water is 1:18. This means for every 1 fl oz of shampoo, we need 18 fl oz of water.

To find out how much shampoo is needed to fill a one-gallon container, we need to set up a proportion:

1 fl oz shampoo / 18 fl oz water = X fl oz shampoo / 128 fl oz water

To solve for X, we can cross-multiply:

18 fl oz water * X fl oz shampoo = 1 fl oz shampoo * 128 fl oz water

18X = 128

X = 7.11 fl oz shampoo

So, we need approximately 7.11 fluid ounces of shampoo to fill a one-gallon container.

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The equation for the surface with all points which are equidistant of (−1,0,0)and the plane x=1 is x² - 2x + y² + z² = 2.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two sides separated by an equal sign (=).

To start with, let's consider the given information. We have been given that all points on the surface are equidistant from (-1,0,0) and the plane x=1. This means that the distance between any point on the surface and (-1,0,0) is the same as the distance between that point and the plane x=1.

We can use the formula for the distance between a point and a plane to derive an equation for the surface. The formula for the distance between a point (x1, y1, z1) and a plane Ax + By + Cz + D = 0 is given by:

distance = |Ax1 + By1 + Cz1 + D| / √(A² + B² + C²)

In our case, the plane is x=1, which can be written as x - 1 = 0. So, A=1, B=0, C=0, and D=-1. The point (-1,0,0) can be substituted as x1=-1, y1=0, and z1=0.

We can simplify the distance formula to:

distance = |x-1|

Now, since all points on the surface are equidistant from (-1,0,0) and x=1, we can set up the following equation:

|x-1| = √( (x+1)² + y² + z² )

Squaring both sides and simplifying, we get:

(x-1)² = x² + 2x + 1 + y² + z²

Rearranging and simplifying, we get the final equation for the surface:

x² - 2x + y² + z² = 2

This is the equation of the surface that contains all points that are equidistant from (-1,0,0) and x=1.

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The negation for the formula is Jxez[~p(x) v ~q(x)] ^ Vxez[~p(x) ^ ~q(x)] ^ Vxez[p(x) v ~q(x)]

Negation is a concept used in mathematics to express the opposite or contradictory statement of a given formula.

To find the negation of this formula, we need to apply De Morgan's laws, which state that the negation of a logical conjunction (and) is a logical disjunction (or) with the negation of each of the operands, and vice versa.

First, let's apply De Morgan's laws to the first expression in the formula:

~[Vx €Z[p(x) ^ q(x)]]

The negation of "for all x in Z, p(x) and q(x)" is "there exists x in Z such that ~(p(x) and q(x))," which can be expressed as:

Jxez[~p(x) v ~q(x)]

Now, let's apply De Morgan's laws to the second expression in the formula:

=> ~[Jx €Z[p(x) v q(x)]]

The negation of "there exists x in Z such that p(x) or q(x)" is "for all x in Z, ~(p(x) or q(x))," which can be expressed as:

=> Vxez[~p(x) ^ ~q(x)]

Finally, let's apply De Morgan's laws to the third expression in the formula:

~[Jx €Z[~p(x) ^ q(x)]]

The negation of "there exists x in Z such that not p(x) and q(x)" is "for all x in Z, ~(not p(x) and q(x))," which can be expressed as:

Vxez[p(x) v ~q(x)]

Putting these three expressions together, we get the negation of the original formula as:

=> Jxez[~p(x) v ~q(x)] ^ Vxez[~p(x) ^ ~q(x)] ^ Vxez[p(x) v ~q(x)]

In this case, the original formula involved three functions (p(x), q(x), and logical operators) that were negated using De Morgan's laws to obtain the final expression.

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Answer:

3(m-7)

Step-by-step explanation:

because 3 times the quantity: m-7

Answer:

6. 3 times the quantity m minus 7

Step-by-step explanation:

You're welcome.

The equation for the pony's path is -

(x - 8)² + (y - 8)² = 128.

The general equation for a circle is -

(x - h)² + (y - k)² = r²

where (h, k) is the center and (r) is the radius.

Given is that the pony is staked at the coordinate point (8, 8).

The general equation for a circle is -

(x - h)² + (y - k)² = r²

We can write the equation for the pony's path as -

(x - 8)² + (y - 8)² = 128

Therefore, the equation for the pony's path is -

(x - 8)² + (y - 8)² = 128.

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Answer:17x25 i think

Step-by-step explanation:

The total area for the figure is given as follows:

288 cm².

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

The dimensions of each rectangle are given as follows:

Hence the total area is given as follows:

A = 8 x 9 + 2 x 9 x 12

A = 288 cm².

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If Mr. Phil T. Rich had a boat load of money. The original value of his estate is $152,000.

Let's call the original value of Mr. Phil T. Rich's estate "x".

After he gave 1/2 of the estate to his wife, he was left with x/2.

After he gave 30,000 to his daughter, he was left with x/2 - 30,000.

After he gave half of what was left to his butler Niles, he was left with (x/2 - 30,000)/2.

After he gave half of what was left to Bubbles, he was left with (x/2 - 30,000)/4.

Finally, after he donated the 8,000 to charity, he was left with (x/2 - 30,000)/4 - 8,000.

We know that the final amount after all these transactions was $0, so we can set up an equation to solve for x:

0 = (x/2 - 30,000$)/4 - 8,000

Multiplying both sides by 4 to isolate x/2:

0 * 4 = (x/2 - 30,000) - 8,000 * 4

Expanding the right side:

0 = (x/2 - 30,000) - 32,000

Adding 30,000 and 32,000 to both sides:

30,000+ 32,000 = (x/2)

Dividing both sides by 1/2:

62,000 * 2 = x

Multiplying both sides by 2:

62,000* 2 * 2 = x * 2

Expanding the left side:

62,000* 4 = x

Dividing both sides by 4:

62,000 * 4 / 4 = x / 4

Expanding the left side:

$62,000 = x

Therefore the original value of Mr. Phil T. Rich's estate was $62,000.

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The interquartile range, IQR=31.

What is interquartile range?

Interquartile range is a measure of statistical dispersion, which is the spread of the data. The interquartile range is calculated by the  difference between the upper and lower quartile. The formula for the interquartile range is given below

                              [tex]IQR=Q_3-Q_1[/tex]

The given data : 45, 21, 3, 15, 32, 97, 68, 27, 29, 52.

Arrange in ascending order,

3, 15, 21, 27 , 29 ,32 , 45 , 52 , 68 , 97

By dividing in to 2 partition as lower half and upper half from let to right.

Lower half = 3, 15, 21, 27 , 29

Upper half = 32 , 45 , 52 , 68 , 97

Lower Quartile[tex]Q_{1}[/tex]  = Median of Lower half of data

⇒[tex]Q_{1}[/tex]= 21 (Median is the middle most term)

Upper Quartile[tex]Q_{3}[/tex] = Median of Lower half of data.

⇒[tex]Q_{3}[/tex]=52 (Median is the middle most term)

Interquartile range = [tex]IQR=Q_3-Q_1[/tex]

                               = 52-21

                               = 31

Hence, the interquartile range IQ=31.

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The random number x satisfies Poisson distribution of probability and the probability that there are 8 occurrences in ten minutes is 0.0241 and The probability that there are less than 3 occurrences is 0.0659.

Given,

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.

1) A Poisson distribution characterizes the random variable x that is provided.

2) Having 8 occurrences in 10 minutes is likely based on the following formula:

P(X = 8) = (e^(-5.3) * 5.3^8) / 8! = 0.0241 (rounded to four decimal places) (rounded to four decimal places)

Consequently,

(a) 0.0241 is the correct response.

3) The likelihood that there are fewer than 3 occurrences is as follows:

P(X 3) = P(X = 0), P(X = 1), and P(X = 2) = (e(-5.3) * 5.30), (e(-5.3) * 5.31), and (e(-5.3) * 5.32), respectively, / 0!, / 1/1, and / 2/ respectively, / 2! = 0.0659 (rounded to four decimal places)

Accordingly,

(a) 0.0659 is the correct response.

The random number x satisfies Poisson distribution of probability and the probability that there are 8 occurrences in ten minutes is 0.0241 and The probability that there are less than 3 occurrences is 0.0659.

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The random number x satisfies Poisson distribution of probability and the probability that there are 8 occurrences in ten minutes is 0.0241 and The probability that there are less than 3 occurrences is 0.0659.

Given,

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of equal length. It is known that the mean number of occurrences in ten minutes is 5.3.

1) A Poisson distribution characterizes the random variable x that is provided.

2) Having 8 occurrences in 10 minutes is likely based on the following formula:

P(X = 8) = ([tex]e^(-5.3)[/tex] * [tex]5.3^8[/tex]) / 8! = 0.0241 (rounded to four decimal places) (rounded to four decimal places)

Consequently,

(a) 0.0241 is the correct response.

3) The likelihood that there are fewer than 3 occurrences is as follows:

P(X 3) = P(X = 0), P(X = 1), and

P(X = 2) = ([tex]e(-5.3)[/tex]* 5.30), ([tex]e(-5.3)[/tex]* 5.31), and ([tex]e(-5.3)[/tex] * 5.32),

respectively, / 0!, / 1/1, and / 2/ respectively, / 2! = 0.0659 (rounded to four decimal places)

Accordingly,

(a) 0.0659 is the correct response.

The random number x satisfies Poisson distribution of probability and the probability that there are 8 occurrences in ten minutes is 0.0241 and The probability that there are less than 3 occurrences is 0.0659.

For similar questions on probability distributions,

brainly.com/question/29204567

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