Determine the indicated probability for a Poisson random variable with the given values of λ and t. Round the answer to four decimal places.
λ=, 0.9, t=8
P (5) =___

Answer:  The length of one side is 9m.

Step-by-step explanation:

If area is 81 square meters, that means A = 81 m^2.

Since A = s^2, we can substitute s^2 for A.  Then

(s^2) = 81 m^2

Take the square root of both sides to solve for s:

(s^2)^(1/2) = (81 m^2)^(1/2)

s = 9 m

The inverse proportionality expression is y =40/x

If the variable y is inversely proportional to x, this is expressed as;

y = k/x

where

k is the constant of proportionality

If y = 5 and x = 8. then;

5 = k/8

k = 5 * 8

k = 40

Determine the inverse proportionality

Recall that y = k/x

y = 40/x

Hence the inverse proportionality expression is y =40/x

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We have produced an orthonormal set of vectors: {(2/√29, -5/√29), (5/√29, 2/√29)}.

(a) To show that the set of vectors in Rn is orthogonal, we need to show that their dot product is zero. Let's calculate the dot product of the given vectors:

(2, -5) · (10, 4) = 2×10 + (-5)×4 = 20 - 20 = 0

Since the dot product is zero, we can conclude that the set of vectors {(2, −5), (10, 4)} is orthogonal.

(b) To normalize the set and produce an orthonormal set, we need to divide each vector by its magnitude. The magnitude of a vector (a, b) is given by √(a^2 + b^2).

So, the normalized vectors are:

v1 = (2, -5) / ||(2, -5)|| = (2/√29, -5/√29)

v2 = (10, 4) / ||(10, 4)|| = (10/√116, 4/√116) = (5/√29, 2/√29)

Now, we can check that both vectors are unit vectors (i.e., their magnitude is 1) and they are still orthogonal:

v1 · v2 = (2/√29)×(5/√29) + (-5/√29)×(2/√29) = 0

Therefore, we have produced an orthonormal set of vectors: {(2/√29, -5/√29), (5/√29, 2/√29)}.

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Answer: 1320 ways

Step-by-step explanation:

In this scenario, 12 finalists are eligible for the money draw and no finalist can win more than one prize.

So for the 1st prize we have 12 finalists

For the 2nd prize we have 11 finalists

And finally, for the 3rd prize we have 10 finalists

Using the multiplication principle:

Total number of ways = 12 x 11 x 10

= 1320

Therefore, there are 1320 ways the first, second, and third prizes be awarded

The length of the side AC in triangle ΔACE found using the midsegment theorem, which indicates that AC is parallel to and twice the length of DF  is 34

Parallel lines are lines that equidistant from each other and that do not intersect.

The information from the question are;

The midpoints of the triangle ΔACE are B, D, and F

The length of the side EC of the triangle ACE = 30

The length of the segment DF of the triangle ΔBDF = 17

The length of the segment AC in the triangle ΔACE is required.

According to the midsegment theorem, the length of the segments formed by joining the midpoints of two sides of a triangle is parallel to the third side and is also half the length of the third side.

Therefore;

The length of the segment DF = 0.5 × The length of the segment AC

DF = 17, by the substitution property, we get;

17 = 0.5 × AC

Multiplying both sides of the equation by 2, we get;

2 × 17 = 2 × 0.5 × AC = 1 × AC = AC

34 = AC

AC = 34 (transitive property)

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Answer:

Step-by-step explanation:

We can use the quadratic formula or factor, This looks hard to factor so we should use the quadratic formula.

ax^2 + bx + c

so

a=4

b=-9

c=2

you can try it by hand or use this:

https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php

you get x=2 and x=0.25 these are the x intercepts (where Y is zero and where the graph crosses the x axis)

so mark x=2 and x=0.25 with a dot on a number line and you can draw a straight line between them since that is the part of the graph that is below the x axis (because the equation has <0) it is a positive parabola because the "a" value is positive and the presence of a "b" value means part of the graph will be below the x axis

The indefinite integral of 8cos(8) yields a power series centered at 0. The first 5 nonzero terms of the power series are: 8x - (16/3!) * x^3 + (256/5!) * x^5 - (2048/7!) * x^7

The first five nonzero terms of the power series are: 8x, 8sin(8x), 0, 0, 0.

The indefinite integral of 8cos(8x) can be expressed as a power series centered at x=0. The power series representation is:

∫8cos(8x) dx = C + ∑((-1)^n * 64^n * x^(2n+1)) / ((2n+1)!),

where C is the constant of integration and the summation is taken over n starting from 0.

To find the power series representation of the indefinite integral, we can use the Maclaurin series expansion for cos(x):

cos(x) = ∑((-1)^n * x^(2n)) / (2n!),

where the summation is taken over n starting from 0.

First, we substitute 8x for x in the Maclaurin series expansion of cos(x):

cos(8x) = ∑((-1)^n * (8x)^(2n)) / (2n!) = ∑((-1)^n * 64^n * x^(2n)) / (2n!).

Now, we integrate the series term by term:

∫8cos(8x) dx = ∫(∑((-1)^n * 64^n * x^(2n)) / (2n!)) dx.

The integral and summation can be interchanged because both operations are linear. Therefore, we get:

∫8cos(8x) dx = ∑(∫((-1)^n * 64^n * x^(2n)) / (2n!)) dx.

The integral of x^(2n) with respect to x is (1/(2n+1)) * x^(2n+1). Thus, the integral becomes:

∫8cos(8x) dx = C + ∑((-1)^n * 64^n * (1/(2n+1)) * x^(2n+1)),

where C is the constant of integration.

Therefore, the full power series representation of the indefinite integral is:

∫8cos(8x) dx = C + ∑((-1)^n * 64^n * x^(2n+1)) / ((2n+1)!).

To find the first 5 nonzero terms of the power series, we evaluate the series for n = 0 to 4:

Term 1 (n = 0): ((-1)^0 * 64^0 * x^(2(0)+1)) / ((2(0)+1)!) = 64x.

Term 2 (n = 1): ((-1)^1 * 64^1 * x^(2(1)+1)) / ((2(1)+1)!) = -2048x^3 / 3.

Term 3 (n = 2): ((-1)^2 * 64^2 * x^(2(2)+1)) / ((2(2)+1)!) = 32768x^5 / 15.

Term 4 (n = 3): ((-1)^3 * 64^3 * x^(2(3)+1)) / ((2(3)+1)!) = -262144x^7 / 315.

Term 5 (n = 4): ((-1)^4 * 64^4 * x^(2(4)+1)) / ((2(4)+1)!) = 1048576x^9 / 2835.

Hence, the first 5 nonzero terms of the power series representation of the integral are:

64x - 2048x^3 / 3 + 32768x^5 / 15 - 262144

x^7 / 315 + 1048576x^9 / 2835.

Therefore, The indefinite integral of 8cos(8) yields a power series centered at 0. The first 5 nonzero terms of the power series are: 8x - (16/3!) * x^3 + (256/5!) * x^5 - (2048/7!) * x^7

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Answer:

Hey y = 16

sorry can't find x and z

Answer:

112 square units.

Step-by-step explanation:

Use the formula for the area of a triangle.

\(A=bh\)

\(b \times h\)

\(14 \times 8\)

\(=112\)

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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Answer: Right/complementary angles

Step-by-step explanation:

Two angles that add up to 90 degrees are called complementary angles.

Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.

In other words, the sum of the measures of complementary angles is always 90 degrees.

Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.

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The function to represent the cost of purchasing x packages of crackers will be f(x)  =  2.49x.

A function in mathematics set up a relatioship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

Given that:-

The practical domain for the function f(x) will be:-

f(x)    =    2.49x.

f(x) is the total cost of purchasing the packages of crackers and x is the number of the crackers.

Therefore the function to represent the cost of purchasing x packages of crackers will be f(x)  =  2.49x.

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The volume of the triangular prism is 171 cubic inches.

To find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism. In this case, the base of the prism has an area of 18 square inches and the height is 9.5 inches. So, the volume of the prism can be calculated as follows:

Volume = Base Area x Height
Volume = 18 sq. in. x 9.5 in.
Volume = 171 cubic inches

Therefore, the volume of the triangular prism is 171 cubic inches.

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Answer:

1. Yes

2. Yes

3. No

4. No

5. No (that is plus not multiply)

The correct answer is (c) analytical. Levels of a variable can have meaning and order when the variable is analytical variable.

Analytical variables are variables that have a meaningful order or ranking, such as height or weight. For example, height is an analytical variable because people can be ranked from shortest to tallest, and each height value is meaningful in relation to other height values.

Prescriptive variables describe the desired or prescribed behavior, such as in a set of rules or guidelines. Categorical variables divide data into categories or groups, such as gender or hair color. Continuous variables have an infinite number of values and can take on any value within a given range, such as temperature or time.

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Answer:

figure 1, 2 respectively

62.5 Answer

Answer:

3.24/2.4=c

Step-by-step explanation:

division

Answer:

BE = (× + 4), ED = (× + 7),

THAT IS ALL I CAN HELP

Answer:

n = m - a

Step-by-step explanation:

Given:

a = m − n

Where,

Actual cost of the item = a

Original price of the item = m

Amount of Coupon = n

Solve the formula for the amount of the coupon

Making n the subject

a = m − n

Subtract m from both sides

a - m = m - n - m

a - m = - n

Divide both sides by -1

(a - m) / -1 = -n / -1

- a + m = n

Can also be written as

n = m - a

Answer:

8 meters

Step-by-step explanation:

Answer:

OK remeber that a all sides of a square are equal so there are 4 sides on a square so u would have to dividde 32 by 4 which is 8

Step-by-step explanation:

Answer:

24 + 40 = 8*(3 + 5)

Step-by-step explanation:

The factors of:

24: 1, 2, 3, 4, 6, 8, 12, 14

40: 1, 2, 4, 5, 8, 10, 20, 40

the prime factors:

24: 2 * 2 * 2 * 3

40: 2 * 2 * 2 * 5

The most shared factors are (2*2*2=8)

Factoring out 8 we have:

24 + 40 = 8*(3 + 5)

The sample proportion of households without fiber cable is approximately 0.313, calculated from a survey of 470 households where 323 had fiber cable.

To find the sample proportion of households without fiber cable, we need to subtract the number of households with fiber cable from the total number of households surveyed and divide it by the total number of households surveyed.

Number of households without fiber cable = Total households surveyed - Number of households with fiber cable

Number of households without fiber cable = 470 - 323 = 147

Sample proportion of households without fiber cable = Number of households without fiber cable / Total households surveyed

Sample proportion of households without fiber cable = 147 / 470 ≈ 0.313

Therefore, the sample proportion of households without fiber cable is approximately 0.313.

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The table of values for the function y = (1/2)^x with x = -2 to 3 x is as shown below

Given that

y= (1/2)^x

To complete the table of values for the function y = (1/2)^x, we can substitute the given values of x into the function and evaluate for y. The table is as follows:

x y

-2 4

-1 2

0 1

1 1/2

2 1/4

3 1/8

Here's how we get each value of y:

Therefore, the table of values for the function y = (1/2)^x with x = -2 to 3 and an increment of 1 in x is as shown above.

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Answer:

Tommy would have to pull at least 40.0000000..... something to beat Artie but the closest whole number is 41 becouse it has to be over 200

Step-by-step explanation:

200 /= 60 + 20 +25 + 55 + x

200/= 160 + x - 160 both sides

40 = x

To derive a recurrence for the average number L(n) of rounds needed to elect a leader in a city with n people, we can consider the following scenario:

In each round, every person in the city randomly chooses another person as their representative. Then, all the chosen representatives vote for a leader, and if there is a single candidate with a majority of votes, that person becomes the leader. Otherwise, a new round is initiated.

Now, let's analyze the probability of electing a leader in one round. For a person to be elected as a leader, they must receive more than half of the votes in that round.

Therefore, the probability of any particular person being elected as a leader in one round is\((1/n) * (1/n) = 1/n^2.\) However, there are n people in the city, so the total probability of electing a leader in one round is n * Hence, we can derive the recurrence relation for L(n) as follows:

L(n) = 1 + (1/n) * L(n-1)

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Given:

Mean absolute deviation (MAD) = 0

One of the data values = 14.

To find:

The statement for other data values.

Solution:

We know that Mean absolute deviation (MAD) represents the average of absolute difference between observations and mean.

\(MAD=\dfrac{\sum |x_i-\overline x|}{n}\)

MAD is 0. It is possible if \(\sum |x_i-\overline x|\). It means all the values of \(|x_i-\overline x|\) are 0.

It means no deviations in mean angle values and all the values are the same.

Therefore, if MAD is 0 and one data value is 14, then all the data values are same, i.e., 14.

I think the answer should be b, since y=3 when x=0, according to the option B.

y = x + 3, B

The surface area is increasing at the rate of (60 x + 150) cm² per second.

Let the side of the cube be x cm.

s = x cm

Surface area of the cube will be:

S = 6 x² cm²

Now, we are given that, the side of the cube is expanding 5 cm per second.

So, the side of the cube after 1 second will be:

s' = x + 5 cm

Surface area will be:

S' = 6 (x + 5)² cm²

S' = (6x² + 150 + 60 x) cm²

Change in the surface area is:

ΔS = (6x² + 150 + 60 x) cm² - 6 x² cm²

ΔS = (60 x + 150) cm²

Therefore, the surface area is increasing at the rate of (60 x + 150) cm² per second.

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Answer:

A. 24x = 192

Step-by-step explanation:

Answer:

A. 24x = 192

Step-by-step explanation:

you would have to multiply 24 x 8 in order to 192!

So yes, the correct answer would be A. 24 x = 192!

Its simple you just have to multiply how many packs x how many crayons he bought! :D