The number of buses arriving at a bus stop in an mm minute interval is a Poisson random variable with average rate 1/101/10 per minute. What is the probability that you observe exactly one bus arrive while standing at the bus stop for 2020 minutes?

The pair of figures is similar by SSS

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Triangles BDC and FGC

When the side lengths of the triangle are compared, we have:

Side lengths of FGC are 5/3 multiplied by the side lengths of BDC

This means that the triangles are similar

And the similarity statement is SSS

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The range of the function g(x) is [300, ∞)

In this question, we have been given that we have deposited $300 into a savings account that earns interest annually.

The function g(x) = 300(1.04)^x used to find the amount of money in the savings account, g(x), after x years.

We need to find the range of the function.

Since a savings account earns interest annually, x can have take values from 0 to infinity.

For x = 0 year,

g(0) = 300(1.04)^0

g = 300 * 1

g = 300

For x tends to ∞, the value of function would be ∞

Therefore, the range of the function g(x) is [300, ∞)

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Sets can be used to explain the situation in quantifiers. The statement "Every student in this class has taken some course in every department in the school of mathematical sciences." can be expressed using quantifiers as:

∀ student ∈ class, ∃ course ∈ department, (student has taken course ∧ department is in school of mathematical sciences)

Explanation:

The universal quantifier "∀" is used to express "Every".

The existential quantifier "∃" is used to express "some".

The set of all students in the class is represented by "student ∈ class".

The set of all courses in each department is represented by "course ∈ department".

The relation "student has taken course" is represented by the binary predicate "student has taken course".

The constraint "department is in school of mathematical sciences" is represented by the predicate "department is in school of mathematical sciences".

Thus, sets can be used to explain the situation in quantifiers.

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In linear equation,  The minimum amount of wax the store owner needs to make 60 candles is 180 grams.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

The number of candles is given as:

n = 60

The amount of wax needed for a candle is not given.

So, we make use of an assumed value

Assume the minimum amount of wax needed to make a candle is 3 grams.

Then, the amount needed for 60 would be:

Amount = 60 * 3

This gives

Amount = 180

Hence, the minimum amount of wax the store owner needs to make 60 candles is 180 grams (using the assumed value)

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The complete question is -

a store owner makes candles by melting and pouring wax identical cylindrical molds are completely full. what is the minimum amount of wax the store owner needs to make 60 candles

The Slope of the line is -3/2

By Substituting x=26

=1/9/8*26+8/3

=-3/2

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a) The probability of event Ak is P(Ak) = \((1/2)^k * (1/2)^{n-k}\) = (1/2)ⁿ. b) The probability of the event Ax-1 Ak is (1/2)^k.

(a) To model the experiment as a Laplace experiment, we can define the sample space as the set of all possible outcomes of tossing a fair coin n times. Each outcome can be represented as a sequence of n coin tosses, where each toss can result in either a head (H) or a tail (T). Therefore, the sample space can be written as:

Ω = {HHHH...HHH, HHHH...HHT, HHHH...HTH, ..., TTTT...TTT}

Since the coin is fair, the probability of obtaining a head in each toss is 1/2, and the probability of obtaining a tail is also 1/2. Thus, each outcome in the sample space is equally likely, and the probability of each outcome is 1/2^n.

For the event Ak, "the first k tosses yield only heads," there is only one outcome that satisfies this event, which is the sequence of k heads followed by (n-k) tails:

Ak = {HH...HTTT...TT}

The probability of this event, P(Ak), can be calculated by considering that each coin toss is independent. Since the probability of obtaining a head in each toss is 1/2, the probability of getting k heads in k tosses is (1/2)^k. The probability of getting (n-k) tails in (n-k) tosses is also (1/2)^(n-k).

(b) The event Ax-1 Ak represents the situation where the first (k-1) tosses yield only heads, and then the kth toss also yields a head. In other words, it means that we obtain k consecutive heads in the first k tosses. This event can be represented as:

Ax-1 Ak = {HH...HH}

The probability of this event, P(Ax-1 Ak), can be calculated in a similar manner as above. Since the first (k-1) tosses yielding heads and the kth toss yielding a head are independent events, the probability is:

P(Ax-1 Ak) = (1/2).

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Answer:

4x

Step-by-step explanation:

Simply add 4 and x, and that is 4x.

The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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Answer:

21% would convert to 0.21 and 0.4% would convert to 0.004

Step-by-step explanation:

-3x+7y = -18 ...1

4x-4y = 8 ...2

...1 × 4

-12x + 28y = -72 ...3

...2 × 3

12x - 12y = 24 ...4

...3 + ...4

28y - 12y = -72 + 24

16y = -48

y = -3

Replace y = -3 in ...2

4x - 4(-3) = 8

4x + 12 = 8

4x = 8 - 12

4x = -4

x = -1

Answer:

\(\huge\boxed{\boxed{(x,y)=(-1,-3)}}\)

Step-by-step explanation:

multiply first equation by 4 and second by 3 respectively:

\( \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}\)

combine the equations:

\( \underline{ \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}} \\ \displaystyle16y = - 48\)

divide both sides by -48:

\( \displaystyle \: \frac{16y}{16} = \frac{ - 48}{16} \\ y = - 3\)

substitute the value of y to the second equation

\( \displaystyle \: 4x - 4. - 3 = 8\)

simplify multiplication:

\( \displaystyle \: 4x + 12 = 8\)

cancel 12 from both sides:

\( \displaystyle \: 4x = - 4\)

divide both sides by 4

\( \displaystyle \: \frac{4x}{4} = \frac{ - 4}{4} \\ x = - 1\)

therefore our solution is

\(\displaystyle (x,y)=(-1,-3)\)

Answer:

the answer is 5

Step-by-step explanation:

it is right jk

Answer:

Step-by-step explanation:

We know area of a rectangle is xy where x and y are its dimensions.

A=xy

If we factor the area we will get the dimensions.

A=15k^4+35k^3+20k^2

(this can be factored in many ways to produce the same area, the answer choices you are given can be any given combination of factors.)

A=15k^4+15k^3+20k^3+20k^2

A=15k^3(k+1)+20k^2(k+1)

A=(15k^3+20k^2)(k+1) (this is one way)

A=5k(3k^2+4k)(k+1)

A=(3k^2+4k)(5k^2+5k) (and another way)

Either expression would give you width and length (or length and width) as they all produce the area of the original equation.

Answer:

yes, they are equivalent

Step-by-step explanation:

solving each expression fully, you will find that both are equal to 77

Answer:

They are equivalent.

Step-by-step explanation:

7⋅11⋅13+13and7⋅6⋅5⋅4⋅3⋅2⋅1+5 are composite numbers.

In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

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Answer:

Shop A = 113 pence

Shop B = 101 pence

Step-by-step explanation:

Given :

Shop A :

5kg for £5.65

Shop B:

2kg for £2.02

Price per kg :

weight / price

100 pence = £1

Shop A :

Price of 1kg :

5.65 / 5 = £1.13 = 113 pence

Shop B:

2.02 / 2 = £1.01 = 1.01 * 100 = 101 pence

Answer:

1

Step-by-step explanation:

Slope (m) of the line can be derived using the following formula below:

\( m = \frac{y2 - y1}{x2 - x1} \)

To solve this, we can pick any two points on the line, and use the coordinates of the points to solve for the slope (m) of the line.

To find the slope (m) of the line given, let's use the coordinates of the points where the line intercepts the y-axis and the x-axis.

Thus, when x = 0, y = 3. Let's make this the first pair of coordinates at the point where the line intercepts the y-axis.

At the point where the line intercepts the x-axis, when x = -3, y = 0.

We now have the following points => in the following format (x, y) as:

Point 1 => (0, 3). Let this be (x1, y1)

Point 2 => (-3, 0). Let this be (x2, y2)

==>Let's find slope (m):

\( m = \frac{y2 - y1}{x2 - x1} \)

\( m = \frac{0 - 3}{-3 - 0} \)

\( m = \frac{-3}{-3} \)

\( m = 1 \)

Slope (m) = 1

The new variance is 0.0625 / n

We can use the following formula to calculate the variance of a data set

variance = (sum of (x - mean)^2) / (number of data points)

where x is a data point and mean is the mean of the data set.

If the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35, we can find the standard deviation as follows

standard deviation = square root of variance = sqrt(0.35) = 0.59

Now, if the price increases by 25 cents a box, the new mean cost will be

new mean = $4.00 + $0.25 = $4.25

To find the new variance, we need to calculate the sum of (x - mean)^2 for the new data set and divide by the number of data points. Let's assume we are still considering the same number of boxes.

sum of (x - mean)^2 = [(4.25 - 4)^2 × n] = 0.0625 × n

where n is the number of data points.

Therefore, the new variance can be calculated as

new variance = (sum of (x - mean)^2) / (number of data points) = 0.0625 / n

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9 meters cost P600

Step-by-step explanation:

3×3 = 9

p200×3 =P600

Answer: each time you roll a 6-sided die is 1/6 percent to get any number  

Step-by-step explanation:

The coordinate system that is an extension of the terrestrial coordinate system on the celestial sphere is called the celestial coordinate system.

The coordinate system that is an extension of the terrestrial coordinate system onto the celestial sphere is known as the celestial coordinate system.

The celestial coordinate system is used to locate and describe objects in the sky, such as stars, planets, and other celestial bodies.

Similar to the terrestrial coordinate system, the celestial coordinate system utilizes a set of coordinates to specify the position of an object. However, due to the spherical nature of the celestial sphere, the celestial coordinate system has some differences.

In the celestial coordinate system, the celestial sphere is divided into two main components: the celestial equator and the celestial poles.

The celestial equator is an imaginary circle that represents the projection of the Earth's equator onto the celestial sphere. It divides the celestial sphere into the northern and southern celestial hemispheres.

To specify the position of an object in the celestial coordinate system, two primary coordinates are used:

declination (DEC) and right ascension (RA).

Declination is similar to latitude and measures the angular distance of an object north or south of the celestial equator, while right ascension is similar to longitude and measures the angular distance of an object eastward from a reference point known as the vernal equinox.

With the celestial coordinate system, astronomers and stargazers can precisely locate and track celestial objects across the sky, enabling them to study and explore the vastness of the universe.

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The candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.

Let x be the quantity of 10% fat-content chocolate.

Fat in 10% fat-content chocolate + Fat in 60% fat-content chocolate = Total fat in 25% fat-content chocolate

0.10x + 0.60(100 - x) = 0.25*100

10x + 60*100 - 60x = 25*100

-50x = 25*100 - 60*100

-50x = 100(25 - 60)

50x = 3500

x = 3500/50

x = 70 kg

This is the quantity of 10% fat-content chocolate required.

100 - x = 30 kg

This is the quantity of 60% fat-content chocolate required.

Therefore, we have found that the candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.

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Denote x2 by y.

(x2-3)7=(y-3)7

This is a binomial expansion in y, and you want the coefficient of y4 because y4=x8

You have 7 terms of (y-3) in (y-3)7.  To get the fourth power of y, you need to choose y from four of the terms.  The number of ways you can do this is the combinations of 7 things taken 4 at a time.  This is:

7!/(4!3!)=35

So, the coefficient of x8 in the given expansion will be 210.

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The entry to record the purchase will include: a debit to Supplies and a credit to Accounts Payable

Now, given: Purchased supplies = $500 (on account).

To find: What does entry to record the purchase include?

Now,

Hence, the entry to record the purchase will include: a debit to Supplies and a credit to Accounts Payable.

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Answer:3 hours

Step-by-step explanation:

-2.5

-2.5

-2.5

=-5 c

Answer:

B

Step-by-step explanation:

Let the number = x

Product: 4 * x

Add 5: 4x + 5

=

3x + 6

Now equate the two parts.

4x + 5 = 3x + 6               Subtract 5 from both sides

4x + 5 - 5 = 3x + 6 - 5   Combine

4x =  3x + 1                    Subtract 3x from both sides

4x-3x=3x -3x + 1          Combine

x = 1

There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

Answer:

if youre talking about line OA, it is

x - 2y =0

The graph of s(x) = -6x + \(8x^2\) + 5x + 3 is concave up at the point with x-coordinate -1. Let us consider the second derivative.

To determine the concavity of a function at a specific point, we need to analyze the second derivative of the function. If the second derivative is positive, the graph is concave up, and if it is negative, the graph is concave down.

Given s(x) = -6x + \(8x^2\) + 5x + 3, let's find the second derivative:

s'(x) = -6 + 16x + 5

s''(x) = 16

The second derivative is a constant, 16, which is positive. Since it is always positive, the graph of s(x) is concave up for all values of x. Therefore, at the point with x-coordinate -1, the graph is also concave up.

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