the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm is:

The equation that represents the total area of the pool and deck is: A(x) = 2x² + 24x + 64.

In algebra, a binomial is a polynomial that consists of two terms connected by either an addition or a subtraction operator. A binomial can be written in the form (ax + b) or (ax - b), where "a" and "b" are constants and "x" is a variable.

Binomials are used in a variety of algebraic operations, such as factoring, expanding, and solving equations. They also appear in binomial probability distributions and binomial theorem.

Let's start by drawing a diagram to visualize the problem:

___________      

|                       |    4 ft

|   _________|_________

|   |                   |                    |

|   |                   |                    |

|  |                    |                    |   2x

|  |                    |                    |

|  |_________|_________ |

|                       |    4 ft

|__________ |

      2w

The rectangular pool is twice as wide as it is long, so we can let the length be x, and the width be 2x.

The deck around the pool is 4 feet wide on each side, so the total width of the pool and deck is (2x + 8), and the total length is (x + 8).

Therefore, the total area of the pool and deck can be represented as:

(2x + 8)(x + 8)

Expanding the expression, we get:

2x² + 24x + 64

So the equation that represents the total area of the pool and deck is:

A(x) = 2x² + 24x + 64

where A(x) is the area of the pool and deck, and x is the length of the pool.

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Answer:

13 bags

Step-by-step explanation:

V = π(2^2)(1/2) = 2π = 6.28 cubic feet

6.28 ÷ .5 = 12.56

So Martin needs to buy at least 13 bags of sand.

As per the query, we have to find a number which is divided by 8 that answers 27, i.e., quotient is 27, and remainder is 4. The number is 220.

In this case, we used it to find the number that was divided by 8 and gave a quotient of 27 and a remainder of 4. As we know the rule:

Dividend = Divisor × Quotient + Remainder

x = 8 × 27 + 4 x = 216 + 4 x = 220.

Hence, the number is 220.

The formula I used is called the division algorithm. It’s a way to divide two numbers and get a quotient and remainder. We can use this formula to solve other division problems with remainders as well.

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The given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.

When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b).

The y value of the y-intercept point is denoted by the symbol b in the formula.

The general form of a linear equation is y-y1=m(x-x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

So, in the given situation:
The point-slope form is: y = mx + b

Then y is y and b is the x value and m is the slope.

Now, insert values as follows:

y = mx + b

140 = -14x + 10

Graph the equation as follows:

(Refer to the graph attached below)

Therefore, the given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.

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The given information says that the number of calls coming to the customer care center of a mobile company per minute is a Poisson random variable with a mean of 5, So the probability that no call comes in a certain minute is 1

                 A Poisson distribution is a probability distribution that shows the probability of a certain number of events occurring within a specific time or space, provided that these events occur at an average rate that is constant throughout the space or time.

             Given a Poisson random variable with mean λ, the probability of observing x occurrences of an event in a certain time interval is given by:

                          P(X = x) = (e^(-λ) * λ^x) / x!,

             where e is Euler's number (approximately equal to 2.71828).

We are required to find the probability that no call comes in a certain minute, i.e., P(X = 0).

Substituting the given values into the Poisson distribution formula:

                     P(X = 0) = (e^(-5) * 5^0) / 0!

                                   = (1 * 1) / 1

                                   = 1

    Therefore, the probability that no call comes in a certain minute is 1.

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Answer:

3.6 miles

Step-by-step explanation:

hope this helps!

A student should score 598 in order to win the award.

To calculate how high should a student score be to win this award, we use the z-score formula.

z=(x-μ)/σ

Where,

μ= Mean of the scores on this exam

σ= Standard deviation of the scores on this exam

z= Z-score

x= Scores on this exam

By substituting the given values in the formula, we get

z=(x-μ)/σ

[tex]= (x-538)/30[/tex]

To find the highest 2.5%, we use the normal distribution table which gives us the Z-score corresponding to 0.975. The highest 2.5% is on each side of the normal distribution curve. Therefore, we have to subtract the area from the highest score, then divide by two.

Subtracting 0.975 from 1 gives us the area to the left of this point on the table which is equal to 0.025.Z = 1.96.

So the score should be one standard deviation above the mean. Thus, the score a student needs to get in the top 2.5% of statewide scores is

   [tex]Z = (x - 538) / 30[/tex]

[tex]1.96 = (x - 538) / 30x - 538 = 1.96 * 30x - 538 = 58.8 + 538x = 597.8[/tex]

The score a student needs to get in the top 2.5% of statewide scores is 598, rounded up to the next integer.

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Answer:

Step-by-step explanation: 14 = x

Answer:

The answer to your question would be 14

Step-by-step explanation:

Simple equation

14 - 10 = 4

I hope this helps and have a wonderful day!

Answer: 126in

Step-by-step explanation:

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5+10=24

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Answer: The answer is 38.5 cm^2

Step-by-step explanation:

Given:

           Radius(r) = 7/2

            Pie (π) = 22/7

We know that:

          The area of Circle is = πr^2 = π * r * r

           So, ans is = (22/7) * 7/2 * 7/2 = 38.5 cm^2

Answer:

A≈ 38.5cm^2

Step-by-step explanation:

Given:

The approximation of pi is 22/7 or 3.141592

The radius is 7/2 or 3.5

Work:

A=πr(2)=π·3.5(2)≈38.48451

now let's round it to 38.5cm^2

The equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1 (option D).

To derive the equation of a line, we need to use the point-slope formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the given values, we have:

y - (-5) = -3(x - 2)

Simplifying this expression, we get:

y + 5 = -3x + 6

y = -3x + 1

Thus, the equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1.

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Complete Question:

Choose the equation below that represents the line passing through the point (2, - 5) with a slope of −3.

A.) y = −3x − 13

B.) y = −3x + 11

C.) y = −3x + 13

D.) y = −3x + 1

Answer:

The answer is y = -3x + 1

The coefficient of determination measures goodness of fit.

The coefficient of determination, often referred to as R-squared, measures the goodness of fit in a regression analysis. It does not measure the independence of variables, economic plausibility, or independence of residuals.

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Answer: 40/7 or 5.7

Step-by-step explanation:

using angle bisector theorem we get,

x/5 = 8/7

Upon substituting our given values in above equation, we will get:

x/5 X 5 = 8/7 X 5

x = 40/7 or 5.7

Answer:

3.3

Step-by-step explanation:

Angle bisector theorem: In a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

       [tex]\dfrac{x}{8-x}=\dfrac{5}{7}[/tex]

Cross multiply,

    x *7 = 5*(8 - x)

        7x = 40 - 5x

   7x + 5x = 40

        12x   = 40

             [tex]x = \dfrac{40}{12}\\\\x = 3.3[/tex]

Answer:

orthocentre

Step-by-step explanation:

this is the answer to your question

To find the probability that at least one of the two cards drawn from a standard deck of 52 playing cards is a spade, we can use the complement rule.

The complement of the event "at least one of the cards is a spade" is "neither of the cards is a spade."

To find the probability that neither of the two cards is a spade, we can multiply the probabilities of drawing a non-spade on the first card and a non-spade on the second card:

P(neither is spade) = (39/52) x (38/51) = 0.4498 (rounded to four decimal places)

P(at least one is spade) = 1 - P(neither is spade)

P(at least one is spade) = 1 - 0.4498

P(at least one is spade) = 0.5502 (rounded to four decimal places)

Therefore, the probability that at least one of the two cards drawn from a standard deck of 52 playing cards is a spade is 0.5502 or approximately 55.02%.

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Maggie is 30 years old, and Bobby is 15 years old if in 3 years, Maggie's age will be 50% greater than Bobby's age and years ago when Maggie was 25 years old, Bobby was 10 years old.

Maggie is 15 years older than Bobby. We have to determine Bobby's age.

Let's suppose that Bobby's age is x, so Maggie's age would be x + 15 years.

1) In 3 years, Maggie's age will be 50% greater than Bobby's age.

The age of Maggie in 3 years would be (x + 15) + 3, and the age of Bobby would be x + 3.

According to the problem, Maggie's age in 3 years would be 50% greater than Bobby's age in 3 years.

So, (x + 15) + 3 = (1.5)(x + 3)

Simplifying the above equation, we get

x + 18 = 1.5x + 4

Now, we will solve for

x.x - 1.5x = -14-0.5x = -14x = 28

Therefore, Bobby is 28 years old now.

2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.

Let's assume that x years ago Maggie was 25 years old. Thus, Bobby was 10 years old at that time.

So, x + 25 = (x + 10) + 15x = 15

Therefore, Maggie is 30 years old now. And Bobby is 15 years old now.

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For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:

P(N=n,K=k) = P(N=n) * P(K=k)If this condition is not satisfied, then N and K are dependent.

The distribution of K given that N=2 can be calculated using the conditional probability formula:

P(K=k|N=2) = P(K=k and N=2) / P(N=2)

Let X be the outcome of the coin flip. Then the joint probability mass function of N and K can be expressed as:

P(N=n,K=k) = P(X=0) for n=0 and k=0

P(N=n,K=k) = P(X=1) for n=1 and k=0, 1

P(N=n,K=k) = P(X=2) for n=2 and k=0, 1, 2

P(N=n,K=k) = P(X=3) for n=3 and k=0, 1, 2

The marginal probability mass function of N can be obtained by summing over all possible values of K:

P(N=n) = P(N=n,K=0) + P(N=n,K=1) + P(N=n,K=2)

The marginal probability mass function of K can be obtained by summing over all possible values of N:

P(K=k) = P(N=0,K=k) + P(N=1,K=k) + P(N=2,K=k) + P(N=3,K=k)

The conditional probability mass function of N given that K=2 can be calculated using Bayes' theorem:

P(N=n|K=2) = P(K=2|N=n) * P(N=n) / P(K=2)

For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:

P(N=n,K=k) = P(N=n) * P(K=k)

If this condition is not satisfied, then N and K are dependent.

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The given equation of the circle is:

[tex] \rm \: x^2 + y^2 = 20[/tex]

We can write this equation in standard form by completing the square:

[tex] \rm x^2 + y^2 = 20[/tex]

[tex] \rm x^2 + y^2 - 20 = 0[/tex]

[tex] \rm (x^2 - 2x + 1) + (y^2 - 20) = 1[/tex]

[tex] \rm (x - 1)^2 + y^2 = 21[/tex]

Therefore, the center of the circle is (1, 0) and the radius is the square root of 21.

Answer: h=4

Step-by-step explanation:

I think the best way to do this is by splitting up the trapezoid into two shapes since it is not a regular trapezoid. We can make a split to form a small right triangle on the left and a regular trapezoid on the right.

Small right triangle on the left:

4 inch side length and 6 inch hypotenuse with the Pythagorean theorem will give us the missing side.

missing side = square root of 6^2-4^2 = [tex]2\sqrt{5}[/tex]

Then the area is [tex]\frac{1}{2}*4*2\sqrt{5}=4\sqrt{5}[/tex]

Regular trapezoid on the right:

Area will be [tex]\frac{6+(17-2\sqrt{5})}{2}*4=46-4\sqrt{5}[/tex]

Summing up the two areas to get the total we have [tex]4\sqrt{5}+46-4\sqrt{5}=46[/tex] in^2.

The variable y is used to represent the worth of the car after t years like an exponential model to reflect the scenario, and the third option, y=28,000(0.91)t, is the correct response.

A = A0(b)t/c is the formula for an exponential model, where A0 denotes the starting quantity of the thing being modeled. t stands for passing time. The quantity at time t is equal to A.

The exponentially decaying formula for an asset's value over time with such a consistent rate of depreciation is: y = a(1-r)t

Where:

Y is equal to the car's value after t years.

In this scenario, the car's original value is $28,000, and its rate of depreciation is 9%, or 0.09 in decimal notation.

t equals the amount of years

The exponential model can be expressed using the following formula: y = 28,000(1-0.09)t

By condensing the formula, we obtain the following result: y = 28,000(0.91)t

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The area of the rectangular section in the garden is Area = (x₂ - x₁) x (y₂ - y₁)

Now, let's look at the rectangular section of the garden represented by the coordinate plane. We are told that the section is represented by Rectangle JKLM. The four corners of this rectangle can be represented by their respective coordinates:

Point J: (x₁, y₁)

Point K: (x₂, y₁)

Point L: (x₂, y₂)

Point M: (x₁, y₂)

To find the area of this rectangle, we need to use the formula:

Area = length x width

The length of the rectangle is the distance between points J and K, which is given by:

Length = x₂ - x₁

The width of the rectangle is the distance between points J and M, which is given by:

Width = y₂ - y₁

Therefore, the area of the rectangle is:

Area = (x₂ - x₁) x (y₂ - y₁)

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Complete Question:

Gina is growing lettuce in a section of a garden. She represents this section with Rectangle JKLM. Each unit in the coordinate plane represents 1 foot.

What is the area of the section where lettuce grows?

This equation represents the linear relationship between the dependent variable (y) and the independent variable (x) with a slope of 2 and a y-intercept of -3.

However, I can provide a general example using common terms in algebra:
Terms: Dependent variable (y), independent variable (x), slope (m), and y-intercept (b).
To represent a linear relationship between two variables, we can use the equation of a straight line, which is often written as:
[tex]y = mx + b[/tex]
Here's what each term in the equation represents:
1. y: This is the dependent variable, meaning its value depends on the value of the independent variable (x). In a graph, it is usually represented on the vertical axis.
2. x: This is the independent variable, which can take any value within a given range. It is usually represented on the horizontal axis in a graph.
3. m: This is the slope of the line, representing the rate at which the dependent variable (y) changes with respect to the independent variable (x). A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.
4. b: This is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
simply plug in the values for the slope (m) and y-intercept (b). For example, if the slope is 2 and the y-intercept is -3, the equation would be:
[tex]y = 2x - 3[/tex]

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the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.

To write a piecewise function to represent the total distance Carrie has traveled after t hours, we need to break down her journey into different parts and calculate the distance covered during each part.

Let's define the three different parts of her journey:

•Part 1: The first hour, during which she averaged 30 miles per hour

•Part 2: The next 4 hours, during which she averaged 65 miles per hour

•Part 3: The remaining 2 hours, during which she averaged 52 miles per hour

For Part 1, the distance covered can be calculated as:

d1 = 30t (where t is the time spent in the first hour, t ≤ 1)

For Part 2, the distance covered can be calculated as:

d2 = 260 + 65(t - 1) (where t is the time spent in the next 4 hours, 1 < t ≤ 5)

For Part 3, the distance covered can be calculated as:

d3 = 520 + 52(t - 5) (where t is the time spent in the remaining 2 hours, 5 < t ≤ 7)

Now, we can combine these three equations to form a piecewise function for the total distance traveled by Carrie:

d(t) = 30t, 0 ≤ t ≤ 1

d(t) = 260 + 65(t - 1), 1 < t ≤ 5

d(t) = 520 + 52(t - 5), 5 < t ≤ 7

Therefore, the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.

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The atmospheric carbon dioxide levels in parts per million (ppm) in a town can be modeled using the function defined by , where is in years and corresponds to 1950.

Substituting in gives , which means that the atmospheric carbon dioxide levels in parts per million (ppm) in the town is 386.50 in 2019.

This means that since 1950, the atmospheric carbon dioxide levels in parts per million (ppm) in the town have increased by 386.50.

This is a significant increase and reflects the growing levels of atmospheric carbon dioxide emissions globally due to human activity, leading to climate change.

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The required amount of money earned on the savings account by the end of the year is $4.50.

To calculate the amount of money earned on a savings account with a given Annual Percentage Rate (APR), we can use the formula:

Interest = Principal x Rate x Time

where:

Principal is the initial amount of money in the account

Rate is the annual interest rate (as a decimal)

Time is the length of time the money is invested (in years)

In this case, the principal is $100, the rate is 4.50% per year (or 0.045 as a decimal), and the time is one year. Therefore, the interest earned can be calculated as:

Interest = $100 x 0.045 x 1

Interest = $4.50

So, the amount of money earned on the savings account by the end of the year is $4.50.

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Answer:

$510,000

Step-by-step explanation:

Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.

Remember, 4 or less, round down. 5 or more, round up.

Since the hundreds digit is 4, we do not need to round.

We only need to change the rest of the digits to 0.

So, our answer would be $510,000.

The area of trapezium CDEF is 30 cm².

The area of a trapezium is given by the formula:

Area = (1/2) x (sum of parallel sides) x (distance between the parallel sides)

where;

So the area of trapezium CDEF is calculated as;

A = ¹/₂ (CD + EF ) x CF

where;

DC= 9 - CB

CB  = 20 - (FA + CF + AB )

CB= 20 - ( 6 + 6 + 6 )

CB= 2

DC = 9 - 2 = 7 cm

A = ¹/₂ (7 + 3 ) x 6

A = 30 cm²

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This means that the line represented by f(x-3) has been shifted down by 39 units compared to the line represented by f(x).

In mathematics, the term "Y-intercept" refers to the point at which a graph or line intersects the y-axis. It is the value of the dependent variable (usually represented by "y") when the independent variable (usually represented by "x") is equal to zero.

For example, the equation of a straight line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept is the value of y when x is equal to zero.

So, if the equation of a line is y = 2x + 5, then the y-intercept is 5, because this is the value of y when x is equal to zero.

To simplify f(x-3), we need to substitute x-3 for x in the expression for f(x):

[tex]f(x-3) = 10(x-3) - 9[/tex]

Expanding the multiplication and simplifying, we get:

[tex]f(x-3) = 10x - 30 - 9[/tex]

[tex]Therefore, f(x-3) = 10x - 39.[/tex]

To determine the slope, we can compare this expression to the standard form of a linear equation, y = mx + b, where m is the slope. We can see that the coefficient of x in the simplified expression is 10, so the slope is 10. This means that the line represented by f(x-3) is steeper than the line represented by f(x).

To determine the y-intercept, we can look at the constant term in the expression. In this case, the constant term is -39. This means that the line represented by f(x-3) has been shifted down by 39 units compared to the line represented by f(x).

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