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 standard fοrm οf the quadratic functiοn is Y = -4(x + 2.5)² + 121

Standard Fοrm: the standard fοrm οf a line is in the fοrm Ax + By = C where A is a pοsitive integer, and B, and C are integers

First, let's expand the expressiοn:

Y = -4(x-3)(x+8)

Y = -4(x² + 8x - 3x - 24)

Y = -4x² - 20x + 96

Y = ax² + bx + c

where a, b, and c are cοnstants.

Tο dο this, we can factοr οut the -4 frοm the first twο terms:

Y = -4(x² + 5x) + 96

Y = -4(x² + 5x + 6.25 - 6.25) + 96

Simplifying the first three terms inside the parentheses, we get:

Y = -4((x + 2.5)² - 6.25) + 96

Expanding the -4 and simplifying, we get:

Y = -4(x + 2.5)² + 121

Therefοre, the standard fοrm οf the quadratic functiοn is:

Y = -4(x + 2.5)² + 121

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The polynomial 7x² - 4 + 6x³ - 4x - x⁴ in standard form is - x⁴ + 6x³ + 7x² - 4x - 4  

Given that

7x² - 4 + 6x³ - 4x - x⁴

The standard form of a polynomial is when the terms are arranged in decreasing order of degree

To rewrite 7x² - 4 + 6x³ - 4x - x⁴ in standard form, we need to rearrange the terms accordingly:

- x⁴ + 6x³ + 7x² - 4x - 4  

Now the terms are in decreasing order of degree, with the highest degree term first

This is the standard form of the polynomial.

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Answer:

1 4/5

Step-by-step explanation:

Answer:

∠D, ∠C, ∠E

Step-by-step explanation:

"The angle opposite to the shortest side is the smallest angle and the side opposite to the longest side is the largest angle."

Therefore, the coordinates of point S after a dilation with the center at the origin and scale factor of 1/2 are (4, -2).

In mathematics, a factor is a number or expression that divides another number or expression without leaving a remainder. For example, 2 and 3 are factors of 6 because 6 can be divided by 2 and 3 without leaving a remainder. In algebra, factors are often used to factorize an expression, which involves breaking it down into its constituent factors. This is a useful technique for simplifying algebraic expressions, solving equations, and finding common factors in polynomials. Factors are also important in number theory, where they are used to study properties of integers and prime numbers.

Given by the question.

To perform a dilation with the center at the origin and scale factor of 1/2, we need to multiply the coordinates of the point by the scale factor.

The coordinates of point S are (8, -4).

After dilation, the x-coordinate will be 1/2 of 8, and the y-coordinate will be 1/2 of -4:

x' = (1/2) * 8 = 4

y' = (1/2) * (-4) = -2

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Answer:

x > 3

Step-by-step explanation:

This is an open circle, meaning there will be no equal sign.

The line is going to the right of 3, meaning x > 3

So, our inequality is x > 3

It is true that the events a and b, relating to Tina being the first woman to finish the 2020 Boston Marathon and the 2021 New York Marathon, are independent.

Independent events are events where the occurrence or non-occurrence of one event does not affect the probability of the occurrence or non-occurrence of the other event. In other words, the outcome of one event has no impact on the outcome of the other event.

In the context of this problem, the outcome of one marathon has no bearing on the outcome of another marathon, hence it is true that the events a and b are independent.

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The probability that the sample mean is greater than 52 is 5.5%.

Given population mean (μ) = 50 and standard deviation (σ) = 10Sample size (n) = 64 Sample mean (X-bar) = 52The formula for finding the probability of a sample mean is greater than a given value is:

P ( X-bar > 52 ) = P ( z > (52-50) / (10/√64) ) = P ( z > 1.6 )The formula for finding the probability of z-score is:

P ( z > 1.6 ) = 1 - P ( z < 1.6 )Now, we need to find the value of P ( z < 1.6 ) from the standard normal distribution table.P ( z < 1.6 ) = 0.9452 (approx)Now, substitute this value in the above equation, we get:

P ( z > 1.6 ) = 1 - 0.9452 = 0.0548 .Therefore, the probability that the sample mean is greater than 52 is 0.0548 or approximately 5.5%.

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The amount of water that the pitcher contained before Mai added more water was 7.8 liters.

Let x be the amount of water the pitcher contained before Mai added more water.

When Mai poured 2.6 liters of water, the total amount of water in the pitcher became x + 2.6 liters.

According to the problem, the pitcher then contained 10.4 liters of water. Therefore, we can write:

x + 2.6 = 10.4

Subtracting 2.6 from both sides, we get:

x = 7.8

Therefore, the pitcher contained 7.8 liters of water before Mai added more water.

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Caden's speed is 10 mph and Rahquez's speed is 16 mph faster, which is 16+6 = 32 mph

Let's use the formula: distance = rate x time

Since Caden and Rahquez are traveling towards each other, their combined distance will be 208 miles. Let's call Caden's speed "x" and Rahquez's speed "x+6", since Rahquez is traveling 6 mph faster than Caden.

Using the formula above, we can set up the equation:

208 = (x + x + 6) * 8

Simplifying, we get:

208 = (2x + 6) * 8

208 = 16x + 48

160 = 16x

x = 10

Therefore, Caden's speed is 10 mph and Rahquez's speed is 32 mph.

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Answer:

The answer is

-7/8 + 3/10

Step-by-step explanation:

See the picture

Hope you understand :)

The 4 is the number the student thought about.

To solve this problem, we will use algebraic expressions. First, let us define the unknown number, x. The problem states that "4 times my number increased by 30 equals 70 decreased by the number." This can be translated into the following equation:

4x + 30 = 70 - x

To solve for x, we need to isolate it on one side of the equation. Let's start by moving all the terms with x to the left side and all the constant terms to the right side.

4x + x = 70 - 30x + 4x + x = 40

Simplifying, we get:

10x = 40

Dividing both sides by 10:

x = 4

Therefore, the number that the student thought of is 4.

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Answer:

A circle has 360 degrees, so 5/6 of the circle can be found by multiplying 360 by 5/6:

5/6 of 360 = (5/6) × 360 = 300

Therefore, the angle measures of 5/6 of the circle is 300 degrees.

Answer:

Step-by-step explanation:

everything is resolved with the expression:

20^2 x 6 = 2400 cm^2

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:

Yes, Justin bought enough

Step-by-step explanation:

if there are 14 screws in a packet and Justin buys 5, all we have to do is multiply 14 x 5

14 x 5 = 70

So Justin bought 2 extra

There are 816 possible five-card hands from a normal deck of cards containing exactly two aces and having exactly two red cards.

There are 80 possible five-card hands from a standard deck of 52 cards that contain exactly two aces and have exactly two red cards.

To calculate this, first count the total number of combinations of two aces from the four aces in the deck. This can be done using the combination formula C(n, r) where n is the number of items (4 aces) and r is the number of items to choose (2 aces). Therefore, the number of combinations of two aces is C(4,2) = 6.

Next, count the number of combinations of two red cards. There are 26 red cards in a deck, which can be divided into the two suits of spades and hearts. For each of these suits, calculate the number of combinations of two cards using the same formula as before, C(n, r). Therefore, the number of combinations of two red cards is C(13,2) * 2 = 156.

Finally, multiply the two values together to get the total number of possible five-card hands with exactly two aces and two red cards. This equals 6 * 156 = 960. This value must be reduced by the number of hands that contain more than two aces and/or more than two red cards. This value can be calculated using the same formula. For instance, the number of hands with three aces is C(4,3) * C(13,2) * 2 = 144. This value must be subtracted from 960, leaving a total of 960 - 144 = 816.

Therefore, there are 816 possible five-card hands from a normal deck of cards containing exactly two aces and having exactly two red cards.

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Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by Free Operant Preference Assessment.

What is a free operant preference assessment? Free operant preference assessment refers to a behavior analysis process used to determine the preferred stimulus of an individual in a naturalistic environment. This method measures the potential and meaningful reinforcers through the observation of a child's free time. A reinforcement is a consequence that strengthens a behavior.The free operant preference assessment is frequently utilized in the autism field to identify reinforcing stimuli. It is a process of assessing a child's preferred items and actions in a naturalistic setting.The free operant preference assessment is conducted in three different stages: Stage 1: involves observation of preferred items and items that are likely to become potential reinforcers, Stage 2: involves assessing for a hierarchy of items and stage 3 involves using the data gathered to plan the student’s schedule, including reinforcement and non-contingent time periods.

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FREE OPERANT PREFERENCE ASSESSMENT. Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by Free Operant Preference Assessment.

A free operant preference assessment is a measure of the attractiveness or preference for various stimuli by measuring an individual's time spent with them.

Free access to different stimuli is given to the individual to determine their preferences, which are subsequently used to reinforce the desired behavior or work on behavior modification through behavior analysis.

The steps to conducting a Free Operant Preference Assessment: Prepare the list of stimuli: Initially, you have to prepare a list of stimuli that you believe may act as a reinforcer for the individual, which may include toys, foods, or other things that the person likes.

Prepare the environment: Arrange the stimuli in a room, and let the individual enter it.

Make sure that there is sufficient space to move around and that the person has free access to all of the stimuli.  

Record the time the individual spends with each stimulus. You can observe the person, either directly or through video recording.

 Based on the data obtained, the most preferred and least preferred stimuli can be identified. Then, these preferred stimuli can be used as potential reinforcers.

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The given statement " the null hypothesis predicts there is a relationship between the variable and a significant difference between the groups." is False because the null hypothesis predicts that there is no relationship between the variables and no significant difference between the groups.

A null hypothesis is a statement that suggests that no relationship exists between two variables. It serves as the baseline assumption and a starting point for researchers to test their alternative hypothesis.

Null hypothesis testing is a statistical method used to compare two mutually exclusive propositions: the null hypothesis and the alternative hypothesis.

In hypothesis testing, the null hypothesis states that there is no significant difference between two groups, while the alternative hypothesis suggests that there is a significant difference between the two groups.

If the observed data deviates significantly from what we would expect under the null hypothesis, we reject it in favor of the alternative hypothesis.

If the observed data does not significantly deviate from what we would expect under the null hypothesis, we fail to reject it.

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We should expect the lahar to arrive at your location at 3:30 pm if we travel down the sandy river at 40 miles an hour.

The given data is as follows:

Length of river = 20 miles

Time = 3 pm

Speed = 40 miles an hour

To calculate the time, we need to use the formula,

Time required = (distance/speed)

It is given that the distance between Mount Hood and your location is 20 river miles, and the speed of the lahar is 40 miles per hour. Therefore, the time it will take for the lahar to arrive is calculated as:

Time required = distance/speed

Time required = 20 miles / 40 miles per hour

Time required = 0.5 hours = 30 min

to determine the expected arrival time at your location,

Total time required = 3.00 + 0.30  =  3.30 pm.

Therefore we can conclude that we should expect the lahar to arrive at your location at 3:30 pm.

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Answer:

Step-by-step explanation:

Given diameter of a beach ball is d=10 inches.Let us find the radius of the beach ball:d=2 r10=2×rr=102∴r=5Therefore, the radius of a beach is 5 inches.Let us find the volume of air contained inside the beach ball:V=43 π×r3=43 π×53=43 π×125=500π3∴V=523.59877Therefore, the volume of air contained inside the beach ball is approximately 523.6 in3.

Answer:

The formula for the volume of a sphere is:

V = (4/3)πr³

We can rearrange this formula to solve for the radius (r):

r = [(3V) / (4π)]^(1/3)

where V is the volume of the sphere.

Substituting the given volume of the beach ball, we get:

r = [(3 × 10,332 in³) / (4 × 3.14)]^(1/3)

r = 10.27 in

Rounding to the nearest tenth, the approximate radius of the beach ball is 10.3 inches.

    the baker needs 15 gallons of milk to make 80 chocolate pies for the community festival. To translate the phrase "9r subtract three fifths greater than 3 and 9 tenths" into an expression, we first need to understand what it's asking us to do.  

  "Three fifths greater than 3 and 9 tenths" means we need to add 3 and 9 tenths to three fifths of 3. Three fifths of 3 is 1.8 (since 3/5 * 3 = 9/5 = 1.8), so we can write:

3 + 9/10 + 1.8

We can simplify this to a single mixed number by adding the whole numbers and the fractions separately:

3 + 1 + 8/10 + 8/5

= 4 + 1 3/5

= 5 3/5

So "three fifths greater than 3 and 9 tenths" is equal to 5 3/5.

Now we can subtract this value from 9r:

9r - 5 3/5

We can simplify this expression further by converting 5 3/5 to a fraction with a common denominator of 5:

9r - 5 3/5 = 9r - (28/5) = (45/5)r - (28/5) = (9r - 28) / 5

So the final expression is:

(9r - 28) / 5

In summary, "9r subtract three fifths greater than 3 and 9 tenths" can be translated to the expression (9r - 28) / 5. This expression represents a quantity that is 9 times "r" minus 5 3/5. We can simplify this expression further by converting the mixed number to an improper fraction and combining the terms, as shown above.

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Answer:

Step-by-step explanation:

A. 5, 2, 2, 5 is a prime factorization of 100 since 5 and 2 are prime factors of 100 and multiplying them gives 100.

B. 2, 5, 10 is not a prime factorization of 100 since 10 is not a prime factor of 100.

C. 5, 10, 2 is not a prime factorization of 100 since 10 is not a prime factor of 100.

D. 5, 2, 5, 2 is not a prime factorization of 100 since it can be simplified as 5x2x5x2 = 100, but it is not a unique prime factorization.

Therefore, the correct answer is A. 5, 2, 2, 5.

1)

A line that fits the whole data set the best.

2)

The line of best fit is y = 5.1 + 0.5x

3)

The equation of best fit is T = 39.6 + 0.225r

4)

The slope of the line of best fit is -0.531.

5)

From the table, it is clear that the s-intercept would be positive.

Barrett's line would have a negative intercept because the slope is negative.

The line of best fit is a straight line that represents the trend or pattern in a set of data. It is also known as the regression line.

This line is determined by analyzing the data and finding the line that comes closest to all of the points in the set. T

We have,

1)

The line of best fit is the line that fits the whole data set the best.

It's the line that comes closest to all of the points in the data set, and it can be used to make predictions or to describe the relationship between the two variables in the data set.

2)

To find the line of best fit, we need to calculate the slope and y-intercept of the line.

Using the least squares method, we find that the slope is 0.5 and the y-intercept is 5.1.

Therefore, the equation of the line of best fit to predict y from x is y = 5.1 + 0.5x.

3)

To find the equation of the line of best fit, we need to calculate the slope and y-intercept of the line.

Using the least squares method, we find that the slope is 0.225 and the y-intercept is 39.6.

Therefore, the equation of the line of best fit to predict T from r is T = 39.6 + 0.225r.

4)

To find the slope of the line of best fit, we need to calculate the covariance and variance of the x and y variables.

Using the least squares method, we find that the slope is -0.531.

5)

From the table, we can see that the s-intercept (the value of s when d is zero) would be positive.

Therefore, a line with a negative slope would have a negative y-intercept, which is not possible.

This means that Barrett's answer is incorrect, and the slope of the line of best fit must be positive.

Thus,

C. a line that fits the whole data set the best.

C. y = 5.1 + 0.5x

A. T = 39.6 + 0.225r

A. -0.531

A. From the table, it is clear that the s-intercept would be positive.

Barrett's line would have a negative intercept because the slope is negative.

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If the number of people arriving for treatment at an emergency room is modeled by a Poisson process with a mean of 5 people per hour, we can use this information to estimate the expected number of people who will arrive during a 45-minute period.

The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time, given the average rate at which the events occur. In this case, the Poisson distribution can be used to estimate the number of people who will arrive during a 45-minute period, given that the mean arrival rate is 5 people per hour.

To calculate the expected number of arrivals, we first need to convert the 45-minute time period into hours. There are 60 minutes in an hour, so 45 minutes is equivalent to 0.75 hours.

Next, we can use the Poisson distribution formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where λ is the mean arrival rate (in this case, 5 people per hour), k is the number of arrivals we are interested in, and e is Euler's number (approximately 2.71828).

Expected number of arrivals = λ * t = 5 * 0.75 = 3.75

Therefore, we can expect approximately 3.75 people to arrive for treatment during a 45-minute period, assuming that the number of arrivals follows a Poisson distribution with a mean of 5 people per hour.

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In a large population, 71% of the people have been vaccinated. if 5 people are randomly selected, 0.997 is the probability that at least one of them has been vaccinated.

To compute the probability that at least one of five people selected at random from a large population has been vaccinated if 71% of the population has been vaccinated.

We need to use the Complement Rule.

This rule tells us that the probability of event A not happening is equal to one minus the probability of event A happening.

P (A) + P (A') = 1

where P(A) is the probability of A happening and P(A') is the probability of A not happening.

We need to compute the probability that none of the five people selected at random have been vaccinated.

Then, we will use the Complement Rule to compute the probability that at least one of them has been vaccinated.

The probability that the first person selected has not been vaccinated is:

P(first person not vaccinated) = 1 - 0.71 = 0.29

The probability that the second person selected has not been vaccinated is:

P(second person not vaccinated) = 1 - 0.71 = 0.29

The probability that the third person selected has not been vaccinated is:

P(third person not vaccinated) = 1 - 0.71 = 0.29

The probability that the fourth person selected has not been vaccinated is:

P(fourth person not vaccinated) = 1 - 0.71 = 0.29

The probability that the fifth person selected has not been vaccinated is:

P(fifth person not vaccinated) = 1 - 0.71 = 0.29

We assume that the selections are made randomly and independently of one another.

Thus, we can multiply the probabilities to get the probability that none of the five people selected have been vaccinated:

P(none vaccinated) = 0.29 × 0.29 × 0.29 × 0.29 × 0.29 = 0.0028

We can use the Complement Rule to compute the probability that at least one of the five people selected has been vaccinated:

P(at least one vaccinated) = 1 - P(none vaccinated)P(at least one vaccinated)

= 1 - 0.0028P(at least one vaccinated)

= 0.9972

Thus, the probability that at least one of five people selected at random from a large population has been vaccinated is approximately 0.997 when rounded to three decimal places.

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1. m may be higher or lower than the population mean.
2. The value of m is not necessarily representative of the population mean.
3. The sampling distribution of m is not necessarily normal.
4. The mean, median, and mode of the sample may all be different.

Assuming that the population from which you select your sample is not normal, the following statements about m (the mean of the sample) are true:
1. m may be higher or lower than the population mean.
2. The value of m is not necessarily representative of the population mean.
3. The sampling distribution of m is not necessarily normal.
4. The mean, median, and mode of the sample may all be different.

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When a population is not normal, it means that the distribution of the data is not symmetric and has non-uniform spread.

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Answer:

To find the vertex and x-intercepts for the quadratic function f(x)=4.9x^2-28x+40:

First, we can find the x-coordinate of the vertex using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function.

In this case, a = 4.9 and b = -28, so:

x = -(-28)/2(4.9) = 2.86

Next, we can find the y-coordinate of the vertex by plugging in this x value into the original function:

f(2.86) = 4.9(2.86)^2 - 28(2.86) + 40 = 6.65

So the vertex is at (2.86, 6.65).

To find the x-intercepts, we can set the function equal to zero and solve for x:

4.9x^2 - 28x + 40 = 0

We can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the coefficients, we get:

x = (28 ± sqrt(28^2 - 4(4.9)(40))) / 2(4.9)

Simplifying:

x = (28 ± sqrt(144.4)) / 9.8

x = 5.36 or 1.43

So the x-intercepts are (5.36, 0) and (1.43, 0).