Use the following information to answer the next five exercises. a hospital is trying to cut down on emergency room wait times. it is interested in the amount of time patients must wait before being called back to be examined. an investigation committee randomly surveyed 70 patients. the sample mean was 1.5 hours with a sample standard deviation of 0.5 hours

Answer:

B

1,4,6,4,1

Step-by-step explanation:

(x+y)^4

x^4+ 4x^3y+ 6x^2y^2+ 4xy^3+ y^4

the coefficients are :1,4,6,4,1

Answer:

3q +9

Step-by-step explanation:

3(q +3)

Distribute

3q+3*3

3q +9

Answer:

\(3q+9\)

Step-by-step explanation:

\(3(q +3)\)

\(3(q) +3(3)\)

\(3q+9\)

Therefore, the probability that more than 35% of the 30 Americans in the sample concur that climate change is a serious threat to humanity is 0.5 or 50%.

The main goal of the mathematical branch known as statistical inference is to estimate the likelihood that a statement is accurate or that a particular event will take place. Any number among 0 and 1, where 1 typically denotes confidence and 0 typically denotes possibility, can be used to symbolise chance.A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

The problem specifies a sample size of n = 30 and a success chance of p = 0.35.

We want to determine the likelihood that the percentage of the 30 Americans sampled who believe that climate change poses an immediate danger to humanity exceeds 35%.

P(p-hat > 0.35)

where p-hat is really the percentage of sample respondents who concur that climate change poses a direct danger to humanity.

The sample proportion P-hat has a standard variation of and a mean of 0.35, both of which are within the normal distribution.

√(p*(1-p)/n) = √(0.35*(1-0.35)/30) = 0.089 is the formula for standard deviation.

As a result, the sample percentage can be standardised as follows:

Standard deviation = (p-hat -0.35) / 0.089 and z = (p-hat - p)

We can also determine the chance as follows:

P(z > (0.35 - 0.35) / 0.089) = P(z > 0) = P(p-hat > 0.35)

Therefore, the likelihood that more than 35% of the 30 Americans in the sample concur that climate change is a serious threat to humanity is 0.5 or 50%.

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The new point will be located at the coordinate (7,8)

Patterns are simply the procedures and the rules that are followed to create a sequence.

From the graph, we have the following highlights

Using the above pattern, the new point will be located at the coordinate (7,8)

See attachment for the next position

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The probability that the firm receives 2 or more complaints in a day is 0.33.

This can be calculated using the Poisson distribution formula. The Poisson distribution is a probability distribution used to calculate the probability of an event occurring a given number of times in a fixed interval of time or space.

It is based on the assumption that the rate of occurrence of an event is constant.

In this case, we are looking at the probability of the firm receiving 2 or more complaints in a day. Let x = 2, where x is the number of complaints in a day. Then, the Poisson distribution formula is: P(x) = (e-λ λx) / x!

Where e = 2.71828 and λ = 3 (the rate of complaints per day).

Plugging in the values, we get: P(2) = (2.71828-3 * 32) / 2! = 0.33. Therefore, the probability that the firm receives 2 or more complaints in a day is 0.33.

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I'm pretty sure the answer is 1/15 or 4/60 because the whole carpet measures 60m and the covered part's area is 4m and that would be 4/60 but simplified 1/15.  Sorry if this is wrong!

To find the fraction of the carpet covered by the rug, we need to determine the area of the rug and divide it by the total area of the carpet.

The area of the square rug can be calculated by squaring its side length: 2m x 2m = 4m². The total area of the rectangular carpet can be found by multiplying its length and width: \(12m x 5m = 60m²\). To find the fraction, divide the area of the rug by the area of the carpet: 4m² / 60m².

To simplify the fraction, we can find the greatest common divisor (GCD) of 4 and 60, which is 4. Dividing both the numerator and denominator by the GCD, we get: \(4m² ÷ 4 / 60m² ÷ 4 = 1m² / 15m²\) . Therefore, the fraction of the carpet covered by the rug is 1/15, which means that 1/15th of the carpet is covered by the rug.

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Answer: 1. 35 5/6 - 4 1/2

2. 1 5/8 - 2/3

3. 1 5/8 + 2/3

4. 35 5/6+4 1/2

Step-by-step explanation:

1. E=Eli. J=Jamison

E=J+4 1/2

35 5/6=J+4 1/2

J=35 5/6 - 4 1/2

2. s=cups of strawberries

b=cups of blueberries

m=more cups of b than s

m=b-s

m=1 5/8 - 2/3

3. o=original length of patio.

i=increase in length of patio

t=total length of patio after increase.

o+i=t

1 5/8 + 2/3=t

4. p=pine tree. a=palm tree. i=inches taller

p+i=a

35 5/6+4 1/2=a

To determine the number of engines that would produce the most revenue for the firm, we need to find the quantity at which the marginal revenue equals zero.

In this case, the marginal revenue is the derivative of the revenue function with respect to the quantity of engines sold.

The revenue for the firm can be calculated by multiplying the quantity of engines sold (q) by the price per engine (p). From the given formula, the price per engine is p = 200 - 2q.

The revenue function, R, can be expressed as R = q * p. Substituting the price formula, we have R = q * (200 - 2q).

To find the quantity that maximizes revenue, we differentiate the revenue function with respect to q, set it equal to zero, and solve for q.

Taking the derivative of R with respect to q, we get dR/dq = 200 - 4q.

Setting dR/dq = 0, we have 200 - 4q = 0. Solving for q, we find q = 50.

Therefore, the firm would generate the most revenue by selling 50 engines to its main client.

At this quantity, the price per engine would be p = 200 - 2(50) = 100 thousand dollars. The total revenue would be R = 50 * 100 = 5000 thousand dollars.

Selling more than 50 engines would result in a decrease in revenue due to the declining price per engine as per the pricing formula.

Selling fewer than 50 engines would also result in a lower revenue due to the missed opportunity to sell more engines at a higher price. Thus, 50 engines is the optimal quantity for maximizing revenue for the firm.

Therefore, selling 50 engines would produce the most revenue for the firm.

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4.82 × 10⁻⁴

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

4.82 x 10^-4

Step-by-step explanation:

8.2 x 10^-4 + .0004= enter into calculator

.000482, move decimal behind first whole number and count places

it moves 4 spaces and because it starts in front of the number your exponent is negative

Answer:

1 m^3

Step-by-step explanation:

Assume hight 4 and ength 4.

2, 1, 1 = 1

Answer:

-14 x -4

Step-by-step explanation:

i did the quiz lol

Answer:

A

Step-by-step explanation:

took the quiz, hope this helps.

Answer: with the discount it'll be $33 and with 6.5% tax it'll be $35.15

Answer:

See explanation

Step-by-step explanation:

( unit 1 ) multiplied by ( unit 2 )

(5.9*10^12) multiplied by 8.9
52.51*10^12 or 5.251*10^13 or 52,510,000,000,000

Answer:

ok here just look at then image i put.

Signature --- INSTA: rowwman

The range or the given data is calculated as 10.2 . Range is the difference between minimum value and maximum value.

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we can make use of the formula for range in statistics which is given as follows:[\large Range = Maximum\ Value - Minimum\ Value\]

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we need to arrange the data in either ascending or descending order, but since we only need to find the range, it is not necessary to arrange the data.

From the data given above, we can easily identify the minimum value and maximum value and then find the difference to get the range.

So, Minimum Value = 1.0

Maximum Value = 11.2

Range = Maximum Value - Minimum Value

                  = 11.2 - 1.0

                     = 10.2

Therefore, the range of the given data is 10.2.

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Step-by-step explanation:

I think there is a mistake in the problem description.

f and p are for the price of 1 yards fencing and 1 post.

and not the amounts.

because the problem description gives us the amounts already (30+8 yards fencing and 4 posts).

based on the 8 more yards of fencing for $256 we know that 1 yard of fencing costs $32.

we know from the beginning

30f + 4p = 1040

and again

8f = 256

f = $32

now using that in the first equation

30×32 + 4p = 1040

960 + 4p = 1040

4p = 80

p = $20

he bought first 30 and then additional 8 yards of fencing for $32 per yard, and 4 posts for $20 per post.

altogether he had to pay 1040+256 = $1296

The volume of the solid generated by revolving the plane region y = 2 - x about the x-axis can be represented by the definite integral ∫[0,2] π(2 - x)² dx.

To find the volume using the shell method, we integrate along the x-axis. The height of each shell is given by the function y = 2 - x, and the radius of each shell is the distance from the axis of revolution (x-axis) to the corresponding x-value.

The limits of integration are from x = 0 to x = 2, which represent the x-values where the region intersects the x-axis. For each x-value within this interval, we calculate the corresponding height and radius.

∫[0,2] π(2 - x)² dx

= π ∫[0,2] (2 - x)² dx

= π ∫[0,2] (4 - 4x + x²) dx

= π [4x - 2x² + (1/3)x³] evaluated from 0 to 2

= π [(4(2) - 2(2)² + (1/3)(2)³) - (4(0) - 2(0)² + (1/3)(0)³)]

= π [(8 - 8 + (8/3)) - (0 - 0 + 0)]

= π [(8/3)]

= (8/3)π

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Maryam received a 71% overall exam percentage score due to her performance on Paper 1, which is worth more points than Paper 2.

We must determine the weighted average of Maryam's results on each paper in order to determine her overall exam % score. We may weight Maryam's results appropriately since Paper 1 accounts for 60% of the total marks and Paper 2 for 40% of the total marks:

Overall percentage score: (65%) = 0.6; (80%) = 0.4.

= 0.6 × 0.65 + 0.4 × 0.80 (converting percentages to decimals) (converting percentages to decimals)

= 0.39 + 0.32

= 0.71

Maryam received a 71% overall exam percentage score as a result. Thus, she performed 71 out of 100 in the test. Given that Paper 1 is worth more points than Paper 2, Maryam's performance on Paper 1 will have a bigger impact on her final score because of the weightings utilized in this computation.

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Complete question is:

An exam is made of two papers that score differently.

Paper 1 has 120 marks.

Paper 2 has 80 marks.

Maryam scores:

65% on Paper 1

80% on Paper 2

Work out Maryam TOTAL percentage score for the exam. You must show your working

Answer:

C

Step-by-step explanation:

C is the only one that matches the data.
C displays an appropriate radius for the data containing 3.1, 3.4, 3.1, 3.9, 4.0, 2.5, 2.8, 3.1, 2.9, 3.6

Answer:

angle x is 60 degrees

Step-by-step explanation:

Complementary angles means the sum of the angles is 90 degrees, so if angle x decreases, angle y must increase.

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

a) The forecast is approximately miles. b) the Mean Absolute Deviation (MAD) based on the forecast is approximately miles. c) The forecast for year 6 is approximately miles. d) the last forecast is 3,468 miles.

a) To calculate the forecast for year 6 using a 2-year moving average, we take the average of the mileage for years 5 and 4. This provides us with the forecasted value for year 6.

b) The Mean Absolute Deviation (MAD) for the 2-year moving average forecast is calculated by taking the absolute difference between the actual mileage for year 6 and the forecasted value and then finding the average of these differences.

c) When using a weighted 2-year moving average, we assign weights to the most recent and previous periods. The forecast for year 6 is calculated by multiplying the mileage for year 5 by 0.40 and the mileage for year 4 by 0.60, and summing these weighted values.

The MAD for the weighted 2-year moving average forecast is calculated in the same way as in part b, by taking the absolute difference between the actual mileage for year 6 and the weighted forecasted value and finding the average of these differences.

d) Exponential smoothing involves assigning a weight (α) to the most recent forecasted value and adjusting it with the previous actual value. The forecast for year 6 is calculated by adding α times the difference between the actual mileage for year 5 and the previous forecasted value, to the previous forecasted value.

In this case, with α=0.20 and a forecast of 3,100 miles for year 1, we perform this exponential smoothing calculation iteratively for each year until we reach year 6, resulting in the forecasted value of approximately 3,468 miles.

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The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.

Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:

= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3

= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]

= (1/3) × [(9/2 + 6) - 0]

= (1/3) × (21/2)

= 7/2

Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

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The probability that a five-card poker hand does not contain the queen of hearts is 47/52.

We have been given that,

Total card to choose = 5

Total cards in a deck = 52

We need to find the probability that a five-card poker hand does not contain the queen of hearts.

The total ways of choosing 5 cards from a deck of 52 cards = \(^{52}C_5\)

The number of queens of hearts in a deck = 1

The number of cards excluding queens of hearts = 52 - 1

                                                                                  = 51

The total ways of choosing 5 cards from 51 cards = \(^{51}C_5\)

Now we find the required probability.

\(\Rightarrow P= ^{51}C_5 \times ^{52}C_5\\\\\Rightarrow P=\frac{51!}{5!(51-5)!} ~\times \frac{52!}{5!(52-5)!}\\\\\Rightarrow P=\frac{47}{52}\)

Therefore, the probability that a five-card poker hand does not contain the queen of hearts is 47/52.

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The price of the article tomorrow will be #4.95.

If an article cost #5 yesterday and has risen by 10% today, it will now cost #5.50. To calculate the price tomorrow, we need to consider that the price will fall by 10%.

To do this, we can first calculate what 10% of #5.50 is, which is #0.55. This means that the price will fall by #0.55 tomorrow, bringing the price down to #4.95.

Therefore, the price of the article tomorrow will be #4.95. This calculation highlights the importance of understanding the impact of percentage changes on prices and how they can impact the overall cost. It also demonstrates the need for individuals to be aware of such changes when making financial decisions.

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Answer:

Sherly's Plumbing is : f(x) = 43x + 30 and Howard's Plumbing is f(x) = 28x + 24

sherly's f(7) = 331 and Howard's f(7) = 220