what is the probability that there will be fewer than 2 arrivals in a given minute?

The 95% confidence interval for the mean tip percentage at the restaurant, using the Restaurant Tips dataset, is (x).  The 95% confidence interval for the mean tip percentage at the restaurant using the RestaurantTips dataset cannot be determined without access to the dataset.

To determine the 95% confidence interval for the mean tip percentage at the restaurant, we can use statistical analysis techniques. However, since the RestaurantTips dataset is not available for reference, we cannot provide an exact confidence interval.

Typically, to calculate a confidence interval, we need the sample mean, standard deviation, sample size, and the level of confidence. The sample mean represents the average tip percentage, the standard deviation indicates the variability of the data, and the sample size determines the precision of the estimate. The level of confidence, in this case, is 95%.

Using the available data, one could calculate the mean and standard deviation of tip percentages and then apply the appropriate statistical formula to compute the confidence interval. However, without access to the dataset, we cannot provide the specific values or calculate the interval.

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The Factoring Trinomials calculator is an incredibly useful tool for those studying mathematics. It can be used to quickly and easily factor any trinomial expression and find the sum of its terms.

All a user needs to do is enter the coefficients of the trinomial into the calculator, and the calculator will display the factors of the expression. This is a great resource for anyone looking to save time on their math homework and practice problems.

It is also a great way to check one’s own work and make sure the answer is correct. The calculator is also easy to use, so anyone with basic math skills can use it. With the Factoring Trinomials calculator, anyone can quickly and easily factor any trinomial expression and find the sum of its terms.

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Answer:

see explanation

Step-by-step explanation:

(a + b)²

= (a + b)(a + b)

Each term in the second factor is multiplied by each term in the first factor, that is

a(a + b) + b(a + b) ← distribute parenthesis

= a² + ab + ab + b² ← collect like terms

= a² + 2ab + b²

Answer:

(a+b) is squared which means (a+b)(a+b)

Lets prove it

= (a+b)(a+b)

= a(a+b) + b(a+b) (Here a will mutiply by (a+b) and b will mutiply with (a+b)

= a²+ab + ab + b²

= a²+ 2ab + b²

Hence proved (a+b)² = a²+ 2ab + b²

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Answer:

12

Step-by-step explanation:

that is because 20 of 60 is 12

60X20/100=12

Answer:

Step-by-step explanation:

when x = 5

then

6 + 2x

= 6 + 2*5

= 6 + 10

= 16

Answer:

y = 1/3x + 8/3

Step-by-step explanation:

The slope of a line that is perpendicular to the line y = -1/3x + 7 is the negative reciprocal of the slope of the given line, which is -3. So, the slope of the perpendicular line is 1/3.

The point where the perpendicular line intersects the given line is also the point where the two lines intersect, which is (4,2) in this case. So, we can use this point to find the equation of the perpendicular line using the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1,y1) is a point on the line.

In our case, the equation of the perpendicular line is:

y - 2 = 1/3(x - 4)

We can simplify this equation to obtain:

y = 1/3x + 8/3

Therefore, the equation of the perpendicular line is y = 1/3x + 8/3.

Answer:

24

Step-by-step explanation:

RSM

the next number in the series is 17.

The given series of numbers is a sequence of prime numbers. To find the next number, we need to identify the next prime number after 13.

The next prime number after 13 is 17.

what is series?

In mathematics, a series is the sum of the terms of a sequence. It is a sequence of numbers that are added together in a specific order. Each term in the series is typically obtained by applying a rule or formula to the preceding terms.

For example, the series 1 + 2 + 3 + 4 + 5 + ... is the sum of all positive integers. In this case, the terms of the series are generated by adding the next positive integer to the sum of the previous terms.

Series can be finite, meaning they have a specific number of terms, or they can be infinite, meaning they continue indefinitely.

Series are an important concept in mathematics and have applications in various fields such as calculus, number theory, and probability.

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The statement that is false of quadrilaterals is C. Adjacent angles in a parallelogram are complementary.

In the tapestry of geometrical relationships, adjacent angles within a parallelogram are not bestowed with the nature of complementarity. Rather, they exhibit a distinct quality known as supplementary.

Unlike the enchanting dance of complementary angles, which combine to form a sum of 90 degrees, adjacent angles in a parallelogram intertwine their measures to yield a sum of 180 degrees. The allure of the parallelogram resides in the congruence of its opposite angles, not the complementarity of its adjacent angles.

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Answer:

The length of the banner is 24 inches and its width is 4 inches.

Step-by-step explanation:

Let the length of the banner be L.

Let the width of the banner be W.

The length is 6 times greater than the width. This means that:

L = 6W

The area of the banner is:

A = L * W = 6W * W = \(6W^2\)

The are of the banner is 96 square inches. This implies that:

\(6W^2\) = 96

=> \(W^2\) = 96 / 6 = 16

W = \(\sqrt{16}\)

W = 4 inches

The length, L, will be:

L = 6 * 4 = 24 inches

The length of the banner is 24 inches and its width is 4 inches.

Answer:

I believe it's A, but I may be wrong. I am sorry if I'm wrong.

Answer:

-8, -3 ,2, 4

Step-by-step explanation:

hope it helps

The value of dy/dt is -2.625 and The value of dx/dt is 0.5833. The derivative of the function h(s) = -4√s by the limit process is h'(s) = -2/√s The following parts can be solved by the concept of Differentiation.

For the first problem, we are given that x and y are both differentiable functions of t, and the equation x^2 + y^2 = 225 holds true. We need to find the values of dy/dt and dx/dt at certain points.

In part (a), we are given x = 9, y = 12, and dx/dt = 7, and we need to find dy/dt. In part (b), we are given x = 12, y = 7, and dy/dt = -2, and we need to find dx/dt.

In the second problem, we need to find the derivative of the function h(s) = -4√s using the limit process.

(a) To solve part (a), we can differentiate the given equation with respect to t using the chain rule as follows:

2x(dx/dt) + 2y(dy/dt) = 0

At x = 9, y = 12, and dx/dt = 7, we can substitute these values and solve for dy/dt:

2(9)(7) + 2(12)(dy/dt) = 0

dy/dt = -63/24 = -2.625

Therefore, the value of dy/dt is -2.625.

(b) To solve part (b), we can again differentiate the given equation with respect to t using the chain rule:

2x(dx/dt) + 2y(dy/dt) = 0

At x = 12, y = 7, and dy/dt = -2, we can substitute these values and solve for dx/dt:

2(12)(dx/dt) + 2(7)(-2) = 0

dx/dt = 14/24 = 0.5833

Therefore, the value of dx/dt is 0.5833.

For the third problem, we need to use the limit process to find the derivative of the function h(s) = -4√s. We start by writing the definition of the derivative:

h'(s) = lim(h -> 0) [h(s+h) - h(s)]/h

Substituting the function h(s) = -4√s, we get:

h'(s) = lim(h -> 0) [-4√(s+h) + 4√s]/h

Multiplying numerator and denominator by the conjugate expression, we get:

h'(s) = lim(h -> 0) [-4√(s+h) + 4√s][(√(s+h) + √s)/(√(s+h) + √s)]/h

Simplifying the numerator, we get:

h'(s) = lim(h -> 0) [-4h]/[h(√(s+h) + √s)]

Cancelling the h's, we get:

h'(s) = lim(h -> 0) [-4]/(√(s+h) + √s)

Substituting h = 0, we get:

h'(s) = -2/√s

Therefore, the derivative of the function h(s) = -4√s by the limit process is h'(s) = -2/√s

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Answer:

Lateral : 103.67 in²

Total : 864 in²

Step-by-step explanation: there you go

Answer:

25% increase

Step-by-step explanation:

Percentage increase = \(\frac{100-80}{80} * 100=\frac{20}{80} * 100 = 25%\)

a=1

Hope this helps

have a great day!

Step-by-step explanation:

Answer:

tuff

Step-by-step explanation:

Answer:

I think you would be right.

a) Rocky Mountain should order 200 tires each time it places an order.

b) The total cost of this policy is $17,160.

a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:

If fewer than 200 tires are ordered: The purchase price is $25 per tire.

If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.

If 8,000 or more tires are ordered: The purchase price is $13 per tire.

Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.

b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:

Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200

Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950

Therefore, the total cost of this policy is $40,950.

Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.

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Using cosine, we can find the hypotenuse by using the formula below;

hypotenuse = adjacent / cos ∅

Using cosine, the hypotenuse side can be solved as follows:

cosine ∅ = adjacent / hypotenuse

cross multiply

hypotenuse cos ∅ = adjacent

divide both sides by cos ∅

hypotenuse cos ∅ / cos ∅ = adjacent / cos ∅

Therefore,

hypotenuse = adjacent / cos ∅

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Answer:

It would be .841

Step-by-step explanation:

There are 1000 meters in a kilometer, and since 841 meters is 841/1000 kilometers, that is how many kilometers you would ride.

Hope this helps!

Answer: To solve for x and y, divide both of the numbers in the equation ONLY by the variable

Step-by-step explanation:

an example, 3y - 9, divide 3y and 9 by 3 the answer would be "y=3"

There are 15,120 ways to distribute the first, second, third, and two fourth prizes among the five different people in the group of nine.

To determine the number of ways to distribute the prizes, we can break down the process step by step: First Prize: There are 9 people in the group, and one of them can be chosen for the first prize. So there are 9 options for the first prize. Second Prize: After the first prize has been awarded, there are 8 remaining people who can be chosen for the second prize. So there are 8 options for the second prize. Third Prize: After the first and second prizes have been awarded, there are 7 remaining people who can be chosen for the third prize. So there are 7 options for the third prize.

Fourth Prizes: There are two fourth prizes to be given. After the first three prizes have been awarded, there are 6 remaining people. The first fourth prize can be given to any one of them, leaving 5 people for the second fourth prize. So there are 6 options for the first fourth prize and 5 options for the second fourth prize. Multiplying the number of options for each step together: Total number of ways = 9 * 8 * 7 * 6 * 5 = 15,120 . Therefore, there are 15,120 ways to distribute the first, second, third, and two fourth prizes among the five different people in the group of nine.

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The correct answer is (0.605,0.635). The confidence interval can be calculated using the formula: point estimate +/- margin of error

where the point estimate is the sample proportion (0.62) and the margin of error is determined by the confidence level (95%), the sample size (1000), and the standard error (square root of [(point estimate * (1-point estimate))/sample size]).

Plugging in the values, we get:

0.62 +/- 1.96 * sqrt[(0.62 * 0.38)/1000]

= 0.62 +/- 0.015

So the 95% confidence interval is (0.605,0.635).
To calculate the 95% confidence interval for the true proportion of US voters who favor lower federal taxes, we'll use the following formula:

Confidence interval = p ± Z * sqrt(p(1-p)/n)

where:
- p is the sample proportion (62% or 0.62)
- Z is the critical value for a 95% confidence interval (1.96)
- n is the sample size (1000)

First, calculate the standard error:

Standard error = sqrt(0.62 * (1 - 0.62) / 1000) = sqrt(0.2356 / 1000) ≈ 0.0153

Next, calculate the margin of error:

Margin of error = 1.96 * 0.0153 ≈ 0.0300

Now, we can find the confidence interval:

Lower limit = 0.62 - 0.0300 = 0.59
Upper limit = 0.62 + 0.0300 = 0.65

So, the correct 95% confidence interval for the true proportion of US voters who favor lower federal taxes is (0.59, 0.65).

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The company make per day is  941.5 feet.

To find the average number of feet of licorice made per day, we can divide the total amount of licorice made by the number of days:

Average = Total amount / Number of days

In this case, the total amount of licorice made is 6,590.7 feet, and the number of days is 7. Plugging in these values into the formula, we get:

Average = 6,590.7 feet / 7 days

Calculating this division gives us:

Average ≈ 941.5286 feet

Rounding this value to the nearest tenth of a foot, the average number of feet of licorice made per day by Max's Licorice Company is approximately 941.5 feet.

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The time taken for the trip if the return trip was 9 hours is 17 hours.

The outward journey used 432 mph. The return journey was 480 mph and this was for 9 hours.

Let the time taken for the initial trip be x. This will be:

x/9 = 432 / 48

Cross multiply

480x = 432 × 9

x = (432 × 9) / 480

x = 8

Therefore, the initial trip was 8 hours.

The time taken for the whole trip will be:

= Outward trip + Return trip

= 8 hours + 9 hours

= 17 hours.

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Answer:

632

Step-by-step explanation:

So you take one from the 3 to make it 2 and add it on to 89 to make 90. next take 10 from 542 and add it to the 90, you get 100. Then 532 + 100 = 632

Hope this helps

Answer:

Step-by-step explanation:

543 + 89

from the 3 and 9 split 9 to get a ten with the 3: 3 + 7 + 2 so 2 goes into the units category of the answer:

..2

Now as 9 > 3 we add 1 to the tens digit

- that is 8 becomes 9.

from the 4 and 9 split 9 to get a ten with  the 4: 6 + 3 so 3 goes into the tens category:

.32.

Now as 9 > 4 we add 1 to the 5, so the answer is 632.

The factors of the polynomial are (x - 4)(x - 4)(x + 7), and the polynomial is completely factored.

For the polynomial x³ - 7x² - 16x + 112, the following statements are true:

1. The factors of the polynomial are (x - 4)(x - 4)(x + 7).

2. The polynomial is completely factored.

To factor the polynomial completely, we can use different factoring techniques such as grouping, factoring by grouping, or synthetic division.

In this case, we observe that the number 4 is a root of the polynomial since when we substitute x = 4 into the polynomial, we get zero.

Using synthetic division or long division, we can divide the polynomial by (x - 4) twice to obtain the factored form (x - 4)(x - 4)(x + 7).

Hence, the factors of the polynomial are (x - 4)(x - 4)(x + 7), and the polynomial is completely factored.

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