in order to reduce the average time customer spends waiting in the queue, the swedish bakery considers replacing tim gonzales (their current server) by john thunderbolt who can serve faster. john thunderbolt can serve a customer in 4 minutes on average (exponentially distributed). what would the new average waiting time in the queue (in minutes)

Answer:

here is the answer :

Step-by-step explanation:

AC=5x-5(similar triangle )

y=10,x=28 (both reasons are similar triangle)

The estimated time for the 100th repetition of this job is approximately 111.11 minutes, assuming a learning curve of 90 percent.

To estimate the time for the 100th repetition of the job, we can use the concept of a learning curve. The learning curve assumes that as the number of repetitions increases, the time required decreases at a constant percentage rate. In this case, the learning curve is 90 percent.

To estimate the time for the 100th repetition, we can use the formula:

Estimated time for the 100th repetition = Time for the 50th repetition / (Learning curve)\(^log2\)(100/50)

Plugging in the given values:

Estimated time for the 100th repetition = 100 minutes / (0.90)\(^log2(100/50)\)

Simplifying the expression:

Estimated time for the 100th repetition ≈ 100 minutes / \((0.90)^1\)

Estimated time for the 100th repetition ≈ 100 minutes / 0.90

Estimated time for the 100th repetition ≈ 111.11 minutes

Therefore, the estimated time for the 100th repetition of this job is approximately 111.11 minutes.

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Answer:

y-intercept = (0, -2)

Step-by-step explanation:

The y-intercept is the y-coordinate of the point (0, b) where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. Looking at your graph, it shows that the line crosses at point (0, -2).

Therefore, the correct answer is (0, -2).

Answer:

8. X + Y = an even number

Step-by-step explanation:

if X and Y are a odd number then if you add them you get an even number

Answer:

\(1)2 ~real ~ solutions\)

\(2) 0 ~ real ~solutions\)

\(3) 1~real ~solutions\)

Step-by-step explanation:.

\(1) x^2+y^2=17\)

\(y=-1/2x\)

\(x^2+1/4x^2=17\)

\(4x^2+x^2=68\)

\(5x^2=68\)

\(x^2=68\)

\(x=\) ± \(\sqrt{68/5}\)

----------------------

\(2) y=x^2-7x+10\)

\(y=-6x+5\)

\(-6x+5=x2-7x+10\)

\(x^2-x+5=0\)

\(a=1\)

\(b=-1\)

\(c=5\)

\(D=b^2-4ac\)

\(=1-20\)

\(=-19\)

\(\sqrt{0} =\sqrt{-19}\)

---------------------

\(3) y=-2x^2+19\)

\(8x-y=-17\)

\(8x+2x^2-9=-17\)

\(8x+2x^2+8=0\)

\(4x+x^2+4=0\)

\(x^2+4x+4=0\)

\(x^2+2x+2x+4=0\)

\(x(x+2)+2(x+2)=0\)

\((x+2)(x+2)^2=0\)

\((x+2)^2=0\)

\(x=-2\)

------------------------------

hope it helps...

have a great day!!!

Answer:

Expressed as a mixed number in its simplest form, 27/4 is equal

to 6 3/4 or six and three quarters.

Step-by-step explanation:

Answer:

first find the profit

profit % is the profit over CP times 100

i. Vectors u and w are orthogonal.

ii. The two vectors orthogonal to v = √(2, -3) are u = (3, 2) and w = (-2, 3).

iii. The two unit vectors orthogonal to 7 are u = (1, -1) / √2 and w = (1, 1) / √2.

i. To show that vectors u = (a, b) and w = (-b, a) are orthogonal, we need to demonstrate that their dot product is zero.

The dot product of u and w is given by:

u · w = (a, b) · (-b, a) = a*(-b) + b*a = -ab + ab = 0

ii. To find two vectors orthogonal to vector v = √(2, -3), we can use the result from part i.

Let's denote the two orthogonal vectors as u and w.

We know that u = (a, b) is orthogonal to v, which means:

u · v = (a, b) · (2, -3) = 2a + (-3b) = 0

Simplifying the equation:

2a - 3b = 0

We can choose any values for a and solve for b. For example, let's set a = 3:

2(3) - 3b = 0

6 - 3b = 0

-3b = -6

b = 2

Therefore, one vector orthogonal to v is u = (3, 2).

To find the second orthogonal vector, we can use the result from part i:

w = (-b, a) = (-2, 3)

iii. To find two unit vectors orthogonal to 7, we need to consider the dot product between the vectors and 7, and set it equal to zero.

Let's denote the two orthogonal unit vectors as u and w.

We know that u · 7 = (a, b) · 7 = 7a + 7b = 0

Dividing by 7:

a + b = 0

We can choose any values for a and solve for b. Let's set a = 1:

1 + b = 0

b = -1

Therefore, one unit vector orthogonal to 7 is u = (1, -1) / √2.

To find the second unit vector, we can use the result from part i:

w = (-b, a) = (1, 1) / √2

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Answer:

b. 0.75 kg

Step-by-step explanation:

1 kilogram is 1000 grams

The correct logarithm form is: a. log5 125 = 3

Question is about finding the logarithm form of 5³ = 125 using the given options.

The correct logarithm form is:

a. log5 125 = 3

Here's the step-by-step explanation:

1. The exponential form is given as 5³= 125.
2. To convert it to logarithm form, you have to express it as log(base) (argument) = exponent.
3. In this case, the base is 5, the argument is 125, and the exponent is 3.
4. Therefore, the logarithm form is log5 125 = 3.

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Answer:

The answer is \(6\frac{5}{8}\)

Step-by-step explanation:

-12 pounds + \(5\frac{3}{8}\)

-12+\(5\frac{3}{8}\)

=-12+5+\(\frac{3}{8}\)

=(-12+5)+\(\frac{3}{8}\)

=(-7)+\(\frac{3}{8\\}\)

=\(-6\frac{5}{8}\)

Mr.Yoo's weight dropped by \(6\frac{5}{8}\)

Answer:

6 5/8 edited--> i didnt see that someone alr answer this

Step-by-step explanation:

Real number \($x^2+y^2= \boxed{158}$\)

Let's start by using the formulas for arithmetic mean and geometric mean:

Arithmetic mean:

\($\frac{x+y}{2}=7 \Rightarrow x+y=14$\)

Geometric mean:

\($\sqrt{xy}=\sqrt{19} \Rightarrow xy=19$\)

Now, we can square the equation for the arithmetic mean:

\($(x+y)^2=14^2 \Rightarrow x^2+2xy+y^2=196$\)

Substituting\($xy=19$\), we get:

\($x^2+y^2+2(19)=196$\)

Simplifying:

\($x^2+y^2= \boxed{158}$\)

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Answer: after 3 seconds

when  the ball hit the ground => - 5t² + 14t + 3 = 0

⇔ (5t + 1)(t - 3) = 0

⇔ t = 3 or t = -1/5

but t  is a positive integer => t = 3

so the ball will hit the ground after 3 seconds

Step-by-step explanation:

The 6√6 in the form √a where a is an integer to be found is √144.

To express 6√6 in the form √a, we need to simplify the expression by factoring out the perfect square

First, we can factor 6 into 2 and

6√6 = 2 × 3 × √6

Next, we can simplify √6 by factoring it into √2 × √3

6√6 = 2 × 3 × √2 × √3 × √2

Now, we can combine the two √2 terms to get

6√6 = 2 × 3 × 2 × √3

Simplifying further, we get

6√6 = 12√3

Therefore, a = 144,since (12√3)^2 = 144 × 3 = 432.

So, 6√6 can be expressed in the form √144.

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The term "p-function" or "p-value" is commonly used in statistics to measure the strength of evidence against the null hypothesis in a hypothesis test. It represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true.

The p-value is used to make decisions about whether to reject or fail to reject the null hypothesis. It is often compared to a predetermined significance level, typically denoted as alpha. If the p-value is less than alpha, it is considered statistically significant, and the null hypothesis is rejected in favor of the alternative hypothesis. On the other hand, if the p-value is greater than or equal to alpha, there is not enough evidence to reject the null hypothesis.

Let's consider an example to better understand the common use of p-values. Suppose we want to test whether a new drug is effective in treating a certain medical condition. The null hypothesis would be that the drug has no effect, while the alternative hypothesis would be that the drug is effective. We collect data from a sample of patients and analyze the results using a statistical test.

After conducting the test, we calculate a p-value of 0.03. If we set our significance level (alpha) to 0.05, we would compare the p-value to alpha. Since the p-value (0.03) is less than alpha (0.05), we would conclude that there is strong evidence to reject the null hypothesis and accept the alternative hypothesis. This suggests that the new drug is effective in treating the medical condition.

In summary, the p-value is a statistical measure that helps us determine the strength of evidence against the null hypothesis in hypothesis testing. It allows us to make informed decisions and draw conclusions based on the data.

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Answer: The answer is provided below

Step-by-step explanation:

A histogram is a diagram which consist of rectangles whereby the area is proportional to frequency of a variable and the width is equal to class interval. A histogram is a commonly used graph that is used to show frequency distributions.

The cumulative histogram is a histogram whereby the vertical axis doesn't gives only the counts for a single bin, but gives the counts for that bin and all the bins for the maller values of a response variable.

Cumulative histograms are similar to normal histograms, but the main difference is that they graph cumulative frequencies unlike histograms that graph just frequencies.

Answer:

1

Step-by-step explanation:

Ratio between ABC and ADE
BC/DE = AB/AE

1/9 = x/9
x=1

Answer:

That's alot of words, kinda hard to understand

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Answer:29.02 in all

Step-by-step explanation:lunch is 8.54 And field trip is 20.48

Answer:

y = 4/3x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (0, -6) and (6, 2)

We see the y increase by 8, and the x increase by 6, so the slope is

m = 8/6 = 4/3

Y-intercept is located at (0, -6)

So, the equation is y = 4/3x - 6

Therefore, the empirical formula of the compound is X169Y.

Since the compound is 13x by mass, we can assume that we have 13 total parts. Let's say x has a mass of m and y has a mass of n. Then we can write:

mass of x = 13m

mass of y = n

We know that the atomic mass of x is 13 times that of y. Therefore:

m = 13n

Substituting m in the first equation, we get:

mass of x = 13(13n) = 169n

mass of y = n

So the total mass of the compound is:

mass of x + mass of y = 169n + n = 170n

Since we have 13 parts, each part has a mass of (170n/13). Therefore, the empirical formula of the compound is:

x: (169n/13) / (170n/13) = 169/170

y: (n/13) / (170n/13) = 1/170

So the empirical formula of the compound is:

x: 169

y: 1

=X169Y

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Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

We need at least 5 tosses to be certain that the probability of getting at least one 6 is greater than or equal to 1/2.

The probability of not getting a 6 on a solitary throw of a fair six-sided kick the bucket is 5/6. Subsequently, the probability of not getting a 6 on n throws is \((5/6)^n\). The probability of getting somewhere around one 6 in n throws is 1 - \((5/6)^n\).

To view the quantity of throws expected as sure that the probability of getting somewhere around one 6 is more prominent than or equivalent to 1/2, we can set the probability equivalent to 1/2 and address for n:

1 - \((5/6)^n\) = 1/2

\((5/6)^n\) = 1/2

Taking the normal logarithm of the two sides, we get:

n ln(5/6) = ln(1/2)

n = ln(1/2)/ln(5/6) ≈ 4.807

Hence, we really want something like 5 throws to be sure that the probability of getting no less than one 6 is more prominent than or equivalent to 1/2.

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a) The affine transformation maps a square in the z-plane to a parallelogram in the w-plane.

b) The image of at least one square is again a square, then u + iv is a linear function of the variable z = x + iy.

Here, we have,

a) To show that an affine transformation converts a square of the plane z = x + iy into a parallelogram of the plane w = u + iv, we need to demonstrate that the four vertices of the square map to the vertices of a parallelogram under the given transformation.

Let's consider the vertices of the square in the z-plane:

A: z = x + iy = (x, y)

B: z = x + iy = (x + 1, y)

C: z = x + iy = (x + 1, y + 1)

D: z = x + iy = (x, y + 1)

Under the affine transformation, the corresponding points in the w-plane will be:

A': w = u + iv = (α₁x + B₁y + γ₁) + i(a₂x + B₂y + γ₂)

B': w = u + iv = (α₁(x + 1) + B₁y + γ₁) + i(a₂(x + 1) + B₂y + γ₂)

C': w = u + iv = (α₁(x + 1) + B₁(y + 1) + γ₁) + i(a₂(x + 1) + B₂(y + 1) + γ₂)

D': w = u + iv = (α₁x + B₁(y + 1) + γ₁) + i(a₂x + B₂(y + 1) + γ₂)

We can simplify these expressions:

A': w = (α₁x + B₁y + γ₁) + i(a₂x + B₂y + γ₂)

B': w = (α₁x + α₁ + B₁y + γ₁) + i(a₂x + a₂ + B₂y + γ₂)

C': w = (α₁x + α₁ + B₁y + B₁ + γ₁) + i(a₂x + a₂ + B₂y + B₂ + γ₂)

D': w = (α₁x + B₁y + B₁ + γ₁) + i(a₂x + B₂y + B₂ + γ₂)

By comparing the coordinates of the transformed points, we can observe that A'B' and CD are parallel and have the same length, while AB' and C'D' are also parallel and have the same length. This implies that the affine transformation maps a square in the z-plane to a parallelogram in the w-plane.

b) If the image of at least one square is again a square, then u + iv is a linear function of the variable z = x + iy.

If the image of a square in the z-plane is again a square in the w-plane, it means that the sides of the transformed parallelogram are parallel and have the same length. This can only occur if the coefficients of the affine transformation are such that the terms involving x and y cancel out in the expressions for u and v.

Considering the general expressions for u and v in terms of x and y:

u = α₁x + B₁y + γ₁

v = a₂x + B₂y + γ₂

To ensure that the transformed shape is a square, the coefficients of x and y should cancel out. This implies that α₁B₂ - a₂B₁ = 0.

If α₁B₂ - a₂B₁ = 0, we can rewrite the expressions for u and v as:

u = α₁(x + iy) + γ₁

v = B₂(x + iy) + γ₂

Notice that the terms involving x and y have completely canceled out. Therefore, the transformed shape can be expressed solely as a function of z = x + iy:

w = u + iv = α₁z + γ₁ + B₂z + γ₂ = (α₁ + B₂)z + (γ₁ + γ₂)

This shows that if the image of at least one square is again a square, then u + iv is a linear function of the variable z = x + iy.

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Answer:

The exterior angle is ∠BDC

Congreunt side is XZ

Step-by-step explanation:

The exterior angle just means the angle facing outside.

And for the congruent one you are right. Because they are put in the same order.

To find the weight of the bowl, we need to first find the volume of the bowl. We can do this by using the formula for the volume of a solid of revolution: The weight of the bowl made out of steel is approximately 0.066 kg.

To find the weight of the bowl, we need to first find the volume of the bowl. We can do this by using the formula for the volume of a solid of revolution:

\(V = \pi \int\limits^b_a { y^2} \, dx\)

In this case, a = 0 and b = 1, since we are revolving the region bounded by y = 20x and y = 20x^2 in the first quadrant about the y-axis. So we have:

\(V = \pi \int\limits^1_o{(20x^2)^2 - (20x)^2 } \, dx\)

\(V = \pi\int\limits^1_0 { 400x^4 - 400x^2 } \, dx\)

\(V = \pi (80/15)\)

\(V = 16\pi /3 m^3\)

Next, we need to find the mass of the bowl, which we can do by multiplying the volume by the density of steel:

m = ρV

m = 8050 * (16π/3)

m ≈ 134,388.09 g

Finally, we convert the mass to kilograms to find the weight of the bowl:

w = m/1000

w ≈ 0.066 kg

Therefore, the weight of the bowl made out of steel is approximately 0.066 kg.

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Answer:

2/3

Step-by-step explanation:

Slope = (-1-(-3))/(3-0) = 2/3

Answer:

slope = 2/3

Step-by-step explanation:

equation: y = x2/3 -3

Answer:

first one is -4+y=20 second is 4+y=-20