We are interested in comparing the fuel efficiencies (measured in miles per gallon) of two "populations" of cars: compact cars (Population 1) and midsized cars (Population 2). These are reported in fuel economy ratings. Assume that the populations are Normal, with means and standard deviations µ1 = 24.5, σ1 = 3.8, µ2 = 21.3, σ2 = 2.7 respectively, all measured in miles per gallon. Suppose we get two independent random samples of the two populations independently, each with sample size n1 = n2 = 8. Let X and Y be the respective sample means.

a. What is the probability distribution of X − Y ?
b. Find P(X> Y ).

Answer:

jonwjwjejejeken 20 ow91

Answer:

Upper Right

Step-by-step explanation:

All of them have different dips, therefore the one facing in a different direction must be the odd one out.

Answer:

top right graph

Step-by-step explanation:

3 of the 4 graphs start at negative infinity for negative x, and approach infinity as x approaches infinity.

The top right graph starts at infinity for negative x and approaches negative infinity as x approaches infinity.

Answer: top right graph

Answer:

60 2/5 x 5 = 60 x 5 + 2/5 x 5

60 x 5 = 300

2/5 x 5 = 2

300 + 2 = 302 so 302 is the answer

302 km for 5 hours

Step-by-step explanation:

Step-by-step explanation:

Km in 1 hour = 60 2/5 = 60.4km

Km in 5 hours = 60.4 x 5 = 302km

Step-by-step explanation:

I think you made a mistake. (3,0) and (3,-12) are two points not possible for an expression.

Repost the question if you can.

To decrease lead times and wasted materials, a doughnut restaurant like Krispy Kreme can use methods such as streamlining the production process, implementing precise measurement and mixing techniques, automating proofing, adopting efficient frying techniques, utilizing glazing automation, and optimizing cooling and packaging processes.

To decrease lead times and wasted materials, a doughnut restaurant like Krispy Kreme can implement the following methods:

1. Streamlined Production Process: By optimizing the workflow and layout of the kitchen, Krispy Kreme can reduce unnecessary movement and improve efficiency. This can include organizing the ingredients and equipment in a logical sequence, minimizing the distance between workstations, and ensuring a smooth flow from one step to the next.

2. Precise Measurement and Mixing: Accurate measurement of ingredients and precise mixing techniques can help minimize wasted materials. Using automated measuring systems or standardized measuring tools can ensure consistency and reduce errors. Additionally, adopting efficient mixing methods, such as high-speed mixers, can decrease mixing time and enhance productivity.

3. Proofing Automation: Implementing automated proofing systems can help control the rising process more precisely. These systems can monitor temperature, humidity, and time to ensure optimal conditions for dough proofing. By automating this step, Krispy Kreme can reduce the risk of over-proofing or under-proofing, which can lead to dough waste.

4. Efficient Frying Techniques: Utilizing advanced frying equipment with precise temperature control and oil circulation can reduce cooking time and minimize the amount of oil required. Maintaining consistent frying conditions can also result in evenly cooked doughnuts and reduce the number of rejects.

5. Glazing Automation: Introducing automated glazing systems can help minimize glaze waste and improve consistency. These systems can accurately apply the desired amount of glaze, reducing excess usage and ensuring uniform coating on each doughnut.

6. Cooling and Packaging Optimization: Efficient cooling methods, such as rapid cooling systems or specialized cooling tunnels, can expedite the cooling process without compromising the quality of the doughnuts. Additionally, optimizing packaging processes, including automated packaging machines, can enhance productivity and reduce material waste.

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Answer:

Your answer is: No solution

Step-by-step explanation:

Hope this helped : )

To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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Step-by-step explanation:

5x64=32066=(320+x} 666x6={320+x)396=320+x=396-320

The correlation coefficient that indicates the strongest relationship between two variables is a. -1.0.

The correlation coefficient is a numerical measure that quantifies the relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

In this case, a correlation coefficient of -1.0 represents a perfect negative correlation, meaning that the two variables have a strong, linear relationship where as one variable increases, the other decreases in a perfectly predictable manner. This indicates a very strong and consistent inverse relationship between the variables.

In comparison, a correlation coefficient of 0.80 indicates a strong positive correlation, but it is not as strong as a perfect negative correlation of -1.0. A correlation coefficient of 0.1 suggests a weak positive correlation, while a correlation coefficient of -0.45 indicates a moderate negative correlation.

Therefore, out of the given options, the correlation coefficient of -1.0 represents the strongest relationship between two variables.

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Answer:

7

Step-by-step explanation:

Answer:

\(x=-20\)

Step-by-step explanation:

\(\frac{x}{5}+7=3\\ \\\frac{x}{5}+7-7=3-7\\ \\\frac{x}{5}=-4\\ \\\frac{x}{5}*5=-4*5\\ \\x=-20\)

Answer:

-20

Step-by-step explanation:

Functions can be represented using equations and graphs Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.

The domain of the function is defined as the set of the numbers we are allowed to put in the function while the range is the assumed data put in the function.

The functions are given as:

\(F(x)=e^{-x}\\\\\\g(x)=-\sqrt{x-4}\)

Using a graphing calculator:

The domain of g(x) is [4, ∞)

The range of g(x) is  [0, ∞)

The domain of f(x) is  (–∞, ∞),

The range of f(x) is  [0, ∞)

Both functions have positive values for their domains

By comparing the above highlights, the true statement between functions g(x) and f(x) is option 3

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Answer:

Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

Step-by-step explanation:

I got it right on the test.

Answer:

slope is 14 and y intercept is 13

Step-by-step explanation:

y=mx=b is slope intercept form

14 is m and 13 is b

m is slope b= y-intercept

After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, \(N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}\). Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

\(\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}\)

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

\(\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}\)

The answer is 35 minutes.

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Answer:

x=5

Step-by-step explanation:

13x-6=8x+19 +6  on both sides

13x=8x+25    -8 on both sides

5x=25       /5 on both sides

x=5

We are given the function h(t) = -t^2 + t + 1 and asked to find the function values for specific inputs. We need to evaluate h(3), h(-1), and h(x+1).

(a) h(3) = -5, (b) h(-1) = -1, (c) h(x+1) = -x^2.

(a) To find h(3), we substitute t = 3 into the function h(t):

h(3) = -(3)^2 + 3 + 1 = -9 + 3 + 1 = -5.

(b) To find h(-1), we substitute t = -1 into the function h(t):

h(-1) = -(-1)^2 + (-1) + 1 = -1 + (-1) + 1 = -1.

(c) To find h(x+1), we substitute t = x+1 into the function h(t):

h(x+1) = -(x+1)^2 + (x+1) + 1 = -(x^2 + 2x + 1) + x + 1 + 1 = -x^2 - x - 1 + x + 1 + 1 = -x^2.

Therefore, the function values are:

(a) h(3) = -5

(b) h(-1) = -1

(c) h(x+1) = -x^2.

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Answer:

(i) \(t = \sqrt{\frac{100}{576} }\)

(ii) \(m = \frac{12nt^2}{5}\)

Step-by-step explanation:

(i) We are given the formula: \(t=\sqrt{\frac{5m}{12n} }\) .

To answer the first question all we have to do is put the values we have been given into the formula. So we put \(m=20\) and \(n=48\) into the formula.

This gives us: \(t=\sqrt{\frac{5*20}{12*48} }\) then simplify to get \(t = \sqrt{\frac{100}{576} }\) . I would just keep it in this form.

(ii) This second part is basically just asking us to rearrange the formula so that we get \(m =\) something.

Start of with: \(t = \sqrt{\frac{5m}{12n} }\)

We need to see how we can start isolating the \(m\) part of the formula. To do this we need to get rid of the square root. So do the inverse of square rooting which is squaring. Squaring both sides we get: \(t^2 = \frac{5m}{12n}\).

When we square the left side we get \(t^2\) but when we square the right side we just cancel out the square root so it leaves us with whatever is inside.

Now we need to continue trying to get \(m\) by itself. We can see that next we need to multiply both sides by \(12n\), which will cancel out the \(12n\) on the right side but multiply the \(t^2\) by \(12n\),

So now we get \(12nt^2 = 5m\).

Finally we can see that we have \(5\) lots of \(m\) but we only want \(m\). Divide both sides by \(5\): \(\frac{12nt^2}{5} = m\)

The main reason behind this is using properties of logarithm .

like

when solving

There you use multiplication property and make addition to multiplication then you get extraneous solution because in plenty of cases they occur

like

But

Same happens in case of logarithm

Answer:

yeah

Step-by-step explanation: l

Answer:

i think its A (edit: im gonna take that back because i was looking at the wrong side, logically it is 12)

Step-by-step explanation:

Answer:

B. 12

Step-by-step explanation:

logically speaking is 12

Answer:

7 m

Step-by-step explanation:

Corresponding sides of similar triangles are in same ratio.

\(\dfrac{QR}{SR}=\dfrac{QP}{ST}\\\\\dfrac{y}{8}=\dfrac{3}{6}\\\\y=\dfrac{3}{6}*8\\\\y=4\\\\\\\)

\(\dfrac{x}{1.5}=\dfrac{6}{3}\\\\x =\dfrac{6}{3}*1.5\\\\x=3\)

x + y = 3 + 4 = 7

Answer:

i think your answer is 7

Answer:

30 meters per second

Step-by-step explanation:

Step 1:

600 ÷ 20 = 30

Answer:

30 meters per second

Hope This Helps :)

Answer:

30 m /s

Step-by-step explanation:

We are looking for the speed

d/t = speed

600m / 20 second

30 m /s

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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Answer:22.5

Step-by-step explanation:

The solution is, : y = 1/3x+6, is the equation of a line that is perpendicular to the line y= -3x+2 and passes through the point (6,8).

We know that,

y = -3x+2 is in slope intercept form  y = mx+b  where m is the slope and b is the y intercept

The slope is -3

Perpendicular lines have slopes that are negative reciprocals

The slope of the perpendicular line is  -1/-3 = 1/3

The equation of the new line is

y = 1/3x +b

Using the point that passes through the line ( 6,8) and substituting in for x and y

8 = 1/3(6) +b

8 = 2+b

8-2 =b

6 =b

The equation becomes

y = 1/3x+6.

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The depth of water in the second cup is 9 cm when the water is transferred from a cylindrical cup with a radius of r cm and a depth of 36 cm.

Given that,

Depth of water in the first cylindrical cup with radius r: 36 cm

Transfer of water from the first cup to another cylindrical cup

Radius of the second cup: 2r cm

The first cup has a radius of r cm and a depth of 36 cm.

The volume of a cylinder is given by the formula:

V = π r² h,

Where V is the volume,

r is the radius,

h is the height (or depth) of the cylinder.

So, for the first cup, we have:

V₁ = π r² 36.

Now, calculate the volume of the second cup.

The second cup has a radius of 2r cm.

Call the depth or height of the water in the second cup h₂.

The volume of the second cup is V₂ = π (2r)² h₂.

Since the water from the first cup is transferred to the second cup, the volumes of the two cups should be equal.

Therefore, V₁ = V₂.

Replacing the values, we have

π r² 36 = π (2r)² h₂.

Simplifying this equation, we get

36 = 4h₂.

Dividing both sides by 4, we find h₂ = 9.

Therefore, the depth of the water in the second cup is 9 cm.

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