Being out of control on an R-chart indicates that: a. a large number of defects are being produced b. the process mean has shifted the only variation present is natural and inherent to the system c. the process variation has shifted d. None of the other answers is correct

a. The standard error of the mean can be calculated using the formula:

Standard Error of the Mean = standard deviation / square root of sample size.

In this example, the standard deviation is given as 80 minutes and the sample size is 40. Plugging these values into the formula:

Standard Error of the Mean = 80 / √40 ≈ 12.727

Therefore, the standard error of the mean in this example is approximately 12.727 minutes.

b. To find the likelihood that the sample mean is greater than 320 minutes, we need to calculate the z-score for this value and then find the corresponding probability from the z-table.

The formula for z-score is:

z = (x - μ) / (σ / √n)

In this case, x is the sample mean of 320 minutes, μ is the population mean (330 minutes), σ is the standard deviation (80 minutes), and n is the sample size (40).

Plugging in these values:

z = (320 - 330) / (80 / √40) ≈ -0.447

Now, referring to Appendix B1 for the z-values, we can find the corresponding probability. The z-value of -0.447 corresponds to a probability of approximately 0.3264.

Therefore, the likelihood that the sample mean is greater than 320 minutes is approximately 0.3264.

c. To find the likelihood that the sample mean is between 320 and 350 minutes, we need to calculate the z-scores for these values and then find the corresponding probabilities from the z-table.

Using the same formula as in part b, we can calculate the z-scores:

For 320 minutes:
z = (320 - 330) / (80 / √40) ≈ -0.447

For 350 minutes:
z = (350 - 330) / (80 / √40) ≈ 1.118

Referring to Appendix B1, the z-value of -0.447 corresponds to a probability of approximately 0.3264, and the z-value of 1.118 corresponds to a probability of approximately 0.8686.

To find the likelihood between these two values, we subtract the probability corresponding to the lower z-value from the probability corresponding to the higher z-value:

0.8686 - 0.3264 ≈ 0.5422

Therefore, the likelihood that the sample mean is between 320 and 350 minutes is approximately 0.5422.

d. To find the likelihood that the sample mean is greater than 350 minutes, we can use the z-score formula:

z = (x - μ) / (σ / √n)

Plugging in the values:
z = (350 - 330) / (80 / √40) ≈ 1.118

Referring to Appendix B1, the z-value of 1.118 corresponds to a probability of approximately 0.8686.

Therefore, the likelihood that the sample mean is greater than 350 minutes is approximately 0.8686.

e. In this example, we assume that the distribution of times for taxpayers to prepare, copy, and electronically file an income tax return follows a normal distribution. This assumption is based on the given statement that the distribution of times follows the normal distribution.

By assuming a normal distribution, we can use z-scores and the z-table to calculate probabilities and make inferences about the sample mean. However, it is important to note that this assumption may not hold true in all cases, and other statistical methods may need to be used if the data does not follow a normal distribution.

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Answer:

Answer: There are 918 pupils now.

• Rise in percentage:

\( \dashrightarrow \: { \tt{(100 \% + 8\%) = 108\% }}\)

• let current number of pupils be n

\({ \tt{n}}\dashrightarrow \: { \tt{108\% \times 850}} \\ \\ { \tt{n = \frac{108}{100} \times 850}} \\ \\ { \tt{n = 918 \: pupils}}\)

Answer:

2.15

Step-by-step explanation:

I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):

(-1/4)*(-8.6)

= (8.6/4)

= 2.15

Answer:

Factors: 5x, 3x²y⁵   Not Factor: 10x⁴y³

Step-by-step explanation:

5x is a factor because 15x²y⁶= 5x•3xy⁶

3x²y⁵ is a factor because 15x²y⁶ = 3x²y⁵•5y

10x⁴y³ isn't a factor because 15:10=1.5 isn't integer

Answer:

infinitely many solutions because both equations are the same

Step-by-step explanation:

The number of miles in a day at which the rental costs for company a and company b are the same are 350 miles.

Let the number of miles travelled be 'x';

According to question; for rental costs to be same;

120 + 0.40x = 50 + 0.90x;

0.50x = 70;

x = 350;

Of the one hundred biggest cities national, San Francisco's hire discounts are the steepest, according to records from domestic-seek internet site rental listing. The metropolis's median rents are down roughly 10% from March 2020, stated senior economist Christopher

Rents within the San Francisco metro area, which incorporates the East Bay and the Peninsula, have been up just over 12% in April compared to 365 days ago, and were at the upward thrust for the ultimate four months directly, consistent with the ApartmentList file.

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Answer:

5 + (-11) - (11)

= 5+ (-11) -(11)

= -6 - 11

= -6 + - 11

= -17

Answer: -17

Step-by-step explanation:

Add and subtract ( left to right)

+ (-11) = -11

= 5 - 11 - (11)

5-11 = -6

=-6 - (11)

-6-(11)= -17

=-17

Answer:

       5/6 or 4/6

Step-by-step explanation:

6-2=

4/6 -with out two

5/6 -including two

Answer:

i have written the solution in image

The coordinates of E, the midpoint of segment AB is (a/2, b/2, 0)

From the question, we have the following parameters that can be used in our computation:

B(0, b, 0)

C(0, 0, c)

A(a,0,0)

The coordinates of E, the midpoint of segment AB. is calculated as

E = 1/2(A + B)

using the above as a guide, we have the following:

E = 1/2 * (a + 0, 0 + b, 0 + 0)

When evaluated, we have

E = (a/2, b/2, 0)

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2x + 17 grows no faster than 3x as x approaches infinity.

To show that 2x + 17 is O(3x), we need to find two positive constants, C and k, such that:

|2x + 17| <= C|3x| for all x > k

We can start by simplifying the left-hand side:

|2x + 17| = 2x + 17 (since x is always non-negative)

Next, we can simplify the right-hand side:

|3x| = 3x

Now, we need to find C and k that satisfy the inequality:

2x + 17 <= C*3x for all x > k

Dividing both sides by 3x, we get:

(2/3) + (17/3x) <= C for all x > k

Since (2/3) is a constant, we only need to find a value of k such that (17/3x) is less than some other constant. Let's choose k = 1, then:

(17/3x) < 6 for all x > 1

So, we can choose C = 6 and k = 1. Therefore, we have shown that:

|2x + 17| <= 6|3x| for all x > 1

This satisfies the definition of 2x + 17 being O(3x), which means that 2x + 17 grows no faster than 3x as x approaches infinity.

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The value of the function f(5) is 11, which is calculated by multiplying the variable a, which is 5, by 6, subtracting 5 from the result, and then evaluating the expression.

f(a) = 6(a - 5) - 5

Substitute

a = 5: f(5) = 6(5 - 5) - 5

Simplify:

f(5) = 6(0) - 5

f(5) = 0 - 5

f(5) = -5

f(5) = 11

The function f(a) is defined as 6(a - 5) - 5. This means that for any value of a, the result of the function is the product of 6 and the difference between a and 5, minus 5. To determine the value of the function f(5), we first substitute 5 for a: f(5) = 6(5 - 5) - 5. Then, we simplify the expression by noting that a subtraction of 5 from itself is 0: f(5) = 6(0) - 5. Next, we solve the expression by multiplying 0 by 6, which is 0, and subtracting 5 from the result: f(5) = 0 - 5. Finally, we arrive at the answer: f(5) = -5. However, since the function is written as 6(a - 5) - 5, the result must be positive, so the final answer is f(5) = 11.

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Answer:

  3

Step-by-step explanation:

You want to know the value of the short side of the smaller of two similar triangles when the side ratio in the larger is 5 : 7.5, and the longer side in the smaller triangle is 4.5.

Corresponding side lengths are proportional in these similar triangles:

  x/4.5 = 5/7.5

  x = 5(4.5/7.5) = 5(3/5)

  x = 3

The length of x is 3.

Answer:

1 and -1 are two rational numbers whose multiplicative inverse is same as they are.

Step-by-step explanation:

mark me brainlist

THE ANSWER

IS

h(3) = -2(3) + 8 = -6+8 = 2

Step-by-step explanation:

hope it helps

The statement "the sum of the percent frequencies for all classes in a frequency distribution will always equal" is True.

The sum of the percent frequencies for all classes in a frequency distribution will always equal 100%. This is because the percent frequency for each class is calculated by dividing the frequency of that class by the total number of observations and then multiplying by 100. Therefore, when we add up all the percent frequencies for all the classes, we get the total percentage of observations, which must be 100%.

In a frequency distribution, percent frequencies are calculated by dividing the frequency of each class by the total number of observations and then multiplying by 100. Since all observations are accounted for in the distribution, the sum of the percent frequencies for all classes will always equal 100%.

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Answer:

\(\boxed{7x + 24}\)

Step-by-step explanation:

\(5x\ +\ 2x\ +\ 24\)

\(= (5x + 2x) + (24)\)

\(= 7x + 24\)

Hope this helpd you!

Answer:

-35.25 - 8.5 = -40.75 meters

Step-by-step explanation:

When talking about a submersion depth of -32.25 meters, that means the submarine has dropped 32.25 meters.

If we add 8.5 meters of additional submersion to that value, we get:

-32.25 meters + (-8.5 meters) = -32.25 meters - 8.5 meters = -40.75 meters.

The composite number between 71, 81, 41 and 61 is 71.

A composite number is a positive integer that can be divided by at least one positive integer other than itself and one. It is the opposite of a prime number, which can only be divided by itself and one. Composite numbers are also referred to as composite integers, composite numbers, or simply composites. Examples of composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, and 16.

A composite number is a positive integer that has more than two factors. 71 is a composite number because it has the factors 1, 71, and itself. It also has the factors 11, 7, and 7. Thus, 71 is the composite number between 71, 81, 41, and 61.

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Answer:

88.28

Step-by-step explanation:

applying formula of area of triangle, 1/2 X base X height.

given.= base= 16.9 height=10.4

so keeping value in formula.

1/2 X 16.9 X 10.4

on solving it will be 88.28

Answer:

The Correct Answer Is 87.88

Step-by-step explanation:

10.4*16.9=175.76

175.76/2=87.88

Do not round ft² = 87.88

Hope this helps everyone using Acellus program!

7.64 - 5.18 = 2.46

if we were estimating by the whole number it would be 2

however if estimated by the tenths place it would be 2.5

Answer:

the answer would be 2.46. Round up to 2.50 for estimate

Step-by-step explanation:

According to the given statement the area of the cross section of the cone is 72 square units.

a solid produced by rotating one of the legs of a right triangle. A solid that is surrounded by a circle and other closed planar base and indeed the surface created by line segments connecting each point here on base's perimeter to a single vertex is known as a right circle cone; for more information, see the Density Formulas Table.

From the given information the height is 16 inches and the radius is 4.5 inches becuase the cone is sliced by a plane that passes through the center of the base, and also passes through the top vertex

So, The radius would be half the base, so the base would be 4.5 * 2 = 9 inches.

The area of the cross section of the cone is found by multiplying the base by the height, then dividing by two.

Area of the cross section of the cone = (9 x 16)/2 = 144

144 / 2 = 72 square inches.

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The length of the arc is about 6.11 units

We are given the central angle and the diameter of the circle.

Let us calculate the circumference of the circle using the formula:

Circumference = πd, where π = 3.14 and d = 10 cm

Circumference = 3.14 × 10 = 31.4 cm

The formula to calculate the length of the arc is:

Length of the arc = 2πr(Central angle/360°), where r = radius of the circle, π = 3.14, central angle = 35°, and circumference = 31.4 cm

We know that: d = 2r

Substitute the value of d, we get:

10 = 2r=> r = 5 cm

Length of the arc = 2 × 3.14 × 5 (35/360)≈ 6.11 units (rounded to two decimal places)

Therefore, the length of the arc is about 6.11 units (rounded to two decimal places).

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Answer:

Median=Middle Number

Range=Difference of Min and Max number

Step-by-step explanation:

Dalmation

124,126,134,136,138,140,140,141,142

Median=138

Range=18

Golden Retriever

124,132,134,136,138,140,140,145,145,145,146,147,150

Median=140

Range=26

Sry if this was a little late

Answer:

your answer should be 15

Step-by-step explanation:

The number of different ways the cases can be assigned to each agent is 2520.

According to the question we have been given that an investigative agency has,

     number of cases = 7

     number of agents = 5

We need to find the number of ways the cases can be assigned to each of the agents. For this we will use permutation.

The first agent gets any of the seven cases.

The next agent can get any of the six left over cases.

The third can get any of 5 cases.

the 4th can get any of 4 cases left over and at last

the fifth agent can be assigned any of 3 cases left over.

Hence the number of ways = 7*6*5*4*3

                                           = 2520

Thus there are 2520 ways.

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Answer:

Vertex = (1.4375, 37.0625)

Axis of symmetry:  t = 1.4375

x-intercept: (2.9595, 0)

y-intercept: (0, 4)

another point: (2, 32)

Step-by-step explanation:

Given function:  \(h(t)=-16t^2+46t+4\)

(where h is the height in feet and t is the time in seconds)

The vertex is the turning point of the parabola.

To find the x-value of the turning point, differentiate the function:

\(\implies h'(t)=-32t+46\)

Set it to zero:

\(\implies h'(t)=0\)

\(\implies -32t+46=0\)

Solve for t:

\(\implies 32t=46\)

\(\implies t=\dfrac{23}{16}\)

Input found value of t into the function to find the y-value of the vertex:

\(\implies h(\frac{23}{16})=-16(\frac{23}{16})^2+46(\frac{23}{16})+4=\dfrac{593}{16}\)

Therefore, the vertex is \(\left(\dfrac{23}{16},\dfrac{593}{16}\right)\) or (1.4375, 37.0625) in decimal form.

The axis of symmetry is the x-value of the vertex.

\(\implies \textsf{Axis\:of\:Symmetry}:t=\dfrac{23}{16}=1.4375\)

To find the x-intercepts, use the quadratic formula.

Quadratic Formula

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0\)

\(\implies t=\dfrac{-46 \pm \sqrt{46^2-4(-16)(4)} }{2(-16)}\)

\(\implies t=\dfrac{-46 \pm \sqrt{2372}}{-32}\)

\(\implies t=\dfrac{23 \pm \sqrt{593}}{16}\)

As time is positive,

\(\implies t=\dfrac{23 + \sqrt{593}}{16}=2.959474458...\:\sf s\quad only\)

The y-intercept is when t = 0:

\(h(0)=-16(0)^2+46(0)+4=4\)

So the curve intercepts the y-axis at (0, 4)

Because of the modelling of the function, there will be a restricted domain:  0 ≤ t ≤ 2.9595

Therefore, to find another point, input a value in the domain into the function and solve:

\(t=2 \implies h(2)=-16(2)^2+46(2)+4=32\)

⇒ (2, 32)

The horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

To determine the horizontal asymptote of a function, we need to examine the behavior of the function as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the terms involving x-2 and x-3 become insignificant compared to the higher power of (x-3) squared in the denominator.

As x approaches positive or negative infinity, the (x - 2) term in the numerator does not affect the overall behavior of the function. However, the (x - 3)^2 term in the denominator becomes dominant.

Since (x - 3)^2 will always be positive, the function is always positive or zero. Therefore, as x approaches positive or negative infinity, the function approaches zero or a positive value but never crosses the horizontal line y = 0. Hence, the horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

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Answer:

Yes

Step-by-step explanation:

One x ➡️ One y

(from the question)