Use the following sample to estimate a population mean μμ.

51.3
59.5
58.1
57.1
55.3
61


Assuming the population is normally distributed, find the 99.9% confidence interval about the population mean. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places.

99.9% C.I. =

Answer:

May be minus

Step-by-step explanation:

minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32

The apothecary system uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.

What is apothecary measurement?

What are the units of the apothecary system?

The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).

Learn more about apothecary system

brainly.com/question/10433943

#SPJ4

Answer:

14

Step-by-step explanation:

okay.. so basically you have 2x+6=34 right? so basically i’m gonna tell you the easiest way to do this

so you’re gonna start off by separating the 2x from the 6=34.

now that you’ve done that, let’s focus on the 6=34. so to get your answer, start by subtracting 6 from 34 so (34 - 6 = 28)

now that you’ve got that, keep the number 28 in mind. youre gonna want to take 2 and multiply by x. but 2x = 28, so what do you multiply by 2 to make 28? 14. so x is 14. to check your work, let’s see.

2 x 14 + 6 = 34?

2 x 14 = 28 + 6 = 34.

34 = 34

so, x is 14. hope this helped!

Answer:

20$

Step-by-step explanation:

\(17 \div \frac{85}{100} = 17 \times \frac{100}{85} = 20\)

Answer:

D) triangle

Step-by-step answer:

A pyramid is a three-dimensional figure with a plane that is parallel to its base.

A three dimensional figure is a figure with a length, width and height. 3D shapes have faces, edges, and vertices.

Rectangle, square and triangle are two dimensional shapes while pyramid is a three dimensional shape.

A pyramid is a three-dimensional figure with a plane that is parallel to its base.

Find out more on Pyramid at: https://brainly.com/question/218706

There is sufficient evidence to support the claim of a greater variance for machine 1

Given: n1=25 , n2​=22

The mean is the sum of all values divided by the number of values:

x1=2.95+3.45+...+3.35+3.12/25≈3.3284

x2​=3.22+3.30+...+3.16+3.33​/22≈3.2782

The variance is the sum of squared deviations from the mean divided by n−1. The standard deviation is the square root of the variance:

s1=√(2.95−3.3284)²+....+(3.12−3.3284)²/25−1≈0.2211

s1​=√25−1(2.95−3.3284)2+....+(3.12−3.3284)2​

​≈0.2211

s2=(3.22−3.3284)2+....+(3.33−3.3284)222−1≈0.0768

s2​=(3.22−3.3284)2+....+(3.33−3.3284)2²/22−1​≈0.0768

Determine the hypotheses:

H0=σ12≤σ22

H1​=σ12​>σ22​

Compute the value of the test statistic:

F=\(\frac{S^1_2}{S^2_2}\) =0.2211²/0.0768²≈8.288

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value with dfn=25−1=24 and dfd=22−1=21:

P<0.01

If the P-value is less than the significance level, reject the null hypothesis.

P<0.01⇒ Reject H0

Complete Question:

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

To learn more about the standard deviation, visit:

brainly.com/question/23907081

#SPJ4

There is sufficient evidence to support the claim of a greater variance for machine 1

Given: n1=25 , n2​=22

The mean is the sum of all values divided by the number of values:

x1=2.95+3.45+...+3.35+3.12/25≈3.3284

x2​=3.22+3.30+...+3.16+3.33​/22≈3.2782

The variance is the sum of squared deviations from the mean divided by n−1. The standard deviation is the square root of the variance:

s1=√(2.95−3.3284)²+....+(3.12−3.3284)²/25−1≈0.2211

s1​=√25−1(2.95−3.3284)2+....+(3.12−3.3284)2​

​≈0.2211

s2=(3.22−3.3284)2+....+(3.33−3.3284)222−1≈0.0768

s2​=(3.22−3.3284)2+....+(3.33−3.3284)2²/22−1​≈0.0768

Determine the hypotheses:

H0=σ12≤σ22

H1​=σ12​>σ22​

Compute the value of the test statistic:

F= \(\frac{S_2^1}{S_2^2}\) =0.2211²/0.0768²≈8.288

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value with dfn=25−1=24 and dfd=22−1=21:

P<0.01

If the P-value is less than the significance level, reject the null hypothesis.

P<0.01⇒ Reject H0

To learn more about Standard deviation:

brainly.com/question/23907081

#SPJ4

Complete Question:

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

Answer:

slope= 3/4 y-intercept= 2  graph is 4,5

Step-by-step explanation:

rise 3 run 4 or up 3 and 4 right

Part 1-The average velocity of the object over the given time intervals is 6m/s.

Part 2- The instantaneous velocity of the object at time t=2sec is 12 m/s.

Given, The displacement of a particle moving in a straight line is given by the function s(t) = 3t².

We have to calculate the following -

Average velocity

Instantaneous velocity

Part 1 - Average Velocity

Average Velocity is the change in position divided by the time it took to change. The formula for the average velocity can be represented as:

v = Δs/Δt

Where v represents the average velocity,

Δs is the change in position and

Δt is the change in time.

Determine the displacement of the particle from t = 0 to t = 2.

The change in position can be represented as:

Δs = s(2) - s(0)Δs = (3(2)² - 3(0)²) mΔs = 12 m

Determine the change in time from t = 0 to t = 2.

The change in time can be represented as:

Δt = t₂ - t₁Δt = 2 - 0Δt = 2 s

Calculate the average velocity as:

v = Δs/Δt

Substitute Δs and Δt into the above formula:

v = 12/2 m/s

v = 6 m/s

Therefore, the average velocity of the object from t = 0 to t = 2 is 6 m/s.

Part 2 - Instantaneous Velocity

Instantaneous Velocity is the velocity of an object at a specific time. It is represented by the derivative of the position function with respect to time, or the slope of the tangent line of the position function at that point.

To find the instantaneous velocity of the object at t = 2, we need to find the derivative of the position function with respect to time.

s(t) = 3t²s'(t) = 6t

The instantaneous velocity of the object at t = 2 can be represented as:

v(2) = s'(2)

Substitute t = 2 into the above equation:

v(2) = 6(2)m/s

v(2) = 12 m/s

Therefore, the instantaneous velocity of the object at t = 2 seconds is 12 m/s.

To know more about velocity refer here:

https://brainly.com/question/31495959

#SPJ11

(4,-12) are the coordinates of the center of the circle.

What is a circle, exactly?

The collection of all points in the plane that make up a circle are all evenly separated from a single point known as the "centre," resulting in a closed two-dimensional structure. Each line that crosses the circle creates the line of reflection symmetry. The rotational symmetry at the centre of each angle is another feature. Following a moving point in a plane while maintaining constant distance from a certain point results in the formation of a circular shape known as a circle.

(x-4)²+(y+12)² = 17²

 The equation of a circle has the following form

  ( x - h)²  + ( y - k)² = r²

where (h, k) is the center of a circle with radius r.

Our equation is

  ( x - 4)² +(y+12)² = 17²

The center is (4,-12).

Learn more about circle

brainly.com/question/29142813

#SPJ1

(a) The marginal pmf of X: fX(1) = 9/32, fX(2) = 11/32

(b) The marginal pmf of Y: fY(1) = 7/64, fY(2) = 9/64, fY(3) = 11/64 fY(4) = 13/64

(c) P(X > Y) = 11/32

(d) P(Y = 2X) = 1/16

(e) P(X + Y = 3) = 1/8

(f) P(X ≤ 3 - Y) = 11/64

(g) X and Y are dependent.

(h) Mean of X (μX) = 41/32, Mean of Y (μY) = 205/64, Variance of X (σX²) = 113/1024 and Variance of Y (σY²) = 8199/8192

(a) To find fX(x), the marginal pmf of X, we sum the joint probabilities for each value of x:

fX(1) = f(1,1) + f(1,2) + f(1,3) + f(1,4) = 3 + 4 + 5 + 6 = 18

fX(2) = f(2,1) + f(2,2) + f(2,3) + f(2,4) = 4 + 5 + 6 + 7 = 22

Therefore, the marginal pmf of X is:

fX(1) = 18/64 = 9/32

fX(2) = 22/64 = 11/32

(b) To find fY(y), the marginal pmf of Y, we sum the joint probabilities for each value of y:

fY(1) = f(1,1) + f(2,1) = 3 + 4 = 7

fY(2) = f(1,2) + f(2,2) = 4 + 5 = 9

fY(3) = f(1,3) + f(2,3) = 5 + 6 = 11

fY(4) = f(1,4) + f(2,4) = 6 + 7 = 13

Therefore, the marginal pmf of Y is:

fY(1) = 7/64, fY(2) = 9/64, fY(3) = 11/64, fY(4) = 13/64

(c) P(X > Y) can be found by summing the joint probabilities where X is greater than Y:

P(X > Y) = f(2,1) + f(2,2) + f(2,3) + f(2,4) = 4 + 5 + 6 + 7 = 22/64 = 11/32

(d) P(Y = 2X) can be found by summing the joint probabilities where Y is twice the value of X:

P(Y = 2X) = f(1,2) = 4/64 = 1/16

(e) P(X + Y = 3) can be found by summing the joint probabilities where X + Y equals 3:

P(X + Y = 3) = f(1,2) + f(2,1) = 4 + 4 = 8/64 = 1/8

(f) P(X ≤ 3 - Y) can be found by summing the joint probabilities where X is less than or equal to 3 - Y:

P(X ≤ 3 - Y) = f(1,1) + f(1,2) + f(2,1) = 3 + 4 + 4 = 11/64

(g) To determine if X and Y are independent or dependent, we compare the joint pmf with the product of the marginal pmfs:

f(x,y) = 32x+y

fX(x) × fY(y) = (9/32) × (7/64) = 63/2048

Since f(x,y) is not equal to fX(x)× fY(y), X and Y are dependent.

(h) To find the means and variances of X and Y, we use the formulas:

Mean of X (μX) = ∑(x × fX(x))

Mean of Y (μY) = ∑(y×fY(y))

Variance of X (σX²) = ∑((x - μX)² * fX(x))

Variance of Y (σY²) = ∑((y - μY)² × fY(y))

Calculating the means:

μX = (1 × (9/32)) + (2 × (11/32)) = 41/32

μY = (1 × (7/64)) + (2× (9/64)) + (3 × (11/64)) + (4 × (13/64)) = 205/64

Calculating the variances:

σX²= ((1 - 41/32)² × (9/32)) + ((2 - 41/32)² × (11/32)) = 113/1024

σY² = ((1 - 205/64)²× (7/64)) + ((2 - 205/64)²× (9/64)) + ((3 - 205/64)² × (11/64)) + ((4 - 205/64)² × (13/64)) = 8199/8192

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ4

Answer:

Step-by-step explanation:

When the balloons collide, they have the same x and y:

-3x^2 + 24x + 3 = y = -4x^2 + 25x + 15

Rearranging like terms together:

(4x^2 - 3x^2) + (24x - 25x) + (3 - 15) = 0

x^2 - x - 12 = 0

(x - 4)(x +3) = 0

x = 4 or -3

As x represents time, it cannot be negative.

The time when the balloons collide is at 4.00 seconds.

The collision means that y is equal

So

As it's time so must be positive

Answer:

16 miles

Step-by-step explanation:

8*2=16

Brainlest pls?

Answer:

1.Conduction

2.the second one

sorry if these are wrong

Step-by-step explanation:

Answer:

#1 Convection

#2 From the hot to the mug

P(at least 1 infected person) = 0.7

Note that:

Probability = (Number of possible outcomes) / (Number of total outcomes)

The crew members = 5

Number of infected crew members = 2

Number of uninfected crew members = 3

We want to select two crew members for a task out of 5

Number of total outcomes = 5C2 (Selecting 2 out of 5)

Note that:

Number of total outcomes = 10

That is, there are 10 ways of selecting 2 crew members from 5

Number of ways of selecting 1 infected person means how we can select two people out of 5 such that 1 one of them will be infected. This means that we will select 1 from the two infected persons, and select the second one from the 3 uninfected persons

Number of ways of selecting 1 infected persons = 2C1 x 3C1

Number of ways of selecting 1 infected persons = 2 x 3

Number of ways of selecting 1 infected persons = 6

Number of ways of selecting 2 infected persons = 2C2

Number of ways of selecting 2 infected persons = 1 way

Probability of selecting 1 infected person = 6/10 = 0.6

Probability of selecting 2 infected person = 1/10 = 0.1

P(at least 1 infected person) = P(1 infected person) + P(2 infected persons)

P(at least 1 infected person) = 0.6 + 0.1

P(at least 1 infected person) = 0.7

Step-by-step explanation:

you can see this either as projection or as 2 similar triangles.

in any case we know that the scale factor is the same for every line and side.

midsegment means that B and D are in the middle of CA and CE. so, the scale factor from CB to CA is 2.

the same scaling factor applies to BD to AE.

AE = 56×2 = 112

9514 1404 393

Answer:

  opposite sides have the same slope, so it is a parallelogram

Step-by-step explanation:

A parallelogram has opposite sides that are parallel. Here, one pair of opposite sides consists of horizontal lines. Both have zero slope, so are parallel.

The other pair of lines each has a "rise" of 3 units for each "run" of 2 units, so the lines have a slope of 3/2. Both lines have the same slope, so are parallel.

Since opposite sides are parallel, the figure is a parallelogram.

The closest to the proportion of orders that are processed in less than 240 seconds is 17%

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the known values in the above equation, so, we have the following representation

z = (240- 276)/38

Evaluate

z = -0.95

The closest proportion is then calculated as:

P(x < 240) = P(z < -0.95)

From the z table of probabilities, we have;

P(x < 240) = 0.17106

This gives

P(x < 240) = 17.106%

Approximate

P(x < 240) = 17%

Hence, the closest proportion is 17%

Read more about probability at:

brainly.com/question/25870256

#SPJ1

Answer:

A

Step-by-step explanation:

4x - 1x = 3x

3 + 2 = 5

therefore your expression would be,

3x + 5

Answer:

A

Step-by-step explanation:

If you combine like terms on all of them, you get

A 3x+5

B 4x+5

C 3x+3

D 4x+5

hope this helps!

Answer:

R

Step-by-step explanation:

It is a triangle, so whichever point is not part of the line MUST be the opposite.

Also I am in geometry too, had my midterm today :D

It should be noted that the place the square root of 75 minus 13 would be plotted on a number line is C. Between −4 and −5, but closer to −4.

It should be noted that a square root simply means the numbers that can be multiplied by itself that will give the original number.

It should be noted that the square root of 75 is 8.66. Therefore, square root of 75 minus 13 would be:

= ✓75 - 13

= 8.66 - 13

= -4.3397

Therefore, it should be noted that the place the square root of 75 minus 13 would be plotted on a number line is vetween −4 and −5, but closer to −4

Learn more about square root on:

brainly.com/question/428672

#SPJ1

Answer:

I, II, III, IV, V, VI, VII, VIII, IX, and X.

Step-by-step explanation:

ik the numerals

Answer:

x=7.48 cm, y=6.94

Step-by-step explanation:

Start by finding the value of x.

Using the Pythagorean Theorem, \(13^{2}+x^{2} =15^{2}\)

\(169+x^{2} =225\\x^2=56\\x=\sqrt{56}\\x=2\sqrt{14}\)

Using this, we can again use the Pythagorean Theorem to find the value of y.

\(2.8^{2} +y^{2} =(2\sqrt{14} )^{2} \\7.84+y^{2} =56\\y^{2} =48.16\\y=\sqrt{48.16}\)

(I rounded to two decimal places, not sure what is required here)

x=7.48 cm

y=6.94 cm

The annual sales of the Hand & Foot Cream are increasing by 151,000 bottles per year. Based on the linear trend equation, the predicted annual sales for year 6 is 1,006,000 bottles.

According to the given linear trend equation F1 = 80 + 151, the constant term 80 represents the initial annual sales at the start of the trend. The coefficient of the independent variable t, which represents the number of years, is 151.

To determine whether the annual sales are increasing or decreasing, we look at the coefficient of t. Since the coefficient is positive (151), it indicates that the annual sales are increasing over time. The coefficient tells us that for every year that passes, the annual sales increase by 151,000 bottles. Therefore, the annual sales are experiencing positive growth.

To predict the annual sales for year 6, we substitute t = 6 into the equation. Plugging in the value, we have F6 = 80 + (151 * 6) = 80 + 906 = 986. Therefore, the predicted annual sales for year 6 is 986,000 bottles.

In conclusion, the annual sales of the Hand & Foot Cream are increasing by 151,000 bottles per year. Based on the linear trend equation, the predicted annual sales for year 6 is 986,000 bottles. This indicates that the product's popularity and demand are growing steadily.

Learn more about linear  equation here:

https://brainly.com/question/32634451

#SPJ11

Answer:

Step-by-step explanation:

The first one

Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.

Given that,

A fair coin is tossed 29 times.

We have to find what is the probability that at most 27 heads occur.

We know that,

A fair coin is tossed 29 times.

n=29

Probability of heads p=1/2

q= 1-p

q=1-1/2=1/2

We get

P (X=x) = ⁿCₓ qⁿ⁻ˣ pˣ

Now, the probability that at most 27 heads occurs is

P(X<27)

=1-[P(X=28)+ P(X=29)]

=1-[²⁹C₂₈(1/2)²⁹⁻²⁸(1/2)²⁸- ²⁹C₂₉(1/2)²⁹⁻²⁹(1/2)²⁹]

=1-[²⁹C₂₈(1/2)²⁹- ²⁹C₂₉(1/2)²⁹]

=1-[28+1](1/2)²⁹

=1-29×0.00000000186

=0.999999945

Therefore, Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ4

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

Answer:

-5

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

hope it helped!! Brainliest? I need em

Answer: For 6 only 1=45degrees 2=45degrees and 3=135 degreed

Step-by-step explanation:

Corresponding and complimentary angles

In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

Learn more about linear equation

brainly.com/question/21835898

#SPJ4    

The scatterplot can show an association or no association, at all.

The type of association shown by the graph that relates variables x and y is no association

When the points on the graph of the scatter plot follows an approximately, straight line; then the relationship is a linear relationship.

If it follows a curve, then it is a nonlinear relationship

If the points are scattered, then it shows no association.

The points on the graph are scattered, and they do not follow a specific pattern.

Hence, the graph shows no association

Read more about scatterplots at:

https://brainly.com/question/6592115