Find the 5 data points needed for a box plot of the given data set: { 8, 19, 11, 20, 2, 14, 17, 9, 15}

Give the answers in order from least to greatest.

Data Point 1:

Data Point 2:

Data Point 3:

Data Point 4:

Data Point 5:

Answer:

Step-by-step explanation:

Answer:

The midpoint is (1,-13.5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(7+-5) /2 = 2/2 =1

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(-12+-15) /2 = -27/2 =-13.5

The midpoint is (1,-13.5)

Answer:

[tex]x<\frac{6}{5}[/tex]

Refer to picture for number line

Step-by-step explanation:

To solve this inequality, we want to isolate the variable. We can do this my getting like terms onto one side

[tex]6x-7<2-\frac{3x}{2}[/tex]       [add both sides by 7]

[tex]6x<9-\frac{3x}{2}[/tex]             [add both sides by 3x/2]

[tex]6x+\frac{3x}{2}<9[/tex]             [multiply both sides by 2]

[tex]12x+3x<18[/tex]          [add]

[tex]15x<18[/tex]                  [divide both sides by 15]

[tex]x<\frac{18}{15}[/tex]                     [simplify]

[tex]x<\frac{6}{5}[/tex]

Now that we have out inequality, we want to graph it. Since we know that [tex]x<\frac{6}{5}[/tex], that means we have an open circle. Since x is less than, the arrow would be pointing left.

Answer:

y = -1.5x - 1

Step-by-step explanation:

We can use the general equation of y = mx + c to form our linear equation as seen on this graph.

Choosing two points on the graph (I will choose 0,-1 and 2,-4) we can find the gradient, m, as the distance between these points

[tex]\frac{Rise}{Run} = \frac{(-1)-(-4)}{(0)-(2)} = \frac{3}{-2} =-1.5[/tex]

We can find the c value by seeing where the graph cuts through the y-axis

This point is -1

Therefore our equation is y = -1.5x - 1

Alternatively, you could write it as [tex]y= -\frac{3}{2} x - 1[/tex]

Answer:

y = -1.5x - 1

Answer:

26 gallons

Step-by-step explanation:

Take the miles and divide by the gallons

455 miles / 17.5 gallons

26 miles per gallon

Answer:

7×(8/6)=9.33

Step-by-step explanation:

7 is whole number

8/6 is the fraction

8/6 is 1.333

so, 7×1.333=9.33

Answer:

a) 0.06% probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years.

b) 90.15% probability that 285 or more companies outsourced some part of their manufacturing process in the past two or three years.

c) 0.23% probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years.

Step-by-step explanation:

For questions a and b, the normal approximation to the binomial is used, while for question c, the central limit theorem is used.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years.

This means that [tex]p = 0.54[/tex]

555 of these companies are contacted.

This means that [tex]n = 555[/tex]

Mean and standard deviation: Normal approximation to the binomial:

[tex]\mu = E(X) = np = 555*0.54 = 299.7[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{555*0.54*0.46} = 11.74[/tex]

a. What is the probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years?

Using continuity correction, this is [tex]P(X \geq 338 - 0.5) = P(X \geq 337.5)[/tex], which is 1 subtracted by the p-value of Z when X = 337.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{337.5 - 299.7}{11.74}[/tex]

[tex]Z = 3.22[/tex]

[tex]Z = 3.22[/tex] has a p-value of 0.9994.

1 - 0.9994 = 0.0006

0.0006*100% = 0.06%

0.06% probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years.

b. What is the probability that 285 or more companies outsourced some part of their manufacturing process in the past two or three years?

Using continuity correction, this is [tex]P(X \geq 285 - 0.5) = P(X \geq 284.5)[/tex], which is 1 subtracted by the p-value of Z when X = 284.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{284.5 - 299.7}{11.74}[/tex]

[tex]Z = -1.29[/tex]

[tex]Z = -1.29[/tex] has a p-value of 0.0985.

1 - 0.0985 = 0.9015

0.9015*100% = 90.15%

90.15% probability that 285 or more companies outsourced some part of their manufacturing process in the past two or three years.

c. What is the probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years?

Now we use the sampling distribution of the sample proportions, which have:

[tex]\mu = p = 0.54[/tex]

[tex]s = \sqrt{\frac{0.54*0.46}{555}} = 0.0212[/tex]

The probability is the p-value of Z when X = 0.48. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.48 - 0.54}{0.0212}[/tex]

[tex]Z = -2.84[/tex]

[tex]Z = -2.84[/tex] has a p-value of 0.0023.

0.0023*100% = 0.23%

0.23% probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years.

Answer:

wheres the picture?

Step-by-step explanation:

Answer: The answer that I got for z was 0.111575, which when you round it to the hundredths place would be 0.11

Answer:

the process capability index of the machine is 2.5

Option c) [More than 2 but less than or equal to 3] is the correct answer

Step-by-step explanation:

Given the data in the question;

process average ( x') = 12.000 ounces

standard deviation σ = 0.002 ounces

the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.

so

Upper specification Limit USL = 12.000 + 0.015 = 12.015 ounces

Lower specification Limit LSL = 12.000 - 0.015 = 11.985 ounces

the process capability index of the machine will be;

Cp = ( process average - Lower specification Limit ) /  3σ

so we substitute

Cp = ( 12 - 11.985 ) / ( 3 × 0.002 )

Cp = 0.015 / 0.006

Cp = 2.5

Therefore, the process capability index of the machine is 2.5

Option c) [More than 2 but less than or equal to 3] is the correct answer

9514 1404 393

Answer:

  3

Step-by-step explanation:

The length of A'B' is 3 units.

The length of AB is 1 unit.

The scale factor is A'B'/AB = 3/1 = 3.

Answer:

[tex]2827.4 \dfrac{ft}{s}[/tex]

Step-by-step explanation:

[tex] A = \pi r^2 [/tex]

[tex] \dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt} [/tex]

[tex] \dfrac{dA}{dt} = 2 \times \pi \times 30~ft \times 15 \dfrac{ft}{s} [/tex]

[tex] \dfrac{dA}{dt} = 2827.4 \dfrac{ft}{s} [/tex]

Answer:

All the angles on the bottom line are 60. The angles on the top line from left to right is 130, 60, 60, 130.

Step-by-step explanation:

Answer:

Volume is 167.6 yd³

Step-by-step explanation:

[tex]{ \boxed{ \bf{volume = \frac{1}{3}\pi {r}^{2} h}}} \\ { \sf{volume = \frac{1}{3} \times 3.14 \times {(4)}^{2} \times 10}} \\ \\ { \sf{volume = 167.6 \: {yd}^{3} }}[/tex]

Answer:

[tex]15x - 5 + x = - 47 \\ 15 + x - 5 = - 47 \\ 16x - 5 = - 47 \\ 16x = - 47 \\ x = \frac{ -16x}{16} = \frac{ - 45}{16} \\ x = - \frac{21}{8} [/tex]

Answer:

The first picture is the solution that I worked out and the second is the graph of the two solutions.

The graph of the solution of inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is as shown below.

"It is a mathematical statement of an order relationship (greater than, greater than or equal to, less than, or less than or equal to) between two numbers or algebraic expressions."

For given question,

We have been given a inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex]

We solve above inequality.

[tex]\Rightarrow -\frac{1}{3} (2x+1) < 3\\\\\Rightarrow \frac{1}{3} (2x+1) > -3\\\\\Rightarrow 2x+1 > -9\\\\\Rightarrow 2x > -10\\\\\Rightarrow x > -5[/tex]

so, the solution of the inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is all points on the X-axis which are greater than x = -5.

The graph of the solution of inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is as shown below.

Learn more about the inequality here:

https://brainly.com/question/19003099

#SPJ2

Answer:

7 and 3 are two numbers that work

Step-by-step explanation:

7-3=4

7×3=21

Answer:

345 bags and would each have 2

Answer:

The solution is defined in the attached file please find it.

Step-by-step explanation:

Answer:

0.0076 = 0.76% probability that all five plants emerged from treated seeds

Step-by-step explanation:

The plants were chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

6 + 6 = 12 seeds, which means that [tex]N = 12[/tex]

6 treated, which means that [tex]k = 6[/tex]

Five sprouted, which means that [tex]n = 5[/tex]

What is the probability that all five plants emerged from treated seeds?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,12,5,6) = \frac{C_{6,5}*C_{6,0}}{C_{12,5}} = 0.0076[/tex]

0.0076 = 0.76% probability that all five plants emerged from treated seeds

Answer:

The two numbers are:

x = 500

y = 125

Step-by-step explanation:

We want to find two numbers x and y, such that:

x + 4*y = 1000

f(x, y) = x*y is maximum.

From the first equation, we can isolate one of the variables to get

x = 1000 - 4y

now we can replace it in f(x, y):

x*y = (1000 - 4*y)*y  = 1000*y - 4*y^2

So now we want to maximize the function:

f(y) =- 4*y^2 + 1000*y

where y must be an integer.

Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.

Remember that for a general quadratic equation:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/(2*a)

so, in the case of:

f(y) =- 4*y^2 + 1000*y

the y-value of the vertex will be:

y = -1000/(2*-4) = 1000/8 = 125

So we found the value of y.

now we can use the equation:

x = 1000 - 4*y

x = 1000 - 4*125 = 1000 - 500 = 500

x = 500

Then the two numbers are:

x =500

y = 125

Answer:

The equation is x + 4 = 0.

Step-by-step explanation:

Point (-4 , 8)

A line parallel to the Y axis has slope is infinite.

The equation of line is

[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]

Answer:

-75/4

Step-by-step explanation:

75 x 100 = 7500

4 x 100 = 400

Answer:

B. 1✓3 in.

Search It ok

I see the answer :)

Answer:

[tex]B)[/tex]

[tex](-1,1)(-3,3)\\\frac{3-1}{-3+1} =-1\\1=1+b\\b=0\\y=-x[/tex]

OAmayOHopeO

Answer:

x = 16

Step-by-step explanation:

7(x + 2) = 6(x + 5)

First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.

7x + 14 = 6x + 30

Next, let's subtract "6x" from both sides of this equation!

x + 14 = 30

Now, we have to subtract "14" from both sides of the equation.

x = 16

Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.

7(16 + 2) = 6(16 + 5)

7(18) = 6(21)

126 = 126

Since our equations equal each other we know that our x-value is correct!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

The alternative hypothesis is [tex]H_1: p > 0.6[/tex].

The critical value is [tex]Z_c = 1.645[/tex]

Step-by-step explanation:

It is claimed that proportion in favor of proportion A is greater than 60%.

This means that at the null hypothesis, we test if the proportion is of at most 60%, that is:

[tex]H_0: p \leq 0.6[/tex]

At the alternative hypothesis, we test if the proportion is more than 60%, that is:

[tex]H_1: p > 0.6[/tex]

What is (are) the critical value?

The critical value is the value of Z with a p-value 1 subtracted by the standard significance level of 0.05, since we are testing if the mean is more than a value, so, looking at the z-table, [tex]Z_c = 1.645[/tex]