We are interested in knowing more about the number of hours students study for ST 311 each week. We know that there are 800 students enrolled in the course, with 35 students per section. We also know that ST 311 students study 10 hours a week on average, and that the standard deviation is 2 hours. We randomly sample 40 students taking the course, and record the average number of hours that they study per week. What is the sample size? A. 35 B. 40 C. 100 D. 800

Answer:

[tex]=13x+5[/tex]

Step-by-step explanation:

[tex]\left(2x+9\right)+\left(11x-4\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=2x+9+11x-4\\\mathrm{Group\:like\:terms}\\=2x+11x+9-4\\\mathrm{Add\:similar\:elements:}\:2x+11x=13x\\=13x+9-4\\\mathrm{Add/Subtract\:the\:numbers:}\:9-4=5\\=13x+5[/tex]

Answer:

  3x²

Step-by-step explanation:

The area is the product of the dimensions of the base:

  area = x(3x) = 3x²

Answer:

The correct answers are B, C, D, B

Step-by-step explanation:

These answers complete the statements that show the difference between the mathematical and reasonable ranges. Good luck! :)

B) Rational Numbers

C) 30,800

D) Real Numbers

B) 800

Correct on edge2020!

Answer:

BCDB

Step-by-step explanation:

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Given:

Total number of glasses = 16

Number of glasses containing prune juice = 4

Number of glasses containing apple juice = 2

To find:  fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice

Solution:

A fraction refers to the parts of a whole. In a fraction, a top number is the numerator, and a bottom number is the denominator.

Number of glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = 16 - 4 - 2 = 10

Total number of glasses = 16

So,

Fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = [tex]\frac{10}{16}=\frac{5}{8}[/tex]

Answer:

Lauren is wrong

Step-by-step explanation:

1. Lauren is wrong

2. What’s the cost of the shirts before tax

Each shirt cost $15 and the total = $15 x 3 = $45

3. How much is the sales tax for all shirts

Sale tax for all shirts is $45 x 0.08 = $3.6

4. What is the total cost of the shirts, including tax?

Total cost  = $45 + $3.6 = $48.60

Answer:

Any values that is greater than 1/2.

Step-by-step explanation:

You have to form an inequality. Given that what values is added to c will satisfy that 3 - 5c is less than 1 - c :

[tex]3 - 5c < 1 - c[/tex]

Next, you have to solve :

[tex] - 5c + c < 1 - 3[/tex]

[tex] - 4c < - 2[/tex]

[tex]c > \frac{ - 2}{ - 4} [/tex]

[tex]c > \frac{1}{2} [/tex]

Answer:

24% of those surveyed liked neither

Step-by-step explanation:

Set concepts:

We use set concepts to solve this question.

I am going to say that:

P(A) is the percentage of people that liked to swim.

P(B) is the the percentage of people that liked to run.

The percentage of people that liked at least one of these activities is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In which [tex]P(A \cap B)[/tex] is the probability that a person liked both these activities.

The percentage of people that liked neither is:

[tex]P = 1 - P(A \cup B)[/tex]

Of those surveyed, 58% said they liked to swim and 36% said they liked to run.

This means that [tex]P(A) = 0.58, P(B) = 0.36[/tex]

18% said they liked both swimming and running

This means that [tex]P(A \cap B) = 0.18[/tex]

What percent of those surveyed liked neither?

At least one:

[tex]P(A \cup B) = 0.58 + 0.36 - 0.18 = 0.76[/tex]

Neither:

[tex]P = 1 - P(A \cup B) = 1 - 0.76 = 0.24[/tex]

24% of those surveyed liked neither

Answer:

117 units cubed.

Step-by-step explanation:

I have attached the work to your problem.

Please see the attachment below.

I hope this helps!

Answer:

117

Step-by-step explanation:

find all the shown surface area

Answer:

relative maximum: x = 1

relative minimum: x = 7

Step-by-step explanation:

Critical points:

Values of x for which f'(x) = 0.

Second derivative test:

For a critical point, if f''(x) > 0, the critical point is a relative minimum.

Otherwise, if f''(x) < 0, the critical point is a relative maximum.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]f(x) = x^{3} - 12x^{2} + 21x - 8[/tex]

Finding the critical points:

[tex]f'(x) = 3x^{2} - 24x + 21[/tex]

[tex]3x^{2} - 24x + 21 = 0[/tex]

Simplifying by 3

[tex]x^{2} - 8x + 7 = 0[/tex]

So [tex]a = 1, b = -8, c = 7[/tex]

[tex]\bigtriangleup = (-8)^{2} - 4*1*7 = 36[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{36}}{2} = 7[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{36}}{2} = 1[/tex]

Second derivative test:

The critical points are x = 1 and x = 7.

The second derivative is:

[tex]f''(x) = 6x - 24[/tex]

[tex]f''(1) = 6*1 - 24 = -18[/tex]

Since f''(1) < 0, at x = 1 there is a relative maximum.

[tex]f''(7) = 6*7 - 24 = 18[/tex]

Since f''(x) > 0, at x = 7 there is a relative minumum.

Answer: statistical

Step-by-step explanation: A statistical – is a question that can be answered by collecting data and that anticipates variability in those data • Statistics – the science of collecting, reviewing, and analyzing data

Answer:

The Answer is 10, 50, and 54

Step-by-step explanation:

You want to figure this answer out by using the Pythagorean Theorem. If 10 squared plus 50 squared does not equal 54 squared, then those side lengths can not make a triangle.  

Answer: 268 hamburgers

Answer:

[tex] y = -\frac{1}{3}x-2[/tex]

Step-by-step explanation:

From the table it is clear that the line is passing through the points [tex] (0,\: -2)= (x_1, \:y_1) \: \&\: (-6, \:0)=(x_2,\:y_2) [/tex]

(There are many other points in the table and any two of them can chosen as per our convenience)

Equation of line in two point form is given as:

[tex] \frac{y-y_1}{y_1 - y_2} = \frac {x-x_1}{x_1 - x_2} \\\\

\therefore \frac{y-(-2)}{-2 - 0} = \frac {x-0}{0 - (-6)} \\\\

\therefore \frac{y+2}{-2} = \frac {x}{0+6)} \\\\

\therefore \frac{y+2}{-2} = \frac {x}{6)} \\\\

\therefore 6(y + 2) = - 2(x)\\

\therefore 6y + 12 = - 2x \\

\therefore 6y = - 2x - 12\\\\

\therefore y = -\frac{2}{6}x-\frac{12}{6}\\\\

\huge \red {\boxed {y = -\frac{1}{3}x-2}} \\\\[/tex]

Answer:

(a)77.4bpm

(b)Mean of Sample 1 = 70.3 beats per minute.  

Mean pulse of sample 2 = 70 beats per minute.

(c)

Step-by-step explanation:

(a)Population mean pulse.

The pulse of the nine students which represent the population are:

[tex]\text{Population Mean} =\dfrac{64+77+89+69+89+65+88+69+87}{9} \\=\dfrac{697}{9} \\\\=77.44[/tex]

The population mean pulse is approximately 77.4 beats per minute.

(b)Sample 1: {Janette,Clarice,Megan}

Mean of Sample 1

[tex]\text{Sample 1 Mean} =\dfrac{65+69+77}{3} \\=\dfrac{211}{3} \\\\=70.3[/tex]

Sample 2: {Janette,Clarice,Megan}

Mean of Sample 2

[tex]\text{Sample 2 Mean} =\dfrac{64+69+77}{3} \\=\dfrac{210}{3} \\\\=70[/tex]

The mean pulse of sample 1 is approximately 70.3 beats per minute.  

The mean pulse of sample 2 is approximately 70 beats per minute.

(c)

Let the amount that Sky receives be S, and the amount that Natalia recieves be N.

[tex] \dfrac{s}{n} = \dfrac{6}{5} [/tex]

[tex]s = n + 3 \\ \\ \dfrac{n + 3}{n} = \frac{6}{5} \\ \\ 5n + 15 = 6n \\ \\ n = 15[/tex]

15 euros

Answer:

Los pinos ocupan [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.

Step-by-step explanation:

Una manera de resolver este problema es la siguiente:

[tex] \\ 1km^{2} = 1km * 1km = 1000m * 1000m = 1000000m^{2}[/tex]

[tex] \\ 2km^{2} = 2km * 1km = 2000m * 1000m = 2000000m^{2} = 2 * 10^{6}m^{2}[/tex]

En palabras, [tex] \\ 2km^{2} = 2000000m^{2}[/tex], o dos kilómetros cuadrados son iguales a 2 millones de metros cuadrados.

Sabemos que:

De esta manera, la parte que ocupan los pinos es el total del bosque menos el área ocupada por las hayas. Por lo tanto, el área ocupada por los pinos es:

[tex] \\ 2000000m^{2} - 380000m^{2}[/tex]

[tex] \\ 1620000m^{2}[/tex]

¿Cuántos metros cuadrados ocupan los pinos?

Los pinos ocupan, entonces, [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.

Step-by-step explanation:

We have,

If a quadratic equation with real coefficients has a discriminant of -36.

The general form of quadratic equation is :

[tex]ax^2+bx+c=0[/tex]

The discriminant of this equation is : [tex]D=b^2-4ac[/tex]

If D=0, it will have 1 real roots

If D>0, it will have 2 real roots

If D<0, it will have no real roots

We have,

D = -36 < 0, so, the quadratic equation will have no real roots.

Answer: 2 ÷ 17

Step-by-step explanation: When you have something in this form, a/b, it means the same thing as a divided by b.

So 2/17 means the same thing as 2 ÷ 17.

Answer:

Step-by-step explanation:

A coin has two faces, a head (H) or tail (T). Tossing a coin twice in succession would give the following sample size;

                                 {HH, HT, TH, TT}

Given that: A = first toss is heads, B = second toss is heads, then:

i. P(A) = {HH, HT} = 2

ii. P(B) = {TH} = 1

iii. P(A∩B) = {HH} = 1

iv. P(B /A) = [tex]\frac{1}{2}[/tex]

Answer:

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

[tex]\mu = 66, \sigma = 2, n = 87, s = \frac{2}{\sqrt{87}} = 0.214[/tex]

Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

This probability is 1 subtracted by the pvalue of Z when X = 66.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{66.5 - 66}{0.214}[/tex]

[tex]Z = 2.336[/tex]

[tex]Z = 2.336[/tex] has a pvalue of 0.99.

1 - 0.99 = 0.01

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Answer:

Yes. Some examples are √2, √3, √5.

You better believe it !  In fact, if you don't count an infinite number of examples, you'll find that MOST of their square roots are irrational.

Let's examine the smallest 1,000 integers . . .

-- They're all rational numbers, but ...

-- only 31 of them have rational square roots !

Answer:

2.9 per hour

Step-by-step explanation:

Divide 69.9 by 24

Answer:

GRAPH OF 3X+2 IS 6

Step-by-step explanation:

Answer:

The graph below

Step-by-step explanation:

Answer:

D. Parabola; 0°

Step-by-step explanation:

Answer:

For this case the mean is given by:

[tex] \mu = p =0.46[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]

Step-by-step explanation:

For this case we have the following info given :

[tex] n = 215[/tex] represent the sample size

[tex]p = 0.46[/tex] represent the proportion of business graduate students from private universities had student loans

For this case we want to find the distribution for the sample proportion and we know that this distribution is given by:

[tex] \hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]

And for this case the mean is given by:

[tex] \mu = p =0.46[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]

Answer:

The mean of this distribution is 0.46 and the standard deviation is 0.034.

Step-by-step explanation:

The Central Limit Theorem estabilishes 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 sampling distributions of samples of size n of a proportion p, the mean is [tex]\mu = p[/tex] and the standard deviation is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]n = 215, p = 0.46[/tex]

So

[tex]\mu = 0.46, s = \sqrt{\frac{0.46*0.54}{215}} = 0.0340[/tex]

The mean of this distribution is 0.46 and the standard deviation is 0.034.

Answer:

Step-by-step explanation:

the data is skewed left

The data in the given set is skewed towards left because the mean of the data is 7.5 and the data is not distributed symmetrically in the given set. Thus, the correct option is C.

Skewed data is the data which creates an asymmetrical, skewed curve on the graph scale. In statistics, the graph of a data set with normal distribution is symmetrical and has a bell-like shape. However, the skewed data has a tail on either side of the graph as well.

Skewness can be demonstrated on a bell curve when the data points are not distributed symmetrically to the left and right sides of the median on the curve. If the bell curve is shifted to the left or towards the right side, it is said to be skewed curve. The two halves of the distribution are not mirror images in the skewed curve because the data are not distributed equally on both sides of the distribution peak.

Therefore, the correct option is C.

Learn more about Skewed data here:

https://brainly.com/question/3907939

#SPJ2

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

The table below contains the overall miles per gallon (MPG) of a type of vehicle. Complete parts a and b below.

28, 34, 28, 20, 21, 31, 28, 24, 34, 35 , 36, 26, 25, 20

a. Construct a 95% confidence interval estimate for the population mean MPG for this type of vehicle, assuming a normal distribution.

b. Choose the correct answer below.

A. We have 95% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval.

B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval. This is the correct answer.

C.95 % of the sample data fall between the limits of the confidence interval.Your answer is not correct.

D. The mean MPG of this type of vehicle for 95?% of all samples of the same size is contained in the interval.

Solution:

a) Mean = (28 + 34 + 28 + 20 + 21 + 31 + 28 + 24 + 34 + 35 + 36 + 26 + 25 + 20)/14 = 27.86

Standard deviation = √(summation(x - mean)²/n

n = 14

Summation(x - mean)² = (28 - 27.86)^2 + (34 - 27.86)^2 + (28 - 27.86)^2 + (20 - 27.86)^2 + (21 - 27.86)^2+ (31 - 27.86)^2 + (28 - 27.86)^2 + (24 - 27.86)^2 + (34 - 27.86)^2 + (35 - 27.86)^2 + (36 - 27.86)^2 + (26 - 27.86)^2 + (25 - 27.86)^2 + (20 - 27.86)^2 = 399.7144

Standard deviation = √(399.7144/14) = 5.34

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 5.34

n = number of samples = 14

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 14 - 1 = 13

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.16

Margin of error = 2.16 × 5.34/√14

= 3.08

The confidence interval is 27.86 ± 3.08

b) B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval.

Step-by-step explanation:

Replace x = 3

f(3) = 2(3) - 2

= 6 - 2

= 4

Answer:

f(3) =4

Step-by-step explanation:

f(x) = 2x - 2

Let x=3

f(3) = 2*3 - 2

     = 6-2

     = 4