A group of professors investigated​ first-year college​ students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 149149 freshmen​ students, 3232 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this​ information, is it correct at the alphaαequals=0.100.10 level of significance to state that more than​ 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary​ systems? State the null and alternative hypotheses. Choos

Answer:

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Step-by-step explanation:

We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.8}{2} = 0.1[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.5 = 0.9[/tex], so [tex]z = 1.282[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.282*\frac{6}{\sqrt{21}} = 1.68[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.

The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Answer:

2

Step-by-step explanation:

-13+3b=-5-b

4b=8

b=2

Answer:

Its depending on the angle

Answer:

0.9940

Step-by-step explanation:

P(at least 1) = 1 − P(zero)

P(at least 1) = 1 − (1 − 0.64)⁵

P(at least 1) = 1 − (0.36)⁵

P(at least 1) = 0.9940

The probability that at least one of them has been vaccinated is 0.9939.

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure. It helps to check the probability of getting “x” successes in “n” independent trials of a binomial experiment.

For the given situation,

Number of people vaccinated = 64% = 0.64

The formula of binomial distribution is

[tex]P(x:n,p) = nC_{x} p^x (1-p)^{n-x}[/tex]

Here x is the number of successes, x ≤ 1

n is the number of trials, n = 5

p is the probability of a success on a single trial, p = 0.64 and

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

The probability is [tex]P(X \leq 1)=1-P(X=0)[/tex]

[tex]P(X=0)= 5C_{0} (0.64)^{0} (1-0.64)^{5-0}[/tex]

⇒ [tex]P(X=0)= 1(1) (0.36)^{5}[/tex]

⇒ [tex]P(X=0)= 0.0060[/tex]

Thus, [tex]P(X \leq 1)=1-P(X=0)\\[/tex]

⇒ [tex]P(X \leq 1)=1-0.0060[/tex]

⇒ [tex]P(X \leq 1)=0.9939[/tex]

Hence we can conclude that the probability that at least one of them has been vaccinated is 0.9939.

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Answer:

Answer:

68.44$

Step-by-step explanation:

x=18*58/100=10.44 $(the tip)

58+10.44=68.44 ( the bill )

Answer:

work is shown and pictured

Answer:

x = 3.6 cm

Step-by-step explanation:

By the theorem of intersecting secants,

"If two secants are drawn from a point outside the circle, product of the lengths of the secant segment and its external segment are equal."

3(3 + y) = 2(2 + 6 + 3)

9 + 3y = 2 × 11

3y = 22 - 9

3y = 13

y = [tex]\frac{13}{3}[/tex] cm = 4.33 cm

Now we will apply theorem of intersecting chords to determine the value of x.

" When two chords intersect each other in a circle, product of their segments are equal"

[tex]x\times 5=6\times 3[/tex]

[tex]x=\frac{18}{5}[/tex]

[tex]x=3.6[/tex] cm

Therefore, x = 3.6 cm and y = 4.33 cm

Answer:

a) (V)  = 904.78 of a sphere = 288pi diameter = 12

(V) = 1728cm^3 of a cube = face diagonal = 16.9cm

b) Difference Volume = 1728-904.78 = 823.22cm^3

Step-by-step explanation:

To find volume of an inscribed sphere within a square cube

We use 4 π/3 * r^3 for the equation

As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3

r^3 = 216

4pi/3 = 4.18

4.18 * 216 = 904.78

This means the answer is 288 pi cm^3.

Answer:

volume of gemstone = 905 cm^3

volume of empty space = 823 cm^3

Step-by-step explanation:

volume of cube = s^3, where s = length of edge

volume of sphere = (4/3)(pi)r^3, where r = radius of sphere

The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.

a)

volume of sphere = (4/3)(pi)r^3

volume of sphere = (4/3)(3.14159)(6 cm)^3

volume of sphere = 905 cm^3

b)

The empty space is the difference between the volume of the cube and the volume of the sphere.

volume of cube = s^3

volume of cube = (12 cm)^3

volume of cube = 1728 cm^3

empty space = volume of cube - volume of sphere

empty space = 1728 cm^3 - 905 cm^3

empty space = 823 cm^3

Answer:

3

Step-by-step explanation:

8-(3a+8)

8-(11a)

8-11a

a=11-8

a=3

Answer:

0

Step-by-step explanation:

8-(3a+8)=0

8-3a-8=0

-3a=0

a=0

Answer:

Search Results

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Which means that the first number is 104, the second number is 104 + 1 and the third number is 104 + 2. Therefore, three consecutive integers that add up to 315 are 104, 105, and 106.

Step-by-step explanation:

Answer:

[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]

And we can find this probability with this difference:

[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(200,50)[/tex]  

Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]

We want to find the following probability:

[tex]P(170<X<220)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

And using this formula we got:

[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]

And we can find this probability with this difference:

[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]

Answer:

  38°

Step-by-step explanation:

The sum of angles that make a line is 180°; the sum of angles in a triangle is 180°. So, we have the following relations:

  2x +y +A = 180

  2y +x + B = 180

  A +B +33 = 180

Adding the first two equations and subtracting the third, we get ...

  (2x +y +A) +(2y +x +B) -(A +B +33) = 180 +180 -180

  3x +3y -33 = 180

  x + y - 11 = 60

  x + y = 71

__

We know vertical angles are congruent, so in triangle QRK, we have ...

  2y +2x +∠K = 180

  ∠K = 180 -2x -2y = 180 -2(x +y) = 180 -2(71)

  ∠JKL = 38°

Answer:

38 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

The variable is

X: average mass of a sample of rocks collected in the waters of a region. (measured in grams)

Variables can be:

Quantitative: they represent number, any characteristic that can be "counted" is a quantitative variable, the most common examples are weight, volume, temperature, height, etc...

There are two types of quantitative variables:

⇒ Discrete variables: The only take certain values within the interval of definition of the variable, for example "number of sales" or "money in a wallet"

⇒ Continuous variables: They can take any value within an interval, in this example that you are working with mass, depending on the precision of the scale the mass can have infinite decimal values.

Qualitative: they represent characteristics that cannot be counted, meaning, they are not represented by numbers. There are many attributes that are qualitative variables, for example: colors, race of an animal, phenotypes, types of business, etc...

1)

The variable in this example is Quantitative, it takes numerical values, and the correct option is:

D. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data.

2)

The values of mass of the rocks can take any value within the range of definition of the variable, they only depend on the precision of the scale used to weight the rocks.

B. Interval, because the differences in the data can be meaningfully measured, but the data do not have a true zero point.

3)

A standard 52-card deck contains 13 cards for each suit (clubs, diamonds, hearts and spades)

To calculate the probability of choosing a card at random and it being a Diamond, supposing that all cards are equally probable, you have to divide the total number of diamonds by the total number of cards in the deck:

P(diamond)= 13/52= 0.25

For items 4) and 5) the contingency tables are attached.

4)

a. and b. are conditional probabilities, to calculate them you have to apply the following formula: [tex]P(A|B)= \frac{P(AnB)}{P(B)}[/tex]

This means that the probability of the event "A" given that event "B" has occurred is equal to the probability of the intersection between events "A" and "B" divided by the probability of event "B"

a. P(A|C)= [tex]\frac{P(AnC)}{P(C)}[/tex]

To calculate the probability of the intersection P(A∩C) you have to divide the observations where both events cross by the total of observations on the table:

P(A∩C)= 10/50= 0.20

The probability of C is found in the margins of the table, in this case you have to divide the total of observations for event C by the total of observations of the table:

P(C)= 21/50= 0.42

Now you can calculate the asked probability:

[tex]P(A|C)= \frac{0.2}{0.42}= 0.48[/tex]

b. P(C|A)= [tex]\frac{P(AnC)}{P(A)}[/tex]

From item a. we already know that P(A∩C)= 10/50= 0.20

The probability of event A is  in the margin of the table and you calculate it as:

P(A)= 27/50= 0.54

Then:

[tex]P(C|A)= \frac{0.20}{0.54} = 0.37[/tex]

c. P(BE)

This symbolized the probability of the events "B" and "E" occurring at the same time, you can also symbolize it as P(B∩E)

To calculate the probability of B and E happening you have to do as follows:

P(B∩E)= 8/50= 0.16

5)

a. P(C|A)= 0.37 (As calculated in 4b.)

b. P(BE) and c. P(EB) ⇒ Both expressions symbolize the intersection between events "B" and "E", P(B∩E)= P(E∩B)= 0.16 (As calculated in 4c.)

I hope this helps!

Answer:

[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.

Step-by-step explanation:

Information given

We have the following data: 54 55 58 59 59 60 61 61 62 65

The sample mean and deviation can be calculated with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}[/tex]

[tex]\bar X=59.4[/tex] represent the sample mean

[tex]s=3.239[/tex] represent the sample standard deviation

[tex]n=10[/tex] sample size  

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic  

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is higher than 55, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 55[/tex]  

Alternative hypothesis:[tex]\mu > 55[/tex]  

Replacing the info given we got:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing the info given we got:

[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55

Answer:

5

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opp /hyp

sin 30 = x / 10

10 sin 30 = x

10 * 1/2 = x

5 =x

Answer:

False.

The null hypothesis failed to be rejected.

At a significance level of 5%, there is not enough evidence to support the claim that the entering class has a mean SAT score that is significantly lower than 1520.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the entering class has a mean SAT score that is significantly lower than 1520.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1520\\\\H_a:\mu< 1520[/tex]

The significance level is 0.05.

The sample has a size n=20.

The sample mean is M=1501.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=53.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{53}{\sqrt{20}}=11.851[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1501-1520}{11.851}=\dfrac{-19}{11.851}=-1.6[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=20-1=19[/tex]

This test is a left-tailed test, with 19 degrees of freedom and t=-1.6, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.6)=0.063[/tex]

As the P-value (0.063) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the entering class has a mean SAT score that is significantly lower than 1520.

Answer:

x=18

Step-by-step explanation:

Step 1: Subtract 2/3x from both sides.

1/2x+4=2/3x+1

-2/3x         -2/3x

= -1/6x+4=1

Step 2: Subtract 4 from both sides.

-1/6x+4=1

-4        -4

= -1/6x=-3

Step 3: Multiply both sides by 6/(-1).

-1/6x=-3

*6/(-1)       * 6/(-1)

        x=18

Answer:

It’s D, 55.

Step-by-step explanation:

After running 45 meters, Juliet runs 55 meters from the beginning of the track

Answer:

a) [tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]

And from the empirical rule we know that this probability is 0.997 or 99.7%

b)[tex] P(195.2 <X<322.2)[/tex]

Using the z score we have:

[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]

[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]

And within one deviation from the mean we have 68% of the values

Step-by-step explanation:

For this case we defien the random variable of interest X as "blood platelet counts" and we know the following parameters:

[tex] \mu = 258.7, \sigma =63.5[/tex]

Part a

We can use the z score formula given by:

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

And we want this probability:

[tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]

And from the empirical rule we know that this probability is 0.997 or 99.7%

Part b

For this case we want this probability:

[tex] P(195.2 <X<322.2)[/tex]

Using the z score we have:

[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]

[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]

And within one deviation from the mean we have 68% of the values

Based on the information given, these are the conclusions we can draw from the 95% confidence interval.

Here, we have,

From the provided 95% confidence interval, we can make the following conclusions:

The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.

The standard error of the difference between the means is 368.41116 dollars.

The degrees of freedom (DF) associated with the confidence interval is 907.34739.

The lower limit of the confidence interval is -206.29374 dollars.

The upper limit of the confidence interval is 1239.7804 dollars.

The confidence interval does not contain zero.

Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.

Based on the information given, these are the conclusions we can draw from the 95% confidence interval.

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The estimated difference in the mean student loans between females and males is 516.74334.

There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.

Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:

The sample difference in means is 516.74334.

The standard error of the difference is 368.41116.

The degrees of freedom (DF) for the analysis is 907.34739.

The lower limit of the confidence interval is -206.29374.

The upper limit of the confidence interval is 1239.7804.

Therefore, we can conclude the following:

The estimated difference in the mean student loans between females and males is 516.74334.

There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.

Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.

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Answer:

63

Step-by-step explanation: The ratio from planet A to B is 100 to 3. If an elephant weight 2100 is planet a, then we are multiplying 21 to hundred. Whatever you do on the left side you have to do it on the right side and if you multiply 21 and 3 on the right side then you get 63.

Answer:

63 pounds

Step-by-step explanation:

The ratio for Planet A to Planet B is

100 : 3

Creating a proportionality with the unknown as x

=> [tex]\frac{100}{3} = \frac{2100}{x}[/tex]

Isolating x would give

x = [tex]\frac{2100 * 3}{100}[/tex]

x = 21 × 3

x = 63 pounds

Answer:

The probability that the event will not happen is [tex]\frac{4}{17}[/tex]

Step-by-step explanation:

The occurrence of an event can be divided into two parts, the event would occur or the event would not occur. But the probability of an event is 1.

From the given question;

The probability of the event = 1

The probability that the event will happen, P = [tex]\frac{13}{17}[/tex]

Thus,

The probability that the event will not happen = probability of the event - probability that the event will happen

                                               = 1 - P

                                               = 1 - [tex]\frac{13}{17}[/tex]

                                               = [tex]\frac{17 - 13}{17}[/tex]

                                               = [tex]\frac{4}{17}[/tex]

Thus, the probability that the event will not happen is [tex]\frac{4}{17}[/tex].

Answer:

option 3

Step-by-step explanation:

x = 2 is a vertical line with an x-intercept of (2, 0) so the answer is Option 3.

Answer:

Option 3

Step-by-step explanation:

The value of x will always be 2. Y can be anything it wants to be and x will still be 2 no matter what, You could pick multiple points on the line for each graph, and only Option 3 will have x always being 2.

Answer:

5

Step-by-step explanation:

Since the diagonals of a parallelogram bisect each other, the two halves must be equal. Therefore:

[tex]15-x=2x \\\\15=3x \\\\x=5[/tex]

Hope this helps!

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

CE = EB since E is the midpoint of CB (proven by AD intersecting it).

If CE=EB, then:

[tex]2x=15-x\\[/tex]

Add [tex]x[/tex] to both sides

[tex]3x=15\\[/tex]

Divide both sides by 3

[tex]x=5[/tex]

Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.

If two angles is said to create a linear pair, the angles are then regarded as supplementary and it is said that their measures often add up to 180°.

Note that Vertical angles are said to be pair of nonadjacent angles created by the crossing or the intersection of any two straight lines.

Since vertical angles are seen if "X" created by two straight lines then when you look at the image attached, you can see that the angle that can from this is Angle EFA.

Therefore, Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.

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Answer:

[tex]\frac{51}{170},\ \frac{52}{170},\frac{53}{170},...................\ \frac{59}{170}[/tex]

Step-by-step explanation:

As mention in the question number is

[tex]\frac{5}{17}\ < \frac{6}{17} \\multiply\ both\ side\ by\ 10\ in\ numerator\ and\ denominator\ we\ get \\\frac{50}{170} <\frac{60 }{170}\\[/tex]

Therefore the number is :

[tex]\frac{51}{170},\ \frac{52}{170},\frac{53}{170},...................\ \frac{59}{170}[/tex]

4yd^2

2yd^2

6yd^2

Step-by-step explanation:

Rule: height x base/2

The area of the big triangle=2 x 4/2 = 4 yd^2

The area of the small one= 2 x2/2 =2yd^2

The total area of the trapezoid is the sum of these areas= 2+4=6yd^2

Answer:

The maximum life expectancy for humans is approximately 87 years.

Step-by-step explanation:

We have to calculate the point in which both linear functions (Life expectancy from birth and Life expectancy from age 65) intersect, as this is the point in which is estimated to be the maximum life expectancy for humans.

NOTE: to simplify we will consider t=0 to the year 1900, so year 2010 becames t=(2010-1900)=110.

The linear function for Life expectancy from birth can be calculated as:

[tex]t=0\rightarrow y=45\\\\t=110\rightarrow y=78.7\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{78.7-45}{110-0}=\dfrac{33.7}{110}=0.3064\\\\\\y=0.3064t+45[/tex]

The linear function for Life expectancy from age 65 can be calculated as:

[tex]t=0\rightarrow y=75\\\\t=110\rightarrow y=84.5\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{84.5-75}{110-0}=\dfrac{9.5}{110}=0.0864\\\\\\y=0.0864t+75[/tex]

Then, the time t where both functions intersect is:

[tex]0.3064t+45=0.0864t+75\\\\(0.3064-0.0864)t=75-45\\\\0.22t=30\\\\t=30/0.22\\\\t=136.36[/tex]

The time t=136.36 corresponds to the year 1900+136.36=2036.36.

Now, we can calculate with any of both functions the maximum life expectancy:

[tex]y=0.0864(136.36)+75\\\\y=11.78+75\\\\y=86.78\approx87[/tex]

The maximum life expectancy for humans is approximately 87 years.

-4-2×-2×64

-4+4×64

-4+256

=252

Answer:  (36)

hope this helps you have a wonderful day

Step-by-step explanation: