A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000 women reported drinking alcohol and 552 of 1000 men reported drinking alcohol. What is the 95% confidence interval of the drinking alcohol percentage difference between women and men

Answer:

  3

Step-by-step explanation:

Those wearing a shirt of another color are ...

  1 - 5/8 -1/4 = 8/8 -5/8 -2/8 = 1/8

of the total number of students in the classroom

  (1/8)×(24 students) = 3 students . . . . wearing another color

_____

Alternate solution

With the given information, you know ...

  (5/8)(24) = 15 . . . students wear blue

  (1/4)(24) = 6 . . . . students wear white

  24 -15 -6 = 3 . . . students wear another color

Answer:

The number which is exactly in between 1/3 and 7/8 will be their average. The average = (1/3 + 7/8) / 2 = (8/24 + 21/24) / 2 = (29/24) / 2 = 29/48.

Answer: 15

Step-by-step explanation:

to find the area multiply the length by height

in this case it’s 5ft and 3ft

5 • 3 = 15

A=15

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Step-by-step explanation:

For this case we have the following info given:

[tex] ME=0.03[/tex] the margin of error desired

[tex]Conf= 0.95[/tex] the level of confidence given

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

the critical value for 95% of confidence is [tex] z=1.96[/tex]

We can use as estimator for the population of interest [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Answer:

The height of the flagpole = 4.50m (3signifiant figures)

Question:

A tree and a flagpole are on the same

horizontal ground. A bird on top of the

tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, Calculate Correct to 3 significant figures the height of the flagpole.

Step-by-step explanation:

First we have to represent the above information with a diagram to enable us solve the question.

Then label them for easy identification.

To determine the distance between the tree and flagpole, we would apply tangent rule.

Let their distance = x

Tan60 = opposite/adjacent

Tan60 = 10.65/y

Tan60 × y = 10.65

y = 10.65/Tan60

y = 10.65/1.7321

y = 6.15m

See attachment for the concluding part

Answer:

[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} =  \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants.

Step-by-step explanation:

Consider the differential equation [tex]y''+6y'+9y = 4e^{x}[/tex]. To find the homogeneus solution, we assume that [tex]y = Ae^{rt}[/tex] and replace it in the equation [tex]y''+6y'+9y = 0[/tex]. If we do so, after using some properties of derivatives and the properties of the exponential function we end up with the equation

[tex]r^2+6r+9 = 0 = (r+3)^2[/tex]

which leads to r = -3. So, one solution of the homogeneus equation is [tex]y_h = c_1e^{-3x}[/tex], where c_1 is a constant.

To use the order reduction method, assume

[tex] y = v(x)y_h(x)[/tex]

where v(x) is an appropiate function. Using this, we get

[tex]y'= v'y+y'v[/tex]

[tex]y''=v''y+y'v'+y''v+v'y'=v''y+2v'y'+y''v[/tex]

Plugging this in the original equation we get

[tex]v''y+2v'y'+y''v + 6(v'y+y'v) +9vy=4e^{x}[/tex]

re arranging the left side we get

[tex]v''y+2v'y'+6v'y+v(y''+6y'+9y)=4e^{x}[/tex]

Since y is a solution of the homogeneus equation, we get that [tex]y''+6y'+9y=0[/tex]. Then we get the equation

[tex]yv''+(2y'+6y)v' = 4e^{x}[/tex]

We can change the variable as w = v' and w' = v'', and replacing y with y_h, we get that the final equation to be solved is

[tex] e^{-3x}w'+(6e^{-3x}-6e^{-3x})w =4e^{x}[/tex]

Or equivalently

[tex]w' = 4e^{4x}[/tex]

By integration on both sides, we get that w = e^{4x}+ k[/tex] where k is a constant.

So by integration we get that v = [tex]e^{4x}{4} + kx+d[/tex] where d is another constant.

Then, the final solution is

[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} =  \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants

Answer:

  see below

Step-by-step explanation:

The construction makes ray BF a bisector of angle ABC. That bisector divides ABC into the two congruent angles DBF and EBF. As a consequence, angle EBF will be half of ABC, not equal to ABC.

Answer:

False, it is easier to isolate x.

Step-by-step explanation:

6y+x=3

x=3-6y

Answer:

4a²

Step-by-step explanation:

(2a)²

Distribute the square to all the terms in the bracket.

2²a²

Solve the powers if possible.

4a²

Answer:

4a²

Step-by-step explanation:

=> [tex](2a)^2[/tex]

=> [tex](2^2*a^2)[/tex]

=> 4 * a²

=> 4a²

Answer:

Step-by-step explanation:

The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm

This means that the required length of computer chips is between 1.1cm - 1.3cm

Where 1.1cm = [1.2 - 0.1]

1.3cm = [1.2 + 0.1]

Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.

The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:

- The length of the chips.

The length of the chips his production team produces should be tailored to meet the length specification of his client.

Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

Random voting:

So 50% of voting yes, 50% no, so [tex]p = 0.5[/tex]

15 members:

This means that [tex]n = 15[/tex]

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

[tex]p = P(X = 0) + P(X = 15)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003[/tex]

[tex]P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003[/tex]

So

[tex]p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006[/tex]

0.006% probability that the final vote count is unanimous.

Answer:

7 donkeys

Step-by-step explanation:

Given

A system consisting of donkeys and tourists

Heads = 50

Legs = 114

Required

Calculate number of donkeys.

Represent donkeys with D and tourists with T.

By means of identification; donkeys and tourists (human) both have 1 head.

This implies that

Number of Heads = D + T

50 = D + T ----- Equation 1

While each donkey have 4 legs, each tourists have 2 legs.

This implies that

Number of legs = 4D + 2T

114 = 4D + 2T ---- Multiply both sides by ½

114 * ½ = (4D + 2T) * ½

57 = 4D * ½ + 2T * ½

57 = 2D + T ----- Equation 2

Subtract equation 1 from 2

57 = 2D + T

- (50 = D + T)

---------------------

57 - 50 = 2D - D + T - T

7 = D

Recall that D represents the number of donkeys.

So, D = 7 implies that

The total number of donkeys are 7

Answer: no, no, no, yes

Step-by-step explanation:

x=-3 is a vertical line. It goes straight up and down at x=-3. In order for the points to be on this line, the x-axis has to be -3. Looking at all the choices, all points are not a solution with the exception of (-3,0) which is right on the line.

Answer:

no no no yes

Step-by-step explanation:

i think

The question is incomplete. The complete question is as follows.

The city of Oakdale wishes to see if there is a linear relantionship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a pont estimate Kilowatt usage when the Temperature is 90 degrees outside?

Temperature(x)                       Kilowatts(y)

        73                                         680

        78                                         760

        85                                         910

        98                                         1510

        93                                         1170

        83                                         888

        92                                         923

        81                                          837

        76                                         600

       105                                        1800

Answer: The point estimate is 1132.5 Kilowatts

Step-by-step explanation: Regression analysis is used to find an equation that fits the data. Once this equation is found, it's used to make predictions. One of the regressions is linear regression.

To find the linear regression model:

1) Create a table with the following: ∑y; ∑x; ∑xy; ∑x²; ∑y²;

2) Use these equations to find coefficients a and b:

a = (∑y)(∑x²) - (∑x)(∑yx) / n(∑x²) - (∑x)²

b = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²

3) Substitute the coefficients into the equation of form: y = a + bx

For the table above, the linear regression equation is:

y = - 2004 + 34.85x

When Temperature is 90, i.e. x = 90:

y = - 2004 + 34.85*90

y = 1132.5

The estimate Kilowatt is 1132.5.

Answer:

Not a random variable

Step-by-step explanation:

The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.

Thus, the last book read by someone in City A is not a random variable.

Answer:

not random

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ \dfrac{4}{5} \ \ \ }[/tex]

Step-by-step explanation:

when the equation is like y = ax + b

the slope is a

in this case we have

[tex]y \ = \ \dfrac{4}{5}x\ \ - \ 3[/tex]

so the slope is

[tex]\dfrac{4}{5}[/tex]

Answer:

b) 0.0608

Step-by-step explanation:

As it is mentioned that the next two days i.e 24 hours, the probability of the rain is uniformly distributed

Therefore the rain probability is

[tex]= \frac{T}{24}[/tex]

where,

T = Length of the time interval

Plus, as we know that rain is independent

So let us assume the rain between the 8: 40 AM and 2: 35 PM on single day is P1 and the time interval is 5 hours 55 minutes

i.e

= 5.91666 hours long.

So, P1 should be

[tex]= \frac{5.91666}{24}[/tex]

= 0.2465

Now we assume the probability of rain on day 2 is P2

So it would be same  i.e 0.2465

Since these events are independent

So, the total probability is

[tex]= 0.2465 \times 0.2465[/tex]

= 0.0608

Hence, the b option is correct

Answer:

y = 5x

Step-by-step explanation:

First, find the slope of the first equation by doing rise/run

This gets you -10/-2 or 5

A parallel line will have the same slope. Since it goes through the origin, the y-intercept and b value will be zero

The equation will be y = 5x

Answer:

please see the attached picture for full solution...

Hope it helps...

Good luck on your assignment....

Answer:

a. They are empty set.

b. they are finite set.

Solution,

a. A={ prime number between 6 and 7}

There are not any number between 6 and 7.

So there will be no Elements.

A={ }

It is empty set.

Empty set are those set which doesn't contain any Element.

b.B={multiples of 2 less than 20}

B={2,4,6,8,10,12,14,16,18}

It is a finite set.

Finite set are those set which we can count easily.

Hope this helps...

Good luck on your assignment...

Answer:

''0 is neither a rational number nor an irrational number.''

Step-by-step explanation:

Zero is a rational number. Zero can be written as a fraction, where p/q = 0, where p = 0 and q is any non-zero integer. Hence, 0 is a rational number.

Answer:

Number of orders seen on last Tuesday = 605

Step-by-step explanation:

Number of orders seen on Tuesday = 600

It is given that it is 0.85% less than last Tuesday.

Let number of sales on last Tuesday = [tex]x[/tex]

As per question statement:

Number of order on last Tuesday - 0.85% of Number of order on last Tuesday = 600

OR

i.e. if we subtract 0.85% of x from x, it must be equal to 600.

[tex]x-\dfrac{0.85}{100}x =600\\\Rightarrow x-\dfrac{0.85}{100}x =600\\\Rightarrow \dfrac{100-0.85}{100}x =600\\\Rightarrow \dfrac{99.15}{100} \times x =600\\\Rightarrow x =\dfrac{600\times 100}{99.15}\\\Rightarrow x =\dfrac{60000}{99.15}\\\Rightarrow x \approx 605[/tex]

So, there were about 605 order seen last Tuesday.

Answer:

1/3

Step-by-step explanation:

hello,

probability of 1 = 1/6

probability of 2 = 1/6

probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0

so the answer is 2/6=1/3

Answer:

a) 6.68% of heights less than 150 centimeters

b) 58.65% of heights between 160 centimeters and 180 centimeters

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

[tex]\mu = 162, \sigma = 8[/tex]

a) The percentage of heights less than 150 centimeters

We have to find the pvalue of Z when X = 150. So

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

[tex]Z = \frac{150 - 162}{8}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% of heights less than 150 centimeters

b) The percentage of heights between 160 centimeters and 180 centimeters

We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.

X = 180

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

[tex]Z = \frac{180 - 162}{8}[/tex]

[tex]Z = 2.25[/tex]

[tex]Z = 2.25[/tex] has a pvalue of 0.9878

X = 160

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

[tex]Z = \frac{160 - 162}{8}[/tex]

[tex]Z = -0.25[/tex]

[tex]Z = -0.25[/tex] has a pvalue of 0.4013

0.9878 - 0.4013 = 0.5865

58.65% of heights between 160 centimeters and 180 centimeters

Answer:

4.92% probability that the third strike comes on the seventh well drilled

Step-by-step explanation:

For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

20% chance of striking oil.

This means that [tex]p = 0.2[/tex]

What is that probability that the third strike comes on the seventh well drilled

2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]

Strike during the 7th drill, with 0.2 probability. So

[tex]P = 0.2P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458[/tex]

Then

[tex]P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492[/tex]

4.92% probability that the third strike comes on the seventh well drilled

Answer:

Dear Yates

Answer to your query is provided below

Total Price for her vehicle will be $20600

Step-by-step explanation:

Edith's trading is worth $8000. So, without the package upgrade of the vehicle delivery charge, her cost is:

$22750 - $8000 = $14750.

Now, add the package upgrade ($5050) and the delivery charge ($800).

$14750 + $5050 + $800 = $20600.

The total cost price of the vehicle after all the expenses is given by the equation A = $ 20,500

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The initial cost of the vehicle is = $ 22,750

Now , Edith has asked for an upgrade to a premium package for which the cost is $5050

So , the new cost of the vehicle = $ 22,750 + $ 5050 = $ 27,800

Now , the delivery charge of the vehicle = $ 700

And , the updated total price = $ 27,800 + $ 700 = $ 28,500

Now , the dealer has offered her $8000

So , the final price of the vehicle = updated total price - $ 8000

On simplifying the equation , we get

The final price of the vehicle A = $ 28,500 - $ 8,000

The final price of the vehicle A = $ 20,500

Hence , the final price of the vehicle is $ 20,500

To learn more about equations click :

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Answer:

0.48% probability that all four are new

Step-by-step explanation:

The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses 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 sucesses.

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:

Total of 10 homes, so N = 10.

We want 4 new, so x = 4.

In total, there are 4 new, so k = 4.

Sample of four homes, so n = 4.

Then

[tex]P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048[/tex]

0.48% probability that all four are new

The calculated probability is "0.0048".

From a total of [tex]N=10\ \ \text{homes},\ r=4[/tex] are completely new while 6 are not.

Let X indicate the series of innovative dwellings in a sample of[tex]n=4[/tex] homes.

X is the next step. Algebraic distribution for parameters[tex]N=10, r=4, \ \ and\ \ n = 4[/tex] Only integer values in this range: can be given to a hypergeometric random variable.

[tex]\to [ \max {(0,\,n+r-N)}, \min {(n,\,r)} ] = [ 0, 4 ] \\\\ \to P( X = 4) \\\\ \to N=10\\\\ \to r=4\\\\ \to n = 4[/tex]

[tex]\to \bold{P(X=k) = \dfrac{\binom{r }{ k}{\binom{N-r} {n-k}}}{\binom{N}{n}}} \\\\\to P(X =4 ) = \dfrac{\binom{r }{ 4}{\binom{N-r} {n-4}}}{\binom{N}{n}} \\\\[/tex]

                   [tex]= \dfrac{\binom{4 }{ 4}{\binom{10-4} {4-4}}}{\binom{10}{4}}\\\\= \dfrac{\binom{4 }{ 4}{\binom{6} {0}}}{\binom{10}{4}} \\\\= \dfrac{ 1 \times 1}{210} \\\\= \dfrac{ 1}{210} \\\\= \dfrac{1}{210} \\\\= 0.004762[/tex]

Using the excel function:

[tex]\text{HYPGEOM.DIST( k, n, r, N. cumulative)}[/tex]  for calculating the [tex]P_{X} (4)[/tex]:

[tex]\to \text{HYPGEOM.DIST( 4, 4, 4, 10, FALSE) = 0.0047619047619}[/tex]

[tex]\to P(X= 4 ) = \frac{1}{210} = { 0.0048 }[/tex]

Find out more information about the probability here:

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Answer:

20-39 ⇒ 5

40-59 ⇒ 3

60-79 ⇒ 5

80-99 ⇒ 10

Answer:

20-39: 5

40-59: 3

60-79: 5

80-99: 10

Step-by-step explanation:

If you just added up, you can find all the values.

Answer:

96 ft^2

Step-by-step explanation:

volume=l^3

l=4

4x4x4=64

Surface area (4x4)=16

16x6=96

Answer:

SA =96 ft^2

Step-by-step explanation:

The volume of a cube is given by

V = s^3

64 = s^3

Take the cube root of each side

64 ^ 1/3 = s^3 ^ 1/3

4 =s

The side length si 4

The surface area of a cube is

SA = 6 s^2

SA = 6 * 4^2

SA = 6 * 16

SA =96 ft^2