Assume that IQ scores are normally distributed, with a standard deviation of 11 points and a mean of 100 points.
If 85 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points?

Answer:

The length of the altitude is 9.3 yards and

The area of the triangle Δ UVW is 139.3 yd².

Step-by-step explanation:

Given

WU = 22 yd

WV = 30 yd

∠ UWV = 25°

To Find:

Altitude, UM = ?

area of the Δ UVW = ?

Construction:

Draw UM perpendicular to WV, that is altitude UM to WV.

Solution:

In right triangle Δ UWM if we apply Sine to angle W we get

[tex]\sin W = \frac{\textrm{side opposite to angle W}}{Hypotenuse}\\ \sin W=\frac{UM}{UW} \\[/tex]

substituting the values we get

[tex]\sin 25 = \frac{UM}{22}\\0.422 = \frac{UM}{22} \\UM = 0.422\times 22\\UM = 9.284\ yd[/tex]

Therefore, the altitude from U to WV is UM = 9.3 yd.(rounded to nearest tenth)

Now for area we have formula

[tex]\textrm{area of the triangle UVW} = \frac{1}{2}\times Base\times Altitude \\\textrm{area of the triangle UVW} = \frac{1}{2}\times VW \times UM\\=\frac{1}{2}\times 30\times 9.284\\ =139.26\ yd^{2}[/tex]

The area of the triangle Δ UVW is 139.3 yd². (rounded to nearest tenth)

Answer:

Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))

1. R is reflexive if for each element a∈B, aRa.

2. R is symmetric if satisfies that if aRb then bRa.

3. R is transitive if satisfies that if aRb and bRc then aRc.

Then, our set B is [tex]\{1,2,3,4\}[/tex].

a) We need to find a relation R reflexive and transitive that contain the relation [tex]R1=\{(1, 2), (1, 4), (3, 3), (4, 1)\}[/tex]

Then, we need:

1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,

2. Observe that

Therefore [tex]\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(4,1),(4,2)\}[/tex] is the smallest relation containing the relation R1.

b) We need a new relation symmetric and transitive, then

and the analysis for be transitive is the same that we did in a).

Observe that

Therefore, the smallest relation containing R1 that is symmetric and transitive is

[tex]\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}[/tex]

c) We need a new relation reflexive, symmetric and transitive containing R1.

For be reflexive

For be symmetric

For be transitive

Then, the smallest relation reflexive, symmetric and transitive containing R1 is

[tex]\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}[/tex]

To find the smallest relation containing given pairs with specific properties, we add missing pairs and ensure all existing pairs satisfy the required properties.

a. To find the smallest relation that is reflexive and transitive, we need to add any missing pairs that would make the relation reflexive and ensure that all existing pairs satisfy the transitive property. In this case, the relation already contains (1, 2), (1, 4), (3, 3), and (4, 1). To make it reflexive, we add (2, 2) and (4, 4). To satisfy the transitive property, we need to add (1, 1), (2, 4), (3, 1), and (4, 2). Therefore, the smallest relation that is reflexive and transitive is {(1, 1), (1, 2), (1, 4), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 4)}.

b. To find the smallest relation that is symmetric and transitive, we need to add any missing pairs that would make the relation symmetric and ensure that all existing pairs satisfy the transitive property. In this case, the relation already contains (1, 2), (1, 4), (3, 3), and (4, 1). To make it symmetric, we need to add (2, 1) and (4, 4). To satisfy the transitive property, we need to add (1, 1), (2, 4), (3, 1), and (4, 2). Therefore, the smallest relation that is symmetric and transitive is {(1, 1), (1, 2), (1, 4), (2, 1), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 4)}.

c. To find the smallest relation that is reflexive, symmetric, and transitive, we need to add any missing pairs that would make the relation reflexive, symmetric, and ensure that all existing pairs satisfy the transitive property. In this case, the relation already contains (1, 2), (1, 4), (3, 3), and (4, 1). To make it reflexive, we add (2, 2) and (4, 4). To make it symmetric, we need to add (2, 1). To satisfy the transitive property, we need to add (1, 1), (2, 4), (3, 1), and (4, 2). Therefore, the smallest relation that is reflexive, symmetric, and transitive is {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 4)}.

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Final answer:

To maximize the enclosed area, each pig pen should have a length of 84 feet and a width of 168 feet.

Explanation:

To find the dimensions of the pig pens that will maximize the enclosed area, we can use the quadratic formula. Let's assume the length of each pen is 'x' feet. Since the two pens share a common side, the combined length of the pens will be '2x' feet. The total length of the fencing, including both sides and the common side, will then be '2x' + 'x' + 'x' = '4x' feet.

According to the problem, the total length of the fencing is 336 feet. Therefore, we can write the equation '4x = 336'. To find the value of 'x', we divide both sides of the equation by 4: 'x = 84'.

So, each pen should have a length of 84 feet and a width of 2x the length, which is '2 × 84 = 168' feet.

Final Answer:

The dimensions for each pig pen that would yield the maximum enclosed area are 84 feet in length and 56 feet in width.

Explanation:

To solve this optimization problem, we can use calculus. Let's denote:
- The length of each pig pen by L
- The width of each pig pen by W
- The total amount of fencing by P, which is 336 feet

Since the two pig pens share a common side, the amount of fencing will be used for 3 widths and 2 lengths. So our perimeter constraint is:
3W + 2L = P

Since we know P is 336 feet, we can write this as:
3W + 2L = 336

We want to maximize the area, A, of the two pens combined. Since the two pens are adjacent and identical, this area can be represented by:
A = 2 * (L * W)

We want to maximize A with respect to our constraint.
First, let's express L in terms of W using our perimeter constraint:
2L = 336 - 3W
L = (336 - 3W) / 2

Now, we can express the area solely in terms of W:
A = 2 * (L * W)
A = 2 * ((336 - 3W) / 2 * W)
A = (336W - 3W^2)

To maximize A, we take the derivative of A with respect to W and set it to zero:
dA/dW = 336 - 6W

Setting dA/dW to zero gives us:
336 - 6W = 0
6W = 336
W = 336 / 6
W = 56

Now we have the width of each pig pen. Next, we'll use the value of W to find L:
L = (336 - 3W) / 2
L = (336 - 3 * 56) / 2
L = (336 - 168) / 2
L = 168 / 2
L = 84

So the dimensions of each rectangular pen that will maximize the area with 336 feet of fencing are:
- Length (L) = 84 feet
- Width (W) = 56 feet

We should verify this solution is a maximum by checking the second derivative of the area function:
d²A/dW² = -6

Since the second derivative is negative, our critical point W = 56 feet corresponds to a maximum. Therefore, the dimensions for each pig pen that would yield the maximum enclosed area are 84 feet in length and 56 feet in width.

Answer: 68C2 = 2278

Step-by-step explanation:

Answer:

the probability that the combined sample tests positive for anemia is ≈ 0,38.

Thus it is 38% likely that such a combined sample to test is positive.

Step-by-step explanation:

The combined sample tests positive if at least one of the 8 women has anemia.

Let p be the probability that a women 65 years of age and older have anemia

Then p=0.1

The probability that one of the 8 women has anemia and others does not is:

p×[tex]p^{7}[/tex] .

Since there are 8 combinations of this probability is possible, the probability that at least one of the 8 woman has anemia is:

8×p×[tex]p^{7}[/tex] =8×0.1×[tex]0.9^{7}[/tex] ≈ 0,3826

The probability that a combined sample of blood from 8 women aged 65 and older tests positive for anemia is approximately 56.95%, making it likely for the sample to test positive. This probability is calculated using the complement rule in probability.

To determine the probability that a combined sample of blood from 8 women aged 65 and older tests positive for anemia, we need to use the complement rule and properties of probability.

Given:
- Probability that one woman has anemia (success): 10% or 0.10
- Probability that one woman does not have anemia (failure): 90% or 0.90
- Number of women sampled: 8

The probability that all 8 women do not have anemia can be calculated as:

[tex](0.90)^8[/tex]

Now let's compute this:

[tex](0.90)^8[/tex]  ≈ 0.4305

This means there is an approximately 43.05% probability that none of the 8 women have anemia. Therefore, the probability that at least one woman in the sample has anemia is:

1 - 0.4305 ≈ 0.5695 or 56.95%

Since the probability is greater than 50%, it's quite likely that such a combined sample will test positive for anemia.

Answer:

P = 0.55   or  55 %

Step-by-step explanation:

First step:  Fred has probability of 0,5 when chossing jar 1 or jar 2

Second step : The probability of chossing one chocolate chp cookie in jar 1 is 3/5 and from the jar 2 is 1/2

Then the probability of Fred to get a chocolate chip cookie is

P ( get a chocolate chip cookie ) =( 0.5 * 3/5) +( 0.5* 1/2)

P = 0.3 + 0.25

P = 0.55   or  55 %

Final answer:

Bob's consumer surplus after a tax is $4, and Lisa's is $1, making the total consumer surplus for both after the tax $5.

Explanation:

Consumer surplus is the difference between the value a consumer places on a good and what they actually pay. Before the government levies a tax, Bob's consumer surplus for a movie ticket is the difference between his valuation of $10 and the market price of $5, which is $5. Lisa's consumer surplus is the difference between her valuation of $7 and the market price of $5, which is $2.

After the government implements a $1 tax on movie tickets, increasing the price to $6, Bob's consumer surplus becomes $4 ($10 - $6), and Lisa's consumer surplus is now $1 ($7 - $6). Thus, the total consumer surplus for Bob and Lisa after the tax is implemented is $5 ($4 for Bob and $1 for Lisa).

Answer:

The answer to your question is [tex]f(x) = \sqrt{x+ 4}[/tex]

Step-by-step explanation:

                                           f(x) = x² - 4

Process

1.- Change f(x) for y

                                           y = x² - 4

2.- Change "x" for "y" and "y" for "x".

                                           x = y² - 4

3.- Make "y" the object of the equation

                                          y² = x + 4

                                          [tex]y = \sqrt{x+ 4}[/tex]

4.- Change "y" for f(x)

                                          [tex]f(x) = \sqrt{x+ 4}[/tex]

Answer:

S=12+7D

Step-by-step explanation:

Linear relationships.

The initial amount of money Ethan has is $12. Each day, he adds up $7 to his savings. At a given day D after his initial funding, he will have added $7D, and he will have in his piggy bank

S=12+7D

For example, on the day D=30 he will have

S=12+7(30)=$222

Answer:

(-2, 2)

Step-by-step explanation:

Well first you would have to graph both inequalities.

y = mx + b

b is the y-axis intercept

m is the slope

Answer: the woman drives 16.9 miles before she stops for coffee

Step-by-step explanation:

A woman drives 169/4 miles to work each day. She stops for coffee at a shop that is 2/5 of the way to her job.

To determine how far the woman drives before she stops for coffee, we will multiply the total miles to her job each day by the fraction of the total miles that she drives before stopping at the coffee shop. It becomes

2/5 × 169/4 = 16.9 miles

Answer:

60 miles/hour

Step-by-step explanation:

840 miles divided by 14 hours

840/14=60 miles per hour

Answer: A) 1260

Step-by-step explanation:

We know that the number of combinations of n things taking r at a time is given by :-

[tex]^nC_r=\dfrac{n!}{(n-r)!r!}[/tex]

Given : Total multiple-choice questions  = 9

Total open-ended problems=6

If an examine must answer 6 of the multiple-choice questions and 4 of the open-ended problems ,

No. of ways to answer 6 multiple-choice questions

= [tex]^9C_6=\dfrac{9!}{6!(9-6)!}=\dfrac{9\times8\times7\times6!}{6!3!}=84[/tex]

No. of ways to answer 4 open-ended problems

= [tex]^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6\times5\times4!}{4!2!}=15[/tex]

Then by using the Fundamental principal of counting the number of ways can the questions and problems be chosen = No. of ways to answer 6 multiple-choice questions x No. of ways to answer 4 open-ended problems

= [tex]84\times15=1260[/tex]

Hence, the correct answer is option A) 1260

To solve the problem, use the combination formula to find the number of ways to choose 6 multiple-choice questions from 9 and 4 open-ended problems from 6, then multiply the results. The answer is  Option(D) 1260.

Solution to the Question

To determine the number of ways to choose 6 multiple-choice questions out of 9, and 4 open-ended problems out of 6, we can use combinations.

The number of ways to choose 6 multiple-choice questions out of 9 is given by the combination formula:

C(9, 6) = 9! / (6! * (9-6)!) = 84.

Similarly, the number of ways to choose 4 open-ended problems out of 6 is given by:

C(6, 4) = 6! / (4! * (6-4)!) = 15.

Now, multiply these two results to get the total number of ways to choose the questions:

84 * 15 = 1260.

Therefore, the answer is A) 1260.

Answer:

  y - 285 = 45(x - 3)

Step-by-step explanation:

The given point is (hours, fee) = (3, 285), and the slope is given as 45 per hour.

The point-slope form of the equation for a line is ...

  y - k = m(x - h) . . . . . . . for a slope m and a point (h, k)

Using the given values, and letting x stand for the number of hours, the equation is ...

  y - 285 = 45(x - 3)

Answer:

y - 285 = 45(x - 3)

Step-by-step explanation:

Answer:

In statistics, the chi-square test is used to prove a specific hypothesis, accepting or rejecting the null one. In order to find enough evidence to prove the hypothesis, we compare two group of frequencies, which belongs to two different groups (like a quasi-experimental design, with a control and experimental group). The researcher have set an expected frequency, based on the hypothesis, and then he/she will observe a frequency from the data recollected.

Therefore, by comparing this two frequencies (the expected with the observed), the researcher is able to demonstrate the hypothesis.

Answer:

Oil: 24 ml; Onion: 56 g; Potatoes: 0.36 kg; Milk: 0.44 l

Step-by-step explanation:

First, we see how much of the soup recipe he wants make.

4 portions out of 20 portions = 4/20 = 1/5 = 0.2

He wants to make 0.2 of the amount of the recipe.

Now we multiply every amount by 0.2

Oil: 0.2 * 120 ml = 24 ml

Onion: 0.2 * 280 g = 56 g

Potatoes: 0.2 * 1.8 kg = 0.36 kg

Milk: 0.2 * 2.2 l = 0.44 l

Richard needs to use a scaling factor to reduce the amounts of each ingredient to make 4 portions of potato soup, resulting in 24 ml oil, 56 g onion, 360 g potatoes, and 0.44 liters of milk. Devon will require 37.5 liters of soup for a party of 100 guests.

To scale down the recipe from 20 portions to 4 portions of potato soup, Richard needs to multiply each ingredient by the scaling factor, which is 4/20 or 1/5. Here's how to calculate the amounts needed:

Therefore, for 4 portions, Richard needs 24 ml of oil, 56 g of onion, 360 g of potatoes, and 0.44 liters of milk.

There are 9 students in only one of the two clubs.

Step-by-step explanation:

Since we have given that

Number of students = 36

Number of students are in chess club = 10

Number of students are in bridge club = 13

Number of students are not in either club = 20

So, Number of students in both the club is given by

[tex]Total=n(chess)+n(bridge)-n(both)+n(neither)\\\\36=10+13-n(both)+20\\\\36=43-n(both)\\\\36-43=n(both)\\\\-7=-n(both)\\\\n(both)=7[/tex]

Number of students only in chess = 10-7 =3

Number of students only in bridge = 13-7=6

Hence, there are 3+6=9 students in only one of the two clubs.

Answer: Option 'd' is correct.

Step-by-step explanation:

Since we have given that

Researcher A :

Mean = 12.4

Standard deviation = 9

sample size = 30

So, the standard error is given by

[tex]\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{9}{\sqrt{30}}\\\\=1.643[/tex]

Researcher B:

Mean = 12.4

Standard deviation = 9

Sample size = 40

So, the standard error is given by

[tex]\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{9}{\sqrt{40}}\\\\=1.423[/tex]

Sample B has smaller standard error than sample A because the sample size was larger than A.

Hence, Option 'd' is correct.

Answer:

B)$96.75

Step-by-step explanation:

5pound bag cost = $13.85

10pound bag cost= $20.43

25pound bag cost = $32.25

The least quantity of bag the customer can by is 65 pounds = (2*25 pound)+ 10 pound + 5pound = $98.78

But careful examination will show actually that since the most the customer can buy is 80 pound, then buying 25pound in three places give him even a lot cheaper than buying the least amount

75 pound = 3*25 pound = 32.25*3 = $96.75.

Therefore the least amount in cost the customer can buy is $96.75

Answer:

Maximum at [tex]x =\frac{\sqrt{7}}{3}[/tex]

Step-by-step explanation:

Given function,

[tex]f(x) = 14x - 6x^3[/tex]

Differentiating with respect to x,

[tex]f'(x) = 14 - 18x^2----(1)[/tex]

For critical values :

[tex]f'(x) = 0[/tex]

[tex]14 - 18x^2 =0[/tex]

[tex]14 = 18x^2[/tex]

[tex]x^2 = \frac{14}{18}[/tex]

[tex]x^2=\frac{7}{9}[/tex]

[tex]x = \pm \frac{\sqrt{7}}{3}[/tex]

Now, differentiating equation (1) again with respect to x,

[tex]f''(x) = -36x[/tex]

Since,

[tex]f''(\frac{\sqrt{7}}{3}) = -36(\frac{\sqrt{7}}{3}) < 0[/tex]

This means that the function is maximum at [tex]x=\frac{\sqrt{7}}{3}[/tex]

While,

[tex]f''(-\frac{\sqrt{7}}{3}) = 36(\frac{\sqrt{7}}{3}) > 0[/tex]

This means that the function is minimum at [tex]x=-\frac{\sqrt{7}}{3}[/tex]

Answer:

A) c(x)=1.50+1.25x

Step-by-step explanation:

The fixed rate (constant) is 1.50 and 1.25 (variable) depending on the number of additional nights, that is, c (x) = 1.25 (x) +1.50 =1.50+1.25x

the answer would be A

The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of p value

hence option (c) is correct  

Test statistic is a way to check the authenticity of null hypothesis that is considered. Test statistic is extremely important to accept and reject the null hypothesis.

The data from the experiment is fed into the equation  and compares your result with the expected results of null hypothesis.

Test statistic is a number calculated from statistical test of a hypothesis.

It shows how closely our  data matches with the distribution expected under null hypothesis of the distribution.

Confidence interval

Confidence interval is the range of  plausible values of a random variable with a certain percentage of confidence level. Confidence level shows that how much certainty or uncertainty in test statistic considering the null hypothesis to be true. It is expressed in percentage. 98% , 95% and  90% Confidence intervals are a few examples.  

p- value is the probability of a happening of a particular event is  a random chance or some other event with similar probability or any rarer event considering null hypothesis to be true.

Alternate hypothesis

Alternate hypothesis is the opposite of Null hypothesis. Null hypothesis is the generally or by default accepted hypothesis which is tested by various statistical tests.

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Answer: $1548

Step-by-step explanation:

We are told the normal rate of payment is $36 per hour

and with an excess of 40 hours the pay will be 1 and a half the normal rate(1.5)

And John works for 42hours

For first we know John worked for an excess of 2 hours

And calculating his pay for 40hours of the normal rate that week, we multiply $36 by 40 which will give $1440

Then the extra 2 hours, the new pay rate will be $36 multiplied by 1.5 which will give $54 per hour

And for the extra 2 hours, John will get extra $54 multiplied by 2 which will give $108

Adding both $1440 and $108, we will get $1548

Answer:

Associative analysis

Step-by-step explanation:

Associative analysis is an approach that is used to analyses the peoples mental representation , focusing on meaning and similarities and differences across the culture.It determined that relationship that is hidden in the large data set.It determine the relationship in between two variable as well.

Answer:

A. maximum value at 30

Step-by-step explanation:

−x² + 10x + 5

First, factor out the leading coefficient from the first two terms:

-1 (x² − 10x) + 5

Take half of the next coefficient, square it, then add and subtract the result.

(-10/2)² = 25

-1 (x² − 10x + 25 − 25) + 5

-1 (x² − 10x + 25) + 25 + 5

-1 (x² − 10x + 25) + 30

Factor the perfect square.

-1 (x − 5)² + 30

The equation is now in vertex form.  This is a downwards parabola with a vertex at (5, 30).  Since the parabola points down, the vertex is a maximum.

The solution to the system of equations represents the break-even point for the production and sale of sweatshirts, indicating the number of units that must be sold to cover production costs.

The solution of the system of equations y=35x and y=-0.05(x-400)^2+9,492 represents the break-even point where the money collected from selling x number of sweatshirts equals the money spent to produce those sweatshirts. In this context, solving the system means finding the number of sweatshirts (x) that need to be sold at $35 each to exactly cover the production costs described by the second equation.

This involves first substituting the expression for y from the first equation into the second equation, then solving for x to find the exact point where income equals expenses. Once x is found, it can be plugged back into either equation to verify the break-even amount of money (y).

Answer:

t=5.20s

Step-by-step explanation:

I think that is the expression because it say he purchases two bags, all the bags are 5.20 so he brought two bags which are school bag and one hand bag the formula I used was y=mx+b but in these case I had to put t=5.20x. I hope this really helped you..

Answer:

Step-by-step explanation:

Anthony purchases two bags. The price of all bags is $5.20

Anthony purchases one school bag and one hand bag. It means that he purchased one handbag and one school bag for a total cost of $5.20

Let s represent the number of school bags and

Let h represent the number of hand bags.

An expression that represents the total cost,T, of the bag will be

T = s + h

Since total cost = $5.20

Then,

5.20 = s + h

Answer:

  13x² -3x

Step-by-step explanation:

A horizontal line from the corner of the "notch" will divide the figure into two rectangles whose dimensions are given. The total area is the sum of the areas of those rectangles. Each area is the product of length and width.

  A = A1 + A2

  = x(3x-7) + 2x(5x+2)

  = 3x² -7x +10x² +4x

  = (3+10)x² +(-7+4)x

  = 13x² -3x

The area is 13x² -3x.