Weights of adult males.
The weights of adult individuals in a certain country are normally distributed with a population mean of μ=172 pounds and a population standard deviation of σ=29 pounds. Suppose n=36 individuals are sampled.
1)
What is the mean of the sampling distribution of the means?

Answer:

x = 11[tex]\sqrt{3}[/tex] , y = 33

Step-by-step explanation:

using the cosine and sine ratios in the right triangle and the exact values

cos60° = [tex]\frac{1}{2}[/tex] , sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{22\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 22[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 11[tex]\sqrt{3}[/tex]

and

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{22\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2y = 22[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 22 × 3 = 66 ( divide both sides by 2 )

y = 33

The probability that exactly one of the two games will be won by Sally. against Martin [tex]= 0.42[/tex] or 42%.

Use the concept of probability defined as:

Probability is the ratio of:

The number of favorable outcomes to the total number of outcomes for the occurrence of an event.

Given that,

Sally plays two games against Martin.

Sally had a chance to win, tie, or drop each game.

The probability that Martin will lose against Sally is [tex]0.3[/tex].

The probability that Martin will lose against Sally in a tie is [tex]0.1[/tex].

We need to calculate the probability that Sally will win exactly one of the two games against Martin.

To calculate the probability that Sally will win exactly one of the two games against Martin:

Use a combination of probabilities.

Since there are 2 games,

So in this case:

There are 2 possible outcomes:

1. When Sally plays, she either loses the first game and wins the second one, or she wins the first game and loses the second one.
The probability of Sally winning the first game and losing the second game can be calculated,

By multiplying the probability of winning (0.3) with the probability of losing,(1 - 0.3 = 0.7).

Similarly,

2. By doubling the likelihood of losing, which is, the chance of Sally losing the first game and winning the second game,

[tex]1 - 0.3 = 0.7[/tex] with the probability of winning (0.3).

To determine the likelihood that Sally will triumph in precisely one of the two games: Add up this probability as follows:

(0.3 x 0.7) + (0.7 x 0.3)  = 0.42

Hence,

The probability that exactly one of the two games will be won by Sally against Martin = 0.42 or 42%.

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Answer: 9%

Step-by-step explanation:

Answer:

y'=3x²

Step-by-step explanation:

[tex]y=ax^{n} \\y'=an*x^{n-1} \\y=x^{3} \\a=1,n=3\\y'=1*3x^{3-1} \\y'=3x^{2}[/tex]

The three numbers which add up to 180 are 90, 34 and 56.

To find the sum of three numbers as 180, we simply add the three numbers together.

In this case, the numbers are given as 128, 90, 34, 80 and 56;

We see that the three numbers whose sum is 180 are 90, 34 and 56,

Let 90 represents one quantity, 34 represents another quantity, and 56 represents yet another quantity.

When we add these three quantities together, we get the total sum of all three quantities, which is 180.

Therefore, the numbers 90, 34 and 56 adds up to 180.

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The given question is incomplete, the complete question is

Which three of these number add up to 180?  128, 90, 34, 80, 56.

Answer:

39

Step-by-step explanation:

[tex]sin(x)=\frac{10}{16}\\ x=sin^{-1} (\frac{10}{16})\\ x=38.682....\\x=39[/tex]

In ∠CAT and ∠TAD is a linear pair.

m ∠CAT = 42° and

m ∠TAD = 135°

Angle:

In Euclidean geometry, an angle is a figure formed by two radii, called sides of the angle, which share a common extremity, called vertex of the angle. The angle formed by two rays is located in the plane containing the rays. Corners are also formed by the intersection of two planes. This is called dihedral angles. Two intersecting curves can also define an angle, which is the angle of the light that hits the corresponding curve at the point of intersection.

Angle is also used to refer to an angle or rotation measurement. This measurement is usually defined as the ratio of an arc's length to its radius and can be drawn. In the case of geometric angles, an arc is centered on a vertex and bounded by an edge. In the case of a rotation, the arc is centered on the center of the rotation and bounded by any other point and its image through the rotation.

According to the angle:

We are given that angle CAT and angle TAD are a linear pair.

m ∠CAT = 42°

and, m ∠TAD = 2x -6

We have to find the measure of angle TAD.

   m ∠CAT + m ∠TAD = 180°

⇒ 42° +m ∠TAD = 180°   (linear pair sum =180 degrees)

⇒ m ∠TAD = 180° - 42°

⇒ m ∠TAD = 135°

Complete Question:

∠CAT and ∠TAD are a linear pair, if M∠CAT = 2x-5 and M∠TAD = 5x+10, what is the measure of ∠CAT and ∠TAD? Draw a picture labelling the given information and show your work

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Improper fraction: 8 21 4 6 7 15 - This fraction is an improper fraction because the numerator (the top number in the fraction) is larger than the denominator (the bottom number in the fraction).

A numerator is the top number in a fraction. It is used to identify the number of parts of a whole that are being considered. For example, in the fraction 3/4, the numerator is 3, which is the number of parts being considered out of the total 4 parts.

Like fractions: 5' 5' 8' 2 - This fraction is a like fraction because the numerators and denominators are the same.
Proper fraction: 2 5 1 9 11 3 12 11 2 - This fraction is a proper fraction because the numerator is smaller than the denominator.
Unlike fraction: 4'4" 7'25'8'513'21' - This fraction is an unlike fraction because the numerators and denominators are different.

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None of above options are correct.

To compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer:

Follow these steps:

STEP 1: Determine the sample proportion (p) and sample size (n).

STEP 2:Calculate the standard error (SE) using the formula

SE = √(p(1-p)/n).

STEP 3: Determine the critical value (z) for a 95% confidence level

(1.96 for a two-tailed test).

STEP 4: Calculate the margin of error (ME) using the formula

ME = z * SE.

STEP 5: Find the confidence interval by adding and subtracting the margin of error from the sample proportion:

CI = (p - ME, p + ME).

Unfortunately, without the sample proportion (p) and sample size (n), it's not possible to compute the confidence interval.

However, once you have these values, you can follow the steps above to find the 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer.

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The answer is 15 sides

The probability that a randomly selected student is either female or a physics major is 27/40 or approximately 0.675.

To find the probability that a randomly selected student is either female or a physics major, we need to add the probability of selecting a female student to the probability of selecting a physics major, but subtract the probability of selecting a student who is both female and a physics major to avoid double-counting.

Let F be the event of selecting a female student, and M be the event of selecting a physics major. We are given that:

P(M) = 15/40 (15 students out of 40 are physics majors)

P(F) = 18/40 (18 students out of 40 are female)

P(F ∩ M) = 6/40 (6 students out of 40 are both female and physics majors)

To find the probability of selecting a student who is either female or a physics major, we use the formula:

P(F ∪ M) = P(F) + P(M) - P(F ∩ M)

Substituting the given probabilities, we get:

P(F ∪ M) = 18/40 + 15/40 - 6/40

Simplifying, we get:

P(F ∪ M) = 27/40

Therefore, the probability that a randomly selected student is either female or a physics major is 27/40 or approximately 0.675.

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The angle AOB will be a right angle if x = 27.5

AOB will be a right angle if the angle AOB is 90°, then we can write the linear equation:

2x + 30 + 2x - 50 = 90

These are the two measures that conform AOB.

Solving that linear equation we will get:

2x + 30 + 2x -50 = 90

4x - 20 = 90

4x = 90 + 20 = 110

x = 110/4 = 27.5

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If XY = 8 and YZ = 4, the length οf XZ is 4√5 cm.

The Pythagοrean theοrem states that in a right-angled triangle, the square οf the length οf the hypοtenuse (c) is equal tο the sum οf the squares οf the lengths οf the οther twο sides (a and b) c² = a² + b².

We can use the Pythagοrean theοrem tο find the length οf the hypοtenuse XZ οf the right-angled triangle XYZ.

In this case, X is the right angle, sο XY is the adjacent side and XZ is the hypοtenuse. YZ is οn the οppοsite side. We are given that XY = 8cm and YZ = 4cm.

So, we have:

XZ² = XY² + YZ²

XZ² = 8² + 4²

XZ² = 64 + 16

XZ² = 80

Taking the square root of both sides, we get:

XZ = √80 = √(16 × 5) = √16 × √5 = 4√5

Therefore, the length of XZ is 4√5 cm.

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Complete question:

If XY=8 and YZ=4 find the length XZ

Let W = width of rectangle

Let W + 2 = length of rectangle = L

Perimeter = 2L + 2W

         56 = 2L + 2W

     since L = W + 2, we can substitute and solve

         56 = 2(W + 2) + 2W

         56 = 2W + 4 + 2W

         56 = 4W + 4

         52 = 4W

          W = 13

      the length 2 more than 13, which is 15

Area = L • W

       = 15 • 13

      = 195

In this scenario, a survey is being conducted to gather information about the fruit and vegetable consumption habits of a population of 200 students. The survey will help to determine the typical servings of fruits and vegetables that students consume in a day.

To ensure that the survey results are accurate and representative of the population, a random sample of students should be selected for the survey. This means that each student in the population has an equal chance of being selected for the survey. The sample size should also be large enough to ensure that the survey results are statistically significant and reliable.

Once the survey has been conducted and the data has been collected, it can be analyzed to determine the average servings of fruits and vegetables that students in the population typically consume in a day. This information can then be used to develop strategies for promoting healthy eating habits among students.

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Answer:

75, 24

Step-by-step explanation:

Answer: 75, 24

Step-by-step explanation:

Let the two numbers be x and y. Then,

1. x+y=99

2. x-y=51

If you add these two equations together, you get:

2x=150

x=75

Plug in x.

75+y=99

y=24

Step-by-step explanation:

The cost of a package containing x comic books and a poster is given by the equation y = 0.91x + 7.08.

Let's start by using the information given to form two equations. Let x be the number of comic books and let y be the cost of package.

From the first sentence, we can form the equation:

y = 7.99 + 2x

From the second sentence, we can form the equation:

y = 16.99 + 11x

Now we can use these equations to find the linear function rule that models the cost of a package containing any number of comic books.

First, we can set the two equations equal to each other since they both represent the cost of a package:

7.99 + 2x = 16.99 + 11x

Solving for x, we get:

9x = 9

x = 1

Now that we know that 1 comic book costs $4, we can substitute that value into either of the original equations to find the cost of a package with a poster and 1 comic book:

y = 7.99 + 2(1) = 9.99

So a package with a poster and 1 comic book costs $9.99.

Finally, we can use the slope of the line to find the linear function rule that models the cost of a package containing any number of comic books. We know that the slope is the change in y over the change in x, or:

m = (16.99 - 7.99)/(11 - 2) = 0.91

So the linear function rule is:

y = 0.91x + 7.08

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The given question is incomplete, the complete question is:

A store sells packages of comic books with a poster. A poster and 2 comics cost ​$7.99. A poster and 11 comics cost ​$16.99. Write a linear function rule that models the cost y of a package containing any number x of comic books.

Answer:

E

Step-by-step explanation:

To solve this question we have to count which one of the options have five red square and which of the options have 7 blue squares.

By looking at the options we can see that E is the only one that matches the requirements!

We have to be careful that we are looking for 5 red squares and not 5 blue squares as our answer would be wrong.

We can find this out in the question, we see that in the question it says red and blue defining that red goes first. This is why we consider red to be 5 and blue to be 7

Hope this helps, have a lovely day! :)

Inverse Statement- If tοday is nοt Sunday, then it is nοt a hοliday. Cοntrapοsitive Statement- If it is nοt a hοliday, then tοday is nοt Sunday.

A cοnditiοnal statement is a type οf lοgical statement that asserts a relatiοnship between twο prοpοsitiοns. It is an "if-then" statement that states that if οne thing is true, then anοther thing is true as well. The hypοthesis is the prοpοsitiοn that is assumed tο be true, while the cοnclusiοn is the prοpοsitiοn that is inferred frοm the hypοthesis.

Other types οf statements include:

Cοnverse: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are swapped.

Inverse: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are negated.

Cοntrapοsitive: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are swapped and negated.

Here,

Cοnditiοnal statement: If tοday is Sunday, then it is hοliday.

Cοnverse: If tοday is a hοliday, then it is Sunday.

Inverse: If tοday is nοt Sunday, then it is nοt a hοliday.

Cοntrapοsitive: If it is nοt a hοliday tοday, then it is nοt Sunday.

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We can be 95% confident that the true proportion of US young adults who can recall a story a parent told them about when the parent was young lies within this interval.

(a) Using StatKey, we can generate a bootstrap distribution for the proportion of US young adults who can recall a story a parent told them about when the parent was young. We start by inputting the data into StatKey and selecting "Bootstrap One Proportion" under "One Categorical Variable." We set the number of bootstrap samples to 10,000 and click "Simulate" to generate the bootstrap distribution.

The resulting bootstrap distribution has a mean of 0.9387 and a standard error of 0.0156.

To find the 95% confidence interval for the proportion, we can use the formula:

proportion ± z × SE

where z is the z-score for a 95% confidence level, which is approximately 1.96.

Plugging in the values, we get:

0.9387 ± 1.96 × 0.0156

which gives us a 95% confidence interval of (0.9084, 0.9689).

(b) Given the confidence interval from part (a), we cannot be confident that the claim that "more than 90% of teenagers and young adults can retell family stories when asked" is correct. The lower bound of the confidence interval is 0.9084, which is below 90%. While the point estimate of 0.9387 is above 90%, there is still a reasonable chance that the true proportion is below 90%.

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The probability of getting 2 tails is option (b) 37.5%

The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.

Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:

P(htt) = 1/2 × 1/2 × 1/2 = 1/8

P(tht) = 1/2 × 1/2 × 1/2 = 1/8

P(tth) = 1/2 × 1/2 × 1/2 = 1/8

So, the probability of getting 2 tails is:

P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8

= 0.375

0.375 multiplied by 100% gives:

P(2 tails) = 37.5%

Therefore, the correct option is (b) 37.5%

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Answer:this is the answer

Step-by-step explanation:

The roots of the given quadratic equation as required to be determined are; Choice D; x = (2 ± i√26) / 3.

As evident from the task content; the roots of the quadratic equation; 3x² + 10 = 4x are to be determined.

Given; 3x² + 10 = 4x

Therefore; 3x² - 4x + 10 = 0 where a = 3, b = -4 and c = 10.

Therefore, using the quadratic formula;

x = ( -b ± √(b² - 4ac) ) / (2a)

We have that;

x = (-(-4) ± √4² - (4×3×10) ) / 2(3)

x = (4 ± 2√-26) / 6

x = (2 ± i√26) / 3

Ultimately, the roots of the given quadratic equations are given as; Choice D; x = (2 ± i√26) / 3.

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After answering the presented question, we can conclude that q (if q is equation greater than n/2) q - n n - q q (if q is less than n/2)

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument[tex]"2x + 3 = 9,"[/tex] for example, states that the sentence[tex]"2x + 3[/tex]" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation[tex]"x^2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

We can simply compare two phrases at a time to arrange them from least to greatest:

If q is bigger than n/2, then q is the largest expression since q > n - q. If q is less than or equal to n/2, the largest expression is n - q, because n - q > q. Depending on the value of q, the greatest expression is either n - q or q.

When we add everything up, we get:

If q is more than n/2, the order is q, q - n, n - q.

If q = n/2, the sequence is q - n, n - q, q.

As a result, the ultimate order is:

q (if q is greater than n/2) q - n n - q q (if q is less than n/2)

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Based on the given options, the correct answer is: OC. Jack interpreted the mean as the median. Half the cats weighed less than 7.96 pounds and half weighed more.

The mean is a measure of central tendency that represents the average of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.

In this case, Jack interpreted the mean of 7.96 as meaning that half the cats weighed less than 7.96 pounds and half weighed more. However, this is incorrect because the mean does not necessarily divide the data set into two equal halves.

The median, on the other hand, is the middle value in a sorted list of numbers. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.

If Jack had interpreted the median as meaning half the cats weighed less than its value and half weighed more, he would have been correct. However, he incorrectly interpreted the mean as the median.

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The ratio between the areas is 4, which means that the area of the large circle is 4 times the area of the other one.

Remember that for a circle of radius R, the area is given by:

A = 3.14*R²

Here we can see that the diameter of the smaller circle is equal to the radius of the larger circle, then if R is the radius of the larger circle, the radius of the smaller one is R/2.

Then the area of the smaller circle is:

a = 3.14*(R/2)² = (1/4)*3.14*R²

The ratio between these two is:

A/a = 3.14*R²/( (1/4)*3.14*R²) = 4

That means that the area of the large circle is 4 times the area of the smaller one.

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(a) Let in the beginning Eric had 3x red pens and Kai had x blue pens

2/5 * 3x = 6x/5
Eric gave 6x/5 red pens to Kai.

Now Eric has 3x - 6x/5 = 9x/5 red pens.

Kai gave x/2 blue pens to Eric

Now Eric has a 9x/5 + x/2 = (18x + 5x)/10 = 23x/10

Now Kai has x - x/2 = x/2 blue pens.

Now Kai has total x/2 + 6x/5 = 17x/10 pens.

required fraction = (x/2)/(17x/10) = x/2 * 10/17x = 5/17

5/17 is the answer.

(b) After another round of transfer Eric has total 23x/10 - 15 pens and Kai has total 17x/10 + 15 pens.

23x/10 - 15 = 17x/10 + 15

(23x - 150)/10 = (17x + 150)/10

23x - 150 = 17x + 150

6x = 300

3x = 150

Eric had 150 pens in the beginning.

A store buys paper at $15 per bundle. It then sells the bundles at a price that includes a 40% markup. The store offers a discount of To off the price of each bundle if two or more bundles are purchased. The price to purchase 3 bundles of paper is $51

$15 x 3 bundles = $45 + 40% markup = $63 - 20% discount = $51.

In short, a purchase price is the economic value, usually defined in fiat currency at a given point in time, for which a buyer purchases a product, service, or asset. The compensation paid for this value can be fiat currency or other, such as services as payment or benefits in kind.the amount of money someone pays for something .The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.

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Answer:

Step-by-step explanation:

5

Answer:Option b. y = 0.

Step-by-step explanation: