the empirical rule says that 95% of the population is within 2 standard deviations of the mean, but when i find the z-scores that mark off the middle 95% of the standard normal distribution i calculate -1.96 and 1.96. is this a contradiction? why or why not? in other words why are the normal distribution calculators not agreeing with the empirical rule?

Answer:

a. Multiply the entire first equation by 3 so that the xs will be eliminated when the two equations are added.

b. Multiply the entire first equation by -2 so that the ys will be eliminated when the two equations are added.

c. y = -5; x = -2

Step-by-step explanation:

a. We're able to cancel a variable when the two variables are the same number with opposite signs (e.g., -3 + 3 = 0, -80 + 80 = 0)

If we multiply the entire first equation by 3, we get

[tex]3(-2x-4y=24)\\-6x-12y=72[/tex]

-6x + 6x = 0

b. We can again use the first equation and multiply it by -2 to cancel out the ys:

[tex]-2(-2x-4y=24)\\4x+8y=-48[/tex]

8y - 8y = 0

c. We can first solve for y by first canceling the xs using the process in part a.

[tex]3(-2x-4y=24)\\\\\\-6x-12y=72\\6x-8y=28\\\\-20y=100\\y=-5[/tex]

We can now plug in -5 for y into the first equation to find x:

[tex]-2x-4(-5)=24\\-2x+20=24\\-2x=4\\x=-2[/tex]

suppose we should solve the following equation:

[tex]s = \frac{13}{2} (12 + 75)[/tex]

which equals 565.5

Answer: 93 grams Zinc

Step-by-step explanation:

cross multiply, and solve for the variable:3(403) = 13(x)3(31) = x93 = x .

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the line passes through the point (-8, 7) and has a slope of -5/4. So we can substitute these values into the slope-intercept form and solve for b:

y = mx + b

7 = (-5/4)(-8) + b

7 = 10 + b

b = -3

Therefore, the equation of the line in slope-intercept form is:

y = (-5/4)x - 3

Answer:

Step-by-step explanation:

First, I believe you would go in and mulitiply that 3 and the 1/6 and from there we will get 0.5. Next you are going to add the 2/5 to that 0.5 and you will get 0.9.

Answer: 0.9

Using empirical rule, the approximate percentage of daily phone calls numbering between 42 and 52 is 68%.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.

Mean = 47

SD = 5

Using Empirical Formula ,approximate percentage of daily phone calls numbering between 42 and 52

Normal Distribution has bell shape curve

The Empirical Rule states that in  a normal distribution

68% of the data falls with in one standard deviation ( -1 to 1)

95%  of data falls with in two standard deviations, and  (-2 to 2)

99.7% of data falls with in three standard deviations from the mean. (-3 to 3)

z score = ( Value - mean)/SD

Calculate z score for 60

Z = (42 - 47)/5

Z = -1

Calculate z score for 66

Z = (52 - 47)/5

Z =  1

As data lies between -1 and 1 hence with in one standard deviation from the mean Hence using Empirical data approximate percentage of daily phone calls numbering between 42 and 52  is 68%.

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d. The expression 7(x + 9) is the product of the constant factor 7 and the 2-term factor x + 9.

As a result, we should not be concerned that the sample does not accurately reflect the population.

We can learn more about average, population, and sample.

What is the population?

The entire group of people, items, or objects that we want to draw a conclusion about is known as the population. For example, if we want to learn about the average age of people in the United States, then the entire population is every individual in the United States.

What is a sample?

A smaller group of individuals, objects, or items that are selected from the population is known as a sample. A random sample is a sample in which every individual in the population has an equal chance of being selected for the sample.

What is an average?

A statistic that summarizes the central tendency of a group of numbers is known as an average.

The mean is the most commonly used average in statistics. The mean is calculated by adding up all the numbers in a group and then dividing by the number of numbers in the group. If we want to learn about the average salary of all teachers in the United States, we'd have to sample every teacher. That's not a feasible option. Instead, we take a smaller sample, which should be representative of the population, and then use the information gathered from that sample to make predictions about the population as a whole.

If we assume that the five teachers in the example are a random sample of all teachers in the United States, then we can conclude that the average salary of all teachers in the United States is around $49,000. As a result, we should not be concerned that the sample does not accurately reflect the population.

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Answer:

Step-by-step explanation:

# elements = 292 - 268 - 1 = 23 elements

G has 2^23 subsets = 8388608

G has 2^23 - 1 proper subsets = 8388607

Answer:

y=6x-8

Step-by-step explanation:

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope m = 6 and a point on the line (1,-2). We can use point-slope form to find the equation and then simplify it to slope-intercept form.

Point-slope form: y - y1 = m(x - x1)

Substitute the values of m, x1, and y1:

y - (-2) = 6(x - 1)

Simplify the right side:

y + 2 = 6x - 6

Subtract 2 from both sides:

y = 6x - 8

This is the equation of the line in slope-intercept form.

Answer:

(a) To find the value of a and d, we use the formula for the sum of first n terms of the arithmetic series A which is given by:Sn = n/2[2a + (n-1)d]We are also given that Sn = 15 + 2n. So we can equate these two expressions to get:15 + 2n = n/2[2a + (n-1)d]Multiplying both sides by 2 and simplifying, we get:30 + 4n = n[2a + (n-1)d]Expanding the brackets and simplifying, we get:2an + nd - d + 30 = 2n^2Rearranging terms, we get:2a = 2n^2 - nd + d - 30Now we also know that the first term of the series A is a. So we can substitute this value of a in the formula above to get:a = (2n^2 - nd + d - 30)/2Simplifying, we get:a = n^2 - (n-1)d - 15Therefore, we have found the values of a and d in terms of n. (b) To find the 20th term of A, we use the formula for the nth term of an arithmetic series which is given by:an = a + (n-1)dSubstituting the value of a and d that we found in part (a) we get:a20 = (20^2 - 19d - 15) + 19dSimplifying, we get:a20 = 391 - dTherefore, the 20th term of A is given by a20 = 391 - d.(c) Given that S2p - 2Sp = 1 + S(p-1), we can use the formula for the sum of first n terms of an arithmetic series which we used in part (a) to get:2p/2[2a + (2p-1)d] - 2p/2[2a + (p-1)d] = 1 + p/2[2a + (p-2)d]Simplifying, we get:2apd = d(p^2 - 3p + 2)Dividing both sides by d and simplifying, we get:2ap = p^2 - 3p + 2Rearranging terms, we get:p^2 - 3p + (2-2ap) = 0This is a quadratic equation with coefficients a=1, b=-3, and c=2-2ap. We can use the quadratic formula to solve for p:p = [3 ± sqrt(9 - 4(1)(2-2ap))]/2Simplifying, we get:p = [3 ± sqrt(4ap + 1)]/2Therefore, we have found the value of p in terms of a.

Rounding off the value of X to the nearest whole number, we get that approximately 35 people would be expected to have consumed alcoholic beverages among 50 randomly selected 18-20 year-olds.

In exercise 3.25, it was learned that about 69.7% of 18-20 year-olds consumed alcoholic beverages in 2008.

Now, consider a random sample of fifty 18-20 year-olds.

It is required to calculate the number of people who would be expected to have consumed alcoholic beverages.

Let X be the number of people who have consumed alcoholic beverages out of 50 randomly selected 18-20 year-olds.

Let p be the proportion of 18-20 year-olds who consumed alcoholic beverages in 2008.

Therefore, the sample proportion is given as \hat{p}

Hence, p=0.69 \hat{p}=X/50

Now, by the properties of the sample proportion, E(\hat{p})=p

Therefore,

E(\hat{p})=E(X/50)

Thus, p=E(X/50) Or, X=50p

Substituting the value of p, we have

X=50(0.697)=34.85

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out of the families that have DS, 20 have both, so subtract them from the absolute to get 124 - 20 = 104.

out of the families that have WII, 20 have both, so subtract them from the all-out to get 186 - 20 = 166.

you presently have 3 classifications that are unadulterated.

104 own DS in particular.

266 own WII in particular.

20 own both.

the complete that possesses either a DS or a WII however not both is equivalent to 104 + 266 = 370.

you need to subtract 20 from every classification since it is remembered for both.

it is remembered for DS and it is remembered for WII.

Market surveys are apparatuses to straightforwardly gather criticism from the interest group to grasp their qualities, assumptions, and prerequisites. Marketers foster previously unheard-of techniques for impending items/benefits however there can be no affirmation about the outcome of these methodologies.

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the complete question is:

A company conducted a marketing survey for families with young children and found that 124 families own a Nintendo DS and 186 families own a Nintendo Wii. If 20 own a Wii and a DS, how many own either a Wii or DS, but not both?

Length of the Sara's rope of 2 1/2 meter in centimeter is 25 centimeters.

To convert 2 1/2 meters to centimeters, we can use the conversion factor 1 meter = 100 centimeters. This means that:

2.5 meters = 2.5 x 100 centimeters

= 250 centimeters

Therefore, the length of the rope is 250 centimeters. It's important to understand and be able to convert between different units of measurement, as this is a common task in many fields such as science, engineering, and finance. For example, in science, it's important to be able to convert between different units of length, mass, and volume when making measurements or analyzing data. Similarly, in finance, it's common to convert between different currencies or units of time when dealing with investments or loans. Being able to make these conversions accurately is essential to avoid errors or misunderstandings. In this case, converting the length of the rope from meters to centimeters allows us to work with a more convenient unit for the task at hand, which is hanging a swing for Sara's sister.

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Answer: He needs 6 baskets

Step-by-step explanation: Its division 24 divided by 4 equals 6

The tip of the woman's shadow is moving away from the pole at a rate of 16/3 ft/s when she is 36 ft from the base of the pole.

Let x be the distance of the woman from the pole, and let y be the length of her shadow on the ground. Since the sun's rays are parallel, the triangles formed by the woman, her shadow, and the pole are similar triangles. Therefore, we can use the following proportion:

(woman's height) / (length of woman's shadow) = (height of pole) / (total length of pole's shadow)

Substituting the given values, we get:

5 / y = 15 / (x + y)

Cross-multiplying and simplifying, we get:

3y = 5(x + y)

3y = 5x + 5y

2y = 5x

y = (5/2)x

We can now differentiate both sides of this equation with respect to time t:

dy/dt = (5/2)dx/dt

We want to find dx/dt when x = 36 ft. To do this, we need to find y when x = 36 ft:

y = (5/2)x = (5/2)(36) = 90 ft

Now we can substitute x = 36 ft and y = 90 ft into the differentiated equation:

dy/dt = (5/2)dx/dt

Solving for dx/dt, we get:

dx/dt = (2/5)dy/dt

We know that dy/dt is the rate at which the woman's shadow is changing, which is given by her walking speed of 4 ft/s. Therefore, dy/dt = 4 ft/s. Substituting this value, we get:

dx/dt = (2/5)(4) = 8/5 ft/s

Therefore, the tip of the woman's shadow is moving away from the pole at a rate of 8/5 ft/s, which is equivalent to 1.6 ft/s or 16/3 ft/s.

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The equation that represents the relationship between the number of hours needed to complete a trip, h, and the driving speed, s, is h = 5/s. This means that the number of hours needed to complete the trip is inversely proportional to the driving speed.

When the driving speed is 60 miles per hour, the number of hours needed to complete the trip is 5 (h = 5/60). If the driving speed is increased to 90 miles per hour, the number of hours needed to complete the trip is 5/90 (h = 5/90).

In general, as the driving speed increases, the number of hours needed to complete the trip decreases.

To summarize, the equation that represents the inverse relationship between the number of hours needed to complete a trip and the driving speed is h = 5/s. This equation can be used to determine the number of hours needed to complete a trip at any given speed.

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To find out whether the community studied in Exercise 13 was unusual or not, a t-test should be utilized to determine whether the average loss observed was significantly different from the regional average.

T-test is a statistical test that assesses whether two population means are statistically different from one another. It is often used in hypothesis testing to determine whether there is a significant difference between two means.

A t-test is utilized when the mean of one variable for two groups is compared to the mean of another variable for those same two groups.

The steps to perform a t-test are given below:

Determine the level of significance (alpha).

Determine the degrees of freedom (DF) for the sample.

Determine the critical value of t.

Calculate the t-value.

Compare the calculated t-value with the critical value of t.

Draw a conclusion as to whether there is a significant difference between the two means or not.

A t-test can be performed using the following formula:

t = (X1 - X2) / [s (1 / n1 + 1 / n2)]

Where:

X1 and X2 are the means of the two samples.

s is the pooled standard deviation of the two samples.

n1 and n2 are the sample sizes for the two groups.

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The sample space for rolling the game piece is S = {A, B, C, D}

In mathematics, a set is a well-defined collection of distinct objects, which can be anything like numbers, letters, people, or even other sets. A set is usually denoted by curly braces {} enclosing its elements separated by commas. For example, the set of natural numbers less than or equal to 5 can be denoted as {1, 2, 3, 4, 5}.

Sets can also be described by various methods such as by listing its elements, by set-builder notation, or by using a Venn diagram to visualize relationships between sets. A set can have any number of elements, including none (empty set), and can also have infinite number of elements.

Sets can be combined through set operations such as union, intersection, and complement. The union of two sets A and B is a set that contains all the elements that belong to either A or B (or both). The intersection of two sets A and B is a set that contains all the elements that belong to both A and B. The complement of a set A is the set of all elements that are not in A.

The sample space for rolling the game piece can be represented by the set of possible outcomes, which are the labels on the faces of the game piece. Therefore, the sample space is:

S = {A, B, C, D}

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The scale ratio that Angie used for the drawing is 25 centimeters : 862 meters.

Scale ratio is a mathematical expression of the relationship between the measurements of an object or space in a drawing or model compared to the measurements of the actual object or space.

A fraction is a mathematical expression that represents a part of a whole. It is written as one number (the numerator) over another number (the denominator), separated by a horizontal or diagonal line.

We can use the scale ratio formula to find the scale that Angie used for the drawing:

Scale ratio = length in drawing / actual length

In this case, the length of the parking lot in the drawing is 348 centimeters, and the actual length of the parking lot is 120 meters. We can convert the units so that they are consistent, for example, by converting the length in the drawing to meters:

Scale ratio = 348 cm / 120 m

Simplifying this ratio, we can convert the length in centimeters to meters by dividing by 100:

Scale ratio = 3.48 m / 120 m

Simplifying further, we can divide both terms by 3.48 to get:

Scale ratio = 1 / 34.48

To express this ratio in the form of a fraction of centimeters to meters, we can multiply the numerator and denominator by 100 to get:

Scale ratio = 100 cm / 3448 cm = 25 / 862

So the scale that Angie used for the drawing is 25 centimeters : 862 meters.

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Stephen needs to lose approximately 13 pounds to reach his desired body fat percentage of 10%.

To calculate how many pounds Stephen needs to lose to reach his desired body fat percentage, we first need to determine his current fat mass and lean mass. We can use the following formula:

Fat mass = body weight x body fat percentage

Lean mass = body weight - fat mass

Using Stephen's current weight of 185 pounds and body fat percentage of 17%, we can calculate his fat mass and lean mass as follows:

Fat mass = 185 x 0.17 = 31.45 pounds

Lean mass = 185 - 31.45 = 153.55 pounds

Next, we can calculate Stephen's desired fat mass using his desired body fat percentage of 10%:

Desired fat mass = 185 x 0.10 = 18.5 pounds

To reach his desired body fat percentage of 10%, Stephen needs to lose the difference between his current fat mass and his desired fat mass:

Pounds to lose = current fat mass - desired fat mass

= 31.45 - 18.5

= 12.95 pounds

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Maggie is 30 years old, and Bobby is 15 years old if in 3 years, Maggie's age will be 50% greater than Bobby's age and years ago when Maggie was 25 years old, Bobby was 10 years old.

Maggie is 15 years older than Bobby. We have to determine Bobby's age.

Let's suppose that Bobby's age is x, so Maggie's age would be x + 15 years.

1) In 3 years, Maggie's age will be 50% greater than Bobby's age.

The age of Maggie in 3 years would be (x + 15) + 3, and the age of Bobby would be x + 3.

According to the problem, Maggie's age in 3 years would be 50% greater than Bobby's age in 3 years.

So, (x + 15) + 3 = (1.5)(x + 3)

Simplifying the above equation, we get

x + 18 = 1.5x + 4

Now, we will solve for

x.x - 1.5x = -14-0.5x = -14x = 28

Therefore, Bobby is 28 years old now.

2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.

Let's assume that x years ago Maggie was 25 years old. Thus, Bobby was 10 years old at that time.

So, x + 25 = (x + 10) + 15x = 15

Therefore, Maggie is 30 years old now. And Bobby is 15 years old now.

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Answer:The given problem can be solved with the help of the following steps:Step 1: Finding the total number of ways to form a hand of four cards from 52 cards can be calculated by using the formula,Number of ways = (52 C 4) = (52! / 4! (52-4)!) = 270725Step 2: Finding the total number of ways to form a hand of four cards containing cards from exactly one suit. For this, we can use the following approach:a) Select one of the four suits available in the deckb) Choose four cards from the selected suitThe total number of ways to form a hand of four cards containing cards from exactly one suit can be calculated by using the following formula,Number of ways = (4 C 1) × (13 C 4) = 4 × (13! / 4! (13-4)!) = 5148Step 3: Finding the probability that the hand contains cards from exactly one suit can be calculated by using the following formula,Probability = (Number of ways to form a hand of four cards containing cards from exactly one suit) / (Total number of ways to form a hand of four cards from 52 cards) = 5148 / 270725 = 0.019Summary:Therefore, the probability that the hand contains cards from exactly one suit is 0.019.

Explanation:

Most people with a mental illness in the United States receive care at some point in their lives, but most receive insufficient or inappropriate care. In any given year, fewer than one-third of people with a diagnosable mental illness obtain treatment.

However, according to a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame.

According to the National Survey on Drug Use and Health (NSDUH), about one in five adults (18.5%) had a mental illness in 2019. It is said that roughly 22.3 million people aged 18 and above received care for a mental health condition in the preceding year.

Treatment may involve medication, therapy, support groups, or a combination of these methods. The majority of people with mental illness may significantly benefit from these treatments.

As per a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame. This statement is true.

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The atmospheric carbon dioxide levels in parts per million (ppm) in a town can be modeled using the function defined by , where is in years and corresponds to 1950.

Substituting in gives , which means that the atmospheric carbon dioxide levels in parts per million (ppm) in the town is 386.50 in 2019.

This means that since 1950, the atmospheric carbon dioxide levels in parts per million (ppm) in the town have increased by 386.50.

This is a significant increase and reflects the growing levels of atmospheric carbon dioxide emissions globally due to human activity, leading to climate change.

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c

Step-by-step explanation:

c because 30 where any marble can be pulled out

To solve triangle ABC, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:

c^2 = a^2 + b^2 - 2ab*cos(C)

We are given B, a, and b, so we can solve for c as follows:

c^2 = 25^2 + 41^2 - 2(25)(41)cos(64)

c^2 = 625 + 1681 - 2135cos(64)

c^2 = 1829 - 2135*cos(64)

c^2 = 311.90

Taking the square root of both sides, we get:

c ≈ 17.7

So the length of side c is approximately 17.7 units.

To find the measures of angles A and C, we can use the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:

a/sin(A) = b/sin(B) = c/sin(C)

We know a, b, and c, and we just solved for c, so we can use the Law of Sines to solve for angles A and C:

a/sin(A) = c/sin(C)

sin(A) = asin(C)/c

A = sin^{-1}(asin(C)/c)

A = sin^{-1}(25*sin(C)/17.7)

Similarly,

b/sin(B) = c/sin(C)

sin(B) = bsin(C)/c

B = sin^{-1}(bsin(C)/c)

B = sin^{-1}(41*sin(C)/17.7)

To find angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:

C = 180 - A - B

Using a calculator, we get:

A ≈ 41.6 degrees

B ≈ 74.1 degrees

C ≈ 64.3 degrees

Therefore, the measures of the angles in triangle ABC are approximately:

A ≈ 41.6 degrees

B = 64 degrees

C ≈ 64.3 degrees

And the lengths of the sides are approximately:

a = 25

b = 41

c ≈ 17.7

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=5\\ y=10 \end{cases} \\\\\\ 10=\cfrac{k}{5}\implies 50=k\hspace{12em}\boxed{y=\cfrac{50}{x}}[/tex]

13/52

52 cards in a deck

13 spades

1-9 of spades

king, queen, jack and ace of spades

that makes 13 spades in a deck of cards

The probability of getting at least one spade when drawing cards at random from a deck of cards without replacement is 0.6492 or 0.65 (rounded to two decimal places).

To find the probability of getting at least one spade, we can first find the probability of getting no spades and subtract it from 1.

The probability of getting no spades in the first draw is 39/52 since there are 13 non-spade cards out of 52 cards in the deck. In the second draw, there are 38 non-spade cards out of 51 since one card has been removed from the deck.

Similarly, in the third draw, there are 37 non-spade cards out of 50. Therefore, the probability of getting no spades in three draws is (39/52) x (38/51) x (37/50) = 0.3508 or 0.35 (rounded to two decimal places).

Finally, we can subtract this probability from 1 to get the probability of getting at least one spade: 1 - 0.3508 = 0.6492 or 0.65 (rounded to two decimal places).

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