3.27 Underage drinking, Part II: We learned In Exercise 3.25 that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 year olds. (a) How many people in the sample would you expect to have consumed alcoholic beverages? (round to one decimal place) (b) Would you be surprised if the sample contained 45 or more people who have consumed alcoholic beverages? - No, it is just as likely as any other outcome - No, 45 or more accounts for six different events -- this wouldn't be surprising - Yes, 45 is more than two standard deviations above the expected value (mean) - Yes, 45 out of 50 is 90% (c) What is the probability that 45 or more people in this sample have consumed alcoholic beverages? Cound to forracina

The sοlutiοns in οrder frοm least tο greatest are:

Lesser x = -4

Greater x = 1

Ascending οrder refers tο the arrangement οf numbers in which the smallest number cοmes befοre the largest.

Tο sοlve fοr x in the equatiοn [tex]x^2 + 3x - 4 = 0[/tex], we can use the quadratic fοrmula:

[tex]x= \frac{(-b+\sqrt{b^{2} -4ac} )}{2a} \\[/tex]

where a, b, and c are the cοefficients οf the quadratic equatiοn[tex]ax^2 + bx + c = 0.[/tex]

In this case, a = 1, b = 3, and c = -4. Substituting these values intο the quadratic fοrmula, we get:

[tex]x = (-3\± \sqrt{(3^2 - 4(1)(-4)))} / 2(1)\\\\x = (-3 \± \sqrt{(25))} / 2\\\\x = (-3 \± 5) / 2[/tex]

This gives twο pοssible sοlutiοns:

x1 = (-3 - 5) / 2 = -4

x2 = (-3 + 5) / 2 = 1

Therefοre, the sοlutiοns in οrder frοm least tο greatest are:

Lesser x = -4

Greater x = 1

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Answer: Incorrect

Step-by-step explanation:

Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.

Answer:

Ngozi is 45 years old

Step-by-step explanation:

N = 2A

AG = 1/3A

A + AG = 30

Subsitute AG with 1/3A.

A + 1/3A = 30

1 1/3 A = 30

A = 22.5

AG = 7.5

Ngozi = 45

Answer:

1,880 sq in ÷ 600 sq in/can ≈ 3.13 cans

If you want you can round that to 4 cans.

Therefore, the exact value of sec²(θ) is 7.

What is trigonometry?

The branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry.

We can use the trigonometric identity:

tan²(θ) + 1 = sec²(θ)

Substituting tan²(θ) = 6 into the identity gives:

sec²(θ) = tan²(θ) + 1

sec²(θ) = 6 + 1

sec²(θ) = 7

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Therefοre, the exact value οf sec²(θ) is 7.

Trigοnοmetry (frοm Ancient Greek τρίγωνον (trígōnοn) 'triangle', and μέτρον (métrοn) 'measure'). is a branch οf mathematics cοncerned with relatiοnships between angles and ratiοs οf lengths. The field emerged in the Hellenistic wοrld during the 3rd century BC frοm applicatiοns οf geοmetry tο astrοnοmical studies.

The Greeks fοcused οn the calculatiοn οf chοrds, while mathematicians in India created the earliest-knοwn tables οf values fοr trigοnοmetric ratiοs (alsο called trigοnοmetric functiοns) such as sine.

Thrοughοut histοry, trigοnοmetry has been applied in areas such as geοdesy, surveying, celestial mechanics, and navigatiοn.

We can use the trigonometric identity:

tan²(θ) + 1 = sec²(θ)

Substituting tan²(θ) = 6 into the identity gives:

sec²(θ) = tan²(θ) + 1

sec²(θ) = 6 + 1

sec²(θ) = 7

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The solution to the system of equations is x = 16/5 and y = 11/5.

Graphing, substitution, elimination, and matrices are the four methods for solving systems of equations.

Using the substitution method, we can find x and y.

To begin, let us solve the first equation for x:

2x + 3y = 13

2x = 13 - 3y

x = (13 - 3y)/2

This expression for x can now be substituted into the second equation:

x - y = 1

[(13 - 3y)/2] - y = 1

To remove the denominator, multiply both sides by 2:

13 - 3y - 2y = 2

Simplifying:

13 - 5y = 2

Taking 13 off both sides:

-5y = -11

-5 divided by both sides:

y = 11/5

Now that we've discovered y, we can plug it back into either of the original equations to find x. Let's look at the first equation:

2x + 3y = 13

2x + 3(11/5) = 13

To eliminate the fraction, multiply both sides by five:

10x + 33 = 65

Taking 33 away from both sides:

10x = 32

Divide both sides by ten:

x = 16/5

As a result, the system of equations solution is x = 16/5 and y = 11/5.

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The residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min is equals to the -2 μm/min.

The residual for each observation in statistics is the difference between predicted values of y (dependent variable) and observed values of y. That is Residual= observed y value − predicted y.

Here, cupric chloride is used to etch circuit boards. The linear regression equation is, y = 2 + (1/5)x

where, x = temperature in °C

y = etching rate in μm/min

Observed value of etching rate of cupric chloride = 5 μm/min for 25°C

To determine the estimated or predicted value of etching rate of cupric chloride, we substite x = 25, in the above linear equation, y = 2 + (1/5)x

=> y = 2 + (1/5)× 25

=> y = 7

So, Predicted Value = 7 μm/min

Observed Value = 5 μm/min.

Residual = Observed Value - Predicted

= 5 - 7 = -2

Hence, required value is -2 μm/min.

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Complete question:

Calculating and interpreting residuals You might need: Calculator Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching rate, in μm/min of the cupric chloride. After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the etching rate from the room temperature: y = 2 + 5/x, What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min. ? Show Calculator

a) Increase in the amount spent on entertainment is $1.82

b) Money spent who doesn't work any hours is $11.36

c) Money spent who works 8 hours is $25.92

The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.

Given line equation is; y = 1.82x + 11.36 Compare with y = mx + c

(a) The slope (m) of the line is 1.82, which means that for every increase of one hour worked, the predicted increase in the amount of money spent on entertainment is $1.82.

(b) For a student who doesn't work any hours, we can substitute x = 0 into the equation of the line of best fit:

y = 1.82x + 11.36

y = 1.82(0) + 11.36

y = 11.36

Therefore, the predicted amount of money spent on entertainment for a student who doesn't work any hours is $11.36.

(c) For a student who works 8 hours, we can substitute x = 8 into the equation of the line of best fit:

y = 1.82x + 11.36

y = 1.82(8) + 11.36

y = 25.92

Therefore, the predicted amount of money spent on entertainment for a student who works 8 hours is $25.92

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The probability that a student selected randomly owns either a laptop or a car is 85%.

Given a survey with a total of 1000 students, the following data was obtained: 750 students own laptops450 students own cars350 students own laptops and cars a university student is selected at random, what is the (empirical) probability that the student owns either a laptop or a car?

For two events A and B, the union of A and B is the probability that event A or event B occurs. It is the addition of the probabilities of each event minus the intersection of the two events. So in this case, the probability of a student owning either a laptop or a car is P(A∪B) = P(A) + P(B) - P(A∩B) where:

P(A) = probability of owning a laptop = 750/1000 = 0.75

P(B) = probability of owning a car = 450/1000 = 0.45

P(A∩B) = probability of owning both a laptop and a car = 350/1000 = 0.35

Now, substituting values into the formula:

P(A∪B) = 0.75 + 0.45 - 0.35= 0.85

Therefore, the probability that a university student selected randomly owns either a laptop or a car is 85%.

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Therefore, the measure of the arc of the circle is 180 degrees.

A circle is a geometrical shape that consists of all points that are equidistant from a single fixed point called the center. It is a closed curve, which means that it has no endpoints and is continuous. The distance between any point on the circle and its center is called the radius of the circle, denoted by the letter 'r'. The diameter of the circle is the distance across the circle through the center and is twice the length of the radius, denoted by the letter 'd'. The circumference of a circle is the distance around the circle and is given by the formula C = 2πr or C = πd, where π (pi) is a mathematical constant approximately equal to 3.14159. Circles are important in mathematics and geometry because of their symmetry, and they are used in a variety of real-life applications such as wheels, clocks, and planetary orbits.

by the question.

To find the measure of the arc of a circle given certain central angles, we need to know the angle measure of the entire circle. Since a circle has 360 degrees, we can add up the given central angles and set them equal to 360 degrees to find the measure of the missing arc.

So, the measure of the missing arc is:

360 - (30 + 100 + 50 + x) = 360 - 180 = 180 degrees

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Answer:392

Step-by-step explanation:

a) It would take one machine 392 minutes.

b) It would take one machine 49 minutes.

Two ratios are said to be equal when a proportion is stated. When comparing two quantities, ratios are used to divide one quantity by the other.

a) Here given that, to produce a batch of newspaper 7 printing machines needed 56 minutes.

Using this relationship, we can set up a proportion:

as given, 7 printing machine needed = 56 minutes

So, 1 printing machine needed = 7 × 56 minutes = 392 minutes

Therefore, it would take one machine 392 minutes to produce the same batch of newspapers.

b) Similarly, to find out for 8 machines to produce the same batch of newspapers, we can use the same relationship:

1 printing machine needed = 392 minutes

So, 8 printing machine needed = (392 / 8) minutes = 49 minutes

Therefore, it would take one machine 49 minutes to produce the same batch of newspapers.

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The crοss-sectiοn in the image  shοwn appears tο be a trapezοid.

A quadrilateral with at least οne pair οf parallel sides. In this crοss-sectiοn, the tοp and bοttοm sides are parallel, while the οther twο sides are nοt parallel is  trapezοid. There are times when people define trapezoids as having at least one pair of opposite sides that are similar, and other times they say there is just one pair.

The parallelogram satisfies the "at least one" interpretation of the definition because it has two pairs of opposite sides that are similar, which qualifies it as both a trapezoid and a parallelogram. The parallelism does not support the "one and only one" interpretation of the description. How students respond to this depends on how they describe themselves.

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The rate of change in candies sold per month is 3 hundred candies.

The momentum of a variable is conveyed by the rate of change, which is used for expressing the percentage change in value over a particular amount of time.

To find the rate of change in candies sold per month, it is necessary to find the slope of the line connecting the two points.

The slope formula is given by: Δ[tex]\frac{y}{x}[/tex][tex]\frac{y2-y1}{x2-x1}[/tex]

Using the coordinates of the points, [tex]\frac{8-2}{6-4} =\frac{6}{2} =3[/tex]

The slope is 3. This means that for every month, the store sells 300 more candies.

Therefore, the rate of change, in candies sold per month is 300.

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Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.

Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.

Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.

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Without specific details it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. So, based on the information we can define some data as below.

A graph in x-y axis plot is a visual representation of functions or data points. The dependent or vertical variable represented by y-axis, while the independent or horizontal variable represented by the x-axis.

Without the specific details of the performance review or the names of the employees, I cannot provide an exact answer. However, based on the information given, we can infer the following:

Person 6 : has a perfect score.

Person 3 : not achieved any of their goals.

Person 5 : excellent personality and very good job knowledge.

Person 4: more interested in hanging out at the water cooler.

Given this information, it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. We also do not have enough information to make an informed judgment about the performance of each employee. It is possible that the review could belong to any of the employees, depending on their individual scores and performance.

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The  value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

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When a data line on a graph slopes down as it goes to the right, it is depicting that the relationship between the variables on the graph is inverse.

An inverse relationship is a kind of correlation between two variables, in which one variable decreases while the other increases, or vice versa. An inverse relationship happens when one variable increases while the other decreases, or when one variable decreases while the other increases.

On a graph, when a data line slopes down as it goes to the right, this is an indication that the relationship between the variables on the graph is inverse. As the values of x increase, the values of y decrease. Therefore, we can conclude that there is an inverse relationship between x and y.

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The iron wrecking ball weighs roughly 191184 grams, which is equivalent to 191.184 kilograms.

To calculate the mass of the iron wrecking ball, we need to use the formula:

mass = density x volume

The density of iron is given as 7.8 g/cm3. The volume of the wrecking ball can be calculated using the formula for the volume of a sphere:

volume = (4/3) x π x radius³

Plugging in the given radius of 18 cm, we get:

volume = (4/3) x π x (18 cm)³

volume = 24488.48 cm³

Now, we can use the formula for mass:

mass = density x volume

mass = 7.8 g/cm³ x 24488.48 cm³

mass = 191183.94 g

Therefore, the mass of the iron wrecking ball is approximately 191184 g or 191.184 kg.

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The points determined by the real numbers 3.2, 9.5, 50, and 263 are all located on the unit circle at their respective distances from the origin.

The unit circle is a circle of radius 1 centered at the origin of a coordinate system, usually the Cartesian coordinate system. In this system, a point (x,y) is determined by its real number x, where x is the horizontal distance from the origin and y is the vertical distance from the origin. For example, the point determined by the real number 3.2 is located at (3.2, 0), since 3.2 is the horizontal distance from the origin. Similarly, the point determined by the real number 9.5 is located at (9.5, 0).

The point determined by the real number 50 is located at (50, 0). Finally, the point determined by the real number 263 is located at (263, 0). The unit circle is often used in trigonometry to describe the position of points on the circle with an angle in standard position (in radians). For example, if the point determined by the real number 3.2 has an angle in standard position of 3.2 radians, then the point located at (3.2, 0) on the unit circle is the same point. Similarly, if the point determined by the real number 9.5 has an angle in standard position of 9.5 radians, then the point located at (9.5, 0) on the unit circle is the same point. The same is true for the points determined by the real numbers 50 and 263, respectively.

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The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.

Answer: 1500000

Step-by-step explanation:

use a calculator

Answer:

1,500,000

Step-by-step explanation:

Breaking it up into an easier problem:

20x50 = 1,000

30x50=1,500

1,000 x 1,500, aka "adding three zeros" to the end of 1,500, as 1,000 is simply 1 x 10 x 10 x 10, and each 10 has one 0 to it.

Thus, the answer is 1,500,000

Answer:

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

Step-by-step explanation:

[tex]735 = 7 \times 105[/tex]

[tex]735 = 7 \times 3 \times 35[/tex]

[tex]735 = 7 \times 3 \times 5 \times 7[/tex]

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

Answer:

(6,12)

Step-by-step explanation:

3x - 6 = 2x

x - 6 = 0

x=6

y=2*6

y=12

You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.

The given expression is equivalent to

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

[tex]a(b+c)=a\times b+a\times c[/tex]

(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2\times x=2x[/tex])

The given expression is [tex]6g-18h[/tex]

We know that we can write

[tex]6=2\times3[/tex]

[tex]18=2\times9=3\times6[/tex]

Thus,

[tex]6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)[/tex]

[tex]6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)[/tex]

[tex]6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)[/tex]

All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.

Thus,

The given expression is equivalent to

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Answer:C & D

Step-by-step explanation:

The histogram that most likely represents a country with a declining population growth rate is one where the bars to the right (representing higher numbers of births or deaths) are lower than the bars to the left.

A declining population growth rate means that the rate at which the population is growing is decreasing, which suggests that the number of births is decreasing or the number of deaths is increasing.

In other words, the shape of the histogram would be skewed to the left, with a long tail on the left-hand side and shorter bars on the right-hand side. This shape suggests that there are fewer births or more deaths, leading to a declining population growth rate.

It is worth noting that a histogram alone may not provide enough information to make definitive conclusions about population growth rates. Other factors such as migration rates and changes in life expectancy can also affect population growth. Therefore, it is important to consider multiple sources of data and statistical methods when analyzing population trends.

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The correct option that expresses the form of the given argument is "d. if c then f."Explanation:In the given argument, it is stated that if cell phone companies screen text messages, then freedom of speech is threatened.

But as cell phone companies do not screen text messages, so freedom of speech is not threatened. This is a conditional argument, and it can be expressed in the form of a hypothetical syllogism.

The hypothetical syllogism is a syllogism that has a conditional statement in its premises. It is also called a chain argument or transitive argument. The form of the hypothetical syllogism is "If A, then B. If B, then C.

Therefore, if A, then C."In the given argument, it can be expressed in the form of the hypothetical syllogism as follows:If cell phone companies screen text messages, then freedom of speech is threatened. If freedom of speech is threatened, then cell phone companies screen text messages. Therefore, if cell phone companies do not screen text messages, then freedom of speech is not threatened.This can also be represented as "if C then F."Therefore, the correct option that expresses the form of the given argument is "d. if c then f."

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To create opposite x terms, we need to multiply the first equation by -5.

How to choose what term to multiply the first equation?

To choose what term to multiply the first equation, we need to consider the coefficients of the variable that we want to eliminate (in this case, the x variable) in both equations. Our goal is to create opposite terms for that variable in the two equations, so that when we add or subtract the equations, that variable will be eliminated.

Determining the number to multiply the first equation by to form opposite terms for the x-variable :

In this case, the coefficient of x in the first equation is 2/5, and the coefficient of x in the second equation is -2.

To create opposite terms for x, we need to find a constant that, when multiplied by the first equation, will result in a coefficient of x that is the negative of the coefficient of x in the second equation (i.e., -2).

To do this, we can divide the coefficient of x in the second equation by the coefficient of x in the first equation, and then multiply the entire first equation by the resulting constant.

In this case, we have:

[tex](-2)/(2/5) = -5[/tex]

Multiplying the first equation by -5 gives:

[tex]-5(2/5)x + (-5)6y = -5(-10)[/tex]

which simplifies to:

[tex]-2x - 30y = 50[/tex]

Now we have two equations with opposite x terms:

[tex]-2x - 4y = 40[/tex]

[tex]-2x - 30y = 50[/tex]

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