Question 10(Multiple Choice Worth 5 points)

(Identifying Functions LC)

The graph represents a relation where x represents the independent variable and y represents the dependent variable.

a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1

Is the relation a function? Explain.

No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.

If Corey buys 27 inches of trim for a craft project, Corey bought 3/4 of a yard of trim for the craft project.

To determine what fraction of a yard Regina buys, we need to know how many inches are in a yard. There are 36 inches in a yard.

To convert 27 inches to yards, we need to divide by 36:

27 ÷ 36 = 0.75 yards

So Corey bought 0.75 yards of trim for the craft project.

To find the fraction of a yard, we need to express 0.75 as a fraction with a denominator of 1:

0.75 = 75/100 = 3/4

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Complete question is:

Corey buys 27 inches of trim for a craft project. What fraction of a yard does Regina buy?

The amount of money with Rocio has 645 euros more than Estefania.

Total amount of money with Estefania has = 2,593 euros

Total amount of money with Rocio has = 3,238 euros

When we compare the amount of money of both Estefania and Rocio

Rocio has more amount of money than Estefania .

3,238 Euros is greater than 2,593 Euros

To find out how much money Rocio has more than Estefania,

= Subtract Estefania's amount of money from Rocio's amount of money.

= 3,238 euros (Rocio's money) - 2,593 euros (Estefania's money)

= 645 euros

Therefore, Rocio has 645 euros more amount of money than Estefania.

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A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611

B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362

The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.

The formula for calculating the standard error of the mean is

SE = σ/√n

where SE is the standard error, σ is the population standard deviation, and n is the sample size.

For n = 30, SE = 4,000/√30 = 729.16

A. For a sample size of n = 60, SE = 4,000/√60 = 516.40

To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error.

For a range of +/- $500, the z-scores are

z = ($51,300 - $51,800) / 516.40 = -0.969

z = ($52,300 - $51,800) / 516.40 = 0.969

Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.

B. For a sample size of n = 120, SE = 4,000/√120 = 368.93

Following the same steps as above, the z-scores for a range of +/- $500 are

z = ($51,300 - $51,800) / 368.93 = -1.364

z = ($52,300 - $51,800) / 368.93 = 1.364

Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.

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Based on the sample of a one-hectare forest community in early August, an estimate can be made for the total number and diversity of shrub species present in the community.

From the sample of the one-hectare forest community, several estimates can be made for the shrubs in the forest community:

Abundance: The abundance of shrubs in the one-hectare forest community can be estimated by multiplying the number of shrubs in the sample by 10 (the number of species represented by the sample). Therefore, an estimate of the total number of shrubs in the one-hectare forest community would be 17 x 10 = 170 shrubs.

Species richness: The sample contained 10 species of shrubs. This can be used as an estimate of the total number of shrub species in the one-hectare forest community.

Diversity: The diversity of the shrub community in the one-hectare forest can be estimated using the data on species richness and abundance. The most commonly used metric for estimating diversity is the Shannon-Wiener diversity index, which takes into account both the number of species and their relative abundance.

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Answer:

(9,8)

Step-by-step explanation:

Solve the first equation

then solve the second equation with the substitute number from the first equation.  

In reference to the given histogram, an absence of bars signifying either 4 or 5 traffic tickets implies that no one from the selection had accumulated this amount.

It should be noted that to make sure our point is accurate, we can sum the heights of the separate bars for 3, 6 and 8 tickets which demonstrate the total people included within the survey who have acquired the relevant number of traffic citations.

The height of the bar for three violations measures out at 1.

Conversely, a measurement of 2 denotes the bar for six infringements.

An assessment of 1 has been given to the bar with regards to eight offences.

Due to the lack of representation mentioned in the histogram concerning both 4 and 5 transgressions, it confirms our inference: nobody from the selection received four or five traffic tickets.

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The model predicts that the player should score around 17.47 points per game based on their 4.1 free throw attempts per game. However, the player's observed score of 13.7 points per game suggests that they may be underperforming compared to what would be expected based on this relationship.

Let us assume that the model predicts a linear relationship between points per game and free throw attempts per game, we can calculate the predicted value of points per game for this player using the regression equation

points per game = slope * free throw attempts per game + intercept

From the given data, we know that the slope of the regression line is 2.6 and the intercept is 7.1. Plugging in the values for this player, we get:

points per game = 2.6 * 4.1 + 7.1 = 17.47

So the model predicts that this player should score approximately 17.47 points per game, which is higher than the observed value of 13.7 points per game. This suggests that this player may be underperforming compared to what would be expected based on their free throw attempts per game.

However, just one player and there may be other factors that could affect their performance beyond just free throw attempts per game.

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The sum of the roots of x² - 9x + 8 is 9. The product of the roots of x² - 9x + 8 is 8.

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.

The expression x² - 9x + 8 can be factored as follows:

x² - 9x + 8 = (x - 1)(x - 8)

To check that this factorization is correct, you can expand the expression using the distributive property:

(x - 1)(x - 8) = x² - 8x - x + 8 = x² - 9x + 8

So the factorization is indeed correct.

The sum of the roots of the quadratic equation ax² + bx + c = 0 is given by -b/a, where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -9, and c = 8, so the sum of the roots is:

-sum of roots = -b/a = -(-9)/1 = 9

Therefore, the sum of the roots of x² - 9x + 8 is 9.

The product of the roots of the quadratic equation ax² + bx + c = 0 is given by c/a. In this case, c = 8 and a = 1, so the product of the roots is:

product of roots = c/a = 8/1 = 8

Therefore, the product of the roots of x² - 9x + 8 is 8.

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Answer:

Step-by-step explanation:

distance traveled by one revolution = circumference of the wheel

= 2πr = 2π(13 inches) = 26π inches

number of revolutions = distance traveled / distance traveled by one revolution

100 feet = 1200 inches

= 1200 inches / 26π inches

≈ 45.91 full revolutions

If in the mail, she received 14 envelopes, and each envelope included $2. 70,Sarah received a total of $37.80 in the mail.

Sarah received a total of 14 envelopes, and each envelope had $2.70. To find out how much money she received in total, we can multiply the number of envelopes by the amount of money in each envelope:

Total money = 14 × $2.70

We can simplify the expression by first multiplying the whole number, 14, by the tenths value of $2.70, which is $0.70:

Total money = $37.80

This amount of money is the sum of all the money in the 14 envelopes she received. It can be useful to double-check the answer by adding up the amounts in each envelope manually, but in this case, it is not necessary since we have already calculated the total.

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Option D is correct, the area of given parallelogram is 30 square inches

Parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Area of parallelogram =bh

=10×3

=30 square inches

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5. The value of x in the figure is

7. Length of arc AD is 125 degrees

8. Angle ROT is 36.87 degrees

The length of chord x is solved using Pythagoras theorem as follows

5.

let x/2 = y then we have

y² = 12² - 9 ² = 144 - 81 = 63

y = √63 = 3√7

and x/2 = y = 3√7. so x = 6√7

7. BD is the diameter hence arc BAD = 180 degrees

if arc ABC is 110 then arc BA = 110 /2 = 55

Arc AD = arc BAD - arc BA

Arc AD = 180 - 55

Arc AD = 125 degrees

8. Angle ROT = arc sin (3/5)

Angle ROT = 36.87 degrees

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Answer:

A. They have different y-intercepts but the same end behavior.

Step-by-step explanation:

From the shape of f we see that its a descending exponential  fnction, so the  factor taken to the power x will be a fraction,  and from the points the eqation is

f(x) = 2(1/4)^x + 2

and the y-intercept is 4

g(x) has y-intercept of 4(1/4)^0 + 2 = 6  so they are different.

As x approaches infinity  both  f and g approach 2 so the end behavior s the same.

The survey found that 86% of 2006 US students in grades 10-12 agreed with the statement "if I make a mistake, I try to figure out where I went wrong." The survey's margin of error is +/- 3.7%, so we can be 95% confident the true proportion falls between 82.3% and 89.7%.

This means that we can be 95% confident that the true proportion of students who agree with the statement lies between 82.3% and 89.7%. This interval is calculated as follows

Subtract the margin of error from the sample proportion to get the lower bound: 86% - 3.7% = 82.3%

Add the margin of error to the sample proportion to get the upper bound: 86% + 3.7% = 89.7%

So, we can say with 95% confidence that the true proportion of students who agree with the statement is somewhere between 82.3% and 89.7%.

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Non-parametric tests are statistical tests that do not require specific assumptions about the population distribution, such as normality or equal variances. They are useful in situations where the data does not meet the assumptions of parametric tests, or when the variables are ordinal or categorical.

There are some additional examples of non-parametric tests.

Hence, non-parametric tests offer a flexible alternative to traditional parametric tests and can be useful in a variety of situations.

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BigDecimal gives you control over how values are rounded. By default option(d) all calculations are exact and rounding occurs.

BigDecimal is a Java class that provides a way to perform exact calculations on decimal numbers with a high degree of precision and control over rounding. Unlike primitive data types, such as double and float, which are prone to rounding errors due to their binary representation, BigDecimal stores numbers using a base-10 representation, allowing for more precise calculations.

Additionally, it allows the programmer to specify rounding rules, such as rounding up or down to a certain number of decimal places, ensuring that the results of calculations are accurate and consistent. This makes BigDecimal a useful tool for applications that require precise numerical calculations, such as financial and scientific applications.

Therefore, the correct option is (d) all calculations are exact and rounding occurs

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The equation that will be  used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ

What is equation?

An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

The population of Log Village is 1800 in 2010, and the population increases each year by 9%.

Initial population(p)= 1800

rate of increase(r)= 9%

Time(t)= x years.

The formula for the population after n years is p(1+r/100)ⁿ.

To determine the equation for the population after x years we have to put the values in the above expression.

So putting all the values we get,

The population, y, of Log Village x years after 2010 is

          y= 1800( 1+9/100)ˣ

          y= 1800(1.09)ˣ

Hence, The equation that will be  used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ

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Sue statement that each piece of pizza has an angle measure of 30º is  incorrect

Assuming the pizza is circular, we know that the total angle measure of a circle is 360 degrees.

If we cut the pizza into halves, we have two equal pieces, each with an angle measure of 180 degrees.

If Sue and her 4 friends share half a pizza, they are sharing one of these equal pieces.

If we divide the 180 degree angle of the piece of pizza by 5 (Sue and her 4 friends plus Sue herself), we get an angle measure of 36 degrees, which is what Sue believes.

Therefore, Sue is incorrect.

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Ryan's gross pay for the last week of April was $864, assuming that 96% of the dolls produced were non-defective.

If Ryan produced 900 dolls during the last week of April and receives $.96 per doll, his gross pay before any defective units are taken into account is:

900 dolls x $0.96/doll = $864

If we need to check if a certain percentage of the dolls produced were defective, we can multiply the gross pay by the percentage of non-defective units to find Ryan's actual gross pay.

For example, if 95% of the dolls produced were non-defective, Ryan's gross pay would be:

$864 x 0.95 = $820.80

Therefore, Ryan's gross pay for the last week of April was $820.80, assuming that 95% of the dolls produced were non-defective.

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The percentage price of the item has decreased by 45%.

What is the definition of percentage?

A percentage is a quantity or ratio that is stated as a fraction of 100.

"%" is the symbol for percentage.

For example, if 25 of 100 students in a class received a "A," we may represent this as a percentage by dividing the number of "A" students by the total number of students and multiplying by 100:

(25/100) x 100% = 25%

This signifies that 25% of the students in the class received a "A".

Now,

To obtain the % drop, subtract the difference between the original and new prices, divide by the original price, then multiply by 100 to get the percentage decrease.

The difference between the original and updated prices is equal to

140 - 77 = 63

So the percentage decrease is:

(63/140) x 100% = 45%

Therefore, the price of the item has decreased by 45%.

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Answer:

73.52 OR 74.00

Step-by-step explanation:

1.) 8 x 1/5 (I prefer converting to decimals first)

2.) 8.00 x 9.19 = 73.52 ----> (Rounding the ones place up) 74.00

The correct answer is: The IQR of 13 is the most accurate to use, since the data is skewed. (Option B).

The correct answer is: Together, Streetcar and Cable Car are the preferred transportation for 168 residents. (Option A).

The correct answer is: The IQR is the best measure of variability, and it equals 6.

1. Since the data is skewed, it is not appropriate to use the range as a measure of variability. The range is sensitive to extreme values and can be misleading in skewed data. The interquartile range (IQR) is a better measure of variability for skewed data since it is not affected by extreme values. Therefore, the charity should use the IQR of 13 as the measure of variability for this data.

2. From the circle graph, we can draw the following conclusion:

Together, Streetcar and Cable Car are the preferred transportation for 27% + 15% = 42% of the residents. 42% of 400 is 168 residents.

3. The line plot shows that the data is discrete and not continuous. Also, the data is not normally distributed and is skewed. Therefore, the range is not an appropriate measure of variability. The interquartile range (IQR) is a better measure of variability for skewed data. The IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data.

From the plot, we can see that Q1 is 2 and Q3 is 8. Therefore, the IQR is 8 - 2 = 6.

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The train travels a distance of 120 kilometers.

To calculate the distance traveled by the train, we can use the formula:

Distance = Speed × Time

Given that the train travels at a consistent speed of 480 km/h and the time is one-fourth of an hour, we can substitute these values into the formula:

Distance = 480 km/h × (1/4) hour

To simplify the calculation, we can convert one-fourth of an hour to minutes. Since there are 60 minutes in an hour, one-fourth of an hour is equal to (1/4) × 60 minutes = 15 minutes.

Now, we can calculate the distance:

Distance = 480 km/h × (1/4) hour

= 480 km/h × (1/4) × 60 minutes / 60 (converting hours to minutes)

= 480 km/h × 15 minutes / 60

= 480 km/h × 0.25

= 120 km

Therefore, distance travelled by train is 120 kilometers.

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Step-by-step explanation:

To find the number that is 175% of 31, we can use the following formula:

175% of X = 31

Mathematically, we can represent 175% as 1.75 (since percentage is a ratio out of 100).

So, the equation becomes:

1.75 * X = 31

To solve for X, we divide both sides of the equation by 1.75:

X = 31 / 1.75

Using a calculator, we can evaluate the right-hand side to find the value of X:

X ≈ 17.714

So, 175% of approximately 17.714 is equal to 31.

Answer:

17.714

Step-by-step explanation:

23. The value for x in triangle is 11.14

24. The value for x in the triangle is 18.3

25. The value for x = 30.4

27 The value for x = 63.413 degrees

23

Cos θ= adj/ hyp

cos 42= x/15

x = 15 cos 42

x = 11.14

24

tan θ= opp/ adj

tan 31= 11/ x

x(tan 31)= 11

x = 11/tan 31

x = 18.3

25

cos θ= adj/ hyp

cos 18= 29/x

x(cos 18) = 29

x = 29/ cos 18

x = 30.4

27

sin x = opp/ hyp

sin x = 17/19

sin x = 0.8947

x = 63.413 degrees

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The value of k is given as follows:

k = 2.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For this problem, we have that the parameters are given as follows:

Hence the equation to obtain k is given as follows:

[tex]\sin{45^\circ} = \frac{\sqrt{2}}{k}[/tex]

[tex]\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{k}[/tex]

k = 2.

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The given information pertains to a sample of einsteinium-253, which naturally loses its mass over time. The initial mass of the sample was 15 grams when it was first measured. The relationship between the elapsed time in weeks, denoted by 't', and the mass of the sample in that week, denoted by 'Mweek(t)', is given by the function.

Mweek(t) = 15 * (0.79)^t.

The daily rate of change in the mass of the sample can be found by taking the derivative of the function with respect to time

Mweek'(t) = 15(0.79)^t ln(0.79)

To find the factor by which the mass decays every day, we can divide the mass at time t by the mass at time t+1.

Mweek(t) / Mweek(t+1) = (15(0.79)^t) / (15(0.79)^(t+1)) = 1/0.79

Therefore, every day, the mass of the sample decays by a factor of approximately 1.26 (rounded to two decimal places).

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The electrician needs approximately 296.26 feet of wire.

The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).

The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.

Using trigonometry, we can write:

sin(17°) = opposite / hypotenuse

where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:

hypotenuse = opposite / sin(17°)

To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:

tan(17°) = opposite / 85

Solving for the opposite side, we get:

opposite = 85 tan(17°)

Substituting this into the formula for the hypotenuse, we get:

hypotenuse = (85 tan(17°)) / sin(17°)

hypotenuse ≈ 296.26 feet

Therefore, the electrician needs approximately 296.26 feet of wire.

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These two events are independent. The action of Rafi downloading a song does not affect the probability of another customer in another city searching for a song on the same site.

The two events, Rafi downloading a song and a customer searching for a song, are independent because the occurrence of one event does not affect the probability of the other event occurring.

In other words, the actions of Rafi do not affect the actions of the customer in another city, and vice versa. The two events are unrelated and can occur simultaneously without affecting each other.

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