Section A: Algebra Question 1: Geometry (10 marks) (a) Which of the following is the definition of a one-to-one function? A. A function with no asymptotes. B. A function that is symmetrical about the y-axis. C. A function where each output is positive. D. A function where each element of the domain gives a unique output (1 mark)

The point (-2, 5) is not included in the solution area

The system of inequalities is given as:

y > 5x + 5

y > -2x+1

See attachment for the graph.

Since the inequalities use the greater than symbol, then the lines of the inequalities would be a dotted line and the upper part would be shaded

The point is given as:

(-2, 5)

The point (-2, 5) is not in the shaded area of the system of inequalities

Hence, the point is not included in the solution area

Mathematically, we have:

5 > 5 * -2 + 5 ⇒ 5 > -5 --- true

5 > -2 * -2 +1 ⇒ 5 > 5 --- false

Since both inequalities are not true, then the point is justified

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Answer:gamble that,on average,will leave a person with the same amount of money.

Step-by-step explanation:

Answer:

k = 5

Step-by-step explanation:

Answer:

en total 6 horas

espero ayudar amiga ;)

Answer:

It's 6 hours cuz 3*2 is 6 so thats twice as much. It will travel 800 kilometers in 6 hours.

Step-by-step explanation:

Therefore, The null hypothesis is that the proportion of customers who try out the samples being offered is 0.15 or less, while the alternative hypothesis is that the proportion is more than 0.15.

The null hypothesis (H0) for this test is that the proportion of customers who try out the samples being offered is 0.15 or less. The alternative hypothesis (Ha) is that the proportion of customers who try out the samples being offered is more than 0.15.
The researcher wants to test whether the proportion of customers who try out the samples being offered is higher than 0.15, which means the null hypothesis states that the proportion is 0.15 or lower. The alternative hypothesis, on the other hand, suggests that the proportion is greater than 0.15. The researcher will conduct a hypothesis test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
Therefore, The null hypothesis is that the proportion of customers who try out the samples being offered is 0.15 or less, while the alternative hypothesis is that the proportion is more than 0.15.

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Answer is 2nd answer

y = (-1/2)x - 7/2 is the equation of the given point and slope.

To graph the point (3, -5) and a line with a slope of -1/2, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents a point on the line, and m represents the slope.

Plugging in the values, we have:

y - (-5) = (-1/2)(x - 3)

Simplifying:

y + 5 = (-1/2)x + 3/2

Subtracting 5 from both sides:

y = (-1/2)x + 3/2 - 5

y = (-1/2)x - 7/2

Now we have the equation y = (-1/2)x - 7/2, which represents a line with a slope of -1/2 passing through the point (3, -5).

To graph the line, plot the point (3, -5) on the coordinate plane and then use the slope to find additional points. For every 2 units you move to the right, move 1 unit down to find other points. Connect the plotted points to draw the line.

The resulting graph will show the point (3, -5) and a line with a slope of -1/2.

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Answer:

θ ≈ 7.43°

Step-by-step explanation:

Given

tan θ = \(\frac{15}{115}\) , then

θ = \(tan^{-1}\) ( \(\frac{15}{115}\) ) ≈ 7.43° ( to 2 dec. places )

¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).

Assuming that the state narcotics bureau has more than 5 agents from which to choose, the number of different possible teams that can be formed is equal to the number of combinations of 5 agents out of the total number of agents the bureau has. This can be calculated using the formula nCr (n choose r), where n is the total number of agents and r is the number of agents in each team, which in this case is 5.

Therefore, the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).

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The volume of the solid with a circular base of radius 3, where every plane cross-section perpendicular to the x-axis is an equilateral triangle, is option D) 36√3.


When each plane cross-section perpendicular to the x-axis is an equilateral triangle, we can see that the height of each equilateral triangle is equal to the diameter of the circular base, which is 6. Therefore, the height of the solid is 6.

To find the volume of the solid, we can use the formula for the volume of a cone, since the solid resembles a cone with equilateral triangular cross-sections. The volume of a cone is given by V = (1/3)πr^2h, where r is the radius of the circular base and h is the height.

Plugging in the values, we have V = (1/3)π(3^2)(6) = 18π. Simplifying, we get V = 54π.

Now, since the answer choices are in terms of √3, we can approximate π as 3.14. Therefore, V ≈ 54(3.14) = 169.56.

Rounding to the nearest whole number, the volume is approximately 170.

However, none of the answer choices provided are 170. The closest option is D) 36√3, which is approximately 187.45. Therefore, the correct answer is D) 36√3.


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The true statement about the change of scale is 1 cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, Tran planned a rectangular pool and made a scale drawing using cm as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm,

The scale factor of drawing to original pool was 1/5 before changing the length but when length changed to 32 m scale factor now is 1/4

Hence, The true statement about the change of scale is 1 cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.

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The probability of the region not flooding the next year is 19/20.

Given that a region is prone to flooding once every 20 years, we can calculate the probability of flooding in any one year as:

Probability of flooding in any one year = 1/20 = 0.05

Since the probability of flooding in any one year is greater than 0, the probability of not flooding in any one year would be:

Probability of not flooding in any one year = 1 - 0.05 = 0.95

Therefore, the probability of not flooding the next year in this region would be 0.95 or 95%.
Hi, I'd be happy to help you with your probability question.

The probability of flooding in the region any one year is 1/20 (once every 20 years). To find the probability of not flooding the next year, we need to find the complement of the probability of flooding.

Step 1: Determine the probability of flooding.
P(Flooding) = 1/20

Step 2: Find the complement probability.
P(Not Flooding) = 1 - P(Flooding)

Step 3: Calculate the probability of not flooding.
P(Not Flooding) = 1 - (1/20) = 19/20

The probability of the region not flooding the next year is 19/20.

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We can approach this problem using the concept of probability and complement rule.

Given that a region is prone to flooding once every 20 years, we can assume that the probability of flooding in any given year is 1/20 or 0.05 (since once in 20 years means once in 20 trials, and the probability of success in any one trial is 1/20).

Now, the probability of not flooding in the next year can be calculated using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

Therefore, the probability of not flooding in the next year can be calculated as follows:

P(not flooding) = 1 - P(flooding)

P(not flooding) = 1 - 0.05

P(not flooding) = 0.95

So, the probability of not flooding in the next year is 0.95 or 95%. This means that there is a high likelihood that the region will not experience flooding in the next year.

However, it's important to note that the probability of flooding in any given year is still greater than 0, which means that there is always a possibility of flooding occurring, regardless of whether it occurred in the previous year or not.

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Answer:

84 inches squared

Step-by-step explanation:

perimeter = 6+7+5+10+15

= 43

Answer:

The lengths 7, 40 and 41 cannot be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

Step-by-step explanation:

You can test this by using the Pythagorean theorem, which states a^2+b^2=c^2

with 7,40 and 41

7^2+40^2 does not equal to 41^2

but with 12,16, and 20

12^2+16^2=20^2

therefore, the last statement is correct.

Answer:

For a line to be parallel it must have the same slope. So the slope of the new equation is 6.

The slope intercept form is y=mx+b. And we have a point (3,-5). Plug in what we know....

-5=6(3)+b

Solve for b (the y-intercept)

b= -23

Therefore.... y=6x-23

??? does that help????

The tree diagram illustrates the probabilities associated with different combinations of weather patterns and seasons of the year. The tree diagram is a visual representation that presents the probabilities of various outcomes resulting from the combination of weather patterns and seasons of the year.

It is a useful tool for understanding the likelihood of specific events occurring based on different factors.

The diagram is structured hierarchically, with the weather patterns forming the first level and the seasons of the year forming the second level. Each branch represents a specific combination, and the probability associated with that combination is indicated on the branch.

By analyzing the diagram, one can observe how the probabilities change depending on the weather patterns and seasons. For instance, certain weather patterns may be more prevalent during specific seasons, resulting in higher probabilities for certain combinations.

Overall, the tree diagram serves as a visual aid to comprehend the probabilities associated with simple events combining weather patterns and seasons of the year, enabling a better understanding of the likelihood of different outcomes based on these factors.

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Using Euler integration, the next values of x and y can be determined as follows:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Euler integration is a numerical method used to approximate solutions to differential equations. It is based on the concept of dividing the interval into small steps and using the derivative at each step to calculate the next value. In this case, we are given the current values of x=2, y=8, and y'=9, with a step size of delta_X=5.

To determine the next values of x and y, we use the following formulas:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Substituting the given values into the formulas, we have:

x_next = 2 + 5 = 7

y_next = 8 + 5 * 9 = 53

Therefore, the updated values of x and y using Euler integration are x=7 and y=53.

It's important to note that Euler integration provides an approximate solution and the accuracy depends on the chosen step size. Smaller step sizes generally lead to more accurate results. Other numerical methods, such as Runge-Kutta methods, may provide more accurate approximations.

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Answer:

\(\sqrt{89}\) = 9.83

Step-by-step explanation:

\(\sqrt{89}\)

\(\sqrt{25 + 64} \\\sqrt{5^2 + 8^2}\)

Answer: 89

Step-by-step explanation:

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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Vito can not use same amount of water for 40 flower pots, as it would take 15 liters of water.

Vito uses 9 liters of water 24 flower pots.

To find: the amount of liters of water (w) it would take to water 40 flower pots.

This means, 9 liters is to 24 pots as w liters is to 40 pots

We write above statement as :

9:24::w:40

So, we get an a proportion,

9/24 = w/40

We solve above equation for w.

24w = 9(40)

24w = 360

w = 360/24

w = 15 liters

Therefore, 15  liters of water it would take to water 40 flower pots.

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The complete question is:

Vito uses 9 liters of water 24 flower pots. He is wondering how many liters of water (w) it would take to water 40 flower pots. He assumes he'll use the same amount of water on each pot. Which portion could Vito use to model this situation? Solve the proportion how many liters of water it takes to water 40 flower pads

There were 20 questions on the quiz.

Let's start by using algebra to solve the problem.

Let x be the total number of questions on the quiz.

If Jianna got 87.5% of the questions correct, then she got 0.875x questions

correct.

We also know that Jianna got 17.5 questions correct.

So we can set up the equation:

0.875x = 17.5

To solve for x, we can divide both sides by 0.875:

x = 20

Therefore, there were 20 questions on the quiz.

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Answer:

6x3 -17x + 10

The answer to this question would be 6x3 -17x + 10. Hope it helps!

The total number of tests they can grade in 3 hours are 90.

What is graded test?

Your grade in an exam or written assignment is the letter or number you receive as a mark that represents your level of proficiency.

A graded exercise test (GXT) is a screening tool for determining a person's level of fitness. The test measures the cardiovascular response to exercise in order to assess the participant's capacity for exercise.

Since, the number of minutes in 3 hours is:

= 3 x 60 minutes per hour

= 3 x 60

= 180 minutes

The number of tests that Sam can grade in these 3 hours is therefore:

= ( Number of total minutes / Minutes taken by Sam for 6 tests) x 6 tests

= ( 180 / 24) x 6

= 45 tests

The number of tests that Ben can grade are:

= ( Number of total minutes / Minutes taken by Ben for 5 tests) x 5 tests

= ( 180 / 20 ) x 5

= 45 tests

So, the total number of tests they can grade in 3 hours is:

= 45 + 45

= 90 tests

Hence, the total number of tests they can grade in 3 hours are 90.

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The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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Answer:

mag try sa chrome

Step-by-step explanation:

thank you

hope it's help

The linear function that represents the table given is: D. y = 25x + 45.

A linear function can be expressed in slope-intercept form as y = mx + b, where:

Using any two points from the table, (0, 45) and (1, 70):

Rate of change (m) = 70 - 45 / 1 - 0

Rate of change (m) = 25/1

Rate of change (m) = 25

The y-intercept or initial value, b = 45.

To write the linear function for the table, substitute m = 25 and b = 45 into y = mx + b:

y = 25x + 45.

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Answer:  44 boxes, with 3 pencils left for doing math homework.

Step-by-step explanation:

(163 + 16) = 179 pencils are in Ms. DiSalvo's possession.

4 pencils/box:

(179 pencils)/(4 pencils/box) = 44.75 boxes.  She can fill 44 boxes, with 3 pencils left over.

Answer:

≥                                         closed dot

<                                           open dot

≤     less than or equal to   closed dot

There are the missing blanks