8. A graph represents the proportional relationship between the number of pages printed, y, and the time in minutes, x. If there is a point on the graph at (4, 720), how many pages can be printed in half a minute?​

The numeric values of the piecewise function in this problem are given as follows:

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

A piecewise function is a function that has different definitions, based on the input x of the function.

For values of x that are of 1 or less, the function is defined as follows:

f(x) = x.

Hence the numeric values in this interval are given as follows:

For values of x that are greater than 1, the function is defined as follows:

f(x) = -x + 4.

Hence, at x = 3, the numeric value of the function is given as follows:

f(3) = -3 + 4 = 1.

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The probability of A and L is 0.25, rounded to two decimal places

To find the probability of A and L, we need to find the number of elements in the intersection of A and L and divide by the total number of elements in the set S.

A = {x ∈ S | x ≥ 21}

= {21, 23, 29, 30}

L = {x ∈ S | x < 25}

= {10, 11, 13, 19, 21, 23}

A ∩ L = {x ∈ S | x ≥ 21 and x < 25}

= {21, 23}

Therefore, the probability of A and L is:

P(A and L) = |A ∩ L|/|S|

= 2/8

= 0.25

Therefore, the required probability of A and L is 0.25, rounded to two decimal places

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The independent variable in the research question is the location of the universities, with SDSU being the specific location of interest. The dependent variable is the time it takes to find a parking spot.

The research question is seeking to compare the time it takes to find a parking spot at SDSU to the time it takes at other San Diego universities, with the location being the independent variable that may affect the dependent variable, which is the time taken to find a parking spot.

By identifying the independent and dependent variables in the research question, researchers can design a study that will collect data on these variables, analyze the data, and

draw conclusions about whether there is a significant difference in the time it takes to find a parking spot at SDSU compared to other universities in San Diego.

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Answer:

Down There

Step-by-step explanation:

Radii:

Circle A - 8

Circle B - 13

Circle C - 17

Circle D - 14

Circle A Area:

(pi)(r)^2, where r = 8

64pi or about 201.06

Circle B Area:

(pi)(r)^2, where r = 13

169pi or about 530.93

Circle C Area:

(pi)(r)^2, where r = 17

289pi or about 907.92

Circle D Area:

(pi)(r)^2, where r = 14

196pi or about 615.75

Circle D is greater than Circle A's area by 132pi or about 414.69.

Mathland Bakery sold 23 apple pies and 13 cherry pies on that day.

Since a represents apple and c represents cherry:

We can now go ahead to solve for a and c using a simultaneous equation approach.

From equation (1)

a = 36 - c

Substituting this expression into equation (2), we get:

Therefore, 13 cherry pies were sold. To find the number of apple pies sold, we can substitute this value of c into equation 1:

Therefore, 23 apple pies were sold.

In other words, Mathland Bakery sold 23 apple pies and 13 cherry pies on that day.

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Answer:

40

Step-by-step explanation:

6:4 = 1,5 which means he grades 1 paper per 1,5 minute. 60:1,5 = 40 papers

Answer:

Step-by-step explanation:

54 - 18 = 36

so...

18 + 36 = 54

x < -2 is the solution for the given inequality.

To solve the inequality:

-3(x - 3) > 5 - 5x

We can start by using the distributive property and simplifying both sides of the inequality:

-3x + 9 > 5 - 5x

Next, we can add 5x to both sides of the inequality to get the x terms on one side:

2x + 9 > 5

Then, we can subtract 9 from both sides of the inequality to isolate the variable:

2x > -4

Finally, we divide both sides by 2, remembering to reverse the inequality because we are dividing by a negative number (-3):

x < -2

Therefore, the solution to the inequality is x < -2.

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The addition of the outlier will affect the distribution in that b) The distribution will become skewed left.

When a score of 12 is added as an outlier, it shifts the distribution of data towards the left-sided direction resulting in skewness. This can be deduced from observing that the median is closer to the lower end of the range of collected data.

Additionally, the introduction of the outlier has substantially decreased the mean value, indicating that the deviation value has pulled the mean downwards and altered the symmetry of the original distribution by making it asymmetrically distributed in a leftward manner.

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The amount to be invested now is  $173.9.

The amount to be invested now can be calculated using the formula for future value of an annuity as shown below;

FV = A x ((1 + r)ⁿ⁻¹) / r

where:

Monthly rate becomes;

r = 6% / 12 = 0.5% = 0.005

The amount is calculated as;

80,000 = A x ((1 + 0.005)¹⁶⁸ ⁻ ¹) / 0.005

80,000 =460A

A = 80,000/460

A = $173.9

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This has to do with the solution the quadratic equation given as: y=x² - 5x -14.

To factorize the quadratic equation - y =  x² - 5x -14, we need to find two numbers that multiply to -14 and add up to -5.

We can list out the factors of -14 as follows:

-1 and 14

1 and -14

-2 and 7

2 and -7

Out of these pairs, the numbers that add up to -5 are -2 and 7.

Therefore, we can factorize the equation as:

y = (x - 2)(x + 7)

To find the zeros or x-intercepts, we set each factor equal to 0 and solve for x:

x - 2 = 0, x + 7 = 0

x = 2, x = -7

So the solutions are (2, 0) and (-7, 0).

The axis of symetry is the average of the x-intercepts

This is (2 - 7)/2 = -2.5.

Substituting this  value into   the equation:

y = (-2.5 )² - 5 (-2.5 ) - 14 = -  20.25

So the vertex is (  -2.5, -20.25).

The domain of the function is all real numbers, since there are no restrictions on the input x.

The range of the function is y ≥ -20.25, since the vertex is the lowest point of the parabola and the graph extends upward from there. See the graph attached.

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Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.

Circumcenter : The point of intersection of the three perpendicular bisectors.

Incenter : The point of intersection of the three angle bisectors.

Centroid : The point of intersection of the three medians.

Orthocenter : The point where all the three altitudes of the triangle meet or intersect each other.

In conclusion, based on the information, Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.

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Answer:

Step-by-step explanation:

...Negative.

Answer:

Negative

Step-by-step explanation:

Answer: red = 9, yellow = 15 green = 24, total = 48 notepads were bought.

Step-by-step explanation:

3 x 3 = 9, so 9 red. 3 x 5 = 15, so 15 yellow. 3 x 8 = 24, so 24 green. In total this is equal to 48 notepads. 9 + 15 + 24 = 48.

The resultant force is gotten  as 173.3780

A resultant force is described as  the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition

we determine resultant force by following these steps:

See attached image for full working

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Answer:

19683

Step-by-step explanation:

3 to the power of 8 is 6561,

so just put 6561 multiplied by itself 3 times.

(6561 X 6561 X 6561).

Answer:

3⁸ × 3 = 19,683

A linear equation is an equation in which each term has at max one degree. The table that represents a linear function is Table 1. Thus, the correct option is A.

We have,

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

For the table to represent a linear function, the function must have a constant slope between any two points.

For the first table, the slope between the first two points is,

m = (7-3)/(2-1) = 4

The slope between the last two points is,

m = (15-11)/(4-3)

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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Answer:

A

Step-by-step explanation:

Expressing the trig ratio as a function of 50°, we have sin310° = sin(360 - 50)°

From the question, we have the following trigonometry function that can be used in our computation:

sin310°

The above expression is a sine function of 310 degrees

By mathematical expression, we have

360 - 50 = 310 degrees

This means that we can replace 310 degrees with (360 - 50) degrees in sin310°

So; in terms of 50 degrees, we have

sin310° = sin(360 - 50)°

Hence, the expression sin310° in terms of 50 degrees is sin(360 - 50)°

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If "∠A" is complementing angle "∠B" and "∠C" is complementing "∠B", then the true statement is (a) ∠A ≅ ∠C, because both the angles have the same measure.

The "Complementary-Angles" are two angles that add up to 90 degrees, which is also known as a right-angle. When two angles are complementary, they are said to complement each other.

Since the angles : ∠A and ∠C are both complementary to ∠B, we can write :

⇒ ∠A + ∠B = 90°,

⇒ ∠B + ∠C = 90°,

Next, We subtract "∠B" from both sides of each equation,
We get;

⇒ ∠A = 90° - ∠B,

⇒ ∠C = 90° - ∠B,

We see that the measure of the angle "A" and angle "C" is same.

Therefore, ∠A and ∠C have the same measure, option (a) is the correct answer.

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The given question is incomplete, the complete question is

If ∠A is a complementary angle of ∠B and ∠C is a complementary angle of ∠B, then which of the following statements is true?

(a) ∠A ≅ ∠C

(b) ∠A ≅ ∠B

(c) ∠A + ∠C ≅ ∠B

(d) ∠B ≅ ∠C

Answer:

[tex]\frac{3}{4} = \frac{6}{8} = \frac{9}{12} = \frac{18}{24} [/tex]

The total amount spent is $9.50.

We have,

2 1/2 yards of fabric cost 7.00.

3 rolls of ribbon cost 2.50.

So, the total amount of money spend

= Cost of fabric + cost of ribbon

= 7 + 2.50

= $9.50

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The factor that one should consider when choosing a career is D. All of the above.

In choosing a career, a student should consider the required education and training involved, the work environment, and their potential earnings.

Other factors to consider include:

Thus, all the listed factors should be considered when choosing a career.

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The number of non-working light bulbs that would be expected in the group of 1,000 light bulbs is: 50 bulbs

In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.

We are told that a sample of 40 bulbs were picked from a box of 1000 bulbs and it was discovered that 2 of the bulbs were not working. Thus:

Fraction of bulbs not working = 2/40 = 0.05

Thus, number of bulbs not working in a sample of 1000 bulbs is:

0.05 * 1000 = 50 bulbs

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The distributive property of multiplication can be used to calculate the sum of the difference between the multiples of the variables expression as follows;

[tex]\sum\limits_{i = 1}^{124} (29\cdot a_i - 13 \cdot b_i)[/tex] = -30

The distributive property states that multiplying the difference between addend by a value produces a result which is equivalent to the multiplication of each addend individually and finding the difference from the resulting values.

The distributive property of multiplication indicates that we get;

Where; [tex]\sum\limits_{i=1}^{124} a_i = -10[/tex], and [tex]\sum\limits_{i=1}^{124} b_i = -20[/tex]

[tex]\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) = 29 \times \sum\limits_{i=1}^{124} a_i - 13 \times \sum\limits_{i=1}^{124} b_i = 29 \times (-20) - 13 \times (-10))[/tex]

29 × (-10) - 13 × (-20) = -30

Therefore;

[tex]\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) =-30[/tex]

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1 inch is the diameter of the driven pulley.

Let's use D to represent the driven pulley's diameter. The speed decrease needed, according to the issue description, is a 4 to 1 reduction.

This implies that the ratio of the diameters is also 4 to 1, as the speeds are inversely proportional to the diameters:

D/4 = 1/4

Multiplying both sides by 4 gives:

D = 1

Therefore, the diameter of the driven pulley should be 1 inch.

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Answer:

1875

Step-by-step explanation:

Yearly income = $90000

Monthly income = 90000÷12 = $7500

Monthly rent = 25%×7500 = $1875

In this table, the constant of proportionality is 15.5.

The constant of proportionality is the ratio that one value has compared to another.

In other words, the constant of proportionality is the quotient of the numerator and the denominator.

The constant of proportionality can also be referred to as the slope, gradient, or unit rate.

X            y         Constant of Proportionality

2          31            15.5 (31/5)

5          77.5        15.5 (77.5/5)

7.5      116.25      15.5 (116.25/7.5)

Thus, the constant of proportionality, which can also be computed as the slope or unit rate is 15.5.

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