1. A company is testing a new energy drink. Volunteers are asked to rate their energy one hour
after consuming a beverage. Unknown to them, some volunteers are given the real energy
drink and some are given a placebo-a drink that looks and tastes the same, but does not have
the energy-producing ingredients. Show your work using the following list of random digits to
assign each participant listed either the real drink or the placebo.
69429 86140 11625 87049 23167
Volunteer
Abby
Barry
87524 24575 87254 97801 82231
Callie
Dion
Ernie
Falco
Garrett
Hallie
Indigo
Jaylene
Real or Placebo
2. The local water authority has received complaints of high levels of iron in the drinking water.
They decide to randomly select 20 houses from each subdivision of 100 houses to visit and test
their water. Describe how to use random numbers to select the 20 houses in each division.
3. A couple is willing to have as many children as necessary to have two girls.
a) Describe a simulation that can be performed to estimate the average number of children
required to have two girls.

The fraction of the school days in February that you walked to school is 7/10 or 0.7 when expressed as a decimal.

The fraction of the school days in February that you walked to school can be represented as:

(number of days you walked) / (total number of school days in February)

Since you walked 14 out of 20 days in February, we can substitute these values into the formula:

(number of days you walked) / (total number of school days in February) = 14 / 20

Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor (2), we get:

(number of days you walked) / (total number of school days in February) = 7 / 10

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Note that where the above function is given, the equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold. See the graph attached.

To change the given equation to slope-intercept form, we need to solve for y.

2x + 3y = 1470

3y = -2x + 1470

y = (-2/3)x + 490

Therefore, the slope of the line is -2/3 and the y-intercept is 490.

To graph this line using the slope-intercept method, we can plot the y-intercept first, which is (0, 490). Then, using the slope of -2/3, we can find another point by moving 2 units to the right and 3 units down from the first point. We can continue this pattern to plot additional points and then draw a straight line through them.

The equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold.

To graph the function, we can plot the intercepts (0, 490) and (735, 0), where 735 is the x-intercept. Then, using the slope of -2/3, we can find other points and draw a straight line through them.

If Sal's total profit on lunch specials for the next month is $1,593, then the equation would be 2x + 3y = 1593. The graphs of the functions for both months would have the same slope of -2/3, indicating that the profit per lunch special sold remains constant.

However, the y-intercept would be different, indicating a different starting profit for the month. The graphs would have different intercepts and intersect the y-axis at different points, reflecting the difference in starting profits.

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Ines has 9/10 liter of juice, if Meg has 3/10 liter of juice left in her bottle and Ines has 3 times as much juice in her bottle as Meg has .

It is need to find how much juice does Ines have.To calculate it, it is need to know how much liter of juice does Meg have. Meg have 3/10 liter of juice left in her bottle, and Ines has 3 times as much juice her bottle as Meg has.

That is Ines has 3 times means multiplying how much juice meg have by 3.

That is Juice left in bottle of Ines = juice left in bottle of Meg * 3 = 3/10 liter x 3 = 9/10 liter. Therefore, Ines has 9/10 liter of juice in her bottle.

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The solution of the given inequality, x - 3 ≤ -2, is solved as the possible value of x which is determined as: x ≤ 1.

Given the inequality x - 3 ≤ -2, to find the solution, wr would have to solve for x as explained below:

x - 3 ≤ -2 [given]

Add 3 to both sides:

x - 3 + 3 ≤ -2 + 3 [addition property of equality]

x ≤ 1

This means that the values of x are less than or equal to 1, which is from 1 below.

Thus, the solution to the inequality is solved by finding the possible value of x, which is x ≤ 1.

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the side length of the large square is equal to 4 divided by the square root of π times the side length of the small square.

what is length  ?

Length is a physical quantity that refers to the measurement of a one-dimensional distance or extent, such as the distance between two points. It is typically measured in units such as meters, feet, inches, or centimeters. Length can be used to describe the size or dimensions

In the given question,

Let's assume that the side length of the small square is equal to the diameter of each small bubble.

When four bubbles in squares collide and merge into one large bubble in a square, the total area of the small squares is equal to the area of the large square. Since the side length of each small square is equal to the diameter of the small bubble, the area of each small square is equal to the square of the diameter of the small bubble.

So, if we let d be the diameter of each small bubble, then the area of each small square is equal to d². Therefore, the total area of the four small squares is equal to 4d², and the area of the large square is equal to the sum of the areas of the four small squares, which is 4d².

The area of a circle is equal to πr², where r is the radius of the circle. If we let R be the radius of the large bubble, then its area is equal to π².

We know that the area of the large square is equal to the area of the large bubble, so we have:

4d² = πR²

Solving for R, we get:

R =√(4d²/π)

R = 2d/√(π)

Since the side length of the large square is equal to twice the radius of the large bubble, we have:

Side length of large square = 2R = 4d/√(π)

Therefore, the side length of the large square is equal to 4 divided by the square root of π times the side length of the small square.

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the backup goalie saved 42 shots. Answer: 42 shots. We can start by setting up an equation using the information given

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written with an equal sign (=) between the two expressions. For example, the equation 2x + 3 = 7 is a statement that asserts that the expression 2x + 3 is equal to 7.

In the given question,

We can start by setting up an equation using the information given:

save percentage = (number of shots saved / total number of shots attempted)

For the backup goalie, we know that their save percentage is 0.560, and we also know the total number of shots attempted on the goal is 75. Let's let the number of shots saved by the backup goalie be represented by the variable "t". Then we can write:

0.560 = t / 75

To solve for t, we can cross-multiply:

0.560 * 75 = t

t = 42

Therefore, the backup goalie saved 42 shots. Answer: 42 shots.

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The geometric term that can be used to describe the crossing sign shown is intersecting lines.

In geometry, intersecting lines are two lines that cross one another at a location known as the point of intersection. It is possible to use the point of intersection to solve issues concerning angles, segments, and geometric shapes because it is the sole point that both lines share.

Two pairs of opposite angles that are equal to one another are formed when two lines connect, giving rise to four angles.

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(a) The expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3).

(b) The least possible integer value of x for the rectangular solid to exist is 4.

a. To express the length, width, and height of the right rectangular prism in terms of x, we can factor the volume expression, 6x³ - 3x² - 45x.

Factoring out the greatest common factor, 3x:

3x(2x² - x - 15)

Now, factor the quadratic expression:

3x(2x² - x - 15)

To factor the quadratic expression further, find two numbers whose product equals the constant term (-15) and whose sum equals the coefficient of the linear term (-1). These two numbers are -5 and 3.

3x(2x + 5)(x - 3)

Thus, the expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3)

b. For the rectangular solid to exist, all dimensions (length, width, and height) must be positive. Let's examine the constraints on x for each dimension:

1. 3x > 0
2. 2x + 5 > 0 → x > -5/2
3. x - 3 > 0 → x > 3

Since x must satisfy all three inequalities, the least possible integer value of x for the rectangular solid to exist is x = 4.

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Answer:

more i formation required

Step-by-step explanation:

Answer:

[tex]8x+71/2[/tex]

Step-by-step explanation:

I did the test

Hope this helps :)

The 10 cupcakes will weigh approximately 25.9 ounces when one cubic inch is about 0. 55 ounces, the diameter of the mold is 3 inches and the height of the mold is 2 inches.

Given data:

Diameter of the mold = 3 inches

Radius = 3/2 = 1.5 inches

Height of the mold = 2 inches.

One cubic inch = 0.55 ounces

π = 3. 14

We need to find how many ounces will 10 cupcakes weigh. to find that we need to find the volume of a cone and the weight of one cupcake. we can find  the volume of a cone given by the formula,

[tex]V = (1/3)πr^2h[/tex]

Where:

r = radius

h = height

By Substituting the r and h values into the formula we get:

[tex]V = (1/3)πr^2h[/tex]

[tex]= (1/3) π ((1.5)^2) × (2)[/tex]

[tex]= (1/3) π×(2.25)×(2)[/tex]

= 1.5π

When one cubic inch of the cone is about 0.55 ounces, the weight of one cupcake is approximately

= 1.5π × 0.55

= 0.825π ounces.

The weight of 10 cupcakes is determined by multiplying by the weight of one cupcake, it is given as:

= 10 × 0.825π

= 8.25π ounces

= 8.25 × 3.14

= 25.9 ounces.

Therefore, the 10 cupcakes will weigh approximately 25.9 ounces.

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Answer:

Congruent, impossible, not congruent.

Step-by-step explanation:

a) Congruent because of AAS congruency.

b) Impossible to tell. There is no congruency rule with 1 angle and 1 side.

c) Not congruent. Sides should not be equal.

Answer:

The triangular prism has two triangular bases and three rectangular lateral faces.

First, we need to find the area of each triangular base. Using the formula for the area of a triangle:

base x height / 2

We can calculate the area of one triangular base as:

(10 x 12) / 2 = 60 units²

Now we need to find the area of each rectangular lateral face. All three faces have the same dimensions of 10 units by 14 units, so the area of each face is:

10 x 14 = 140 units²

To find the total surface area of the prism, we add up the areas of both triangular bases and all three rectangular faces:

Total surface area = 2 x (area of triangular base) + 3 x (area of rectangular face)

Total surface area = 2 x 60 units² + 3 x 140 units²

Total surface area = 120 units² + 420 units²

Total surface area = 540 units²

Therefore, the surface area of the triangular prism is 540 square units.

the inflection points are x = 0 and x = 2, and the intervals of concavity are (-∞, 0) and (2, ∞) for concave down, and (0, 2) for concave up.

To find the inflection points and intervals of concavity of the function f(x) = x^4 - 4x^3, we need to find its second derivative.

f'(x) = 4x^3 - 12x^2
f''(x) = 12x^2 - 24x

The inflection points occur where f''(x) = 0 or is undefined. Therefore, we set 12x^2 - 24x = 0 and solve for x.

12x(x - 2) = 0
x = 0 or x = 2

These are the two possible inflection points.

To determine the intervals of concavity, we need to look at the sign of the second derivative in each interval. We can use test points to determine the sign.

Test point x = 1:
f''(1) = 12 - 24 = -12, so the function is concave down on the interval (-∞, 0) and concave up on the interval (0, ∞).

Test point x = 3:
f''(3) = 108 - 72 = 36, so the function is concave up on the interval (2, ∞) and concave down on the interval (-∞, 2).

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Answer:V≈339.29m³

Step-by-step explanation:

V=π(d

2)2h=π·(6

2)2·12≈339.29201m³ Pls if you can answer my question if you have txvs.

The 25 fluid ounces is greater than one pint is correct statement .

Relation between fluid ounces and pint ,

There are 16 fluid ounces in one pint.

Conversion of fluid ounces to pint

This implies that,

1 fluid ounces is equal to  one by sixteen pint.

To be precise,

25 fluid ounces is equal to 25 / 16pints

⇒  25 fluid ounces is equal to 1.5625.

However, since 1.5625 is greater than 1,

This implies that 25 fluid ounces is greater than 1 pint.

So, 25 fluid ounces is greater than 1 pint.

Because 25 is greater than 16.

And 1 pint is not greater than 25 fluid ounces.

Therefore, the 25 fluid ounces is greater than one pint.

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We have found the altitude of the aircraft, we can determine its distance from station P, which is simply the value of d1

We can use the concept of triangulation to find the distance of the aircraft from station P. Let's assume that the aircraft is at point A, and let d1 and d2 be the distances of the aircraft from stations P and Q, respectively. Then we have:

[tex]d1^2 + h^2 = r1^2 ------ (1)\\d2^2 + h^2 = r2^2 ------ (2)[/tex]

where h is the altitude of the aircraft, r1 and r2 are the distances from the aircraft to stations P and Q, respectively. We want to find d1, which is the distance of the aircraft from station P.

We know that the distance between the two radar stations is 120 miles, so we have:

[tex]r2 = r1 + 120 (3)[/tex]

Subtracting equation (1) from equation (2), we get:

[tex]d2^2 - d1^2 = r2^2 - r1^2\\d2^2 - d1^2 = (r1+120)^2 - r1^2\\d2^2 - d1^2 = 120*240 + 120^2\\d2^2 - d1^2 = 40800[/tex]

Adding equations (1) and (3), we get:

[tex]2h^2 + 2*r1*120 = r1^2 + (r1+120)^2\\2h^2 + 2*r1*120 = 2*r1^2 + 120^2\\2h^2 = 4*r1^2 - 2*r1*120 + 120^2\\h^2 = 2*r1^2 - r1*120 + 120^2 / 2\\h^2 = r1^2 - r1*60 + 120^2 / 4[/tex]

Substituting h^2 into equation (1), we get:

[tex]d1^2 + (r1^2 - r1*60 + 120^2 / 4) = r1^2\\d1^2 = r1*60 - 120^2 / 4\\d1^2 = 15*r1^2 - 18000[/tex]

Substituting d2^2 - d1^2 from the previous calculation, we get:

[tex]d2^2 - (15*r1^2 - 18000) = 40800\\d2^2 = 15*r1^2 + 58800[/tex]

Now we have two equations with two unknowns (d1 and r1). Solving for r1 in equation (4) and substituting into equation (5), we get:

[tex]d2^2 = 15*(d1^2 + 120*d1) + 58800\\d2^2 = 15*d1^2 + 1800*d1 + 58800\\15*d1^2 + 1800*d1 + 58800 - d2^2 = 0[/tex]

This is a quadratic equation in d1, which can be solved using the quadratic formula:

[tex]d1 = (-b \± sqrt(b^2 - 4ac)) / 2[/tex]

where a = 15, b = 1800, and c = 58800 - d2^2. Note that we should take the positive root, since d1 is a distance and therefore cannot be negative.

Once we have found d1, we can use equation (1) to find h, the altitude of the aircraft, as:

[tex]h = sqrt(r1^2 - d1^2)[/tex]

Finally, the distance of the aircraft from station P is simply d1.

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To get it why radians  have fractional answers, one can use the unit of a circle .  the unit circle could be a circle with a radius of 1, centered at the root of a coordinate plane. To measure points in radians on the unit circle, we measure the  arc length of the comparing other part of the circle, as shown within the image attached:

Radian measures angles based on arc length equal to the radius of a circle, resulting in fractions for non-whole arcs. The unit circle has a radius of 1 and is centered at the origin.

This explains why radians can be fractional. To measure angles in radians, we use arc length on the unit circle. Most angles correspond to fractions of a full circle, like π/2 for a quarter circle.

The angle in radians for one-eighth of a circle is approximately 0.79 (π/4), as most circle arcs are not exact multiples of the radius. Most circle arcs cannot be expressed as a whole number of radii.

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The approximate area of the figure is 40 square meters. So, the correct answer is B).

Recall the formula for the area of a kite, which is

Area = (1/2) x Base x Height

where "Base" is the length of one of the diagonals and "Height" is the length of the other diagonal.

Identify the base and height of the given kite from the problem statement. Here, it is given that the height is 10 meters and the base is 8 meters.

Substitute the values of the base and height into the formula for the area of a kite

Area = (1/2) x 8 meters x 10 meters

Simplify the expression by multiplying the base and height together and dividing by 2

Area = 40 square meters

Round the answer to the nearest whole number or keep the answer as a decimal, depending on the instructions of the problem.

Therefore, the approximate area of the given kite is 40 square meters. So, the correct answer is B).

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The area of the triangle ∆WXY is derived to be 5.7 to the nearest tenth.

When two side length of a triangle and the angle between them is given, the area is half the multiplication of the two sides and the sine of the angle.

Area of the triangle = 1/2 × 4.7 × sin162

Area of the triangle = 11.4738/2

Area of the triangle = 5.7369.

Therefore, the area of the triangle ∆WXY is derived to be 5.7 to the nearest tenth.

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For the given case, there is evidence that the true mean number of hours of screen time for US adults is greater than 3.5.

Here, the researcher is 95% confidence interval from 3.6 hours to 8.1 hours captures  y = the true mean amount of daily screen time for US adults.
If 3.5 hours falls below this interval, it is likely that the true mean number of hours of screen time for US adults is greater than 3.5 hours.

A confidence interval is a measure of values that is used to evaluate a statistical parameter which tends to involve the true form of the parameter a predetermined proportion of the time if the procedure of searching the group of values is repeated numerous times.

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Answer:

Step-by-step explanation:

git

The total length of the race is approximately 28.24 miles.

To determine the total length of the race, we can use the given information: Piotr has completed 24 miles, which represents 85% of the race. We can set up a proportion to find the total length. Let 'x' represent the full length of the race:

(24 miles) / x = 85% / 100%

To solve for 'x', we can first convert the percentage to a decimal by dividing 85 by 100, resulting in 0.85:

24 / x = 0.85

Next, we can cross-multiply:

0.85 * x = 24

Now, we can solve for 'x' by dividing both sides by 0.85:

x = 24 / 0.85

x ≈ 28.24 miles

Therefore, the total length of the race is approximately 28.24 miles. Piotr has completed 85% of this distance, which means he has run 24 miles and has around 4.24 miles remaining to finish the race.

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The estimated population proportion is 0.622, with a margin of error of +/- 0.096.

The value of the population proportion of people from Hawaii who exercised for at least 30 minutes a day 3 days a week can be estimated using the sample proportion of 62.2%. However, we need to calculate the margin of error to determine a range in which the true population proportion is likely to fall.

Using the formula for the margin of error:

Margin of error = z*sqrt(p*(1-p)/n)

where z is the z-score for the desired level of confidence (let's use 95% confidence, which corresponds to a z-score of 1.96), p is the sample proportion (0.622), and n is the sample size (100).

Plugging in the values, we get:

Margin of error = 1.96*sqrt(0.622*(1-0.622)/100) = 0.096

So the margin of error is 0.096, meaning that we can be 95% confident that the true population proportion of people from Hawaii who exercise for at least 30 minutes a day 3 days a week falls within a range of 0.622 +/- 0.096.

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Answer:

62.29

Step-by-step explanation:

100 - 3(4.25) - 13 - 4(2.99)

= 100 - 12.75 - 13 - 11.96

= 62.29

explanation in the picture

the answer is

62,29

The amplitude of the current I is 16.9 Amperes

To find the amplitude of the current I in the given circuit with an alternating current E(t) = 120sin(12t), inductance L = 0.31 H, resistance R = 7 ohms, and capacitance C = 0.029 F, we need to determine the impedance (Z) of the circuit first.

The impedance Z can be calculated using the formula:

Z = √((R²) + (XL - XC)²)

Where XL is the inductive reactance, and XC is the capacitive reactance. XL can be calculated as:

XL = 2πfL

And XC can be calculated as:

XC = 1/(2πfC)

Here, f is the frequency of the alternating current, which can be determined from the given function E(t) = 120sin(12t) as:

f = 12/(2π) = 1.91 Hz

Now, we can calculate XL and XC:

XL = 2π(1.91)(0.31) = 3.74 ohms

XC = 1/(2π(1.91)(0.029)) = 2.89 ohms

Next, we can find the impedance Z:

Z = √((7²) + (3.74 - 2.89)²) = √(49 + 0.72) = 7.1 ohms

Finally, we can find the amplitude of the current I using Ohm's law:

I = E(t)/Z

Since we're looking for the amplitude, we only need the maximum value of E(t), which is 120 V:

I = 120/7.1 = 16.9 A

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The discrepancy in the results: The theoretical probability may not be calculated correctly and enough trials have not been performed to give the desired result

In the given scenario, 81% of money spent at full-service restaurants in America is through debit, credit, or pre-paid cards. However, one restaurant found that 421 out of 973 customers used these payment methods. Possible reasons for the discrepancy in the results are:

1. The theoretical probability may not be calculated correctly: The 81% figure might not accurately represent the actual proportion of customers using cards in full-service restaurants. It could be due to incorrect data collection or interpretation.

3. Enough trials have not been performed to give the desired result: The data from one restaurant for one week might not be enough to accurately reflect the overall trend. A larger sample size and longer time frame would give a more accurate representation.

It's important to note that there might not necessarily be a discrepancy in the result; it could be a difference due to variations in individual restaurant data compared to the overall average.

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The required answer is the nearest hundred dollars: $902.09 is approximately $900.

To find the value of the car 20 years after it was purchased, we can use the formula for exponential decay:

Value = Initial value * (1 - Depreciation rate) ^ (time elapsed / time for depreciation)

1. Determine the depreciation rate: The car's value depreciates by one half every 3.5 years, so the depreciation rate is 50% or 0.5.
Depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wears, and second, the allocation in accounting statements of the original cost of the assets to periods in which the assets are used (depreciation with the matching principle).

Depreciation is thus the decrease in the value of assets and the method used to reallocate, or "write down" the cost of a tangible asset (such as equipment) over its useful life span

2. Calculate the number of depreciation periods: Since the car's value halves every 3.5 years, we need to find out how many 3.5-year periods are in 20 years. To do this, divide 20 by 3.5: 20 / 3.5 ≈ 5.71 periods.

3. Use the exponential decay formula:
Value = 29,000 * (1 - 0.5) ^ (5.71)
Value ≈ 29,000 * (0.5) ^ (5.71)
Value ≈ 29,000 * 0.0311
Value ≈ 902.09

4. Round the value to the nearest hundred dollars: $902.09 is approximately $900.

So, the value of the car 20 years after it was purchased is approximately $900.

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Answer:

Step-by-step explanation:

To find the equation that has the same solution as x^2 - 10x - 3 = 5, we can start by simplifying the left side of the equation by adding 8 to both sides:

x^2 - 10x - 3 = 5

x^2 - 10x - 8 = 0

Now we need to find an equation with the same solutions as this simplified equation. We can do this by factoring the quadratic equation into two linear factors:

x^2 - 10x - 8 = 0

(x - 2)(x - 8) = 0

Therefore, the solutions to the equation x^2 - 10x - 3 = 5 are x = 2 and x = 8. We can write two equations that have these solutions:

(x - 2) = 0

(x - 8) = 0

So the two equations that have the same solution as x^2 - 10x - 3 = 5 are x - 2 = 0 and x - 8 = 0. These equations can be simplified as x = 2 and x = 8, which are the same solutions as the original quadratic equation. Therefore, the equations x - 2 = 0 and x - 8 = 0 have the same solution as x^2 - 10x - 3 = 5.

(x - 5)^2 = 33

For the solutions to the inequality *> 145, you can consider the given terms: 1. Fractions larger than 14 1/2: These are solutions since 14 1/2 is equivalent to 145/2, which is smaller than 145. 2.

Decimals larger than 14 1/2: These are also solutions as any decimal larger than 14.5 (14 1/2 as a decimal) will be greater than 145/2 and thus smaller than 145. 3. Whole numbers larger than 14 1/2: These are solutions as well, since any whole number greater than 14 is greater than 14 1/2 and therefore greater than 145/2. The numbers that are not solutions to the inequality are: 1. Fractions smaller than 14 1/2 2. Decimals smaller than 14 1/2 3. Whole numbers smaller than 14 1/2 These values are all less than 145/2 and therefore do not satisfy the inequality *> 145.

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Answer:

a)

[tex]m = \frac{15 - 10}{4 - 2} = \frac{5}{2} [/tex]

[tex]10 = \frac{5}{2} (2) + b[/tex]

[tex]10 = 5 + b[/tex]

[tex]b = 5[/tex]

[tex]y = \frac{5}{2}x + 5[/tex]

b) The function is already given.

c)

[tex]m = \frac{100 - 40}{30 - 10} = \frac{60}{20} = 3 [/tex]

[tex]100 = 3 (30) + b[/tex]

[tex]100 = 90 + b[/tex]

[tex]b = 10[/tex]

[tex] y = 3x + 10[/tex]