I. Linear functions - Complete the table by writing the Slope-Intercept form, identifying the slope, and finding the
y
-intercept for each equation given. Indicate if an answer does not exist.

Y= 3.2

When \( y \) varies directly as \( x \) and inversely as \( z \), the equation is given by:
\( y = \frac{kx}{z} \)

Where \( k \) is a constant.

Substituting the given values of \( x \), \( y \) and \( z \), we get:
\( 24 = \frac{k(120)}{16} \)

Solving for \( k \):
\( k = \frac{24*16}{120} = 4.8 \)

Substituting the values of \( k \), \( x \) and \( z \) into the equation, we get:
\( y = \frac{(4.8)*4}{15} \)

Therefore, the value of \( y \) when \( x=4 \) and \( z=15 \) is \( 3.2 \).

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Question Number 5.

The first and second numbers in the exponential sequence are 10 and 5, respectively.

In the exponential sequence given by a, b, c, d, ..., where a and b are the first two numbers. We know that the third number is given by b * c/a, and the fourth number is given by c * d/b.

the third number = 100

the fourth number = 500,

So b * c/a = 100

c * d/b = 500

rearranging the first equation :

c = 100a/b

Substituting this into the second equation, we then have

d = 500b/a

The sequence is then written as a, b, 100a/b, 500b/a, ...

We then proceed to  find a and b,

a, b, 100a/b, 500b/a, ...

a, b, 100a/b, 500b/a, ... = a, b, 100a/b, 500b/a, ...

100a/b = 100

500b/a = 500

Solving for a and b, we have:

a = 10

b = 5

In conclusion, the first and second numbers in the exponential sequence  are 10 and 5.

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Solution:

Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.

What is equation of a straight line?

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

After 2 months, Javier has saved a total of $920. Therefore, we can write the following equation:

2m = 920

Simplifying this equation, we get:

m = 460

This means that Javier is saving $460 each month.

After 4 months, Javier has saved a total of $1030. Using the same logic as before, we can write:

4m = 1030

Simplifying this equation, we get:

m = 257.5

This means that Javier is saving $257.5 each month.

To model the relationship between the amount of money Javier has saved and the number of months he has saved for, we can use the equation of a straight line:

y = mx + b

where y is the amount of money saved, x is the number of months, m is the monthly savings rate, and b is the starting amount saved.

Using the values we found earlier, we can write two equations:

y = 460x + b (for the first two months)

y = 257.5x + b (for the first four months)

To find the value of b, we can substitute the values of x and y for one of the points:

920 = 460(2) + b

Simplifying, we get:

b = 0

So the final equation that models the relationship between the amount of money Javier has saved and the number of months he has saved for is:

y = 460x (for the first two months)

y = 257.5x (for the first four months)

This means that Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.

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1.) The total number of ways in which the books can be arranged so that mathematics and physics cannot touch = 478,961,280.

2.) The total number of ways the books can be arranged when math and physics books touch = 479,001,600

Permutation is defined as the expression that shows how objects can be arranged in a definite order.

The total number of mathematics books = 5

The total number of astronomy books = 4

The total number of physics = 3

The total number of books that the student has in possession = 5+4+3 = 12.

The arrangement of the books so that math and physics cannot touch = 12!-8!

= 479001600 - 40320

= 478,961,280

The arrangement of the books so that math and physics can touch = 12! = 479,001,600

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O(n

A brute force algorithm for the 3-center problem would involve trying every combination of three points in the set of given points, calculating the cost for each combination using Equation (1), and then returning the combination with the minimum cost. The algorithm can be expressed as follows:

The computational complexity of this algorithm is O(n

combinations of three points from a set of n points.

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Answer: 1. x < 22       2. First option          3. x ≥ 5

Step-by-step explanation:

Closed dots means equal to or less/greater than.

Open dots means only less/greater than.

1. Open dot and arrow points left so x < 22

2. Only greater than so first option (Open dot and arrow points right)

3. Closed dot and arrow points right so x ≥ 5

Hope this helps!

Kevin's assertion is untrue. The perimeter of two rectangles can be the same although their lengths and widths differ.

The area of a planar figure is the space enclosed by its perimeter. An enclosed figure's area is the total number of unit squares that completely encircle its surface. Cm2 and m2 are two square measures. Only two dimensions are available for measuring a shape's area.

Kevin's claim is incorrect. Two rectangles can have the same perimeter but different lengths and widths.

For example, consider two rectangles with perimeters of 26 meters:

Rectangle A: Length = 8 meters, Width = 5 meters

Rectangle B: Length = 9 meters, Width = 4 meters

Both rectangles have a perimeter of 26 meters (8+5+8+5=26 and 9+4+9+4=26), but they have different lengths and widths.

Kevin's claim is not true in general.

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Mohal would expect to earn $265 in a day when he waits on 16 tables, and he would expect to earn $15tt + $25 in a day when he waits on tt tables

Earnings or wages refer to the amount of money an individual receives in exchange for their work or services. This can include a regular salary or hourly wage, as well as bonuses, commissions, and other forms of compensation.

Earnings or wages are typically determined by a variety of factors, including the type of work being performed, the level of skill and experience required, the local job market, and the employer's policies and practices. In some cases, earnings may be negotiated between the employer and the employee, while in other cases they may be set by industry standards or government regulations.

To calculate Mohal's expected earnings in a day when he waits on 16 tables, we can use the formula:

Total earnings = Guaranteed wage + Tips

Guaranteed wage = $25

Tips = $15 x Number of tables

Number of tables = 16

So, Total earnings with 16 tables = $25 + ($15 x 16) = $265

To calculate Mohal's expected earnings in a day when he waits on tt tables, we can use the same formula:

Total earnings = Guaranteed wage + Tips

Guaranteed wage = $25

Tips = $15 x Number of tables

Number of tables = tt

So, Total earnings with tt tables = $25 + ($15 x tt) = $15tt + $25

Therefore, Mohal would expect to earn $265 in a day when he waits on 16 tables, and he would expect to earn $15tt + $25 in a day when he waits on tt tables.

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Answer:

Total earnings with 16 tables: 265

Total Earnings with t tables: 15t+25

Step-by-step explanation:

The number of sodas sold is 83 and the number of hot dogs sold is 52.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's call the number of sodas sold "x".

According to the problem, the number of hot dogs sold is 31 less than the number of sodas sold, so we can write the number of hot dogs sold as "x - 31".

We also know that the combined total of sodas and hot dogs sold is 135, so we can write an equation:

x + (x - 31) = 135

Simplifying this equation:

2x - 31 = 135

Adding 31 to both sides:

2x = 166

Dividing both sides by 2:

x = 83

So the number of sodas sold is 83.

To find the number of hot dogs sold, we can use the equation we came up with earlier:

x - 31 = 83 - 31 = 52

So the number of hot dogs sold is 52.

Therefore, the number of sodas sold is 83 and the number of hot dogs sold is 52.

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The perimeter of Raina's pigpen is 1020 feet.

Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all sides of the shape. Perimeter is typically measured in units such as inches, feet, meters, or centimeters, depending on the system of measurement being used.

To find the perimeter of the rectangular pigpen, we need to add up the lengths of all four sides. The formula for the perimeter of a rectangle is:

perimeter = 2 * length + 2 * width

Plugging in the values we know, we get:

perimeter = 2 * 325 + 2 * 185

perimeter = 650 + 370

perimeter = 1020

Therefore, the perimeter of Raina's pigpen is 1020 feet.

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Answer:

8x²y + 14xy - 6xy²

Step-by-step explanation:

To expand the bracket, you need to multiply each term inside the bracket by 2xy, then recombine the terms.

2xy * 4x = 8x²y

2xy * 7 = 14xy

2xy * -3y = -6xy²

Final answer: 8x²y + 14xy - 6xy²

Answer:

8x^2y+14xy-6xy^2

Step-by-step explanation:

2xy( 4x+7-3y)

Distribute the 2xy to each term inside the parentheses.

2xy * 4x + 2xy +7 + 2xy * -3y

8x^2y+14xy-6xy^2

Sure, here are the answers to Exercises 4.4 1 for Propositions 1.5 through 1.8:

Proposition 1.5: If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths and angles but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same side lengths and angles can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the side lengths and angles of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.6: If two triangles have two angles and a side of one equal to two angles and a side of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same angle measures and side lengths but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same angle measures and side lengths can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the angle measures and side lengths of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.7: If two triangles have two sides and an angle of one equal to two sides and an angle of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths and angle measures but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same side lengths and angle measures can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the side lengths and angles of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.8: If two triangles have three sides of one equal to three sides of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere

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Measure of ∟A is 119°

To solve for x, we must use the fact that the angles have the same measure, so ∟A = ∟B.

Substitute 7x + 24° for ∟A and 3x + 92° for ∟B and set them equal to each other:

7x + 24° = 3x + 92°

Subtract 3x from both sides:

7x - 3x = 92° - 24°

4x = 68°

Divide both sides by 4 to solve for x:

x = 17°

Now that we have x, we can substitute 17° for x into the original equation for ∟A to find its measure:

∟A = 7x + 24°

∟A = 7(17°) + 24°

∟A = 119°

Therefore, the measure of ∟A is 119°.

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Answer:

3,200 kK

Step-by-step explanation:

Typically, only about 10% of the energy available at one trophic level is transferred to the next trophic level. This is known as the 10% rule, and it means that herbivores will only be able to incorporate about 10% of the energy available in the big bluestem grasses.

Therefore:

32,000 kJ x 0.10 = 3,200 kJ

The difference from part (b) is that Beth has a much higher initial wealth, so the negative expected value of the gamble has a smaller impact on her overall utility.

This is not a fair gamble because the expected value of the gamble is negative. The expected value of a gamble is calculated by multiplying the probability of each outcome by the value of that outcome and summing the results. In this case, the expected value is 0.4(-$100) = -$40. Since the expected value is negative, the gamble is not fair.

Anh will not join this gamble because her expected utility from the gamble is lower than her utility from her initial wealth. Her expected utility from the gamble is

0.4u(-$100) = 0.4v(-$100) = -40v.

Her utility from her initial wealth is

u($100) = v($100) = 100v.

Since -40v < 100v, her expected utility from the gamble is lower than her utility from her initial wealth, so she will not join the gamble.

Chris will not join this gamble because his expected utility from the gamble is lower than his utility from his initial wealth. His expected utility from the gamble is

0.4u(-$100) = 0.4e^(-100c) = -40e^(-100c).

His utility from his initial wealth is

u($0) = e^(0c) = 1.

Since -40e^(-100c) < 1, his expected utility from the gamble is lower than his utility from his initial wealth, so he will not join the gamble.

Beth will not join this gamble because her expected utility from the gamble is lower than her utility from her initial wealth. Her expected utility from the gamble is

0.4u(-$100) = 0.4v(-$100) = -40v.

Her utility from her initial wealth is

u($10000) = v($10000) = 10000v.

Since -40v < 10000v, her expected utility from the gamble is lower than her utility from her initial wealth, so she will not join the gamble.

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Answer:

Mate show the full picture please..half of the question is not shown.

Step-by-step explanation:

Step-by-step explanation:

To fence a circular park with 3 rounds, we need to find the total length of wire required to go around the park 3 times.

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, π is the constant pi, and d is the diameter.

Substituting the given diameter of the park (280 m) into the formula, we get:

C = π * 280 m

≈ 879.65 m

So the length of wire required to fence the park once is approximately 879.65 m.

To fence the park three times, we need to multiply this length by 3:

3 rounds of wire = 3 * 879.65 m

= 2638.95 m

Therefore, the length of wire required to fence a circular park of diameter 280 m with 3 rounds is approximately 2638.95 m.

The missing side lengths are computed below

Triangle 22

The side length x can be calculated using

sin(30) = 9/x

So, we have

x = 9/sin(30)

Evaluate

x = 18

For length y, we have

y = √(18² - 9²)

Evaluate

y = 9√3

Triangle 23

The side length y can be calculated using

sin(30) = y/√3

So, we have

y = √3 * sin(30)

Evaluate

y = 1/2√3

For length x, we have

x = √(√3² + (1/2√3)²)

Evaluate

x = √(15/4)

x = 1/2√15

Triangle 24

The side length y can be calculated using

cos(60) = y/2√3

So, we have

y = 2√3 * cos(60)

y = √3

For x, we have

x = √((2√3)² - (√3)²)

x = √9

x = 3

Triangle 25

The side length x can be calculated using

cos(60) = 5/x

So, we have

x = 5/cos(60)

x = 10

For y, we have

y = √(10² - 5²)

y = 5√3

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The probability of getting two heads and three tails in a single throw of five unbiased coins is 0.3125.

The probability of getting two heads and three tails in a single throw of five unbiased coins can be calculated using the formula:

P = (5! / (2! * 3!)) * (0.5)^2 * (0.5)^3

Where 5! is the factorial of 5, 2! is the factorial of 2, and 3! is the factorial of 3.

First, calculate the factorial of 5, 2, and 3:

5! = 5 * 4 * 3 * 2 * 1 = 120
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6

Next, plug these values into the formula:

P = (120 / (2 * 6)) * (0.5)^2 * (0.5)^3

Simplify:

P = (120 / 12) * (0.25) * (0.125)

P = 10 * 0.25 * 0.125

P = 0.3125

Therefore, the probability of getting two heads and three tails in a single throw of five unbiased coins is 0.3125.

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Answer: 6

Step-by-step explanation:

Let's start with what we know. We have the following equation:

x^2 + 7 = 43

Now, we subtract 7 from both sides.

x^2 = 36

Then we take the square root of both sides giving our final answer:

x = 6.

The  general form of an explicit function for what the nth term of any arithmetic sequence would bean = a + (n-1)*d

An explicit function is a mathematical function containing only the independent variable or variables —opposed to an implicit function which is written in terms of both dependent and independent variables

The general arithmetic progression can be written as:

T₁ ,  T₂,   T₃,   T₄,   ......,  Tn.

Where n is any term

Now since a = 1 and d = common difference, The general arithmetic progression can be written as:

a, a+d,  a+2d,  a+3d, a+4d, a+(n-1)*d

Thus, the explicit function becomes a+(n-1)*d

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Answer:

The brain of the newborn baby has a mass of about 377 grams.

Step-by-step explanation:

Fractions are written as a ratio of two integers. For instance, a/b is a fraction.

Given the following parameters

Body mass = 2900 grams.

If the Brain mass of a newborn baby is about 13% of the mass of the newborn, then the mass of the brain is given as;

mass of brain = 13% of 2900

Mass of brain = 0.13 * 2900

Mass of brain = 377grams

Simplifying the equation of v 4. 4 ( v - 16. 8 ) - -2. 3 = 3. 62, we find that v = 21.45.

To solve for v, we will use the following steps:

Simplify the left-hand side of the equation by distributing the 4.4:

4.4v - 73.92 + 2.3 = 3.62

Simplify further by combining like terms:

4.4v - 71.62 = 0

Add 71.62 to both sides of the equation:

4.4v = 71.62

Solve for v by dividing both sides by 4.4:

v = 71.62 / 4.4

v = 16.27727...

Round the answer to two decimal places:

v = 21.45

Therefore, the solution to the equation 4.4(v - 16.8) - (-2.3) = 3.62 is v = 21.45.

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a. The probability that a student makes more than $30,000 is 0.0668.

b. The probability that a student makes between $27,000 and $32,000 is 0.9545.

c. The probability that a student makes less than $23,150 is 0.0062.

Probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various events. Statistics is the study of occurrences that follow a chance distribution.

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The correct matches for the vocabulary would be :

Apathy is a lack of interest or passion for anything. The line "Ahmein doesn't care if he does well or not" describes apathy since Ahmein is apathetic about whether he succeeds or fails.

Being competent is having the knowledge and skills required to complete a task successfully which describes Javier as he is aware that he can construct a birdhouse.

Expectations are convictions or presumptions regarding future events. Value is a term used to describe something's importance or worth.

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Answer:

1. apathy = Trudy doesn't care about doing well in school.

2. competent = Javier knows he is able to build a birdhouse.

3. expectations = fear of failure or success

4. autonomy = Alfonzo likes to make choices on his own.

5. stress = Quincy feels anxious and distressed about a test.

Answer:

scalene triangle

Step-by-step explanation:

in a scalene triangle, all the sides are not equal

IH is not equal to HJ and also is not equal to JI