A newspaper charges $50 per half-page ad and $80 per full-page ad. Gavin has a budget of $750 to purchase 12 advertisements.
Define a variable for each unknown. Write a system of equations to represent the situation.

How many half-page advertisements does Gavin purchase? Show your work.

How many full-page advertisements does Gavin purchase? Show your work. (no links please, and no nonsense answers)

Answer:

360

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

120% of 300

Answer:

1,2,4,6,7

Step-by-step explanation:

The given shape is a pentagon, an irregular polygon, and also convex.

A Polygon is considered to be Concave if its diagonal can lie outside the Polygon as well.

A polygon is considered to be Convex if all of its diagonals lie within it.

A polygon is considered to be regular if it is convex and has equal sides and angles.

If all of the angles and sides of a polygon are not equal, it is said to be irregular.

Here,

The given shape has five sides, which means this is a pentagon.

The given shape has unequal sides, which means this is an irregular pentagon.

The given shape has it's all its diagonals lying inside, which means this is a convex pentagon.

Thus, the given shape is a pentagon, an irregular polygon, and also convex.

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Answer:

25x-10y-30

Step-by-step explanation:

5(5x - 2y - 6)=(5*5x)(-5*2y)(-5*6)=25x-10y-30

Answer:

-8 ,-4, 0, 2

Step-by-step explanation:

Answer:

-8,-4,0,2

Step-by-step explanation:

Answer:

3rd

Step-by-step explanation:

x & y are both negative in 3rd

Answer:

rotate it once to the right and you will get the vertices

Step-by-step explanation:

Answer:

r = qr - 5p - 4

Step-by-step explanation:

3r + 4 = qr - 5p

Subtract:

3r = qr - 5p - 4

Divide:

r = qr - 5p - 4

Answer:

  (18π +4) cm ≈ 60.55 cm

Step-by-step explanation:

You want the perimeter of a figure bounded by two semicircles and a straight line segment.

The perimeter of the figure is the sum of the lengths of the curves and lines that form its boundary. Here, one boundary is a semicircle of diameter 16 cm, another boundary is a semicircle of diameter 20 cm, and a straight line forms the remaining boundary.

The length of a semicircle is half the circumference of a full circle of the same diameter:

  boundary length = 1/2(πd)

The smaller semicircle has a length of ...

  boundary length (small) = 1/2π(16 cm) = 8π cm

The larger semicircle has a length of ...

  boundary length [large] = 1/2π(20 cm) = 10π cm

The length of the line segment is the difference of the diameters:

  line segment length = (20 cm) -(16 cm) = 4 cm

The perimeter is the sum of these lengths:

  P = boundary length (small) + boundary length (large) + line segment length

  P = (8π +10π +4) cm = 18π +4 cm ≈ 60.55 cm

The perimeter of the figure is about 60.55 cm.

__

Additional comment

The perimeter is closer to 60.549 cm, so rounds to 60.5 cm.

The statement that describes the end behavior of the graph f(x) = -4x³ + 28x² + 32x + 64.

The graph increases to left and decreases to right.

The end behavior of a polynomial function is given by the limits of the function as x approaches infinity, meaning that only the term with the highest exponent is considered for the calculation of the limit.

In this problem, the function is defined as follows:

f(x) = -4x³ + 28x² + 32x + 64.

Considering only the highest exponent, we have that:

f(x) = -4x³.

Hence the behavior of the graph of the function at the left tail is given as follows:

lim x -> -∞ f(x) = -4(-∞)³ = -4 x (-∞) = ∞.

(increases to the left).

At the right tail, the behavior is given as follows:

lim x -> ∞ f(x) = -4 x (∞)³ = -4 x (∞) = -∞.

(decreases to right).

The problem is incomplete, hence we suppose that it asks for us to describe the end behavior of the graph.

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Answer:b

Step-by-step explanation:

The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.

The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.

In this case, applying the EDD rule, the sequence of jobs would be as follows:

D (Due on Friday 10th June)

F (Due on Tuesday 14th June)

E (Due on Wednesday 15th June)

C (Due on Friday 17th June)

G (Due on Thursday 16th June)

H (Due on Saturday 18th June)

A (Due on Monday 13th June)

B (Due on Monday 20th June)

By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.

Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.

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The third-degree Maclaurin polynomial for f(x) = sin(x) is P3(x) = x - (x^3) / 6.

To find the nth Maclaurin polynomial for the function f(x) = sin(x) when n = 3, we need to compute the polynomial up to the third-degree term.

The Maclaurin polynomial for a function f(x) centered at x = 0 is given by the formula:

Pn(x) = f(0) + f'(0)x + (f''(0)x^2) / 2! + (f'''(0)x^3) / 3! + ...

Let's calculate the nth Maclaurin polynomial for f(x) = sin(x) when n = 3:

First, we find the values of the function and its derivatives at x = 0:

f(0) = sin(0) = 0

f'(x) = cos(x), so f'(0) = cos(0) = 1

f''(x) = -sin(x), so f''(0) = -sin(0) = 0

f'''(x) = -cos(x), so f'''(0) = -cos(0) = -1

Using these values, we can write the Maclaurin polynomial:

P3(x) = 0 + 1x + (0x^2) / 2! + (-1x^3) / 3!

Simplifying further, we have:

P3(x) = x - (x^3) / 6.

Therefore, the third-degree Maclaurin polynomial for f(x) = sin(x) is:

P3(x) = x - (x^3) / 6.

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The solution of each part of the question is given below:

a. Let C be the event that a person smokes cigars, and let S be the event that a person smokes cigarettes. The percentage of Americans who smoke either cigars, cigarettes, or both can be calculated as P(C U S), where U represents the union of two events. From the given information, P(C) = 15% and P(S) = 35%. The probability that a person smokes both cigars and cigarettes is 7%, so P(C ∩ S) = 7%.

P(C U S) = P(C) + P(S) - P(C ∩ S)

P(C U S) = 15% + 35% - 7% = 43%

So, 43% of Americans smoke either cigars, cigarettes, or both.

b. The percentage of Americans who smoke neither cigars nor cigarettes can be calculated as P(C' ∩ S'), where C' represents the complement of event C (not smoking cigars) and S' represents the complement of event S (not smoking cigarettes).

P(C' ∩ S') = 100% - P(C U S)

P(C' ∩ S') = 100% - 43% = 57%

So, 57% of Americans smoke neither cigars nor cigarettes.

c. The percentage of Americans who smoke cigars but not cigarettes can be calculated as P(C ∩ S').

P(C ∩ S') = P(C) - P(C ∩ S)

P(C ∩ S') = 15% - 7% = 8%

So, 8% of Americans smoke cigars but not cigarettes.

d. The conditional probability that a person smokes cigarettes given that he smokes cigars can be calculated as P(S | C), where S represents the event that a person smokes cigarettes and C represents the event that a person smokes cigars.

P(S | C) = P(S ∩ C) / P(C)

P(S | C) = 7% / 15% = 0.47

So, the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars is 0.47, or 47%.

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X would equal 8

Step-by-step explanation:

5-3(8) = -19

5 multiplied by negative 3 times 8 equals negative 19

negative 3 times 8 equals negative 24 plus 5 equals 19

a) For the given savings account with an annual percentage rate of 5.5% compounded quarterly, the values to be used are a = $2,500, r = 0.055, and k = 4.

b) After 10 years, Karla will have approximately $11,374.46 in the account.

c) The annual percentage yield (APY) for the savings account is approximately 5.614%.

a) In the exponential formula A(t) = a(1 + r/k)^(kt), we substitute the values: a = $2,500 (the principal amount), r = 0.055 (the annual percentage rate), and k = 4 (since the interest is compounded quarterly).

b) To calculate the amount of money Karla will have in the account after 10 years, we substitute t = 10 into the formula:

A(10) = 2500(1 + 0.055/4)^(4*10) ≈ $11,374.46

The answer is rounded to the nearest penny.

c) The annual percentage yield (APY) represents the actual or effective annual percentage rate, considering all compounding in a year. To calculate it, we can use the formula:

APY = (1 + r/k)^k - 1

Substituting the given values, we have:

APY = (1 + 0.055/4)^4 - 1 ≈ 0.05614

The answer is rounded to 3 decimal places, so the APY for the savings account is approximately 5.614%.

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Answer:

+13 or just 13

Answer:

Step-by-step explanation:

y = 3x + 5

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 5 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, thus

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (- 1, 2) into the partial equation

2 = - 3 + c ⇒ c = 2 + 3 = 5

y = 3x + 5 ← equation of parallel line

Answer:

y=3x-26

Step-by-step explanation:

Hi there!

We are given the line y=3x+5, and we want to write an equation that is parallel to that line, and goes through the point (9, 1)

Parallel lines have the same slope; so let's find the slope of y=3x+5

The line is written in the format y=mx+b, where m is the slope and b is the y intercept

Since 3 is in the place of where m is in the equation, the slope of the line is 3.

Because we are given the point (9,1) and the slope 3, we can write the equation using point-slope form, which is \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point

We have everything we need to write the equation in point-slope form, let's just label their values to avoid any confusion:

m=3

\(x_1=9\\y_1=1\)

Substitute these values into the formula above:

\(y-y_1=m(x-x_1)\)

y-1=3(x-9)

The equation can be left as that, or you can re-write it into slope-intercept form (y=mx+b form) if you wish

In order to do that, we first need to open up the parentheses by multiplying x and -9 by 3:

y-1=3x-27

Add 1 to both sides

y=3x-26

Hope this helps!

Answer:

ig its a translation bc its not rotated, reflected or dilated

Step-by-step explanation:

hope this helps

The critical numbers of the function f(θ) = 2cos(θ) + sin^2(θ) on the interval 0 ≤ θ < 2π are:
θ = 0 (smaller value)
θ = π (larger value)

To find the critical numbers of the function f(θ) = 2cos(θ) + sin^2(θ) on the interval 0 ≤ θ < 2π, follow these steps:

1. Find the derivative of f(θ) with respect to θ. This will give us f'(θ).
f'(θ) = -2sin(θ) + 2sin(θ)cos(θ)

2. Set f'(θ) to 0 and solve for θ. This will give us the critical numbers.
0 = -2sin(θ) + 2sin(θ)cos(θ)

Factor out the common term 2sin(θ):
0 = 2sin(θ)(1 - cos(θ))

Now, set each factor to 0:
2sin(θ) = 0
1 - cos(θ) = 0

Solve for θ:
sin(θ) = 0
cos(θ) = 1

3. Determine θ values within the given interval (0 ≤ θ < 2π):
For sin(θ) = 0, θ = 0, π
For cos(θ) = 1, θ = 0

4. Identify the smallest and largest critical numbers.
θ = 0 (smallest value)
θ = π (largest value)

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The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.

To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.

Given the system:

x + y = 8

y = 3x

Substituting the value of y from the second equation into the first equation, we have:

x + (3x) = 8

4x = 8

x = 2

Now, substitute the value of x into the second equation to solve for y:

y = 3(2)

y = 6

Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.

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Answer:

c.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

8/17 (Answer B)

Step-by-step explanation:

There are a total of 34 students, of whom 16 are girls.

The desired probability is 16/34, which reduces to 8/17 (Answer B)

There are 18 boys and 16 girls in social studies class. A student is chosen at random to represent the class at History Day. What is the probability that a girl will be chosen?

A) 7/34

B) 8/17

C) 10/17

D) 9/34

Answer: C, 10/17

Answer:

B) 3b. 10b

Step-by-step explanation:

B) 3b. 10b = (3x10)(bxb) = 30b²

The limit of the function in this problem is given as follows:

lim x->0 f(x) = 1/2.

Following the standard procedure to obtain the limit of the function, merely obtaining the numeric value at x = 1, the limit is undetermined at x = 0, as follows:

0/0.

Hence the can apply the L'Hospital Rule, trying to find the derivative at the numerator and the denominator, hence:

At x = 0, the limit would again assume an undetermined value of 0/0, hence the L'Hospital Rule is applied again, hence:

Now the function is:

f(x) = cos(2x)sqrt(cos(2x))/2.

Since cos(x) = 0, the numeric value at x = 0 is given as follows:

f(0) = 1/2.

Which is the limit.

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Alice can be expected to win approximately 5 games out of the 7 games she plays.

If historically Alice wins 70% of the time, we can expect her to win 70% of the games she plays. If Alice and Bob play 7 games of chess, we can calculate how many games Alice can be expected to win by multiplying the total number of games (7) by the probability of Alice winning (70% or 0.7):

Expected number of games Alice wins = 7 * 0.7 = 4.9

Since we cannot have a fraction of a game, we can round the expected number of games Alice wins to the nearest whole number. Therefore, Alice can be expected to win approximately 5 games out of the 7 games she plays.

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The mathematicians credited with developing the mathematical models that predict population growth in each of two competing species are Rosenzweig and MacArthur(OPTION A).

These two scientists developed a theory known as the "competitive exclusion principle," which states that two species competing for the same resources cannot coexist indefinitely. Instead, one species will eventually outcompete and displace the other species.
Rosenzweig and MacArthur's model is based on the Lotka-Volterra equations, which are a set of differential equations that describe the dynamics of predator-prey relationships. They extended this model to include two competing species and developed the concept of the "ecological niche" – the specific set of environmental conditions under which a species can survive and reproduce.
Their model predicts that the two species will reach a stable equilibrium, where their populations remain relatively constant over time. However, the exact outcome of the competition depends on several factors, including the initial population sizes of the two species, the relative strengths of their ecological niches, and the availability of resources.
Overall, Rosenzweig and MacArthur's mathematical model has been influential in the field of ecology, providing a framework for understanding how competing species interact and how ecosystems evolve over time.

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The analysis of the sample data and the hypothesis test conducted do not provide sufficient evidence to reject the null hypothesis that the average speed of all cars traveling down the specified stretch of highway is greater than 71 mph.

Through the hypothesis test, the null hypothesis (H₀) was tested against the alternative hypothesis (H₁). The null hypothesis states that the average speed of all cars on the highway is not greater than 71 mph, while the alternative hypothesis suggests that the average speed is indeed higher than 71 mph.

The results of the hypothesis test failed to produce a p-value that was lower than the chosen significance level. This indicates that there is insufficient evidence to reject the null hypothesis. Failing to reject the null hypothesis does not prove that the average speed is exactly 71 mph, but it suggests that the data does not provide strong enough support to conclude that the average speed is significantly greater than 71 mph.

Several factors could contribute to this outcome, including the sample size, data collection methodology, or limitations in the study design. It is important to acknowledge the possibility of a type II error, which means that we might have failed to reject a false null hypothesis. To obtain more reliable insights, further research or a larger sample size may be necessary to assess the average speed of cars on the specified stretch of highway more accurately.

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The second number in terms of n is x = n - 8.

Let the second number be x.

The fact that the first number is eight more than the second number is clear.

n = x + 8.    ...(1)

It is given that the third number is five more than the first number

n + 5 = y     ...(2)

We want to solve for x in terms of n, so we can use the first equation to get x in terms of n:

From equation 1 and 2

n + 5 = y = (x + 8) + 5

n + 5 = x + 13

x = (n + 5) - 13

x = n - 8

Therefore, the second number in terms of n is x = n - 8.

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If two lines intersect, then the vertical angles formed must be both equal in measure.

The  intersection of a line can be described as when two or more lines cross each other in a plane as a result of this they are been referred to as   intersecting lines.

Therefore, intersecting lines share a common point, hence , If two lines intersect, then the vertical angles formed must be both equal in measure.

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The coordinates of triangle A'B'F' after the given sequence of transformations are:

A'(6, 7), B'(6, 3), and F'(3, 3).

To find the coordinates of triangle A'B'F' after the given sequence of transformations, we need to apply each change one by one and record the resulting coordinates.

Reflection over the x-axis:

When we reflect a point over the x-axis, its y-coordinate changes sign while its x-coordinate remains the same. So, the coordinates of A, B, and F after the reflection are:

A(-6, -7), B(-6, -3), and F(-3, -3).

Rotation of 180° about the origin:

When we rotate a point 180° about the origin, it's x-coordinate and y-coordinate change sign. So, the coordinates of A', B', and F' after the rotation is:

A'(6, 7), B'(6, 3), and F'(3, 3).

1/3 Dilation about the origin:

When we dilate a point about the origin by a scale factor of 1/3, both its x-coordinate and y-coordinate are multiplied by 1/3. So, the coordinates of A", B", and F" after the dilation is:

A"(2, 7/3), B"(2, 1), and F"(1, 1).

Therefore, the diagram of the final transformation is given in the attached image.

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