Michael has $15 and wants to buy a combination of cupcakes and fudge to feed at least three siblings. A cupcake costs $2, and a piece of fudge costs $3
This system of inequalities models the scenario:
2x + 3y <15
x+y≥ 3
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points).
***PLEASE MAKE IT EASY FOR ME SO ITS EASY TO TYPE*** 15 POINTS

The length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."

The Pythagorean theorem, which asserts that given a right triangle, the sum of the squares of the two shorter sides (a and b), is equal to the square of the hypotenuse (c), can be used to determine the length of the triangle's hypotenuse (c).

a = 10 feet

b = 20 feet

Using the Pythagorean theorem, we can calculate c as follows:

c^2 = a^2 + b^2

c^2 = 10^2 + 20^2

c^2 = 100 + 400

c^2 = 500

To find c, we take the square root of both sides:

c = √500

c ≈ 22.36

Rounding the answer to the nearest whole number, we get c ≈ 22.

Therefore, the length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."

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Answer:

B

Step-by-step explanation:

[tex]\frac{x^6-4x^4+3x^2}{5x^2}[/tex]

factor out the common factor of x² from each term on the numerator

= [tex]\frac{x^2(x^4-4x^2+3)}{5x^2}[/tex] ( cancel x² on numerator/ denominator )

= [tex]\frac{x^4-4x^2+3}{5}[/tex]

Answer:

[tex](x +5)^2+(y-1)^2=25[/tex]

Step-by-step explanation:

To determine the equation of the graphed circle, we need to find the coordinates of its center and the length of its radius.

The center of the circle is a single point that lies at an equal distance from all points on the circumference of the circle.

From inspection of the graphed circle, we can see that its domain is [-10, 0] and its range is [-4, 6].  The x-coordinate of the center is the midpoint of the domain, and the y-coordinate of the center is the midpoint of the range.

[tex]x_{\sf center}=\dfrac{-10+0}{2}=-5[/tex]

[tex]y_{\sf center}=\dfrac{-4+6}{2}=1[/tex]

Therefore, the center of the circle is (-5, 1).

The radius of the circle is the distance from the center to all points on the circumference of the circle. Therefore, to calculate the length of the radius, find the distance between x-coordinate of the center and one of the endpoints of the domain.

[tex]r=0-(-5)=5[/tex]

Therefore, the radius of the circle is r = 5.

To determine the equation of the circle, substitute the center and radius into the standard formula.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

As h = -5, k = 1 and r = 5, then:

[tex](x - (-5)^2+(y-1)^2=5^2[/tex]

[tex](x +5)^2+(y-1)^2=25[/tex]

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x +5)^2+(y-1)^2=25}[/tex]

Answer:

0

Step-by-step explanation:

Use the following models to show the equivalence of the fractions 35 and 610 a) Set model

The best deal over 5 years would be investing at 7.8% compounded quarterly.

Although the interest rates of 7.87% compounded semi-annually and 7.72% compounded every minute may appear slightly higher, the frequency of compounding plays a significant role in determining the overall return.

Compounding more frequently leads to a higher effective annual rate. In this case, compounding quarterly provides a greater compounding frequency than semi-annual or minute-by-minute compounding, resulting in higher returns over time.

When interest is compounded quarterly, the compounding occurs four times a year, whereas semi-annual compounding only occurs twice a year. Compounding every minute may seem more frequent, but the actual effect on the return is minimal since there are a large number of minutes in a year.

Therefore, the 7.8% compounded quarterly is the best deal over 5 years as it offers a higher effective annual rate compared to the other options.

In summary, investing at 7.8% compounded quarterly is the most advantageous choice over a 5-year period. The frequency of compounding plays a crucial role in determining the overall return, and compounding quarterly provides a greater compounding frequency compared to semi-annual or minute-by-minute compounding.

It is essential to consider both the interest rate and the compounding frequency when evaluating investment options to make an informed decision.

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Answer:  the correct answer is 5/2

Step-by-step explanation:

To find the slope of a line perpendicular to a given line, we can use the property that the product of the slopes of two perpendicular lines is equal to -1.

The given line has an equation of y = -2/5x + 4/5.

The slope of this line can be determined by comparing it to the slope-intercept form (y = mx + b), where "m" represents the slope. In this case, the slope of the given line is -2/5.

To find the slope of the line perpendicular to this line, we take the negative reciprocal of the given slope. The negative reciprocal of -2/5 is 5/2.

The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

[tex]y = 20000(0.95)^5[/tex]

Calculating the expression, we find:

[tex]y ≈ 20000(0.774)[/tex]

Simplifying further, we get:

[tex]y ≈ 15480[/tex]

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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The break-even sales (units) when the variable costs are decreased by $4 is approximately 47,714 units.

To find the break-even sales (units) when the variable costs are decreased by $4, we need to calculate the new unit variable costs and then use the break-even formula.

Fixed costs (F) = $334,000

Unit selling price (P) = $22

Unit variable costs (V) = $19

Change in unit variable costs = $4

New unit variable costs (V') = V - Change in unit variable costs

= $19 - $4

= $15

Now, let's calculate the break-even sales (units) using the formula:

Break-even sales (units) = Fixed costs / (Unit selling price - Unit variable costs)

Break-even sales (units) = $334,000 / ($22 - $15)

= $334,000 / $7

= 47,714.29

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Answer:

Its b i bealive

Step-by-step explanation:

The linear inequality represented by the graph is y < 3x + 2. Option A.

To determine the linear inequality represented by the graph, let's analyze the given information and the slope-intercept form of a linear equation (y = mx + b), where m represents the slope and b represents the y-intercept.

We are given two points on the line: (-3, -7) and (0, 2). Using these points, we can calculate the slope (m) as follows:

m = (y2 - y1) / (x2 - x1)

= (2 - (-7)) / (0 - (-3))

= 9 / 3

= 3

Therefore, the slope of the line is 3.

Next, we can substitute the slope and one of the given points into the slope-intercept form to find the y-intercept (b). Let's use the point (0, 2):

y = mx + b

2 = 3(0) + b

2 = b

So, the y-intercept (b) is 2.

Now we have the equation of the line: y = 3x + 2.

The shaded region is to the left of the line. To express this region as an inequality, we need to find the inequality symbol. Since everything to the left of the line is shaded, we need the inequality to represent values less than the line.

Therefore, the correct inequality is y < 3x + 2.

Hence, the linear inequality represented by the graph is y < 3x + 2. So Option A is correct.

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Note the complete question is

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.

Which linear inequality is represented by the graph?

A.) y < 3x + 2

B.) y > 3x + 2

C.) y < 1/3x + 2

D.) y > 1/3x + 2

The line of best fit for the data in this problem is given as follows:

y = -0.5x + 60.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

Two points on the scatter plot are given as follows:

(30, 45) and (60, 30).

When x increases by 30, y decays by 15, hence the slope m is given as follows:

m = -15/30

m = -0.5.

Hence:

y = -0.5x + b.

When x = 30, y = 45, hence the intercept b is obtained as follows:

45 = -15 + b

b = 60.

Thus the function is given as follows:

y = -0.5x + 60.

The data is given by the image presented at the end of the answer, and the problem asks for the line of best fit for the data.

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Answer:

34.45%

Step-by-step explanation:

A tree diagram shows all possible outcomes of two or more events.

Each branch is a possible outcome and is labelled with the probability of that outcome.

Draw lines (branches) to represent the first event (main meal). Write the outcomes on the ends of the branches: "sandwich" and "slice of pizza". Write the given probabilities on the branches.

Draw the next set of branches to represent the second event (side).  Write the outcomes on the ends of the branches: "chips" and "veggies with hummus". Write the given probabilities on the branches.

We assume that the events in this scenario are independent, so the probability of the first event happening has no impact on the probability of the second event or the third event happening.  Therefore, to find the probability of each combination of events, multiply along the branches.

Sandwich and chips = 35% × 47% = 16.45%

Sandwich and veggies with hummus = 35% × 53% = 18.55%

Slice of pizza and chips = 65% × 47% = 30.55%

Slice of pizza and veggies with hummus = 65% × 53% = 34.45%

Therefore, the probability that Sophie selects a slice of pizza and veggies is 34.45%.

The probability that Sophie selects a slice of pizza and veggies is 34.45%.

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

The probability of pizza and veggies  is calculated as

P = Pizza * Veggies

Substitute the known values in the above equation, so, we have the following representation

P = 65% * 53%

Evaluate

P = 34.45%

Hence, the probability that Sophie selects a slice of pizza and veggies is 34.45%.

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Answer:

I have not comed across this question before

Answer:

  x = 4

Step-by-step explanation:

You want the value of x in the figure of a circle with intersecting secants.

The product of lengths from the near and far circle intercepts to the point where the secants intersect is the same for both secants:

  6(6+10) = 8(8+x)

  6·16 = 8·(8+x)

  12 = 8 +x . . . . . . . divide by 8

  4 = x . . . . . . . . . . subtract 8

The length x is 4 units.

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Answer:

x=3

Step-by-step explanation:

You can get the answer by substituting the value of x in the equations, your aim is to find a number that will make both equations equal zero.

The numeral 7,001 eight is equal to 3585 in base ten.

To convert the numeral 7,001 in base eight to base ten, we need to multiply each digit by the corresponding power of eight and sum them up.

Starting from the rightmost digit, we have:

[tex]1 * 8^0 = 1\\0 * 8^1 = 0\\0 * 8^2 = 0\\7 * 8^3 = 3584[/tex]

Adding these values together, we get:

1 + 0 + 0 + 3584 = 3585

Therefore, the numeral 7,001eight is equal to 3585 in base ten.

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The first mechanic worked for 12 hours, and the second mechanic worked for 8 hours.

Let's assume the first mechanic worked for x hours. Since the first mechanic charged $75 per hour, their earnings can be represented as 75x dollars.

Similarly, the second mechanic worked for (20 - x) hours, and at a rate of $95 per hour, their earnings can be represented as 95(20 - x) dollars.

According to the problem, the combined earnings of both mechanics are $1800. Therefore, we can write the equation:

75x + 95(20 - x) = 1800

Simplifying this equation, we get:

75x + 1900 - 95x = 1800

-20x = -100

x = 5

Substituting x back into the equation, we find that the first mechanic worked for 5 hours, and the second mechanic worked for (20 - 5) = 15 hours.

Therefore, the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours.

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The system of inequalities shown in this problem is defined as follows:

d) y < 1 and y ≥ x.

The line in the image has an intercept of zero and slope of 1, hence it is given as follows:

y = x.

Points above the solid line are plotted, hence the first condition is:

y ≥ x.

The upper bound, represented by the dashed horizontal line, is y = 1, hence the second condition is:

y < 1.

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Answer:

A requested task is subject to be reported when it has been completed according to the instructions provided.

To demonstrate this with chain of thought reasoning:

1. The task requested will have details outlining what needs to be done.

2. To fulfill the request of the task, the instructions outlined must be followed.

3. Once all instructions are met, the task is complete.

4. Completion of the task means it is subject to be reported.

Step-by-step explanation:

Answer:

[tex]f(x) = - 3 {x}^{2} - 6x - 1[/tex]

Answer:

5n - 8 = 37

5n = 45

n = 9

The number is 9.

Answer:

Step-by-step explanation:

To graph the solution to the compound inequality 3 - x < 22 or 4x + 2 > 10, we need to graph the individual inequalities and find the overlapping region.

First, let's graph the inequality 3 - x < 22:

Subtract 3 from both sides to isolate x:

-x < 19

Multiply both sides by -1, which reverses the inequality direction:

x > -19

This means that x is greater than -19, but not including -19. So, we will have an open circle at -19 and shade everything to the right of it.

Next, let's graph the inequality 4x + 2 > 10:

Subtract 2 from both sides to isolate 4x:

4x > 8

Divide both sides by 4:

x > 2

This means that x is greater than 2, but not including 2. So, we will have an open circle at 2 and shade everything to the right of it.

Combining the two inequalities, we need to find the overlapping region. Since both inequalities have an open circle at their endpoint, we will use a dashed line to represent them.

The graph should look like this:

markdown

Copy code

 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

  +                                                     +

  |                                                     |

  |                                                     |

  +---------------------------------|-------------------->

                                      -19       2

The shaded region will be to the right of -19 and to the right of 2, including all numbers greater than those values.

Therefore, the correct answer is:

O A. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Each person runs 1/3 of a mile when Jeff catches up to Roger.

================================================

Explanation

x = number of minutes that Jeff runs

x+1 = number of minutes Roger runs

Roger has the head start of 1 minute, so he has been running for 1 minute longer compared to Jeff.

Roger runs 1 mile in 9 minutes. His unit rate is 1/9 of a mile per minute.

Jeff's unit rate is 1/6 of a mile per minute.

Let's set up a table with what we have so far

[tex]\begin{array}{|c|c|c|c|} \cline{1-4} & \text{Distance} & \text{rate} & \text{time}\\\cline{1-4}\text{Jeff} & d & 1/6 & \text{x}\\\cline{1-4}\text{Roger} & d & 1/9 & \text{x}+1\\\cline{1-4}\end{array}[/tex]

The distance equation for Jeff is d = (1/6)x

The distance equation for Roger is d = (1/9)(x+1)

note: distance = rate*time

Both runners travel the same distance when Jeff catches up to Roger, so both "d"s are the same value at this specific moment. Set the right hand sides equal to each other and solve for x.

(1/6)x = (1/9)(x+1)

18*(1/6)x = 18*(1/9)(x+1)

3x = 2(x+1)

3x = 2x+2

3x-2x = 2

x = 2

Jeff runs for 2 minutes when he catches up to Roger.

----------

Check:

Jeff runs for 2 minutes, at 1/6 of a mile per minute, so he runs 2*(1/6) = 2/6 = 1/3 of a mile.

Roger runs for 2+1 = 3 minutes (remember he gets the head start) at 1/9 of a mile per minute, so he has run 3*(1/9) = 3/9 = 1/3 of a mile as well.

Both men have run the same distance which confirms Jeff catches up to Roger at this point. The answer is confirmed.

The correct answer is an option (d): Impossible.

Both the geometric mean and harmonic mean require positive values. However, in the given set of values, we have negative values (-11 and -14), which makes it impossible to calculate the geometric mean and harmonic mean. Therefore, the correct answer is that it is impossible to calculate the geometric mean and harmonic mean for the given values.

Step-by-step explanation:

a. 4/64= 1/16 for red marble

b. 40/64= 5/8 black marbles

c. 20/64= 5/16 blue marble

d. highest: black marble

e. lowest: red marble

Answer:

Step-by-step explanation: