Describe the graph that would be used to solve the equation -x^2+4=x+2 using a system of equations. How will you use the graph to find the solution(s)?

[tex]{\huge{\green{\maltese}}}[/tex][tex]{\huge{\green{\mathbb{ANSWER}}}}[/tex]

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There are a total of 29 students in the class.

The probability of selecting an accounting major on the first pick is 9/29.

After the first pick, there are 28 students remaining, 8 of whom are accounting majors.

The probability of selecting another accounting major on the second pick is 8/28.

Using the multiplication rule, the probability of selecting two accounting majors is:

(9/29) * (8/28) = 0.079

Rounded to three decimal places, the probability is 0.079.

Answer:

1) [tex]\sqrt{53}(\cos286^\circ+i\sin286^\circ)[/tex]

2) [tex]\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i[/tex]

Step-by-step explanation:

Problem 1

[tex]z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)[/tex]

Problem 2

[tex]\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i[/tex]

[tex]\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i[/tex]

[tex]\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5[/tex]

Note that [tex]\text{cis}\,\theta=\cos\theta+i\sin\theta[/tex] and [tex]125=125(\cos0^\circ+i\sin0^\circ)[/tex]

The probability of drawing either a heart or a queen from a standard deck of 52 playing cards is 4/13.

In a standard deck of 52 playing cards, there are 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards, including the ace, numbered cards from 2 to 10, and the face cards (jack, queen, and king).

We are interested in finding the probability of drawing either a heart or a queen from the deck.

First, let's determine the total number of favorable outcomes, i.e., the number of cards that are either hearts or queens.

There are 13 hearts in the deck, and there are 4 queens (one queen for each suit). However, we need to subtract the queen of hearts from the count because it has already been counted as a heart. So, the total number of favorable outcomes is 13 + 4 - 1 = 16.

Next, let's determine the total number of possible outcomes, which is the number of cards in the deck, 52.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:

Probability = Favorable outcomes / Possible outcomes

          = 16 / 52

          = 4 / 13

Therefore, the correct answer is d. 4/13.

The probability of drawing either a heart or a queen from a standard deck of 52 playing cards is 4/13.

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The length of the field is greater than the width by the expression [tex](14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).[/tex]

1. The length of the field is represented by the expression [tex]14x - 3x^2 + 2y.[/tex]

2. The width of the field is represented by the expression [tex]5x - 7x^2 + 7y[/tex].

3. To find the difference between the length and width, we subtract the width from the length: ([tex]14x - 3x^2 + 2y) - (5x - 7x^2 + 7y[/tex]).

4. Simplifying the expression, we remove the parentheses: [tex]14x - 3x^2 + 2y - 5x + 7x^2 - 7y.[/tex]

5. Combining like terms, we group the [tex]x^2[/tex] terms together and the x terms together: [tex]-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.[/tex]

6. Simplifying further, we add the coefficients of like terms:[tex](7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).[/tex]

7. The simplified expression becomes: [tex]4x^2 + 9x - 5y.[/tex]

8. Therefore, the length of the field is greater than the width by the expression [tex]4x^2 + 9x - 5y.[/tex]

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Answer:

[tex]P_{B}[/tex] = 80

Step-by-step explanation:

given 2 similar figures with ratio of sides = a : b

then ratio of perimeters is also a : b

here ratio of sides = 24 : 15 = 8 : 5

the ratio of perimeters is also 8 : 5

then by proportion

[tex]\frac{ratioA}{P_{A} }[/tex] = [tex]\frac{ratioB}{P_{B} }[/tex] , that is

[tex]\frac{8}{128}[/tex] = [tex]\frac{5}{P_{B} }[/tex] ( cross- multiply )

8 [tex]P_{B}[/tex] = 5 × 128 = 640 ( divide both sides by 8 )

[tex]P_{B}[/tex] = 80

Answer: The answer is B

Step-by-step explanation:

Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

If the scatter points lie on a straight line then it indicates a perfect linear relationship between the two variables.

When drawing a scatter diagram, if the scatter points lie on a straight line then it indicates a perfect linear relationship. A scatter plot is a diagram used to show the relationship between two sets of data. Scatter plots are used to examine the correlation or association between two variables. A scatter plot is a set of points plotted on a horizontal and vertical axes. The position of each point on the graph represents the value of the two variables.
Scatter diagrams can reveal correlation between variables. There are three types of correlation, namely:
Positive correlation: Both variables increase or decrease at the same time. The line of best fit slopes upward.
Negative correlation: One variable increases as the other decreases. The line of best fit slopes downward.
No correlation: There is no relationship between the two variables. Points are scattered randomly throughout the graph.
If the scatter points lie on a straight line, it indicates a perfect linear relationship between the two variables. The line of best fit is a straight line, showing a strong correlation between the variables. The correlation coefficient value (r) for this type of relationship would be either +1 or -1.
Skewness refers to the degree of asymmetry in a set of data. It describes how the data is distributed. None of these and no relationship refers to the absence of correlation between two variables.

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Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=5\\ b=11\\ h=4 \end{cases} \implies A=\cfrac{4(5+11)}{2}\implies A=32~cm^2[/tex]

The quadratic expression [tex]x^2[/tex] - 4x + 6 is already in standard form.

To determine if the given quadratic expression [tex]x^2[/tex] - 4x + 6 is in standard form, we need to compare it with the general form of a quadratic equation, which is a[tex]x^2[/tex] + bx + c = 0.

In the given expression, we have:

a = 1 (coefficient of [tex]x^2[/tex])

b = -4 (coefficient of x)

c = 6 (constant term)

Since all the coefficients are already in their respective positions and the terms are arranged in decreasing order of exponents, the expression [tex]x^2[/tex]- 4x + 6 is indeed in standard form.

To summarize, the quadratic expression [tex]x^2[/tex] - 4x + 6 is already in standard form, as the terms are arranged in decreasing order of exponents (from highest to lowest) and the coefficients are in their respective positions.

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The measure of angle F to the nearest degree is approximately 78 degrees.

To determine the measure of angle F, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab*cos(C)

In this case, we have a triangle with sides FG = 7 yd, FH = 6 yd, and GH = 5 yd. We want to find the measure of angle F.

Let's label angle F as angle C, side FG as side c, side FH as side a, and side GH as side b. Plugging the given values into the Law of Cosines equation:

c^2 = a^2 + b^2 - 2abcos(C)

7^2 = 6^2 + 5^2 - 265cos(C)

49 = 36 + 25 - 60cos(C)

49 = 61 - 60cos(C)

60cos(C) = 61 - 49

60cos(C) = 12

cos(C) = 12/60

cos(C) = 0.2

To find the measure of angle C (angle F), we can take the inverse cosine (cos^-1) of 0.2:

C = cos^-1(0.2)

C ≈ 78.46 degrees

Therefore, the measure of angle F to the nearest degree is approximately 78 degrees.

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We can see here that Malcolm is correct in his statement but his reasoning or conclusion to the answer is wrong.

Malcolm believes that since 8 > 7 and 11 > 10 then 8/11 > 7/10. This reason is wrong because:

1. It does not work for all numbers and and not the basis to determine.

2. If we follow that reasoning, we will have issues:

For example:

2/10 < 1/3

yet 2 > 1 and 10 > 3

Thus, Malcolm's reasoning is not correct. He is making a false analogy. Just because two things are similar in one way does not mean that they are similar in all ways.

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The answer in its simplest form is 6/25.

The relative frequency of the spinner landing on the blue section can be obtained from the given table as follows:

| Colour | Number of Times | Relative Frequency |

|    Blue  |                6             |             6/25 |

|     Red  |                9             |             9/25 |

| Green  |                4             |             4/25 |

| Yellow |               6              |             6/25 |

The total number of times the spinner landed on all four colors is the sum of the values in the "Number of Times" column, which is: 6 + 9 + 4 + 6 = 25. Therefore, the relative frequency of the spinner landing on the blue section is: 6/25So,

Relative frequencies, on the other hand, do not employ raw counts. Instead, they use percentages, proportions, or fractions to compare the count for one type of event to the entire number of events. The word "relative" refers to a specific tally in relation to the overall number, which is where it is used.

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The triangles RST and VUT in the figure are congruent

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

The triangle (see attachment)

By definition, we have

"If two sides in one triangle are congruent to two sides in another triangle and the included angle in both are congruent, then the two triangles are congruent"

This means that they are congruent by the SAS  statement

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Answer:

Anthony T. answered • 03/17/21

TUTOR 5 (52)

Patient Math & Science Tutor

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First, let's ask ourselves what do we want to know? We want to know how many cups of small and large lemonades were sold. Let's let S = # of small cups, and L the # of large cups.

It says she sold a total of 155 cups; that means S + L = 155. So this is one equation.

Next it says she made a total of $265. The small cups sold for $1.25 each, so she made $1.25S amount of money on these. It also says she sold large cups for $2.50 each, so she made $2.50L on these.

So, if we add up the money she made from each size, we can say 1.25S + 2.50L = 265.

Now we have two equations with 2 unknowns, and we can solve by either elimination or substitution. Let's solve it by substitution.

As S + L =155, L = 155 - S. Put this expression for L into the second equation.

1.25S + 2.50(155-S) = 265. Now solve this for S.

You should get S = 98 small cups. So, from the equation S + L = 155, solve for L which gives

L = 57 large cups. You can prove this by substituting these numbers in the second equation.

The same principles apply to other problems of this type.

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{7}=\cfrac{28}{x}\implies x^2=196\implies x=\sqrt{196}\implies x=14[/tex]

After evaluating, we got T(2, -2, 3) = (9, 6, 0).

To find the image of the vector (2, -2, 3) under the linear transformation T, we need to use the given information about the transformation of the standard basis vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1).

The transformation of a vector can be obtained by multiplying the vector by the corresponding columns of the transformation matrix. In this case, the transformation matrix can be constructed using the images of the standard basis vectors as follows:

| 2 -1 1 |

| 1 1 2 |

| 3 0 -2 |

To evaluate T(2, -2, 3), we perform matrix multiplication as follows:

| 2 -1 1 | | 2 | | 9 |

| 1 1 2 | x | -2 | = | 6 |

| 3 0 -2 | | 3 | | 0 |

Multiplying the matrices, we get:

22 + (-1)(-2) + 13 = 9,

12 + 1*(-2) + 23 = 6,

32 + 0 + (-2)*3 = 0.

Therefore, T(2, -2, 3) = (9, 6, 0).

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Answer: 3

Step-by-step explanation:  List out 2, 3, 1, 3, 3, 5 and 4

Then order them in ascending order: 1, 2, 3, 3 ,3 4, 5

The find the middle number : 3

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

Iris should use an income value of approximately $3,137.50 when making her budget.

When making her budget as a freelancer, Iris should use an income value that reflects her average earnings over the past four months. By calculating the average income, Iris can have a more stable and reliable estimate for her budget planning.

To determine the average income, Iris needs to add up the total income earned over the four months and divide it by the number of months. Summing up the income values, we get:

$2700 + $4600 + $3550 + $1700 = $12,550

Next, dividing the total income by four (the number of months), we find:

$12,550 / 4 = $3,137.50

Therefore, Iris should use an income value of approximately $3,137.50 when making her budget. This average value allows her to account for fluctuations in her monthly income and provides a more accurate representation of her earning potential.

It is important for Iris to consider her expenses and financial goals when budgeting. By using the average income, she can create a budget that balances her income and expenses, allowing her to allocate funds appropriately for various needs such as bills, savings, investments, and personal expenses.

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The probable question may be:

Iris is a working freelancer and has been tracking her monthly income for the last four months, which are $2700, $4600, $3550, and $1700. What income value should she use when making her budget?

Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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Answer:

3x² - 4x - 5

Step-by-step explanation:

Definitions:

Long Division Method of dividing polynomials:

Given:

Rearrange the dividend in descending order of the exponents:

6x³ - 17x² + 2x  + 15

Now use the method of long division to divide (6x³ - 17x² + 2x  + 15) by (2x - 3):

[tex]\large \begin{array}{r}3x^2-4x-5\phantom{)}\\2x-3{\overline{\smash{\big)}\,6x^3-17x^2+2x+15\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-9x^2)\phantom{-b)))))))).)}}\\-8x^2+2x+15\phantom{)}\\-~\phantom{()}\underline{(-8x^2+12x)\phantom{)))..}}\\-10x+15\phantom{)}\\-~\phantom{()}\underline{(-10x+15)\phantom{}}\\0\phantom{)}\\\end{array}[/tex]

Therefore, the quotient is:

[tex]\boxed{\boxed{3x^2-4x-5}}[/tex]

788,954 in word form is "seven hundred eighty-eight thousand, nine hundred fifty-four."

Answer:

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. If a spherical balloon has a radius of 165 mm, then the volume of air used to fill the balloon is V = (4/3)π(165)^3 = 18805165.33 cubic millimeters or approximately 18805165.33 mL.

Step-by-step explanation:

The value of x, considering the segment addition postulate in this problem, is given as follows:

x = -6.

The segment addition postulate is a geometry axiom that states that when a line segment is divided into a number of smaller segments, the total length is given by the sum of the lengths of each of the smaller segments.

For this problem, we have that two segments, with lengths x + 14 and x + 13, are added to form a segment with length of 15, hence the value of x is obtained as follows:

x + 14 + x + 13 = 15

2x + 27 = 15

2x = -12

x = -6.

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The team has failed to meet his quality goal of achieving a quality score above 0.95 in the last four weeks.

The table shows the weekly goals and their respective scores:

Weekly Goals:

Job Satisfaction Score > 4.50, Absence Rate ≤ 0.03, Quality Score > 0.95, Output Score > 9Week Job Sat Score

To compare the quality score for the past four weeks, we have:

Quality Score in Week 2 = 0.88

Quality Score in Week 3 = 0.89

Quality Score in Week 5 = 0.92

Quality Score in Week 6 = 0.83

Quality Score in Week 7 = 0.91

Quality Score in Week 8 = 0.92

Quality Score in Week 9 = 0.83

Since, the goal was Quality Score > 0.95,

To see how your team is doing against your quality goals over the last four weeks, you need to compare your quality score each week to your goal of 0.95. The Quality Scores for the past 4 weeks are:

Week 23: 0.88

Week A: 0.89

Week 56: 0.90

Week 78: 0.92

We are counting quality scores each week with a goal of 0.95. increase. , you can see that none of the quality values ​​meet or exceed the target.

As a result, the team has failed to meet his quality goal of achieving a quality score above 0.95 in the last four weeks.

It can be observed that the team was not able to achieve the quality goal in any of the weeks (Week 2 to Week 9).

Therefore, it can be concluded that the team was not able to achieve the quality goal in the past four weeks.

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The correct equation that represents the line is Oy = (-1/3)x + 5.

To find the equation of the line that passes through the points (-6, 7) and (-3, 6), we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y_1 = m(x - x_1)

where (x1, y1) is a point on the line and m is the slope of the line.

Let's use the first point (-6, 7) as (x_1, y_1). The coordinates of the point are x_1 = -6 and y_1 = 7.

Next, we need to find the slope (m) of the line using the two given points. The slope is calculated using the formula:

m = (y_2 - y_1) / (x_2 - x_1)

Let's use the second point (-3, 6) as (x_2, y_2). The coordinates of the point are x_2 = -3 and y_2 = 6.

Plugging the values into the slope formula, we get:

m = (6 - 7) / (-3 - (-6))

m = -1 / (3)

m = -1/3

Now, we have the slope (m) and a point (x_1, y_1). We can substitute these values into the point-slope form equation:

y - 7 = (-1/3)(x - (-6))

Simplifying the equation:

y - 7 = (-1/3)(x + 6)

y - 7 = (-1/3)x - 2

y = (-1/3)x - 2 + 7

y = (-1/3)x + 5

Therefore, the equation that represents the line passing through the points (-6, 7) and (-3, 6) is:

y = (-1/3)x + 5

The right equation to express the line among the available possibilities is Oy = (-1/3)x + 5.

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The variance of X-bar is 12.25.

To find the variance of the sample mean (X-bar) for a normally distributed population, we can use the formula:

Variance of X-bar = (Population Variance) / (Sample Size)

In this case, the population mean (μ) is 138 and the standard deviation (σ) is 14. The population variance (σ^2) can be calculated as the square of the standard deviation, which gives us 14^2 = 196.

Since we are sampling with a batch size of 16, the sample size is also 16.

Now we can substitute these values into the formula:

Variance of X-bar = 196 / 16 = 12.25

Therefore, the variance of X-bar is 12.25.

It's important to note that the sample mean (X-bar) is an unbiased estimator of the population mean (μ). The smaller the sample size, the greater the variability of X-bar around the population mean.

As the sample size increases, the variance of X-bar decreases, indicating a more precise estimate of the population mean.

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