Choose all of the points where the graph of the line 3x + 2y = 6 and the graph of the parabola y = x2 - 4x + 3 interact

The standard deviation is 7.35.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79

Determine the difference between each value and the mean and then square the result:

(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)²  + (84- 79)²  + (68 - 79)²  +( 75- 79) ²

64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√432 / 8 = 7.35

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A speedup of 2 suggests that the program is efficiently utilizing the additional computational resources provided by the second computer, resulting in a significant reduction in computation time.

A speedup of 2 indicates that the program running on two computers in parallel is approximately twice as fast as running it on a single computer. In other words, the distributed computing techniques and parallel processing allow the mathematician to solve the systems of linear equations in half the time compared to running the program on a single computer.

Speedup is a measure of the improvement achieved by using parallel computing techniques. It quantifies the ratio of the time required to execute a task sequentially (on a single computer) to the time required to execute the same task in parallel (using multiple computers). A speedup of 2 suggests that the program is efficiently utilizing the additional computational resources provided by the second computer, resulting in a significant reduction in computation time.

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The ratios involved in the ROI formula are the net profit and the investment cost.

The ROI (Return on Investment) formula includes the following ratios:

Net Profit: The net profit represents the profit gained from an investment after deducting expenses, costs, and taxes.

Investment Cost: The investment cost refers to the total amount of money invested in a project, including initial capital, expenses, and any additional costs incurred.

The ROI formula is calculated by dividing the net profit by the investment cost and expressing it as a percentage.

ROI = (Net Profit / Investment Cost) * 100%

Therefore, the ratios involved in the ROI formula are the net profit and the investment cost.

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The Coase theorem suggests that in situations like this, bargaining between the two parties can lead to an efficient outcome. In this case, the smoker and non-smoker (roommate and you) could negotiate to find a solution that minimizes the total cost to both parties.

For example, the smoker could agree to smoke outside or use an air purifier, while the non-smoker could offer to pay a portion of the cost of these solutions. Ultimately, the Coase theorem suggests that as long as property rights are clearly defined and transaction costs are low, the two parties can negotiate to find a mutually beneficial solution to the problem of smoking in the apartment.

1. Clearly defining property rights: Establish whether the apartment has a non-smoking policy or if you have the right to a smoke-free environment within your living space.

2. Engaging in negotiation: Communicate your concerns to your roommate and discuss the negative effects of their smoking on you.

3. Finding a mutually beneficial solution: Both parties can negotiate and arrive at a compromise. This could include your roommate agreeing to smoke outside, designating a specific area for smoking, or using a smoke-filtering device. In some cases, you may also consider offering compensation or splitting the costs of a smoke-filtering device.

By following these steps, both you and your roommate can reach an efficient solution that reduces the cost imposed on you due to your roommate's smoking.

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The observed and expected frequencies for the green candies is C. Observed: 93 Expected: 103.6

The number of participants or observations included in a study is referred to as the sample size. Usually, n is used to represent this number. Research results are directly impacted by sample size calculations. Very small sample sizes compromise a study's internal and external validity. Small differences frequently become statistically significant differences in very large samples.

Sample size = 518

The number of green candies observed/counted is = 93

That's an approximated value for 18% of the 518 candies

18/100 × 518 = 93.24 ≅ 93

Note, the symbol ≅ means 'approximately equal to. Since the candy company claims that the distribution of each color is exactly 20%, the expected frequency for green candies is:

20% of 518

= 20/100 × 518

= 103.6

The correct option is C.

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Complete question

Karen recorded the results for a sample of 518 candies.

Color Counts Sample Proportion

(p with hat on top)

Red 130 25%

Yellow 109 21%

Green 93 18%

Orange 114 22%

Purple 72 14%

The candy company claims that the distribution of each color is exactly 20%. Select the observed and expected frequencies for the green candies.

a.) Observed: 103.6 Expected: 93

b.) Observed: 93 Expected: 93.2

c.) Observed: 93 Expected: 103.6

d.) Observed: 72 Expected: 93.2

Answer:

\( \dfrac{2(\sqrt{a} - 3)}{a - 9} \)

Step-by-step explanation:

\((\dfrac{1}{\sqrt{a}-3}+\dfrac{1}{\sqrt{a} +3}) \times (1 - \dfrac{3}{\sqrt{a}}) =\)

\(= \dfrac{1}{\sqrt{a}-3} +\dfrac{1}{\sqrt{a} +3}} - \dfrac{3}{\sqrt{a}(\sqrt{a}-3)} - \dfrac{3}{\sqrt{a}(\sqrt{a} +3)}\)

\(= \dfrac{\sqrt{a}(\sqrt{a}+3)}{(\sqrt{a}-3)\sqrt{a}(\sqrt{a}+3)}+\dfrac{\sqrt{a}(\sqrt{a}-3)}{(\sqrt{a} +3)\sqrt{a}(\sqrt{a}-3)}\)

\(~~~~~- \dfrac{3(\sqrt{a}+3)}{\sqrt{a}(\sqrt{a}-3)(\sqrt{a}+3)}-\dfrac{3(\sqrt{a}-3)}{\sqrt{a}(\sqrt{a} +3)(\sqrt{a}-3)}\)

\( = \dfrac{a + 3\sqrt{a} + a - 3\sqrt{a} - 3\sqrt{a} - 9 - 3\sqrt{a} + 9}{\sqrt{a}(\sqrt{a} +3)(\sqrt{a}-3)} \)

\( = \dfrac{2a - 6\sqrt{a}}{\sqrt{a}(\sqrt{a} +3)(\sqrt{a}-3)} \)

\( = \dfrac{2(a - 3\sqrt{a}}{(a - 9)\sqrt{a}} \)

\( = \dfrac{2(\sqrt{a}\sqrt{a} - 3\sqrt{a}}{(a - 9)\sqrt{a}} \)

\( = \dfrac{2\sqrt{a}(\sqrt{a} - 3)}{(a - 9)\sqrt{a}} \)

\( = \dfrac{2(\sqrt{a} - 3)}{a - 9} \)

By analyzing the population equation we can see that:

Here we have the population equation:

\(p(t) = \frac{500}{1 + 4.55e^{-0.5*t}}\)

a) When does the growth rate start to decrease?

The rate of change will be:

\(p'(t) = 0.5*\frac{500}{(1 + 4.55e^{-0.5*t})^2}*4.55e^{-0.5*t}\)

Below, you can see the graph of it, and there you can see that for t > 0 the rate always decreases.

b) The initial population is what we get when we evaluate p(t) in t = 0

\(p(t) = \frac{500}{1 + 4.55e^{-0.5*0}} = \frac{500}{1 + 4.55} = 91\)

c) What is the maximum population?

It is 500 (asymptotically), which is the value that we get when we take the limit of t to infinity.

d) The population after 2 years is given by:

\(p(t) = \frac{500}{1 + 4.55e^{-0.5*2}} = 187\)

So after two years, there will be 187 birds.

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Answer:

C

Step-by-step explanation:

Linear functions will be greater than exponential functions at first- however, exponential equations will gradually surpass the linear equation.

Answer:

ASA

Step-by-step explanation:

the angles of the vertex are vertical angles, so they are congruent.

We have a congruent side between two congruent angles

Therefore, the value of the given integral is 2π/3 (2^6 - 1)

Given integral is S y²z² dS where S is the part of the cone y = x² + z² given by 0 ≤ y ≤ 4.So, x² + z² ≤ y, i.e., z² ≤ y - x².At y = 4, z² = 4 - x², i.e., z = (4 - x²)^(1/2).

The surface area of the cone is  S = πrℓ where r is the radius and ℓ is the slant height. Here, the radius r = x² + z² and the slant height ℓ = √(x² + y² + z²).Therefore, ℓ² = x² + y² + z².⇒ ℓ² = x² + y² + (4 - x²)⇒ ℓ² = y + 4.This gives us the relation, z = [(y + 4) - y]^(1/2) = 2^(1/2).Given integral is S y²z² dS, therefore,  ∫∫S y²z² dS = ∫∫D y² (2^(1/2))^2 dAwhere D is the projection of S onto the xy-plane.D is given by  x² + z² ≤ y and 0 ≤ y ≤ 4.

Substituting z² = y - x², we get x² + y - x² ≤ y.⇒ y ≤ y.This is true for all values of y. Therefore, the projection of S onto the xy-plane is the region enclosed by the parabolic cylinder x² = 4y. We use polar coordinates to evaluate the integral.We get ∫∫S y²z² dS = ∫(0 to 2π) ∫(0 to 2) r^5 sin²θ cos²θ dr dθ = 2π/3 (2^6 - 1).Therefore, ∫∫S y²z² dS = 2π/3 (2^6 - 1).

Let's begin with the given integral,S y²z² dS where S is the part of the cone y = x² + z² given by 0 ≤ y ≤ 4.In order to find the solution of the given problem, we need to find the values of x and z.So, x² + z² ≤ y, i.e., z² ≤ y - x².At y = 4, z² = 4 - x², i.e., z = (4 - x²)^(1/2).Now, let's find the surface area of the cone using the formula  S = πrℓ where r is the radius and ℓ is the slant height. Here, the radius r = x² + z² and the slant height ℓ = √(x² + y² + z²).Therefore, ℓ² = x² + y² + z².⇒ ℓ² = x² + y² + (4 - x²)⇒ ℓ² = y + 4.This gives us the relation, z = [(y + 4) - y]^(1/2) = 2^(1/2).Now, we have all the values required to evaluate the integral. Let's do that. The integral is given by, ∫∫S y²z² dS = ∫∫D y² (2^(1/2))^2 dA

where D is the projection of S onto the xy-plane. D is given by  x² + z² ≤ y and 0 ≤ y ≤ 4.Substituting z² = y - x², we get x² + y - x² ≤ y.⇒ y ≤ y.This is true for all values of y. Therefore, the projection of S onto the xy-plane is the region enclosed by the parabolic cylinder x² = 4y. We use polar coordinates to evaluate the integral.We get ∫∫S y²z² dS = ∫(0 to 2π) ∫(0 to 2) r^5 sin²θ cos²θ dr dθ = 2π/3 (2^6 - 1)

.Therefore, the value of the given integral is 2π/3 (2^6 - 1)

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(1) We incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.

(2) The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.

1) Assume you predicted the variable "Number of Promotion Earned" by regressing it against just two other variables, "Income in $s" and "Years of Experience."

When compared to the beta for years of experience, the income beta is quite modest. You incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.

But until we standardize the variables, this is incorrect. Then they can be put side by side.

2) As HR, I was questioned about whether employees who earn more money perform better. Do those with higher salaries complete the same task more quickly? I've been given data with two columns: "HIGH" salary people's income, and "LOW" salary people's income.

I conduct an ANOVA method test on two groups of individuals and track their typical completion time. The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.

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The complete question is:

First, how can graphics and/or statistics be used to misrepresent data? Where have you seen this done? Second, image that you are a human resources (HR) analyst reporting to a recently hired supervisor. Your supervisor has asked you to provide an example of data processed by HR. Describe one type of data that an HR department may process, and discuss a corresponding statistical method that may be used to summarize the data.

Answer:

4

Step-by-step explanation:

the second column and the second row so, the answer is 4

Answer:

Step-by-step explanation:

sin A = \(\frac{opposite side}{Hypotenuse}\)

Sin 29 = \(\frac{y}{500}\)

0.4848 * 500 = y

y = 242.4 ft

Answer:

Y=242.4

Step-by-step explanation:

due to the association property the angle at the bottom left is 29 degrees

since sine property is oposite over hypothesis we get

sine(29)=y/500

500sin(29)=y

Y=242.4

If the exchange rate were 5 Egyptian pounds per US dollar, a watch that costs $25 US dollars would cost 125 Egyptian pounds.

The exchange rate is the price at which one currency can be exchanged for another. In this case, the exchange rate is 5 Egyptian pounds per US dollar. This means that one US dollar can be exchanged for 5 Egyptian pounds.

To find out how much a watch that costs $25 US dollars would cost in Egyptian pounds, we need to multiply the cost in US dollars by the exchange rate:

$25 x 5 = 125 Egyptian pounds

Therefore, if the exchange rate were 5 Egyptian pounds per US dollar, a watch that costs $25 US dollars would cost 125 Egyptian pounds.

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Answer:

Your Y-intercept is 4/3.

Step-by-step explanation:

The X intercept would be 0 and the Y intercept is 4/3, making the coordinate (0, 4/3).

Answer:

999,000

Step-by-step explanation:

We need to find the number that is one thousand (1,000) less than one million (1,000,000).

Answer:

999000

Step-by-step explanation:

1 million - 1000 or 1 million less is 100,000

The extracellular fluid volume (A) for the data (a) A = 0.02154 *  72^0.6469 * 178^0.7236. (b) A = 0.02154 * 65^0.6469 * 140^0.7236. (c) A = 0.02154 * 70^0.6469 * 160^0.7236. (d) Substitute your own weight and height values into the equation: A = 0.02154 * (Your Weight)^0.6469 * (Your Height)^0.7236

To find the extracellular fluid volume (A) for the given data, we can substitute the values of height (h) and weight (w) into the formula A = 0.02154w^0.6469h^0.7236.

(a) For Height = 178 cm and Weight = 72 kg:

A = 0.02154 * 72^0.6469 * 178^0.7236

(b) For Height = 140 cm and Weight = 65 kg:

A = 0.02154 * 65^0.6469 * 140^0.7236

(c) For Height = 160 cm and Weight = 70 kg:

A = 0.02154 * 70^0.6469 * 160^0.7236

To find your own extracellular fluid volume, you need to substitute your own height and weight into the formula:

(d) For Your Height and Your Weight:

A = 0.02154 * (Your Weight)^0.6469 * (Your Height)^0.7236

By substituting the given values into the formula, you can calculate the respective extracellular fluid volumes for each case.

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The area enclosed by the given ellipse is A = πab.



We can start by noting that the given equations for the ellipse are in parametric form, with t representing the angle parameter. To find the area enclosed by the ellipse, we can use the formula for the area of a sector of an ellipse, which is given by:

A = ½ abθ

where a and b are the lengths of the major and minor axes of the ellipse, respectively, and θ is the central angle that the sector subtends. In our case, we want to find the area enclosed by the entire ellipse, which corresponds to a full 360-degree rotation. Thus, we have:

A = ½ ab(2π) = πab




To fully understand how we arrived at the formula for the area of a sector of an ellipse, we can look at the geometry of the ellipse itself. An ellipse is defined as the set of all points in a plane whose distances from two fixed points (called the foci) sum to a constant. Alternatively, we can think of an ellipse as a stretched circle, with one axis longer than the other. The lengths of the major and minor axes are denoted by a and b, respectively.

Now, consider a sector of the ellipse, defined by two rays emanating from one of the foci and intersecting the ellipse at two points. Let the central angle that the sector subtends be denoted by θ,

To find the area of this sector, we can first find the area of the corresponding sector of a circle, with radius a. This is given by:

A_circle = ½ a²θ

However, since our sector is part of an ellipse, we need to adjust this formula to take into account the fact that the radius varies along the ellipse. Specifically, the radius at any point on the ellipse is given by:

r = a√[1 - (sin t)²]

(where t is the angle that the point makes with the x-axis). To account for this, we need to multiply the area of the circle sector by a scaling factor that accounts for the variation in radius. This factor is simply the ratio of the length of the minor axis to the length of the major axis:

scaling factor = b/a

Thus, the area of the sector of the ellipse is given by:

A_ellipse = ½ a²θ (b/a)

= ½ abθ


In summary, to find the area enclosed by an ellipse given in parametric form, we can use the formula A = πab, which is derived from the formula for the area of a sector of an ellipse. This formula takes into account the varying radius of the ellipse and the lengths of the major and minor axes.

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From the given values, we know there are 2 defective resistors and 9 not defective. then, we have

where

denote the combinations of 9 elements taking in 3, that is 3 good resistor from the 9 which are not defective. Similarly,

denotes the combinations of 2 elements taking in 1, that is, 1 defective resistor form the 2 defective resistors.

Then, we have

then, the answer is

Answer:

35°

Step-by-step explanation:

As we know vertically opposite angles are equal . So ,

x + 90= 125

x = 125-90 = 35°

Answer:

35

Step-by-step explanation:

125 + 90(APC) + DPA + EPB + x = 360

215 + DPA + EPB + x = 360

DPA = 180 - 125 = 55

EPB = DPA

EPB = 55

X = 90(EPC) - EPB

X = 90 - 55

X = 35

OR easy way

DB is a straight line so angels on it add up to 180

EPB = 180 - 125

EPB = 55

X = 90(EPC) - EPB

X = 90 - 55

X = 35

Answer:

4x=>-74

Step-by-step explanation:

x+23=>18

4(x+23)=>18

4x+92=>18

collect like terms

4x=>18-92

4x=>-74

Answer is 4 (x + 23 ) ≥ 18

Step by step

4 times the sum of a number and 23

4(x + 23)

Is at least 18

≥ 18

Your inequality

4 (x + 23 ) ≥ 18

to solve, distribute

4x + 92 ≥ 18

subtract 92 from both sides

4x + 92 - 92 ≥ 18 - 92

simplify

4x ≥ -74

divide both sides by 4 to solve for x

4/4 x ≥ -74/4

x ≥ 18.5

18.5 is equal to or greater than 18 so problem solved

** We used ≥ in this inequality which means at least (equal to) this number or greater

Answer:

15.9

Step-by-step explanation:

Answer:

\(\frac{1}{2}, \frac{1}{4}\)

Step-by-step explanation:

I hope this helps!

Answer:

x = ¾-a

Step-by-step explanation:

x + a = ¾

Subtract a from each side

x + a -a= ¾-a

x = ¾-a

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

\(x+a=\dfrac{3}{4}\\\\x=\dfrac{3}{4}-a\\\\x=\dfrac{3-4a}{4}\)

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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The real zeros of f(x) = x^3 - 7x^2 - 41x - 33 are -3, 1, and -11.

The rational zeros theorem states that if a polynomial function has a rational zero, it can be expressed as the ratio of a factor of the constant term to a factor of the leading coefficient.

In the case of f(x) = x^3 - 7x^2 - 41x - 33, the constant term is -33 and the leading coefficient is 1.

The factors of the constant term -33 are ±1, ±3, ±11, and ±33.

The factors of the leading coefficient 1 are ±1.

So, the possible rational zeros are:

±1, ±3, ±11, ±33

To determine if any of these are actual zeros of the function, we can substitute them one by one into f(x) and check if the result is equal to zero.

By testing these values, we find that the real zeros of f(x) are:

x = -3

x = 1

x = -11

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A sample statistic is a numerical descriptive measure of a sample.

Therefore, a  sample statistic is a numerical descriptive measure of a sample.

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The complete question is given below:

What is a sample statistic?

A _____descriptive measure of  a _____.

Give three examples. (Select all that apply.)