1. What properties of quadratic functions cause this "death ray" effect?

2. Using the diagram below, what is the point called where the sun's rays are concentrated? Will the "death ray" always hit the same spot? Why?

2. Could this property of quadratic functions be helpful in a different situation? Explain

Answer:

He owns about 4.17% or 4% so the others own about 95.83% or 96% but sense it rounds to the nearest tenth your answer would be 95.8%

Step-by-step explanation:

You can figure this out by doing 11,919 divided by 285,763 in order to figure out the percentage of the company he owns and then just do 100 - your answer.

Step-by-step explanation:

First, we need to find out how much money the three other individuals invested in the company. To do that, we'll subtract Fred's investment from the total investment:

Total investment = 285,763

Fred's investment = 11,919

Investment from the three other individuals = Total investment – Fred's investment

Investment from the three other individuals = 285,763 – 11,919

Investment from the three other individuals = 273,844

Now, to calculate the percentage of ownership for the three individuals, we'll divide their combined investment by the total investment and multiply by 100:

Percentage of ownership = (Investment from the three other individuals / Total investment) * 100

Percentage of ownership = (273,844 / 285,763) * 100

Percentage of ownership ≈ 95.8%

So, the three other individuals own approximately 95.8% of the company. Since the question asks to round to the nearest tenth, the answer is 95.8%.

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &7 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 7} \implies \boxed{A \approx 3969.39} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2800\\ r=rate\to 5.2\%\to \frac{5.2}{100}\dotfill &0.052\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]A = 2800\left(1+\frac{0.052}{4}\right)^{4\cdot 7}\implies A=2800(1.013)^{28} \implies \boxed{A \approx 4019.97} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 4019.97 ~~ > ~~ 3969.39 \end{array}}~\hfill[/tex]

The salary plus benefits and the cost of living index for the two cities indicates;

1) Phoenix

2) San Antonio; $25,262.37, Phoenix; $21,901.35

3) San Antonio, because of the higher adjusted salary

The cost of living index is a measure of how expensive it is to reside in a city, compared with the national average costs.

1) The cost of living index for the cities indicates that Phoenix, with a cost of living index of 96.2 is more expensive to live in than San Antonio, Texas with a cost of living index of 85.3

2) The job offers can be evaluated by converting the salary from one city to another as follows;

(Salary in City A) × (Cost of living index for City B)/(Cost of living index for City A)

Therefore, we get;

San Antonio: ($17,000 + $5,400)×96.2/85.3 ≈ $25,262.37

Phoenix: ($23,500 + $1,200)*85.3/96.2 ≈ $21,901.35

3) The job offer that is better, based on the conversion of the job offers into adjusted salary for the two Cities of $25,262.37 vs $21,901.35, indicates that the San Antonio job offer is better

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The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.

We have,

We can use the inverse square law to find the distance to the star:

Luminosity / (4π(distance)²) = Apparent brightness

Rearranging this formula to solve for the distance, we get:

distance = √(Luminosity / (4π (Apparent brightness)))

Plugging in the given values, we get:

distance = √(8.0 × 10^{26} / (4π (1.5 × 10^{-12}))

Simplifying this expression, we get:

distance = 3.04 × 10^{20} meters

Converting this distance to kilometers, we get:

distance = 3.04 × 10^{17} kilometers

To convert this distance to light-years, we divide by the speed of light in kilometers per year:

distance = (3.04 × 10^{17}) / (9.46 × 10^{12})

Simplifying this expression, we get:

distance = 32.2 light-years

Therefore,

The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.

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Answer:

BF×BA= DF×CF

9×2=3x

x = 6

AB=9

CD=11

Answer:

Step-by-step explanation:

The measures of the marked angles in the figure are:

x = 0.8°

6x + 8° = 12.8°

x + 12° = 12.8°

We have that:

x + 12° and 6x + 8°.

We equate the expression: 6x + 8° = x + 12°

We then  solve for x:

6x - x = 12° - 8°

5x = 4°

We then divide  both sides by 5:

x = 4° / 5

x = 0.8°

We get the  measure of the marked angle for

6x + 8°:

6(0.8°) + 8° = 4.8° + 8° = 12.8°

We also get the measure of the marked angle as:

x + 12°:

0.8° + 12° = 12.8°

In conclusion, an  angle is formed when two straight lines or rays meet at a common endpoint.

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The domain and the range of the table of values are Domain = {-15, 0, 9, 33, 44, 45} and Range = {21, 33, 57, 15, 97, 46}

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

The table of values

The above table of values can be represented as a list of ordered pairs

The rule of a table of values is that

using the above as a guide, we have the following:

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About 71 members of the group are expected to be between 51 years old and 59 years old.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Considering the mean of 55 years and the standard deviation of 4 years, ages between 51 and 59 years are within one standard deviation of the mean, hence the percentage is of:

68%.

Out of 104 people, the number of people with ages in the range is given as follows:

0.68 x 104 = 71 people. (rounded to the nearest integer).

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Answer:If the Diameter of a circle is 22 inches, the area will be 380.13in².

Step-by-step explanation:

These are the formulas you use:

Area=pi*Radius^2  or A=pi*Radius*Radius

Diameter=2*Radius

A=1

4*pi*Diameter*2=1 2

4*pi*222=380.13271in

380.13271in is approximately 380.13in².

Shakira needs to rent a car for one day and she is trying to decide which car rental company to use. Alpha Car Rental offers a Porsche for $29.17 per day, plus 57 cents per mile. Beta Car Rental also offers the same car for $50.23 per day, plus 44 cents per mile.

To determine which car rental is a better deal, Shakira needs to calculate at what number of miles the prices for both Alpha and Beta Car Rental are the same. To do this, she can use the following equation:

The variable of x is the number of miles. This equation simplifies to x = 21.06 miles. Therefore, at 21.06 miles, Alpha and Beta Car Rental will be the same price.

The expected value of the investment is $600,000.

The expected value of the investment is calculated by multiplying the possible outcomes by their respective probabilities and summing them up. In this case, the possible outcomes are a success or a failure, with probabilities of 0.3 and 0.7 respectively.

If the company succeeds, the investment will be worth $2,000,000. If it fails, the investment will be worth $0. Therefore, the expected value is:

(0.3 x $2,000,000) + (0.7 x $0) = $600,000

This means that the expected value of the investment is $600,000.

Since the expected value of the investment is positive, Mr. Sharp should invest the $100,000. However, it's important to note that expected value is just an estimate and does not guarantee a positive return on investment. There is always a risk associated with any investment, and Mr. Sharp should carefully consider his risk tolerance and financial goals before making any investment decisions.

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The rule for this translation. and the coordinates of the image point are  (x, y) = (x + 4, y - 5); (7, -6)

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

translated to the right 4 units and down t units

Mathematically, this can be expressed as

(x, y) = (x + 4, y - 5)

Given that

A = (3, -1)

And, we have

(x, y) = (x + 4, y - 5)

This means that

A' = (3 + 4, -1 - 5)

Evaluate

A' = (7, -6)

So, the image point is A' = (7, -6)

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Question

ABC is translated 4 units to the right and 5 units down. Answer the questions to find the coordinates of A after the translation.

A = (3, –1)

Answer:(-4,0) (2,0)

Step-by-step explanation:

the points will be (-4,0) & (2,0) while the parabola is concave up

Answer: Thats a Trapezoid

Step-by-step explanation:

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

The equivalent expression is the one in the last option:

[tex]\sqrt[10]{y}[/tex]

Here we want to find an expression equivalent to:

[tex](\frac{1}{\sqrt{y} } )^{-1/5}[/tex]

Remember the two rules for exponents that we need to use here:

[tex]x^{-n} = (1/x)^n[/tex]

[tex]x^{1/n} = \sqrt[n]{x}[/tex]

Using the first rule, we can rewrite our expression as:

[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5}[/tex]

Now we can rewrite the root of a root to get:

[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5} = \sqrt[5]{\sqrt{y} } = \sqrt[10]{y}[/tex]

Where in the last step we just multiplied the exponents for the roots, we can see that the correct option is the last one.

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The statements that justify why the table does not represent a probability distribution are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Considering that the number of outcomes cannot be negative, negative probabilities do not exist.

For a distribution, the sum of all the probabilities must be of one, hence:

-1/3 + 2/5 + 1/5 + 2/5 = 1 - 1/3 = 2/3 -> Different of one.

The table is given by the image presented at the end of the answer.

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The annual deposit for John for total amount of annuity is A = $ 29,060.29

Given data ,

To determine the annual deposit amount needed for John to have a total of $500,000 by the time he retires, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where FV is the future value, P is the annual deposit, r is the annual yield (interest rate), and n is the number of years.

In this case, we are given:

FV = $500,000

r = 5% = 0.05

n = 25 years

Substituting these values into the formula, we have:

$500,000 = P * [(1 + 0.05)^25 - 1] / 0.05

And , the value of P is

P = ($500,000 x 0.05) / [(1.05^25) - 1]

P ≈ ($25,000) / (1.858734... - 1)

P ≈ ($25,000) / 0.858734...

P ≈ $29,060.29

Hence , John must deposit approximately $29,060.29 into the retirement account each year to accumulate a total of $500,000 by the time he retires in 25 years

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1. f(x) =  (2x² + 4x + 4) / x³ = 0; as lim x→∞, and lim x→-∞

2. g(x)  = (2x²  +  4x  + 4)/x² = ∞; as lim x→∞, and lim x→-∞]

3.  h(x)  = (2x²  +  4x  + 4)/x = ∞ as lim x→∞, and -∞ as lim x→-∞.

To find the end behavior of each of the functions, we can take the limit as x approaches infinity and negative infinity.

For  f(x)  = (2x²  +  4x  + 4)/x³;

lim x→∞ (2x² + 4x + 4) / x³ = 0

lim x→-∞ (2x² + 4x + 4) / x³ = 0

f(x) approaches zero as x approaches positive or negative infinity.

For  g(x)  = (2x²  +  4x  + 4)/x²;

lim x→∞ (2x² + 4x + 4) / x² = ∞

lim x→-∞ (2x² + 4x + 4) / x² = ∞

g(x) approaches infinity as x approaches positive or negative infinity.

For  h(x)  = (2x²  +  4x  + 4)/x

lim x→∞ (2x² + 4x + 4) / x = ∞

lim x→-∞ (2x² + 4x + 4) / x = -∞

h(x) approaches infinity as x approaches positive infinity, and negative infinity as well, but with a negative sign.

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Answer:

4π cm

Step-by-step explanation:

A minute hand travels a full revolution along a circular path in 60 minutes

The distance from the center to the tip of the minute hand = 8 cm

We can consider the movement of the minute hand as being on the circumference of  a circle with radius = 8 cm

Circumference = 2π · r

=  2π · 8

= 16π

I5 minutes = 15/60 = 1/4th

So in 15 minutes the minute hand will cover only 1/4th of the full circle

Therefore distance traveled by tip of minute hand

= 1/4 x 16π = 4π cm

Seattle's sales were approximately 33.33% larger than Portland's.

Portland's sales were approximately 25% smaller than Seattle's.

Portland's sales were approximately 75% of Seattle's sales.

We have,

a)

Seattle's sales were larger than Portland's by:

= (380,000 - 285,000)

= $95,000.

To calculate the percentage difference, we can use the formula:

Percentage difference = (Difference / Original value) x 100

Percentage difference = (95,000 / 285,000) * 100 ≈ 33.33%

b)

Portland's sales were smaller than Seattle's by (380,000 - 285,000) = $95,000.

To calculate the percentage difference, we can use the formula:

Percentage difference = (Difference / Original value) x 100

Percentage difference = (95,000 / 380,000) x 100 ≈ 25%

c)

Portland's sales were a certain percentage of Seattle's sales.

To calculate this percentage, we can use the formula:

Percentage = (Portland sales / Seattle sales) * 100

Percentage = (285,000 / 380,000) * 100 ≈ 75%

Therefore,

Seattle's sales were approximately 33.33% larger than Portland's.

Portland's sales were approximately 25% smaller than Seattle's.

Portland's sales were approximately 75% of Seattle's sales.

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Answer:

x=0, y=6

x=4, y=0

x=8, y=-6

Step-by-step explanation:

6x + 4y = 24

6(0) + 4y = 24

y = 6

So x=0, y=6

y=0

6x+4y=24

6x+4(0)=24

6x=24

x=4

When x=4, y=0

x=8

6x+4y=24

6(8) + 4y = 24

48 + 4y = 24

4y = 24-48

4y = -24

y = -24/4

y = -6

When x = 8, y = -6

C. The total profit, if all shares for both stocks are sold at the close of business on day 7, is $587.62

D. The best day to sell TechCo shares would be day 7, as it had the highest closing price. For HealthCo, day 7 would also be the best day to sell.

E. There is no difference in profit or loss compared to part C.

Part 2

A. Diversity can be evaluated based on the portfolio in question

B. By analyzing the types of assets present in the portfolio, it is possible to determine where potential risks may originate.

C. The individual carrying a particular portfolio can be characterized based on their risk tolerance, financial goals, and stage of life.

Part 1:

A. TechCo (TCO) and HealthCo (HCO) have their shares priced at $100 and $50 respectively.

Name of Stock Symbol Quantity of Shares Purchased Purchase Price per Share Total Purchase Value

TechCo TCO 75 $100 $7,500

HealthCo HCO 150 $50 $7,500

B. Here is an illustration of the potential ending values:

Name of Stock Closing Price Day 1 Closing Price Day 2 Closing Price Day 3 Closing Price Day 4 Closing Price Day 5 Closing Price Day 6 Closing Price Day 7

TechCo $101 $99 $100 $98 $102 $101 $103

HealthCo $51 $50 $52 $49 $51 $52 $54

C. If we sell all shares on day 7, we can calculate the profit/loss and the brokerage fee:

TechCo: 75 shares * $103/share = $7,725

HealthCo: 150 shares * $54/share = $8,100

Total = $7,725 + $8,100 = $15,825

Brokerage fee = $15,825 * 1.5% = $237.38

Profit = $15,825 - $15,000 (initial investment) - $237.38 (brokerage) = $587.62

D. The best day to sell TechCo shares would be day 7, as it had the highest closing price. For HealthCo, day 7 would also be the best day to sell.

E. Since we've already assumed selling on the best day, there is no difference in profit or loss compared to part C.

Part 2:

A. Diversity can be evaluated based on the portfolio in question. A portfolio that encompasses investments in a variety of sectors, asset classes, and regions would exhibit a high level of diversity.

B. By analyzing the types of assets present in the portfolio, it is possible to determine where potential risks may originate.

An investment portfolio that primarily consists of stocks or other assets with high risks would be considered as an aggressive portfolio. A portfolio that primarily consists of bonds or low-risk assets is considered to be a conservative one.

A balance between the two would be a moderate portfolio.

C. The individual carrying a particular portfolio can be characterized based on their risk tolerance, financial goals, and stage of life.

For example, a young professional with a high-risk tolerance might carry an aggressive portfolio to maximize growth, while a retired individual might have a conservative portfolio to preserve their capital.

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Using the law of sines, the value of a in the given triangle, to the nearest tenth, is calculated as: 19.9.

The law of sines that we would apply is given as:

sin A/a = sin B/b = sin C/c.

Given the following:

a = ?

A = 64 degrees

b = 17

B = 50 degrees

Plug in the values into the equation, sin A/a = sin B/b:

sin 64/a = sin 50/17

Cross multiply:

a * sin 50 = sin 64 * 17

Divide both sides by sin 50

a * sin 50 / sin 50 = sin 64 * 17 / sin 50

a ≈ 19.9 [nearest tenth]

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The value of a to the nearest tenth is 20.0

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Using sine rule to solve for a;

The side opposite to angle 64 is a and the side opposite to angle 50 is 17

a/sinA = b/sinB

a/sin64 = 17/sin50

asin50 = 17sin64

0.766a = 17 × 0.899

0.766a = 15.283

a= 15.283/0.766

a = 20.0( nearest tenth)

Therefore the value of a is 20.0

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The missing measurements on the triangle are given as follows:

m < H = 65º, y = 32.2, c = 35.5.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The sum of the internal angle measures of a triangle is of 180º, hence the measure of angle H is given as follows:

m < H + 25 + 90 = 180

m < H = 65º.

Regarding the angle of 25º, we have that 15 is the opposite side, while y is the adjacent side, hence the measure of y is given as follows:

tan(25º) = 15/y

y = 15/tangent of 25 degrees

y = 32.2.

Applying the Pythagorean Theorem, the value of c is obtained as follows:

c² = 15² + (32.2)²

[tex]c = \sqrt{15^2 + 32.2^2}[/tex]

c = 35.5.

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(a). The ratio of blue marbles to all marbles as 5/14.

(b). The number of blue marbles by the number of red marbles: 5/9

(a) The ratio of blue marbles to all marbles in the bag is 5/14.

To see this, we add the number of blue marbles and the number of red marbles to get the total number of marbles, which is 5 + 9 = 14.

Then we can express the ratio of blue marbles to all marbles as 5/14.

(b) The ratio of blue marbles to red marbles is 5/9. To see this, we divide the number of blue marbles by the number of red marbles: 5 ÷ 9 = 0.55555..., which we can simplify to 5/9.

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Answer: D: 1/5

Step-by-step explanation:

sinx = 5/13

this ratio is special; it is a 5-12-13 right triangle, (pythagorean triple).

there is also a formula to find tan(x/2); It is tan(x/2) = ±[tex]\sqrt{\frac{1-cosx}{1+cosx} }[/tex]

the + or - sign is decided by the quadrant the half angle is in;

since x is in quad one, it is somewhere between 0 and pi/2. To find the half angles position, simply divide it; x/2 is somewhere between 0/2 and pi/4.

so its also in the first quadrant. Since tangent is positive in the first quadrant, we will take the positive answer:

One more thing. we need the cosx in our formula. cosx will be 12/13, since this is a special right triangle as we said before.

tan(x/2) = [tex]\sqrt{\frac{1-12/13}{1+12/13} }[/tex]

tan(x/2) = [tex]\sqrt{\frac{1/13}{25/13} }[/tex]

tan(x/2)= [tex]\sqrt{1/25}[/tex]

tan(x/2) = 1/5

Option D is the answer :)

From the first equation, we can rearrange to get x = 12 + y.

Substituting that into the second equation, we get y^2 = 5(12 + y - 2) = 50 + 5y.

This simplifies to y^2 - 5y - 50 = 0.

Using the quadratic formula, we can solve for y to get y = 10 or y = -5.

Therefore, two possible values of y are 10 and -5.