How does value of a affect the
parabola?

The management salary is $19,429

What is ratio?

Ratio is the quantitative relationship between two numbers which shows the number of times an amount or a number is contained within the other amount or number.

In this case, a ratio  of 8:7 shows the number of times the management salaries is contained within the management trainee salary

The management salary has a  value of 8 whereas the management trainee salary has a value of 7 as shown below:

salary ratio=management salary/management trainee salary

salary ratio=8/7

management salary=unknown(assume it is X)

management trainee salary=$17,000

8/7=X/$17,000

cross multiply

8*$17,000=7*X

X=8*$17,000/7

X=$19,429

The fact that annual management trainee salary is $17,000 means that the management salary is $19,429 annually.

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(a) The ratio of the areas, A2/A1, is: A2/A1 =\((16πr1^2)/(4πr1^2) = 4\)

(b)  The ratio of the areas A2/A1 is 4, and the ratio of the volumes V2/V1 is 8.

(a) To find the ratio of the areas, A2/A1, we need to substitute the radii of sphere 2 and sphere 1 into the formula for surface area.

Let's denote the radius of sphere 1 as r1 and the radius of sphere 2 as r2, where r2 = 2r1.

For sphere 1:

A1 =\(4πr1^2\)

For sphere 2:

A2 = \(4πr2^2 = 4π(2r1)^2 = 4π(4r1^2) = 16πr1^2\)

Therefore, the ratio of the areas, A2/A1, is:

A2/A1 =\((16πr1^2)/(4πr1^2) = 4\)

(b) Similarly, to find the ratio of the volumes, V2/V1, we substitute the radii into the formula for volume.

For sphere 1:

V1 = \((4/3)πr1^3\)

For sphere 2:

V2 = \((4/3)πr2^3 = (4/3)π(2r1)^3 = (4/3)π(8r1^3) = (32/3)πr1^3\)

Therefore, the ratio of the volumes, V2/V1, is:

V2/V1 = \(((32/3)πr1^3)/((4/3)πr1^3) = 8\)

So, the ratio of the areas A2/A1 is 4, and the ratio of the volumes V2/V1 is 8.

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Answer:

5

Step-by-step explanation:

The mode is the most commonly occurring number in a set of numbers. In this one it is 5.

The square of the length of the chord that is a common external tangent of the other two circles with radii of 3 and 6 is 45.

Given that circles of radii 3 and 6 are externally tangent to each other and internally tangent to a circle of radius 9. The circle of radius 9 has a chord that serves as a common external tangent for the other two circles. The task is to find the square of the length of this chord.

The distance between the centers of the circles of radii 3 and 6 can be found by adding their radii: d1 = 3 + 6 = 9 units.

Since the circles are internally tangent to the circle of radius 9, the distance between their centers can be found by subtracting their radii from the radius of the larger circle: d2 = 9 - 3 - 6 = 0 units.

The chord is a common external tangent of the circles, and its length can be found by doubling the distance between the center of the circle of radius 9 and the chord: Chord length = 2 × h.

To find the height (h) of the triangle formed by the chord and the center of the circle of radius 9, we can use the formula h = (r1 + r2 - R) / 2, where r1 and r2 are the radii of the smaller circles, and R is the radius of the larger circle. In this case, h = (3 + 6 - 9) / 2 = 0.
Since h is zero, it means that the chord passes through the center of the circle of radius 9. Therefore, its length will be the diameter of the circle of radius 9.

The square of the length of the chord can be found using the Pythagorean theorem. Let's denote the length of the chord as d.

- We know that r1 + h = R, so h = R - r1 = 9 - 3 = 6.

- Using the Pythagorean theorem: d = sqrt(R² - h²) = √(9² - 6²) = √(81 - 36) = √(45).

Therefore, the square of the length of the chord is d^2 = 45.

In summary, the square of the length of the chord that serves as a common external tangent for the circles of radii 3 and 6, and is internally tangent to a circle of radius 9, is 45.

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Answer:

b = 8.485

c = 23.995 ≈ 24

Step-by-step explanation:
Part b:

\(\sqrt{(10-4)^2+(9-3)^2}\)

√(36 + 36)

= 8.485

Part c:

Base = \(\sqrt{(6-2)^2+(1-5)^2}\)

Base = 5.656

Area = Base x Height x 0.5

Area = 5.656 x 8.485 x 0.5

Area = 23.995 ≈ 24

Answer:pl z give me brainliest the crown next to the stars when two people answer :) have a good day ;)

Step-by-step explanation:

hope this helped

Answer:

60% of 20 is 12

40% of 20 is 8

12 in California

8 in Alaska

Answer:

w = 144

Step-by-step explanation:

11 + w/8*6 = 14

w/8*6 = 3

w/48 = 3

w = 144

The probability that more than 12 particles occur in the area of a disk under the study is 0.20844.

The number of particles follows a Poisson Distribution.

A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as  \(P(X = x) = e^{-\lambda} \frac{\lambda^{x}}{x!}\) .

In the question, x = 12.

λ = 100*0.1 = 10.

To find : P(X > 12)

P(X > 12) = 1 - P(X ≤ 12) = 1 - poissoncdf(10,12)

As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).

Therefore, P(X > 12) = 1 - 0.79156 = 0.20844.

Therefore, the probability that more than 12 particles occur in the area of a disk under the study is 0.20844.

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Answer: y=-6x-7

Step-by-step explanation:

Slope-intercept form is y=mx+b. This means, we want to isolate y.

18x+3y=-21                   [subtract both sides by 18x]

3y=-18x-21                    [divide both sides by 3]

y=-6x-7

Now, our equation is in slope-intercept form.

Answer:

im pretty sure its c or rotation

Step-by-step explanation:

the 95% confidence interval for the average textbook cost at the BC bookstore is approximately $77.76 to $82.64.

The point estimate for the average textbook cost at the BC bookstore is the sample mean, which is 80.2. Therefore, the point estimate is 80.2 (to 3 decimals).

To calculate the 95% confidence interval, we need to determine the margin of error and then construct the interval using the sample mean, the margin of error, and the appropriate critical value based on the standard normal distribution.

The margin of error can be calculated using the formula:

Margin of Error = z * (standard deviation / sqrt(sample size))

Given that the sample size is 170, the standard deviation is 14.2, and we want a 95% confidence interval, we need to find the corresponding critical value, denoted as z*.

The critical value for a 95% confidence interval is found by subtracting half of the confidence level (0.05) from 1 and then finding the z-score associated with that cumulative probability. Looking up the value in a standard normal distribution table, we find that the z-score is approximately 1.96.

Now, we can calculate the margin of error:

Margin of Error = 1.96 * (14.2 / sqrt(170))

Margin of Error ≈ 2.44 (to 3 decimals)

Finally, we can construct the 95% confidence interval using the sample mean and the margin of error:

95% Confidence Interval = (Sample Mean - Margin of Error, Sample Mean + Margin of Error)

95% Confidence Interval = (80.2 - 2.44, 80.2 + 2.44)

95% Confidence Interval ≈ (77.76, 82.64) (to 3 decimals)

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Answer:

113.1 inches squared

Step-by-step explanation:

Answer:

the answer is 113.1

Step-by-step explanation:

given

d=12

diameter is half of the radius

so

r=6

now we apply the formula

A=22/7 × 6×6

=792/7

=113.1

i hope the answer is right

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

Step-by-step explanation:

add all of them up,  Julie,   6 + 12 + 3 + 4 = 25  

there are 25 total students.  now divide each of the number of people that speak that language by the total students

6/25 = .24 = 24%

12/25= .45 = 48%

3/25 = .12 = 12%

4/25 = .16 = 16%

Also, if you want to just check,  see if the percentages add to 100%

Using the relative frequency concept, it is found that the relative frequencies for students speaking each language is:

--------------------------------

A relative frequency of a to b is a/b, that is, the number of desired outcomes divided by the number of total outcomes.

--------------------------------

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Given:

The inequality is:

\(-4x-7y<15\)

To find:

The whether (-6,3) is a solution of given inequality of not.

Solution:

We have,

\(-4x-7y<15\)

We need to check the inequality for point (-6,3).

Substitute \(x=-6, y=3\) in the given inequality.

\(-4(-6)-7(3)<15\)

\(24-21<15\)

\(3<15\)

This statement is true. It means the point (-6,3) satisfies the given inequality.

Therefore, the correct option is A. Yes, the ordered pair is a solution.

Answer:

(1) - C, \((3,\frac{\pi}{6})\)

(2) - B, \((0,-2)\)

Step-by-step explanation:

\(\text{Using the following conversions:}\\\boxed{\left\begin{array}{ccc}\text{\underline{Rect. to Polar:}}\\(x,y)\rightarrow(r, \theta)\\\\r=\sqrt{x^2+y^2}\\\\\theta=\tan^{-1}(\frac{y}{x})\end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Polar to Rect.:}}\\(r, \theta)\rightarrow(x,y)\\\\x=r\cos \theta\\\\y=r \sin\theta\end{array}\right}\)

Note that when doing these calculations, make sure your calculator is in radians mode.

Question #2:

Given:

\((\frac{3\sqrt{3} }{2} ,\frac{3}{2} ) \ \text{in} \ (x,y)\)

\((\frac{3\sqrt{3} }{2} ,\frac{3}{2} )\\\\\Rightarrow r=\sqrt{(\frac{2\sqrt{2} }{2})^2+(\frac{3}{2})^2} \\\\\Longrightarrow r=\sqrt{\frac{27}{4} +\frac{9}{4} } \\\\\Longrightarrow r=\sqrt{9}\\\\\therefore \boxed{ r=3}\\\\\Rightarrow \theta=\tan^{-1}(\frac{\frac{3}{2}}{\frac{3\sqrt{3} }{2}})\\\\\Longrightarrow \theta=\tan^{-1}(\frac{\sqrt{3} }{3})\\\therefore \boxed{\theta=\frac{\pi}{6} }\)

Thus, the correct option is C.

\(\boxed{\boxed{(3,\frac{\pi}{6})}}\)

Question #3:

Given:

\((2,\frac{3\pi}{2} ) \ \text{in} \ (r,\theta)\)

\((2,\frac{3\pi}{2} ) \\\\\Rightarrow x=(2)\cos(\frac{3\pi}{2})\\\\\Longrightarrow x=(2)(0)\\\\\therefore \boxed{x=0}\\\\\Rightarrow y=(2)\sin(\frac{3\pi}{2})\\\\Longrightarrow y=(2)(-1)\\\\\therefore \boxed{y=-2}\)

Thus, the correct option is B.

\(\boxed{\boxed{(0,-2)}}\)

Answer:

5832

Step-by-step explanation:

54+27=81x72=5832

Answer:

Bond

Step-by-step explanation:

A promissory note or a promise to repay a certain amount of money at some point in the future is basically a bond.

A bond is a debt security that represents a loan made by an investor to a borrower, which is usually a corporation or government agency. It is a fixed-income investment, meaning that the borrower promises to pay a specific amount of interest over a set period of time and return the principal amount of the loan on the date of maturity. Bonds are issued for various purposes, such as raising capital, funding new projects, or refinancing debt.

CD (Certificate of Deposit) is a savings instrument issued by a bank or credit union that generally pays a fixed rate of interest over a set term. Mutual fund is an investment vehicle that pools money from multiple investors to purchase a portfolio of securities, such as stocks, bonds, or both. Stock is an ownership share in a company that represents a claim on part of the company's assets and earnings.

The value of chi-square statistic (\(X^{2}\)) is 11.26

As per the given question

the sample space of all the four cases are 30

the proportions that land upright are the same when the dropping height is 3, 5, 10, and 20 cm.

the formula of chi-squared test is

\(X^2=\sum\frac{(O_i-E_i)^2}{E}\)

where

\(X^{2}\) is chi-square

\(O_i\) is the observed value

\(E_i\) is the expected value

the upright observed value are 20,23,27,29

the upright expected values are 24.75

now

the chi-square at 3cm height is

\(X^2=\(\frac{(20-24.75)^2}{24.75}\)

=> \(X^2=0.91\)

the chi- square at 5cm height is

\(X^2=\(\frac{(23-24.75)^2}{24.75}\)

=> \(X^2=0.12\)

the value of chi-square at 10cm is

\(X^2=\(\frac{(27-24.75)^2}{24.75}\)

=>\(X^2=0.20\)

the value of chi-square at 20cm is

\(X^2=\(\frac{(29-24.75)^2}{24.75}\)

=> \(X^2=1.97\)

the not upright observed values are

10,7,3,1

the not upright expected values are 5.25

the chi-square test at 3cm height is

\(X^2=\(\frac{(10-5.25)^2}{5.25}\)

=> \(X^2=4.30\)

the chi-square test at 5cm height is

\(X^2=\(\frac{(7-5.25)^2}{5.25}\)

=> \(X^2=0.58\)

the chi-square test at  10cm height is

\(X^2=\(\frac{(3-5.25)^2}{5.25}\)

=> \(X^2=0.96\)

the chi-square test at 20 cm is

\(X^2=\(\frac{(1-5.25)^2}{5.25}\)

=> \(X^2=3.44\)

now,

the total

chi-square value at 3cm height is

=>X^2=0.91+4.30

=> \(X^{2}\)= 5.21

chi-square at 5cm height is

=> \(X^{2}=0.12+0.58\)

=> \(X^2=0.71\)

chi-square at 10cm is

=> \(X^{2}=0.20+096\)

=> \(X^2=1.16\)

chi-square at 20 cm is

=> \(X^{2}=0.73+3.44\)

=> \(X^{2}=4.17\)

now ,

the total chi-square statistic is

=>\(X^{2}=\)5.21+0.71+1.17+4.17

=>\(X^{2}=\) 11.26

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Knowing that a circle has a radius of 6 inches, the area of a sector with a central angle of 120º is 12π square inches.

The area of a sector can be found using the formula:
Area of sector = (Central angle/360°) × π × r²

Where "central angle" is the angle of the sector in degrees and "r" is the radius of the circle.

In this case, the central angle is 120° and the radius is 6 inches. Plugging these values into the formula, we get:
Area of sector = (120°/360°) × π × 6²
Area of sector = (1/3) × π × 36
Area of sector = 12π square inches

Therefore, the area of the sector bounded by a central angle measuring 120° in a circle with a radius of 6 inches is 12π square inches.

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Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

Answer:

\( \sf \: c) \: 3(4x) + 3(5y) \)

Step-by-step explanation:

Now we have to,

→ find the equivalent expression.

The expression is,

→ 3(4x + 5y)

Let's solve the problem,

→ 3(4x + 5y)

→ (3 × 4x) + (3 × 5y)

→ 3(4x) + 3(5y)

Hence, option (c) is correct.

Answer:

0.4141 rounded to the nearest thousandth is 0.414.

Step-by-step explanation:

Since the number is 0.4141, and the number following the thousandths place is under 5, the thousandth place stays the same. If it were 5 or over, it would round up making it 0.415, but it's not so it is 0.414.

Answer:

-125

Step-by-step explanation:

Each term is 7 less than the previous term.

1st term: 15

2nd term: 15 - 7

3rd term: 15 - 7 - 7 = 15 - 2(7)

4th term = 15 - 7 - 7 - 7 = 15 - 3(7)

Notice that each term is 15 minus a multiple of 7. The multiple is obtained by multiplying 7 by 1 less than the term number.

The formula is:

\( a_n = 15 - 7(n - 1) \)

For the 21st term, multiply 7 by 20, and subtract from 15.

7 × 20 = 140

15 - 140 = -125

Using the formula:

\( a_{21} = 15 - 7(21 - 1) = 15 - 7(20) = 15 - 140 = -125 \)

Answer: -125

Answer:

C.

the temperatures of temperate rainforests are generally lower than those of tropical rainforests.

The radius of convergence, r, is 2. The series converges for values of x within the interval (-2, 2).

To find the radius of convergence, we can use the ratio test. Consider the series:

∑ (-1)^n * (x^n) / (2^n * ln(n))

Applying the ratio test:

lim |(-1)^(n+1) * (x^(n+1)) / (2^(n+1) * ln(n+1))| / |(-1)^n * (x^n) / (2^n * ln(n))|

= lim |x / 2 * ln(n+1) / ln(n)|

As n approaches infinity, the limit simplifies to:

| x / 2 |

For the series to converge, this limit must be less than 1:

|x / 2| < 1

Solving for x, we have:

-1 < x/2 < 1

Multiplying by 2, we get:

-2 < x < 2

Therefore, the radius of convergence, r, is 2. The series converges for values of x within the interval (-2, 2).

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The minimum is 29 cm and it represents the sensor's minimum height above the ground.

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.

In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.