A searchlight has a parabolic reflector that forms a "bowl", which is 9 in wide from rim to rim and 3
in deep. If the filament of the light bulb is located at the focus, how far from the vertex of the
reflector is it? (round to at least 3 decimal places)

The value of "c" such that the random variable cY has an x² distribution is 4.

To find the value of "c" such that the random variable cY has a chi-squared (x²) distribution, we need to consider the properties of the chi-squared distribution and the given expression for Y.

The chi-squared distribution with "k" degrees of freedom is obtained by summing the squares of "k" independent standard normal random variables. Each standard normal variable contributes one degree of freedom to the chi-squared distribution.

In the given expression for Y, we have two squared terms: (X₁ + X₃ + X₅ + X₇)² and (X₂ + X₁ + X₆ + X₈)². To obtain an x² distribution, we need to rewrite the expression in terms of squared standard normal random variables.

To achieve this, we can divide each squared term by its corresponding degrees of freedom and take the square root:

Y = (X₁ + X₃ + X₅ + X₇)² + (X₂ + X₁ + X₆ + X₈)²

= (1/4)(X₁ + X₃ + X₅ + X₇)² + (1/4)(X₂ + X₁ + X₆ + X₈)²

Now, we can rewrite Y as:

Y = (1/4)χ²₁ + (1/4)χ²₁

Here, χ²₁ and χ²₂ represent chi-squared random variables with 1 degree of freedom each.

To obtain an x² distribution, we need to make the coefficients of the chi-squared random variables equal to their degrees of freedom. In this case, we want the coefficient to be 1.

So, setting the coefficient of χ²₁ to 1, we get:

(1/4) = 1/c

Solving for "c", we find:

c = 4

For such more question on value:

https://brainly.com/question/843074

#SPJ8

Answer:6.25

Step-by-step explanation:1.25x5=6.25

Answer:

$6.25

Step-by-step explanation:

1.25 × 5 = 6.25

hope this helps...

The result of  the expression 2 + 5^3 is 127.

To solve the expression 2 + 5^3, you need to follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

In this case, the exponentiation should be performed first.

Step 1: Calculate 5^3

5^3 means raising 5 to the power of 3, which is equivalent to multiplying 5 by itself three times: 5 * 5 * 5 = 125.

Step 2: Add 2 to the result from Step 1.

2 + 125 = 127.

Therefore, the result of 2 + 5^3 is 127.

For more such questions on result , Visit:

https://brainly.com/question/29248277

#SPJ11

The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

Learn more about area of square on https://brainly.com/question/27683633

#SPJ1

Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Step-by-step explanation:

16 - 10 × 1/5 + 13

16 - 5 + 13

11 + 13

24

Step-by-step explanation:

10/5=2

16-2+13=27.

d. 27

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

Answer:

Option B

Step-by-step explanation:

<r = 32 degrees (alternate angles )

<r = <n = 32 degrees (vertical angles)

Find the number of girls by subtracting number of boys from total:

726 - 340 = 386 girls

Divide number of girls by total students:

386/726 = 0.53168

Multiply by 100 get get percent:

0.53168 x 100 = 53.168%

Round to the nearest whole percent: 53% are girls

Answer:

The formula for finding the area of a circle using its radius is:

The formula for finding the area of a circle using its radius is:A = πr²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14

Step-by-step explanation:

Hope it Helps

The formula for finding the area of a circle using its radius is π * r².

The formula for finding the area of a circle using its diameter is (π/4) * d².

The formula for finding the area of a circle using its radius is:

A = π * r²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

r represents the radius of the circle.

If you have the diameter of the circle instead of the radius, you can use the following formula:

A = (π/4) * d²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

d is the diameter of the circle.

For more information on the Area of Circle, click:

https://brainly.com/question/14068861

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

1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)

2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).

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

4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)

5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)

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

7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)

8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)

For more such questions on length, click on:

https://brainly.com/question/28322552

#SPJ8

To multiply a whole number, and a fraction, we can proceed as follows:

1. In general, we only need to multiply the whole number times the numerator of the fraction as follows:

2. And then, we can simplify the fraction.

If we have that:

In this case, we can first

It should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

In geometry, it should be noted that a polygon is a plane figure which is described by a finite number of straight line segments that are connected in order to form a closed polygonal chain.

In this case, the bounded plane region, the bounding circuit, may be called a polygon. Also, a similarity transformation is the conformal mapping whose transformation matrix are identical.

In this case, it should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

Learn more about polygon on:

https://brainly.com/question/24966296

#SPJ1

Answer: 9 shirts I think

Step-by-step explanation: 54/6=9

SOLUTION

From

Now, we will substitute 1.97 for x into y

Since y which is the height of the arrow is 66.02 feet, and the tree is 68 feet tall, the arrow can not pass over the tree. Because for the arrow to pass over the tree, its height must be above 68 feet tall.

Answer: $26

Step-by-step explanation:

Since the 7 tickets cost $168, the value of each ticket will then be:

= $168/7

= $24

Each ticket cost $24

If one friend gave him $50, the change that the friend will collect will be:

= $50 - $24

= $26

Therefore, Edward should return $26 to the person.

Answer:

\(a_{n}\) = 6n - 2

Step-by-step explanation:

Because you can use the formula \(a_{n}\) = a1 + d (n - 1) to identify the arithmetic sequence :)

Answer:

f (Common Difference) = 6

Step-by-step explanation:

10 - 4 = 6

16 - 10 = 6

22 - 16 = 6

and so on...

Answer:

slope = - 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 7) and (x₂, y₂ ) = (2, - 5)

m = \(\frac{-5-7}{2-(-2)}\) = \(\frac{-12}{2+2}\) = \(\frac{-12}{4}\) = - 3

A range of 2 reveals that the smallest and largest data values are 2 units away from each other.

Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.

Range = highest value - lowest value

To learn more about range, please check: https://brainly.com/question/12372689

#SPJ1

Answer:

y=2

Step-by-step explanation:

A horizontal line can be represented as y = a number.

Therefore D. y=2 is a horizontal line.

Answer:

The exact values of the tangent, secant and cosine of angle theta are, respectively:

\(\cos \theta = -\frac{11}{61}\)

\(\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}\)

\(\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}\)

Step-by-step explanation:

The components of the unit vector are \(x = -\frac{11}{61}\) and \(y = -\frac{60}{61}\). Since \(r = 1\), then \(x = \cos \theta\) and \(y = \sin \theta\). By Trigonometry, tangent and secant can be calculated by the following expressions:

\(\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}\)

\(\sec \theta = \frac{1}{\cos \theta} = \frac{1}{x}\)

Now, the exact values of the tangent, secant and cosine of angle theta are, respectively:

\(\cos \theta = -\frac{11}{61}\)

\(\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}\)

\(\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}\)

Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

To learn more about measurement refer to:

https://brainly.com/question/777464

#SPJ1

Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

Define measurement?

To learn more about measurement refers to:

https://brainly.com/question/1613675

#SPJ1

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

The commission earn by Mrs. Parker earn last month is $ 4,582.35

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula's percentage?

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Given that:

Total sales = $53,910

Commission = 8.5%

Commission in cash = 53910 * 0.085 = 4,582.35

Hence commission earn by Mrs. Parker earn last month is $ 4,582.35

Learn more about percentage

https://brainly.com/question/24877689

#SPJ1

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

Answer:

0.3

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

I hope this is what you where asking for?

Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2. Therefore, option D is correct.

Given that the point A is at -4 and the point B is at 6.

We need to find the point that divides AB into a 3:2 ratio.

One way to find the point that divides AB into a 3:2 ratio is to divide AB into 5 equal parts.

Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2.

Therefore, option D is correct.
Option A is incorrect because the point that divides AB into a 3:2 ratio is not 0.Option B is incorrect because the point that divides AB into a 3:2 ratio is not 3.Option C is incorrect because the point that divides AB into a 3:2 ratio is not 1.

For more such questions on divides , Visit:

https://brainly.com/question/30126004

#SPJ8

Answer:

the shoes

Step-by-step explanation:

the shoes never changed, and the amount money sarah has remaining will depend on the shoes.