A flashlight can light a circular area of up to 6 feet in diameter. What is the maximum area that can be lit? Round to the nearest tenth if needed!

Answer: 19.1 is correct

Step-by-step explanation:

where a and c are the lengths of two sides of the triangle and C is the angle between them. To use this formula, we need to find side b and angle A.

We can use the Law of Cosines to find side b:

We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.

We have,

To generate numbers between 1 and 6 in Matlab, we can use the "randi" command.

To generate 10 numbers, we can use:
```matlab
numbers10 = randi([1, 6], [1, 10]);
mean10 = mean(numbers10);
disp(mean10);
```

To generate 100 numbers, we can use:
```matlab
numbers100 = randi([1, 6], [1, 100]);
mean100 = mean(numbers100);
disp(mean100);
```

To generate 1000 numbers, we can use:
```matlab
numbers1000 = randi([1, 6], [1, 1000]);
mean1000 = mean(numbers1000);
disp(mean1000);
```

After running these commands, we will get the means for generating 10, 100, and 1000 numbers between 1 and 6.

As mentioned in the question, the mean of rolling a die is 3.5.

Therefore,

We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.

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The blanks are filled as follows

1. Commutative

2. Distributive

3. Identity

4. Associative

5. Commutative

6. Inverse

7. Identity

8. Associative

9. Distributive

10. A. Identity

11. A. Identity

12. B. Commutative

13. C. Associative

14. E. Distributive

The distributive law of multiplication is a distinct attribute in mathematics that distinguishes how multiplication interacts with the operations of addition or subtraction.

It is exemplified in the problem as

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The required pair of points that are both located less than 3 units from points (3, 8) is (2, 7).

Following the condition given in the question,
Assuming there are 3 points on the graph beside (3, 8) are (2, 7), (5, 5), and (6, 10)

The distance formula between two points is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, for each point, we can plug in the coordinates and simplify the following:

Point (2, 7):

d = √[(2 - 3)² + (7 - 8)²]

d = √[1² + 1²]

d = √2  (<3)

Points (6, 10):

d = √[(6 - 3)² + (10 - 8)²]

d = √[3² + 2²]

d = √13  (>3)

Point (5, 5):

d = √[(5 - 3)² + (5 - 8)²]

d = √[2² + 3²]

d = √13   (>3)

Point (1, 1):

d = √[(1 - 3)² + (1 - 8)²]

d = √[(-2)² + (-7)²]

d = √53  (>3)

Thus, the pair of points that are both located less than 3 units from points (3, 8) is (2, 7).

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If the company has 33% more employees than it did a year ago and there are currently 66,500 employees, the number of employees the company had a year ago was proportionately, 50,000 employees.

Proportion refers to the ratio of one quantity or value compared to another.

Proportions are fractional values, representing using fractions, decimals, or percentages.

The current population of a company's employees = 66,500

The percentage increase in the population from last year's = 33%

Proportionately, last year's population = 100%, while this year's population is 133% (100 + 33).

If 66,500 = 133% (1.33), then 100% = 50,000 (66,500 ÷ 1.33)

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The ratio of sec θ is determined as 5/3.

option A.

The ratio is sec θ is calculated by applying the following method;

sec θ =  1/cosθ

Given that tanθ = -4/3 = oppo/adjacent

The hypotenuse side is calculated by applying Pythagoras theorem as shown below;

h = √ 4² + 3²

h = 5

The ratio of sec θ is calculated as follows;

sec θ =  1/cosθ

1/cosθ = 1/(3/5)

1/cosθ = 5/3

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Answer:

A,E

Step-by-step explanation:

Operation: Minus

To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.

6.8 km - 2.3 km = 4.5 km

Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.

Answer:

a and e

Step-by-step explanation:

got it right on homework

Answer:No, X=-3, yly =-4,0,4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The third side of Patricia's garden should be approximately 10.64 feet long.

To determine the length of the third side of Patricia's garden, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we have two known side lengths (6 feet and 7 feet) and the angle between them (110 degrees).

The Law of Cosines states that for a triangle with side lengths a, b, and c, and angle C opposite side c:

c² = a² + b² - 2ab*cos(C)

We want to find the length of the third side, so let's call it c. Plugging in the known values:

c² = 6² + 7 - 267*cos(110°)

Simplifying the equation:

c² = 36 + 49 - 84*cos(110°)

Now, we can calculate the value of cos(110°) using a calculator or trigonometric tables. Once we have that value, we can substitute it back into the equation to find c². Taking the square root of c² will give us the length of the third side.

Note: The value of cos(110°) is approximately -0.342.

c² = 36 + 49 - 84*(-0.342)

c² ≈ 36 + 49 + 28.248

c^2 ≈ 113.248

Taking the square root:

c ≈ √113.248

c ≈ 10.64

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The amount of money Laurie would pay to have the pond cleaned is equal to $3,161.85.

In Mathematics and Geometry, the volume of a hemisphere can be calculated by using the following mathematical equation (formula):

Volume of a hemisphere = 2/3 × πr³

Where:

r represents the radius.

Note: Radius = diameter/2 = 13/2 = 6.5 feet.

By substituting the given parameters into the formula for the volume of a hemisphere, we have the following;

Volume of a hemisphere = 2/3 × 3.14 × (6.5)³

Volume of a hemisphere = 574.881 ft³

Cost = 5.50 × 574.881 ft³

Cost = $3,161.85

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The calculated value of the probability of winning is 3.06501854e-7

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

Select 6 numbers out of 39 to win

This means that when a number is selected, the number is returned and the total numbers reduces by 1

i.e. P(Current) = n/(39 - n)

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

P(Win) = 6/39 * 5/38 * 4/37 * 3/36 * 2/35 * 1/34

Evaluate the product of tthe expressions

So, we have

P(Win) = 3.06501854e-7

Hence, the probability of winning is 3.06501854e-7

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Complete question

In a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win You purchase one lottery ticket What is the probability that you will win?

The probability of winning is

The value of x is 13°

When two lines intersect, four angles are formed. There are two pairs of nonadjacent angles. These pairs are called vertical angles.

In a coordinate plane, a line parallel to the Y-axis is called Vertical Line. It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate.

We have:

The angles are:

m ∠ A=(2x−2) ∘ and ∠ B=(3x−15) ∘

We have to find the value of x

Now, We know that :

m ∠A = m ∠B  (Def. of Vertical Angles)

(2x−2) = (3x−15)

Combine the like terms:

2x - 3x = -15 + 2

-x = -13

x = 13

The value of x is 13°

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The numeric value of the function graphed is given as follows:

f(-8) = 6.

The expression for the numeric value of the function in this problem is given as follows:

f(-8).

This means that the input is given as follows:

x = -8.

Passing a vertical line through x = -8, the value of y in which the vertical line crosses the graph is given as follows:

y = 6.

Hence the numeric value is given as follows:

f(-8) = 6.

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We can actually see here that the triangle ABC is an isosceles triangle. This is because two sides of the triangle are equal.

An isosceles triangle is actually a geometric shape having three sides, two of which are equal in length. Consequently, two of the angles that are across from those sides are also equal.

In order to prove that the triangle is an isosceles triangle, we will find the following:

Distance between  vertices A and B:

AB = √((8-5)² + (8-3)²) = √(3² + 5²) = √34 = 5.83mm

Then, we also find the distance between vertices B and C:

BC = √((11-5)² + (3-3)²) = 6mm

Finally, we find the distance between vertices A and C:

AC = √((11-8)² + (3-8)²) = √(3² + 5²) = √34  = 5.83mm

Thus, we see here that AB and AC are actually equal which makes the triangle an isosceles.

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It is essential to maximize the volume for a fixed surface area for cost and material waste.

Because it can help to optimize the efficiency of material usage and minimize the cost of production.

In many manufacturing and construction processes, the cost of materials is a significant expense.

By maximizing the volume of an object for a fixed surface area, we can reduce the amount of material needed to construct the object.

This means that we can save money on material costs and reduce waste by using fewer materials overall.

In addition, minimizing the surface area of an object for a fixed volume can also help to reduce production costs.

This is because the surface area of an object is often a factor in determining the time and labor required to produce it.

By minimizing the surface area, we can reduce the amount of time and labor needed to produce the object.

Which can help to reduce production costs.

Therefore, maximizing volume for fixed surface area is an essential consideration in many manufacturing and construction processes.

It help to optimize material usage, minimize waste, and reduce production costs.

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Answer:

2(1/2)(11)(13) + 2(1/2)(10)(13.2) + 10(11)

= 143 + 132 + 110 = 385 square feet

B is the correct answer.

Answer:

I Think 62°

Step-by-step explanation:

a) The probability that the student was female is 43/76

b) The probability that the student was female AND got a "C" is 9/38

c) The probability that the student was female OR got a "C" is 45/76

We have,

             A   B   C  

Male     16  15  2  33

Female 14  11  18  43

Total     30 26 20 76

a) The probability that the student was female

= 43/76

b) The probability that the student was female AND got a "C"

= 18/76

= 9/38

c) The probability that the student was female OR got a "C"

= 43 /76 + 20/76 - 18/76

= 45/76

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Answer:

< QPR = 36

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

< QPR = 1/2 ( 72)

< QPR = 36

Answer:

a  

Step-by-step explanation:

Answer:

[tex]1 \frac{7}{20} [/tex]

Step-by-step explanation:

Well you should find a common denominator for 10, 4 and 5 first to be able to mix them. Let's take 20 because it's the smallest number we can convert 10, and 4 and 5 to.

So

[tex] \frac{3 \times 2}{10 \times 2} + \frac{1 \times 5}{4 \times 5} + \frac{4 \times 4}{5 \times 4} [/tex]

And you get

6/20 + 5/20 + 16/20 (now you can add them because they all have 20 as denominator) so = 27/20 = 1 7/20

The mean is 270.75 and the median is 271. While there is no single mode, then we conclude that our mode is 264 and 294 respectively.

By definition:

Mean is the sum of all the numbers in the set divided by the total number of numbers.

Median is the middle value in the set when the numbers are arranged in order.

Mode is the number that appears most frequently in the set.

If we re-arrange the data given in ascending order, we have:

264 264 267 269 273 276 294 297

To calculate Mean:

Add up all the numbers and divide by the total number of numbers:

Mean = (264 + 264 + 267 + 269 + 273 + 276 + 294 + 297) / 8

Mean = 270.75

To calculate Median:

We need to find the middle number in the set. Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers:

Median = (269 + 273) / 2

Median = 271

To calculate Mode:

We need to determine which number appears most frequently in the set. In this case, there are two numbers that appear twice (264 and 294), and the rest of the numbers appear only once. Therefore, there is no single mode for this data set.

Mode = 264 and 294

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The radius of the circle is approximately 7.9 feet.

The arc length formula (if θ is in degrees) is expressed as:

s = 2πr × (θ/360°)

Where r is radius and θ is the central angle subtended by the arc.

Given that:

Arc length s = 9ft

Central angle subtended by the arc = 65°

Radius r = ?

Plug the given values into the above formula.

s = 2πr × (θ/360°)

9ft = 2 × 3.14 × r × (65/360°)

r = 9ft / 1.133888

r = 7.9 ft

Therefore, the radius is 7.9 ft.

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Result:

sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).

For us to write the expression, we shall use this formular formula:

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

where:

a = tan⁻¹(x)

b = tan⁻¹(y)

Next, we have:

tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))

= (x - y) / (1 + xy)

From both sides, we have sine:

sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))

So, sin(tan⁻¹(x) - tan⁻¹(y))  

= sin(tan⁻¹(x) - tan⁻¹(y))

= (x - y) / (1 + xy) in terms of x and y.

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The actual distance between the two cities is  [tex]7\frac{1}{2}[/tex] miles .

A scale drawing is the reduced version of a larger image. The scale drawing is reduced at a constant proportion to the original image using a scale. An example of a scale drawing is a map of the city.

Actual distance between the cities can be determined by multiplying the distance in the scale drawing by the scale.

Actual distance = 1[tex]\frac{1}{2}[/tex] x 5

= [tex]\frac{3}{2}[/tex] x 5 = [tex]\frac{15}{2}[/tex] = [tex]7\frac{1}{2}[/tex] miles

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An appropriate tip for a waiter at a restaurant is at least 15% of the total bill. For a tab of $20, the tip would be:

Tip amount = 15% of $20

Tip amount = 0.15 x $20

Tip amount = $3

Therefore, the total amount of money that should be left, including tip, is:

$20 (tab) + $3 (tip) = $23.

The number of users that are 30 and older is 10,500.

We have,

From the histogram,

The number of users that are 30 and older.

= 7 + 9 + 3 + 2

= 21

Now,

The percentage of 30 and older users.

= 21/50 x 100
= 21 x 2

= 42%

Now,

Total users = 25,000

So,

The percentage of 30 and older users.

= 42% of 25,000

= 42/100 x 25,000

= 42 x 250

= 10500

Thus,

The number of users that are 30 and older is 10,500.

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Answer:

289

Step-by-step explanation:

Let's call the height of the building "h" and the distance from the point on the ground to the base of the building "d".

From the point on the ground, the distance to the top of the antenna is d + 138, and the distance to the bottom of the antenna is d.

Using trigonometry, we can set up two equations:

tan(30.5°) = (d + 138) / h (1)

tan(23.5°) = d / h (2)

We can solve equation (2) for d:

d = h tan(23.5°)

Substituting this into equation (1), we get:

tan(30.5°) = (h tan(23.5°) + 138) / h

Simplifying:

tan(30.5°) = tan(23.5°) + 138/h

tan(30.5°) - tan(23.5°) = 138/h

h = 138 / (tan(30.5°) - tan(23.5°)) ≈ 289.12 feet

Therefore, the height of the building is approximately 289.12 feet.

Answer: In one week, Nursen saves $5 and shares $3.75, so she has $5 + $3.75 = $8.75 per week.

She spends $4.95 on bus fare, so she has $8.75 - $4.95 = $3.80 per week to spend.

This week, Nursen earned $24 babysitting, so she has an additional $24 to spend.

Therefore, Nursen has $3.80 + $24 = $27.80 to spend.

Step-by-step explanation:

Answer:

To solve m^2 - 6m = 3 using the quadratic formula, we first need to put the equation in standard form, which is ax^2 + bx + c = 0.

m^2 - 6m - 3 = 0

Now we can identify a, b, and c:

a = 1, b = -6, c = -3

Next, we can plug these values into the quadratic formula:

m = (-b ± sqrt(b^2 - 4ac)) / 2a

m = (-(-6) ± sqrt((-6)^2 - 4(1)(-3))) / 2(1)

m = (6 ± sqrt(48)) / 2

Simplifying the square root of 48, we get:

m = (6 ± 4sqrt(3)) / 2

Now we can simplify by factoring out a 2 from the numerator:

m = 3 ± 2sqrt(3)

So the solutions to the equation are:

m = 3 + 2sqrt(3) or m = 3 - 2sqrt(3)

Step-by-step explanation:

Answer: 3±2√3

Step-by-step explanation:

see image for explanation

Let me know if you more explanation with simplifying the root.  That is a whole lesson in itself.