3. Solve using the Laws of Sines Make a drawing to graphically represent what the following word problem states. to. Two fire watch towers are 30 miles apart, with Station B directly south of Station A. Both stations saw a fire on the mountain to the south. The direction from Station A to the fire was N32 W. The direction from Station B to the fire was N40 ° E. How far (to the nearest mile) is Station B from the fire?

Answer:

x=6.54138

x=0.458619

Step-by-step explanation:

using the Quadratic Formula where

a = 1, b = -7, and c = 3

x=−b±\(\sqrt{b^{2} -4ac}\)/2a

x=−(−7)±√[(−7)2−4(1)(3)]/2(2)

x=7±√(49−12)/2

x=7±√37/2

The discriminant b2−4ac>0

so, there are two real roots.

Cannot Simplify the Radical:

x=\(\frac{7+-\\\sqrt{37} }{2}\)

which becomes

x=6.54138

x=0.458619

There are 8 to take Lara and Hayden to volunteer the same number.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Lara already volunteered 50 hours and will volunteer 5 hours more each week.

And, Hayden already volunteered to 10 hours and will volunteer 10 hours each week .

Now, For Lara;

⇒ 50 + 5x

And, For Hayden;

⇒ 10 + 10x

So, For same number of volunteer is,

⇒ 50 + 5x = 10 + 10x

⇒ 50 - 10 = 10x - 5x

⇒ 40 = 5x

⇒ x = 40/5

⇒ x = 8

Thus, There are 8 to take Lara and Hayden to volunteer the same number.

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Answer:

Step-by-step explanation:

Answer:

m(arc AC) = 72°

m(arc BD) = 108°

m∠DEB = 90°

Step-by-step explanation:

Ratio of the measure of arc AC, arc BC, arc BD and arc AD = 4 : 2 : 6 : 8

Since, m(arc AC) + m(arc CB) + m(arc BD) + m(arc AD) = 360°

By the property of ratio,

Measure of arc AC = \(\frac{4}{4+2+6+8}\times (360^0)\)

                               = \(\frac{4\times 360}{20}\)

                               = 72°

Measure of arc BD = \(\frac{6}{4+2+6+8}\times (360^0)\)

                               = \(\frac{6\times 360}{20}\)

                               = 108°

Measure of ∠DEB = \(\frac{1}{2}m(arcAC + arc BD)\)

                              = \(\frac{1}{2}(72+108)\)

                              = 90°

Answer:

y=3x+10

Step-by-step explanation:

2=-12+b

b=10

If angle BOC in circle is 68° then the measure of angle BAC is 34°.

Given that angle BOC in the circle is 68°.

We have to find the angle BAC.

We have that m∠BOC=arc BC ------by central angle.

we have m∠BOC=68°.

therefore arc BC=68°.

We know that the inscribed angle is half that of the arc it comprises so m∠BAC=1/2 *(arc BC)-----1

In geometry one of the theorem states states that angle at the center of a circle is twice angle at the circumference.

We have that arc BC=68°

substitute arc BC in equation 1 to get the measurement of ∠BAC.

m∠BAC=\(68/2\)

=34°

Hence if angle BOC in circle is 68° then the measure of angle BAC is 34°.

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Answer:

78 cm³ of space is left inside the closet.

Step-by-step explanation:

Given that,

A closet is is 5 feet wide, 3 feet long, and 6 feet tall. A box with dimensions 2 ft × 3 ft × 2 ft is inside the closet.

We need to find the space is left inside the closet around the box.

Space left = volume of the closet - volume of the box

= 5×3×6 - 2×3×2

= 90 - 12

= 78 cm³

So, 78 cm³ of space is left inside the closet.

Answer:The answer would be 6a(4b4 +2b3 -3b2)

Step-by-step explanation:All you have to do is take 6a out of each number and put the 6a outside of parenthesis and put the rest of the equation in parenthesis.

Step-by-step explanation:

An index number is a method of evaluating variations in a variable or group of variables in regards to geographical location, time, and other features. The base value of the index number is usually 100, which indicates price, date, level of production, and more. There are various kinds of index numbers.

Answer:

I don't understand but I believe the answer is 16y^8

Step-by-step explanation:

Answer: (4 x a x a x a x a) x (4 x a x a x a x a)

HOPE THIS HELPS

Answer:

go to khan academy on you tube he's really good at explaining stuff also sorry that's all i got...

Step-by-step e

Answer: A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

Step-by-step explanation:

To calculate the costs for carpeting, wallpapering, painting, and the overall cost of the project, we need to determine the areas that need to be covered and the corresponding prices for each material.

Given dimensions:

Room length: 26 feet

Room width: 18 feet

Room height: 9 feet

Door dimensions:

Height: 6 feet 6 inches

Width: 4 feet

Window dimensions (each):

Width: 2 feet

Height: 2 feet 6 inches

A: Carpeting the floor:

To find the area of the floor, we multiply the length and width of the room:

Floor area = Length × Width = 26 feet × 18 feet = 468 square feet.

To convert to square yards (since the carpet is sold per square yard), we divide by 9:

Floor area in square yards = 468 square feet / 9 = 52 square yards.

Cost to carpet the floor = Floor area in square yards × Cost per square yard = 52 square yards × $18.00 = $936.00.

B: Wallpapering the walls:

To find the area of the walls, we calculate the perimeter of the room (2 × (Length + Width)) and multiply it by the height of the room:

Wall area = Perimeter × Height = 2 × (26 feet + 18 feet) × 9 feet = 396 square feet.

Cost to wallpaper the walls = Wall area × Cost per square foot = 396 square feet × $0.75 = $297.00.

C: Painting the ceiling:

To find the area of the ceiling, we multiply the length and width of the room:

Ceiling area = Length × Width = 26 feet × 18 feet = 468 square feet.

Since a quart of paint covers 88 square feet, we need to determine the number of quarts required:

Number of quarts = Ceiling area / Coverage per quart = 468 square feet / 88 square feet = 5.32 quarts.

Since a gallon contains 4 quarts, the number of gallons required is 5.32 quarts / 4 quarts = 1.33 gallons.

Cost to paint the ceiling = Number of gallons × Cost per gallon = 1.33 gallons × $25.00 = $33.25.

D: Cost of the entire project:

Total cost = Cost to carpet the floor + Cost to wallpaper the walls + Cost to paint the ceiling

= $936.00 + $297.00 + $33.25 = $1266.25.

Therefore:

A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

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The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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Answer:

1/3 or one third

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

2/6 = ?

You can simplify this fraction

2/6 = 1/3

Answer:

30 days

Step-by-step explanation:

1 way:

18 cars/6 days = 3 cars/1 day

90cars/3 cars a day= 30 days

another way:

90 cars/18 cars= 5

6 days * 5= 30 days

We can calculate the percent change dividing the change by the original amount of people attending the exhibit.

The increase is 298-152 = 146.

Then, we can calculate the percent change as:

There was a 96% increase in the number of people attending the exhibit.

Answer:

point

Step-by-step explanation:

Answer:

90 degree angle

Step-by-step explanation:

Answer:

6/4

Explanation:

If Alex can file the papers in the cabinets for 6 hours and 4 hours with Millie, then the fraction to represent the papers filed with Millie would be 6/4.

Hope this helps!

Answer:

27

Step-by-step explanation:

3x + 9 = 90

3x = 90 - 9

3x = 81

x =27

Answer:

Obtuse

Step-by-step explanation:

1 angle over 90

Answer:

4

Step-by-step explanation:

I like to use the FOIL method! I've attached a quick picture of how it works below, but basically you multiply the first terms. Next, multiply the outside/outer terms. Then, multiply the inside/inner terms. Lastly, you multiply the last terms.

In this question, the binomial is (x + 2)².

You can expand this to be (x + 2)(x + 2).

When you expand it using the FOIL method, you get x times x, which is x².

Next, the outside/outer terms are x and 2, which is 2x.

Then, you multiply the inside/inner terms 2 and x, which is 2x.

Last, you multiply the last terms, which are 2 and 2, which is 4.

When you put them together, it looks like this:

x² + 2x + 2x + 4.

You can simplify this to x² + 4x + 4.

So your answer is 4.

The number of suspects had less than two prior arrests are 3.

Given that, While reviewing the previous day’s arrest report.

Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.

Here, x+y=5 -----(i)

2x+3y=12 -----(ii)

From equation (i), x=5-y in equation (ii), we get

2(5-y)+3y=12

10-2y+3y=12

10+y=12

y=2

Substitute y=2 in equation (i), we get

x+2=5

x=3

Therefore, the number of suspects had less than two prior arrests are 3.

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Answer:

4.92% probability that the third strike comes on the seventh well drilled

Step-by-step explanation:

For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

20% chance of striking oil.

This means that \(p = 0.2\)

What is that probability that the third strike comes on the seventh well drilled

2 stikers during the first 6 drills(P(X = 2) when n = 6)\)

Strike during the 7th drill, with 0.2 probability. So

\(P = 0.2P(X = 2)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458\)

Then

\(P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492\)

4.92% probability that the third strike comes on the seventh well drilled

The area of the triangle in the shaded region is derived to be 12.5 square units.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

For the triangle in the shaded region;

base = 5 units

height = 5 units

area of the triangle = 1/2 × 5 units × 5 units

area of the triangle = 25/2

area of the triangle = 12.5 square units

Therefore, the area of the triangle in the shaded region is derived to be 12.5 square units.

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Answer:

(26 x $1,334) + ( 19 x $ 749) = $48,915

Step-by-step explanation:

All together she spent $45,915. She spent $34, 684 on treadmills and $14,231 on Stationary bikes.

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Peace and Love

The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.

Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.

As p is a prime number, and 2 is the smallest prime number, so, p\(\geq\)2

So, the positive divisors of the integer n are: 1,p,p².

As σ(n) represents the sum of all positive divisors of the integer n.

σ(n)=1+p+p²

In order to prove that σ(n) < 2n,for all n of the form n = p².

1+p+p²<2p²

p²-p-1>0

It is know that, p\(\geq\)2.

So, p²-p-1\(\geq\)1

Thus, σ(n) < 2n holds true for all n of the form n = p².

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Answer:

x=8

Step-by-step explanation:

2.5x+17+21x−25=180

Simplify 2.5x+17+21x−25

23.5x−8=180

Move all terms not containing x to the right side of the equation.

23.5x=188

Divide each term by 23.5 and simplify.

x=8

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The amount that Bob will have on deposit after seven years is
$ 313,742,585,000.

What is compound interest and how is it calculated?
Interest that is added to a loan or deposit sum is known as compound interest. The interest calculated on the principle and the interest accrued over the prior period is known as compound interest. It differs from simple interest in that simple interest does not take the principal into account when calculating the interest for the following month. In math, compound interest is typically represented by the letter C.I.
Mathematically, the amount A after the compound interest is imposed can be calculated as:
Amount, A = P [1 + (r/t)]ⁿ, where P = principal, r = rate of interest, t =  number of times interest is compounded per year, n = time in years.

Given, the principal Bob shall deposit = P = $ 5000
Rate of interest paid to Bob in percentage = r =12
Number of times interest is compounded per year = t = 1
Time of deposit in years = n = 7
Let the amount that Bob will have on deposit after seven years be = A
Substituting all the given values in the formula established in the literature part, we get,
A = 5000 [1 + (12/1)]⁷ = 5000*13⁷ = 313,742,585,000
Therefore, the amount that Bob will have on deposit after seven years is $ 313,742,585,000.

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