Solve the following triangle. B = 60° C = 50°, b=9 A 0° AR (Simplify your answer.) a (Type an integer or decimal rounded to two decimal places as ne C (Type an integer or decimal rounded to two dec"

Answer:

A

Step-by-step explanation:

Its a positive slope and you go up 2 and to the right 5

We need to operate the next matrixes.

First, subtract the next matrixes:

13 10 7

6 8 1

2 5 0

-

3 -2 6

14 -6 11

8 -12 9

=

13-3 10-(-2) 7-6

6-14 8-(-6) 1-11

2-8 5-(-12) 0-9

=

10 12 1

-8 14 -10

-6 17 -9

Now, the result adds to the next matrix:

10 12 1

-8 14 -10

-6 17 -9

+

6 10 15

10 0 9

1 0 7

=

10+6 12+10 1+15

-8+10 14+0 -10+9

-6+1 17+0 -9+7

=

16 22 16

2 14 -1

-5 17 -2

Therefore, the correct answer is the first one.

Answer:

49/100

Step-by-step explanation:

Answer:

Decimal Fraction Percentage

0.49 49/100 49%

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

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The sets of numbers that could not represent the three sides of a triangle is {7,21,28}

Each side of a triangle that is considered legal must have a length that is less than the total of the lengths of the other two sides. hence, the longest side must be shorter than the total length of the other two sides.

fFor  option A , biggest side =11 and this can be seen to be greater than  9+ 11 = 20, so that is valid

for  option B  the biggest side  is 28 which is considered to be less equal to 21 +7 = 28, so that is  invalid

for option C the biggest side 39 which is considered to be not  less than 13 + 28 = 41, so that is invalid

for  option D, the biggest side 18 is less than 5 + 14  = 19, so that is valid

Therefore, option B is correct.

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Som needs 16 gallons of gas to travel 100 miles. Here's how to solve it:Given :Som's car uses 40 gallons of gas to travel 250 miles.

If Som currently has 10 gallons of gas in his car, we need to calculate the amount of gas needed to travel 100 miles. Solution: We can solve the problem by using a proportion.

This gives us the equation:40/250 = x/100 where x is the number of gallons of gas needed to travel 100 miles. To solve for x, we can cross-multiply to get.

\(40 x 100 = 250 x40 x 100 / 250 = x16 = x\)

Som needs 16 gallons of gas to travel 100 miles.

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Answer:

C.  37.5

Step-by-step explanation:

From inspection of the given triangle, we can see that the straight line that divides the triangle into two smaller triangles is an angle bisector since it divides the angle into two congruent angles.

Angle Bisector Theorem

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

\(\implies x:15=40:16\)

Solve for x:

\(\implies \dfrac{x}{15}=\dfrac{40}{16}\)

\(\implies \dfrac{x}{15}=2.5\)

\(\implies x=2.5\times 15\)

\(\implies x=37.5\)

Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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Answer:

Alternate Interior ∠s: 3 & 5, 4 & 6.

Corresponding ∠s: 1 & 5, 2 & 6, 3 & 8, 4 & 7.

Alternate Exterior ∠s: 1 & 8, 2 & 7.

Consecutive ∠s: 3 & 6, 4 & 5.

Step-by-step explanation:

Alternate interior angles must both be in between the parallel lines, it is almost like you are flipping the angle over the line, then moving it down, if that makes any sense.

Corresponding angles correspond, which means that they are the same (of course), but it is like you go directly down to the similar angle. You can visually see that angles are the same, an example is 1 & 5.

Alternate exterior angles are similar to alternate exterior angles, but they must be on the exterior of the parallel lines. Once again, it is like you are flipping the angle of the line, then turning it downwards, if it makes any sense that way to you.

Consecutive angles are always in between the two parallel lines on the same side. They add up to 180. So 4 & 5 is a good example.

Good luck.

it is seen that if the number of people in the group is n = 23, the probability that at least two people will have the same birthday is at least 1/2.

Let P(A) be the probability that in a randomly selected group of n people, at least two people have the same birthday.

If we assume that the year has 365 days, then the number of ways to select n people with different birthdays is n x (n-1) x (n-2) x ... x (n-364).

the probability of selecting n people with different birthdays is P(A') = n(n - 1)(n - 2)...(n - 364)/365nThen, the probability that at least two people in a group of n have the same birthday is given by P(A) = 1 - P(A').

We need to find the smallest value of n such that P(A) ≥ 1/2.Let's solve for this.Let us find n such that P(A) ≥ 1/2.

By using the complement rule, 1-P(A') = P(A).Then:1 - n(n - 1)(n - 2)...(n - 364)/365n ≥ 1/2n(n - 1)(n - 2)...(n - 364)/365n ≤ 1/2(2)n(n - 1)(n - 2)...(n - 364) ≤ 365n/2Now, take the natural logarithm of both sides and simplify as follows:ln[n(n - 1)(n - 2)...(n - 364)] ≤ ln[365n/2]nln(n) - ln[(n - 1)!] - ln[(n - 2)!] - ... - ln[2!] - ln[1!] ≤ ln[365n/2]

Therefore, we need at least 23 people in the group for the probability of two or more people having the same birthday to be at least 1/2.

This is because n = 23 is the smallest number for which the inequality holds, and therefore, it is the smallest number of people required to ensure that the probability of two or more people having the same birthday is at least 1/2.

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Answer:

The number used to multiply the lengths of a figure to make it smaller or larger.

Step-by-step explanation:

You're welcome.

The product of the smallest and largest integer is 672

Represent the smallest even integer with x.

So, the other even integers are x + 2 and x + 4

The sum is represented as

x + x + 2 + x + 4 = 18 + 5/2x

Evaluate the like terms

3x + 6 = 18 + 5/2x

Evaluate the like terms

1/2x = 12

Multiply by 2

x = 24

The largest integer is x + 4

So, we have

x + 4 = 24 + 4

x + 4 = 28

The product of the smallest and largest integer is

Product = 24 * 28

Evaluate

Product = 672

Hence, the product of the smallest and largest integer is 672

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Answer:

-44

Step-by-step explanation:

(-4+1)+(10-51)

-4+1+10-51

-3-41

-44

To find the probability that exactly 15 lights out of 20 have a useful life of at least 1000 hours, we can plug in the values: P(X = 15) = (20 choose 15) * 0.8^15 * 0.2^5

Given that the probability that a fluorescent light has a useful life of at least 1000 hours is 0.8, we can use the binomial distribution formula to find the probabilities that among 20 such lights, a certain number will have a useful life of at least 1000 hours. The formula is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the number of lights that have a useful life of at least 1000 hours, n is the total number of lights (20 in this case), k is the number of lights with a useful life of at least 1000 hours, p is the probability that a single light has a useful life of at least 1000 hours (0.8), and (n choose k) is the binomial coefficient.

For example, to find the probability that exactly 15 lights out of 20 have a useful life of at least 1000 hours, we can plug in the values:

P(X = 15) = (20 choose 15) * 0.8^15 * 0.2^5

Using a calculator or a statistical software, we can find that this probability is approximately 0.202. Similarly, we can find the probabilities for other values of k, such as P(X = 10), P(X = 5), or P(X = 0). The probabilities will follow a binomial distribution, which is a discrete probability distribution that models the number of successes in a fixed number of trials.
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Answer:

14 is the rate of change; he can harvest 14 acres per day

Step-by-step explanation:

The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of amount $50 and a 25% markup on the selling price.

$50 / 0.25 = $200

To calculate the cost of the Nike baseball gloves with a markup of 25% and a margin of $50, use the following formula:

Cost = (Price + Markup) / (1 + Markup Percentage)

Cost = ($50 + $50) / (1 + 0.25)

Cost = $100 / 1.25

Cost = $80

Therefore, the manager can afford to pay amount $80 for each baseball glove.

The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of $50 and a 25% markup on the selling price.

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Answer: 62

Step-by-step explanation: In the red empty spot, the #5 would go there and in the blue spot the #6 would go there. 8x2=16 and 16+16= 32: t=This is for the to rectangle shapes on both sides. Now for the square in the middle, since the red spot is 5 and the blue is 6, 5x6= 30. So, 30+32=62.

Answer:

Step-by-step explanation:

The line is passing through 2 points: (0,9 and (3,3)

slope=(9-3)/(0-3)=-2

equation is : y-9=-2(x-0) or y=-2x+9

Answer:

0,0

1,1.5

2,3

3,4.5

4,6

5,7.5

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Step 1:

- 8 = - ( x + 4 )

Step 2:

- 8 = - x - 4

Step 3:

- 4 = - x

Answer:

x = 4

Hope This Helps :)

Answer: (17 , 5)

18 + 16 / 2 = 17

0 + 10 / 2 = 5

Answer:

Step-by-step explanation:

F = (18, 0 )  as ( x1 , y1)

G = (16 , 10) as (x2, y2 )

mid = (x1+x2) / 2 ,( y1 + y2) / 2

mid = (18+16)/2 , (0+10)/2

mid = 34/2 , 10 /2

mid =( 17, 5)

Answer:

A system of linear equations is a collection of two or more linear equations, and a solution to a system of linear equations consists of values of each of the unknown variables in the system that satisfies all of its equations, or makes them true.

The theorem states that if T is a translation along a line l, then T is also a translation along any line l' that is parallel to l.

To prove the theorem, let's consider a translation T along a line l. By definition, a translation preserves distances and directions. Now, let's consider a line l' that is parallel to l.

Since l' is parallel to l, any point on l' will have the same distance and direction from the corresponding point on l. In other words, for any point P on l', there exists a corresponding point Q on l such that the distance and direction between P and Q are the same.

Now, when we apply the translation T along l, it will move every point on l by the same distance and in the same direction. Since l' is parallel to l, the corresponding points on l' will also be moved by the same distance and in the same direction. Therefore, T is also a translation along l'.

Hence, we have proved that if T is a translation along a line l, then T is also a translation along any line l' that is parallel to l.

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The Taylor series has convergence within the disk centered at z₀ = 0 with a radius of 1.

The convergence properties of a Taylor series depend on the function being approximated and the point around which the series is being expanded.

The Taylor series for the function 1/(1 + z) around z₀ = 0 is as follows:

1/(1 + z) = 1 - z + z² - z³ + z⁴ - ...

The series converges if the absolute value of the ratio of successive terms is less than 1, i.e.

|(-1)ⁿ zⁿ⁺¹ / (-1)ⁿ⁺¹ zⁿ| < 1

|z| < 1

So, the Taylor series converges in the disk of radius 1 centered at z₀ = 0.

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Answer:

18 bags of skittles

Step-by-step explanation:

19-7.25-0.5x=2.75

=> -0.5x=-9

=> x=18

Answer:

4/125

Step-by-step explanation:

Answer:

-y=3,7

Step-by-step expl