Mathematics High School

Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) What is Miguel’s expected value from playing the game? answer= $2 Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? answer= $2 What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point. Let X = the points you have after one spin. Fill out the missing values in the table. Xi P(xi) If you take one spin, what is your expected value? What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 What is the expected value for each choice? Should he pass the ball or take the shot himself? Explain. Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values. If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?

Answers

Answer 1
1) We have that there are in total 6 outcomes If we name the chips by 1a, 1b, 3 ,5 the combinations are: 1a,3 \ 1b, 3 \1a, 5\ 1b, 5\ 3,5\1a,1b. Of those outcomes, only one give Miguel a profit, 1-1. THen he gets 2 dollars and in the other cases he lose 1 dollar. Thus, there is a 1/6 probability that he gets 2$ and a 5/6 probability that he loses 1$.
2) We can calculate the expected value of the game with the following: E=[tex] \frac{1}{6}*2- \frac{5}{6} *1[/tex]. In general, the formula is [tex]E= \sum{p*V}[/tex] where E is the expected value, p the probability of each event and V the value of each event. This gives a result of E=2/6-5/6=3/6=0.5$ Hence, Miguel loses half a dollar ever y time he plays.
3) We can adjust the value v of the winning event and since we want to have a fair game, the expecation at the end must be 0 (he must neither win or lose on average). Thus, we need to solve the equation for v:
0=[tex] \frac{1}{6}v -\frac{5}{6} =0 [/tex]. Multiplying by 6 both parts, we get v-5=0 or that v=5$. Hence, we must give 5$ if 1-1 happens, not 2.
4) So, we have that the probability that you get a red or purple or yellow sector is 2/7. We have that the probability for the blue sector is only 1/7 since there are 7 vectors and only one is blue. Similarly, the 2nd row of the table needs to be filled with the product of probability and expectations. Hence, for the red sector we have 2/7*(-1)=-2/7, for the yellow sector we have 2/7*1=2/7, for the purple sector it is 2/7*0=0, for the blue sector 1/7*3=3/7. The average payoff is given by adding all these, hence it is 3/7.
5) We can approach the problem just like above and set up an equation the value of one sector as an unknown. But here, we can be smarter and notice that the average outcome is equal to the average outcome of the blue sector.  Hence, we can get a fair game if we make the value of the blue sector 0. If this is the case, the sum of the other sectors is 0 too (-2/7+0+2/7) and the expected value is also zero.
6) We want to maximize the points that he is getting. If he shoots three points, he will get 3 points with a probability of 0.30. Hence the average payoff is 0.30*3=0.90. If he passes to his teammate, he will shoot for 2 points, with a success rate of 0.48. Hence, the average payoff is 0.48*2=0.96. We see that he should pass to his player since 0.06 more points are scored on average.
7) Let us use the expections formula we mentioned in 1. Substituting the possibilities and the values for all 4 events (each event is the different profit of the business at the end of the year).
E=0.2*(-10000)+0.4*0+0.3*5000+0.1*8000=-2000+0+1500+800=300$
This is the average payoff of the firm per year.
8) The firm goes even when the total profits equal the investment. Suppose we have that the firm has x years in business. Then x*300=1200 must be satisfied, since the investment is 1200$ and the payoff per year is 300$. We get that x=4. Hence, Claire will get her investment back in 4 years.
Answer 2

Answer:

To check all the events (6), we label the chips. Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices. Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.

The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)

We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one. The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$. In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on. On average, Miguel loses half a dollar every time he plays.

Related Questions

The area of a rectangle is 28^2 , and the length of the rectangle is 1ft more than double the width. find the dimensions of the rectangle.

Answers

either 29 or 32 either way i die soon so bye

Please I need help with this.

Answers

1. 2 ( C)
2. 2x^2-9x+10 (B)
3. -1 (D)
4. 40x^2+22x-6 (B)
5.x^2-2x+4-(14/x+2) (A)

The triangle and the rectangle have the same perimeter.

Answers

Amazing I am so happy for you

PLEASE I NEED MAJOR HELP (PICTURE IS DOWN BELOW)

Answers

26. 

You simply read the table on this one
Hi! :)

To solve this problem, you need to put it into a proportion. 

Since you want to find how many high school students will have an art major out of 1,000 people, you will want to find the current ratio of art majors to all majors, so we can solve the proportion. 

Add all the values together. 

26+24+16+21+18+20= 125

26/125 <-- art majors over all majors 

[tex] \frac{26}{125} = \frac{x}{1000} [/tex]

Cross multiply. 

125*x= 1000*26

125*x= 26,000

x= 208

208 out of the 1,000 students will most likely want to pursue an art major. 

Hope this helps!

A gift box is 12 inches long, 8 inches wide and 2 inches high. how much wrapping paper needed to wrap the box?

A.) 272 inches
B.) 192 inches
C.) 384 inches
D.) 184 inches

Answers

It is B.) 192 inches. 

Matt's Ice Cream Shoppe has 7 cups of sprinkles to use on sundaes for the rest of the day. If each sundae is served with
1/8

cup of sprinkles, how many sundaes can they serve?

Answers

Final answer:

Matt's Ice Cream Shoppe can serve 56 sundaes with 7 cups of sprinkles, assuming each sundae uses 1/8 cup of sprinkles.

Explanation:

The question asks: How many sundaes can Matt's Ice Cream Shoppe serve with 7 cups of sprinkles if each sundae is served with 1/8 cup of sprinkles?

To find the answer, we divide the total amount of sprinkles by the amount used per sundae. Here's the calculation:

Total amount of sprinkles = 7 cups.Amount of sprinkles per sundae = 1/8 cup.Number of sundaes that can be served = Total amount of sprinkles ÷ Amount of sprinkles per sundae = 7 cups ÷ 1/8 cup = 56 sundaes.

Therefore, Matt's Ice Cream Shoppe can serve a total of 56 sundaes with their current stock of sprinkles.

Matt's Ice Cream Shoppe can serve 56 sundaes with the 7 cups of sprinkles they have.

To find out how many sundaes Matt's Ice Cream Shoppe can serve with 7 cups of sprinkles, we need to divide the total amount of sprinkles by the amount of sprinkles used per sundae.

Given:

- Total amount of sprinkles: 7 cups

- Amount of sprinkles per sundae: [tex]\( \frac{1}{8} \)[/tex] cup

Let ( x ) be the number of sundaes that can be served.

We can set up the equation:

[tex]\[ \text{Total amount of sprinkles} = \text{Amount of sprinkles per sundae} \times \text{Number of sundaes} \][/tex]

[tex]\[ 7 = \frac{1}{8} \times x \][/tex]

Now, to solve for ( x ), we can multiply both sides of the equation by 8:

[tex]\[ 7 \times 8 = x \][/tex]

[tex]\[ x = 56 \][/tex]

Therefore, Matt's Ice Cream Shoppe can serve 56 sundaes with the 7 cups of sprinkles they have.

How can i find one side of a triangle with another side and an angle?

Answers

If you only have two of the six measures of a triangle, you cannot find the others. You need at least 3 measures, including at least one side, in order to solve a triangle.

You can always use the Law of Cosines (if you have sufficient information), or the Law of Sines (if you have sufficient information).

Wyatt's dog is tethered to a post in his yard. If the rope tied to the dog is 12 feet long, how many square yards does the dog have access to? (Use 3.14 for π.)

https://clackamasweb.owschools.com/media/g_mat08_ccss_2016/7/img_circle_quiz.gif
452.16 yd 2 50.24 yd 2 75.36 yd 2 25.12 yd 2

Answers

Solution:

Wyatt's dog is tethered to a post in his yard.

The rope tied to the dog is 12 feet long.

we have been asked to find

How many square yards does the dog have access to?

when Wyatt's dog is tethered to a post in his yard, then that dog can move along that post only and the area covered will be a circle with radius 12ft.

So Area access to dog in ft^2 [tex] = \pi r^2=\pi 12^2=144 \pi [/tex]

But it ask for area in yards, so we will have to use conversion formula

[tex] 1ft=0.33333yard [/tex]

Area access to dog in yards[tex] =144*3.14*(0.33333)^2=50.24 \ Yards [/tex]

Answer:

Wyatt's dog is tethered to a post in his yard.

The rope tied to the dog is 12 feet long.

we have been asked to find

How many square yards does the dog have access to?

when Wyatt's dog is tethered to a post in his yard, then that dog can move along that post only and the area covered will be a circle with radius 12ft.

So Area access to dog in ft^2  

But it ask for area in yards, so we will have to use conversion formula

Area access to dog in yards

Step-by-step explanation:

Use the given point on the terminal side of angle 0 to find the value of the trigonometric function indicated.
1)tan0;(10,-18)
2)tan0;(4,3)

Answers

1 is tan 0 = -18/10 = -9/5
2 is tan 0 = 3/4

In general, an angle with a terminal side on the point (x, y) the tan of that line is the fraction y/x

When a number is subtracted from x the result is 6. What is that number

Answers

Hey there!!

I'm pretty sure the number is 9 and x is 3 so it equals 6.

hope this helps!!

Good luck:) 
Let n represent the number of interest. The problem statement tells you
.. x - n = 6
.. x - 6 = n . . . . . add n-6

The number is x-6.

A certain species of fish require 1.5 1.5 cubic feet of water per fish to maintain a healthy environment. find the maximum number of fish you could put in a tank measuring 6 6 feet by 3 3 feet by 4 4 feet.

Answers

(6 ft)*(3 ft)*(4 ft) * (1 fish)/(1.5 ft^3) = (6*3*4/1.5) fish = 48 fish

A negative correlation means that ________. select one:
a. high values of one variable are associated with low values of the other
b. high values of one variable are associated with high values of the other
c. low values of one variable are associated with low values of the other
d. there is no relationship between the two variables

Answers

The answer is A- High Values of one variable are associated with low values of the other.
Negative correlation is a relationship between two variables wherein if the value of one variable increases, the value of the other variable decreases, and vice versa.
Final answer:

A negative correlation means that high values of one variable are associated with low values of the other. This suggests that as one variable increases, the other decreases respectively and vice versa, which can be seen in various real-world scenarios such as the relationship between time spent studying and number of mistakes made on a test.

Explanation:

In the context of statistics and data analysis, a negative correlation means that high values of one variable are associated with low values of the other. This implies that as one variable increases, the other decreases correspondingly and vice versa. For instance, if we were examining the relationship between time spent studying and number of mistakes made on a test, a negative correlation might indicate that the more time a student spends studying, the fewer mistakes they make on the test. This is indicative of a negative correlation because as the value of one variable (study time) increases, the value of the other variable (mistakes) decreases.

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Austin rented a truck for one day. there was a base fee of $15.99 , and there was an additional charge of 82 cents for each mile driven. austin had to pay $123.41 when he returned the truck. for how many miles did he drive the truck?

Answers

123.41 - 15.99 = 107.42 / 0.82 = 131

131 Miles

Given the lease terms below, find the total lease cost, assuming that the deposit is nonrefundable.
Terms:
Length of lease: 36 months
MSRP of the car: $21,400
Purchase value of the car after lease: $17,100
Down payment: $1500
Monthly payment: $272
Security deposit: $350
Acquisition fee: $700

Answers

Answer: The total cost of the lease is $12,342.

To find the total cost of the lease, we have to add up all the costs that you will be responsible for.

You will have to pay the down payment, the monthly payment, security deposit and the acquisition fee.

However, don't forget that you have to multiply the monthly payment by 36 months.

1500 + 36(272) + 350 + 700 =12342

Final answer:

The total lease cost is the sum of the down payment, nonrefundable security deposit, acquisition fee, and the total payments over the lease term which amounts to $12,342.

Explanation:

The total lease cost can be calculated by adding all fees, the nonrefundable deposit, monthly payments, and any other additional costs. We start by adding the down payment, security deposit, and acquisition fee:

Down payment: $1500Security deposit (nonrefundable): $350Acquisition fee: $700

The monthly payment over the term of the lease is calculated by multiplying the monthly payment amount by the number of months in the lease term:

Monthly payment: $272Length of lease: 36 months

Multiplying the monthly payment by the lease term gives us the total amount paid over the course of the lease:

272 * 36 = $9792

Adding all the costs together gives us the total lease cost:

Total lease cost = Down payment + Security deposit + Acquisition fee + Total monthly paymentsTotal lease cost = $1500 + $350 + $700 + $9792Total lease cost = $12342

Note that this calculation assumes that the security deposit is nonrefundable, which is often the case in a car lease. It's also important to note that additional costs may apply, such as excess mileage fees or wear and tear.

Aldo drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Aldo drove home, there was no traffic and the trip only took 5 hours. If his average rate was 21 miles per hour faster on the trip home, how far away does Aldo live from the mountains? Do not do any rounding.

Answers

8x = 5(x+21)
8x = 5x +105
3x = 105
x = 105 /3
x = 35

8 x 35 = 280 miles away

The distance of Aldo's house from the mountains when calculated using the parameters is; 280 miles

How to Solve Algebra Word Problems?

We know that distance is given by;

Distance = speed * time

Distance with traffic = 8x

Distance without Traffic plus average rate = 5(x + 21)

Thus;

8x = 5(x + 21)

8x = 5x + 105

3x = 105

x = 105/3

x = 35

Thus;

Distance from his house = 5(35 + 21) = 280 miles

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What's the probability of getting at least k heads in n coin flips?

Answers

Half of n time k = 1/2 n * k

A cube 3 1/2 inches long V = _____ cubic inches

Answers

The side of cube is given as 3 1/2 inches.

converting 3 1/2 into mixed fraction we have 7/2 inches.

on dividing 7 by 2 we get 3.5 inches

Formula to find volume of cube is given by:

[tex] V = a^{3} [/tex]

where "a" is length of side.

Plugging the value of a in the formula we have,

[tex] V = (3.5)^{3} [/tex]

Volume of cube is 42.875 cubic inches.

HELP PLEASE CAN SOMEONE TAKE A LOOK?

1. The investment you make into a start=up company is also known as ____ (1point)
A. Venture Capital
B. first-time investment
C. entrepreneurial capital
D. beginning capital

Answers

The investment you make into a start-up company is also known as *A.) Venture capital 
 Venture capital-capital invested in a project in which there is a substantial element of risk, typically a NEW or expanding business

Kendall says the sum of (6x^2+4xy+2y^2) and (4x^2-2xy-3y^2) is (10x^2+2xy-5y^2) what error did Kendall make

Answers

(6x^2 + 4xy + 2y^2) + (4x^2 - 2xy - 3y^2)
=
(10x^2 + 4xy - y^2)

Kendall assumed the 2y^2 was negative and not positive leading her to create the error of -5y^2

Hope this helps :)
Final answer:

The error made was in the summation of the y^2 terms in each expression, leading to an incorrect final sum of the two expressions.

Explanation:

Kendall's error lies in incorrectly adding the terms that contain y^2. Specifically, Kendall summed 2y^2 from the first expression and -3y^2 from the second expression, but mistakenly calculated the result as -5y^2 instead of the correct -y^2. Remember, when performing operations with similar terms, you must carry the correct sign along with each term.

So, the correct sum of (6x^2+4xy+2y^2) and (4x^2-2xy-3y^2) is (10x^2+2xy-y^2).

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Using the properties of equality, fill the blanks with the correct value to show the solution for y.
3(y-2)=18
3y-___=18
3y=___

Answers

3(y-2)=18
3y-6=18
3y=24
y=8
y=8 if you solve it it will equal to it welcome :D

A _____________ is a three-dimensional form that has length and width but minimum thickness.

Answers

A plane is a three-dimensional form that has length and width by minimum thickness. 

I don't know: Person 1, person 2, and person 3 made $660, if the ratio is 3:4:5, how much did person 1 person 2, and person 3 get?

Answers

3:4:5 = 3+4+5 = 12

660/12 = 55

55*3 = 165
55*4 = 220
55*5 = 275

person 1 = 165
Person 2 = 220
 person 3 = 275

Manny Brought a brand new car in 2012 for $28750. if the car depreciates by 12% each year, write n exponential function to model the situation, then find the value of the car in 2018

Answers

The formula for exponential decay is 
[tex]y=a(1-r)^{x} [/tex]

where  a is the initial value (28750)
r is the rate of decrease (0.12)
x is the time, in this case in years (6 .  2018-2012 = 6 years)

[tex]y=28750(1-0.12)^{6} [/tex]

y ≈ 13351.62

Value of the car in 2018 after depreciation by 12% each year is equals to $13351.5

What is exponential decay?

" Exponential decay is the decrease in the value of the product at a constant rate over a period of time interval."

Formula used

y = a (1 - r)ⁿ

a = Initial value

r =rate of depreciation

n = time

y = exponential function

According to the question,

Cost of new car 'a' = $28750

Rate of depreciation 'r' = 12%

2018 - 2012 = 6years

n = 6

Substitute the given values in the formula we get,

Exponential function

    y = 28750 [1 - (12 / 100)]⁶

⇒ y = 28750 ( 1 - 0.12)⁶

⇒ y = 28750 ( 0.88)⁶

⇒ y = 28750 (0.4644)   ( up to four decimals)

⇒ y = $13351.5

Hence, value of the car in 2018 after depreciation by 12% each year is equals to $13351.5

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Please help, I’m so confused :/

Answers

[tex] \tan x = \dfrac{\sin x}{\cos x} [/tex]

[tex] \tan x = \dfrac{\frac{5}{13}}{\frac{12}{13}} [/tex]

[tex] \tan x = \dfrac{5}{13} \times \dfrac{13}{12} [/tex]

[tex] \tan x = \dfrac{5}{12} [/tex]
[tex]cos x = \frac{a}{h} [/tex] , so a = 12, h = 13
[tex]sinx= \frac{o}{h} [/tex], so o = 5, h = 13
[tex]tanx = \frac{o}{a} [/tex]
[tex]tanx = \frac{5}{12} [/tex] 

Or 

[tex]tanx = \frac{sinx}{cosx} [/tex]
[tex]tanx = \frac{ \frac{5}{13}}{ \frac{12}{13} } [/tex]
[tex]tanx = \frac{5}{12} [/tex] 

Use the complex zeros(1/2, -3+7i, -3-7i) to factor f(x)=-2x^3 - 11x^2 -110x +58

Answers


P(x)=-(2x^3+11x^2+110x-58)
P(1/2)=-(2*1/8+11*1/4+110*1/2-58)=0
P(x)=(1/2-x)(2x²+12x+116) (using synthetic division)
P(x)=(1-2x)(x²+6x+58)=(1-2x)(x+3+7i)(x+3-7i)

I'd like to point out that Caylus' posting is correct using complex factors.

one may note that it could also be simplified to 

[tex]\bf f(x)=(1-2x)(x+3+7i)(x+3-7i) \\\\\\ f(x)=(1-2x)[(x+3)+(7i)][(x+3)-(7i)] \\\\\\ f(x)=(1-2x)~~[\stackrel{\textit{difference of squares}}{(x+3)^2-(7i)^2}] \\\\\\ f(x)=(1-2x)[(x^2+6x+9)-(7^2i^2)] \\\\\\ f(x)=(1-2x)[(x^2+6x+9)-(49\cdot -1)] \\\\\\ f(x)=(1-2x)[(x^2+6x+9)-(-49)] \\\\\\ f(x)=(1-2x)[(x^2+6x+9)+49] \\\\\\ f(x)=(1-2x)(x^2+6x+58)[/tex]

please help me with algebra 2?! i am so lost on how to do this!
1.Multiply and simplify if possible.

four square root of eleven•four square root of ten
(1 point)

11four square root of ten
11
10
four square root of one hundred ten

2.What is the simplest form of the expression?

cubed root of twenty four times a to the tenth times b to the sixth
(1 point)

3a3b2cubed root of two a
2a3bcubed root of a
2a3b2cubed root of three a
none of these

Answers

Question 1: 
- both squared roots are multiplied by 4, therefore you can regroup: 4·(√11·√10)
- since they are both squared roots, you can multiply the two numbers: 4·√(11·10)
- therefore the answer is: 4·√110

Question 2:
- first thing, you need to factorize the number: 24=2³·3
- then, highlight the exponents multipes of 3: ∛(2³·3·a^9·a·b^6)
- now you can take outside the cubic root everything that has an exponent multiple of 3, dividing the exponents by 3: 2·a³b²·∛3·a

A student received a 75% on an exam. If there were 20 questions on the exam, which ratio would show the number of questions answered correctly to the total number of questions? A. 20:5 B. 5:20 C. 15:20 D. 20:15

Answers

C, 15:20.

The student missed 5 questions.

Hope this helped!
For this case what you can do is the following rule of three:
 100% ---> 20
 75% -----> x
 Clearing the value of x we have:
 x = (75/100) * (20)
 x = 15
 This number represents the number of correct answers.
 We have then that the ratio is:
 15:20
 Answer: 
 A ratio that would show the number of questions answered correctly to the total number of questions is: 
 C. 15:20

Divide. 5x3y3z - 6x4y2z2 + 4xy3z xyz

Answers

Final Answer:

The result of dividing [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz is [tex](5x^2y^2 - 6x^3yz + 4y^2z).[/tex]

Explanation:

To divide [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz, we'll divide each term in the polynomial by xyz separately.

First, let's divide [tex]5x^3y^3z by xyz: (5x^3y^3z) / (xyz) = 5x^2y^2.[/tex]

Then, divide [tex]-6x^4y^2z^2 by xyz: (-6x^4y^2z^2) / (xyz) = -6x^3yz.[/tex]

Lastly, divide [tex]4xy^3z by xyz: (4xy^3z) / (xyz) = 4y^2z.[/tex]

Thus, the resulting polynomial after division is [tex]5x^2y^2 - 6x^3yz + 4y^2z.[/tex]This is derived from individually dividing each term in the polynomial by xyz, simplifying each term, and collecting like terms together to obtain the final result.

In this process, division by xyz means dividing each term of the polynomial by the factors x, y, and z, and simplifying the expression. By doing so, we obtain a simplified form of the polynomial where each term is reduced by the common factors x, y, and z, resulting in the expression [tex](5x^2y^2 - 6x^3yz + 4y^2z)[/tex] as the quotient.

Complete question:

Divide [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz.

Two planes start from the same airport and fly in opposite directions. the second plane starts 1/2 hour after the first plane, but its speek is 50 miles per hour faster. find the air speed of cach plan, if 2 hours after the first plante departs, the plans are 2000 miles apart

Answers

First plane
t = 2 hours.
r = r

Second plane
t = 1.5 hours
(30 minutes = 1/2 hour. the second plain has been in the air 2 - 1/2 hour = 1.5 hours. )
r = r + 30

Equation
2 * r + 1.5(r  + 50) = 2000
2r + 1.5r + 75 = 2000
3.5r = 2000 - 75
3.5r = 1925 
r = 1925 / 3.5
r = 550

the first plane was going 550 mph
the second plan was going 600 mph

PLEASE ANSWER ASAP.

Find the area of the triangle QRS.

Area = square units

Answers

Answer:area is 140

Step-by-step explanation:

Answer:

Area= 140 square units

Step-by-step explanation:

q(-9, 5). r(6,10). s(2,-10).

find the area of the triangle QRS.

Area=140 square units

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