Answer:
-40x(x+1)
Step-by-step explanation:
Find [g•h](x) and [h•g] (x)
g(x)=2x
h(x)=-10x-10
[g•h](x) = 2x(-10x-10)= -20x^2-20x = -20x(x+1)
[h•g](x) = (-10x-10)2x= -10x(2x)-10(2x) = -20x^2-20x
[g•h](x) and [h•g] (x)
and means addition
-20x^2-20x + (-20x^2-20x)
-20x^2-20x-20x^2-20x
choose like terms
-20x^2-20x^2-20x-20x
-40x^2-40x
-40x(x+1)
Sebastian gathered data by surveying his neighbors comparing how much time they spend on the internet to how much mail they receive in a week. Explain the steps Sebastian should take in order to analyze the data.
Step-by-step explanation:
1. The first is a tabulation of the data, in an organized, clear and concise way for each event.
2. After tabulation, for a better understanding of the data, statistical data, such as the mean, median, and standard deviation of each event, should be collected.
3. Finally, graph the data obtained to see the trend of both cases and thus have a very precise way to make the comparison of both events
A tour bus normally leaves for its destination at 5:00 p.m. for a 200 mile trip. This week however, the bus leaves at 5:40 p.m. To arrive on time, the driver drives 10 miles per hour faster than usual. What is the bus’s usual speed?
Answer:
The usually speed of the bus is 50 miles/h.
Step-by-step explanation:
Let the usual speed of the bus be x mile/hour.
We know that
[tex]speed=\frac{distance}{time}[/tex]
[tex]\Rightarrow time = \frac{distance}{speed}[/tex]
The bus travels 200 miles.
To reach its destination it takes time [tex]=\frac{200}{x}[/tex] h
This week however the bus leaves at 5:40.
The bus late 40 minutes [tex]=\frac{40}{60} h[/tex] [tex]= \frac{2}{3}h[/tex]
Now the speed of the bus is = (x+10) miles/h
The new time to reach the destination is [tex]=\frac{200}{x+10}[/tex] h
According to the problem,
[tex]\frac{200}{x}-\frac{200}{x+10}=\frac{2}{3}[/tex]
[tex]\Rightarrow 200[\frac{x+10-x}{x(x+10)}]=\frac{2}{3}[/tex]
[tex]\Rightarrow 200[\frac{10}{x^2+10x}]=\frac{2}{3}[/tex]
⇒2(x²+10x)=200×10×3
⇒x²+10x = 3000
⇒x²+10x -3000=0
⇒x²+60x-50x-3000=0
⇒x(x+60)-50(x+60)=0
⇒(x+60)(x-50)=0
⇒x= -60,50
∴x=50 [since speed does not negative]
The usually speed of the bus is 50 miles/h.
The bus's usual speed is 60 mph.
To find the bus's usual speed, we can set up an equation based on the given information. Let the usual speed be x mph. Then, the time taken to travel 200 miles at the usual speed is 200/x. The time taken to travel the same distance at the increased speed (x+10) mph is 200/(x+10). Since the bus left late, these times should be equal, leading to the equation 200/x = 200/(x+10). Solving this equation, we find that x = 60 mph, which is the usual speed of the bus.
) One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players exceeded $1.1 million.
Answer:
Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.
Step-by-step explanation:
We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.
Suppose a sample of 400 major league players was taken.
Let [tex]\bar X[/tex] = sample average salary
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean salary = $1.5 million
[tex]\sigma[/tex] = standard deviation = $0.9 million
n = sample of players = 400
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P([tex]\bar X[/tex] > $1.1 million)
P([tex]\bar X[/tex] > $1.1 million) = P( [tex]\frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }[/tex] > [tex]\frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} }[/tex] ) = P(Z > -8.89) = P(Z < 8.89)
Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.
Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.
The approximate probability that the average salary of the 400 players exceeded $1.1 million will be "1".
ProbabilityAccording to the question,
Standard deviation, σ = 0.9
Mean, μ = 1.5
Let,
The salaries for professional sports player be "x".
Now,
The probability will be:
= P ([tex]\bar x[/tex] > 1.1)
= P ([tex]\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{1.1 - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex])
By substituting the values,
= P (Z > [tex]\frac{1.1 -1.5}{\frac{0.9}{\sqrt{400} } }[/tex])
= P (Z > -8.89)
By using the table,
= 1
Thus the above answer is correct.
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PLLLLLZ HELP I HAVE A DEADLINE Write a recursive formula for finding the nth term of each arithmetic sequence. 15.75, 14.25, 12.75, …
a1 = 15.75, an = an – 1 + 1.5
a1 = 12.75, an = an – 1 – 1.5
a1 = 11.25, an = an – 1 + 1.5
a1 = 15.75, an = an – 1 – 1.5
Answer: D. a1=15.75,an = an -1 -1.5
Step-by-step explanation:
Sorry about the no explanation, but the answer is correct.
The correct recursive formula for the arithmetic sequence 15.75, 14.25, 12.75, … is a1 = 15.75, an = an-1 - 1.5. This means the first term is 15.75 and each following term is 1.5 less than the previous term.
Explanation:The question asks for a recursive formula for the arithmetic sequence provided. An arithmetic sequence is a sequence of numbers wherein the difference between any two consecutive terms is constant. In this case, the common difference (d) is -1.5, because each term decreases by 1.5 from the previous term. Every term in the sequence follows the pattern of the first term, plus the common difference (d) multiplied by (n-1), where n is the term number.
To write a recursive formula for the sequence, we express the nth term (an) as the sum of the (n-1)th term and the common difference. Thus, the recursive formula for the sequence is: a1 = 15.75, an = an-1 - 1.5. This tells us that the first term a1 equals 15.75, and any term an (after the first term) is 1.5 less than the term before it(an - 1).
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Find a. If necessary, round your answer to the nearest hundredth.
Sorry the picture was upside down. :(
Answer:
The answer to your question is a = 4.81
Step-by-step explanation:
Process
1.- The angle B and 43° are supplementary
B + 43° = 180°
B = 180 - 43
B = 137°
2.- Calculate angle C
The sum of the internal angles in a triangle equals 180°
A + B + C = 180°
29 + 137 + C = 180
- Solve for C
C = 180 - 29 - 137
C = 14°
3.- Use the law of signs to find a
a / sin A = c / sin C
a / sin 29 = 2.4 / sin 14
- Solve for a
a = 2.4 sin 29 / sin 14
- Simplification
a = 2.4 (0.485) / 0.242
- Result
a = 4.809
The probability that a randomly selected car will be in an accident in the next year in a particular country is 0.0467. If four cars are randomly selected, find the probability that at least one has an accident during the coming year. Round to 4 decimals.
To find the probability that at least one of four cars has an accident, calculate the probability that no cars have accidents and subtract from 1. The probability is approximately 0.1785 after rounding to four decimal places.
Explanation:The probability that at least one of four randomly selected cars will be in an accident in the next year can be found by using the complement rule. The complement of at least one car being in an accident is that no cars are in an accident. We can calculate the probability of no accidents occurring and then subtract from 1 to find the desired probability.
First, we calculate the probability of a single car not being in an accident. This is 1 - 0.0467 = 0.9533. We then raise this probability to the power of four to represent all four independent events (four car selections): (0.9533)4.
Probability of no accidents = 0.95334 ≈ 0.8215 (rounded to four decimals).
Now, we subtract this from 1 to find the probability that at least one car has an accident in the coming year.
Probability at least one accident = 1 - Probability of no accidents = 1 - 0.8215 = 0.1785 (rounded to four decimals).
A shade of paint is made by evenly mixing m gallons of white paint, costing $12 a gallon, with n gallons of blue paint, costing $30. What is the cost, in dollars per gallon, of the resulting mixture?
Answer:
The cost of mixture is
[tex]\dfrac{12m + 30n}{m+n}\text{ dollars per gallon}[/tex]
Step-by-step explanation:
We are given the following in the question:
Cost of white per gallon = $12 a gallon
Amount of white paint in the mixture = m gallons
Total cost of white paint =
[tex]12\times m = 12m\$[/tex]
Cost of blue per gallon = $30 a gallon
Amount of blue paint in the mixture = n gallons
Total cost of blue paint =
[tex]30\times n = 30n\$[/tex]
Total cost of mixture =
Total cost of white paint + Total cost of blue paint
[tex](12m + 30n)\text{ dollars}[/tex]
Total amount of mixture =
Amount of white paint in the mixture + Amount of blue paint in the mixture
[tex]=(m+n)\text{ gallons}[/tex]
Cost of mixture per gallon =
[tex]=\dfrac{\text{Total cost}}{\text{Total amount}}\\\\=\dfrac{12m + 30n}{m+n}\text{ dollars per gallon}[/tex]
is the required cost of mixture.
Help please!!!!! Show work
Solve the equation
6(k+5)=66
Answer:
6
Step-by-step explanation:
6(k+5) = 6
k+5 = 66/6
k+5 = 11
k = 11-5
k = 6
In a poll conducted by a certain research center, 824 adults were called after their telephone numbers were randomly generated by a computer, and 10% were able to correctly identify the president. Identify the type of sampling used.
Answer:
Step-by-step explanation:
Hello!
Using a computer program 824 telephone numbers were randomly selected and a survey was conducted.
The sampling method used is the "simple random sampling" where the experimental units are randomly selected from the population without any kind of restriction and each unit has the same chance of being selected.
I hope it helps!
Factor the expression. 35g^2 – 2gh – 24h^2
(7g + 6)(5g + 4h2)
(7g + 6h)(5g – 4h)
(7g – 6h)(5g + 4h)
(7g – 6)(5g + 4)
Option C: [tex](7 g-6 h)(5 g+4 h)[/tex] is the correct answer.
Explanation:
The given expression is [tex]35 g^{2}-2 g h-24 h^{2}[/tex]
We need to determine the factor of the expression.
Now, let us break the given expression into two groups.
Hence, we get,
[tex]35 g^{2}+28 g h-30 g h-24 h^{2}[/tex]
Simplifying, we get,
[tex]\left(35 g^{2}+28 g h\right)+\left(-30 g h-24 h^{2}\right)[/tex]
Let us factor out 7g from the term [tex]\left(35 g^{2}+28 g h\right)[/tex]
Hence, we have,
[tex]7 g(5 g+4 h)+\left(-30 g h-24 h^{2}\right)[/tex]
Similarly, let us factor out -6h from the term [tex]\left(-30 g h-24 h^{2}\right)[/tex]
Thus, we have,
[tex]7 g(5 g+4 h)-6 h(5 g+4 h)[/tex]
Now, we shall factor out the term [tex]5g+4h[/tex] , we get,
[tex](7 g-6 h)(5 g+4 h)[/tex]
Thus, the factorization of the given expression is [tex](7 g-6 h)(5 g+4 h)[/tex]
Therefore, Option C is the correct answer.
Answer:
Option C is the correct answer.
Step-by-step explanation:
Out of 3000 light bulbs that were tested, 126 were defective. find the prbability of defective and non defective
Answer:
P(defective) = 126/3000 = 0.042
P(not defective) = 1 - P(defective)
= 1 - 0.042 = 0.958
A box contains three coins: two regular and one fake one-sided coin (P(H) = 1) You pick a coin at random and toss it. What is the probability that it lands tails up? You pick a random coin and after tossing get H. What is the probability that the coin is not fake?
Answer:
0.50
Step-by-step explanation:
Given that a box contains three coins: two regular and one fake one-sided coin (P(H) = 1) You pick a coin at random and toss it.
Probability of selecting any one coin = 1/3
The coins are regular 1, regular 2 , fake
P for head 0.5 0.5 1
Probability for head = [tex]\frac{1}{3} (1+0.5+0.5) = 0.6667[/tex]
using total probability theorem for mutually exclusive and exhaustive)
Probability that coin is not fake/head = [tex]\frac{0.5+0.5}{1+0.5+0.5} \\= 0.5[/tex]
Jerome took $20 to the store to buy a book and some CDs. If he buys a book that costs $4.50, write an inequality to find the most he could spend on CDs.
Answer:
y[tex]\leq[/tex]15.5
Step-by-step explanation:
The Total Amount taken to the store by Jerome = $20
He buys a book worth $4.50
Let y be the most he could spend on CDs
Since he is spending on books and CDs, the amount spent cannot be more than total sum he has, therefore:
y+$4.50[tex]\leq[/tex]20
This is because he could spend either less than $20 or exactly $20
y[tex]\leq[/tex]20-4.50
y[tex]\leq[/tex]15.5 is the inequality to find the most he could spend on CDs.
Tina bake some cookies 1/2 of her cookies with peanut butter 1/2 of the peanut butter cookies also have chocolate chips what fraction of the cookies were peanut butter and have chocolate chips
Answer: 1/4
Step-by-step explanation:
so if 1/2 of 1/2 of cookies are with choclate chips therefore saying 1/2 cookies is the same as 2/4 cookies and since half of the cookies are with choclate chips so there are 1/4 cookies with choclate chips nd are peanut butter please mark brainliest.
Answer:1/4
Step-by-step explanation: Half of the cookies baked were peanut butter cookies. 1/2 of the peanut butter cookies have chocolate chips. 1/2 divided by 1/2 is 1/4. 1/4 of the total cookies baked are peanut butter chocolate chip cookies.
The width of a rectangular prism is six times its length. The height is five times its length. If its length is m units, what is m units; what is the volume of the prism?
Answer:
[tex]30m^3[/tex] cubic units.
Step-by-step explanation:
Let m represent length of the rectangular prism.
We have been given that the width of a rectangular prism is six times its length, so width of the prism would be [tex]6m[/tex].
We are also told that the height is five times its length, so height of the prism would be [tex]5m[/tex].
We know that volume of rectangular prism is height times width times length.
[tex]\text{Volume of rectangular prism}=lwh[/tex]
[tex]\text{Volume of rectangular prism}=m\cdot 6m\cdot 5m[/tex]
[tex]\text{Volume of rectangular prism}=30m^3[/tex]
Therefore, the volume of the given rectangular prism would be [tex]30m^3[/tex] cubic units.
1/5+1/7+3/21 the answer is
Answer:
17/35Step-by-step explanation:
We need to get all the fractions with a common denominator before we can solve the problem.
The only fractions that have a common multiple are 1/7 and 3/21, so we'll add these first and then add 1/5.
1/7 = 3/21
Add
[tex]\frac{3}{21} + \frac{3}{21} =\frac{6}{21}[/tex]
6/21 = 30/105
1/5 = 21/105
[tex]\frac{30}{105} + \frac{21}{105} = \frac{51}{105}[/tex]
Simplify
[tex]\frac{51}{105} / \frac{3}{3} =\frac{17}{35}[/tex]
ANSWER: 17/35I'm always happy to help :)
simplify by dividing
3/5 ÷ -4/9
1. -27/20
2. 27/20
3. -12/45
4. 12/45
Answer:
The answer to your question is -27/20
Step-by-step explanation:
Divide 3/5 ÷ - 4/9
Process
1.- Just multiply the numerator of the first fraction by the denominator of the second fraction.
3 x - 9 = -27
2.- Multiply the denominator of the first fraction by the numerator of the second fraction.
5 x 4 = 20
3.- Join both results
-27/20
At the zoo there are two different tours. One leaves every 30 minutes and one leaves every 45 minutes. If they both leave at 8:00am, at what time will they be the same again
The two zoo tours start at 8:00 am, one leaves every 30 minutes and the other every 45 minutes. The next time they will coincide, or leave at the same time, is at 9:30 am.
Explanation:The tours in the zoo that are mentioned in your question represent two different intervals, 30 minutes and 45 minutes. To figure out when these tours will coincide again, we actually need to find a common multiple of the two intervals. The smallest common multiple of 30 and 45 minutes is 90 minutes or 1 hour and 30 minutes.
So, if both tours start at 8:00 am, they will sync again 90 minutes later, which is 9:30 am. Therefore, the two tours will depart together again at 9:30 am.
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50 POINTS Find the perimeter of the polygon if B = D
Answer:
92 cm
Step-by-step explanation:
2[ (2×11.5) + 10.5 + 12.5 ]
92
Karen started walking at 1 mile per hour. After she walked 2.5 miles, her friend Ned started walking along the same route at a piece of 1 mile per hour. If they continue to walk at the same rate, will Ned ever catch up to Karen? Explain.
Answer: No, Ned will never catch up to Karen.
Step-by-step explanation:
Karen started walking at 1 mile per hour.
Time = distance/speed
If she walks 2.5 miles, it means that the time she spent walking is
2.5/1 = 2.5 hours.
After she walked 2.5 miles, her friend Ned started walking along the same route at a speed of 1 mile per hour. Since Ned is walking at 1 mile per hour which is even slower than Karen's speed, it means that for every 1 mile that Ned walks, Karen walks 2.5 miles. Therefore, if
they continue to walk at the same rate, Ned will never catch up to Karen.
Teddy called the movie theater to find out how much tickets cost for him and his seven friends to go to the new hero movie. He remembered that the total was $60 if they go to the early movie but not how much each ticket is. Select which equation can be used so that he can tell his friends how much money the
Answer:
7.5
Step-by-step explanation:
If 8 people are going to the movie theater including Teddy, then we have to divide 60 by 8 which equals 7.5.
Carl and rick are traveling to a store 5 miles away. Carl is riding a bike, so he's going 12 mph faster than rick. If it takes rick 45 minutes, how long it take carl?
Answer:
Therefore Carl takes[tex]=16.07 mins[/tex]
Step-by-step explanation:
Speed : speed is the ratio of distance to time.
[tex]speed=\frac{distance}{time}[/tex]
The S.I unit of speed = m/s
The C.G.S unit of speed = cm/s
12 mph means 12 miles per hour.
Let the speed of Carl be x.
Carl is going 12mph faster than Rick.
Then the speed of Rick is = (x-12)mph
We know that,
[tex]time =\frac{distance}{speed}[/tex]
[tex]Time =\frac{5}{x-12}[/tex] h
45 minutes = [tex]\frac{45}{60}[/tex] h
According to the problem,
[tex]\frac{5}{x-12} =\frac{45}{60}[/tex]
[tex]\Rightarrow 45(x-12)=5\times60[/tex]
[tex]\Rightarrow45x-540 = 300[/tex]
[tex]\Rightarrow 45x=300+540[/tex]
[tex]\Rightarrow x=\frac{840}{45}[/tex]
We know that,
[tex]time =\frac{distance}{speed}[/tex]
Therefore Carl takes [tex]=\frac{5}{\frac{840}{45} } h[/tex] [tex]=\frac{5\times 45\times 60}{840} mins[/tex] [tex]=16.07 mins[/tex]
Carl will take approximately 16.08 minutes to travel the 5 miles to the store.
Step 1:
Determine Rick's speed.
Since Rick travels 5 miles in 45 minutes, we first convert 45 minutes to hours: 45 minutes ÷ 60 minutes/hour = 0.75 hours. Then, we find Rick's speed: Speed = Distance ÷ Time = 5 miles ÷ 0.75 hours = 6.67 mph.
Step 2:
Determine Carl's speed.
Since Carl is riding a bike 12 mph faster than Rick, we add 12 mph to Rick's speed to find Carl's speed: Carl's speed = Rick's speed + 12 mph = 6.67 mph + 12 mph = 18.67 mph.
Step 3:
Calculate Carl's time.
Now that we know Carl's speed, we can calculate how long it will take him to travel 5 miles. Time = Distance ÷ Speed = 5 miles ÷ 18.67 mph ≈ 0.268 hours.
Step 4:
Convert Carl's time to minutes.
To convert hours to minutes, we multiply by 60: 0.268 hours × 60 minutes/hour ≈ 16.08 minutes.
Step 5:
Interpret the result.
It will take Carl approximately 16.08 minutes to travel 5 miles to the store.
The population of United States is about 3×10(to the power of 8). The population of Kazakhstan is about 1.5×10(to the power of 7). How many times greater is the population of United States then Kazakhstan?
Answer:
The answer to your question is 20 times
Step-by-step explanation:
Data
United States' population = 3 x 10⁸
Kazakhstan's population = 1.5 x 10⁷
Process
1.- To solve this problem, just divide the United States' population by Kazakhstan's population.
3 x 10⁸ / 1.5 x 10⁷ = 20
2.- Conclusion
The population of the United States is 20 times greater than Kazakhstan's population.
List the first twenty counting numbers in the indicated base below. twelve (Only digits 0, 1, 2, 9, A, B are used in base twelve.) What are the first twenty counting numbers in base twelve? (Use a comma to separate answers as needed.)
Answer:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, 17, 18
Step-by-step explanation:
The first twenty counting numbers in base ten are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. If we convert each of these numbers to base twelve, then we will get the first twenty counting numbers in base twelve. We now proceed with the conversion below.
The first twelve digits of base 12 are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B.
12 in base 10 = 10 in base 12 since 12/12 = 1 R 0.
13 in base 10 = 11 in base 12 since 13/12 = 1 R 1.
14 in base 10 = 12 in base 12 since 14/12 = 1 R 2.
15 in base 10 = 13 in base 12 since 15/12 = 1 R 3.
16 in base 10 = 14 in base 12 since 16/12 = 1 R 4.
17 in base 10 = 15 in base 12 since 17/12 = 1 R 5.
18 in base 10 = 16 in base 12 since 18/12 = 1 R 6.
19 in base 10 = 17 in base 12 since 19/12 = 1 R 7.
20 in base 10 = 18 in base 12 since 20/12 = 1 R 8.
So the next 8 counting numbers of base 12 are 10, 11, 12, 13, 14, 15, 16, 17, 18.
The student requested the first twenty numbers in the base twelve system. In this system, the digits 0 to 9 are used as in decimal, but 'A' represents ten and 'B' represents eleven. The sequence starts with 0 and follows with 1, 2, ... 9, A, B, 10 (twelve in decimal), up to 17 (nineteen in decimal).
The student asked for the first twenty counting numbers in base twelve, also known as the duodecimal system. In this system, we use the digits 0, 1, 2, ..., 9, A, and B, where A represents ten and B represents eleven in decimal. Here is the list:
0123456789AB1011121314151617After the number B, the numbers continue with 10 (equivalent to twelve in decimal), then 11 (thirteen), and so on until 17, which is nineteen in decimal.
2/3 of the students study a language 2/5 of the students study french Find the ratio of students who study french to students who do not study french.
Answer:
Therefore the ratio of students who study french to students who do not study french is 4:11.
Step-by-step explanation:
Given that [tex]\frac2 3[/tex] of the students study a language. [tex]\frac2 5[/tex] of the students study french.
Consider total number of student be x.
The number of student who study language [tex]= \frac2 3\times x[/tex]
Again [tex]\frac2 5[/tex] of the students study french.
The number of student who study french [tex]= \frac2 3\times x\times \frac25[/tex]
[tex]=\frac{4}{15}x[/tex]
The number of student who do not study french
[tex]=x-\frac{4}{15}x[/tex]
[tex]=\frac{x(15-4)}{15}[/tex]
[tex]=\frac{11x}{15}[/tex]
Therefore the ratio of students who study french to students who do not study french is
[tex]=\frac{4}{15}x:\frac{11}{15}x[/tex]
=4:11
Answer:
(2/3)(300)= 200, study a language. Of those, 2/5, so (2/5)(200)= 80, study French. The other 300- 80= 220 students do not study French. The ratio of students who study French to those who do not is 80 to 220 which can be reduced to 8 to 22 and then 4 to 11.
Suppose the position of an object moving in a straight line is given by s (t )equals 4 t2+ 5 t+ 5. Find the instantaneous velocity when t equals 2. What expression can be used to find the instantaneous velocity at the given time?
Answer:
[tex] v(t) = 8t +5[/tex]
And that represent the instantaneous velocity at a given time t.
And then we just need to replace t =2 in order to find the instantaneous velocity and we got:
[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]
Step-by-step explanation:
For this case we have the position function s(t) given by:
[tex] s(t) = 4t^2 + 5t+5[/tex]
And we can calculate the instanteneous velocity with the first derivate respect to the time, like this:
[tex] v(t) = s'(t)= \frac{ds}{dt}[/tex]
And if we take the derivate we got:
[tex] v(t) = 8t +5[/tex]
And that represent the instantaneous velocity at a given time t.
And then we just need to replace t =2 in order to find the instantaneous velocity and we got:
[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]
What is 6:12 in simplest form?
A.2
B.21
C. 12
D. 12.6
Answer:
It’s B
Step-by-step explanation:
Answer: 1:2 or 1/2
Step-by-step explanation:
6:12
Step 1: find a common divisible value, in this case, it is 6
Step2: divide through 6
1:2 or 1/2
Amber can paint a room in 20 hours. Christy can paint the same room in 16 hours. How long does it take for both amber and christy to paint the room if they are working together?
Answer: it will take them 8.89 hours
Step-by-step explanation:
Amber can paint a room in 20 hours. This means that Amber's working rate per hour is 1/20
Christy can paint the same room in 16 hours. This means that Christy's working rate per hour is 1/16
If they work together, they would be working simultaneously and their unit rates is additive. This means that their combined rate would be
1/20 + 1/16
Assuming it takes t hours for both of them to paint the room working together. It means that their combined working rate per hour is 1/t. Therefore
1/20 + 1/16 = 1/t
(16 + 20/320 = 1/t
36/320 = 1/t
t = 320/36
t = 8.89 hours
Amber and Christy can paint a room together in approximately 8.89 hours by combining their work rates. Each has individual work rates of 1/20 and 1/16, respectively, and their combined work rate is 9/80 of a room per hour.
To determine how long it will take for Amber and Christy to paint the room when working together, we can use the concept of combined work rates. First, we calculate each person's individual work rate. Amber's work rate is 1 room per 20 hours (1/20), and Christy's work rate is 1 room per 16 hours (1/16).
Adding their rates together gives us the combined work rate:
Combined rate = Amber's rate + Christy's rate
Combined rate = 1/20 + 1/16
To add these fractions, we need a common denominator, which in this case is 80:
Combined rate = (4/80) + (5/80) = 9/80
This means that together, Amber and Christy can paint 9/80 of the room per hour. To find the total time required to paint the entire room, we take the reciprocal of the combined work rate:
Total time = 1 / (Combined rate)
Total time = 1 / (9/80)
Total time = 80/9
Total time = 8.89 hours (rounded to two decimal places)
Therefore, Amber and Christy will be able to paint the room together in approximately 8.89 hours.
What is the slope of the line whose equation is y−4= StartFraction 5 Over 2 EndFraction.(x−2)?
Answer:
m=5/2
Step-by-step explanation:
If [tex]y-4=\frac{5}{2}(x-2)[/tex], to find the slope, we first express the equation of the line in the slope-intercept form
y=mx+c, where
c=intercept on the y-axis
m=gradient/slope
[tex]y-4=\frac{5}{2}(x-2)\\y=\frac{5}{2}(x-2)+4\\y=\frac{5}{2}x-5+4\\y=\frac{5}{2}x-1[/tex]
Comparing with y=mx+c, the slope of the line, m=5/2
Answer:
5/2
Step-by-step explanation:
LOGARITHMS, CONIC SECTIONS, SEQUENCES
Evaluating an exponential function with base e that models a real...
The number of milligrams D (n) of a drug in a patient's bloodstream h hours after the drug is injected is modeled by the following function.
D(h) =40e-0.5h
Find the initial amount injected and the amount in the bloodstream after 7 hours.
Round your answers to the nearest hundredth as necessary.
Initial amount:
milligrams
Amount after 7 hours:
milligrams
X
5
?
Explanation
Check
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Answer:
(a) 40 milligrams
(b) 1.21 milligrams
Step-by-step explanation:
Exponential Function
It's commonly used to model real situations in life, like this one proposed in the question where the number of milligrams of a drug D(h) in a patient's bloodstream h hours after the drug is injected is modeled by the following function.
[tex]D(h) =40e^{-0.5h}[/tex]
(a) The initial amount injected to the patient can be found when h=0
[tex]D(0) =40e^{-0.5(0)}=40e^{0}=40[/tex]
Initial amount: 40 milligrams
(b) Let's plug h=7
D(7) =40e^{-0.5(7)}=40e^{-3.5}=1.21
The amount in the bloodstream after 7 hours is 1.21 milligrams