Answer:
840
Step-by-step explanation:
Total number of gifts (teddy bears)= 4
Total number of nieces = 7
We need to find the number of ways to give the 4 teddy bears to 4 of the 7 nieces, where no niece gets more than one teddy bear.
Number of possible ways to give first teddy = 7
It is given that no niece gets more than one teddy bear.
The remaining nieces are = 7 - 1 = 6
Number of possible ways to give second teddy = 6
Now, the remaining nieces are = 6 - 1 = 5
Similarly,
Number of possible ways to give third teddy = 5
Number of possible ways to give fourth teddy = 4
Total number of possible ways to distribute 4 teddy bears is
[tex]Total=7\times 6\times 5\times 4=840[/tex]
Therefore total possible ways to distribute 4 teddy bears are 840.
Final answer:
There are 35 different ways to give 4 identical teddy bears to 4 of the 7 nieces where no niece receives more than one teddy bear. The calculation is done using combinations formula C(7, 4).
Explanation:
To determine the number of different ways the 4 teddy bears can be given to 4 out of 7 nieces where each niece gets only one teddy bear, we use combinations. Combinations are a way of selecting items from a group, where the order does not matter. In mathematics, this is denoted as C(n, k), which represents the number of combinations of n items taken k at a time.
In this case, we want to find C(7, 4), because we have 7 nieces (n=7) and we are choosing 4 of them (k=4) to each receive one teddy bear. This is calculated by:
C(7, 4) = 7! / (4! * (7-4)!) => C(7, 4) = (7 * 6 * 5 * 4!) / (4! * 3!). Since 4! in the numerator and denominator cancel each other out, it simplifies to:
C(7, 4) = 7 * 6 * 5 / (3 * 2 * 1) = 35
Therefore, there are 35 different ways to give the 4 identical teddy bears to 4 of the 7 nieces when no niece gets more than one teddy bear.
which expression has the greatest value |-21|, |14|, |30|, |-45|
Answer:
|-45|
Step-by-step explanation:
In mathematics, the absolute value of a real number is the numeric value of the number, regardless the sign, either this is positive or negative.
The absolute value function can be definied as:
|a|=a si a ≥0|a|=-a si a <0Using this definition, we have:
|-21| = -(-21) = 21
|14| = 14
|30| = 30
|-45| = -(-45) = 45
Therefore, the expression |-45| has the greatest value.
Rosie washes clothes for two families the first family pays her $500 more per month than the second. Her total earning per month is $3200. How much does she earn from each families?
Answer:
Family 1: $1.850Family 2: $1.350Step-by-step explanation:
We know that the total monthly payment is 3200, so if we call Pa (family A`s payment) and Pb (Family B's payment) the payments:
Pa+Pb=3200also, Pa = Pb+500So if we replace Pa in the first ecuation:
Pb+500+Pb=32002Pb= 3200-500Pb=2700/2= $1.350then Pa+Pb=3200 => Pa= 3200-1350= $1.850
Good Luck!
Write x'" = x + t as a first order system
Answer:
y = x'
z = y'
z' = x + t
Step-by-step explanation:
Hi!
You need to define two new variables y and z:
y = x'
z = y'
Then:
z = y' = x''
z' = x''' = x + t
Now you have a system of 3 equations with only first derivatives
A snorkeler dives for a shell on a reef. After entering the water, the diver decends 11/3 ft in one second. Write an equation that models the divers position with respect to time.
Answer:
[tex]h(t)=-\dfrac{11}{3}t[/tex]
Step-by-step explanation:
A snorkeler dives for a shell on a reef. After entering the water, the diver decends [tex]\frac{11}{3}[/tex] ft in one second.
Let t be the time passed after entering the water, in seconds, and h(t) be the position of the snorkeler under the water, in feet.
The initial position of the snorkeler was 0 feet under the water.
An equation that models the divers position with respect to time is
[tex]h(t)=0-\dfrac{11}{3}t\\ \\h(t)=-\dfrac{11}{3}t[/tex]
Here the position is negative, because the diver decends (he deepens under the water)
A bacteria culture starts with 200 bacteria and grows at a rate proportional to its size. After 6 hours there will be 1200 bacteria (1) Express the population after I hours as a function of t. population: p(tepe (1.066-21) (unction of t) (b) What will be the population after 7 hours? 348125.2 (c) How long will it take for the population to reach 1750 ? Note: You can earn partial credit on this problem.
Answer:
We are given that the rate of change is proportional to its size S
So, [tex]\frac{dS}{dt} \propto S[/tex]
[tex]\frac{dS}{dt} = kS[/tex]
[tex]\frac{dS}{S} = kdt[/tex]
Integrating both sides
[tex]\log(S)= kt + log c[/tex]
[tex]\frac{S}{S_0}=e^{kt}[/tex]
[tex]S=S_0 e^{kt}[/tex]
S is the population after t hours
[tex]S_0[/tex] is the initial population
Now we are given that After 6 hours there will be 1200 bacteria
[tex]1200=200 e^{6k}[/tex]
[tex]6=e^{6k}[/tex]
[tex]6^{\frac{1}{6}=e^{k}[/tex]
So, [tex]S=200 \times 6^{\frac{t}{6}[/tex]
a)Now the population after t hours as a function of t; [tex]S=200 \times 6^{\frac{t}{6}[/tex]
b) What will be the population after 7 hours?
Substitute t = 7 hours
A bacteria culture starts with 200 bacteria
[tex]S=200 \times 6^{\frac{7}{6}}[/tex]
[tex]S=1617.607[/tex]
c) How long will it take for the population to reach 1750 ?
[tex]1750=200 \times 6^{\frac{t}{6}[/tex]
[tex]\frac{1750}{200} =6^{\frac{t}{6}[/tex]
[tex]8.75 =6^{\frac{t}{6}[/tex]
[tex]t=7.26[/tex]
So, it will take 7.2 hours for the population to reach 1750
Final answer:
To determine the population growth function in terms of time and find the population after a specific duration, use the exponential growth formula N(t) = N0 x 2^t. Calculate the growth rate using given data points like the initial and final population. Finally, substitute the desired time into the population function to find the population at that specific time.
Explanation:
The population of bacteria after t hours can be represented by the formula N(t) = N0 x 2t.
(a) To express the population after t hours as a function of t, you can use the given data points to find the growth rate. For the provided data, the growth rate is calculated as r = log2(1200/200) / 6 = 0.1333 per hour.
(b) To find the population after 7 hours, substitute t=7 into the function: N(7) = 200 x 27x0.1333 = 3481.49.
c) To find out how long it will take for the population to reach 1750, we get
p(t)=1750 and solving it
t ≈7.846
I need to find the standard for Hamilton's method to figure out how many teachers should be at each school
Answer:
The standard divisor is 22.48.
Step-by-step explanation:
There are a total of 3259 students at the 5 schools. Then dividing that number by the number of teachers (145) we get the "standard divisor" of ...
3259/145 ≈ 22.48
__
By Hamilton's method, that divisor is used to divide the number of students at each school, and the result is rounded down. This is the initial allocation of teachers to schools. The remainders from the division are examined. Starting with the largest and working down, one additional teacher is assigned until all the unassigned teachers have been assigned.
For this problem, the initial assignment results in 142 teachers being assigned, so there are 3 more that can be allocated. In order, the highest three remainders are associated with the number of students at East, Central, and South. Each of those schools gets one more teacher than the number initially assigned. The final allocation of teachers is highlighted in the attachment.
You're driving into Canada and trying to decide whether to fill your gas tank before or after crossing the border. Gas in the United States costs $2.58/gallon, in Canada it's $1.29/L, and the Canadian dollar is worth 79¢ in U.S. currency. Where you should fill up?
Answer:
It is more convenient to fill up in the United States.
Step-by-step explanation:
We convert a US gallon to liters:
1 Gallon equals 3.78541 liters.
Therefore, 1 US Gallon costs (3.78541) x (1.29) = 4.8831789 Canadian dollars.
Now we convert the price of a US gallon in Canadian territory to US dollars:
4.8831789 * 0.79 = 3.85771133 US dollars.
Conclusion: A gallon purchased in the United States costs 2.58 US dollars, while a gallon in Canada is equivalent to 3.85771133 US dollars. This way it is more convenient to fill up in the United States.
It would be more economical to fill up the gas tank in the United States before crossing into Canada.
To determine whether it is more cost-effective to fill up the gas tank in the United States or Canada, we need to convert the Canadian gas price into U.S. dollars per gallon. The price of gas in Canada is $1.29 per liter. Since 1 gallon is equal to 3.78541 liters, the price per gallon in Canada would be $1.29 × 3.78541 = $4.88238 CAD. Now, we need to convert this price into USD, knowing the Canadian dollar is worth 79¢ in U.S. currency. Therefore, $4.88238 CAD × 0.79 = $3.85728 USD per gallon.
The price of gas in the United States is $2.58 per gallon. When comparing the two prices, it is clear that $2.58 per gallon in the United States is cheaper than the converted price of gas in Canada ($3.85728 per gallon in USD). Hence, it would be more economical to fill up the gas tank in the United States before crossing into Canada.
The 1992 world speed record for a bicycle (human-powered vehicle) was set by Chris Huber. His time through the measured 200 m stretch was a sizzling 6.509 s, at which he commented,"Cogito ergo zoom!" (I think, therefore I go fast!). a.) What was Chris Huber’s speed in meters per second(m/s)? b) In 2001, Sam Whittingham beat Huber’s record by 19.0 km/h. What was Whittingham’s time through the 200 m? (answer hours)
Answer:
a) 30.726m/s and b) 5.5549s
Step-by-step explanation:
a.) What was Chris Huber’s speed in meters per second(m/s)?
Given the distance and time, the formula to obtain the speed is
[tex]v=\frac{d}{t}[/tex].
Applying this to our problem we have that
[tex]v=\frac{200m}{6.509s}= 30.726m/s[/tex].
So, Chris Huber’s speed in meters per second(m/s) was 30.726m/s.
b) What was Whittingham’s time through the 200 m?
In a) we stated that [tex]v=\frac{d}{t}[/tex]. This formula implies that
[tex]t=\frac{d}{v}[/tex].First, observer that [tex]19\frac{km}{h} =19,000\frac{m}{h}=\frac{19,000}{3,600}m/s= 5.2777m/s[/tex].
Then, Sam Whittingham speed was equal to Chris Huber’s speed plus 5.2777 m/s. So, [tex]v=30.726\frac{m}{s} +5.2777\frac{m}{s}= 36.003 m/s.[/tex]
Then, applying 1) we have that
[tex]t=\frac{200m}{36.003m/s}=5.5549s.[/tex]
So, Sam Whittingham’s time through the 200 m was 5.5549s.
Please help me with geometry. Theres only 3 questions i need help with
Which of the following angles have equal measure when a pair of parallel lines are crossed by a transversal?
supplementary angles
complementary angles
corresponding angles
adjacent angles
Answer:
corresponding angles
Step-by-step explanation:
Corresponding angles are congruent where a transversal crosses parallel lines. Such a geometry has 4 pairs of corresponding angles. The corresponding angles of each pair are congruent.
Answer:
corresponding angles
Step-by-step explanation:
Construct a truth table for the logical operator NOR.
Answer:
NOR Gate
Step-by-step explanation:
NOR gate is a two input gate.
It is defined as the complement of (X or Y), where X and Y are the inputs of the gate.
X Y X+Y Complement(X+Y) NOR
1 1 1 0 0
1 0 1 0 0
0 1 1 0 0
0 0 0 1 1
Ut is an operator which gives a value of 1 only when the bvoth the inputs are 0.
A truth table for the logical operator NOR is:
P Q NOR
T T F
T F F
F T F
F F T
How to construct a Truth Table?
A truth table is a mathematical table used in logic to show all possible combinations of truth values for the input variables of a Boolean function and their corresponding output.
To construct a truth table for the logical operator NOR, we can use the following table:
P Q NOR
T T F
T F F
F T F
F F T
The NOR operator returns true only when both inputs are false. Otherwise, it returns false.
This can also be expressed as ¬(P ∨ Q), which is logically equivalent to P NOR Q.
In art class Ms smith is working on polygons. She want the students to Create a picture of the polygons. She points out to the class That there is are three sides to a triangle, 4 sides on a quadrilateral , 5 sides on a pentagon, and six sides on a hexagon, How many more side are on a hexagon than on a quadrilateral
Answer:
There are two more sides on a hexagon than on a quadrilateral
Step-by-step explanation:
If the hexagon has 6 sides, and the quadrilateral has 4, then 6-4=2
Determine the sum of the first k odd positive integers for a number of values of k. What generalizations occur to you? Are your inferences correct for all positive integers k?
Answer:
[tex]S_{n} = \sum_{k=1}^{n} (2k-1) = n^2[/tex]
Step-by-step explanation:
Let's take a look at the first few odd numbers and their sum.
Lets define [tex]O_{k}[/tex] as the [tex]kth[/tex] odd number as:
[tex]O_{k} = 2k-1[/tex]
So we have:
[tex]O_{1} = 1\\O_{2} = 3\\O_{3} = 5\\O_{4} = 7\\[/tex]
And lets define the sum of all the odd numbers from [tex]k=1[/tex] to [tex]k=n[/tex] as:
[tex]S_{n} = \sum_{k=1}^n O_{k} = \sum_{k=1}^n (2k-1)[/tex]
Lets now check some values of said sum:
[tex]S_{1} = 1\\S_{2} = 1 + 3 = 4\\S_{3} = 1 + 3 + 5 = 9\\S_{4} = 1+3+5+7 = 16[/tex]
We can then observe than the sum up to [tex]n[/tex] equals [tex]n^2[/tex]
Let us then prove that this is the case by Induction.
First of all, we can prove this by an Induction Proof because we are taking all positive Integers. This is, we are working with the set of natural numbers [tex]\mathbb{N}[/tex].
We want to prove that
[tex]P(n) = S_{n} = \sum_{k=1}^n = n^2 \forall n\in \mathbb{N}[/tex]
This is, we want to prove that the sum of all odd numbers from [tex]1[/tex] to [tex]n[/tex] equals [tex]n^2[/tex] for all natural numbers.
Now, in order to prove something by Induction we need to check 2 things:
[tex]1) The\ base\ case . \ The\ statement\ holds\ for\ n=1\\2) The\ inductive\ step.\ Prove\ that\ if\ the\ statement\ holds\ for\ n\ then\ it\ must\ hold\ for\ n+1\\[/tex]
[tex]P(1)[/tex] is immediate:
[tex]P(1) = \sum_{k=1}^1 2k-1 = 1 = 1^2[/tex]
Now let's assume the statement holds for [tex]P(n)[/tex] and let's take a look at [tex]P(n+1)[/tex]
[tex]P(n+1) = \sum_{k=1}^{n+1} 2k-1[/tex]
And we can rewrite it by taking the last term out as:
[tex]P(n+1) = \sum_{k=1}^n 2k-1 \ + 2.(n+1) - 1[/tex]
And by inductive hypothesis we know that [tex]\sum_{k=1}^n 2k-1 = n^2[/tex]
and then:
[tex]P(n+1) = \sum_{k=1}^n 2k-1 \ + 2.(n+1) -1 = n^2 + 2n +2 -1 = n^2 +2n +1 = (n+1)^2[/tex]
And we have the proof we were looking for!
Janet Woo decided to retire to Florida in 6 years. What amount should Janet invest today so she can withdraw $51,500 at the end of each year for 20 years after she retires? Assume Janet can invest money at 6% compounded annually. (Use the Table 13.2 and Table 12.3.) Present value ??
Answer:
$293,562.707
Step-by-step explanation:
As for the provided details we know,
Janet needs $51,500 from end of 7th year for upcoming 20 years.
The present value of 20 installments of $51,500 shall be @ 6% from year 7 to year 8.0858
Thus total value = $51,500 [tex]\times[/tex] 8.0858 = $416,418.7
Now the compound interest factor for 6 year @ 6 % = 1.4185
Thus, value to be invested today = $416,418.70/1.4185 = $293,562.707
As this when compounded annually will provide the balance as required at the end of 6 years.
A local fraternity is conducting a raffle where 50 tickets areto be sold--one per customer. There are three prizes to beawarded. If the four organizers of the raffle each buy oneticket, what is the probability that the four organizers
a) win all of the prizes?
b) win exactly two of the prizes?
c) win exactly one of the prizes?
d) win none of the prizes?
The answers:
a) (4) / (19600)
b) (276) / (19600)
c) (4140) / (19600)
d) (15180) / 19600)
Answer:
The answers are the same you stated.
The calculations are in the step-by-step explanation
Step-by-step explanation:
There are 3 prizes to be distributed among 50 tickets. The order these prizes are distributed does not matter. So the total number of prizes is a combination of 3 from 50.
The formula for a combination of n from m is:
[tex]C(m,n) = \frac{m!}{n!(m-n)!}[/tex]
So, the total number of prizes is:
[tex]T = C(50,3) = \frac{50!}{3!(50-3)!} = \frac{50*49*48*47!}{3!*47!} = 19600[/tex]
what is the probability that the four organizers
a) win all of the prizes?
The number of ways that the four organizers can will all of the prizes is a combination of 3 from 4.
[tex]C(4,3) = \frac{4!}{3!1!} = 4[/tex]
The probability that the win all of the prizes is the number of ways that they can win all the prizes divided by the total numbers of ways that the prizes can be distributed.
[tex]P = \frac{4}{19600}[/tex]
b) win exactly two of the prizes?
The total outcomes(total number of ways that the prizes can be distributed) is 19600.
For them to win exactly two of the prizes, we have a combination of 2 from 4(two organizers win prizes) multiplied by a combination of one from 46(one non-organizers wins a prize), so:
[tex]C(4,2)*C(46,1) = \frac{4!}{2!2!}*\frac{46!}{1! 45!} = 6*46 = 276[/tex]
The probability that they win exactly two of the prizes is
[tex]P = \frac{276}{19600}[/tex]
c) win exactly one of the prizes?
The total outcomes(total number of ways that the prizes can be distributed) is 19600.
For them to win exactly one of the prizes, we have a combination of 1 from 4(one organizer wins a prize) multiplied by a combination of two from 46(two non-organizers win prizes), so:
[tex]C(4,1)*C(46,2) = \frac{4!}{1!3!}*\frac{46!}{2! 44!} = 4*1035 = 4150[/tex]
The probability that they win exactly one prize is
[tex]P = \frac{4150}{19600}[/tex]
d) win none of the prizes?
The total outcomes(total number of ways that the prizes can be distributed) is 19600.
For them to win none of the prizes, we have a combination of 3 from 46(3 prizes distributed among 46 non-organizers). So:
[tex]C(46,3) = \frac{46!}{43!3!} = 15180[/tex]
The probability that they don't win any prize is:
[tex]P = \frac{15180}{19600}[/tex]
The probabilities of winning all of the prizes, winning exactly two of the prizes, winning exactly one of the prizes, and winning none of the prizes are [tex]\rm \dfrac{4}{19600},\dfrac{276}{19600},\dfrac{4140}{19600}, \ and \ \dfrac{15180}{19600}[/tex] respectively.
What is probability?Probability means possibility. It deals with the occurrence of a random event. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
A local fraternity is conducting a raffle where 50 tickets are to be sold one per customer.
There are three prizes to be awarded.
If the four organizers of the raffle each buy one ticket.
The total outcomes will be
[tex]\rm ^{50}C_3 = \dfrac{50!}{47! *3!}\\\\\rm ^{50}C_3 = 19600[/tex]
a) win all of the prizes.
The number of ways the four organizers can win all the prizes is given by
[tex]\rm ^4C_3 = \dfrac{4!}{3! *1!}\\\\\rm ^4C_3 = 4[/tex]
Then the probability of winning all the prizes will be
[tex]\rm Probability = \dfrac{4}{19600}[/tex]
b) win exactly two of the prizes.
The number of ways is 2 from organizers and 1 from non-organizers given by
[tex]\rm ^4C_2 * ^{46}C_1 = \dfrac{4!}{2! *2!}*\dfrac{46!}{45! *1!}\\\\\rm ^4C_2 * ^{46}C_1 = 276[/tex]
Then the probability of 2 from organizers and 1 from non-organizers will be
[tex]\rm Probability = \dfrac{276}{19600}[/tex]
c) win exactly one of the prizes.
The number of ways is 1 from organizers and 2 from non-organizers given by
[tex]\rm ^4C_1 * ^{46}C_2 = \dfrac{4!}{1! *3!}*\dfrac{46!}{44! *2!}\\\\\rm ^4C_1 * ^{46}C_2 = 4140[/tex]
Then the probability of 1 from organizers and 2 from non-organizers will be
[tex]\rm Probability = \dfrac{4140}{19600}[/tex]
d) win none of the prizes.
The number of ways is 3 from non-organizers given by
[tex]\rm ^{46}C_3 = \dfrac{46!}{43! *3!}\\\\\rm ^{46}C_3 = 15180[/tex]
Then the probability of 3 from non-organizers will be
[tex]\rm Probability = \dfrac{15180}{19600}[/tex]
Thus, The probabilities of winning all of the prizes, winning exactly two of the prizes, winning exactly one of the prizes, and winning none of the prizes are [tex]\rm \dfrac{4}{19600},\dfrac{276}{19600},\dfrac{4140}{19600}, \ and \ \dfrac{15180}{19600}[/tex] respectively.
More about the probability link is given below.
https://brainly.com/question/795909
A piece of toast came out of the toaster very overcooked.
What kind of change occurred?
chemical change
change in reaction
phase change
physical change
Answer:
It is a chemical change ⇒ 1st answer
Step-by-step explanation:
* Lets explain the statements to solve the problem
- A chemical change occurs when a new substance is formed through
a chemical reaction
- Ex: cooking an egg
- Change of reaction is the rate of reaction it can be decreases or
increasing
- A phase change is a change from one state to another without a
change in chemical composition
- Ex: Condensation: the substance changes from a gas to a liquid
- A physical change, such as a state change or dissolving, but does
not create a new substance
- Ex: Breaking a glass
* Lets solve the problem
- A piece of toast came out of the toaster very overcooked.
∵ It is like the cooking an egg
∴ It is a chemical change
Answer:
Chemical
Step-by-step explanation:
Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual
has a Visa credit card and B be the analogous event for a MasterCard. Suppose that , P(A)= 0.6 and P(B)=0.4.
a. Could it be the case that P( A ∩ B )=0.5, why or why not?
b. From now on, suppose that P( A ∩ B )=0.3 What is the probability that student has one of these two types of cards?
c. What is the probability that the selected student has neither type of card?
d. Describe in terms of A and B the event that the select student has a visa card, but not a mastercard? and then calulate the probability of this event.
e. Calcuate th probability that the selected student has exactly one of the two types of cards?
Answer:
(a) P( A ∩ B )=0.5 is not possible.
(b) 0.7
(c) 0.3
(d) 0.3
(e) 0.4
Step-by-step explanation:
Given information: The alphabet A and B represents the following events
A : Individual has a Visa credit card.
B: Individual has a MasterCard.
P(A)= 0.6 and P(B)=0.4.
(a)
We need to check whether P( A ∩ B ) can be 0.5 or not.
[tex]A\cap B\subset A[/tex] and [tex]A\cap B\subset B[/tex]
[tex]P(A\cap B)\leq P(A)[/tex] and [tex]P(A\cap B)\leq P(B)[/tex]
[tex]P(A\cap B)\leq 0.6[/tex] and [tex]P(A\cap B)\leq 0.4[/tex]
From these two inequalities we conclude that
[tex]P(A\cap B)\leq 0.4[/tex]
Therefore, P( A ∩ B )=0.5 is not possible.
(b)
Let [tex]P(A\cap B)=0.3[/tex]
We need to find the probability that student has one of these two types of cards.
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Substitute the given values.
[tex]P(A\cup B)=0.6+0.4-0.3=0.7[/tex]
Therefore the probability that student has one of these two types of cards is 0.7.
(c)
We need to find the probability that the selected student has neither type of card.
[tex]P(A'\cup B')=1-P(A\cup B)[/tex]
[tex]P(A'\cup B')=1-0.7=0.3[/tex]
Therefore the probability that the selected student has neither type of card is 0.3.
(d)
The event that the select student has a visa card, but not a mastercard is defined as
[tex]A-B[/tex]
It can also written as
[tex]A\cap B'[/tex]
The probability of this event is
[tex]P(A\cap B')=P(A)-P(A\cap B)[/tex]
[tex]P(A\cap B')=0.6-0.3=0.3[/tex]
Therefore the probability that the select student has a visa card, but not a mastercard is 0.3.
(e)
We need to find the probability that the selected student has exactly one of the two types of cards.
[tex]P(A\cap B')+P(A\cap B')=P(A\cup B)-P(A\cap B)[/tex]
[tex]P(A\cap B')+P(A\cap B')=0.7-0.3[/tex]
[tex]P(A\cap B')+P(A\cap B')=0.4[/tex]
Therefore the probability that the selected student has exactly one of the two types of cards is 0.4.
At lunchtime, Ciaran buys a sandwich.
He can choose white bread or brown bread.
What is the probability that he chooses brown bread?
Answer:
1/2.
Step-by-step explanation:
There are 2 choices and he has to choose 1 , so the answer is 1/2.
Assuming Ciaran has no preference for white or brown bread, and each choice is equally likely, the probability of choosing brown bread is 1/2 or 50%.
The probability that Ciaran chooses brown bread depends on the assumption that he has no preference and that the choices are equally likely. If the only options available to Ciaran are white bread or brown bread, and each choice is equally likely, then the probability of choosing one over the other is 1 out of the total number of options.
In this case, there are 2 options (white or brown), so the probability that Ciaran will choose brown bread is 1/2 or 0.5, which can also be expressed as a 50% chance.
Problem 4.28: People with type O-negative blood are
universaldonors. That is, any patient can receive a transfusion
ofO-negative blood. Only 7% of the American population
haveO-negative blood. If 10 people appear at random to give blood,
whatis the probability that at least 1 of them is a
universaldonor?
Answer: 0.516
Step-by-step explanation:
Binomial probability distribution formula to find the probability of getting success in x trial:-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where n is the number of trials , p is the probability of getting success in each trial.
Given : People with type O-negative blood are universal donors.
The proportion of the American population have O-negative blood =0.07
For n=10, the probability that at least 1 of them is a O-negative blood :-
[tex]P(x\geq1)=1-P(x=0)\\\\=1-[^{10}C_0(0.07)^0(1-0.07)^{10}]\\\\=1-[(1)(1)(0.93)^{10}]\ \ \ [\text{ Since}^nC_0=1]\\\\=1-0.483982307179\approx1-0.4840=0.516[/tex]
Hence, the probability that at least 1 of them is a universal donor = 0.516
what is the value of cos (L)?
Use the roster method to write each of the given sets. For some exercises you may need to consult a reference, such as the Internet or an encyclopedia. (Enter EMPTY for the empty set.)
The set of natural numbers x that satisfy x + 2 = 1
There are no natural numbers that satisfy the equation x + 2 = 1. Therefore, using the roster method, the set is empty.
Explanation:The question requires us to use the roster method to write the set of natural numbers x that satisfy the equation x + 2 = 1. Natural numbers, by definition, are counting numbers starting from 1. They are non-negative and do not include zero. So, if we try to find a natural number x that satisfies the equation x + 2 = 1, we see that x would need to be -1 (since -1 + 2 equals 1). However, -1 is not a natural number. Therefore, there are no natural numbers that satisfy the equation, so the set is empty.
Learn more about the Roster Method here:https://brainly.com/question/28709089
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The set of natural numbers x that satisfy x + 2 = 1. The correct answer is EMPTY.
To solve the equation x + 2 = 1 for natural numbers x we would first try to isolate x subtracting 2 from both sides of the equation:
x + 2 - 2 = 1 - 2
x = -1
However, natural numbers are defined as the set of positive integers, starting from 1 and increasing indefinitely.
Since the solution to the equation x = -1 is not a positive integer, it does not belong to the set of natural numbers. Therefore, there is no natural number x that satisfies the equation x + 2 = 1
Since there are no elements that satisfy the condition, the set is empty. Hence, the correct representation of the set using the roster method is EMPTY.
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 8686 people in the 18-21 age bracket and finds that 4343 of them respond and 4343 refuse to respond. When 276276 people in the 22-29 age bracket are contacted, 258258 respond and 1818 refuse to respond. Suppose that one of the 362362 people is randomly selected. Find the probability of getting someone in the 18 dash 2118-21 age bracket or someone who respondedresponded.
Answer:
0.9503
Step-by-step explanation:
First of all, there are some wrong figures in the original text. Because there is a total of 362362 people, the figures should be 86086 (people in the 18-21 age bracket), 43043 (people in the 18-21 age bracket who respond) and 43043 people in the 18-21 age bracket who refuse to respond. In the same way, because there are 276276 people in the 22-29 age bracket, it should be 18018 and not 1818 who refuse to respond in this subset of people. Now, let's define the following events:
R: a person respond
A: a person belongs to the 18-21 age bracket. So,
The number of people who respond is 43043 + 258258 = 301301, so
P(R) = 301301/362362 = 0.8315
P(A) = 86086/362362 = 0.2376
P(R | A) = 43043/86086 = 0.5
We are looking for P(A∪R) = P(A) + P(R) - P(A∩R),
P(A∩R) = P(R | A)P(A) = (0.5)(0.2376) = 0.1188, so,
P(A∪B) = 0.2376 + 0.8315 - 0.1188 = 0.9503
1,787 pages in 11 days = pages in 1 month
assuming 30 days per month.
[tex]\bf \begin{array}{ccll} pages&days\\ \cline{1-2} 1787&11\\ x&30 \end{array}\implies \cfrac{1787}{x}=\cfrac{11}{30}\implies 53610=11x \\\\\\ \cfrac{53610}{11}=x\implies 4873\frac{7}{11}=x[/tex]
Answer: 4873.64
Step-by-step explanation:
I'm assuming that you're asking how many pages there are in a month. On average, the typical month is 30 days, correct? We can plug this information into proportions.
1787/11 = x/30
1787 multiplied by 30 is 53610, and that divided by 11 would be 4873.64, when rounded to the nearest hundredth.
I hope that helped!
Solve the initial value problem: dydx+5y=7 y(0)=0
Answer:
Given differential equation,
[tex]\frac{dy}{dx}+5y=7[/tex]
[tex]\frac{dy}{dx}=7-5y[/tex]
[tex]\implies \frac{dy}{7-5y}=dx[/tex]
Taking integration both sides,
[tex]\int \frac{dy}{7-5y}=\int dx[/tex]
Put 7 - 5y = u ⇒ -5 dy = du ⇒ dy = -du/5,
[tex]-\frac{1}{5} \int \frac{du}{u} = \log x + C[/tex]
[tex]-\frac{1}{5} \log u = \log x + C[/tex]
[tex]-\frac{1}{5}\log(7-5y) = \log x + C---(1)[/tex]
Here, x = 0, y = 0
[tex]\implies -\frac{1}{5} \log 7= C[/tex]
Hence, from equation (1),
[tex]-\frac{1}{5}\log(7-5y)=\log x -\frac{1}{5}log 7[/tex]
[tex]\log(7-5y)=\log (\frac{x}{7^\frac{1}{5}})[/tex]
[tex]7-5y=\frac{x}{7^\frac{1}{5}}[/tex]
[tex]7-\frac{x}{7^\frac{1}{5}}=5y[/tex]
[tex]\implies y=\frac{1}{5}(7-\frac{x}{7^\frac{1}{5}})[/tex]
Suppose you buy a new car whose advertised mileage is 20 miles per gallon (mpg). After driving your car for several months, you find that its mileage is 16.4 mpg. You telephone the manufacturer and learn that the standard deviation of gas mileages for all cars of the model you bought is 1.14 mpg. a. Find the z-score for the gas mileage of your car, assuming the advertised claim is correct. b. Does it appear that your car is getting unusually low gas mileage? a. zequals nothing (Round to two decimal places as needed.) b. Does it appear that your car is getting unusually low gas mileage? Yes No
Answer:
a) The z-score for the mileage of the car is -3.16
b) It appears that the car is getting unusually low gas mileage.
Step-by-step explanation:
The z-score formula is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which: X is the mileage per gallon we are going to find the z-score of, [tex]\mu[/tex] is the mean value of this mileage and [tex]\sigma[/tex] is the standard deviation of this value.
a. Find the z-score for the gas mileage of your car, assuming the advertised claim is correct.
The gas mileage for you car is 16.4 mpg, so [tex]X = 16.4[/tex]
The advertised gas mileage is 20 mpg, so [tex]\mu = 20[/tex]
The standard deviation is 1.14 mpg, so [tex]\sigma = 1.14[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma} = \frac{16.4 - 20}{1.14} = -3.16[/tex]
b. Does it appear that your car is getting unusually low gas mileage?
The general rule is that a z-score lower than -1.96 is unusually low. So yes, it appears that the car is getting unusually low gas mileage.
To find the z-score for the gas mileage of your car, use the formula z = (x - μ) / σ. A z-score of -3.16 indicates that your car is getting unusually low gas mileage as it is more than 3 standard deviations below the mean.
Explanation:To find the z-score for the gas mileage of your car, we can use the formula:
z = (x - μ) / σ
where x is the observed mileage, μ is the mean mileage, and σ is the standard deviation.
In this case, since the advertised mileage is 20 mpg, we have:
z = (16.4 - 20) / 1.14 = -3.16
For part b, a z-score of -3.16 indicates that your car is getting unusually low gas mileage as it is more than 3 standard deviations below the mean. Therefore, the answer is Yes.
Look online for the growth of the trunk of a tree. Estimate how much time does it take for a water oak to grow one inch in diameter. Estimate the growth rate over a year
Answer:
Explained
Step-by-step explanation:
The trunk of a tree grows in two different ways, first in height and second in diameter.Usually tree grows one ring per year in diameter. So, counting the number of rings we can determine the age of a tree. Both height and diameter growth does not occur at the same rate. Tree grows more in height than in their diameter. Mature trees usually grows 1 inch in diameter every year.
Water oak gains 24 inches in height every year and 1.5 inch growth in diameter annually, meaning if we divide 1.5 inches by 12 months we gets 0.125 inches growth monthly. So a water oak tree needs only 8 months to grow 1 inch in diameter.
suppose you deposit $1000 in an account paying 4.6% annual interest compounded continuously. How long will it take for the money to double?
Answer: About 16 years
Step-by-step explanation:
The formula to find the compound amount if compounded continuously is given by :-
[tex]A=Pe^{rt}[/tex], where P is Principal amount, r is the rate of interest ( in decimal) and t is time ( in years).
Given : P= $1000 ; r= 4.6%=0.046
let t be the time it will take to double the amount, the we have
[tex]2(1000)=(1000)e^{0.046\times t}[/tex]
Dividing 1000 both sides, we get
[tex]2=e^{0.046 t}[/tex]
Taking natural log on each side, we get
[tex]\ln2=\ln(0.046\times t)\\\\\Rightarrow\ 0.6931=0.046t\\\\\Rightarrow\ t=\dfrac{0.6931}{0.046}=15.0673913043\approx16\text{ years}[/tex]
Hence, it will take about 16 years to double the amount.
Express the following relations in the set builder notation. Then, determine whether it is reflexive, symmetric, transitive. Please show work.
a.) One number is less than or equal to another.
b.) One integer is a factor of another.
c.) Two integers are unequal.
d.) One set is a subset of another.
Answer:
a)Reflexive, not symmetric, transitive
b)Reflexive, not symmetric, transitive
c)Not reflexive, symmetric, not transitive
d)Reflexive, not symmetric, transitive
Step-by-step explanation:
a)
[tex]R=\left \{ (a,b)\epsilon \mathbb{R} \times \mathbb{R} \mid a \leq b\right \}[/tex]
The relation R is reflexive for
[tex]a\leq a[/tex] for every real number a
it is not symmetric because 0 is less than 1, but 1 is not less than 0
it is transitive
[tex]a\leq[/tex] and [tex] b\leq c\Rightarrow a\leq c[/tex]
So if aRb and bRc, then aRc
b)
[tex]R=\left \{ (m,n)\epsilon \mathbb{Z} \times \mathbb{Z} \mid \exists k\in \mathbb{Z} \ni m=kn \right \}[/tex]
R is reflexive because m=1.m for every integer m
R is not symmetric: 2 is a factor of 4, but 4 is not a factor of 2
R is transitive: if mRn and nRp if m=kn and n=qp, so m=(kq)p and kq is an integer , so mRp
c)
[tex]R=\left \{ (m,n)\epsilon \mathbb{Z} \times \mathbb{Z} \mid m\neq n\right \}[/tex]
R is obviously not reflexive because all numbers equals themselves
R is symmetric: if a different to b, then b different to a
R is not transitive: 1R2 and 2R1 (because 1 different to 2), but 1 = 1
d)
[tex]R=\left \{ A,B\mid A\subseteq B \right \}[/tex]
R is reflexive for every set A is a subset of itself
R is not symmetric {1,2} is a subset of {1,2,3} but {1,2,3} is not a subset of {1,2}
R is transitive: if A is subset of B and B is subset of C, then A is subset of C
Plot another sin function of 20% higher frequency over the same range.
Step-by-step explanation:
The frequency of sine function is given by the number of periods in a given range. For example:
Frequency for [tex]sin(x)[/tex] is 1 in the interval [tex][0,2\pi][/tex].This means that, if we want another sine function with frequency 20% higher, we need that function to have a frequency of 1.2 in the interval [tex][0,2\pi][/tex].
To be easier to see we will consider interval [tex][0,10\pi][/tex] instead of [tex][0,2\pi][/tex]. In this interval [tex]sin(x)[/tex] has 5 periods, therefore our new sine function should have 6 periods.
Finally, as we can see in the graph, the function [tex]sin(\frac{6}{5}x )[/tex] (in blue) has a frequency 20% higher than [tex]sin(x)[/tex] (in red). This can be easily seen counting the number of periods between 0 and [tex]10\pi[/tex] for both functions. 5 for [tex]sin(x)[/tex] and 6 for [tex]sin(\frac{6}{5} x)[/tex].
Suppose a manufacturer sells a product as $2 per unit. If q units are sold, (a) write the total revenue function, (b) and find the marginal revenue function. What does the constant marginal revenue function mean?
Answer:
We are given that a manufacturer sells a product as $2 per unit.
Quantity = q units
So, Total revenue = [tex]\text{Cost per unit} \times quantity[/tex]
Total revenue = [tex]2q[/tex]
So, the total revenue function is [tex]2q[/tex]
Marginal revenue is the derivative of the revenue functions
So, Marginal revenue = [tex]\frac{dR}{dq} =2[/tex]
The marginal revenue function is 2
The constant marginal revenue function mean that the revenue earned by the addition of the output is constant.