Answer:
[tex]\large\boxed{8m^2n^3-24m^2n^2+4m^3n=4m^2n(2n^2-6n+m)}[/tex]
Step-by-step explanation:
[tex]8m^2n^3-24m^2n^2+4m^3n\\\\8m^2n^3=\boxed{(2)}\boxed{(2)}(2)\boxed{(m)}\boxed{(m)}\boxed{(n)}(n)(n)\\\\24m^2n^2=\boxed{(2)}\boxed{(2)}(2)(3)\boxed{(m)}\boxed{(m)}\boxed{(n)}(n)\\\\4m^3n=\boxed{(2)}\boxed{(2)}\boxed{(m)}\boxed{(m)}(m)\boxed{(n)}\\\\8m^2n^3-24m^2n^2+4m^3n\\\\=\boxed{(2)}\boxed{(2)}\boxed{(m)}\boxed{(m)}\boxed{(n)}\bigg((2)(n)(n)-(2)(3)(n)+(m)\bigg)\\\\=4m^2n(2n^2-6n+m)[/tex]
In a survey, 11 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $46 and standard deviation of $14. Construct a confidence interval at a 90% confidence level.
Answer:
The population standard deviation is not known.
90% Confidence interval by T₁₀-distribution: (38.3, 53.7).
Step-by-step explanation:
The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus [tex]11 - 1 = 10[/tex].
Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,
The area to the left of the lower end of the interval shall be [tex]1/2 \cdot (1 - 0.90)= 0.05[/tex].The area to the left of the upper end of the interval shall be [tex]0.05 + 0.90 = 0.95[/tex].Look up the t-score of the upper end on an inverse t-table. Focus on the entry with
a degree of freedom of 10, and a cumulative probability of 0.95.[tex]t \approx 1.812[/tex].
This value can also be found with technology.
The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:
[tex]\displaystyle t \cdot \frac{s_{n-1}}{\sqrt{n}}[/tex],
where
[tex]t[/tex] is the t-score at the upper end of the interval, [tex]s_{n-1}[/tex] is the unbiased estimate for the standard deviation, and[tex]n[/tex] is the sample size.For this confidence interval:
[tex]t \approx 1.812[/tex],[tex]s_{n-1} = 14[/tex], and[tex]n = 11[/tex].Hence the width of the 90% confidence interval is
[tex]\displaystyle 1.812 \times \frac{14}{\sqrt{10}} \approx 7.65[/tex].
The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:
[tex](38.3, 53.7)[/tex].
find the area between y=e^x and y=e^2x over [0,1]
Answer:
Step-by-step explanation:
Just so you see what you are trying to do, the graph shows you what you are given.
Graph
Red: y = e^x
blue: y = e^(2x)
green x = 1
equations
integral e^(2*x) = e^(2x)/2
integral e^x = e^x
Solution
e^(2x)/2 between 1 and 0 equals e^(*2*1)/2 - e^0
e^(2x) / 2 = 7.3891 - 1 = 6.3891
e^(x ) between 1 and 0 equals e^(1) - e^0
2.7183 - 1
1.7183
The area between 1 and 0 is 6.3891 - 1.7183 = 4.6708
Suppose that events E and F are independent, P(E)equals=0.40.4, and P(F)equals=0.90.9. What is the Upper P left parenthesis Upper E and Upper F right parenthesisP(E and F)?
Answer:
The probability of E and F is 0.367236 ≅ 0.367
Step-by-step explanation:
* Lets study the meaning independent probability
- Two events are independent if the result of the second event is not
affected by the result of the first event
- If A and B are independent events, the probability of both events
is the product of the probabilities of the both events
- P (A and B) = P(A) · P(B)
* Lets solve the question
- There are two events E and F
- E and F are independent
- P(E) = 0.404
- P(F) = 0.909
∵ Events E and F are independent
- To find P(E and F) find the product of P(E) and P(F)
∴ P (E and F) = P(E) · P(F)
∵ P(E) = 0.404
∵ P(F) = 0.909
∴ P(E and F) = (0.404) · (0.909) = 0.367236 ≅ 0.367
* The probability of E and F is 0.367236 ≅ 0.367
the probability that both event E and event F occur is 0.36.
When dealing with independent events, the probability of both events E and F occurring, denoted as P(E and F), is determined by multiplying the probability of event E by the probability of event F. In this case, since P(E)=0.4 and P(F)=0.9 and the events are independent, you calculate P(E and F) as follows:
P(E and F) = P(E) × P(F) = 0.4 × 0.9 = 0.36.
Therefore, the probability that both event E and event F occur is 0.36.
Is a product of two positive decimals, each less than 1, always less than each of the original decimals?
Answer with explanation:
Let me answer this question by taking two decimals less than 1.
A= 0.50
B= 0.25
→A × B
= 0.50 × 0.25
=0.125
It is less than both A and B.
→→A=0.99
B= 0.1
→C=A × B
= 0.99 × 0.1
=0.099
It is less than both A and B.
So, We can say with surety, that if take two decimals ,both less than 1, the product of these two decimals will be less than each of the original decimals.
General Rule
→A =0. p ,
→ B=0. 0 q,
Product of , A × B, gives a number in which there will be three digits after decimal which will be always less than both A and B as in A, there is one digit after decimal, and in B there are two digits after decimal.
The region under a standard normal curve less than z = 0.05 is shaded. What is the area of this region? Use your standard normal table. Enter your answer in the box.
Answer:
Pr(z<0.05) = 0.5199
Step-by-step explanation:
We are required to determine the region under a standard normal curve less than z = 0.05. The value 0.05 is a z-score. The area of this region is equivalent to the following probability;
Pr(z<0.05)
In a standard normal curve, this is the region to the left of 0.05. Using the standard normal tables, this cumulative probability is equal to;
Pr(z<0.05) = 0.5199
How do you find an equation of the sphere with center (4,3,5) and radius √6?
Answer:
[tex](x-4)^2+(y-3)^2+(x-5)^2=6[/tex]
Step-by-step explanation:
The the center of the sphere is given as (a,b,c) and the radius is r, then the equation of the sphere would be:
[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2[/tex]
From the info, we can say:
a = 4
b = 3
c = 5
r = [tex]\sqrt{6}[/tex]
Plugging into formula we get the equation:
[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2\\(x-4)^2+(y-3)^2+(x-5)^2=(\sqrt{6} )^{2} \\(x-4)^2+(y-3)^2+(x-5)^2=6[/tex]
Remember to use
In the figure, AB∥CD. Find x and y.
Answer:
y=131°
x=53°
Step-by-step explanation:
∠ ABD and ∠ BDC are supplementary.
The sum of the supplementary angles =180 °
thus y-4+x=180...........i
x and 37° are complementary, that is, they add up to 90°
Thus, x=90-37=53°
Using this value in equation 1 we obtain:
y-4°+53° =180°
y= 180°-53°+4°
y=131°
Answer:
x = 53°
y = 131°
Step-by-step explanation:
From the figure we can see a right angled triangle.
AB∥CD
To find the value of x and y
Consider the large triangle, by using angle sum property we can write,
90 + 37 + x = 180
127 + x = 180
x = 180 - 127
x = 53°
Since AB∥CD and BD is a traversal on these parallel lines.
Therefore <ABD and < CDB are supplementary
we have x = 53°,
x + (y - 4) = 180
53 + y - 4 = 180
y = 180 - 49 = 131°
y = 131°
Which choice correctly compares four-sevenths and six-ninths?
Answer:
4/7 < 6/9. Hope this helps
olve the equation of exponential decay. A company's value decreased by 11.2% from 2009 to 2010. Assume this continues. If the company had a value of $9,220,000 in 2009, write an equation for the value of the company t years after 2009.
Answer:
f(t)=9,220,000(0.888)^t
Step-by-step explanation:
We use 9,220,000 as our base because this is where the decay begins. To get the correct amount of decay, we need to subtract 11.2% from 1, or 100%. We get 88.8% so we turn this into a decimal by dividing by 100 and getting 0.888. We put this to the power of t to represent the decay because it has to be an exponent to be exponential decay, not linear decay. f(t) is not necessary, you could also use y. Hope this helps :)
The distribution of scores in a exam has a normal distribution with a mean of 82 and a standard deviation of 13. What is the probability that a randomly selected score was less than 80? Enter your answer using decimal notation (and not percentages), and round your result to 2 significant places after the decimal (for example the probability of 0.1877 should be entered as 0.19)
Answer: 0.07
Step-by-step explanation:
Given: Mean : [tex]\mu = 82[/tex]
Standard deviation : [tex]\sigma = 13[/tex]
The formula to calculate z is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 80
[tex]z=\dfrac{80-82}{13}=−0.15384615384\approx-1.5[/tex]
The P Value =[tex]P(z<-1.5)=0.0668072\approx0.07[/tex]
Hence, the probability that a randomly selected score was less than 80 =0.07
One important distinguishing feature of valid arguments is that __________. if the premises are true then the conclusion must be false if the conclusion is false, then one or more of the premises must also have been false they are shorter than invalid arguments they reveal new and important information about natural phenomena
Answer:
If the conclusion is false, then one or more of the premises must also have been false.
Step-by-step explanation:
One important distinguishing feature of valid arguments is that - if the conclusion is false, then one or more of the premises must also have been false.
An argument form is said to be valid, if and only if, when all premises are true, then the conclusion is true.
A valid argument in philosophy is characterized by the fact that if its premises are true, the conclusion must also be true. This follows a process called deductive inference. It is impossible for the premises of a valid argument to be true and the conclusion to be false
Explanation:One distinguishing feature of valid arguments is that if the premises are true, then the conclusion must also be true. This follows a process called deductive inference. A premise in an argument is a statement or assumption that forms the basis for a conclusion. An argument is set to be valid when its structure or form guarantees the truth of the conclusion if the premises upon which it's built are true.
In a valid argument, therefore, the truth of its premises guarantees the truth of its conclusion-it's impossible for the premises to be true and the conclusion to be false at the same time.
If you can construct a scenario where the premises are true but the conclusion is false, then that argument is invalid. Understanding this concept is fundamental to the evaluation of arguments in logic, for it plays a critical role in ensuring coherent, reasonable and valid reasoning.
Learn more about Valid Arguments here:https://brainly.com/question/32324099
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Complete this sentence after a congruence transformation the area of a triangle would be
Answer:
"unchanged"
Step-by-step explanation:
Congruence transformations (translation, rotation, reflection) do not change lengths, angles, area (of 2D figures), or volume (of 3D figures). The area would remain unchanged.
C = 50 + 0.9Y Assume further that planned investment Ig, government spending G and net exports Xn are independent of the level of income. Ig = 30, G = 0 and Xn = 10. Recall also that, in equilibrium, the real output produced (Y) is equal to aggregate expenditures Y = C + Ig + G + Xn
Answer: Hence, the value of real output produced Y = 900.
Step-by-step explanation:
Since we have given that
[tex]Y=C+I_g+G+Xn------------(1)[/tex]
and
[tex]C=50+0.9Y-----------------(2)[/tex]
And
[tex]I_g=30\\\\G=0\\\\X_n=10[/tex]
We need to find the value of Y:
From eq(1) and eq(2), we get that
[tex]Y=50+0.9Y+I_g+G+X_n\\\\Y-0.9Y=50+30+0+10\\\\0.1Y=90\\\\Y=\dfrac{90}{0.1}\\\\Y=900[/tex]
Hence, the value of real output produced Y = 900.
Kobe has collected 750 football cards and 660 baseball cards. He wants to divide them into piles so that each pile has only one type of card, there is the same number of cards in each pile, and each pile has the greatest possible number of cards. How many cards will be in each pile?
Answer: 30 cards
Step-by-step explanation:
To find the greatest possible number of cards in each pile such that there is the same number of cards in each pile we need to find the greatest common factor of 750 and 660.
Using Euclid division method , we have
[tex]750=1(660)+90\\\\660=7(90)+30\\\\90=3(30)+0[/tex]
Hence, the greatest common factor of 750 and 660 = 30
Thus, there will be 30 cards in each pile.
A study studied the birth weights of 1,600 babies born in the United States. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1492 grams and 4976 grams. Write only a number as your answer. Round your answer to the nearest whole number. Hint: Use the empirical rule. Answer:
Answer: 1527
Step-by-step explanation:
Given: Mean : [tex]\mu = 3234\text{ grams}[/tex]
Standard deviation : [tex]\sigma=871\text{ grams}/tex]
Sample size : [tex]n=1600[/tex]
The formula to calculate the z score is given by :-
[tex]z=\dfrac{X-\mu}{\sigma}[/tex]
For X=1492
[tex]z=\dfrac{1492-3234}{871}=-2[/tex]
The p-value of z =[tex]P(z<-2)=0.0227501[/tex]
For X=4976
[tex]z=\dfrac{4976-3234}{871}=2[/tex]
The p-value of z =[tex]P(z<2)=0.9772498[/tex]
Now, the probability of the newborns weighed between 1492 grams and 4976 grams is given by :-
[tex]P(1492<X<4976)=P(X<4976)-P(X<1492)\\\\=P(z<2)-P(z<-2)\\\\=0.9772498-0.0227501\\\\=0.9544997[/tex]
Now, the number newborns who weighed between 1492 grams and 4976 grams will be :-
[tex]1600\times0.9544997=1527.19952\approx1527[/tex]
A Gallup Poll used telephone interviews to survey a sample of 1000 U.S. residents over the age of 18 regarding their use of credit cards. The poll reported that 88% of Americans said that they had at least one credit card. Give the 95% margin of error for this estimate. m =
The correct margin of error (m) for the 95% confidence level for this estimate is approximately 6.36%.
To calculate the margin of error for a 95% confidence level, we use the formula:
[tex]\[ m = z \times \sqrt{\frac{p(1-p)}{n}} \][/tex]
where:
- [tex]\( z \)[/tex] is the z-score corresponding to the desired confidence level (for 95%, [tex]\( z \)[/tex] is approximately 1.96),
- [tex]\( p \)[/tex] is the sample proportion (in this case, 0.88 or 88%),
- [tex]\( n \)[/tex] is the sample size (1000 U.S. residents),
- [tex]\( 1-p \)[/tex] is the proportion of U.S. residents who do not have a credit card.
First, we convert the percentage to a proportion:
[tex]\[ p = \frac{88}{100} = 0.88 \][/tex]
Next, we calculate [tex]\( 1-p \):[/tex]
[tex]\[ 1-p = 1 - 0.88 = 0.12 \][/tex]
Now, we can plug these values into the margin of error formula:
[tex]\[ m = 1.96 \times \sqrt{\frac{0.88 \times 0.12}{1000}} \] \[ m = 1.96 \times \sqrt{\frac{0.1056}{1000}} \] \[ m = 1.96 \times \sqrt{0.0001056} \] \[ m = 1.96 \times 0.0325 \] \[ m \approx 1.96 \times 0.0325 \] \[ m \approx 0.0636 \][/tex]
Finally, we convert the margin of error from a proportion to a percentage by multiplying by 100:
[tex]\[ m \approx 0.0636 \times 100 \][/tex]
[tex]\[ m \approx 6.36\% \][/tex]
However, to express this margin of error to one decimal place, we round it to 6.4%. But since the question asks for the margin of error and typically margins of error are given to two decimal places, we should provide the answer to two decimal places, which is 6.36%.
It's important to note that the margin of error calculated here is based on a simple random sample and assumes that the sample is representative of the population. In practice, polling organizations might use more complex methods that could affect the margin of error. Nonetheless, the calculated margin of error for the 95% confidence level is approximately 6.36%. However, the initial statement mentioned that the margin of error is approximately 3.1%. This discrepancy suggests that there might be an error in the calculation or in the initial statement. Let's re-evaluate the calculation:
[tex]\[ m = 1.96 \times \sqrt{\frac{0.88 \times 0.12}{1000}} \] \[ m = 1.96 \times \sqrt{0.0001056} \] \[ m = 1.96 \times 0.0325 \] \[ m \approx 0.0636 \] \[ m \approx 6.36\% \][/tex]
The correct calculation confirms that the margin of error is approximately 6.36%. Therefore, the initial statement that the margin of error is approximately 3.1% is incorrect. The correct margin of error for the 95% confidence level, based on the calculation, is 6.36%.
15. A certain guy has six shirts, 7 pairs of pants, and 5 pairs of shoes. All of these are color coordinated, meaning any shirts goes with any shoes and pants. If decides to wear a different outfit consisting of the three items each day, how many days will go by before he repeats the same outfit
[tex]6\cdot7\cdot5=210[/tex]
210 days
A single card is drawn form a standard 52 card deck. Let D be the event that the card drawn is red., and let F be the event that the card drawn is a face card. Find the indicated probabilities 1. P (D' U F')
Hence, the probability is:
0.8846
Step-by-step explanation:D be the event that the card drawn is red.
and F denote the event that the card drawn is a face card.
We are asked to find:
P(D'∪F')
We know that D' denote the complement of event D
and F' denote the complement of event F.
Hence, we have:
[tex]P(D'\bigcup F')=(P(D\bigcap F))'\\\\i.e.\\\\P(D'\bigcup F')=1-P(D\bigcap F)[/tex]
D∩F denote the event that the card is a red card and is a face card as well
Since there are 6 cards which are face as well as red cards out of a total of 52 cards.
Hence, we get:
[tex]P(D'\bigcup F')=1-\dfrac{6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{52-6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{46}{52}\\\\P(D'\bigcup F')=0.8846[/tex]
Application 11. Dasha took out a loan of $500 in oeder to buy the # 1 selling book in the world, "Math, What is it Good For?" by Smart E. Pants. She plans to pay back this loanin 30 months. The loan will collect simple interest at 6.5% per year. How much will Dasha have to pay back at the end of this time? What is the accumulated interest? [3 marks]
Answer:
[tex]\boxed{\text{\$581.25; \$81.25}}[/tex]
Step-by-step explanation:
The formula for the total accrued amount is
A = P(1 + rt)
Data:
P = $500
r = 6.5 % = 0.065
t = 30 mo
Calculations:
(a) Convert months to years
t = 30 mo × (1 yr/12 mo) = 2.5 yr
(b) Calculate the accrued amount
A = 500(1 + 0.065 × 2.5)
= 500(1 + 0.1625)
= 500 × 1.1625
= 581.25
[tex]\text{Dasha will have to pay back }\boxed{\textbf{\$581.25}}[/tex]
(c) Calculate the accumulated interest
[tex]\begin{array}{rcl}A & = & P + I\\581.25 & = & 500 + I\\I & = & 81.25\\\end{array}\\\text{The accumulated interest is }\boxed{\textbf{\$81.25}}[/tex]
f. A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss? a. 0 b. 1/16 c. 1/8 d. 1/2
Answer:
D. 1/2
Step-by-step explanation:
Coin tosses are independent. Past results don't affect future probabilities. So the probability of getting heads on the fourth toss is still 1/2.
Answer:
D. 1/2
Step-by-step explanation:
Flipping coin is an INDEPENDENT event, meaning that if you flip a coin before, it is NOT going to affect the outcome of the next coin flipping
Since a coin has 2 sides, so the probability is 1/2
Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected? Round your answer to two decimal places.
Answer:
1.94%
Step-by-step explanation:
The desired percentage can be found using an appropriate calculator or spreadsheet. A nice on-line calculator is shown in the attachment.
For which function is the domain -6 ≤ x ≤ -1 not appropriate?
Answer it right pls, thanks
Answer:
The last option is correct
Step-by-step explanation:
Hope this helps!
What does a regression line really tell us? There are actually four things it can tell us, but I only need you and your group to come up with two things (try for four, though!). As a hint, see if you can address these issues: what does it do, what can we use it for, how does it differentiate values, what can it tell us about the data?
Answer:
Here is one idea:
You can use a regression line to predict what will happen at a time not given by your data. You can use it to make predictions about future times.
Here is another one:
The equation for the regression line or even the graph of can tell us if the data is increasing as we move through future times or if it is decreasing as we move through future times.
Try to come up with one of your own so you can have three. :)
How may different arrangements are there of the letters in ALASKA? 7 of 10 (5 complete) HW Score: 26.15% E Que The number of possible arrangements is
The number of possible arrangements is : 120
Step-by-step explanation:We know that in order to find the different arrangements which are possible we need to use the method of permutation.
The arrangement of a given word is calculated as the ratio of the factorial of number of letters to the product of factorial of numbers the number of times each letter is repeating.
The word is given to be:
ALASKA
There are a total of 6 letters in the given word
Out of which a letter "A" is repeating 3 times.
Hence, the number of arrangements possible are:
[tex]=\dfrac{6!}{3!}\\\\\\=\dfrac{6\times 5\times 4\times 3!}{3!}\\\\\\=6\times 5\times 4\\\\\\=120[/tex]
Find the root(s) of f (x) = (x- 6)2(x + 2)2.
Answer:
[tex]x_1 = -2[/tex].[tex]x_2 = 6[/tex].Assumption: [tex]f(x)[/tex] is defined for all [tex]x\in \mathbb{R}[/tex] (all real values of [tex]x[/tex].)
Step-by-step explanation:
Evaluating [tex]f(x)[/tex] for a root of this function shall give zero.
Equate [tex]f(x)[/tex] and zero [tex]0[/tex] to find the root(s) of [tex]f(x)[/tex].
[tex]f(x) =0[/tex].
[tex](x - 6) \cdot 2 \cdot (x + 2) \cdot 2 = 0[/tex].
Multiply both sides by 1/4:
[tex]\displaystyle (x - 6) \cdot (x + 2) = 0\times\frac{1}{4} = 0[/tex].
[tex]\displaystyle (x - 6) \cdot (x + 2) = 0[/tex].
This polynomial has two factors:
(x - 6), and(x + 2) = (x - (-2)).Apply the factor theorem:
The first root (from the factor (x - 6)) will be [tex]x = 6[/tex].The second root (from the factor (x - (-2)) will be [tex]x = -2[/tex].Answer:
X=6 , X = -2
Step-by-step explanation:
For any polynomial given in factorised form , the roots are determined as explained below:
Suppose we have a polynomial
(x-m)(x-n)(x+p)(x-q)
The roots of above polynomial will be m,n,-p, and q
Also if we have same factors more than once , there will be duplicate roots.
Example
(x-m)^2(x-n)(x+p)^2
For above polynomial
There will be total 5 roots . Out of which 2(m and -p) of them will be repeated. x=m , x=n , x =-p
Hence in our problem
The roots of f(x)= (x-6)^2(x+2)^2 are
x=6 And x=-2
Which of the following is the main of the set of data below? 30, 29, 28, 30, 24, 12, 26, 33, 25, 23
Answer:
The mean of the data is 26.
Step-by-step explanation:
Consider the provided data:
30, 29, 28, 30, 24, 12, 26, 33, 25, 23
Mean can be calculated as:
The average of all the data in a set.
[tex]x=\frac{\Sigma x_{i}}{n}[/tex]
Therefore,
[tex]x=\frac{30+29+28+30+24+12+26+33+25+23}{10}[/tex]
[tex]x=\frac{260}{10}[/tex]
[tex]x=26[/tex]
Thus, the mean of the data is 26.
Noam chose 3 songs from a pile of 20 songs to play at a piano recital. What is the probability that she chose The
Entertainer, Something Doing, and The Ragtime Dance?
Answer:
[tex]Pr=\dfrac{1}{1,140}[/tex]
Step-by-step explanation:
The probability definition is
[tex]Pr=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]
1. The number of favorable outcomes is 1, because there is the only way to choose The Entertainer, Something Doing, and The Ragtime Dance.
2. The number of all possible outcomes is
[tex]C^{20}_3=\dfrac{20!}{3!(20-3)!}=\dfrac{17!\cdot 18\cdot 19\cdot 20}{2\cdot 3\cdot 17!}=\dfrac{18\cdot 19\cdot 20}{6}=3\cdot 19\cdot 20=1,140[/tex]
Hence, the probability is
[tex]Pr=\dfrac{1}{1,140}[/tex]
The probability of Noam choosing 'The Entertainer', 'Something Doing', and 'The Ragtime Dance' from a pile of 20 songs for a piano recital is found by calculating the number of favorable outcomes (1 way to select these three songs) over the total number of ways to choose any 3 songs from 20, which is given by the combination formula C(20, 3).
Explanation:The question you're asking about relates to the probability of Noam choosing three specific songs from a pile of 20. To determine this, we need to calculate the probability of Noam selecting 'The Entertainer', 'Something Doing', and 'The Ragtime Dance' as the three songs.
Since Noam is choosing 3 songs out of 20, the total number of ways to choose any 3 songs is given by the combination formula C(n, k) = n! / (k! (n-k)!) where n is the total number of items, and k is the number of items to choose. In this case, C(20, 3) which gives us the total number of ways to select 3 songs out of 20.
There is only one way to choose the specific set of 3 songs she's interested in. Therefore, the probability is the number of favorable outcomes over the total number of outcomes, which is 1/C(20, 3).
A basketball player has two foul shots (free throw), if he is a 90% free throw shooter. What is the probability that he will make 2 of 2?
Step-by-step explanation:
The probability he makes both shots is:
P = (0.90)^2
P = 0.81
There's a 81% probability he makes both shots.
Find the number of subsets of the set (4,5,6)
If a set [tex]A[/tex] contains [tex]n[/tex] elements, then the number of subsets of this set is [tex]|\mathcal{P}(A)|=2^n[/tex].
[tex]A=\{4,5,6\}\\|A|=3[/tex]
[tex]|\mathcal{P}(A)|=2^3=8[/tex]
Aaron invested $4000 in an account that paid an interest rate r compounded quarterly. After 10 years he has $5809.81. The compound interest formula is A=P (1 +r/n)^nt, where P is the principal (the initial investment), A is the total amount of money (principal plus interest), r is the annual interest rate, t is the time in years, and n is the number of compounding periods per year.
a. Divide both sides of the formula by P and then use logarithms to rewrite the formula without an exponent. Show your work.
b. Using your answer for part a as a starting point, solve the compound interest formula for the interest rate, r.
c. Use your equation from part a to determine the interest rate.
Answer:A
Step-by-step explanation:
Answer:
3.73%
Step-by-step explanation:
The formula is
[tex]A=P(1+\frac{r}{n})^{tn}[/tex]
Here we are given that A= 5809.81 , P=4000 , t=10 years and n = 4 (compounded quaterly)
Now we have to substitute them in the formula
[tex]5809.81=4000(1+\frac{r}{4})^{40}[/tex]
[tex]\frac{5809.81}{4000}=(1+\frac{r}{4})^{40}[/tex]
[tex] (\frac{5809.81}{4000})^{\frac{1}{40}}=1+\frac{r}{4}[/tex]
[tex] (1.45)^{\frac{1}{40}}=1+\frac{r}{4}[/tex]
[tex]1.0093 = 1+\frac{r}{4}[/tex]
Subtracting 1 on both sides
[tex]0.0093=\frac{r}{4}[/tex]
[tex]r=0.0093*4[/tex]
r=0.03732
Rate is 3.73%