Answer: Probability that both are non smokers is 0.48.
Step-by-step explanation:
Since we have given that
Number of male smokers = 102
Number of male non smokers = 408
Total male = 102+408=510
Number of female smokers = 240
Number of female non smokers = 360
Total female = 240+360 = 600
According to question,
A male student and a female student from the college are randomly selected for a survey,
So, Probability that both are non smokers is given by
P(both are smokers ) = P(Male smoker) × P(female smoker)
[tex]P(both)=\dfrac{360}{600}\times \dfrac{408}{510}\\\\P(both)=\dfrac{146880}{306000}\\\\P(both)=0.48[/tex]
Hence, probability that both are non smokers is 0.48.
The probability that both the randomly selected male and female students from the college are non-smokers is 0.48.
Explanation:To compute the probability that both the randomly selected male and female students are non-smokers, we start by finding the total number of male and female students. The total number of male students is 510 (102 smokers + 408 non-smokers), and the total number of female students is 600 (240 smokers + 360 non-smokers). Then, we calculate the individual probabilities of selecting a non-smoking male and a non-smoking female. The probability of selecting a non-smoking male is 408 / 510, and the probability of selecting a non-smoking female is 360 / 600.
To find the combined probability, we multiply these individual probabilities. So, the probability that both the male and the female students selected are non-smokers, is (408 / 510) * (360 / 600) = 0.8 * 0.6 = 0.48.
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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. :)
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
A Straight fence is to be Constructed from post 6 inches wide by which are Separated by Chain link sections that are 4 feet long . If, the Fence must begin and end with a post . So, Which of the Following Could not be the Length of the Fence ... Remember 1 Foot = 12 Inches .
Answer:
any length less then 5 ft
Suppose you are to throw a dart at a circular dart board with radius 2 inches. Let (X, Y ) denote the point that you hit on the board (you can assume the board is centered at the origin (0, 0), and that the dart hits somewhere on the board uniformly at random). (a) Find the joint PDF of X and Y . (b) Find the marginal PDFs of X and Y . (c) Find the conditional PDFs fX|Y and fY |X. (d) Suppose that the “bulls eye” on the target consists of a small circle centered at the origin with radius 0.25. Explain how you would use one of these PDFs to compute the probability of a dart hitting the bulls eye. Find this probability an even easier way. (e) What is the probability that X > 1? (f) If you know that X = 1, what is the PDF of Y conditioned on this fact? What’s the probability that Y > 0.3 conditioned on this fact?
a. All points on the board are equally likely to be hit with a probability of 1/(area of board), or
[tex]f_{X,Y}(x,y)=\begin{cases}\dfrac1{4\pi}&\text{for }x^2+y^2\le4\\\\0&\text{otherwise}\end{cases}[/tex]
b. To find the marginal distribution of [tex]X[/tex], integrate the joint distribution with respect to [tex]y[/tex], and vice versa. We can take advantage of symmetry here to compute the integral:
[tex]\displaystyle\int_y f_{X,Y}(x,y)\,\mathrm dy=2\int_0^{\sqrt{4-x^2}}\frac{\mathrm dy}{4\pi}=\frac{\sqrt{4-x^2}}{2\pi}[/tex]
[tex]f_X(x)=\begin{cases}\dfrac{\sqrt{4-x^2}}{2\pi}&\text{for }-2\le x\le2\\\\0&\text{otherwise}\end{cases}[/tex]
and by the same computation you would find that
[tex]f_Y(y)=\begin{cases}\dfrac{\sqrt{4-y^2}}{2\pi}&\text{for }-2\le y\le2\\\\0&\text{otherwise}\end{cases}[/tex]
c. We get the conditional distributions by dividing the joint distributions by the respective marginal distributions:
[tex]f_{X\mid Y=y}(x)=\dfrac{f_{X,Y}(x,y)}{f_Y(y)}[/tex]
[tex]f_{X\mid Y=y}(x)=\begin{cases}\dfrac1{2\sqrt{4-y^2}}&\text{for }-2\le y\le2\text{ and }x^2\le4-y^2\\\\0&\text{otherwise}\end{cases}[/tex]
and similarly,
[tex]f_{Y\mid X=x}(y)=\begin{cases}\dfrac1{2\sqrt{4-x^2}}&\text{for }-2\le x\le2\text{ and }y^2\le4-x^2\\\\0&\text{otherwise}\end{cases}[/tex]
d. You can compute this probability by integrating the joint distribution over a part of the circle (call it "B" for bullseye):
[tex]\displaystyle\iint_Bf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^{2\pi}\int_0^{0.25}\frac r{4\pi}\,\mathrm dr\,\mathrm d\theta=\frac1{64}[/tex]
(using polar coordinates) The easier method would be to compute the area of a circle with radius 0.25 instead, then divide that by the total area of the dartboard.
[tex]\dfrac{\pi\left(\frac14\right)^2}{\pi\cdot2^2}=\dfrac1{64}[/tex]
e. The event that [tex]X>1[/tex] is complementary to the event that [tex]X\le1[/tex], so
[tex]P(X>1)=1-P(X\le1)=1-F_X(1)[/tex]
where [tex]F_X(x)[/tex] is the marginal CDF for [tex]X[/tex]. We can compute this by integrate the marginal PDF for [tex]X[/tex]:
[tex]F_X(x)=\displaystyle\int_{-\infty}^xf_X(t)\,\mathrm dt=\begin{cases}0&\text{for }x<-2\\\\\dfrac12+\dfrac1\pi\sin^{-1}\dfrac x2+\dfrac{x\sqrt{4-x^2}}{4\pi}&\text{for }-2\le x<2\\\\1&\text{for }x\ge2\end{cases}[/tex]
Then
[tex]P(X>1)=1-F_X(1)=\dfrac13-\dfrac{\sqrt3}{4\pi}\approx0.1955[/tex]
f. We found that either random variable conditioned on the other is a uniform distribution. In particular,
[tex]f_{Y\mid X=1}(y)=\begin{cases}\dfrac1{2\sqrt3}&\text{for }y^2\le3\\\\0&\text{otherwise}\end{cases}[/tex]
Then
[tex]P(Y>0.3\mid X=1)=1-P(Y\le0.3\mid X=1)=1-F_{Y\mid X=1}(0.3)[/tex]
where [tex]F_{Y\mid X=x}(y)[/tex] is the CDF of [tex]Y[/tex] conditioned on [tex]X=x[/tex]. This is easy to compute:
[tex]F_{Y\mid X=1}(y)=\displaystyle\int_{-\infty}^yf_{Y\mid X=1}(t)\,\mathrm dt=\begin{cases}0&\text{for }y<-\sqrt3\\\\\dfrac{y+\sqrt3}{2\sqrt3}&\text{for }-\sqrt3\le y<\sqrt3\\\\1&\text{for }y\ge\sqrt3\end{cases}[/tex]
and we end up with
[tex]P(Y>0.3\mid X=1)=\dfrac{10-\sqrt3}{20}\approx0.4134[/tex]
Final answer:
The joint PDF for a uniform distribution on a circular dart board is constant within the dart board and zero outside. Marginal and conditional PDFs are derived from the joint PDF. To compute probabilities such as the bulls eye hit or X > 1, integrate the corresponding PDF over the relevant range.
Explanation:
Finding the Joint and Marginal PDFs, and Conditional Probabilities
The joint probability density function (PDF) of X and Y for a uniform distribution over a circular dart board with radius 2 inches is constant within the circle and zero outside. First, we calculate the area of the circle, A = πr² = π(2)² = 4π square inches. The joint PDF f(x, y) will be 1/A for all points inside the dart board, and 0 otherwise.
The marginal PDFs are derived by integrating the joint PDF over the other variable. For instance, fX(x) is found by integrating f(x, y) over y, and fY(y) is found by integrating f(x, y) over x.
The conditional PDFs fX|Y and fY|X are derived from the joint PDF divided by the marginal PDF of the conditioned variable.
To find the probability of hitting the bulls eye, a circle of radius 0.25 inches, you'd integrate the joint PDF over the area of the bulls eye or simply calculate the area ratio of the bulls eye to that of the entire dart board.
The probability that X > 1 is found by integrating fX(x) from 1 to 2. If you know that X = 1, the conditional PDF of Y is fY|X(y|X=1). The probability that Y > 0.3 given X = 1 is calculated by integrating this conditional PDF from 0.3 to the upper limit set by the circle's boundary.
Factor the higher degree polynomial
5y^4 +11y^2 +2
Answer:
[tex]\large\boxed{5y^4+11y^2+2=(y^2+2)(5y^2+1)}[/tex]
Step-by-step explanation:
[tex]5y^4+11y^2+2=5y^4+10y^2+y^2+2=5y^2(y^2+2)+1(y^2+2)\\\\=(y^2+2)(5y^2+1)[/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%.
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]
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
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.
given the function f(x) = log base 4(x+8) , find the value of f^-1(2)
Answer:
The value of [tex]f^{-1}(2)=8[/tex]
Step-by-step explanation:
* Lets revise how to find the inverse function
- At first write the function as y = f(x)
- Then switch x and y
- Then solve for y
- The domain of f(x) will be the range of f^-1(x)
- The range of f(x) will be the domain of f^-1(x)
* Now lets solve the problem
- The inverse of the logarithmic function is an exponential function
∵ [tex]f(x)=log_{4}(x + 8)[/tex]
- Write the function as y = f(x)
∴ [tex]y=log_{4}(x+8)[/tex]
- Switch x and y
∴ [tex]x=log_{4}(y+8)[/tex]
- Lets solve it to find y
# Remember: [tex]log_{a}b=n=====a^{n}=b[/tex]
- Use this rule to find y
∴ [tex]4^{x}=(y + 8)[/tex]
- Subtract 8 from both sides
∴ [tex]4^{x}-8=y[/tex]
∴ [tex]f^{-1}(x)=4^{x}-8[/tex]
- Lets substitute x by 2
∴ [tex]f^{-1}(2)=4^{2}-8[/tex]
- The value of 4² = 16
∴ [tex]f^{-1}(x)=16-8=8[/tex]
* The value of [tex]f^{-1}(2)=8[/tex]
To find the inverse of the function f(x) = log base 4 of (x+8) when evaluated at 2, we solve the equation log base 4 of (x+8) = 2 to find x. This gives us x = 8, so f^-1(2) = 8.
To find the value of f-1(2) for the function f(x) = log4(x+8), we first need to understand that f-1(x) denotes the inverse function of f(x). This means that if f(a) = b, then f-1(b) = a. To solve for f-1(2), we set f(x) equal to 2 and solve for x:
log4(x+8) = 2
42 = x+8 (using the property that if logb(a) = c then bc = a)
16 = x+8
x = 16 - 8
x = 8
Therefore, f-1(2) = 8.
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]
True or False? For any integer m, 6m(2m + 10) is divisible by 4. Explain
Answer:
True
Step-by-step explanation:
6m (2m + 10)
= (6m)(2m) + (6m)(10)
= 12m² + 60m
= 4(3m² + 15m)
Because we factored out a "4" in the expression, by observation, we can see that regardless of what value of integer m is chosen, the entire expression is divisible by the "4" which has been factored out of the parentheses. Hence it is True.
What is the divisibility test of 4?
If a number's last two digits are divisible by 4, the number is a multiple of 4 and totally divisible by 4.
Solving the problem.6m(2m+10) = 6m cannot be said to be always divisible by 4 but is divisible by 2 as 6m = 2*3m
(2m+10) cannot say if it is divisible by but can say is divisible by 2 as we can take 2 commons from both the integer and rewrite it as 2*(m+5).
Hence multiplying both the numbers we get = 2*3m*2(m+5) and now we group 2's together we get 4*3m*(m+5), as the whole number is multiplied by 4 it is at least divisible by 4 once.
Hence proved that 6m(2m+10) is divisible by 4 and the answer is true.
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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.
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
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.
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
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%
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.
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]
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.
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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.
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]
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].
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 :)
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.
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]
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.
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
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).