Answer:
The probability is 0.7449
Step-by-step explanation:
Given
[tex]n = 12[/tex] ---- total
[tex]r = 5[/tex] --- selection
[tex]Genre =\{Rap(4), Country (5), Heavy\ metal (3)\}[/tex]
Required
Probability of buying at least 1 of each genre
First, we calculate the total possible selection.
To select 5 CDs from a total of 12, we use:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
[tex]^{12}C_5 = \frac{12!}{(12 - 5)!5!}[/tex]
[tex]^{12}C_5 = \frac{12!}{7!5!}[/tex]
Expand
[tex]^{12}C_5 = \frac{12*11*10*9*8*7!}{7!*5*4*3*2*1}[/tex]
[tex]^{12}C_5 = \frac{12*11*10*9*8}{5*4*3*2*1}[/tex]
[tex]^{12}C_5 = \frac{95040}{120}[/tex]
[tex]^{12}C_5 = 792[/tex]
So, the total selection is:
[tex]Total = 792[/tex]
To select at least 1 from each genre, there are 6 possible scenarios.
And they are:
[tex]\begin{array}{ccc}{Heavy\ Metal (3)} & {Rap (4)} & {Country(5)} & {3} & {1} & {1} & 2 & {1} & {2} & {2} & {2} & {1}& {1} & {2} & {2}& {1} & {3} & {1}& {1} & {1} & {3} \ \end{array}[/tex]
The possible selections for the given scenario is:
[tex]Possible = ^3C_3* ^4C_1 * ^5C_1 +^3C_2* ^4C_1 * ^5C_2 +^3C_2* ^4C_2 * ^5C_1 +^3C_1* ^4C_2 * ^5C_2 +^3C_1* ^4C_3 * ^5C_1 +^3C_1* ^4C_1 * ^5C_3[/tex]
Using a calculator, we have:
[tex]Possible = 1*4*5 +3*4*10 +3*6*5 +3*6*10+3*4*5+3*4*10[/tex]
[tex]Possible= 20 +120 +90 +180+60+120[/tex]
[tex]Possible = 590[/tex]
The probability is then calculated using:
[tex]Pr = \frac{Possible}{Total}[/tex]
[tex]Pr = \frac{590}{792}[/tex]
[tex]Pr = 0.7449[/tex]
find the area, seventh grade math problem please help
Answer:
78 ft²
Step-by-step explanation:
[tex]A=\frac{a+b}{2} h[/tex]
[tex]A=\frac{11+15}{2}6[/tex]
78
Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X). We have another thermometer that is much cheaper and lighter, but of unknown precision (Y). We would like to know if we can (reliably) bring the lighter thermometer with us into the field. So, we set up an experiment where we expose both thermometers to 31 different temperatures and measure the temperature with each. We get the following observations
x = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120
y = 0.02, 3.99, 7.91, 12.03, 16.09, 20.00, 23.98, 28.09, 31.94, 36.03, 40.00, 44.05, 47.95, 52.00, 55.87, 59.90, 63.91, 67.95, 72.11, 76.02, 80.01, 84.10, 88.06, 91.74, 96.02, 99.95, 103.87, 108.01, 111.99, 116.04, 120.03
We want to decide if these thermometers seem to be measuring the same temperatures. Let's use the thershold α= 0.1.
Required:
Write down the appropriate hypothesis tests for β1.
Answer:
a)H0: β1= 1 and Ha: β1 ≠1
b) The test statistic is____.t= b- β/ sb
c) The p-value is____.0.999144
(d) Therefore, we can conclude that:_____. there is not enough evidence to reject the null hypothesis.
The data provides no evidence at the 0.1 significance level that these thermometers are not consistent.
Step-by-step explanation:
This is called testing hypotheses about β, the population regression co efficient.
The null and alternate hypotheses are
H0: β1= 1 and Ha: β1 ≠1
The significance level is ∝=0.1 and ∝/2 is 0.05
The critical region at t ∝/2 (29)= t ≤ - 1.699 , t ≥ 1.699
The test statistic is
t= b- β/ sb
which has t distribution with υ= 31-2= 29 degrees of freedom.
Calculations
Ŷ = a +bX
b = SPxy /SS x= Σ(xi-x`)(yi-y`)/Σ(xi-x`)²
b = 39671.6/39680= 0.9998
a = y` - bx`
x`= 60
y`= 59.989
a = 59.989 -0.9998*60 = 0.001734
Syx²= Σ( yi -y`)²/ n-2= 39663.3857/ 29=1367.68965
Syx= 36.9822
Sb= Syx/ √∑ (x-x`)²
Sb= 36.9823/ √39680
Sb= 36.9823/ 199.984
Sb= 0.18493
x-x` y-y` (x-x`)² (x-x`)(y-y`)
-60 -59.969 3600 3598.1419
-56 -55.999 3136 3135.9458
-52 -52.079 2704 2708.1097
-48 -47.959 2304 2302.0335
-44 -43.899 1936 1931.5574
-40 -39.989 1600 1599.5613
-36 -36.009 1296 1296.3252
-32 -31.899 1024 1020.769
-28 -28.049 784 785.3729
-24 -23.959 576 575.0168
-20 -19.989 400 399.7806
-16 -15.939 256 255.0245
-12 -12.039 144 144.4684
-8 -7.989 64 63.9123
-4 -4.119 16 16.4761
0 -0.08903 0 0
4 3.921 16 15.6839
8 7.961 64 63.6877
12 12.121 144 145.4516
16 16.031 256 256.4955
20 20.021 400 400.4194
24 24.111 576 578.6632
28 28.071 784 785.9871
32 31.751 1024 1016.031
36 36.031 1296 1297.1148
40 39.961 1600 1598.4387
44 43.881 1936 1930.7626
48 48.021 2304 2305.0065
52 52.001 2704 2704.0503
56 56.051 3136 3138.8542
60 60.041 3600 3602.4581
∑0 0 39680 (SSx) 39671.6 (SPxy)
Putting the values
The test statistic is
t= b- β/ sb
t= 0.9998-1/ 0.18493
t=-0.0010815
Since the calculated t=-0.0010815 does not lie in the critical region t ∝/2 (29)= t ≤ - 1.699 , t ≥ 1.699 we conclude that these thermometers seem to be measure temperatures.
The p-value is ≈ 0.999144
there is not enough evidence to reject the null hypothesis.
Which expression is equivalent to7sqrt x^2/ 5 sqrt y^3
?Assume y/=0,
Answer:
7sq rt = 2.6457513110645907 = sqrt y^3
Step-by-step explanation:
Given the following regression output, what is the expected value for the change in daily circulation (the dependent variable) if a newspaper had 35 winners and finalists between 2004 and 2014 and 14 winners and finalists between 1990 and 2003?
Model parameters (Change in Daily Circulation, 2004-2013):
Source Value Standard error t Pr > |t| Lower Upper
bound (95%) bound (95%)
Intercept -0.328 0.042 -7.890 <0.0001 -0.412 -0.244
Pulitzer Prize
Winners and
Finalists,
1990-2003 -0.015 0.008 -1.873 0.067 -0.030 0.001
Pulitzer Prize
Winners and
Finalists,
2004-2014 0.024 0.008 2.837 0.007 0.007 0.040
Pulitzer Prize
Winners and
Finalists,
1990-2014 0.000 0.000
Answer:
0.512 ; - 0.538
Step-by-step explanation:
Using the standard linear regression relation :
y = bx + c
b slope ; c = intercept ; y = dependent ; x = independent variable.
For finalist between 2004 - 2014 ;
y = 0.024x - 0.328
x = 35
y = 0.024(35) - 0.328
y = 0.512
For finalist between 1990 - 2014 ; with 14 winners ; change in daily circulation :
y = -0.015x - 0.328
x = 14.
y = -0.015(14) - 0.328
y = - 0.538
PLEASE HELP WITH THIS ASPA 3/8 divided by-3/5
Answer:
Step-by-step explanation:
HELP! i will give Brainly, if anyone could give me the full equation :) only answer if you’re sure...
Answer:
y=-3/4x+3
Step-by-step explanation:
Slope is rise over run, so -3/4. Y-intercept is at (0, 3)
y=-3/4x+3
#2Need help ???!!! For an exam. Please don’t send any links !!! Cannot open. Thank you and answer below please and thank!
the width of a rectangular yard is 3 yards more than twice its length. the perimeter of the garden is 192 yards
Answer:
Step-by-step explanation:
W = 2L + 3, and:
P = 2W + 2L = 192
Substituting 2L + 3 for W, we get:
P = 2(2L + 3) + 2L = 192, or
4L + 6 + 2L = 192, or:
6L = 186
L = 186/6 = 31
The length is 31, the width is 62 + 3, or 65
Therefore, the perimeter P is P = 2(31) + 2(65) = 130 + 62 = 192 (OK!)
1. The amount of time Mr. Smith spends exercising each day is
approximately normally distributed with a mean of 30 minutes and a
standard deviation of 10 minutes. On approximately what percent of the
days in a year does Mr. Smith exercise for between 10 minutes and 40
minutes?
Answer:boy
Step-by-step explanation:boy
Mr. Smith exercises for between 10 and 40 minutes on 77.45 percent of the days in a year.
Given that his exercising time follows a normal distribution with a mean of 30 minutes and a standard deviation of 10 minutes.
Here we have to find the percentage of days in a year that Mr. Smith exercises for between 10 and 40 minutes,
First, we need to standardize the values of 10 and 40 minutes using the formula,
⇒ z = (x - μ) / σ
where x is the value we want to standardize,
μ is the mean,
And σ is the standard deviation.
For x = 10:
⇒ z = (10 - 30) / 10
= -2
For x = 40:
⇒ z = (40 - 30) / 10
= 1
Now, we need to find the probability of Mr. Smith exercising between -2 and 1 standard deviations from the mean.
We can use a standard normal distribution table or a calculator to find this probability.
Using a standard normal distribution table,
we can find the probability of z being between -2 and 1 is about 0.7745. This means that on approximately 77.45% of the days in a year, Mr. Smith exercises for between 10 and 40 minutes.
Therefore,
Mr. Smith exercises for between 10 and 40 minutes on approximately 77.45% of the days in a year.
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ2
Tommy the Dunker's performance on the basketball court is influenced by his state of mind: If he scores, he is twice as likely to score on the next shot as he is to miss, whereas if he misses a shot, he is five times as likely to miss the next shot as he is to score.
(a) If Tommy has missed a shot, what is the probability that he will score two shots later?
(b) In the long term, what percentage of shots are successful?
What is the converse of the statement below?
“If today is Friday, then tomorrow is Saturday."
Answer:
C (Sorry if its incorrect)
Step-by-step explanation:
I believe its C
Becuase a converse is switching the hypothis and conclusion around
Calvin wrote inequalities to compare the heights, in feet, of rivers above or below flood stage.
Select all of the inequalities that are correct.
A. -10 > -9
B. 1> -18
C. -25 > -30
D. 3 < -5
E. -10 < 3
Answer:
I'm not 100% sure but I think its B. 1> -18
Enter in the missing numbers to create equivalent ratios. HELPPPPPPPPPPPPPPPPPPPP
Can someone help me with this?
Answer:
I can help you via Watsapp
Find the lateral area and the surface area of the composite solid. Keep answer in exact form.
10 cm
12 cm
1
1
1
1
32 cm
10 cm
Lateral Area
Surface Area
Answer:
a) Lateral area of the solid = 2011.43 [tex]cm^{2}[/tex]
b) Surface area of the solid = 2544 [tex]cm^{2}[/tex]
Step-by-step explanation:
a) Lateral area of the figure = 2[tex]\pi[/tex]rh
where; r is the radius of the cylinder, and h is its height.
Lateral area of the figure = 2 x [tex]\frac{22}{7}[/tex] x 10 x 32
= 2011.43 [tex]cm^{2}[/tex]
b) The surface area = 2[tex]\pi[/tex]r(r + h) - 2([tex]\frac{1}{2}[/tex] x b x h)
= 2[tex]\pi[/tex]r(r + h) - (b x h)
The height of the isosceles triangle can be determined by applying the Pythagoras theorem to have,
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]h^{2}[/tex]
100 = 36 + [tex]h^{2}[/tex]
[tex]h^{2}[/tex] = 100 - 36
= 64
h = [tex]\sqrt{64}[/tex]
= 8
h = 8 cm
The surface area of the solid = 2 x [tex]\frac{22}{7}[/tex] x 10 (10 + 32) - 12 x 8
= 2640 - 96
= 2544
The surface area of the solid is 2544 [tex]cm^{2}[/tex].
The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration -
a, over time, t. Which is an equivalent equation solved for a?
Ofv=a
10-v=a
O a
(+v=a
o {+v=a
Answer:
A
Step-by-step explanation:
f = v + at
f - v = at
(f-v)/t = a
Answer:
(f - v) / t = a
Step-by-step explanation:
Solving for the equation for a means taking all integers or values on the other side of the equation for a
To do this we must do it mathematically.
f = v + at
f - v = at
(f - v) / t = a
Right circular cylinder has volume and radius. Right circular cylinder is similar to cylinder and has volume. Find the radius of cylinder.
Answer: where’s the picture
Step-by-step explanation:
Hum
Plz help me well mark brainliest if correct.....????
Answer:
The answer would be C. 31
Step-by-step explanation:
Answer:
Hello There!!
Step-by-step explanation:
15 Girls like fantasy books and 16 boys like fantasy books so in total the students that like fantasy books are 31.
hope this helps,have a great day!!
~Pinky~
h
If the original principal of Jimmy
Christensen's account balance today
is $3,450.00, the balance after 2 years is
$3,485.95, and he made no other deposits,
how much interest did he earn?
A $123.95
B $34.95
C $3,485.95
D$35.95
Round to the nearest whole dollar: 2.89
Answer:
I believe it would be $3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Because 0.89 is greater than 0.5, we have to round up. Therefore, the answer is 3.
If this helps please mark as brainliest
Find the equation of the exponential function represented by the table below:
Answer:
y = 0.2(0.5)^x
Step-by-step explanation:
Exponential function are of the form
y = ab^x
----------------------
To find "a" plug in x = 0 y = 0.2
0.2 = a(0.2)^0
0.2 = a
-------------------------
To find "b" plug in another point and a = 0.2
using x = 2, b = 0.05
0.05 = 0.2b^2
Divide both sides by 0.20
.25 = b^2
Take the square root of both sides
0.5 = b
-----------------------------
With a = 0.2 and b = 0.5 the equation becomes
y = 0.2(0.5)^x
8+12/-4=5 please help
Answer:
you use the bodmas 12/-4p plus 8 =s
Step-by-step explanation:
hop it helps
Add the following and simplify if possible.
Answer:
2x+3
Step-by-step explanation:
When Natalie runs the 400 meter dash, her finishing times are normally distributed with a mean of 71 seconds and a standard deviation of 2.5 seconds. What percentage of races will her finishing time be between 71 and 77 seconds, to the nearest tenth?
Answer:
49.2%
Step-by-step explanation:
solve the quadratic equation by completing the square: 6x²-11x-10=0
Step-by-step explanation:
6x² - 11x - 10 =0{use splitting middle term method} -60x²| |
-4. +15
(6x² - 4x) (15x - 10)2x( 3x - 2 ) +5( 3x - 2)(2x + 5) (3x - 2)2x = -5 or 3x = 2x = -5 or x = 2there fore x = 2Plz help me well mark brainliest if correct!!...
9514 1404 393
Answer:
B) fifth grade boys
Step-by-step explanation:
55 tickets is halfway between the lines marked 50 tickets and 60 tickets. The bar that comes closest to that value is the right-most green bar, representing ...
fifth-grade boys
A spinner is made of three equal sections blue green and red if I spend spend 180 times how many times I expect to get red as outcome
Consider the three points (-7, -7), (21, 14), (49, 35). Part A: Which of the following points are on the same line that passes through the (-7, -7), (21, 14), (49, 35)? Select all that apply. A. (5, 9) B. (5, 2) C. (17, 11) D. (4, 3) E.) (33, 23) Part B: Show or explain how you determined which points were on the line and which were not on the line.
Answer:
A. (5, 9)
Step-by-step explanation:
Line A passes through the point (-8, 3) and is perpendicular to the line represented by the equation
y = -4x + 9. Line A can be expressed as an equation of the form y = mx + b.
Part A
What is the value of m for line A?
Part B
What is the value of b for line A?
Answer:
Did u get the answers ?
Step-by-step explanation:
I need help lol
Answer: A: -4 B:-29
Step-by-step explanation:
Help with Math Question 1
Answer:
Step-by-step explanation:
X is also 67° Like the interior angle