Solution :
Defining the following events as :
B : Being a Business major
α : Studying at the library
∴ Given that :
[tex]$P(B) = \frac{45}{100}$[/tex]
= 0.45
Again, P [ Studying at the library | Being a Business major ] = 2 P [ Studying at the library | Being a non business major ]
[tex]$P[ \alpha | B] = 2 P[\alpha | B^C]$[/tex] .......(1)
Again,
[tex]$P[\text{Studying at the library } | \text{ Being a business major}] = \frac{1}{2} = 0.50$[/tex]
[tex]$P(\alpha | B) = 0.50$[/tex]
From (1), we get
[tex]$P(\alpha | B^C) = \frac{1}{2} . P(\alpha | B)$[/tex]
[tex]$=\frac{1}{2} \times 0.50$[/tex]
= 0.25
Therefore, we need,
= P[ The students is a Business major | The student studies at the library ]
[tex]$=P(B | \alpha)$[/tex]
By Bayes theorem
[tex]$=\frac{P(B). P(\alpha | B)}{P(B).P(\alpha | B) + P(B^C). P(\alpha | B^C)}$[/tex]
[tex]$=\frac{0.45 \times 0.50}{0.45 \times 0.50 + 0.55 \times 0.25}$[/tex]
= 0.6207
We are given a jar full of thousands of red and blue marbles. We want to estimate the unknown proportion pof red marbles in the jar. To do this, we randomly draw 100 marbles and count reds: it so happens we drew 45 reds. Enter values in decimal form, rounded to four decimal places (or more).
We estimate the proportion of reds in the jar to be
Attach a give-or-take value to this estimate. (That is, estimate the standard error.)
For a 96% confidence interval, about how many standard errors should be added to and subtracted from the estimate?
Set up an approximate 96% confidence interval for the unknown proportion of reds in the jar.
Answer:
(0.3478, 0.5522)
Step-by-step explanation:
Given:
Total number of red marbles, x = 45
Total number of marbles, n = 100
Phat = x / n = 45 / 100 = 0.45
The confidence interval, C.I is given by :
Phat ± Zcritical * standard error
Phat ± Zcritical * √Phat(1 - Phat) / n
Zcritical at 96% = 2.0537
The standard error = √Phat(1 - Phat) / n
S.E = √(0.45 * 0.55) / 100 = 0.0497493
C.I = 0.45 ± (2.0537 * 0.0497493)
C.I = 0.45 ± 0.10217013741
C. I = (0.3478, 0.5522)
Một công ty sản xuất một thùng hình trụ tròn không có nắp và có thể tích 8x ft Chi phí sản xuất đáy là 2 USD / ft ?, chi phí sản xuất mặt bên là 4,8 USD / ft . Hỏi chi phí tối ưu nhất để sản xuất cái thằng này là bao nhiêu USD ?,
Answer:
nsjdjdnajakla ,bxn. dnsksksvhdjeke dkekdkbdjdls d
In a die game, you roll a standard 6-sided die twice. If the second number rolled is the same as the first number rolled, you win $25. Otherwise, you lose $2. If you were to play the game 100 times, how much money can you expect to make
Answer:
You can expect to make $250.
Step-by-step explanation:
Possible outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Probability of the second number rolled being the same as the first number rolled:
6 outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
Out of 36, thus:
[tex]p = \frac{6}{36} = \frac{1}{6}[/tex]
Expected value of 1 game:
1/6 probability of earning $25.
5/6 probability of losing $2.
Thus:
[tex]E = 25\frac{1}{6} - 2\frac{5}{6} = \frac{25 - 10}{6} = 2.5[/tex]
100 games:
100*2.5 = 250
You can expect to make $250.
I are these orders pairs a function
х,у
0,9
2,8.
4,7
6,6
8,5
10,4
9514 1404 393
Answer:
yes
Step-by-step explanation:
No x-value is repeated, so these ordered pairs do represent a function.
Determine if the graph of y=x/x^2-4 is symmetrical with respect to the x-axis, the y-axis, or the origin.
a. about the x-axis
b. about the y-axis
c. about the origin
d. all of these
e. none of these
please help i’ll also rate brainliest
9514 1404 393
Answer:
c. about the origin
Step-by-step explanation:
The function is odd: replacing x with -x gives the negative of the function value:
f(-x) = -f(x)
Odd functions are symmetrical about the origin.
Find the answer for x and y
Answer:
x = 57
y = 57
Step-by-step explanation:
because of the two parallel lines :
41+y+8+74 = 180 add like terms
y + 123 = 180 subtract 123 from both sides
y = 57
x - 3 + 41 + y + 8 = 180 because they make a straight line
x + y + 46 = 180
x + 57 + 46 = 180
x + 123 = 180 subtract 123 from both sides
x = 57
find r and s on the triangle
Answer:
r=24
s=21
Step-by-step explanation:
I use proportion of 2 to 3
I multiply 16 and 3/2 to get r
r=24
I multiply 14 and 3/2 to get s
s=21
How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer to the nearest square inch.
Answer: About 63 in²
Step-by-step explanation:
Area of circle = π · r²
r = radius lengthπ ≈ 3.14Area of large pizza:
[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]
Area of small pizza:
[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]
Difference in area:
[tex]113.04-50.24=62.8[/tex]
A campus deli serves 101 customers over its busy lunch period from 11:30 am to 1:30 pm. A quick count of the number of customers waiting in line and being served by the sandwich makers shows that an average of 18 customers are in process at any point in time. What is the average amount of time (in minute) that a customer spends in process?
Answer:
21.38 minutes
Step-by-step explanation:
the total number served = 101
teh number of hours that is spent in serving from 11.30 to 1.30 = 2 hours
Lq = average number of those that are in line = 18 customers
from here we are to find the flow rate
= [tex]\frac{total served}{service hour}[/tex]
= 101/2 = 50.5
the average time in waiting =
Lq/flow rate
= 18/50.5
= 0.3564 hours
convert to minutes = 0.3564 * 60 minutes
= 21.38 minutes
After analyzing a data set using the one-way ANOVA model, the same data are analyzed using the randomized block design ANOVA model. SS (Treatment) in the one-way ANOVA model is ________ the SS (Treatment) in the randomized block design ANOVA model.
a. Always equal to.
b. Always greater than.
c. Always less than.
d. Sometimes greater than.
Answer: Always equal to
Step-by-step explanation:
A one way analysis of variance refers to the technique that is used in knowing if there's significant difference between two samples means.
Based on the options given, it should be noted that SS (Treatment) in the one-way ANOVA model is always equal to the SS (Treatment) in the randomized block design ANOVA model.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd
9514 1404 393
Answer:
3/2
Step-by-step explanation:
Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.
[tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]
rope price of length 45cm 25 cm and 81 cm have to be cut into same size pieces what is the smallest price length possible
= 2025
When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)
For this, you divide the given lengths using the numbers that divides all through.
I have added an image to this answer. Go through it for more explanation
Solve.
x² + 5x – 2=0
Answer:
1
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
2
+
5
−
2
=
0
x^{2}+5x-2=0
x2+5x−2=0
=
1
a={\color{#c92786}{1}}
a=1
=
5
b={\color{#e8710a}{5}}
b=5
=
−
2
c={\color{#129eaf}{-2}}
c=−2
=
−
5
±
5
2
−
4
⋅
1
(
−
2
)
√
2
⋅
1
Step-by-step explanation:
this should help
This is Some next level Geometry
Step-by-step explanation:
Measure of Angle 1 is 115 due to corresponding angles postulate
Measure of Angle 2 is 65 is linear pair postulate.
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the binomial quadratic expressions with their factored form.
Answer:
x²-36 and (x-6)(x+6)
9x-1 and(3x-1)(3x+1)
4x² -16 and 4(x-2)(x+2)
Step-by-step explanation:
when you multiply(x+6)(x-6)
you get x²-36,this is known as difference of two squares ie (a+b)(a-b)=(a²-b²)=0
x(x-6)+6(x-6)
x²-6x+6x-36
x² -36
the second the same explanation as the first
for the third, multiply (x+2)(x-2) it will give x²-4
then multiply this by 4 which is = 4x² - 16
Use AABC to find the value of sin B.
Answer:
35/37
Step-by-step explanation:
sin(B)=(AC)/(AB) = 35/37
A research center poll showed that 76% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
Answer:
6/25
Step-by-step explanation:
P(have belief) =76/100 = 19/25
P (does not have belief) = 1-19/25 = 6/25
What are 3 ratios that are equivalent to 8 :5
Answer:
Step-by-step explanation:
8/5 = 16/10 = 24/15
8:5 = 16:10 = 24:15
The profits for video game companies depend on what game platform the game runs on, which can either be a portible system with a built in screen, or a standard system that you have to hook up to a television. The profit off of a portible game system is $72, while the profit from a standard game system is $90. The store manager has to make at least $360 per day in order to keep the store open. Which graph represents this inequality? Write the inequality that represents the number of games that must be sold everyday to meet or beat the sales goal.
Step-by-step explanation:
1. A helicopter is at a position from two VORS (VHF Omnidirectional
Radio Range, an aircraft navigation system operating in the VHF band -
not covered in chapter) as in the diagram shown below. Given the angles
shown, find the third angle.
Helicopter
74.0°
66.0°
VOR
VOR
The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees
The diagram is not shown; however, the question can still be answered.
The given angles are:
[tex]\theta_1 = 74.0^o[/tex]
[tex]\theta_2 = 66.0^o[/tex]
Represent the third angle as [tex]\theta_3[/tex]
The helicopter and the 2 VORs form a triangle.
So, we make use of the following theorem to calculate the third angle
[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle
Substitute known values
[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]
[tex]140.0^o + \theta_3= 180^o[/tex]
Collect like terms
[tex]\theta_3= 180 -140.0^o[/tex]
[tex]\theta_3= 40^o[/tex]
Hence, the third angle is 40 degrees.
Learn more about angles in a triangle at:
https://brainly.com/question/14780489
) How many different three-letter initials can people have: , (b) How many different three-letter initials with none of the letters repeated can people have: , (c) How many different three-letter initials with letters repeated begin with an X: , (d) How many different three-letter initials begin with a F and end in a D:
Solution :
a).
The different three letter initials that people have is :
= 26 x 26 x 26
= [tex]26^3[/tex]
= [tex]17576[/tex]
b). The first place to be fill in26 ways.
The second place to be filled in 25 ways
The third place to be filled in 24 ways.
Therefore, total number of three letter initial with no repetition is :
= 26 x 25 x 24
= [tex]15600[/tex]
c). The total number of three letter initial begin with X = 1 x 26 x 26
= [tex]676[/tex]
d). The total number of the three letter initials that begin with letter 'F' an end with letter 'D' is = 1 x 26 x 1
= [tex]26[/tex]
In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty-four gearboxes are in stock, 6 with improperly drilled holes. Five gearboxes must be selected from the 24 that are available for installation in the next five robots. (Round your answers to four decimal places.) (a) Find the probability that all 5 gearboxes will fit properly. (b) Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxes.
Answer:
The right answer is:
(a) 0.1456
(b) 18.125, 69.1202, 8.3139
Step-by-step explanation:
Given:
N = 24
n = 5
r = 7
The improperly drilled gearboxes "X".
then,
⇒ [tex]P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}[/tex]
(a)
P (all gearboxes fit properly) = [tex]P(x=0)[/tex]
= [tex]\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}[/tex]
= [tex]0.1456[/tex]
(b)
According to the question,
[tex]X = 91+5[/tex]
Mean will be:
⇒ [tex]\mu = E(x)[/tex]
[tex]=E(91+5)[/tex]
[tex]=9E(1)+5[/tex]
[tex]=9.\frac{nr}{N}+5[/tex]
[tex]=9.\frac{5.7}{24} +5[/tex]
[tex]=18.125[/tex]
Variance will be:
⇒ [tex]\sigma^2=Var(X)[/tex]
[tex]=V(9Y+5)[/tex]
[tex]=81.V(Y)[/tex]
[tex]=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}[/tex]
[tex]=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}[/tex]
[tex]=69.1202[/tex]
Standard deviation will be:
⇒ [tex]\sigma = \sqrt{69.1202}[/tex]
[tex]=8.3139[/tex]
What is the sine ratio for
Answer:
the since ratio is 5/4
Step-by-step explanation:
hope this is helpful ask manyPlease help!! The question is the image below VVV
Answers are also images after the picture.
Step-by-step explanation:
When adding two fractions with different bases (bottom numbers), we can use this function:
[tex]\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}[/tex]
So, to apply this to the given question:
[tex]\frac{x+3}{x-6} +\frac{1}{x-2}[/tex]
= [tex]\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}[/tex]
From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.
Multiply top using: (a + b)(c + d) = ac + ad + bc + bd= [tex]\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}[/tex]
Simplify.= [tex]\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}[/tex]
Remove parentheses.= [tex]\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}[/tex]
Simplify again.= [tex]\frac{x^2 +2x-12}{(x-6)(x-2)}[/tex]
Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.
Factor.= [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]
Answer:
A) [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]
need some help with this :)
===========================================================
Explanation:
All direct variation equations are of the form y = kx, for some constant k.
We know that y = -8 and x = 4 pair up together. Let's use these two values to find k
y = kx
-8 = k*4
-8/4 = k
-2 = k
k = -2
Therefore, we go from y = kx to y = -2x
We can then find y when x = -4
y = -2x
y = -2*(-4)
y = 8
Answer:
y∝x
y=kx
k=y/x
by putting values
k=-8/4
k= -2
now ,if x= -4
as, y=kx
hence, y= (-2)(-4)
y=8
Step-by-step explanation:
Rose walks 2 2/3 km in three-fifths of an hour. If her speed remains unchanged, how many kilometres can she walk in one and three quarters of an hour? Express your answer as a mixed number in lowest terms
Answer:
Distance = 7 7/9 Km
Step-by-step explanation:
Given the following data;
Distance = 2⅔ = 8/3 Km
Time = ⅗ hour
First of all, we would find her speed;
Speed = distance/time
Speed = (8/3)/(3/5)
Speed = 8/3 * 5/3
Speed = 40/9 km/h
Next, we would find the distance covered when time = 1¾ hours
Distance = speed * time
Distance = 40/9 * 1¾
Distance = 40/9 * 7/4
Distance = 10/9 * 7
Distance = 70/9
Distance = 7 7/9 Km
A popular brand of pen is available in 13 colors and 2 writing tips. How many different choices of pens do you have with this brand?
There are ___ different choices of pens with this brand.
Answer:
7
Step-by-step explanation:
i had it
Find the missing side of the right triangle.
Answer:
√202
Step-by-step explanation:
since it's the hypotenuse you are required to find
x²=11²+9²
x²=121+81
√x²=√202
x=√202
I hope this helps
what is the prime product of 120
Answer:
[tex]2^{3} * 3 * 5[/tex]
Step-by-step explanation:
I will give you brainliest if you answer this correctly
Answer:
Mark Brainliest please
The answer is 1
Step-by-step explanation:
(1 — x^ m-n) ^-1 + (1- x ^n-m)^ -1
1/[1-x^(m-n)] + 1/[1-x^(n-m)]
1/[1-x^m × x^(-n)] + 1/[1-x^n × x^(-m)]
x^n/(x^n - x^m) + x^m/(x^m - x^n)
x^n/(x^n - x^m) - x^m/(x^n - x^m)
Now taking the LCM here, we get
(x^n - x^m)/(x^n - x^m)
