You want to go to graduate school, so you ask your math professor, Dr. Emmy Noether, for a letter of recommendation. You estimate that there is a 80% chance that you will get into a graduate program if you receive a strong recommendation, a 60% chance that you will get into a graduate program if you receive a moderately good recommendation, and 5% chance that you will get into a graduate program if you receive a weak recommendation. Furthermore, you estimate that the probabilities that a recommendation will be strong, moderately good, and weak are 0.7, 0.2, and 0.1, respectively. Based on these estimates, what is the probability that you will get into a graduate program. Given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation? Suppose you didn't receive an offer to attend a graduate program. Given that, what is the probability that you received a moderately good recommendation?
Answer:
a
[tex]P(G) = 0.69[/tex]
b
[tex]P(S | G) = 0.81[/tex]
c
[tex]P(M|G') = 0.26[/tex]
Step-by-step explanation:
From the question we are told the
The probability of getting into getting into graduated school if you receive a strong recommendation is [tex]P(G |S) = 0.80[/tex]
The probability of getting into getting into graduated school if you receive a moderately good recommendation is [tex]P(G| M) = 0.60[/tex]
The probability of getting into getting into graduated school if you receive a weak recommendation is [tex]P(G|W) = 0.05[/tex]
The probability of getting a strong recommendation is [tex]P(S) = 0.7[/tex]
The probability of receiving a moderately good recommendation is [tex]P(M) = 0.2[/tex]
The probability of receiving a weak recommendation is [tex]P(W) = 0.1[/tex]
Generally the probability that you will get into a graduate program is mathematically represented as
[tex]P(G) = P(S) * P(G|S) + P(M) * P(G|M) + P(W) * P(G|W)[/tex]
=> [tex]P(G) = 0.7 * 0.8 + 0.2 * 0.6 + 0.1 * 0.05[/tex]
=> [tex]P(G) = 0.69[/tex]
Generally given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation is mathematically represented as
[tex]P( S|G) = \frac{ P(S) * P(G|S)}{ P(G)}[/tex]
=> [tex]P(S|G) = \frac{ 0.7 * 0.8 }{0.69}[/tex]
=> [tex]P(S | G) = 0.81[/tex]
Generally given that you didn't receive an offer to attend a graduate program the probability that you received a moderately good recommendation is mathematically represented as
[tex]P(M|G') = \frac{ P(M) * (1- P(G|M))}{(1 - P(G))}[/tex]
[tex]P(M| G') = \frac{ 0.2 * (1- 0.6)}{ (1 - 0.69)}[/tex]
[tex]P(M|G') = 0.26[/tex]
Consider the ratio of 153 per 108. Write this ratio in different forms below. A ratio written as a reduced fraction: ____ A ration written as a decimal rounded to the hundredths: ___
Answer:
17/12 and 1.42Step-by-step explanation:
Ratios can be used to compare values and also can be written in various forms.
Given the following example
the ratio of 153 per 108.
153:108
A. this ratio can expressed in the reduced fraction as
dividing both the numerator and the denominator by a common factor of 3 will give
=153/108 = 51/36
we can further divide by a common factor of 3 to further reduce the ratio
= 51/36= 17/12
hence the ratio expressed as a reduced fraction is 17/12
B. ration written as a decimal rounded to the hundredths:
A ratio written as a decimal rounded to the hundredths:
to express the ratio as a decimal we have to divide the numerator by the value of the denominator i.e 153/108= 1.4166
to the nearest hundredth we have 1
1.42
it’s more than one answer by the way
Answer:
Step-by-step explanation:
1. The speed at which an automated assembly line produces a product follows a normal distribution with mean production time of 32.20 seconds and standard deviation of 1.05 seconds. A full production run from this line consists of 20 completed products. What is the probability that a full production run will take less than 32 seconds on average to produce?2. Recent homebuyers from a local developer allege that 30% of the houses this developer constructs have some major defect that will require substantial repairs. To test this allegation, we randomly sample 20 homes constructed by the developer and find that two of the homes did indeed have some major defect. If the allegation is correct, what is the probability of observing at most two defective homes out of a random sample of 20?3.It is believed that 15% of people who fly on commercial airliners are "very concerned" about the safety of the carrier they have chosen. If this is accurate, what is the probability that out of 150 randomly selected people who fly on commercial airliners, between 20 and 25 of them are "very concerned" about the safety of the carrier which they have chosen?
Answer: Probability = 0.2
Step-by-step explanation:
Given data:
Mean production time = 32.20 seconds
Standard deviation = 1,05seconds
probability that a full production run will take less than 32 seconds on average to produce
= P(Xbar<32)
= P(Z<-0.8518)
= 0.2
| 1) Simplify: 12+8/2x3-(42+3)
2) Simplify: 3
1 3
—+-
5
с
3) What is 23% of 80?
а
5/6
b
4) Using the image, name a
pair of corresponding angles.
I
5) Simplify: V169
Answer:
1 no. answer is -21
Step-by-step explanation:
According to BODMAS
12 + 8 / 2 * 3 - (42 + 3)
= 12 + 8 / 2 * 3 - 45
= 12 + 4 * 3 - 45
= 12 + 12 - 45
= 24 - 45
= -21
Find the output, d, when the input, t, is 11. d= -20+11t d= ______
Answer:
d = 101
Step-by-step explanation:
d= -20+11t
Let t=11
= -20 + 11(11)
= -20 + 121
101
Answer:
the output is 101
Step-by-step explanation:
d= -20+11t
in the question it is given that t=11
substituting t=11 in the given equation
d=-20+11(11)d=-20+121d=101so the output is 99
hope it will help ^_^
Sebastian picked 21 white cabbages. He picked 12 red cabbages. How many cabbages did Sebastian pick
Answer:
Step-by-step explanation:
32 cabbages
21+12=32
a. How many ways can the letters of the word ALGORITHM be arranged in a row?
b. How many ways can the letters of the word ALGORITHM be arranged in a row if A and L must remain together (in order) as a unit?
c. How many ways can the letters of the word ALGORITHM be arranged in a row if the letters GOR must remain together (in order) as a unit?
Answer: a) 362880 b) 40320 c)720
Step-by-step explanation:
a) There are 9 letters in the word ALGORITHM. Pls note that all 9 letters are different.
So to find the number of the ways which the letters can be arranged lets imagine , that in 1st place can stay any of 9 letters, in second place any of remaining 8 letters, in 3-rd place - any of 7 letters etc
So total number of the ways is
N= 9*8*7*6*5*4*3*2*1=9!=362880
b) If A and L must remain togetherin order AL ( LA is forbidden !) so we can imagine that AL is 1 special letter.
So total number of the letters is 8. Similarly to a) we can find the number of the ways as:
N=8*7*6*5*4*3*2*1=40320
c) Similarly to b) lets imagine that GOR is 1 special letter. So there are only 7 letters . Similarly to a) the number of the ways is
N=7*6*5*4*3*2=720
Step-by-step explanation:
a.362880 b.40320. c.720
Consider the first order differential equation
y′ + t/t2 − 25y = et/t − 9
For each of the initial conditions below, determine the largest interval a
a. y(-7) = 6.4.
b. y(-2. 5) = -0.5.
c. y(0) = 0.
d. y(4.5) = -2.1.
e. y(14)= 1.7.
Answer:
For y(-7) =6.4
The largest interval is between
[tex]-\infty \to -5[/tex]
For y(-2.5) = -0.5.
The largest interval is between
[tex]-5 \to 5[/tex]
For y(0) = 0
The largest interval is between
[tex]-5 \to 5[/tex]
For y(4.5) = -2.1.
The largest interval is between
[tex]-5 \to 5[/tex]
For y(14)= 1.7.
The largest interval is between
[tex]9 \to \infty[/tex]
Step-by-step explanation:
From m the question we are told that
The first order differential equation is [tex]\frac{y' - t}{ t^2 -25} = \frac{e^t}{t-9}[/tex]
Now the first step is to obtain the domain of the differential equation
Now to do that let consider the denominators
Now generally
[tex]t^2 - 25 \ne 0[/tex] side calculation
=> [tex]t\ne \pm5[/tex] [tex]t^2 - 25 = 0[/tex]
[tex]t = \pm 5[/tex]
Also [tex]t-9\ne 0[/tex] [tex]t -9 = 0[/tex]
=> [tex]t\ne 9[/tex] [tex]t= 9[/tex]
This means that this first order differential equation is discontinuous at
[tex]t = -5 , \ \ t = 5 \ \ t = 9[/tex]
[tex]This \ is \ illustrated \ below \ \\ ------------------\\\. \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ |\\. \ -5 \ \ \ \ \ \ \ \ \ \ \ \ 5 \ \ \ \ \ \ \ \ \ \ \ \ \ 9[/tex]
So
For y(-7) =6.4
The largest interval is between
[tex]-\infty \to -5[/tex]
For y(-2.5) = -0.5.
The largest interval is between
[tex]-5 \to 5[/tex]
For y(0) = 0
The largest interval is between
[tex]-5 \to 5[/tex]
For y(4.5) = -2.1.
The largest interval is between
[tex]-5 \to 5[/tex]
For y(14)= 1.7.
The largest interval is between
[tex]9 \to \infty[/tex]
The GCF is 3x...
Express each term as the product of the GCF and its other factors.
15x^2+6x=3x(__)+3x(__)
An electronics store received two shipments of radios. Of the 250 radios in the first shipment, exactly 6% were damaged. In the second shipment, 4% of the radios were damaged. A total of 24 radios were damaged. How many radios in the combined shipments were NOT damaged? A. 466 B. 441 C. 451 D. 460
Answer:
Total number of not damaged = 451
C. 451
Step-by-step explanation:
In the first shipment, 6% of the 250 radios where damaged.
Number of damaged= 6/100 * 250
Number of damaged= 6*2.5
Number of damaged= 15 radios.
Number of not damaged= 250-15
Number of not damaged = 235 radios
In the second shipment, 4% of the radios were damaged
Let the number of second shipment= y
0.04 of y where damaged
Total number of radio damaged= 24
15 + 0.04y = 24
0.04y= 24-15
0.04y = 9
Y= 9/0.04
Y= 225
Number of radio in the second shipment= 225
Number of damaged in the second shipment= 0.04*225
Number of damaged in the second shipment= 9
Number of not damaged in the second shipment= 225-9
Number of damaged in the second shipment= 216
Total number of not damaged
= 235+216
= 451
Total number of not damaged= 451
HELP ME OUT! Triangle ABC is transformed by a rotation about the
origin, and then a translation.
The first transformation is a rotation of
degrees.
The second transformation is a translation that moves
units left and
units down.
Answer : 180 degrees
2 units left
5 units down
Your welcome ❤️
Answer:
The first transformation is a rotation of 180
degrees.
The second transformation is a translation that moves
2 units left and 5 units down.
Step-by-step explanation:
Please help I’m confused.
Answer:
What is the most common month? That is the answer
Step-by-step explanation:
Answer:
January is the most common month
Step-by-step explanation:
january=7
march=4
august=3
april=5
june=5
july=4
november=1
december=6
may=2
october=1
february=1
What is the product of the polynomials below?
(6x2-3x-6)(4x2 +5x+4)
A. 24x4 +18x2 – 15x2 - 42x-2
B. 24x4 +18X? – 15x? - 36x - 24
C. 24x4 +18x3 - 15x2 - 42x - 24
D. 24x4 +18x? - 15x2 - 36x-2
Answer:
C :) try the box method! it always works for alot of people but i prefer diatrubuative method
what is the common like term for 11 a^2v-12ab^2
Answer:
a
Step-by-step explanation:
There are no like terms here, hence no "common like term."
__
The terms have a greatest common factor of 'a', so the expression could be written as ...
a(11av -12b^2)
The greatest common factor is 'a'.
the sum of fifty and a
Answer:
a + 50
Step-by-step explanation:
Step 1: Translate word into math
sum = +
fifty = 50
a = a
Step 2: Combine
a + 50
Answer:
a + 50
Step-by-step explanation:
Step 1: Translate word into math
sum = +
fifty = 50
a = a
Step 2: Combine
a + 50
Brainliest to best PLEASE!!
Step-by-step explanation:
This is the answer i guess thank me if its right
What is the answer? Step by step.
Answer:
420 in^2
Step-by-step explanation:
The area of the rectangle before removing the circles is
A = l*w
A = 24*22
=528
The area of one of the circles is
A = pi r^2
The diameter is 6 so the radius is 6/2 = 3
= 3.14 * ( 3) ^2
=28.26
There are 4 circles
4* 28.26
113.04
Subtract the area of the 4 circles from the rectangle
528-113.04
414.96
415 in ^2
The best estimate is 420
Help, Find the domain of the function
Answer:
(-∞,∞)
Step-by-step explanation:
This would form a roughly parabolic shape that extends infinitely along the x-axis. It would reach a height of ³√2 on the y-axis. Because it extends infinitely left and right, it would have an infinite domain. In interval notation, this would be (-∞,∞)
(3 + 2i) + (4 – 5i) solve the equation .
Answer:
7 - 3 i
Step-by-step explanation:
Simplifying
(3 + -2i) + (4 + -5i) = 0
Remove parenthesis around (3 + -2i)
3 + -2i + (4 + -5i) = 0
Remove parenthesis around (4 + -5i)
3 + -2i + 4 + -5i = 0
Reorder the terms:
3 + 4 + -2i + -5i = 0
Combine like terms: 3 + 4 = 7
7 + -2i + -5i = 0
Combine like terms: -2i + -5i = -7i
7 + -7i = 0
Solving
7 + -7i = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -7i = 0 + -7
Combine like terms: 7 + -7 = 0
0 + -7i = 0 + -7
-7i = 0 + -7
Combine like terms: 0 + -7 = -7
-7i = -7
Divide each side by '-7'.
i = 1
Simplifying
i = 1
5.71 x 0.8 = 3.26 x 1.45 True or false Need answers quick!!
Answer:
False
Step-by-step explanation:
All you want to do is times 5.71 by 0.8. Once you do that, you'll get 4.568. Then you times 3.26 by 1.45 which gets you 4.727, 4.568 does not = 4.727 which makes the statement false.
Which of the following numbers has the highest value? Select one
a. 0.97
b. 0.79
C 0.95
d. 0.89
The tank of a small airplane holds 48 gallons of fuel. Seven gallons will be used for takeoff and landing. While in the air, the plane will consume an average of 10 gallons of fuel per hour. What is the maximum number of hours the plane can remain in the air?
A. 5.5
B. 4.8
C. 6.0
D. 4.1
Step-by-step explanation:
If x is the number of hours, then:
48 = 10x + 7
41 = 10x
x = 4.1
A photocopy of a polygon was reduced to 70% of its original size. Then, the copy was again reduced to 70% of its size.
a.is the second photocopy similar to the original?
b.what is the ratio of the corresponding sides of the second photocopy to the original?
Step-by-step explanation:
Step 1 of 4
a) Yes, since the photo copy, is same which is reduced by 80% it remains similar. Because the angles stay the same and the ratios responding sides are proportional.
The following is the figure:

a). Photocopy of a polygon reduced the size of the original polygon by
70%.
But the shape and angles of the the polygon remains unchanged.
Therefore, all the photocopies will be similar to the original polygon.
b). Let the measure of a side of the original polygon measures 'x' unit.
Size of the original polygon gets reduced by 70% in the photocopy.
Then the measure of the side in the photocopy = x - (70% of x)
= [tex]x-\frac{70x}{100}[/tex]
= [tex]x-0.7x[/tex]
= [tex]0.3x[/tex] units
Size of the second photocopy was reduced again by 70%.
Therefore, measure of the side of the second polygon = [tex]0.3x-(\frac{70}{100}\times 0.3x)[/tex]
= [tex]0.3x-0.21x[/tex]
= [tex]0.09x[/tex] units
Ratio of the corresponding sides of the second photocopy and the
original = [tex]\frac{0.09x}{x}[/tex]
= 0.09 : 1
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Find an equation of the line graphed below: (picture included)
Answer:
Step-by-step explanation:
1/x + 1/y =9/11 (x+y)/x.y=9/11 11x+11y=9x.y
F(x)=11x/(9x-1)
Answer:
Step-by-step explanation:
(-5,-3) (1,0)
(0+3)/(1+5)= 3/6 = 1/2
y - 0 = 1/2(x - 1)
y = 1/2x - 1/2
In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows:
∬Df(x,y)dA=∫5_0∫(2/5)y_0 f(x,y)dxdy+∫7_5∫(7−y)_0 f(x,y)dxdy.
Sketch the region D and express the double integral as an iterated integral with reversed order of integration.
∫b_a∫g2(x)_g1(x) f(x,y)dydx
a= b=
g1(x)= g2(x)=
Answer
[tex]a=0[/tex], [tex]b=2[/tex]
[tex]g_1(x)=\frac{5x}{2}[/tex], [tex]g_2(x)=7-x[/tex]
Step-by-step explanation:
Given that
[tex]\int \int Df(x,y)dA=\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy+\int_5^7\int_0^{7-y} f(x,y)dxdy\; \cdots (i)[/tex]
For the term [tex]\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy[/tex].
Limits for [tex]x[/tex] is from [tex]x=0[/tex] to [tex]x=\frac {2y}{5}[/tex] and for [tex]y[/tex] is from [tex]y=0[/tex] to [tex]y=5[/tex] and the region [tex]D[/tex], for this double integration is the shaded region as shown in graph 1.
Now, reverse the order of integration, first integrate with respect to [tex]y[/tex] then with respect to [tex]x[/tex] . So, the limits of [tex]y[/tex] become from [tex]y=\frac{5x}{2}[/tex] to [tex]y=5[/tex] and limits of [tex]x[/tex] become from [tex]x=0[/tex] to [tex]x=2[/tex] as shown in graph 2.
So, on reversing the order of integration, this double integration can be written as
[tex]\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx\; \cdots (ii)[/tex]
Similarly, for the other term [tex]\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy[/tex].
Limits for [tex]x[/tex] is from [tex]x=0[/tex] to [tex]x=7-y[/tex] and limits for [tex]y[/tex] is from [tex]y=5[/tex] to [tex]y=7[/tex] and the region [tex]D[/tex], for this double integration is the shaded region as shown in graph 3.
Now, reverse the order of integration, first integrate with respect to [tex]y[/tex] then with respect to [tex]x[/tex] . So, the limits of [tex]y[/tex] become from [tex]y=5[/tex] to [tex]y=7-x[/tex] and limits of [tex]x[/tex] become from [tex]x=0[/tex] to [tex]x=2[/tex] as shown in graph 4.
So, on reversing the order of integration, this double integration can be written as
[tex]\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy=\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx\;\cdots (iii)[/tex]
Hence, from equations [tex](i)[/tex], [tex](ii)[/tex] and [tex](iii)[/tex] , on reversing the order of integration, the required expression is
[tex]\int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx+\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx[/tex]
[tex]\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\left(\int _ {\frac {5x}{2}}^5 f(x,y)+\int _5 ^ {7-x} f(x,y)\right)dydx[/tex]
[tex]\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^{7-x} f(x,y)dydx\; \cdots (iv)[/tex]
Now, compare the RHS of the equation [tex](iv)[/tex] with
[tex]\int_a^b\int_{g_1(x)}^{g_2(x)} f(x,y)dydx[/tex]
We have,
[tex]a=0, b=2, g_1(x)=\frac{5x}{2}[/tex] and [tex]g_2(x)=7-x[/tex].
The required values are,
[tex]a=0\\b=2\\g_1(x)=\frac{5x}{2} \\g_2(x)=7-x[/tex]
Double Integral:Double integral is mainly used to find the surface area of a 2d figure, and it is denoted using ‘ ∫∫’. We can easily find the area of a rectangular region by double integration.
Given function is,
[tex]\int \int_Df(x,y)dA=\int_{0}^{5}\int_{0}^{2y}f(x,y)dxdy+\int_{5}^{7}\int_{0}^{7-y}f(x,y)dxdy[/tex]
We can write the double integral as a single term by reversing the order as,
[tex]\int_{a}^{b}\int_{g_1(x)}^{g_2(x)}f(x,y)dydx=\int_{0}^{2}\int_{\frac{5x}{2}}^{7-x}f(x,y)dydx)[/tex]
The region D is attached below.
Hence, we get the values,
[tex]a=0\\b=2\\g_1(x)=\frac{5x}{2} \\g_2(x)=7-x[/tex]
Learn more about the topic Double Integral:
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What is the y-intercept of the graph
of 3x - 4y = 12
Pls help
Answer:
Hey there!
3x-4y=12
-4y=-3x+12
y=3/4x-3
So the y-intercept is -3.
Let me know if this helps :)
Answer:
The y-intercept is at (0, -3).
Step-by-step explanation:
Where the graph intercepts the y axis x = 0 so we have the equation:
3(0) - 4y = 12
-4y = 12
y = 12/ -4
y = -3.
if D equals 4x + 10 e f equals 2x - 1 + d f equals 9 x - 15 find DF
Answer:
4x+10+2x-1=9x-15;
6x+9=9x-15;
6x-9x=-15-9;
-3x=-24;
3x=24;
from which
x=24:3=8
Then:
DF=9x-15=(9×8)-15=72-15=57
Was this helpful
Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73B. 1.21C. 1.32D. 1.89
Complete question :
A : 2.7, 3.7, 5.6, 2.6, 2.7
B : 5.1, 4.0, 3.9, 3.8, 5.2
Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73B. 1.21C. 1.32D. 1.89
Answer: A.1.73
Step-by-step explanation:
Given the data:
A : 2.7, 3.7, 5.6, 2.6, 2.7
B : 5.1, 4.0, 3.9, 3.8, 5.2
Difference betweenA and B (A - B) :
Xd = (A - B) = - 2.4, -0.3, 1.7, - 1.2, - 2.5
Sum of (A - B) = Σ Xd = (-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5) = - 4. 7
Md = ΣXd / n = - 4.7 / 5 = - 0.94
Xd - Md = (-2.4 + 0.94), (-0.3 + 0.94), (1.7 + 0.94), (-1.2 + 0.94), (-2.5 + 0.94)
(Xd - Md) = - 1.46, 0.64, 2.64, - 0.26, - 1.56
(Xd - Md)^2 = (-1.46)^2 + 0.64^2 + 2.64^2 + (-0.26)^2 + (-1.56)^2
Σ(Xd - Md)^2 = (2.1316 + 0.4096 + 6.9696 + 0.0676 + 2.4336) = 12.012
Standard deviation = √[Σ(Xd - Md)^2 / (n-1)]
Standard deviation= √12.012 / 4
Standard deviation = 1.7329
Standard deviation= 1.73
8+(-8) + a = simplified
Answer:
Just a
Step-by-step explanation:
8+(-8) they cancel each other out so 0+a = a