Answer:
10
Step-by-step explanation:
it is 10 cause 634+10=644
Answer:
10
Step-by-step explanation:
What is the missing addend?
We can fill in the blank with x
634+x=644
Now we need to get x to the other side
The rule to do this is what we do on one side we have to do the same thing to the other side
so if we subtract 634 on one side we also have to do that on the other side as well:
634-634+x=644-634
634-634 is 0
So it is
x=644-634
644-634 is 10
x=10
So the missing addend is 10
Hope this helps!
Suppose a certain study reported that 27.7% of high school students smoke.
Random samples are selected from high school that has 632 students.
(i) If a random sample of 60 students is selected, what is the probability that
fewer than 19 of the students smoke?
(ii) If a random sample of 75 students is selected, what is the probability that
more than 17 of the students smoke?
The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.
Given:
Probability of student smoke,
P = 27.7%
= 0.277
Number of students (n) = 632
[tex]q = 1-p[/tex]
[tex]=1-0.277[/tex]
[tex]=0.723[/tex]
(i)
Here,
Number of students (n) = 60
then,
⇒ [tex]n_P=60\times 0.277[/tex]
[tex]=16.62[/tex]
⇒ [tex]n_q=60\times 0.723[/tex]
[tex]=43.38[/tex]
We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.
Now,
[tex]\mu = n_P= 16.62[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]= \sqrt{60\times 0.277\times 0.723}[/tex]
[tex]=3.9664[/tex]
Now,
⇒ [tex]P(X<19) = P(X<18.5)[/tex]
[tex]=P(Z_{18.5})[/tex]
The Z-score is:
= [tex]\frac{18.5-16.62}{3.4664}[/tex]
= [tex]0.5423[/tex]
hence,
The probability will be:
⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]
or,
⇒ [tex]P(Z<19) = 0.7062[/tex]
(ii)
Here,
Number of students (n) = 75
[tex]\mu = n_P = 75\times 0.277[/tex]
[tex]=20.775[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]=\sqrt{75\times 0.277\times 0.723}[/tex]
[tex]=3.8756[/tex]
Now,
⇒ [tex]P(X>17) = P(X> 17.5)[/tex]
[tex]=1-P(X \leq 17.5)[/tex]
[tex]=1-P(Z_{17.5})[/tex]
The Z-score is:
= [tex]\frac{17.5-20.775}{3.8756}[/tex]
= [tex]-0.9740[/tex]
then, [tex]P(Z_{17.5}) = 0.165[/tex]
hence,
The probability will be:
⇒ [tex]P(X>17) = 1-0.165[/tex]
[tex]=0.835[/tex]
Learn more about Probability here:
https://brainly.com/question/9825651
What is the volume of a cone with a radius of 4 inches and height of 11?
Answer:
184.22
Step-by-step explanation:
Complete the equation describing how X and Y are related X= -2, -1, 0, 1,2,3. Y= -8, -5,-2,1,4,7
Answer:
y = 3x - 2
Happy Studying
Which is equal to (3x + 2)(x – 3)?
Please answer asappp
(3x +2)(x -3)
FOIL method
3x^2 -9x + 2x -6
3x^2 -7x -6
Your answer: 3x^2 -7x -6
Area and perimeter please?
Answer:
Area = 240 cm²
Perimeter = 80 cm
Step-by-step explanation:
✔️ Area of the triangle = ½*base*height
base of the triangle = 24 cm
height = 20 cm
Plug in the known values
Area = ½*24*20
= 12*20
Area = 240 cm²
✔️Perimeter of the triangle = sum of all the three sides that make up the triangle
Perimeter = 22 + 24 + 34
= 80 cm
If 3(nP2 + 24)=2nP2, find the positive value of n
Answer:
[tex]n = 8[/tex]
Step-by-step explanation:
Given
[tex]3(^nP_2 + 24) = ^{2n}P_2[/tex]
Required
Find n
To do this, we simply apply permutations formula
[tex]nP_r = \frac{n!}{(n -r)!}[/tex]
So, we have:
[tex]3 * [\frac{n!}{(n -2)!} + 24] = \frac{2n!}{(2n -2)!}[/tex]
Expand
[tex]3 * [\frac{n * (n - 1) * (n - 2)!}{(n -2)!} + 24] = \frac{2n * (2n - 1) * (2n - 2)}{2n - 2}[/tex]
[tex]3 * [n * (n - 1) + 24] = 2n * (2n - 1)[/tex]
[tex]3 * [n^2 - n + 24] = 4n^2 - 2n[/tex]
Open bracket
[tex]3n^2 - 3n + 72 = 4n^2 - 2n[/tex]
Collect like terms
[tex]3n^2 - 4n^2- 3n+2n + 72 = 0[/tex]
[tex]-n^2- n + 72 = 0[/tex]
Expand
[tex]-n^2 -9n + 8n + 72 = 0[/tex]
Factorize
[tex]-n(n +9) - 8(n + 9) = 0[/tex]
Factor out n + 9
[tex](-n -8)(n + 9) = 0[/tex]
Split
[tex](-n -8)= 0 \ or\ (n + 9) = 0[/tex]
Solve for n
[tex]n =8\ or\ n = -9[/tex]
The positive value is [tex]n = 8[/tex]
Determine the sum of the measures of the exterior angles of a convex hexagon (6-sided polygon).
A. 540
B. 720
C. 1,080
D. 360
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Answer:
(d) 360°
Step-by-step explanation:
The sum of exterior angles of any convex polygon is 360°.
Hi. I need help with part b thank you so much if you can do so
9514 1404 393
Answer:
Yes, that distance is the hypotenuse of a right triangle whose sides are known
Step-by-step explanation:
The diagram seems to show the path of the ball as being two segments that are at right angles to each other. Then the direct-line distance to the hole from the tee is the hypotenuse (part A) of the triangle.
Since the leg lengths are known, the Pythagorean theorem can be used (part B) to find the length of the hypotenuse. (The answer to Part B is also the answer to Part C.)
Find the missing side lengths leave your answer as a racials simplest form
Answer:
y=3 and x=3*sqrt(3)
Step-by-step explanation:
sin(30)=y/6
1/2=y/6, y=3. As it's a right angled triangle, 6^2-3^2=x^2, x=3*sqrt(3)
Answer:
x = 3 sqrt(3)
y = 3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 30 = y /6
6 sin 30 = y
6 (1/2) = y
3 = y
cos theta = adj / hyp
cos 30 = x /6
6 cos 30 =x
6 ( sqrt(3)/2) =x
3 sqrt(3) = x
f(x) = 1 + 9. Find f '(x) and its domain.
A. f-1 (z) = (x – 9)?: x2 9
B. f-1(x) = (x – 9)?; x20
c. f-1 (2) = x2 – 9;x2 9
D. f-1 (x) = x2 – 9; x2 0
Answer:
B
Step-by-step explanation:
f(x) = sqrt(x) + 9
f(x) - 9=sqrt(x)
f^(-1)(x)=(x-9)^2 and it's domain is greater than 0
ABC are points; (2,3), (4,7), (7,3) respectively. Find the equation of the line through the point (3,-5) which is parallel to the line with the equation 3x+2y-5=0
Answer:
y = -3x/2 - 1/2
Step-by-step explanation:
slope m = -3/2
-5 = (-3/2)×3+b
or, b = -1/2
putting it into y = mx + b
y = -3x/2 - 1/2
Answered by GAUTHMATH
Draw a frequency polygon for the following data:
Marks
0 - 10
10 - 20 20 - 30 30 - 40 40 - 5050 - 60
错误。
No. of Students
7
15
22
30
16
10
Answer:
See attachment
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Required
The frequency polygon
We have:
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
First, we calculate the midpoint of each class
[tex]\begin{array}{ccccccc}{Midpoint} & {(0+10)/2} & {(10+20)/2} & {(20+30)/2} & {(30+40)/2} & {(40+50)/2} & {(50+60)/2}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
[tex]\begin{array}{ccccccc}{Midpoint} & {5} & {15} & {25} & {35} & {45} & {55}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Lastly, we plot the midpoint against the frequency of students (see attachment)
A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 11.3. In his class, an "A" is any exam score of 90 or higher. This quarter she has 22 students in her class. What is the probability that 6 students or more will score an "A" on the final exam?
prob =
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
---------------
For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.
Additionally, to find the proportion of students who scored an A, the normal distribution is used.
----------------
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success.
----------------
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
----------------
Proportion of students that scored an A:
Scores have a mean of 79 and a standard deviation of 11.3, which means that [tex]\mu = 79, \sigma = 11.3[/tex]
Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 79}{11.3}[/tex]
[tex]Z = 0.97[/tex]
[tex]Z = 0.97[/tex] has a p-value of 0.8340.
1 - 0.8340 = 0.166
The proportion of students that scored an A is 0.166.
----------------
Probability that 6 students or more will score an "A" on the final exam:
Binomial distribution.
22 students, which means that [tex]n = 22[/tex]
The proportion of students that scored an A is 0.166, which means that [tex]p = 0.166[/tex]
The probability is:
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184[/tex]
[tex]P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807[/tex]
[tex]P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687[/tex]
[tex]P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239[/tex]
[tex]P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117[/tex]
[tex]P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517[/tex]
Then
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551[/tex]
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449[/tex]
Thus
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
For a problem that used the normal distribution, you can check https://brainly.com/question/15181104, and for a problem that used the binomial distribution, you can check https://brainly.com/question/15557838
Mr. Rowley has 16 homework papers and 14 exit tickets to return. Ms. Rivera has 64 homework papers and 60 exit tickets to retum. For each teacher, write a ratio to represent the number of homework papers to number of exit tickets they have to return. Are the ratios equivalent? Explain.
Answer:
Mr. Rowley=16:14
=8:7
Ms.Rivera= 64:60
=16:15
Một tàu biển trị giá 2.500.000 USD đang chở các lô hàng A, B,C có giá trị lần lượt là 100.000 USD; 300.000USD, 500.000USD và tiền cước chưa thu thuộc chủ tàu là 60.000 USD. Trong hành trình đi từ Indonesia về cảng Sài Gòn tàu bị mắc cạn, vỏ tàu bị thủng, nước tràn vào làm hư hỏng một số hàng hóa. Để cứu tàu và hàng, thuyền trưởng quyết định bịt lỗ thủng bằng các phương tiện trên tàu và vứt một số hàng để tàu nhẹ bớt, đồng thời thuyền trưởng cũng cho máy tàu làm việc vượt công suất nhằm giúp tàu thoát cạn. Sau sự việc, các tổn thất được xác định như sau:
- Vỏ tàu thủng dự kiến phải sửa chữa hết 100.000 USD
- Máy tàu hư do hoạt động quá công suất và dự kiến phải sửa hết 250.000 USD
- Lô hàng B bị nước tràn vào giảm giá trị thương mại 100%.
- Lô Hàng A bị vứt xuống biển toàn bộ.
- Thiệt hại để cứu tàu và chi phí cho thủy thủ trong việc cứu tàu là 10.000 USD.
a. Hãy xác định các tổn thất riêng của các bên
b. Hãy xác định tổng tổn thất chung của các bên
c. Hãy xác định giá trị chịu phân bổ tổn thất chung (giá trị đóng góp của từng chủ thể trên tàu)
d. Hãy xác định các khoản đóng góp vào tổn thất chung của các bên
Answer:
ask in English then I can help
I need help ASAP thank you
Answer:D) Under-root 25.Under-root 3
Step-by-step explanation
Under-root 25 = 5
Answer:
Answer D and B.
Step-by-step explanation:
[tex]{ \bf{5 \sqrt{3} }} \\ = { \bf{ \sqrt{ {5}^{2} } \times \sqrt{3} }} \\ = { \bf{ \sqrt{25} . \sqrt{3} }}[/tex]
What dimensions would you need to calculate the volume of a basketball?
radius and height
length, width and slant height
radius
length, width, and height
Answer:
Radius on it's own is enough
Step-by-step explanation:
you could get the radius from the other informations, but after all you will calculate the volume with it and not the otheds, so just take radius. a sphere is, in terms of information, the simplest 3D-body to describe, like with a circle in 2D
The dimensions would you need to calculate the volume of a basketball is Radius on its own is enough
We have given that,
radius and height
length, width, and slant height
radius
length, width, and height
We have to determine the dimensions would you need to calculate the volume of a basketball.
What is the dimension?
Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction.
you could get the radius from the other information, but after all, you will calculate the volume with it and not the others, so just take the radius.
A sphere is, in terms of information, the simplest 3D body to describe, like a circle in 2D.
To learn more about the dimension visit:
https://brainly.com/question/26740257
#SPJ2
One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.
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Answer:
90°, 60°, 30°
Step-by-step explanation:
The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.
The first angle is 3 ratio units, or 90°.
The second angle is 2 ratio units, or 60°.
The third angle is half that, or 30°.
The three angles are 90°, 60°, 30°.
Which quadrilateral has equal diagonals
Select one:
a. trapezoid
b. rectangle
c. parallelogram
d. rhombus
Answer:
Option b: Rectangle
Explanation:
Give branliest pls ;)
6. On a number line, point A has a coordinate of -6, and point B has a coordinate of 2. Which is the coordinate of point M, the midpoint of AB ?
A) 0
B) -2
C) -3
D) 4
9514 1404 393
Answer:
B) -2
Step-by-step explanation:
The midpoint is the average of the end points.
M = (A +B)/2
M = (-6 +2)/2 = -4/2 = -2
The coordinate of M is -2.
Please help me with 9 I really need it
Answer:
605 boys.
Step-by-step explanation:
5:7 means 5 parts consists of boys and 7 parts consist of girls.
Since 7 parts = 847, 1 part = 121 and 5 parts = 605
Hence there are 605 boys.
Hope you have a nice day :)
By how many minutes is 2¾h longer than 1h 55min?
Three numbers form an arithmetic sequence whose
common difference is 3. If the first number is
increased by 1, the second increased by 6, and
the third increased by 19, the resulting three
numbers form a geometric sequence. Determine
the original three numbers.
Let x be the first number in the sequence. Then the first three numbers are
{x, x + 3, x + 6}
The next sentence says that the sequence
{x + 1, x + 9, x + 25}
is geometric, which means there is some fixed number r for which
x + 9 = r (x + 1)
x + 25 = r (x + 9)
Solve for r :
r = (x + 9)/(x + 1) = (x + 25)/(x + 9)
Solve for x :
(x + 9)² = (x + 25) (x + 1)
x ² + 18x + 81 = x ² + 26x + 25
8x = 56
x = 7
Then the three numbers are
{7, 10, 13}
Mathematics question help
Distance Formula: [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
Point 1: (9,0)
Point 2: (5,-8)
D = sqrt[ (5 - 9)^2 + (-8 - 0)^2 ]
D = sqrt[ (-4)^2 + (-8)^2 ]
D = sqrt[ 16 + 64]
D = sqrt(80)
Hope this helps!
In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.
Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
[tex]f(t) = 10000(0.9407)^t[/tex]
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
[tex]f(t) = f(0)(1-r)^t[/tex]
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that [tex]f(0) = 10000[/tex], thus:
[tex]f(t) = 10000(1-r)^t[/tex]
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
[tex]f(2) = 8850[/tex]
We use this to find 1 - r.
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]8850 = 10000(1-r)^2[/tex]
[tex](1-r)^2 = \frac{8850}{10000}[/tex]
[tex](1-r)^2 = 0.885[/tex]
[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]
[tex]1 - r = 0.9407[/tex]
Thus
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]f(t) = 10000(0.9407)^t[/tex]
Convert 15,000 meters to centimeters.
15,000 centimeters
150,000 centimeters
15,000,000 centimeters
1,500,000 centimeters
Answer:
1500000
Step-by-step explanation:
1 metre = 100 cm
15000metre =15000*100
=1500000
what is the least common factor for 9 8 7
Answer:504
This is the answer
504
The question is in the screenshot
Answer:
AC is about 4.29
Step-by-step explanation:
we need to use simple trigonometry for this problem
the tangent of an angle is the ratio between the opposite side and the adjacent side
so the tangent of the angle 35º is BC / AC
tan(35) is about 0.7
this means that BC / AC = 0.7
we know BC is 3
so 3 / AC = 0.7
3 = 0.7(AC)
AC is about 4.29
According to Zimmels (1983), the sizes of particles used in sedimentation experiments often have a uniform distribution. In sedimentation involving mixtures of particles of various sizes, the larger particles hinder the movements of the smaller ones. Thus, it is important to study both the mean and the variance of particle sizes. Suppose that spherical particles have diameters that are uniformly distributed between 0.02 and 0.08 centimeters. Find the mean and variance of the volumes of these particles. (Recall that the volume of a sphere is (4/3) πr3) Round your answers to four decimal places.
E(Y)= ___ x10−5 cm3
V(Y) = ___ x10−9
The expected value of a normal distribution is the mean of the distribution, while the variance measures the squared deviation of a value from the expected value. The expected value and the variance are: [tex]13.6190 \times 10^{-5}[/tex] and [tex]580.8000 \times 10^{-9}[/tex]
Given that, the diameters are:
[tex]d_1 = 0.02[/tex]
[tex]d_2 = 0.08[/tex]
The radius is:
[tex]r = \frac{d}{2}[/tex]
So, we have:
[tex]r_1 = \frac{0.02}{2} = 0.01[/tex]
[tex]r_2 = \frac{0.08}{2} = 0.04[/tex]
The volume of the sphere is:
[tex]V = \frac{4}{3} \times \pi \times r^3[/tex]
For [tex]r_1 = 0.01[/tex], the volume is:
[tex]V_1 = \frac{4}{3} \times \frac{22}{7} \times 0.01^3 = 0.419047 \times 10^{-5}[/tex]
For [tex]r_2 = 0.04[/tex], the volume is
[tex]V_2 = \frac{4}{3} \times \frac{22}{7} \times 0.04^3 = 26.819047 \times 10^{-5}[/tex]
The mean of a uniform distribution is:
[tex]E(y) = \frac{a + b}{2}[/tex]
In this case, the mean is:
[tex]E(y) = \frac{V_1 + V_2}{2}[/tex]
So, we have:
[tex]E(y) = \frac{0.419047 \times 10^{-5} + 26.819047 \times 10^{-5}}{2}[/tex]
[tex]E(y) = \frac{27.238094\times 10^{-5} }{2}[/tex]
[tex]E(y) = 13.619047 \times 10^{-5}[/tex]
Approximate
[tex]E(y) = 13.6190 \times 10^{-5}[/tex]
The variance of a uniform distribution is:
[tex]V(y) = \frac{(b-a)^2}{12}[/tex]
In this case, the volume is:
[tex]V(y) = \frac{(V_2-V_1)^2}{12}[/tex]
So, we have:
[tex]V(y) = \frac{(26.819047 \times 10^{-5}- 0.419047 \times 10^{-5})^2}{12}[/tex]
[tex]V(y) = \frac{(26.4 \times 10^{-5})^2}{12}[/tex]
[tex]V(y) = \frac{(696.96 \times 10^{-10})}{12}[/tex]
[tex]V(y) = 58.08000 \times 10^{-10}[/tex]
Rewrite as:
[tex]V(y) = 580.8000 \times 10^{-9}[/tex]
Hence, the expected value and the variance of the sphere are:[tex]13.6190 \times 10^{-5}[/tex] and [tex]580.8000 \times 10^{-9}[/tex]
Learn more about expected values and variance at:
https://brainly.com/question/4470015
*20 points*
What is the probability of drawing yellow marble followed by a red marble from a bag containing 12 yellow marbles, 14 red marbles, and 15 green marbles if the first marble is not replaced?
a. 192/1,849
b. 18/43
c. 21/205
Answer:
c: 21/205
Step-by-step explanation:
The probability of choosing a yellow marble first is 12/41 bc there are 12 yellow marbles and 41 marbles to choose from.
The probability of choosing a red marble is 14/40 bc there are 14 red marbles and 40 marbles to choose from( since you have removed the marble you first chose so there are 40 marbles left).
Multiplying these two together, 12/41 * 14/40 = 168/1640, simplified it's 21/205.
