Find the slope of the line that passes through (10, 10) and (8, 11).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
= -1/2
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (11-10)/(8-10)
= 1/-2
= -1/2
a) One of two boxes contain 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1/3 for box 1 and 2/3 for box 2. A box is selected at random and a ball is selected at random from it. a) Given that the ball selected is red, what is the probability it was selected from the first box? b) Given that the ball selected is red, what is the probability it was selected from the second box? c) Compare the results in parts a) and b) and explain the answer.
Answer:
The answer is below
Step-by-step explanation:
Let B₁ represent box 1, B₂ represent box 2, E₁ represent the event of selecting box 1, E₂ represent the event of selecting box 2 and R represent the event of selecting a red ball.
Given that:
Probability of selecting box 2 P(E₂) = 2/3, Probability of selecting box 1 = P(E₁) = 1/3
Probability of selecting red ball from box 1 = P(R | E₁) = 4/6 [4 red balls out of 4 red, 2 green]
Probability of selecting red ball from box 2 = P(R | E₂) = 2/6 [2 red balls out of 2 red, 4 green]
a)
Given the ball is red, the probability it was selected from the first box is:
[tex]P(E_1|R)=\frac{P(R|E_1)P(E_1)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)} =\frac{2/3*1/3}{(2/3*1/3)+(1/3*2/3))} =\frac{1}{2}[/tex]
b)
Given the ball is red, the probability it was selected from the second box is:
[tex]P(E_2|R)=\frac{P(R|E_2)P(E_1)}{P(R|E_2)P(E_2)+P(R|E_1)P(E_1)} =\frac{1/3*2/3}{(1/3*2/3)+(2/3*1/3))} =\frac{1}{2}[/tex]
c)
We can see that both probabilities are equal. Although we have more red balls in box 1 (twice as much) than in box 2 but the probability of selecting from box 2 (is twice as much) than from selecting from box 1.
The probability that the ball selected is red and it is selected from the first box is 1/2 and the probability that the ball selected is red and it is selected from the second box is 1/2.
Given :
One of the two boxes contains 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1/3 for box 1 and 2/3 for box 2.a) The probability that the ball selected is red and it is selected from the first box is:
[tex]P(E_1|R)=\dfrac{P(R|E_1)P(E_1)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)}[/tex]
[tex]P(E_1|R)=\dfrac{\dfrac{2}{3}\times \dfrac{1}{3}}{\dfrac{2}{3}\times \dfrac{1}{3}+\dfrac{1}{3}\times \dfrac{2}{3}}[/tex]
[tex]P(E_1|R)=\dfrac{1}{2}[/tex]
b) The probability that the ball selected is red and it is selected from the second box is:
[tex]P(E_2|R)=\dfrac{P(R|E_2)P(E_2)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)}[/tex]
[tex]P(E_2|R)=\dfrac{\dfrac{2}{3}\times \dfrac{1}{3}}{\dfrac{2}{3}\times \dfrac{1}{3}+\dfrac{1}{3}\times \dfrac{2}{3}}[/tex]
[tex]P(E_2|R)=\dfrac{1}{2}[/tex]
c) The probability that the ball selected is red and it is selected from the first box and the probability that the ball selected is red and it is selected from the second box is the same.
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Please help! :( If AJKL = ARST, which congruences are true by CPCTC? Check all that apply.
A. ZL ZR
B. KL: ST
C. KZS
D. JK = RS
E. JL - RS
F. LJ2S
Step-by-step explanation:
I just got it on a pex. JK=RS. KL=ST. K=S. those are the answers
The congruences that are true by CPCTC are:
∠L = ∠R
KL ≅ ST
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
If ΔJKL = ΔRST, then the corresponding parts of the triangles are congruent.
CPCTC stands for "corresponding parts of congruent triangles are congruent,"
So we can use this property to determine which congruences are true.
∠L = ∠R:
This is true by CPCTC because they are corresponding angles in congruent triangles.
JK ≅ RS:
This is not true by CPCTC because they are not corresponding sides in congruent triangles.
KL ≅ ST:
This is true by CPCTC because they are corresponding sides in congruent triangles.
JL ≅ RS:
This is not true by CPCTC because they are not corresponding sides in congruent triangles.
∠L = ∠S:
This is not necessarily true just by the fact that ΔJKL = ΔRST.
It could be true in some cases, but it is not guaranteed by CPCTC.
Therefore,
The congruences that are true by CPCTC are:
∠L = ∠R
KL ≅ ST
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Half of my weight is equal 3/4 of my brother's weight. If my brother weighs 64kg; what is my weight
Answer:
96kg
Step-by-step explanation:
3/4 of 64 is 48
2 × 48 = 96kg
The data in the line plot show how many pages each student read last night. Which is the best measure of variability?
A. interquartile range
B. mean
C. median
D. range
Which is the graph of the function f(x) = x2 + 2x + 3? On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (negative 1, 2), and goes through (0, 3). On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (1, 2), and goes through (2, 3). On a coordinate plane, a parabola opens up. It goes through (negative 4, 3), has a vertex at (negative 2, negative 1), and goes through (0, 3). On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (2, negative 1), and goes through (4, 3). AAAAAAA
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Please help me with this and explain how you got the answer thank you
What is the slope of line m?
On a coordinate plane, a straight line goes through (negative 2, 1), (0, 0), and (2, negative 1).
Given:
A straight line goes through (-2,1), (0,0), and (2,-1).
To find:
The slope of the given line.
Solution:
Slope formula
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Consider any two points from the given points.
The line goes through (-2,1) and (0,0). So, the slope of the line is
[tex]m=\dfrac{0-1}{0-(-2)}[/tex]
[tex]m=\dfrac{-1}{2}[/tex]
Therefore, the slope of the line is [tex]m=-\dfrac{1}{2}[/tex].
Answer:
its 2/3
Step-by-step explanation:
. You need 1/12 yard of ribbon to make one bow. You have 5/6 yard of ribbon. How many bows are you able to make with the ribbon you have? *
Answer:
You can make 14 with some ribbon left over.
Step-by-step explanation:
What are the zero(s) of the following function: f(x)= -8X - 4?
Robin made a cuboid of plasticine. Length, breadth, and height of the cuboid are
3 cm, 2 cm, 3 cm respectively. How many such cuboids will he need to make a
perfect cube?
Answer:
75
Step-by-step explanation:
Tom purchased 5 football games for 10.88 each and 5 pokemon games for 11.87 each with 6 20 bills. How much change did tom get
Answer:
5*10.88 + 5*11.87=113.75
120-113.75=6.25
$6.25
Step-by-step explanation:
(fractions 5th grade) 3/9 + 2/3
Answer:
1
Step-by-step explanation:
Simplify 3/9 by 3 -> 1/3
Now that both fractions have the same denominator, you can add them.
1/3 + 2/3 = 3/3 or 1
What is the correct solution to the
inequality?
Answer:
the correct answer is D
Step-by-step explanation:
help please. pleasee i will mark brain please
Answer:
A=3
B=3
C=2.5
D=5
E=1
F=2
G=4
Here you go! Happy to help!
Step-by-step explanation:
47) How much does 75 gallons of water weigh
Answer:
It weighs 850 pounds
Step-by-step explanation:
Have a nice day
There are less 32 students in Mr. B’s math class
Answer:
-32????
Step-by-step explanation:
I don't see an actual question here, so my three answers that I got from this post are:
-32
<32
>-32
A teacher is making 7 identical supply boxes
for each table in her classroom. Each box
contains some pencils and 11 pens. The
teacher uses a total of 182 pencils and pens.
Determine the number of pencils that are in
each box.
Answer:
26
Step-by-step explanation:
182 pencils devided by 7 identical boxes
182÷7
=26 pencils are in each box
Answer:
15 pencils in each box
Step-by-step explanation:
If each box has 11 pens,then there are 77 pens
In total 182 pencils and pens
182-77 = 105 (105 pencils)
105/7 = 15
15x7 = 105
11x7 = 77
105 +77 = 182
he FDAL level for insect filth in chocolate is 0.6 insect fragments (larvae, eggs, body parts, and so on) per grams. Suppose that there is an average of 0.57 insect fragments per gram of chocolate bar and the distribution is following a Poisson distribution. Compute the probabilities that the number of insect fragments in a 50-gram sample of chocolate bar are:
Answer:
Step-by-step explanation:
[tex]\text{To find :} \\ \\ 1.) \ \ \text{More than 20} \\ \\ 2) \text{Less than 30 } \\ \\ 3) \ \text{Within the range of }( \mu - \sigma , \mu +\sigma)[/tex]
[tex]\ \ \ Since \ \ X \ \text{follows a poisson distribution and;} \\ \\ X\sim Poisson (0.57) per \ gram \\ \\ X \sim Poisson (28.5) \ per \ 50 \ grams \\ \\[/tex]
[tex]1) \ \ \ \text{The probability } P(X>20) = \sum \limits ^{50}_{x=21} \dfrac{e^{-28.5}\times 28.5^x}{x!} \\ \\ \mathbf{ = 0.9389}[/tex]
[tex]2) P( X<30) = \sum \limits ^{29}_{x=0} \dfrac{e^{-28.5}\times 28.5^x}{x!} \\ \\ \mathbf{=0.5861}[/tex]
[tex]\text{3) Since then mean}\ \mu = 28.5 \\ \\ \sigma =\sqrt{28.5} = 5.339 \\ \\ \mu - \sigma = 28.5 -5.339= 23.161 \\ \\ \mu + \sigma = 28.5 + 5.339 = 33.839[/tex]
∴
[tex]P(23.161 < X< 33.839) = \sum \limits ^{33}_{24} \dfrac{e^{-28.5}\times 28.5^x}{x! } \\ \\ = P(X\le 33) - P( X \le 23) \\ \\ = 0.82678 - 0.1750 \\ \\ \mathbf{= 0.6516}[/tex]
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Answer:y+2=7/3(x-2)
Step-by-step explanation:
You plug the x, y and the slope on the point-slope formula, which is y-y1=m(x-x1)
Y1 is -2, x1 is 2 and slope(m) is 7/3
Answer: y+2=7/3(x-2)
Step-by-step explanation: I used a coordinate plane
Plz mark me brainliest
city workers recorded the number of squirrels in a park over a period of time. At the first count, there were
30 total squirrels. After 1 year, the city workers recorded a total of 60 squirrels, and after 2 years there were
120
a. Write a function that represents the population of squirrels recorded over x number of years,
b. Assuming the same growth rate and no squirrel dies, what will the squirrel population be in 6 years?
Justify your answer mathematically
Function:
A. x times 60 = the amount of squirrels in that year
Answer
B. 6 X 60 = 360
Step-by-step explanation
Years | Squirrels
______________
1 | 60
---------------------------
2 | 120
-------------------------
3 | 180
-------------------------
4 | 240
-------------------------
5 | 300
-----------------------
6 | 360
what is 261.8 rounded to the nearest tenth
is it 261.80?
A rectangular garden is 20 ft longer than it is wide. Its area is 800 ft 2 . What are its dimensions?
how many 5 digits numbers can be created using digits 1,2,3,7, and 6 without repeating any digits within that 5-digit number?
There are 5 numbers that can be used.
The first digit can be 1 of 5
The second digit can be 1 of 4
The third digit is 1 of 3
The fourth digit is 1 of 2
The fifth digit is 1 of 1
Total digits that can be created = 5 x 4 x 3 x 2 x1 = 120
Find the area of the figure. Use 3.14 for A. N 8 m 12 m
Answer: 105m²
Formula for Area of Circle: A = π r²
so, A = 3.14 (6)² (I got 6 because radius is half the diameter)
Don't forget to divide the final area of the circle in half, because It's only a semicircle.
Formula for Triangle: A = [tex]\frac{bh}{2\\}[/tex]
so, A = [tex]\frac{6(8)}{2}[/tex] (again, the "6" is just the diameter divided in half which forms the base of ONE triangle.)
You need to multiply the final area of the triangle by 2 since there are 2 triangles.
Step-by-step explanation:
Cos Milky said it. Trust Milky. Milky smart.
Answer:
deez nù Tx. . .
Step-by-step explanation:
source:trust me bro
PLEASE HELP ME THANKS SO Much
9514 1404 393
Answer:
(b) x = 7, AB = 9, AC = 12
Step-by-step explanation:
ΔAEB ~ ΔCDB so corresponding sides are proportional.
AB/CB = AE/CD
(x+2)/(x -4) = 12/4
x +2 = 3(x -4) . . . . . . multiply by x-4
x +2 = 3x -12 . . . . . . eliminate parentheses
14 = 2x . . . . . . . . . . . add 12-x
7 = x . . . . . . . . . . . . . divide by 2
AB = x +2 = 7 +2 = 9
BC = x -4 = 7 -4 = 3
AC = AB +BC = 9 +3 = 12
__
In summary, ...
x = 7, AB = 9, AC = 12 . . . . . matches the 2nd choice
_____
Additional comment
Please note the other choices make no sense.
(a) AB = x +2 = -5 +2 = -3 ≠ -9
(c) AC = 2x-2 = 2(7) -2 = 12 ≠ 9
(d) segment lengths are never negative in a geometrical figure
please help me! no links please im begging u ;(
9514 1404 393
Answer:
x = 70
Step-by-step explanation:
The angle between the tangents is the supplement of the intercepted arc:
x° = 180° -110°
x° = 70°
__
Alternate solution
The exterior angle x° is half the difference of the intercepted arcs. Long arc ACB is 360° -110° = 250°, so we have ...
x° = (250° -110°)/2 = 140°/2
x° = 70°
__
If you work this alternate solution generically, you find it is the same as the first solution.
x = ((360 -AB) -AB)/2 = (360 -2AB)/2 = 180 -AB
For this question, if the answer is not a whole number, enter it as a fraction using / as the fraction bar.
Rajek, a truck driver, hauls containers for his customers. One customer wants to know the total amount of cardboard that can fit in a container at one time. The truck Rajek uses is shown below.
The base of the container has an area of 50 1/4 square feet.
Answer:
226 1/8
Step-by-step explanation:
Substitute the measurements of the container into the formula.
The amount of cardboard Rajek can fit in the container at one time is cubic feet.
The total surface area of the container is 9L + 9W + 50 1/4
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
To find the total amount of cardboard that can fit in the container at one time, we need to find the surface area of the container.
The container has a rectangular base with an area of 50 1/4 square feet.
Let's assume the length of the base is L and the width is W.
We know that:
L x W = 50 1/4
We also know that the height of the container is 4(1/2) feet, which is equivalent to 9/2 feet.
The container has two identical sides, which are rectangles with a length of L and a height of 9/2 feet.
The surface area of one side is:
L x (9/2) = (9/2)L
The container also has two identical ends, which are rectangles with a width of W and a height of 9/2 feet.
The surface area of one end is:
W x (9/2) = (9/2)W
Finally, the container has a top, which is a rectangle with a length of L and a width of W.
The surface area of the top is:
L x W
To find the total surface area of the container, we add up the surface area of each of these parts:
Total surface area = 2(L x (9/2)) + 2(W x (9/2)) + (L x W)
Simplifying this expression, we get:
Total surface area = 9L + 9W + LW
We know that L x W = 50 1/4, so we can substitute this into the equation:
Thus,
The total surface area of the container is 9L + 9W + 50 1/4
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please help a bro brainiest
3^-x=243
Answer:
x=-240
Step-by-step explanation:
Answer: [tex]x = - 5[/tex]
Step-by-step explanation:
[tex]3^{-x} = 243[/tex]
[tex]3^{-x} = 3^{5}[/tex]
[tex]-x = 5[/tex]
[tex]x = -5[/tex]
what is the measure of angle k?
9514 1404 393
Answer:
59°
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
∠N +∠L = 180°
(a +16) +(a -18) = 180
2a = 182 . . . . . . . . . . add 2
a = 91 . . . . . . . . . . . . divide by 2
Then the measure of angle M is ...
∠M = (a+30)° = (91 +30)° = 121°
and angle K is its supplement.
∠K = 180° -121°
∠K = 59°