Answer:
0.207 = 20.7% probability that exactly 10 of these are from the second section
Step-by-step explanation:
The students are chosen without replacement, which means that the hypergeometric distribution is used.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] 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]
In this question:
20 + 30 = 50 total students, which means that [tex]N = 50[/tex]
30 students from the second section, which means that [tex]k = 30[/tex]
First 15 graded projects, so sample of 15, which means that [tex]n = 15[/tex]
a. What is the probability that exactly 10 of these are from the second section
This is P(X = 10).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 10) = h(10,50,15,30) = \frac{C_{30,10}*C_{20,5}}{C_{50,15}} = 0.207[/tex]
0.207 = 20.7% probability that exactly 10 of these are from the second section
Falisha spent 2/5 of her money on a bag. she gave 2/3 of the remaining amount to her sister. What fraction of her money was she left with?
Answer:
1/5
Step-by-step explanation:
After spending 2/5 of her money on a bag, she has 3/5 of the original amount of money left. As she gave 2/3 of the remaining amount of money to her sister, she gave 2/5 of the original amount of money to her sister (3/5 × 2/3 = 2/5). Therefore, there's only 1/5 (1 - 2/5 - 2/5 = 1/5) of the original amount of money left in her bag.
the area of a 12-cm-wide rectangle is 288 cm^2 what is its length?
Answer:
24cm
Step-by-step explanation:
The area of the rectangle is length × breadth. You already know the area and the breadth, so you can find the length.
288cm² = length × 12cm
length = 288cm² ÷ 12cm
= 24cm
Washe
car alone, ustin takes
45 hours
had
takes tos hours.
How
donde long does the car
by
does it take Justin's
hiods?
Washing car alone it takes Justin 4.5 hours. If his dad helps him it takes 1.5 hours. His long does it take Justin’s dad to wash the car by himself?
Answer:
it takes his dad 3 hours
Step-by-step explanation:
4.5-1.5 =3
Chandler, Jamal, Allison, and Qi are given the following problem. In 1982, Wayne Gretsky set a record for the greatest number of hockey goals in one season with 92 goals. If a player has scored 60 goals this season and averages 2 goals per game, how many additional games must he play to break the record? Each student writes an inequality to represent the situation. Chandler wrote 60 + 2g ≥ 92 Jamal wrote 60 + 2g > 92 Allison wrote 60 + 2g < 92 Qi wrote 60 + 2g ≤ 92 Whose inequality is CORRECT? A. Qi B. Chandler C. Allison D. Jamal
Answer:
The correct answer is B.
Step-by-step explanation:
Since Chandler, Jamal, Allison, and Qi are given the following problem: "In 1982, Wayne Gretsky set a record for the greatest number of hockey goals in one season with 92 goals. If a player has scored 60 goals this season and averages 2 goals per game, how many additional games must he play to break the record? ", And each student writes an inequality to represent the situation:
Chandler wrote 60 + 2g ≥ 92
Jamal wrote 60 + 2g> 92
Allison wrote 60 + 2g <92
Qi wrote 60 + 2g ≤ 92
To determine whose inequality is correct, the following calculation must be performed:
92 - 60 = 32
32/2 = 16
Chandler: 60 + 2x16 ≥ 92
Thus, Chandler wrote the correct option.
In Nebraska, Mr. Dukarelli's 11th grade class consisting of 27 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average 11th grade class size in the state is 27. If the students in Mr. Dukarelli's class are representative of students in the state's 11th grade classes and there are 1600 11th grade in the state, which of the following best estimates the number of 11th grade students in the state who have fewer than two siblings? SHOW YOUR WORK PLEASE!!
a. 18,200
b. 28,300
c. 30,600
d. 43,200
95141 1404 393
Answer:
b. 28,300
Step-by-step explanation:
The estimated number of 11th grade students in the state is ...
(1600 classes)(27 students/class) = 43,200
About 34.6% are estimated to have 2 or more siblings, so the remaining 100%-34.6% = 65.4% are estimated to have fewer than 2 siblings.
Translated to a number of students, that percentage is ...
0.654 × 43,200 = 28,252.8 ≈ 28,300
A good estimate of the number of students with fewer than 2 siblings is 28,300.
List the transformation on the function f(x)
y= -4/5 f(x+5)-3
Answer:
Move the graph 5 units left, 3 units down, with a slope of -4/5
Step-by-step explanation:
inside parenthesis is the opposite so instead of 5 units right its 5 units left
and the 3 outside the parenthesis stays as is moving the graph down
and the -4/5 represents the slope of the function
Rory earned an 84% on his test. He answered 21 questions correctly. How many total questions were on the
test? Round to the nearest tenth if necessary
Answer:
25 questions,
$18.75
Step-by-step explanation:
Remember, to change percents to decimals, divide the number by 100 and remove the parentheses.
1. 84%, or 21 questions of Roy's test were correct.
Let's set the number of questions on the test as "x". We can then write this equation:
84% * x = 21
Simplify.
0.84 * x = 21
Divide both sides by 0.84
x = 25
There were 25 questions on the test.
2. Cheesecake Factory question
We need to find 15% of 125.
15% * 125 =
0.15 * 125 =
18.75
They need to leave a $18.75 tip.
I hope this helps! Feel free to ask any questions!
Find the surface area of a cone that has a slant height of 6 inches and a base with a diameter of 3 inches.
Answer:
Step-by-step explanation:
radius r = 1.5 in
slant height ℓ = 6 in
lateral area LA = πrℓ
= π(1.5)(1.5)
= 2.25π
≅ 7.07 in²
base area BA = πr²
= π1.5²
≅ 7.07 in²
surface area SA = LA + BA
= 7.07 + 7.07
≅ 14.14 in²
You bought $2000 worth of stocks in 2012. The value of the stocks has been decreasing by 10% each year
Part A
Write an exponential function to represent this scenario...
Format for answer...
A(T) = a (1 + r)
Part B
What will your stock be worth in 2017? Round your answer to the nearest cent.
Answer:
a(t)= 2000(1+r)^T
*make sure to add the power to t
a(t)=2000(1+.10)^5
= 3221.02
Hope this helps!
The exponential decay function is given by y=2000×0.9ˣ and the stock will be worth $1180.98 after a period of 5 years.
What is exponential decay function?In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)ˣ wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.
Given here: The value of the stock in 2012 was $2000 and the value decreases each year by 10%
We know the exponential decay is given by y=a(1-b)ˣ
where x is the number of years and 1-b is the decreasing factor
Thus based on the given information we can construct the exponential decay function as y=2000(1-10%)ˣ
or y=2000×0.9ˣ
Therefor in 5 years i.e in 2017 the stock will be worth
y=2000×0.9⁵
=$1180.98
Hence, The exponential decay function is given by y=2000×0.9ˣ and the stock will be worth $1180.98 after a period of 5 years.
Learn more about functions here:
https://brainly.com/question/28303908
#SPJ2
Can someone help me with this pls?
Answer:
D. 8
Step-by-step explanation:
Given:
A(4, 4)
B(8, 4)
C(12, 0)
Midsegment length = ½((Bx - Ax) + (Cx - 0))
Where,
Ax = 4
Bx = 8
Cx = 12
Substitute
Midsegment length = ½((8 - 4) + (12 - 0))
= ½(4 + 12)
= ½(16)
Midsegment length = 8
Rotational symmetry of 2D shapes
Choose all that apply
Answer:
B and C
Step-by-step explanation:
I think that this is right.
A pentagon's lines of symmetry go thru an angle and the middle of a side. Every 72 degrees, the pentagon in split into identical halves. Same with 144 because it is basically 2 72 degree rotations.
Answer:
72
Step-by-step explanation:
The order of rotational symmetry of a regular pentagon is 5.
To find the angle of rotation we divide 360 by the number of sides
360/5=72
so the angle of rotation is 72 degrees.
PLEASE HELP!!!!!! WILL GIVE BRAINLIEST!!!!!!!!!!
Alicia is writing the program for a video game. For one part of the game she uses the rule to move points on the screen.
(a) What output does the rule give when the input is ? Show your work.
(b) What output does the rule give when the input is ? Show your work.
(c) Is the rule a function? Explain why it is or why it is not
Answer:
a) (-9, 4)
b) (0, 0)
c) No
Step-by-step explanation:
PLEASE I NEED HELP CLICK ON THIS IMAGE
Answer:11
Step-by-step explanation:smart
60 degrees,60 degrees,4cm Do the following conditions make a unique triangle, more than one triangle or no triangle possible?
NOT NECESSARILY would a triangle be equilateral if one of its angles is 60 degrees. To be an equilateral triangle (a triangle in which all 3 sides have the same length), all 3 angles of the triangle would have to be 60°-angles; however, the triangle could be a 30°-60°-90° right triangle in which the side opposite the 30 degree angle is one-half as long as the hypotenuse, and the length of the side opposite the 60 degree angle is √3/2 as long as the hypotenuse. Another of possibly many examples would be a triangle with angles of 60°, 40°, and 80° which has opposite sides of lengths 2, 1.4845 (rounded to 4 decimal places), and 2.2743 (rounded to 4 decimal places), respectively, the last two of which were determined by using the Law of Sines: "In any triangle ABC, having sides of length a, b, and c, the following relationships are true: a/sin A = b/sin B = c/sin C."¹
Please help What’s the answer?
Answer:
A. x=54 And
B. x= 89
these numbers are less then hundred.
< this sign prove that what is the less number of given question.
need help answering this
Answer:
what ur yourgrade?
Step-by-step explanation:
Answer:
5) x=19 ft.
6) x=3 cm.
7) x=50 ft.
8) 56 mm.
Explanation:
All of these problems require proportions. For example, in #5, the smaller rectangle has a width of 8 ft. and a length of 24 in. and the larger rectangle has a length of 57 in. but the width is not given. Now, we know that [tex]\frac{8}{24}[/tex][tex]=\frac{x}{57}[/tex]. Cross-multiply to get 456=24x. Divide 24 on both sides to get x=19 ft.
there are 50 petals on 10 purple orchids each purple orchid has the same number of petals find the number of petals on the purple orchid
Answer:
5 petals per purple orchid
Step-by-step explanation:
because if they all have the same amount of petals then you divide the total petals (50) by the number of orchids (10) and get the (5) orchid petals per purple orchid.
2
A person that is 6 feet tall casts a shadow that is 2.5 feet long. At the same time, a 120 foot tall building casts a shadow. What is the length of the shadow?
feet
Answer:
The building's shadow is 50 ft
Step-by-step explanation:
[tex]\frac{6}{2.5} =\frac{120}{x} \\\\6x=300\\x=50[/tex]
Please Help I will Give Brainest and 100 points and no fake answers
Step-by-step explanation:
[tex] \sqrt{3} is \: between1.7and1.8[/tex]
Which is the lower rate 165 students on 5 buses or 140 students on 4 buses
Answer:
140 students on 4 buses
Gary can paint a garage in 8 hours. Gary van do it in 6 hours. How long will it take if they all paint together?
ill mark brainlist plss help
Answer:
64 ft²
Step-by-step explanation:
Given
Length of a square (L) = 8 ft
Area of the square is
= L²
= 8²
= 64 ft²
Hope it will help :)❤
I need help with this!!
9514 1404 393
Answer:
C y = -5x +6
Step-by-step explanation:
It often works well to try the answer choices and see what works.
Using the first point, we find ...
A y = -1/5(-2) +6 ≠ 16
B y = 6(-2) -1/5 ≠ 16
C y = -5(-2) +6 = 16 . . . . . this equation works
D y = 6(-2) -5 ≠ 16
__
You can also go to the trouble to determine the equation. The slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (11 -16)/(-1 -(-2)) = -5/1 = -5 . . . . . tells you C is correct
The y-intercept can be found from ...
b = y -mx
b = 16 -(-5)(-2) = 16 -10 = 6
Then the equation is ...
y = mx + b
y = -5x +6 . . . . . matches choice C
Rob was tasked to graph this system of equations:
6x + 2y = 5
y + 3x = 2
How many times will these lines intersect?
Answer:
6x + 2y =5
y + 3x= 2
Step-by-step explanation:
ill mark brainlist plss help
Robin weighs her math textbook and finds that it is 2 kilograms. How many grams does her textbook weigh?
Answer:
2000
Step-by-step explanation:
1 kilogram is 100 grams therefore 2 kilo grams is equal to 2000 grams
The word kilo means thousand in Greek and i think French
:)
Answer:
2,000 grams :)
A first-aid cream contains amounts of the active ingredient (in mg) that vary Normally with unknown mean m and standard deviation s from tube to tube. You select a simple random sample of 9 tubes and assess the quantity of active ingredient they contain. The 9 amounts, in mg, are 23 24 23 29 28 26 27 28 26 Based on these data, a 99% confidence interval for the population mean m has margin of error of ____ mg.
Answer:
2.5 mg
Step-by-step explanation:
Given the data:
23 24 23 29 28 26 27 28 26
The sample standard deviation, s
s = sqrt[Σ(x - mean)²] ÷ (n - 1)
Mean, m = ΣX / n
n = 9
Mean = 234 /9 = 26
Using a calculator :
s = 2.236
The margin of error, MOE
MOE = Tcritical * s/sqrt(n)
Tcritical at df = (n-1) = 9-1 = 8 , α = 0.01 = 3.35536
MOE = 3.35536 * 2.236/sqrt(9)
MOE = 3.35536 * 2.236/3
MOE = 3.35536 * 0.7453333
MOE = 2.50086
MOE = 2.5
Which expression is equivalent to 7 (x y)?
1. 7 x + y
2. 7 x minus y
3. x (7 y)
4. StartFraction x y Over 7 EndFraction
Answer:
option c.
x(7y)
................
What number can you multiply ONE equation by in the following system to obtain a matching
coefficient? (Elimination)
4x+3y=8
2x+5y=12
(Worth 10 points )
Answer:
Multiply the second equation by 2
Step-by-step explanation:
Given
[tex]4x + 3y = 8[/tex]
[tex]2x + 5y =12[/tex]
Required
Get matching coefficient for elimination
[tex]4x + 3y = 8[/tex]
[tex]2x + 5y =12[/tex]
The coefficient of x in both expressions are factors.
So, we can multiply the second equation by 2 to get the coefficient of x in the first.
i.e.
[tex]2 * (2x + 5y = 12)[/tex]
[tex]4x + 10y = 24[/tex]
So, the system becomes:
[tex]4x + 3y = 8[/tex]
[tex]4x + 10y = 24[/tex]
Now, x can be eliminated
Emilio spent $21 at the state
fair. He paid $3 for admission and bought
12 tickets for rides. Solve the equation
12t +3= 21 to find the cost of each
ticket
Answer:
t = $1.5Steps:
12t+3 = 21
12t = 21-3
12t = 18
t = 18/12
t = 3/2
t = $1.5