Answer:
0.5944 = 59.44% probability that the team has at least 2 grade 11 students
Step-by-step explanation:
The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes 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 successes.
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]
We have that:
6 + 8 = 14 students, which means that [tex]N = 14[/tex]
6 grade 11 students means that [tex]k = 6[/tex]
Teams of 4 members means that [tex]n = 4[/tex]
What is the probability that the team has at least 2 grade 11 students?
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[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 = 0) = h(0,14,4,6) = \frac{C_{6,0}*C_{8,4}}{C_{14,4}} = 0.0699[/tex]
[tex]P(X = 1) = h(1,14,4,6) = \frac{C_{6,1}*C_{8,3}}{C_{14,4}} = 0.3357[/tex]
Then
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0699 + 0.3357 = 0.4056[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4056 = 0.5944[/tex]
0.5944 = 59.44% probability that the team has at least 2 grade 11 students
What is the surface area of the rectangular prism?
5 ft
5 ft
8 ft
10.6.23
Question Help
Becky would like to be a millionaire in 40 years. How much would she need to invest quarterly in a sinking
fund paying a 3% interest rate compounded quarterly to accumulate $1,000,000 in 40 years?
I = $ 1,200,000.00
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 3%/100 = 0.03 per year,
then, solving our equation
I = 1000000 × 0.03 × 40 = 1200000
I = $ 1,200,000.00
The simple interest accumulated
on a principal of $ 1,000,000.00
at a rate of 3% per year
for 40 years is $ 1,200,000.00.
The terms central location or central tendency relate to the way quantitative data tend to cluster around some middle or central value.
a. True
b. False
Answer:
A: True
Step-by-step explanation:
It's true because central tendency is defined as a branch of descriptive statistics that shows the centre of the data distribution.
This central tendency could be mean, median or mode.
A recent study at Winthrop University was done to determine the ratio of democrats to republicans. Use the information in each problem to come up with an appropriate sample size to accurately estimate the mean. Let a republican represent a success r. If no preliminary sample is taken, how large should the sample be to be 90% sure that the estimate is within .03 of the population proportion?
Answer:
A sample of 752 should be taken.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
No preliminary sample is taken
This means that [tex]\pi = 0.5[/tex]
How large should the sample be to be 90% sure that the estimate is within .03 of the population proportion?
This is n for which M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645*0.5[/tex]
[tex]\sqrt{n} = \frac{1.645*0.5}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2[/tex]
[tex]n = 751.7[/tex]
Rounding up:
A sample of 752 should be taken.
5.Square Given:a =12m,A=
Pa help po
If s=side, then each side is 12m.
It got cut off but
12mx12m=144m^2 because mxm=m^2.
heart if helpful
Determine the location and absolute maximum and absolute minimum for the given function f(x)=(_x+2)^4 where 0
Answer:
the minimum is 0 and the maximum is 16.
Step-by-step explanation:
For a function f(x), the maximum is defined as:
f(xₐ)
such that:
f(xₐ) ≥ f(x) for every value of x in the domain.
And the minimum is:
f(xₙ)
Such that:
f(xₙ) ≤ f(x)
for every value of x.
Now, in this case we have the function:
f(x) = (-x + 2)^4 in the range 0 < x < 3
First, let's analyze our function.
We can see that the exponent is even, then:
f(x) = (-x + 2)^4
Can be equal to zero or larger than zero.
Then the minimum will be f(x) = 0
To find this, we need to find the value of x such that:
-x +2 = 0
2 = x
Then the minimum is:
f(2) = (-2 + 2)^4 = 0
For the maximum, we can just play with the other values in the range and see which one gives the larger value of f(x).
Again, because f(x) = (-x + 2)^4 , the maximum will be at the value of x such that:
|-x + 2| is maximized.
As we have a negative sign multiplying x, the smaller value in the range:
x = 0
is the one that maximizes that:
|-0 + 2| = |2| = 2
Evaluating f(x) in x = 0 we get:
f(0) = (0 + 2)^4 = 16
Then the minimum is 0 and the maximum is 16.
Question 8 of 10
Suppose f(x) = x2 and g(x)= Which statement best compares the
graph of g(x) with the graph of f(x)?
O A. The graph of g(x) is the graph of Ax) shifted units left.
O B. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 5.
O c. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 5.
O D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 5.
SUBMIT
9514 1404 393
Answer:
B. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5
Step-by-step explanation:
Replacing x by x/5 in a function causes its graph to be stretched horizontally by a factor of 5. This is because x must be 5 times as large in order for the function argument to be the same.
Following is a portion of the regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal. When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as
Answer:
Matched samples
Step-by-step explanation:
A matched sample is obtained when pairing of treatment values for each subject or observation is performed. This sample obtained from a matched pair is usually called dependent sample and is usually done when each subject in an experiment is subjected to two different treatments usually at different time or stage. Hence, matched samples are used in matching observations to tie different groups.
Using Figure 1, complete the following function.
sin θ=
A. u/r
B. v/r
C. u/v
D. r/v
E. v/u
F. r/u
Given:
A figure of right triangle with terminal angle [tex]\theta[/tex], base u, perpendicular v and hypotenuse r.
To find:
The value of [tex]\sin \theta[/tex].
Solution:
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
Substituting Perpendicular = v and hypotenuse = r in the above formula, we get
[tex]\sin \theta=\dfrac{v}{r}[/tex]
The value of [tex]\sin \theta[/tex] is [tex]\dfrac{v}{r}[/tex].
Therefore, the correct option is B.
if loga (n) = 16, find loga (sqrtt n)
Answer:
8
Step-by-step explanation:
by definition:
[tex]log_an=16\\\\log_a\sqrt{n}=log_a n^{\frac{1}{2}}=\frac{1}{2}log_a n=\frac{1}{2}(16)=8[/tex]
A rectangular farm has an area of 1/2 square miles. If its length is 1/3 miles, what is its width?
Classify the following triangle. Check all that apply.
Answer:
This triangle is a right triangle
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Answer:
[tex]\frac{x2}{a} - \frac{y2}{b2} = 1[/tex]
Step-by-step explanation:
A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.
The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:
[tex]\frac{X2}{16} - \frac{b}{4} = 1[/tex]
The coordinates of the foci is at (±c, 0), where c² = a² + b²
Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:
I don't feel like explaining so...
a. = 4
The foci c is at +/-2√5, using c² = a² + b²:
B = 2
Substituting the value of a and b to get the equation of the hyperbola:
[tex]\frac{x2}{a2} - \frac{y2}{b2} = 1[/tex]
[tex]\frac{x2}{16} - \frac{b2}{4} = 1[/tex]
In terms of \piπ, how much bigger is the area of a pizza with a diameter of 18 in. than the area of pizza with a diameter of 10 in.?
Answer:
56л
Step-by-step explanation:
area of a pizza of 18 in= лr²
r=18/2=9
area= л×9²
=81л
area of a pizza of 10in=
r=10/2=5
area=л×5²
=25л
difference=81л-25л
=56л
Espanol
At the movie theatre, child admission is $5.70 and adult admission is $9.40. On Sunday, 135 tickets were sold for a total sales of S1080.30. How many adult
tickets were sold that day?
9514 1404 393
Answer:
84 adult tickets
Step-by-step explanation:
Let 'a' represent the number of adult tickets sold. Then (135-a) is the number of child tickets sold, and total revenue is ...
5.70(135 -a) +9.40(a) = 1080.30
3.70a = 310.80 . . . . . . . . subtract 769.50 and simplify
a = 310.80/3.70 = 84
84 adult tickets were sold on Sunday.
as central angle is to 360 degrees.Arc length is to
A.circumference
B.area
C.sector
D. Diameter
If central angle is 360° then Arc length is circumference.
What is the central angle of a Circle?
An angle with the circle's center as its vertex is referred to as a central angle. The radius refers to each side of the angle that extends outward from the center to a particular point on the circle.
What is circumference?A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.
How to solve it?Since, when considering the circle's central angle we consider 360° which is the central angle of the whole circle.
So, when considering the arc length of a sector, we consider the arc length of the whole circle which is the circumference.
Learn more about circles here-
brainly.com/question/11833983
#SPJ2
At the market, he spends $5.58 on red potatoes and $4.68 on yellow potatoes. If each type of potato costs $0.90 per pound, how many total pounds of potatoes does he buy?
Answer:
11.4pounds
Step-by-step explanation:
(5.58+4.68)÷0.90
＝11.4(pounds)
What is the factored form of x2 − 4x − 5? (x + 5)(x − 1) (x + 5)(x + 1) (x − 5)(x − 1) (x − 5)(x + 1)
Pls help again thanks
Answer:
d.156.
x+24=180 ( being staright angle)
you and your four friends go to the water park. it is $10 each for tickets, and y dollars for lunch.
a. use the distributive property to write and simplify an expression for the total the group pays.
b. how much does the group pay when the lunches cost $4?
Answer:
56 dollars
Step-by-step explanation:
idfk 56 dollars is the answer tho
What is the slope of the line that passes through the points (3, 2) and (-1,-4)?
m=
Answer:
3/2
Step-by-step explanation:We know that,
Slope of the straight line passing through the points (x1,y1) and (x2,y2) is
m=y2-y1/x2-x1
Here,
Given, x1= 3,x2= 1
and y1= 2,y2= -4
so, the slope of the straight line is,
m= -4-2/-1-3
=3/2
Solve for x:
х/2 = 8
O A) X= 17
OB) x = 18
OC) x = 16
OD) x = 12
Hi there!
»»————- ★ ————-««
I believe your answer is:
C) x = 16
»»————- ★ ————-««
Here’s why:
We will use inverse operations to solve for 'x'.⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\\frac{x}{2}=8\\-------\\\rightarrow{\frac{x}{2}=8}\\\\\rightarrow(\frac{x}{2}})*2=8*2\\\\\rightarrow\boxed{x=16}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x = 16
Step-by-step explanation:
х/2 = 8
Multiply each side by 2
x/2*2 = 8*2
x = 16
Garcia bought 3 packs of red notebooks, 5 packs of yellow notebooks, and 8 packs of green notepads. There were 3 notepads in each package. How many notepads in all?
What is the expression?
The answer is 48 notepads.
Daniel and Joe watched a beetle and a spider on the sidewalk. The beetle crawled 1/2 of a yard and the spider crawled 1/8 of a yard. How much farther did the beetle crawl than the spider?
Answer: 3/8 yard
Step-by-step explanation:
Since the beetle crawled 1/2 of a yard and the spider crawled 1/8 of a yard. To calculate how much farther the beetle crawl than the spider, we will have to subtract 1/8 from 1/2. This will be:
= 1/2 - 1/8
= 4/8 - 1/8
= 3/8 yard
Therefore, the beetle covered 3/8 yard more.
English
v
Which table represents a linear function?
2
y
х
y
22
y
22
y
1
0
0
0
0
ol
1
هدايا
2
1
1
1
1
1
3
이
4
2
3
2
0
2
ا م ا
3
8
3.
6
3
1
3
7
Answer:
2 y x
Step-by-step explanation:
What is the value of h?
Answer:
35
All angles of a triangle = 180 degrees subtract 40 from 180 and you get 140
180-40=140 because the other angles are equal with the same equation to get them divide 140 by 2 140/2=70 then you have to get h alone so you divide by the other 2 in the equation 70/2=35 h=35
Answer:
55
Step-by-step explanation:
In triangle ABC (LET'S SAY TRIANGLE IS ABC)
Angle A=40
Angle B = Angle C = x (since 2h is beside B and C both)
40+x+x=180 (Angle sum property)
40+2x=180
2x=140
x=70
2h+70=180 (Angle in a straight line=180)
2h=110
h=55
Express the area of the entire rectangle.
Your answer should be a polynomial in standard
form. X+9 top x+2
Pls help i will mark the brainliest!
Explanation:
The blue rectangle is x*x = x^2 in areaThe pink rectangle has area of x*9 or 9xThe green rectangle has area 2*x or 2xThe orange rectangle has area 2*9 = 18Add up those areas to get the final answer
x^2+9x+2x+18 = x^2+11x+18
note the like terms 9x and 2x combine to 11x
Evaluate the variable expression when a = -2, b = 5, C = -5, and d = 3.
-4b + 1 (ac + bd)
5
5
Answer:
-4(5)+1(-2*-5+5*3)
Step-by-step explanation:
-20+1(10+15)
-19(25)
-475
Answer:
5
Step-by-step explanation:
Given :- a = -2 , b = 5 , c = -5 & d = 3
Solution :-
- 4 b + 1 ( ac + bd )- 4 ( 5 ) + 1 ( (-2)(-5) + (5)(3))-20 + -2 × -5 + 3 × 5-20 + 10 + 15- 20 + 255Three coins are flipped. What is the probability that all three coins will match?
Answer:
25%
Step-by-step explanation:
We can also show this from the results table below: There are 8 possible outcomes for tossing three coins. Two of these outcomes are either all heads or all tails, Therefore there is a 28=14=0.25=25% chance of getting all heads or all tails.
Help me with my geometry homework
Answer:
10.5 is the answer
Step-by-step explanation:
i hope it helps u
Answer:
is the answer y=7? if correct its ok but if the answer didn't match then plesse let me know
