Answer:
[tex]Probability =0.1744[/tex]
Step-by-step explanation:
Given
Total
[tex]American = 11[/tex]
[tex]Canadian = 18[/tex]
Selection
[tex]American = 0[/tex]
[tex]Canadian = 4[/tex]
Required
Determine the probability of selecting a 4 committee member that are Canadian.
First, we calculate total possible selection.
[tex]Total = American + Canadian[/tex]
[tex]Total = 11 + 18[/tex]
[tex]Total = 27[/tex]
Number of ways to select 4 from 27 is:
[tex]^{27}C_4 = \frac{27!}{(27-4)!4!}[/tex]
[tex]^{27}C_4 = \frac{27!}{23!4!}[/tex]
[tex]^{27}C_4 = \frac{27*26*25*24*23!}{23!4!}[/tex]
[tex]^{27}C_4 = \frac{27*26*25*24}{4!}[/tex]
[tex]^{27}C_4 = \frac{27*26*25*24}{4*3*2*1}[/tex]
[tex]^{27}C_4 = \frac{421200}{24}[/tex]
[tex]^{27}C_4 = 17550[/tex]
Next, we calculate ways of selecting 4 Canadians from 18 is:
[tex]^{18}C_4 = \frac{18!}{(18-4)!4!}[/tex]
[tex]^{18}C_4 = \frac{18!}{14!4!}[/tex]
[tex]^{18}C_4 = \frac{18*17*16*15*14!}{14!4!}[/tex]
[tex]^{18}C_4 = \frac{18*17*16*15}{4!}[/tex]
[tex]^{18}C_4 = \frac{18*17*16*15}{4*3*2*1}[/tex]
[tex]^{18}C_4 = \frac{73440}{24}[/tex]
[tex]^{18}C_4 = 3060[/tex]
The required probability is:
[tex]Probability =\frac{3060}{17550}[/tex]
[tex]Probability =0.1744[/tex]
30 POINTS WOWWWWWW plz answer :)
Answer:
Step-by-step explanation:
Write the slope intercept form of the equation of the line through the given points
Answer:
9) y = -3x - 4
10) y = -1/3x + 14/3
11) y = x - 1
12) y = -7/5x - 18/5
13) y = 3/5x + 9/5
14) y = -2x - 3
Step-by-step explanation:
For this explanation, let's use the last problem as the example. You would use the formula y=mx+b. The first thing you would need to find would be the slope, or m. So, you would find the slope and conclude the answer is -2. After that, you would solve for b and get the answer. Hope this helped!
Solve using Graphing. x-y=-7 2x+9y=19
Answer:
(-4, 3)
General Formulas and Concepts:
Algebra I
Solving systems of equations by graphingStep-by-step explanation:
Where the 2 lines intersect would be the solution set to the systems of equations.
Hong made $323 for 17 hours of work
At the same rate, how much would he make for 7 hours of work
Answer:
$153
Step-by-step explanation:
323/17=19
19x7=153
Marcus can drive his boat 36 miles down the river in 3 hours but takes 4 hours to return upstream. Find the rate of the boat
in still water and the rate of the current.
Answer:
With river 12 miles per hour
Against river 9 miles per hour
wv = water velocity vsw = boat velocity in still water
vsw +wv = 12 mph
vsw -wv = 9 mph
2 * vsw = 21 mph
boat velocity in still water = 10.5
Since vsw + wv = 12 then
water velocity = 1.5 mph
Step-by-step explanation:
Answer:
speed in still water: 10.5 Current: 1.5
Step-by-step explanation:
The side lengths of a triangle are 5, 8, and 12. Is this a right triangle?
O A. No, because 52 + 32 + 122.
OB. No, because 5+ 8 + 12.
C. Yes, because 52 + 82 = 122.
O D. Yes, because 52 + 82 < 122
Answer:
A) No...
Step-by-step explanation:
We can check if this triangle is a right triangle by using the Pythagorean Theorem.
a² + b² = c² where a and b are the legs of the right triangle, and c is the hypotenuse (longest side)Using 5 for a, 8 for b, and 12 for c, let's see if this satisfies the equation:
5² + 8² = 12²Simplify.
25 + 64 = 144 89 = 144We can see that 89 ≠ 144, so this leaves us with answer choices A and B. I think you meant to write < for the last + sign.
Seeing as the sum of the two lengths of the triangle is greater than the third side length, this creates a normal triangle. This cannot be the correct answer choice since this only satisfies the requirements for a triangle, but not a right triangle.
This leaves us with answer choice A. 52 + 32 ≠ 122 and 52 + 32 < 122. (I'm not sure why the squares of the side lengths are not used, but this should be the correct answer.)
Valeria is playing with her accordion. The length of the accordion A(t)A(t)A, left parenthesis, t, right parenthesis (in \text{cm}cmstart text, c, m, end text) after she starts playing as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\cos(b\cdot t)+da⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. At t=0t=0t, equals, 0, when she starts playing, the accordion is 15\text{ cm}15 cm15, start text, space, c, m, end text long, which is the shortest it gets. 1.51.51, point, 5 seconds later the accordion is at its average length of 21\text{ cm}21 cm21, start text, space, c, m, end text. Find A(t)A(t)A, left parenthesis, t, right parenthesis. \textit{t}tstart text, t, end text should be in radians.
Answer:
−6cos( π/3 t)+21
Step-by-step explanation:
The length of the accordion is −6cos( π/3 t)+21.
How to derive a sinusoidal expression?We must figure out the periodic phenomenon's amplitude, period, and vertical shift in order to create a sinusoidal function that models it. Additionally, we must choose between using a sine or a cosine function and calculate the ensuing phase shift.
Given
A = 5+1 = 6
Shift = 21
ω =- π/3[because of 4th quadrant]
exp = Asin[-ωt] + shift
=-Acosωt + shift = -6cosπ/3 t + 21
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SOLVE FOR X. pls i need help
Scrat the squirrel has a few nuts. When he put them in groups of 5 nuts, two nuts were left, and
when he laid them out in groups of 3 nuts, there were no nuts left. How many nuts among the
options provided below could belong to Scrat?
Answer:
The options are not shown, so i will solve this in a general way.
Let's suppose that there are N nuts
If we divide the N nuts into groups of 5, there will be a remainder of 2 nuts.
If we divide the N nuts into groups of 3, there is no remainder.
This means taht N is a multiple of 3. then we can write:
N = 3*k
where k is a random integer.
Now, we know that when we divide N by 5, there is a remainder of 2 nuts, this means that N is equal to a multiple of 5 plus 2, then we can write:
N = 5*j + 2
where j is a random integer.
Now we only need to find a pair of k and j (both positive integers) such that:
3*k = 5*j + 2
We can rewrite this as:
k = (5/3)*j + (2/3)
Now we could just input different values of j, and see if k is also an integer:
j = 2
k = (5/3)*2 + 2/3 = 10/3 + 2/3 = 12/3 = 4
Then the pair j = 2, k = 4 is a possible solution.
N = 3*k = 3*4 = 12
N = 5*j + 2 = 5*2 + 2 = 12
From this we can conclude that N = 12, so Scrat has 12 nuts.
Now with the equation
k = (5/3)*j + (2/3)
We can find other possible combinations of j and k, that will give different values for N.
for example, if j = 5:
k = (5/3)*5 + 2/3 = 25/3 + 2/3 = 27/3 = 9
Then the pair j = 5, k = 9 is also a possible solution:
N = 3*k = 3*9 = 27
N = 5*j + 2 = 5*5 + 2 = 27
In this case, Scrat has 27 nuts.
A rectangular mat has an area of 7/12 in2. The length of the mat is 5/6 in. What is the width of the mat
The width of the mat with the given area and length is 7/10 in.
What is the width of the mat?The area of a rectangle is expressed as;
A = l × w
Where l is length and w is width.
Given the data in the question;
Area A = 7/12 in²Length l = 5/6 inWidth w = ?We plug our given values into the above equation and solve for w.
A = l × w
7/12 = 5/6 × w
w = 7/12 ÷ 5/6
w = 7/12 ÷ 6/5
w = 42/60
w = 7/10 in
Therefore, the width of the mat with the given area and length is 7/10 in.
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What is the answer to this question?
Answer:
the answer is the top right option
Step-by-step explanation:
50. If angles are complementary, what’s value of x?
Answer:
x = 14
Step-by-step explanation:
For complementary angles, the sum of two angles is equal to 90 degrees.
We have,
[tex]m\angle ABC = 4x-10\\\\m\angle DBC = x+30[/tex]
ATQ,
[tex]4x-10+x+30=90[/tex]
Taking like terms together,
4x+x =90-30+10
5x = 70
x = 14
So, the value of x is 14.
What is the probability of picking a yellow marble and a blue marble of the yellow marble is replaced ?
Answer:
50%
Step-by-step explanation:
please answer fast!!
I am really confused and I don't know what to do.
Answer:
C
Step-by-step explanation:
Ed use 3 2/3 cups of peanut butter and 2 cups of powdered sugar to make 1 batch of peanut butter fudge. How much more peanut butter will Ed use than powdered sugar to make 3 batches of fudge?
Answer:
Ed will use 5 more peanut butter than powdered sugar to make 3 batches of fudge(11-6=5)
Step-by-step explanation:
3 2/3 cups of peanut butter (x)
2 cups of powdered sugar(y)
for every one batch you need 2 cups, and for 3 batches you need 6 cups of powdered sugar(2*3=6)
and for every batch you need 32/3 cups of peanut butter and for three batches you need (3 2/3 *3)= 11/3 *3=33/3=11 cups of peanut butter to make the fudge
Ed will use 5 more peanut butter than powdered sugar to make 3 batches of fudge(11-6=5)
A dragon lived in a cave.
The dragon doubled in size every day.
After 20 days the dragon filled the cave.
After how many days did the dragon half-fill the cave?
Answer: After 19 days, the dragon filled half of the cave.
Step-by-step explanation:
The dragon doubled in size every day and after 20 days he filled the cave.
So, one day before, the dragon occupied half of the cave.
20 - 1 = 19 [days]
After 19 days did the dragon half-fill the cave.
The dragon doubles in size every day, and after 20 days, it completely fills the cave.
To find out when the dragon half-filled the cave, we need to determine how many days it took for the dragon to reach half of the cave's capacity.
we know that,
On the 20th day, the dragon filled the entire cave.
and, The dragon doubled in size every day.
so, we have,
On the 19th day, the dragon's size would have been half of what it was on the 20th day.
On the 18th day, the dragon's size would have been half of what it was on the 19th day.
And so on...
We can see that every day before the 20th day, the dragon's size was halved.
So, on the 19th day, the dragon's size was half of the size it was on the 20th day.
Therefore, on the 19th day, the dragon half-filled the cave, and on the 20th day, it filled the entire cave.
Hence, After 19 days did the dragon half-fill the cave.
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Beth put $8,000 in a savings account. At the end of a year
the account had earned $720 in interest. What was the
yearly interest rate on the account?
Answer:
It's %9.0.
Step-by-step explanation:
4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.
[2]
a. Draw a picture of the rectangle
[4]
b. Write an EXACT expression for the base and the height of the rectangle.
[2]
C. Use your expressions to find the EXACT area of the rectangle.
9514 1404 393
Answer:
a) see attachment
b) base: 4, height: 4√3
c) area: 16√3
Step-by-step explanation:
a) The figure is drawn in the attachment
__
b) The side lengths of a 30-60-90 right triangle have the ratio ...
1 : √3 : 2
Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.
__
c) The area is the product of base and height:
A = bh
A = 4(4√3) = 16√3 . . . . square units
Find the slope of the line.
please help
will mark brainlyest
Answer:
m = 1
Step-by-step explanation:
slope = (y₂-y₁)/(x₂-x₁)
m = (4 - -1) / 1 - -4) = 5/5 = 1
These are so annoying
Answer:
a=4
b=6
perimiter=38
Step-by-step explanation:
you take the side lengths by it and you can subtract and stuff then you add them all up to find the perimeter
Answer:
3-9=6 and 6-10=4
Step-by-step explanation
part of b is cut by 3 as u can see above and 9 is at the bottom on which the part is cut, as for the other one 10 is the main line and is cut by 6. so u just have minus the main line aka the long line by a parallel line next to it
Find the value of x. 1) m angle2=3x-6 120° 2 B) 10 D) 6 A) 12 C) -11
Find the value of x
Answer:
x=20°
Step-by-step explanation:
The triangle is equilateral. (All sides are the same).
Each angle in an equilateral triangle is 60.
3x=60
x=20°
if 50% is 10 what is 100%
Answer:
20
Step-by-step explanation:
Please help me asap this is due in 10 min Ill also mark brainliest
As we know that formula of area of circle is πr²
So let's apply formula
π×8.6×8.6
=232.2
=200 is the nearest hundredth.
You have to do rest of all through this method.
determine the slope of the linear graph y=12x+7
Answer:
12x
Step-by-step explanation:
3x-2y=1x+4y=33 elimination process
Answer:
x = 5 ; y = 7
Step-by-step explanation:
3x - 2y = 1 --------------------(I)
x + 4y = 33 ------------(II)
Multiply equation (II) by (-3) and then add. So, x will be eliminated and we can find the value of y
(I) 3x - 2y = 1
(II)*(-3) -3x -12y = -99 {Now add}
- 14y = -98
y = -98/14
y = 7
Plugin y = 7 in equation (I)
3x - 2*7 = 1
3x - 14 = 1
3x = 1 + 14
3x = 15
x = 15/3
x = 5
Is this correct? If not plz get answers 25points!!!
That is correct.
Sqrt 5 x sqrt20
Apply the radical rule to get sqrt( 5 x 20)
Simplify to get sqrt(100)
Sqrt(100) = 10
What is the constant of proportionality for the table? What does it represent? Reminder: k= y/x
Answer:
The constant of proportionality is 5. It represents the cups of yellow paint needed for 1 cup of blue paint.
A manufacturer knows that their items have a normally distributed length, with a mean of 16.2 inches, and standard deviation of 0.9 inches. If one item is chosen at random, what is the probability that it is less than 16.4 inches long
Answer:
57.926%
Step-by-step explanation:
Calculation for the probability that it is less than
16.4 inches long
Using this formula
z = (X - μ) / σ
Where,
X represent Date=16.4
μ represent Mean=16.2
σ represent Standard deviation=0.9 inches
Let plug in the formula
z = (16.4 - 16.2) /0.9 inches
z=0.2/0.9 inches
z = 0.2
Using Z-score table to find the area of 0.2
z=0.57926*100
z=57.926%
Therefore the probability that it is less than
16.4 inches long is 57.926%
Geometry question plz help
Answer:
I think A
Step-by-step explanation:
