Answer:
10 students play sudoku and checkers
Step-by-step explanation:
First find the number of students that play sudoku
2/5 * 30
12
of those 12 students, 5/6 play checkers
12 * 5/6 = 10
10 students play sudoku and checkers
Suppose that Haley encounter two traffic lights on her commute to GGC campus. Based on
her past experience, she judge that the probability is 0.35 that the first light will be red when she gets to it,
0.45 that the second light will be red, and 0.20 that both lights will be red. Let R1 denote the event that the
first light is red, and let R2 denote the event that the second light is red.
a) Determine the probability that at least one light will be red. (Show how you calculate this.)
b) Determine the conditional probability that the second light will be red given that the first light is
red. (Show how you calculate this.)
c) Are the events R1 and R2 independent? Justify your answer numerically.
d) Are the events R1 and R2 disjoint (mutually exclusive)? Justify your answer numerically.
Answer:
Explained below.
Step-by-step explanation:
The information provided is,
P (R₁) = 0.35
P (R₂) = 0.45
P (R₁ ∩ R₂) = 0.20
(a)
Compute the probability that at least one light will be red as follows:
P (at least one light will be red) = P (R₁ ∪ R₂)
= P (R₁) + P (R₂) - P (R₁ ∩ R₂)
= 0.35 + 0.45 - 0.20
= 0.60
Thus, the probability that at least one light will be red is 0.60.
(b)
Compute the conditional probability that the second light will be red given that the first light is red as follows:
[tex]P(R_{2}|R_{1})=\frac{P(R_{1}\cap R_{2})}{P(R_{1})}[/tex]
[tex]=\frac{0.20}{0.35}\\\\=0.571428\\\\\approx 0.57[/tex]
Thus, the conditional probability that the second light will be red given that the first light is red is 0.57.
(c)
If two events, say A and B are independent then:
P (A|B) = P (A).
The value of P (R₂ | R₁) = 0.57.
And the value of P (R₂) = 0.45
P (R₂ | R₁) ≠ P (R₂)
Thus, the events R₁ and R₂ are not independent.
(d)
If two events, say A and B are mutually exclusive then:
P (A ∩ B) = 0
The value of P (R₁ ∩ R₂) = 0.20.
Thus, the events R₁ and R₂ are not mutually exclusive.
In a chemistry class, 12 L of a 12% alcohol solution must be mixed with a 20% solution to get a 14% solution. How many liters of the 20% solution are needed?
4 liters of 20% solution are needed to get a 14% solution.
Suppose x liters of 20% solution is needed to get a 14% solution.
What is a solution?The solution is a homogenous mixture of two or more substances in relative amounts.
So, according to the question
Final concentration of solution = 14%
So, 12% of 12 + 20% of x = 14% of (12+x)
12*12/100 + 20*x/100 = 14*(12+x)/100
144 + 20x = 168 + 14x
6x =24
x=4
4 liters of 20% solution is needed to get a 14% solution.
Therefore, 4 liters of 20% solution is needed to get a 14% solution.
To get more about mixtures and alligations visit:
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pleas help ill give brainiest
Given:
Initial amount in the account = $1,000
Interest rate = 3.25%
Since the type of interest is simple, 3.25 % of 1000 will be added to that account every year with no increase in the incrementing amount
Amount increased in 18 years:
Amount increased every year = 3.25 * 1000 / 100 = $32.5
Amount increased in 18 years = amount gained in 1 year * 18
Amount increased in 18 years = 32.5 * 18 = $585
Total amount in John's bank account at the age of 18:
Initial amount + amount increased in 18 years
1000 + 585
$1,585
The following table shows the cost of 444 party favor packs. For example, the Slinky costs \$9$9dollar sign, 9 for a pack of 555.
Toy pack Cost (dollars) Quantity
Slinky 999 555
Wind-up robot 161616 888
Yo-yo 151515 666
Emoji beach ball 333 222
Which toy pack has a cost of \$2.50$2.50dollar sign, 2, point, 50 per toy
Answer:
yoyo
Step-by-step explanation:
Answer: the answer is yo-yo
Step-by-step explanation:
because they say the 6-yo-yo cost 15 dollars. So if you take 6 and multiply it by 2.5 it gives you 15 dollars. Hope this helps
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
Answer:
I think it might be zero
Step-by-step explanation:
you might want to look into this all the way beforyou trust put it into*
How many 2/3 go into 4
Answer:
it goes into 4, 6 times
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] ÷ [tex]4[/tex]
Hope this helps
solve the following equation 5+7=11+7
Answer:
The equation, 5+7=11+7 solved step by step is:
5 plus 7, which equals 12.
And then, 11 plus 7, which equals 18.
You put it all together, it turns into 12=18 which isn't true.
So, your problem is not real.
Step-by-step explanation:
Your question has no answer because the two sides aren't equal.
Hope this helped! :)
How many proportional relationships are shown in the coordinate plane below? Please answer quick
Answer:
The answer is 1
Step-by-step explanation:
There is 1 proportional relationship in the graph
Find the critical t-value for a 98% confidence interval estimation if the sample size equals 11. (Round your solution to 4 decimal places)
Answer:
2.764
Step-by-step explanation:
Critical value = tα/2, degrees of freedom
Degrees of freedom = n - 1
n = 11
Degrees of freedom = 11 - 1
= 10
tα/2 = 100 - 98%/2
= 2%/2
= 1%
= 0.01
Critical value = 0.01, 10
Using the Critical T value table, the Critical T value for
two tails( a degree of significance of 0.02 and degree of freedom of 10) or one tail (0.01, 10) = 2.764
Changing Scales in Scale Drawings- (question in picture attachment)
i dont get it
Step-by-step explanation:
A triangle has two sides of length 2 and 15. What compound inequality describes the possible
lengths for the third side, X?
Answer:
13<X<17
Step-by-step explanation:
Triangular Inequalities state that a side is always greater than the absolute value of the difference of the other two sides and less than the sum of the other two sides. You use the inequality |a-b|<c<a+b with a, b, and c as the lengths of the sides.
When you plug in the numbers, (X being c, 2 being b, and 15 being a) you get
|15-2|<X<15+2
|13|<X<17
Which brings us to our final answer of:
13<X<17
Ivan has 32 baseballs and 48 basketballs. If he wants to divide them into identical groups without any balls left over, what is the greatest number of groups Ivan can make
Here we will show you step-by-step with detailed explanation how to calculate 48 divided by 32 using long division.
Before you continue, note that in the problem 48 divided by 32, the numbers are defined as follows:
48 = dividend
32 = divisor
Step 1:
Start by setting it up with the divisor 32 on the left side and the dividend 48 on the right side like this:
3 2 ⟌ 4 8
Step 2:
The divisor (32) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:
0
3 2 ⟌ 4 8
Step 3:
Multiply the divisor by the result in the previous step (32 x 0 = 0) and write that answer below the dividend.
0
3 2 ⟌ 4 8
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.
0
3 2 ⟌ 4 8
- 0
4
Step 5:
Move down the 2nd digit of the dividend (8) like this:
0
3 2 ⟌ 4 8
- 0
4 8
Step 6:
The divisor (32) goes into the bottom number (48), 1 time(s). Therefore, put 1 on top:
0 1
3 2 ⟌ 4 8
- 0
4 8
Step 7:
Multiply the divisor by the result in the previous step (32 x 1 = 32) and write that answer at the bottom:
0 1
3 2 ⟌ 4 8
- 0
4 8
3 2
Step 8:
Subtract the result in the previous step from the number written above it. (48 - 32 = 16) and write the answer at the bottom.
0 1
3 2 ⟌ 4 8
- 0
4 8
- 3 2
1 6
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 48 divided by 32 calculated using Long Division is:
1
16 Remainder
Charlie has 468 onions to sell. He puts 12 onions in each bag, and he sells the bags for $8 each. What is the answer?
Answer:
312 $
Step-by-step explanation:
468 / 12 = 39 bags
8 x 39 = 312 $
so the answer is 312$
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7 + (−3) simplify
please
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
When you add a negative number, you're basically subtracting it.
7 - 3 = 4
Hope this helps! Good luck :)
Review the proof of de Moivre’s theorem (not in order).
Proof of de Moivre's Theorem
[cos(θ) + isin(θ)]k + 1
A = [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1
B = cos(kθ + θ) + isin(kθ + θ)
C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]
D = [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]
E = cos[(k + 1)θ] + isin[(k + 1)θ]
Which steps must be switched to put the proof in order?
steps B and C
steps B and D
steps C and D
steps C and E
Answer:
steps B and D
Step-by-step explanation:
the correct chart is below :)
The steps which must be switched to put the proof in order are steps B and D
Since [cos(θ) + isin(θ)]k + 1
= [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1
= [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]
= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]
= cos(kθ + θ) + isin(kθ + θ)
= cos[(k + 1)θ] + isin[(k + 1)θ]
Since the step after A is [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)] = D, and the step after C is cos(kθ + θ) + isin(kθ + θ) = B.
So, steps B and D must be switched.
The steps which must be switched to put the proof in order are steps B and D.
Learn more about De Moivre's theorem here:
https://brainly.com/question/11889817
What’s 1 times 5 times 2?
Answer:
10
Step-by-step explanation:
Answer:10
Step-by-step explanation:1×5=5×2=10
Find the remainder when f(x) is divided by g(x) given that f(x) = 4x3 − 5x2 − 3x + 2 and g(x) = x − 3.
Given:
[tex]f(x)=4x^3-5x^2-3x+2[/tex]
[tex]g(x)=x-3[/tex]
To find:
The remainder when f(x) is divided by g(x).
Solution:
According to remainder theorem, if f(x) is divides by (x-c), then remainder is f(c).
Using remainder theorem, if [tex]f(x)=4x^3-5x^2-3x+2[/tex] is divides by [tex]g(x)=x-3[/tex], then remainder is f(3).
Substitute x=3 in f(x).
[tex]f(3)=4(3)^3-5(3)^2-3(3)+2[/tex]
[tex]f(3)=4(27)-5(9)-9+2[/tex]
[tex]f(3)=108-45-7[/tex]
[tex]f(3)=56[/tex]
Therefore, the required remainder is 56.
Find the integers that are closest to 65 (the number in the middle)
Step-by-step explanation:
Divisors of the Positive Integer 65:
1,5,13,65
Sum of all the Divisors of 65, including itself:
84
Sum of the Proper Divisors of 65:
19
Properties of the number 65:
The integer 65 is an odd number.
The integer 65 is a Composite number.
19 is less than 65, so 65 is a deficient number.
1) Suppose you buy a laptop costing $1850 at a store charging 12% add-on interest, and you make a $500 down payment.
Find the exact value using trigonometric identities.
1850 , 0.12 , − o n , 500 a
What type of number is V40?
Choose all answers that apply:
А
Whole number
B
Integer
С
Rational
D
Irrational
PLEASE ANSWER!!!
Answer:
A, B, and C
Step-by-step explanation: I'm going to assume the V is a typo. 40 is a whole number (it isnt a fraction or decimal), an integer, and rational because it is a real number and ends.
Tim used the expression n3 to determine the volume of a cube where n represents a side length of the cube. Using this expression, what is the volume, in cubic inches, of a cube with a side length of 3.5 inches?
Answer:
4
Step-by-step explanation:
Answer:
Step-by-step explanation:
An airplane cover 1020km in an hour. How much distance will it cover in 25/6 hours
Answer:
4250 km
Step-by-step explanation:
If we convert 25/6 into a mixed fraction, we get 4 1/6. Since we already know the plane goes for four hours already, we can multiply 1020 km x 4. That would give us 4080. Now that we converted the equation into a mixed fraction, we also know that the plane goes for an extra 1/6 hour. We divide 1020/6 because it is a sixth of an hour and the plane can travel 1020 in an hour. We get 170 km for 1/6 of an hour.
4080km + 170km= 4250 km
Given : An airplane cover 1020km in an hour.
To Find : How much distance will it cover in 25/6 hours .
Solution : It is given that an airplane covers 1020 km in one hour , this implies that the speed of the airplane is 1020km/hr .
Now , it is asked to find that how much distance it will cover in 25/6 hours .
Here ,
Speed = 1020km/hr .Time = 25/6 hr .Distance = ? .★ We know a relation between speed , distance & time as ,
[tex]\boxed{\red{\bf Distance = Speed \times time }}[/tex]
⇒ Distance = Speed × Time .
⇒ Distance = 1020km/hr × 25/6 hr .
⇒ Distance = 4250 km .
Hence the distance travelled is 4250km.
I need help !!!!!!!
Given , KM = 22
Then JL =
This trapezoid is an isosceles trapezoid which means its diagonals will be equal . So ,
KM = JL ( the diagonals in an isosceles trapezoid are congruent )
22 = JL
JL = 22
Therefore , JL = 22 .
Solution (6) :Given , DF = 8.7
Then , EG =
Since this trapezoid is an isosceles trapezoid , its diagonals will be equal . So ,
DF = EG ( the diagonals in an isosceles trapezoid are congruent )
8.7 = EG
EG = 8.7
Therefore , EG = 8.7 .
The length of a rectangle is 10 meters more than the width. If 3 meters is added to both the length and the width, the new area will be 299 square meters. Find the length and width of the original rectangle.
HELP HELP HELP HELP
Answer:
L = 20
W = 10
Step-by-step explanation:
L = (w + 10)
NL = (w + 13)
Divide 299 by 13:
299 ÷ 13 = 23
So, 23 x 13 = 299
L = 23
W = 13
Subtract 3 from both to get the original length and width
What is the answer to -1x(-2)
Answer: 2x
Step-by-step explanation:
Answer:
2x
Step-by-step explanation:
Since there's two negative signs, the product should be positive. Just multiply 1x and 2 together to get the answer. :D
What is the value of 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5) when x = 5?
Answer:
96
Step-by-step explanation
4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5)
4(5 - 2)(5 + 3) = 12(8) = 96
7(5 - 2)(5 - 5) = 0
- 6(5 - 3)(5 - 5)= 0
96+0-0 = 96
Find the value of f'(4) when
f(x)=5/3x^3/2+8x^1/2
. (2 points each) How many ways are there to choose a dozen (12) donuts from 18 varieties if(a) there are no two donuts of the same variety
Answer:
There are 455 ways
Step-by-step explanation:
Here, we want to find the number of ways to select 12 donuts out of 18 donuts given that all the donuts are different
Mathematically, that would be;
18 C 2
= 18!/(18-12)!12! = 18!/6!12! = 455
a child walks 3/10 of a mile in 1\5 hour. At this rate, how far will the child walk in 1 hour
Answer:
1½ mile
Step-by-step explanation:
Given
3/10 mile = ⅕ hour
Required
Determine the distance in 1 hour
Since rate is constant, we have:
3/10 mile = ⅕ hour
Multiply both sides by 5
5 * 3/10 mile = ⅕ hour * 5
15/10 mile = 5/5 hour
3/2 mile = 1 hour
1½ mile = 1 hour
Hence,the child will walk 1½ mile in 1 hour