Answer:
0.1733 = 17.33% probability the first stack was selected.
Step-by-step explanation:
To solve this question, it is needed to understand conditional probability, and the hypergeometric distribution.
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]
Conditional probability:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Probability of all red cards for the first stack:
For this, we use the hypergeometric distribution, as the cards all chosen without replacement.
7 + 4 = 11 cards, which means that [tex]N = 11[/tex].
7 red, which means that [tex]k = 7[/tex]
3 are chosen, which means that [tex]n = 3[/tex]
We want all red, so we find P(X = 3).
[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 = 3) = h(3,11,3,7) = \frac{C_{7,3}*C_{4,0}}{C_{11,3}} = 0.2121[/tex]
Conditional probability:
Event A: All red
Event B: From the first stack.
Probability of all red cards:
0.2121 of 50%(first stack)
1 of 50%(second stack). So
[tex]P(A) = 0.2121*0.5 + 1*0.5 = 0.60605[/tex]
Probability of all red cards and from the first stack:
0.21 of 0.5. So
[tex]P(A \cap B) = 0.21*0.5 = 0.105[/tex]
What is the probability the first stack was selected?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.105}{0.60605} = 0.1733[/tex]
0.1733 = 17.33% probability the first stack was selected.
Find the x and y intercepts of the equation. Express your answers as points. 5 x + 7 y = − 140
Answer:
x-intercept(s): (-28, 0)
y-intercept(s): (0, -20)
Step-by-step explanation:
Try This Answer.
hey this is my first post, does anyone know how to do this and find V?
Answer:
16
Step-by-step explanation:
8/1/2
8 divided by 1/2
8 x 2/1 = 16
Answer:
Step-by-step explanation:
P=8/V
1/2=8/V
do cross multiplication
2*8=V*1
16=V
PLZ SOLVE. DONT BE WRONG PLEASEEEE I NEDD ED THIS
Answer:
288
Step-by-step explanation:
Take the area of every individual section, and add them together.
24
24
100
80
60
Find the volume of the rectangular pyramid below.
Answer:
315 yd cubed
Step-by-step explanation:
To find the volume of the pyramid, we first need to consult the equation below. Thebase is for the rectangular portion, then after multiplied by the height it is divided by 3 to get the pyramid.
[tex]\frac{1}{3} (B * H )[/tex]
To get the base, we multiply the length by the width.
21 * 9 = 189
189 * 5 = 945
945 divided by 3 = 315
Answer:
Let's find the base area:
21 x 9 = 189
Now let's multiply the base area by the height:
189 x 5 = 945
Now let's divide by 3( x 1/3 ):
945 divided by 3(x 1/3) = 315 yd^3 is your answer
Step-by-step explanation:
Formula area of a rectangular Pyramid(just like any other pyramid):
BH x 1/3
To find base we multiply length by width just using the basic formula of finding area of a rectangle.
Then we multiply our base area by our height.
One we've done that we now divide by 3(multiplying by 1/3)
3) Which inequality represents this scenario?
The weight of a book may be no more than 3.3 pounds.
A) w > 3.3
B) w< 3.4
C) w <3.3
D) w < 3.3
Answer:
w < 3.3
C) w < 3.3
D) w < 3.3
Answer: [tex]w \le 3.3[/tex]
=====================================================
Explanation:
w is the weight and it may be no more than 3.3 pounds. This is the same as saying that 3.3 pounds is the highest it can go. Think of it as the ceiling.
w = 3.3 is possible or anything smaller than it is possible.
So w is 3.3 or smaller meaning we write the inequality [tex]w \le 3.3[/tex]
The answer is not w < 3.3 because that would exclude 3.3 itself.
The answer is between choices C and D. It seems like one of those inequality signs should have an underline.
Metric Units of Length
1 km = 103 m = 1,000 m
1 m= 102 cm = 100 cm
1 m = 103 mm = 1,000 mm
1 cm = 10 mm
Which of the following tells how to change a measurement from millimeters to meters?
O Divide by 10
O Multiply by 10
O Divide by 1,000
O Multiply by 1,000
Answer:
devide by 1000 is answer
Answer:
divide by 1000
Step-by-step explanation:
1m=1000mm
? = 10mm
10m*1m/1000
=
Need help
7th grade
Vertical angles
Answer:
a) 90°
b) 90° - 35° = 55°
c) 65° - 40° = 25°
d) 90° - 65° = 25°
e) 180° - 65° = 115°
f) 180° - 35° = 145°
g) 180° - 40° = 140°
h) 65° + 35° = 100°
180° - 100° = 80°
i) 90° - 40° = 50°
j) 35° + 40° = 75°
180° - 75° = 105°
(the answer is written in bold)
Add.
2
1
3x² - 4x-4
3x² +8x+4
+.
Simplify your answer as much as possible.
NO LINKS please and thank you
Answer:
6x²+4x
Step-by-step explanation:
The given expressions are 3x²- 4x-4 and 3x²+8x+4.
We need to add these two expressions.
3x²- 4x-4 + 3x²+8x+4 = 3x² + 3x² -4x+8x-4+4
= 6x²+4x
On adding the given expressions, we get the value as 6x²+4x. Hence, the sum of the given expressions is equal to 6x²+4x
I'm kinda lost here, what do I do when the quadrant is given? CanI have some of these solved at least with steps?
Answer:
See Explaination
Step-by-step explanation:
According To Question
In Quadrant-1 (0* to 90*) ( All the Trignometry Functions are Positive )In Quadrant-2 (90* to 180*) (Only Sine & Cosecant are Positive)In Quadrant-3 (180* to 270*) (Only Tangent & Cotangent Are Positive)In Quadrant-4 (270* to 360*) ( Only Cosine & Secant Are Positive)(Diagram, Please Find In Attachment)
Question 38 . Cos ∅ = 12/13 ∅ in Quadrant-4(Where only Cos & Sec are Positive all other Functions Are Negative in this Quadrant)
Now ∅ Represent a Right Angle Triangle with Base=12 Perpendicular=5 & Hypothenese=13
other Five Trignometry Functions Are as FollowSin∅ = -5/13 , Cosec∅=-13/5 , Tan∅=-5/12 , Cot∅=-12/5 & Sec∅=13/12
Question 39 . SinX=-3/4 X Lies in Quadrant-3(Where only Tan & Cot are Positive all other Functions Are Negative in this Quadrant)
Now For Other Trignometry FunctionsFind By Using Basic Formulas
[tex]SinX^{2}+CosX^{2}=1[/tex] ↔ Put Value of Sin∅=-3/4
We get CosX= ±[tex]\frac{\sqrt{5} }{4}[/tex] (but X Lies in Quadrant-3 Where Cosine Is Negative , So Neglect CosX= +[tex]\frac{\sqrt{5} }{4}[/tex])
So CosX= -[tex]\frac{\sqrt{5} }{4}[/tex] ...... now you get the point . All Questions Will Solve like This .
The table shows the coordinates of some rides on a map of the fairgrounds. Which quadrant shows the roller coaster
Answer:
Quadrant IV shows the roller coaster.
Step-by-step explanation:
Since you see R in quadrant 4, which has the coordinates 1,-6, it is in the 4th quadrant, or Quadrant IV.
What two numbers add to 7 and multiply to -44
Answer:
The numbers are 11 and -4
Step-by-step explanation:
Given
Let the two numbers be [tex]x[/tex] and [tex]y[/tex]
such that:
[tex]x + y = 7[/tex]
[tex]x*y = -44[/tex]
Required
Find x and y
Make y the subject in: [tex]x + y = 7[/tex]
[tex]y = 7 - x[/tex]
Substitute [tex]y = 7 - x[/tex] in [tex]x*y = -44[/tex]
[tex]x(7-x) = -44[/tex]
Open bracket
[tex]-x^2 +7x = -44[/tex]
Rewrite as:
[tex]x^2 -7x -44=0[/tex]
Expand
[tex]x^2 +4x-11x -44=0[/tex]
Factorize
[tex]x(x +4)-11(x +4)=0[/tex]
Factor out x + 4
[tex](x -11)(x +4)=0[/tex]
Solve for x
[tex]x =11; x =-4[/tex]
Recall that:
[tex]y = 7 - x[/tex]
So:
[tex]y = 7-11 = -4[/tex]
or
[tex]y = 7--4 = 11[/tex]
Distribute and combine HELP NOW!!
Answer:
9x + 8
Step-by-step explanation:
2(3x + 1) + 5x + 9 - 2x - 3
⇒ 6x + 2 + 5x + 9 - 2x - 3
⇒ 9x + 8
Algebra
2(3x+1)=6x+2
Then combine like terms.
6x+2+5x+9-2x-3
9x+8
21× 1 2/14. step by step explanation pls!
Answer:
18
Step-by-step explanation:
21 = 3 x 7
12 = 2 x 6
4 = 2 x 7
( 21 x 12 ) / 14
= ( 3 x 7 x 2 x 6 ) / ( 2 x 7 )
= 3 x 6
= 18
Answer:
18
Step-by-step explanation:
See image attached for guide
21 x 1 2/14
Make 1 2/14 an improper fraction, add the denominator 1 under 21:
21/1 x 16/14
Multiply numerator x numerator, do the same for denominator:
21 x 16= 336
1 x 14 = 14
336/14
Simplify:
336/14 = 24
Hope this helps
Matthew is organizing textbooks on his bookshelf. He has a Spanish textbook, a biology textbook, and a history textbook. How many different ways can he line the textbooks up on his bookshelf?
Answer:
I think he can line them up a total of 6 times?
Answer:
6
Step-by-step explanation:
An engine encounters a standard environment with a probability of 0.9, and a severe environment with a probability of 0.1. In a normal environment the probability of failure is 0.03, whereas in the severe environment this probability is 0.5.
i. What is the probability of failure?
ii. Given that failure has occurred, what is the probability that the environment encountered was severe?
Answer:
.077
.64935
Step-by-step explanation:
Let F= failure
let S= severe
we are given that
p(F|S')= .03
p(F|S)= .5
For the first question we are looking for f
we can solve for it by using the law of total probability
so in theory we want
F∩S+F∩S'
Using the conditional probability formula we can solve for the intersections
.03*.9+.5*.1= .077
2.
For this question we are looking for S|F
to solve this use bayes thereom
[tex]S|F=\frac{F|S*S}{F|S*S+F|N*N}=\frac{.5*.1}{.5*.1+.9*.03}=.649[/tex] (or 50/77)
What is an algebraic expression for the quotient of w and 7 ? A. W-7 B. W+7 C.W/7 D.7w
Answer:
the answer for this is C.
Step-by-step explanation:
quotient is the number gotten by dividing a number by another.this is why it is C.
1. Annel sells a phone which costs $180 and earns 5% commission. What is the dollar
amount of commission that Annel earns?
A $189
B $9
C $109
D $90
Answer:
B) $9
Step-by-step explanation:
5% can also be written as 0.05
Dividing a percentage by 100 gives you decimal form.
The question is asking for the amount of commission earned, not the total amount. This means that all we have to do is do:
$180 x 0.05 = $9
7. CHALLENGE: Use the digits 0 to 9 to make the equation true. You don't need to use all thedigits you can only use each digit once.
20 = ___+(___-___)×___
9514 1404 393
Answer:
20 = 2 + (7 -4) × 6
Step-by-step explanation:
The Order of Operations requires the parentheses be evaluated first, then the multiplication performed. Finally, the addition is performed.
If each of the blanks is filled with a single digit, the result of the multiplication must be a composite number greater than 10. Those are 12, 14, 15, 16, 18, 20. For the expression shown above, we have chosen to make the product be 18. That means the first blank is filled with 2 and the remaining blanks must evaluate to one of the products 2×9 or 3×6.
We have chosen 6 for the last blank, so the two blanks in parentheses must have a difference of 3. The digits 2 and 6 cannot be used, leaving possible choices as (3-0), (4-1), (7-4), (8-5).
Our final expression is chosen to be ...
20 = 2 +(7 -4)×6
Following a strategy of product differentiation, Westwood Corporation (W) makes a high-end kitchen range hood, KE8. W’s data for 2012 and 2013 follow on the next slide.In 2013, W produced no defective units and reduced direct materials usage per unit of KE8. Conversion costs in each year are tied to manufacturing capacity. Selling and customer service costs are related to the number of customers that the functions are designed to support. W has 23 customers (wholesalers) in 2012 and 25 customers in 2013.
Units of KE8 produced and sold 40,000 42,000
Selling Price $100 $110
Direct Materials (sq ft) 120,000 123,000
DM cost per sq ft $10 $11
Manufacturing capacity for KE 850,000units 50,000units
Conversion Costs $1,000,000 $1,100,000
CC per unit $20 $22
Selling & Customer Service capacity 30customers 29customers
Selling & Customer Service Costs$720,000 $725,000
Cost per customer$24,000 $25,000
Required:
(1) Describe elements you would expect to see in W’s BSC.
(2)Calculate the growth, price recovery and productivity components that explain the change in the 2012 to 2013 income. Can you use the worksheet to get the variances?(3) Suppose during 2013, the market size for high-end rangehoods grew 3% and all increases in market share are due to W’s product differentiation strategy. How much of the change in OI is due to the industry market size factor, cost leadership and product differentiation?
(4) How successful was the strategy implementation?
I need help is using double-angle formulas to simplify trig expressions.
Answer:
the answer is c
Step-by-step explanation:
(1-cosb²)/sinx²
Please show work thank you
Answer: 70 mph
Step-by-step explanation:
Perimeter of a rectangle is 11 inches. The length of the rectangle is 1/2 inches what is the width of the rectangle?
Answer:
=5
Step-by-step explanation:
perimeter= 2(L)+2(W)
11 =2(1/2)+2W
11=1+2W
11-1=2W
10=2W
Both sides divided by 2
therefore The width is 5
The ages of the members of a family are 46, 48, 21, 12, 15, and 8. what is the mean age?
Answer:mean means to average. in order to average, add all the numbers then divide by how many numbers you have.
All these ages add up to 150. because there are 7 ages, divide by 7. this is 21.4 which can be rounded to about 21
46 + 48 + 21 + 12 + 15 + 8 = 150
150 ÷ 7= 21.4285 = 21
Step-by-step explanation:
I tried to complete this question on determining a trigonometry equation on a graph but I got the wrong answer. What did I do wrong?
Answer:
[tex]y=2\sin(x)-1[/tex]
Step-by-step explanation:
Let's break it down:
In the sinusoidal function [tex]y=a\sin b(x-c)+d[/tex]:
[tex]a[/tex] represents Amplitude [tex]b[/tex] represents a constant related to the Period[tex]c[/tex] represents Phase Shift [tex]d[/tex] represents Vertical ShiftTo find Amplitude, divide the entire height of the function (from top to bottom) by two, or find the vertical distance between the horizontal line of symmetry and the highest/lowest point of the wave. In this case, Amplitude is 2.
To find [tex]b[/tex], use [tex]T=\frac{2\pi}{b}[/tex], where [tex]T[/tex] is the period of the function. To find the period, count the horizontal distance of the length of one complete cycle. In this case, period is [tex]2\pi[/tex] and therefore
[tex]2\pi=\frac{2\pi}{b},\\b=\frac{2\pi}{2\pi}=1[/tex].
To find Phase Shift, find the horizontal shift from the parent function [tex]y=\sin x[/tex]. In this case, there is no phase shift.
To find Vertical Shift, find the vertical shift from the parent function [tex]y=\sin x[/tex]. In this case, vertical shift is -1.
Thus, we've found:
[tex]a=2[/tex] [tex]b=1[/tex] [tex]c=0[/tex] [tex]d=-1[/tex]Substituting these values into [tex]y=a\sin b(x-c)+d[/tex] , we get:
[tex]y=2\sin 1(x-0)-1=\boxed{y=2\sin(x)-1}[/tex]
Which graph best represents the equation f(x) = 2(5)^x
Answer:
H
Step-by-step explanation: 6 4 17 30
if x = 0 f(0) = 2×5^0
= 2 × 5
= 10
H is the only graph that equals 10 at x=0
Answer:
See the image below for the answer:)
Step-by-step explanation:
Hope this was helpful.
PLESE HURRY
If f(x) = (-x)3, what is f(-2)?
-8
-6
6
8
Answer:
8
Step-by-step explanation:
f(x) = (-x)^3
Let x = -2
f(-2) = (- -2)^3
= (2)^3
= 8
Plsss help me I’m so confused! Brainlist!!!!! Plsss ASAP, or I’m going to fail my class!!!
Answer:
the median is 12
the mean is 11.16
I believe the answer is:
Median: 12 hours
Mean: 11.2 hours
Hope this helps! :D
Helen gathered 37 mushrooms in 3 hours. how many mushrooms did she gather if she gathered 7 more mushrooms in the second hour than the first hour and 6 more in the third hour than in the first hour?
pls help!
Step-by-step explanation:
How many mushrooms did she gather every hour, if she gathered 7 more mushrooms in the second hour than in the first hour, and 6 more in the third hour than in the first hour? = 8.
What set or sets does negative squareroot of 20 belong to? is it a real number, rational, integer, whole number, irrational, or natural?
Answer:
Real number and Irrational number
Step-by-step explanation:
Given
[tex]-\sqrt{ 20[/tex]
Required
The set it belongs to
First, solve the expression
[tex]-\sqrt{ 20} = -4.472136[/tex]
The above number is not an integer and it is not whole or natural because it has decimal points
It is not a rational number because it cannot be expressed as a simple fraction
However, the number can be categorized as either irrational or real because of the level of the decimal point in the result
Write an equitation for each problem and solve; someone help! I have until 4!
Taxi Word Problem
C = 3.50 + .50m + 3
C = 3.50 + .50(13) + 3
C = 3.50 + 6.50 + 3
C = 13
The total cost will be $13.00
Rock Climbing Word Problem
Trina: 5 + 3.25h = 21.25
Now, subtract 5 from both sides.
3.25h = 16.25
Now, divide both sides by 3.25.
h = 5
Trina spent 5 hours at the facility.
Ralph: 21.25 - 5/ 3.25 = h
Subtract 5 from 21.25
16.25/ 3.25 = h
Now divide
5 = h
Ralph will spend 5 hours at the facility to spend the same amount as Trina.
I hope I helped you in time! Good Luck!!