Solution :
P(H) = 0.7 ; P(T) = 0.3
If heads, then Urn H, 1 blue and 4 red marbles.
If tails, then Urn T , 3 blue and 1 red marbles.
a).
P ( choosing a Red marble )
= P (H) x P( Red from Urn H) + P (T) x P( Red from Urn T)
[tex]$=0.7 \times \frac{4}{5} + 0.3 \times \frac{1}{4}$[/tex]
= 0.56 + 0.075
= 0.635
b). If P (B, if coin showed heads)
If heads, then marble is picked from Urn H.
Therefore,
P (Blue) [tex]$=\frac{1}{5}$[/tex]
= 0.2
c). P (Tails, if marble was red)
[tex]$=P (T/R) = \frac{P(R/T)}{P(R)} \ P(T)$[/tex]
Where P (R/T) = P ( red, if coin showed tails)
[tex]$=\frac{1}{4}$[/tex]
= 0.25 (As Urn T is chosen)
P (R) = P (Red) = 0.635 (from part (a) )
P (T) = P (Tails) = 0.3
∴ [tex]$P(T/R) = \frac{0.25 \times 0.3}{0.635}$[/tex]
= 0.118
Bob purchased 2 hot dogs and 1 hamburger for S10. Later that day, Bob had to purchase more food and
Bot 1 hot dog and 3 hamburgers for S15. What were the prices of the hamburger and hot dogs?
Answer:
Hotdog: $3.00
Hamburger: $4.00
Step-by-step explanation:
For the first time that Bob buys food, we can make an equation to find how much a single hotdog and a single hamburger costs, where:
x = cost of a hotdog
y = cost of a hamburger
He bought 2 hotdogs and 1 hamburger for $10, so the equation for his first time buying food is:
2x + y = 10
For the second time buying food, he bought 1 hotdog and 3 hamburgers for $15, so his equation would be:
x + 3y = 15
To find the value for x and y we need to solve this system of equations using the two equations we just came up with. We can do this multiple ways, but I'll be demonstrating the substitution method.
Using the second equation, we can solve for x by simply subtracting 3y from both sides:
x = 15 - 3y
We can then insert this value of x into the first equation so that way we are only dealing with one variable to solve - y:
2(15-3y) + y = 10
Distribute out the 2 into the paratheses, combine like terms, and then solve for y:
30 - 6y + y = 10
30 - 5y = 10
-5y = -20
y = 4
This means the cost for one hamburger is $4. But we still need to find the price of one hotdog, so we can insert this value of y into the equation we came up with earlier for x, and then solve for x:
x = 15 - 3y
x = 15 - 3(4)
x = 15 - 12
x = 3
So the price of one hotdog is $3 and the price of one hamburger is $4. Hope this helps.
Find the coefficient of x in the polynomial ( 4y - 13 - 5z - 4x )
[tex]\large\huge\green{\sf{Answer:-}}[/tex]
the coefficient of x in the polynomial ( 4y - 13 - 5z - 4x ) is -4Answer:
[tex]\huge\boxed{\sf -4}[/tex]
Step-by-step explanation:
The given polynomial is:
4y - 13 - 5z - 4x
Coefficient:
The term/number (along with the sign) with that certain variable is called coefficient.
x has the coefficient of :
-4 (number along with x)
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807When Damian runs the 400 meter dash, his finishing times are normally distributed
with a mean of 60 seconds and a standard deviation of 1 second. Using the empirical
rule, determine the interval of times that represents the middle 99.7% of his finishing
times in the 400 meter race.
The middle 99.7% is within 60 seconds to 63 seconds.
The empirical rule states that for a normal distribution, 68% are within one standard deviation from the mean, 95% are within two standard deviations from the mean and 99.7% are within three standard deviations from the mean.
Given that:
mean (μ) = 60 seconds, standard deviation (σ) = 1 second
99.7% are within three standard deviations = μ ± 3σ = 60 ± 3(1) = (57, 63)
The middle 99.7% is within 60 seconds to 63 seconds.
Find out more at: https://brainly.com/question/4518679
Layla borrowed some money from her friend in order to help buy a new video game
system. Layla agreed to pay the friend back some amount every week until her loan
was paid off. Let L represent the amount Layla owes her friend after t weeks. A graph
of L is shown below. Write an equation for I then state the y-intercept of the graph
and determine its interpretation in the context of the problem.
The linear equation for this scenario is L = -20t + 140. Layla owes her friend $140 and pays the friend $20 per week.
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
Let L represent the amount Layla owes her friend after t weeks.
Using the point from the graph (0, 140) and (7, 0):
L - 140 = [(0 - 140)/(7 - 0)](t - 0)
L - 140 = -20t
L = -20t + 140
The y intercept is 140
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Frederico's checking account balance is -$15, and Neela's checking account balance is -$285. How many times the balance of Frederico's checking account is Neela's checking account balance? A. -19 B. -270 C. 270 D. 19
Answer:
2
Step-by-step explanation:
the answer is 2 because I need points for my brainly so I can get a 100 on this assignment
plssss help, need major help with the second question // 25 points
Answer:
22
Step-by-step explanation:
9 + 8 + 14 = 22
I hope this helps!
what is 3 1/3 - 1 1/2
Answer:1.833333
Step-by-step explanation:
How Much Percentage is 7 out of 45.99?
Answer: 0.152207 %
Step-by-step explanation: divide the amount by the total to get the percentage.
The perimeter of a rectangle is 20/33 feet. The length of three sides together is 16/33 feet.
What is the length of the fourth side?
40 feet
4/33feet
16/33feet
20/33feet
Calvin and Sanjay are each thinking of a number. If you multiply Sanjay’s number by 3 and subtract
2, you get Calvin’s number. If you take half of Calvin’s number and then subtract 2, you get Sanjay’s
number. What number is each thinking of?
Answer:
Calvin's number: 16 Sanjay's number: 6
Step-by-step explanation:
6 x 3 = 18, 18 - 2 = 16
16 / 2 = 8, 8 - 2 = 6
A Car’s rectangular gas tank has dimensions 30 cm by 25 cm by 42 cm.
(a) Calculate the capacity in liters, of the tank.
(b) If gasoline cost $154 per liter, what is the cost of filling the tank?
Answer:
$4851
Step-by-step explanation:
rectangular prism volume = length x width x height
1 litre = 1000 cm³
cost = $per litre x litres
v = l x w x h
30cm x 25cm x 42cm = 31500cm³
litres = cm³ / 1000
31500cm³ / 1000 = 31.5 litres
31.5 x $154 = $4851
If I take 1 hour to cook a batch of cookies and I have 15 ovens working 24 hours a day every day for 5 years, how long does it take me to make 6000000 batches of cookies?
Answer:
Approximately 40,069 days
arithmetic sequence, can anyone help with this questions plz?
Answer:
Add 2/3
Step-by-step explanation:
2/3 + 2/3 = 4/3 + 2/3 = 6/3 (or 2) + 2/3 = 8/3 +2/3 = 10/3
Please help with this question
Answer:
D
Step-by-step explanation:
The first equation would have to have a y-intercept of 4, and the second equation would have to have a y-intercept of -1.
-hope it helps
Answer: what the actual fudge is this?? i am a former harvard professer for math and I have never seen such a monstrocity of a math question, but the answer is the first one.
Step-by-step explanation:
The solution is -1/2.
Which multiplication equation has the given solution?
Answer:
5x=-(5/2) ~~ first choice
Step-by-step explanation:
divide both sides by 5
-> x=(5/2)/5
simplify the above
-> x = - (5/2x5)
simplify
-> x = -(5/10)
simplify and solve
=> x = - 1/2
(basically trial and error)
I need the answer asap and the demonstration please
Answer:
4
Step-by-step explanation:
Use system of equations to solve for x.
If you live 1.5 miles from school and you walk at a rate of 3mph, when should you leave home in order to arrive at school by 9:00?
Work Shown:
time = distance/speed
time = (1.5 miles)/(3 mph)
time = (1.5/3) hours
time = 0.5 hours
time = 30 minutes
It takes 30 minutes to walk to school, so you should leave a half hour before 9:00. Subtracting 30 minutes from 9:00 gets you to 8:30. If anything, you should start a little bit before 8:30 just in case something might slow you down for one reason or another.
What is the area of a triangle with a base of √10 and a height of √13
Answer:
5.691
Step-by-step explanation:
v10=3.162 and v13=3.605
so 3.162x3.605= 11.383
the 11.383 divided by 2 = 5.691
my bro has homework and he needs help but I don't have the time to help him
Answer: 25
Step-by-step explanation:
Subtract 46.50 - 46.25 and you’ll get 25
Carlos is at the store buying pencils. There is a package with 4 pencils that
costs $5 or a package with 5 pencils that costs $6. Which package is the
better buy?
A. The $6 package, because each pencil costs $1.20.
B. The $6 package, because each pencil costs $0.83.
C. The $5 package, because each pencil costs $1.25.
D. The $5 package, because each pencil costs $0.80.
Answer:
The best answer would be A. because 6 divided by 5 is 1.20. Pls give me brainliest because i am trying to rank up.
Step-by-step explanation:
What is the slope of the line?
Answer:
1/3
Step-by-step explanation:
m = (y2-y1)/(x2-x1)
m = (0- -3)/(5- -4)
m = 3/9 = 1/3
Enrique bought a football and a puzzle at a store.
He paid $15.35 for the football.
He paid a total of $24.02 for the football and the puzzle.
How much did Enrique pay for the puzzle, in dollars and cents?
Answer:
8 dollars and 67 cents...8.67
Step-by-step explanation:
5 dollar bill
3 one dollar bills
2 quarters
1 dime
1 nickel
2 pennies
1/3(x+6)=2/3(x-9)
multi step equation
[tex]\dfrac13(x+6) = \dfrac 23 (x-9) \\\\\\\implies x+6 = 2(x-9)~~~~;[ \text{Multiplying both sides by 3}]\\\\\implies x +6 = 2x -18\\\\\implies 2x -x = 6+ 18 \\\\\implies x = 24[/tex]
Monica says,"if 4 bottles cost $10, then 2 bottles cost $5 + $20." Is Monica correct? Explain
6 grade shiiii, help me out doe, thanks luvs <33.
Answer:
Monica is not correct.
Step-by-step explanation:
First of all, if 4 bottles only cost $4, then how would only 2 cost more? (She said the two bottles would be $25, which doesn’t make sense.)
CAN SOMEONE ANSWER THIS!!!!!!!!
Answer:
Step-by-step explanation:
2 now help me :(
PLEASE HELP DUE NOW!!
Answer:
✓ C. f(x)= sqrt 1/x
Step-by-step explanation:
i hoep this answer your question
Pls help I’ll brainlest ASAP
Answer:
slope = change over y/change over x
point 1: (-3,-4)
point 2: (2,3)
(-4-3)/(-3-2)=(-7)/(-5)=7/5
y=mx+b -> m=slope, b=y-intercept
y=(7/5)x+b
plug in one of the points
3=(7/5)*2+b
3=14/5+b
b=1/5
slope = 7/5, y-intercept = (0,1/5)
From a hot-air balloon, Grayson measures a 29^{\circ} ∘ angle of depression to a landmark that’s 1004 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
The balloon’s vertical distance above the ground is 556 feet
The set up will form a right triangle.
Given the following parameters
Angle of depression = 29 degreesHorizontal distance = 1004 feetTo get the height above the ground, we will use the SOH CAH TOA identity as shown;
Opposite = h
Adjacent = 1004 feet
Tan theta = h/1004
Tan 29 = h/1004
h = 1004 tan 29
h = 1004(0.5543)
h = 556.52 feet
Hence the balloon’s vertical distance above the ground is 556 feet
Learn more on angle of depression here: https://brainly.com/question/23497407
0.03249 in standard form to 3 significant figures is
(A) 3.24 × 10−1
(B) 3.24 × 10−2
(C) 3.25 × 10−2
(D) 3.25 × 10−3
The domain of y = cosx is the set of real numbers. True False
Answer:
true
Step-by-step explanation:
