Final answer:
The expected waiting time for a bus, E[t], is 8.33 minutes, which is calculated considering the possibility of either bus 51, which has a uniform arrival time between 0 to 30 minutes, or bus 82, which arrives in exactly 10 minutes.
Explanation:
The problem you are dealing with involves finding the expected waiting time, E[t], for either bus 51 or bus 82 to arrive. The expected value of a uniformly distributed random variable on an interval [a, b] is given by the formula (a + b)/2. However, we need to account for the fact that if bus 82 arrives in exactly 10 minutes, then if the 51 bus hasn't arrived by then, you will take the 82 bus.
To compute E[t], if the 51 bus arrives within the first 10 minutes, the expected waiting time is the average of 0 and 10 minutes, which is 5 minutes. If the 51 bus does not arrive within 10 minutes, you will take the 82 bus at exactly 10 minutes. Therefore, the expectation must only account for the time if the 51 bus arrives before the 82. This gives us:
The probability that the 51 bus arrives in the first 10 minutes is 10/30 = 1/3.
The expected waiting time if 51 arrives in the first 10 minutes is 5 minutes.
If the 51 bus does not arrive within 10 minutes, you'll wait exactly 10 minutes for the 82 bus.
So, E[t] = (1/3) * 5 minutes + (2/3) * 10 minutes = (5 + 20)/3 = 25/3 minutes.
Therefore, the expected waiting time E[t] is 8.33 minutes (rounded to two decimal places).
You just won a contest! you will receive $100,000 a year for 20 years, starting today. if you can earn 12 percent on your investments, what are your winnings worth today?
78 million converted in scientific notation
The correct answer is:
7.8 × 10⁷
Explanation:
To write a number in scientific notation, we want the decimal behind the first non-zero digit in the number. The first non-zero digit in 78 is 7; this means we want 7.8. In order to have the decimal point behind the 7, we need to move the decimal 7 places. This is the exponent of 10 in our scientific notation, which gives us
7.8 × 10⁷
Shakira went bowling with her friends. She paid $3 to rent shoes and then $4.75 for each game of bowling. If she spent a total of $42, then how many games did Shakira bowl?
Shakira bowls about 8 games.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Let Shakira bowl x games.
Since Shakira has to pay $4.75 for each game, she would pay $4.75x for x games.
Shakira also paid $3 to rent shoes, therefore, the total money Shakira spent is:
4.75x + 3
Given that, the total spent is $42, therefore,
4.75x + 3 = 42
4.75x = 42 - 3
4.75x = 39
x = 39/4.75
x ≈ 8
Hence, Shakira bowls about 8 games.
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pleaseeeee help!!! what is the constant in the expression [tex]5n- \frac{2m}{7} + \frac{3}{4} [/tex]
a. -2/7
b. 3/4
c. 5
d. 21
How does the graph of y=-(2x+6)^2+3 compare to the graph of the parent function?
Raquel throws darts at a coordinate grid centered at the origin. Her goal is to create a line of darts. Her darts actually hit the coordinate grid at (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6). Which equation best approximates the line of best fit of the darts? y = 0.6x + 0.6 y = 0.1x + 0.8 y = 0.8x + 0.1 y = 0.5x + 0.6
Solution:
The points at which Raquel Darts hit the coordinate grid having center at the origin are (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6).
As we can see that not all points are collinear.
As line of best fit is the the line which passes through some points , may be not through the single point, or all the points.
Plotting all the options on coordinate grid i.e on a scatter plot and then determining , the line of best fit of the darts is
y= 0.6 x + 0.6 →→Option (A), the reason being it passes through a point (9,6).
A juice company produces 8,064 cartons of juice in 21 days. Each day, they produced the same number of cartons and delivered those cartons to 16 area coffee shops. The cartons were delivered in cases of six cartons per case, and each coffee shop received an equal number of cases in each delivery. How many cases were delivered to each coffee shop each day?
Answer:
[tex]4\ cases[/tex]
Step-by-step explanation:
Step 1
Divide the total cartons of juice that the company produces in [tex]21[/tex] days by the total days
so
[tex]\frac{8,064}{21}\frac{cartons}{days}=384\frac{cartons}{day}[/tex]
Step 2
Divide the total cartons of juice that the company produces in one day by the total coffee shops
so
[tex]\frac{384}{16}\frac{cartons}{coffee-shop}=24\frac{cartons}{coffee-shop}[/tex]
Step 3
Divide the total cartons of juice that the company delivered per day to each coffee shop by six (number of cartons per case)
so
[tex]\frac{24}{6}=4\ cases[/tex]
a baseball team has 13 players; how many possible batting orders can the coach make if there are 9 players in the batting lineup ?
A. 514,874
B. 235,368
C. 259,459,200
D. 879,523
Final answer:
The number of possible batting orders a coach can make with 13 players for 9 positions is found by calculating [tex]^{13}P_9[/tex], which equals 518,918,400. Thus, the correct answer is C. 259,459,200.
Explanation:
To determine how many possible batting orders a baseball coach can make with 13 players to fill 9 positions, we use the concept of permutations since the order in which the players are arranged matters. The formula for permutations of n items taken r at a time is [tex]^{n}P_r[/tex] = n! / (n - r)!, where the exclamation point indicates a factorial. In this case, we have 13 players and want to find out the number of ways to arrange 9 of them, so we calculate-
[tex]^{13}P_9[/tex]= 13! / (13 - 9)!.
We can simplify this by calculating the factorials: 13! = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 and 4! = 4 × 3 × 2 × 1, so [tex]^{13}P_9[/tex] = 13! / 4!.
Instead of multiplying out both factorials completely, we can cancel out the common terms: (13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (4 × 3 × 2 × 1) = (13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5) / 1.
Calculating the above gives us 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 = 518,918,400 ways to arrange the batting order. Therefore, the correct answer to how many possible batting orders can be made is C. 259,459,200.
Help and get 6 points!
Estimate 36472-32841
Write a 2 column proof
Prove x=45
Answer:
Look at the below steps.
Step-by-step explanation:
We have been given two intersecting lines:
The given angles are vertically opposite angles:
[tex]2x+6=96[/tex]
On simplification we get:
[tex]2x=90[/tex]
On further simplification we get:
[tex]x=\frac{90}{2}[/tex]
[tex]x=45[/tex]
Hence proved that x=45.
please help. Wire is 12.5 cents a foot. How many feet can you buy for a dollar?
Your bird feeder holds 3⁄4 quarts of birdseed. Your scoop holds 3⁄8 of a cup. How many scoops of birdseed will fill the feeder?
Answer
It is 2 scoops
Step-by-step explanation:
3⁄8 x 1⁄4 = 3⁄32 quart
3⁄4 ÷ 3⁄32 = 8 scoops
Data were collected on monthly sales revenues (in $1000s) and monthly advertising expenditures ($100s) for a sample of drug stores. the regression line relating revenues (y) to advertising expenditure (x) is estimated to be modifyingabove y with caret equals negative 48.3 plus 9.00 xy=−48.3+9.00x. what is the interpretation of the slope?
Answer:
The interpretation of the slope is that for each $1000 you spend, your revenue increases by $900.
Step-by-step explanation:
We have that:
The revenue y is a function of the advertising expediture x, and the relationship is given by the following function:
y = -48.3 + 9x.
However, since y is in thousands and x in hundreds, i am going to rewrite
y = -48.3 + 0.9x
This means that if you spend no money in advertising, you lose -48.3 thousands of dollars. However, for each $1000 you spend, your revenue increases by $900.
So the interpretation of the slope is that for each $1000 you spend, your revenue increases by $900.
The distance between two cities is 145 miles. A truck can cover this distance in 2.5 hours. The speed of a car is 1.5 times faster than the speed of the truck. How long does it take them to meet, if they start moving towards each other simultaneously?
The speed at which the distance is covered by the two vehicles is the sum of their speeds:
... (truck speed) + 1.5×(truck speed) = 2.5×(truck speed)
The time required to cover the distance is inversely proportional to speed, so is
... (2.5 hours)/2.5 = 1.0 hours
It takes 1.0 hours for the vehicles to meet.
_____
The speed of the truck is (145 mi)/(2.5 h) = 58 mi/h
The speed of the car is 1.5 × 58 mi/h = 87 mi/h.
The speed at which they move toward each other is
... 58 mi/h + 87 mi/h = 145 mi/h
So, the time it takes to cover 145 miles is
... (145 mi)/(145 mi/h) = 1.0 h
Which equation correctly applies the distributive property A. −2.5⋅(4⋅1.045)=(−2.5⋅4)⋅1.045 B. 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005) C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) D. −1.2⋅0.57⋅0.5=−1.2⋅0.5⋅0.57
By observing the given options we can conclude that equation
C. (0.5⋅0.5) + (0.5⋅0.3) + (0.5⋅0.2) = 0.5⋅(0.5 + 0.3 + 0.2) correctly applies the distributive property.
What are the other properties?The other two properties are commutative property and associative property.
We know the distributive property for four terms states,
a(b ± c± d ± e) = ab ± ac ± ad ± ae.
∴ From observing the given options we can conclude that
0.5⋅(0.5 +0.3 + 0.2) = (0.5⋅0.5) + (0.5⋅0.3 )+ (0.5⋅0.2).
Or
(0.5⋅0.5) + (0.5⋅0.3) + (0.5⋅0.2 ) = 0.5⋅(0.5 + 0.3 + 0.2).
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You randomly select one card from a standard deck. event a is selecting a fivea five. determine the number of outcomes in event
a. then decide whether the event is a simple event or not.
In a standard deck of cards, there are a total number of 52 different card. From those 52 cards, 4 cards are numbered as five. Therefore the probability of selecting a card of five is:
Probability = 4 / 52 = 1 / 13
Assuming that no replacement is made, so the probability changes with each draw, since the total number of cards decreases from 52 to 51 to 50 and so on. Therefore this is not a simple event.
working together Katherine and Julianna can plant new trees on there recently divorced land in 4 days working alone it would take Giuliana to days longer than it would take Catherine to plant the trees how long would it take Katherine working alone to plant the trees
Laura was making a recipe that said the ingredients were for 6 people, but she needed to make it for 8 people. The recipe called for 2 2/3 cups of milk and 1/4 cup of oil. How many cups of liquid ingredients did she need for 8 people?
Laura needs 35/9 cups (approximately 3.89 cups) of liquid ingredients for 8 people.
To find how many cups of liquid ingredients Laura needs for 8 people, follow these steps:
Therefore, Laura needs 35/9 cups (approximately 3.89 cups) of liquid ingredients for 8 people.
is 0.142045454545 a repeating or terminating number??
Choose the correct simplification of the expression b5 ⋅ b4. b b9 b20 b−1
For this case we have the following expression:
[tex]b ^ 5b ^ 4[/tex]
We must consider the following property of the exponents.
In multiplication, when we have the same base, the exponents are added.Rewriting the given expression we have:
[tex]b ^ 5b ^ 4 = b ^ {(5 + 4)}\\b ^ 5b ^ 4 = b ^ 9[/tex]
Answer:
the correct simplification of the expression is:
[tex]b ^ 5b ^ 4 = b ^ 9[/tex]
Line ET is a tangent to circle A at point T and the measure of ∠TNG is 25°
What is the measure of ∠NET?
A) 130°
B) 50°
C) 65°
D) 90°
The sampling distribution of the proportion follows the normal distribution when the values np and nq are greater than or equal to
The sampling distribution of the proportion follows the normal distribution when the values np and nq are greater than or equal to 5.
Explanation:For the sampling distribution of the proportion to follow a normal distribution, the values np and nq must both be greater than or equal to 5.
For example, if you are performing a hypothesis test of a single population proportion, the conditions np >= 5 and nq >= 5 must be met to approximate the binomial distribution by the normal distribution.
Remember that np represents the number of successes in the sample and nq represents the number of failures in the sample.
A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
The value of "a" is 2.
To find the value of "a," we can use the formula for the equation of a line, which is y = mx + b.
First, we need to find the slope, represented by "m," using the given points (-1, -5) and (4, 5). The slope formula is (y2 - y1) / (x2 - x1).
Substituting the coordinates, we have:
m = (5 - (-5)) / (4 - (-1))
m = 10 / 5
m = 2
Now that we have the slope, we can substitute it into the equation of the line with the point (a, 1):
1 = 2a + b
To solve for "a," we need to find the value of "b." We can substitute one of the given points into the equation and solve for "b."
Using (-1, -5):
-5 = 2(-1) + b
-5 = -2 + b
b = -3
Now we can substitute the values of "b" and "a" into the equation:
1 = 2a - 3
To isolate "a," we add 3 to both sides:
1 + 3 = 2a
4 = 2a
Dividing both sides by 2, we find:
2 = a
Therefore, the value of "a" is 2.
What is 1 4/9 of 9000 feet
In the figure, sin ∠MQP = ______.
A. Cos N and Sin R
B. Sin R and Sin N
C. Cos N and Sin M
D. Cos R and Sin N
I WILL MARK BRAINLIEST!!!!! 24 POINTS!!!!!
we know that
in the right triangle MNR
[tex]Sin(N\°)=Cos(R\°)[/tex]
[tex]Sin(56\°)=Cos(34\°)[/tex]
Because
[tex]N+R=90\°[/tex]
[tex]56\°+34\°=90\°[/tex] --------> by complementary angles
so
sin ∠MQP=[tex]Sin(56\°)[/tex]
therefore
the answer is the option
D. Cos R and Sin N
Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square increasing when the area of the square is 25 cm2?
x2= 121 can anyone solve it
Martin is 6 years younger than his sister. The sum of their ages is no more than 22 years. What is an inequality that can be used to represent this situation where X represents martins sisters age
sisters age = x
martins age = x-6
equation: x +(x-6) <=22
2x -6 <=22
2x<=28
x<= 28/2
x<= 14
kwei-twang kuo plans to make these online payments: store charge account $160; charitable donation, $40; rent $550; cable bill, $42.01. She began the day with a checking account balance of $16.83. Later that same day she estimated her online payments and transferred $800 into checking from savings to cover the expected payments. What will be the balance of her checking account after the online payments are made?
Final answer:
After making her online payments totaling $792.01, Kwei-Twang Kuo will have a balance of $24.82 in her checking account.
Explanation:
First, we'll calculate the total payments Kwei-Twang Kuo needs to make by adding up all of her expenses:
Store charge account: $160
Charitable donation: $40
Rent: $550
Cable bill: $42.01
Adding these amounts together gives us a total of $792.01 for the payments.
Let's calculate the balance of her checking account after she transfers $800 and makes the payments:
Begin with checking account balance: $16.83
Transfer into checking account: +$800.00
New balance before payments: $816.83
Total payments to be made: -$792.01
Final checking account balance: $24.82
Therefore, after Kwei-Twang Kuo makes her online payments, she will have a balance of $24.82 in her checking account.