Answer:
Probability of a train on line A arriving on time: 80%
Probability of any train arriving on time: 96%
Step-by-step explanation:
If 18 of the 90 incoming trains on line A arrive late, we have that 90 - 18 = 72 trains of the 90 arrive on time, so the probability of a train on line A arriving on time is:
P(A) = 72/90 = 0.8 = 80%
on line B, we have that 70 - 14 = 56 trains of the 70 arrived in time, so the probability of a train from line B arriving on time is:
P(B) = 56/70 = 0.8 = 80%
To find the probability of any train arriving on time, we can use this formula:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.8 + 0.8 - 0.8*0.8
P(A or B) = 1.6 - 0.64 = 0.96 = 96%
The probability that a train on line A arrives on time is 0.8 or 80%. The probability that any train arrives on time, considering both line A and line B, is also 0.8 or 80%.
Explanation:To calculate the probability that a train on line A arrives on time, we subtract the number of trains that arrive late from the total number of trains on line A:
Probability = (Total trains on line A - Trains on line A that are late) / Total trains on line A
Probability = (90 - 18) / 90
Probability = 72 / 90
Probability = 0.8 or 80%
To calculate the probability that any train arrives on time at the station, we need to consider the total number of trains arriving on time for both lines:
Total trains on time = (Total trains on line A - Trains late on line A) + (Total trains on line B - Trains late on line B)
Total trains on time = (90 - 18) + (70 - 14) = 72 + 56 = 128
Then, we divide the number of trains on time by the total number of trains:
Probability = Total trains on time / Total trains
Probability = 128 / (90 + 70)
Probability = 128 / 160
Probability = 0.8 or 80%
Factor completely
x^2-14x+45
n^2+4n-32
Answer:
1. (x+9)(x-5)
2. (x+8)(x-4)
Step-by-step explanation:
use x-box method to simplify both problems
Final answer:
To factor the quadratic expressions, we look for pairs of numbers that multiply to give the constant term and add to give the coefficient of the middle term, resulting in the expressions (x - 9)(x - 5) for the first and (n + 8)(n - 4) for the second.
Explanation:
The question relates to factoring quadratic expressions, which is a fundamental skill in algebra. Specifically, we are looking to factor the expressions [tex]x^2[/tex] - 14x + 45 and [tex]n^2[/tex] + 4n - 32 completely. Factoring involves finding two binomial expressions that multiply together to give the original quadratic expression.
To factor [tex]x^2[/tex] - 14x + 45, consider two numbers that multiply to 45 and add to -14. These numbers are -9 and -5. Therefore, the factored form is (x - 9)(x - 5).
To factor [tex]n^2[/tex] + 4n - 32, we again look for two numbers that multiply to -32 and add to 4. These numbers are 8 and -4. Thus, the factored form is (n + 8)(n - 4).
Question 5: The top 5% of the 4,200 students at your college will receive a
$200 tuition refund. How many students will receive the refund?
What is 10% of 4200?
Your answer
How many students will receive the refund?
Your answer
Answer:
2,100 students will receive the funds.10% of 4200 is 420.
Step-by-step explanation:
How do you know if an event is likely to happen or unlikely to happen?
Answer:
You will know if an event is unlikely or unlikely to happen if the following events that happen follow behind it.
Step-by-step explanation:
A zip line starts 28 feet in the air and
ends 11 feet in the air. The zip line drops
at an angle of 85 degrees 85°. How long
is the zip line cable when completely
taut (no rider)?
Given:
A zip line goes from 28 feet to 11 feet in the air. The angle of depression is 85°.
To find:
The length of the zip line where there is no rider.
Solution:
A right-angled triangle can be formed using the given data.
The difference in height between the start and end of the zipline is [tex]28-11=17[/tex]. The angle of the triangle is 85°.
Assume the zip line is x feet long.
The adjacent side of the triangle measures 17 feet, the hypotenuse of the triangle measures x feet, and the angle of the triangle is 85°.
To determine x, we calculate the cos of the given angle.
[tex]cos \theta = \frac{adjacentside}{hypotenuse} .[/tex]
[tex]cos 85 = \frac{17}{x} , x = \frac{17}{cos85}, cos85= 0.0871.[/tex]
[tex]x = \frac{17}{0.0871} = 195.1779.[/tex]
Rounding this off, we get the length of the zip line when there is no rider is 195.18 feet long.
The length of the zip line when there is no rider is 195.18 feet long.
Calculation of the length of the zip line:Here the difference is
= 28 - 11
=17
And, The angle of the triangle is 85°.
Here we Assume the zip line should be x feet long.
Now
The length should be
[tex]cos\ 85 = 17\div x\\\\x = 17\div 0.0871[/tex]
= 195.18
Hence, The length of the zip line when there is no rider is 195.18 feet long.
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Question 2 of 10
2 Points
The circle below is centered at the point (-2, 1) and has a radius of length
What is its equation?
(x+1)++
O
B. (x - 2)2 + (y + 1)
O
c. (x + 2)2 + (y- 1)2 =
O
D. (x - 1)2 + (y + 2)2
O
Answer:
B is the answer to this problem
On a separate sheet of paper graph the following function. In the answer box describe the function.
f(x) = 2[x] – 3
Answer:
Answer
Step-by-step explanation:
The function is a greatest integer function, which is a step function.
The function f(x) = 2[x] - 3 features a step-like graph due to the floor function [x]. To graph it, calculate f(x) for integer values, plot the points, and draw horizontal lines between them. The function's range in this context is specified to be between 0 and 20.
Explanation:The function given is f(x) = 2[x] - 3, where [x] denotes the greatest integer function, also known as the 'floor' function, which returns the greatest integer less than or equal to x. This type of function creates a step-like graph. When graphing this function, you'll notice that for every integer value of x, the function will take on a constant value until the next integer is reached, at which point it will jump up to the next 'step'.
To graph this function, you should first calculate the values of f(x) at various integer points within the given range. Then plot these points on a coordinate plane and create horizontal lines to represent the function's value between each pair of consecutive integer x values. For non-integer values of x, the function value will be based on the floor of x. Label your graph with f(x) and x. Make sure to scale the x and y axes with the maximum values, considering that in this case we are dealing with 0 ≤ x ≤ 20.
Someone please help meee!!
Answer:x=9
Step-by-step explanation:
Add the numbers and the x's
39x+369= 6 angles
Formula 6-2=4×180=720
39x+369=720
-369. -369
39x =351
Divide by 39
X=9
look at these equations:
A = B+12 B = C+4
Write an equation to show the relation ship between A and C
Answer:
A = C + 16
Step-by-step explanation:
Given
A = B + 12 and B = C + 4, then substitute B = C+ 4 into A, that is
A = C + 4 + 12
A = C + 16
what is the coordinate if (2,2) is reflected over the line x=2
Answer:
-2,2
Step-by-step explanation:
Find the slope of the line that passes through the two points given
SW. *
(4,3) & (3,-2)
Answer:
5
Step-by-step explanation:
The slope between (4,3) (3,-2) can be found using the following formula
m = (y2-y1)/(x2-x1)
=(-2-3)/(3-4)
= (-5)/(-1)
=5
2 Find the mystery numbers for each pair of clues. A product is the number you get
when you multiply numbers. A sum is a number you get when you add numbers.
a Use these clues to help
• The product of these two numbers
is 12.
• The sum of these two numbers is 7.
6 Use these clues to help
• The product of these two numbers
is 8.
• The sum of these two numbers is 9.
The numbers are
and
The numbers are
and
Answer:
4 and 3 at least i think
Step-by-step explanation:
Answer asap please :/
Answer:
the first answer is correct
Step-by-step explanation:
Answer:
The correct function is
A. y = -0.5x+100
Help !!!!!!!!!!!!!!!!!!!!!!
5.Last Sunday, 4 of the houses had some cars parked outside. If there
were 4 cars outside each house. How many cars were there in total?
Solve: n^2/2 -2 = 5n/6
Answer:
n = -4/3 or n = 3
Step-by-step explanation:
Multiply by 6 to eliminate fractions, then put into standard form.
3n^2 -5n -12 = 0
3n^2 -9n +4n -12 = 0 . . . . . separate -5n into two terms to facilitate factoring
3n(n -3) +4(n -3) = 0 . . . . . factor pairs of terms
(3n +4)(n -3) = 0 . . . . . . . . . factor out the common factor
n = -4/3 or 3 . . . . . . . values that make the factors be zero
Ginny has a package of 80 cards. There are 40 yellow cards
and 40 red cards.
If she randomly picks 4 cards, how many cards should she
expect to be yellow?
Answer:
8?
you gotta do the math.
Johnny paid $19 for a pair of jeans. It was originally $33. What percent discount did he receive?
Answer:
Approximately 42.42%
Step-by-step explanation:
If you subtract 42.42% from 33 it equals approx 19.
What does b equal in this equation 3=3/4(b-8)
Look at the attached picture⤴
Hope it will help u....:)
What fraction goes in the box to make it correct?
7
×
□
=
1
Answer: 1/7
Do Keep Change Flip
Keep: 7
Change: ÷ into ×
Flip: 7/1 into 1/7
Your new problem: 7×1/7
Multiply
7/1×1/7=7/7
7/7=1
The fraction that will fit into the box to make the equation correct is: [tex]\mathbf{\frac{1}{7}}[/tex]
Let the missing fraction that will fit in the box be represented as x.
Thus, let's find x in the equation, 7 × x = 1
Solve for the value of x to get the fraction that will fit in to make the equation correct.
[tex]7 \times x = 1[/tex]
Divide both sides by 7[tex]\frac{7x}{7} = \frac{1}{7} \\\\[/tex] (division property of equality)
[tex]\mathbf{x = \frac{1}{7}}[/tex]
Therefore the fraction that will fit into the box to make the equation correct is: [tex]\mathbf{\frac{1}{7}}[/tex]
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(2c + 4) + (3m + 5) = simply your answer
Hi there! hopefully this helps!
-------------------------------------------------------------------------------------------------------------
Answer: 2c + 9 + 3m
Find the value of x in the triangle
Answer:
x=32 degrees
Step-by-step explanation:
a triangle sum up to 180 degrees.
to find x
42+ x+106 =180
Subtract the numbers to let x stand on its own
x= 180 - 106- 42
x=32
Answer:
32⁰
Step-by-step explanation:
By angle sum property :
106 + 42 + x = 180
x = 180 - 148
x = 32⁰
A tile store charges $607.50 to install 135 square feet of tile. Assuming they charge the same rate
per square foot regardless of the amount of tile installed, how much would they charge to install
840 square feet of tile?
Translate to a proportion:
square feet
square feet
They would charge
to install 840 square feet of tile.
The unit price for installation per square foot of tile is
Answer:
the tile is 4.50 per square foot to install
it will cost 3780.00 to install 840 square feet
Step-by-step explanation:
divide 607.50 by 135 to find out the price per square foot to install
multiply the price per square foot by the number of square feet you are installing so 4.50 X 840
Please help me answer the question.
Answer:
63
Step-by-step explanation:
Each side is bigger by a factor of 9, i.e. 10*9=90, etc.
so 7 * 9 = 63
A cylinder has height 10 cm and volume 42 cm'. An enlargement of the
cylinder has height 25 cm. Calculate the volume of the enlarged cylinder.
ANSWER:
Given f(n) is a geometric sequence where f(3)=32 and f(9)=72, find f(16).
I think the answer may be 64/27, but I don't know for sure.
Answer:
f(16)=162
Step-by-step explanation:
-In a geometric sequence, the quotient between any tow consecutive numbers is called the common ratio,r:
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
Given that f(3)=32 and f(9)=72, we can find the common ratio as below:
[tex]r=\frac{a_n}{a_{n-1}}\\\\\therefore \frac{f(9)}{f(3)}=r^6\\\\\frac{72}{32}=r^6\\\\r^6=2.25\\\\r=2.25^{1/6}[/tex]
#We substitute and use the same formula to find the nth term:
[tex]a_n=ar^{n-1}[/tex]
let f(3) be a(the first term):
[tex]a_n=ar^{n-1}\\\\a_{16}=32(2.25^{1/6})^{16-3-1}\\\\a_{16}=32(2.25^{1/6})^{12}\\\\\\=162[/tex]
Hence, f(16)=162
What is the growth factor of y=70(2)^x
Answer:
100% growth rate or it doubles
Step-by-step explanation:
This is of the form
y = ab^x
where a is the initial value and
b is the growth/decay factor
b>1 growth
b<1 decay
Since b>1 it is growth
We determine the growth rate by
b-1
2-1 =1
Multiply by 100%
1*100% = 100 % growth rate
QueSLIUI
A friend asks to borrow $250 for 18 months and agrees to pay 12% annual simple interest. How much interest will you
earn?
Round your answer to the nearest dollar.
Provide your answer below:
Answer:
$90 of interest will be earned.
Step-by-step explanation:
We are given the following in the question:
Principal,P = $250
Time, T = 18 months = 3 years
Rate, R = 12% = 0.12
Formula for simple interest:
[tex]I =\dfrac{P\times R\times T}{100}[/tex]
Putting values, we get,
[tex]I =\dfrac{250\times 12\times 3}{100} = \$90[/tex]
Thus, interest of $90 will be earned.
A bus with kids and a truck with their bags started moving from the school to the camp at the same time. The speed of the bus was 60 mph. The speed of the truck was 45 mph. It took kids 3 hours to reach the camp. How long did they have to wait for their bags?
The kids have to wait for 1 hour to get their bags.
Step-by-step explanation:
Given that,
A bus with kids and a truck with their bags started moving from the school to the camp at the same time.
The speed of the bus was 60 mph.It took kids 3 hours to reach the camp.To find the distance traveled by the bus :
⇒ Distance = Speed × Time
⇒ 60 × 3
⇒ 180 m
∴ The distance is 180 m.
To find the time taken by the truck to reach the camp :
The speed of the truck was 45 mph.We found the distance as 180 m.Time taken = distance / speed.
⇒ 180 / 45
⇒ 4 hours.
∴ The time taken by the truck to reach the camp is 4 hours.
To find how long the kids have to wait for their bags :
The time taken by the truck to reach the camp - the time it took for the kids to arrive.
⇒ 4 hours - 3 hours
⇒ 1 hour.
∴ The kids have to wait for 1 hour to get their bags.
The bus traveled 180 miles to the camp in 3 hours at 60 mph, while the truck took 4 hours at 45 mph to cover the same distance. Hence, the kids had to wait 1 hour for their bags to arrive.
Travel Time and Waiting Time
To determine how long the kids had to wait for their bags, we need to calculate the time it took for the truck to reach the camp.
The bus travels at a speed of 60 mph and it took the kids 3 hours to reach the camp. The distance to the camp can be calculated using the formula:
Distance = Speed × TimeTherefore, the distance is 60 mph × 3 hours = 180 miles.Next, we calculate the time it took for the truck, traveling at 45 mph, to cover the same distance:
Time = Distance / SpeedThus, the truck's travel time is 180 miles / 45 mph = 4 hours.Since the kids took 3 hours to reach the camp and the truck took 4 hours, the kids had to wait for:4 hours - 3 hours = 1 hour.Therefore, the kids had to wait for 1 hour for their bags to arrive.
What is the radius and diameter of the following circle?
11 cm
?
Radius-
Diameter-
Answer:
Radius: 5.5
Diameter: 22
Step-by-step explanation:
You spend $62 on a game, receive $50 for painting a fence, and give $10 to your friend. You have $44 left.
How much money did you start with?
Answer:
You started with $66.
Step-by-step explanation:
The equation would be:
[tex]x-62+50-10=44\\ x-22=44\\ x=66\\[/tex]
To check the answer:
[tex]66-62+50-10=44\\4+50-10=44\\54-10=44\\44=44[/tex]
We started with $66 initially.
What is Algebra?Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations. The idea that there is such a separate branch of mathematics, as well as the term algebra to identify it, came about gradually through time. It tries to find solutions to equations that contain one or more unknown quantities. Although early mathematicians would not have been familiar with such a concept, the word "equation" is frequently employed to conveniently represent these operations when discussing the early history of algebra.
As per the given data:
Money spend on game (g) = $62
Money received for painting a fence (p) = $50
Money given to friend (f) = $10
Money left = $44
To find out the money we had initially:
Let's assume we had $x.
Money left = x - g + p - f
44 = x - 62 + 50 - 10
44 = x - 22
x = $66
Hence, We started with $66 initially.
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