[tex]\frac{1}{15}[/tex] or 6.67%
Step-by-step explanation:In practice, the relative frequency of an event happening is the same as the probability that that event happened. In other words, the terms "relative frequency" and "probability" can be used interchangeably.
Now, the probability P(A) of an event A happening is given by;
P(A) = [tex]\frac{number-of-outcomes-in-the-event-A}{number-of-outcomes-in-the-sample-space}[/tex]
From the question;
The event A is the situation of local residents having a post office box. Therefore the;
number-of-outcomes-in-the-event-A = 8 [since only 8 of the local residents have a post office box]
number-of-outcomes-in-the-sample-space = 120 [since there are altogether 120 local residents]
Therefore,
P(A) = [tex]\frac{8}{120}[/tex]
P(A) = [tex]\frac{1}{15}[/tex]
The relative frequency that a local resident does not have a post office box for receiving a mail is therefore, [tex]\frac{1}{15}[/tex]
PS: Sometimes it is much more convenient to express relative frequencies as percentage. Therefore, the result above expressed in percentage gives:
[tex]\frac{1}{15} * 100%[/tex]% = 6.67%
a percent measures a rate a) per unit b)per 10 unit c) per 100 unit d) per 1000 unit
Answer:
[tex]\boxed{Option \ C}[/tex]
Step-by-step explanation:
Percentage means "out of hundred" So measuring the rate in percentage we've to find it using "per 100 units".
Answer:
c) per 100 unit
Step-by-step explanation:
a percent measures a rate:
per cent ⇒ per 100
The correct answer is option c.
PLEASEE HEEELP! In the normal distribution, 68% of the data lies within 1 standard deviation A: __/6 of the mean, 95% of the data lies within 2 standard deviations of the mean, and 99.7% of the data lies within 3 standard deviations of the mean. Answer the following question without using the Z-table. If scores on a test are normally distributed with mean 1100 and standard deviation 100, what percentage of the test scores are: a) more than 1300? b) less than 1100?
Answer:
a) 2.5% b) 50%
Step-by-step explanation:
1300 is two standard deviations higher than the mean. Since 95% of the data is covered within two standard deviations to the left and right of the mean, 5% is not covered. So, we have 2.5% leftover on the left side of the curve, under 900, and 2.5% leftover on the right side of the graph that is above 1300.
The mean is 1100, so anything above or below the mean is exactly 50% in a normal distribution.
Answer:
Step-by-step explanation:
This is the Empirical Rule.
68% of the data lies within 1 standard deviation of the mean, and so on.
If the mean is 1100 and the standard deviation is 100, 1300 represents two standard deviations above the mean. Using a calculator with distribution functions, we type in normcdf(2,10000), obtaining 0.023. This tells us that 2.3 percent of test scores are more than 1300.
Less than 1100: Since the mean is 1100, the area under the standard normal curve is exactly 0.5 (corresponding to 50% of data are less than 1100).
If the Mega-Print 3000 printer can print a large document in one fourth the time of the Super-Print 1000 printer, and the printers working together can print the document in 6 hours, how long would it take the slower printer alone to print the document?
==================================================
Explanation:
Ignore the values 3000 and 1000 as they are simply labels for the printer names (or brand models). I'll call the two printers A and B for simplicity.
Printer A can produce a large document in 1/4th the time printer B can do the same job. So we can say x = (1/4)y where x and y are the times it takes for both printers to do the job if they work alone. Solving for y gets us y = 4x.
Printer A can do the full job, on its own, taking x hours. It's rate is 1/x jobs per hour. Printer B's rate is 1/y = 1/(4x) jobs per hour for similar reasons.
Their combined rate is
1/x + 1/(4x) = 4/(4x) + 1/(4x) = 5/(4x)
Set this equal to 1/6 and solve for x. The 1/6 represents the combined rate based on how they can work together to get the job done in 6 hours.
-----------
5/(4x) = 1/6
5*6 = 4x*1 .... cross multiply
30 = 4x
4x = 30
x = 30/4 ... divide both sides by 4
x = 7.5
Printer A takes 7.5 hours to do the job alone
y = 4x
y = 4*7.5
y = 30
Printer B takes 30 hours to get the job done if it worked alone
-----------
Note how
1/x + 1/y = 1/7.5 + 1/30 = 4/30 + 1/30 = 5/30 = 1/6
so this confirms we have the right answer.
Which number is the largest 1.2 x 104, 4.5 x 10–3, 3.8 x 103, 7.5 x 103
The correct answer is the last one, 7.5 x 104. (the sum is 772.5)
Step-by-step explanation:if you multiply it the sum is 772.5, and all the other ones sum is less than 772.5
I hope this helped (:
Write an equation in standard form of the line passing through the points (4, 3) and (7, 9).
The equation is
(Type your answer in standard form.)
Answer:
2x -y = 5
Step-by-step explanation:
The 2-point form of the equation of a line is a useful starting point.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (9 -3)/(7 -4)(x -4) +3
y = 6/3(x -4) +3 = 2(x -4) +3 = 2x -8 +3
Adding 5-y, we get ...
2x -y = 5
Which expression can be used to find the surface area of the following square pyramid?
Answer:
Step-by-step explanation:
expression for surface area = a² + a √(a²/4+h²)
=4² + 2(4) √(4²/4+5²)
=16 + 8 √(16/29)
= 24 √0.55
= 20.65
Graphs are sometimes______by the way they present information.
Answer:
Misleading?
Step-by-step explanation:
Graphs can have mislabeled axes or different values on the axes, making them hard to understand.
I think this is the right answer, but the question was way too vague. Next time, put some options or at least explain the problem better.
At the grocery store, you can purchase lemons at 2 for $0.99. you can also buy a bag of 6 lemons for $2.50. Which is the better buy?
Answer:
Purchasing the bag of 6 lemons is the better buy.
Step-by-step explanation:
There are two ways that we can do this: find the unit rate or find how the LCM.
---
The first way is more orthodox, and you should definitely use it in harder problems. We can set up two ratios like so.
2 : 0.99
6 : 2.5
Let's simplify the ratios so the left side is one.
2 : 0.99 = 1 : 0.495 by dividing both sides by 2.
6 : 2.5 = 1 : 0.41666... by dividing both sides by 6.
Comparing the two ratios, we can conclude that the second one is smaller, therefore the bag of 6 lemons costs less.
---
The second way, although not very efficient with big numbers, works well with small numbers like these.
First, we need to find the LCM, or the least common multiple. The LCM of 2 and 6 is 6, as 6 is a multiple of both 2 and itself.
Now we must make the amount of lemons match each other so we can compare the price.
2 : 0.99 = 6 : 2.97 by multiplying by 3.
The second ratio stays the same.
2.50 is smaller than 2.97, so the second ratio is smaller than the first, reaching our previous conclusion.
---
I hope this helps, let me know if you need any more clarification.
What is the inverse of the function f(x)=-\dfrac{1}{2}(x+3)f(x)=− 2 1 (x+3)f, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, plus, 3, right parenthesis
Answer:
The inverse of the function is
-2x-3
Step-by-step explanation:
The inverse of the function f(x) = -\dfrac{1}{2}(x+3) is f(x)⁻¹ = -2x - 3
What is the inverse of a function?The inverse of a function is a function that gives us the actual value for which the desired function has a given result.
The given function is:
[tex]\mathbf{ f(x)=-\dfrac{1}{2}(x+3)}[/tex]
To find the inverse, we need to follow the following steps
replace the role of f(x) by y;[tex]\mathbf{ y=-\dfrac{(x+3)}{2}}[/tex]
Swap x and y variables[tex]\mathbf{ x=-\dfrac{(y+3)}{2}}[/tex]
Solve for y;2x = - (y + 3)
2x = -y - 3
y = -2x - 3
Writing back in inverse notation, we have:
f(x)⁻¹ = -2x - 3
Learn more about the inverse of a function here:
https://brainly.com/question/2873333
#SPJ2
Is (3,1), (7,2) , (11,3) , (18,5) linear?
Answer:
It is not linear.
Step-by-step explanation:
If you plug in the coordinates into a graphing calculator, you'll see that after the point (7,2), the line starts to increase. A linear function on a graph is going to be a straight line, not increasing or decreasing. It's consistent. I hope this was helpful.
Howard is playing in a high school basketball game that is halfway through the
third quarter.
1) What fractional part of the game is left?
2) If there are 12 minutes of playing time left in the game, how many minutes
of playing time are there in the whole game?
(Please help me solve it)
Answer:
96 minutes in the whole game or 1 hour and 36 minutes and 1/8 of the game is left.
Step-by-step explanation:
So we know that there are 4 quarters in a game. So if they're halfway through the 3rd quarter with 12 minutes left in the game, that means half a quarter equals 12 minutes. That means a full quarter equals 24 minutes. Then we do 24 *4 which is 96. So there are 96 minutes in the whole game and there 1/8 of the game left since 96/8=12.
Hope this helped
Gary runs a recycling centre for a local charity.
New staff have to take part in 7 hours of training before they can
work at the centre,
Gary needs to arrange a training programme for new staff.
The training programme will start on Monday 5th September
Each training day:
1) starts at 10 am and must finish by 5 pm
2)has sessions in 2 hour blocks which include a 15 minute
break
3)has a 1 hour break for lunch
The 15 minute breaks and
lunch do not count towards the 7 hours of training
At the end of the training there will be a 90 minute assessment.
Gary needs to know the least number of days he needs to allocate
for the 7 hours of training and the assessment.
Plan a training programme for Gary.
Show the start and finish times for the sessions on your plan.
Answer:
Just use 2 days
Step-by-step explanation:
Train for 2
Break
Train for 2
Break
Lunch
Day 2:
Train for 2
Break
Lunch
Exams
find the nth term of this sequence, 3, 6, 9, 12
Answer:
[tex]\large\boxed{\sf n^{th} \ term =3n}}[/tex]
Step-by-step explanation:
Find common difference from subtracting any term in the sequence with the previous term.
[tex]\large{\sf 6-3}=3[/tex]
Apply nth term formula.
[tex]\large{\sf a_n=a_1+(n-1)d[/tex]
[tex]\large{\sf d=3 \ \ a_1=3}[/tex]
[tex]\large{\sf a_n=3+(n-1)3[/tex]
[tex]\large{\sf a_n=3+3n-3[/tex]
[tex]\large{\sf a_n=3n}[/tex]
Answer:
a(n) = 3 + 3(n -1)
Step-by-step explanation:
Note that each new term is found by adding 3 to the previous term. The first term is 3 and the common difference is 3. Thus, the formula for the nth term is
a(n) = a(1)+d^(n - 1)
or, in this case,
a(n) = 3 + 3(n -1)
1) Assume that Mike can walk 3 km per hour. If he had been walking for 5 hours away from the trail, create a table
of values to express how far he walked and graph his progress.
Answer:
see below for a table; see second attachment for a graph
Step-by-step explanation:
Each of the distance values in km in the table will be 3 times the time value in hours.
The slope of the line on the graph is 3. The practical domain of the distance function is 0 to 5 hours.
help me plz i want help
Answer:
1/24
Step-by-step explanation:
You can see that there are 24 possible combinations by counting the results on the right. Only 1 spells AXEL - the first one. So its:
1/24
Anna baked
3
33 batches of cookies with
c
cc cookies in each batch. She then ate
8
88 cookies!
How many cookies does Anna have left?
Answer:
3c-8
Step-by-step explanation:
how would you solve this problem?
Answer:
a) 6x²/2x³-4
b) [tex]2ln (2x^3-4)+ C[/tex]
Step-by-step explanation:
a) Given the ln(2x³-4). We will use the chain rule in differentiating the function
If y = ln(2x³-4);
u = 2x³-4; du/dx = 3(2)x³⁻¹
du/dx = 6x²
y = ln u; dy/du = 1/u
According to chain rule, dy/dx = dy/dy*du/dx
dy/dx = 1/u * 6x²
dy/dx = 1/2x³-4 * 6x²
dy/dx = 6x²/2x³-4
Hence, the derivative of the given function is 6x²/2x³-4
b) Given an integral function [tex]\int\limits {\frac{12x^2}{2x^3-4} } \, dx[/tex], the integral problem can be solved using integration by substitution method as shown below;
From the question, let y = 2x³-4... 1, dy/dx = 6x²
dx = dy/6x² ... 2
Substituting equation 1 and 2 into the question given;
[tex]\int\limits {\frac{12x^2}{y} } \,\frac{dy}{6x^2} \\\\= \int\limits {\frac{2dy}{y} } \\\\= 2 \int\limits {\frac{dy}{y} }\\\\= 2lny + C\\substituting\ y = 2x^3-4\ into\ the \ resulting\ function\\\\= 2ln (2x^3-4)+ C[/tex]
Pls answer no explanation needed!!
Answer:
12pi.
Step-by-step explanation:
The area of the circle is pi * r^2.
r = 4.
pi * 4^2 = pi * 16 = 16pi.
There is 3/4 of the circle. (3/4) * 16pi = 3 * 4pi = 12pi.
Hope this helps!
Answer:
37.68
Step-by-step explanation:
4^2=16
16x3.14=50.24
50.24/2=25.12
25.12/2=12.56
25.12+12.56=37.68
please answer need help
Answer
2/15 or 0.13
Step By Step
2/3 ÷ 5
Rewrite the division as a fraction.
Rewrite the division as a fraction.2/3/5
Multiply the numerator by the reciprocal of the denominator.
2/3 x 1/5
= 2/15
The result can be shown in multiple forms.
The result can be shown in multiple forms.Exact Form:
2/15
Decimal Form:
Decimal Form:0.13
You pack sandwiches for a mountain hike with your friends. Each sandwich takes 222 slices of bread, and each hiker eats one sandwich. How many slices of bread are used for nnn hikers? Write your answer as an expression.
Answer:
This question contains some errors; the correct question is:
You pack sandwiches for a mountain hike with your friends. Each sandwich takes 2 slices of bread, and each hiker eats one sandwich. How many slices of bread are used for n hikers? Write your answer as an expression.
The answer is:
(2n) slices of bread for n hikers
Step-by-step explanation:
According to the question, sandwiches packed for a mountain hike with friends is made of two (2) slices of bread.
Each hiker gets one sandwich
This, n hikers will get n× 1 sandwich
= (n) sandwiches.
If 1 sandwich contains 2 slices of bread, then (n) sandwiches for n hikers will contain:
(2 × n) slices of bread
That is, (2n) slices of bread.
The expression is (2n).
HELP FIRST GET BRAINLLEST Which of the statements below are true? Select all that apply. A) Tom's friends are taller than Sam's friends B) Sam's tallest friend is 72 inches tall C) Sam's friends are taller than Tom's friends. D) Tom's tallest friend is over 70 inches tall
Answer:
B and C are true
Step-by-step explanation:
hope this helps :)
Answer:
I agree, B & C
Step-by-step explanation:
FIRST GETS BRAINLLEST Each group of students receives a bag that has 9 red cubes, 5 green cubes, and 11 blue cubes. If each group makes 1000 pulls and replaces the cube after each pull, how many times would you expect them to draw a blue cube?
Answer:
440 blue cubes
Step-by-step explanation:
We can put it in a ratio of 9:5:11. Add those up we get 25. Then we do 1000/25 which if 40. So each number in the ratio equals 40. Then we do 11*40 and we get 440.
Answer:
440 times
Step-by-step explanation:
First, you need to find the total number of cubes each student receives (25)
Now you put it into a ratio of blue cubes to the total number of cubes
11 : 25
After that you make another ratio and solve for x
x : 1000
25x = 11000
x = 440
A
85°
O A. 45
o
E
O B. 32.5
B
C. 52.5
D. 65
SUBMIT
Answer:
A
Step-by-step explanation:
The formula for external arc measures ia 1/2(x-y) where x is 85 and y is the smaller arc. Knowing the actual angle measurement, we can see that we have 1/2(85 - y) = 20; y = 45. Answer A is your answer.
Given: f(x) = x2, g(x) = x + 6, h(x) = 7
Find g{fſh(x)}}.
20
169
55
Answer:
20 or 55
Step-by-step explanation:
It depends because i am not sure what f(x) is.
Case 1: f(x)=x^2
We know h(x)=7 hence f(h(x))=7^2=49 hence g(f(h(x)))=49+6=55
Case 2: f(x)=x*2
We know h(x)=7 hence f(h(x))=2*7=14 hence g(f(h(x)))=14+6=20
Note: x^2 is x to the power of 2 while x*2 is x times 2.
Consider the following function. F(x)=3/2+4 Using the given function, plot all the ordered pairs for the values in the domain below. (-8,-4,-2,0,2,4)
Answer:
zephyr
Step-by-step explanation:
ez i am god of thunder
HELP ME THE ANSWER IS NOT 36 OR 12 DO THE RSM ANSWER!!! Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $36 when they begin and $36 when they end, what is the total amount that all three friends have?
Answer:
$252
Step-by-step explanation:
Let the initial amount of money Ami, Jan and Toy have initially be A, J and T respectively.
Please see attached picture for full solution.
Answer:
$252
Step-by-step explanation:
Step 1Toy has $36 and gets $36 from Ami. Now he has $36*2= $72
Step 2Toy gets $72 from Jan to double his money and now has $72*2= $144
Step 3Toy gives enough money to Ami and Jan to double their money
Toy has $36 at the end, so he has given $144 - $36= $108 to Ami and Jan
Since he doubles their money by giving $108, they now have
$108*2= $216Now we add the amount Toy has at the end to the amount Ami and Jan have at the end to get final amount:
$216+$36= $252So the friends have $2527 movie tickets cost $35
Unit rate
Answer:
$5 per ticket
Step-by-step explanation:
If you put it into a ratio of movie tickets to cost it will be 7 : 35
When you simplify it the ration will be 1 : 5
Answer:
$5 per ticket . # Unit rate.
Step-by-step explanation:
7 tickets costs =$35
therefore, 1 ticket cost = $35÷ 7
= $5
is 4(x+2)+3x+7 equivalent to 7x+14
Answer:
No equal
Step-by-step explanation:
If you multiply through you get
4x+8+3x+7 which equals
7x+15 which is not equal to 7x+14
Answer:
NoStep-by-step explanation:
Let's solve:
[tex]4(x + 2) + 3x + 7[/tex]
Distribute 4 through the parentheses
[tex] = 4x + 8 + 3x + 7[/tex]
Collect like terms
[tex] = 7x + 8 + 7[/tex]
Add the numbers
[tex] = 7x + 15[/tex]
Hope this helps..
best regards!
13. If 16 people are needed to run 7 machines, how many people are needed to run 35 machines?
Answer:
80
Step-by-step explanation:
16 people =7
7*5= 16*5
35=80 people
Answer:
80 people are required to run 35 machines
Step-by-step explanation:
Write and solve an equation of ratios:
p 35
------- = -----
16 7
where p is the number of people needed to run 35 machines.
Cross-multiplying yields 7p = 16(35), or p = 16(5), or p = 80
80 people are required to run 35 machines.
What is the slope of the line ?
Answer:
The slope is 1
Step-by-step explanation:
there's actually a trick you can do to find the slope. if you go from where the y-intercept is and go over to the x- intercept it will give you the slope hope this helps you