Answer:
a) Megan's total so far is 3 km more than necessary for an average of 15 km
b) 22 km
Step-by-step explanation:
a) The total of differences from 15 is ...
-1 + 8 + (-2) +(-2) = 3
Since this is more than 0, Megan's average is more than 15.
__
b) The total of differences from 17 is ...
-3 +6 -4 -4 = -5
To increase her average to 17 km, Megan must walk 17+5 = 22 km on Friday.
_____
Comment on the approach
In general, I find it easier mentally to deal with small numbers than with larger ones. So adding small differences can be easier than computing larger sums.
a) By computing the difference from the supposed average, we have effectively found the difference of the sum of values from the total necessary to give the required average. That is, Megan's average would be 15 if her total distance were 4·15 = 60. Her total distance is (4·15 +3) = 63, so her average is more than 15.
b) By finding out how much the total is below that necessary for the desired average, we determine the amount above that average the final number needs to be.
(14 -17) +(23 -17) +(13 -17) +(13 -17) +(Friday -17) = 0 . . . . the Friday value to make an average of 17
14 +23 +13 +13 +Friday = 5·17 . . . . . . . add 5·17
(14 +23 +13 +13 +Friday)/5 = 17 . . . . . . shows the Friday amount gives the required average
Friday = 17 -((14 -17) +(23 -17) +(13 -17) +(13 -17)) . . . . first equation rearranged to show how we computed Friday
Friday = 17 -(-5) = 17 +5 = 22
A club consisting of 6 juniors and 8 seniors is to be formed from a group of 13 juniors and 16 seniors. How many different clubs can be formed from the group?
Answer: 22,084,920 different clubs
Step-by-step explanation:
The club must have 6 juniors and 8 seniors
We have a total of 13 juniors and 16 seniors.
Now, we know that the possible combinations of N objects into a group of K is equal to:
[tex]C = \frac{N!}{(N-K)!*K!}[/tex]
For the juniors we have N = 13 and K = 6
[tex]Cj = \frac{13!}{7!*6!} = \frac{13*12*11*10*9*8}{6*5*4*3*2*1} = 1716[/tex]
For the seniors we have N = 16 and K = 8
[tex]Cs = \frac{16!}{8!8!} = \frac{16*15*14*13*12*11*10*9}{8*7*6*5*4*3*2*1} = 12870[/tex]
Now, as the group consist on both combinations togheter, the number of different clubs that can be formed are:
C = Cj*Cs = 1,716*12,870 = 22,084,920
Max and Leah each have a lemonade stand . Max sold 12 glasses the first hour and 10 glasses each hour after that . Leah sold 8 glasses the first hour and 10 glasses each hour after that . How many glasses will each person have sold after 5 hours?
Answer:
120
Step-by-step explanation:
find the square root of 6.4 upto two decimal place
Answer:
2.53
Step-by-step explanation:
Solve the system of equations by elimination.
2x + 2y = -2
3x - 2y = 12
Answer:
Step-by-step explanation:
2x + 2y = -2
3x - 2y = 12
5x = 10
x = 2
2(2) + 2y = -2
4 + 2y = -2
2y = -6
y = -3
(2, -3)
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECT PLEASE EXPLAIN WHY YOU ARE CORRECT
Answer:
In a typical kite as shown in picture, it is symmetric around PQ and PQ is perpendicular with RN.
=> Two right triangles PNT and PRT are congruent.
=> angle PRT = angle PNT = 34 deg
=> angle RPT = 90 - angle PRT = 90 - 34 = 56 deg
=> Option A is correct.
Hope this helps!
:)
Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?
Answer:
{6-√21, 6+√21}
Step-by-step explanation:
It usually works well to put the x-terms on one side of the equal sign. Then add the square of half the x-term coefficient.
x^2 -12x = -15 . . . . . . subtract 12x
The x-term coefficient is -12, so the square of half that is (-12/2)^2 = 36. Adding 36, we have ...
x^2 -12x +36 = -15 +36
(x -6)^2 = 21
x -6 = ±√21 . . . . . take the square root
x = 6 ±√21 . . . . . add 6
The solution set is ...
{6-√21, 6+√21}
Look at this triangle.
B
8 cm
A
22 cm
С
Work out length AB.
Answer:
23,41 cm (if it's a square triangle)
Step-by-step explanation:
a²+b² = c²
22²+8² = c²
√548 = √c²
23,41 = c
Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3]
Answer:
g(x), f(x), h(x)
Step-by-step explanation:
The required functions sequence are -x³, -x² and -|x|.
Three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3].
Rate of change is defined as the change in value with rest to the time is called rate of change.
Question seems to be incomplete, we assumed three functions -x³, -x² and -|x|.
Now, the function has fastest decreasing average rate of change is -x³
and the function has slowest decreasing average rate of change is -|x| on the interval [0, 3]. While plotting on graph.
Thus, the required functions sequence are -x³, -x² and -|x|.
Learn more about rate of change here: https://brainly.com/question/13103052
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is the origin Located at the point (1,1)
Answer:
No, the origin is Located at (0,0)
Answer:
no
Step-by-step explanation:
The origin is located at the center of a graph, at (0, 0)
Factor completely: x^2 - 5x - 6
Answer:
x×x-5x-6
x × -4X - 6
Step-by-step explanation:
x×x-5x-6
x × -4X - 6
What is 100 times 10
Answer:
Your answer will be 1,000
Step-by-step explanation:
One thousand
Hope this helps : )
Answer:
1000
Step-by-step explanation:
Add 100 10 times and you will get 1000
What is the area of the triangle?
A triangle with a base of 30 centimeters, height of 18 centimeters, and side length of 24 centimeters.
Answer:
270cm^2
Step-by-step explanation:
The side length is irrelevant and does not matter.
The area of a triangle is found by multiplying the base by the height and then dividing that by two.
For this problem it would be...
30*18=540
540/2=270
So the area would be 270cm^2
Answer:
270
Step-by-step explanation:
It is known that a particular project can be completed by nine employees working eight hours a day for twenty five days. To speed completion of the project in a particular town, the supervisor is being provided with twelve workers, and is being asked to complete the project in fifteen days. How many hours a day must the employees worl each day, in order to finish on time?
In order to wipe out the whole job, it takes
(9 persons) x (8 hours/day) x (25 days) = 1,800 person-hours .
12 workers working for 15 days will accomplish
(12 persons) x (H hours/day) x (15 days) = 180H person-hours of work.
180H person-hours = 1,800 person-hours
H = 10
The 12-person team must work 10 hours/day to make this scheme all work out.
What'll really happen:
-- In order to keep tabs on the project and make sure it gets done on the accelerated schedule, the managers in Chicago in suits will assign the supervisor to complete the project in 14 days instead of 15, and they'll require him to send them a status report twice each day.
-- After completing and emailing the Noon status report each day, the supervisor will put on his hard-hat and PPE, and head out to work alongside the 12 sweating workers, who will all begin to sag when they pass 9 hours each day.
-- Day #12 will be solid torrential rain, and no progress will be possible. The men will want to get some rest, but Chicago will call a Zoom meeting to deliver a motivational pep-talk. Attendance will be mandatory.
-- Days #13 and #14 will stretch to 12 hours, but the project will finish in the allotted 14 days.
-- On Day #15, in Chicago, the customer will treat the managers to a fine dinner, drinks, and a Bulls game, in appreciation for completing the project in 15 days. In the field, the supervisor and the 12 workers will get to sleep in for a whole hour later than usual, before they clean up the job site and begin the long drive home.
(Been there. Done that.)
What’s the length of the apothem in this pentagon if all sides are 10in?
Answer:
10 inches
Step-by-step explanation:
It is 10 inches as you have chosen because the length from the midpoint to a side or the apothem is the length of one side. As given, a side length is 10 inches so, the length of the apothem is 10 inches.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Answer:
[tex]5\sqrt{3} inches[/tex]
Step-by-step explanation:
A long year-end status report for work is 144 pages long. You need to print 16 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.54 each.
Give your answer to the nearest cent, only for the paper you use (partial reams are OK)
Submit Question
Answer: The paper going to cost $16.31 for those reports.
Step-by-step explanation:
Given, the length of a long year-end status report for work = 144
If we ned to print 16 copies for a meeting next week, the total number of pages required = 16 *144
= 2304
Since, the paper is sold in reams of 500 pages = $3.54
Then, cost of one page = (Cost of a ream of 500 pages) ÷ 500
= $3.54 ÷ 500
= $ 0.00708
Cost of total number of pages required = 2304x (cost of one page)
= 2304 x ($ 0.00708)
= $ 16.31232 ≈ $16.31
Hence, the paper going to cost $16.31 for those reports.
The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. A juice box is selected at random. What is the probability of the complement of choosing an orange juice box? (first answer will get brainliest)
1/18
4/9
5/9
17/18
Answer:
[tex] p(O)=\frac{8}{18}=\frac{4}{9}[/tex]
And since we want the complement of choosing an orange juice box the answer would be:
[tex] P(O') =1 - P(O) = 1-\frac{4}{9}= \frac{5}{9}[/tex]
And the nest answer for this case is:
5/9
Step-by-step explanation:
For this case we know that we have 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes, so then the size of the sample space is:
[tex] 8+4+6= 18[/tex]
Then we can find the probability of selecting an orange juice box with the definition of Laplace given by:
[tex] p =\frac{possible}{total}[/tex]
And for this case the possible cases are 4 and the total 18 so then the probability is given by:
[tex] p(O)=\frac{8}{18}=\frac{4}{9}[/tex]
And since we want the complement of choosing an orange juice box the answer would be:
[tex] P(O') =1 - P(O) = 1-\frac{4}{9}= \frac{5}{9}[/tex]
And the nest answer for this case is:
5/9
Help please?????????????
Answer:
1 gal 9 qt
Step-by-step explanation:
Answer:
1.75 US Gallons
Step-by-step explanation:
(3 gal 2 qt) - (1 gal 3 qt) =
1.75 US gallons
Can u add this up.
My brain cant handle it.
Answer:
976
Step-by-step explanation:
triangle= 1/2(24)14 times 2
square or rectangle= 10(14), 10(25), 10 (25)
How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 60 tissues during a cold. Suppose a random sample of 10 comma 000 people yielded the following data on the number of tissues used during a cold: x overbar equals 53 comma s equals 23. We want to test the alternative hypothesis Upper H Subscript a: muless than60. State the correct rejection region for alpha equals 0.05 .
Answer:
Null hypothesis: [tex] \mu \geq 60[/tex]
Alternative hypothesis: [tex] \mu <60[/tex]
Since the sample size is large enough we can assume that the distribution for the statistic is normal so then in order to find the critical value for this test taking in count the significance level given of 0.05 we need to look in the normal standard distribution a value who accumulates 0.05 of the area in the left and would be:
[tex] z_{crit}= -1.64[/tex]
Step-by-step explanation:
For this case we have the following data given:
[tex] \bar X = 53[/tex] represent the sample mean
[tex] s = 23[/tex] represent the sample deviation
[tex]n = 10000[/tex] represent the sample size.
We want to test for this case if the true mean is less than 60 so then the system of hypothesis are:
Null hypothesis: [tex] \mu \geq 60[/tex]
Alternative hypothesis: [tex] \mu <60[/tex]
Since the sample size is large enough we can assume that the distribution for the statistic is normal so then in order to find the critical value for this test taking in count the significance level given of 0.05 we need to look in the normal standard distribution a value who accumulates 0.05 of the area in the left and would be:
[tex] z_{crit}= -1.64[/tex]
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet
and the volume of each large box is 22 cubic feet. A total of 22 boxes of paper were
shipped with a combined volume of 324 cubic feet. Write a system of equations that
could be used to determine the number of small boxes shipped and the number of
large boxes shipped. Define the variables that you use to write the system.
Answer:
Small Boxes: 10
Large boxes: 12
Step-by-step explanation:
A show has 4,320,000 viewers for it's season premiere express this number using scientific notation
Answer:
4.32 × 10^6= 4.32 × 10^6
(scientific notation)
= 4.32e6
(scientific e notation)
= 4.32 × 10^6
(engineering notation)
(million; prefix mega- (M))
= 4320000
(real number)
Hence number using scientific notation is 4.32*[tex]10^{6}[/tex]
What is scientific notations?When a number between 1 and 10 is multiplied by a power of 10, it is written in scientific notation. 650,000,000, for example, can be expressed as 6.5 108 in scientific notation. Sal Khan and the CK-12 Foundation collaborated on this project.
How to solve?Given 4,320,000 which can be broken in 432*10000
Which can be written as 432*[tex]10^{4}[/tex]
432 can be written as 4.32*100*[tex]10^{4}[/tex]=4.32*[tex]10^{6}[/tex]
Hence number using scientific notation is 4.32*[tex]10^{6}[/tex]
Learn more about scientific notationhttps://brainly.com/question/1767229
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Situation:
A hiker in Africa discovers a skull that
contains 79% of its original amount of C-
14.
N = Noe
kt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
find the age of the skull to the nearest year
Answer:
about 2357 years
Step-by-step explanation:
You want to find t such that ...
0.79 = e^(-.0001t)
Taking natural logs, we get ...
ln(0.79) = 0.0001t
ln(0.79)/-0.0001 = t = 2357 . . . years
Answer:
See image
Step-by-step explanation:
choose a number between 67 and 133 that is a multiple of 2,8 and 16 .
Answer:
80
Step-by-step explanation:
Since 2 and 8 are factors of 16, you only need to find a multiple of 16 in between 67 and 133 which is simple. I chose 80.
Answer:
128
Step-by-step explanation:
It's asking you to find a number between 67 and 133 that you could divide by 2, 8 and 16 and won't get a remainder.
128 can be divided by 2, 8 and 16 without a remainder.
^picture attached above
I need some help now !!! please (math)
- I need to know the Slope and y-intercept (ordered pair)?
- I also need to know the equation of the line is?
Please someone help me
Answer:
the slope is either -2/1 or -1/2
Step-by-step explanation:
hope this helped sorry i didnt know the y intercept but i think its 0
Please help with this magic square
Answer:
-0.06 left-middle
0.28 right-middle
0.03 right-top
0.1 middle-top
0.12 middle-bottom
Step-by-step explanation:
column-row
2. The National Safety Council routinely analyzes the benefit of seat belt use on driver safety. Their data showed that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed. Test the hypothesis (at 95% confidence) that there is no difference in the proportion of deaths between the 2 groups. What do you conclude? Calculate the margin of error (E) at 95%.
Answer:
We conclude that there is difference in the proportion of deaths between the 2 groups.
Step-by-step explanation:
We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.
Let [tex]p_1[/tex] = proportion of deaths when drivers were not wearing seat belts.
[tex]p_2[/tex] = proportion of deaths when drivers were wearing seat belts.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex] {means that there is no difference in the proportion of deaths between the 2 groups}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex] {means that there is difference in the proportion of deaths between the 2 groups}
The test statistics that would be used here Two-sample z test for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of deaths when drivers were not wearing seat belts = [tex]\frac{31}{2823}[/tex] = 0.011
[tex]\hat p_2[/tex] = sample proportion of deaths when drivers were wearing seat belts = [tex]\frac{16}{7765}[/tex] = 0.002
[tex]n_1[/tex] = sample of drivers not wearing seat belts = 2823
[tex]n_2[/tex] = sample of drivers wearing seat belts = 7765
So, the test statistics = [tex]\frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }[/tex]
= 4.438
The value of z test statistics is 4.438.
Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that there is difference in the proportion of deaths between the 2 groups.
Also, Margin of error (E) = [tex]1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }[/tex]
= [tex]1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }[/tex]
= 0.00397
Solve for p. 6p-2(p+4)=12
Answer:
p=5
Step-by-step explanation:
please mark brainliest
Sam buys 4 boxes of the Crispy Crunch Cereal at Store A. What
fraction of the original price of each box of cereal does he pay per
box? Enter your answer and explanation in the box.
B 1 u
X, Ω
Store Discounts
Sam shops at three stores and each store is having its own
sale as described below.
Store A Crispy Crunch Cereal: Buy 3 boxes, get 4th free!
Store B: Take off the original price of one item!
Store C: Mystery Discount! Percent off your total purchase will
be revealed at the register!
Answer: 3/4 of the original price.
Step-by-step explanation:
Ok, so Sam buys 4 boxes in Store A.
We know that in Store A you can get 4 boxes paying only for 3.
If P is the price of a Box, then he got 4 boxes and paid 3*P
then the amount that he paid for each box is equal to the total amount that he paid divided the number of boxes that he received.
this is: 3P/4 = (3/4)*P
Meaning that he paid 3/4 of the original price for each box.
a.
Does there appear to be a linear trend between the temperature, t and the soft drink sales, g? Is there an exact linear fit?
No, there does not appear to be a linear trend.
b. No, there does not appear to be a linear trend; the fit is not exact
Yes, there appears to be a linear trend and the fit is exact.
d. Yes, there appears to be a linear trend, but the fit is not exact.
C.
Answer:
d. Yes, there appears to be a linear trend, but the fit is not exact.
Step-by-step explanation:
³d what is the anwser
Answer:
75%
Step-by-step explanation:
48 of 64 times 100
48/64 × 100
0.75 × 100
75
So 75% of the bottle of orange juice is water
Hope this helps!!