Answer:
The speed of the boat is 20 km/hr
Step-by-step explanation:
Let s be the speed of boat in still water
Let d be the distance
Upstream speed = s-4
Jane took 30 min to drive her boat upstream to water-ski at her favorite spot.
So, Distance traveled in upstream =[tex]Speed \times time =(s-4) \times \frac{30}{60}[/tex]
Downstream speed = s+4
So, Distance traveled in downstream = [tex]Speed \times time =(s+4) \times \frac{20}{60}[/tex]
So, [tex](s-4) \times \frac{30}{60}=(s+4) \times \frac{20}{60}[/tex]
30s-120=20s+80
10s=200
s=20
Hence The speed of the boat is 20 km/hr
Candice is preparing for her final exam in Statistics. She knows she needs an 65 out of 100 to earn an A overall in the course. Her instructor provided the following information to the students. On the final, 200 students have taken it with a mean score of 57 and a standard deviation of 6. Assume the distribution of scores is bell-shaped. Calculate to see if a score of 65 is within one standard deviation of the mean.
Answer:
a. 72
b. 816
c. 570
d. 30
Step-by-step explanation:
Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.
Please refer the figure for a better understanding.
a. In a normal distribution, Mean = Median = Mode
Therefore, Median = Mean = 72
b. We have to know that 68% of the values are within the first standard deviation of the mean.
i.e., 68% values are between Mean Standard Deviation (SD).
Scores between 63 and 81 :
Note that 72 - 9 = 63 and
72 + 9 = 81
This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.
Now, Scores between 63 and 81 =
= 68 X 12 = 816.
That means 816 students have scored between 63 and 81.
c. We have to know that 95% of the values lie between second Standard Deviation of the mean.
i.e., 95% values are between Mean 2(SD).
Note that 90 = 72 + 2(9) = 72 + 18
Also, 54 = 63 - 18.
Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to of the values.
Therefore, Scores between 72 and 90 =
= 570.
That is a total of 570 students scored between 72 and 90.
d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.
In this case, 5 % of the values lie between below 54 and above 90.
Since, we are asked to find scores below 54. It should be 2.5% of the values.
So, Scores below 54 =
= 2.5 X 12 = 30.
That is, 30 students have scored below 54.
Step-by-step explanation:
It is found that score of 62 is not within one standard deviation of the mean.
What is z - score?The Z-score measures how many standard deviations the measure is from the mean. If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have [tex]X \sim N(\mu, \sigma)[/tex]then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
In a set with mean and standard deviation, the z- score of a measure X is given by:
[tex]Z = \dfrac{X - \mu}{\sigma},[/tex]
Z-score, we look at the z-score table and find the p-value associated with this z-score.
Given that Mean score of 54 and a standard deviation of 6.
This means to see if a score of 62 is within one standard deviation of the mean.
Is Z between -1 and 1 when X = 62.
[tex]Z = \dfrac{X - \mu}{\sigma},\\Z = \dfrac{62 - 54}{6},[/tex]
Z = 1.33
Therefore, It is found that score of 62 is not within one standard deviation of the mean.
Learn more about z-score here:
https://brainly.com/question/21262765
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Write the equation of the line that passes through the points (1,-5)(1,−5) and (-9,2)(−9,2). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
y+5 = -0.7 (x-1)
Step-by-step explanation:
m = (change in y) / (change in x) = (2-(-5)) / (-9-1) = 7 / (-10) = -0.7
PLEASE HELP!!
Sorry for all the tabes I'm working on a presentation at the same time.
Answer:
0.5
Step-by-step explanation:
use rise over run, from (-6,0) to (0,3) it rises 3 and runs 6. 3/6 = 1/2.
Answer:
the slope is two
Step-by-step explanation:
rise over run
Find the slope of the line
graphed below.
Answer:
[tex]\frac{3}{5}[/tex] or 0.6
Step-by-step explanation:
This problem requires the slop formula which is [tex]\frac{y2-y1}{x2-x1}[/tex]
You start with the first point which is (-1,1). This will be x1 and y1.
The next point is (4,4). This will be x2 and y2.
You plug these values into your equation which gives you [tex]\frac{4-1}{4-(-1)}[/tex]
To solve, you evaluate, [tex]\frac{4-1}{4-(-1)}[/tex] = [tex]\frac{3}{5}[/tex] or 0.6
Find the exponential function that satisfies the given conditions: initial value = 70, decreasing at a rate of 0.43% per week
Answer choices:
A) f(t) = 70 x 0.9957^t
B) f(t) = 70 x 1.43^t
C) f(t) = 0.43 x 0.3^t
D) f(t) = 70 x 1.0043^t
Answer:
a- just took the test
Step-by-step explanation:
-3/7 % -1/2 =??
What is the answer to this equation
Answer:
-0.21428571428
A diver swims 5.875 feet up to the surface of the water. Which number represents the diver’s position in relation to the surface before swimming to the top?
-5.9 feet
Negative 5 and three-fourthsfeet
-58 feet
Negative 5 and StartFraction 7 over 8 EndFractionfeet
Answer:
Negative 5 and 7 over 8
Step-by-step explanation:
Answer:
Negative 5 and StartFraction 7 over 8
Step-by-step explanation:
M/x =n-p, x for p ??
Answer:
the answer is A) X=m/n-p
Step-by-step explanation:
m/x=n-p
n-p=m/X
(n-p)×x=m
X=m/n-p
A farm has 56 horses and sheep in all. There are 8 fewer sheep than horses. How many horses are there on the farm?
Answer:
32 Horses
Step-by-step explanation:
32-8=24
There are 32 horses and 24 sheep (As you can see there are 8 fewer sheep than horses)
I sort of guess and checked:
I tried to think of 2 numbers that added to 56 but one number was 8 less than the other one.I figured out that 32 and 24 fit this description :)
Emilia wrote a total of 12 pages over 4 hours. After spending 6 hours writing this week, how
many pages will Emilia have written in total? Assume the relationship is directly proportional.
Answer:
30 pages
Step-by-step explanation:
Knowing she wrote 12 pages in 4 hours, we can do 12/4 to get 3 pages per hour. Multiply 3 pages by the 6 hours she spends writing and you get 18 pages in 6 hours. Add 12 pages and 18 pages and you have 30 pages.
An oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day. For each additional well that is drilled, the average production per well decreases by 25 barrels per day.
Required:
How many additional wells should be drilled to obtain the maximum amount of oil per day?
Answer:
The additional wells for maximum amount of oil per day is 3 wells.
Step-by-step explanation:
Given;
initial number of wells, n = 6
total production, T = 1800
average production per well, = 1800/6 = 300 barrels per day
Let the additional well = y
total number of wells after optimization = 6 + y
new production per well = 300 - 25y
new total production = (6+y)(300-25y)
t = 1800 - 150y + 300y - 25y²
t = 1800 + 150y - 25y²
dt / dy = 150 -50y
for maximum value, dt/dy = 0
150 - 50y = 0
50y = 150
y = 150 / 50
y = 3
Therefore, the additional wells for maximum amount of oil per day is 3 wells.
33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
Given that an oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day, and for each additional well that is drilled, the average production per well decreases by 25 barrels per day, to determine how many additional wells should be drilled to to obtain the maximum amount of oil per day, the following calculation must be performed:
1800 x 6 = 10800 1200 x 30 = 36000 1000 x 38 = 38000 950 x 40 = 38000 900 x 42 = 37800 975 x 39 = 38025
Therefore, 33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
Learn more in https://brainly.com/question/13581736
Sophia says that you can solve the problem in the Example by multiplying both quantities in the ratio 60:36 by one-sixth. Is Sophia correct?
Answer:
Sophia is not correct
Step-by-step explanation:
The given situation represent the problem of a ratio and it is predicted to do the simplify the ratio by determining the smallest possible values
Here it can be presented 60:36 as a fraction i.e. [tex]\frac{60}{36}[/tex]
Now the fraction should be fall by dividing both the numerator and denominator by a common factor i.e. 6
Now after dividing it, the fraction would be [tex]\frac{10}{6}[/tex]
Now it can be further reduced by a common factor i.e. 2
So now the fraction is [tex]\frac{5}{2}[/tex]
Thus, the ratio is 5:2
Hence, she is not correct
Multiply. Express your answer in simplest form. 9 1/6 × 1 1/11. A. 10 B. 9 1/66 C. 10 1/17 D. 10 5/6
Answer:
9 1/66
Step-by-step explanation:
9 x 1 is 9 so its that but to add more proof the problem is 9 1/6, 1 1/11 multiply 6 and 11 it is 66 so the answer is 9 1/66
The distance from a point to two is five units. The point could be located at
-7
-6
6
-3
NEXT QUESTION
O ASK FOR HELP
Answer:
The correct answer is -3
Step-by-step explanation:
attached is a number line to show diagrammatically how to count five units from the chosen point to point 2 on a number line.
Moving five units from -3 to 2 on a number line is given as follows:
-3 ⇒ -2 ⇒ -1 ⇒ 0 ⇒ 1 ⇒ 2
From the motion expression shown above, moving from -3 to 2 involves moving 5 units.
another way of determining the correct answer is to find the difference in interval between the two points as shown below:
Let the point be x
2 - x = 5 units
2 - 5 = x
∴ x = -3
Answer:
-3
Step-by-step explanation:
it was on quiz baby
A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax?
O $1.26
O $5.40
O $19.26
O $30.60
Answer:
1
Step-by-step explanation:
1.26
A nursery owner buys 8 panes of glass to fix some damage to his greenhouse. The 8 panes cost
$19.60. Unfortunately, he breaks 3 more panes while repairing the damage. What is the cost of
another 3 panes of glass?
Another 3 panes of glass cost $
Answer:
$8.85
Step-by-step explanation:
Step-by-step explanation: well if you take 23.60 and divide it by 8 you would get 2.95 times that by three and you would get 8.85 and there's your answer.
Answer:
7.35
because my kid got the question wrong
When holding your arms horizontal, your body is the line of reflection. true or false?
Answer:
true
Step-by-step explanation:
Your arms would be the line and your body would be the y-axis, and your arms are on either side of the y-axis which means your body is the line of reflection
Hope this helps.
One package of blackberries costs $3. How many packages of blackberries can you buy for $15?
Answer:
5 packages
Step-by-step explanation:
One package of blackberries cost $3
Let x represent the number of packages that will cost $15
1 = $3
x= $15
3x= 15
Divide both sides by the coefficient of x which is 3
3x= 15/3
x= 5
Hence 5 packages of blackberries will cost $15
A worker at one farm is paid $486 for the week, plus $0.03 for every pound
of apples she picks. At another farm, a worker is paid $490 for the week, plus
$0.02 for every pound of apples. For how many pounds of apples are the workers
paid the same amount?
Answer:sorry this probably is t the most helpful but the closest i could get was 399 lbs. it’s is st$497.7 for one and $$497.8.
Step-by-step explanation:
uestion 1:
Damon wants to sell his motorcycle that he paid $4,000 for 3 years ago. The motorcycle depreciated (decreased in value) at a constant rate each month over a 3-year period. If x represents the monthly depreciation amount, write an expression that shows how much Damon can sell his motorcycle for today.
Answer:
4,000 -x3
Step-by-step explanation:
x times 3 is equal to the decrease so therefore you take the decrease away form 4/oo
Answer:
3y-x=4,000
Step-by-step explanation:
a. Suppose a BMW dealer in Fullerton, CA is trying to calculate the probability of his car sale for next week. The dealer knows that the sale of car is normally distributed with mean 50 and variance 9. The variance 9 was calculated from the weekly car sale data of 20 weeks, as the population variance is not known to the dealer. What is the probability that the dealer will sell 51 or more cars next week? (Hint: use t distribution) (15)
Answer:
0.45576
Step-by-step explanation:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
Standard Deviation = √variance
Mean = 50
= √9
= 3
z = 51 - 50/3
= 0.11111
Probability value from Z-Table:
P(x<51) = 0.54424
P(x>51) = 1 - P(x<51)
= 1 - 0.54424
= 0.45576
The probability that the dealer will sell 51 or more cars is 0.45576
It too Mrs. phillips 1.6 hours to run the 13.2 miles. What was his average speed
Answer:
13.2 miles/ 1.6 hours= 8.25 miles/hour.Mr. Phillips's speed was 8.25
Multiply: -12y(y - 6) Enter the correct answer.
Simplify 2x^3 х 3x^2
Answer:
ans = 6x4
Step-by-step explanation:
(2x2)(3x2)
first multiply the coefficients
(2*3) = 6
next multiply the variables
(x2*x2) = x2+2 = x4
productofcoeficients,productofvariables
= 6x4
There are 100 students at a school and three dormitories A, B, and C with capacities of 25, 35, and 40, respectively.
Required:
a. How many ways are there to fill up the dormitories?
b. Suppose that, of the 100 students, 50 are men and 50 arewomen and that A is an all-men's dorm, B is an all-women's dorm andC is co-ed. How many ways are there to fill thedormitories?
Answer:
a
[tex]N = 7.0 *10^{44} \ Ways [/tex]
b
[tex]U = 2.85 *10^{26}\ ways [/tex]
Step-by-step explanation:
From the question we are told that
The number of students are n = 100
The number of dormitories is k = 3
The capacity of the first dormitory is A = 25
The capacity of the second dormitory is B = 35
The capacity of the third dormitory is c = 40
Generally the number of way to fill the dormitory up is mathematically represented as
[tex]N = \frac{n!}{A! B!C!}[/tex]
=> [tex]N = \frac{100!}{25! 35! 40!}[/tex]
Here ! stands for factorial, so we will be making use of the factorial functionality in our calculators to evaluated the above equation
=> [tex]N = \frac{100!}{25! 35! 40!}[/tex]
[tex]N = \frac{9.332622* 10^{157}}{[1.551121* 10^{25}]* [1.0333148* 10^{40}] * [8.1591528*10^{47}]}[/tex]
[tex]N = 7.0 *10^{44} \ Ways [/tex]
From the question we are told that there are 50 men and 50 women and
A is all-men's dorm and B is all-women's dorm while C is co-ed
So
When A is filled , the number of men that will be remaining to fill dorm C is 50-25 = 25
While when B is filled the number of women that will be remaining to fill dorm C is 50-35 = 15
Generally the number of ways there to fill the dormitories is equivalent to the number of ways of selecting the 25 men and 35 women to fill dormitory A and B plus one more way which is filling dorm C with the remaining students this is mathematically represented as
[tex]U = ^{50}C_{35} * ^{50}C_{25} + 1[/tex]
Here C stands for combination hence we will be making use of the combination functionality in our calculators
[tex]U = 2.250829575* ^{12} * 1.264106064 * 10^{14} + 1[/tex]
=> [tex]U = 2.85 *10^{26}\ ways [/tex]
M is the midpoint of line segment PQ. MQ = 5x + 8 and PQ = 6x + 65, find x
Answer:
freeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
trump 20202020202020020202020
Wade picked 4 pints of blackberries. His friend, Matt, picked 6 pints. How
many pints did they pick altogether?
There is a paper attached only 5 questions :)
Answer:
Question 1: 20,160 cookies
Question 2: 37,600 letters
Question 3: 252,396 squares on each tablecloth
Question 4: 138,762 points
Question 5: 4,652,352 shrimp
Step-by-step explanation:
Question 1: Multiply 315 and 64 to get amount of cookies
Question 2: Multiply 940 and 40 to get the number of letters
Question 3: Multiply 36 and 7,011
Question 4: Multiply 26 and 5,337 to get the number of points
Question 5: Multiply 96 and 48,462 to get the number of shrimp the chef prepared.
:)
please help me with this question
Answer:
2c^2
Step-by-step explanation:
c3-c1=c2
d2-d2=0
8/4=2
Help. (Math) The following construction was performed. What distance did the compass have to be set to sweep the two arcs through point T?
1. RP
2. QR
3. QT
4. QP