1.) The probability that the sample mean will be greater than 48 minutes is 0.9332.
2.) The probability of the sample mean being between 44 and 49 minutes is 0.6687.
3.) The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean.
To solve this problem, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means tends to be approximately normally distributed, regardless of the shape of the original population, when the sample size is large enough.
1.) Probability of sample mean > 48 minutes:
To calculate this probability, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, the population mean (μ) is 45 minutes, the population standard deviation (σ) is 12 minutes, and the sample size (n) is 36. We want to find the probability of the sample mean being greater than 48 minutes.
Calculating the z-score:
z = (48 - 45) / (12 / √36) = 3 / 2 = 1.5
Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.5 is approximately 0.9332. Therefore, the probability that the sample mean will be greater than 48 minutes is approximately 0.9332.
2.) Probability of sample mean between 44 and 49 minutes:
To calculate this probability, we need to find the z-scores for both 44 and 49 minutes and then calculate the area between those z-scores.
Calculating the z-scores:
For 44 minutes:
z1 = (44 - 45) / (12 / √36) = -1 / 2 = -0.5
For 49 minutes:
z2 = (49 - 45) / (12 / √36) = 4 / 2 = 2
Using the standard normal distribution table or calculator, we find the probabilities corresponding to z1 and z2:
P(z < -0.5) ≈ 0.3085
P(z < 2) ≈ 0.9772
The probability of the sample mean being between 44 and 49 minutes is approximately P(-0.5 < z < 2) = P(z < 2) - P(z < -0.5) ≈ 0.9772 - 0.3085 = 0.6687.
3.)Conclusion from 100 samples with a mean of 65 minutes:
If 100 samples were collected, and the sample mean was 65 minutes, we would need to assess whether this value is significantly different from the population mean of 45 minutes.
To make this assessment, we can calculate the z-score for the sample mean of 65 minutes:
z = (65 - 45) / (12 / √36) = 20 / 2 = 10
The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean. This is an extremely large deviation, suggesting that the sample mean of 65 minutes is highly unlikely to occur by chance.
Given this, we can conclude that the sample mean of 65 minutes is significantly different from the population mean. It may indicate that there is a systematic difference in the delivery times between the sample and the population, possibly due to factors such as increased demand, traffic, or other external variables
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Question 3 of 10
The circle below is centered at the point (4, 3) and has a radius of length 5.
What is its equation?
D. (x-4)2 + (y-3)2 = 52
10
OA. (x-3)2 + (y - 3)² =
52
OB. (x+4)2 + (y - 3)² =
25
O C. (x-4)2 + (y + 3)² =
52
Answer:
D.
[tex](x - 4) {}^{2} + (y - 3) {}^{2} = 5 {}^{2} [/tex]
The equation of the circle centered at point (4, 3) with a radius of length 5 is (x - 4)² + (y - 3)² = 5².
What is the equation of the circle with the given parameters?The standard form equation of a circle with center (h, k) and radius r is:
( x - h )² + ( y - k )² = r²
Given that circle has a center at point (4, 3 ).
Hence:
h = 4
and k = 3
Also given that, the radius has a length of 5
r = 5
Plug these values into the above formula and simplify the equation:
( x - h )² + ( y - k )² = r²
( x - 4 )² + ( y - 3 )² = 5²
Expanding and simplifying, we get:
(x - 4)² + (y - 3)² = 25.
Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 5².
Option D) (x - 4)² + (y - 3)² = 5² is the correct answer.
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Identify the following errors as systematic or random.
a. A micropipet is improperly calibrated, and the balance dispensed is always smaller than expected.
b. The last digit on a pH meter fluctuates up and down as a measurement is taken.
c. A thermometer is placed such that the bulb makes poor contact with the measured substance, giving erratic temperature reading.
d. A few drops of water are on a balance pan, causing the mass output on the balance to be high each time it is used.
Answer:
systematic errors [ A, C], Random errors [B, D]
Step-by-step explanation:
Random errors are errors that cause certain fluctuations around the true values of substances that are measured, as a result of difficulties being experienced while taking measurements. Systematic errors are mostly associated with the calibration of equipment. It seen to cause consistent deviations from the true value that can be gotten during measurement.
In most cases, random errors cannot be avoided while systematic errors can.
Solve the equation.
x^2 − 4x + 4 = 3
What does -1/5 (-2 1/4) equal?
Answer:
Step-by-step explanation:
Change 0.150 to a fraction.
Step-by-step explanation:
150/1000 and then you you have to simplify it
<1 and <2 are vertical angles. If m<4=
(6x + 11)' and m<2= (10x - 91°, find m<1.
Answer:
Something
Step-by-step explanation:
Something and something and thats it!
Solving the equation
Answer:
-40
Step-by-step explanation:
We multiply both sides by 5:
x = -5 * 8
so x = -40
Jerry was paid $47.00 for 4 hours of work. Leigh-Anne received $84.35 for 7 hours. Who had the greater rate of pay? By how much?
Answer:
Jerry was paid $10.75 an hour and Leigh-Anne was paid $12.05 hourly
Step-by-step explanation:
what 23 div 57 times 7
Answer:
187.285714286
Step-by-step explanation:
Step-by-step explanation:
27/57= 0.40350877193
0.40350877193x7=
2.82456140351
rounded ver- 2.82
Josh added 18 fish to his pond over a period of 6 days. He added the same number of fish each day. What was the change in the number of fish in the pond each day?
Answer:
he put 3 fish everyday for 6 days
PLEASE HELP!!!
Equation: 2 (1/2x + 1) = -3 (2x - 1) +4 (2x + 1)
Answer Choices:
A. 5
B. All real numbers
C. No solution
D. None of the above
I got D but I wanted some confirmation. I feel like I got it wrong... Thanks!
Answer:
Step-by-step explanation:
2(1/2x+1) = -3(2x-1)+4(2x+1)
Distributive Property 1x+2 = -6x+3+8x+4
Combine Like Terms. 1x+2 = 2x+7
Subtract 1x from both sides 2 = x+7
Subtract 7 from both sides -5 = x
Thus the solution is non of the above
If 1 yard = 3 feet and 1 mile = 5,280 feet, how many yards are there in 4 miles?
7,040 yards
15,840 yards
21,120 yards
63,360 yards
Help me please!!
Answer:
7040
Step-by-step explanation:
You do 5280 times 4 which is 21120. Then you do 21120 divided by 3 and get 7040.
What values of B make the equation 7+4-2-B=13-9 true?
Answer:
solution:
Here,7+4-2-8=13-9
or, 9-B=4
or, -B=4-9
or-B=-5
*B= 5
What is the difference between climate and weather?
Answer:
B
Step-by-step explanation:
Climate happens over a long period of time.
Weather varies day to day.
Ex: South Texas has a hot humid summer (climate)
Ex: It is 89 degrees in California today (weather)
A. Find the Mode, Median, Mean and Range. Show your work.
1. 24, 31, 12, 38, 13, 15, 46, 62.
2. 17, 66, 14, 79, 47, 95, 32, 21, 10, 58.
3. 53, 22, 76, 46, 68, 32, 15, 29.
4. 17, 24, 8, 19, 6, 34, 10, 28, 12.
5. 5, 8, 9, 10, 11, 15, 21, 32.
6. 28, 15, 15, 46, 27, 21, 24
B. Find the mode, median, and range
7) 5.2, 5.7, 5.2, 4.3, 3.6, 3.8, 2.7, 4.2, 4.3, 3.9, 4.2
8) 18.1 , 18.6, 18.2, 18.1, 18.9, 18.6, 18.7, 18.3, 18.2, 18.6, 18.6
C. Find the mode and median for each data.
9) 2/9 , 7/9, 5/9, 1/9, 3/9, 8/9
10) 1/4, 1/11, 1/6, 1/9, 1/3 , 1/10
A.
1. Mode: No mode. Median: 24. Mean: 30.875. Range: 50.
2. Mode: No mode. Median: 33.5. Mean: 43.9. Range: 85.
3. Mode: No mode. Median: 46. Mean: 43.571. Range: 61.
4. Mode: No mode. Median: 17. Mean: 18. Range: 28.
5. Mode: No mode. Median: 10.5. Mean: 13.5. Range: 27.
6. Mode: 15. Median: 22.5. Mean: 25.857. Range: 31.
B.
7. Mode: 4.3. Median: 4.2. Range: 2.1.
8. Mode: 18.6. Median: 18.6. Range: 0.8.
C.
9. Mode: No mode. Median: 4/9.
10. Mode: No mode. Median: 5/24.
Determine whether the equations are parallel or not for y= 3x-2 and y= 1/3x -11
Answer:
To know if these lines are parallel, you just have to look at the slope. In this case they are not.
Step-by-step explanation:
The slope is the number in front of your x. So for the first formula the slope is 3 and for the second one it is 1/3. The slope tells you in which direction the line goes, so if they are the same, that means that the lines are parallel. In this case the slopes are not the same, so the lines are not parallel.
Answer:
not parallel
Step-by-step explanation:
while the lines have a different y-intercept they do not have the same slope which they would need to be parallel. With two different slopes the lines will eventually cross.
Mrs. Thomas has $71.00 to purchase bottles of juice for her class. If the bottles of juice cost $3.55 each, how many
bottles can she buy?
O 2 bottles
O 5 bottles
O 20 bottles
O 25 bottles
Yesterday, Charlie had k baseball cards. Today, he got 24 more. Using k
Subtitute 2x+y=7 and 3x-y=8
Answer:
x = 3 , y = 1
Step-by-step explanation:
2x + y = 7
3x + y = 8
solution
2x + y = 7-----------(1)
3x - y = 8------------(2)
from equation 1
2x + y = 7
y = 7 - 2x-------------(3)
substitute equation 3 into equation 2
3x - y = 8
3x - (7 - 2x) = 8
3x - 7 + 2x = 8
3x + 2x = 8 + 7
5x = 15
divide through by the coefficient of x
5x/5 = 15/5
x = 3
to find y
substitute x into equation 1
2x + y = 7
2(3) + y = 7
6 + y = 7
y = 7 - 6
y = 1
What is the slope for the function y = -5x^2 + 2 at the point x = 1?
Answer:
y = 27
Step-by-step explanation:
just multiply 5(1) then do Pemdas
ASAP JUST ANSWER NO WORK
Answer: C
Step-by-step explanation:
Examine the division problem.
StartFraction 15 over 4 EndFraction divided by (negative StartFraction 5 over 8 EndFraction
To solve the problem, you first must find the reciprocal of the second fraction. Which reciprocal fraction should you use?
Negative StartFraction 5 over 1 EndFraction
Negative one-fifth
Negative StartFraction 5 over 8 EndFraction
Negative StartFraction 8 over 5 EndFraction
Answer:d -8/5
i just toke the test and got it right
Answer:
Actually its negative 6 -6
Step-by-step explanation:
Multiplying a number by its reciprocal always results in a product of 1. What number must be multiplied by 4 5/8 to create a product of 1?
First, turn 4 5/8 into an improper fraction.
4 = 32/8
(The fraction bar is basically division)
32/8 + 5/8 = 37/8
Now, flip it to find the answer.
6/37
That is the answer.
Hope I helped
what is length?define
Step-by-step explanation:
the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of an object.
Answer:
the measurement or extent of something from end to end.
Solve the expression when x = 4 and y = -2 x² - 2xy + y² 36
Answer:Did u mean plus 36
Step-by-step explanation:
Omar wants to measure the width of a river. He marks off two right triangles, as shown in the figure. The base of the larger triangle has a
length of 64 m, and the base of the smaller triangle has a length of 31 m. The height of the smaller triangle is 19.8 m. How wide is the
river? Round your answer to the nearest meter. (The figure is not drawn to scale.)
19.8 m
River
A
31 m
64 m
?
A
m
X
Ś
Answer:
41 meters
Step-by-step explanation:
[tex]\frac{31}{64}[/tex] = [tex]\frac{19.8}{x}[/tex]
31x = (19.8)(64)
31x = 1267.2 Divide both sides by 31 and round
x = 41
the percentage of registered voters who voted in this election was 55%, up 17% from the last election. what was the percentage that voted at the last election?
Answer:
0.38 or 38%
Step-by-step explanation:
Because I subtracted 17% from 55% and got 0.38 Then, I turned the decimal 0.38 into the percentage 38%.
4.
If 75 persons can perform a piece of work in 12 days of 10 hours, how many men will
perform a piece of work twice as great in tenth part of time, if they work the same
number of hours a day, supposing that two of the second set can do as much work as
three of the first set?
1
n.1.1
Answer: dont know
Step-by-step explanation:
henry and his brother each start a savings account. henry begins with $200 and deposits $25 each month. his brother begins with $150 and deposits $35 each month. after how many months will the two brothers have the same in their savings account ?
Answer:
Henry after 2 months: 250
His brother after 2 months: 220
Step-by-step explanation:
Henry started with $200 so add $25 twice (for 2 months) and get $250 dollars after 2 months.
His brother started with $150 so add $35 twice and get $220 dollars after 2 months
I've done every problem I only need with the help this problem
Answers:
[tex]\displaystyle \lim_{x \to 2^{+}} f(x) = 1\\\\\displaystyle \lim_{x \to 2^{-}} f(x) = 1\\[/tex]
Both result in the same limit value. This allows us to say [tex]\displaystyle \lim_{x \to 2} f(x) = 1[/tex] without the plus or minus over the 2.
The left and right hand limits may not always match like this.
==================================================
Explanation:
The notation [tex]\displaystyle \lim_{x \to 2^{+}} f(x)[/tex] means that we are approaching x = 2 from the right hand side. This is from the positive direction. So we start at say x = 3 and move to x = 2.5 then to x = 2.1 then to x = 2.01 and so on.
Because we started with values x > 2, we will use the third definition of the piecewise function
if x > 2, then f(x) = 3x-5
Plug in x = 2 to get
f(x) = 3x-5
f(2) = 3(2)-5
f(2) = 6-5
f(2) = 1
This shows [tex]\displaystyle \lim_{x \to 2^{+}} f(x) = 1[/tex]
-----------------------------
For the other limit, we're approaching x = 2 from the negative side. So we could start at say x = 0, then move to x = 1, then to x = 1.5 then to x = 1.9 then to x = 1.99, and so on.
We're using x values such that x < 2 now.
So we'll be using the first definition of the piecewise function
If x < 2, then f(x) = x^2 - 3
f(x) = x^2-3
f(2) = 2^2-3
f(2) = 4-3
f(2) = 1
We end up with [tex]\displaystyle \lim_{x \to 2^{-}} f(x) = 1[/tex]
---------------------------------
Both right hand limit and left hand limit result in the same value
Because [tex]\displaystyle \lim_{x \to 2^{+}} f(x) = \displaystyle \lim_{x \to 2^{-}} f(x) = 1[/tex]
We can shorten that to [tex]\displaystyle \lim_{x \to 2^{}} f(x) = 1[/tex] meaning we can approach x = 2 from either direction to arrive at the same limiting value.
A thing to notice is that f(2) is not equal to 1. Instead the second line of the piecewise function says f(2) = 3.
The fact that the limit as x approaches 2 and f(2) don't agree means this function is not continuous at x = 2.
The graph shows this. We have a removable discontinuity where we effectively picked the point off the graph and move it upward.
See the diagram below.
