Answer:
7 years old
Step-by-step explanation:
Robert's mother pours a cup of milk for him and realizes that cup has a small crack so she pour the milk into another cup. Robert is not upset because he knows that the amount of milk has remained same.
As Robert is 7 year old . He can groups the milk in the cup according to size , shape and color. He has a better understanding of numbers and can understand problems easily.
Robert's recognition of the conservation of volume implies he is at least 7 years old, the age at which children typically enter the concrete operational stage and understand this concept.
Explanation:The question asks us to determine Robert's age based on his understanding of the concept of conservation of volume. According to developmental psychology, children gain the ability to understand that a change in the form of an object does not necessarily imply a change in the volume or quantity after a certain age. This concept is typically acquired during the concrete operational stage of development, which is from about 7 to 11 years old. Since Robert recognizes that the same amount of milk remains constant despite being poured into cups of different shapes, we can infer that Robert is at least in the concrete operational stage of development. Thus, Robert is at least 7 years old.
which of the following rain-related losses WOULD be covered under this renters insurance policy?
a. Your laptop is ruined because you left your window open during a moderate rain shower
b. Your mattress is ruined because part of the apartment's roof blew off during a major rainstorm, creating
a stream of water landing directly on your bed
C. Your carpet is ruined because your roommate negligently left her wet boots, umbrella, and raincoat
sitting in a pile on the rug all afternoon
d. You lose a day's wages because a horrible rainstorm makes it impossible to get to your job
Answer:I think this is the nswer
Step-by-step explanation:
C. Your carpet is ruined because your roommate negligently left her wet boots, umbrella, and raincoat
sitting in a pile on the rug all afternoon
The statement of rain-related losses that WOULD be covered under this renters insurance policy is when your mattress is ruined because part of the apartment's roof blew off during a major rainstorm, creating a stream of water landing directly on your bed.
What is the renter's insurance policy?Basically, the renter's insurance is similar to the homeowner's insurance, but it is for people who rent or lease properties, such as houses and apartments. A renter's insurance refers to an insurance policy that can cover theft, water backup damage, certain natural disasters, bodily injuries and more in a rented property.
If we rent an apartment, home or even a dorm, the renter's insurance are more recommended for protecting your space and belongings in the event of a covered accident. Therefore, the Option B is correct.
Missing options "a. Your laptop is ruined because you left your window open during a moderate rain shower b. Your mattress is ruined because part of the apartment's roof blew off during a major rainstorm, creating a stream of water landing directly on your bed C. Your carpet is ruined because your roommate negligently left her wet boots, umbrella, and raincoat sitting in a pile on the rug all afternoon D. You lose a day's wages because a horrible rainstorm makes it impossible to get to your job"
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Police estimate that 84% of drivers wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. If they stop 140 cars,
what is the probability they find at least 27 drivers not wearing their seatbelts?
Use a Normal approximation.
Answer:
0.8802
Step-by-step explanation:
given that the Police estimate that 84% of drivers wear their seatbelts.
when they stop 140 cars, no of trials = no of cars checked = 140
Each car is independent of the other
Hence X no of cars with drivers wearing seat belts is binomial with p = 0.85
Required probability =
the probability they find at least 27 drivers not wearing their seatbelts
Since normal approximation is required we can approximate to
X is Normal with mean = np = [tex]140(0.84)\\=117.6[/tex]
std dev = [tex]\sqrt{npq} =4.338[/tex]
Required probability =atelast 27 drivers not wearing their seatbelts
= P(X>(140-27))
= P(X>113)
[tex]=P(X>112.5)\\=1- 0.1198\\=0.8802[/tex]
Carol has two cats rover and Bobo. Rover eat three fourths of a can of cat food each day and bobo eat a half of a can of cat food each day. Cat food cost five dollars for three cans. It's is only sold in three can packs. How much does it cost carol for a sixty day supply of cat food for her two cats.
Answer: A sixty day supply of cat food for her two cats will cost her $125
Step-by-step explanation:
Carol has two cats Rover and Bobo.
Let x = the quantity of a can of fast food.
Rover eats three fourths of a can of cat food each day. This means that Rover eats 3x/4 each day. Bobo eats a half of a can of cat food each day. This means that bobo eats x/2 each day.
Cat food costs five dollars for three cans. This means that 3x = 5
Total number of cans consumed by both dogs in a day is 3x/4 + x/2 =5x/4
That means the cost per day would be
(5x/4 × 5)/3x = 25x/4 ×1/3x
= 25/12
It costs her $25/12 per day
To determine the cost for 60 days, we would multiply the cost per day by 60. It becomes
25/12 × 60 = $125
Suppose that F′(x)=f(x) and G′(x)=g(x). Which statements are true? A. If F and G differ by a constant, then f=g. B. If f and g differ by a constant, then F=G. C. If f=g, then F=G. D. None of the above
Answer: The correct option is
(A) If F and G differ by a constant, then f = g.
Step-by-step explanation: According to the given condition, we have
[tex]F'(x)=f(x)~~~\textup{and}~~~G'(x)=g(x).[/tex]
We are to select the correct statement.
Let F(x) = p(x) and G(x) = p(x) + c, c - constant.
Then, we get
[tex]F'(x)=p'(x)~~~\textup{and}~~~G'(x)=p'(x).[/tex]
Therefore,
[tex]F'(x)=G'(x)\\\\\Rightarrow f(x)=g(x)\\\\\Rightarrow f=g.[/tex]
Thus, if F and G differ by a constant, then f = g.
Option (A) is CORRECT.
A recipe for brownies calls for 2/3 Cup of chocolate chips for a batch of two dozen brownies. How many chocolate chips will be needed to make 18 brownies.
Answer:
6 cups
Step-by-step explanation:
[tex](18 \times \frac{2}{3} ) \div 2 = [/tex]
[tex]12 \div 2 = [/tex]
[tex]6[/tex]
In the July 2007 issue, Consumer Reports examined the calorie content of two kinds of hot dogs: meat (usually a mixture of pork, turkey, and chicken) and all beef. The researchers purchased samples of several different brands. The meat hot dogs averaged 111.7 calories, compared to 135.4 for the beef hot dogs. A test of the null hypothesis that there's no difference in mean calorie content yields a P-value of 0.124. Would a 95% confidence interval for μMeat −μBeef include 0? Explain.
Answer:
Since we FAIL to reject the null hypothesis, then if we construct an interval of 95% of confidence, the 0 should be included, because on the test hypothesis we conclude that there would be no significant difference between the means of the two groups analyzed, and the results obtained on the hypothesis test needs to be consistent with the confidence interval.
Step-by-step explanation:
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
[tex]\bar x_{meat}=111.7[/tex] represent the sample mean of calories for the meat hot dogs
[tex]\bar x_{beef}=135.4[/tex] represent the sample mean of calories for the beef hot dogs
The system of hypothesis on this case would be:
Null hypothesis: [tex]\mu_{meat}-\mu_{beef}=0[/tex]
Alternative hypothesis: [tex]\mu_{meat}-\mu_{beef}\neq 0[/tex]
On this case we have the p value obtained, after calculate the statistic and we got that [tex]p_v =0.124[/tex] if we select a 5% significance level [tex]\alpha=0.05[/tex] we see that [tex]p_v >\alpha[/tex] and on this case we can FAIL to rejec the null hypothesis, so there is not a significant difference between the mean of the two tpes of hot dogs analyzed at 5% of significance.
And since we FAIL to reject the null hypothesis, then if we construct an interval of 95% of confidence, the 0 should be included, because on the test hypothesis we conclude that there would be no significant difference between the means of the two groups analyzed, and the results obtained on the hypothesis test needs to be consistent with the confidence interval.
A 95% confidence interval for μMeat - μBeef including 0 indicates no significant difference in calorie content between meat and beef hot dogs.
Explanation:A 95% confidence interval for μMeat - μBeef that includes 0 suggests that there is no significant difference in the mean calorie content between meat and beef hot dogs. In this case, the difference in mean calorie content between the two types of hot dogs is not statistically significant, as the null hypothesis is not rejected. The P-value of 0.124 suggests that there is a 12.4% chance of observing a difference in mean calorie content as extreme as the one observed if the null hypothesis were true. Therefore, we cannot conclude that there is a significant difference in the mean calorie content between meat and beef hot dogs.
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Which of the following items are elements of a monthly checking account statement? I. A period (beginning date and ending date) II. A beginning balance and ending balance. III. A detailed list of debits and credits during the period.
Answer:
the answer is d.
Step-by-step explanation:
Monthly checking account statements include:
- A period
- A beginning balance and an ending balance
- A detailed list of debits and credits during the period
so it is d since it is all three.
How many milligrams of zinc ions do the trout need to be exposed to in order for them to survive exactly one minute after exposure?
Answer:
1770
Step-by-step explanation:
No calculator is needed.
When you fill in the numbers, you get ...
1 = (x/1770)^(-0.8)
The only way the value will be 1 is if the fraction is 1:
x/1770 = 1
The only way the fraction will be 1 is x = 1770.
1770 mg Zn ions per liter will be lethal in 1 minute.
_____
Check
You know the answer will be slightly more than 1743 from your answer to the second part of the first question.
On march 4 1999 the new england journal of medicine published a research article by Dr Douglas Jorenby and colleague comparing different treatments to help patients stop smoking.
Is this a question or a statement?
ILL MARK BRAINLIEST!
The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 36
52 40
50 34
47 39
51 44
48 41
53 40
53 38
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
The answer is mean.
What are mean, median, and mode?Mean is the most commonly used measure of central tendency. It represents the average of the given collection of data. Median: Given that the data collection is arranged in ascending or descending order, the following method is applied:
• If number of values or observations in the given data is odd, then the median is given by [(n+1)/2]th observation.
• If in the given data set, the number of values or observations is even, then the median is given by the average of (n/2)th and [(n/2) +1]th observation.
Given here: Shop A Shop B
55 36
52 40
50 34
47 39
51 44
48 41
53 40
53 38
Total = 409 312
Since the data is not skewed mean will provide more accurate data then median.
Therefore the respective means are Shop A =51.125 Shop B=39
Hence, The answer is mean.
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Is dollars 250 is to be divided among Neymar Rohit Sharma and Nadal so that Neymar gets two parts Rohit gets three parts and Nadal gets 5 parts how much money will we get? What will it be in percentage
Answer:
Step-by-step explanation:
Total amount of money to be shared among Neymar, Rohit Sharma and Nadal is $250
Neymar gets two parts. This means that Neymar gets 1/2 × total amount of money.
Neymar gets 1/2 × 250 = 125
The percentage will be amount that Neymar gets divided by the total amount and multiplied by 100. It becomes
125/250 × 100 = 50%
Rohit gets three parts. This means that Rohit gets 1/3 × total amount of money.
Rohit gets 1/3 × 250 = 83.33
The percentage will be amount that Rohit gets divided by the total amount and multiplied by 100. It becomes
83.33/250 × 100 = 33.33%
Nadal gets five parts. This means that Nadal gets 1/5 × total amount of money.
Nadal gets 1/5 × 250 = 50
The percentage will be amount that Nadal gets divided by the total amount and multiplied by 100. It becomes
50/250 × 100 = 20%
Answer:
Neymar: $50, 20%Rohit: $75, 30%Nadal: $125, 50%Step-by-step explanation:
A total of 10 parts are allocated to Neymar, Rohit, and Nadal, so each part represents 1/10 of the amount, or 10%.
Neymar gets 2 parts, or 20% of $250, so gets $50.
Rohit gets 3 parts, or 30% of $250, so gets $75.
Nadal gets 5 parts, or 50% of $250, so gets $125.
_____
Comment on the question
The question seems incomplete in that there are 4 names, but only 3 allocations.
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If sin θ = 3/5, and lies in Quadrant II, what are the exact values of sin 2θ, cos 2θ , and tan 2θ ?
Thank you in advance!
Answer:
sin2θ = -24/25
cos2θ = 7/25
tan2θ = -24/7
Step-by-step explanation:
sinθ = 3/5
θ is in Quadrant II. So 2θ is in Quadrant III or IV. So sin2θ is negative. Nothing can be said about cos and tan yet.
sin135 = 0.707 > 3/5.
So θ > 135.
2θ lies in Quadrant IV. So cos2θ is positive and tan2θ is negative.
cosθ = √(1 - sin²θ)
= -4/5
sin2θ = 2sinθcosθ = 2x(3/5)x(-4/5) = -24/25
cos2θ = 1 - 2sin²θ = 1 - 2x(3/5)² = 7/25
tan2θ = sin2θ/cos2θ = -24/7
What is the angle in the picture below called?
A. a reflex angle
B. a straight angle
C. an acute angle
D. a right angle
Answer:
b
Step-by-step explanation:
Answer:straight angle
Step-by-step explanationbecause it’s straight
Plz explain and prove the triangles congruence.
Answer:
[tex]\overline {JL} \cong \overline{MO}[/tex] is the only correct statement.
Step-by-step explanation:
When the two triangles are congruent then their Vertices are correspondence to each other. the correspondence of vertices are as
For, Δ JKL ≅ Δ MNO
J ↔ M
K ↔ N
L ↔ O
The true statement with respect to the correspondence are as
For, Δ JKL ≅ Δ MNO
∠JKL ≅ ∠MNO
∠JLK ≅ ∠MON
∠KJL ≅ ∠NMO
[tex]\overline {JL} \cong \overline{MO}[/tex]
[tex]\overline {KL} \cong \overline{NO}[/tex]
[tex]\overline {JK} \cong \overline{MN}[/tex]
These all are corresponding parts of congruent triangles (c.p.c.t).
A paper airplane was thrown from the top of a tall building, The height of the paper airplane above the ground can be found using the function y= -1.5x+60, where x is the time in seconds the airplane has been in the air.
Answer:
How many seconds did it take the paper airplane to reach the ground?
40 Seconds.
Step-by-step explanation:
When the paper airplane touches the ground is equivalent to having a height equal to zero (y=0). So replacing in the equation:
[tex]y= -1.5x+60\\0= -1.5x+60\\1.5x=60\\x=\frac{60}{1.5} \\x=40[/tex]
The function y= -1.5x+60 describes the downward trajectory of a paper airplane. The '-1.5' represents the falling speed per second, and '+60' represents the initial height. To find the paper airplane's height at any time, substitute the time into the equation.
Explanation:The question deals with the concept of linear equations and gravity, a physics concept represented in mathematical terms. The function y= -1.5x+60 describes the trajectory of a paper airplane thrown from a building. This function means that the height y of the airplane above the ground, after x seconds, decreases by 1.5m each second, starting from an initial height of 60m.
The coefficient -1.5 represents the speed of the plane, which is downwards due to negative sign. After each second, the paper airplane will be 1.5 m lower than it was the previous second. The '+60' means the paper airplane was initially 60m off the ground.
To use this function for any given time (x), simply substitute the time into the equation. For example, for 5 seconds (x=5), the height y would be -1.5*5+60 = -7.5 + 60 = 52.5m
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What are the coordinates of the circumcenter of the triangle ?
Answer:
A=(-1,3)
B=(5,3)
C=(5,-5)
Step-by-step explanation:
Answer:
The answer to your question is (2, -1)
Step-by-step explanation:
1.- Find half points
AB
Between A and B there are 6 units, then the half point is three units from point A to the right
(2, 3)
BC
Between B and C there are 8 units, then the half point is four units below the point B.
(5, -1)
AC
Xm = -1 + 5 / 2 = 4 / 2 = 2
Ym = 3 - 5 / 2 = - 2 / 2 = - 1
(2, -1)
2.- Find the equations of the mediatrices
AB
x = 2 because the line must be perpendicuar to AB
BC
y = - 1 because the line must be perpendicular to BC
AC
slope m =[tex]\frac{-5 - 3}{5 + 1}[/tex]
m = [tex]\frac{-8}{6}[/tex]
m = [tex]\frac{-4}{3}[/tex]
mediatrix AC
y + 1 = -4/3 (x -2)
3y + 3 = -4x + 8
4x + 3y = 8 - 3
4x + 3y = 5
3.- Find the circumcenter
When x = 2
4(2) + 3y = 5
8 + 3y =5
3y = 5 - 8
3y = -3
y = -3/3
y = -1
When y = -1
4x + 3(-1) = 5
4x - 3 = 5
4x = 5 + 3
4x = 8
x = 8/4
x = 2
Circumcenter (2, -1)
The diameter of a cylindrical construction pipe is 5 ft. If the pipe is 21 ft long, what is its volume?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
412 ft³
Step-by-step explanation:
Diameter = 5 ft
Radius = D/2 = 5/2 = 2.5 ft
Volume of a Cylinder = 2πr²*h
Plug in values
2(3.14)(2.5)^2*21 = 412.33 ft^3
Volume of the pipe is 412 cubic feet rounded to nearest whole number.
The volume of the cylindrical construction pipe is 330 cubic feet.
To find the volume of a cylindrical construction pipe, we can use the formula:
Volume = π * [tex](radius)^2[/tex] * height
Given that the diameter is 5 ft, the radius of the pipe is half of the diameter, which is 2.5 ft.
The height of the pipe is given as 21 ft.
Plugging these values into the volume formula:
Volume = 3.14 *[tex](2.5)^2[/tex] * 21 = 330 ft³
Therefore, the volume of the cylindrical construction pipe is 330 cubic feet.
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The table shows the amount of money made by a summer blockbuster in each of its fi...
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If you all could help him, that would be great! Thanks mates!
that's cool I saw what you did your a nice friend lol
Answer:
dam it
Step-by-step eddqowd23r43tttt5xplanation:
You spend 15 minutes reading email. You then spend 3 hours watching television. Write the ratio of the amount of time spent reading email to the amount of time spent watching television as a fraction in simplest form. The ratio in simplest form is nothing.
The amount of time spent reading email to the amount of time spent watching television is 1/12
Step-by-step explanation:
Given
Time to read email = 15 minutes
Time on television = 3 hours = 3*60 minutes = 180 minutes
Ration is the fraction between two things. In this case, the ration is from the amount of time spent reading email to the amount of time spent watching television
So,
Required ratio will be: 15/180
Simplifying => 1/12
So,
The amount of time spent reading email to the amount of time spent watching television is 1/12
Keywords: Ratio, fractions
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Show that 6^3-1 is divisible by 5 using our identities
Answer:
Step-by-step explanation:
a³-b³=(a-b)(a²+ab+b²)
6³-1=6³-1³=(6-1)(6²+6*1+1²)=5×43
so 6³-1 is divisible by 5.
[tex]\displaystyle 6^3 - 1 = 216 - 1 = 215[/tex]
The number 215 is divisible by 5 because it ends in 5, according to the divisibility rules.
I am joyous to assist you anytime.
8.90 × 10^6 L has __ significant figures.
Answer:3 significant figures
Step-by-step explanation:got it right!!
Earches related to bus traveled at an average rate of 60 miles per hour and then reduced its average rate to 40 miles per hour for the rest of the trip. If the 288 dash mile trip took 6 hours, determine how long the bus traveled at each rate.
Answer: the bus traveled 144 miles at a speed of 60 miles per hour and 144 miles at a speed of 40 miles per hour
Step-by-step explanation:
The bus traveled at an average rate of 60 miles per hour and then reduced its average rate to 40 miles per hour for the rest of the trip.
Let x miles = distance travelled at 60 miles per hour.
Let y miles = distance travelled at 40 miles per hour.
Total distance travelled = 288 miles.
Therefore,
x + y = 288 - - - - - - - 1
Total time spent in travelling 288 miles = 6 hours
Speed = distance /time
Time = distance / speed
Time spent when travelling x miles at a speed of 60 miles per hour = x/60
Time spent when travelling y miles at a speed of 40 miles per hour = y/40
Since total time is 6 hours, this means that
x/60 + y/40 = 6
(2x + 3y)/120 = 6
2x + 3y = 6 × 120 = 720 - - - - - - - 2
Substituting x = 288-y from equation 1 into equation 2, it becomes
2(288-y) + 3y= 720
576 - 2y + 3y = 720
- 2y + 3y = 720 - 576
y = 144 miles
x = 288 - y = 288-144
x = 144 miles
A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 4.7 minutes and the standard deviation was 0.50 minutes.
(a) What fraction of the calls last between 4.7 and 5.5 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)Fraction of calls (b) What fraction of the calls last more than 5.5 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)Fraction of calls (c) What fraction of the calls last between 5.5 and 6 minutes? (Round z-score computation to 2 decimal places and final answer to 4 decimal places.)Fraction of calls
(d) What fraction of the calls last between 4 and 6 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)Fraction of calls (e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 3% of the calls. What is this time? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.)Duration
Answer:
a) 0.4452
b) 0.0548
c) 0.0501
d) 0.9145
e) 6.08 minutes or greater
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 4.7 minutes
Standard Deviation, σ = 0.50 minutes.
We are given that the distribution of length of the calls is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(calls last between 4.7 and 5.5 minutes)
[tex]P(4.7 \leq x \leq 5.5) = P(\displaystyle\frac{4.7 - 4.7}{0.50} \leq z \leq \displaystyle\frac{5.5-4.7}{0.50}) = P(0 \leq z \leq 1.6)\\\\= P(z \leq 1.6) - P(z <0)\\= 0.9452 - 0.5000 = 0.4452 = 44.52\%[/tex]
[tex]P(4.7 \leq x \leq 5.5) = 44.52\%[/tex]
b) P(calls last more than 5.5 minutes)
[tex]P(x > 5.5) = P(z > \displaystyle\frac{5.5-4.7}{0.50}) = P(z > 1.6)\\\\P( z > 1.6) = 1 - P(z \leq 1.6)[/tex]
Calculating the value from the standard normal table we have,
[tex]1 - 0.9452 = 0.0548 = 5.48\%\\P( x > 5.5) = 5.48\%[/tex]
c) P( calls last between 5.5 and 6 minutes)
[tex]P(4.7 \leq x \leq 5.5) = P(\displaystyle\frac{5.5 - 4.7}{0.50} \leq z \leq \displaystyle\frac{6-4.7}{0.50}) = P(1.6 \leq z \leq 2.6)\\\\= P(z \leq 2.6) - P(z <1.6)\\= 0.9953 - 0.9452 = 0.0501 = 5.01\%[/tex]
[tex]P(5.5 \leq x \leq 6) = 5.01\%[/tex]
d) P( calls last between 4 and 6 minutes)
[tex]P(4 \leq x \leq 6) = P(\displaystyle\frac{4 - 4.7}{0.50} \leq z \leq \displaystyle\frac{6-4.7}{0.50}) = P(-1.4 \leq z \leq 2.6)\\\\= P(z \leq 2.6) - P(z <-1.4)\\= 0.9953 - 0.0808 = 0.9145 = 91.45\%[/tex]
[tex]P(4 \leq x \leq 6) = 91.45\%[/tex]
e) We have to find the value of x such that the probability is 0.03.
P(X > x)
[tex]P( X > x) = P( z > \displaystyle\frac{x - 4.7}{0.50})=0.03[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 4.7}{0.50})=0.03 [/tex]
[tex]=P( z \leq \displaystyle\frac{x - 4.7}{0.50})=0.997 [/tex]
Calculation the value from standard normal z table, we have,
P(z < 2.75) = 0.997
[tex]\displaystyle\frac{x - 4.7}{0.50} = 2.75\\x = 6.075 \approx 6.08[/tex]
Hence, the call lengths must be 6.08 minutes or greater for them to lie in the highest 3%.
The fraction of calls that last between 4.7 and 5.5 minutes is 0.4452, the fraction of calls that last more than 5.5 minutes is 0.0548, the fraction of calls that last between 5.5 and 6 minutes is 0.0501, the fraction of calls that last between 4 and 6 minutes is 0.9145, and the length of the longest 3% of the calls is 5.85 minutes.
Explanation:To solve this problem, we can use the standard normal distribution table by converting the given values into z-scores. The z-score formula is: z = (x - μ) / σ where x is the given value, μ is the mean, and σ is the standard deviation. Let's calculate the fractions for each part of the question:
(a) Between 4.7 and 5.5 minutes:
Calculate the z-score for 4.7 minutes: z = (4.7 - 4.7) / 0.5 = 0Calculate the z-score for 5.5 minutes: z = (5.5 - 4.7) / 0.5 = 1.6Use the z-score table to find the area to the left of 1.6: 0.9452Subtract the area to the left of 0 from the area to the left of 1.6: 0.9452 - 0.5 = 0.4452(b) More than 5.5 minutes:
Calculate the z-score for 5.5 minutes: z = (5.5 - 4.7) / 0.5 = 1.6Find the area to the left of 1.6 using the z-score table: 0.9452Subtract the area to the left of 1.6 from 1: 1 - 0.9452 = 0.0548(c) Between 5.5 and 6 minutes:
Calculate the z-score for 5.5 minutes: z = (5.5 - 4.7) / 0.5 = 1.6Calculate the z-score for 6 minutes: z = (6 - 4.7) / 0.5 = 2.6Find the area to the left of 1.6 using the z-score table: 0.9452Find the area to the left of 2.6 using the z-score table: 0.9953Subtract the area to the left of 1.6 from the area to the left of 2.6: 0.9953 - 0.9452 = 0.0501(d) Between 4 and 6 minutes:
Calculate the z-score for 4 minutes: z = (4 - 4.7) / 0.5 = -1.4Calculate the z-score for 6 minutes: z = (6 - 4.7) / 0.5 = 2.6Find the area to the left of -1.4 using the z-score table: 0.0808Find the area to the left of 2.6 using the z-score table: 0.9953Subtract the area to the left of -1.4 from the area to the left of 2.6: 0.9953 - 0.0808 = 0.9145(e) The longest 3% of the calls:
Find the z-score for an area of 0.97 using the z-score table: 1.88Use the z-score formula to find the time value: x = z * σ + μSubstitute z = 1.88, σ = 0.5, μ = 4.7 into the formula: x = 1.88 * 0.5 + 4.7 = 5.85So, the time for the longest 3% of the calls is 5.85 minutes.
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Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 22.1 in. and a standard deviation of sigma equals 1.2 in. These data are often used in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater)less than or equals0.01 and a value is significantly low if P(x or less)less than or equals0.01. Find the back-to-knee lengths separating significant values from those that are not significant. Using these criteria, is a back-to-knee length of 24.2 in. significantly high?
In a normal distribution, the back-to-knee lengths that separate significant values from others are 24.896 inches (upper percentile) and 19.304 inches (lower percentile) respectively. Using these limits, a back-to-knee length of 24.2 inches is not considered significantly high.
Explanation:To find the back-to-knee lengths that separate significant values from those that are not, we need to find the values of x for which P(x ≥ some value) ≤ 0.01, and P(x ≤ some value) ≤ 0.01.
These values are known as the upper and lower percentiles, respectively, and can be obtained by transforming to a standard normal distribution (with a mean of 0 and a standard deviation of 1) using z-scores.
Let's use the standard normal table to find z-scores corresponding to 0.01 in the upper side and lower side of the distribution. You would find that the z-score which has an area of 0.01 in the upper tail is approximately 2.33, and in the lower tail it is -2.33.
Now, we can use these z-scores to calculate respective back-to-knee lengths. The formula for a z-score is z = (x - μ) / σ, where μ is the mean, σ is the standard deviation, and x is the observation. Solving for x gives us x = zσ + μ.
Upper percentile, x = (2.33*1.2) + 22.1 = 24.896 inches.
Lower percentile, x = (-2.33*1.2) + 22.1 = 19.304 inches.
So, any back-to-knee length above 24.896 inches or below 19.304 inches can be considered statistically significant. Therefore, a back-to-knee length of 24.2 inches would not be considered significantly high as it is less than 24.896 inches.
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In order to find the separating lengths for significant values in a normal distribution, we need to find the values corresponding to z-scores for probabilities 0.01 and 0.99. To know if a back-to-knee length of 24.2 in. is significantly high, compare the probability P(X>=24.2) with 0.01.
Explanation:In the problem presented, the information is about the normal distribution of the back-to-knee length of a group of adults. A normal distribution graph has its highest point at the mean, which in this case is 22.1 in., and it decrease on either side. The standard deviation, which measures the spread of the values, is given as 1.2 in.
For a value to be considered significantly high, the probability P(x or higher) should be less than or equal to 0.01. Similarly, for a value to be significantly low, P(x or lower) should also be less or equal to 0.01.
To find the back-to-knee lengths separating the significant values from non-significant, one can use the z-scores associated with the probabilities 0.01 and 0.99 (since the total probability of a normal distribution is 1). So, the lengths in question will be the ones that correspond to these z-scores.
Provided, a z-score is a value's number of standard deviations from the mean. If z is the z-score, μ is the mean, σ is the standard deviation, and x is the value, the formula is z=(x-μ)/σ.
Regarding the specific measurement of 24.2 in., we would need to calculate the probability P(X>=24.2) using the given mean and standard deviation in Z-score formula. If P(X>=24.2) is less than 0.01, then 24.2 in. can be considered as significantly high.
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For a continuous random variable x, the height of the function at x is a. 0.50, since it is the middle value. b. a value less than zero. c. the probability at a given value of x. d. named the probability density function f(x).
Answer:
Answer is a continuous random variable x the height of the function named the probability density function f(x)
Step-by-step explanation:
A continuous random variable takes infinite number of possible values.
example include height , weight amount of sugar in an orange time required to run a mile.
Continues random variable named probability function f(x).
The height of a function at a certain value of x in the case of a continuous random variable represents the probability density at that point, not the actual probability. The area under the curve of the function between two points gives the actual probability that x falls between those points. The total probability (the total area under the curve) is always 1.
Explanation:For a continuous random variable x, the height of the function at a certain value of x is named the probability density function f(x) which describes the probabilities for continuous random variables. The value does not represent a direct probability but the density of probability around that point, and the area under the curve between two given points gives the probability that x would fall between those points. This is represented by the notation P(c < x < d), where c and d are the boundaries of the interval.
It is essential to note that for any specific value of a continuous random variable, the probability is always 0, represented as P( x = c )= 0, which means the height of the function at a particular x does not represent the exact probability at that point but just the density.
The total probability of a continuous random function is always 1, thus, the total area under the probability density function curve equals one. And the value of the function at any given point can be less or greater than 1 given the function's shape and range.
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A new Firestone tire is guaranteed to last for 40,000 miles. The actual mean life of the tires is 47,000 miles with a standard deviation of 4,000 miles.
a) What percent of the tires will last for at least 40,000 miles?
b) What percent of the tires will not last for at least 40,000 miles?
c) What is the probability that a tire will last for more than 50,000 miles?
d) The Firestone Company wants to advertise how long some of their tires last. They decide to state how long the top 3% of their tires will last. How many miles will the top 3% of their tires last?
Answer:
a) 95.99%
b) 4.01%
c) 00.62%
Step-by-step explanation:
Explanation is given in the attachments.
A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 36 grams. Write an exponential equation f(t) representing this situation. (Let f be the amount of radioactive substance in grams and t be the time in minutes.)
Answer:
f(t) = 250[tex]e^{-0.007752t}[/tex]
Step-by-step explanation:
Let f(t) = [tex]\alpha[/tex][tex]e^{\beta t }[/tex]
where f is the amount of radioactive substance in grams
and t is the time in minutes
initially (at t=0), f = 250 grams
⇒f(0) = 250 grams
⇒[tex]\alpha[/tex][tex]e^{0\beta}[/tex] = 250
⇒[tex]\alpha[/tex][tex]e^{0}[/tex] = 250
⇒[tex]\alpha[/tex] = 250 grams {∵[tex]e^{0} = 1[/tex]}
⇒f(t) = 250[tex]e^{\beta t }[/tex]
At t = 250 minutes, f = 36 grams
⇒f(250) = 36 grams
⇒250[tex]e^{250\beta}[/tex] = 36
⇒[tex]e^{250\beta}[/tex] = [tex]\frac{36}{250}[/tex] = 0.144
⇒250[tex]\beta[/tex] = ㏑ 0.144 = -1.938
⇒[tex]\beta[/tex] = -[tex]\frac{1.938}{250}[/tex] = -0.007752 [tex]min^{-1}[/tex]
∴f(t) = 250[tex]e^{-0.007752t}[/tex]
The pH of solution A is 2.4, while the pH of solution B is 9.4.
(a) What are their hydrogen-ion concentrations?
(b) How many times greater is the hydrogen-ion concentration of solution A than that of solution B?
(c) By how many orders of magnitude do the concentrations differ?
Answer:
The answer to your question is below
Step-by-step explanation:
pH definition
pH = - log [H⁺]
a) For pH = 2.4, solution A
2.4 = -log[H⁺]
[H⁺] = antilog⁻².⁴
[H⁺] = 0.00398
For pH = 9.4, solution B
[H⁺] = antilog⁻⁹.⁴
[H⁺] = 3.98 x 10⁻¹⁰
b) Divide hydrogen-ion concentration of solution A by hydrogen-ion concentration of solution B.
0.00398 / 3.98 x 10⁻¹⁰
10000000 times
c) By 7, because 7 is the number of zeros
A local news agency conducted a survey about unemployment by randomly dialing phone numbers until they had gathered responses from 1000 adults in their state. In the survey, 19% of those who responded said they were not currently employed. In reality, only 6% of the adults in the state were not currently employed at the time of the survey. Which of the following best explains the difference in the two percentages?
(a) The difference is due to sampling variability. We shouldn't expect the results of a random sample to match the truth about the population every time.
(b) The difference is due to response bias. Adults who are employed are likely to lie and say that they are unemployed.
(c) The difference is due to undercoverage bias. The survey included only adults and did not include teenagers who are eligible to work.
(d) The difference is due to nonresponse bias. Adults who are employed are less likely to be available for the sample than adults who are unemployed.
(e) The difference is due to voluntary response. Adults are able to volunteer as a member of the sample.
Answer:
Option d is right
Step-by-step explanation:
Given that a local news agency conducted a survey about unemployment by randomly dialing phone numbers until they had gathered responses from 1000 adults in their state. In the survey, 19% of those who responded said they were not currently employed. In reality, only 6% of the adults in the state were not currently employed at the time of the survey.
The reason more approporiate woul dbe
(d) The difference is due to nonresponse bias. Adults who are employed are less likely to be available for the sample than adults who are unemployed.
would be the correct option.
Adults who are employed will lie is absurd may be reverse true. Since survey done for adults, eligible teenagers also included. Voluntary response is also wrong as given 1000 persons selected.
The difference in percentages is due to sampling variability. Random sampling may not perfectly represent the population, resulting in differences in the percentages.
Explanation:The difference in percentages is best explained by (a) sampling variability. When conducting a survey, it is expected that there will be some variability between the sample results and the true population values. Even with random sampling, there is a chance that the sample may not perfectly represent the entire population. In this case, the survey respondents may not be an accurate reflection of the overall population, resulting in a difference in the percentages.
For example, if the survey happened to include a higher proportion of unemployed individuals in the sample, the percentage of unemployed respondents would be higher than the true population percentage.
Sampling variability is common in statistics and can be mitigated by increasing the sample size to reduce the margin of error.
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Marcella burgess deposited $15000 for two months in a money market account that pays simple interest for the first moth marcella earned 3.87 annual interest she earned 3.47 annual interest for the second month interest is not compounded what total interest did marcella earn in two months
Answer:
$91.76
Step-by-step explanation:
Interest the first month was ...
I = Prt
I = $15000(0.0387)(1/12) = $48.375 ≈ $48.38
Interest in the second month was ...
I = $15000(0.0347)(1/12) = $43.375 ≈ $43.38
So the total interest amount is ...
$48.38 +43.38 = $91.76
Marcella earned $91.76 in two months.
_____
Comment on rounding
We have assumed that Marcella's account statement will report the interest rounded to 2 decimal places (cents). Hence she obtains the benefit from rounding for both months.
If there is no statement, so that rounding is not required until the end of the second month, then she may not have that extra penny in her account.