The probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.
What is probability ?
Probability cam be defined as ratio of number of favorable outcomes, total number of outcomes
We can solve this problem by using the central limit theorem. According to the theorem, if we have a large enough sample size, the distribution of sample means will be approximately normal, regardless of the underlying distribution of the population.
The mean of the sample means will be equal to the population mean, and the standard deviation of the sample means (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a sample size of 20, which is not very large, but we can still use the central limit theorem as an approximation. The population mean is 48 minutes, and the population standard deviation is 15 minutes. The standard error of the sample mean is:
SE = σ / sqrt(n) = 15 / sqrt(20) = 3.354
To find the probability that the mean completion time for the sample is greater than 60 minutes, we need to standardize the sample mean using the formula:
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error of the sample mean.
Plugging in the values, we get:
z = (60 - 48) / 3.354 = 3.57
We can now look up the probability of getting a z-score greater than 3.57 in a standard normal distribution table (or use a calculator). The probability turns out to be very small, approximately 0.0002 or 0.02%.
Therefore, the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.
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Find X correct to 2 decimal places.
NOTE: The triangle is NOT drawn to scale.
The length of the side 'х' is 79.20 units to two decimal places.
What is angle?Angle is a two-dimensional figure that is formed by two straight lines intersecting each other. It can also be defined as the amount of rotation between two lines or planes. An angle is measured in degrees, with a full rotation being 360°.
The given triangle is a right-angled triangle as it has an angle of 64° which is a right angle. The angle 35° and 113 are the other two angles of the triangle. To find the length of the side 'х', we need to use the Pythagorean Theorem. The Pythagorean Theorem states that "the square of the hypotenuse is equal to the sum of the squares of the other two sides".
In this case, the hypotenuse is 113, and the other two sides are 'х' and the perpendicular side opposite to the angle of 35°. Therefore, using the Pythagorean Theorem, we can say:
113² = х² + (perpendicular side)²
Using the trigonometric ratio sine, we can calculate the length of the perpendicular side opposite to the angle 35°, which is equal to the sine of 35° multiplied by the hypotenuse.
(perpendicular side) = sin 35° × 113
Therefore, the equation for the triangle now becomes:
113² = х² + (sin 35° × 113)²
Simplifying the equation and solving for 'х' gives us:
х² = 113² - (sin 35° × 113)²
х = √(113² - (sin 35° × 113)²)
Finally, substituting the values, we get:
х = √(113² - (sin 35° ×113)²)
= √(12,841 - (0.5736 × 113)²)
= √(12,841 - 6,539.7808)
= √6,301.2192
= 79.20
Therefore, the length of the side 'х' is 79.20 units to two decimal places.
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7. From the observation deck of a skyscraper, Matthew
measures a 45° angle of depression to a ship in the harbor
below. If the observation deck is 1053 feet high, what is
the horizontal distance from the base of the skyscraper out
to the ship? Round your answer to the nearest tenth of a
foot if necessary.
The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.
What are the trigonometric ratios?Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slanted side is called the hypotenuse.
Let d the horizontal distance from the base of the skyscraper out to the ship. Since the angle of depression is 45°, hence:
[tex]\text{Angle} = 90 - 45 = 45^o[/tex]
Using trigonometric ratio:
[tex]tan(45) = \dfrac{d}{1053}[/tex]
[tex]d = 1053\ \text{feet}[/tex]
The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.
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The scheme that you thought of is to start saving 10% of your allowance in the first week of every month, then add 10% more every week for the 3 weeks. And the cycle goes on for 12 months of a year. If you're weekly allowance is 500, how much will you be able to earn after a year? Show your computation here
Using percentage concept, we would have saved 2784.6 dollars after a year
How much is saved at the end of the yearTo calculate how much you will have saved after a year, we can break down the savings for each week of each month, and then add up the total. Here's how it works:
We can use percentage to calculate how much is saved each week
In the first week of each month, you save 10% of your weekly allowance, which is 10 percent of 500 = 50 dollars.
In the second week of each month, you save 10% more than the previous week, which is 10% of (500 + 50) = 55 dollars.
In the third week of each month, you save 10% more than the previous week, which is 10% of (500 + 50 + 55) = 60.5 dollars.
In the fourth week of each month, you save 10% more than the previous week, which is 10% of (500 + 50 + 55 + 60.5) = 66.55 dollars.
So in total, you save 50 + 55 + 60.5 + 66.55 = 232.05 dollars per month.
Over the course of a year, you will have saved 232.05 dollars per month * 12 months = 2784.6 dollars.
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What is the shape of each cut surface? What are its dimensions?
Answer:
1. The shape of each cut surface is the same shape as the base it is parallel to: a rectangle. It is an 8" by 10" rectangle
Step-by-step explanation:
The coefficient of variation for a poisson distribution with A=5 is
The coefficient of variation for a Poisson distribution with A=5 is equal to 1/A, which is equal to 0.2.
What is Poisson distribution?Poisson Distribution is a type of probability distribution used for independent events which occur at a known average rate within a given interval of time or space. It is used to model the number of times an event is likely to occur within a specified period of time or space. It is used in fields such as healthcare, quality control, finance, and engineering.
Coefficient of variation (CV) is a measure of relative variability or dispersion. It is a measure of the relative dispersion of a set of data points around its mean. It is calculated by dividing the standard deviation of the data points by the mean.
The coefficient of variation for a Poisson distribution with A=5 is equal to 1/A, which is equal to 0.2. This means that the relative variability of a Poisson distribution with A=5 is 0.2. This is because the standard deviation of a Poisson distribution is equal to the square root of the mean, and in this case, the mean is 5. Therefore, the standard deviation is the square root of 5, or 2.236. When divided by the mean, the coefficient of variation is 0.2.
In general, the coefficient of variation is used to compare the variability of two different datasets. A low coefficient of variation indicates that the data points are relatively close to the mean and that there is not much variability in the data. A high coefficient of variation indicates that the data points are further away from the mean and that there is a greater amount of variability in the data.
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Lin says that 4÷3/4 equals 5 1/4 because there are five groups of 3/4 and 1/4 left. Do you agree with Lin?
The result is 5 1/3, not 5 1/4 as Lin suggested.
No, I don't agree with Lin's statement. Lin's explanation is incorrect.
When evaluating the expression 4 ÷ (3/4), we need to remember the order of operations, which states that we should perform the division before the multiplication.
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Therefore:
4 ÷ (3/4) = 4 * (4/3)
Now we can simplify the expression:
4 * (4/3) = (4 * 4) / 3 = 16 / 3
The result, 16/3, is an improper fraction. To convert it to a mixed number (a whole number and a fraction), we divide the numerator (16) by the denominator (3):
16 ÷ 3 = 5 with a remainder of 1
The quotient is 5, and the remainder is 1. Therefore, the result is 5 1/3, not 5 1/4 as Lin suggested.
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which reason justifies
Laars earns an annual salary of $90,000. Determine his gross earnings per pay period under each of the following payment frequencies: a. Monthly b. Semi-monthly c. Biweekly d. Weekly
Answer:
To determine Laars' gross earnings per pay period under different payment frequencies, we need to divide his annual salary of $90,000 by the number of pay periods in a year for each frequency.
a. Monthly: Laars will receive 12 paychecks per year, one per month.
Gross earnings per pay period = $90,000 / 12 = $7,500 per month
b. Semi-monthly: Laars will receive 24 paychecks per year, two per month.
Gross earnings per pay period = $90,000 / 24 = $3,750 per semi-monthly period (twice per month)
c. Biweekly: Laars will receive 26 paychecks per year, one every two weeks.
Gross earnings per pay period = $90,000 / 26 = $3,461.54 per biweekly period (every two weeks)
d. Weekly: Laars will receive 52 paychecks per year, one per week.
Gross earnings per pay period = $90,000 / 52 = $1,730.77 per weekly period (every week)
Therefore, Laars' gross earnings per pay period are $7,500 per month, $3,750 per semi-monthly period, $3,461.54 per biweekly period, and $1,730.77 per weekly period.
Select the expression that results in a rational number.
Answer:
The answer is A
Step-by-step explanation:
thats all
A recipe calls for 2 cups of peanuts for 3 cups of flour. Using the same recipe, how many cups of flour will you need for 5 cups of peanuts?
A triangle has a base of 8 cm and a height of 12 cm.
What is the area of the triangle?
________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
(No picture of the question was given)
________________________________
Answer:
A = 48 cm²
Step-by-step explanation:
A = (1/2)bh
A = (1/2)(8 cm)(12 cm)
A = 48 cm²
Answer:
48cm^2
Step-by-step explanation:
8×12=96
96÷2=48cm^2
Can someone help me solve this
Answer:
2520
because we need to multiply all the lengths to take out volume of piramid
When Silvia feeds her cat, she places food in
3 different locations. She wondered if her cat was equally likely to eat first from each of the locations, so she tallied which location her cat chose first in a sample of
30 feedings. Here are the results along with a chi-square goodness-of-fit test:
-------------------------kitchen-----bedroom-----Living room
Hypothesized:-----0.333--------0.333---------0.333
Observed-----------13--------------13--------------4
Expected------------10--------------10-------------10
Components-------0.9------------0.9------------3.6
chi-squared statistic = 5.4, df = 2
p-value =0.067
Assume that all conditions for inference were met.
At the 0.05 significance level, what should Silvia conclude about her cat's feeding preferences?
A: There is sufficient evidence to conclude that her cat prefers to eat first from some locations more than others.
B: There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others.
C: There is sufficient evidence to conclude that her cat is equally likely to eat first from each of the locations.
D: No conclusions can be made from this test, because one of the observed counts is too low for the calculations to be accurate.
for my khan bros (ignore this part):
When Silvia feeds her cat, she places food in
3
33 different locations. She wondered if her cat was equally likely to eat first from each of the locations, so she tallied which location her cat chose first in a sample of
30
3030 feedings. Here are the results along with a chi-square goodness-of-fit test:
Location Kitchen Bedroom Living room
Hypothesized
0.333
0.3330, point, 333
0.333
0.3330, point, 333
0.333
0.3330, point, 333
Observed
13
1313
13
1313
4
44
Expected
10
1010
10
1010
10
1010
Components
0.9
0.90, point, 9
0.9
0.90, point, 9
3.6
3.63, point, 6
�
2
=
5.4
,
DF
=
2
χ
2
=5.4, DF=2\chi, squared, equals, 5, point, 4, comma, start text, space, D, F, end text, equals, 2
P-value
=
0.067
P-value=0.067start text, P, negative, v, a, l, u, e, end text, equals, 0, point, 067
Assume that all conditions for inference were met.
At the
�
=
0.05
α=0.05alpha, equals, 0, point, 05 significance level, what should Silvia conclude about her cat's feeding preferences?
Choose 1 answer:
Choose 1 answer:
B .The results of the chi-square goodness-of-fit test, with a chi-squared statistic of 5.4 and a p-value of 0.067, Silvia cannot reject the null hypothesis that her cat is equally likely to eat first from each of the three locations at the 0.05 significance level.
Therefore, the correct answer is B: There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others. It is important to note that while the p-value is relatively close to the significance level of 0.05, it does not meet the threshold for statistical significance, and the sample size may not be large enough to draw definitive conclusions about the cat's feeding preferences.
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Answer: There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others.
Step-by-step explanation: Since the P-value is greater than the significance level, we can't reject the null hypothesis. In this context, the null hypothesis is that cat is equally likely to choose each of the locations. (Got it right on Khan academy)
Please help me Geometric Sequences
Which is the bette buy 3 pints of
at $3.60 or 6 pints are all at $8.10
Answer:
It is better to buy 6 pints at $8.10
Step-by-step explanation:
To compare the cost per pint in each option, we can divide the total cost by the total number of pints.
For the first option, buying 3 pints at $3.60, the cost per pint is shown by the following:
3 pints ÷ $3.60 = $0.83 / pint
For the second option, buying 6 pints at $8.10, the cost per pint is shown by the following:
6 pints ÷ $8.10 = $0.74 / pint
Therefore, buying 6 pints at $8.10 is less expensive per pint than buying 3 pints at $3.60. Each pint when buying 3 at a time costs $0.83 whereas each pint when buying 6 at a time costs $0.74.
Choose True or False for each statement.
a. The numbers 0.3 and 0.3. . . are equal to the same fraction.
b. The number 0.111000111000 . . . is a repeating decimal.
c. The fraction 1/9 is equal to a repeating decimal.
d. The fraction 2/11 is equal to 0.1818 . . . .
Answer:
a. True. Both 0.3 and 0.3... represent the decimal expansion of one-third, which is equivalent to the fraction 1/3.
b. True. The number 0.111000111000... is a repeating decimal, with a repeating block of three digits (111) that starts repeating from the fourth decimal place.
c. True. The fraction 1/9 is equal to the repeating decimal 0.1111..., where the digit 1 repeats infinitely.
d. True. To convert the fraction 2/11 to a decimal, we can perform long division. We get a repeating decimal expansion of 0.181818... where the digits 18 repeat infinitely. Therefore, the statement is true.
Step-by-step explanation:
is -2-3=-2+-3 justify your answer
Answer:
- 2 - 3 is the same thing as -2 + -3. This is because taking away 3 is the same thing as adding - 3. -2 -3 is just a more simplified version of -2 + -3.
Hope this helps!
please help me I need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
reflection around the y-axis
Step-by-step explanation:
you really don't see that the picture just flipped from left to right and vice versa (around a central vertical mirror line through the black center dot) ?
to make it simple I just declare this line to be the y-axis.
A neighborhood group goes to the movies every Saturday night. Last week, they purchased 29 adult tickets and 17 youth tickets for $254. This week they purchased 21 adult tickets and 22 youth tickets for $213. Find the cost of one adult ticket.
The cost of one adult ticket is $7.
What is the cost of one adult ticket?The first step is to set up a pair of linear equations that represent the information in the question.
29a + 17y = 254 equation 1
21a + 22y = 213 equation 2
Where:
a = cost of one adult tickety = cost of one youth ticketThe elimination method would be used to solve the equations
Multiply equation 1 by 22:
638a + 374y = 5588 equation 3
Multiply equation 2 by 17:
357a + 374y = 3621 equation 4
Subtract equation 4 from equation 3
1967 = 281a
Divide both sides of the equation by 281
1967 / 281 = a
a = 7
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Please help me Graph this in a line graph(economics)
The Pound to Australian Dollar (GBP/AUD) exchange rate has been going up besides the drop in UK business optimism. The CBI business optimism index dropped from 0 to -22 in the first quarter, which shows the negative impact of the recent lockdown. However, this had been changed by the idea of greater US fiscal stimulus measures and the global economic outlook improving. On the other hand, the Australian Dollar (AUD) struggled to find support despite the December unemployment rate decreasing from 6.8% to 6.6%. This shows that the labor market remains elevated by previous trends, weighing on AUD exchange rates. The retail sales trends for December is expected to show a -2.5% monthly contraction, signaling a continued impact of Covid-19. The UK PMIs could also have an impact on the GBP/AUD exchange rate, with signs of the UK economy likely to limit any potential gains.
The correct answer is interval 2. A function is a rule that relates each element in one set, called the domain, to exactly one element in another set, called the range.
What is function?It is a mathematical expression that takes an input, performs a calculation and produces an output.
In order to determine if dy/dx>0 and d2y/dx2<0 over interval 2, we must take the first and second derivatives of the function y=f(x). The first derivative of the function is dy/dx=2x-3 and the second derivative of the function is d2y/dx2=2.
Now, if we look at the graph, we can see that the function is increasing from 0 to 3 and then decreasing from 3 to 6. This means that over interval 2, which is from 3 to 6, the first derivative, dy/dx, must be negative. This means that dy/dx<0 over interval 2.
Furthermore, the second derivative, d2y/dx2, must be negative over interval 2 since the graph is decreasing over this interval. This means that d2y/dx2<0 over interval 2.
Therefore, the correct answer is interval 2 since it is the only interval for which both dy/dx>0 and d2y/dx2<0 are true.
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how can you help me understand is .0362 less than .05
Answer: Please refer to the step by step explanation :)
Step-by-step explanation:
To understand how .0362 is less than .05, let’s pretend the 6 and the 2 don’t exist for right now. So, now we have .03 and .05. Since three is a lesser number than five, this has to mean .03 is less than .05. Reapplying the 6 and 2, .0362 must be less than .05.
The graph shows the relationship between time and
distance for Mason's training run.
The graph represents a proportional relation
The unit rate is 200The unit rate represents a speed of 200 metersminDoes the graph represent a proportional relationFrom the question, we have the following parameters that can be used in our computation:
The graph
We can see that the lines pass through the origin
This means that the graph is a proportional relationship
The unit rate of the relationFrom the graph. we have
(x, y) = (2, 400)
So, the unit rate is
Rate = 400/2
Rate = 200
What the unit rate representsThe interpretation of this is that Mason's speed is 200 meters per minute
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Find the Pearson correlation coefficient r for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
(1,6),(2,10),(3,4),(4,4),(5,8),(6,2),(7,2)
In response to the query, we can state that Therefore, the Pearson correlation coefficient r for the given points is approximately -0.758.
what is correlation?The relationships between various variables are described by correlations. Expressions might be strong, weak, positive, or negative. 1 = Correlation does not always imply causation. Correlation is a statistical indicator of the linear relationship between two variables (that is, do they change at a constant rate).
1 6 -3 1 9 1 -3
Σx = 28
Σy = 36
n = 7
Therefore, the correlation coefficient r for the given points is approximately -0.758.
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*Brady has a bankruptcy on his credit report, so he pays higher interest rates on his current loans. He calculates that the extra money he pays in additional interest each year, if invested at the rate of 3% for one year, could earn him simple interest totaling $210. How much does Brady pay in additional interest each month?
Hint: Use the simple interest formula I=P*r*t where P is principal amount, r is rate, and t is time. In this case, for Brady I is the simple interest $210, P is what you are trying to find, r is the rate of 3% (make sure to convert to decimal), and t is time in years, 1 year.
After you find P, divide it by 12 and that is your answer. Round it to the nearest cent.
Brady pays an additiοnal interest οf $583.33 each mοnth.
What is the interest?Tο calculate simple interest, multiply the principal amοunt by the interest rate and the time. The fοrmula written οut is "Simple Interest = Principal x Interest Rate x Time." This equatiοn is the simplest way οf calculating interest.
Let x be the additiοnal interest Brady pays each mοnth.
Since there are 12 mοnths in a year, the tοtal additiοnal interest he pays in a year is 12x.
Accοrding tο the prοblem, if Brady invests this additiοnal interest at the rate οf 3% fοr οne year, he will earn $210 in simple interest. Using the simple interest fοrmula, we have:
I = Prt
210 = 12x0.031
Simplifying this equatiοn, we get:
210 = 0.36x
Dividing bοth sides by 0.36, we get:
x = $583.33
Therefοre, Brady pays an additiοnal interest οf $583.33 each mοnth.
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PLEASE HELP!!! ASAP, THANK U
Which system of equations has the solution (4, -3)
A. y = -2x + 5 and x + y = 1
B. y = 2x - 5 and x - y = 1
C. y = -5x + 2 and 2x + y = 2
D. y = 5x - 2 and 2y - x = 2
Answer:
A.Y=-2x+5 and x+y=1 is the system of equation has the solution.i am sorry if iam wrong.
A(-4,-6) and B (3,2) find midpoint of AB
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 3 -4}{2}~~~ ,~~~ \cfrac{ 2 -6}{2} \right) \implies \left(\cfrac{ -1 }{2}~~~ ,~~~ \cfrac{ -4 }{2} \right)\implies \left(-\frac{1}{2}~~,~~-2 \right)[/tex]
solve:
f(x)=3x^2-2x+4
x=2
Answer:
to find f(2), we need to substitute x=2 into the equation:
f(2) = 3(2)^2 - 2(2) + 4
Simplifying:
f(2) = 3(4) - 4 + 4
f(2) = 12
Therefore, f(2) = 12.
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]f(2) = (3)(2^2) - 2(2) +4[/tex]
[tex]= 12 - 4+ 4[/tex]
[tex]= 12[/tex]
This is not a math question, but can someone please tell me how to put my questions in the high school section instead of the college one?
Answer:
it should give you the option right before you post the answer, what subjectand grade level
Step-by-step explanation:
Evaluate 11.1x + 10.7y when x = 7 and y = 8 11.1) + 10.7 +85.6
Answer:
To evaluate 11.1x + 10.7y when x = 7 and y = 8, we simply substitute these values into the expression and simplify:
11.1(7) + 10.7(8) = 77.7 + 85.6 = 163.3
Therefore, 11.1x + 10.7y evaluates to 163.3 when x = 7 and y = 8.
Step-by-step explanation: