Answer: Density = 1,282.26 kg/m^3
Step-by-step explanation:
Density = 80 lb/ft^3
We know that:
1lb = 0.4536 kg.
1ft^3 = 0.0283 m^3
then we can write:
1 = (0.4536kg)/(0.0283 m^3)*(1ft^3/lb)
we can multiply our equation by this, and it wont be affected, then we have:
Density = 80 lb/ft^3 = 80 lb/ft^3 (0.4536kg)/(0.0283 m^3)*(1ft^3/lb)
Density = 1,282.26 kg/m^3
Amanda is constructing equilateral triangle JKL inscribed in circle M. To construct the inscribed polygon, she is going to use a compass to partition the circle into congruent arcs. To what width should she set the compass when partitioning the circle? A. The width must be equal to the radius of circle M. B. The width must be equal the diameter of circle M. C. The width can be equal to either the radius or the diameter of circle M. D. The width can be any size greater than the radius but less than the diameter of circle M. E. The width must be less than the radius of circle M. help meee please!!!!!!!!!!!!!!!!!
Given:
An equilateral triangle JKL inscribed in circle M.
Solution:
To draw an equilateral triangle inscribed in circle follow the steps:
1: Draw a circle with any radius.
2. Take any point A, anywhere on the circumference of the circle.
3. Place the compass on point A, and swing a small arc crossing the circumference of the circle.
Remember the span of the compass should be the same as the radius of the circle.
4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.
5. Repeat this process until you return to point A.
6. Join the intersecting points on the circle to form the equilateral triangle.
So the correct option is A. The width must be equal to the radius of circle M.
Still timed. More math needing help with, i'll double points and mark brainliest! 1. (y - 6) (y + 3) 2. (4x - 5) (x - 7) 3.(3x - 2) ( 4x - 1)
Answer:
1. y² - 3x - 18
2. 4x² - 33x + 35
3. 12x² - 11x + 2
Step-by-step explanation:
All we do with these questions are expanding the factored binomials. Use FOIL:
1. y² + 3y - 6y - 18
y² - 3y - 18
2. 4x² - 28x - 5x + 35
4x² - 33x + 35
3. 12x² - 3x - 8x + 2
12x² - 11x + 2
Answer:
1) (y-6) (y+3)
=> [tex]y^2+3y-6y-18[/tex]
=> [tex]y^2-3y-18[/tex]
2) (4x-5) (x-7)
=> [tex]4x^2-28x-5x+35[/tex]
=> [tex]4x^2-33x+35[/tex]
3) (3x - 2) ( 4x - 1)
=> [tex]12x^2-3x-8x+3[/tex]
=> [tex]12x^2-11x+3[/tex]
Can somebody help me with this question
The scientist performs additional analyses and observes that the number of major earthquakes does appear to be decreasing but wonders whether the relationship is statistically significant. Based on the partial regression output below and a 5% significance level, is the year statistically significant in determining the number of earthquakes above magnitude 7.0?Dependent Variable: Earthquakes above Magnitude 7.0 Coefficients Standard t Stat P-value Lower 95% Upper 95% ErrorIntercept 64.67 38.08 4.32 89.22 240.12Year -0.07 0.02 -3.82 -0.11 -0.04
Answer:
Step-by-step explanation:
Hello!
A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.
^Y= 164.67 - 0.07Xi
Y: earthquake above magnitude 7.0
X: year
The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0
The hypotheses are:
H₀: β = 0
H₁: β ≠ 0
α: 0.05
The statistic for this test is a student's t: [tex]t= \frac{b - \beta }{Sb} ~~t_{n-2}[/tex]
The calculated value is in the regression output [tex]t_{H_0}= -3.82[/tex]
This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.
The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:
p-value: [tex]P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq 3.82)[/tex]
As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.
If you want to use the rejection region approach, the sample size is also needed to determine the critical values.
But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.
Using the CI, the decision rule is as follows:
If the CI includes the "zero", do not reject the null hypothesis.
If the CI doesn't include the "zero", reject the null hypothesis.
The calculated interval for the slope is: [-0.11; -0.04]
As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.
At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.
I hope this helps!
(full output in attachment)
slope of (-2, -5) and (1, -3)
Start by making a table for the ordered pairs with the x-values
in the left column and the y-values in the right column.
--x--|--y--
-2 | -5
1 | -3
|
|
Now remember that the slope is equal to the rate of change
or the change in y over the change in x.
We can see that the y-values go from -5 to -3 so the change in y is 2.
The x-values go from -2 to 1 so the change in x is 3.
So the change in y over the change in x is 2/3.
This means that the slope is also equal to 2/3.
If someone weighs 130 kilos what is the conversion in lbs
Answer:
286.60
Please tell me if I'm wrong.
Suppose a polling agency reported that 44.4% of registered voters were in favor of raising income taxes to pay down the national debt. The agency states that results are based on telephone interviews with a random sample of 1049 registered voters. Suppose the agency states the margin of error for 95% confidence is 3.0%. Determine and interpret the confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.
Answer:
95% of confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.
(0.414 ,0.474)
Step-by-step explanation:
Step(i):-
Given sample proportion
p⁻ = 44.4 % = 0.444
Random sample size 'n' = 1049
Given margin of error for 95% confidence level = 3 % = 0.03
Step(ii):-
95% of confidence interval for the proportion is determined by
[tex](p^{-} - Z_{\alpha }\sqrt{\frac{p^{-} (1-p^{-} }{n} } , p^{-} + Z_{\alpha }\sqrt{\frac{p^{-} (1-p^{-} }{n} })[/tex]
we know that
Margin of error for 95% confidence level is determined by
[tex]M.E = Z_{\alpha }\sqrt{\frac{p^{-} (1-p^{-}) }{n} }[/tex]
Step(iii):-
Now
95% of confidence interval for the proportion is determined by
[tex](p^{-} - M.E, p^{-} + M.E)[/tex]
Given Margin of error
M.E = 0.03
Now 95% of confidence interval for the proportion
[tex](0.444 - 0.03, 0.444+ 0.03)[/tex]
(0.414 ,0.474)
Conclusion:-
95% of confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.
(0.414 ,0.474)
Plz. Can anyone explain and tell the answer of this question.I promise I will mark it as brainliest Question.
Answer:
x = 15
y = 90
Step-by-step explanation:
Step 1: Find x
We use Definition of Supplementary Angles
9x + 3x = 180
12x = 180
x = 15
Step 2: Find y
All angles in a triangle add up to 180°
3(15) + 3(15) + y = 180
45 + 45 + y = 180
90 + y = 180
y = 90°
What’s the probability of getting each card out of a deck?
Determine the probability of drawing the card(s) at random from a well-shuffled regular deck of 52 playing cards.
a. a seven __________
b. a six of clubs. ___________
c. a five or a queen ___________
d. a black card. ___________
e. a red card or a jack. ___________
f. a club or an ace. ___________
g. a diamond or a spade. ___________
Answer:
a. 1/13
b. 1/52
c. 2/13
d. 1/2
e. 15/26
f. 17/52
g. 1/2
Step-by-step explanation:
a. In a deck of cards, there are 4 suits and each of them has a 7. Therefore, the probability of drawing a 7 is:
P(7) = 4/52 = 1/13
b. There is only one 6 of clubs, therefore, the probability of drawing a 6 of clubs is:
P(6 of clubs) = 1/52
c. There 4 fives (one for each suit) and 4 queens in a deck of cards. Therefore, the probability of drawing a five or a queen is:
P(5 or Q) = P(5) + P(Q)
= 4/52 + 4/52
= 1/13 + 1/13
P(5 or Q) = 2/13
d. There are 2 suits that are black. Each suit has 13 cards. Therefore, there are 26 black cards. The probability of drawing a black card is:
P(B) = 26/52 = 1/2
e. There are 2 suits that are red. Each suit has 13 cards. Therefore, there are 26 red cards. There are 4 jacks. Therefore:
P(R or J) = P(R) + P(J)
= 26/52 + 4/52
= 30/52
P(R or J) = 15/26
f. There are 13 cards in clubs suit and there are 4 aces, therefore:
P(C or A) = P(C) + P(A)
= 13/52 + 4/52
P(C or A) = 17/52
g. There are 13 cards in the diamonds suit and there are 13 in the spades suit, therefore:
P(D or S) = P(D) + P(S)
= 13/52 + 13/52
= 26/52
P(D or S) = 1/2
The Mathalot Company makes and sells textbooks. They have one linear function that represents the cost of producing textbooks and another linear function that models how much income they get from those textbooks. Describe the key features that would determine if these linear functions ever intercepted. (10 points)
What is the first step when solving the equation below for x?
4
0.2
= 1.9
Add 1.9 to both sides of the equation.
Divide each side of the equation by 4.
Add 0.2 to both sides of the equation.
Subtract 0.2 from both sides of the equation.
Step-by-step explanation:
4x + 0.2=0.9
transposing 0.2 to RHS
=> 4x =0.9-0.2 => 4x=0.7
transposing 4 to RHS
=> x=0.7÷4
=> x=0.175
if it helps plzz mark it as brainliest
Answer: add 0.2
Step-by-step-explanation:
"Tegan is trying to decide if a coin is fair. She flips it 100 times and gets 63 heads. Please explain why it might make sense to view 63 heads as enough evidence to conclude the coin is unfair."
Answer:
Should be a 50/50 chance
Step-by-step explanation:
When you flip a coin there are 2 possible chances, heads or tails. That means that out of 100 there should a 50/50 chance to get both. By Tegan getting 63 heads it show how the mentailty that it should be a perfect 50/50 chnace to get heads is not real and therefore not fair.
(but in real life this is what happens. Its not fair).
Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). f(x) = (-2/x) – 1; g(x) = -2/(x+1) Choices: a. g(x) has to be: (1+x)/2 b. g(x) has to be: x/2 c. g(x) has to be: 2 – (1/x) d. Inverses
Answer:
(f o g) = x, then, g(x) is the inverse of f(x).
Step-by-step explanation:
You have the following functions:
[tex]f(x)=-\frac{2}{x}-1\\\\g(x)=-\frac{2}{x+1}[/tex]
In order to know if f and g are inverse functions you calculate (f o g) and (g o f):
[tex]f\ o\ g=f(g(x))=-\frac{2}{-\frac{2}{x+1}}-1=x+1-1=x[/tex]
[tex]g\ o\ f=g(f(x))=-\frac{2}{-\frac{2}{x}+1}=-\frac{2}{\frac{-2+x}{x}}=\frac{2x}{2-x}[/tex]
(f o g) = x, then, g(x) is the inverse of f(x).
Leo takes 15 minutes to cycle to school at an average speed of 12 km/h. He will need only ___hours if he cycle at 18 km/h. Express your answer as a common fraction.
Answer:
1/6 hours
Step-by-step explanation:
It takes leo 15 minutes = 15/60 = 0.25 hours to circle to school with speed of
12km/hr .
Distance covered = speed*Time.
Distance covered = 12*0.25
Distance covered= 3 km
So the distance to be covered each time is 3km.
If speed increase to 18 km/he
Time taken = distance/speed
Time taken = 3/18
Time= 1/6 hour
Or 1/6 * 60 = 60/6 = 10 minutes
Which equation represents a line that passes through (2,-2) and has a slope of 3?
y-2 = 3(x +
y – 3 = 2(x + ?)
y +
= 3(x - 2)
y +
= 2(x - 3)
At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answer to four decimal places.
Answer:
(0.6231 , 0.6749)
Step-by-step explanation:
With the information we have, it is impossible to solve the exercise, therefore I was looking for information to complete it and we have to:
the sample proportion is 64.9%, or 0.649 plus the sample size is 1300 (n)
Now, we have that the standard error is given by:
SE = (p * (1 - p) / n) ^ (1/2)
replacing
SE = (0.649 * (1 - 0.649) / 1300) ^ (1/2)
SE = 0.0132
Now we have that confidence level is 95%, hence α = 1 - 0.95 = 0.05
α / 2 = 0.05 / 2 = 0.025, Zc = Z (α / 2) = 1.96
With this we can calculate margin of error like so:
ME = z * SE
ME = 1.96 * 0.0132
ME = 0.0259
Finally the interval would be:
CI = (p - ME, p + ME)
CI = (0.649 - 0.0259, 0.649 + 0.0259)
CI = (0.6231, 0.6749)
The nth term of a geometric sequence is given by an = 27(0.1)n - 1. Write the first five terms of this sequence.
Answer:
The first first five terms of this sequence are
27 ,2.7 ,0.27 ,0.027 , 0.0027Step-by-step explanation:
[tex]a(n) = 27(0.1)^{n - 1} [/tex]
where n is the number of term
For the first term
n = 1
[tex]a(1) = 27(0.1)^{1 - 1} = 27(0.1) ^{0} [/tex]
= 27(1)
= 27Second term
n = 2
[tex]a(2) = 27(0.1)^{2 - 1} = 27(0.1)^{1} [/tex]
= 27(0.1)
= 2.7Third term
n = 3
[tex]a(3) = 27(0.1)^{3 - 1} = 27(0.1)^{2} [/tex]
= 0.27Fourth term
n = 4
[tex]a(4) = 27(0.1)^{4 - 1} = 27(0.1)^{3} [/tex]
= 0.027Fifth term
n = 5
[tex]a(5) = 27(0.1)^{5 - 1} = 27(0.1)^{4} [/tex]
= 0.0027Hope this helps you
What is the value of x?
Enter your answer in the box.
Answer:
x=11
Step-by-step explanation:
Since the lines in the middle are parallel, we know that both sides are proportional to each other.
6:48 can be simplified to 1:8
Since we know the left side ratio is 1:8, we need to match the right side with the same ratio
We can multiply the ratio by 5 to match 5:3x+7
5:40
5:3x+7
Now we can set up the equation: 40=3x+7
Subtract 7 from both sides
3x=33
x=11
It was found that the mean length of 200 diodes (LED) produced by a company
was 20.04 mm with a standard deviation of 0.02mm. Find the probability that a diode
selected at random would have a length less than 20.01mm
Answer:
6.68% probability that a diode selected at random would have a length less than 20.01mm
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 20.04, \sigma = 0.02[/tex]
Find the probability that a diode selected at random would have a length less than 20.01mm
This is the pvalue of Z when X = 20.01. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20.01 - 20.04}{0.02}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% probability that a diode selected at random would have a length less than 20.01mm
Bailey and Jade both play basketball. The table and graph show the total number of games that each of their teams won over six weeks. A coordinate plane labeled Jade's Team. The x-axis is labeled Weeks and the y-axis is labeled Wins. Points plotted are (1, 0), (2, 1), (3, 3), (4, 5), (5, 6), and (6, 7). Bailey’s Team Number of weeks Wins 1 2 2 2 3 3 4 4 5 4 6 6 After which week had the two teams won the same number of games? week 1 week 2 week 3 week 5
Answer:
Week 3
Step-by-step explanation:
Week one was 1,0
Week two was 2,1
Week three was 3,3 which is the same number the teams have won
Therefore the answer is week 3
Hope this helps
The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Suppose that 43 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
What is the distribution of XX? XX ~ N(_______,_________)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(______,_________)
If a single randomly selected individual is observed, find the probability that this person consumes is between 61.4 mL and 62.8 mL. ________
For the group of 43 pancake eaters, find the probability that the average amount of syrup is between 61.4 mL and 62.8 mL. _________
For part d), is the assumption that the distribution is normal necessary? No Yes
please only answer if you are able to answer all parts correctly
Answer:
(a) X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).
[tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
Step-by-step explanation:
We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.
Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.
(a) Let X = amount of syrup that people put on their pancakes
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount of syrup = 63 mL
[tex]\sigma[/tex] = standard deviation = 13 mL
So, the distribution of X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).
Let [tex]\bar X[/tex] = sample mean amount of syrup that people put on their pancakes
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount of syrup = 63 mL
[tex]\sigma[/tex] = standard deviation = 13 mL
n = sample of people = 43
So, the distribution of [tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)
P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X [tex]\leq[/tex] 61.4 mL)
P(X < 62.8 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{62.8-63}{13}[/tex] ) = P(Z < -0.02) = 1 - P(Z [tex]\leq[/tex] 0.02)
= 1 - 0.50798 = 0.49202
P(X [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{13}[/tex] ) = P(Z [tex]\leq[/tex] -0.12) = 1 - P(Z < 0.12)
= 1 - 0.54776 = 0.45224
Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL)
P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL) = P([tex]\bar X[/tex] < 62.8 mL) - P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL)
P([tex]\bar X[/tex] < 62.8 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{62.8-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z < -0.10) = 1 - P(Z [tex]\leq[/tex] 0.10)
= 1 - 0.53983 = 0.46017
P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.81) = 1 - P(Z < 0.81)
= 1 - 0.79103 = 0.20897
Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
Which comparison is correct?
0.298 < 0.289
0.420 > 0.42
1.32 < 1.319
d) 3.544 > 3.455
Step-by-step explanation:
Option D is the correct answer because 3.544 is greater than 3.455
Option D is true in given comparison.
Here,
We have to find the correct comparison.
What is Decimal expansion?
The decimal expansion terminates or ends after finite numbers of steps. Such types of decimal expansion are called terminating decimals.
Now,
In option D;
The one tenth of 3.544 is 5 and place value of one tenth number in 3.455 is 4.
Clearly, 5 > 4
So, 3.544 > 3.455
Hence, option D; 3.544 > 3.455 is true.
Learn more about the Decimal expansion visit:
https://brainly.com/question/26301999
#SPJ2
A car travelling from Ibadan to Lagos at 90 km/hr
takes 1 hour 20 min. How fast must one travel to
cover the distance in one hour?
Answer:
A velocity of 120km/h is needed to cover the distance in one hour
Step-by-step explanation:
The velocity formula is:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.
This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]
We use this to find d.
[tex]v = \frac{d}{t}[/tex]
[tex]90 = \frac{d}{1.3333}[/tex]
[tex]d = 90*1.3333[/tex]
[tex]d = 120[/tex]
The distance is 120 km.
How fast must one travel to cover the distance in one hour?
Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{120}{1}[/tex]
[tex]v = 120[/tex]
A velocity of 120km/h is needed to cover the distance in one hour
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. Click on the datafile logo to reference the data. 6 4 6 8 7 7 6 3 3 8 10 4 8 7 8 7 5 9 5 8 4 3 8 5 5 4 4 4 8 4 5 6 2 5 9 9 8 4 8 9 9 5 9 7 8 3 10 8 9 6Develop a 95% confidence interval estimate of the population mean rating for Miami.
Answer:
The 95% confidence interval for the population mean rating is (5.73, 6.95).
Step-by-step explanation:
We start by calculating the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=6.34.
The sample size is N=50.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=50-1=49[/tex]
The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.01 \cdot 0.305=0.61[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95[/tex]
The 95% confidence interval for the mean is (5.73, 6.95).
If TU = 6 units, what must be true? SU + UT = RT RT + TU = RS RS + SU = RU TU + US = RS
Answer:
Since RT = 12, TU = 6 and RS = 24, T and U are the midpoints of RS and TS respectively. This means that SU + UT = RT.
Answer:
su+ut=rt
Step-by-step explanation:
HELP!!!! 25 POINTS AND BRAINLIEST ANSWER!!!!
Look at photo above!
Answer:
8.96 seconds
Step-by-step explanation:
A triangle has sides of lengths 9, 7, and 12. Is it a right triangle? Explain.
Answer:
Yes based on the numbers .
Step-by-step explanation:
Answer:Yes
Step-by-step explanation:Based on the number given, it shows that there is a hypotenuse (The longest side of a right triangle, in this case being 12), And opposite (Another part of the right triangle, that could be either 9 or 7), and the adjacent (The line next to the opposite, which could be 9 or 7)
A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/14. Find the two integers.
Answer:
The integers are 7 and 14.
Step-by-step explanation:
y = 2x
1/y + 1/x = 3/14
1/(2x) + 1/x 3/14
1/(2x) + 2/(2x) = 3/14
3/(2x) = 3/14
1/2x = 1/14
2x = 14
x = 7
y = 2x = 2(7) = 14
Answer: The integers are 7 and 14.
The required two integers are 7 and 14
This is a question on word problems leading to the simultaneous equation:
Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1
Also, if the sum of the reciprocals of the two positive integers is 3/14, then:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2
Substitute equation 1 into 2
[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]
Find the LCM of 2y and y
[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]
Substitute y = 7 into equation 1:
Recall that x = 2y
[tex]x = 2(7)\\x = 14[/tex]
Hence the required two integers are 7 and 14.
Learn more here: https://brainly.com/question/17671977
is a parallelogram sometimes always or never a trapezoid
yes
Step-by-step explanation:
parallelogram are quadrilaterals with two sets of parallel sides. since square must be quadrilaterals with two sets of parallel sides ,then all squares are parallelogram ,a trapezoid is quadrilateral.
Not sure how to solve this
Answer:
x y
8 -2
0 0
12 3
Step-by-step explanation:
The equation you are given is:
[tex] y = \dfrac{1}{4}x [/tex]
To find y, replace the given x-value in the table with x in the equation, and solve for y.
When x = -8, you get, replacing x with -8:
[tex] y = \dfrac{1}{4}(-8) [/tex]
Simplify:
[tex] y = -2 [/tex]
This gives you the line in the table:
-8 -2
When x = 0, you get, replacing x with 0:
[tex] y = \dfrac{1}{4}(0) [/tex]
Simplify:
[tex] y = 0 [/tex]
This gives you the line on the table:
0 0
To find x, replace the given y-value in the table with y in the equation, and solve for x.
When y = 3, you get, replacing y with 3:
[tex] 3 = \dfrac{1}{4}x [/tex]
Simplify:
[tex] 3 \times 4 = \dfrac{1}{4}x \times 4 [/tex]
[tex] 12 = x [/tex]
This gives you the line in the table:
12 3