Complete Question
In a random sample of ten people, the mean driving distance to work was 23.1 miles and the standard deviation was 6.6 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 99% confidence interval for the population mean Interpret the results. Identify the margin of error.
Answer:
The 99% confidence interval is [tex]16.32< \mu <29.88[/tex]
The interpretation is that there is 99% confidence that the true mean lies within the limits
The margin of error is [tex]E = 6.783[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 23.1[/tex]
The standard deviation is [tex]\sigma = 6.6 \ miles[/tex]
The sample size is n = 10
Generally the degree of freedom is mathematically represented as
[tex]df = n-1[/tex]
=> [tex]df = 10-1[/tex]
=> [tex]df =9[/tex]
Given that the confidence level is 99% , the n the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha =1\%[/tex]
[tex]\alpha =0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] with a df of 9 from from the student t-distribution table the value is
[tex]t _{\frac{\alpha }{2} , df } = 3.250[/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , df } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 3.250 * \frac{6.6 }{\sqrt{10} }[/tex]
[tex]E = 6.783[/tex]
The 99% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]23.1 - 6.78 < \mu <23.1 + 6.78[/tex]
=> [tex]16.32< \mu <29.88[/tex]
The interpretation is that there is 99% confidence that the true mean lies within the limits
The blue dot is at what value on the number line?
Answer:
-19
Step-by-step explanation:
By looking at the 2 numbers provided, -10 and -4, you can work out that there is a gap of 6 numbers as(-4) - (-10) = 6
There are 2 intervals between -10 and -4, so each interval is
6/2 = 3
a gap of 3
This means the number to the left of -4 is -7, then -10 which works.
From there, you count how many intervals there is between -10 and the ?
There are 3 intervals, so you have to decrease -10 by -3x3 or -9
Therefore the ? is -19
Another way is to just count it directly
The number directly left of -10 is going to be -13, then -16 and finally -19
WILL GIVE BRAINILY 5 STARS AND THANKS FOR CORRECT ANSWER ITS PRETTY EASY If it is 3:00 p.m. and you move the minute hand of the clock 270 degrees clockwise, what time will it be?
Answer:
3:45 pm
Step-by-step explanation:
Every 90 degree = 15 minutes
270 degrees = 15 x 3 = 45 minutes
3:00 + 0:45 = 3:45 pm
Hope this helps!
Answer:
3:45 pm
Step-by-step explanation:
∆T = (270/360)° × 60 minutes
=45 mins
Time = 3hrs + 45 mins
3:45 pm
Is the constant of proportionality in gallons per minute the same for every row? What does this say about the relationship of the amount of water to time?
Answer:
Yes, the constant of proportionality is the same for the three rows.
The relationship between amount of water (W) in terms of time (t) can be written as:
W = 16.5 t
Step-by-step explanation:
To find the constant of proportionality, find the number of gallons per minute for each row:
First row: 16.5 gal in 1 minute means: 16.5 Gal/min
Second row: 24.75 gallons in 1.5 minutes means 24.75/1.5 = 16.6 Gal/min (same proportionality as above)
Third row: 33 gallons in 2 minutes means: 33/2 = 16.5 Gal/min (again same proportionality)
Then: Yes, the constant of proportionality is the same for the three rows.
Therefore the amount (W) of water in gallons per time (t) in minutes can be written as the product of 16.5 times time (t):
W = 16.5 t
Answer:
The numbers prove that there is a proportional relationship between the gallons of water and the time in minutes. The bathtub fills at a constant rate.
Step-by-step explanation:
If P is the midpoint of XY, XP = 8x - 2 and PY = 12x - 30, find the
value of x.
Answer:
x=7
Step-by-step explanation:
If P is the midpoint of XY, then XP = PY:
8x - 2 = 12x - 3012x -8x = 30 -24x = 28x= 28/4x= 7the sum of two numbers is twenty-four. The second number is equal to twice the first number.
Answer:
The two numbers are: 8 and 16.
Step-by-step explanation:
Let the two unknown numbers be a and b.
The sum of the two number is 24. In other words:
[tex]a+b=24[/tex]
The second number is equal to twice the first number. In other words:
[tex]a=2b[/tex]
This is a system of equations. Solve by substitution:
[tex]a+b=24\\a=2b\\\\2b+b=24\\3b=24\\b=8\\a=2b\\a=2(8)=16[/tex]
Which graph represents a linear function that has a slope of 0.5 and a y-intercept of 2?
On a coordinate plane, a line goes through points (negative 2, 0) and (0, 1).
On a coordinate plane, a line goes through points (0, 2) and (4, 0).
On a coordinate plane, a line goes through points (0, 2) and (2, 3).
On a coordinate plane, a line goes through points (negative 4, 0) and (0, 2).
Answer:
f(x)=1/2x+2
Step-by-step explanation:
Using formula y=mx+b.
m is 0.5 or 1/2 as stated above
f(x)= 1/2x+b
If it were y=1/2x, it would intersect at 0,0 and we want 0,2
so b should be 2
therefore
Y=1/2x+2
or
f(x)=1/2x+2
Answer:
D
Step-by-step explanation:
The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.2 grams with a standard deviation of 0.18 grams. Enter your responses as a decimal with 4 decimal places. (a) What is the probability that a randomly chosen mouse has a mass of less than 19.99 grams?
Answer:
12.1%
Step-by-step explanation:
Given that:
Mean (μ) = 20.2 grams and standard deviation (σ) = 0.18 grams.
The z score is a score used to determine the number of standard deviations by which the raw score is above or below the mean. A positive z score means that the raw score is above the mean and a negative z score means that the raw score is below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For x < 19.99 g:
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{19.99-20.2}{0.18} \\\\z=-1.17[/tex]
From the normal distribution table, P(x < 19.99) = P(z < -1.17) = 0.1210 = 12.1%
The probability that a randomly chosen mouse has a mass of less than 19.99 grams is 12.1%
Rewrite to make true: The sequence 8,8,8,8,8, ... is neither arithmetic or geometric.
Answer:
8,8,-8,-8,8, ... is neither arithmetic nor geometric
Step-by-step explanation:
8,8,-8,-8,8, ...
This sequence is neither arithmetic nor geometric
We could also write
8,8,8,8,8, ... this is geometric since we multiply by 1 each time
Solving a word problem with three unknowns using a linear...
Rachel, Trey, and Deshaun sent a total of 98 text messages during the weekend. Trey sent 4 times as many messages as Deshaun. Rachel sent 10 fewer
messages than Deshaun. How many messages did they each send?
Number of text messages Rachel sent:
221
Х
?
Answer:If Rachel texted 221 text messages, then Deshaun texted 231 text messages, and Trey texted 924 text messages.
Step-by-step explanation:
221+10=231, 321 times 4 equal 924
what is the least number to be added to 1500 to make it a perfect square?
Answer:
21
Step-by-step explanation:
√1500 = 38.7
Round to nearest whole number
≈39
39²-1500
= 1521 - 1500
= 21
check to see whether 5 is a solution: 10 + 7g < 44
Answer:
Not a solution
Step-by-step explanation:
We want to check and see if 5 is a solution to the inequality. Therefore, we must substitute 5 into the inequality.
[tex]10+7g < 44[/tex]
Plug 5 in for g.
[tex]g=5[/tex]
[tex]10+7(5) < 44\\[/tex]
First, multiply 5 and 7.
[tex]10 + (7*5) < 44[/tex]
[tex]10 + 35 < 44[/tex]
Next, add 10 and 35.
[tex](10+35) < 44[/tex]
[tex]45 < 44[/tex]
This statement is not true. 45 is not less than 44. Therefore, 5 is not a solution.
Answer:
it is not a solution
Step-by-step explanation:
By replacing the letter g with a 5 the answer would be 45<44 which is not true
Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed Show Your Work
Answer:
The removed number is 11.
Step-by-step explanation:
Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :
[tex]let \: x = total \: values[/tex]
[tex] \frac{x}{5} = 7[/tex]
[tex]x = 7 \times 5[/tex]
[tex]x = 35[/tex]
Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :
[tex]let \: y = removed \: number[/tex]
[tex] \frac{35 - y}{4} = 6[/tex]
[tex]35 - y = 6 \times 4[/tex]
[tex]35 - y = 24[/tex]
[tex]35 - 24 = y[/tex]
[tex]y = 11[/tex]
Okay, let's slightly generalize this
Average of [tex]n[/tex] numbers is [tex]a[/tex]
and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.
Solution:
If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]
Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]
For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .
so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]
or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]
Simplify the equation, and solve for [tex]x[/tex] to get,
[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]
Hope you understand it :)
The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form.
[(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)
(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]
[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]
a. MP
b. DS
c. MT
d. Conj
e. HS
Answer:
e. HS
Step-by-step explanation:
The argument:
[(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)
(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]
[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]
is an instance of one of hypothetical syllogism (HS).
Hypothetical syllogism contains conditional statements for its premises.
Let
p = [(P ≡ T) • (H • N)]
q = (T ⊃ ~S)
r = [(H ∨ E) ∨ R]
The this can be interpreted as:
p ⊃ q
q ⊃ r
p ⊃ r
This interprets that:
If p then q
but if q then r
therefore if p then r
Thus, in logic HS is a valid argument form:
p → q
q → r
∴ p → r
Note that ⊃ symbol is used to symbolize implication relationships. This is used in conditional statements which are represented in the if...then... form. For example p ⊃ q means: if p then q. So the type of Hypothetical syllogism used in this is conditional syllogism.
There are three parts of syllogism:
major premise
minor premise
conclusion
An example is:
If ABC is hardworking, then ABC will go to a good college.
Major premise: ABC is hardworking.
Minor premise: Because ABC is hardworking , ABC will score well.
Conclusion: ABC will go to a good college.
Example of Hypothetical syllogism:
If AB is a CD, then EF is a GH
if WX is a YZ, then AB is a CD
therefore if WX is a YZ, then EF is a GH
This can be understood with the help of an example:
If you study the topic, then you will understand the topic.
If you understand the topic, then you will pass the quiz.
Therefore, if you study the topic, then you will pass the quiz.
Find the probability that when a couple has four children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
Answer:
The probability that at least, one of the four children the couple has is a boy is 0.8.
Step-by-step explanation:
Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..
Note that it is possible to have the following for 4 children:
1. 4 boys, 0 girls
2. 3 boys, 1 girl
3. 2 boys, 2 girls
4. 1 boy, 3 girls
5. 0 boys, 4 girls.
To have at least, one boy, out of the 5 options, only 4 is possible.
1. 4 boys, 0 girls.........YES
2. 3 boys, 1 girl ...........YES
3. 2 boys, 2 girls.........YES
4. 1 boy, 3 girls.............YES
5. 0 boys, 4 girls..........NO
The probability is therefore,
(Probability of event = 4) ÷ (Total possible outcome = 5)
P = 4/5 = 0.8
Find the Value of X 1. Solve for X algebraically. 2. Using complete sentences, describe your method for finding X.
The value of x using complete sentences is 40 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees. A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
We are given that;
The measure of angles 75,50 and 85
Now,
In triangle 1
50+75+y=180
y=180-125
y=55
In triangle 2
55+85+x=180
140+x=180
x=40
Therefore, by angle sum properties of triangle answer will be 40 degrees.
Learn more about the triangles;
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The data given below consists of the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12. Find the z-score corresponding to the median of school allergies. You may use your calculator to find the mean and standard deviation.
Answer:
z -score = 0.0459
Step-by-step explanation:
Given that:
the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12.
The objective is to find the z- score , but before we can do that , we need to determine the mean and the standard deviation of the sample.
Mean = sum of the sample/ total number of the sample
Mean = (3+9+ 5+ 5+ 14+ 10+ 5+ 11+ 9+ 6+ 1+ 8+ 10+ 7+ 9+13+ 18+ 9+ 8+11+ 9+ 7+ 6+ 14+ 12)/25
Mean = 219/25
Mean = 8.76
Standard deviation = [tex]\sqrt{\dfrac {\sum (x_i - \mu)^2}{N}}[/tex]
Mean (in order )= 1, 3,5,5,5,6,6,7,7,8,8,9,9,9,9,9,10,10,11,11,12,13,14,14,18)
Standard deviation = [tex]\sqrt{\dfrac { (8.76 - 1)^2}{25} + \dfrac { (8.76 - 3)^2}{25} +\dfrac { (8.76 - 5)^2}{25} +...+ \dfrac { (8.76 - 18)^2}{25} }[/tex]
Standard deviation = 5.2174
The standard z score formula is:
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
where X = median (13th observation ) = 9
[tex]z = \dfrac{9- 8.76}{5.2174}[/tex]
[tex]z = \dfrac{0.24}{5.2174}[/tex]
z -score = 0.0459
1
1
A baseball weighs approximately
3
pound. A golf ball weighs about pound.
10
What expression can be used to find the combined weight of a baseball and a golf ball?
Answer:
6 pounds 10 ounces
Step-by-step explanation:
I take this to mean "a baseball weighs approximately 3 pounds and a golf ball three pounds ten ounces."
Adding these two weights together, we get 6 pounds 10 ounces.
perform the following division (-2/3) ÷ (4/7)
Answer:
-7/6
Step-by-step explanation:
-2/3 x 7/4 = -14/12 = -7/6
Answer: -7/6
Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).
Remember that dividing by a fraction is the same thing
as multiplying by the reciprocal of the fraction.
Before multiplying however, notice that we
can cross-cancel the 2 and 4 to 1 and 2.
So multiplying across the numerators and denominator and
remembering our negative in the first fraction, we have -7/6.
i will give brainliest and 5 stars if you help ASAP
Answer:
BC = 13.4
Step-by-step explanation:
its a law of cosines S-A-S
a² = b² + c² - 2bc cosA
a² = 12.6² + 4.6² - ( 2 * 12.6 * 4.6 * cos 90 )
a² = 179.92
a = sqrt (179.92)
a = 13.4
What is the solution of the linear equation? LaTeX: 5k\:+\:3.8\:=\:3k\:+\:95 k + 3.8 = 3 k + 9 Group of answer choices 26 6.4 .065 2.6
Answer:
[tex]k = 2.6[/tex]
Step-by-step explanation:
Given
[tex]5k + 3.8 = 3k + 9[/tex]
Required
Solve
[tex]5k + 3.8 = 3k + 9[/tex]
Collect like terms
[tex]5k -3k+ 3.8 = 3k -3k + 9[/tex]
[tex]2k+ 3.8 = 9[/tex]
Subtract 3.8 from both sides
[tex]2k+ 3.8 - 3.8= 9 - 3.8[/tex]
[tex]2k= 9 - 3.8[/tex]
[tex]2k = 5.2[/tex]
Divide through by 2
[tex]k = 5.2/2[/tex]
[tex]k = 2.6[/tex]
1 - Dada a função f(x)= -Ix²-5x+4I, determine o valor de função para x = -1. * 1 ponto a) -10 b) 10 c) 9 d) -9 e) -8
Option a) -10
[tex] f(x)=-|x^2-5x+4|[/tex]
put $x=-1$
$f(-1)=-|(-1)^2-5(-1)+4|$
$\implies f(-1)=-|1+5+4|=-|10|=10$
Answer:
option a
Step-by-step explanation:
Option a) -10
put $x=-1$
$f(-1)=-|(-1)^2-5(-1)+4|$
$\implies f(-1)=-|1+5+4|=-|10|=10$
Find the distance of the translation.
Round your answer to the nearest hundredth.
Which is greater 9/20 or 60%
Answer:
60%
Step-by-step explanation:
9/20 is 45%
Answer:
60 %
Step-by-step explanation: If you divide 9/20, it equals to 0.45, makes it 45% and the number 45 in general is smaller than 60. Thus, 60% is greater than 9/20. I hope this helps.
A 2-column table with 9 rows. The first column is labeled year with entries 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010. The second column is labeled pounds of trash with entries 3.25, 3.25, 3.66, 3.83, 4.57, 4.52, 4.74, 4.69, 4.44. The table shows the average number of pounds of trash generated per person per day in the United States from 1970 to 2010. Use the statistics calculator to calculate the mean and median. Round the answers to the nearest hundredth. Median = Mean =
Answer:
Median: 4.44
Mean: 4.11
On edge
Step-by-step explanation:
The mean and median of the data is
Mean ≈ 4.1 pounds
Median = 4.44
How to find mean and median of a data?The ratio of the total number of observations to the sum of the observations is known as the mean.
The median is a value for an ordered data collection that has the same amount of observations on its left and right (in either ascending or descending order).
We have the following data:
3.25, 3.25, 3.66, 3.83, 4.57, 4.52, 4.74, 4.69, 4.44
So, Mean of the data is
= sum/number of observations
= (3.25 + 3.25 + 3.66 + 3.83 + 4.57 + 4.52 + 4.74 + 4.69 + 4.44) / 9
= 36.95 / 9
= 4.10555
Now, Arranging the data in ascending order gives
3.25, 3.25, 3.66, 3.83, 4.44, 4.52, 4.57, 4.69, 4.74
Here mid value is the 5th value from both end.
Thus, median of the data set = 4.44
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Find an equation in slope-intercept form of the line that has slope –9 and passes through point A(-9,-1)
Answer:
y = -9x - 82
Step-by-step explanation:
Line with slope m=-9 passing through A(x1, y1) =A(-9,-1)
y-y1 = m(x-x1)
Substitute values
y-(-1) = -9(x-(-9)
y+1 = -9x -81
y = -9x - 82
please help !! Solve –2.5x ≤ 25
Answer:
x ≥-10
Step-by-step explanation:
–2.5x ≤ 25
Divide each side by -2.5, remembering to flip the inequality
–2.5x/-2.5 ≥ 25 /-2.5
x ≥-10
Answer:
[tex]x\leq -10[/tex]
Step-by-step explanation:
[tex]-2.5x\leq 25[/tex]-----> Multiply by -1:
[tex]2.5x\geq -25[/tex]-----> Divide by 2.5:
[tex]x\geq -10[/tex]
Hope this helps!
Carol owns a BBQ company that sells brisket for $11.75 per pound (after it is smoked for 10 hours). She buys the brisket for an AP$ of $4.72 per pound and they weigh 10.4 lbs each. Once they are done smoking, they weigh 6.24 lbs each.
What is the yield % of the briskets after Carol is done smoking them?
Answer: 60%
Step-by-step explanation:
Given, AP$ of Brisket = $4.72
Weight of each brisket on purchase : 10.4 lbs
Weight of each brisket after smoking : 6.24 lbs
Yield % of the briskets after Carol is done smoking them=[tex]\dfrac{\text{Weight after smoking}}{\text{Weight on purchase}}[/tex]
[tex]\dfrac{6.24}{10.4}\times100\\\\=60\%[/tex]
Hence, the yield % of the briskets after Carol is done smoking them = 60%
please Factor 12n - 18.
Answer:
[tex]\large \boxed{6(2n-3)}[/tex]
Step-by-step explanation:
[tex]12n-18[/tex]
Factor out 6 from each term.
[tex]6(2n)+6(-3)[/tex]
Take 6 as a common factor.
[tex]6(2n-3)[/tex]
Answer:
[tex] \boxed{3(4n - 6)}[/tex]Step-by-step explanation:
[tex] \mathsf{12n - 18}[/tex]
In such expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor
Factor out 3 from the expression
[tex] \mathsf{ = 3(4n - 6)}[/tex]
Hope I helped!
Best regards!
4x + 1 -5x =2x +4(x-5)
Answer:
x = 3
Step-by-step explanation:
To answer for x first distribute the 4 in the parenthesis
4x + 1 - 5x = 2x +4x - 20
Next add or subtract the x's
-x + 1 = 6x - 20
Now subtract 6x and 1 on both sides to get x on the left and the rest on the right
-7x = -21
Lastly, divide -7 on both sides
x = 3
PLZZZZZZZZ HELP ME I WILL GIVE BRAINLIEST TO THE FASTEST AND MOST ACCURATE
Answer:
10/1 +54/-6
Step-by-step explanation:
Is this the answer?
