A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
A. (195 - 286) + 1.992 underroot46/45 + 58/40
B. (286 - 195) + 1.992 underroot46^2/45+ 58^2/40
C. (195 - 286)+ 1.992 underrot 140² 158²/45+40
D. (286 - 195) + 1.992 46 1582 45 +40
E. (195-286) +1.992 462 + 58 45 40
Answer:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
Step-by-step explanation:
Given that:
NEWER CARS:
Sample size = n1 = 45
Standard deviation s1 = 46
Mean = m1 = 195
OLDER CARS:
Sample size = n2 = 40
Standard DEVIATION s2 = 58
Mean = m2 = 286
Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025
Confidence interval is calculated thus : (newer--older)
(m1 - m2) ± Tcritical * standard error
Mean difference = m1 - m2; (195 - 286)
Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)
Standard error (E) = sqrt((s1²/n1) + (s2²/n2))
E = sqrt((46^2/45) + (58^2/40))
Hence, confidence interval:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
Given that:The first sample consists of owners of newer cars
First sample's size = [tex]n_1 =45[/tex]First sample's mean = [tex]\overline{x_1}=\$195[/tex]First sample's standard deviation = [tex]s_1 = \$46[/tex]The second sample consists of owner of older cars.
Second sample's size = [tex]n_2 = 40[/tex]Second sample's mean = [tex]\overline{x_2}=\$286[/tex]Second sample's standard deviation = [tex]s_2 = \$58[/tex]To find:95% confidence interval for difference between both samples' means.
Calculations and Explanations:Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.
The CI is given as:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)
Thus,
[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]
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Select the correct answer.
Which graph represents this equation?
y- 4=-3(x+5)
Step-by-step explanation:
The given expression is :
y- 4=-3(x+5)
⇒ y-4 = -3x-15
⇒y+3x = -15 + 4
⇒ y+3x= -11
We need to draw the graph for this equation. The attached figure shows the graph for this equation.
Using partial quotients, which would be the best choice for the first number to subtract in the division problem 858 +26?
Answer:
780
Step-by-step explanation:
We want to use partial quotients in the division problem 858 ÷ 26.
In partial quotients method, what we do is to repeatedly subtract from the dividend easy multiples of the divisor.
In this case, the dividend is 858 and the divisor is 26.
Thus, the first easy multiple of the divisor we can use will be 30 because 30 × 26 = 780 yields the closest value to 858.
Therefore, the best choice for first number to subtract is 780
Answer: 780
Step-by-step explanation:
The best choice for the division problem will be 780.
The data set shows the numbers of flowers that students on a field trip correctly identified. What is the mode of the data set? 0 7 3 9 5 0 10 5 8 6
Answer:
The mode is the value that appears most frequently in a data set
Step-by-step explanation:
so it will be 0 and 5
Answer:
0 and 5
explanation:
i don’t understand this , what’s the answer?
The temperature in a chemical reactor was measured every half hour under the same conditions. The results were 78.1°C, 79.2°C, 78,9°C, 80.2°C, 78.3°C, 78.8°C. 79.4°C.
the mean ?
Answer:
72.2
Step-by-step explanation:
The mean of the data is 78.98.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
For example,
To calculate the mean,
= (3 + 11 + 4 + 6 + 8 + 9 + 6 = 47). Then you divide the total sum by the number of scores =(47 / 7 = 6.7).
Given:
Data: 78.1°C, 79.2°C, 78,9°C, 80.2°C, 78.3°C, 78.8°C. 79.4°C.
Now, the mean of the data
= Sum of data/ Total number of data
= 78.1+ 79.2+ 78.9+ 80.2+ 78.3+ 78.8+ 79.4 / 7
= 552.9/7
= 78.98
Hence, the mean of the data is 78.98.
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Find the value of 8C0
Answer:
[tex]^8C_0=1[/tex]
Step-by-step explanation:
In this problem, we need to find the value of [tex]^8C_0[/tex].
The formula for the combination is given by :
[tex]C(n,r)=\dfrac{n!}{r!(n-r)!}[/tex]
We have,
n = 8 and r = 0
[tex]C(8,0)=\dfrac{8!}{0!(8-0)!}\\\\=\dfrac{8!}{8!}\ (\because\ 0!=1)\\\\=1[/tex]
So, the value of [tex]^8C_0[/tex] is 1.
Helppp pleaseeee xxxxx
Answer:
[tex] h = 3\sqrt{3} [/tex]
[tex] c = 4\sqrt{2} [/tex]
Step-by-step explanation:
✔️Finding h using trigonometric ratio:
Reference angle = 60°
Opposite = h
Adjacent = 3
Thus:
[tex] tan(60) = \frac{h}{3} [/tex]
[tex] \sqrt{3} = \frac{h}{3} [/tex] (tan 60 = √3)
Multiply both sides by 3
[tex] 3\sqrt{3} = h [/tex]
[tex] h = 3\sqrt{3} [/tex]
✔️Finding c using trigonometric ratio:
Reference angle = 45°
Hypotenuse = 8
Adjacent = c
Thus:
[tex] cos(45) = \frac{c}{8} [/tex]
[tex] \frac{\sqrt{2}}{2} = \frac{c}{8} [/tex] (cos 45 = √2/2)
Multiply both sides by 8
[tex] \frac{\sqrt{2}}{2} \times 8 = c [/tex]
[tex] \sqrt{2} \times 4 = c [/tex]
[tex] c = 4\sqrt{2} [/tex]
Is this a function?
Answer:
yes
Step-by-step explanation:
Help please!!!
Triangle ABC is similar to triangle PQR, as shown below
Answer:
b:q
Step-by-step explanation:
im pretty sure its that. ive learned this before.
if you flipped them so that c and r were facing the same direction, then b and q would be too.
can someone please answer as soon as possible
Answer:
A) {-1,2,8}
Step-by-step explanation:
fill in all domain values in f(x) and you get:
f(-1) = -1
f(0) = 2
f(2) = 8
The set of results is the range.
Evaluate the expression 2l + 2w for l = 5.7 and w = 6.2.
Answer:
so 5.7 square root is 2.45 so minus that by 2K and you get 3.4
Step-by-step explanation:
The average amount of money spent for lunch per person in the college cafeteria is $6.35 and the standard deviation is $2.31. Suppose that 41 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
What is the distribution of X?X ~ N(,)
What is the distribution of x¯? x¯ ~ N(,)
For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.1605 and $6.757.
For the group of 17 patrons, find the probability that the average lunch cost is between $6.1605 and $6.757.
Answer:
(6.35, 5.34)
(6.35, 0.99)
0.10253
0.3984
Step-by-step explanation:
Given that :
μ = 6.35
σ = 2.31
n = 41
What is the distribution of X?X ~ N(,)
X :
Mean of distribution = μ= 6.35
The variance = σ^2 = 2.31^2 = 5.3361 = 5.34
X ~ N = (6.35, 5.34)
What is the distribution of x¯? x¯ ~ N(,)
The mean = μ = 6.35
The standard deviation of the mean = σ/sqrt(n) = 6.35/sqrt(41) = 0.9917 = 0.99
X ~N = (6.35, 0.99)
find the probability that this patron's lunch cost is between $6.1605 and $6.757.
P(6.1605 < x < 6.757)
Obtain the standardized scores:
Z = (x - μ) / σ ; (6.1605 - 6.35) / 2.31 = - 0.082
P(Z < - 0.082) = 0.46732 (Z probability calculator)
(6.757 - 6.35) / 2.31 = 0.176
P(Z < 0.176) = 0.56985 (Z probability calculator)
P(Z < 0.176) -P(Z < - 0.082)
0.56985 - 0.46732 = 0.10253
For the group of 17 patrons, find the probability that the average lunch cost is between $6.1605 and $6.757.
P(6.1605 < x < 6.757) ; n = 17
Obtain the standardized scores:
Z = (x - μ) / σ/sqrt(n) ; (6.1605 - 6.35) / 2.31/sqrt(17) = - 0.338
P(Z < - 0.338) = 0.36768 (Z probability calculator)
(6.757 - 6.35) / 2.31/sqrt(17) = 0.726
P(Z < 0.726) = 0.76608 (Z probability calculator)
P(Z < 0.726) -P(Z < - 0.338)
0.76608 - 0.36768 = 0.3984
Answer:
he did a good job
Step-by-step explanation:
What is the equation in slope-intercept form of the line that passes through the point (6, 1) and is parallel to the line represented by
y = -3x + 2?
Enter your answer by filling in the boxes.
Simplify (6x−3)−(9x+2)
15x−5
15x−1
−3x−1
−3x − 5
Answer:
- 3x - 5
Step-by-step explanation:
(6x-1) -9x-2
=-3x-5
At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?
Answer: It is a function because at any given time the oven was exactly one temperature.
Step-by-step explanation:
It is given that:
At 5:00 p.m., Antonio turned on the oven.
The oven remained at 400°F for 45 minutes until Antonio turned it off.
It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m.
Helppp pleaseee I don’t understand
Answer:
I think it is all false. 45 minutes is 19 and 55 is 23
The graph of a logarithmic function is shown below...
On a coordinate plane, a curve starts at y = negative 2 in quadrant 4 and curves up into quadrant 1 and approaches y = 2.
What is the domain of the function?
A. x 0
C. x < 1
D. all real numbers
Answer:
ITS B GOOD SIR!! I JUST FINISHED THE TEST
Step-by-step explanation:
huhjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj
The domain of the function is [tex]x\geq 0[/tex]
To understand more, check below explanation.
Domain of function:The input values for which any function is defined, that input values aree known as the domain of function.
For any graph of a function, the x- axis values are the domain of the function.
From the given graph it is observed that, the input values for the function is [tex]x\geq 0[/tex].
Hence, the domain of the function is [tex]x\geq 0[/tex].
Learn more about the domain and range of the function here:
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What is the solution of the following system y=-2x=8 16+4x=2y
Question 13 (3 points)
Intel's microprocessors have a 1.2% chance of malfunctioning. Determine the
probability that a random selected microprocessor from Intel will not malfunction.
Write the answer as a decimal.
Answer:
sorry
Step-by-step explanation:
What is probability? Put simply, it is the chance of an event occurring. Probability is often expressed in quantifiable terms as either a percentage or a decimal: for example, the chance of a coin landing as heads is 50% . It is impossible to be certain you can correctly predict whether the coin will land heads or tails, which makes the act of flipping the coin a random event. We can however, calculate the probability of the coin landing heads or tails.
The probability that a random selected microprocessor from Intel will not malfunction 98.8% or 0.988
Given that Intel's microprocessors have a 1.2 % chance of malfunctioning
The chance or probability of happening ant event A is given by equation (1)
[tex]\rm Probability\; of \; happening \; of \; event \; A = P(A).........(1) \\The \; Probability \; of \; same \; event \; not \; happening = P(\bar A) = 100 - P(A) ........(2) \\Where \; P(A) \; is\; expressed \; in \%[/tex]
Let one Intel microprocessor be selected at random then from equations (1) and (2) we can write that
P( Malfunctioning of Intel's microprocessor) + P( Non malfunctioning of Intel's microprocessor) = 100 %
According to the given situation From equations (1) and (2) we can write that
[tex]\rm 1.2\% + P( Non\; malfunctioning\; of \; Intel's\; microprocessor) = 100\% \\ \\ P( Non \; malfunctioning\; of \; Intel's\; microprocessor) = 100\% - 1.2 \% \\P( Non \; malfunctioning\; of \; Intel's\; microprocessor) = 98.8\% = 0..988[/tex]
So we can conclude that the probability that a random selected microprocessor from Intel will not malfunction 98.8% or 0.988
For more information please refer to the link given below
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Please help me answer this :)!
I will give braisnlt
Answer: I don't see anything
Step-by-step explanation:
Please Help: Adelle solved the equation 4x/7-6= -20 as shown. Fill in the correct justification for each step. Will Mark Brainliest. Only answer if you are extremely 100%. Have to pass math. No Plagiarism Please.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the equation :
4x / 7 - 6 = - 20
4x / 7 = - 20 + 6 (move - 6 to the right hand side, the - sign attached to 6 changes to positive)
4x / 7 = - 14 ( - 20 + 6 = - 14)
4x = - 98 ( multiply both sides by 7 in other to isolate 4x)
x = - 24.5 (Divide both sides by 4, in other to isolate x and obtain it's value).
Combine the like terms to create an equivalent expression.
5 + 3t +4-t
Answer:
2t + 9
Step-by-step explanation:
5 and 4 are like terms. 3t and -t are like terms
= 2t + 9
or 9 + 2t
Answer:
2t + 9
Step-by-step explanation:
5 + 4 = 9
3t - 1t = 2t
Select all expressions that are equivalent to 8.8.8.8.8
Answer:
the first one
the third one
and the forth one
Step-by-step explanation:
they all add up to the same amount
Water freezes at 32° Fahrenheit, which is 0° Celsius. Water boils at 212 Fahrenheit, which is 100 Celsius. Which temperature would be the best estimate for water at room temperature in Celsius
Answer:
20
Step-by-step explanation:
I don't really know how to explain this beyond either memorizing this or remembering that Fahrenheit is around 70 degrees and estimating it.
The heights of dogs, in inches, in a city are normally distributed with a population standard deviation of 7 inches and an unknown population mean. If a random sample of 20 dogs is taken and results in a sample mean of 21 inches, find a 95% confidence interval for the population mean. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.
Answer:
The 95% confidence interval is [tex] 17.932 < \mu < 20 + 22.068[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma =7 \ inches[/tex]
The sample size is n = 20
The sample mean is [tex]\= x = 20[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{7 }{\sqrt{20} }[/tex]
=> [tex]E = 2.068[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 20 - 2.068 < \mu < 20 + 2.068[/tex]
=> [tex] 17.932 < \mu < 20 + 22.068[/tex]
Can somebody help me pls
the answer can vary between x=−1 or x=2 or x=−3 or x=3
explanation:
x4−x3−11x2+9x+18=0
Step 1: Factor left side of equation.
(x+1)(x−2)(x+3)(x−3)=0
Step 2: Set factors equal to 0.
x+1=0 or x−2=0 or x+3=0 or x−3=0
x=−1 or x=2 or x=−3 or x=3
PLZ HELP ASAP WILL GIVE BRAINLIEST
which list orders the numbers from least to greatest
Answer:
-5, -2, 1, 3
Step-by-step explanation:
mark the points on the number line and go from left to right. The points on the left are always less than the right
Answer:
the person above me is right mark me brainiest for being right
Step-by-step explanation:
Bo big cookies for two hours and 30 minutes he finished baking at 8:30 PM when did bo start baking
Answer:
6:00 pm
Step-by-step explanation: