Answer:
a
The point estimate of the population mean is [tex]\= x = 56[/tex]
b
The 80% confidence level is [tex]50.57 < \mu < 61.43[/tex]
c
There is 80% confidence that the true population mean lies within the confidence interval.
Step-by-step explanation:
From the question we are told that
The sample size is n = 18
The standard deviation is [tex]\sigma = 18 \ L[/tex]
The sample mean is [tex]\= x = 56[/tex]
Generally the point estimate of the population mean is equivalent to the sample mean whose value is [tex]\= x = 56[/tex]
Given that the confidence interval is 80% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 80[/tex]
[tex]\alpha = 20 \%[/tex]
[tex]\alpha = 0.20[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 1.28[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.28 * \frac{18 }{\sqrt{18} }[/tex]
=> [tex]E = 5.43[/tex]
Generally the 80% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]56 - 5.43 < \mu < 56 + 5.43[/tex]
=> [tex]50.57 < \mu < 61.43[/tex]
The interpretation is that there is 80% confidence that the true population mean lies within the limit
34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles.
Required:
Construct a binomial distribution using n= 0.6 and p=0.34
Answer:
solution below
Step-by-step explanation:
The question says 6 working mother's were selected so n = 6 not 0.6
We are expected to find
P(X = 0,1,2,3,4,4,6)
1. When x = 0
6C0*(0.34)⁰*(0.66)⁶
= 1 *1* 0.827
= 0.0827
2. When X = 1
6C1*(0.34)¹*(0.66)⁵
= 6 x 0.34 x 0.252
= 0.2555
3. When X = 2
6C2*(0.34)²*(0.66)⁴
= 15 x 0.1156 x 0.1897
= 0.3289
4. When x = 3
6C3*(0.34)³*(0.66)³
20 x 0.039304 x 0.2875
= 0.2599
5. When X = 4
6C4*(0.34)⁴*(0.66)²
= 15 x 0.01336 x 0.4356
= 0.8729
6. When x = 5
6C5*(0.34)⁵*(0.66)¹
= 6 x 0.0045 x 0.66
= 0.01782
7. When x = 6
6C6*(0.34)⁶*(0.66)⁰
1 x 0.0015 x 1
= 0.0015
In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of men and women favoring a higher legal drinking age is different at (alpha 0.05).
Answer:
Step-by-step explanation:
Given that:
Let sample size of women be [tex]n_1[/tex] = 1000
Let the proportion of the women be [tex]p_1[/tex] = 0.65
Let the sample size of the men be [tex]n_2[/tex] = 1000
Let the proportion of the mem be [tex]p_2[/tex] = 0.60
The null and the alternative hypothesis can be computed as follows:
[tex]H_0: p_1 = p_2[/tex]
[tex]H_0a: p_1 \neq p_2[/tex]
Thus from the alternative hypothesis we can realize that this is a two tailed test.
However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]
p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]
p = [tex]\dfrac{650+600 } {2000}[/tex]
p = 0.625
The standard error of the test can be computed as follows:
[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]
[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]
[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]
[tex]SE = \sqrt{0.234375 (0.002)}[/tex]
[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]
[tex]SE = 0.02165[/tex]
The test statistics is :
[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]
[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]
[tex]z =\dfrac{0.05}{0.02165}[/tex]
[tex]z =2.31[/tex]
At level of significance of 0.05 the critical value for the z test will be in the region between - 1.96 and 1.96
Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96
Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that the percentage of men and women favoring a higher legal drinking age is different.
Identify the inverse function of f(x) = VX - 2 + 3.
Answer:
[tex]\huge\boxed{f^{-1}(x) = (x-3)^2+2}[/tex]
Step-by-step explanation:
[tex]f(x) = \sqrt{x-2} + 3[/tex]
Replace y = f(x)
[tex]y = \sqrt{x-2} + 3[/tex]
Exchange x and y
[tex]x = \sqrt{y-2}+3[/tex]
Solve for y
[tex]x = \sqrt{y-2}+3[/tex]
Subtracting both sides by 3
[tex]x - 3 = \sqrt{y-2}[/tex]
Taking square on both sides
[tex](x-3)^2 = y -2[/tex]
Adding 2 to both sides
[tex]y = (x-3)^2+2[/tex]
Substitute y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = (x-3)^2+2[/tex]
Answer:
[tex] \boxed{ {f}^{ - 1} (x) = {(x - 3)}^{2} + 2}[/tex]Option D is the correct option
Step-by-step explanation:
[tex] \mathsf{f(x) = \sqrt{x - 2} + 3}[/tex]
Replace f(x) with y
[tex] \mathsf{y = \sqrt{x - 2} + 3}[/tex]
Interchange variables
[tex] \mathsf{x = \sqrt{y - 2} + 3}[/tex]
[tex] \mathsf{{(x - 3)}^{2} = {( \sqrt{y - 2)} }^{2} }[/tex]
[tex] \mathsf{ {(x - 3)}^{2} = y - 2}[/tex]
[tex] \mathsf{ y = {(x - 3)}^{2} + 2}[/tex]
Replace y with f ⁻¹( x )
[tex] \mathsf{ {f}^{ - 1} (x) = {(x - 3)}^{2} + 2}[/tex]
Hope I helped!
Best regards!
An individual is teaching a class on Excel Macros. The individual plans to break the class up into groups of 4 and wants each group to have 2 exercises to practice on, with no group doing the same exercise. The individual wants to know how many exercises he will need. Solve for the dependent variable (y) if the independent variable is 16.
Answer:
32
Step-by-step explanation:
If there are 16 independent variables (groups) then there would need to be 2 unique exercises x 16 groups = 32 exercises. If the independent variable is the number of students, then they would only need 8.
The Total Exercises each group will do 2x/4
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Total exercises individual need is y = 4x/2
y - 4x/2
The No. of groups = 4
Each group has to do exercises = 2
Total no. of exercises individual need is y
Total Exercises each group will do 2x/4
Total exercises individual need
y = 2x/4 (4)
y - 4x/2
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
Which of the following is the correct notation of the complex number?
Answer:
-84 + 10i
Step-by-step explanation:
Standard Complex Form: a + bi
Step 1: Evaluate
√-100 = √-1 x √100 = i x 10 = 10i
-84 = -84
Step 2: Combine
10i - 84
Step 3: Rearrange
-84 + 10i
Answer:
Last Option
Step-by-step explanation:
√-100 - 84
(√(100×-1)) - 84
(√100)(√-1)-84
√-1 = i
10i - 84 or -84 + 10i
Jupiter orbits the sun at a rate of 8 miles per second. How far does Jupitertravel in one day? Tip: There are 86400 seconds in a day.
Answer:
Jupiter travels 691200 miles a day
Step-by-step explanation:
I just did 86400 x 8
Plz give brainliest
please show me step by step
Answer:
Step-by-step explanation:
Picture
If you want to turn a ball into a giant water balloon, how many cubic feet of lake water can you fill it with if the radius of this balloon is 1.5 feet?
Answer:
14.13 cubic feet of lake water can fill the given balloon.
Step-by-step explanation:
concept used:
volume of sphere = 4/3 [tex]\pi r^3[/tex]
where r is the radius of sphere
we take [tex]\pi[/tex] = 3.14
_____________________________________
shape of balloon can be taken as spherical.
Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.
Given radius of balloon = 1.5 feet
Thus, volume of balloon = 4/3 [tex]\pi[/tex] 1.5^3 = 4/3*3.14*1.5^3
volume of balloon = 42.39/3 = 14.13 cubic feet
Thus, 14.13 cubic feet of lake water can fill the given balloon.
Suppose that 10% of all steel shafts produced by a process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. What is the (approximate) probability that X is:
a. Less than 30?
b. Between 15 and 25 (inclusive)?
Answer:
a?
Step-by-step explanation:
The sum of two numbers is 21. Five times the first number added to 2 times the second number is 66. Find the two numbers.
Which is one of the transformations applied to the graph of f(x) = X^2 to change it into the graph of g(x) = -x^2 +16x - 44
Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
Step-by-step explanation:
Let's construct g(x) in baby steps.
Ok, we start with f(x) = x^2
The first thing we have is a horizontal translation of A units (where A is not known)
A vertical translation of N units to the right, is written as:
g(x) = f(x - N)
Then we have:
g(x) = (x - A)^2 = x^2 - 2*A*x + A^2
Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.
Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)
Then if we apply also a reflection over the x-axis, we have:
g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44
Then:
2*A = 16
A*A = 44.
The first equation says that A = 16/2 = 8
But 8^2 is not equal to 44.
Then we need another constant coefficient, which is related to a vertical translation.
If we have a relation y = f(x), a vertical translation of N units up, will be
y = f(x) + N.
Then:
g(x) = -f(x - A) + B
-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44
Now we have:
2*A = 16
-A^2 + B = - 44
From the first equation we have A = 8, now we replace it in the second equation and get:
-8^2 + B = -44
B = -44 + 64 = 20
Then we have:
The transformation is:
First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
6x — Зу = 5
y - 2x = 8
How many solutions does the system have?
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Answer:
none
Step-by-step explanation:
Multiplying the second equation by -3 gives ...
6x -3y = -24
Values of x and y that satisfy this equation cannot also satisfy the first equation ...
6x -3y = 5
There are no solutions to this system of equations.
__
The equations describe parallel lines. There is no point of intersection.
A simple random sample of 28 Lego sets is obtained and the number of pieces in each set was counted.The sample has a standard deviation of 12.65. Use a 0.05 significance level to test the claim that the number of pieces in a set has a standard deviation different from 11.53.
Answer:
Step-by-step explanation:
Given that:
A simple random sample n = 28
sample standard deviation S = 12.65
standard deviation [tex]\sigma[/tex] = 11.53
Level of significance ∝ = 0.05
The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.
The null hypothesis and the alternative hypothesis can be computed as follows:
Null hypothesis:
[tex]H_0: \sigma^2 = \sigma_0^2[/tex]
Alternative hypothesis:
[tex]H_1: \sigma^2 \neq \sigma_0^2[/tex]
The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.
[tex]X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}[/tex]
[tex]X_0^2 = \dfrac{(28-1)(12.65)^2}{(11.53)^2}[/tex]
[tex]X_0^2 = \dfrac{(27)(160.0225)}{132.9409}[/tex]
[tex]X_0^2 = \dfrac{4320.6075}{132.9409}[/tex]
[tex]X_0^2 = 32.5002125[/tex]
[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}[/tex]
[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}[/tex]
From the chi-square probabilities table at 0.975 and degree of freedom 27;
[tex]X^2_{0.975 , 27}[/tex] = 14.573
[tex]X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}[/tex]
[tex]X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}[/tex]
From the chi-square probabilities table at 0.975 and degree of freedom 27;
[tex]X^2_{0.025 , 27}=[/tex] 43.195
Decision Rule: To reject the null hypothesis if [tex]X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}[/tex] ; otherwise , do not reject the null hypothesis:
The rejection region is [tex]X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573[/tex]
Conclusion:
We fail to reject the null hypothesis since test statistic value 32.5002125 lies between 14.573 and 43.195.
4. Write 3x(x + 4)(x - 1) in standard form.
3x3 + 9x2 - 12x
3x3
- 12x + 9x2
3x3 + 9x2 - 12x + 1
1 - 12x + 9x2 + 3x3
Answer:
i thank the ans id 450
Step-by-step explanation:
What number comes next in this series 7,10,10,13,16,16,
(-1, 4) and (-2, 2).
Answer:
Slope : 2
slope-intercept: y = 2x + 6
Point-slope (as asked): y - 4 = 2 (times) (x + 1)
standered: 2x - y = -6
Step-by-step explanation:
A state lottery sells instant-lottery scratch tickets. 12% of the tickets have prizes. Neil goes to the store and buys 10 tickets. What is the probability that exactly three of Neil's tickets will have prizes?
Answer:
The probability of success is .12
The probability of failure is .88
According to the binomial theorem the probability of 3 success is
10! / (3! * 7!) * .12^3 * .88^7 = .085
Help me with this question for 10 points please
9514 1404 393
Answer:
(a) 10 cm
Step-by-step explanation:
Since C is the midpoint of AB, the triangle shown is 1/4 of the rectangular area shown. When the tank is sitting horizontally on its 100 cm side, the water height will be 1/4 of the 40 cm height of the tank. It will be 10 cm.
__
More elaborate explanation
Triangle area = 1/2(AD)(AC) = 1/2(AD)(1/2(AB)) = 1/4(AD)(AB)
Whole tank area = (AD)(AB)
So, the triangle area is 1/4 the whole tank area. When the tank is tipped back to horizontal, the water area will still be 1/4 the whole tank area, so will be ...
water area = (1/4(AD))(AB)
and the height will be 1/4(AD) = 1/4(40 cm) = 10 cm
One of two small restaurants is chosen at random with equally likely probability, and then an employee is chosen at random from the chosen restaurant. Restaurant #1 has 10 full-timers and 6 part-timers. Restaurant #2 has 7 full-timers and 9 part-timers. What is the probability that Restaurant #1 was chosen at random, given that a full-time employee was chosen? Your answers should be rounded to 4 digits after the decimal.
Answer:
P(1 |F) = 10/17
Step-by-step explanation:
Let events
1 = restaurant 1
2 = restaurant 2
F = full-time worker chosen
P = part-time worken chosen
P(1 and F) = 1/2 * 10/16 = 5/16
P(2 and F) = 1/2 * 7/16 = 7/32
P( (1 or 2) and F ) = P(F) = 5/16+7/32 = 17/32
P(1 | F) Probability of choosing restaurant 1 given a full-time was chosen
= P(1 and F) / P(F)
= 5/16 / (17/32)
= 5/16 * 32/17
= 10 / 17
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is?
Answer:
1.56x+10.15
Step-by-step explanation:
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
The simplified form of (5.23x + 3.76) – (3.67x – 6.39) is 1.56x + 10.15.
The radar system beeps once every second. How many times will it beep in 3 days?
Answer:
259200
Step-by-step explanation:
so there are 86400 in one day. multiply by 3.
Answer:
259200
Step-by-step explanation:
60x24x3x60=
True or false? If it is false, replace the underlined word with the correct word. (Constant is underlined) The constant term in a polynomial expression is a number that is not multiplied by a
variable.
Answer:
true
Step-by-step explanation:
what else would it be. that is exactly the reason why we have constants.
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
awnser asap
Answer:
Mr. Shim would record the number +10 or 10 for Ben because of the word "more".
For Gail, Mr. Shin would record the number -8 because of the word, "less''.
Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.
I hope this helps better
r-(-4x - (y + y)); use x = -4, and y = -3 evaluate
Answer:
insert values of x and y
r - ( -4(-4) - ( -3-3))
r - ( 16 +6 )
r - 22
Doneeeeeeeeeeeeeeeeee3
Jimmy measured to find the total number of square inches that covered the top of a rectangular table.
Which was Jimmy measuring?
0
A. area
B. circumference
C. distance
D. perimeter
E. volume
Answer: it is a
Step-by-step explanation:
What is the y value when x is -5? What about 5?
I’ve done all three functions and the answers are -9, 24 and -4 but I don’t know which one to answer as the y value with. Please help.
What is the slope of the line shown below?
A. -3/2
B. 3/2
C. 2/3
D. -2/3
Answer:
2/3
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= (1- -7)/(9 - -3)
= ( 1+7)/( 9+3)
= 8/12
Simplifying
= 2/3
Answer:
C. 2/3
Step-by-step explanation:
You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.
y2 is equal to the y coordinate of the second point: 1
y1 is equal to the y coordinate of the first point: -7
x2 is equal to the x coordinate of the second point: 9
x1 is equal to the x coordinate of the first point: -3
So if you plug these values into the equation, you will get:
1 - (-7)/ 9- (-3)
= 1 + 7/ 9 + 3
= 8/12
= 2/3
Which, if any, pair of sides are parallel? AB II DC and AD II BC Cannot be determined AB II DC only AD II BC only
Answer:
120%
Step-by-step explanation:
Given the central angle, name the arc formed.
Major arc for ∠EQD
A. EQDˆ
B. GDFˆ
C. EGDˆ
D. EDˆ
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Answer:
C. EGD
Step-by-step explanation:
A major arc is typically named using the end points and a point on the arc. Here, the end points are E and D, and points on the major arc include C, G, and F. The major arc ED could be named any of
arc ECDarc EGD . . . . choice Carc EFDOf course, the reverse of any of these names could also be used: DCE, DGE, DFE.
fill in the missing. 1:1000=1cm:_?
Answer:
meter
10 meters
Or
a dekameter