Answer: [tex]\boldsymbol{37.5} < \mu < \boldsymbol{44.5}[/tex]
===========================================================
Explanation:
At a 90% confidence level, the z critical value is roughly z = 1.645. Use a reference table or a calculator to determine this. Despite not knowing what sigma is, we can use a z interval here because n > 30. If the sample size n was smaller than 30, then we'd have to use a T distribution instead.
We'll plug that z value, along with the other given values, into the formula for the lower boundary L of the confidence interval.
[tex]L = \text{lower boundary}\\\\L = \overline{x} - z*\frac{s}{\sqrt{n}}\\\\L = 41 - 1.645*\frac{12}{\sqrt{31}}\\\\L = 41 - 3.545\\\\L = 37.455\\\\L = 37.5\\\\[/tex]
This value is approximate.
Do the same for the upper boundary as well
[tex]U = \text{upper boundary}\\\\U = \overline{x} + z*\frac{s}{\sqrt{n}}\\\\U = 41 + 1.645*\frac{12}{\sqrt{31}}\\\\U = 41 + 3.545\\\\U = 44.545\\\\U = 44.5\\\\[/tex]
This value is also approximate.
We have 90% confidence that the population mean [tex]\mu[/tex] (greek letter mu) is somewhere between L = 37.5 and U = 44.5
Therefore, we would write the 90% confidence interval as [tex]\boldsymbol{37.5} < \mu < \boldsymbol{44.5}[/tex]
This is the same as writing the confidence interval in the form [tex](\boldsymbol{37.5} , \boldsymbol{44.5})[/tex]. Both forms are two different ways to say the same thing. The first form being [tex]L < \mu < U[/tex] while the second form is [tex](L,U)[/tex].
Side note: The value 3.545 calculated earlier is the approximate margin of error.
Calculate 1.015 to the power of 72
Answer:
2.92 rounded
Step-by-step explanation:
:))
last one i’m almost done.
Answer:
AFC
Step-by-step explanation:
You can tell by the angles
Jonas is conducting an experiment using a 10-sided die. He determines that the theoretical probability of rolling a 3 is StartFraction 1 over 10 EndFraction. He rolls the die 20 times. Four of those rolls result in a 3. Which adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer?
A.He can decrease the sample space.
B.He can increase the sample space.
C.He can decrease the number of trials.
D.He can increase the number of trials.
Answer:
A. He can decrease the simple spacw
Answer:
D. He can increase the number of trials
Choose the missing step in the given solution to the
inequality -X - 10 > 14 + 2x.
_X
- 10 > 14 + 2x
-3X - 10 > 14
x<-8
0 -3x > 24
0 -3x > 4
0-3x>.
- 4
0 -3x < 24
Answer:
Step-by-step explanation:
expand and simplify
(y – 2) (+1) (y+3)
Answer:
y² + y - 6
Step-by-step explanation:
(y - 2)(+ 1)(y + 3) simplifies to
(y - 2)(y + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
y(y + 3) - 2(y + 3) ← distribute parenthesis
= y² + 3y - 2y - 6 ← collect like terms
= y² + y - 6
Your deductible expenditures are $8236 for interest on a home mortgage, $3528 for contributions to charity, and $634 for state income taxes. Your filing status entitles you to a standard deduction of $12,200. Should you itemize your deductions rather than claiming the standard deduction? If so, what is the difference?
Answer:
yes 198
Step-by-step explanation:
2) Subtract and simplify. 11 7\10 − 7 3\10 =
Answer:
4 2/5
Step-by-step explanation:
11 7/10
- 7 3/10
----------------
4 4/10
4 4/10 = 4 2/5
1. If something gets 1 percent better each day, how long will it take it to become 100 percent better than it already is? Round to the nearest day.
2. How many times better will it be in 365 days? Round to the nearest percent.
Answer:
it would take 100 days for it to get better that just makes sense I think and for number two it would be 365% better
Step-by-step explanation:
What is the rectangular form of theta = 3pi/4?
Please answer this question if you 100% know this answer.
a. x - y = 0
b. x - y = 1
c. x + y = 0
d. x + y = 1
The answer was not a.
Answer:
c. x + y = 0
Step-by-step explanation:
The terminal ray of the angle θ = 3π/4 extends to the upper left through the 2nd quadrant with a slope of -1. It lies on the line ...
y = -x
x + y = 0 . . . . . . add x to get this standard form equation
Solve the equation.
2x - 3 + 4x = 21
A)x = -12
B)x= -6
C)x= 4
D)x = 6
Answer:
C. X=4
Step-by-step explanation:
The American customer satisfaction index scores of McDonalds restaurants grew from 61 in 2002 to 71 in the year 2014. Find the average rate of change for the data. Show work.
Answer:
[tex]\large\sf{average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}[/tex]
Step-by-step explanation:
Given the American customer satisfaction index scores that increased from 61 in 2002, to 71 in 2014:
In order to solve for the average rate of change, we could simply use the average rate of change formula:
Average rate of change = Change in output/Change in input
[tex]\huge\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}}[/tex]
Let (x₁, y₁) = (61, 2002)
(x₂, y₂) = (71, 2014)
Substitute these values into the average rate of change formula:
[tex]\BIGG\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}\:=\frac{2014\:-\:2002}{71\:-\:61}\:=\:\frac{12}{10}\:=\:\frac{6}{5}}[/tex]
[tex]\large\bf\sf{Therefore,\:the\:average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}[/tex].
Anyone know the answer to this plz
Answer:
Domain: -10 < x < 10
Range: -2 < y < 8
Step-by-step explanation:
Hope this helps!
Last year, wind turbines along a hilly ridge had an average output of 390 kilowatt hours per
year. The turbines were upgraded, and now their average annual output is 30% more. What
is the new average yearly output?
kilowatt hours
Submit
Answer:
507 KW/hStep-by-step explanation:
Initial output:
390 KW/hUpgraded output:
30% moreFind the upgraded output in number:
390 + 30% of 390 =390 + 390*30/100 =390*1.3 =507Average output=390KW
Updated percentage=30%
Updated output:-
[tex]\\ \sf\longmapsto 30\%\:of\:390[/tex]
[tex]\\ \sf\longmapsto 0.3(390)[/tex]
[tex]\\ \sf\longmapsto 117[/tex]
New output=390+117=507KW
the interval [2, 4] is divided into n equal subintervals of length delta x. What is delta x (in terms of k and n)
Each subinterval would have length ∆x = (4 - 2)/n = 2/n
solve for x, x-c=r+d/y
Answer:
D
Step-by-step explanation:
x - c = (r + d)/y for x
x = (r +d)/y + c common denominator : (c/1) (y/1) = yc
x = (r + d)/y + yc
x = (yc + r + d)/ y
Line l is a reflection in the x-axis of line k. Write an equation that represents line k.
Answer:
(-4,3)
Step-by-step explanation:
nejsjsjssjsususheheueueyeehejebebe
Answer: y = (5/3)x + -1
Step-by-step explanation:
The slope is -5/3, so since its a reflection in the x - axis, the new slope would be the opposite, 5/3. Now for the +1, you just have to find the y intercept by plotting the dots at the opposite version of the y number that is already there. For example because the point (0,1) has 1 as its y number, you make it into -1, and for example if you have the point (3,-4) since -4 is the y number you change it to 4.
A 6 sided die is rolled 2 times. What is the probability of getting a 1 both times ?
Answer:
Step-by-step explanation: If you roll the die twice, the probability of getting a even number both times is (1/2)(1/2) ... A probability experiment consists of rolling a 6 sided die
PLEASE HELP WITH THIS ONE QUESTION
Answer:
g(x) = x(x-2)^2(x-3) -3
Step-by-step explanation:
the translation from f(x) to g(x) is right 1 down 3.
vertical translations are easier since you just add the amount to everything. so we have f(x) - 3 = (x-1)^2(x-2)(x+1) -3.
for the horizontal translation, we make every x into x-1, so now we have (x-1-1)^2 (x-1-2) (x-1+1) - 3 or (x-2)^2(x-3)x -3
looking at the answers it is g(x) = x(x-2)^2(x-3) -3
after how many years will £6,000.00 yield a simple interest of £900.00 at 3%
Answer:
add 1 Century to divide £6 000 000
Answer:
the answer to your question is 105 I think sorry if it's not
The bag has 99 buttons. Draw more buttons so there are 105 buttons in all. Write the numbers as you count.
Answer:
100 101 102 103 104 105
Step-by-step explanation:
im kinda confused
1. Find the coordinates of all points where the lines
x + y = 8, y = 5, and x = 1 intersect.
Answer:
(3)1. Find the coordinates of all points where the lines
x + y = 8, y = 5, and x = 1 intersect.
Step-by-step explanation:
this answer
The coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect are (0, 5), (1, 0), (3, 5) and (1, 7).
Given that;
The equation of lines is,
x + y = 8
y = 5
x = 1
Now all the coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect are find as,
x + y = 8
Put y = 5;
x + 5 = 8
x = 8 - 5
x = 3
Put x = 1;
1 + y = 8
y = 8 - 1
y = 7
Therefore, the points are (0, 5), (1, 0), (3, 5) and (1, 7).
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Jett is 6 feet 2 inches tall. How tall is he in inches ?
Answer:
74in
Step-by-step explanation:
Jett is 74 inches tall, as of the given unit conversion condition.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
1 feet = 12 inches
So,
6 feet 2 inch = 6 feet + 2 inch
= 6 × 12 inch + 2 inch
= 72 + 2
= 74 inches
Thus, Jett is 74 inches tall, as of the given unit conversion condition.
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A snack company makes packages of grapes and honeydew slices. The weight of an individual package of
grapes, G, is approximately Normally distributed with a mean of 3.25 ounces and a standard deviation of 0.91
ounces. The weight of an individual package of honeydew slices, H, is approximately Normally distributed with a
mean of 4.51 ounces and a standard deviation of 2.02 ounces. Assume G and H are independent random
variables. Let D=G-H. What is the probability that a randomly selected package of grapes weighs more than a
randomly selected package of honeydew slices?
O 0.127
O 0.230
0.284
0.334
Using the normal distribution, it is found that there is a 0.284 = 28.4% probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X. When two normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.In this problem, for each variable, [tex]\mu_G = 3.25, \sigma_G = 0.91, \mu_H = 4.51, \sigma_H = 2.02[/tex]
For the subtraction, we have that:
[tex]\mu_D = \mu_G - \mu_H = 3.25 - 4.51 = -1.26[/tex]
[tex]\sigma_D = \sqrt{\sigma_G^2 + \sigma_H^2} = \sqrt{0.91^2 + 2.02^2} = 2.2155[/tex]
The probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices is P(D > 0), which is 1 subtracted by the p-value of Z when X = 0.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-1.26)}{2.2155}[/tex]
[tex]Z = 0.57[/tex]
[tex]Z = 0.57[/tex] has a p-value of 0.7157.
1 - 0.715 = 0.284
0.284 = 28.4% probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices.
A similar problem is given at https://brainly.com/question/24663213
Are the two triangles congruent?
Choose 1 answer:
(Choice A)
A-Yes
B-No
C-There is not enough information to say.
Assignments
In a lottery, the top cash prize was $633 million, going to three lucky winners. Players pick four different numbers from 1 to 52 and one number from 1 to 41
A player wins a minimum award of $400 by correctly matching two numbers drawn from the white balls (1 through 52) and matching the number on the gold ball (1
through 41). What is the probability of winning the minimum award?
Study Plan
Gradebook
The probability of winning the minimum award is
(Type an integer or a simplified fraction
The probability of winning the minimum award is very small, approximately 1 in 185 million.
To calculate the probability of winning the minimum award, we need to determine the number of possible outcomes and the number of favorable outcomes.
To win the minimum award, the player needs to match two of the white ball numbers and the gold ball number.
There are (4 choose 2) ways to choose two of the four white ball numbers, and there is only one way to choose the gold ball number. Therefore, the number of favorable outcomes is (4 choose 2) × 1.
So, the probability of winning the minimum award is:
(favorable outcomes) / (total outcomes)
= [(4 choose 2) × 1] / [(52 choose 4) × 41]
= (6 × 1) / (26,827,440 × 41)
= 6 / 1,100,701,040
≈ 0.0000000054 or 5.4 × 10⁻⁹
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can someone PLEASE help me with this!? I’ve been trying to find the answer but I just couldn’t find it. I’m behind in math and this was due four days ago!!
Answer:
{-2}
Step-by-step explanation:
Answer:
B)-2
Step-by-step explanation:
In functions, X is your input. Y is the output unless specifically stated otherwise :P
Brainliest? <3
If
x
=
4
and
y
=
7
, evaluate the following expression:
2
(
4
x
+
3
y
)
Answer:
expression.
2(4x+3y)
2(4(4)+3(7))
2(16+21)
2( 37)
74
Both questions 7 and 8
9514 1404 393
Answer:
7. $10,459.28
8. $30,060.93
Step-by-step explanation:
Your table 12-2 will tell you the present-value multiplier of the annual payment for a 10-year annuity due will be ...
7%: 7.515232
11%: 6.537048
__
7. The 11% table value will be used with a payment of $1600 to find the present value:
6.537048 × $1600 = $10,459.28 . . . present value of the annuity due
__
8. The 7% table value will be used with a payment of $4000 to find the present value:
7.515232 × $4000 = $30,060.93 . . . present value of the annuity due
Find the equation of the line through (2,1) which is parallel to the line y=−7x−1.
Give your answer in the form y=mx+b
Answer:
y=-7x+15
Step-by-step explanation:
1. What kind of sequence is this? 44, 57, 70, 83, .. arithmetic ,geometric,
both , neither
Answer:
arithmetic
Step-by-step explanation:
arithmetic
There is a common difference of 13 between each term.