Answer:
a) The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.
b) [tex]T_c = 2.4469[/tex]
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 7 - 1 = 6
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469, and the answer to question b is [tex]T_c = 2.4469[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{0.23}{\sqrt{7}} = 0.21[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1.4 - 0.21 = 1.19 pounds.
The upper end of the interval is the sample mean added to M. So it is 1.4 + 0.21 = 1.61 pounds.
The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.
I RLLY NEED HELP!!!!!!
Answer:
Angle ADB = 60 degrees
Step-by-step explanation:
This is a 60 60 60 triangle, which means all of its angles equal 60 degrees. Therefore angle ADB is 60 degrees.
Mathew travels 42/50 meters in 26/30 minutes. Find the speed of Mathew in meters per second
Answer:
Step-by-step explanation:
Find the scale factor where the pre-image is the large triangle and the image is the small triangle.
A. 4/5
B. 3/2.4
C. 2.4/3
D. 5/4
Answer:
Option B
Step-by-step explanation:
If the larger triangle (Preimage) is dilated by a scale factor 'k' to form the image triangle (small triangle),
Scale factor = [tex]\frac{\text{Length of one side of the image triangle}}{\text{Length of one side of the preimage}}[/tex]
k = [tex]\frac{3}{2.4}[/tex]
Therefore, Option B will be the correct option.
michael has an average of 68% in his 3 papers but that is below the pass mark of 70%. what must be his least score in the fouth paper to enable him pass?
Answer:
72%
Step-by-step explanation:
68% + x/2 = 70%
68 + x = 140
x = 72
I am authoring you to offer free insurance for a year the regular price is 6.99 this will save the customer almost_ a year
Hari earns Rs 4300 per month. He spends 80% from his income. How much does he save in a year? please give answer in step by step explaination
Answer:
4300 x 12= 51600
20/100 x 51600
10,320 Rs (also pay bohat kam hai :D )
Drag each tile to the correct location on the image. Each tile can be used more than once, but not all images will be used.
Consider function f.
f(x) = 3√8x+4. PLZ HELP
Answer:
Switch x and y, and solve for y
[tex]f^{-1}(x) =\frac{(x -4)^3}{8}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 3\sqrt{8x} + 4[/tex]
Required
Complete the steps to determine the inverse function
Solving (a): Complete the blanks
Switch x and y, and solve for y
Solving (b): Determine the inverse function
[tex]f(x) = \sqrt[3]{8x} + 4[/tex]
Replace f(x) with y
[tex]y = \sqrt[3]{8x} + 4[/tex]
Switch x and y
[tex]x = \sqrt[3]{8y} + 4[/tex]
Now, we solve for y
Subtract 4 from both sides
[tex]x -4= \sqrt[3]{8y} + 4-4[/tex]
[tex]x -4= \sqrt[3]{8y}[/tex]
Take cube roots of both sides
[tex](x -4)^3= 8y[/tex]
Divide both sides by 8
[tex]\frac{(x -4)^3}{8} = y[/tex]
So, we have:
[tex]y =\frac{(x -4)^3}{8}[/tex]
Hence, the inverse function is:
[tex]f^{-1}(x) =\frac{(x -4)^3}{8}[/tex]
Answer:
x
y
f^-1(x)= 1/8(x-4)^3 (plug in choices to match)
Step-by-step explanation:
You see, the guy above me already got it right. 1/8(x-4)^3 and (x-4)^3/8 are essentially the same thing. The only difference is either dividing by 8 and multiplying by 1/8, and that's only a visual difference.
Người ta thống kê được rằng mỗi chuyến bay có chừng 0,5% hành khách bị mất hành lí và giá trị trung bình mà khách đòi bồi thường cho mỗi hành lí bị mất là 1 triệu đồng. Một dịch vụ muốn tăng thêm giá vé để bù đắp cho số chi phí này.Vậy nên tăng thêm giá mỗi vé là bao nhiêu ?
Answer:
tăng lên 5.000 nghìn đồng
Step-by-step explanation:
mỗi chuyến bay có 0.5% hành khách mất hành lí
mỗi người đòi bồi thường 1.000.000 đồng
do đó vẽ mỗi người tăng lên :0.5%×1.000.000=5.000
Which inequality is shown in the graph?
I need help plz
Answer:
I am pretty sure it is B.
Step-by-step explanation:
This is a line with a positive slope, therefore we can discard c and d.
the sign < will mean that the shaded in area will be on your right side.
help please will give brainiest asap
Answer:
C
Step-by-step explanation:
Let me know if you need an explanation
A function of the form f(x)=ab^x is modified so that the b value remains the same but the a value is increased by 2. How do the domain and range of a new function compare to the domain and range of the original function?
Answer:
The domain and range remain the same.
Step-by-step explanation:
Hi there!
First, we must determine what increasing a by 2 really does to the exponential function.
In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).
Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).
The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.
The range remains the same as well; for the original function, it would have been [tex]y\neq 0[/tex]. Because increasing a by 2 does not move the entire function up or down, the range remains the same.
I hope this helps!
obtain the value of X for which (X+1),(X-5),(X-2) is a geometric progression.hence find the sum of the first 12 terms of the progression.
If x + 1, x - 5, and x - 2 are in a geometric progression, then there is some constant r for which
x - 5 = r (x + 1)
==> r = (x - 5) / (x + 1)
and
x - 2 = r (x - 5)
==> r = (x - 2) / (x - 5)
Then
(x - 5) / (x + 1) = (x - 2) / (x - 5)
Solve for x :
(x - 5)² = (x - 2) (x + 1)
x ² - 10x + 25 = x ² - x - 2
-9x = -27
x = 3
It follows that the ratio between terms is
r = (3 - 5) / (3 + 1) = -2/4 = -1/2
Now, assuming x + 1 = 4 is the first term of the G.P., the n-th term a(n) is given by
a(n) = 4 (-1/2)ⁿ⁻¹
The sum of the first 12 terms - denoted here by S - is then
S = 4 (-1/2)⁰ + 4 (-1/2)¹ + 4 (-1/2)² + … + 4 (-1/2)¹¹
Solve for S :
S = 4 [(-1/2)⁰ + (-1/2)¹ + (-1/2)² + … + (-1/2)¹¹]
(-1/2) S = 4 [(-1/2)¹ + (-1/2)² + (-1/2)³ + … + (-1/2)¹²]
==> S - (-1/2) S = 4 [(-1/2)⁰ - (-1/2)¹²]
==> 3/2 S = 4 (1 - 1/4096)
==> S = 8/3 (1 - 1/4096)
==> S = 1365/512
The population of a strain of bacteria doubles in a culture. At noon there were 80 bacteria present and by 4:00 PM there were 20 480 bacteria. Determine algebraically the doubling period. Hint: You DO NOT need to use systematic trials.
Answer:
t = 1/2 hour
Step-by-step explanation:
20480 = 80[tex]x^{t }[/tex]
20480 = 80[tex]x^{4 }[/tex]
20480/80 = [tex]x^{4 }[/tex]
256 = [tex]x^{4 }[/tex]
x = 4
doubling period
2 = [tex]4^{t}[/tex]
t = 1/2 hour
Solve equation by using the quadratic formula
Answer:
x = -2
Step-by-step explanation:
x^2 + 4x + 4 = 0
quadratic formula:
-b +or- sqrt(b^2-4ac)/2a
-4 +/- sqrt ((-4)^2-4*1*4)/2*1
-4+/- sqrt(16-16) / 2
-4 +/- 0 / 2
-4/2
-2
Which of the following scatterplots do not show a clear relationship and would not have a trend line?
Answer:
the second one
Step-by-step explanation:
it is not going in any general direction
Answer:
B
Step-by-step explanation:
Please help due tomorrow
Answer: x= 2.5, y = 10
Step-by-step explanation:
I'm going to assume that these photocopies are proportional in relations to each other.
If they're proportional, you can set up two proportions:
[tex]1) \frac{x}{5} =\frac{3}{6} \\\\2) \frac{5}{y} =\frac{3}{6}[/tex]
And cross-multiply:
[tex]1) 6x = 5*3 \\\\2) 3y = 5*6[/tex]
Then solved for x and y:
[tex]1) 6x = 15\\x=\frac{15}{6} =\frac{5}{2} =2.5 \\\\2) 3y = 30\\y=\frac{30}{3} =10[/tex]
Line Lis perpendicular to the y-axis. If the line contains point(0, -9), what is the equation of Line ?
O1
y = 0
2
x = 0
O
a
3
X = -9
4
y = -9
Answer:
y = -9
Step-by-step explanation:
perpendicular to the y-axis means it is parallel to the x-axis.
so, it is a flat line, which means the slope is 0 (it has the save y value for every x value).
therefore the equation is
y = 0×x + b
of simply
y = b
to get b we look at the point we know about (0, -9).
-9 = b
aha !
so, the line equation is simply
y = -9
There is a close relationship between the air pressure inside a hurricane and its maximum sustained wind speed: y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots (nautical miles per hour).
What does the slope of the line represent?
A. the change in wind speed for every 1 kPa increase in air pressure
B. the wind speed of a hurricane with an air pressure of 1000 kPa
C. the wind speed of a hurricane with an air pressure of 0 kPa
D. the change in wind speed for every hour
Answer:
A. the change in wind speed for every 1 kPa increase in air pressure
Step-by-step explanation:
The equation of a straight line is given by:
y = mx + b;
where y, x are variables, m is the slope (rate of change) of the line and b is the y intercept (value of y when x = 0)
Given the line y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots.
The slope of the line is -1.22. The slope means that there is a decrease in wind speed by 1.22 miles per hour for every increase of 1 kPa in air pressure.
round 3/5 to 3 decimal points
Answer:
3/5=0.600
Step-by-step explanation:
I hope this answer helps
The answer is 0.6.
Upto 3 decimal places it is 0.600.
How long will it take the same crew to clear the entire plot of 2 1/2 acres?
Answer:
1. 15 days
2. 0.17 acre.
Step-by-step explanation:
1. Determination of the number of days.
From the question given above,
The crew clears ⅓ acre of land in 2 days.
Therefore, the crew will clear 2½ acres in = (2½ × 2) / ⅓
= (5/2 × 2) × 3
= 15 days
Thus, the crew will clear 2½ acres in 15 days
2. Determination of the acre of land.
From the question given above,
The crew clears ⅓ acre of land in 2 days.
Therefore, the crew will clear X acre of land in 1 day i.e
X acre of land = ⅓ ÷ 2
X acre of land = ⅓ × ½
X acre of land = 1/6
X acre of land = 0.17 acre
Thus, the crew will clear 0.17 acre of land in 1 day
if( x) means 10 what's (x) divide my 2
Answer:
If you meant that the value of (x) is equal to 10, and you want that value divided by 2, then that would be easy!
10/2 is equal to 5.
If you meant something else, please let me know! :)
if (a + b) = 73 and a b =65 find value of a²+ b²
Step-by-step explanation:
Here,
by formula a^2+b^2=(a+b)^2-2ab
so,
or,(a+b)^2-2ab
or,(73)^2-2×65
or,5329-126
=5203 is the answer
Which number can be distributed across two terms
inside parentheses? 3/5 V
X-6
18-4x-1
5
tep 2 Combine like terms that are on the same side of
the equation. Which terms can be combined?
18 and -1
3/5x and 4x
6 and 1
Check
Intro
9514 1404 393
Answer:
3/5 can be distributed (correct answer is shown)18 and -1 can be combinedStep-by-step explanation:
The only factor outside parentheses that contain 2 terms is the factor 3/5. It can be distributed. (The correct response is shown.)
3/5 can be distributed
__
The only like terms that reside on the same side of the equal sign are ...
18 and -1
12,963 rounded to the nearest hundredth
9514 1404 393
Answer:
12,963.00 (in the US)12,96 (some other places)Step-by-step explanation:
In the US, a decimal point is represented by a period. This value is interpreted as an integer with no fractional part, so the fractional part is zero:
12,963.00
__
Some other places, a comma is used to identify the beginning of the decimal fraction. In that form, this number has a fractional part that has 3 as its thousandths digit. The value of 3 is less than 5, so the number is simply truncated at the hundredths place.
12,96
If the thousandths digit were 5 or greater, then 1 hundredth would be added to the truncated number.
GIVING 10 POINTS ANSWER ASAP PLEASE
Simplify the following rational expression.
\dfrac{n^2-225}{n^2+30n+225}=
n
2
+30n+225
n
2
−225
=start fraction, n, squared, minus, 225, divided by, n, squared, plus, 30, n, plus, 225, end fraction, equals
Which values of nnn make the expression undefined?
Answer:
the answer is n, 225 so u can use another app to make sure u find ur answer
A basketball player is fouled while attempting to make a basket and receives two free throws. The opposing coach believes there is a 32% chance that the player will miss both shots, a 22% chance that he will make one of the shots, and a 46% chance that he will make both shots.
Required:
a. Construct the appropriate probability distribution.
b. What is the probability that he makes no more than one of the shots?
c. What is the probability that he makes at least one of the shots?
Simplify the trigonometric expression cos(2x)+1 using Double-Angle identities
9514 1404 393
Answer:
C. 2cos²(x)
Step-by-step explanation:
The relevant identities are ...
cos(2x) = cos²(x) -sin²(x)
cos²(x) = 1 -sin²(x)
__
Then the expression can be simplified to ...
cos(2x) +1 = (cos²(x) -sin²(x)) +1 = cos²(x) +(1 -sin²(x)) = cos²(x) +cos²(x)
= 2cos²(x)
five eights of the people on a hike were children. there are 20 children on the hike. how many people total
Answer:
There were a total of 32 people on the hike.
Step-by-step explanation:
Represent the number of people total by p. Then:
(5/8)p = c = the number of children
Since there are 20 children on the hike, (5/8)p must equal 20:
(5/8)p = 20
Solve for p by multiplying both sides by (8/5):
(8/5)(5/8)p = 20(8/5), or
p = 32
There were a total of 32 people on the hike.
Rewrite the fraction in the sentence below as a percentage. From 125 yards away, a marksman hit 11/20 of the targets last year.
Answer:
Step-by-step explanation:
11/20 = 55/100 = 55%
The 450 juniors at East HS drink a total of 1500 cartons of milk per 5-day week. If the average senior drinks milk at the same rate as the average junior, what is the average number of total cartons of milk the 600 seniors drink each school day?
Answer:
I believe it’s 900
Step-by-step explanation:
Find out how much milk per student for one day then time 5 the times 600 if I’m wrong please let me know
The average number of total cartons of milk the [tex]600[/tex] seniors drink each school day will be [tex]400[/tex].
What is average?The average is the sum of the numbers divided by total numbers .
We have,
Number of juniors [tex]=450[/tex]
Number of Seniors [tex]=600[/tex]
And,
Cartons of milk Juniors drink in [tex]5[/tex] days [tex]=1500[/tex] cartoons
So,
Cartons of milk Juniors drink in [tex]1[/tex] day [tex]=\frac{1500}{5} =300[/tex]
So,
The average Cartons of milk Juniors drink in [tex]1[/tex] day [tex]=\frac{300}{450} =\frac{2}{3}[/tex]
And,
According to the question,
The average Cartons of milk Juniors drink in [tex]1[/tex] day [tex]=[/tex] The average Cartons of milk Seniors drink in [tex]1[/tex] day
i.e.
The average Cartons of milk Seniors drink in [tex]1[/tex] day [tex]=\frac{2}{3}[/tex]
So,
Number of total cartons of milk the [tex]600[/tex] seniors drink each school day [tex]=\frac{2}{3}*600=400[/tex]
Hence we can say that the average number of total cartons of milk the [tex]600[/tex] seniors drink each school day will be [tex]400[/tex].
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