Answer:
(- 2, 4 )
Step-by-step explanation:
Given the 2 equations
3x + 5y = 14 → (1)
y = [tex]\frac{1}{2}[/tex] x + 5 → (2)
Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)
3x + 5([tex]\frac{1}{2}[/tex] x + 5) = 14
3x + [tex]\frac{5}{2}[/tex] x + 25 = 14
[tex]\frac{11}{2}[/tex] x + 25 = 14 ( subtract 25 from both sides )
[tex]\frac{11}{2}[/tex] x = - 11 ( multiply both sides by 2 )
11x = - 22 ( divide both sides by 11 )
x = - 2
Substitute x = - 2 into (2) for corresponding value of y
y = [tex]\frac{1}{2}[/tex] × - 2 + 5 = - 1 + 5 = 4
solution is (- 2, 4 )
The librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant took a sample and found the mean to be 880 books. She provides the librarian with an interval estimate of between 790 and 970 books checked out per day. An efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress is
Answer:
a. 880
Step-by-step explanation:
Options are "a. 880 b. 90 c. 790 d. None of these choices"
Interval estimate of between 790 and 970 books checked out per day.
Lower limit is 790, Upper limit is 970
Point estimate of μ(x) = [Upper limit + Lower limit} / 2
Point estimate of μ(x) = [970 + 790] / 2
Point estimate of μ(x) = 1760/2
Point estimate of μ(x) = 880
So, the efficient, unbiased point estimate of the number of books checked out each day at the New York City Public Library is 880.
The U.S. Department of Agriculture records data on farm acreage and number of farms by county for every county in the country. This takes considerable time and energy, and the results for each update (usually occurring approximately every five years) are a long time in process. A quicker way to update the data is by sampling. The table below shows the number of counties in each geographic region and a summary of farm acres (in thousands) for independent random samples of 22 counties from each region.
Region Number of counties
North Central 1052
North East 210
South 1376
West 418
Required:
a. Estimate the mean acreage for each region, with a margin of error.
b. Estimate the total acreage for each region, with a margin of error.
c. Estimate the difference between mean acreage for the North Central region and the South, with a margin of error.
d. Estimate the difference between mean acreage for the North East and the West, with a margin of error.
e. Estimate the mean acreage per county across the United States, with a margin of error.
Solution :
From the table,
Number of countries = [tex]$N_i$[/tex]
Mean = [tex]$\overline Y_i$[/tex]
Standard deviation = [tex]$\sigma_i$[/tex]
Margin of error of B = 50,000 acres
So we determine the [tex]$\text{sample size n}$[/tex] and then allocate the four regions of [tex]$n_1, n_2, n_3$[/tex] and [tex]$n_4$[/tex].
Under the [tex]$\text{proportional allocation}$[/tex], the [tex]$\text{equation}$[/tex] for the value of [tex]$n_1$[/tex] which yields [tex]$V(\overline Y_{st}) = D = \frac{B^2}{H}$[/tex] is given by :
[tex]$n=\frac{\sum_{K=1}^L N_K \sigma^2_K}{ND+\frac{1}{N}\sum_{K=1}^L N_K \sigma^2_K}$[/tex]
Let us complete the numerator
[tex]$\sum_{K=1}^L N_K \sigma^2_K = N_1\sigma_1^2 + N_2\sigma_2^2 + N_3\sigma_3^2 + N_4\sigma_4^2$[/tex]
[tex]$= 1052 \times (271)^2 + 210 \times (79)^2 + 1376 \times (244)^2 + 418 \times (837)^2 $[/tex]
= 453329920
The bound on the error of estimation is B = 50,000 acres
Hence we get
[tex]$D=\frac{B^2}{H}$[/tex]
[tex]$=\frac{50000^2}{4}$[/tex]
= 625,000,000
[tex]$n=\frac{\sum_{K=1}^L N_K \sigma^2_K}{ND+\frac{1}{N}\sum_{K=1}^L N_K \sigma^2_K}$[/tex]
[tex]$=\frac{453329920}{3056 \times 625 + \frac{1}{3056} \times 453329920}$[/tex]
= 220.24044
≈ 221 (approximately)
Therefore, the sample size under the proportional allocation from each stratum are given by :
[tex]$n_1=n\left[\frac{N_1}{\sum_{K=1}^\mu N_K}\right]$[/tex]
[tex]$=221\left[\frac{1052}{3056}\right]$[/tex]
≈ 76
[tex]$n_2=n\left[\frac{N_2}{\sum_{K=1}^\mu N_K}\right]$[/tex]
[tex]$=221\left[\frac{210}{3056}\right]$[/tex]
≈ 15
[tex]$n_3=n\left[\frac{N_3}{\sum_{K=1}^\mu N_K}\right]$[/tex]
[tex]$=221\left[\frac{1376}{3056}\right]$[/tex]
≈ 100
[tex]$n_4=n\left[\frac{N_4}{\sum_{K=1}^\mu N_K}\right]$[/tex]
[tex]$=221\left[\frac{418}{3056}\right]$[/tex]
≈ 30
Thus, we should select 76 counties from North central region, 15 counties from the north east region, 100 from south region and 30 from west region.
We can also estimate mean acreage of each county across all the county with a margin of error of 50,000 acres.
please help
thank you
Answer:
Step-by-step explanation:
-4<n≤5
The Smiths painted their house blue. The complete predicate of this sentence is _____.
Smiths
the Smiths
Solve the following: You purchase a set of Bluetooth earbuds for $45 and use a $5 off manufacturer's coupon. If sales tax is 8.25%, how much do you pay for the earbuds? Include the dollar sign in your answer and round to two decimal places.
Answer:
43.3
Step-by-step explanation:
45-5=40,
0.0825*40=3.3
40+3.3=43.3
Donna is participating in a 6-day cross-country biking challenge. She biked for 51, 62, 61, 47, and 63 miles on the first five days. How many miles does she need to bike on the last day so that her average (mean) is 56 miles per day?
Answer:
52 miles
Step-by-step explanation:
total miles needed to average 56
56 * 6 = 336
miles after 5 days
51 + 62 + 61 + 47 + 63 = 284
miles needed on last day
336 - 284 = 52 miles
What are the coordinates of the turning point of the parabola whose equation is y=-x^2+4x+1
PLEASEEE ANSWERRRRRR
Answer:
The maximum of the parabola lands at (2,5).
The coordinates of the turning point of the parabola whose equation is y=-x²+4x+1 are (2, 5)
What is Coordinate system?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points.
The equation of Parabola is y=-x²+4x+1
The turning point (vertex) is the point where the derivative is equal to zero.
y=-x²+4x+1
Differentiate the equation
dy/dx=-2x+4
Now equate dy/dx with zero
dy/dx=0
-2x+4=0
-2x=-4
x=2
Now put x value in the equation
y=-(2)²+4(2)+1
y=-4+8+1
y=5
Hence the coordinates of the turning point of the parabola whose equation is y=-x²+4x+1 are (2, 5)
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Which of the following is the point and slope of the equation y + 2 = 2(x - 8)?
-8, 2), 2
(2, -8), 2
(8, -2), 2
(-2, 8), 2
plzzzzz help me i have no clue
Answer: Maybe a
Step-by-step explanation:
I mean it is confusing but still look over it
Answer:
The bottom one looks correct
Step-by-step explanation:
Any number from 1-infinity will make that true
The sales tax in your city is 8.8\%8.8%8, point, 8, percent, and an item costs \$63$63dollar sign, 63 before tax.
How much tax would you pay on that item?
9514 1404 393
Answer:
$5.54
Step-by-step explanation:
8.8% of $63 is ...
0.088×$63 = $5.544
The tax is rounded to the nearest cent, so you would pay $5.54 in tax.
Answer: 5.54
Step-by-step explanation: khan said it was correct
hrutoday? eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Ica ingin membuat sebuah lampion
berbentuk kubus, panjang rusuknya 15
dm, maka volume lampion Ica adalah
... m?
a. 45
b. 3,375
c. 33,75
d. 3,375
Well the answer is 3,375
Mr. Halsey leans a ladder against an 11.5 foot wall the bottom the of the ladder is 3.5 ft from the base of the wall as shown what is the approximate length of the ladder
Hence, the approximate length of the ladder is [tex]12ft[/tex].
What is the approximation value?
An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding.
A calculation can be approximated by rounding the values within it before performing the operations.
Here given that,
[tex](x)^2=(11.5)^2+(3.5)^2\\X^2=132.25+12.25\\X^2=144.5 \\X=\sqrt{144.5}\\X=12 feet[/tex]
Hence, the approximate length of the ladder is [tex]12ft[/tex].
To know more about the approximation value
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Find the surface area of the rectangular prism (type the number
only)
2.6
4.2 ft
6.8 ft
HELP
-61=-3(1-5p)+4(-8-7p)
Answer: hello! have a good day! :)))
P = 2
Find the value of the following by suitable rearrangement. Mention the
property used.
a. 25 x 679 x 4
b. 2917 x 102 - 2917 x 2
(a) 67900
(b) 291700
Step-by-step explanation:(a) 25 x 679 x 4
Rearrange the terms starting with the smallest
4 x 25 x 679
The property used here is the commutative property of multiplication which states that the order in which these numbers are multiplied does not matter.
Now solve
4 x 25 x 679 = 67900
(b) 2917 x 102 - 2917 x 2
Factor out the common terms
2917(102 - 2)
Using the distributive property which states that when a number is multiplied by the sum or difference of two numbers, the result is the same as multiplying each of the two numbers by the number and then adding or subtracting the products.
Now solve
2917(102 - 2) = 2917(100)
= 291700
I have no idea pls help
Answer:
Area= 90
Step-by-step explanation:
triangle area: (b x h) / 2
(12 x 15) / 2
(180) / 2
a= 90
What is the area of the polygon?
Answer:
[tex]154m^{2}[/tex]
Step-by-step explanation:
8 · 7 = 56m (horizontal rectangle shape) the width was given by subtracting the total of the width (23m) minus (16m).
5 · 8 = 40m (square shape) Subtract 8m - 3m = 5m.
6 · 8 = 48m (square shape to the left of the polygon)
2 · 5 = 10m (small rectangle shape bottom left) 8 - 6 = 2 for the length and 5 for the width by 8 - 3 = 5
56m + 40m + 48m + 10m = 154 [tex]m^{2}[/tex]
So what would be the answer?
Answer:
i
Step-by-step explanation:
Answer:
did you forget a picture?
Step-by-step explanation:
if you did, either add it in the comments, or make a new question
Which expression is NOT equal to 28?
A (9 + 25 = 5) x 2
B. [(13 – 4x2) – 1] x 7
C. 42 = 6 + 28 = 4
D. 7 [8 - (12 - 4x 2)]

Answer:
aaaaa
Step-by-step explanation:
Answer:
I think it’s A
Step-by-step explanation:
Match each pair of Lines to the correct description
parallel lines
EP and CD
perpendicular lines
GH and EF
neither parallel nor
perpendicular lines
AB and CD
Answer:
Parallel = AB and CD
Perpendicular = EF and CD
Neither: GH and EF
Step-by-step explanation:
Parallel lines will go on forever without touching, they are aligned with each other.
Perpendicular lines intersect with 4 right angles
The Parallel lines are AB and CD and Perpendicular lines are EF and CD.
It is required to find the solution.
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
The given figure shown as four lines are given AB , CD ,EF , CD ,GH and EF.
According to given question we have
Parallel = AB and CD
Perpendicular = EF and CD
Neither parallel nor perpendicular lines: GH and EF
Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions
Perpendicular lines are lines that intersect at a 90-degree angle.
Therefore , the Parallel lines are AB and CD and Perpendicular lines are EF and CD.
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if a +b+c = 0 then the value of a²+b²+c²/bc+ca+ab
pls solve and give the explanation
Answer:
[tex]\frac{a^2 + b^2 +c ^2}{a*b + a*c + b*c} = -2[/tex]
Step-by-step explanation:
if:
a + b + c = 0
then we can rewrite:
c = -a - b
Now we can replace this in our expression:
[tex]\frac{a^2 + b^2 + c^2}{a*b + a*c + b*c} = \frac{a^2 + b^2 + (-a - b)^2}{a*b + a*(-a - b) + b*(-a - c)}[/tex]
Now we can rewrite:
(-a - b)^2 = a^2 + 2*a*b + b^2
Then we can rewrite our expression as:
[tex]\frac{a^2 + b^2 + a^2 + b^2 + 2*a*b}{a*b - a^2 - a*b - b^2 - b*a}[/tex]
Let's keep simplifying this:
[tex]\frac{2*(a^2 + b^2 + a*b)}{-a*b - b^2 - a^2}[/tex]
Here is easy to see the simplification we need to do, as we have the same factor in the denominator as in the numerator (just a different of sign).
[tex]\frac{2*(a^2 + b^2 + a*b)}{-a*b - b^2 - a^2} = \frac{2*(a^2 + b^2 + a*b)}{-(a^2 + b^2 + a*b)} = -2[/tex]
Then the expression is equal to -2
[tex]\frac{a^2 + b^2 +c ^2}{a*b + a*c + b*c} = -2[/tex]
PLEASE HELP ME IT'S MY LAST GRADE
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Is 5pi/3 the same as 5/3 radians?
Best answer gets brainliest!!
Please help me fast i need help
First question: less or greater
Second question: decrease or increase
Third question: would or would not
fourth question: correct or incorrect
You have to choose the answer's
Ok
Answer:
Look at the image.
Step-by-step explanation:
I really need help on this if someone knows the answer pls help
Answer:
14.75
Step-by-step explanation:
x = 1*1*0.5 = 0.5
y = 1.5*1.5 = 2.25
g = ((2.5+1.5)\2) * 2 = 4
t = 4*2 = 8
total = 0.5 +2.25 +4 +8 - 14.75
Help Please?! ?????????????
Answer:
Ed's answer of [tex]\frac{3}{8}[/tex] is correct because he divided [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{3}[/tex] to get his answer.
Step-by-step explanation:
To solve for m in [tex]\frac{2}{3}m=\frac{1}{4}[/tex] you want to isolate m by dividing by [tex]\frac{2}{3}[/tex] on both sides, therefore he divided [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{3}[/tex] to get his answer of [tex]\frac{3}{8}[/tex], and his answer is correct.
Eight new graduates are hired by an engineering firm. Each is assigned at random to one of eight cubicles arranged in a row in the back of the room that houses the engineering staff. Two of the graduates are Bill and Cathy. What is the probability that they are assigned adjacent cubicles
Answer:
the probability that they are assigned adjacent cubicles is 1 ÷ 4
Step-by-step explanation:
Given that
There is 8 new graduates are hired
2 of the graduates are bill and cathy
And, each one is assigned on random basis
We need to find out the probability
So,
= (2) (7!) ÷ (8!)
= (2) ÷ (8)
= 1 ÷ 4
Hence, the probability that they are assigned adjacent cubicles is 1 ÷ 4
The same would be relevant
What is another way to write 5/5? *
Answer:
Hello! answer: 1
Step-by-step explanation:
5/5 is 1 whole so you could write it as 1 because 5/5 is worth 100%
The histogram shows the ages of the players in an adult volleyball league. Which of the
following statements is true?
Volleyboll Players Ages
The older the age group, the greater the
number of players
5
There are 30 players between ages 20 and 25.
Number of Players
More than half of the players are under age
40.
20% 30% 50's 70's
Age Group
There must be 5 players between 50 and 55.
Answer:
More than half of the players are under age
40.
Step-by-step explanation:
Evaluating the expression : More than half of the players are under age 40.
Below 40s :
Number of players in 20s = 19
Number of players in 30s = 24
(19 + 24) = 43 players
40s and above :
40s = 8 players
50s = 10 players
60s = 5 players
70s = 2 players
(8 + 10 + 5 + 2) = 25 players
Hence, total number of players below 30s is more Than half of the total players