The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the standard deviation is 1.4 gallons and the mean is 15.9 gallons per day. If they are using a 80% level of confidence, how large of a sample is required to estimate the mean usage of water
Answer:
A sample of 164 is needed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.8}{2} = 0.1[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.1 = 0.9[/tex], so [tex]z = 1.28[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How large of a sample is required to estimate the mean usage of water
We need a sample of n.
n is found when [tex]\sigma = 1.4, M = 0.14[/tex]. So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.14 = 1.28*\frac{1.4}{\sqrt{n}}[/tex]
[tex]0.14\sqrt{n} = 1.28*1.4[/tex]
[tex]\sqrt{n} = \frac{1.28*1.4}{0.14}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.28*1.4}{0.14})^{2}[/tex]
[tex]n = 163.84[/tex]
Rounding up
A sample of 164 is needed.
Graph the systems of equations to find the solution.
There are 60 students in a choir. Of those students, 55% of them warm up before a performing. How many students warm up before performing
New York and Chicago are 800 miles apart. A train leaves New York for Chicago and travels at an average speed of 50 mph. Another train leaves Chicago for New York at the same time and travels at an average spped of 40 mph. How far apart will the two trains be after six hours?
Answer:
60
Step-by-step explanation:
50 x 6 = 300
40 x 6 = 240
300 - 240= 60
The cost of making copies at Store W is $14 regardless of the number of copies. The cost of making copies at Store Z is 60cents per copy plus a $2 charge for the use of the machine. The total cost, c, of making n copies at either store can be represented by an equation. Write and graph a system to find how many copies you have to make for the cost to be the same at both stores. Use pencil and paper. If you have to make a small number of copies which store should you go to? If you have to make a large number of copies which store should you go to? Explain.
Answer:
store w: c = $14
store z: c = 0.60n + 2
Step-by-step explanation:
i had a similiar question with different numbers so i just changed the numbers for ur equation :)
The equation to make for the cost to be the same at both stores would be; 14 = 0.60n + 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given that cost of making copies at Store W is $14 regardless of the number of copies. And the cost of making copies at Store Z is 60 cents per copy plus a $2 charge for the use of the machine.
The total cost, c, of making n copies at either store can be represented by an equation as;
The store w:
c = $14
The store z:
c = 0.60n + 2
Solving for n then
14 = 0.60n + 2
0.60n = 12
n = 20
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Expressed in simplest form,(3x^3)(2y)^2(4x^4) is equivalent to
Answer:
Step-by-step explanation:
3[tex]x^{3}[/tex][tex](2y)^{2}[/tex]4[tex]x^{4}[/tex]
So I wrote down exactly above how the eq. is put in the question, note that the 2y is the only coefficient that is inside of the parenthesis, I hope that is how the question is asked. The 3 and 4 coefficient are NOT part of the exponential part.. is my point.. which will make a big difference if they were.
anyway
3[tex]x^{3}[/tex]4[tex]y^{2}[/tex]4[tex]x^{4}[/tex]
48[tex]y^{2}[/tex][tex]x^{3}[/tex][tex]x^{4}[/tex] ( b/c the x bases are the same we can just add the exponents)
48[tex]y^{2}[/tex][tex]x^{3+4}[/tex]
48[tex]y^{2}[/tex][tex]x^{7}[/tex] ( this is your answer )
side note: an important learning point that was implied above is that you could rewrite the expression as 48[tex]y^{2}[/tex][tex]x^{2}[/tex][tex]x^{2}[/tex][tex]x^{2}[/tex][tex]x^{1}[/tex]... why would you want to write it that way? b/c often a square is needed to make a problem work out easier.
as in Cos^2(Ф) + Sin^2(Ф) = 1 but that's another question L :P
(if you're read this far.. good for you.. if it's the 1st time you've heard of that rule for exponents then ask your teacher / professor if I can have 1/2 of their pay since I am doing their job :D )
what is the oxidation number of carbon
+4
The oxidation number of C must be +4, to make the oxidation number of the ion the same as its charge.
number of C must be + 4 to make the oxidation number of the ion the same as its charge
What is the solution for 7 +2x/5=13
Answer:
The correct answer is,
[tex]x = \frac{65}{37} [/tex]
What is the outlier in the following data set? 12,24,15,63,12,22,26,15,30
Answer:
63
Step-by-step explanation:
very far from thesecond largest number
hope this helps <3
What happens when you add and subtract like fractions
Answer:hey must have the same denominator (the bottom value). If the denominators are already the same then it is just a matter of either adding or subtracting the numerators (the top value). If the denominators are different then a common denominator needs to be found.
Step-by-step explanation:
Are these ratios equivalent?
6 centiliters every 2 months
48 centiliters every 16 months
question is provided in the picture! please provide the work too! thanks (: ASAP
Answer:
the answer is -10 over 21
Freddy went to the museum and bought a reduced copy of a painting he saw in a exhibit. If the actual painting is 12 inches high, how wide is it ?
Answer:
It is probably 6 inches wide. I tried my best
Step-by-step explanation:
what’s the equation of the following
[tex] \bold {m = \frac{rise}{run} } \\ m = \frac{0 - ( -2)}{0 - 10} \\ m = \frac{0 + 2}{ - 10} \\ m = \frac{2}{ - 10} \\ m = - \frac{1}{5} [/tex]
From the slope-intercept form.[tex]y = mx + b \\ m = slope \\ b = y - intercept[/tex]
Because the graph passes origin point (0,0). Therefore the value of b is 0.
Answer[tex] \large \boxed {y = - \frac{1}{5} x}[/tex]
(GIVING BRAINLIEST!!)
Choose the equation that represents the fraction one twelfth.
12 ÷ 1 = ________
12 ÷ 11 = ________
1 ÷ 12 = ________
11 ÷ 12 = ________
The first equation (12÷1) represents the fraction one twelfth since it can be written as 1/12.
Hope it helps!
Answer:
The one that represents the fraction one twelfth is the 3rd option down 1 divided by 12
Step-by-step:
1 divided by 12 gives u the decimal for 1/12.
how do I write 10b4 + 3b2 - 11 in quadratic form
Answer:
46b-11
Step-by-step explanation:
If a solution has 24g of sugar in 130ml of water, what is its concentration?
Answer: concentration = 15.58%
Step-by-step explanation:
Given: mass of sugar = 24 g = 24 ml [ ∵ 1 g = 1 ml]
Volume of solution = Quantity of water + quantity of solute
= 130 +24 ml
= 154 ml
Concentration = [tex]\dfrac{mass\ of\ solute}{Volume\ of\ solution}\times100[/tex]
[tex]=\dfrac{24}{154}\times 100\\\\\approx15.58\%[/tex]
Hence, the concentration =15.58%
what is the volume of the right cone shown below?
Answer:
A it's a because 45 x 10³ is 75
A miniature golf course has a special group rate. You can pay $20 plus $3 per person when you have a group of 5 or more friends. Let be the number of friends and be the total cost.
1) Determine which variable is independent and which is dependent.
2) Write an equation that models the situation.
Please help me.
1 - Dependent Variable
2- 3x + 20 = 35
Find the value of ƒ(5) if
Question 12 options:
A)
19
B)
-5
C)
3
D)
7
Answer:
the value of ƒ(5) is 19
Step-by-step explanation:
Answer:
dk
Step-by-step explanation:
HELP! I need help very quick! Please
Answer:
1st is 15 dollar I am looking for 2nd 1by2 dollar 3rd no
Wyatt can buy T-shirts in packs of 5 for $8.15 or in packs of 2 for $5.86. How much money does he save by buying 20 T-shirts at the better price?
Answer:
Wyatt saves $26 if he uses the 5 for $8.15
Step-by-step explanation:
Use the numbered angles in the diagram to answer the question.
Which angles are congruent? How do you know?
8. Write an algebraic expression to represent each
word expression.
e. fourteen less than three times a number n
Vector addition obeys rules that are different from those for the addition of two scalar quantities.
a. True
b. False
Answer:
false
Step-by-step explanation:
false
how to calculate area when you are given volume of 182m3 and height of 2.8m
Hey there!
We simply have to do 182/2.8, and you will get the area (65m^2).
We know that the formula for area is length x width, and the formula for volume is length x width x height. In the volume formula, we can see it can also be area x height to get volume. So, we know that area x height = volume, right? And in this equation, we are given volume and height. If V = ha, with V = volume; h = height; a = area, we can divide "h" on both sides, and we get V/h = a, or volume divided by height is area. To solve for the above equation, we can plug the numbers in the formula: 182/2.8 = a, or 65 = a.
Hope this helps! Have an amazing day, and remember, you've got this!
SOS! Can some please help me!
Answer:
8.9
Step-by-step explanation:
1. DE:BC=AD:AB
2. AD=AB+BD, but according to the conditions AB=5, then
AD=5+BD.
3. after the substitution DE=16; BC=9; AB=5 and AD=5+BD into the formula:
16:9=(5+BD):5;
[tex]\frac{16}{9} =\frac{BD+5}{5};[/tex]
BD=80/9 - 5≈3.9.
4. if AD=AB+BD, then AD=5+3,9=8,9
Answer:
8.9 is your answer to the question
y = -2, 3y-4 evaluate it please
5 percent of adults participate in at least 30 minutes from of exercise each day. How likely is it that a randomly chosen adult will exercise 30 minutes each day
Answer:
5% probability that the adult will exercise 30 minutes each day
Step-by-step explanation:
The exercise states that 5 percent of adults participate in at least 30 minutes from of exercise each day.
The interpretation of this is that if we choose a randomly selected adult, there is a 5% probability that the adult will exercise 30 minutes each day.
Compute $\left(\sqrt{675} - \sqrt{363}\right)^2$.
Answer:
( √675 - √363 )²
= (( 988 - ( √363 × 363 ))
= (( 988 - 131.769 ))
= - 130.781
The expression equivalent to the given one is - 130.781.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple,
We have given an expression;
( √675 - √363 )²
= (( 988 - ( √363 × 363 ))
= (( 988 - 131.769 ))
= - 130.781
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