A sample of 50 drills had a mean lifetime of 12.17 holes drilled when drilling a low-carbon steel. Assume the population standard deviation is 6.37.Construct a 95% confidence interval for the mean lifetime of this type of drill
Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:
Sample mean of [tex]\overline{x} = 12.17[/tex]Population standard deviation of [tex]\sigma = 6.37[/tex]Sample size of [tex]n = 50[/tex].The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which z is the critical value.
We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.
In this problem, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.
Then:
[tex]M = 1.96\frac{6.37}{\sqrt{50}} = 1.77[/tex]
The confidence interval is the sample mean plus/minutes the margin of error, hence:
[tex]\overline{x} - M = 12.17 - 1.77 = 10.4[/tex]
[tex]\overline{x} + M = 12.17 + 1.77 = 13.94[/tex]
The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
A similar problem is given at https://brainly.com/question/22596713
How much should you invest at 2.6% simple interest in order to earn $75 interest in 8 months?
Answer: Total interest will $1800 after 5 years.
Step-by-step explanation: It is given that the principle amount is $6000.
Rate of interest rate is 6% per annum.
Total interest is $1800.
Formula for simple interest is
Where, P is principle, r is rate of interest in percent and t is time in years.
Substitute P=6000, r=6 and I=1800 in the above formula.
Divide both sides by 360.
Therefore the total interest will $1800 after 5 years.
From 77 books to 128 books
By selling a cow for Rs 144, there is a profit of the same percentage as its cost price. Find the cost price.
Answer:
Step-by-step explanation:
☼︎Answer:The cost price of cow = Rs.80
Explanation:
☼︎Given :-By selling a cow for Rs 144, there is a profit of the same percentage as its cost price.☼︎To Find:-The cost price.☼︎Let:-The cost price of cow = Rs.x☼︎Solution :-[tex] \sf x + x \: of \: x\%= 144 \\ \\ \sf \implies x + \frac{x \times x}{100} = 144 \\ \\ \sf \implies {x}^{2} + 100x - 14400 = 0 \\ \\ \sf \implies x(x - 80) + 180(x - 80) = 0 \\ \\ \sf \implies x + 180 = 0 \\ \\ \sf \implies x = - 180 \\ \\ \sf \therefore \: {\boxed{ \sf \pink{x = 80}}}[/tex]
Hence:The cost price of cow =Rs80
Step-by-step explanation:
The cost price of cow =Rs80
Please help missed this lesson
Answer:
m∠XYW = 32°, m∠WYZ= 85°
Step-by-step explanation:
6x+44-10x+65=117
-4x+109=117
-4x=117-109
=8
x=-8÷4
=-2
Hence, ∠XYW = (6x+44)°
= [6(-2)+44]°
= (-12+44)°
= 32°
Hence, ∠WYZ = 117° - 32°
= 85°
Pls Help
________________
under the supremacy clause, can the states ignore federal laws? (its a yes or no question not a paragraph from g00gle)
Answer:
no
Step-by-step explanation:
no
please help i'll mark brainliest
Answer
Isosceles
Step-by-step explanation:
You know two points for the leg (4,3) and (3,4). If you look at the x coordinate you know that one of the legs will be longer than the other because 4>3. So the triangle is isosceles.
8. A freight company charges a flat insurance fee to deliver a package anywhere in the continental United States, plus an additional charge for each pound the package weighs. The graph shows the relationship between the weight of the package and the total cost to ship it. Based on the graph, how much would it cost to ship a . 25-pound box?
(A) $37.00
(B) $48.00
(C) $62.50
(D) $74.50
Answer:
D 74.5
Step-by-step explanation:
Solution 1:
Observing the graph we know that when weight is 0lb we need to pay a $12 flat fee.
When weight=2 lb we notice that the total cost would be $17.
Take out the flat fee:
17-12 = $5.
So, for every 2 lb we need to pay an extra $5; therefore for every lb we need to pay $2.5.
25lb * $2.5/lb = $62.5
Add flat fee: 62.5+12=$74.5
Solution 2:
use linear equation to solve the problem.
1. Find the equation of the graph.
- pick 2 pts (0,12) and (2, 17)
2. Set up equation:
[tex]y=ax+b[/tex] and since the graph goes through (0,12)
thus [tex]y=ax+12[/tex]
3. plug in
- Plug in (2,17)
- [tex]17=2a+12[/tex] and [tex]a=2.5[/tex]
- so [tex]y=2.5x+12[/tex] where x is the weight and y is the total cost in dollar.
4. solve for x=25
[tex]y=2.5*25+12=74.5[/tex]
Divide (5x +39x+27) + (x+7) Your answer should give the quotient and the remainder. Quotient: Remainder:
Answer:
45x + 34
Step-by-step explanation:
this is your answer!
How long is a line of 1 million centimeter cubes be?
Answer:
1m cm
10m mm
Step-by-step explanation:
Write the equation in slope-intercept form of the line that passes through the
given points.
7. (-1,3) and (-3, 1)
8. (-4, 8) and (4, 6)
9. (9, 2) and (-3,-2)
7. y=x+4
8. y=(-1/4)x+7
9. y=(-1/3)x-1
SESSION 4
NDIV
4 Franklin uses 3 eggs to make a large omelet and 2 eggs to make a small omelet.
How many eggs does he need to make 5 large omelets and 4 small omelets?
14 eggs
B 22 eggs
© 23 eggs
0 26 eggs
Answer:
Which traits did Ben Franklin want to develop in himself?
Generosity, kindness, tolerance
Helpfulness, love, involvement
Acceptance and knowledge of the world
Temperance, efficiency, sincerity, and the avoidance of idleness and extravagance
Step-by-step explanation:
How many degrees are in 11.6pi
Step-by-step explanation:
[tex]11.6\pi × \dfrac{180°}{\pi} = 2088°[/tex]
Answer:
11.6 z × 180° / z = 2088°
[tex]11.6\pi \: \: \: \times \: \: \frac{180}{\pi} = 2088\pi \\ \\ \\ \\ i \: hope \: it \: is \: helpfull[/tex]
4% of a number is what fraction of that number?
Answer:
1 / 25
Step-by-step explanation:
4% in fraction form is 1 / 25
Hello there! (:
4% =4/100
Our fraction can be simplified:
2/50
Divide by 2, because it's not it its simplest form:
1/25
Hope it helps!
#CarryOnLearning
[tex]SparklingFlower[/tex]
Determine if the equation x-3y^2=1
Add 3y² to both sides of the equation.
x = 1 + 3y²
- Vocab
· Equation
A mathematical statement that says two expressions have the same value; any number sentence with an = .
· Expression
A mathematical symbol, or combination of symbols, representing a value, or relation.
· Combination
A selection in which order has no importance.
Which of the following statment is not true?
A. 0.6 = [tex]\frac{3}{5}[/tex]
B. 0.125 = [tex]\frac{1}{8}[/tex]
C. 2.015 = [tex]2 \frac{1}{100}[/tex]
D. 10.38 = [tex]10 \frac{19}{50}[/tex]
Answer:
The answer is C
Step-by-step explanation:
ABD IS TRUE
I’m sorry to ask, but can anyone please help me solve this. It would be greatly appreciated! Thank you to anyone who does! :))
Answer:
No need to apologize!! im pretty sure its
Step-by-step explanation:
X=80/10
X=8 MG OF VITAMIN C IN AN APPLE.
A cheetah can run 50 mph at this rate how many minutes would it take a cheetah to run 2.5 miles
Answer:
3 minutes
Step-by-step explanation:
time = distance / speed
t = 2.5 / 50
t = 0.05 hours
0.05 hr * 60minutes /hr = 3 minutes
3 minutes
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of
$1625. What was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour?
Note that the ALEKS graphing calculator can be used to make computations easier.
oo
Answer:
The first mechanic charges $45/hour while the second mechanic charges $50/hr
Step-by-step explanation:
X = rate of first mechanic
Y = rate of second mechanic
X + Y = 95 ---> Y = 95 - X
20X +5Y = 1150
Substituting the first equation into the second,
20X + 5(95 - X) = 1150
20X + 475 - 5X = 1150
15X + 475 = 1150
15x = 1150 - 475
15x = 675
X = 675/15 = 45 --> y = 95 - 45 = 50
CHECK: Plugging these results into the second equation:
20*45 + 5*50 = 900 + 250 = 1150
YES! Success! It checks!
So the first mechanic charges $45/hour while the second mechanic charges $50/hr! :)
Graph y < 1 -3x. Plz help me I will give branilest
Answer: Someone tell me if i'm wrong but from this I think it might be the fourth one (?)
Step-by-step explanation:
y=1
A straight line in slope (m) and intercept (c) form is:y=mx +c
In this example, y is a straight line of slope 0 and y −intercept of 1 ∴ y =0⋅
x+1
Hence, the graph of y a is straight line parallel to the x −axis through the point
(0,1)
In the series finale of 'Breaking Wind', ratings
were up 125% from last year's season finale.
10.5 million people watched this year. How
many people watched last year?
Answer:
3937500
Step-by-step explanation:
People watched last year = x
if ratings were up 125% x increased by x and 25% of x
25% of 10.5 million is 2625000
x increased by itself and 2625000
x*2+2625000 = 10500000
cancel out 2625000 by subtracting to both sides
10500000 - 2625000 = 7875000
x*2 = 7875000
cancel out 2 by dividing 2 on both sides
7875000/2 = 3937500
x = 3937500
A yacht will be leaving from Port Destiny and traveling on a straight line to an island 20
miles east and 60 miles north of the port. Find an equation h(x) for the line representing the path of the yacht. Assume Port Destiny is at the point (0,0) on a coordinate axis, East is to the right on the
horizontal axis, West is to the left on the horizontal axis, North is up on the vertical axis, and South is down on
the vertical axis.
h(x) =
9514 1404 393
Answer:
h(x) = 3x
Step-by-step explanation:
You want the equation of a line between the points (0, 0) and (20, 60). The slope of that line is ...
m = (y2 -y1)/(x2 -x1) = (60 -0)/(20 -0) = 60/20 = 3
The y-intercept is 0, so the slope-intercept equation of the line is ...
h(x) = 3x
A basket contains 12 red balls and 8 yellow balls. One ball is picked at random and not replaced, and then a second ball is picked at random from the remaining balls. What is the probability of a red ball followed by a yellow ball
Answer:
12/20, 8/19
Step-by-step explanation:
The first basket contains 48 peaches. The second basket contains 50 peaches. How many peaches must you transfer from the first basket to the second on so that the number of peaches in the second basket is 6 times that of the first one?
Answer:
Hence, answer is 34 peaches
Step-by-step explanation:
Analysis : Total peaches = 48 + 50
= 98
Let first one contained x peaches
: second basket will contain 6x peaches
--> x + 6x = 98
--> 7x = 98
--> x = 98/7 = 14
: 48 - 14 = 34 peaches will transfer from the first basket to second one
Can someone please tell me the steps I would have to take in order to answer the question below?
Answer:
Step-by-step explanation:
Add all sides together and set equal to 360
x+1 + x+2 + x+3 + x+4 =360
Combine Like Terms
4x + 10 = 360
get rid of the ten on both sides
4x = 350
Divide both sides by 4
x = 87.5
The picture is up there
Answer: [tex]2\sqrt{3}[/tex]
Step-by-step explanation:
Simplify the following radical:
[tex]\sqrt{12}[/tex]
Find the prime factors of 12:
2² × 3
[tex]\sqrt{2^{2} (3)}[/tex] = [tex]2\sqrt{3}[/tex]
please help its a growth and decay problem
simplify (-x+8x-12)/(x^(2)-4x-12)
Answer:
[tex]\frac{7x-12}{(x-6)(x+2)}[/tex]
Step-by-step explanation:
We solve this equation by combining like terms [tex](-x+8x)=7x[/tex]
Now we rewrite the equation [tex]\frac{7x-12}{x^2-4x-12}[/tex]
We factorize [tex]x^2-4x-12[/tex] and we get [tex](x-6)(x+2)[/tex]
So our simplified answer would be [tex]\frac{7x-12}{(x-6)(x+2)}[/tex]
Write each fraction as a percent 2/7 round decimal to nearest 100
Answer:
3 okkkkkkkkkyy667yytrty
Answer:
0.29
Step-by-step explanation:
2/7=0.285 or 2÷7= 0.285
then round to the nearest 100th
0.29
