The breaking strengths of cables produced by a certain manufacturer have a mean, , of pounds, and a standard deviation of pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be pounds. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the mean breaking strength has increased
The question is incomplete. The complete question is :
The breaking strengths of cables produced by a certain manufacturer have a mean of 1900 pounds, and a standard deviation of 65 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 150 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1902 pounds. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the mean breaking strength has increased?
Solution :
Given data :
Mean, μ = 1900
Standard deviation, σ = 65
Sample size, n = 150
Sample mean, [tex]$\overline x$[/tex] = 1902
Level of significance = 0.01
The hypothesis are :
[tex]$H_0 : \mu = 1900$[/tex]
[tex]$H_1 : \mu > 1900$[/tex]
Test statics :
We use the z test as the sample size is large and we know the population standard deviation.
[tex]$z=\frac{\overline x - \mu}{\sigma / \sqrt{n}}$[/tex]
[tex]$z=\frac{1902-1900}{65 / \sqrt{150}}$[/tex]
[tex]$z=\frac{2}{5.30723}$[/tex]
[tex]$z=0.38$[/tex]
Finding the p-value:
P-value = P(Z > z)
= P(Z > 0.38)
= 1 - P(Z < 0.38)
From the z table. we get
P(Z < 0.38) = 0.6480
Therefore,
P-value = 1 - P(Z < 0.38)
= 1 - 0.6480
= 0.3520
Decision :
If the p value is less than 0.01, then we reject the [tex]H_0[/tex], otherwise we fail to reject [tex]H_0[/tex].
Since the value of p = 0.3520 > 0.01, the level of significance, then we fail to reject [tex]H_0[/tex].
Conclusion :
At a significance level of 0.01, we have no sufficient evidence to support that the mean breaking strength has increased.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
Slope = 2
Step-by-step explanation:
To find the slope of the line, you need to plot two points
My own two points will be: [tex](1,2)[/tex] and [tex](2,4)[/tex]
Now use the Slope-Formula to identify the slope of the line
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-2}{2-1}[/tex]
[tex]m=\frac{2}{1}[/tex]
[tex]m=2[/tex]
so the slope of the line in simplest form will be 2.
Give an example of a function with both a removable and a non-removable discontinuity.
Answer:
(x+5)(x-3) / (x+5)(x+1)
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
Multiply the polynomial 4x(2x+3) (show work pls)
Answer:
8^2+12x
Step-by-step explanation:
4x(2x+3)
=4x times 2x+4x times 3
=4 times 2xx+4 times 3x
Answer:
8x^2 +12x
Step-by-step explanation:
Step 1) Multiply each term in the parentheses by 4x
4xx2x+4xx3
Step 2) Calcuate the product
8x^2 +12x
You can afford a $950 per month mortgage payment. You've found a 30 year loan at 8% interest. a) How big of a loan can you afford? b) How much total money will you pay the loan company? c) How much of that money is interest?
Answer:
129469.3194
342000
212530.6806
Step-by-step explanation:
Going to assume that the 8% is a nominal, montly rate
which means the effective monthly rate is .08/12= .006667
using the annuity immediate formula...
a.)
[tex]950(\frac{1-(1+.006667)^{-30*12}}{.006667})=129469.3194[/tex]
b.) we would pay 950*30*12= 342000
c.) the amount in interest would be 342000-129469.3194=212530.6806
a) The loan one can afford is $1,29,460.2
b) The total amount of money paid to the loan company over the life of the loan is $342,000.
c) $212539.8 of the total amount paid is interest.
To determine the answers to these questions, we'll need to use the formula for calculating a fixed monthly mortgage payment:
[tex]M = \frac{P \times r \times (1 + r)^n}{((1 + r)^n - 1)}[/tex]
where:
M is the monthly payment,
P is the principal loan amount,
r is the monthly interest rate (annual interest rate divided by 12),
and n is the total number of payments (number of years multiplied by 12).
Given:
Monthly payment (M) = $950
Loan term = 30 years
Interest rate = 8% per year
a) How big of a loan can you afford?
Let's calculate the principal loan amount (P):
First, we need to convert the annual interest rate to a monthly interest rate:
r = 0.08 / 12
= 0.00667
n = 30 years × 12 months
n= 360
Using the formula and plugging in the values we have:
[tex]950 = \frac{P \times 0.00667 \times (1 + 0.00667)^{360}}{((1 + 0.00667)^{360} - 1)}[/tex]
[tex]950 = \frac{P \times 0.00667 \times 10.948}{10.948 - 1}[/tex]
[tex]950=\frac{P \times 0.07302316}{9.948}[/tex]
[tex]950\times9.948 = 0.0730P[/tex]
Divide by 0.073:
Now we can solve for P:
[tex]P=\frac{9450.6}{0.0730}[/tex]
[tex]P = 1,29,460.2[/tex]
Therefore, you can afford a loan amount of $1,29,460.2
b) The total amount paid to the loan company can be calculated by multiplying the monthly payment by the total number of payments:
Total amount = Monthly payment × Total number of payments
Total amount =[tex]$950 \times 360[/tex]
Total amount = [tex]342,000[/tex]
Therefore, the total amount of money paid to the loan company over the life of the loan is $342,000.
c) To find out how much of the total amount paid is interest, we can subtract the principal loan amount from the total amount:
Interest = Total amount - Principal loan amount
Interest = [tex]342,000 - 129460.2[/tex]
=$212539.8
Therefore, $212539.8 of the total amount paid is interest.
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Help asap! Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and an extra 25¢ for each mile over 250. For what number of miles traveled in one day would the unlimited mileage plan save Lia money? (Show work)
Answer:
The unlimited mileage plan would save money for Lia from 410 miles onwards.
Step-by-step explanation:
Since Lia can rent a van for either $ 90 per day with unlimited mileage or $ 50 per day with 250 free miles and an extra 25 ¢ for each mile over 250, to determine for what number of miles traveled in one day would the unlimited mileage plan save Lia money, the following calculation must be performed:
90.25 - 50 = 40.25
40.25 / 0.25 = 161
161 + 250 = 411
Therefore, the unlimited mileage plan would save money for Lia from 410 miles onwards.
if TS is a midsegment of PQR find TS
Answer:
B. 7
Step-by-step explanation:
Recall: according to thee Mid-segment Theorem of a triangle, the Mid-segment of a triangle is half the length of the base of the triangle
Base length of the traingle, RQ = 14 (given)
Mid-segment = TS
Therefore,
TS = ½(RQ)
Plug in the value
TS = ½(14)
TS = 7
WILL GIVE BRAINLIEST!!!
Write as a polynomial: 14b + 1 - 6(2 - 11b)
Answer:
80b-11
Step-by-step explanation:
14b + 1 - 6(2 - 11b)
Distribute
14b+1-12+66b
Combine like terms
80b-11
Answer:
80b - 11
Step-by-step explanation:
what is the problem ?
just multiply it out and combine terms.
14b + 1 - 6(2 - 11b) = 14b + 1 - 12 + 66b = 80b - 11
An amusement park offers 2 options on tickets into the park. People can either buy 5 admission tickets for $130 or buy 1 admission ticket for $30. How much money will a group of 5 people save by buying 5 admission tickets for $130?
Answer:
You could save $20
Step-by-step explanation:
For buying them separately for $30 each for 5 people it would be $150 but if you buy the first option you would get 5 admission tickets for only $130
Answer:
20 dollars
Step-by-step explanation:
for the first deal is 5 for $130
and the second is for $30
$30 times 5 (the number of people) = $150
$150-$130= is 20
answer: $20
For which equation is (4, 3) a solution?
Answer:
4 over 3
because is in side the bracket is part of inequalities
An airplane can travel 350 mph in still air. If it travels 1995 miles with the wind
in the same length of time it travels 1505 miles against the wind, what is the speed of the wind?
Answer:
49 mph
Step-by-step explanation:
RT=D
T = D/R
[tex]\frac{1995}{(350 + x) } =\frac{1505}{350-x}[/tex]
1995(350-x) = 1505(350+x)
x=49
Put the equation y = x^2- 14x + 48 into the form y = (x-h)^2+k
please help me!
Answer:
Step-by-step explanation:
Answer:
[tex]y=(x-7)^2-1[/tex]
Step-by-step explanation:
We want to convert the equation:
[tex]\displaystyle y=x^2-14x+48[/tex]
Into vertex form, given by:
[tex]\displaystyle y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.
Method 1) Vertex Formulas
Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.
Recall that the vertex is given by:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]
To find the y-coordinate, substitute this value back into the equation. Hence:
[tex]y=(7)^2-14(7)+48=-1[/tex]
Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.
And since we already determined a = 1, our equation in vertex form is:
[tex]\displaystyle y=(x-7)^2-1[/tex]
Method 2) Completing the Square
We can also complete the square to acquire the vertex form. We have:
[tex]y=x^2-14x+48[/tex]
Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:
[tex]y=(x^2-14x)+48[/tex]
Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.
We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:
[tex]y=(x^2-14x+49)+48-49[/tex]
Factor using the perfect square trinomial and simplify:
[tex]y=(x-7)^2-1[/tex]
We acquire the same solution as before, with the vertex being (7, -1).
Iceberg lettuce is grown and shipped to stores for about 40 cents a head, and consumers purchase it for about 92 cents a head. Find the percent increase.
Answer: 130%
Step-by-step explanation:
percent increase = x[tex]40 + 40(x) = 9240\\40(1 + x) = 92\\1+x=\frac{92}{40} \\x=\frac{92}{40} -1=2.3-1=1.3[/tex]
x = 1.3 = 130%
For two consecutive numbers, five times the number that is less is 3 more than 4 times the greater number, What are the numbers
This is due on 7/1/2021 at 8AM PST. Someone please help?
According to Okun's law, if the unemployment rate goes from 5% to 3%, what will be the effect on the GDP?
A. It will increase by 7%.
B. It will decrease by 7%.
C. It will decrease by 1%.
D. It will increase by 1%.
Answer:
D. It will increase by 1%.
Step-by-step explanation:
Given
[tex]u_1 = 5\%[/tex] --- initial rate
[tex]u_2 = 3\%[/tex] --- final rate
Required
The effect on the GDP
To calculate this, we make use of:
[tex]\frac{\triangle Y}{Y} = u_1 - 2\triangle u[/tex]
This gives:
[tex]\frac{\triangle Y}{Y} = 5\% - 2(5\% - 3\%)[/tex]
[tex]\frac{\triangle Y}{Y} = 5\% - 2(2\%)[/tex]
[tex]\frac{\triangle Y}{Y} = 5\% - 4\%[/tex]
[tex]\frac{\triangle Y}{Y} = 1\%[/tex]
This implies that the GDP will increase by 1%
Answer: A. It will increase by 7%.
Step-by-step explanation: I took this course!
Which one is the correct answer? help pls!!
Answer:
(2k, k)
Step-by-step explanation:
x + y = 3k
x - y = k
Add the equations.
2x = 4k
x = 2k
2k + y = 3k
y = k
Answer: (2k, k)
What equation can I use to pick numbers 1-70 if they're picked randomly
9514 1404 393
Answer:
you cannot use an equation to pick random numbers
Step-by-step explanation:
"Picked randomly" and "using an equation" are mutually exclusive. A random number cannot be predicted, so an equation cannot be used to generate it.
That being said, many programming languages make use of a "linear congruential generator" for generating random numbers. Such a generator generates a next number (x') from a previous number (x) using the equation ...
x' = (a·x +c) mod m
Numbers generated in this way are called "pseudo-random numbers." The sequence of generated numbers will repeat at some point, and the statistics of generated numbers may or may not be suitable for any given application. (For example, sequential numbers may tend to be correlated.) The distribution of numbers is inherently uniform, so if you need other distribution, you need to perform some math on what you get from a linear congruential generator. Methods are available for approximating about any kind of distribution you might want.
This is not the only "equation" that can be used, and is certainly not the best.
__
A variety of different values of a, c, m are used in generators of this type. Some are better than others at producing what looks like randomness. Here's a set of numbers you can try: (no claim is made regarding suitability for your purpose)
a = 1140671485c = 12820163m = 2^24 = 16777216This will produce numbers in the range 0–16777215. To get numbers in the range of 1-70, you can map these to your range in any suitable fashion. For example, you could add 1 to the integer part of the result from division by 239675.
Below is a graph of the sorted output of 200 values in the range 1–70 from the generator described here. You can see the distribution is approximately linear, and that some values are missing while others show up more often than average. (You expect this with random numbers.) The seed for these numbers (first value of x) is 1337457.
__
There is a web site available that will produce random numbers to your specification, based on the background noise of the universe. They are truly random.
Carlos has an aquarium which is 45 cm long, 32 cm wide, and 35 cm high. How much water can the aquarium hold?
Answer:
volume =l×b×h
45cm×32cm×35cm=48,960cm³
Find the slope of the line containing the pair of points.
(-3,1) and (1, - 11)
Answer:
Step-by-step explanation:
slope = (y2 - y1)/(x2 - x1)
x2 = -3
x1 = 1
y2 = 1
y1 = - 11
slope = (1 - - 11) / (-3 - 1)
slope = 12 / - 4
slope = - 3
The variance of the scores on a skill evaluation test is 143,641 with a mean of 1517 points. If 343 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 36 points
Answer:
The probability that the mean of the sample would differ from the population mean by less than 36 points=0.9216
Step-by-step explanation:
We are given that
The variance of the scores on a skill evaluation test=143,641
Mean=1517 points
n=343
We have to find the probability that the mean of the sample would differ from the population mean by less than 36 points.
Standard deviation,[tex]\sigma=\sqrt{143641}[/tex]
[tex]P(|x-\mu|<36)=P(|\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}|<\frac{36}{\frac{\sqrt{143641}}{\sqrt{343}}})[/tex]
[tex]=P(|Z|<\frac{36}{\sqrt{\frac{143641}{343}}})[/tex]
[tex]=P(|Z|<1.76)[/tex]
[tex]=0.9216[/tex]
Hence, the probability that the mean of the sample would differ from the population mean by less than 36 points=0.9216
6. Aerial photography is to be taken of a tract of land that is 8 x 8 mi2. Flying height will be 4000 ft above average terrain, and the camera has focal length of 6 inches. If the focal plane opening is 9 x 9 in., and minimum side overlap is 30%, how many flight lines will be needed to cover the tract for the given data
Answer:
the number of flight lines needed is approximately 72
Step-by-step explanation:
Given the data in the question;
Aerial photography is to be taken of a tract of land that is 8 x 8 mi²
L × B = 8 x 8 mi²
Flying height H = 4000 ft = ( 4000 × 12 )inches = 48000 in
focal length f = 6 in
[tex]l[/tex] × b = 9 × 9 in²
side overlap = 30% = 0.3
meaning remaining side overlap = 100% - 30% = 70% = 0.7
{ not end to end overlap }
we take 100% { remaining overlap }
[tex]l[/tex]' = 9 × 100% = 9 in
b' = 9 × 70% = 6.3 in
Now the scale will be;
Scale = f/H
we substitute
Scale = 6 in / 48000 in = 1 / 8000
so our scale is; 1 : 8000
⇒ 1 in = 8000 in
⇒ 1 in = (8000 / 63360)mi
⇒ 1 in = 0.126 mi
so since
L × B = 8 x 8 mi²
[tex]l[/tex]' = ( 9 × 0.126 mi ) = 1.134 mi
b' = ( 6.3 × 0.126 mi ) = 0.7938 mi
Now we get the flight lines;
N = ( L × B ) / ( [tex]l[/tex]' × b' )
we substitute
N = ( 8 mi × 8 mi ) / ( 1.134 mi × 0.7938 mi )
N = 64 / 0.9001692
N = 71.0977 ≈ 72
Therefore, the number of flight lines needed is approximately 72
To find the quotient of 8 divided by one-third, multiply 8 by
O One-eighth
O One-third
O 3
O 8
Answer:
3
Step-by-step explanation:
Skip,Flip,Multiply Method
[tex] \frac{8}{ \frac{1}{3} } = \frac{8}{1} \times 3 = 24[/tex]
Answer:
3
Step-by-step explanation:
If f(x)=5x and g(x)=2x-1, what is the composition f(g(x))?
Answer:
10x-5
Step-by-step explanation:
f(x)=5x
g(x)=2x-1
To create a composite function, replace x in f(x) with g(x)
f(g(x)) = 5(g(x) = 5(2x-1) = 10x-5
the graph function f(x) is illustrated in figure below (-2,1) ,(-1,2) ,(1,2) ,(2,3) .Use the transformation techniques to graph the following functions
a) y=f(x)-2
b) y=f(-x)
Answer:
a) y = f(x) - 2 (x, y) ⇒ (x, y - 2)b) y = f(-x) (x, y) ⇒ (-x, y)a) y=f(x)-2
(-2, 1) → (-2, 1 - 2) = (-2, -1)(-1, 2) → (-1, 2 - 2) = (-1, 0)(1, 2) → (1, 2 - 2) = (1, 0)(2, 3) → (2, 3 - 2) = (2, 1)b) y=f(-x)
(-2, 1) → (-(-2), 1) = (2, 1)(-1, 2) → (-(-1), 2) = (1, 2)(1, 2) → (-1, 2)(2, 3) → (-2, 3)mrs cabrini needs 2 quarts of tomato sauce to make a large batch of her spaghetti sauce. she has 1 1/4 quarts of her own. she borrows 1/2 quart from the neighbor across the hall and 3/8 quart from the neighbor next door . how many quarts does she have in all of her own .
Answer:
Mrs. Cabrini has a total of 2 1/8 quarts of tomato sauce.
Step-by-step explanation:
Since Mrs. Cabrini needs 2 quarts of tomato sauce to make a large batch of her spaghetti sauce. she has 1 1/4 quarts of her own, and she borrows 1/2 quart from the neighbor across the hall and 3/8 quart from the neighbor next door, to determine how many quarts does she have in all of her own must perform the following calculation:
1/4 = 0.25
1/2 = 0.5
3/8 = 0.375
0.25 + 0.5 + 0.375 = X
1.125 = X
1 + 1,125 = 2,125
Therefore, Mrs. Cabrini has a total of 2 1/8 quarts of tomato sauce.
Get brainly if right!! Plsss help
The 8t h term in the arithmetic sequence is 17, and 12t h term is 25. Find the first
term, and the sum of the first 20 terms.
Step-by-step explanation:
t8 = a1 + (n - 1)*d
t8 = 17
17 = a1 + 7*d
t12 = 25
25 = a1 + 11d
17 = a1 + 7d Subtract
8 = 4d Divide by 4
8/4 = 4d/4
2 = d
17 = a1 + 7d
17 = a1 + 7*2
17 = a1 + 14 Subtract 14
3 = a1
Sum 20 terms
The 20 term = a1 + 19*2
The 20 term = 3 + 38
= 41
Sum = (a1 + a20) * 20 / 2
Sum = (3 + 41)* 20/2
Sum = 44 * 10
Sum = 440
Please help solve this problem.
Answer:
Ang hirap naman niyan bakit kaya lahat na module mahirap
ANSWER ASAP IM BEING TIMED
IF I GET AN A ON THIS I WILL DO ANOTHER POINT FREE DROP, PLEASE SHOW YOUR WORK
The lengths of three sides of a quadrilateral are shown below:
Side 1: 1y2 + 3y − 6
Side 2: 4y − 7 + 2y2
Side 3: 3y2 − 8 + 5y
The perimeter of the quadrilateral is 8y3 − 2y2 + 4y − 26.
Part A: What is the total length of sides 1, 2, and 3 of the quadrilateral? (4 points)
Part B: What is the length of the fourth side of the quadrilateral? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Answer:
Part A
(1y^2+3y-6)+(4y-7+2y^2)+(3y^2-8+5y)
6y^2+12y-21
The farmer is buying fence panels.
He needs a total length of 200 m of fence panels.
Each fence panel is 2.5 m in length.
Work out how many fence panels the farmer will need to buy?
Answer:
80 panels
Step-by-step explanation
Can someone help me out here please? I do not know how to solve this problem nor where to start?
Answer:
200 test tubes will fill the container
Step-by-step explanation:
Hi there!
We need to find out how many 5 milliliter tubes will fill a 1 liter container
First, let's convert everything to the same unit, as the tubes and the container are in different units.
Let's do milliliters, as those are smaller than liters and we will avoid having decimals.
there are 1,000 milliliters in a liter (the unit prefix "milli-" means "thousand")
Let's say the number of test tubes needed to fill the container is x
As each tube has 5 milliliters of water, 5x milliliters will equal 1,000 milliliters (1 liter)
as an equation, that's
5x=1,000
divide both sides by 5
x=200
So that means 200 test tubes will fill the container
Hope this helps! :)
Answer:
Here is how to start
Step-by-step explanation: 7 2 13 42
1 milliliter is one one thousands of a liter 1 milliliter = 0.001 liter
1000 milliliter is equal to 1 liter
How many 5 milliliter test tubes are in 1 liter?
1000 milliliter / 5 milliliter per test tube = ________ test tubes