The probability that a randomly chosen light bulb will last less than 1460 hours is 0.0322, rounded to the nearest thousandth
The formula for calculating the z-score is:
z = (x - μ) / σ
Where: x = the value we want to find the probability
μ = the mean of the distribution.
σ = the standard deviation of the distribution.
Now for the probability that a randomly chosen light bulb will last less than 1460 hours,
Here, x = 1460
μ = 1600
σ = 75
Plugging in the values, we get:
z = (1460 - 1600) / 75
= -1.8667
Now, The cumulative probability represents the area under the curve to the left of the z-score.
Looking up the z-score -1.8667 in the standard normal distribution table, we find that the cumulative probability is 0.0322.
Therefore, the probability that a randomly chosen light bulb will last less than 1460 hours is 0.0322, rounded to the nearest thousandth.
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write as a polynomial (-2x^2+x+1)-(x^2-x+7)-(4x^2+2x+8)
Answer:
The answer would be -7x^2 - 14!
Step-by-step explanation:
We can remove the parentheses by distributing the subtraction sign! -2x^2 + x + 1 - x^2 + x - 7 - 4x^2 - 2x - 8. Simplifying this gives us -7x^2 - 14. Hope this helped! :)
Need help please due in 1 hour and 30 mins
Answer:
the answer of that is number C
Use the substitution method to solve this system.
y = 2x+4
3x+y = 9
Answer:
x = 1; y=6
Step-by-step explanation:
y = 2x +4
3x + y = 9
Substitute 2x+4 for y in 3x+y = 9
3x + y = 9
3x + 2x+4 = 9
5x + 4 = 9
5x = 9-4
5x = 5
5x/5 = 5/5
x = 1
Substitute 1 for x in y = 2x +4
2(1) + 4
2 + 4
= 6
Answered by Gauthmath
Can someone do #2?❤️
Answer:
b
Step-by-step explanation:
A proportional relationship is a straight line. Is must also go through the point (0,0)
b
Answer:
Step-by-step explanation:
A proportional relationship is a straight line. Is must also go through the point (0,0)
which ecpression is the simplest form of 3(3x-4)-5(x+3)
[tex]\boxed{ \sf{Answer}} [/tex]
[tex] \sf \: 3(3x - 4) - 5(x + 3) \\ \sf =( 3 \times 3x) - (3 \times 4) + ( - 5 \times x) +( - 5 \times 3 ) \\ \sf = 9x - 12 - 5x - 15 \\ \sf = 9x - 5x - 12 - 15 \\ = \underline{ \bf 4x - 27}[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
[tex]\\ \sf\longmapsto 3(3x-4)-5(x+3)[/tex]
[tex]\\ \sf\longmapsto 9x-12-5x-15[/tex]
[tex]\\ \sf\longmapsto 9x-5x-15-12[/tex]
[tex]\\ \sf\longmapsto (9-5)x-27[/tex]
[tex]\\ \sf\longmapsto 4x-27[/tex]
Can someone please help me thanks in advance!
Step-by-step explanation:
Bro your question is quiet blur... Please help me out..
hope it Wonderful.
^_^....!_!_
ALGEBRA 2 SIMPLIFY THE EXPRESSION
Step-by-step explanation:
here's the answer to your question
Một tàu biển trị giá 2.500.000 USD đang chở các lô hàng A, B,C có giá trị lần lượt là 100.000 USD; 300.000USD, 500.000USD và tiền cước chưa thu thuộc chủ tàu là 60.000 USD. Trong hành trình đi từ Indonesia về cảng Sài Gòn tàu bị mắc cạn, vỏ tàu bị thủng, nước tràn vào làm hư hỏng một số hàng hóa. Để cứu tàu và hàng, thuyền trưởng quyết định bịt lỗ thủng bằng các phương tiện trên tàu và vứt một số hàng để tàu nhẹ bớt, đồng thời thuyền trưởng cũng cho máy tàu làm việc vượt công suất nhằm giúp tàu thoát cạn. Sau sự việc, các tổn thất được xác định như sau:
- Vỏ tàu thủng dự kiến phải sửa chữa hết 100.000 USD
- Máy tàu hư do hoạt động quá công suất và dự kiến phải sửa hết 250.000 USD
- Lô hàng B bị nước tràn vào giảm giá trị thương mại 100%.
- Lô Hàng A bị vứt xuống biển toàn bộ.
- Thiệt hại để cứu tàu và chi phí cho thủy thủ trong việc cứu tàu là 10.000 USD.
a. Hãy xác định các tổn thất riêng của các bên
b. Hãy xác định tổng tổn thất chung của các bên
c. Hãy xác định giá trị chịu phân bổ tổn thất chung (giá trị đóng góp của từng chủ thể trên tàu)
d. Hãy xác định các khoản đóng góp vào tổn thất chung của các bên
Answer:
ask in English then I can help
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. THIS IS NOT A TEST OR AN ASSESSMENT!! Please help me with these math problems. Chapter 12 part 2 PLEASE SHOW WORK!!!
4a. a_n = 2(1/3 + a_n-1), a_1 = 4
4b. a_n= n/(a_n-1), a_1 = 6
4c. 1/6, 2/3, 8/3, . . .
Problem 4a
The instructions are incomplete. You set up the recursive formula, but didn't ask any question about said formula.
I'll assume that your teacher wants you to list out a few terms. I'll list out the first five terms.
The notation a_1 = 4 is the same as writing [tex]a_1 = 4[/tex] where the '1' is a subscript. It tells us that the first term is 4.
The nth term a_n or [tex]a_n[/tex] is defined as such
[tex]a_n = 2*(1/3 + a_{n-1})\\\\[/tex]
Notice how if we replaced n with 2, then we get
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_2 = 2*(1/3 + a_{2-1})\\\\a_2 = 2*(1/3 + a_1)\\\\[/tex]
So the second term is directly tied to the first term, or it is dependent on it.
We'll replace a_1 with 4 to get the following
[tex]a_2 = 2*(1/3 + a_1)\\\\a_2 = 2*(1/3 + 4)\\\\a_2 = 2*(1/3 + 12/3)\\\\a_2 = 2*(13/3)\\\\a_2 = 26/3\\\\[/tex]
So the second term is 26/3.
As you can guess, the third term is going to be found in a similar fashion
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_3 = 2*(1/3 + a_{3-1})\\\\a_3 = 2*(1/3 + a_2)\\\\a_3 = 2*(1/3 + 26/3)\\\\a_3 = 2*(27/3)\\\\a_3 = 2*(9)\\\\a_3 = 18\\\\[/tex]
So 18 is the third term.
We'll repeat for n = 4 to get the fourth term.
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_4 = 2*(1/3 + a_{4-1})\\\\a_4 = 2*(1/3 + a_3)\\\\a_4 = 2*(1/3 + 18)\\\\a_4 = 2*(1/3 + 54/3)\\\\a_4 = 2*(55/3)\\\\a_4 = 110/3\\\\[/tex]
The fourth term is 110/3.
Lastly, we'll plug in n = 5
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_5 = 2*(1/3 + a_{5-1})\\\\a_5 = 2*(1/3 + a_4)\\\\a_5 = 2*(1/3 + 110/3)\\\\a_5 = 2*(111/3)\\\\a_5 = 2*(37)\\\\a_5 = 74\\\\[/tex]
The fifth term is 74.
Answer: The first five terms are 4, 26/3, 18, 110/3, 74==============================================================
Problem 4b
Again, the instructions are missing. I'll assume the same thing as problem 4a.
[tex]a_1 = 6[/tex] is the first term
Plug n = 2 into the first equation to get
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_2 = \frac{2}{a_{2-1}}\\\\a_2 = \frac{2}{a_{1}}\\\\a_2 = \frac{2}{6}\\\\a_2 = \frac{1}{3}\\\\[/tex]
The second term is 1/3.
Repeat for n = 3
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_3 = \frac{3}{a_{3-1}}\\\\a_3 = \frac{3}{a_{2}}\\\\a_3 = \frac{3}{1/3}\\\\a_3 = 3\div\frac{1}{3}\\\\a_3 = 3\times\frac{3}{1}\\\\a_3 = 9\\\\[/tex]
The third term is 9
Repeat for n = 4.
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_4 = \frac{4}{a_{4-1}}\\\\a_4 = \frac{4}{a_{3}}\\\\a_4 = \frac{4}{9}\\\\[/tex]
The fourth term is 4/9
Repeat for n = 5
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_5 = \frac{5}{a_{5-1}}\\\\a_5 = \frac{5}{a_{4}}\\\\a_5 = 5 \div a_{4}\\\\a_5 = 5 \div \frac{4}{9}\\\\a_5 = 5 \times \frac{9}{4}\\\\a_5 = \frac{5}{1} \times \frac{9}{4}\\\\a_5 = \frac{5*9}{1*4}\\\\a_5 = \frac{45}{4}\\\\[/tex]
Answer: The first five terms are 6, 1/3, 9, 4/9, 45/4==============================================================
Problem 4c
I'm not much help here for this problem. Not only are the instructions missing, but it's not clear how this sequence is set up. If I had to guess, it's somehow recursively defined. How exactly, I'm not sure. I would ask your teacher for any clarification.
what is the value of k
Answer:
(A)
Step-by-step explanation:
M=-2
therefore
x¹=3, y¹=-12, x²=6 y²=k
M=(y²-y¹)/(x²-x¹)
-2=(k+12)/(6-3)
-2×3=k+12
-6=k+12
k=-18
In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 2000. In 2001, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 and p2 be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.
Required:
Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared with the proportion in 1999
Answer:
The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
1999:
20 out of 100 in the bottom third, so:
[tex]p_1 = \frac{20}{100} = 0.2[/tex]
[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
2001:
10 out of 100 in the bottom third, so:
[tex]p_2 = \frac{10}{100} = 0.1[/tex]
[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
Test if proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
At the null hypothesis, we test if the proportion is still the same, that is, the subtraction of the proportions in 1999 and 2001 is 0, so:
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternative hypothesis, we test if the proportion has been reduced, that is, the subtraction of the proportion in 1999 by the proportion in 2001 is positive. So:
[tex]H_1: p_1 - p_2 > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.1 - 0}{0.05}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of at least 0.1, which is the p-value of z = 2.
Looking at the z-table, the p-value of z = 2 is 0.9772.
1 - 0.9772 = 0.0228.
The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Question 7 of 10
What is the slope of the line described by the equation below?
y-9 = -2(x-8)
Answer:
The slope is -2 and a point on the line is (8,9)
Step-by-step explanation:
The equation is in point slope form
y -y1 = m(x-x1) where (x1,y1) is a point on the line and m is the slope
y-9 = -2(x-8)
The slope is -2 and a point on the line is (8,9)
The product of two positive integer numbers is 30 and the sum of the same two numbers is 11. Find the
numbers.
Answer:
5 and 6
Step-by-step explanation:
call them a and b, respectively
we have a*b=30 -> a=30/b
a+b=11 -> b+ 30/b=11
b=6 and a=5
How to change unit from feet to cm
to change unit from feet to cm just divide the length value by 30.48......
Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected and the diameter is measured. The resulting data (in millimeters) are as follows: No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24 Use the data above to calculate a 95% two-sided confidence interval on the mean rod diameter. Assume the data are normally distributed. (a) Calculate the sample mean and standard deviation. Round the sample mean and the sample standard deviation to 2 and 3 decimal places respectively (e.g. 98.76 and 98.765). (b) Calculate the 95% two-sided confidence interval on the true mean rod diameter. Round your answers to 3 decimal places (e.g. 98.765).
Answer:
(8.213 ; 8.247)
Step-by-step explanation:
Given the data :
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24
Sanple size, n = 15
Sample mean, xbar = Σx / n = 123.45 / 15 = 8.23
The sample standard deviation, s = √(x -xbar)²/n-1
Using calculator :
Sample standard deviation, s = 0.03116
s = 0.031 (3 decimal places)
The 95% confidence interval :
C.I = xbar ± (Tcritical * s/√n)
Tcritical at 95%, df = 15 - 1 = 14
Tcritical = 2.145
C.I = 8.23 ± (2.145 * 0.031/√15)
C.I = 8.23 ± 0.0171689
C.I = (8.213 ; 8.247)
If 10 wholes are divided into pieces that are one half of a whole each how many pieces are there?
9514 1404 393
Answer:
20
Step-by-step explanation:
A whole can be divided into two pieces that are each 1/2 of the whole.
(10 wholes) × (2 pieces per whole) = 20 pieces
For what numbers is f(0) = sec 0 not defined?
Answer:
stundeez
Step-by-step explanation:
Nicki Minaj hdhsbskdhsnsk
in isosceles triangle XYZ, angle X=117°. calculate angleZ
Answer:
31.5
Step-by-step explanation:
Angle Z+ Angle X+ Angle Y=180
As the triangle is isosceles, Z=X, hence Z=63/2=31.5
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____. a. parabolic band of points b. band of points having a slope consistent with that of the regression equation c. horizontal band of points centered near 0 d. widening band of points
Answer:
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____.
c. horizontal band of points centered near 0
Step-by-step explanation:
This residual graph or plot shows the residual values (or the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line) on the vertical axis and displays the independent variable on the horizontal axis. A linear regression model becomes appropriate for a dataset when the points are randomly dispersed around the horizontal axis near 0; otherwise, a nonlinear model becomes more appropriate.
How does the area below the mean compare to the area above the mean in a normal distribution?
A. the areas are always equal regardless of the mean
B. the areas are sometimes equal depending upon the standard deviation of the distribution
C. the area above the mean is larger since the values are larger as you move above the mean
D. the areas are sometimes equal depending upon the value of the mean
Answer:
A.
Step-by-step explanation:
that is the definition of "mean". it cuts the possible outcomes weighed with their probabilities (actual occurrences vs. possible occurrences) in 2 halves.
The areas are always equal regardless of the mean.
option (a) is correct.
What is normal distribution?A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
The standard normal distribution is a probability distribution, so the area under the curve between two points tells you the probability of variables taking on a range of values. The total area under the curve is 1 or 100%.
Therefore ,the areas are always equal regardless of the mean.
Learn more details about normal distribution:
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Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. ASAPostulate
Answer:
SR = LK
Step-by-step explanation:
ASA means angle - (included) side - angle.
we got 2 angles confirmed, so all we need is the confirmation of the side between the 2 angles.
simplify using the laws of exponents (4^3)^-2 × (2^3)^4 ×(8/15)^-2
Answer:
[tex] \dfrac{225}{64} [/tex]
Step-by-step explanation:
[tex] (4^3)^{-2} \times (2^3)^4 \times (\dfrac{8}{15})^{-2} = [/tex]
[tex]= (2^2)^{-6} \times 2^{12} \times (\dfrac{15}{8})^{2}[/tex]
[tex]= 2^{-12} \times 2^{12} \times \dfrac{225}{64}[/tex]
[tex] = \dfrac{225}{64} [/tex]
The half-life of a radioactive substance is 20 years. If you start with some amount of this substance, what fraction will remain in 180 years?
Answer:
1/512
Step-by-step explanation:
Let staring fraction = x
Half-life = 20 years ; this is the time taken for an element to decrease to half of its original size
Hence,
After 20 years - - - > x/2
After 40 years - - - - > x/2 ÷ 2 = x/2 * 1/2 = x /4
After 60 years - - - - > x/4 ÷ 2 = x/4 * 1/2 = x/8
After 80 years - - - - -> x/8 ÷ 2 = x/8 * 1/2 = x / 16
After 100 years - - - > x/16 * 1/2 = x/32
After 120 years - - - - > x/32 * 1/2 = x/64
After 140 years - - - - -> x / 64 * 1/2 = x / 128
After 160 years - - - - - > x / 128 * 1/2 = x/256
After 180 years - - - - > x/256 * 1/2 = x / 512
Hence, the fraction after 180 years = 1/512
Solve |6k + 12| + 9 = 9 for k.
Step-by-step explanation:
6k + 12 + 9=9
6k + 12 = 9 - 9
6k + 12 = 0
12 = -6k
12/-6 = -6k/-6
2/-1 = k
k = -2
Answer:
k=-2
Step-by-step explanation:
6k+12+9=9
subtract 9 from both sides
6k+12=0
subtract 12 from not sides
6k= -12
divide both sides by 6 (isolating the variable)
k= -12/6
simplify
k= -2
Hi I need help could someone please help me
Answer:
it's hypotenuse
Step-by-step explanation:
There are two rectangles Jared is examining. He knows the width of the first rectangle measures
2.48 cm, and the length is twice its width.
Jared also knows that the width of the second rectangle is equal to the length of the first rectangle,
and that the area of the second rectangle is 9.92. Given this information, find the length of the
second rectangle for Jared.
1st rectangle:
width: 2.48cm
length: 4.96
2nd rectangle:
width: 4.96 (equals to the length of the 1st rectangle)
area: 9.92
length: 9.92/4.96 = 2
6/5w-7 = blank/ 49-35w
Answer:
Resolver para x
x=8869w/5 - 343
Step-by-step explanation:
simplificando ambos lados de la ecuación, entonces aislar la variable. x
by selling a purse for rupees 250 Rajan loses one sixth of what cost should find the cost price of the first her loss percentage
Answer:
300, 16.67%
Step-by-step explanation:
Let x be the cost price. x-(1/6)x=250. 5x/6=250. x=300. Losss percentage is 16.67%
Which best represents data that is not likely to be clustered?
A. a low MAD and IQR
B. low MAD and a great IQR
C. a low IQR and a great MAD
D. a great MAD and IQR
Answer: guess it your self
Step-by-step explanation:
Melinda takes out a loan to purchase a car. The balance on her loan after x months is represented by the equation y = 10,000 – 250x and the value of the car after x months is represented by y = 8,000 – 50x. Which statement describes when Melinda’s loan will be equal to the value of the car?
After 10 months, the loan and value of the car will both be equal to $7,500.
After 12 months, the loan and value of the car will both be equal to $7,000.
After 14 months, the loan and value of the car will both be equal to $6,500.
After 16 months, the loan and value of the car will both be equal to $6,000.
Answer:
After 10 months, the loan and value of the car will both be equal to $7,500.
Step-by-step explanation:
Value of the loan after x months:
[tex]y_l = 10000 - 250x[/tex]
Value of the car after x months:
[tex]y_c = 8000 - 50x[/tex]
Which statement describes when Melinda’s loan will be equal to the value of the car?
They are equal when:
[tex]y_l = y_c[/tex]
So
[tex]10000 - 250x = 8000 - 50x[/tex]
[tex]200x = 2000[/tex]
[tex]x = \frac{2000}{200}[/tex]
[tex]x = 10[/tex]
Equal after 10 months:
Value of [tex]y(10) = 8000 - 50(10) = 7500[/tex]
Thus, the correct option is:
After 10 months, the loan and value of the car will both be equal to $7,500.
