Answer:
you have to solve for z, z = 6\root(5)(i), this to the power of 5 equals 77761
Step-by-step explanation:
Marc is sending his sister a parcel through the post. the parcel weighs 2.451kg. round this to 1 decimal place
Answer:
2.5 kg
Step-by-step explanation:
2.451
Find the number in the tenth place 4 and look one place to the right for the rounding digit 5.
Round up if this number is greater than or equal to 5 and round down if it is less than 5.
Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 2 and a mean diameter of 200 inches.
If 83 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches? Round your answer to four decimal places.
Answer:
0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
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]
Standard deviation of 2 and a mean diameter of 200 inches.
This means that [tex]\sigma = 2, \mu = 200[/tex]
83 shafts
This means that [tex]n = 83, s = \frac{2}{\sqrt{83}}[/tex]
What is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches?
Mean between 200 - 0.2 = 199.8 inches and 200 + 0.2 = 200.2 inches, which is the p-value of Z when X = 200.2 subtracted by the p-value of Z when X = 199.8.
X = 200.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{200.2 - 200}{\frac{2}{\sqrt{83}}}[/tex]
[tex]Z = 0.91[/tex]
[tex]Z = 0.91[/tex] has a p-value of 0.8186
X = 199.8
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{199.8 - 200}{\frac{2}{\sqrt{83}}}[/tex]
[tex]Z = -0.91[/tex]
[tex]Z = -0.91[/tex] has a p-value of 0.1814
0.8186 - 0.1814 = 0.6372
0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.
Complete the table of inputs and outputs for the given function. g(x) = 3 - 8x g() 0 -5 3 Reset
Answer:
Step-by-step explanation:
Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A0 after time t. b) It is found that 8 lb of A will reduce to 4 lb in 4.6 hr After how long will there be only 1 lb left?
a) Choose the equation that gives A in terms of A0, t, and k, where k > 0.
b) There will be 1 lb left after 14 hr (Do not round until the final answer. Then round to the nearest whole number as needed.)
Answer:
(a) [tex]A = A_0 * e^{kt}[/tex]
(b) There will be 1lb left after 14 hours
Step-by-step explanation:
Solving (a): The equation
Since the substance decomposes at a proportional rate, then it follows the following equation
[tex]A(t) = A_0 * e^{kt}[/tex]
Where
[tex]A_0 \to[/tex] Initial Amount
[tex]k \to[/tex] rate
[tex]t \to[/tex] time
[tex]A(t) \to[/tex] Amount at time t
Solving (b):
We have:
[tex]t = 4.6hr[/tex]
[tex]A_0 = 8[/tex]
[tex]A(4.6) = 4[/tex]
First, we calculate k using:
[tex]A(t) = A_0 * e^{kt}[/tex]
This gives:
[tex]A(4.6) = 8 * e^{k*4.6}[/tex]
Substitute: [tex]A(4.6) = 4[/tex]
[tex]4 = 8 * e^{k*4.6}[/tex]
Divide both sides by 4
[tex]0.5 = e^{k*4.6}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.5) = \ln(e^{k*4.6})[/tex]
This gives:
[tex]-0.6931 = k*4.6[/tex]
Solve for k
[tex]k = \frac{-0.6931}{4.6}[/tex]
[tex]k = -0.1507[/tex]
So, we have:
[tex]A(t) = A_0 * e^{kt}[/tex]
[tex]A(t) = 8e^{-0.1507t}[/tex]
To calculate the time when 1 lb will remain, we have:
[tex]A(t) = 1[/tex]
So, the equation becomes
[tex]1= 8e^{-0.1507t}[/tex]
Divide both sides by 8
[tex]0.125= e^{-0.1507t}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.125)= \ln(e^{-0.1507t})[/tex]
[tex]-2.0794= -0.1507t[/tex]
Solve for t
[tex]t = \frac{-2.0794}{-0.1507}[/tex]
[tex]t = 13.7983[/tex]
[tex]t = 14[/tex] --- approximated
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
x + y - z = -2
2x - y + 3z = 9
x - 4y - 2z = 1
Answer:
(x, y, z) =(1, -1,2)
Step-by-step explanation:
.............
Công thức tính hiệu suất
Answer:
Công thức tính hiệu quả công việc là tỷ lệ giữa đầu ra và đầu vào được biểu thị bằng phần trăm. ... Công thức hiệu quả công việc là hiệu quả = đầu ra / đầu vào, và bạn có thể nhân kết quả với 100 để tính hiệu quả công việc theo tỷ lệ phần trăm.
The moment generating function for health care costs experienced by a policyholder is given as follows:
Mx(t)= (4/4-t)^3
An insurer reimburses the policyholder for 70% of health care costs experienced by the policyholder. Calculate the expected reimbursement by the insurer for a policyholder.
Answer:
0.525 = 52.5%
Step-by-step explanation:
Moment generating function ( Mx(t) ) = ( 4 / 4-t)^3
Reimbursement by Insurer = 70%
Determine the expected reimbursement by insurer for policyholder
d/dx (Mx(t) ) = d/dt ( 4 / 4-t)^3 = d/dt (1 - t/4 )^-3
= 3/4 ( 1 - t/4 )^-4 = 3/4
as t → 0
Given that the insurer reimburses 70% = 0.7
expected reimbursement = 0.7 * 3/4 = 0.7 * 0.75 = 0.525
construct a scale of A-sharp major on a treble staff in ascending order only
Answer: In the picture from the basic music theory website's page on a-sharp major scale
Step-by-step explanation: music theory
A company wants to estimate, at a 95% confidence level, the proportion of all families who own its product. A preliminary sample showed that 30.0% of the families in this sample own this company's product. The sample size that would limit the margin of error to be within 0.047 of the population proportion is:
Answer:
The sample size is of 366.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A preliminary sample showed that 30.0% of the families in this sample own this company's product.
This means that [tex]\pi = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The sample size that would limit the margin of error to be within 0.047 of the population proportion is:
This is n for which [tex]M = 0.047[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.047 = 1.96\sqrt{\frac{0.3*0.7}{n}}[/tex]
[tex]0.047\sqrt{n} = 1.96\sqrt{0.3*0.7}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.047}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.047})^2[/tex]
[tex]n = 365.2[/tex]
Rounding up:
The sample size is of 366.
Rewrite the following subtraction problem as an addition problem.
Answer:
x+129=592
Step-by-step explanation:
add 129 to each side
when is 9+10 really equal to 21
Answer:
9 + 10 = 21
Step-by-step explanation:
9 + 10 = 21
Factor out 9 and 10
9 = 3 · 3 10 = 2 · 5
Next multiply 3 by 2
3 × 2 = 6
Then multiply 3 by 5
3 · 5 = 15
Finally add the products
15 + 6 = 21
y=x+9x solve for x. Please and Thank you.
Answer:
x=y/10
Step-by-step explanation:
y=10x
y/10=x
x=y/10
Hope this is helpful
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {\: x = \frac{y}{10}}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]y = x + 9x\\[/tex]
[tex]➺ \: y = 10x\\[/tex]
[tex]➺ \: x = \frac{y}{10}\\ [/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Simplify 3/4 X 14/ 15 .
Can someone please answer this please
Answer: I don't know but i have the formula.
Step by Step: [tex]A=\frac{1}{2}b h[/tex]
HELP PLEASE ASAP What is the product of any integer and -1?
Answer:
A
Step-by-step explanation:
The product is opposite of the integer
For example
2 * -1 = -2
What is the measure of each exterior angle of the right triangle?
x =
y =
z =
Answer:
x = 90
y = 134
z = 136
Step-by-step explanation:
Sum of interior angles of a triangle are 180
Linear angles are 180
So 180 - 90 = 90
180 - 44 = 136
180 - 90-44 = 46
180 - 46 = 134
How do I solve this and do the explanation of it
Answer:
180-66
114
hope it helps mark as brainlist
7/7q+21= x /5q^2-45 then x=?
Answer:
x = 5q - 15
Step-by-step explanation:
[tex]\frac{7}{7q+21}=\frac{x}{5q^{2}-45}\\\\\frac{7}{7(q+3)}=\frac{x}{5 (q^{2} -9)}\\\\frac{1}{q+3}=\frac{x}{5*(q^{2}-3^{2})}\\\\\frac{1}{q+3}=\frac{x}{5(q+3)(q-3)}\\\\\frac{1}{q+3}*5*(q+3)(q-3)=x\\\\5(q-3)=x\\\\x= 5q-15[/tex]
Please answer this!!! WILL GIVE BRAINLIEST
Answer:
p > 9
Step-by-step explanation:
First let's note down-
George- has 23$
Total cost of m+p= more than $14
Second, let's subtract 23 and 14 to get what the glue costs.
23 - 14 = 9
So now we can cross out choice A and D.
Third, now earlier I said more than $14, this is the key part to find what we are going to choose.
more than = >
now we just plug in the variable,
p > 9
Hope this helps!
Please reach out to me if you still don't understand :)
Find cos 0.
53
45
28
Whoever helps gets Brainliest!!! PLEASE HELP!!!
John throws a biased four-sided dice.
The probabilities of getting each number are summarised in the table below.
Number
1
2
3
4
Probability
0.2
x
0.2
0.2
Work out the probability that the dice lands on 2.
Answer:
0.4
Step-by-step explanation:
0.2+0.2+0.2=0.6
1.0-0.6=0.4
This isn't 0.2 like the others which is why it's a biased dice like it says.
What's the LCM of 16,24,40
Step-by-step explanation:
explanation is in the attachment
hope it is helpful to you
The length of the longer leg of a right triangle is 6 inches more than twice the length of the shorter leg. The length of the hypotenuse is 9 inches more than twice the length of the shorter leg. Find the side lengths of the triangle.
9514 1404 393
Answer:
15 in, 36 in, 39 in
Step-by-step explanation:
The Pythagorean theorem tells us that for short side x, the relation is ...
(2x +9)² = (2x +6)² +x²
4x² +36x +81 = 4x² +24x +36 +x²
x² -12x -45 = 0 . . . . . subtract the left-side expression
(x -15)(x +3) = 0 . . . . factor
x = 15 . . . . . . . . . . . the positive value of x that makes a factor zero
The side lengths of the triangle are 15 inches, 36 inches, and 39 inches.
Write an explicit formula for an, the nth term of the sequence 63,21,7
Answer:
63/3=2121/3=77/3=7 -3
5)
I
6
50°
16x + 2
B) 9
A) -10
C) 4
D) 8
Answer:
c is answer
Step-by-step explanation:
c is ans because it is simple c only serves the need of questions and satisfy it
Answer:
D) 8
Step-by-step explanation:
Liner pair meaning that the angles have a sum of 180. So you add them together to get the equation 16x+52=180 an16x=128 and then you divide both sides by 16 to get x equal to 8. Hope I helped and post more questions :)
How much in earning can PNG make in a year in cocoa export of 400 000 tonnes at K2 353 per tonne ? (2 marks)
Answer: K941,200,000
Step-by-step explanation:
From the question, we are to calculate the amount of earning that PNG can make in a year in cocoa export of 400 000 tonnes at K2 353 per tonne.
This will be:
= Number of tonnes × Amount per ton
= 400000 × k2353
= K941,200,000
Therefore, the answer is K941,200,000
determine the general term of this sequence 2;10;18;26;.........;394
Answer:
Tn=8n-6
Step-by-step explanation:
this is arithmetic sequence so first we check our difference by saying
T2-T1=T3-T2
10-2=18-10
so difference =8 nd a=2
Formula for arithmetic is Tn=a + (n-1)d
then substitute Tn=2 + (n-1)(8)
Tn=2 + 8n-8
Tn=8n-6
simplify: 6x²+35x-6÷ 2x²-72
Step-by-step explanation:
this will be the answer of the question where quotient is 3 and the remainder is 35x + 210
Answer:
[tex]\frac{6x - 1}{2(x - 6)}[/tex]
Step-by-step explanation:
[tex]6x^2 + 35x - 6 \ \div \ 2x^2 - 7 2\\\\6x^2 + 36x - x - 6 \ \div \ 2(x^2 - 36)\\\\6x(x + 6) - 1(x + 6) \ \div \ 2(x^2 - 6^2)\\\\(6x - 1)(x + 6) \ \div \ 2(x- 6)(x+ 6) \ \ \ \ \ \ \ \ \ \ [ \ x^2 -a^2 = (x-a)(x+a) \ ]\\\\\frac{(6x - 1)(x + 6) }{2(x- 6)(x+ 6)} = \frac{6x - 1}{2(x-6)}[/tex]
X^2+9x+20 divided by x+5
Answer:
x ≠ -5
Step-by-step explanation:
The easiest way is to factor the numerator.
x2 + 9x + 20 = (x + 4)(x + 5)
Then
(x2 + 9x + 20)/(x + 5) = (x + 4)(x + 5) / (x + 5) = x + 4,
with the restriction that x ≠ -5