Answer:
[tex]g'(x) = \frac{x^2}{100} +2[/tex]
Step-by-step explanation:
Given
[tex]g(x) = 10\sqrt{x - 2[/tex]
Required
Determine the inverse function
[tex]g(x) = 10\sqrt{x - 2[/tex]
Replace g(x) with y
[tex]y = 10\sqrt{x -2[/tex]
Swap the positions of x and y
[tex]x = 10\sqrt{y -2[/tex]
Divide through by 10
[tex]\frac{x}{10} = \sqrt{y - 2[/tex]
Square of both sides
[tex]\frac{x^2}{100} = y - 2[/tex]
Make y the subject
[tex]y = \frac{x^2}{100} +2[/tex]
Replace y with g'(x)
[tex]g'(x) = \frac{x^2}{100} +2[/tex]
Hence, the inverse function is: [tex]g'(x) = \frac{x^2}{100} +2[/tex]
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 148 millimeters, and a standard deviation of 7 millimeters. If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 2.2 millimeters? Round your answer to four decimal places.
Answer:
0.0802 = 8.02% probability that the sample mean would differ from the population mean by more than 2.2 millimeters
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 estabilishes 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.
Their current steel bolts have a mean diameter of 148 millimeters, and a standard deviation of 7 millimeters.
This means that [tex]\mu = 148, \sigma = 7[/tex]
Sample of 31:
This means that [tex]n = 31, s = \frac{7}{\sqrt{31}}[/tex]
What is the probability that the sample mean would differ from the population mean by more than 2.2 millimeters?
Less than 148 - 2.2 = 145.8 or more than 148+2.2 = 150.2. Due to the simmetry of the normal distribution, these probabilities are the same, which means that we find one and multiply by 2.
Probability of being less than 145.8:
The pvalue of Z when X = 145.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{145.8 - 148}{\frac{7}{\sqrt{31}}}[/tex]
[tex]Z = -1.75[/tex]
[tex]Z = -1.75[/tex] has a pvalue of 0.0401
2*0.0401 = 0.0802
0.0802 = 8.02% probability that the sample mean would differ from the population mean by more than 2.2 millimeters
It’s the end of the year I’m really not trying so anybody just help really
Answer: its D
Step-by-step explanation: because a - x - is a positive so you add them
"A driving instructor is investigating whether the time a driver spends in a driverâs education course improves their score on the driverâs test. The instructor randomly selected 10 drivers from a driverâs education course and recorded the number of hours each driver attended the driverâs education course and their corresponding score on the driverâs test. Assuming all conditions for inference are met, which of the following significance tests should be used for the investigation?"
a. A chi-square test of independence
b. A two-sample t-test for a difference between means
c. A two-sample z-test for a difference between proportions
d. A linear regression t-test for slope
e. A matched pairs t-test for a mean difference
Answer:
e. A matched pairs t-test for a mean difference
Step-by-step explanation:
When the observations from two samples are paired either naturally or by design we find the differences between the two observations of each pair.Treating the differences as a random sample from a normal population with mean ud= u1-u2 and unknwn standard deviation σd we perform one sample t- test on them. This is called the paired difference t- test or a paired t- test.
Suppose 10 young recruits are given a physical training by the Army . Their weights are recorded before and after the training. These observations constitutes natural pairing .
When we eliminate the undesireable sources of variation to take observations in pairs , this is called pairing by design.
A bag of marbles contains 10 blue marbles, 62 yellow marbles, 34 green marbles, 71 orange marbles, and 23 red marbles. What percentage of the gumballs are yellow?
A.200%
B.62%
C.31%
D.85%
Answer:
your answer is C. 31%
percentage of yellow marbles =
[tex] \frac{62}{10 + 62 + 34 + 71 + 23} [/tex] × 100
[tex] \frac{62}{200} [/tex] × 100
[tex]31\%[/tex]
help please. will give Brainly.
Answer:
a10 = 15
an = 6n - 45
Step-by-step explanation:
a12 = 27 = a + 11d - eq 1
a14 = 39 = a + 13d - eq 2
eq 2 - eq 1
2d = 12
d = 6
a + 11(6) = 27
a + 66 = 27
a = -39
a10 = a + 9d = -39 + 9(6) = 15
Tn = a + (n-1)d
-39 + 6(n - 1)
-39 + 6n -6
an = 6n - 45
A simple random sample of 150 people who completed the ESPN 2019 Tournament Bracket was selected, and 81 out of the 150 people who completed the ESPN 2019 Tournament Bracket had their choice to become the national champion make the Final Four. If appropriate, use this information to calculate and interpret a 90% confidence interval for the proportion of all people who completed the ESPN 2019 Tournament Bracket whose choice to become the national champion made the Final Four.
Answer:
The answer is "0.54 and (0.4733, 0.6067)".
Step-by-step explanation:
Please find the complete question in the attachment file.
In question 1:
[tex]\to x=81\\\\ \to n=150\\\\ \to \hat{p}=\frac{x}{n}=\frac{81}{150}=0.54\\\\[/tex]
Hence the choice A is correct.
In point b:
Calculating Critical Value:
[tex]\to (Z_{\alpha/2})=1.64 \ \ \ \ \ \ \ \ \ \ (use \ \ z\ \ table)\\\\[/tex]
Calculating the Confidence intervals:
[tex]=\hat{p} \pm Z_{\alpha/2}\times \sqrt{\frac{\hat{p} \times (1-\hat{p}))}{n}}\\\\ =0.54 \pm 1.64\times \sqrt{\frac{0.0.54 \times (1-0.54)}{150}}\\\\ =0.54 \pm 0.0667\\\\ =(0.4733, 0.6067)\\\\[/tex]
Hence the choice a is correct.
The correct confidence interval is (0.4733, 0.6067).
What is the z critical value?The z critical test is conducted when the population standard deviation on a normal distribution is known and the sample size is greater than or equal to 30.
x = 81
n = 150
p = x/n =81/ 150
p = 0.54
So, the correct choice is A.
In point b
Critical Value:
[tex]Z_{\alpha /2} = 1.64[/tex]
the Confidence intervals:
= p±[tex]Z_{\alpha /2} \times \sqrt{\frac{p \times (1-p)}{n} }[/tex]
= 0.54 ± [tex]\\1.64 \times \sqrt{\frac{0.54 \times (1-0.54)}{150} }[/tex]
= 0.54 ± 0.0667
= (0.4733, 0.6067)
Hence, the choice A is correct.
Therefore, the correct confidence interval is (0.4733, 0.6067).
Learn more about critical value:
https://brainly.com/question/5425085
find the probability. PLZ HELP
Answer:
Probability that [tex]-5 \leq x \leq 5[/tex] is 0.3
Step-by-step explanation:
From the table, we have that the probability is:
[tex]P(-5 \leq x \leq 5) = P(x = -5) + P(x = 0) + P(x = 5)[/tex]
With the values given
[tex]P(-5 \leq x \leq 5) = P(x = -5) + P(x = 0) + P(x = 5) = 0.15 + 0.05 + 0.1 = 0.3[/tex]
So
Probability that [tex]-5 \leq x \leq 5[/tex] is 0.3
What is the answer please help if you put a link I will report
Answer:
true.
Step-by-step explanation:
Hi! I was wondering if someone could explain how to find a percent of a large number. I think you're supposed to multiply a number by a decimal, but I don't remember. Please give an example and no links. Thanks so much!
Answer:
Yes, you're correct.
An example would be, say, 345. You want to find 60%. So you multiply 345 by 0.60.
Answer:
Give other answer brainliest!!!!
Step-by-step explanation:
Good work
plese help me
21,382.62 ÷ 10,000
Answer:
2.138262
Please mark my answer as the brainliest for further answers :)
Answer:
2.138262
Step-by-step explanation:
21,382.62 ÷ 10,000
Find arc DC please help me
Answer:
arc ABC = 196°
arc DC = 360 - 196 - 70 = 94° (which looks out of proportion, but so does angle D)
Step-by-step explanation:
arc ABC = 2(∠D) = 2(98°) = 196°
If x = -6, which inequality is true?
-5 – 3x > 10
-3 – 5x < -14
1 – 2x > 13
Answer:
1-2x>13
Step-by-step explanation:
1-2x>13
-2x>13-1
-2x>12
x>-12/2
x<-6
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. A hypothesis test is performed to determine if the additional training was effective in lowering the defect rate. The correct value of the Z-statistic is
Answer:
The correct value of the Z-statistic is z = -1.56
Step-by-step explanation:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective.
This means that the null hypothesis is:
[tex]H_{0}: p = 0.08[/tex]
A hypothesis test is performed to determine if the additional training was effective in lowering the defect rate.
This means that the alternate hypothesis is:
[tex]H_{a}: p < 0.08[/tex]
z-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.08 is tested at the null hypothesis:
This means that [tex]\mu = 0.08, \sigma = \sqrt{0.08*0.92}[/tex]
After training was implemented, a sample of 450 chips revealed only 27 defects.
This means that [tex]n = 450, X = \frac{27}{450} = 0.06[/tex]
The correct value of the Z-statistic is
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.06 - 0.08}{\frac{\sqrt{0.08*0.92}}{\sqrt{450}}}[/tex]
[tex]z = -1.56[/tex]
Which table values would use to graph y=x^2 + 3 (with work please)
In semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. The etch rate is an important characteristic in this process and known to follow a normal distribution. Two different etching solutions have been compared, using two random samples of 10 wafers for each solution. Assume the variances are equal. The etch rates are as follows (in mils per minute):
Solution 1 Solution 2
9.9 10.6 10.5 10.2
9.4 10.3 10.6 10.2
9.3 10.0 10.7 10.7
9.6 10.3 10.4 10.4
10.2 10.1 10.5 10.3
Required:
a. Construct normal probability plots for the two samples. Do these plots provide support for the assumptions of normality and equal variances? Write a practical interpretation for these plots.
b. Do the data support the claim that the mean etch rate is the same for both solutions? In reaching your conclusions, use α = 0.05 and assume that both population variances are equal. Calculate a P-value.
c. Find a 95% confidence interval on the difference in mean etch rates
im really smart (no im not thats why im here)
Which is the best reason why step 1 is a good first step in the solution shown?`
WILL GIVE BRIANELIST
Answer:
Multiplying by 5 isolates the x on one side of the equation
Step-by-step explanation:
This is so you can solve for the variable x. By isolating you get the get the variable on its own so you know what the varible itself is equal to, which in this case is 75.
Answer:
Multiplying by 5 isolates x on one side of the equation
Step-by-step explanation:
When you solve equations like that, your goal is to get the variable by itself
SALE
75% off
original price!
The original price of a red clay pot is $40. What is the sale price?
Order these numbers from least to greatest:
|-17|
|-18|
-18
|19|
20
Answer: -18, l-17l, l-18l, l19l, 20
Step-by-step explanation: You can just think of the ones in absolute value brackets as positive.
there are 10 students in miss mendoza's remedial class. how many ways can she choose 3 students to clean the room?
Answer:
im pretty sure thats 30
Step-by-step explanation: 3*10=30
-12.3 + 7v = 10.1 solve for V
Answer:
v=3.2
Step-by-step explanation:
Let's solve your equation step-by-step.
−12.3+7v=10.1
Step 1: Simplify both sides of the equation.
7v−12.3=10.1
Step 2: Add 12.3 to both sides.
7v−12.3+12.3=10.1+12.3
7v=22.4
Step 3: Divide both sides by 7.
7v /7 = 22.4 /7
v=3.2
brainliest?
Car A is traveling east at a steady speed of 40 miles per hour. After 2 hours, it is 95 miles easy of Jhonstown. Car B is traveling east on the same road. its distance of Jhonstown is represented by the graph.
Answer:
B
Step-by-step explanation:
hope i helped
PLEASE HELP I HAVE NO IDEA HOW TO DO SLOPES
Step-by-step explanation:
(0, 4) (4, 0)
(0-4)/(4-0) = -4/4= -1 is the slope
simplify 14x(7xy^14)(-9x^-7 y^-3)
Answer:
-882y^11/x^5
Step-by-step explanation:
Please help givin brainliest
Answer:
Answer H
Step-by-step explanation:
13 points pls help me quick
Answer:
Right Angles: C, F
Obtuse Angles: E, B
Acute Angles: A, D
Step-by-step explanation:
Right Angles are angles that are exactly 90 degrees.
Obtuse Angles are angles that are bigger than 90 degrees.
Acute Angles are angles that are smaller than 90 degrees.
Answer:
a . C and F .
b. B and E .
c. A and D .
Step-by-step explanation:
Hope this helps .
The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150. Which of the following is not a feasible purchase combination?
a. 100K - 90Q <= 18,000
b. 90K + 100Q <= 18,000
c. 300K + 90Q <= 18,000
s. 500K + 100Q <= 18,000
e. 100K + 90Q <= 18,000
Answer:
500K + 100Q <= 18,000 ( D )
Step-by-step explanation:
king bed ( K ) requires = 100 cubic feet
Queen bed ( Q ) requires = 90 cubic feet
Total available space = 18,000 cubic feet
Revenue of king size bed = $300
Revenue of queen size bed = $150
Hence the NOT feasible purchase combination
= 500K + 100Q <= 18,000
because 500 of king size bed + 1000 of queen size is > 18,000
what is 10 / 2 + (2x4) -3 ?
Answer:
10
Step-by-step explanation:
10 / 2 = 5
(2x4) = 8
(5 + 8) - 3
13 - 3
10
Answer:
10
Step-by-step explanation:
5+8-3=10
Find -3(6m-8)+(-4+2m).
Answer: − 16 m + 20
Step-by-step explanation:
Answer:
m = 5/4
Step-by-step explanation:
What do you get when you round 2932.62 to the nearest hundredth please provide step by step explanation too.
Answer:
you get 2932.6
Step-by-step explanation:
you basically just round it down because it isn't 5 or above.
please mark brainliest
An international company has 22,900 employees and one country. If this represents 21.6% of the companies employees how many employees does it have in total? Round answer to the nearest whole number.