Answer:
i. X represents the difference between the mean entry-level mechanical engineering salary and the mean entry-level electrical engineering salary.
ii. t distribution with df = 96
iii. t = -2.38
iv. p-value = 0.0190
v. Alpha = 0.05
i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).
ii. We used the t-distribution for the test due to unknown population standard deviations and relatively small sample sizes.
iii. The calculated test statistic is -2.1095.
iv. The degrees of freedom for the t-distribution are approximately 113242.
v. The p-value associated with the test statistic and degrees of freedom is approximately 0.0001.
i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).
ii. We will use the t-distribution for the test since the population standard deviations are unknown, and the sample sizes are relatively small (less than 30).
iii. The test statistic for this hypothesis test is calculated as:
[tex]t = (X - Xe) / \sqrt(s_m^2 / n_m) + (s_e^2 / n_e))}[/tex]
Where:
X = sample mean for mechanical engineering
Xe = sample mean for electrical engineering
Sm = standard deviation for mechanical engineering
Se= standard deviation for electrical engineering
nm = sample size for mechanical engineering
ne = sample size for electrical engineering
t = (46100 - 46900) / √(3450² / 46) + (4230² / 52))
= -800 / √(3450² / 46) + (4230² / 52))
= -800 / 379.4303
= -2.1095
iv.
Calculating the degrees of freedom:
df = (3450² / 46 + 4230² / 52)² / ((3450² / 46)² / (46 - 1) + (4230² / 52)² / (52 - 1))
= (119023.913 + 180714.2308)² / ((119023.913)² / 45 + (180714.2308)² / 51)
= 113242.1436
The degrees of freedom are approximately 113242.
Now, we need to find the p-value associated with the test statistic and degrees of freedom.
We can use a t-distribution table to look up the p-value.
Since the test is one-tailed and the test statistic is negative, we will look up the p-value in the left tail of the t-distribution with the given degrees of freedom.
Assuming the p-value is less than 0.0001, we can state that the p-value is approximately 0.0001.
v. To conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.
So, the significance level (alpha) is given as 5%.
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A student is taking a multiple-choice test in which each question has four possible answers. She knows the answers to 5 of the questions, can narrow the choices to 2 in 3 cases, and does not know anything about 2 of the questions. What is the probability that she will correctly answer A) 10, b) 9, c) 8 d) 7, e) 6, and f) 5 questions?
Do not need to answer every part if they are worked the EXACT same way.
the probability that she will correctly answer
A) 10 questions = 0
b) 9 questions = 0.00003
c) 8 questions = 0.00039
d) 7 questions =0.00309
e) 6 questions = 0.01622
f) 5 questions = 0.0584
Here the total number of question is 5+3+2= 10, and every question has four possible answers, for this problem, we will be using the binomial distribution, the formula is :
[tex]C_{n,k}[/tex][tex]p^{k}[/tex][tex]q^{n-k}[/tex] ,here C is the combination, p is the probability of success and q is the probability of having the success
for the given situation :
the p = 1/ 4 whereas, q=3/4
here n =10
now for different values of k which is the number of successes, we substitute the know values in the formula, and we get
P(k=10) = 0
P(k=9) = 0.00003
P(k=8) = 0.00039
(P=7)= 0.00309
(P=6)=0.01622
(P=5)= 0.0584
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42,786,950 writen in scientific notation
Answer: 4.278695 × 10^7
Step-by-step explanation:
Answer: 4.2786950x10^7 or 4.2x10^7
Step-by-step explanation:
To convert a number to scientific notation, move the decimal.
42,786,950
At the and of this number, there is an understood decimal. To find the scientific notation version of it, move the decimal over to the left until you have only one digit to the left of the decimal, as such...
4.2786950
To then find what the exponent you're multiplying by, you count how many places you moved the decimal.
So in the end, you get 4.2786950x10^7
Which of the following graphs show the most reliable results (the x-axis shows the original text scores, and the y-axis shows the re-test scores).
The following is the graph that displays the most trustworthy findings:
Choice C
A correlation coefficient is defined.
A measure of correlation between two variables, the correlation coefficient between two variables assumes values between -1 and 1.
The relationship is direct proportional if it is positive, and inverse proportional if it is negative.
Strong correlation exists between two variables if the correlation coefficient's absolute value is higher than 0.6.
This description leads us to conclude that the graph with the highest correlation coefficient is the most accurate, making Option C the proper choice.
Lack of Information
The two solutions to this problem are as follows:
Option B: Create a graph with a r = 0 correlation coefficient.
Option C: Create a graph with a r = 0.87 correlation coefficient.
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how would you explain the difference between qualitative and quantitative data sources? how would you explain the difference between qualitative and quantitative data sources?
Qualitative data is used to represents the qualities , intention of human behavior and is basically based on observations and interview using open ended questions where as quantitative data is based on the statistical and mathematical data.
Explanation:
Difference between Quantitative and Qualitative data sources:
Qualitative data sources:
It represents the subjective approachBased on open-ended question.It represents the human behavior.Quantitative data sources:
It represents the objective approach.Based on Statistical and mathematical data.Represents using graphs.Therefore, qualitative data is used to represent the human behavior while quantitative data is for statistical and mathematical data.
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Find the mean absolute deviation: 5, 11, 2, 7, 16. the mean is 8.2
the mean absolute deviation is 4.24
What Is Mean Absolute Deviation?
Mean absolute deviation (MAD) is a measure of the average absolute distance between each data value and the mean of a data set. Similar to standard deviation, MAD is a parameter or statistic that measures the spread, or variation, in your data.
the given mean absolute deviation 5,11,2,7,16
mean = [tex]\frac{5+11+2+7+16}{5}[/tex]
mean = 8.2
Hence, the mean absolute deviation is given by:
[tex]M_{d}[/tex] = |5-8.2| + |11-8.2| +|2-8.2| +|7-8.2|+|16-8.2| / 5
= 4.24
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when three positive integers $a, b$, and $c$ are multiplied together, their product is $100$. suppose $a < b < c$. in how many ways can the numbers be chosen?
Together the numbers a , b and c can be chosen in 4 ways.
Given:
when three positive integers $a, b$, and $c$ are multiplied together, their product is $100$ and a < b < c .
The positive divisors of 100 are :
1 , 2 , 4 , 5 , 10 , 20 , 25 , 50 , 100.
It is clear that :
10 ≤ c ≤ 50.
so we apply from c value 10.
if c = 10 , then ( a , b , c ) = ( 2 , 5 , 10 )
if c = 20 , then ( a , b , c ) = ( 1 , 5 , 10 )
if c = 25 , then ( a , b , c ) = ( 1 , 4 , 25 )
if c = 50 , then ( a , b , c ) = ( 1 , 2 , 50 )
we can observe ways = 4.
Therefore the number of ways is 4.
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Fill in the Table Values pls
Answer:45 76 97 790 9786 99780 533455 6687878
Step-by-step explanation:
can y’all help me with these three questions
(x^4+6x^3-x^2-5x+1)/(x-2)
PLEASE HELP SYNTHETIC DIVISION
Answer:
x^3+8x^2+15x+25+51
x-2
a. a rectangular solar panel is made up of small squares. a particular solar panel is 5 squares by 27 squares. in what other rectangular arrays could the squares have been arranged? b. if there were 23 squares, how many rectangular arrays can there be?
(a) The rectangular arrays could the squares have been arranged as
1 by 135, 3 by 45, 5 by 27, 9 by 15, 15 by 9.
(b) The rectangular arrays is of 1 by 23.
What is solar panel?
An assembly of photovoltaic solar cells installed on a frame (often rectangular) is known as a solar cell panel, solar electric panel, photo-voltaic (PV) module, PV panel, or solar panel. A well-organized collection of PV panels is known as a photovoltaic system or solar array. Sunlight is used by solar panels to collect radiant energy, which is then transformed into direct current (DC) power.
(a) Let a particular solar panel is 5 squares by 27 squares.
5 by 27 = 135 which can be arranged as,
1 by 135
3 by 45
5 by 27
9 by 15
15 by 9
(b) There were 23 squares.
The factors of 23 are 1, 23 only so there can be only 1 rectangular array of 1 by 23.
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A line's y-intercept is 6, and its slope is 1. What is its equation in slope-intercept form?
Answer:y=x+6
Step-by-step explanation:
y= slopex+y-intercept
three points are chosen randomly and independently on a circle. what is the probability that all three pairwise distances between the points are less than the radius of the circle?
There is a 1/12 chance that the three pairwise distances between the locations are smaller than the radius of the circle.
Here,
The first point can be placed anywhere on the circle because it doesn't matter where it is chosen.
A total of 120 degrees and a probability of 1/3 must be provided by the next point, which must be within an arc of 60 degrees on either side. The second point must be 60 degrees or less from the first two.
The third point can be located within an arc with a minimum area of freedom of 60 degrees and a chance of 1/6 if the first two locations are separated by 60 degrees. The third point can be located with a maximum degree of freedom of a 120 degree arc and a 1/3 chance if the first two points are the same.
Up to a maximum of 60 degrees away from the starting point, the likelihood changes linearly.
By averaging the probabilities at either end, we may discover 1/4, the typical likelihood we can position the third point based on a fluctuating second point.
The overall probability is 1 1/3 4 = 1/12.
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Joey ha 8 pair of ock in hi drawer. Five of the pair are white. What percent of joey ock are colored?
Using percentages, we know that Joey has 37.5% of colored pairs of socks.
What is the percentage?%, which is a relative figure used to denote hundredths of any quantity.
Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance.
Finding the percentage of a whole in terms of 100 is what percentage calculation is.
Both manual calculation and the use of internet calculators are options.
So, the percentage of colored pair of socks are:
We know that Joey has a total of 8 pairs of socks.
We also know that 5 pairs of socks are white.
Hence, the colored pair of socks will be:
8 - 5 = 3
Calculate its percentage as follows:
3/8 * 100
0.375 * 100
37.5%
Therefore, using percentages, we know that Joey has 37.5% of colored pairs of socks.
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A company that manufactures memory chips for digital cameras uses the formula c = 3√n(40 6√n +9 4√n) to determine the cost, c, in dollars, for producing n chips. This formula can be written as c = 120 3√n +27 4√nb, where a and b are constants.
What are the values of a and b?
**answer choices in pic
The values of a and b are 3 and 2.
What is Expression?An expression is combination of variables, numbers and operators.
Given,
A company that manufactures memory chips for digital cameras uses the formula [tex]c=3\sqrt{n} (40\sqrt[6]{n}+9\sqrt[4]{n} )[/tex]
The cost, c, in dollars, for producing n chips.
We need to solve for values a and b.
[tex]c=3\sqrt{n} (40\sqrt[6]{n}+9\sqrt[4]{n} )[/tex]
[tex]c=3\sqrt{n} (40\sqrt[6]{n})+3\sqrt{n} (9\sqrt[4]{n} )[/tex]
[tex]c=120\sqrt{n} \sqrt[6]{n} +27\sqrt{n} \sqrt[4]{n}[/tex]
[tex]c=120n^{\frac{7}{2}} +27n^{\frac{5}{2}}[/tex]
c=[tex]120n^{\frac{3a}{2} } +27n^{\frac{4b}{2} }[/tex]
By solving this we get a=3 and b=2
Hence, the value of a and b is 3 and 2.
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6. Olumide plays the piano and guitar. For every 5 minutes of piano practice, he spends 8) minutes practicing guitar. How many minutes will Olumide practice piano if he spends 64 minutes practicing guitar?
He will practice 40 m on piano if he spends 64 m practicing on guitar. It can be solve by the concept of word problems on multiplication of fraction.
What is fraction?
Fraction is a part of a whole number or quantity. It is written as 3/8, 4/9, etc.
Piano practice time = 5 m
Guitar practice time = 8 m
If he spend 8 minute practicing on guitar then he will spend on piano practice = 5 m
If he spend 1 minute practicing on guitar then he will spend on piano practice = 5m/8m
If he spend 64 minute practicing on guitar then he will spend on piano practice
[tex]=\frac{5m}{8m}64m\\=40 m[/tex]
Hence, he will practice 40 m on piano if he spends 64 m practicing on guitar. It can be solve by the concept of word problems on multiplication of fraction.
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a large study in the uk was done to determine if there was a link between cell phone usage and brain cancer. the study set out to determine if using a cell phone more, increased the likelihood of getting brain cancer. the study took about 800,000 women and asked them to report their cell phone use in 1999, 2005, and again in 2009. in 2009, they recorded the proportion of women who had developed brain cancer. their conclusion was "in this large prospective study, mobile phone use was not associated with increased incidence of glioma, meningioma or non-cns cancers." is this an observational study or an experiment? justify your answer.
The given case study can be categorized as an observational study .A correctly conducted observational study will never attempt to influence participants' reactions, in contrast to experimental designs, which by definition apply a treatment condition to some individuals.
It is debatable whether cell phones and cancer are related. Studies on cellphones and cancer have been conducted for a long time, with varying degrees of success. There isn't now agreement on the potential cancer risk posed by cellphone use.
The growth of cancer linked to cellphone use appears to be the main cause for concern regarding smartphones and cancer. Despite the fact that cellphone use wasn't prevalent in the 1970s, some research indicates a slight rise in the prevalence of cancer since that decade.
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5 added to the difference between a number an 12
Answer:
x-7
Explanation:
Subtract 5 5 from both sides of the equation. Subtract 5 5 from 12 12 . Divide each term in −x=7 by −1 and simplify. Divide each term in −x=7
In a hypothesis test for population proportion, you calculated the p-value is 0. 01 for the test statistic, which is a correct statement of the p-value?.
According to the hypothesis test, the correct statement of the p-value is mean value is against null hypothesis.
Hypothesis test:
In statistics, hypothesis test means a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution.
Given,
Here we need to find the correct statement of the p-value for the a hypothesis test for population proportion, you calculated the p-value is 0. 01 for the test statistic.
While we looking into the given question we have identified the value of p value of the test statistic is 0.01.
Then the correct statement of the p-value less than 0.01 will under normal circumstances mean that there is substantial evidence against the null hypothesis.
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Use point-slope form to write the equation of a line that passes through the point (-13,-19) with the slope 7/6
Answer: [tex]y = \frac{7}{6}x - \frac{23}{6}[/tex]
Work Shown:
[tex]y - y_1 = m(x - x_1)\\\\y - (-19) = \frac{7}{6}(x - (-13))\\\\y + 19 = \frac{7}{6}(x + 13)\\\\y + 19 = \frac{7}{6}x + \frac{7}{6}*13\\\\y + 19 = \frac{7}{6}x + \frac{91}{6}\\\\y = \frac{7}{6}x + \frac{91}{6} - 19\\\\y = \frac{7}{6}x + \frac{91}{6} - 19*\frac{6}{6}\\\\y = \frac{7}{6}x + \frac{91}{6} - \frac{114}{6}\\\\y = \frac{7}{6}x + \frac{91-114}{6}\\\\y = \frac{7}{6}x - \frac{23}{6}\\\\[/tex]
A ski rental service charges a $37.30 initial flat rate and then an additional $2.70 per hour. In this situation, what is the value of the y-intercept?
what is the equation in point-slope form of a line that passes through the points (7, −8) and (−4, 6) ? responses y+6=−23(x−4) y plus 6 equals negative fraction 2 over 3 end fraction open parenthesis x minus 4 close parenthesis y+6=−1411(x−4) y plus 6 equals negative fracion 14 over 11 end fraction open parenthesis x minus 4 close parenthesis y−6=−23(x+4) y minus 6 equals negative fraction 2 over 3 end fraction open parenthesis x plus 4 close parenthesis y−6=−1411(x+4)
The equation of the line that passes through the points (7, -8) and (-4, 6) in point slope form is y - 6 = -14/11(x + 4)
The coordinates of the first point = (7, -8)
The coordinates of the second point = (-4, 6)
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (6-(8) / (-4-7)
= 6+8 / -4-7
= 14 / -11
= - 14/11
Point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the value in the equation
y - 6 = -14/11(x - (-4))
y - 6 = -14/11(x + 4)
Therefore, the equation of the line is y - 6 = -14/11(x + 4)
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which sentance describe points that miguel should consider in the goal setting process before he starts to invest
PLEASE HELP I'M SO STRESSED
SOLVE FOR X PLEASE HELP ME
Answer:
Step-by-step explanation:
39.06
Joseph has a loyalty card good for a 9% discount at his local grocery store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $37? Round to the nearest cent.
Answer: $40.33
Step-by-step explanation:
9% of $37 = 3.33
37 + 3.33 = 40.33
What is the equation of a line perpendicular to 3z + 4y - 12and passes thru the point (3.2)? Write the equation in slope-intercept form (y=mx+b)
Answer:
Step-by-step explanation:
After you know the equation of this line, you will be able to figure out the equation of the line that runs perpendicular to it. [11] To simplify. y − 6 = 3 2 ∗ ( x − 4) {\displaystyle {y}- {6}= {\frac {3} {2}}* ( {x}-4)} , first multiply all of the numbers in parentheses by the outer value to get.
How much would $300 invested at 4% interest compounded monthly be worth after 8 years? round your answer to the nearest cent.
The amount will be $412.91 after 8 years if $300 is invested at 4% interest compounded monthly.
Given:
Principal (P) = $300
rate of interest (r) = 4%
time (t) = 8 years.
compounded monthly.
Amount (A) = ?
we know the formula as:
A(t) = P(1+r/n)^nt
we know t=8
A(8) = 300(1+0.04/12)^12(8)
A(8) = 300(1+0.04/12)^96
A(8) = 300(1.033)^96
A(8) = $412.91
Hence amount after 8 years will be $412.91.
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how do the results compare to your hypothesis? explain why your hypothesis was or was not supported by the results.
To compare result to hypothesis, we will start by providing the key result from the each model and then compare and contrast them.
A hypothesis is usually a prediction based on some evidence. Hypothesis must be tested and once tested they can be supported by evidence if a statement is made that cannot be tested or disproof then it is not hypothesis
To compare we will start by providing the key result from the each model and then compare and contrast them then you can then provide any interpretation or future direction to some of the comparison
To prove or disprove your hypothesis you need to be able to do an experiment and take that measurement or make observation to see how two things are related
If you have hypothesis is not supported by the result of the experiment you should really realize the data in order to figure out why your result disprove your hypothesis
You should not alter the observation or experiment so that you reserve proof your hypothesis
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one hundred subjects are to be assigned to two groups for an experiment that requires a completely randomized design
The subjects in Group 1 are those with the 50 lowest four-digit numbers. Group 2 is given the remaining subjects.
An experiment that is conducted at random?What a Random Situation Is Exactly. Any clearly defined procedure that yields an observable result that could not be entirely predicted beforehand is considered a random experiment. In order to avoid any ambiguity or surprise, a random experiment must be clearly defined.
List the subjects in alphabetical order by name.
A four-digit number at random, between 0001 and 9999 (inclusive), should be given to each subject using a table of random numbers.
Leaving out 4 digit that have already been allocated.
The subjects in Group 1 are those with the 50 lowest four-digit numbers. Group 2 is given the remaining subjects.
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PLEASE HELP ME !!!!!
1 ) The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 24 inches long and vibrates 128 times per second, what is the length of a string that vibrates 64 times per second?
48 inches
46 inches
42 inches
55 inches
------------------------------------------------------------------
2 ) The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute - rpm) and the cube of the diameter. If the shaft of a certain material 3 inches in diameter can transmit 45hp at 100 rpm, what must the diameter be in order to transmit 60hp at 150rpm?
24
[tex]\sqrt[3]{150}[/tex]
[tex]2\sqrt[3]{3}[/tex]
[tex]4\sqrt[3]{6}[/tex]
Answer:
[tex]\textsf{1)\quad 48\;inches}[/tex]
[tex]\textsf{2)\quad$2\sqrt[3]{3}$\; inches}[/tex]
Step-by-step explanation:
Question 1Define the variables:
Let x be the length of the string.Let y be the rate of vibration of a string under constant tension.The rate of vibration of a string under constant tension varies inversely with the length of the string:
[tex]\boxed{y \propto \dfrac{1}{x} \implies y=\dfrac{k}{x}\quad\text{for a constant $k$}}[/tex]
Given values:
x = 24 inchesy = 128 times per secondSubstitute the given values of x and y into the formula and solve for k:
[tex]\implies 128=\dfrac{k}{24}[/tex]
[tex]\implies k=128 \cdot 24[/tex]
[tex]\implies k=3072[/tex]
Therefore, the equation is:
[tex]y=\dfrac{3072}{x}[/tex]
To find the length of a string that vibrates 64 times per second, substitute y = 64 into the equation and solve for x:
[tex]\implies 64=\dfrac{3072}{x}[/tex]
[tex]\implies x=\dfrac{3072}{64}[/tex]
[tex]\implies x=48[/tex]
Therefore, the length of a string that vibrates 64 times per second is 48 inches.
---------------------------------------------------------------------------------------------
Question 2Define the variables:
Let y be the horsepower (hp) that a shaft can safely transmit.Let v be the speed of the shaft (in rpm).Let d be the diameter of the shaft (in inches).The horsepower that a shaft can safely transmit varies jointly with its speed and the cube of the diameter:
[tex]\boxed{y \propto vd^3 \implies y=kvd^3\quad\text{for a constant $k$}}[/tex]
Given values:
y = 45 hpv = 100 rpmd = 3 inchesSubstitute the given values of y, v and d into the formula and solve for k:
[tex]\implies 45=k \cdot 100 \cdot 3^3[/tex]
[tex]\implies 45=k \cdot 100 \cdot 27[/tex]
[tex]\implies 45=2700k[/tex]
[tex]\implies k=\dfrac{45}{2700}=\dfrac{1}{60}[/tex]
Therefore, the equation is:
[tex]y=\dfrac{vd^3}{60}[/tex]
To find the diameter of the shaft in order to transmit 60 hp at 150 rpm, substitute y = 60 and v = 150 into the equation and solve for d:
[tex]\implies 60=\dfrac{150d^3}{60}[/tex]
[tex]\implies 3600=150d^3[/tex]
[tex]\implies d^3=\dfrac{3600}{150}[/tex]
[tex]\implies d^3=24[/tex]
[tex]\implies d=\sqrt[3]{24}[/tex]
[tex]\implies d=\sqrt[3]{8 \cdot 3}[/tex]
[tex]\implies d=\sqrt[3]{8} \sqrt[3]{3}[/tex]
[tex]\implies d=\sqrt[3]{2^3} \cdot \sqrt[3]{3}[/tex]
[tex]\implies d=2\sqrt[3]{3}[/tex]
Therefore, the diameter of a shaft that transmits 60 hp at 150 rpm is 2³√3 inches.
(5p³z-9z+9) - (p³z + 5z - 4)
Answer:
4p³z - 14z +13
Step-by-step explanation:
(5p³z -9z +9) - (p³z +5z -4)
the - multiplies the bracket
5p³z -9z +9 -p³z -5z +4
collect like terms
5p³z -p³z -9z -5z +9+4
4p³z - 14z +13