College Math Questions: Expert Solutions & Tips

Create a 2nd order, homogeneous, linear IVP, that is not guaranteed to have a unique solution at $x_0=3$

Let B and C be the following ordered bases of ${\displaystyle R^3:}$
$B=(\left[\begin{array}{c}1\\ 4\\ -\frac{4}{3}\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 8\end{array}\right],\left[\begin{array}{c}1\\ 1\\ -2\end{array}\right])$
$C=(\left[\begin{array}{c}1\\ 1\\ -2\end{array}\right],\left[\begin{array}{c}1\\ 4\\ -\frac{4}{3}\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 8\end{array}\right])$ Find the change of coordinate matrix I_{CB}

If ${\displaystyle n=110}$ and ${\displaystyle \hat{p}}$ (p-hat) ${\displaystyle =0.66}$, construct a ${\displaystyle 95\mathrm{\%}}$ confidence interval. Give your answers to two decimals ${\displaystyle ?<p<?}$

A normal population has mean ${\displaystyle \mu =20}$ and standard deviation ${\displaystyle \sigma =4}$.
What proportion of the population is less than 18?

A population of values has a normal distribution with ${\displaystyle \mu =120.6}$ and ${\displaystyle \sigma =48.5}$. You intend to draw a random sample of size ${\displaystyle n=105}$.
Find the probability that a sample of size ${\displaystyle n=105}$ is randomly selected with a mean greater than 114.9.
${\displaystyle P\left(M>114.9\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

A population of values has a normal distribution with ${\displaystyle \mu =239.5}$ and ${\displaystyle \sigma =32.7}$. You intend to draw a random sample of size ${\displaystyle n=139}$.
Find the probability that a sample of size $n=139$ is randomly selected with a mean greater than 235.9.
${\displaystyle P\left(M>235.9\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

Find the sum of the given vectors
${\displaystyle 50N\mathrm{\angle }{320}^{\circ }+170N\mathrm{\angle }{150}^{\circ }}$
$Rx=?$
$Ry=?$
$R=?$
$\theta =?$

Is $Z_3\oplus Z_9,$ isomorpbic to
$Z_{27}?$
Decide and answer why exactly?

Solve differential equation $dy/dx=e^{4}x(y-3)$

To find: The exact circumference of the circle with diameter 20 inches and approximate the circumference.

A random sample of ${\displaystyle n_1=16}$ communities in western Kansas gave the following information for people under 25 years of age.
${\displaystyle X_1:}$ Rate of hay fever per 1000 population for people under 25
$\begin{array}{|cccccccc|}\hline 97& 91& 121& 129& 94& 123& 112& 93\\ 125& 95& 125& 117& 97& 122& 127& 88\\ \hline\end{array}$
A random sample of ${\displaystyle n_2=14}$ regions in western Kansas gave the following information for people over 50 years old.
${\displaystyle X_2:}$ Rate of hay fever per 1000 population for people over 50
$\begin{array}{|ccccccc|}\hline 94& 109& 99& 95& 113& 88& 110\\ 79& 115& 100& 89& 114& 85& 96\\ \hline\end{array}$
(i) Use a calculator to calculate ${\displaystyle {\bar{x}}_1,s_1,{\bar{x}}_2,\text{and}{s}_2.}$ (Round your answers to two decimal places.)
(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use ${\displaystyle \alpha =0.05.}$
(a) What is the level of significance?
State the null and alternate hypotheses.
${\displaystyle H_0:{\mu }_1={\mu }_2,H_1:{\mu }_1<{\mu }_2}$
${\displaystyle H_0:{\mu }_1={\mu }_2,H_1:{\mu }_1>{\mu }_2}$
${\displaystyle H_0:{\mu }_1={\mu }_2,H_1:{\mu }_1\ne {\mu }_2}$
${\displaystyle H_0:{\mu }_1>{\mu }_2,H_1:{\mu }_1={\mu }_{12}}$
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations,
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations,
The Student's t. We assume that both population distributions are approximately normal with known standard deviations,
What is the value of the sample test statistic? (Test the difference ${\displaystyle {\mu }_1-{\mu }_2}$. Round your answer to three decimalplaces.)

What is the value of the sample test statistic? (Test the difference ${\displaystyle {\mu }_1-{\mu }_2}$. Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
P-value ${\displaystyle >0.250}$
${\displaystyle 0.125<P-\text{value}<0,250}$
${\displaystyle 0,050<P-\text{value}<0,125}$
${\displaystyle 0,025<P-\text{value}<0,050}$
${\displaystyle 0,005<P-\text{value}<0,025}$
P-value ${\displaystyle <0.005}$
Sketch the sampling distribution and show the area corresponding to the P-value.
P.vaiue Pevgiue
P-value f P-value

Find the inverse Laplace transform of
$\frac{6s+15}{(s^2+25)}$
$s>0$

Find derivatives of the functions defined as follows. $(y=-{10}^{3x^2-4})$

Differentiate between univariate, bivariate and multivariate data.

Identify the variable being measured.

A population of values has a normal distribution with ${\displaystyle \mu =116.3}$ and ${\displaystyle \sigma =27.5}$. You intend to draw a random sample of size ${\displaystyle n=249}$.
Find the probability that a single randomly selected value is greater than 117.3.
${\displaystyle P\left(X>117.3\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $(A\text{ and }B)=P(A)\cdot P(B)P(A\text{ and }B)=P(A)\cdot P(B).$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.

1. Find each of the requested values for a population with a mean of $?=40$, and a standard deviation of $?=8$ A. What is the z-score corresponding to $X=52?$ B. What is the X value corresponding to $z=-0.50?$ C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of $M=42$ for a sample of $n=4$ scores? E. What is the z-scores corresponding to a sample mean of $M=42$ for a sample of $n=6$ scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: $a.-2.00b.1.25c.3.50d.-0.34$ 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $\mu =78$ and $\sigma =12$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $82,74,62,68,79,94,90,81,80$. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $\$12(\mu =42,\sigma =12)$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is $44.50 from tips. Test for a difference between this value and the population mean at the $\alpha =0.05$ level of significance.

Trust Fund A philanthropist deposits $5000 in a trust fund that pays 7.5% interest, compounded continuously. The balance will be given to the college from which the philanthropist graduated after the money has earned interest for 50 years.
How much will the college receive?

Write the first order differential equation for $y=2-{\int }_0^x(1+y(t))\sin tdt$