Answer:
The graphs of the equations intersect each other at two places.
The correct answer is the graphs of the equations intersect each other at two places.
Why does an equation have 2 solutions?A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solutions.
How do you know if a graph has two solutions?Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
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On the cone below, the length of CB is 6 inches.
What is the length of the diameter of the cone?
• 3 inches
• 6 inches
• 12 inches
• 24 inches
Answer:
12 inchesStep-by-step explanation:
CB is the radius. It is equal to BD. So, the diameter CD is ...
6 inches + 6 inches = 12 inches
The diameter is always twice the length of the radius.
The diameter of this cone is 12 inches.
The titanium content of an alloy is being studied in the hope of ultimately increasing the tensile strength. An analysis of six recent heats chosen at random produces the following titanium contents.6.6% 9.1% 7.0% 6.3% 8.5% 10.0%
What is the value of the test statistic, if the alternative hypothesis is the mean titanium content is greater than 9.5%? Round your final answer to two decimal places.
Answer:
[tex]t=\frac{7.917-9.5}{\frac{1.501}{\sqrt{6}}}=-2.58[/tex]
[tex]p_v =P(t_{5}<-2.58)=0.03[/tex]
If we compare the p value with a significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v < \alpha[/tex] so we can conclude that we can reject the null hypothesis, and there is enough evidence to conclude that the true mean is significantly lower than 9.5% at 0.05 of signficance
Step-by-step explanation:
Data given and notation
Data: 6.6% 9.1% 7.0% 6.3% 8.5% 10.0%
We can calculate the mean and the sample deviation with the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s = \sqrt{\frac{\sum_{i=1}^n (X-i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=7.917[/tex] represent the sample mean
[tex]s=1.501[/tex] represent the sample standard deviation
[tex]n=6[/tex] sample size
[tex]\mu_o =9.5[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the true mean os greater or not than 9.5%, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 9.5[/tex]
Alternative hypothesis:[tex]\mu < 9.5[/tex]
We don't know the population deviation, so for this case we can use the t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{7.917-9.5}{\frac{1.501}{\sqrt{6}}}=-2.58[/tex]
Calculate the P-value
The degrees of freedom are given by:
[tex] df = n-1 = 6-1=5[/tex]
Since is a lower tailed test the p value would be:
[tex]p_v =P(t_{5}<-2.58)=0.03[/tex]
In Excel we can use the following formula to find the p value "=T.DIST(-2.58,5,TRUE)"
Conclusion
If we compare the p value with a significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v < \alpha[/tex] so we can conclude that we can reject the null hypothesis, and there is enough evidence to conclude that the true mean is significantly lower than 9.5% at 0.05 of signficance
The test statistic of the sampling will be -2.58.
How to calculate the test statistic?The following can be deduced from the information:
Mean = 7.917
Degree of freedom = 6 - 1 = 5
P value = 0.975 > 0.05
The test statistic will be:
= (7.917 - 9.5) / (1.501 / ✓56)
= -2.58
In conclusion, the test statistic is -2.58.
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Harold took 5 hours to paint 3 same-sized walls. If he works at the same rate, how long will it take him to paint 18 walls of the same size?
Answer:
30 hours
Step-by-step explanation:
We can use ratios to solve
5 hours x hours
-------------- = -------------
3 walls 18 walls
Using cross products
5*18 = 3x
Divide each side by 3
5*18/3 = 3x/3
30 =x
Answer:It will take Harold 30 hours to paint all 18 of the walls
Step-by-step explanation:Your multiplying the amount of walls he is painting by 6 so you do the same to the amount of hours he is painting
-4 = 5 + x
I don’t know how to do this
Ionizing radiation is being given increasing attention as a method for preserving horticultural products. A study reports that 153 of 180 irradiated garlic bulbs were marketable (no external sprouting, rotting, or softening) 240 days after treatment, whereas only 117 of 180 untreated bulbs were marketable after this length of time.
Does this data suggest that ionizing radiation is beneficial as far as marketability is concerned? Use a=.05.
Answer:
Yes, there is enough evidence to support the claim that ionizing radiation is beneficial in terms of marketability.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that ionizing radiation is beneficial in terms of marketability.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]
Being π1: the true proportion of treated bulbs that can be comercialized after 240 days, and π2: the true proportion of untreated bulbs that can be comercialized after 240 days.
The significance level is 0.05.
The sample 1, of size n1=180 has a proportion of p1=0.85.
[tex]p_1=X_1/n_1=153/180=0.85[/tex]
The sample 2, of size n2=180 has a proportion of p2=0.65.
[tex]p_2=X_2/n_2=117/180=0.65[/tex]
The difference between proportions is (p1-p2)=0.2.
[tex]p_d=p_1-p_2=0.85-0.65=0.2[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{153+117}{180+180}=\dfrac{270}{360}=0.75[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.75*0.25}{180}+\dfrac{0.75*0.25}{180}}\\\\\\s_{M_d}=\sqrt{0.001+0.001}=\sqrt{0.002}=0.0456[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.2-0}{0.0456}=\dfrac{0.2}{0.0456}=4.382[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=P(t>4.382)=0.000008[/tex]
As the P-value (0.000008) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that ionizing radiation is beneficial in terms of marketability.
Final answer:
The observed marketable rate of irradiated garlic bulbs suggests that ionizing radiation is beneficial to their marketability compared to untreated bulbs, and this could be statistically tested for significance.
Explanation:
The student's data indicates that irradiated garlic bulbs have a significantly higher rate of remaining marketable (85%) after 240 days compared to unirradiated bulbs (65%). Using a significance level of α = 0.05, we can infer a positive effect of ionizing radiation on the marketability of garlic bulbs. To statistically confirm this observation, one could perform a hypothesis test (such as a chi-squared test for independence) to determine if the difference in marketability between the treated and untreated groups is significant.
How long is a pipeline that runs diagonally across a square field 6 kilometers on a side?
Answer: the square root of 72 which is approximately 8.5
Step-by-step explanation:
When draw a line diagonally in a square you get 2 right triangles so you can do pathogream theorem on them so a squared plus b squared equals c squared. In this case 6^2 + 6^2 = c^2. By solving you get the answer
The length of the pipeline running diagonally across the square field is 8.485 kilometers.
What is Pythagoras theorem?The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the sides of the square field are each 6 kilometers long. Let's sides of the square as a, b, and c, where c is the length of the diagonal (the pipeline) and a and b are the sides of the square.
Using the Pythagorean theorem, we have:
c² = a² + b²
Since the square field is a square, all sides are equal, so a = b = 6 kilometers.
c² = 6² + 6²
c² = 36+ 36
c² = 72
c = 8.485 Km
Therefore, the length of the pipeline running diagonally across the square field is 8.485 kilometers.
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Little Book LTD has total assets of $860 000. There are 75 000 shares of stock outstanding, total book value of $750 000 with a market value of $12 a share. The firm has a profit margin of 6.5% and a total asset turnover of 1.5.
a) Calculate the company’s EPS?
b) What is the market –to- book ratio?
a) Little book LTD earning per share is $1.118 per share.
Explanation:
To calculate earning per share we will use following formula:[tex]\frac{NET INCOME}{WEIGHTED AVERAGE SHARE OUTSTANDING}[/tex]
Now to find net income we will take help of asset turnover ratio :[tex]\frac{NET SALES}{TOTAL ASSET}[/tex]
NOTE : LET x BE THE NET SALES DURING THE YEAR.
Asset turnover ratio = [tex]\frac{x}{860000}[/tex]
1.5 × $860000 = x
x (net sales) = $1290000
Outstanding shares = 75000 shares
So Net Income = $1290000×.065
= $83850
Now Earning per share = [tex]\frac{83850}{75000}[/tex]
Earning per share = $1.118
b) Market to Book Ratio will be 1.2 for Little Book LTD.
Explanation:
Market to Book Ratio =[tex]\frac{MARKET CAPITALIZATION}{TOTAL BOOK VALUE}[/tex]
Market Capitalization = $ 75000× $ 12
= $900000
So, Market To Book Ratio =[tex]\frac{900000}{750000}[/tex] = 1.2
So , Market To Book Ratio is 1.2 for little book ltd.
Tony buys a pair of running shoes f 80$ he pays 9%sales tax how much does the pair of shoes cost in total?
A log is 16m long, correct to the nearest metre. It has to be cut into fence posts which must be 70cm long, correct to the nearest 10cm. What is the largest number of fence posts that can possibly be cut from the log?
Answer:
25 posts
Step-by-step explanation:
So the number of fence post would be the total length of the log divided by the length of each post. As the log is 16m and is corrected to the nearest metre, it could possibly be 16.499m. As for the post that is 70 cm long and corrected to the nearest 10cm, it may as well be 65 cm (or 0.65m) each post
So the max number of fence point once can possibly cut from the log would be
16.499 / 0.65 = 25 posts
HELPPP. find the volume of the solid with a radius of 9in and a height of 29in.
Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that EXACTLY 10 will show that the above three food items were ordered
Answer:
18.59% probability that EXACTLY 10 will show that the above three food items were ordered
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they order the above food items, or they do not. The probability of a customer ordering these items is independent of other customers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink.
This means that [tex]p = 0.6[/tex]
If a random sample of 15 cash register receipts is selected, what is the probability that EXACTLY 10 will show that the above three food items were ordered
This is P(X = 10) when n = 15. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{15,10}.(0.6)^{10}.(0.4)^{5} = 0.1859[/tex]
18.59% probability that EXACTLY 10 will show that the above three food items were ordered
If a radius is 1.5 inches, what is the diameter?
Answer:
The diameter is 3 inches
Step-by-step explanation:
If you are calculating a circle, one of the main rules you should know is that the diameter is double the radius. In this case the radius is 1.5 inches long. If you need the diameter, you need to double that figure; in this case the answer is 3 inches
Answer:
3 inches
Step-by-step explanation:
diameter is twice the length of the radius
1.5x2=3
I need help for this question because I need to understand this topic!
You and your family decide to go on a camping trip. As long as it stays above 58°F, your baby brother will get to come along. The function T(x) represents the temperature in degrees Fahrenheit, where x is the number of hours you are at the campsite. It is supposed to be the coldest 3 hours after you arrive. Use T(x) = x4 – 2x3 + x2 + 27 to determine the lowest temperature tonight. Will your brother get to go on the trip?
Answer:
yes, brother can go
Step-by-step explanation:
Apparently, you're not to think to deeply about this function. Rather, you are to take the question at face value. It is asking if the value of T(3) is more than 58.
Evaluation of polynomials is facilitated by writing them in "Horner form."
T(x) = ((x -2)x +1)x^2 +27
T(3) = ((3 -2)3 +1)9 +27 = (3 +1)9 +27 = 36 +27
T(3) = 63
The coldest temperature is supposed to be 63 degrees, which is above 58 degrees. Baby brother can come along.
Answer:
yes, the little brother can go
Step-by-step explanation:
the lowest will be 63 degrees so the baby can go
The square of 9 less than a number is 3 less than the number. What is the number?
0
-12 or 7
-12 or -7
-7 or 12
7 or 12
Answer: D. 7 or 12
Step-by-step explanation: on edgenuity 2020 :))
Using the "opposite operation" to "undo" and isolate the variable
when solving an equation is more commonly called applying the ...
Answer: inverse operation
Step-by-step explanation:
here you go
Ryan spent 24 months living in San Diego.
What would happen to the number of units if she measured the time in years?
Answer:
nothing
Step-by-step explanation:
nothing
A shipping company is creating their own shipping boxes. They have created a box with a volume of 800in^3, a helght of 8 inches and a base perimeter of 40 inches.
The machine malfunctioned, and in order to be fixed the correct dimensions of the box needed to be input. What length and width would a worker need to input in
order to fix the machine?
Length:?
inches width:?
Answer:
Length=10 Inches
Width=10 Inches
Step-by-step explanation:
Volume of the box [tex]=800in^3[/tex]
Height=8 Inches
Base Perimeter =40 Inches
Volume of a box=lbh
SInce h=8 in, V=800.
Then:
8bl=800
bl=100
[tex]l=\frac{100}{b}[/tex]
Base Perimeter=40 Inches
Perimeter of the Base= 2(l+b)
Therefore: 2(l+b)=40
Substituting [tex]l=\frac{100}{b}[/tex]
[tex]2(\frac{100}{b}+b)=40\\\frac{100+b^2}{b}=20\\$Cross Multiply\\100+b^2=20b\\b^2-20b+100=0\\$Solving the quadratic equation \\b^2-10b-10b+100=0\\b(b-10)-10(b-10)=0\\(b-10)(b-10)=0\\b-10=0 (Twice)\\b=10 \:Inch[/tex]
Recall:
[tex]l=\frac{100}{b}=\frac{100}{10}\\l=10 Inch[/tex]
Therefore:
Length=10 Inches
Width=10 Inches
Which is the answer?
Answer:
B is the correct answer.
Step-by-step explanation:
15 times 5 plus 450
= 525
25 times 5 plus 400
= 525
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 425 babies were born, and 340 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective? 0.75less than pless than 0.85 (Round to three decimal places as needed.) Does the method appear to be effective? No, the proportion of girls is not significantly different from 0.5. Yes, the proportion of girls is significantly different from 0.5.
Answer:
0.75<p<0.85
Yes,the proportion of girls is significantly different from 0.5.
Step-by-step explanation:
We calculate the proportion of girls:
[tex]p=\frac{340}{425}\\\\\\\\=0.8[/tex]
#We then calculate the confidence interval as follows:
[tex]CI=p\pm z(ME)\\\\=p\pm z_{0.005}\sqrt{\frac{p(1-p)}{n}}\\\\=0.8+2.576\times \sqrt{\frac{0.8\times 0.2}{425}}\\\\=0.8\pm0.05\\\\=[0.75,0.85][/tex]
Hence, the proportion's confidence interval at 99% is 0.75<p<0.85
#We then state our hypothesis to validate the claim:
[tex]H_o:p=0.5\\H_a:p>0.5\\\\p=0.8(True \ mean)[/tex]
Since the confidence interval does not contain 0.5, which is the the 50% chance of having a girl, then it can be concluded the proportion of girls is significantly different from 0.5.
City cabs charges a $2.75 pickup fee and $1.50 per mile traveled. Diego’s dare for a cross-town cab ride is $19.25. How far did he travel in the cab
Diego’s travel distance can be determined by first subtracting the pickup fee from the total fare and then dividing this result by the cost per mile. In this case, Diego traveled a total of 11 miles.
Explanation:To calculate Diego’s travel distance, begin by subtracting the pickup fee from the total fare. The pickup fee is $2.75 and the total fare is $19.25, so this calculation gives us $19.25 - $2.75 = $16.50. Next, divide this result by the cost per mile to determine the total distance traveled. As City cabs charge $1.50 per mile, this calculation is $16.50 ÷ $1.50 = 11. So, Diego traveled 11 miles in the cab.
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Diego traveled 11 miles in the city cab, as calculated by subtracting the fixed pickup fee from the total fare and then dividing by the cost per mile.
City cabs charges a $2.75 pickup fee and $1.50 per mile traveled. If Diego's fare for a cross-town cab ride is $19.25, the question asks us to calculate how far he traveled in the cab. To solve this, we need to use the equation of the total fare which is:
Total fare = Pickup fee + (Cost per mile × Number of miles)
Let 'x' be the number of miles Diego traveled. Using the above equation and substituting the given values, we have:
$19.25 = $2.75 + ($1.50 × x)
To find 'x', we will subtract the pickup fee from the total fare and then divide the result by the cost per mile:
$19.25 - $2.75 = $1.50 × x
$16.50 = $1.50 × x
x = $16.50 / $1.50
x = 11
Therefore, Diego traveled 11 miles in the cab.
Which is a correct first step for solving this equation?
2 + 7 = 2x + 5 - 43
Answer:
Combine the like terms
Step-by-step explanation:
2 + 7 = 2x + 5 - 43
The first step is to combine the like terms
9 = 2x - 38
A force can
___act by itself.
•
A. Sometimes
•
B. Maybe
C. Never
D. Maybe
The hours on a clock face are 30 apart. What is the angle a line from one o'clock to 6 o'clock make with a horizontal line
The angle between a line from 1 o'clock to 6 o'clock and a horizontal line is 150 degrees.
* The clock face has hours spaced 30 degrees apart.
* You want to find the angle between a line from 1 o'clock to 6 o'clock and a horizontal line.
1. **Finding the angle between consecutive hours:** Each hour on the clock face is 30 degrees apart from its neighbors. Therefore, the angle between 1 o'clock and 2 o'clock is 30 degrees, and the angle between 2 o'clock and 3 o'clock is also 30 degrees, and so on.
2. **Calculating the angle from 1 o'clock to 6 o'clock:** To get from 1 o'clock to 6 o'clock, we must move five hour marks counter-clockwise. Since each hour mark represents 30 degrees, moving five marks corresponds to an angle of 5 * 30 degrees = 150 degrees.
Therefore, the angle between a line from 1 o'clock to 6 o'clock and a horizontal line is 150 degrees.
a music company signed 12 new artists to its label in 2002. Out of the 12, 10 artists have hit songs. Write a ratio to compare the number of artists with hit songs to the total number of artists signed in 2002.
To compare the number of artists with hit songs to the total number of artists signed, write a ratio using the two numbers. The ratio of artists with hit songs (10) to total artists signed (12) simplifies to 5:6 after dividing by the greatest common factor.
Explanation:The student has asked to write a ratio comparing the number of artists with hit songs to the total number of artists signed by a music company in 2002. To do this, we take the number of artists with hit songs and place it in the numerator (top part) of the ratio and the total number of artists in the denominator (bottom part).
To write the ratio in its simplest form, we divide the numerator and the denominator by their greatest common factor if necessary. In this case, the ratio is already in the simplest form.
Step-by-Step Solution:
Number of artists with hit songs: 10
Total number of artists signed: 12
Write the ratio as 10:12
Simplify the ratio by dividing both numbers by 2, the greatest common factor, to get 5:6
So, the simplified ratio of the number of artists with hit songs to the total number of artists signed is 5:6.
Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a population standard deviation of 47 pounds. Suppose we take a sample of 30 new players and we find that the average weight from that sample is 237 pounds. We are interested in seeing if the weight of NFL players is decreasing
a.What is the standard error?
b.What is the margin of error at 90% confidence?
c. Using my sample of 30, what would be the 90% confidence interval for the population mean?
Answer:
a) The standard error would be of 8.58 pounds.
b) The margin of error is 14.11 pounds.
c) The 90% confidence interval for the population mean is between 232.89 pounds and 261.11 pounds
Step-by-step explanation:
a.What is the standard error?
The standard error is
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample. So
[tex]s = \frac{47}{\sqrt{30}} = 8.58[/tex]
The standard error would be of 8.58 pounds.
b.What is the margin of error at 90% confidence?
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*s = 1.645*8.58 = 14.11[/tex]
The margin of error is 14.11 pounds.
c. Using my sample of 30, what would be the 90% confidence interval for the population mean?
Lower bound: Sample mean subtracted by the margin of error.
247 - 14.11 = 232.89 pounds
Upper bound
247 + 14.11 = 261.11 pounds
The 90% confidence interval for the population mean is between 232.89 pounds and 261.11 pounds
Answer:
a) The standard error would be of 8.58 pounds.
b) The margin of error is 14.11 pounds.
c) The 90% confidence interval for the population mean is between 232.89 pounds and 261.11 pounds
Step-by-step explanation:
The high price of medicines is a source of major expense for those seniors in the United States who have to pay for these medicines themselves. A random sample of 1800 seniors who pay for their medicines showed that they spent an average of $ 4600 last year on medicines with a standard deviation of $ 800 . Make a 90 % confidence interval for the corresponding population mean.
Answer:
[tex]4600-1.646\frac{800}{\sqrt{1800}}=4568.96[/tex]
[tex]4600+1.646\frac{800}{\sqrt{1800}}=4631.04[/tex]
We are confident at 90% that the true mean for the amount spent on medicines is between (4568.96 and 4631.04)
Step-by-step explanation:
Information given
[tex]\bar X=4600[/tex] represent the sample mean for the amount spent on medicines
[tex]\mu[/tex] population mean
s=800 represent the sample standard deviation
n=1800 represent the sample size
Solution
The confidence interval for the true population mean is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
We can calculate the degrees of freedom with:
[tex]df=n-1=1800-1=1799[/tex]
We know that the Confidence level is 0.90 or 90%, the value of significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,1799)".And we see that [tex]t_{\alpha/2}=1.646[/tex]
Replcing in the formula for the confidence interval we got:
[tex]4600-1.646\frac{800}{\sqrt{1800}}=4568.96[/tex]
[tex]4600+1.646\frac{800}{\sqrt{1800}}=4631.04[/tex]
We are confident at 90% that the true mean for the amount spent on medicines is between (4568.96 and 4631.04)
Let X equal the number of flips of a fair coin that are required to observe
tails-heads on consecutive flips.
(a) Draw a tree diagram?
(b) Find the pmf of X
(c) Find the values of (i) P(X = 0) and (ii) P(X > 4)
(d) Find E(X + 1)^2
(e) Find Var(kX - k), where k is a constant.
Answer:
(a) I attached a photo with the diagram.
(b) [tex]f(x) = \big( \frac{1}{2} \big)^{x-1}[/tex]
(c) 1/4
(d) 4
(e) [tex]k^2/2[/tex]
Step-by-step explanation:
(a) I attached a photo with the diagram.
(b) The easiest way to think about this part is in terms of combinatorics. Think about it like this.
To begin with, look at the three each level of the three represents a possible outcome of throwing the coin n-times. If you throw the coin 3 times at the end in total there are 8 possible outcomes. But The favorable outcomes are just 2.
1 - Your first outcome is HEADS and all the others are different except the last one.
2 - Your first outcome is TAILS and all the others are different except the last one.
Therefore the probability of the event is
[tex]f(x) = P(X=x) = \frac{2}{2^x} = \frac{1}{2^{x-1}} = \big( \frac{1}{2} \big)^{x-1}[/tex]
(c)
P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.
[tex]E(X > 4) = 1 - P(X \leq 3) = 1 - ( P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3))\\= 1 - ( \frac{1}{2} + \frac{1}{4} ) = \frac{1}{4}[/tex]
(d)
Remember that this is a geometric distribution therefore
[tex]E[X] = p/(1-p)[/tex], in this case [tex]p = 1/2[/tex] so [tex]E[X] = 1[/tex] and
[tex]E[X+1]^2 = ( E[X] +1 )^2 = (1+1)^2 = 2^2 = 4[/tex]
Also
(e)
This is a geometric distribution so its variance is
[tex]Var(X) = \frac{1-p}{p^2} = 1/2 / 1/4 = 1/2[/tex]
And using properties of variance
[tex]Var(kX - k ) = Var(kX) = k^2 var(X) = k^2 /2[/tex]
To find the required answers, we create a tree diagram to visualize the possibilities of flipping a fair coin. Then, we determine the probability mass function (pmf) of X, finding the probabilities associated with each outcome. We find that P(X=0) is not possible and P(X>4) is 0. We also calculate E((X+1)^2) and Var(kX-k) using the formulas for expected value and variance of a discrete random variable.
Explanation:To answer the question, we first need to understand the possibilities when flipping a coin. Let H represent a heads and T represent a tails. The possibilities are: HT, TH, and HH. Now, let's create a tree diagram to visualize the possibilities:
(b) To find the probability mass function (pmf) of X, we need to determine the probability of each outcome. Since the coin is fair, each outcome has a probability of 1/2. Therefore, the pmf of X is: P(X=1) = 1/2, P(X=2) = 1/4, P(X=3) = 1/4.
(c) (i) P(X=0) is not possible because we need to observe tails-heads in consecutive flips. (ii) P(X>4) is the probability of observing tails-heads after at least 4 flips, which is 0 since tails-heads can occur in the 2nd or 3rd flip.
(d) To find E((X+1)^2), we need to multiply each possible outcome by its corresponding probability, square it, and then sum them up. E((X+1)^2) = (0+1)^2 * P(X=1) + (1+1)^2 * P(X=2) + (2+1)^2 * P(X=3).
(e) Var(kX-k) = k^2 * Var(X), where Var(X) is the variance of X. Since X is a discrete random variable, Var(X) = E(X^2) - (E(X))^2.
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What are the values of a,b, , and c in the quadratic equation 0 = 5x - 4x ^ 2 - 2 O a = 5b = 4 c = 2 2 a = 5 , b = - 4 , c = - 2 a = - 4 , b = 5 c = - 2 a = 4 , b = - 5 c = - 2
The cost of a cell phone increases about 13.7% each year. About how much would a $350 cell phone cost 20 years from
now?
Answer:
350(1.137)^20=4563.28232
solve for x log3(x)=6
Use log definition: if logₐ(b) = c then b = a^c
log₃(x) = 6 → x = 3⁶
x = 3⁶ → x = 726
Therefore, x = 726
Best of Luck!