Answer:
Probabilty of not poor= 0.75
Step-by-step explanation:
total of 11332 bonds.
7311 are good risk.
1182 are medium risk.
Poor risk
= total risk-(good risk+ medium risk)
= 11332-(7311+1182)
= 11332-8493
= 2839.
Poor risk = 2839
Probabilty that the ball choosen at random is not poor= 1 - probability that the ball is poor
Probability of poor = 2839/11332
Probabilty of poor= 0.2505
Probabilty that the ball choosen at random is not poor= 1- 0.2505
= 0.7495
To two decimal place= 0.75
A model of a house was built using the scale 5 in: 25 ft. If a window in the model is 1.5 in. wide, how wide is the actual window?
Answer:
7.5 feet
Step-by-step explanation:
Scale of the Model =5 in: 25 ft.
If we divide both sides by 5
[tex]\dfrac{5 in.}{5} : \dfrac{25 ft.}{5}\\\\$1 inch: 5 feet[/tex]
If a window on the model is 1.5 inch wide, from the unit ratio derived above we then have that:
1 Inch X 1.5 : 5 feet X 1.5 feet
1.5 Inch : 7.5 feet
Therefore, if a window in the model is 1.5 in. wide, the actual window is 7.5 feet wide.
What is ansewer 1/6 of 30
Answer:
5
Step-by-step explanation:
The right answer is 5.
look at the attached picture
Hope it helps...
Good luck on your assignment
5. Which statement is true about the triangles?
Hey there! I'm happy to help!
It appears that we are trying to figure out which triangles are similar, which means that their side lengths have the same ratio. In ΔABC, we see that two sides have a length of 10 and the shorter has a length of 5. This means that the ratio between the long sides and the short sides must be 2:1 to be similar to this triangle.
Let's look at ΔJKL. Our long side has to be double our short side. If we double 2.5, it will be 5, not six, so JKL is not similar with ABC.
Now, let's look at ΔDEF. We see that it's long sides are double the short sides because 6 is double three. This means that the triangles ABC and DEF are similar.
The answer is A) ΔABC ~ ΔDEF.
I hope that this helps! Have a wonderful day!
Factories A and B produce computers. Factory A produces 3 times as many computers as factory B. The probability that an item produced by factory A is defective is 0.03 and the probability that an item produced by factory B is defective is 0.045. A computer is selected at random and it is found to be defective. What is the probability it came from factory A?
Answer:
P(A∣D) = 0.667
Step-by-step explanation:
We are given;
P(A) = 3P(B)
P(D|A) = 0.03
P(D|B) = 0.045
Now, we want to find P(A∣D) which is the posterior probability that a computer comes from factory A when given that it is defective.
Using Bayes' Rule and Law of Total Probability, we will get;
P(A∣D) = [P(A) * P(D|A)]/[(P(A) * P(D|A)) + (P(B) * P(D|B))]
Plugging in the relevant values, we have;
P(A∣D) = [3P(B) * 0.03]/[(3P(B) * 0.03) + (P(B) * 0.045)]
P(A∣D) = [P(B)/P(B)] [0.09]/[0.09 + 0.045]
P(B) will cancel out to give;
P(A∣D) = 0.09/0.135
P(A∣D) = 0.667
A study is done by a community group in two neighboring colleges to determine which one graduates students with more math classes. College A samples 11 graduates and finds the mean is 4 math classes with a standard deviation of 1.5 math classes. College B samples 9 graduates and finds the mean is 3.5 math classes with a standard deviation of 1 math class. The community group believes that a student who graduates from college A has taken more math classes, on the average. Test at a 10% significance level. Assume the requirements for a valid hypothesis test are satisfied.
Answer:
[tex]t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890[/tex]
The p value for this case would be:
[tex]p_v =P(t_{18}>0.890)=0.193[/tex]
The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B
Step-by-step explanation:
Information given
[tex]\bar X_{1}=4[/tex] represent the mean for sample A
[tex]\bar X_{2}=3.5[/tex] represent the mean for sample B
[tex]s_{1}=1.5[/tex] represent the sample standard deviation for A
[tex]s_{2}=1[/tex] represent the sample standard deviation for B
[tex]n_{1}=11[/tex] sample size for the group A
[tex]n_{2}=9[/tex] sample size for the group B
[tex]\alpha=0.1[/tex] Significance level provided
t would represent the statistic
Hypothesis to test
We want to verify if the student who graduates from college A has taken more math classes, on the average, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2} \leq 0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}> 0[/tex]
The statistic is given by:
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)
And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=11+9-2=18[/tex]
Replacing we got:
[tex]t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890[/tex]
The p value for this case would be:
[tex]p_v =P(t_{18}>0.890)=0.193[/tex]
The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B
Solve the formula d = rt for r
Answer: r=d/t
Step-by-step explanation:
This is an equation manipulation problem. Since you are looking for r, you want to get it alone. To do so, you would divide t on both sides. Therefore, you get r=d/t.
Solve the quadratic equation 3x² + 2x-4=0
Give your answers to 2 decimal places.
3x² + 2x - 4 = 0
Δ = b² - 4.a.c
Δ = 2² - 4 . 3 . -4
Δ = 4 - 4. 3 . -4
Δ = 52
x = (-b +- √Δ)/2a
x' = (-2 + √52)/2.3
x'' = (-2 - √52)/2.3
x' = 0,8685170918213297
x'' = -1,5351837584879966
2 Decimal places
x' = 0,87
x'' = -1,54
Answer: .8685
Step-by-step explanation:
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 222 days and standard deviation sigma equals 15 days.
What is the probability that a random sample of 26 pregnancies has a mean gestation period of 216 days or less?
The probability that the mean of a random sample of 26 pregnancies is less than 216 days is approximately
Answer:
[tex] z = \frac{216-222}{\frac{15}{\sqrt{26}}}= -2.040[/tex]
And we can find this probability on this way:
[tex]P(z<-2.040)=0.0207[/tex]
Step-by-step explanation:
Let X the random variable that represent the lenghts of the pregnencies of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(222,15)[/tex]
Where [tex]\mu=222[/tex] and [tex]\sigma=15[/tex]
We are interested on this probability
[tex]P(\bar X<216)[/tex]
The z score formula is given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score we got:
[tex] z = \frac{216-222}{\frac{15}{\sqrt{26}}}= -2.040[/tex]
And we can find this probability on this way:
[tex]P(z<-2.040)=0.0207[/tex]
Consider a sample with data values of 10, 20, 12, 17, and 16. (a) Compute the mean and median. Mean = Median = (b) Consider a sample with data values 10, 20, 12, 17, 16, and 12. How would you expect the mean and median for these sample data to compare to the mean and median for part a (higher, lower, or the same)? The input in the box below will not be graded, but may be reviewed and considered by your instructor. Compute the mean and median for the sample data 10, 20, 12, 17, 16, and 12. If required, round your answers to one decimal place.
Answer:
Step-by-step explanation:
Consider a sample with data values of 10, 20, 12, 17, and 16. (a) Compute the mean and median. Mean = Median = (b) Consider a sample with data values 10, 20, 12, 17, 16, and 12.
Mean = Total of values/ Total number of observations
Total of values = 10+20+12+17+16 = 75
Total number of observations = 5
Mean = 75/5 = 15
Median:
Arrange in ascending order = 10, 12,16,17,20
Median = [n+1] / 2
N = number of observation = 5
Median = [5+1]/2 = 3rd observation
Median = 16
Find the value of x that will make a || B
Answer:
x = 30
Step-by-step explanation:
4x + 2x = 180
6x = 180
x = 30
If the sinA=3/5 and the cos=4/5 then what is tan A
Answer:
tanA = sinA / cosA = 3/5 / 4/5 = 3/4.
Can someone help me pls, I will really appreciate it
Use the law of cosines to find the missing length, which we'll call [tex]d:[/tex]
[tex]d^2=100^2+120^2-2(100)(120)\cos 45^\circ[/tex]
[tex]d^2=24400-12000\sqrt{2}[/tex]
[tex]\boxed{d\approx 86\text{ cm}}.[/tex]
One of the reasons health care costs have been rising rapidly in recent years is the increasing cost of malpractice insurance for physicians. Also, fear of being sued causes doctors to run more precautionary tests (possibly unnecessary) just to make sure they are not guilty of missing something. These precautionary tests also add to health care costs. Data in the Excel Online file provided below are consistent with findings in the Reader's Digest article and can be used to estimate the proportion of physicians over the age of 55 who have been sued at least once.
Required:
a. Formulate hypotheses that can be used to see if these data can support a finding that more than half of physicians over the age of 55 have been sued at least once.
b. Use Excel or Minitab and the file LawSuit to compute the sample proportion of physicians over the age of 55 who have been sued at least once. What is the p-value for your hypothesis test?
c. At α= 0.01, what is your conclusion?
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
b) Sample proportion (p) = 0.6
Sample size (n) = 200
P-value = 0.0029
c) Conclusion: there is enough evidence to support the claim that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.
Step-by-step explanation:
The question is incomplete: there is no attached file with the data.
a) We want to test if more than half of the physiscians over the age of 55 have been sued at least once.
Then, the claim that will be stated in the alternative hypothesis should be that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.
The null hypothesis should state that this proportion is not signficantly different from 0.5.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
b) As we do not have the file, we will work with a sample with size n=200 and sample proportion of 0.6.
This sample proportion can be calculated from the data as
[tex]p=x/n=120/200=0.6[/tex]
where x is the number of subjects in the sample that have been sued at least once.
The claim is that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
The significance level is 0.01.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.6-0.5-0.5/200}{0.035}=\dfrac{0.098}{0.035}=2.758[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.758)=0.0029[/tex]
As the P-value (0.0029) is smaller than the significance level (0.01), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.
watching tv: in 2012, the general social survey asked a sample of 1310 people how much time they spend\t watching tv each day. The mean number of hours was 2.8 with a standard deviation of 2.6. A sociologist claims that people watch a mean of 3 hours of TV per day. Do the data provide sufficient evidence to conclude that the mean hours of TV watched per day is less the claim? Use the a=0.5 level of significance and the P-value method with the TI-84 Plus calculator.
(a) State the appropriate null and alternate hypotheses.
H0: Mu = 3
H1: Mu < 3
This hypothesis test is a _____ test.
(b) Compute the P-value. Round the answer to at least four decimal places
P-value =
Answer:
a) Null hypothesis:[tex]\mu \geq 3[/tex]
Alternative hypothesis:[tex]\mu < 3[/tex]
This hypothesis test is a left tailed test.
b) [tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =P(z<-2.784)=0.0027[/tex]
We can conduct the test with the Ti84 using the following steps:
STAT>TESTS>T-test>Stats
We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.
And we got the same results.
Step-by-step explanation:
Information given
[tex]\bar X=2.8[/tex] represent the sample mean
[tex]s=2.6[/tex] represent the population standard deviation
[tex]n=1310[/tex] sample size
[tex]\mu_o =3[/tex] represent the value to test
[tex]\alpha=0.5[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Part a) System of hypothesis
We want to test if the true mean is less than 3, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 3[/tex]
Alternative hypothesis:[tex]\mu < 3[/tex]
This hypothesis test is a left tailed test.
Part b
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =P(z<-2.784)=0.0027[/tex]
We can conduct the test with the Ti84 using the following steps:
STAT>TESTS>T-test>Stats
We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.
And we got the same results.
Given: g(x) = Square Root of x - 4 and h(x) = 2x - 8. What are the restrictions on the domain of gxh? x is greater than or equal to what?
[tex]g(x) = \sqrt{x - 4}[/tex]
[tex]h(x) = 2x - 8[/tex]
g x h = [tex]\sqrt{x-4}.(2x-8)[/tex]
Looking at the equation we know that there's no way to have a negative root, so we need x - 4 to be greater than or equal to 0
[tex] x - 4 \geq 0[/tex]
[tex]x \geq 4[/tex]
Answer:
It's 6
Step-by-step explanation:
HELP PLEASE!! Stefano owns a restaurant where his customers create their own pasta dishes. The customer chooses exactly one type of noodle, sauce, vegetable, and meat. The following table shows the options available to customers. HELP PLEASE!! WILL GIVE EXTRA POINTS
Answer:
180 ways
Step-by-step explanation:
U just multiply the number of sauce, noodle, vegetable, and meat
So 3 times 3 times 4 times 5
Correct me if this is wrong
Answer:
180
Step-by-step explanation:
you multiply 3X3X4X5 thus it equals 180
The area of the surface of a circular pond is needed. A measure about the pond gives a circumference of about 47 feet. Find the area.
Answer:
55.95 ft²
Step-by-step explanation:
Circumference formula: C = 2πr => r = C / (2π)
Area formula: A = πr²
Substituting C / (2π) for r in the above equation, we get:
C 47 ft
A = π( ----------- )² = π ( -------------- )²
2π (2π)
or ...
π(47 ft)² 2209 ft²
A = ---------------------- = -------------------- = 55.95 ft²
4π² 4(3.14159)²
Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 78 students shows that 36 have jobs. Do the data indicate that more than 35% of the students have jobs
Answer:
[tex]z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074[/tex]
Now we can calculate the p value with this probability:
[tex]p_v =P(z>2.074)=0.019[/tex]
If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.
Step-by-step explanation:
Information given
n=78 represent the random sample taken
X=36 represent the students with jobs
[tex]\hat p=\frac{36}{78}=0.462[/tex] estimated proportion of students with jobs
[tex]p_o=0.35[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the proportion of students with jobs is higher than 0.35, the system of hypothesis are:
Null hypothesis:[tex]p \leq 0.35[/tex]
Alternative hypothesis:[tex]p > 0.35[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074[/tex]
Now we can calculate the p value with this probability:
[tex]p_v =P(z>2.074)=0.019[/tex]
If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.
Members of a public speaking club are competing to see who can recite a speech fastest. Who speaks the most words per minute?
Bailey
Gail
Naomi
Wade
Answer:
Wade
Step-by-step explanation:
Wade equals to 165
Naomi equals to 112
Gail equals to 123
And bailey equals to 150
the value pi/24 is a solution for the equation 4 cos^4 (4x)-3
Answer:
False
Step-by-step explanation:
4 cos^4 (4x)-3 = 0
Substitute into the equation
4 cos^4 (4pi/24)-3 = 0
4 cos^4 (pi/6)-3 = 0
Take the cos pi/6
4 ( sqrt(3)/2) ^4 -3 =0
Take it to the 4th power
4 ( 9/16) -3 =0
9/4 -3 =0
9/4 - 12/4 = 0
-3/4 =0
False
Answer:
THE ANSWER IS TRUE.
Step-by-step explanation:
I did this on my homework.
What is 719 ÷ 47
I don't know the answer so I will keep on typing untill it reached 20 words:)
Answer:
719/47 is 15.29787234
The average life expectancy in a certain country is 50.2 years. Estimate the country's life expectancy in hours by rounding the life expectancy to the nearest year.
Given a+b=7 and a–b=3, find: 3a÷3b
Answer & Step-by-step explanation:
We are given two equations...
a + b = 7
a - b = 3
We are asked to find 3a ÷ 3b. In order to find the value of a and b, we have to rearrange one of the equations so it will be easier to find the values of the variables. Let's rearrange the second equation.
a - b = 3 → a = 3 + b
Now that we have an equation that shows the value of a, we can use this equation and plug it into the first equation.
a + b = 7
a = 3 + b
(3 + b) + b = 7
3 + 2b = 7
2b = 4
b = 2
We have the value of b. Now, we have to find the value of a by plugging b into the second equation.
a - b = 3
b = 2
a - 2 = 3
a = 5
Now that we have the values of both variables, we can plug them into (3a÷3b)
3a ÷ 3b
3(5) ÷ 3(2)
15 ÷ 6
5/2 or 2.5
So, 3a ÷ 3b equals 5/2 or 2.5
Find the measurements (the length L and the width W) of an inscribed rectangle under the line with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
The question is incomplete. Here is the complete question.
Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -[tex]\frac{3}{4}[/tex]x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answer: L = 1; W = 9/4; A = 2.25;
Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:
A = x.y
A = x(-[tex]\frac{3}{4}.x + 3[/tex])
A = -[tex]\frac{3}{4}.x^{2} + 3x[/tex]
To maximize, we have to differentiate the equation:
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{d}{dx}[/tex](-[tex]\frac{3}{4}.x^{2} + 3x[/tex])
[tex]\frac{dA}{dx}[/tex] = -3x + 3
The critical point is:
[tex]\frac{dA}{dx}[/tex] = 0
-3x + 3 = 0
x = 1
Substituing:
y = -[tex]\frac{3}{4}[/tex]x + 3
y = -[tex]\frac{3}{4}[/tex].1 + 3
y = 9/4
So, the measurements are x = L = 1 and y = W = 9/4
The maximum area is:
A = 1 . 9/4
A = 9/4
A = 2.25
What is the product x^2-16 over 2x+8 • x^3-2x^2+x over x^2+3x-4
Answer:
[tex]\dfrac{x^3-5x^2 +4x}{2x+8}[/tex]
Step-by-step explanation:
The basic idea is to factor each expression and cancel common factors from numerator and denominator.
[tex]\dfrac{x^2-16}{2x+8}\cdot\dfrac{x^3-2x^2 +x}{x^2+3x-4}=\dfrac{(x-4)(x+4)}{2(x+4)}\cdot\dfrac{x(x-1)^2}{(x+4)(x-1)}\\\\=\dfrac{(x-4)x(x-1)}{2(x+4)}\cdot\dfrac{(x+4)(x-1)}{(x+4)(x-1)}\\\\=\boxed{\dfrac{x^3-5x^2 +4x}{2x+8}}[/tex]
Please number them but left to right from the top please.
Answer: Three have a right angle. These are the green rectangle, the pinkish square, and the orange trapezoid.
Step-by-step explanation:
5- How many 50ml glasses can you fill from a 2 litre bottle?
Answer:
2 litre = 200 ml
so 200/50 = 4 glasses
Answer:
It's 40 of 50ml glass
Step-by-step explanation:
It's basically 2 litre/50ml
But 1000ml = 1 litres ;
Meaning 2 litres = 1000 × 2 = 2000ml
Therefore 2 litre/50ml = 2000/50
= 40
A yogurt costs 45p. How many yogurts can be bought for ten pounds?
Step-by-step explanation:
21
may be, I am not sure about this answer. But it can be
A missiles is fired at a target and the probability that the target is hit is 0.7 . Find how many missiles should be fired so that the probability that the target is not hit is less than 0.001 .
Answer:
(C)
Step-by-step explanation:
We want the probability of at least one hit in
missiles to be at least 80%.
i need help on this. ive been struggling. TwT
lateral area
surface area
volume
Answer:
total surface area Stot = 753.9816 m2
lateral surface area Slat = 351.85808 m2
top surface area Stop = 201.06176 m2
bottom surface area Sbot = 201.06176 m2
Answer:
Lateral area = 352 Square m
Surface area = 756. 3 square m
Volume = 1408 cubic m
Step-by-step explanation:
[tex]lateral \: area = 2\pi \: rh \\ = 2 \times \frac{22}{7} \times \frac{16}{2} \times 7 \\ = 22 \times 16 \\ = 352 \: {m}^{2} \\ \\ surface \: area = 2\pi \: r(h + r) \\ = 2 \times 3.14 \times 8(7 + 8) \\ = 6.28 \times 8 \times 15 \\ = 6.28 \times 120 \\ = 756.3 \: {m}^{2} \\ \\ volume = \pi {r}^{2} h \\ = \frac{22}{7} \times {8}^{2} \times 7 \\ = 22 \times 64 \\ = 1408 \: {m}^{3} \\ [/tex]