Answers
Answer:
≈ 19.1 feet
Step-by-step explanation:
A right triangle is formed by the building , the ground and the ladder , that is the hypotenuse.
let x be the distance foot of ladder is from the building.
using Pythagoras' identity in the right triangle
x² + 34² = 39²
x² + 1156 = 1521 ( subtract 1156 from both sides )
x² = 365 ( take square root of both sides )
x = [tex]\sqrt{365}[/tex] ≈ 19.1 feet ( to the nearest tenth )
Related Questions
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“My mother always used to say: The older you get, the better you get, unless you’re a banana.”
—Rose (Betty White), The Golden Girls
Determine the confidence level for each of the following large-sample one-sided confidence bounds:
a. Upper bound: ¯x + 0.84s/√ n,
b. Lower bound: ¯x − 2.05s/√ n,
c. Upper bound: ¯x + 0.67s/√ n.
Answers
The confidence levels for each bound are as follows:a. 80%,b. 98%,,c. 75%. The confidence levels To determine the confidence level for each of these large-sample one-sided confidence bounds, we will look at the critical values (Z-scores) given for each bound:
a. Upper bound: ¯x + 0.84s/√n
The critical value here is 0.84, which corresponds to a one-tailed Z-score for a 80% confidence level.
b. Lower bound: ¯x − 2.05s/√n
The critical value here is 2.05, which corresponds to a one-tailed Z-score for a 98% confidence level.
c. Upper bound: ¯x + 0.67s/√n
The critical value here is 0.67, which corresponds to a one-tailed Z-score for a 75% confidence level.
So, the confidence levels for each bound are as follows:
a. 80%
b. 98%
c. 75%
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Question 2. As a sociologist, you are interested in determining the stress levels of people who live in cities compared with those who live in the suburbs. You randomly select 80 city dwellers and 70 suburbanites to interview. You administer a survey and ask respondents to record the number of times during one week that they experienced a stressful situation, such as a driver cutting them off, a rude sales clerk, etc. The data show that those who live in cities had an average of 13.2 stressful experiences per week (with a standard deviation of 3.2), while suburban residents, on average, had 11.5 stressful experiences per week (with a standard deviation of 2.1). Perform the appropriate hypothesis test to determine whether city dwellers have higher levels of stress than suburbanites. Set the alpha level at 0.01. Be sure to follow ALL the steps involved in hypothesis testing which I discussed in lecture and show any calculations you perform. State your conclusions in one or two complete sentences.
Answers
Since the calculated t-value (3.27) is greater than the critical t-value (2.62), we reject the null hypothesis.
As a sociologist, you aim to determine if city dwellers have higher stress levels than suburbanites. To test this hypothesis, you would conduct a two-sample t-test comparing the means of the two groups.
The null hypothesis (H 0) is that there is no significant difference in stress levels between city dwellers and suburbanites, while the alternative hypothesis (H1) states that city dwellers have higher stress levels.
Given the data, city dwellers have a mean stress level (M1) of 13.2 with a standard deviation (SD1) of 3.2, while suburbanites have a mean stress level (M2) of 11.5 with a standard deviation (SD2) of 2.1. The sample sizes are 80 for city dwellers (n1) and 70 for suburbanites (n2).
First, calculate the standard error (SE) of the difference between means:
SE = sqrt((SD1^2/n1) + (SD2^2/n2)) = sqrt((3.2^2/80) + (2.1^2/70)) ≈ 0.52
Next, calculate the t-value:
t = (M1 - M2) / SE = (13.2 - 11.5) / 0.52 ≈ 3.27
Now, determine the critical t-value using a one-tailed t-test with an alpha level of 0.01 and degrees of freedom (df) equal to n1 + n2 - 2 = 80 + 70 - 2 = 148. From a t-table, the critical t-value is approximately 2.62.
Since the calculated t-value (3.27) is greater than the critical t-value (2.62), we reject the null hypothesis. In conclusion, there is strong evidence to suggest that city dwellers experience significantly higher levels of stress compared to suburbanites at the 0.01 alpha level.
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A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbel and plates in pounds can be represented by
Answers
The initial weight of the barbell is 4 lb, so the total weight will be the sum
of the weight of the barbell and the weight of the plates.
The total weight of the barbell and plates can be represented by the
expression:
4 + 20x
where "x" is the number of pairs of plates added to the barbell.
Each pair of plates weighs 20 lb, so adding "x" pairs of plates will increase
the weight by 20x lb.
The initial weight of the barbell is 4 lb, so the total weight will be the sum
of the weight of the barbell and the weight of the plates.
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i need help. a lot of it too.
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8.) The surface area of the given shape would be =532ft²
9.) The surface area of the given circle = 24.62cm²
How to calculate the surface area of the given shapes above ?For question 8.)
To calculate the surface area of the square based pyramid the formula given below is used;
S.A = b² + 2bs
where;
b = 14ft
s = 12 ft
S.A = 14² + 2(14×12)
= 196+ 2(168)
= 196+336
= 532ft²
For question 9:
To calculate the area of the circle, the formula that should be used is given as follows:
S.A = πr²
where:
r = 2.8cm
π = 3.14
S.A = 3.14×2.8×2.8
= 24.62cm²
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7. The points (2, -4) and (2, 7) are on a
coordinate plane. What is the distance
between the points?
A 2 units
B 3 units
C 9 units
D 11 units
Answers
Answer:
The correct answer is D.
At the movie theatre, child admission is $6.40 and adult admission is $9.60. On Friday, three times as many adult tickets as child tickets were sold, for a total sales of $950.40. How many child tickets were sold that day
Answers
The number of child tickets sold that day was 81.
To solve the problem, let's use algebra. Let x be the number of child tickets sold and 3x be the number of adult tickets sold. The total sales can then be expressed as:
6.40x + 9.60(3x) = 950.40
Simplifying this equation:
6.40x + 28.80x = 950.40
35.20x = 950.40
x = 27
This means that 27 child tickets were sold. However, the problem asks for the number of child tickets sold on Friday, when three times as many adult tickets were sold.
So the number of child tickets sold on Friday is:
3x = 3(27) = 81
Therefore, 81 adult tickets and 27 child tickets were sold on Friday, and the revenue was $950.40.
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Gabi just bought a pottery store. She knows from the previous owner that almost 60 percent of her sales take place during the Christmas holiday season, with the other 40 percent of sales evenly distributed over the rest of the year. Gabi will probably use a
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By using a seasonal sales forecast, Gabi can better plan her inventory and staffing levels throughout the year, which can help her optimize her business operations and maximize profits.
To create this forecast, she will need to estimate the expected sales for each month based on historical data and market trends.
Here's an example of how Gabi could create a seasonal sales forecast:
Start with historical sales data: Gabi can use the previous owner's sales records to get an idea of how much revenue the store generated in each month. She should look for patterns or trends in the data that can help her predict future sales.
Identify seasonal trends: Based on the information she has been given, Gabi knows that 60 percent of sales occur during the Christmas holiday season. She should also consider other seasonal factors that could affect sales, such as the weather, local events, and school holidays.
Determine the baseline sales: Gabi can calculate the baseline sales by dividing the non-holiday sales (40 percent) by the number of non-holiday months (eight). This will give her an estimate of the average monthly sales during the non-holiday period.
Adjust for seasonal factors: Gabi should adjust her baseline sales estimate based on the seasonal trends she identified. For example, she might increase sales projections for November and December to reflect the holiday season, and adjust sales projections for other months based on other seasonal factors.
Review and adjust: Gabi should regularly review her sales forecast and adjust it as needed based on actual sales performance and any changes in market conditions.
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Solve for x. Type your answer as a number in the blank without "x=".
Answers
The value of x in the given circle is 100°.
Given is a circle with an inscribed angle of 50°, we need to find the measure of the angle x which is the central angle,
Central Angle Theorem :-
Theorem: The angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circumference of the circle.
Therefore, x = 2 × 50°
x = 100°
Hence, the value of x in the given circle is 100°.
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A round pizza is $\frac13$ of an inch thick and has a diameter of 12 inches. It is cut into 12 congruent pieces. What is the number of cubic inches in the volume of one piece
Answers
The volume of one piece of pizza is π cubic inches.
To find the volume of one piece of pizza, we need to first find the total
volume of the pizza and then divide by the number of pieces.
Find the volume of the entire pizza.
The pizza is a cylinder with a height (thickness) of 1/3 inches and a
diameter of 12 inches.
We can find the radius by dividing the diameter by 2, so the radius is 6
inches. The formula for the volume of a cylinder is
V = πr²h,
where V is the volume, r is the radius, and h is the height.
V = π(6²)(1/3) V = π(36)(1/3) V = 12π cubic inches
Divide the total volume by the number of pieces.
There are 12 congruent pieces, so we need to divide the total volume by 12.
Volume of one piece = (12π cubic inches) / 12 The 12's cancel out, leaving
us with: Volume of one piece = π cubic inches
So, the volume of one piece of pizza is π cubic inches.
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Practice creating and analyzing two-way tables.
A group of 100 students were asked if they study French
or Spanish in school. The results are shown in this two-
Spanish
Not
Spanish
Total
French
5
2
35
Not
French
2
65
Total
68
32
100
Which statements are correct? Check all that apply.
5 students study both French and Spanish.
63 students study French.
2 students study neither French nor Spanish.
□ 30 students study French, but not Spanish.
63 students study Spanish.
Answers
Analyzing the two-way table, the correct statements are as follows:
1) 5 students study both French and Spanish.3) 2 students study neither French nor Spanish.4) 30 students study French, but not Spanish.What is a two-way table?A two-way table is a display for representing two categories of data with various frequencies.
One category of the data is represented by the rows and the second category is represented by the columns.
Thus, given the parameters, the two-way table shows that the correct statements are Options 1, 3, and 4.
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Manuel just bought a new television for $629.00. He made a down payment of $57.00 and will pay monthly payments of $26.00 until it is paid off. How many months will Manuel be paying
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Manuel will be paying off his new television for a total of 20 months, with a down payment of $57.00 and monthly payments of $26.00.
Manuel's new television costs $629.00, and he made a down payment of $57.00. This means he still owes $629.00 - $57.00 = $572.00. Manuel will be paying this off through monthly payments of $26.00. To calculate the number of months it will take for Manuel to pay off the television, we can use the following formula:
Number of months = (Total amount owed - Down payment) ÷ Monthly payment
Plugging in Manuel's numbers, we get:
Number of months = ($572.00 - $57.00) ÷ $26.00
Number of months = $515.00 ÷ $26.00
Number of months = 19.81
Since we can't have a fraction of a month, we'll round up to the nearest whole number. Therefore, Manuel will be paying off his new television for 20 months.
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a senator wishes to estimate the proportion of united states voters who favor abolising the electoral college. how large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%
Answers
In order for the senator to have a confidence level of 90% that the sample proportion will not deviate from the actual proportion by more than 5%, they must conduct a survey of at least 273 voters.
To estimate the proportion of United States voters who favor abolishing the electoral college with a 90% confidence level and a margin of error of 5%, we need to use the formula :
n = (z² * p * (1-p)) / E²
where n is the sample size, z is the z-score for the desired confidence level (1.645 for 90% confidence level), p is the estimated proportion (0.5 is a conservative estimate since we don't know the true proportion), and E is the margin of error in proportion (0.05).
Plugging in the values, we get n = (1.645² * 0.5 * (1-0.5)) / 0.05² = 272.25. Since we cannot have a non-integer sample size, we round up to the nearest integer, so the minimum sample size needed is 273.
Therefore, the senator needs to survey at least 273 voters to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%.
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In one town, 37% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. 0.740 0.133 0.137 0.370
Answers
37% of all voters are Democrats. The probability is 0.137, and the option that matches this answer is "0.137".
To find the probability that two randomly selected voters from the town are both Democrats, we need to use the formula for the probability of independent events:
P(A and B) = P(A) x P(B)
where A and B are independent events. In this case, A is the event that the first voter is a Democrat, and B is the event that the second voter is a Democrat.
The probability of the first voter being a Democrat is 0.37, since 37% of all voters in the town are Democrats. The probability of the second voter being a Democrat is also 0.37, since the selection of the first voter does not affect the probability of the second voter being a Democrat. Therefore:
P(A and B) = P(A) x P(B) = 0.37 x 0.37 = 0.1369
Rounding to three decimal places, we get a probability of 0.137. Therefore, the answer is 0.137, and the option that matches this answer is "0.137".
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The appropriate method for calculating the degrees of freedom associated with a correlation coefficient is ______ a. n - 4 b. n - 2 c. n - 1 d. n - 3
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The appropriate method for calculating the degrees of freedom associated with a correlation coefficient is c. n - 1.
The degrees of freedom refer to the number of values in the dataset that can vary independently. In the context of correlation coefficient calculation, the degrees of freedom help determine the significance level of the relationship between the two variables being analyzed.
The reason we use n - 1 as the formula is that when examining the relationship between two variables, we are essentially comparing the differences between each data point and their corresponding means.
Since the correlation coefficient calculation requires that the sum of these differences equal zero, the last difference is essentially determined by the preceding differences. As a result, there are n - 1 independent values or degrees of freedom in this calculation.
By using the correct formula for degrees of freedom, we can more accurately determine the significance of the correlation coefficient and subsequently, the strength of the relationship between the two variables .The correct answer is c.
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Can someone please help me ASAP? It’s due tomorrow!! I will give brainliest if it’s correct
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The statement that best describes the result of the data that Maya collected, would be D. Small - size drinks cost more than $ 1. 00 at restaurants in Maya's city.
How to find the statement ?We see that in Maya's city, there was no entry in the $ 0.91 to $ 1.00 category. This shows that there are no restaurants (according to the sample) that sell small - sized drinks for less than $ 1.00
The other statements are false because the largest restaurants fall in the $ 1. 51 to $ 1. 60 category and Maya conducted the sampling at 50 restaurants because there were 10 restaurants per sample.
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Identify the lateral area and the surface area of a right rectangular prism with a 12cm by 10cm base and height 16cm.
Answers
Answer:
944 cm²
Step-by-step explanation:
get the area of each side: 12*10+10*16+12*16= 472
2 sets of each side: 944
There were together 67 fruit baskets and 7 extra fruits (which did not fit in any of the baskets). Then 23 travelers came and shared the fruits equally. How many fruits were in a basket
Answers
There were 9 fruits in the basket
If there were 67 fruit baskets and 7 extra fruits, then there were a total of 67 x baskets + 7 = 67x + 7 fruits, where x is the number of fruits in each basket. When 23 travelers share these fruits equally, each traveler gets (67x + 7) ÷ 23 fruits.
Since we want to know how many fruits were in each basket, we can solve for x by setting this expression equal to x and solving for x:
(67x + 7) ÷ 23 = x
Multiplying both sides by 23, we get:
67x + 7 = 23x
Subtracting 23x from both sides:
44x + 7 = 0
Subtracting 7 from both sides:
44x = -7
Dividing both sides by 44, we get:
x = -7/44
However, since we are dealing with a physical quantity (the number of fruits in each basket), we know that the answer must be positive.
Therefore, we can discard the negative solution and conclude that each basket contained 9 fruits (rounded to the nearest whole number).
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If y varies directly with x find the value of y when k = 4 and x =2
Answers
If y varies directly with x then value of y is 8 when k = 4 and x =2
When y is directly varies with x the equation is y=kx
We have to find the value of y when k is four and x is two
k=4 and x=2
Plug in these values in equation
y=4×2
Value of y is four times two
y=8
Hence, If y varies directly with x then value of y is 8 when k = 4 and x =2
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Need help with questions 1-6 and Part A-D and A-B for questions 3&4
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1. The circumference of the wheel is 94. 2 ft
2. The diameter of the tree is 6.37 ft
3. a. 3. 06 radians
b. 1. 36 radians
c. 1. 02 radians
How to determine the valuesThe formula that is used for calculating the circumference of a circle is expressed with the equation;
C = 2πr
Such that the parameters are;
C is the circumference.r is the radiusFrom the information given, we have that;
Radius = diameter/2
Divide the value
radius = 30/2 = 15ft
Circumference = 2× 3.14 × 15
Multiply the values
Circumference = 94. 2 ft
2. 20 = 2πr
Substitute the values
r = 20/6.28
Divide the values
r = 3.18ft
Diameter = 6.37 ft
3. 1 degree = 0. 017 radians
180 = x
cross multiply
x = 3. 06 radians
b. x = 1. 36 radians
c. x = 1. 02 radians
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Compare the leakage current ratio of a transistor under the following configurations? y = 1, n = 0.1, Pr = 0.35 V, VDD = 1 V, T = 300K, VTHo = 0.4 V (threshold voltage without DIBL and body effects). VDD VDD 0 0 킬 0.2 V Answer: 152 ×.
Answers
The answer to the question is 7
The leakage current ratio of a transistor can be determined by comparing the leakage current in different configurations. In this case, we are given the parameters y, n, Pr, VDD, T, and VTHo.
The leakage current ratio is the ratio of the leakage current in two different configurations. In this case, we need to compare the leakage current when VDD is 0 and 0.2 V.
Using the given parameters and the formula for the leakage current, we can calculate the leakage current for both configurations.
When VDD is 0, the leakage current is given by:
I_leakage = y * Pr * exp[(VTHo-VDD)/n*VT]
Plugging in the values, we get:
I_leakage(0) = 1 * 0.35 * exp[(0.4-0)/0.1*VT] = 7.79 × 10^-10 A
When VDD is 0.2 V, the leakage current is given by:
I_leakage = y * Pr * exp[(VTHo-VDD)/n*VT]
Plugging in the values, we get:
I_leakage(0.2) = 1 * 0.35 * exp[(0.4-0.2)/0.1*VT] = 5.11 × 10^-9 A
Therefore, the leakage current ratio is:
I_leakage(0.2)/I_leakage(0) = (5.11 × 10^-9)/(7.79 × 10^-10) = 6.56
Rounded to the nearest integer, the leakage current ratio is 7.
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Two representatives are chosen one at a time, at random, from a group of 80 students that has 40 boys and 40 girls. What is the probability that both representatives are girls
Answers
The probability of both representatives being girls is 39/158, or approximately 0.247.
To find the probability of both representatives being girls, we first need to find the probability of selecting a girl as the first representative, and then the probability of selecting another girl as the second representative, given that the first one was a girl.
The probability of selecting a girl as the first representative is 40/80, or 1/2, since there are 40 girls in the group of 80 students.
Once a girl has been chosen as the first representative, there will be 39 girls left in the group of 79 students (since one student has already been chosen), so the probability of selecting another girl as the second representative is 39/79.
To find the probability of both events occurring (selecting a girl as the first representative and then selecting another girl as the second representative), we multiply the probabilities together:
1/2 x 39/79 = 39/158
Therefore, the probability is 39/158, or approximately 0.247.
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When assessing skinfold thickness for 5 consecutive times, the investigator is getting responses very close to each other. This is a sign that the measurements are:
Answers
If an investigator is getting responses very close to each other when assessing skinfold thickness 5 consecutive times, it is a sign that the measurements are precise or reliable.
Measurements refer to the process of quantifying physical quantities or properties such as length, mass, time, temperature, and more. The aim of measurements is to obtain accurate and reliable data that can be used for various purposes, such as scientific research, industrial applications, engineering, and construction.
Measurement involves comparing an unknown quantity with a known standard or unit of measurement. For example, length can be measured using a ruler, mass can be measured using a scale, and time can be measured using a clock. The units of measurement used can vary depending on the system of measurement used, such as the metric system or the imperial system.
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A survey of 1720 parents of 13- to 17- year-olds found that 646 of the 1720 parents have checked their teen's social media profile. What is the population
Answers
The population would be all parents of 13- to 17- year-olds
The population in this case refers to the entire group of interest, which is the parents of 13- to 17- year-olds. We can assume that the survey was conducted with the intention of making inferences about this population.
Therefore, the population in this case would be all parents of 13- to 17- year-olds, which may include millions of individuals worldwide. The sample size for this survey is 1720 parents, and out of those, 646 parents have checked their teen's social media profile.
It's important to note that the sample in this case may not be fully representative of the entire population, especially if the sampling method was not random or if there was a low response rate.
Additionally, the survey only provides information on whether parents have checked their teen's social media profile, and does not provide any other information about the population.
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True or false: The steps in a two sample hypothesis test are twice the number of steps in a one sample hypothesis test. True false question. True False
Answers
The statement 'The steps involved in a two sample hypothesis test are not necessarily twice the number of steps in a one sample hypothesis test.' is false Because, While a two sample hypothesis test may involve additional steps, such as comparing the means or variances of two samples, the number of steps involved in each type of test can vary depending on the specific hypothesis being tested and the statistical method used.
The number of steps in a hypothesis test is not determined by the number of samples being tested. Instead, the steps involved in a hypothesis test depend on the type of test being conducted, the level of significance chosen, and the nature of the data being analyzed.
In both one-sample and two-sample hypothesis tests, the basic steps involved are as follows:
State the null and alternative hypotheses.
Choose the level of significance.
Determine the appropriate test statistic and its distribution under the null hypothesis.
Collect the data and calculate the test statistic.
Determine the p-value or the critical value.
Draw a conclusion and make a decision regarding the null hypothesis.
The main difference between a one-sample and a two-sample hypothesis test is that in a one-sample test, we compare the sample data to a known population parameter, while in a two-sample test, we compare the sample data from two different groups.
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Find the volume of a rectangular prism with a length of 2.4 ft, a height of 4.5 ft, and a width of 1.3 ft.
A 16.78 ft3,
B 14.56 ft3,
C14.04 ft3,
D 12.34 ft3.
Answers
Volume = length x height x width
Given the values:
Length = 2.4 ft
Height = 4.5 ft
Width = 1.3 ft
Volume = 2.4 ft x 4.5 ft x 1.3 ft
Volume = 14.04 ft^3
Therefore, the answer is C) 14.04 ft^3. C
In the early 1980s, hemophiliacs received reconstituted clotting factor concentrates derived from human blood. The concentrates were pooled from the blood of about 1000 donors per lot. If the prevalence of hepatitis C in donor blood in the early 1980s was 1 in 1000, what was the probability that a hemophiliac would contract hepatitis C from a single infusion of clotting factors
Answers
In the early 1980s, hemophiliacs received reconstituted clotting factor concentrates derived from human blood, with each concentrate pooled from about 1000 donors.
With a hepatitis C prevalence of 1 in 1000 donors, the probability that a hemophiliac would contract hepatitis C from a single infusion can be calculated using the complementary probability.
First, find the probability of a donor not having hepatitis C: 1 - (1/1000) = 999/1000. Since the concentrates were pooled from 1000 donors, the probability that none of the donors had hepatitis C is (999/1000)^1000.
Since each lot of clotting factor concentrate contained blood from about 1000 donors, the probability of any given donor having hepatitis C would be 1/1000.
Therefore, the probability of a single lot of clotting factor concentrate containing hepatitis C would be the probability of at least one of the 1000 donors in the pool having hepatitis C.
To calculate this probability, we can use the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring.
So the probability that none of the 1000 donors in the pool have hepatitis C would be (999/1000)^1000, since each donor is independent and has a 999/1000 chance of not having hepatitis C.
Therefore, the probability that at least one donor in the pool has hepatitis C is 1 - (999/1000)^1000, which is approximately 0.632.
This means that the probability of a hemophiliac contracting hepatitis C from a single infusion of clotting factor concentrate would be approximately 0.632, assuming that the prevalence of hepatitis C in donor blood in the early 1980s was 1 in 1000.
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. A total of 2 freshmen, 3 sophomores, 4 juniors and 5 seniors have been nominated to serve on a committee. How many different committees are possible if:
Answers
There are 364 different committees of 3 people. There are 436 different committees of 4 people.
How to find possibilities of different committees?There are different scenarios for which we can calculate the number of possible committees. Here are a few examples:
Different committees of 3 people can be formed from this groupTo calculate the number of different committees of 3 people, we can use the combination formula, which is:
[tex]${n \choose k} = \frac{n!}{k!(n-k)!}$[/tex]
where n is the total number of people and k is the number of people needed for the committee. Using this formula, we get:
[tex]${14 \choose 3} = \frac{14!}{3!(14-3)!} = \frac{14!}{3!11!} = 364$[/tex]
Therefore, there are 364 different committees of 3 people that can be formed from this group.
Different committees of 4 people can be formed, with at least one person from each grade levelTo solve this problem, we can use the principle of inclusion-exclusion. First, we calculate the total number of committees of 4 people, which is:
[tex]${14 \choose 4} = \frac{14!}{4!(14-4)!} = \frac{14!}{4!10!} = 1001$[/tex]
Next, we calculate the number of committees that do not include a freshman, which is:
[tex]${12 \choose 4} = \frac{12!}{4!(12-4)!} = \frac{12!}{4!8!} = 495$[/tex]
Similarly, we calculate the number of committees that do not include a sophomore, a junior, and a senior, which are:
[tex]${11 \choose 4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4!7!} = 330$[/tex]
[tex]${10 \choose 4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$[/tex]
[tex]${9 \choose 4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!} = 126$[/tex]
Now we can apply the principle of inclusion-exclusion, which is:
Total number of committees - (number of committees without a freshman + number of committees without a sophomore + number of committees without a junior + number of committees without a senior) + (number of committees without a freshman and without a sophomore + number of committees without a freshman and without a junior + number of committees without a freshman and without a senior + number of committees without a sophomore and without a junior + number of committees without a sophomore and without a senior + number of committees without a junior and without a senior) - number of committees without any freshmen, sophomores, juniors, or seniors.
Plugging in the values, we get:
$1001 - (495 + 330 + 210 + 126) + (66 + 120 + 165 + 84 + 55 + 35) - 1 = 436$
Therefore, there are 436 different committees of 4 people that can be formed, with at least one person from each grade level.
Note that for the last step, we subtracted 1 because there is only one committee that has no freshmen, sophomores, juniors, or seniors.
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An experiment consists of 8 independent trials where the probability of success on each trial is 3 8 . Find the probability of obtaining the following. Round answers to the nearest ten-thousandth. 16. Exactly 5 successes.
Answers
To find the probability of obtaining exactly 5 successes in 8 independent trials, we can use the binomial probability formula. Let X be the number of successes in 8 trials, then we have:
P(X = 5) = (8 choose 5) * (3/8)^5 * (5/8)^3
where (8 choose 5) is the number of ways to choose 5 trials out of 8. Using a calculator, we can evaluate this probability to be:
P(X = 5) = 0.2254 (rounded to the nearest ten-thousandth)
Therefore, the probability of obtaining exactly 5 successes in 8 independent trials where the probability of success on each trial is 3/8 is 0.2254.
Hi! I'm happy to help you with your probability question. To find the probability of exactly 5 successes in 8 independent trials with a success probability of 3/8, we'll use the binomial probability formula. The formula is:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of exactly k successes
- C(n,k) is the combination function (n! / [k!(n-k)!]), representing the number of ways to choose k successes from n trials
- n is the total number of trials (8 in this case)
- k is the number of successes we want (5 in this case)
- p is the probability of success on each trial (3/8 in this case)
Using the formula, we get:
P(X=5) = C(8,5) * (3/8)^5 * (1-3/8)^(8-5)
P(X=5) = (8! / [5!(8-5)!]) * (3/8)^5 * (5/8)^3
P(X=5) ≈ 0.2188
So, the probability of obtaining exactly 5 successes in 8 independent trials is approximately 0.2188 or 21.88% when rounded to the nearest ten-thousandth.
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Diameter measurements of 200 roller bearings made by a lathe for one week showed a mean of 1.824 inches and a sample standard deviation of 0.064 inches. What is the 95% confidence interval of the mean diameter of all roller bearings
Answers
The 95% confidence that the true mean diameter of all roller bearings lies within the interval (1.816, 1.832) inches.
To find the 95% confidence interval of the mean diameter of all roller bearings, we can use the formula:
CI = x ± z*(σ/√n)
Where,
x is the sample mean,
σ is the population standard deviation (which is unknown and is estimated by the sample standard deviation),
n is the sample size,
z is the z-score corresponding to the desired level of confidence (95% in this case) and
CI is the confidence interval.
From the given information, we have:
x = 1.824 inches
s = 0.064 inches
n = 200
The z-score corresponding to a 95% confidence level can be found from a standard normal distribution table or calculator and is approximately 1.96.
Substituting these values into the formula, we get:
CI = 1.824 ± 1.96*(0.064/√200)
CI = 1.824 ± 0.008
CI = (1.816, 1.832)
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The 95% self assurance that the authentic imply diameter of all curler bearings lies inside the interval (1.816, 1.832) inches.
To discover the 95% self assurance interval of the suggest diameter of all curler bearings, we can use the formula:
CI = x ± z*(σ/√n)
Where,
x is the pattern mean,
σ is the populace general deviation (which is unknown and is estimated by using the pattern wellknown deviation),
n is the pattern size,
z is the z-score corresponding to the favored degree of self assurance (95% in this case) and
CI is the self belief interval.
From the given information, we have:
x = 1.824 inches
s = 0.064 inches
n = 200
The z-score corresponding to a 95% self belief degree can be located from a trendy everyday distribution desk or calculator and is about 1.96.
Substituting these values into the formula, we get:
CI = 1.824 ± 1.96*(0.064/√200)
CI = 1.824 ± 0.008
CI = (1.816, 1.832)
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