It is more difficult to establish nonspuriousness in quasi-experiment designs, where do not use randomization to assign subjects to treatment and comparison groups. So, option(c) is right.
The prefix quasi means "resembling". Thus, quasi-experimental research is a type of research which resembles to experimental research but it is not a true experimental research. These designs are similar to true experiments but lack random assignment to experimental and control groups. A true experiment, a quasi-experimental design, aims to establish a cause-and-effect relationship between an independent and a dependent variable. Aim of these experiments is to evaluate interventions but without use of randomization. Subjects are assigned to groups based on non-random criteria. Since the independent variable is measured, not manipulated, they are best thought of as correlational research. Thus, the correct answer is to determine a relationship between two variables that is not caused by variation in a third variable, i.e, Nonspuriousness.
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Complete question :
Because quasi-experimental designs do not use randomization to assign subjects to treatment and comparison groups, it is more difficult to establish:
a. Association
b. Time order
c. Nonspuriousness
d. Causal mechanism
e. Context
How many ways are there to arrange 12 (distinct) people in a row so that Dr. Tucker is 3 positions away from Dr. Stanley (i.e., 2 people are inbetween Dr. Tucker and Dr. Stanley), e.g., . . . . T _ _ S . . . .
There are 3,628,800 ways to arrange 12 distinct people in a row so that Dr. Tucker is 3 positions away from Dr. Stanley.
To count the number of arrangements of 12 people with Dr. Tucker and Dr. Stanley positioned 3 apart, we can treat Dr. Tucker and Dr. Stanley as a single block of two people, and then arrange the resulting 11 blocks in a row.
Since Dr. Tucker and Dr. Stanley can occupy any of the 10 possible positions (the first two positions, the second and third, and so on up to the last two positions), there are 10 ways to form this block.
After the block is formed, we are left with 10 remaining people to arrange in the remaining 10 positions. There are 10! ways to arrange these people, so the total number of arrangements is:
10 x 10! = 3,628,800
Therefore, there are 3,628,800 ways to arrange 12 distinct people in a row so that Dr. Tucker is 3 positions away from Dr. Stanley.
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we use a bode plot to show filter characteristics because the use of logarithms creates plots that can be approximated with straight lines. true false
It is true that we use a bode plot to show filter characteristics because the use of logarithms creates plots that can be approximated with straight lines.
We use a bode plot to display the frequency response of a filter. The frequency response of a filter is a complex function, and its plot can be difficult to analyze. However, by using logarithmic scales on the frequency and amplitude axes, we can transform the complex function into a simpler form that can be approximated with straight lines. This simplification is particularly useful because it allows us to easily identify the characteristics of the filter, such as its cutoff frequency, bandwidth, and phase shift. Therefore, the use of logarithmic scales is essential in creating a bode plot, and it is why we use this type of plot to show filter characteristics.
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A
E
B
6
C
In triangle ABC shown, what is the length of
side AC?
Answer:
8
Step-by-step explanation:
6^2+8^2=10^2 So, the answer is 10.
An isosceles triangle has an angle that measures 132°. What measures are possible for the other two angles? Choose all that apply.
The measures of the angles of the isosceles triangle is x = 24°
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of ∠ABC = 132°
And , the triangle is isosceles
So , the measure of ∠BAC + ∠ACB + ∠ABC = 180°
And , ∠BAC = ∠ACB
So , 2x + 132° = 180°
2x = 48°
Divide by 2 on both sides , we get
x = 24°
Hence , the isosceles triangle is solved
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Use technology to find the indicated area under the standard Normal curve. Include an appropriately labeled sketch of the Normal curve and shade the appropriate region. a. Find the area in a standard Normal curve to the left of 1.96. b. Find the area in a standard Normal curve to the right of 1.96. Remember that the total area under the curve is 1.
The area to the left of 1.96 for part a and the area to the right of 1.96 for part b. Remember to label the curve, x-axis, and shaded areas appropriately.
To find the indicated areas under the standard Normal curve, you can use technology such as a calculator, spreadsheet software, or an online tool like a z-score calculator.
a. To find the area to the left of 1.96, input the z-score (1.96) into the calculator. The result is approximately 0.975. This means that about 97.5% of the area under the curve is to the left of 1.96.
b. To find the area to the right of 1.96, subtract the area found in part a from the total area under the curve (1). So, 1 - 0.975 = 0.025. This means that about 2.5% of the area under the curve is to the right of 1.96.
In your sketch, draw a standard Normal curve and mark 1.96 on the x-axis. Shade the area to the left of 1.96 for part a and the area to the right of 1.96 for part b. Remember to label the curve, x-axis, and shaded areas appropriately.
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What is 4 hours and 45 minutes as a fraction in simplest form?
O 4 2/3
O 4 3/4
O 4 5/9
O 4 1/2
To convert 4 hours and 45 minutes to a fraction, we need to first convert the minutes to hours by dividing by 60 and then add the result to the 4 hours.
4 hours and 45 minutes = 4 + 45/60 hours = 4 + 0.75 hours
Now, we can write this as a fraction by expressing the decimal part as a fraction:
4 + 0.75 = 4 + 3/4 = (4*4 + 3)/4 = 19/4
Therefore, 4 hours and 45 minutes is equal to 19/4 when expressed as a fraction in simplest form.
The answer is (B) 4 3/4.
6. A semi trailer has a length of 36 feet, a width of 92.5 inches and a height of 102 inches. Using the
box at the front of the classroom, determine how many of the boxes could fit into the trailer.
Answer:
The maximum number of boxes that will fit inside the trailer will be 952.
Step-by-step explanation:
Volume of single box = a² = (1.5)² = 2.25 square feet.
Volume of cargo space = L x B x H = (28 x 8.5 x 9) = 2142 square feet.
The maximum number of boxes that will fit inside the trailer will be -
n = {(L x B x H)/a²}
n = (2142/2.25)
n = 952
True or False: In order to take the final exam, I must complete each lesson quiz in order with a passing score of 100% before I can attempt the final.
Answer:
Yes! It is TRUE
Hope my answer helps you ✌️
To determine whether there is sufficient evidence to support the mayor's claim that over 47% of the residents favor construction of a new community, we need to perform a hypothesis test.
Let's define the null hypothesis (H0) and the alternative hypothesis (H1) as follows:
H0: The proportion of residents favoring construction of a new community is 47% or less.
H1: The proportion of residents favoring construction of a new community is greater than 47%.
We will conduct a one-tailed test since we are interested in determining if the proportion is greater than 47%.
Next, we need to gather a sample of residents and determine the proportion in favor of construction. Let's assume we collect a random sample of residents and find that 53 out of 100 residents favor the construction.
To perform the hypothesis test, we will use a significance level (α) of 0.10. Using this information, we can calculate the test statistic and compare it to the critical value or p-value to make a decision.
The test statistic for testing a proportion is given by:
z = (p - P) / sqrt((P * (1 - P)) / n)
where p is the sample proportion, P is the hypothesized proportion under the null hypothesis, and n is the sample size.
Let's calculate the test statistic:
p = 53 / 100 = 0.53 (proportion from the sample)
P = 0.47 (hypothesized proportion under the null hypothesis)
n = 100 (sample size)
z = (0.53 - 0.47) / sqrt((0.47 * (1 - 0.47)) / 100)
= 0.06 / sqrt(0.2494 / 100)
= 0.06 / 0.04994
= 1.2012
To determine whether there is sufficient evidence to support the mayor's claim, we compare the test statistic (z = 1.2012) to the critical value from the standard normal distribution at the 0.10 significance level. The critical value for a one-tailed test at a significance level of 0.10 is approximately 1.28.
Since the test statistic (1.2012) is less than the critical value (1.28), we fail to reject the null hypothesis. This means that there is not sufficient evidence at the 0.10 level to support the mayor's claim that over 47% of the residents favor construction of a new community.
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The sportsbook at the High Roller Casino put the odds of a certain baseball team to win the World Series at 1:25 (1 to 25). Based on those odds, what is the probability that this baseball team will win the World Series
The probability that this baseball team will win the World Series, based on the provided odds, is 1/26 or approximately 0.0385 (rounded to four decimal places).
To determine the probability of the baseball team winning the World Series based on the odds given by the sportsbook, we can use the formula:
Probability = (Number of ways the event can occur) / (Total number of possible outcomes)
In this case, the "event" is the baseball team winning the World Series, and the "total number of possible outcomes" is the number of teams participating in the World Series. Assuming there are 30 teams in the Major League Baseball, the total number of possible outcomes is 30.
To calculate the number of ways the event can occur, we can use the odds provided by the sportsbook. The odds of 1:25 mean that for every 25 times the event does not occur (i.e. the baseball team does not win the World Series), it occurs once (i.e. the baseball team wins the World Series). Therefore, the number of ways the event can occur is 1.
Using the formula above, we can now calculate the probability:
Probability = 1 / 30
Therefore, the probability of the baseball team winning the World Series based on the odds of 1:25 is approximately 0.04 or 4%.
Hi! You've asked about the probability of a certain baseball team winning the World Series, given that the sportsbook at the High Roller Casino has set the odds at 1:25.
To find the probability, you'll need to use the odds provided. In this case, the odds are 1 to 25, meaning there's 1 chance of winning for every 25 chances of losing. To calculate the probability, you can use the following formula:
Probability = Number of winning outcomes / (Number of winning outcomes + Number of losing outcomes)
In this case, the number of winning outcomes is 1, and the number of losing outcomes is 25. Plugging these numbers into the formula, you get:
Probability = 1 / (1 + 25)
Probability = 1 / 26
So the probability that this baseball team will win the World Series, based on the provided odds, is 1/26 or approximately 0.0385 (rounded to four decimal places).
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To calculate the probability of a baseball team winning the World Series based on odds of 1:25, we need to convert the odds to a probability. The formula for converting odds to probability is:
Probability = 1 / (odds + 1)
Using this formula, we can calculate the probability of the baseball team winning the World Series as follows:
Probability = 1 / (1 + 25) = 0.038
Therefore, the probability of the baseball team winning the World Series based on the odds of 1:25 is 0.038 or 3.8%.
it is important to understand that odds and probability are two different ways of expressing the likelihood of an event occurring. Odds are typically expressed as a ratio of the number of ways an event can happen to the number of ways it cannot happen. Probability, on the other hand, is expressed as a number between 0 and 1 that represents the likelihood of an event occurring.
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The ratio of the amount o rice Max has to the amount of rice Victor has to the amount of rice Roman has is 3:2:4, If Victor gives 1/4 of hs rice to Roman, what will the new ratio of the amounts of Max's rice to Victor's rice be
The new ratio of the amounts of Max's rice to Victor's rice to Roman's rice is 2:1:3.
Given, that ratio of rice between max, victor and roman
Ratio : A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Let the amount of rice that Max, Victor, and Roman have as 3x, 2x, and 4x, respectively.
The total ratio of the amounts of rice is 3+2+4 = 9,
So each "part" of the ratio is 1/9.
If Victor gives 1/4 of his rice to Roman, he will give away
(1/4) × (2x) = 1/2x rice to Roman, and he will be left with
(3/4) × (2x)
= 6/4x
= 3/2x rice.
Roman will receive 1/2x rice from Victor and will have
4x + 1/2x = 9/2x rice in total.
So the new amounts of rice that Max, Victor, and Roman have are 3x, 3/2x, and 9/2x, respectively.
The new ratio of the amounts of rice is (3x):(3/2x):(9/2x).
To simplify this ratio, we can multiply all parts by 2 to get:
6x:3x:9x
And then divide all parts by 3x to get:
2:1:3
Hence, the new ratio of the amounts of Max's rice to Victor's rice to Roman's rice is 2:1:3.
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The new ratio of the amount of rice that Max has to the amount that Victor has after Victor gives away 1/4 of his rice to Roman is 2:1.
Explanation:Let's assume the amount of rice Max, Victor, and Roman have are 3x, 2x, and 4x units respectively. Now, if Victor gives 1/4 of his rice to Roman, Victor's amount will decrease by 1/4*2x = 0.5x, therefore, Viktor will have 2x - 0.5x = 1.5x units of rice. So, the new ratio of the amount of rice Max to the amount of rice Victor will be 3x:1.5x or, simplifying, 2:1.
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Neck cancer is a rare (<10% of the total population). If a case-control study were conducted and an odds ratio obtained, which relative measure would it most likely be estimating
If a case-control study were conducted to investigate the relationship between an exposure and a rare disease like neck cancer, the most likely relative measure that would be estimated is the odds ratio.
This is because the prevalence of neck cancer in the general population is low, which means that the incidence rate is also low. As a result, it is difficult to calculate the relative risk directly in a case-control study. Instead, the odds ratio is used as a measure of association between the exposure and the disease outcome.
The odds ratio is calculated by comparing the odds of exposure in cases to the odds of exposure in controls. The odds ratio can provide an estimate of the strength and direction of the association between the exposure and the disease outcome in the population being studied.
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The grocery store has bulk pecans on sale, which is great since you're planning on making 4 pecan pies for a wedding. How many pounds of pecans should you buy
You would need to buy about 1.5 pounds of pecans to make the 4 pecan pies.
To determine how many pounds of pecans you should buy for making 4 pecan pies for a wedding, you need to have an idea of the quantity of pecans required to make one pie. Typically, a single pecan pie recipe calls for 1 ½ cups of pecans. However, the actual amount of pecans needed depends on the size of the pie you are making. For instance, if you are making a deep-dish pecan pie, you may need to increase the amount of pecans.
Assuming that you are making standard-sized pies, each requiring 1 ½ cups of pecans, you will need a total of 6 cups of pecans to make 4 pies. A standard 1-pound bag of pecans contains around 4 cups of pecans. Hence, you would need to buy about 1.5 pounds of pecans to make the 4 pecan pies.
However, if you prefer to add more pecans to your pies, you may want to purchase additional bags of pecans. In such a case, it is advisable to purchase an extra half-pound of pecans for every extra cup of pecans you intend to use.
In conclusion, to make 4 pecan pies for a wedding, you should purchase 1.5 pounds of pecans.
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How much is considered the maximal amount of medically unsupervised weight an adult should lose in one week
The maximal amount of medically unsupervised weight loss that an adult should aim for in one week is generally 1-2 pounds (0.5-1 kg). This is because losing weight too quickly can be harmful to your health and lead to a number of negative side effects, such as muscle loss, fatigue, dehydration, and gallstones.
It's important to note that the amount of weight an individual can lose in a week can vary depending on factors such as their starting weight, body composition, and overall health. In some cases, a doctor or other medical professional may recommend a faster rate of weight loss under close supervision, but this is generally reserved for people who are severely overweight or have medical conditions that require rapid weight loss.
Ultimately, it's important to approach weight loss in a healthy and sustainable way, with a focus on making long-term lifestyle changes rather than relying on quick fixes or fad diets. A balanced diet, regular exercise, and a consistent sleep schedule are all important components of a healthy weight loss plan.
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Both the z and t distributions have the following properties: Multiple select question. bimodal skewed symmetric around 0 with asymptotic tails bell-shaped
False.
The statement is incorrect because neither the z nor the t distribution is necessarily skewed symmetric. While they are both bell-shaped and have asymptotic tails, the shape of the distribution depends on the degrees of freedom for the t distribution and the mean and standard deviation for the z distribution.
The z and t distributions share several properties, which include:
1. Skewed: Both distributions are not skewed, as they are symmetric around 0.
2. Symmetric around 0: Both the z (standard normal) and t distributions are symmetric around 0, which means that they have equal probability on both sides of 0.
3. Asymptotic tails: Both distributions have asymptotic tails, which means that the tails of the distributions approach but never touch the horizontal axis.
4. Bell-shaped: Both the z and t distributions are bell-shaped, with a peak at the center (0) and tails extending to the left and right.
So, the correct properties for both z and t distributions are: symmetric around 0, asymptotic tails, and bell-shaped.
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I'm 2nd place in math for iready in school and now im getting stuff i dont understand please help TvT
The graph of function is |x + 2| – 5= -(x - 1)(x - 3) which is represented in the graph option A is correct.
What is a function ?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we can see in the graph, there are two graphs of a function shown.
First one is a graph of a mod function and second one is a graph of a quadratic equation.
|x + 2| – 5= -(x - 1)(x - 3)
f(x) = |x + 2| - 5
g(x) = -(x - 1)(x - 3)
Thus, the graph of function is |x + 2| – 5= -(x - 1)(x - 3) which is represented in the graph option A is correct.
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what might you conclude if a random sample of 29 time intervals between eruptuions has a mean greater than 106
If a random sample of 29 time intervals between eruptions has a mean greater than 106, it may be concluded that the average time between eruptions is longer than 106 units of time. However, it is important to note that the sample size of 29 may not be representative of the entire population of time intervals between eruptions, and therefore the conclusion drawn may not be entirely accurate.
Additionally, it is important to consider the variability of the data. If the standard deviation of the sample is high, it may indicate that there is a wide range of time intervals between eruptions, making it difficult to draw a definitive conclusion. On the other hand, if the standard deviation is low, it may indicate that the time intervals are more consistent, and the conclusion drawn may be more reliable.
Overall, it is important to consider both the mean and variability of the sample when drawing conclusions about the population of time intervals between eruptions. Further research and analysis may be necessary to validate the findings and provide a more accurate answer.
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A lump sum of $1000 is invested at 4.6% compounded continuously. (a) Write the function for the model that gives the future value of the investment in dollars after t years.
The investment would be worth about $1315.94. Similarly, we can find the future value at any other time by plugging in the appropriate value of t.
To find the future value of an investment that is compounded continuously, we can use the formula:
A = Pe^(rt)
Where A is the future value, P is the initial principal, r is the annual interest rate, and t is the time in years.
In this case, we have P = $1000, r = 0.046 (since the interest rate is 4.6%), and t is the number of years. Plugging these values into the formula, we get:
A = 1000*e^(0.046t)
This is the function for the model that gives the future value of the investment in dollars after t years. To find the future value at a specific time, we just need to substitute the value of t into the function and evaluate it. For example, if we wanted to find the value after 5 years, we would plug in t = 5:
A = 1000*e^(0.046*5) = 1000*e^(0.23) ≈ $1315.94
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The heights of juniors at a certain high school have a mean of 65.5 inches, with a standard deviation of 3.5 inches. What is the probability that a randomly selected junior at this school is at least 72.5 inches tall
The probability that a randomly selected junior at this school is at least 72.5 inches tall is,
= 2.275%
We have to given that;
The heights of juniors at a certain high school have a mean of 65.5 inches, with a standard deviation of 3.5 inches.
Hence, We can formulate;
Let x be the height of a junior.
X ~ n (65.5, 3.5)
P (x > 72.5) - 1 - P (x < 72.5)
= 1 - P [z < (72.5 - 65.5)/3.5]
= 1 - P (z < 2)
= 1 - 0.92725
= 0.02275
= 2.275%
Thus, The probability that a randomly selected junior at this school is at least 72.5 inches tall is,
= 2.275%
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The number of private donations received by non-government disaster relief organizations can be modeled as
f(x) = 0.1xe−0.06x thousand donations
where x is the number of hours since a major disaster has struck.
(a) Write an expression for the rate of change in donations. (Round all numerical values to three decimal places.)
f '(x) =
(b) At what time is the rate of change of donations zero? (Round your answer to three decimal places.)
hours after the major disaster strikes
(c) What is the donation level at the time found in part (b)? (Round your answer to three decimal places.)
thousand donations
Note that
a) f'(x) = 0.0xe^(-0.06x) + 0.1e^(-0.06 x) thousands donations per hours.
b) the rate of change of donations is zero at approximately 51.24 hours after the major disaster
c) donation level in part (B) is 1.58.
How can one arrive at this?(a) The rate of change of donations can be found by taking the derivative of the function f (x ) .....
f'(x ) = (0.1 x)(-0.06)e^(-0.06 x) + e^(-0.06 x)(0.1)
Simplifying:
f'(x) = 0.01e^( -0.06x )(10 - x)
So the expression for the rate of change in donations is f' ( x) = 0.01e^( -0.06x)( 10 - x).
(b) To find when the rate of change of donations is zero, we need to solve the equation f'(x) = 0:
0.01e^(-0.06x)(10 - x) = 0
10 - x = 0
x = 10
So the rate of change of donations is zero 10 hours after the major disaster strikes.
(c) To find the donation level at the time found in part (b), we substitute x = 10 into the original function f(x):
f(10) = 0.1(10)e^(-0.06(10)) = 0.635
So the donation level at 10 hours after the major disaster strikes is 0.635 thousand donations.
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1. Travis is testing how far he can throw a baseball to prepare himself for the season. He makes 16
throws and records the length of each throw in feet. The results are provided in the accompanying table.
236 240 232 242 238 235 228 245
247 239 234 238 241 227 243 238
Travis says that the histogram provided below could be used to represent the data.
Show whether the histogram Travis created is correct and, if not, explain how the histogram could be corrected.
Answer:
It is incorrect
Step-by-step explanation:
225 - 229: 2, where as he shows none
230 - 234: 2, which he shows correctly
235 - 239: 6, which he shows incorrectly as 2
240 - 244: 4, which he shows incorrectly as 6
245 - 249: 2, which he shows incorrectly as 4
250 - 254: 0, which he shows incorrectly as 2
Using the iterative formula xn+1=3√7−4xn starting with x0=1.25, find a solution to x3+4x−7=0 rounded to 3 DP.
The solution to x³ + 4x - 7 = 0 is x₃ = 1.709 by using iterative formula.
We can use the given iterative formula to find a sequence of approximations to the solution of the equation x³ + 4x - 7 = 0, starting with x₀ = 1.25.
First, we compute x₁ = 3√(7 - 4x₀)
= 3√(7 - 4(1.25))
= 1.771
Next, we compute x₂ = 3√(7 - 4x₁)
= 3√(7 - 4(1.771))
= 1.652
Solution x₃ = 3√(7 - 4x₂) = 3√(7 - 4(1.652)) = 1.709
We continue this process until we get the desired level of accuracy.
Therefore, the solution to x³ + 4x - 7 = 0, rounded to 3 decimal places, is x₃ = 1.709.
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Solve by compleating the square
x^2-8x+3=0
4 ± √13.
Step:
To solve the equation x^2 - 8x + 3 = 0 by completing the square, we first move the constant term to the right side of the equation to obtain x^2 - 8x = -3. Then, we take half of the coefficient of x, which is -4, and square it to get 16. We add 16 to both sides of the equation, which gives x^2 - 8x + 16 = 13. The left side of the equation can be factored as (x - 4)^2, which gives us (x - 4)^2 = 13. Finally, we take the square root of both sides to get x - 4 = ±√13, and our solutions are x = 4 ± √13.
A man usually rides his bike 9 kilometers per hour, yet the wind slows him to 6.76 kilometers for 26 minutes and 5.55 kilometers for 10; how long until he gets home 11.54 kilometers away
It will take approximately 51.25 minutes for the man to get home at his usual speed of 9 kilometers per hour.
Step 1: Convert the given time in minutes to hours
26 minutes = 26/60 hours = 0.4333 hours
10 minutes = 10/60 hours = 0.1667 hours
Step 2: Calculate the distance covered during each time interval
First interval: 6.76 km/h * 0.4333 hours = 2.9276 km
Second interval: 5.55 km/h * 0.1667 hours = 0.9256 km
Step 3: Add the distances together to find the total distance covered
2.9276 km + 0.9256 km = 3.8532 km
Step 4: Calculate the remaining distance to reach home
11.54 km - 3.8532 km = 7.6868 km
Step 5: Calculate the time it takes to cover the remaining distance at the usual speed
Time = Distance / Speed
Time = 7.6868 km / 9 km/h = 0.8541 hours
Step 6: Convert the time in hours back to minutes
0.8541 hours * 60 = 51.246 minutes
So, it will take approximately 51.25 minutes for the man to get home at his usual speed of 9 kilometers per hour.
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How many people surveyed did not choose a rainbow color (red, orange, yellow, green, blue, or purple) as their favorite
Students were surveyed about their favorite colors. 1/4 of the student preferred red, 1/8 of the students preferred blue, and 3/5 of the remaining students preferred greed, then 10 students surveyed did not choose a rainbow color as their favorite.
Let's use algebra to solve for the total number of students surveyed:
Let x be the total number of students surveyed.
Then, the number of students who preferred red is (1/4)x.
The number of students who preferred blue is (1/8)x.
The remaining students are (x - (1/4)x - (1/8)x) = (5/8)x.
Out of these remaining students, 3/5 preferred green, so we can set up the equation:
(3/5)(5/8)x = 15
Simplifying, we get:
(3/8)x = 15
Multiplying both sides by 8/3, we get:
x = 40
Therefore, there were 40 students surveyed in total. To find the number of students who did not choose a rainbow color as their favorite, we need to subtract the number of students who preferred red, blue, green, or purple from the total number of students:
Number of students who did not choose a rainbow color = x - (1/4)x - (1/8)x - 15 = 40 - 10 - 5 - 15 = 10
Therefore, 10 students surveyed did not choose a rainbow color as their favorite.
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From a bag containing 15 red balls ,12green balls ,18 black balls and 9blue balls ,a ball is drawn at random. If the probability of drawing that specific coloured ball is 5/18,then ball of which colour has been drawn ?
Where X has 9 balls in the bag. Looking at the options, we see that only the black balls have 9 balls in the bag, so the ball drawn must be black. the answer is black.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Let's assume that the ball drawn is of color X. Then, we can use the formula for probability:
P(X) = Number of balls of color X / Total number of balls
We are given that P(X) = 5/18, so we can write:
Number of balls of color X / Total number of balls = 5/18
Multiplying both sides by the total number of balls, we get:
Number of balls of color X = (5/18) * Total number of balls
Now we can substitute the given values:
Number of balls of color X = (5/18) * (15 + 12 + 18 + 9) = 9
So the ball drawn is of color X, where X has 9 balls in the bag. Looking at the options, we see that only the black balls have 9 balls in the bag, so the ball drawn must be black. Therefore, the answer is black.
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E52 Find the number of integers in the set {1,2,3,..., 210} that are divisible (a) by exactly one of 2, 3, 5, and 7; (b) by exactly two of 2,3,5, and 7.
The number of integers in the set divisible by exactly one of 2, 3, 5, and 7 is therefore 211 and the total number of integers in the set divisible by exactly two of 2, 3, 5, and 7 is 101
To count the integers in the set {1, 2, 3, ..., 210} that are divisible by exactly one of 2, 3, 5, and 7, we need to use the principle of inclusion-exclusion.
The number of integers in the set divisible by 2 is 105.
The number of integers in the set divisible by 3 is 70.
The number of integers in the set divisible by 5 is 42.
The number of integers in the set divisible by 7 is 30.
The number of integers in the set divisible by 2 and 3 is 35.
The number of integers in the set divisible by 2 and 5 is 21.
The number of integers in the set divisible by 2 and 7 is 15.
The number of integers in the set divisible by 3 and 5 is 14.
The number of integers in the set divisible by 3 and 7 is 10.
The number of integers in the set divisible by 5 and 7 is 6.
The number of integers in the set divisible by exactly one of 2, 3, 5, and 7 is therefore:
105 + 70 + 42 + 30 - (35 + 21 + 15 + 14 + 10 + 6) = 211.
(b) To count the integers in the set {1, 2, 3, ..., 210} that are divisible by exactly two of 2, 3, 5, and 7, we can count the number of integers in the set that are divisible by each pair of these primes and add up the results.
The number of integers in the set divisible by 2 and 3 is 35.
The number of integers in the set divisible by 2 and 5 is 21.
The number of integers in the set divisible by 2 and 7 is 15.
The number of integers in the set divisible by 3 and 5 is 14.
The number of integers in the set divisible by 3 and 7 is 10.
The number of integers in the set divisible by 5 and 7 is 6.
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how many rectangles can you make with 17 squares
FIND THE EXPLICIT FORMULA 39,46,53,60....
The explicit formula for the given sequence is:
an = 39 + (n-1)7, where n is the position of the term in the sequence.
The given sequence is an arithmetic sequence where each term is obtained by adding a common difference 'd' to the preceding term.
To find the explicit formula for this sequence, we need to find the value of 'd' and the first term 'a1'.
We can find the common difference 'd' by subtracting any two consecutive terms in the sequence.
Let's subtract the second term from the first term:
46 - 39 = 7
This means the common difference 'd' is 7.
To find the first term 'a₁', we can substitute any of the given terms in the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n-1)d
Let's use the first term of the sequence, which is 39, and substitute n = 1 and d = 7:
39 = a₁ + (1-1)7
39 = a₁
So the first term of the sequence is 39.
Now we can write the explicit formula for the nth term of the sequence:
an = 39 + (n-1)7
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A triangular sail has sides of 12 ft, 28 ft, and 32 ft. If the longest side of a similar sail measures 28 ft, what is the measure of its shortest side
The measure of the shortest side of the larger sail is 12 ft
How to find the shortest side of triangular sail?We can use the property that similar triangles have corresponding sides in proportion to solve this problem.
Let the length of the shortest side of the larger sail be x.
Since the two sails are similar, we can set up the proportion:
12 : 28 : 32 = x : 28 : y
where y is the length of the remaining side of the larger sail.
We can then use cross-multiplication to solve for y:
12 * 28 = 28 * x
336 = 28x
x = 12
So the length of the shortest side of the larger sail is 12 feet.
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URGENT PLEAS HELP MEEE
The graph of functions y = f (x) - 2 and y = - f(x) are shown in image.
Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
The graph of function y = f (x) is shown in figure.
Now, We know that;
Function y = f (x) - 2 is 2 unit down to the function y = f (x).
And, Function y = - f (x) is opposite the graph of function y = f (x).
Hence, The graph of functions y = f (x) - 2 and y = - f(x) are shown in image.
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