Answer:
Scale factor of dilation is
Step-by-step explanation:
Cross multiplication gets:
QR = 3 * Q'R'
Q'R' = 1/3 * QR
So it's 1/3
Answer:
A
C
D
Step-by-step explanation:
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Explanation:
We have two workers, more or less. Worker A gets the job done in 5 hours. Worker B comes along to help. If A and B work together, they get the job done in 4 hours. This assumes neither worker hinders the other.
Worker A's rate is 1/5 of a job per hour. In other words, after 1 hour, 1/5 of the job is done.
The combined rate is 1/4 for similar reasoning
Worker B's rate is 1/x where x represents how long it takes worker B to get the job done on its own.
The equation to solve is
1/5 + 1/x = 1/4
Note how 1/5 and 1/x represents the sum of the individual rates to get the combined rate 1/4
To solve this equation, it helps to clear out the fractions. Multiply every term by the LCD 20x
20x(1/5 + 1/x) = 20x(1/4)
20x(1/5) + 20x(1/x) = 20x(1/4)
4x + 20 = 5x
From here you can probably see solving this is relatively easy
4x+20 = 5x
20 = 5x-4x
20 = x
x = 20
Therefore, it will take 20 hours for worker B to get the job done on its own.
Going back to the processing context, it takes 20 hours for the new processor to download the movie. This is where the new processor is working alone without help from the original processor.
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Side note: downloading a movie really depends on internet speed rather than processor speed.
10×10=100
there is 100 pencils in total
Answer:
We conclude that the population mean is not equal to 17.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 17
Sample mean, = 14.12
Sample size, n = 40
Alpha, α = 0.05
Population standard deviation, σ = 4
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
a) Formula:
Putting all the values, we have
b) P-value can be calculated from the standard z-table.
P-value = 0.0000
c) Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17
d) Now,
e) Rejection Rule:
We reject the null hypothesis if it is less than lower critical value and greater than the upper critical value
If the z-statistic lies outside the acceptance region which is from -1.96 to +1.96, we reject the null hypothesis.
f) Since the calculated z-stat lies outside the acceptance region, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17.
The test statistic is -1.78 and the p-value is 0.0761, indicating that we fail to reject the null hypothesis. Therefore, it cannot be concluded that the population mean is not equal to 17.
The test statistic can be calculated using the formula:
test statistic = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
Plugging in the given values, we get:
test statistic = (14.12 - 17) / (4 / sqrt(40))
Calculating this gives us a test statistic value of -1.78.
The p-value can be calculated using the test statistic. We need to find the probability that a test statistic at least as extreme as -1.78 would occur assuming the null hypothesis is true. Using a standard normal distribution table or software, we find the p-value to be approximately 0.0761.
Since the p-value is greater than the significance level (alpha = 0.05), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the population mean is not equal to 17.
#SPJ11
Answer:
-60.
Step-by-step explanation:
Let the unknown number be x.
Number is increased by 26 = x+26
Then result is tripled = 3(x+26)
Then the result is increased by 72 = 3(x+26)+72
Final result is of the number =
Isolate variable terms.
Multiply both sides by 2.
Divide both sides by 5.
Therefore, the required number is -60.
Answer:
I'm not sure