Answer:
N(t) = N0·e^(kt)107,672Step-by-step explanation:
a) Your question supplies the formula for N(t):
N(t) = N0·e^(kt)
__
b) Given the initial population and doubling time (in months), the population function can also be written as ...
N(t) = 10,000·2^(t/14) . . . . . t in months
Then in 4 years the population will be ...
N(48) = 10,000·2^(48/14) ≈ 107,672.02
The population 4 years from now will be approximately 107,672 people.
_____
Comment on the formula for N(t)
In order to use the formula of the first part in answering the second part, we need to find the value of k. It will be an irrational number. In order to obtain accurate results in the second part, k would need to be good to at least 6 significant digits. Its value, for t in months, is ...
k = ln(2)/14 ≈ 0.0495105
For t in years, it is 12 times this value, or ...
k ≈ 0.594126
The advice not to do any rounding (even for the value of k) is appropriate.
__
As we can see from the above, it is not necessary to determine k in order to answer the question in part b.
The population of a city with exponential growth can be expressed as [tex]N(t) = N0 * e^(^k^t^)[/tex]. The growth factor k is found to be approximately 0.592. Using this, the population 4 years later is found to be approximately 43609.
Explanation:The population of a city showing exponential growth can be expressed as [tex]N(t) = N0 * e^(^k^t^)[/tex] where N(t) is the population at time t, N0 is the initial population, e is the natural logarithmic base (approx. 2.71828), and k is the growth rate.
Given that the population doubled in 14 months, which is about 1.17 years, we have: 2*N0 = N0 * [tex]e^(^1^.^1^7^k^)[/tex]. Solving this equation for k, we get k = ln(2)/1.17. Hence, the growth rate (k) is approximately 0.592.
To find the population 4 years from now, we substitute t=4 and k=0.592 into the equation. So, N(4) = 10000 * [tex]e^(^4^*^0^.^5^9^2^)[/tex]. After calculating, we get a population of approximately 43609.
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Which product is shown on this number line
Answer:
Would ypu plz show us the number line so at least i could answer the question
Consider the expression 63+81. How can you use the distributive property and the GFC to find an equivalent expression? Explain how you can check your answer.
Answer:
(See explanation)
Step-by-step explanation:
The expression is simplified as follows:
[tex]63 + 81[/tex]
[tex]9 \times (7+9)[/tex]
[tex]9\times 16[/tex]
[tex]144[/tex]
This answer can be checked by summing the previous formula:
[tex]63 + 81[/tex]
[tex]144[/tex]
A pathologist knows that 14.9% of all deaths are attributable to myocardial infarctions (a type of heart disease). (Either you have myocardial infarction or you don’t)
a. Find the mean and standard deviation for the number of such deaths that will occur in typical region with 5000 deaths.
b. In one region, 5000 death certificates are examined, and it is found that 896 deaths were attributable to myocardial infarction. Is there cause for concern? Why or why not?
Answer:
a) The mean number is 745 and the standard deviation is 25.18.
b) 896 deaths is a significantly high number, which means that there is cause for concern.
Step-by-step explanation:
For each death, there are only two possible outcomes. Either it is attributable to myocardial infarctions, or it is not. The probability of a death being attributable to myocardial infarctions is independent of other deaths. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
A value X is significantly high is:
[tex]X > E(X) + 2\sqrt{V(X)}[/tex]
In this problem:
[tex]p = 0.149, n = 5000[/tex]
a. Find the mean and standard deviation for the number of such deaths that will occur in typical region with 5000 deaths.
[tex]E(X) = np = 5000*0.149 = 745[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5000*0.149*0.851} = 25.18[/tex]
The mean number is 745 and the standard deviation is 25.18.
b. In one region, 5000 death certificates are examined, and it is found that 896 deaths were attributable to myocardial infarction. Is there cause for concern? Why or why not?
Is 896 a significantly high number?
[tex]E(X) + 2\sqrt{V(X)} = 745 + 2*25.18 = 795.36[/tex]
895 > 795.36
896 deaths is a significantly high number, which means that there is cause for concern.
correct 0.00578 to 2 significant figures,
Answer:
It is 0.578
Step-by-step explanation:
0.00578
to 2 significant figures
0.00578
0.578
Final answer:
0.00578 rounded to two significant figures is 0.0058, as you only count the first two non-zero digits and apply the standard rules of rounding off.
Explanation:
To correct the number 0.00578 to two significant figures, we need to identify the first two non-zero digits as those are the ones considered significant. Here, the non-zero digits are 5 and 7. Therefore, to maintain two significant figures, we need to round the third digit (8), keeping in mind the rules of rounding: if the third digit is 5 or more, we round up the second digit by 1.
In this case, since the third digit is 8, which is more than 5, we round up the second digit by 1. Hence, the number becomes 0.0058. Since we must retain only two significant figures, we do not count the zeros before the '5' as they are merely placeholders. Finally, to two significant figures, 0.00578 is correctly rounded to 0.0058.
1.25=0.75+r what is R?
Look at the attached picture ⤴
Hope it will help u...
Answer:
0.5
Step-by-step explanation:
you have to combine like terms
65% of what number is 78?
A. 120
B. 143
C. 785
D. 5,070
Answer:
D
Step-by-step explanation:
65% × 78 =
(65 ÷ 100) × 78 =
(65 × 78) ÷ 100 =
5,070 ÷ 100 =
50.7;
Answer:
A 120
Step-by-step explanation:
you divide 120 by 0.65 to find 78
point
1. Challa drank 6,500 mL of water before her soccer game. She drank the
water out of 1 liter bottles. How many bottles of water did she drink? Hint: 1
liter= 1000 ml
Answer:
6.5 bottles
Step-by-step explanation:
convert liters to ml 1 bottle= 1000ml
divide how much she drank by 1000ml
6500÷1000=6.5
1) The world's smallest mammal is the bumblebee bat. The mean weight of 200 randomly selected bumblebee bats is 1.659 grams, with a standard deviation of 0.264 grams.
(a) Find a 99.9% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal).
(b) Find a 99% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal).
(c) Find a 95% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal).
(d) Find an 80% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal).
2) Dr. Clifford Jones claims that the mean weight of bumblebee bats is 1.7 grams. We are interested in whether it's less than he claims.
Using the t-distribution technique, is there evidence that bumblebee bats weigh less on average than he claims, at each of the following levels?
Answer:
For values
99.9%==1.659±0.061499%==1.659±0.048190%==1.659±0.036680%=1.659±0.0239Hence the Dr.Clifford Jones claim is wrong about the bats mean weight
Step-by-step explanation:
Given:
Mean=1.659 grams
Standard deviation: 0.264
No of samples=200
To find :
Confidence intervals at
1)99.9% 2)99% 3)95% 4)80% and
Whether the Dr. Clifford with 1.7 mean weight is less or not?
Solution:
We know interval estimation is given by ,
E=mean±Z value*{standard deviation/Sqrt(N)}
Now For Z value 99.9% =3.291
E=1.659±3.291{0.264/Sqrt(200)}
=1.659±0.0614
i.e.C.I.[1.6 to 1.72]
Now for Z value 99 % =2.576
E=1.659±2.576{0.264/Sqrt(200)}
=1.659±0.0481
i.e. C.I[1.61,1.71]
Now for Z value at 95% =1.96
E=1.659±1.96*(0.264/sqrt(200))
=1.659±0.0366
i.e. C.I.[1.62,1.7]
Now ofr Z value at 80% =1.28
E=1.659±1.28*(0.264/sqrt(20))
=1.659±0.0239
i.e. C.I.[1.64,1.68]
Using t distribution as ,
value for mean =1.7
raw i.p=1.659
Degree of freedom =N-1=200-1=199
Hence
t-score is similar to zscore
T-score =(Raw input -mean)/(standard deviation/Sqrt(n))
=(-1.7+1.659)/(0.264/Sqrt(200))
=-2.19721
Consider 1 tailed ,
p value =P(Z≤-2.19721)
=0.0143
i.e P value is 0.0143
Hence The result is not significant at p<0.01
To find the confidence interval for the mean weight of all bumblebee bats, use the formula: Confidence Interval = Xbar ± (Z-Value) * (Standard Deviation / sqrt(n)). To test whether bumblebee bats weigh less on average than Dr. Clifford Jones claims, use the t-distribution technique.
Explanation:To find the confidence interval for the mean weight of all bumblebee bats, we will use the formula:
Confidence Interval = Xbar ± (Z-Value) * (Standard Deviation / sqrt(n))
where Xbar is the sample mean, Z-Value is the critical value from the standard normal distribution table, Standard Deviation is the population standard deviation, and n is the sample size.
(a) For a 99.9% confidence interval, the Z-value corresponding to a 99.9% confidence level is 3.291. Using the given values, the confidence interval can be calculated as follows:
Confidence Interval = 1.659 ± (3.291) * (0.264 / sqrt(200)) = 1.659 ± 0.1153
So the 99.9% confidence interval for the mean weight of all bumblebee bats is (1.543, 1.774).
(b) For a 99% confidence interval, the Z-value corresponding to a 99% confidence level is 2.576. Using the given values, the confidence interval can be calculated as follows:
Confidence Interval = 1.659 ± (2.576) * (0.264 / sqrt(200)) = 1.659 ± 0.0942
So the 99% confidence interval for the mean weight of all bumblebee bats is (1.565, 1.753).
(c) For a 95% confidence interval, the Z-value corresponding to a 95% confidence level is 1.96. Using the given values, the confidence interval can be calculated as follows:
Confidence Interval = 1.659 ± (1.96) * (0.264 / sqrt(200)) = 1.659 ± 0.0734
So the 95% confidence interval for the mean weight of all bumblebee bats is (1.586, 1.732).
(d) For an 80% confidence interval, the Z-value corresponding to an 80% confidence level is 1.282. Using the given values, the confidence interval can be calculated as follows:
Confidence Interval = 1.659 ± (1.282) * (0.264 / sqrt(200)) = 1.659 ± 0.0547
So the 80% confidence interval for the mean weight of all bumblebee bats is (1.604, 1.714).
2) To test whether bumblebee bats weigh less on average than Dr. Clifford Jones claims, we will use the t-distribution technique. We will set up the following hypotheses:
Null hypothesis (H0): The mean weight of bumblebee bats is equal to 1.7 grams.
Alternative hypothesis (Ha): The mean weight of bumblebee bats is less than 1.7 grams.
We will use a one-tailed test since we are only interested in whether the bats weigh less on average. Calculate the test statistic t using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(n))
where the sample mean is 1.659 grams, the hypothesized mean is 1.7 grams, the sample standard deviation is 0.264 grams, and the sample size is 200. Using these values, the test statistic can be calculated as follows:
t = (1.659 - 1.7) / (0.264 / sqrt(200)) = -2.524
Using a t-table or calculator, we can find the critical value for a one-tailed test with a significance level of 0.05 and 199 degrees of freedom to be approximately -1.652.
Since the test statistic t is less than the critical value, we reject the null hypothesis. Therefore, there is evidence to suggest that bumblebee bats weigh less on average than Dr. Clifford Jones claims at a significance level of 0.05.
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Moon Corp. has a required return on debt of 10 percent, a required return on equity of 18
percent, and a 34 percent tax rate. Moon's management has concluded that a financing mix
of 50 percent debt, 50 percent equity is desirable. Given this information, should Moon
accept this investment?
Answer:
The optimal capital structure of a firm is the best mix of debt and equity financing that maximizes a company’s market value while minimizing its cost of capital. In theory, debt financing offers the lowest cost of capital due to its tax deductibility. However, too much debt increases the financial risk to shareholders and the return on equity that they require. Thus, companies have to find the optimal point at which the marginal benefit of debt equals the marginal cost.
Step-by-step explanation:
The mean amount of time it takes a kidney stone to pass is 14 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let X=time to pass the kidney stone. Round all answers to two decimal places.
The probability that a person will take longer than 21 days to pass it is 0.12
Explanation:
Given:
Mean time, μ = 14 days
Standard deviation, ρ = 6 days
Let x be the time to pass the kidney stones.
Probability that a person will take longer than 21 days to pass it.
We need to find z score first
Z score = [tex]\frac{x - u}{p}[/tex]
Z score = [tex]\frac{21-14}{6}[/tex]
= 1.166
Probability that a person will take longer than 21 days to pass it = P(x > Z)
= P(x > 1.16)
= 0.12
Therefore, the probability that a person will take longer than 21 days to pass it is 0.12
A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample mean will be used to estimate the population mean. What is the expected value of LaTeX: \overline{x}x ¯?
Answer:
[tex]\bar{x}= 200[/tex]
Step-by-step explanation:
We are given the following in the question:
Population mean = 200
Population standard deviation = 50
Sample size, n = 100
We have to estimate the expected value of the sample mean.
The best point estimate for the sample mean is the population mean.
Thus, we can write:
[tex]\bar{x}= \mu = 200[/tex]
Thus, the expected value of the sample mean is 200.
Tameka makes a 4% commission selling electronics. How much commission does she make if she sells a flatscreen TV for $8000?
Answer:
Step-by-step explanation:
8000x0.04=
$320
Answer:
$320.
Step-by-step explanation:
.04 x 8000 = 320
Feel free to let me know if you need more help! :)
Approximate the integral R f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2), and (0, 2) into eight equal squares and finding the sum 8 f(xi, yi) ΔAi i = 1 where (xi, yi) is the center of the ith square. Evaluate the iterated integral and compare it with the approximation. (Round your answers to one decimal place.) 1 4 4 0 2 x2y dy dx 0
Answer:
The final approximation integral answer is 1.8975
Seating played eight basketball games this season. Her point total for each game were 8,14,4,7,6,14,4 and 7. What was the mean number of points she scored per game?
Answer:
The mean number of points she scored per game was 8.
Step-by-step explanation:
The mean number of points scored per game is the sum of total points scored divided by the number of games played:
Her point total for each game were 8,14,4,7,6,14,4 and 7.
This means that there were 8 total games.
She scored 8+14+4+7+6+14+4+7 = 64 total points
64/8 = 8
The mean number of points she scored per game was 8.
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:
rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 5 and width of 1
Write an equation to determine the area, A, of the patio that will be painted.
Answer:
Answer: A = (x + 20)(x + 10) − 12 is the correct answer
Step-by-step explanation:
We would take the length and width of the patio and subtract it by the area that does not need to be painted.
I got this right on the test!
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Step-by-step explanation:
The number of years of education of self-employed individuals in the U.S. has a population mean of 13.6 years and a population standard deviation of 3.0 years. If we survey a random sample of 100 self-employed people to determine the average number of years of education for the sample, what is the mean and standard deviation of the sampling distribution of x-bar (the sample mean)? Enter your answers below to one decimal place, e.g. 0.1.
Answer:
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
The mean is given by:
[tex] \bar X = 13.6[/tex]
And the deviation is given by:
[tex]\sigma_{\bar X} =\frac{3}{\sqrt{100}}= 0.3[/tex]
Step-by-step explanation:
For this case we define the random variable X as "number of years of education of self-employed individuals in the U.S." and we know the following properties:
[tex] E(X) = 13.6 , Sd(X) = 3[/tex]
And we select a sample of n = 100
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
Solution to the problem
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
The mean is given by:
[tex] \bar X = 13.6[/tex]
And the deviation is given by:
[tex]\sigma_{\bar X} =\frac{3}{\sqrt{100}}= 0.3[/tex]
Answer:
a) Mean of the sampling distribution = 13.6 years
b) Standard deviation of the sampling distribution = 0.3
[tex]\bar {x} = N(13.6, 0.3)[/tex]
Step-by-step explanation:
Population mean, [tex]\mu = 13.6 years[/tex]
Population standard deviation, [tex]\sigma = 3.0 years[/tex]
Sample size, n = 100
a) Mean of the sampling distribution = mean of the normal distribution
[tex]\mu_{s} = \mu\\\mu_{s} = 13.6 years[/tex]
b) Standard deviation of the sampling distribution, [tex]\sigma_{s} = \frac{\sigma}{\sqrt{n} }[/tex]
[tex]\sigma_{s} = \frac{3}{\sqrt{100} } \\\sigma_{s} = \frac{3}{10} \\\sigma_{s} = 0.3[/tex]
Mollie is training for a race. She will swim, bike and run during the race. One week, she swims 1 2/4 miles and bikes 22 3/4 miles. She also runs during rhe week. The total distance she swims, bikes, and runs during the week is 30 2/4 miles. How far does she run during the week?
Sari Tagore obtains a $1000 loan to purchase a laser printer. Her interest rate is 7% ordinary interest for 108 days.
Answer: the interest owed is $21
Step-by-step explanation:
The question is incomplete. The complete question is:
Sari Tagore obtains a $1000 loan to purchase a laser printer. Her interest rate is 7% ordinary interest for 108 days. What is the interest owed?
Solution:
When calculating ordinary interest, we assume that a year has 360 days. We would apply the formula for determining simple interest which is expressed as
I = PRT/100
Where
I represents interest paid on the loan
P represents principal or amount borrowed.
R represents interest rate
T represents duration in years
From the information given,
P = 1000
R = 7%
T = 108 days. Converting to years, it becomes 108/360
Therefore
I = (1000 × 7 × 108/360)/100
I = $21
The box show the weights in pounds of the dogs in two different animal shelters. Which describes the spread of the data in the two box plots?
Answer: A ( the data in shelter A show more spread than the data in shelter B )
Step-by-step explanation:
Answer: A
Step-by-step explanation: shelter A
The basketball team scored a total of 79 points last game. They made 35 shots, including 2-point shots and 3-point shots. How many 2-point shots did they make? How many 3-point shots did they make?
The number of 2-point shots and the number of 3-point shots if, The basketball team scored a total of 79 points last game, They made 35 shots, including 2-point shots and 3-point shots, are 26 and 9 respectively.
What is the equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
The basketball team scored a total of 79 points last game,
They made 35 shots, including 2-point shots and 3-point shots,
Write the equation as shown below,
x + y = 35
2x + 3y = 79
Here, x is the number of 2-point shots and y is the number of 3-point shots,
Solve the equation by elimination method,
y = 9, x = 35 - 9 = 26
Thus, the number of 2-point shots is 26 and the number of 3-point shots is 9.
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25t - 87.5 = 12.5
What is the answer
8-35. Use your knowledge of polygons to answer the questions below, if possible.
hapter 1
a. How many sides does a polygon have if the sum of the measures of the interior angles is 1980°? 900°?
hapter 2
b. If the exterior angle of a regular polygon is 90°, how many sides does it have? What is another name for this shape?
c. Each interior angle of a regular pentagon has measure 2x + 4°. What is x? Explain how you found your answer.
hapter 3
apter 4
apter 5
apter 6
apter 7
d. The measures of four of the exterior angles of a pentagon are 57, 74, 56, and 66. What is the measure of the remaining angle?
e. Find the sum of the interior angles of an 11-gon. Does it matter if it is regular or not?
The number of sides of a polygon can be determined from the total interior angle or each exterior angle. The interior angle measures of a regular polygon can be used to find unknown quantities. The sum of the interior angles in an 11-gon is 1620° regardless of whether it is regular or irregular.
Explanation:a. The sum of the interior angles of a polygon is given by the formula (n-2) * 180°, where n is the number of sides. To find the number of sides, you rearrange the formula to n = (sum of angles/180) + 2. For 1980°, n = (1980/180) + 2 = 13. For 900°, n = (900/180) + 2 = 7.
b. The sum of the exterior angles of any polygon is always 360°. If each exterior angle is 90°, divide 360 by 90 to get 4. This polygon has 4 sides, so it's a square.
c. In a regular pentagon, each interior angle is 108°. So, if 2x + 4 = 108°, solve for x to find x = 52°.
d. The sum of the exterior angles of a polygon is also 360°. If four of them are 57, 74, 56, and 66, add these up and subtract from 360 to find the remaining angle. It's 107°.
e. The sum of the interior angles of an 11-gon (n = 11) is (11-2) * 180 = 1620°. This is the same whether the polygon is regular or not.
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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x, y, z) = x2y2z2; x2 + y2 + z2 = 4
Final answer:
To find the extrema of the function f(x, y, z) = x²y²z² subject to the constraint x² + y² + z² = 4, one must apply the method of Lagrange multipliers and solve for the critical points that satisfy both the original function and the constraint.
Explanation:
To find the maximum and minimum values of the function f(x, y, z) = x²y²z² subject to the constraint x² + y² + z² = 4 using Lagrange multipliers, we need to set up the Lagrange function, also known as the Lagrangian, which incorporates the original function and the constraint. The Lagrangian for this problem is L(x, y, z, λ) = x²y²z² + λ(4 - x² - y² - z²), where λ is the Lagrange multiplier.
We then take the partial derivatives of L with respect to x, y, z, and λ and set them equal to zero:
∂L/∂x = 2xyz² - 2xλ = 0
∂L/∂y = 2xy²z - 2yλ = 0
∂L/∂z = 2xyz² - 2zλ = 0
∂L/∂λ = 4 - x² - y² - z² = 0
By solving this system of equations, we can find the values of x, y, z, and λ that maximize or minimize the function f under the given constraint.
To rationalize the denominator of StartFraction 5 minus StartRoot 7 EndRoot Over 9 minus StartRoot 14 EndRoot EndFraction , you should multiply the expression by which fraction?
A. StartFraction 5 + StartRoot 7 EndRoot Over 9 minus StartRoot 14 EndRoot EndFraction
B. StartFraction 9 minus StartRoot 14 EndRoot Over 9 minus StartRoot 14 EndRoot EndFraction
C. StartFraction 9 + StartRoot 14 EndRoot Over 9 + StartRoot 14 EndRoot EndFraction
D. StartFraction StartRoot 14 EndRoot Over StartRoot 14 EndRoot EndFraction
Answer:
[tex](C)\dfrac{9+\sqrt{14} }{9+\sqrt{14} }[/tex]
Step-by-step explanation:
To rationalize the expression:
[tex]\dfrac{5-\sqrt{7} }{9-\sqrt{14} }[/tex]
In order to rationalize any Surdic expression, what is needed is to multiply both the numerator and the denominator of the rational function by the conjugate of the denominator.
In the example above:
The denominator is: [tex]9-\sqrt{14}[/tex]
Its conjugate therefore is: [tex]9+\sqrt{14}[/tex]
Therefore, we multiply the fraction by the expression:
[tex]\dfrac{9+\sqrt{14} }{9+\sqrt{14} }[/tex]
Answer:
c
Step-by-step explanation:
Most alpine skiers and snowboarders do not use helmets. Do helmets reduce the risk of head injuries? A study in Norway compared skiers and snowboarders who suffered head injuries with a control group who were not injured. Of 578 injured subjects, 96 had worn a helmet. Of the 2992 in the control group, 656 wore helmets. STATE: Is helmet use less common among skiers and snowboarders who have head injuries? Follow the four‑step process to answer the questions about this study. (Note that this is an observational study that compares injured and uninjured subjects. An experiment that assigned subjects to helmet and no‑helmet groups would be more convincing.) PLAN: Let p1 and p2 be the proportion of injured skiers and snowboarders who wear helmets and the proportion of uninjured skiers and snowboarders who wear helmets, respectively. Select the correct hypotheses for your test.
This problem can be solved by Conducting a Chi-square test for independence to explore the relationship between helmet usage and head injuries. We state our null and alternative hypotheses, then we carry out our plan by calculating the observed and expected counts, the test statistic, and the p-value. The conclusion is drawn based on the computed p-value.
Explanation:The purpose of this analysis is to see if there is a relationship between the use of helmets and head injuries in skiers and snowboarders. In this case, we are dealing with two categorical variables: injury status (injured or not injured) and helmet use (helmet used or not). This falls under the field of statistics in math, specifically, Chi-square test for independence is appropriate here.
Step 1 - STATE: We're comparing the proportion of helmet users among skiers and snowboarders who have head injuries (p1) with the proportion of helmet users among uninjured skiers and snowboarders (p2). The null hypothesis is that the two proportions are equal, i.e., p1 = p2, while the alternative is that they are not equal, i.e., p1 ≠ p2.
Step 2 - PLAN: We are to use a Chi-square test for independence to investigate if helmet use is independent of injury status.
Step 3 - SOLVE: Calculate the observed and expected counts, the test statistic, and the p-value. The observed counts are given in the problem: 96 out of 578 injured subjects used helmets and 656 out of 2992 uninjured subjects used helmets. Expected counts and the test statistic would require a detailed calculation that isn’t shown here.
Step 4 - CONCLUDE:
The conclusion depends on the computed p-value. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that helmet use is less common among skiers and snowboarders who have head injuries. However, bear in mind that correlation does not imply causation, and this is an observational study, not an experiment.
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Find f(127)
f(x) = 8 /143 – x
Answer:
C 32
Step-by-step explanation:
[tex]f(x) = 8 \sqrt{143 - x} \\ f(127) = 8 \sqrt{143 - 127} \\ f(127) = 8 \sqrt{16} \\ f(127) = 8 \times 4 \\ \huge \red{ \boxed{ f(127) = 32}}[/tex]
What two numbers multiply to -36 and add to 5
Answer: 9 and -4
Step-by-step explanation:
9 and 4 are both factors of 36, however we want to multiply to -36 so one of them must be a negative.
The two must also add up to 5, so that means -9 and 4 would not work as those would add to -5, leaving 9 and -4 left as the answer.
The value of two numbers multiply by -36 and added to 5 would be - 36 and 5.
Used the concept of the equation that states,
Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that,
The multiplication of two numbers = - 36
The addition of two numbers = 5
Let us assume that the two numbers are x and y.
Hence the equations become,
x + y = 5 .. (i)
And, xy = - 36 .. (ii)
From (i);
x = 5 - y
Substitute the above value in (ii);
(5 - y)y = - 36
5y - y² = - 36
y² - 5y - 36 = 0
y² - (9 - 4)y - 36 = 0
y² - 9y + 4y - 36 = 0
y (y - 9) + 4 (y - 9) = 0
(y + 4) (y - 9) = 0
This gives,
y = - 4
y = 9
Substitute both the values in (i);
Put x = - 4
x - 4 = 5
x = 9
Put x = 9;
x + 9 = 5
x = - 4
Therefore, the two numbers are 9 and - 4.
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Y=4x+6
Y=3x+19
What is the x coordinate of the solution to the system(s)
A) 13
B) 58
C) -13
D) -13
Answer: A.13
Step-by-step explanation:
The number of blogs (or weblogs) grew rapidly for several years. According to one report, since early 2004 the number of blogs has doubled in size every six months.
What is the percentage increase from March 2004 to March 2006?
Answer:
1500%
Step-by-step explanation:
From March 2004 - March 2006, this is 2 years. The number of "6-month" period there are in 2 years is:
2* 12 = 24 months
24/6 = 4 "6 month periods"
So, it doubles "4" times in that time frame.
Let Initial population be 100 (In March 2004).
1 times double = 100 * 2 = 200
2 times double = 200 * 2 = 400
3 times double = 400 * 2 = 800
4 times double = 800 * 2 = 1600
So, population goes from 100 to 1600. How much percentage increase is that?
To get percentage increase, we find the increase and divide by original (initial amount). Then multiply by 100 to get percentage. So,
1600 - 100 = 1500 increase
1500/100 = 15
15 * 100 = 1500%
Percentage increase in the number of blogs from March'04 to March'06 will be 1500%.
Exponential growth function: Exponential growth function is given by,
[tex]P(t)=P_0(1+r)^t[/tex]
Here, [tex]P(t)=[/tex] Final value
[tex]P_0=[/tex] Initial value
[tex]r=[/tex] Growth rate
[tex]t=[/tex] Period of 6 months
Given in the question,
"Number of blogs are doubled in every six months"
[tex]P(t)=2P_0[/tex]
[tex]2P_0=P_0(1+r)^1[/tex]
2 = (1 + r)
r = 1 Or 100%
Therefore exponential function will be,
[tex]P(t)=P_0(2)^t[/tex]
To find the increase in blogs from March 2004 to March 2006,
Number of six monthly periods in 2 years = 4
[tex]P(4)=P_0(2)^4[/tex]
P(4) = 16(P₀)
Percentage increase in blogs = [tex]\frac{P(4)-P_0}{P_0}\times 100[/tex]
[tex]=\frac{16P_0-P_0}{P_0}\times 100[/tex]
= 1500%
Therefore, percentage increase in the number of blogs will be 1500%.
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Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produ confidence interval
we are 95% confident that a randomly selected taxi fare will be between S2051 and S2421
95% of all taxi fares are between S2051 and S2421
We are 95% confident that the average tau fare between Logan Airport and downtown Boston will fall between S2051 and S2421.
The mean amount of a taxi fare is S22.31, 95% of the time
Answer:
Step-by-step explanation:
Hello!
The variable of the study is
X: taxi fare from Logan Airport to downtown Boston.
This variable has a normal distribution
Suppose a sample of 7 taxi fares was taken and a 95%CI for the population mean was calculated obtaining:
$[20.51; 24.21]
The confidence level is a way of estimating the value of a population parameter of interest just like the point estimation. The difference is that instead of obtaining one value that may or may not be close to the true value of the parameter you obtain the range of values the parameter may take with a certain level of confidence.
The confidence level of an interval is the probability under which it is built. This probability indicates that if they build 100 confidence intervals, we expect 95 to contain the value of the parameter of interest we are trying to estimate.
As mentioned before in this case the parameter of interest is:
μ: population mean of taxi fares from Logan Airport to downtown Boston
And the 95% CI can be interpreted as:
We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.
I hope this helps!