Answer:
If [tex]K[/tex] is a constant of integration, then
[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]
Step-by-step explanation:
According to the information of the problem we know that
[tex]{\displaystyle \frac{dP}{dt} = P(a-bP) }[/tex]
Remember that in general a Bernoulli equation is an equation of the type
[tex]y' + p(x)y = q(x)y^n[/tex]
And the idea to solve the equation is to substitute
[tex]{ \displaystyle v = y^{1-n}}[/tex]
Now for this case
[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]
Then we substitute
[tex]v = P^{1-2} = P^{-1}[/tex]
Therefore
[tex]P = v^{-1}[/tex]
and if you compute the derivative of that you get that
[tex]{\displaystyle \frac{dP}{dt} = -v^{-2} \frac{dv}{dt}}[/tex]
Now you substitute that onto the original equation and get
[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]
[tex]{\displaystyle -v^{-2} \frac{dv}{dt} - v^{-1} = -bv^{-2}[/tex]
If you multiply everything by [tex]-v^2[/tex] you get that
[tex]{\displaystyle \frac{dv}{dt} + v = b }[/tex]
That's a linear differential equation and the solution would be
[tex]v = {\displaystyle \frac{b}{a} + Ke^{-at}} = P^{-1}[/tex]
Where [tex]K[/tex] is a constant of integration, then
[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]
The given logistic equation is a Bernoulli equation, which can be solved using a substitution of variables method.
Explanation:The given differential equation is a Bernoulli equation, which is a nonlinear first-order ordinary differential equation of the form dy/dx = P(x)y + Q(x)y^n, where n is a constant. To solve it, we can use a substitution of variables by setting y = u^(1-n). Applying this substitution to the logistic equation, we get du/dx = (1-n)a*u + (1-n)b*u^(2-n), which can be solved using separation of variables method.
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The National Assessment of Educational Progress (NAEP) gives a math assessment every year to 12th graders in the U.S. On the math test, a score above 275 indicates that a student has the skills to balance a checkbook. For a random sample of 500 young men, the mean NAEP math score is 272 with a standard deviation of 78. Do we have evidence to support the claim that young men nationwide have a mean score below 275? The null and alternative hypotheses are H 0: μ = 275, H a: μ < 275. The level of significance is 5%. The t-test statistic is −0.86 with a P-value of 0.20. What is the correct conclusion? Group of answer choices The evidence suggests that young men nationwide have a mean score less than 275. We do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide. The evidence suggests that young men nationwide have a mean score equal to 275. It is likely that these 500 young men have a mean score less than 275.
We do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide.
Explanation:The null hypothesis (H0) is that the mean NAEP math score for young men nationwide is 275. The alternative hypothesis (Ha) is that the mean score is less than 275. The level of significance is 5%.
The t-test statistic is -0.86 and the p-value is 0.20. Since the p-value is greater than the significance level (0.20 > 0.05), we fail to reject the null hypothesis. This means we do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide.
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Consider the graph of the quadratic function y = 2(x + 3)2 – 3 with two real zeros. What number can be added to the right side of the equation to change it to a function with one real zero?.
Answer: 3
Step-by-step explanation:
Answer: I am pretty sure it is 3 but I apologize if it is incorrect.
Step-by-step explanation:
Find the measure of x
A. x=2
B. x = 6
C. x=8
D. X=10
Answer:
x = 6º
Step-by-step explanation:
120º = 15(x + 2)
120 = 15x + 30
15x = 120 - 30
15x = 90
x = 90/15
x = 6º
The measure of x is 6°, which corresponds to option B: x = 6, using the property of parallel lines.
We can observe that the given lines are parallel cut by a transversal.
So, the angles 120° and 15(x + 2) are alternate exterior angles which are equal.
So, 120° = 15(x + 2)
To find the value of x:
1. Start by isolating the variable x on one side of the equation.
Subtract 30 from both sides to move the constant term to the other side:
120° - 30° = 15(x + 2) - 30°
2. Simplify the equation:
90° = 15(x + 2)
3. Now, divide both sides of the equation by 15 to solve for x:
(90°) / 15 = (15(x + 2)) / 15
4. Calculate:
90° / 15 = 6°
So, x = 6°.
Therefore, the correct answer is: B. x = 6.
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8 people share 1 pizza. How much each person receive ?
Answer:
1
Step-by-step explanation:
because one pizza is cut into 8 so
1 piece would be even
=1
The amount of pizza received by each person is 0.125.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The number of pizza is 1.
And, the total number of people is 8.
Now, the share of each people can be obtained as follows,
Consider that each people get the equal share.
The arithmetic operation used in this case is division.
Then, the problem can be solved by dividing 1 by 8 as follows,
⇒ 1 ÷ 8 = 1/8 = 0.125
The result of the division is a decimal number which shows that the amount of pizza for each people is the smallest part less than the whole.
Hence, the share of pizza received by each person is 0.125.
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Solve for v.
7(v-3)+7v = 21
Simplify your answer as much as possible.
Answer:
v = 3
Step-by-step explanation:
7(v - 3) + 7v = 21
distribute the 7 into the parentheses
7v -21 +7v = 21
combine like terms
14v - 21 = 21
add 21 on both sides
14v + 21 - 21 = 21 + 21 which equals 14v = 42
divide both sides by 14 to isolate v
14v/14 = 42/14
v = 3
hope this helps :)
Senior management of a consulting services firm is concerned about a growing decline in the firm’s weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the management randomly selected a sample of size 50 from the available frame. The sample mean and sample standard deviations were 46.4 and 7.2 hours, respectively. Construct a 97% confidence interval for the standard deviation of the number of hours this firm’s employees spend on work-related activities in a typical week
With 97% confidence, we estimate that the true standard deviation of the firm's employees' work hours lies within the range of approximately 5.832 to 7.950 hours per week.
To construct a 97% confidence interval for the standard deviation [tex](\(\sigma\))[/tex], we use the chi-square distribution. The formula for the confidence interval is given by:
[tex]\[ \left( \sqrt{\frac{(n-1)s^2}{\chi_{\alpha/2}^2}}, \sqrt{\frac{(n-1)s^2}{\chi_{1-\alpha/2}^2}} \right) \][/tex]
where [tex]\(n\)[/tex] is the sample size, [tex]\(s\)[/tex] is the sample standard deviation, [tex]\(\alpha\)[/tex]is the significance level, and [tex]\(\chi_{\alpha/2}^2\)[/tex] and [tex]\(\chi_{1-\alpha/2}^2\)[/tex] are the chi-square critical values.
Given that [tex]\(n = 50\)[/tex] , [tex]\(s = 7.2\)[/tex] , and [tex]\(\alpha = 0.03\)[/tex] (97% confidence level corresponds to [tex]\(\alpha/2 = 0.015\))[/tex] , we look up the critical values from the chi-square distribution table. For 49 degrees of freedom (50-1), the critical values are approximately 31.449 and 71.420.
Substitute these values into the formula:
[tex]\[ \left( \sqrt{\frac{49 \times 7.2^2}{31.449}}, \sqrt{\frac{49 \times 7.2^2}{71.420}} \right) \][/tex]
The formula for the confidence interval is:
[tex]\[ \left( \sqrt{\frac{(n-1)s^2}{\chi_{\alpha/2}^2}}, \sqrt{\frac{(n-1)s^2}{\chi_{1-\alpha/2}^2}} \right) \][/tex]
Given:
[tex]\[ n = 50, \ s = 7.2, \ \alpha = 0.03 \][/tex]
For 49 degrees of freedom (50-1), the chi-square critical values are approximately 31.449 [tex](\(\chi_{\alpha/2}^2\))[/tex] and 71.420 [tex](\(\chi_{1-\alpha/2}^2\))[/tex] .
Now, substitute these values into the formula:
[tex]\[ \left( \sqrt{\frac{49 \times 7.2^2}{31.449}}, \sqrt{\frac{49 \times 7.2^2}{71.420}} \right) \][/tex]
Calculating this yields approximately (5.832, 7.950).
Therefore, the 97% confidence interval for the standard deviation of the weekly work hours is approximately (5.832, 7.950).
In summary, with 97% confidence, we estimate that the true standard deviation of the firm's employees' work hours lies within the range of approximately 5.832 to 7.950 hours per week.
A recent Gallup poll found that 36% of U.S. teens aged from 13 to 17 years old have a computer with [(6)] Internet access in their rooms. The poll was based on a random sample of 1028 teens. (a) In words, determine the population parameter, p, that this sample is estimating. [1] (b) Produce a 99% confidence interval for the population proportion, p, and interpret what it means in [3] this context. Round your answers to three decimals. (c) How big of a sample must we take in order to ensure that we are within 1% of the true proportion [2] with 99% confidence
Answer:
Step-by-step explanation:
a) The population parameter is the population proportion.
b) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 1028
p = 36/100 = 0.36
q = 1 - 0.36 = 0.64
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.99 = 0.1
α/2 = 0.01/2 = 0.005
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.995
The z score corresponding to the area on the z table is 2.58. Thus, confidence level of 99% is 2.58
Therefore, the 99% confidence interval is
0.36 ± 2.58 × √(0.36)(0.64)/1028
The lower limit of the confidence interval is
0.36 - 0.039 = 0.321
The upper limit of the confidence interval is
0.36 + 0.039 = 0.399
Therefore, with 99% confidence interval, the proportion of U.S. teens aged from 13 to 17 years old that have a computer with Internet access in their rooms is between 0.321 and 0.399
c) for a margin of error of 1%, that is 1/100 = 0.01, then
0.01 = 2.58 × √(0.36)(0.64)/n
0.01/2.58 = √0.2304/n
0.00387596899 = √0.2304/n
Square both sides
0.00001502314 = 0.2304/n
n = 0.2304/0.00001502314
n = 15336
A study of the effect of exposure to color (red or blue) on the ability to solve puzzles used 42 subjects. Half the subjects (21) were asked to solve a series of puzzles while in a red-colored environment. The other half were asked to solve the same series of puzzles while in a blue-colored environment. The time taken to solve the puzzles was recorded for each subject. The 21 subjects in the red-colored environment had a mean time for solving the puzzles of 9.64 seconds with standard deviation 3.43; the 21 subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.65.
The two-sample t statistic for comparing the population means has value _____ (± 0.001).
Answer:
The two-sample t statistic for comparing the population means is -3.053.
Step-by-step explanation:
We are given that the time taken to solve the puzzles was recorded for each subject.
The 21 subjects in the red-colored environment had a mean time for solving the puzzles of 9.64 seconds with standard deviation 3.43; the 21 subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.65.
Let [tex]\mu_1[/tex] = average time taken to solve the puzzle in red-colored environment.
[tex]\mu_2[/tex] = average time taken to solve the puzzle in blue-colored environment.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that there is no difference in time taken to solve both the puzzles}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex] {means that there is difference in time taken to solve both the puzzles}
The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_-_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample average time for solving the puzzles in the red-colored environment = 9.64 seconds
[tex]\bar X_2[/tex] = sample average time for solving the puzzles in the blue-colored environment = 15.84 seconds
[tex]s_1[/tex] = sample standard deviation for red-colored environment = 3.43 seconds
[tex]s_2[/tex] = sample standard deviation for blue-colored environment = 8.65 seconds
[tex]n_1[/tex] = sample of subjects in the red-colored environment = 21
[tex]n_2[/tex] = sample of subjects in the blue-colored environment = 21
Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(21-1)\times 3.43^{2}+(21-1)\times 8.65^{2} }{21+21-2} }[/tex] = 6.58
So, test statistics = [tex]\frac{(9.64-15.84)-(0)}{6.58 \sqrt{\frac{1}{21}+\frac{1}{21} } }[/tex] ~ [tex]t_4_0[/tex]
= -3.053
The value of two-sample t test statistics is -3.053.
Find all nth roots. Write your answers in polar form.
−√2+i√2, n=5
Answer:
help me and I will help you
The amount of chill is _ times the amount of cream cheese
Answer:
6 Chili / 3 cream cheese = 2 Timeschilli compared to cream cheese.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
There are 6 for chilli and 3 for cream cheese.
3 *2 is 6, there fore it is 2 times as much
Hope this is helpful! :)
Order the numbers from least to greatest typical number of hours of sleep per employee
Answer:What?
Step-by-step explanation:
How is the graph of y =(x-1)2 - 3 transformed to produce the graph of y = 5(X+4)??
The graph is translated left 5 units, compressed vertically by a factor of 5, and translated up 3 units.
The graph is stretched vertically by a factor of 3, translated left 5 units, and translated up 3 units
The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units
The graph is stretched horizontally by a factor of 2, translated left 5 units, and translated down 3 units
Answer:
The graph is translated left 5 units, compressed vertically by a factor of 5, and translated up 3 units.Step-by-step explanation:
The initial function is
[tex]y=(x-1)^{2} -3[/tex]
The transformed function is
[tex]y=5(x+4)^{2}[/tex]
Notice that the first function represents a parabola with vertex at (1, -3), and the secong function represents a parabola with vertex at (-4, 0). That means the function was shifted three units up and 5 units to the left. Additionally, the function was compressed by a scale factor of 5, because that's the coffecient of the quadratic term.
Therefore, the right answer is the first choice.
Answer:
A.
Step-by-step explanation:
The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.
If g(x) = x square - 2x + 11, find g(-2)
Answer:
g(-2) = 19
Step-by-step explanation:
g(x) = x ^2 - 2x + 11,
Let x= -2
g(-2) = (-2)^2 -2(-2) +11
= 4 +4 +11
=19
Answer:
-2
Step-by-step explanation:
what’s the value of x?
Answer:
D
Step-by-step explanation:
Answer:
x = 29.1m
Step-by-step explanation:
X= 71 x =
Y = y = 28.2 m
Z = z = 20.9 m
[tex]x^{2} = y^{2} + z^{2} - 2yz cos x\\(28.2 )^{2} + (20.9)^{2} - 2(28.2 )(20.9) cos (71)\\795.24 + 436.81 - 1178.76cos(71)\\1232.05 - 1178.76 cos (71)\\{1232.05-383.767}\\\\\sqrt{x^{2} } = \sqrt{1232.05 - 383.767}\\ x = 29.1[/tex]
Jesse has 252 inches of string how many yards of string does he have
Answer:
7 yards
Step-by-step explanation:
252/12=21 21/3=7
8300 dollars is placed in an account with an annual interest rate of 6.5%. How much
will be in the account after 14 years, to the nearest cent?
Answer:
(About) 20043.46 after 14 years
Step-by-step explanation:
~ Let us apply a compound interest formula not through substituting values, but through a similar way of following this formula ~
1. First let us assign the values:
interest ⇒ 6.5 percent ( % ), principle number - start value ⇒ $ 8300, time ⇒ 14 years
2. Now let us convert interest ⇒ decimal form: 0.065
3. Add 1 to this value 0.065 ⇒ 1 + 0.065 = 1.065
4. Now let us take 1.065 exponentially to the power of itself 14 times, or in other words to the power of time ( 14 years ): 1.065^ 14 = 2.414874185.......
5. Multiply this infinite number by the principle number P, or most commonly known as the start value: 2.414874185....... * 8300 ⇒
(About) 20043.46 after 14 years
Using the formula for compound interest and substituting accordingly, the given investment grows to approximately 18,108.80 dollars after 14 years.
Explanation:To solve this, we'll use the formula for compound interest, which is P(1 + r/n)^(nt), where P is the principle amount (initial investment), r is the annual interest rate, n is the number of times that interest is compounded per unit t, and t is the time the money is invested for.
In this case, P = 8300 dollars, r = 6.5/100 = 0.065 (we need the rate in decimal form), n = 1 (since the interest is given annually), and t = 14 years.
Substitute these values into the formula:
A = 8300(1 + 0.065/1)^(1*14) which simplifies to A = 8300(1.065)^14.
Using a calculator, A ≈ 18,108.80 dollars. So, after 14 years, the account will have approximately 18,108.80 dollars.
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Mr. Ramirez purchased 20 concert tickets for a total of $225. The concert tickets costs $15 for adults and $10 for children under the age of 12. Write the system of equations and solve algebraically.
Answer:
C = 15
Step-by-step explanation:
Let A = # of adults and C = # of children.
A + C = 20
15A + 10C = 225
There are several ways to solve this system; here is one of them.
From the first equation: C = 20 - A
Substitute into the second equation: 15A + 10(20 - A) = 225
Multiply, collect terms, and subtract 200 from each side: 5A = 25 => A = 5
Since C = 20 - A, C = 15
The number of children's ticket bought is 15 and the number of adult tickets bought is 5.
The system of equations that can be derived from the question are:
a + b = 20 equation 1
15a + 10b = 225 equation 2
Where:
a = number of children's ticket bought
b = number of adult tickets bought
In order to determine the value of b, multiply equation 1 by 15.
15a + 15b = 300 equation 3
Subtract equation 2 from 3
5b = 75
b = 15
In order to determine the value of a, substitute for b in equation 1
a + 15 = 20
a = 20 - 15
a = 5
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What must be true regarding the distribution of the population? A. The population must be normally distributed and the sample size must be large. B. There are no requirements on the shape of the distribution of the population. C. The population must be normally distributed. nothing Your answer is correct.D. Since the sample size is large enough comma the population distribution does not nbsp need to be normal.
Answer:
C. The population must be normally distributed.
Step-by-step explanation:
Population distribution have to do with the classification of people living in a particular geographical area into different segment such as Age, Occupation, Sex, Geographical location.
For instance
If Age distribution is use, the total number of people living in say New york will classified into 0-10 11-19years 20-29years and so on
Sex distribution involves distribution into the male and Female Category
Occupation distribution of Population involves classification of occupant of an area according to their Job.. I.e.Drives-15 people, Lawyer =2 people and so on.
Geographical location distribution of population involves the classification of people living in a particular country according to their geographical names. I.e. Abuja=3.5million people etc.
The requirements on the distribution of the population can vary depending on the analytical methods being used. Some methods require the population to be normally distributed, while others, such as those based on the Central Limit Theorem, can work reliably with large sample sizes regardless of whether the population is normally distributed.
Explanation:In the field of statistics, when you are drawing conclusions or inferences from a dataset (sample), there are different requirements depending on the method used. Generally speaking, the assumption about the distribution of the population can vary.
For instance, if you are using methods based on the Central Limit Theorem (CLT), you might not require the population to be normal if your sample size is sufficiently large, as per option D. This is because the CLT states that if the sample size is large enough, the distribution of the sample means will approximate a normal distribution, regardless of the shape of the population distribution.
However, some analytical methods might require the population to be normally distributed for the method to produce reliable results. So, although there is not a one-size-fits-all answer, the requirements on the distribution of the population depend largely on the analytical methods being used.
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Todos los días, Luna utiliza 12 regaderas de medio litro para regar su jardín. ¿Cuántos litros de agua utiliza al día?
The question in English:
Every day Luna uses 12 half-liter watering cans to water her garden. How many liters of water does she use per day?
Answer:
Español:
Luna utiliza 6 litros de agua al día.
¡Espero que esto ayude!
English:
Luna uses 6 liters of water a day.
Hope this helps!
The amount water used by Luna is equivalent is 6 liters.
What is water?Water is a tiny molecule. It consists of three atoms : two of hydrogen and one of oxygen. Water molecules cling to each other because of a force called hydrogen bonding.
Given is that every day, Luna uses 12 half-liter watering cans to water her garden.
The amount water used by Luna is equivalent to -
A{w} = 1/2 x 12
A{w} = 6 liters
Therefore, the amount of water used by Luna is equivalent is 6 liters.
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{Question in english -
Every day, Luna uses 12 half-liter watering cans to water her garden. How many liters of water she use per day?}
An aquarium manager wants to study gift shop browsing. She randomly observes 120 couples that visit the aquarium with children and finds that 107 enter the gift shop at the end of their visit. She randomly observes 76 couples that visit the aquarium with no children and finds that 59 enter the gift shop at the end of their visit. Find the lower bound of the 95% confidence interval for the difference in population proportions of couples with children that enter the gift sho
Answer:
95% confidence interval for the difference in population proportions of couples with children and with no children is [0.00134 , 0.219].
Step-by-step explanation:
We are given that an aquarium manager wants to study gift shop browsing.
She randomly observes 120 couples that visit the aquarium with children and finds that 107 enter the gift shop at the end of their visit. She randomly observes 76 couples that visit the aquarium with no children and finds that 59 enter the gift shop at the end of their visit.
Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportions is given by;
P.Q. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of couples that visit the aquarium with children who enters the gift shop at the end of their visit = [tex]\frac{107}{120}[/tex] = 0.89
[tex]\hat p_2[/tex] = sample proportion of couples that visit the aquarium with no children who enters the gift shop at the end of their visit = [tex]\frac{59}{76}[/tex] = 0.78
[tex]n_1[/tex] = sample of couples that visit the aquarium with children = 120
[tex]n_2[/tex] = sample of couples that visit the aquarium with no children = 76
Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.
So, 95% confidence interval for the difference between population proportions, is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < [tex]{(\hat p_1-\hat p_2)-(p_1-p_2)}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95
P( [tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < [tex](p_1-p_2)}[/tex] < [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95
95% confidence interval for [tex](p_1-p_2)}[/tex] =
[[tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex],[tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex]]
= [ [tex](0.89-0.78)-1.96 \times {\sqrt{\frac{0.89(1-0.89)}{120}+ \frac{0.78(1-0.78)}{76}} }[/tex] , [tex](0.89-0.78)+1.96 \times {\sqrt{\frac{0.89(1-0.89)}{120}+ \frac{0.78(1-0.78)}{76}} }[/tex] ]
= [0.00134 , 0.219]
Therefore, 95% confidence interval for the difference in population proportions of couples with children and with no children is [0.00134 , 0.219].
PLEASE HELP ME I WILL MARK BRAINLIEST!!!
Answer:
v= 205.3
Step-by-step explanation:
The formula to solve a pyramid is v=(l*h*w)/3.
11*7*8=616
616/3=205.333.... (repeating 3)
about 205.3
~sorry I couldn't draw it out~
We randomly place 200 balls independently in 100 boxes in the most natural uniform way. That is, each ball is placed independently from the rest of the balls in such a way that the probability to put it into the ith box is one-percent (1 ≤ i ≤ 100). Let X denote the number of empty boxes at the end. What is the expected value of X? I also want the numerical value.
Answer:
The expected value of X is 13.4.
Step-by-step explanation:
For each boox any time a ball is placed, there are only two possible outcomes. Either the ball is put into the box, or it is not. The boxes are independent. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
200 balls placed in boxes:
This means that [tex]n = 200[/tex]
For each box, the ball has 1/100 probability of being put there:
This means that [tex]p = \frac{1}{100} = 0.01[/tex]
The probability of a box being empty:
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.01)^{0}.(0.99)^{200} = 0.1340[/tex]
Let X denote the number of empty boxes at the end. What is the expected value of X?
Each box has a 0.1340 probability of being empty at the end.
There are 100 boxes.
So
0.1340*100 = 13.4
The expected value of X is 13.4.
30 points!!!!!!! EASY MATH!!!!!!!!!! PLZ HELP!!!!
f(x)=(x+1)^2
What is the domain of f?
Answer:
Domain: all real values
Step-by-step explanation:
f(x)=(x+1)^2
The domain is the values for x
We can use any value for x in the equation
Domain: all real values
Answer:
All real values of x
Step-by-step explanation:
f(x) = (x + 1)² is defined for all x
Hence the domain includes all real values of x
A random sample of size 13 is selected from men with hypertension. For each person, systolic blood pressure was measured right before and one hour after taking the medicine. The mean reduction of the blood pressures was 10.1 and the standard deviation of the difference was 11.2. Test if there is sufficient evidence to conclude that the hypertension medicine lowered blood pressure. What is the value of the test statistic (round off to second decimal place)
Answer:
Yes, hypertension drugs lowers blood pressure.
Step-by-step explanation:
Claim: The hypertension medicine lowered blood pressure.
The null and alternative hypothesis is
H0:\mu_{d}\geq 0
H1:\mu_{d}< 0
Level of significance = 0.05
Sample size = n = 13
Sample mean of difference = \bar{d} = 10.1
Sample standard deviation of difference = s_{d} = 11.2
Test statistic is
t=\frac{\bar{d}}{s_{d}/\sqrt{n}}
t = ((10.1) / (11.2 /squre root of 13)) = 3.251
Degrees of freedom = n - 1 = 13 - 1 = 12
Critical value =2.179( Using t table)
Test statistic | t | > critical value we reject null hypothesis.
In Conclusion: The hypertension medicine lowered blood pressure
How many times greater is 70 million than 4 million?
Answer:
66 million
Step-by-step explanation:
4 million on 70 million is 66 million
Answer:
17.5
Step-by-step explanation:
hope we can be friends
can i please get brainliest
Complete the square for the expression
x
2
+8x
x2+8x
. Then factor the trinomial.
Answer:
x^2+8x+16
(x+4)^2
Step-by-step explanation:
x^2 +8x
Take the coefficient of the x term
8
Divide by 2
8/2 =4
Square it
4^2 =16
x^2+8x+16
We can factor it into
(x+8/2) ^2
(x+4)^2
Final answer:
Completing the square for the expression x² + 8x involves adding and subtracting 16 to form the perfect square trinomial (x + 4)² and then subtracting 16. The factored form of the resulting trinomial is (x + 4)² - 16.
Explanation:
To complete the square for the expression x² + 8x, we need to find a number that, when added to 8x, will make the expression a perfect square trinomial. The number we're looking for is ²⁄8², which is 16. So, we add and subtract 16 within the expression to maintain equality.
The expression becomes x² + 8x + 16 - 16. Now the first three terms form a perfect square trinomial (x + 4)², and we still have -16. The expression is (x + 4)² - 16.
To factor the trinomial, we write it as the square of a binomial: (x + 4)². Hence, the expression x² + 8x can be written as (x + 4)² - 16, which is the factored form of the trinomial resulting from the completion of the square.
5.62 (6.2+6.2) divided by 2
Look at the attached picture z
⤴
Hope it will help u...
Help anyone can somebody explain the answer please
Answer:
D
Step-by-step explanation:
8^2+x^2=16^2
It takes 15 hours for 4 men to paint a room.
How many men would be needed to paint the room in 10 hours?
Answer:
6
Step-by-step explanation:
If there was one man, he would have taken 15×4= 60 hours
To complete the job in 10 hours, 60÷10 = 6 men will be needed
To paint the room in 10 hours instead of 15, the calculation shows that 6 men would be needed. This is determined through the concept of work rate and inverse proportions, calculating the total man-hours and then dividing by the desired hours.
The question involves determining the number of men needed to paint a room in 10 hours, given it takes 15 hours for 4 men to paint the same room. This problem can be solved using the concept of work rate and inverse proportions, which is a common method in Mathematics to deal with time and work problems. First, we calculate the work rate of the 4 men together and then find how many men would be needed to complete the job in 10 hours at a proportional rate.
Calculation steps:
Identify the original work rate: 4 men take 15 hours.Compute the total man-hours required for the job: 4 men × 15 hours = 60 man-hours.To find the time it would take for an unknown number of men to complete the same task in 10 hours, set up the equation: x men × 10 hours = 60 man-hours.Solving for x gives x = 60 man-hours / 10 hours = 6 men.Therefore, 6 men would be needed to paint the room in 10 hours.
Find the value of x
Answer:
x = 66
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360 degrees
103+133+58+x = 360
Combine like terms
294+x = 360
Subtract 294 from each side
294+x-294 = 360-294
x = 66