Answer:
For this case we have the following info related to the time to prepare a return
[tex] \mu =90 , \sigma =14[/tex]
And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. 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]
And the standard deviation would be:
[tex]\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2[/tex]
And the best answer would be
b. 2 minutes
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
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".
Solution to the problem
For this case we have the following info related to the time to prepare a return
[tex] \mu =90 , \sigma =14[/tex]
And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. 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]
And the standard deviation would be:
[tex]\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2[/tex]
And the best answer would be
b. 2 minutes
A report on the U.S. economy indicates that 28% of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities judged to be especially economically depressed and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities? What are the correct null and alternative hypotheses for testing such a claim?
Answer:
For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:
NUll hypothesis: [tex]p \leq 0.28[/tex]
Alternative hypotheis: [tex] p >0.28[/tex]
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Solution to the problem
For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:
NUll hypothesis: [tex]p \leq 0.28[/tex]
Alternative hypotheis: [tex] p >0.28[/tex]
Sergio weighed 2.9 kg at birth. Convert this to grams.
Answer:
2900g
Step-by-step explanation:
1kg=1000g
2.9(1000)
=2900g
Round your answer to the nearest hundredth.
Step-by-step explanation:
cosB=4/5
B=36.86°
Hope it helps u
Use the data table provided to calculated the values requested below. Provide all answers to three decimal places.
Has at least 1 child Has no children Total
Supports bans 1739 3089 4828
Does not support bans 746 1142 1888
Total 2485 4231 6716
1. Conditional proportion of support for the ban among those with at least one child: ________
2. Conditional proportion of support for the ban among those with no children: __________
3. Difference in proportion of supporters for the ban between those with at least one child and those with no children (at least 1 child - no children): ___________
4. Relative risk of supporting the ban for those with at least one child compared to those with no children: _________
Answer:
1) 0.700
2) 0.730
3) 0.030
4) 0.959
Step-by-step explanation:
1) proportion of support for the ban with at least one child =
[tex]\frac{no of support atleast 1 child}{Total no of atleast 1 child\\}[/tex]
= [tex]\frac{1739}{2485}[/tex]
= 0.700
2) proportion of support for the ban with no child =
= [tex]\frac{no of support with no child}{Total of no child}[/tex]
= [tex]\frac{3089}{4231}[/tex]
= 0.730
3) Difference in proportion of supporters for the ban between those with atleast one child and those with no child
= 0.700 - 0.730
= -0.03
4) Relative risk = [tex]\frac{proportion with atleast on child}{proportion with no child}[/tex]
= [tex]\frac{0.700}{0.730}[/tex] = 0.959
Credit card balances follow a nearly normal distribution with a mean of $2,900 and a standard deviation of $860. A local credit union believes their customers are carrying an above average credit card balance, so they carry out a study to determine their customers' debt. If the study results in a standard error of $43, what sample size was used in the study
Answer:
A sample size of 400 was used in the study.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation(standard error) [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, we have that:
[tex]\sigma = 860, s = 43[/tex]
We have to find n.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]43 = \frac{860}{\sqrt{n}}[/tex]
[tex]43\sqrt{n} = 860[/tex]
[tex]\sqrt{n} = \frac{860}{43}[/tex]
[tex]\sqrt{n} = 20[/tex]
[tex](\sqrt{n})^{2} = 20^{2}[/tex]
[tex]n = 400[/tex]
A sample size of 400 was used in the study.
Gianna bought some new bracelets for $29.99 and a sales tax of $2.40 was added to the cost. What was the sales tax rate (percent)? Round to the nearest percent.
Answer:
8% is the final answer.
Step-by-step explanation:
(2.4/29.99)x100
=0.08x100
=8%
A teaching assistant collected data from students in one of her classes to investigate whether study time per week (average number of hours) differed between students in the class who planned to go to graduate school and those who did not. Complete parts (a) through (C). Data Full data set Graduate school: 13, 7, 15, 10, 5, 5, 2, 3, 12, 16, 15, 39, 8 14, 10, 17, 3, 27, 15, 5, 5 No graduate school: 6, 8, 14, 6, 5, 13, 10, 10, 13, 5 Find a 95% confidence interval comparing the population means. Interpret. Find a 95% confidence interval comparing the population means. The 95% confidence interval for (mu _1 - mu _2) is (1.6, 7.0) (Round to the nearest tenth as needed.)
The given 95% confidence interval of (1.6, 7.0) for the difference between the average weekly study times (mu_1 - mu_2) means we are 95% confident that students planning to attend graduate school study between 1.6 to 7 hours more per week on average than those who do not.
Explanation:The teaching assistant is comparing the average weekly study times between students intending to go to graduate school and those who are not with the use of data. The relevant statistical concept in this context is the confidence interval for the difference in population means.
The given 95% confidence interval for the difference between the average weekly study times (mu_1 - mu_2) is (1.6, 7.0). This interval was calculated from the provided data, and it provides a statistical estimation that, in this context, means we are 95% sure that students who plan to attend graduate school study between 1.6 to 7 hours more per week on average compared to those who do not plan to go to graduate school.
To interpret this, you can say that we are 95% confident that the true difference in average weekly study times between the two groups falls within this interval. As the entire interval is positive, we may infer that those planning for graduate school likely study more on average than their peers not planning for graduate school.
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1x2x2x2..........50=50!
Martha’s annual salary last year was $72,000. What was her gross pay each month?
Answer:
$6000
Step-by-step explanation:
so she made 72000 in a year, a year as 12 months so to find the monthly rate we just need to divide 72000 by 12 which gives 6000
Answer:
The Correct answer is 6000
Step-by-step explanation:
All you do is divide all the months in a year by how much she got paid to find salary.
Based on the graph of an exponential function f(x)=b^x, for b >0, describe how you can verify that the output of the function can NEVER be equal to zero.
Answer:
see the explanation
Step-by-step explanation:
we know that
The equation of a exponential growth function is given by
[tex]f(x)=a(b^x)[/tex]
where
a is the initial value or y-intercept
b is the factor growth (b>0)
In this problem
a=1
so
[tex]f(x)=b^x[/tex]
we know that
The graph of the function has no x-intercept
Remember that the x-intercept of a function is the value of x when the value of the function is equal to zero
That means ----> The output of the function can NEVER be equal to zero
Verify
For f(x)=0
[tex]0=b^x[/tex]
Apply log both sides
[tex]log(0)=xlog(b)[/tex]
Remember that
log 0 is undefined. It's not a real number, because you can never get zero by raising anything to the power of anything else.
Final answer:
Exponential functions with a positive base can never output zero due to their growth pattern.
Explanation:
Exponential functions of the form f(x) = b^x, where b is greater than 0, never output zero.
To verify this, consider that any positive number raised to any power will never result in zero, as it will approach zero but never reach it. For example, 2^x will grow rapidly but never touch zero. This property holds true for all exponential functions with a positive base.
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Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 12.
Answer:
35/36
Step-by-step explanation:
total outcome: 6 x 6 = 36
getting 12: 1/36
getting less than 12: 1 - 1/36 = 35/36
Answer:
35/36
Step-by-step explanation:
The sum can be between 2 and 12.
P(sum < 12) = 1 - P(sum = 12)
Sum = 12: (6,6)
P(sum < 12) = 1 - 1/36
35/36
equation of a line that has a slope of -2 and passes through the point (-1,8)
Answer:
y= -2x +6
Step-by-step explanation:
Since we have a point, and the slope, we can use the point slope formula
[tex]y-y_{1} =m(x-x_{1} )[/tex]
m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point
In this case, m is -2, y1 is 8, and x1 is -1, so we can substitute them in
y-8= -2(x--1)
Now, we need to solve for y
y-8=-2(x+1)
Distribute the -1
y-8= -2x-2
Add 8 to both sides
y= -2x +6
Over which interval on the x-axis is there a negative rate of change in the function?
–2 to –1
–1.5 to 0.5
0 to 1
0.5 to 1.5
Answer:
A -2 to -1
Step-by-step explanation:
> (889 x 27) + 50 is __
than 889 x 27
+27 more
+
50 less
• 27 less
27 less
50 more
Answer:
50 is more than 27
Step-by-step explanation:
27 comes before 50
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.3 minutes and a standard deviation of 2.6 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
Answer:
a) 0.6062
b) 0.9505
c) 0.679
Step-by-step explanation:
The customer service center in a large new york department store has determined tha the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.3 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be
(a) less than 10 minutes?
(b) longer than 5 minutes?
(c) between 8 and 15 minutes?
a) The Z score (z) is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex],
Where:
μ is the mean = 9.3 minutes,
σ is the standard deviation = 2.6 minutes and x is the raw score
[tex]z=\frac{x-\mu}{\sigma}=\frac{10-9.3}{2.6}=0.27[/tex]
From the z tables, P(X < 10) = P(z < 0.27) = 0.6062 = 60.62%
b) The Z score (z) is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex],
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-9.3}{2.6}=-1.65[/tex]
From the z tables, P(X > 5) = P(z > -1.65) = 1 - P(z < -1.65) = 1 - 0.0495 = 0.9505 = 95.05%
c) For 8 minutes
[tex]z=\frac{x-\mu}{\sigma}=\frac{8-9.3}{2.6}=-0.5[/tex]
For 15 minutes
[tex]z=\frac{x-\mu}{\sigma}=\frac{15-9.3}{2.6}=2.19[/tex]
From the z tables, P(8< X < 15) = P(-0.5 < z < 2.19) = P(z < 2.19) - P(z< -0.5) = 0.9875 - 0.3085 = 0.679 = 67.9%
The question pertains to finding a probability concerning the time taken to resolve a customer's complaint. The time follows a normal distribution with a mean of 9.3 minutes and a standard deviation of 2.6 minutes. We need to calculate the Z-score with the required time, mean and standard deviation, which can then be referenced on a standard normal distribution table to find the probability.
Explanation:The question is about finding the probability of the time spent with a customer in a Customer Service Center of a department store in New York, given that the time that is spent follows a normal distribution with a mean of 9.3 minutes, and a standard deviation of 2.6 minutes.
To calculate this, we'll use the standard normal distribution, Z-score, which standardizes the distribution. The Z-score is a measure of how many standard deviations an element is from the mean. It can be calculated by using the formula: Z = (X - μ) / σ
where X is the time about which we want to find the probability, μ is the mean, and σ is the standard deviation.
Unfortunately, the exact time (X) you want to find the probability for was not provided in your question. However, assuming X to be a given time, t, you substitute t, 9.3 (the mean), and 2.6 (the standard deviation) into the formula to get a Z-score. Then, by referencing the Z-score on a standard normal distribution table, you can find the probability for a complaint taking at an amount of time, t, to be resolved.
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Many variants of poker are played with both cards in players’ hands and shared community cards. Players’ hand are some combination of the two sets of cards. For parts (a) and (b), consider playing such that Anna, Brad, Charlie, and Dre each have 2 cards for themselves, and build a 5 card hand out of those 2 cards and 3 shared cards. Assume a standard 52-card deck is being used.
What is the probability that Anna has a flush, where her 2 cards and the 3 community cards share a suit?
Answer:
Step-by-step explanation:
Given that Anna has a flush, this means that the three shared cards and the 2 cards with Anna has the same suit, therefore given this condition the probability that Brad also has a flush is computed here as:
= Probability that Brad has the same suit cards as those shared cards and Anna
= Probability that Brad selected 2 cards from the 8 cards remaining of that suit
= Number of ways to select 2 cards from the 8 cards of that same suit / Total ways to select 2 cards from the remaining 47 cards
= 0.0259
Therefore 0.0259 is the required probability here.
the little calculation is shown in the picture attached
What is the slope of the line shown on the graph?
a 5/4
b 4/5
c -5/4
d -4/5
Answer:
B
Step-by-step explanation:
Take 2 points and use the slope formula
The 2 points: (0,0) and (5,4)
The slope formula is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{2} }[/tex]
We can say (0,0) is our first point, and (5,4) is our second, and substitute them in. y2 is 4, y1 is 0, x2 is 5, and x2 is 0.
[tex]m=\frac{4-0}{5-0}[/tex]
[tex]m=\frac{4}{5}[/tex]
So, the slope if 4/5, or choice B
i need points please if i have 0 and you give me 10 then how much do i have?
Answer:
10 :/
Step-by-step explanation:
If you have 0 and I give you 10, then you have 10 because 0+10 is 10.
You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of x. If two or more points share the same value of x, list those points starting with the smallest value of y. If any blanks are unused, type an upper-case "N" in them. Point 1: (x,y)= ( , )
Answer:
The solutions listed from the smallest to the greatest are:
x: [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: -1 1 -1 1
Step-by-step explanation:
The slope of the tangent line at a point of the curve is:
[tex]m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
[tex]m = -\frac{\cos 2\theta}{\sin \theta}[/tex]
The tangent line is horizontal when [tex]m = 0[/tex]. Then:
[tex]\cos 2\theta = 0[/tex]
[tex]2\theta = \cos^{-1}0[/tex]
[tex]\theta = \frac{1}{2}\cdot \cos^{-1} 0[/tex]
[tex]\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]
[tex]\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]
The first four solutions are:
x: [tex]\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: 1 -1 1 -1
The solutions listed from the smallest to the greatest are:
x: [tex]-\sqrt{2}[/tex] [tex]-\sqrt{2}[/tex] [tex]\sqrt{2}[/tex] [tex]\sqrt{2}[/tex]
y: -1 1 -1 1
Using derivatives of the parametric curves and the solving a trigonometric equation, it is found that the points (x,y) are:
[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
Given two parametric curves x(t) and y(t), the slope of the tangent line is given by:
[tex]m = \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
The tangent line is horizontal for:
[tex]\frac{dy}{dt} = 0, \frac{dx}{dt} \neq 0[/tex]
In this problem, since we are working with trigonometric functions sine and cosine, they will never be simultaneously 0, hence, the equation of interest is:
[tex]\frac{dy}{dt} = 0[/tex]
Then:
[tex]y(t) = \sin{2\theta}[/tex]
[tex]\frac{dy}{d\theta} = 2cos{2\theta}[/tex]
Hence:
[tex]2\cos{2\theta} = 0[/tex]
[tex]\cos{2\theta} = 0[/tex]
[tex]\cos{2\theta} = \cos{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]2\theta = \frac{k\pi}{2}[/tex]
[tex]\theta = \frac{k\pi}{4}, k = 1, 3, 5, \cdots[/tex]
Hence, the points (x,y) are:
[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]
[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]
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A clothing store is having a sale on shirts and jeans.Five shirts and 3 pairs jeans cost $220. Six shirts and 2 pairs of jeans cost $200. How much is the cost of one shirt? How much is the cost of pair of jeans?
Answer:
Shirt: $20
Trouser: $40
Step-by-step explanation:
5x + 3y = 220
6x + 2y = 200
3x + y = 100
y = 100 - 3x
5x + 3(100 - 3x) = 220
5x + 300 - 9x = 220
4x = 80
x = 20
y = 100 - 3(20)
y = 40
The cost of a shirt is $20 and the cost of pair of a jeans is $40.
Given that, five shirts and 3 pairs of jeans cost $220. Six shirts and 2 pairs of jeans cost $200.
We need to find the cost of one shirt and the cost of pair of jeans.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1.
A linear equation in two variables is of the form Ax + By + C = 0, in which A, B, and C are real numbers and x and y are the two variables, each with a degree of 1. If we consider two such linear equations, they are called simultaneous linear equations.
Let the cost of a shirt be x and the cost of pair of jeans be y.
Now, five shirts and 3 pairs of jeans cost $220.
That is, 5x+3y=220------(1)
Six shirts and 2 pairs of jeans cost $200.
6x+2y=200------(2)
Multiplying the equation (1) with 2, we get 10x+6y=440------(3)
Multiplying the equation (2) with 3, we get 18x+6y=600------(4)
Now, equation (4)-(3) is 8x=160
⇒x=$20
Substitute x=20 in equation (1), we get 5(20)+3y=220
⇒y=$40
Therefore, the cost of a shirt is $20 and the cost of pair of a jeans is $40.
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What is the factored expression of 6k+21?
A. 3(2k+6)
B. 3(k+6)
C. 3(2k+7)
Answer:
the answer is C. 3(2k + 7) i hope this helps! :)
Step-by-step explanation:
trying to find 6k + 21
given 3(2k + 6)
distribute the 3 to both inside the parenthesis 6k + 18
given 3(k + 6)
distribute the 3 to both inside the parenthesis 3k + 18
given 3(2k + 7)
distribute the 3 again to both inside of the parenthesis 6k + 21
Answer:
C. 3(2k+7)
Step-by-step explanation:
you should mark me brainliest lol
If you deposit $5,000 into an account that pays 4% simple interest, what will the balance be in 6 years?
Answer:
$6,200 i hope this helps! :)
Step-by-step explanation:
the 4% interest of the $5000 4% of 5000 = 200
multiply by 6 for the 6 years 200 * 6 = 1200
add the 1200 to the 5000 5000 + 1200 = 6,200
In a certain power plant it was found necessary to store some water in a vertical tank 5 inches in diameter and 10 ft. long at a temperature of 200 degrees F. When the water temperature dropped to 125 degrees F it was necessary to replenish the tank with hot water. Observations showed that it cooled 10 degrees F in 1 hour 15 minutes at an outside temperature of 75 degrees F. How long will it take to cool to 125 degrees F when the 100 drop in 1.25 hours occurs with the initial water temperature of 2000 F.
Answer:
It takes approximately 13.737 hours for the 200 degree water to cool down to 125 degrees.
Step-by-step explanation:
Recall Newton's Law of heating and cooling for an object of initial temperature [tex]T_0[/tex], in an ambient temperature [tex]T_a[/tex]:
[tex]T(t)=T_a+(T_0-T_a)\,e^{-kt}[/tex]
where t is the time elapsed.
We know the ambient temperature and the initial temperature of the object, but we don't know the value of the constant "k" that describes the cooling process. We can obtain such value (k) by using the information that the 200 degrees water cooled 10 degrees in 1.25 hours.
In such case we have:
[tex]T(t)=T_a+(T_0-T_a)\,e^{-kt}\\200-10=75+(200-75)\,e^{-k(1.25)}\\190=75+125\,e^{-k(1.25)}\\190-75=125\,e^{-k(1.25)}\\115=125\,e^{-k(1.25)}\\\frac{115}{125}= e^{-k(1.25)}\\0.92=e^{-k(1.25)}\\ln(0.92)=-k\,(1.25)\\k=\frac{ln(0.92)}{-1.25} \\k=0.0667[/tex]
Therefore, we have now the complete expression for the cooling process:
[tex]T(t)=75+125\,e^{-0.0667\,t}[/tex]
To find the time it takes to cool the 200 degree water down to 125 degrees, we use:
[tex]125=75+125\,e^{-0.0667\,t}\\125-75=125\,e^{-0.0667\,t}\\50=125\,e^{-0.0667\,t}\\\frac{50}{125} =e^{-0.0667\,t}\\0.4=e^{-0.0667\,t}\\ln(0.4)=-0.0667\,\,t\\t=\frac{ln(0.4)}{-0.0667} \\t=13.737\,\,hours[/tex]
It is estimated that the total time Americans will spend on taxes this year is 7.8 billion hours! According to the White House budget office, tax work accounts for approximately 80% of the paperwork burden of the federal government. If 7.8 billion hours is 80% of the total time spent on federal government paperwork, how many hours are equivalent to 50% of the total time spent on federal government paperwork?
Answer:
4.875 billion hours
Step-by-step explanation:
-Let X be the total time spent on taxes and 7.8 billion (80%) is time on paper work.
#We equate and cross multiply to get the total time on taxes:
[tex]0.8=7.8\\1=X\\\\\therefore X=\frac{1\times 7.8}{0.8}\\\\\\=9.75[/tex]
-let y be the 50% amount of time spent. we equate to find it in actual hours:
[tex]1=9.75\\0.5=y\\\\y=\frac{9.75\times 0.5}{1}\\\\=4.875[/tex]
Hence, 50% of the time is equivalent to 4.875 billion hours
-2/7х=-1/3, срочно(если что это дроби)
To solve the equation -2/7x=-1/3 for x, you would divide both sides by -2/7. This translates to multiplication of -1/3 by the reciprocal of -2/7 which is -7/2. By performing this multiplication, x equals to 7/6.
Explanation:The equation at question here is -2/7x=-1/3. To solve for x, we need to isolate x on one side of the equation. To do this, we can divide both sides of the equation by -2/7, which is the coefficient of x in the equation. Performing this operation (also known as the division property of equality), we get:
x = (-1/3) ÷ (-2/7)
When we divide by a fraction, it's the same as multiplying by its reciprocal, so:
x = (-1/3) * (-7/2)
Performing this multiplication gives x = 7/6.
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Model Price ($) Model Price ($) Retail Outlet Deluxe Standard Retail Outlet Deluxe Standard 1 39 27 5 40 30 2 39 29 6 39 35 3 46 35 7 35 29 4 38 31 The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10.
To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.
Explanation:To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.
The null hypothesis (H0) is that the mean difference is equal to $10, while the alternative hypothesis (Ha) is that the mean difference is not equal to $10.We calculate the sample mean difference and the standard deviation of the differences.We calculate the t-statistic using the formula: t = (sample mean difference - hypothesized mean difference) / (standard deviation of the differences / sqrt(n)), where n is the number of pairs of observations.We compare the t-statistic to the critical value from the t-distribution with n-1 degrees of freedom at a significance level of 0.05.If the absolute value of the t-statistic is greater than the critical value, we reject the null hypothesis and conclude that the mean difference is not equal to $10. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean difference is not equal to $10.smaller and larger solution
(x+6)(-x+1)=0
Answer:
x = -6,1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Use a series to estimate the following integral's value with an error of magnitude less than 10 Superscript negative 5. Integral from 0 to 0.5 sine x squared dx Integral from 0 to 0.5 sine x squared dxalmost equals nothing (Do not round until the final answer. Then round to five decimal places as needed.)
Answer:
Hey Tamia,
the answer is 0.4969564
Please rate me as brainiest as the answer explanation is in attached picture, which will clear every step.
Thanks
Step-by-step explanation:
To estimate the integral within an error rate, use the power series expansion of sin(x) to construct an equivalent series for sin(x²). Add terms until the error is less than [tex]10^{-5}[/tex]. Integrate each term from 0 to 0.5.
Explanation:To estimate the value of the integral ∫ from 0 to 0.5 sin(x²) dx with an error of magnitude less than 10^-5, we can use a power series expansion of sin(x). The power series expansion is given as sin(x) = x - x³/3! + x⁵/5! - x⁷/7! + .... Now since we are interested in sin(x²), we just replace x in the above series with x²: sin(x²) = x² - (x²)³/3! + (x²)⁵/5! - (x²)⁷/7! + .... This series can be truncated at any term, and the remaining terms would represent the error in your approximation. We keep adding terms until we reach an error less than [tex]10^{-5}[/tex]. Finally, integrate term by term from 0 to 0.5 to get the approximate value of the original integral.
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Describe how you would find 24+ 36 using mental math
To solve 24+36 using mental math, break it down into simpler steps. First, add 20 + 30 = 50. Then, add 4 + 6 = 10. Finally, combine 50 + 10 to get 60.
Explanation:To solve the equation 24+36 using mental math, you can break it down into simpler steps. First, add the tens together: 20 + 30 = 50. Then add the remaining units: 4 + 6 = 10. Finally, combine these results: 50 + 10 = 60. Therefore, 24 + 36 equals 60 when using mental math strategies.
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(Photo attached) Trig question. Please explain and thanks in advance! :)
Answer:
0.2036
Step-by-step explanation:
u = arcsin(0.391) ≈ 23.016737°
tan(u/2) = tan(11.508368°)
tan(u/2) ≈ 0.2036
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You can also use the trig identity ...
tan(α/2) = sin(α)/(1+cos(α))
and you can find cos(u) as cos(arcsin(0.391)) ≈ 0.920391
or using the trig identity ...
cos(α) = √(1 -sin²(α)) = √(1 -.152881) = √.847119
Then ...
tan(u/2) = 0.391/(1 +√0.847119)
tan(u/2) ≈ 0.2036
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Comment on the solution
These problems are probably intended to have you think about and use the trig half-angle and double-angle formulas. Since you need a calculator anyway for the roots and the division, it makes a certain amount of sense to use it for inverse trig functions. Finding the angle and the appropriate function of it is a lot easier than messing with trig identities, IMO.