Answer:
6 minutes
Step-by-step explanation:
Since it's you have 10 dollars in one hour, and you want to find 1/10th of the dollar value, you'd multiply 1/10th, or 0.1 by the time as well. I converted it into minutes because we're finding a smaller unit of time than 1 hour.
60 min x 1/10 (or 60 min/10)= 6 minutes
I hope this helped!
6 minutes
If it takes 1 hour to earn $10, we convert that 1 hour to 60 minutes. Now we will divide 60 by 10, and that gives you 6. Therefore every 6 minutes you earn $1.
Hope this helps!
Let F = sin ( 8 x + 5 z ) i − 8 y e x z k . F=sin(8x+5z)i−8yexzk. Calculate div ( F ) div(F) and curl ( F ) . and curl(F). (Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answer:
Required results are [tex]\nabla .\vec{F}[/tex]=8\cos(8x+5z)-8ye^x[/tex] and [tex]\nabla\times \vec{F}=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]
Step-by-step explanation:
Given vector function is,
[tex]\vec{F}=\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k}[/tex]
To find [tex]\nabla .\vec{F}[/tex] and [tex]\nabla \times \vec{F}[/tex] .
[tex]\nabla .\vec{F}[/tex]
[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]
[tex]=\frac{\partial}{\partial x}(\sin(8x+5z))-\frac{\partial}{\partial z}(8ye^xz)[/tex]
[tex]=8\cos(8x+5z)-8ye^x[/tex]
And,
[tex]\nabla \times \vec{F}[/tex]
[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})\times(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]
[tex]\end{Vmatrix}[/tex]
[tex]=\uvec{i}\Big[\frac{\partial}{\partial y}(-8ye^xz)\Big]-\uvec{j}\Big[\frac{\partial}{\partial x}(-8ye^xz)-\frac{\partial}{\partial z}(\sin(8x+5z))\Big]+\uvec{k}\Big[-\frac{\partial}{\partial y}(-\sin(8x+5z))\Big][/tex]
[tex]=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]
Hence the result.
The mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100. What is the z-score (value of z) for an income of $1,100
Answer:
The z-score (value of z) for an income of $1,100 is 1.
Step-by-step explanation:
We are given that the mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100.
Let X = group of weekly incomes of a large group of executives
So, X ~ N([tex]\mu=1,000 ,\sigma^{2} = 100^{2}[/tex])
The z-score probability distribution for a normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean income = $1,000
[tex]\sigma[/tex] = standard deviation = $100
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, we are given an income of $1,100 for which we have to find the z-score (value of z);
So, z-score is given by = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{1,100-1,000}{100}[/tex] = 1
Hence, the z-score (value of z) for an income of $1,100 is 1.
The z-score for an income of $1,100 is 1.0.
The z-score is a measure of how many standard deviations a particular value, in this case, income, is from the mean of a normally distributed dataset. The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
x is the value being evaluated.μ is the mean of the distribution.σ is the standard deviation of the distribution.Given the mean (μ) is $1,000 and the standard deviation (σ) is $100, we can substitute these values into the formula to find the z-score of an income of $1,100.
z = ($1,100 - $1,000) / $100
z = $100 / $100
z = 1
Therefore, the z-score for an income of $1,100 is 1.0. This means the income of $1,100 is one standard deviation above the mean.
According to industry sources, online banking is expected to take off in the near future. The projected number of households (in millions) using this service is given in the following table. (Here, x = 0 corresponds to the beginning of 1997.)
Year, x 0 1 2 3 4 5
Households, y 4.5 7.5 10.0 13.0 15.6 18.0
(a) Find an equation of the least-squares line for these data. (Give numbers to three decimal places.)
y(x) =
(b) Use your result of part (a) to estimate the number of households using online banking at the beginning of 2007, assuming the projection is accurate.
Answer:
(a) The least-square regression line is: [tex]y=4.662+2.709x[/tex].
(b) The number of households using online banking at the beginning of 2007 is 31.8.
Step-by-step explanation:
The general form of a least square regression line is:
[tex]y=\alpha +\beta x[/tex]
Here,
y = dependent variable
x = independent variable
α = intercept
β = slope
(a)
The formula to compute intercept and slope is:
[tex]\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \end{aligned}[/tex]
The values of ∑X, ∑Y, ∑XY and ∑X² are computed in the table below.
Compute the value of intercept and slope as follows:
[tex]\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}[/tex]
The least-square regression line is:
[tex]y=4.662+2.709x[/tex]
(b)
For the year 2007 the value of x is 10.
Compute the value of y for x = 10 as follows:
[tex]y=4.662+2.709x[/tex]
[tex]=4.662+(2.709\times10)\\=4.662+27.09\\=31.752\\\approx 31.8[/tex]
Thus, the number of households using online banking at the beginning of 2007 is 31.8.
Consider the function on the interval (0, 2π). f(x) = x − 2 sin x (a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)
Answer:
Increasing:
[tex](\frac{\pi}{3},\frac{5\pi}{3})[/tex]
Decreasing
[tex](0,\frac{\pi}{3})[/tex] U [tex](\frac{5\pi}{3},2\pi)[/tex]
Step-by-step explanation:
Increasing and Decreasing Intervals
To find if a function is increasing in a point x=a, we evaluate the first derivative in x=a and if:
f'(a) >0, the function is increasing f'(a) <0, the function is decreasing f'(a) =0, the function has a critical pointFor continuous functions, we can safely assume between a given critical point and the next one, the function keeps its behavior, i.e. it's increasing or decreasing in the interval formed by both points.
So, we find the critital points of
[tex]f(x)=x-2sinx[/tex]
Taking the derivative
[tex]f'(x)=1-2cosx[/tex]
Equating to 0
[tex]1-2cosx=0[/tex]
Solving
[tex]\displaystyle cosx=\frac{1}{2}[/tex]
There are two solutions in the interval [tex](0,2\pi)[/tex]
[tex]\displaystyle x=\frac{\pi}{3},\ x=\frac{5\pi}{3}[/tex]
Now we compute the second derivative
[tex]f''(x)=2sinx[/tex]
Evaluating for both critical points
[tex]\displaystyle f''(\frac{\pi}{3})=2sin\frac{\pi}{3}=\sqrt{3}[/tex]
Since it's positive, the point is a minimum
[tex]\displaystyle f''(\frac{5\pi}{3})=2sin\frac{5\pi}{3}=-\sqrt{3}[/tex]
Since it's negative, the point is a maximum
In the interval
[tex](0,\frac{\pi}{3})[/tex]
the function is decreasing
In the interval
[tex](\frac{\pi}{3},\frac{5\pi}{3})[/tex]
the function is increasing
In the interval
[tex](\frac{5\pi}{3},2\pi)[/tex]
the function is decreasing
First, you need to find the derivative of the function f(x) = x - 2sin(x).
Using the rules of calculus, the derivative of x is 1 and the derivative of -2sin(x) is -2cos(x). Therefore, the derivative of the function, denoted as f'(x), is given by:
f'(x) = 1 - 2cos(x).
To determine where the function is increasing or decreasing, we need to find the critical points, the x-values where the derivative of the function is equal to zero or undefined.
Setting the derivative equal to zero and solving:
1 - 2cos(x) = 0.
2cos(x) = 1.
cos(x) = 1/2.
The solutions to this equation on the interval 0 to 2π are x = π/3 and x = 5π/3.
With these critical points, we have divided the entire interval into three subintervals:
(0, π/3), (π/3, 5π/3), and (5π/3, 2π).
We now determine the sign of the derivative on each of these intervals. We pick a "test point" from each interval and substitute it into the derivative.
From (0, π/3), we pick x = π/6, and find that f'(π/6) is positive.
From (π/3, 5π/3), we pick x = π, and find that f'(π) is negative.
From (5π/3, 2π), we pick x = 3π/2, and find that f'(3π/2) is positive.
By the First Derivative Test, a positive derivative indicates that the function is increasing on that interval and a negative derivative indicates that the function is decreasing on that interval.
Therefore, the function increases on the intervals (0, π/3) and (5π/3, 2π),
and decreases on the interval (π/3, 5π/3).
#SPJ3
A population of rabbits oscillates 19 above and below average during the year, hitting the lowest value in january. the average population starts at 650 rabbits and increases by 160 each year. find an equation for the population p in terms of the months since january t
The equation we've developed to represent the rabbit population over time, where 't' is the number of months since January, is P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650. This equation covers the oscillations in the population and the steady yearly increase.
Explanation:The subject matter falls under the discipline of Mathematics, particularly in the topics involving functions. We can create a sinusoidal (sine or cosine) function to represent the oscillation of the population of rabbits.
Given that the population fluctuates 19 above and below the average, and the average increases by 160 each year, this suggests a sinusoidal period of 12 months (a year) with a vertical shift (midline) that increases linearly.
Considering t as the number of months since January, the equation for the population P in terms of the months since January t would be:
P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650
The 19 is the amplitude, (2π/12)t - π/2 represents the sinusoidal oscillation adjusted to start at the minimum in January, (160t/12) is the yearly change in population that increases per month, and 650 is the average population at the start.
Learn more about Sinusoidal Functions here:https://brainly.com/question/32049339
#SPJ3
To find the population equation in terms of months since January considering oscillations and growth, use the formula p(t) = 650 + 160t + 19sin(2πt/12).
Population Equation: The equation for the population p in terms of the months since January t can be written as p(t) = 650 + 160t + 19sin(2πt/12). This equation takes into account the initial population of 650 rabbits, an increase of 160 rabbits per year, and the oscillation of 19 above and below the average population.
The fuel tanks on some ships are spheres of which only the top halves are above deck. If one of these tanks is 96 ft in diameter, how many gallons of fuel does it hold? Use
1 ft3 ≈ 7.5 gal
Answer:
720
Step-by-step explanation:
96 * 7.5
The number 0.05891 can be expressed using scientific notation as
Answer:
5.892×10^-2
Step-by-step explanation:
Scientific notation has one digit to the left of the decimal point. To write the number in scientific notation, it can work to start by writing the number with that as one of the factors:
0.05891 = 5.891 × 0.01
= 5.891 × 1/10^2
= 5.891 × 10^-2
__
You can also enter this number into your calculator and change the display mode to SCI.
_____
It helps to understand the decimal place-value number system in terms of the power of 10 that multiplies each number place.
find the area of a rhombus with a perimeter equal to 40 and a diagonal equal to 14 cm.
Answer:
about 100 cm²
Step-by-step explanation:
The side length of the rhombus is 1/4 of the perimeter so is 10 cm. The length of half of the other diagonal will be the length of the leg of a right triangle with hypotenuse 10 and leg 7 (half the given diagonal).
d= √(10² -7²) = √51
Then the area of the rhombus is the product of this and the given diagonal:
A = (14 cm)(√51 cm) ≈ 99.98 cm²
The area of the rhombus is about 100 cm².
The circumference of the inner circle is 88 ft. The distance between the inner circle and the outer circle is 3 ft. By how many feet is the circumference of outer circle greater than the circumference of the inner circle? Use StartFraction 22 Over 7 EndFraction
for pi. (3.14)
Answer:
18.86 feet
Step-by-step explanation:
The circumference of the inner circle is 88 ft.
Circumference of a Circle[tex]=2\pi r[/tex]
Therefore:
[tex]2\pi r =88\\r=88 \div (2*\frac{22}{7})=14 ft[/tex]
Radius of the inner circle=14 feet
If the distance between the inner circle and the outer circle is 3 ft, the radius of the outer circle=14+3 =17 feet.
Therefore. circumference of the outer Circle[tex]=2\pi r[/tex]
[tex]=2*\frac{22}{7}*17=106.86 ft[/tex]
Difference in Circumference=106.86-88 =18.86 feet
The circumference of the outer circle is greater than that of the inner circle by 18.86 feet.
18.9
Step-by-step explanation:
The demand of the computers is surely increasing in recent years. A survey shows that this phenomenon can be calculated by the function D(t) = 23.2sqrt(5 + 2.7t) Here, D represents the demand (measured by millions ) and t the time (measured by years ). It will take years that the demand of the computers reaches 132.2 millions . Round your answer to one decimal point
Answer:
10.2
Step-by-step explanation:
Apparently, you want to find the solution for ...
132.2 = 23.2√(5 +2.7t)
132.2/23.2 = √(5 +2.7t) . . . . divide by 23.2
(132.2/23.2)² = 5 +2.7t . . . . . square both sides
(132.2/23.2)² -5 = 2.7t . . . . . subtract 5
((132.2/23.2)² -5)/2.7 = t . . . . divide by the coefficient of t
10.2 ≈ t
It will take about 10.2 years for the demand for computers to reach 132.2 million.
He purchased $12.00 worth of lemons and $4.00 worth of glasses to make the lemonade.
He adds $0.02 worth of sugar to each glass of lemonade.
He sells each glass of lemonade for $0.25.
What is the minimum number of glasses of lemonade that Michael needs to sell to begin to make a profit?
The student must sell at least 70 glasses of lemonade at $0.25 each, considering the initial costs of $16.00 and the additional $0.02 cost per glass for sugar, to begin to make a profit.
Explanation:To calculate the minimum number of glasses of lemonade that must be sold to start making a profit, we need to consider the total costs and the revenue per glass. The student spent $12.00 on lemons and $4.00 on glasses, totaling $16.00 in costs. Additionally, each glass of lemonade has an added cost of $0.02 for sugar. The revenue from selling one glass of lemonade is $0.25.
To break even, the total revenue must equal the total costs. As costs are fixed at $16.00 and the variable cost is $0.02 per glass, we can set up the equation: (Number of glasses × $0.25) - (Number of glasses × $0.02) = $16.00. This simplifies to (Number of glasses × $0.23) = $16.00, and solving for Number of glasses gives us Number of glasses = $16.00 / $0.23, which is approximately 69.57 glasses. Since you can't sell a fraction of a glass, rounding up means the student needs to sell at least 70 glasses to begin to make a profit.
Graphing Quadratic Equations, if you have a graph, how do you find zeros?
Answer:
look for the x-intercepts
Step-by-step explanation:
A "zero" is a value of x where the function value is zero. On a graph, that point is where the graph meets the x-axis. Every x-intercept is a zero of the function.
__
If there are no x-intercepts, then there are no real zeros. The roots (zeros) will be complex.
3. For the school Band, Marcia decides to order t-shirts for all of the participants. It will
cost $4 per shirt for the medium size and $5 per shirt for the large size. Marcia orders
a total of 70 T-shirts and spends $320. Determine the two linear equations to
represent the information. [4A) **Hint: One equation is for amount of t-shirts and the second is
for money. YOU DO NOT NEED TO SOLVE,
Let x represent number of medium size shirts
Let y represent total large size shirts
Answer:
4x+5y = 320
x+y = 70
Step-by-step explanation:
We need one equation for the total number of shirts, and one for the total cost.
Total number = 70
So that means medium shirts + large shirts = 70
So our first equation is x+y = 70
Total cost = $320
So that means $4 times medium shirts + $5 times large shirts = 320
So our second equation is 4x+5y = 320
1. Heather rode her horse 2 kilometers down the mountain side trail. Hailey rode 1900 meters on her horse on the same trail. Who rode the farthest and how much farther did they ride in kilometers?
Answer:
Heather rode the farthest
She rode 0.1km farther than Hailey.
Step-by-step explanation:
This is a conversion of units question.
Heather rode her horse 2 kilometers.
Hailey rode 1900 meters on her horse.
Each km has 1000 meters.
So 1900 meters = 1900/1000 = 1.9 km
This means that Hailey rode for 1.9 km.
Heather rode the farthest(2km is greather than 1.9km)
2 - 1.9 = 0.1km
She rode 0.1km farther than Hailey.
The number of guppies that a fish tank can safely hold depends on its volume.A fish tank should have a volume of 576 cubic inches to safely hold 3 guppies.how many guppies can a fish tank that is 24 inches long, 12 inches wide, and 16 inches highly safely hold?
Answer:
24 guppies
Step-by-step explanation:
Assuming a linear relationship, the volume required per guppy is given by:
[tex]g=\frac{576\ in^3}{3\ guppies}\\ g= 192\ in^3/guppy[/tex]
The volume of the fish tank is given by the product of its length, by its width and its height:
[tex]V = 24*12*16\\V=4,608\ in^3[/tex]
The number of guppies that this tank can safely hold is:
[tex]n=\frac{V}{g}=\frac{4,608}{192} \\n=24\ guppies[/tex]
The tank can safely hold 24 guppies.
The life span of a battery is the amount of time the battery will last. The distribution of life span for a certain type of battery is approximately normal with mean 2.5 hours and standard deviation 0.25 hour. Suppose one battery will be selected at random. Which of the following is closest to the probability that the selected battery will have a life span of at most 2.1 hours?A:0.055B: 0.110C: 0.445D: 0.890E: 0.945
Answer:
A:0.055
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 2.5, \sigma = 0.25[/tex]
Which of the following is closest to the probability that the selected battery will have a life span of at most 2.1 hours?
This is the pvalue of Z when X = 2.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.1 - 2.5}{0.25}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a pvalue of 0.0548
So the correct answer is:
A:0.055
what is one thousand five hundred divided by five equal
Answer: 300
We know that 5×3=15. Since we are trying to get 1500 we Multiply 300×5 and get 1500.
How do we know?
As you can see if you cross out 2 of the 0 in 300 you have 3×5. When you multiply it you get 15.Also if you cross out 1 of the 0 in 300 you have 30×5. When you multiply that you get 150.As you see when you still multiply either of those problems you have 15 in it. So we should know 300×5=1500.
Note: We can also multiply 500×3 and get 1500. You still get the same answer but just switched numbers.
Answer:
[tex]300[/tex]
Step-by-step explanation:
[tex] \frac{1500}{5} = 300[/tex]
It's very easy to find if you use a calculator.
To know whether that the answer is correct or wrong you can do like this.
[tex]300 \times 5 = 1500[/tex]
hope this helps
thanks.
Which fraction is equivalent to 3/4+1/6
Answer:
1/2
Step-by-step explanation:
Answer:
11/12
Step-by-step explanation:
If you convert 3/4 and 1/6,
you will get 9/12+2/12.
If you add both of them, you will get your answer.
A survey of 1000 air travelers1 found that prefer a window seat. The sample size is large enough to use the normal distribution, and a bootstrap distribution shows that the standard error is . Use a normal distribution to find a 90% confidence interval for the proportion of air travelers who prefer a window seat. Round your answers to three decimal places.
Answer:
90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)
Step-by-step explanation:
We have the following data:
Sample size = n = 1000
Proportion of travelers who prefer window seat = p = 60%
Standard Error = SE = 0.015
We need to construct a 90% confidence interval for the proportion of travelers who prefer window seat. Therefore, we will use One-sample z test about population proportion for constructing the confidence interval. The formula to calculate the confidence interval is:
[tex](p-z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}}, p+z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}})[/tex]
Since, standard error is calculated as:
[tex]SE=\sqrt{\frac{p(1-p)}{n} }[/tex]
Re-writing the formula of confidence interval:
[tex](p-z_{\frac{\alpha}{2}} \times SE, p+z_{\frac{\alpha}{2}} \times SE)[/tex]
Here, [tex]z_{\frac{\alpha}{2}}[/tex] is the critical value for 90% confidence interval. From the z-table this value comes out to be 1.645.
Substituting all the values in the formula gives us:
[tex](0.6 - 1.645 \times 0.015, 0.6 + 1.645 \times 0.015)\\\\ = (0.575, 0.625)[/tex]
Therefore, the 90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)
Steroids, which are dangerous, are sometimes used to improve athletic performance. A study by the National Athletic Trainers Association surveyed random samples of 1679 high school freshmen and 1366 high school seniors in Illinois. Results showed that 34 of the freshmen and 24 of the seniors had used anabolic steroids. Estimate at a 95% confidence level the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois.
Answer:
At 95% confidence level, the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois is -7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237
Step-by-step explanation:
Here we are required to construct the 95% confidence interval of the difference between two proportions
The formula for the confidence interval of the difference between two proportions is as follows;
[tex]\hat{p}_1-\hat{p}_2\pm z^{*}\sqrt{\frac{\hat{p}_1\left (1-\hat{p}_1 \right )}{n_{1}}+\frac{\hat{p}_2\left (1-\hat{p}_2 \right )}{n_{2}}}[/tex]
Where:
[tex]\hat{p}_1 = \frac{34}{1679}[/tex]
[tex]\hat{p}_2 = \frac{24}{1366}[/tex]
n₁ = 1679
n₂ = 1366
[tex]z_{\alpha /2}[/tex] at 95% confidence level = 1.96
Plugging in the values, we have;
[tex]\frac{34}{1679}- \frac{24}{1366} \pm 1.96 \times \sqrt{\frac{ \frac{34}{1679}\left (1- \frac{34}{1679}\right )}{1679}+\frac{\frac{24}{1366} \left (1-\frac{24}{1366} \right )}{1366}}[/tex]
Which gives;
-7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237.
At 95% confidence level, the difference between the proportion of freshmen using steroids in Illinois and the proportion of seniors using steroids in Illinois = -7.01135×10⁻³ < [tex]\hat{p}_1-\hat{p}_2[/tex] < 1.237.
Drains A and B are used to empty a swimming pool. Drain A alone can empty the pool in 4.75 hours. How long will it take drain B alone to empty the pool if it takes 2.6 hours when both drains are turned on?
B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and it takes 2.6 hours when both drains are turned on.
Step-by-step explanation:
The given is,
A alone can empty the pool in 4.75 hours.
It takes 2.6 hours when both drains are turned on.
Step:1
One hour work drains A and B =
One hour work of drain A + One hour work of Drain B.........(1)
One hour work of Drain A = [tex]\frac{1}{4.75}[/tex]
One hour of ( A + B ) = [tex]\frac{1}{2.6}[/tex]
Equation (1) becomes,
One hour work of B = One hour work of ( A + B )
- One hour work of A
Substitute the values,
One hour work of B = [tex]\frac{1}{2.6} - \frac{1}{4.75}[/tex]
= [tex]\frac{4.75-2.6}{(4.75)(2.6)}[/tex]
= [tex]\frac{2.15}{12.35}[/tex]
= [tex]\frac{1}{5.744}[/tex]
One hour work of B = [tex]\frac{1}{5.744}[/tex]
B alone can empty the pool in 5.744 hours
Result:
B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and it takes 2.6 hours when both drains are turned on.
Choose the correct graph of the following condition.
Answer:
the correct graph is pictured below
Step-by-step explanation:
the graph is below
A radioactive substance decays according to the following function, where yo is the initial amount present, and y is the amount present at time t (in days).
y= y_o e^0.072t.
Find the half-life of this substance. Do not round any intermediate computations, and round your answer to the nearest tenth. days
Answer:
[tex]t_{1/2} \approx 9.6\,days[/tex]
Step-by-step explanation:
The time constant of the radioactive constant is:
[tex]\tau = \frac{1}{0.072}\,days[/tex]
[tex]\tau = 13.889\,days[/tex]
The half-life of the substance is:
[tex]t_{1/2} = \tau \cdot \ln 2[/tex]
[tex]t_{1/2} = (13.889\,days)\cdot \ln 2[/tex]
[tex]t_{1/2} \approx 9.6\,days[/tex]
Researchers are interested in whether having an older sibling provides people a model for stable relationships in adolescence. They gather random samples of people with either older siblings or not and measure the number of relationships they have as teenagers. For individuals with no older siblings (N=16), they find an average of 5 relationships (s=1.4) For individuals with older siblings (N=20), they find an average of 3.5 relationships (s=0.8). Test the null hypothesis that the number of adolescent relationships is equal between those with an older sibling and those without (alpha=0.05).
Answer:
Step-by-step explanation:
So, we do not have enough evidence to conclude that the number of adolescent relationships is equal between those with an older sibling and those without.
check the attached file for explanation and solution
Hopefully that’s better :)))
Answer: Top right, a rectangle has all the properties of a square
Step-by-step explanation: A rectangle does not have all the properties of a square.
which expressions are equivalent to 7•7•7•7•7•7
Answer:7^6
Step-by-step explanation:
Answer:
7^6
Step-by-step explanation:
A company receives shipments of a component used in the manufacture of a high-end acoustic speaker system. When the components arrive, the company selects a random sample from the shipment and subjects the selected components to a rigorous set of tests to determine if the components in the shipments conform to their specifications. From a recent large shipment, a random sample of 250 of the components was tested, and 24 units failed one or more of the tests.
a) What is the point estimate of the proportion of components in the shipment that fail to meet the company's specifications?
b) What is the standard error of the estimated proportion?
c) At the 98% level of confidence, what is the margin of error in this estimate?
d) What is the 95% confidence interval estimate for the true proportion of components, p, that fail to meet the specifications?
e) If the company wanted to test the null and alternative hypotheses: H_0: p = 0.10 against H_a: p notequalto 0.10 at the alpha = 0.05 level of significance, what conclusion would they draw?
Step-by-step explanation:
a) 24 / 250 = 0.096
b) Standard error for a proportion is:
σ = √(pq/n)
σ = √(0.096 × 0.904 / 250)
σ = 0.0186
c) At 98% confidence, the critical value is 2.326. The margin of error is therefore:
2.326 × 0.0186 = 0.0433
d) At 95% confidence, the critical value is 1.960. The margin of error is therefore:
1.960 × 0.0186 = 0.0365
So the confidence interval is:
(0.0960 − 0.0365, 0.0960 + 0.0365)
(0.0595, 0.1325)
e) 0.10 is within the 95% confidence interval, so the null hypothesis would not be rejected.
Final answer:
a) The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is 9.6%. b) The standard error of the estimated proportion is 1.9%. c) The margin of error at the 98% confidence level is 4.4%. d) The 95% confidence interval estimate for the true proportion is approximately 5.9% to 13.3%. e) The null hypothesis that the proportion is 0.10 is rejected if the z-test statistic falls outside the range (-1.96, 1.96).
Explanation:
a) Point estimate:
The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is the number of failed components divided by the total number of components tested. In this case, the point estimate is 24/250 = 0.096, or 9.6%.
b) Standard error:
The standard error of the estimated proportion is calculated using the formula SE = sqrt((phat * (1 - phat)) / n), where phat is the point estimate and n is the sample size. In this case, the standard error is sqrt((0.096 * (1 - 0.096)) / 250) = 0.019, or 1.9%.
c) Margin of error:
The margin of error is determined by multiplying the standard error by the appropriate critical value from the standard normal distribution. For a 98% confidence level, the critical value is approximately 2.33. Therefore, the margin of error is 2.33 * 0.019 = 0.044, or 4.4%.
d) Confidence interval:
The 95% confidence interval estimate for the true proportion of components that fail to meet the specifications is given by the formula phat +/- z * SE, where phat is the point estimate, z is the appropriate critical value from the standard normal distribution (for 95% confidence, z is approximately 1.96), and SE is the standard error. Therefore, the confidence interval is 0.096 +/- 1.96 * 0.019, or approximately 0.059 to 0.133.
e) Hypothesis test:
To test the null hypothesis H_0: p = 0.10 against the alternative hypothesis H_a: p != 0.10, we can use a two-tailed z-test. The test statistic is calculated as (phat - p_0) / sqrt((p_0 * (1 - p_0)) / n), where p_0 is the null hypothesis value (0.10), phat is the point estimate, and n is the sample size. The critical value for a significance level of 0.05 is approximately 1.96 from the standard normal distribution. If the test statistic is outside the range (-1.96, 1.96), we reject the null hypothesis. In this case, if the test statistic falls outside the range (-1.96, 1.96), we would reject the null hypothesis and conclude that the true proportion of components that fail to meet the specifications is not 0.10.
Write the equation of the tangent line to the curve x^2/8 - y^2/4 =1 at the point (4,2) by using the following facts. The slope m of the tangent line to a hyperbola at the point (x, y) is: m=b^2x/a^2y for x^2/a^2 -y^2/b^2=1 m=a^2x/b^2y for y^2/a^2 - x^2/b^2 =1
Answer:
[tex]y=x-2[/tex]
Step-by-step explanation:
So we are given the formula for the slope of a hyperbola in this form:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex].
That formula for the slope is [tex]m=\frac{b^2x}{a^2y}[/tex]
If we compare the following two equations, we will be able to find [tex]a^2[/tex] and [tex]b^2[/tex]:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
[tex]\frac{x^2}{8}-\frac{y^2}{4}=1[/tex]
We see that [tex]a^2=8[/tex] while [tex]b^2=4[/tex].
So the slope at [tex](x,y)=(4,2)[/tex] is:
[tex]m=\frac{b^2x}{a^2y}=\frac{4(4)}{8(2)}=\frac{16}{16}=1[/tex].
Recall: Slope-intercept form of a linear equation is [tex]y=mx+b[/tex].
We just found [tex]m=1[/tex]. Let's plug that in.
[tex]y=1x+b[/tex]
[tex]y=x+b[/tex]
To find [tex]b[/tex], the [tex]y[/tex]-intercept, we will need to use a point on our tangent line. We know that it is going through [tex](4,2)[/tex].
Let's enter this point in to find [tex]b[/tex].
[tex]2=4+b[/tex]
Subtract 4 on both sides:
[tex]2-4=b[/tex]
Simplify:
[tex]-2=b[/tex]
The equation for the tangent line at [tex](4,2)[/tex] on the given equation is:
[tex]y=x-2[/tex]
Answer: y = x - 2
Step-by-step explanation:
First you take the derivative of each term. d/dx(x²/8) - d/dx(y²/4) = d/dx(1)
x/4 - (y/2)dy/dx = 0
Then you solve for dy/dx: dy/dx = x/2y
Plug in the values: dy/dx = 1
To find the y-intercept, plug in values for y = mx+ b. 2 = 4 + b, b = -2
The equation is y = x - 2
Use the following to answer question 39: The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what is the probability that students scored less than 60
Answer:
The probability of students scored less than 60 = .0768
Step-by-step explanation:
Given -
Mean score [tex](\nu )[/tex] = 70
standard deviation [tex](\sigma )[/tex] = 7
Let X be the score of students
the probability that students scored less than 60 =
[tex]P(X< 60)[/tex] = [tex]P(\frac{X - \nu }{\sigma}< \frac{60 - 70}{7})[/tex]
= [tex]P(z < \frac{60 - 70}{7})[/tex] put[ Z= [tex]\frac{X - \nu }{\sigma}[/tex]]
= [tex]P(z < -1.428)[/tex] using z table
= .0768
-4x + (-3) =x +3 What is X equivalent to
Answer: x= −6 /5 is the answer
Answer:
x= -1 1/5 or x= -1.2
Step-by-step explanation:
-4x+-3=x+3
-5x-3=3
-5x=6
-x=6/5
x=-6/5
x=-1 1/5
or x=-1.2
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