Answer:
For this case since since they not want to differentiate between the campuses, so is good to use a simple random sampling or SRS, that is a procedure in order to select a sample of size n from a population of size N known, and each element of the population have the sample probability of being selected [tex]p=\frac{1}{N}[/tex]
So then the administrator can select a random sample of n students from all the campuses from the CSU University and obtain the distance from hometwon to campuses for the selected sample and then calculate the average and use this to inference.
Other possibility is use a systematic random sampling for example they can define a random number k and they can select 1 student each k individuals and then create a random sample of size n and calculate the average for this in order to do inference.
The convenience sampling is not too useful since is not a probabilistic method.
Step-by-step explanation:
For this case we can clasify this study as an enumerative study and inferential since they want to identify the average distance between the hometowns of students and their campuses.
For this case the sampling frame represent all the 23 campuses, and is known for the researcher,
For this case since since they not want to differentiate between the campuses, so is good to use a simple random sampling or SRS, that is a procedure in order to select a sample of size n from a population of size N known, and each element of the population have the sample probability of being selected [tex]p=\frac{1}{N}[/tex]
So then the administrator can select a random sample of n students from all the campuses from the CSU University and obtain the distance from hometwon to campuses for the selected sample and then calculate the average and use this to inference.
Other possibility is use a systematic random sampling for example they can define a random number k and they can select 1 student each k individuals and then create a random sample of size n and calculate the average for this in order to do inference.
The convenience sampling is not too useful since is not a probabilistic method.
Different sampling methods that can be employed to estimate the average distance between CSU student hometowns and their campuses include Simple Random Sampling, Stratified Random Sampling, Cluster Sampling, and Systematic Sampling. Each has its own advantages and potential drawbacks.
Explanation:There are several sampling methods that can be employed to gauge the average distance between student hometowns and their respective California State University (CSU) campuses.
A Simple Random Sampling method could be applied, where every student from every campuse has the exact same chance of being selected. However, this method may not give a representative sample if certain campuses have more or less students than others.
Another method is Stratified Random Sampling, where students are first divided into groups or 'strata' based on their campus, and then random samples are taken from each stratum. This ensures a balanced sample from all campuses.
Then comes the Cluster Sampling, it divides the student population into 'clusters' based on their hometown, and then randomly selected clusters are surveyed. It would be useful for large-scale surveys.
Last is Systematic Sampling. In this method, every nth student on a list would be selected. This approach ensures evenly distributed selection of students across the whole population but requires a complete listing of all students at the CSU campuses.
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Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = 25x and y = x2 25 . Find V by slicing.
Answer:
[tex]volume\ = \pi \frac{625^2}{6}[/tex]
Step-by-step explanation:
See the attached figure.
y₁ = 25x and y₂ =x²
The intersection between y₁ and y₂
25x = x²
x² - 25x = 0
x(x-25) = 0
x = 0 or x =25
y = 0 or y =25² = 625
The points of intersection (0,0) and (25,625)
To find the volume of the solid obtained by rotating about the y-axis the region bounded by y₁ and y₂
y₁ = 25x ⇒ x₁ = y/25 ⇒ x₁² = y²/625
y₂ =x² ⇒ x₂ = √y ⇒ x₂² = y
v = ∫A(y) dy = π ∫ (x₂² - x₁²) dy
∴ V =
[tex]\pi \int\limits^{625}_0 {y-\frac{y^2}{625} } \, dy =\pi( \frac{y^2}{2} -\frac{y^3}{3*625} ) =\pi (\frac{625^2}{2} -\frac{625^3}{3*625}) =\pi ( \frac{625^2}{2}-\frac{625^2}{3}) =\pi \frac{625^2}{6}[/tex]
To find the volume of the solid formed by rotating the region bounded by y = 25x and y = x²25 about the y-axis, one needs to calculate the area of a typical slice, then integrate this area over the range of x-values.
Explanation:To find the volume V of the solid obtained by rotating the region bounded by y = 25x and y = x225 about the y-axis, we can apply the method of slicing.
First, we need to find the area A(x) of a typical slice perpendicular to the x-axis. Here we have two functions, finding the x- values where these functions intersect gives the bounds on the integral for the volume.
We can find the area A(x) = pi*(outer radius)2 - pi*(inner radius)2 = pi[(25x)ˆ2 - (xˆ2 * 25)ˆ2].
To find V, we integrate A(x) over the interval of x-values. This will give us the exact volume of the solid.
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A person walks in the following pattern: 2.4 km north, then 1.9 km west, and finally 4.7 km south. (a) How far and (b) at what angle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point?
Answer:
a) Figure attached
b) For this case w have that A =(2.4 km)j, B= (-1.9 km) i , C= (-4.7 km)j
And the final position vector can be calculated adding the 3 vectors like this:
[tex] s = A +B+C[/tex]
[tex] s= (-1.9 km)i +(2.4 -4.7 km) j= (-1.9km)i + (-2.3 km)j[/tex]
We can find the magnitude of s like this:
[tex] |s| = \sqrt{(-1.9)^2 +(-2.3)^2}=2.983[/tex]
And then we can find the angle with this formula:
[tex] \theta = \tan^{-1} (\frac{-2.3 km}{-1.9 km})=50.44 [/tex]
The other possibility is [tex] \theta = 50.44+180 =230.44[/tex]
And since they want the angle measured from East the correct angle would be [tex] \theta = 230.44[/tex]
Step-by-step explanation:
Part a
On the figure attached we have the vectors for the pattern described.
Part b
For this case w have that A =(2.4 km)j, B= (-1.9 km) i , C= (-4.7 km)j
And the final position vector can be calculated adding the 3 vectors like this:
[tex] s = A +B+C[/tex]
[tex] s= (-1.9 km)i +(2.4 -4.7 km) j= (-1.9km)i + (-2.3 km)j[/tex]
We can find the magnitude of s like this:
[tex] |s| = \sqrt{(-1.9)^2 +(-2.3)^2}=2.983[/tex]
And then we can find the angle with this formula:
[tex] \theta = \tan^{-1} (\frac{-2.3 km}{-1.9 km})=50.44 [/tex]
The other possibility is [tex] \theta = 50.44+180 =230.44[/tex]
And since they want the angle measured from East the correct angle would be [tex] \theta = 230.44[/tex]
Can some body pls help me
Answer:
Step-by-step explanation:
The diagram consists of different boxes if the same sizes. Each box is a square with sides measuring 1 cm. The area of each box would be
1 × 1 = 1cm^2
The area of the parallelogram is the total number of squares that it contains. To determine this, the first step is to count the total number of complete squares. Looking at the diagram, there are 11 complete squares. This means
11 × 1 = 11 square units.
The next step is to count the number of incomplete squares and divide by 2. The number of incomplete squares are 8
8/2 = 4
4 × 1 = 4 square units
The area of the parallelogram would be
11 + 4 = 15 square units
the absolute value of a complex number z=a+bi, denoted |z|, is given by the formula
|z|=square root a^2+b^2.
find six distinct complex numbers (which are neither purely imaginary nor purley real) such that each has an absolute value of 7.
Step-by-step explanation:
You need to find six combinations of a and b such that a² + b² = 7.
a = 1, b = √6
a = √2, b = √5
a = √3, b = 2
a = 2, b = √3
a = √5, b = √2
a = √6, b = 1
Suppose x x represents the value of some varying quantity. As the value of x x varies from 3.5 to 8.
What is the change in the value of x x?
Answer: The change in the value of x would be : [tex]\Delta x=4.5 [/tex] .
Step-by-step explanation:
We know that if y represents the value of some varying quantity, then as the value of y varies from p to q.
The change in the value of y is given by :-
[tex]\Delta y=q-p[/tex] [Next value - previous value]
Given : x represents the value of some varying quantity.
So , As the value of x varies from 3.5 to 8.
The change in the value of x is given by :-
[tex]\Delta x=8-3.5=4.5 [/tex]
Hence, the change in the value of x would be : [tex]\Delta x=4.5 [/tex]
Sarah inherited a sum of 1,539 dollars with an interest rate of 1% per year what is the accrued value after 5 years, 10 years, and 15 years. Show all work.
Answer:
The accrued value after 5 years is $1,605.95.
The accrued value after 10 years is $1,672.9.
The accrued value after 15 years is $1,739.85.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex].
In this problem, we have that:
[tex]P = 1539, I = 0.01[/tex]
Accrued value after 5 years
This T when t = 5. So
[tex]E = P*I*t[/tex]
[tex]E = 1339*0.01*5 = 66.95[/tex]
The total is
[tex]T = E + P = 66.95 + 1539 = 1605.95[/tex]
The accrued value after 5 years is $1,605.95.
Accrued value after 10 years
This T when t = 10. So
[tex]E = P*I*t[/tex]
[tex]E = 1339*0.01*10 = 133.9[/tex]
The total is
[tex]T = E + P = 133.9 + 1539 = 1672.9[/tex]
The accrued value after 10 years is $1,672.9.
Accrued value after 15 years
This T when t = 15. So
[tex]E = P*I*t[/tex]
[tex]E = 1339*0.01*15 = 200.85[/tex]
The total is
[tex]T = E + P = 200.85 + 1539 = 1739.85[/tex]
The accrued value after 15 years is $1,739.85.
which is the equation of a libe that has a slope of 1/2 and passes through (2,-3)
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
The slope is given as 1/2 and the line passes through (2, - 3)
To determine the intercept, we would substitute x = 2, y = - 3 and m= 1/2 into y = mx + c
y = mx + c. It becomes
- 3 = 1/2 × 2 + c = 1 + c
c = - 3 - 1 = - 4
The equation becomes
y = x/2 - 4
New drug strategies have centered on cholesterol ______ statins. Select one:
a. lowering b. raising c. destroying d. improving
Answer: lowering
Step-by-step explanation:
Statins are drugs that are administered in order to help reduce cholesterol level in the body. Statins achieves this by making it impossible for the body to have access to substances that helps to produce cholesterol. This drug reduces cholesterol up to 50% and are taken once every day. Examples includes rosuvastatin, pitavastatin, simvastatin.
Let S = {2,4,6} and T = {1,3,5}. Use the set-roster notation to write each of the following sets, and indicate the number of elements that are in each set?
a. S X T
b. T X S
c. S X S
d. T X T
Answer:
a. [tex]S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}[/tex] . Set S × T has 9 elements.
b. [tex]T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}[/tex]. Set T × S has 9 elements.
c. [tex]S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}[/tex] . Set S × S has 9 elements.
d. [tex]T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}[/tex] . Set T × T has 9 elements.
Step-by-step explanation:
The given sets are S={2,4,6} and T={1,3,5}.
We need to find the set-roster notation to write each of the following sets, and the number of elements that are in each set.
a.
[tex]S\times T=\{(s,t)|s\in S and t\in T\}[/tex]
[tex]S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}[/tex]
Set S × T has 9 elements.
b.
[tex]T\times S=\{(t,s)|s\in S and t\in T\}[/tex]
[tex]T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}[/tex]
Set T × S has 9 elements.
c.
[tex]S\times S=\{(s,s)|s\in S \}[/tex]
[tex]S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}[/tex]
Set S × S has 9 elements.
d.
[tex]T\times T=\{(t,t)|t\in T\}[/tex]
[tex]T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}[/tex]
Set T × T has 9 elements.
Using the set roster notation, the number of elements in each of the sets would be the product of the number of elements in each individual set, which is 9.
S = {2, 4, 6}T = {1, 3, 5}A.) S × T :
{2, 4, 6} × {1, 3, 5}
{(2, 1), (2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6, 5)}
Number is of elements = 9
B.) T × S :
{1, 3, 5} × {2, 4, 6}
{(1,2), (1,4), (1,6), (3,2), (3,4), (3, 6), (5, 2), (5,4), (5,6)}
Number is of elements = 9
C.) S × S :
{1, 3, 5} × {1, 3, 5}
{(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 3), (5, 1), (5, 3), (5, 5)}
Number is of elements = 9
D.) T × T :
{2, 4,6} × {2, 4, 6}
{(2,2), (2, 4), (2, 6), (4,2), (4, 4), (4, 6), (6,2), (6, 4), (6,6)}
Number is of elements = 9
Hence, the distribution of values of each set.
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A quantity and its 2/3 are added together and from thesum 1/3 of the sum is subtracted, and 10 remains.What is the quantity?
Answer:
[tex]14\frac{1}{3}[/tex]
Step-by-step explanation:
Let's write this out as an equation. Let the unknown quantity be x:
[tex]x+\frac{2}{3} - \frac{1}{3} (x+\frac{2}{3}) = 10\\\\3x+2-x -\frac{2}{3} = 30\\\\9x+6-3x-2=90\\\\6x= 86\\\\x = \frac{86}{6} =\frac{43}{3} =14\frac{1}{3} \\[/tex]
Answer: the quantity is 9
Step-by-step explanation:
Let x represent the quantity.
A quantity and its 2/3 are added together. The 2/3 of the number is 2/3 × x = 2x/3
The sum of the quantity and its 2/3 would be
x + 2x/3 = (3x + 2x)/3 = 5x/3
From the sum, 1/3 of the sum is subtracted. 1/3 of the sum would be
1/3 × 5x/3 = 5x/9
Subtracting 1/3 of the sum from the sum, it becomes
5x/3 - 5x/9 = (15x - 5x)/9 = 10x/9
If the remainder is 10, it means that
10x/9 = 10
Crossmultiplying
10x = 9 × 10 = 90
x = 90/10
x = 9
Charlie is a car salesman. He earns $800 plus a 9% commission on all of his sales for the week. If Charlie received a paycheck for 1,916 this week, how much were his total sales?
Answer:
$12,400
Step-by-step explanation:
Given:
Week earning + 9% commission = $1,916
Weekly Earning = $800
Commission for the Week = $1,916 - $800 = $1,116
Let total sales for the week = x
Therefore, x = ($1,116 * 100)/9
x = $12,400
Answer:
$12400
Step-by-step explanation:
Wages = Basic pay + Commission
1916 = 800 + 9%A
Let A be the total sales
9%A = 1916 - 800
9%A = 1116
A = $12400
Lisa put tulips and roses into vases. Each vase has 12 flowers. The red vase has 7 tulips. the blue vase has twice as mnay roses as the red vase. How many roses are in the blue vase?
Answer:
10 roses
Step-by-step explanation:
To find the number of roses in the blue vase, we double the number of roses in the red vase. Since the red vase has 5 roses, the blue vase contains 10 roses.
Explanation:The student's question is about determining the number of roses in the blue vase given certain conditions about the number of flowers in vases. We know that each vase has 12 flowers, the red vase has 7 tulips, and thus 5 roses because the total is 12. The blue vase has twice as many roses as the red vase, so we need to double the number of roses in the red vase to find that number.
Since the red vase has 5 roses, the blue vase will have twice as many, which is 10 roses.
Here's the calculation step by step:
Subtract the number of tulips from the total flowers in the red vase to find the number of roses: 12 flowers - 7 tulips = 5 roses.Multiply the number of roses in the red vase by 2 to find the number in the blue vase: 5 roses x 2 = 10 roses.A prize was awarded to 56 women and 642 men.
a. What fraction of the prize winners were women?
b. What fraction were men?
SIMPLIFY EACH plz
Find the Surface area
Answer:
27m²
Step-by-step explanation:
surface area is area of all sides
these is two triangles and a rectangle
area of triangle = (base x height) /2 = (3 x 4)/2= 12/2 =6
area of rectangle = length x breadth = 5x3 = 15
surface area = area of triangle + area of triangle + area of rectangle
6 + 6 + 15 = 27m²
math answers- the length of segment AB is 3.6. the length of segment AC is 11.8. what is the length of segment BC? write and solve a decimal addition equation and a decimal subtraction equation.
Answer:
answer is AC^2
Step-by-step explanation:
Observations on burst strength (Ib/in2) were obtained both for test nozzle closure welds and for production canister nozzle welds. Test 7200 6100 7300 7300 8000 7400 7300 7300 8000 6700 8300 5250 5625 5900 5900 5700 6050 5800 6000 5875 6100 5850 6600 Cannister A comparative boxplot is given below. Test Nozde Cannister 5000 000006000 Bunt strength (b, m Comment on interesting features (the cited article did not include such a picture, but the authors commented that they had looked at one). (Select all that apply.) The production canister welds have consistently lower burst strengths than the test nozze welds. The production canister weids have much more variable burst strengths The test nozzle welds data contain 2 outliers. test nozzle welds have much more variable burst strengths. The production canister welds have much higher burst strengths. The production canister welds data contain 2 outiers.
Answer:
1) The production canister welds have consistently lower burst strengths than the test nozze welds.
2) The production canister weids have much more variable burst strengths.
3) The test nozzle welds data contain 2 outliers.
4) Test nozzle welds have much more variable burst strengths.
5) The production canister welds have much higher burst strengths.
6) The production canister welds data contain 2 outiers.
Step-by-step explanation:
Hello!
The boxplots summarize the information of test nozzle closure welds and production canister nozzle welds.
The boxplot for the test nozzle closure welds shows that the first quartile and second quartile are close to each other but the third quartile is more separated to them, meaning that the data contained in the box is asymmetric, the data seems to have less variability between C₁ and C₂ and more between C₂ and C₃, the box is right-skewed.
The left whisker is larger than the right one, there are no outliers in the sample, due to most of the data being comprehended below C₁, the overall distribution of the data set is left-skewed, with large variability.
The boxplot for production cannister nozzle welds shows that the box is small (the variability of the data set is low) and symmetric, with C₂ in the middle of it and C₁ and C₃ are equidistant to the second quartile.
The whiskers of the box are small but they have almost the same length, showing that there is the same amount of data in them, this adds to the overall symmetry of the data set.
Finally, this data set shows two outliers, these values are far from the box, meaning that they are relatively extreme unusual values in regards to the rest of the sample but their distance to the box seems to be equal wich adds to the conclusion of the symmetrical distribution, with low variability of the data set.
I hope it helps!
Find the matrix P that multiplies (x; y; z) to give (y; z; x). Find the matrix Q that multiplies (y; z; x) to bring back (x; y; z).
Answer:
[tex]P = \left[\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{array}\right][/tex]
[tex]Q = \left[\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{array}\right][/tex]
Step-by-step explanation:
[tex]P*\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}y\\z\\x\end{array}\right][/tex]
[tex]Q*\left[\begin{array}{c}y\\z\\x\end{array}\right]=\left[\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{array}\right] \left[\begin{array}{c}y\\z\\x\end{array}\right] = \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]
Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than 1.15 is:_________
Answer:
0.8749
Step-by-step explanation:
Problems of normally distributed samples can be 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 = 0, \sigma = 1[/tex]
The probability that Z is less than 1.15 is:
This is the pvalue of Z = 1.15, which is 0.8749.
The probability that Z is less than 1.15: P(Z < 1.15) = Φ(1.15) ≈ 0.8749 or 87.49%
For a standard normal distribution with a mean of 0 and a standard deviation of 1, the probability that the random variable Z is less than 1.15 can be calculated using the standard normal cumulative distribution function (CDF).
The standard normal CDF gives the probability that a standard normal random variable takes a value less than or equal to a given value. We can use a standard normal distribution table or a calculator/software to find the value of the CDF at the desired point.
Let's denote the CDF of the standard normal distribution as Φ(z). Then, the probability that Z is less than 1.15 is given by:
P(Z < 1.15) = Φ(1.15)
Using a standard normal distribution table or calculator, we find that Φ(1.15) ≈ 0.8749.
Therefore, the probability that Z is less than 1.15 is approximately 0.8749 or 87.49%.
Suppose the length of the vegetable garden is increased by 50%. The new length can be written as (3y + 5) + 1 2(3y + 5) or 1.5(3y + 5). Explain why both expressions are correct. Then write the new length of the garden in simplified form.
Answer:
Given:
Length of the garden is represented by :
[tex]3y+5[/tex]
The length is increased by 50%.
To find the new length.
Solution:
1) The original length = [tex]3y+5[/tex]
The increase in length will be = [tex]50%[/tex] of [tex]3y+5[/tex]
⇒ [tex]\frac{50}{100}(3y+5)[/tex]
⇒ [tex]\frac{1}{2}(3y+5)[/tex]
The new length = Original length + Increased length = [tex](3y+5)+ \frac{1}{2}(3y+5)[/tex]
2) Let the original length = 100%
Increase percent of length = 50%
Total percent of length = [tex]100\%+50\%=150\%[/tex]
New length = [tex]150%[/tex] of [tex]3y+5[/tex]
⇒ [tex]\frac{150}{100}(3y+5)[/tex]
⇒ [tex]1.5(3y+5)[/tex]
Thus, the new length of the garden can be represented by both expression :
[tex](3y+5)+ \frac{1}{2}(3y+5)[/tex] or [tex]1.5(3y+5)[/tex]
The list of individuals from which a sample is actually selected is called the sampling frame. Ideally, the frame should list every individual in the population, but in practice this is often difficult. A frame that leaves out part of the population is a common source of undercoverage.
Suppose that a sample of households in a community is selected at random from the telephone directory.
What types of people do you think are likely to live in these households?These people will probably be underrepresented in the sample. (Select all that apply.)1.People with extra time on their hands.2.People without the extra income to keep a phone line will largely comprise the population without a phone line.3.Very busy people or those interested in maintaining privacy will largely comprise those with unlisted numbers.4.People who do not like to take surveys are likely to live in these households.
Answer:
Step-by-step explanation:
answer to Step 1
Households with unlisted numbers or without telephones.
answer to Step 2
2.People without the extra income to keep a phone line will largely comprise the population without a phone line.
3.Very busy people or those interested in maintaining privacy will largely comprise those with unlisted numbers.
Solve the right triangle
SR =sin (angle) = opposite leg/ hypotenuse
sin(52) = SR/ 7.6
SR = 7.6 x sin(52)
SR = 5.988 ( round answer as needed.)
QR = cos(angle) = adjacent leg / hypotenuse
Cos(52) = QR/ 7.6
QR = 7.6 x cos(52)
QR = 4.679. ( round answer as needed).
Angle S = 180 - 90 -52 = 38 degrees
A mathematician tells her son, "I will give you $100 only if you pass the class." Being a mathematician, she means exactly what she said. Check all true statements about this situation. a. If she ended up paying him $100, he must have passed the class. b. Her statement defined passing the class as a necessary condition for receiving the $100. c. if he passes the class, she will pay him $100. d. Her statement defined passing the class as a sufficient condition for receiving the 100 e. He will not get the s 100 unless he passes the class. f. If she didn't pay him $100, that means he didnt pass the class. . g. If he doesn't pass the class, she will definitely not pay him $100. h. If he passes the class, she may pay him $100.
Answer: C. If he passes the class, she will pay $100.
A. If she ended up paying $100, he must have passed the class.
Step-by-step explanation:
For a statement to be true, one assumption might imply the other assumption. In this case, A and C fulfills it.
Final answer:
The mathematician's statement makes passing the class a necessary condition for her son to receive $100. If he received the money, he must have passed the class, but not receiving the money does not conclusively prove he did not pass. The statement does not make passing the class a sufficient condition, as there could be other requirements.
Explanation:
The statement made by the mathematician to her son is a classic example of a conditional statement in logic, particularly looking at necessary and sufficient conditions. To analyze the truth of the given statements, we must understand the relationship between passing the class and receiving the $100.
a. If she ended up paying him $100, he must have passed the class. This is true. The payment is made on the condition of passing the class, so if he got paid, it means the condition was met.b. Her statement defined passing the class as a necessary condition for receiving the $100. This is true. 'Necessary condition' means without passing the class, he cannot get the $100.c. If he passes the class, she will pay him $100. This seems true based on the statement; however, we do not know if there are other conditions or possibilities so this could be false.d. Her statement defined passing the class as a sufficient condition for receiving the $100 False. Her statement does not guarantee that passing the class is all that is required for him to receive the $100; there might be other conditions.e. He will not get the $100 unless he passes the class. True. This is another way of saying that passing the class is a necessary condition.f. If she didn't pay him $100, that means he didn't pass the class. False. Not receiving the $100 could also occur due to other conditions not being met.g. If he doesn't pass the class, she will definitely not pay him $100. True. This is the definition of a necessary condition for the payment being made.h. If he passes the class, she may pay him $100. True. This acknowledges the possibility of passing the class leading to payment but does not imply it is a guarantee.Which of the following equations is also true?
Answer:
cos 38 = 17/c
Step-by-step explanation:
cos 38 = 17/c is the correct statement
Find the solution of the system of equations 3x+4y=10 and x−y=1. Give the x value followed by the y value, separated by a comma
Answer:
Solution of the system is (2,1).
Step-by-step explanation:
We are given the following system of equation:
[tex]3x+4y=10\\x - y = 1[/tex]
We would use the elimination method to solve the following system of equation.
Multiplying the second equation by 4 and adding the two equation we gwt:
[tex]3x + 4y = 10\\4\times (x-y = 1)\\\Rightarrow 4x - 4y = 4\\\text{Adding equations}\\3x + 4y + (4x-4y) = 10 + 4\\7x = 14\\\Rightarrow x = 2\\\text{Substituting value of x in second equation}\\2 - y = 1\\\Rightarrow y = 1[/tex]
Solution of the system is (2,1).
Answer: the solution is (2, 1)
Step-by-step explanation:
The given system of simultaneous equations is given as
3x+4y=10 - - - - - - - - - - - - -1
x−y=1 - - - - - - - - - - - - 2
We would eliminate x by multiplying equation 1 by 1 an equation 2 by 3. It becomes
3x + 4y = 10
3x - 3y = 3
Subtracting, it becomes
7y = 7
Dividing the left hand side and the right hand side of the equation by 7, it becomes
7y/7 = 7/7
y = 1
Substituting y = 1 into equation 2, it becomes
x - 1 = 1
Adding 1 to the left hand side and the right hand side of the equation, it becomes
x - 1 + 1= 1 + 1
x = 2
help pls asap in Ixl for geometry
Answer:
Step-by-step explanation:
Triangle QRS is a right angle triangle.
From the given right angle triangle
RS represents the hypotenuse of the right angle triangle.
With 30 degrees as the reference angle,
QR represents the adjacent side of the right angle triangle.
QS represents the opposite side of the right angle triangle.
To determine QR, we would apply trigonometric ratio
Cos θ = adjacent side/hypotenuse side. Therefore,
Cos 30 = QR/14
√3/2 = QR/14
QR = 14 × √3/2
QR = 14√3/2 = 7√3/2
A population model for two species can describe either competition for resources (an increase in one species decreases the growth rate in the other) or cooperation for resources (an increase in one species increases the growth rate in the other) For the systems below identify the parameters as growth rates, carrying capacities, and measure of interactions between species. Determine if the species compete of cooperate r, = 31-334-5ry 50 y (a) Growth Rate Constants (b) Carrying Capacity Constants: (c) Interaction Constants: Note: Your answers must be numbers, (which may include 0). If there is more than one answer, separate your answers with commas (d) Choose One Note: You can eam partial credit on this probiem.
(a) Growth Rate Constants: 6
(b) Carrying Capacity Constants: 0
Interaction Constants: 3
The species compete since the interaction constant is positive, indicating competition for resources between the two species.
For the given system:
[tex]\[ x' = 6x \][/tex]
[tex]\[ S_{xy} = 32y^2 - 8y - 8 + 3xy - 31 \][/tex]
(a) Growth Rate Constants: The growth rate constant for species [tex]\(x\)[/tex] is [tex]\(6\)[/tex].
(b) Carrying Capacity Constants: There is no explicit term indicating a carrying capacity for either species in the given equations, so the carrying capacity constants are both [tex]\(0\)[/tex].
Interaction Constants: The interaction constant between the two species can be identified from the term [tex]\(S_{xy}\)[/tex], which is [tex]\(3\)[/tex] in this case.
So, the answers are:
(a) Growth Rate Constants: [tex]\(6\)[/tex]
(b) Carrying Capacity Constants: [tex]\(0\)[/tex]
Interaction Constants: [tex]\(3\)[/tex]
The species compete since the interaction constant is positive.
Complete Question :
Population models for two species can report either competition for resources (an rise in one species recede the growth rate in the other) or cooperation for asset (an rise in one species rise the growth rate in the other). For the systems below, identify the boundary as growth rates, carrying capacities, and measures of interconnection between species. Determine if the species compete or cooperate. x' = 6x Sxy = 32y^2 - 8y - 8 + 3xy - 31 (a) Growth Rate Constants: (b) Carrying Capacity Constants: interconnection Constants: Note: Your answers must be numbers (which may include 0). If there is more than one answer, different your answers with commas. Choose One: - The Species Do Not Interact - One species take part, the other Cooperates - Help Both Species Cooperate - Both Species Compete.
PLEASE HELP! See attached image for the equation!
Answer:
Step-by-step explanation:
The first step is to rearrange the given quadratic equation so that it will take the form of the standard quadratic equation which is expressed as
ax² + bx + c = 0
The given quadratic equation is expressed as
2 = - x + x² - 4
Rearranging it, we would subtract 2 from the left hand side and the right hand side of the equation. It becomes
2 - 2 = - x + x² - 4 - 2
- x + x² - 6 = 0
x² - x - 6
a = 1
b = - 1
c = - 6
Substituting into the quadratic formula, it becomes
x = [- (- 1) ± √(- 1)² - 4(1)(- 6)] /2(1)
The table below shows selected points from a function.
The rate of change for the interval shown in the table is
A. constant
B. not constant
part b
A. linear
B. not linear
The rate of change is A. constant, B. linear
Step-by-step explanation:
Rate of change is the ratio of change in value of y with corresponding value of x
Rate of change=Δy/Δx
Rate of change=5-2/4-1 =3/3=1
The rate of change is constant in the given interval and linear with a positive slope.
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Keywords: function,rate of change,interval,table
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Determine if the statement is true or false. A system in echelon form can have more variables than equations. True False Justify your answer.
Answer:
Yes
Step-by-step explanation:
A system in echelon form can have more variables than equations. ... Every linear system with free variables has infinitely many solutions. True, a free variable can take any value, and so there are infinitely many solutions. Any linear system with more variables than equations cannot have a unique solution.
Find the third Taylor polynomial P3(x) for the function f(x) = (x-1)ln(x) about x0 = 1.
(a) Use P3(0.5) to approximate f(0.5). Find an upper bound for error |f(0.5) - P3(0.5)| using the error formula, and compare it to the actual error.
(b) Find a bound for the error |f(x) - P3(x)| in using P3(x) to approximate f(x) on the interval [0.5,1.5].
(c) Approximate \int_{0.5}^{1.5}f(x)dx using \int_{0.5}^{1.5}P_{3}(x)dx .
(d) Find an upper bound for the error in (c) using \int_{0.5}^{1.5}|R_{3}(x)dx| , and compare the bound to the actual error.
Answer:
A) The actual error |f(0.5) - P3(0.5)| is 0.0340735. The error using Taylor's error formula R₃(0.5) is 0.2917.
B) Te error in the interval [0.5,1.5] is 0.0340735.
C) The approximate integral using P₃(x) is 1/12
D) The real error between the two integrals is 4.687·10^(-3) while the error using \int_{0.5}^{1.5}|R_{3}(x)dx| is 0.018595
Step-by-step explanation:
A) To determine the error we first have to write the third grade Taylor polynomial P3(x):
[tex]P_n(x)=\displaystyle\sum_{k=0}^N \frac{f^{k}(a)}{k!}(x-a)[/tex] with N=3
[tex]P_3(x)=\displaystyle\sum_{k=0}^3 \frac{f^{k}(1)}{k!}(x-1)=(x-1)^2-\frac{1}{2} (x-1)^3[/tex]
The error for the third grade Taylor polynomial R₃(x) is represented as the next term non-written in the polynomial expression near to the point x:
[tex]R_3(x)=\displaystyle \frac{f^{4}(x)}{4!}(x-a)=\frac{1}{24} (\frac{2}{x^3}+\frac{6}{x^4})(x-1)^4[/tex]
Therefore the real error is:
[tex]Err(0.5)=|f(0.5)-P_3(0.5)|=0.0340735[/tex]
The error of the Taylor polynomial R₃(0.5) is:
[tex]R_3(0.5)=\displaystyle \frac{1}{24} (\frac{2}{0.5^3}+\frac{6}{0.5^4})(0.5-1)^4=0.2917[/tex]
B) The error in the interval [0.5,1.5] is the maximum error in that interval.
This is found in the extremes of the intervals. We analyze what happens in X=1.5:
[tex]Err(1.5)=|f(1.5)-P_3(1.5)|=0.01523[/tex]
[tex]R_3(1.5)=\displaystyle \frac{1}{24} (\frac{2}{1.5^3}+\frac{6}{1.5^4})(1.5-1)^4=\frac{1}{216}=4.63\cdot 10^{-3}[/tex]
Both of these errors are smaller than Err(0.5) and R₃(0.5). Therefore the error in this interval is Err[0.5,1.5] is Err(0.5).
C) The approximation of the integral and the real integral is:
[tex]I_f=\displaystyle\int_{0.5}^{1.5} f(x)\, dx=\int_{0.5}^{1.5} (x-1)ln(x)\, dx=0.08802039[/tex]
[tex]I_{p3}=\displaystyle\int_{0.5}^{1.5} P_3(x)\, dx=\int_{0.5}^{1.5} (x-1)^2-0.5(x-1)^3\, dx=1/12=0.0833333[/tex]
D) The error in the integrals is:
[tex]Errint=|I_f-I_{p3}|=4.687\cdot10^{-3}[/tex]
[tex]Errint(R_3)=\displaystyle\int_{0.5}^{1.5} R_3(x)\, dx=\int_{0.5}^{1.5} \frac{1}{24} (\frac{2}{x^3}+\frac{6}{x^4})(x-1)^4\, dx=0.018595[/tex]