(a) With 98% confidence, the true average student loan debt for university students in Canada falls between $25,883.5 and $26,116.5.
(b) No, this does not contradict the reported average of $26,500.
(a) To construct a 98% confidence interval, we can use the formula:
CI = [tex]\bar{x}[/tex] ± z* (σ/√n)
where [tex]\bar{x}[/tex] is the sample mean, σ is the population standard deviation (unknown), n is the sample size, and z* is the z-value from the standard normal distribution that corresponds to the desired level of confidence (98% in this case).
Substituting the given values, we get:
CI = 26,000 ± 2.33 * (500/√64)
CI = 26,000 ± 116.5
CI = (25,883.5, 26,116.5)
Therefore, we can say with 98% confidence that the true average student loan debt for university students in Canada falls between $25,883.5 and $26,116.5.
(b) No, this does not contradict the reported average of $26,500. The reported average is within the confidence interval we calculated, which means that it is a plausible value for the true average. The sample mean of $26,000 is slightly lower than the reported average, but this could be due to random sampling error.
Overall, we cannot make a definitive conclusion about the true average based on this sample alone, but we can say with 98% confidence that it falls within the range of $25,883.5 to $26,116.5.
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(1 point) Consider the function f(x, y) = xy + 33 – 48y. f har ? at (-43,0) f has at (0,4). a maximum a minimum a saddle some other critical point no critical point f ha: at (463,0). f has at (0,0). f has ? at (0, –4).
At point (-43,0), f has a maximum. At point (0,4), f has a minimum. At point (463,0), f has a maximum. At point (0,0), f may have a critical point. none of the given points are critical points of the function f (x, y) = xy + 33 - 48y.
Hi! To analyze the critical points of the function f(x, y) = xy + 33 - 48y, we first need to find the partial derivatives with respect to x and y:
fx = ∂f/∂x = y
fy = ∂f/∂y = x - 48
Now, we can analyze the given points:
1. (-43, 0)
At this point, fx = 0 and fy = -48. Since both partial derivatives are not equal to 0, this point is not a critical point.
2. (0, 4)
At this point, fx = 4 and fy = 0. Again, both partial derivatives are not equal to 0, so this is not a critical point.
3. (463, 0)
At this point, fx = 0 and fy = 463 - 48 = 415. Since both partial derivatives are not equal to 0, this is not a critical point.
4. (0, 0)
At this point, fx = 0 and fy = -48. Since both partial derivatives are not equal to 0, this is not a critical point.
5. (0, -4)
At this point, fx = -4 and fy = -48. Again, both partial derivatives are not equal to 0, so this is not a critical point.
In summary, none of the given points are critical points of the function f(x, y) = xy + 33 - 48y.
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A company knows that unit cost and unit revenue from the production and sale of x units are related by C. + 10621. Find the rate of change of revenue per unit when the 102.000 cost per unit is changing by $8 and the revenue is $4,000 O A $102.00 OD $160.00 OC. $577.05 OD. $1,052.10
The rate of change of revenue per unit is $8 when the unit cost is changing by $8 and the revenue is $4,000.
We are given that the unit cost (C) and unit revenue (R) are related by the equation C = R + 10621.
We want to find the rate of change of revenue per unit, dR/dx, when the unit cost (C) is changing by $8 per unit and the revenue (R) is $4,000.
1. Differentiate the given equation with respect to x: dC/dx = dR/dx
2. Plug in the given values: dC/dx = $8 (cost per unit is changing by $8) R = $4,000 (revenue per unit)
3. Solve for the cost per unit (C) using the equation
C = R + 10621
C = $4,000 + 10621
C = $14,621
4. Since dC/dx = dR/dx, and we know dC/dx = $8,
we can find the rate of change of revenue per unit (dR/dx) when the cost per unit is changing by $8: dR/dx = $8
Thus, the rate of change of revenue per unit is $8 when the unit cost is changing by $8 and the revenue is $4,000.
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You doing the practice 1
Using the intersection of sets we find that A ∩ B = {1, 3}
What is a set?A set is a collection of well ordered items.
Givent hat set A = {x| x is an od number greater than 0 and less than 10} and set B = {1, 2, 3, 4}, we desire to find A ∩ B. We proceed as follows.
First since set A = {x| x is an odd number greater than 0 and less than 10}, its elements are A = {1, 3, 5, 7, 9}
Also, set B = {1, 2, 3, 4}
Since we require A ∩ B which is the intersection of both sets and is the elements that both sets have in common. Since both sets have element 1 and 3 in common, we have that
A ∩ B = {1, 3}
So, A ∩ B = {1, 3}
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Find the mass of each object. (Round answers to two decimal places.)
A thin copper wire 3.75 feet long (starting at a = 0) with density function given by
p(t) = 5x^2 + 4x lb/ft.
The mass of the copper wire is approximately 131.77 lb.
To find the mass of the copper wire, we will first need to calculate its mass per unit length using the given density function[tex]p(t) = 5x^2 + 4x lb/ft,[/tex] and then integrate the function over the length of the wire.
Write down the given density function: [tex]p(t) = 5x^2 + 4x lb/ft[/tex]
2. Write down the limits of integration, which correspond to the length of the wire:
a = 0, b = 3.75 feett.
Set up the integral to find the mass of the wire:
Mass = ∫[p(t) dt] from a to b.
Plug in the density function and limits:
Mass = ∫[tex][5x^2 + 4x dx][/tex]from 0 to 3.75
Integrate the function: Mass = (5/3)x^3 + 2x^2 | from 0 to 3.75
Substitute the upper limit and then subtract the result of the lower limit:
Mass =[tex][(5/3)(3.75)^3 + 2(3.75)^2] - [(5/3)(0)^3 + 2(0)^2][/tex]
Perform the calculations and round to two decimal places:
Mass ≈ 131.77 lb.
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The monthly income of a man is Rs 53000. He deposits 20% of his yearly income in civil investment fund and 10% in charity. If 1 % social security tax should be paid on First Rs 300000and 15% tax is imposed yearly ,how much tax should he pay?
The man needs to pay a total tax of Rs 69780 (3000 for social security and 66780 for yearly tax).
How to find the tax should he pay?To find the tax, let's find the man's yearly income:
Yearly income = Monthly income x 12
Yearly income = 53000 x 12 = 636000
Next, let's find how much he deposits in civil investment fund and charity:
Amount deposited in civil investment fund = Yearly income x 20%
Amount deposited in civil investment fund = 636000 x 0.2 = 127200
Amount deposited in charity = Yearly income x 10%
Amount deposited in charity = 636000 x 0.1 = 63600
Now, let's calculate the total taxable income:
Total taxable income = Yearly income - Amount deposited in civil investment fund - Amount deposited in charity
Total taxable income = 636000 - 127200 - 63600 = 445200
Since the man's taxable income is above Rs 300000, he needs to pay 1% social security tax on Rs 300000:
Social security tax = 1% of 300000 = 3000
Now, let's calculate the yearly tax imposed at a rate of 15%:
Yearly tax = Total taxable income x 15%
Yearly tax = 445200 x 0.15 = 66780
Therefore, the man needs to pay a total tax of Rs 69780 (3000 for social security and 66780 for yearly tax).
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Ben practises playing the Oboe daily.
The time (in minutes) he spends on
daily practice over 28 days is as follows:
10, 15, 30, 35, 40, 40, 45, 55, 60, 62,
64, 64, 66, 68, 70, 70, 72, 75, 75, 80,
82, 84, 90, 90, 105, 110, 120, 180
a Find the median time.
b
Find the lower quartile.
c Find the upper quartile.
d
Find the range.
Determine whether there
outliers in the data.
e
(2 marks)
(2 marks)
(2 marks)
(2 marks)
are any
(4 marks)
f Draw a box-and-whisker diagram for
the above data.
(3 marks)
Therefore, (70+72)/2 = **71 minutes** is the median time. B)42.5 minutes as a result. C,D)The range is determined by deducting the dataset's smallest value from highest value.
A)When the data are organized in order of magnitude, the median time is the middle value. The median in this situation is the average of the 14th and 15th values, which are 70 and 72, respectively. There are 28 data points in this situation. Therefore, (70+72)/2 = **71 minutes** is the median time.
b) The median of the lowest half of the data constitutes the lower quartile (Q1). We must arrange the data in descending order of magnitude before determining the median of the first half of the data in order to determine Q1. is the average of the seventh and eighth values, which are 40 and 45, respectively, in the first half of the data, which consists of 14 values. Q1 = (40+45)/2 = **42.5 minutes as a result.
b) The median of the upper half of the data constitutes the upper quartile (C). We must first organise the data in descending order of magnitude before determining the median of the remaining data in order to determine Q3. Q3 is the average of the seventh and eighth values from the last, which are 90 and 105, respectively, in the second half of the data, which consists of 14 values. Q3 = (90+105)/2 = **97.5 minutes**3 as a result.
d) The range is determined by deducting the dataset's smallest value from highest value.
In this instance, Ben's practise time can be anywhere from **10 minutes** to **180 minutes**. Range then equals maximum value - minimum value, which in this case is 180 - 10 = **170 minutes**
e) Extreme values that are beyond the typical range of a dataset's values are known as outliers. We can use a criterion that states that any value that sits more than 1.5 times the interquartile range (IQR) below Q1 or above Q3 is regarded as an outlier to ascertain whether there are outliers in this dataset. When Q1 is subtracted from Q3, the result is the IQR: Q3 - Q1 = 97.5 - 42.5 = **55 minutes**3. By using this rule, we can see that the dataset contains the outliers **180** and **120** minutes.
IQR stands for what?The term "interquartile range" is IQR. It is a measure of variability that is based on quartilizing a dataset. The first quartile (Q1) is subtracted from the third quartile to determine the IQR. (Q3). It is a representation of the middle 50% of the data's range.
f) A box-and-whisker plot illustrates a dataset's quartiles, outliers, and range1. For Ben's practice, here's how to create a box-and-whisker plot:
- Create a number line with all the values Ben practised with.
- Draw a box spanning Q1 through Q3.
- Inside the box, at the location of Q2, draw a vertical line. (the median).
Draw whiskers from the box's two ends to all values that are not outliers.
- Place every outlier on the graph as a separate point, outside of any whiskers.
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Question 10(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 11(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10, 16, 20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 14, with a median of 14
Bus 18, with a mean of 12
Bus 14, with a mean of 14
Bus 18, with a median of 12
Question 13(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5
The drive-thru is able to estimate their wait time more consistently will be A. Burger Quick, because it has a smaller IQR.
What is the IQR?The interquartile range (IQR) is a measure of variability that represents the range of values in the middle 50% of scores in a distribution. It is used when the data is skewed and the median is a better measure of central tendency than the mean.
In this scenario, Burger Quick has an IQR of 14.5, while Fast Chicken has an IQR of 4.5.
The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
For Burger Quick, Q1 is 9.5 and Q3 is 24, so the IQR is 24 - 9.5 = 14.5. For
Fast Chicken, Q1 is 10 and Q3 is 14.5, so the IQR is 14.5 - 10 = 4.5.
Therefore, Burger Quick has a larger IQR than Fast Chicken, indicating that its data is more consistent and less spread out. This means that Burger Quick is better able to estimate its wait time consistently.
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Rewrite 32 1/2 as a radical form
Therefore, 32 1/2 can be written as a radical form of 32 + √2.
What is fraction?In mathematics, a fraction is a numerical quantity that represents a part of a whole or a ratio between two numbers. Fractions are written in the form of one integer, called the numerator, written above a line, and another integer, called the denominator, written below the line. The denominator represents the total number of equal parts into which a whole is divided, while the numerator represents the number of those parts being considered.
Here,
We can write 32 1/2 as a mixed number, which is equivalent to the fraction 65/2. To express 65/2 as a radical form, we can simplify the fraction by finding a perfect square that divides evenly into both the numerator and the denominator. In this case, 4 is a perfect square that divides into 64 (the nearest perfect square to 65) and 2, so we can write:
65/2 = (64 + 1)/2
= 64/2 + 1/2
= 32 + 1/2
Now, we can express the fraction 1/2 as a radical by taking the square root of the denominator, which gives:
32 1/2 = 32 + √2
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Find the cost of one dozen exercise books, if 3 similar exercise books cost $2.70.
Answer:
$10.8
Step-by-step explanation:
We know that 3 books are $2.70, so 1 book is 2.70/3 which is $0.9
1 dozen = 12
To find the price of 12 books, we multiply by the cost of 1 book
12 * 0.9 = $10.8
Determine the distance between the points (−3, −6) and (5, 0).
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - (-3)~~)^2 + (~~0 - (-6)~~)^2} \implies d=\sqrt{(5 +3)^2 + (0 +6)^2} \\\\\\ d=\sqrt{( 8 )^2 + ( 6 )^2} \implies d=\sqrt{ 64 + 36 } \implies d=\sqrt{ 100 }\implies d=10[/tex]
Use the properties of sigma notation and the summation formulas to evaluate the given sum: 15 [ili2 – 21 +1) – 4] i=1
The sum is equal to 18600.
How to find summation?
Let's first simplify the expression inside the brackets:
(i^2 - 21 + 1) - 4 = i^2 - 24
Now we can write the sum using sigma notation:
15 Σ (i^2 - 24), i=1
Using the summation formulas of the first n squares, we have:
Σ i^2 = n(n+1)(2n+1)/6
So, substituting n = 1 to 15, we get:
15 Σ i^2 = 15 Σ n(n+1)(2n+1)/6
Now, let's use the formula for the sum of the first n integers:
Σ i = n(n+1)/2
Substituting n = 1 to 15, we get:
Σ i = 1 + 2 + ... + 15 = 15(15+1)/2 = 120
Substituting these formulas into our original expression, we have:
15 Σ (i^2 - 24), i=1
= 15 [Σ i^2 - 24Σ i], i=1
= 15 [15(15+1)(2(15)+1)/6 - 24(120)]
= 15 [1240]
= 18600
Therefore, the sum of 15 (i^2 - 24) from i = 1 to 15 is equal to 18600.
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Find the volume of this cylinder using 3.14 as pi
13 ft
20 ft
The value of the volume of the cylinder is 706. 5 cm³
How to determine the valueThe formula for the volume of a cylinder is expressed as;
V = πr²h
Such that the parameters are;
V is the volume of the cylinderπ takes the value 3.14r is the radius of the cylinderh is the height of the cylinderNow, substitute the values into the formula, we get;
Volume, V = 3.14 × 5² × 9
Find the square value and substitute
Volume, V = 3.14 × 25 × 9
Multiply the values
volume, V = 706. 5 cm³
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What is the vertex, Line of symmetry, and how many x intercepts are there?
The vertex is the highest or lowest point on the parabola, the line of symmetry is a vertical line passing through the vertex and dividing the parabola into two equal halves, and the number of x-intercepts depends on the discriminant of the quadratic equation.
The vertex is a point on a parabola where the curve changes direction. It is the highest or lowest point on the curve, depending on whether it opens up or down. The vertex is represented as (h, k), where h is the x-coordinate and k is the y-coordinate.
The line of symmetry is a vertical line that divides the parabola into two equal halves. It passes through the vertex and is equidistant from the two arms of the parabola. The equation of the line of symmetry is x = h.
The number of x-intercepts is determined by the equation of the parabola. If the discriminant of the quadratic equation is positive, then the parabola intersects the x-axis at two distinct points, and there are two x-intercepts. If the discriminant is zero, then the parabola touches the x-axis at one point, and there is one x-intercept. If the discriminant is negative, then the parabola does not intersect the x-axis, and there are no x-intercepts.
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Los 2/3 mas la edad de Juan es igual a los 3/5 menos la edad de Julia. ¿Que fraccion representa la edad de juan respecto a la edad de Julia?
The fraction representing Juan's age relative to Julia's age is -1/10. This means that Juan's age is one-tenth less than Julia's age.
Let's start by translating the given statement into an equation:
[tex]2/3J = 3/5 - 2/3Jl[/tex]
where J is Juan's age and Jl is Julia's age.
Now we can simplify this equation by first multiplying both sides by 15 (the least common multiple of 3 and 5) to get rid of the denominators:
[tex]10J = 9 - 10Jl[/tex]
Next, we can isolate J on one side of the equation by adding 10Jl to both sides:
[tex]10J + 10Jl = 9[/tex]
Finally, we can factor out a 10 from the left-hand side:
[tex]10(J + Jl) = 9[/tex]
Dividing both sides by 10, we get:
[tex]J + Jl = 9/10[/tex]
Now we can express Juan's age as a fraction of Julia's age by dividing both sides of this equation by Jl:
[tex]Jl/Jl + J/Jl = 9/10Jl[/tex]
Simplifying this, we get:
1 + J/Jl = 9/10
Subtracting 1 from both sides, we get:
[tex]J/Jl = 9/10 - 1[/tex]
[tex]J/Jl = -1/10[/tex]
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Olivia finds a combination of two different transformations that moves ABCD onto A" B" C" D". What is one way she might have done this?
One way Olivia might have achieved this is by performing a translation followed by a rotation.
How could Olivia have combined two different transformations to move ABCD onto A" B" C" D"?One way Olivia might have achieved the transformation of ABCD onto A" B" C" D" is by performing a translation followed by a rotation. Here's a possible approach:
Translation: Olivia could have first translated ABCD by shifting the entire figure in a specific direction (up, down, left, or right) by a certain distance. This would result in a new position for each vertex of ABCD, creating a new figure.Rotation: After the translation, Olivia could have performed a rotation around a point, such as the origin or a specific vertex. The rotation would change the orientation of the translated figure, aligning it with the desired position of A" B" C" D".By combining these two transformations, Olivia could have successfully moved ABCD onto A" B" C" D" and achieved the desired configuration. It's important to note that there could be other valid combinations of transformations as well.
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4x + 8y = 3x + 7y + 14; y=2
Answer:
Step-by-step explanation:
as we alderdy have value of y,we can substuite it in the place of y
4x+8(2)=3x+7(2)+14
4x+16=3x+14+14
4x-3x=28-16
x=12
a) ¿Cuál es el coeficiente del término 23x5?
Answer:
El coeficiente del término 23x^5 es 23.
Step-by-step explanation:
If the circumference of a circle is 50. 4 ft, what is its area? (Use π = 3. 14) *
2 points
50. 24 sq ft
113. 04 sq ft
202. 24 sq ft
314 sq ft
If the circumference of a circle is 50. 4 ft, its area is 202.24 sq ft. Correct option is C: 202.24 sq ft.
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. We are given that the circumference is 50.4 ft, so we can solve for the radius:
50.4 = 2πr
r = 50.4 / (2π)
r ≈ 8.02 ft
Now we can use the formula for the area of a circle: A = πr²
A = 3.14 * (8.02)²
A ≈ 202.24 sq ft
Therefore, the answer is option C: 202.24 sq ft.
Alternatively, to find the area of a circle with a circumference of 50.4 ft, we will first find the radius using the formula for circumference (C = 2πr) and then use the formula for the area of a circle (A = πr²). Using π = 3.14:
Solve for the radius (r):
C = 2πr
50.4 = 2(3.14)r
r = 50.4 / (2 * 3.14)
r ≈ 8 ft
Calculate the area (A):
A = πr²
A = 3.14 * (8²)
A = 3.14 * 64
A ≈ 201.06 sq ft
The closest answer among the options provided is 202.24 sq ft. Correct option is C: 202.24 sq ft.
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A van can ferry a maximum of 12 people. By setting up an inequality, find the maximum number of vans that are needed to ferry 80 people
By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.
To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.
Since a van can ferry a maximum of 12 people, we can write the inequality as:
12v ≥ 80
Now, let's solve for "v":
Divide both sides of the inequality by 12.
v ≥ 80/12
Simplify the inequality.
v ≥ 6.67
Since we cannot have a fraction of a van, we need to round up to the nearest whole number:
v ≥ 7
Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.
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An investor purchases 500 shares of Exxon-mobil stock at $98. 93 per share. His broker charges 2% of the cost of the stock. What is the cost of the stock?
The cost of the stock for the investor would be calculated as follows:
Cost of 1 share = $98.93
Number of shares purchased = 500
Total cost of the stock = Cost per share x Number of shares
Total cost of the stock = $98.93 x 500
Total cost of the stock = $49,465
The broker charges 2% of the cost of the stock, so the broker's fee would be calculated as:
Broker's fee = 2% x Total cost of the stock
Broker's fee = 2% x $49,465
Broker's fee = $989.30
Therefore, the total cost of the stock for the investor including the broker's fee would be:
Total cost of the stock + Broker's fee = $49,465 + $989.30
Total cost of the stock + Broker's fee = $50,454.30
So the cost of the stock for the investor including the broker's fee is $50,454.30.
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Use substitution to find the indefinite integral. szve ? 2 zV9z+ - 5 dz [21922-5 Zy9z 9z- 5 dz = =]
To solve this problem, we can use substitution. Let u = 9z - 5, then du/dz = 9 and dz = du/9.
Using this substitution, we can rewrite the integral as:
∫(2/(u+5))(1/9)du
Simplifying this expression:
(2/9) ∫(1/(u+5))du
We can then solve this integral by using the formula for the natural logarithm:
(2/9) ln|u+5| + C
Substituting back in for u:
(2/9) ln|9z| + C
2 zV9z+ - 5 dz is (2/9) ln|9z| + C.
Consider the integral:
∫2z√(9z² - 5) dz
We can use the substitution method. Let's choose the substitution:
u = 9z² - 5
Now, differentiate u with respect to z:
du/dz = 18z
Solve for dz:
dz = du/(18z)
Now, substitute u and dz back into the integral and simplify:
∫(2z√u) * (du/(18z)) = (1/9)∫√u du
Now, integrate with respect to u:
(1/9)(2/3)(u^(3/2))/(3/2) + C = (2/27)u^(3/2) + C
Finally, substitute back the original expression for u:
(2/27)(9z² - 5)^(3/2) + C
So, the indefinite integral is:
(2/27)(9z² - 5)^(3/2) + C
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help me Find the y-intercept of the parabola y = x^2 + 29/5 .
Answer:
(0,5.8)
Step-by-step explanation:
What is the slope of the line that passes through the points (9, 1) and (10, -1)?
Write your answer in simplest form.
Answer:
m=2
Step-by-step explanation:
When do you hit the water and what is your maximum height above the pool?
The time till you hit the water, given your height above the water, would be 0.76 seconds.
The maximum height above the pool you would get is 15.39 feet.
How to find the maximum height and time ?We are given h ( t ) = - 16 t ² + 5t + 15
You hit the water at 0 so the formula is:
0 = - 16 t ² + 5t + 15
Using the quadratic equation, we can solve:
t = ( - b ± √ ( b ² - 4 ac ) ) / 2a
t = ( - 5 ± √ ( 5 ² - 4 ( - 16 ) ( 15 ) )) / 2 (- 16)
t = (- 5 ± √ 985 ) / -32
t = 0. 76 seconds
The vertex of the parabolic function would be:
= - b / 2a
= - 5 / ( 2 x - 16 )
= 0. 15625 seconds
Maximum height is therefore:
= -16 ( 0. 15625 ) ² + 5 ( 0. 15625 ) + 15
= 15.39 feet
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can someone pls help with this
A linear function would be the best fit for the data.
A function that would be the best for this data is: D. y = -4/25(x) + 10
The amount of snow that would be on the ground when the temperature reaches 55° is 1.2 inches.
How to determine the line of best fit?In this scenario, the temperature would be plotted on the x-axis (x-coordinate) of the scatter plot while the snow (inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the temperature and the snow (inches), an equation for the line of best fit is given by:
y = -0.16x + 10
y = -4/25(x) + 10
When x = 55, the amount of snow is given by;
y = -4/25(55) + 10
y = 1.2 inches.
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A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 0.5 s and t=1.4 s? Use Galileo's formula u(t) = -32t ft/s.
Answer = _______
The distance is negative because it's a fall, so the cat falls 27.36 ft between t = 0.5 s and t = 1.4 s.
To find the distance the cat falls between t = 0.5 s and t = 1.4 s, we need to use the formula for velocity and distance.
we first need to find the position at each of these times using the given formula u(t) = -32t ft/s.
The formula for distance fallen is:
distance(t) = initial position + initial velocity × t + (1/2) × acceleration × t²
Since the cat falls with zero initial velocity and starts from the tree, we can simplify the formula:
distance(t) = (1/2) × acceleration × t²
First, let's find the velocity of the cat at t = 0.5 s and t = 1.4 s using Galileo's formula:
u(0.5) = -32(0.5) = -16 ft/s
and, u(1.4) = -32(1.4) = -44.8 ft/s
Now, we can use the formula for distance:
distance = (velocity at t = 0.5 s + velocity at t = 1.4 s) / 2 x (t = 1.4 s - t = 0.5 s)
⇒ distance = (-16 ft/s + (-44.8 ft/s)) / 2 x (1.4 s - 0.5 s)
⇒ distance = (-60.8 ft/s) / 2 x (0.9 s)
⇒ distance = -27.36 ft/s x s
Therefore, the cat falls 27.36 feet between t = 0.5 s and t = 1.4 s.
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Patrick buys a tissue box in the shape of a cube. how many cubic centimeters of space do the tissues occupy if the box it half full
The total cubic centimeters of space the tissue box requires is 500 cubic centimeters, under the condition that the box is half full.
The volume of a cube is evaluated by multiplying its length by its width by its height. If all sides of a cube are equal,
we can use the formula
V = s³
here
s = length of one side of the cube.
If we let s be the length of one side of the cube and V be its volume,
V = s³
If we know that the tissue box is half full, then let us consider that half of its volume is occupied by tissues. Then
V' = 0.5 × V
Staging V = s³ in the equation
V' = 0.5 × s³
s = 10 cm (given)
V' = 0.5 × 1000 = 500 cubic centimeters
Hence, if Patrick's tissue box has a volume of 1000 cubic centimeters and it is half full, then the tissues occupy 500 cubic centimeters of space.
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The complete question is
Patrick buys a tissue box in the shape of a cube of side 10 centimeters. How many cubic centimeters of space do the tissues occupy if the box is half full? Show all work
The surface area of a triangular pyramid is 450 square meters. The surface area of a similar triangular pyramid is 50 square meters.
What is the ratio of corresponding dimensions of the smaller pyramid to the larger pyramid?
The ratio of the corresponding dimensions of the smaller pyramid to the larger pyramid is 1/3.
What is a dimension?Dimension is the measure of the distance or length of an obeject.
To calculate the ratio of the corresponding dimensions of the smaller pyramid to the larger pyramid, we use the formula below
Formula:
l/L = √(a/A) ........................ Equation 1
Where:
l/L = Ratio of the dimension of the smaller pyramid to the larger onea = Area of the smaller pyramidA = Area of the larger pyramidFrom the question,
Given:
a = 50 m²A = 450 m²Substitute these values into equation 1
l/L = √(50/450)l/L = √(1/9)l/L = 1/3Learn more about dimension here: https://brainly.com/question/27404871
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Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?
Answer:
The total amount Joe spent on gasoline and oil can be determined by the expression: 2.85g + 3.15c. This expression represents the cost of g gallons of gasoline at $2.85 per gallon plus the cost of c cans of oil at $3.15 per can.
Step-by-step explanation:
This year, a French restaurant used 377,020 ounces of cream. That is 50% less than last year, when the restaurant had a different menu. How much cream did the restaurant use last year?
the restaurant used 754,040 ounces of cream last year.
What is an Equations?
Equations are statements in mathematics that consist of two algebraic expressions separated by an equals (=) sign, indicating the equivalence between the expressions on either side. Equations can be solved to determine the value of a variable that represents an unknown quantity. A statement that does not have an "equal to" symbol is not considered an equation and is instead referred to as an expression.
If the restaurant used 50% less cream this year compared to last year, then it means that this year's usage is 50% of last year's usage.
Let x be the amount of cream used last year.
Then we can set up the following equation:
x * 50% = 377,020
To solve for x, we need to isolate it on one side of the equation.
x * 50% = 377,020
x = 377,020 / 50%
To convert 50% to a decimal, we divide it by 100:
x = 377,020 / 0.5
x = 754,040
Therefore, the restaurant used 754,040 ounces of cream last year.
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