Answer:
2(M - 14) = 64
M - 14 = 32
M = 46
What else would need to be congruent to show that ABC=AXYZ by SAS?
A. ZB=LY
B. BC = YZ
C. C= LZ
D. AC = XZ
Given:
AB XY
BC=YZ
To show that ABC ≅ AXYZ by SAS, we would need to establish that angle BAC ≅ angle XYZ.
To show that triangles ABC and AXYZ are congruent by the Side-Angle-Side (SAS) criterion, we need to establish that two corresponding sides and the included angle are congruent.
Given AB ≅ XY and BC ≅ YZ, we already have two corresponding sides congruent.
To complete the congruence by the SAS criterion, we need to establish that the included angles are congruent. In this case, the included angle is angle BAC (or angle XYZ).
Therefore, to show that ABC ≅ AXYZ by SAS, we would need to establish that angle BAC ≅ angle XYZ.
None of the answer choices directly addresses the congruence of the angles. So, none of the given options (A, B, C, D) are sufficient to show the congruence of the triangles by SAS.
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labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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Suppose that an object is thrown upward from ground level with an initial velocity of 160ft/sec. Its height after t seconds is a function h given by h(t)=-16t^2 +160t.
a) Find an equivalent expression for h(t) by factoring out a common factor with a negative coefficient.
b) Check your factoring by evaluating both expressions for h(t) at t=1.
The factored expression is
a) The factored expression for h(t) is -16t(t - 10), obtained by factoring out a common factor of -16 and a common factor of t from the original expression -16t^2 + 160t.
b) Both the original expression -16t^2 + 160t and the factored expression -16t(t - 10) yield the same result of 144 when evaluated at t = 1, confirming the correctness of the factoring.
a) To factor out a common factor with a negative coefficient from the expression h(t) = [tex]-16t^2 + 160t[/tex], we can rewrite it as:
h(t) = [tex]-16(t^2 - 10t)[/tex]
Now, let's focus on factoring the quadratic expression inside the parentheses. We can factor out a common factor of t:
h(t) = -16t(t - 10)
Therefore, the factored expression for h(t) is -16t(t - 10).
b) To check the factoring by evaluating both expressions for h(t) at t = 1, we substitute t = 1 into the original expression and the factored expression and compare the results.
Using the original expression:
h(1) = [tex]-16(1)^2 + 160(1)[/tex]
h(1) = -16 + 160
h(1) = 144
Using the factored expression:
h(1) = -16(1)(1 - 10)
h(1) = -16(1)(-9)
h(1) = 144
Both expressions yield the same result of 144 when evaluated at t = 1. Therefore, the factoring is correct.
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The following is a list of shoe sizes for a group of 13 people.
4.5, 9.5, 8, 6.5, 10, 7, 8.5, 6, 7.5, 9, 6, 7, 11
Which of the following box plots best represents the numerical data?
A box plot using a number line from 3 to 12.25 with tick marks every one-fourth unit. The box extends from 6.25 to 9.25 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 11. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 11.25 with tick marks every one-fourth unit. The box extends from 6.25 to 8.75 on the number line. A line in the box is at 7.25. The lines outside the box end at 4.5 and 10. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 13 with tick marks every one-half unit. The box extends from 6.5 to 9 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 12. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 12.5 with tick marks every one-fourth unit. The box extends from 6.25 to 8.75 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 10.5. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
The box plot that best represents the numerical data is: A. A box plot using a number line from 3 to 12.25 with tick marks every one-fourth unit. The box extends from 6.25 to 9.25 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 11. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
How to complete the five number summary of a data set?In order to determine the five-number summary for the survey, we would arrange the data set in an ascending order:
4.5,6,6,6.5,7,7,7.5,8,8.5,9,9.5,10,11
Based on the information provided about the list of shoe sizes for a group of 13 people, we would use a graphical method (box plot) to determine the five-number summary for the given data set as follows:
Minimum (Min) = 4.5.
First quartile (Q₁) = 6.25.
Median (Med) = 7.5.
Third quartile (Q₃) = 9.25.
Maximum (Max) = 11.
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Sam is a waiter at a local restaurant where he earns wages of $7 per hour. Sam figures that he also earns about $5 in tips for each person he serves. Sam works 6 hours on a particular day. If n represents the number of people Sam serves that day, which of the following functions could Sam use to figure E , his total earnings for the day?
The function Sam can use to figure his total earnings for the day, based on the number of people he serves, is E(n) = 42 + 5n.
To calculate Sam's total earnings for the day, we need to consider both his hourly wages and the tips he receives based on the number of people he serves. Let's break it down step by step.
First, we know that Sam earns $7 per hour as his wage. Since he works for 6 hours, his earnings from wages alone would be $7 multiplied by 6, which equals $42.
Next, Sam also earns about $5 in tips for each person he serves. We can represent the number of people Sam serves as "n". Therefore, his total tip earnings would be $5 multiplied by "n", which gives us 5n.
To calculate Sam's total earnings for the day, we add his earnings from wages and tips together. So the function representing his total earnings, "E", can be written as:
E(n) = 7(6) + 5n
Simplifying further, we get:
E(n) = 42 + 5n
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Find the center of the ellipse defined by the equation... 100 points
Answer:
(-4,4)
Step-by-step explanation:
You rewrite the terms:
(x + 4)^2 => [x - (-4)]^2
(y - 4)^2 => [y - (4)]^2
so h = -4 and k = 4
so center of ellipse is (h,k) or (-4,4)
Answer:
Center = (-4, 4)
Step-by-step explanation:
The standard form of the equation of an ellipse with center (h, k) is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
The given equation is:
[tex]\dfrac{(x+4)^2}{25}+\dfrac{(y-4)^2}{9}=1[/tex]
Comparing the given equation with the standard form, we can see that h = -4 and k = 4. Therefore, the center (h, k) of the ellipse is (-4, 4).
The diagonal of rectangle ABCD measures 2 inches in length. What is the length of line segment AB?
Answer:
AB = √3
Step-by-step explanation:
Since ABCD is a rectangle, all angles are 90°
∠CDA = 90°
⇒ ∠CDB + ∠BDA = 90
⇒ ∠BDA = 60
In ΔABD,
sin(∠BDA) = opposite/ hypotenuse = AB / BD
⇒ sin(60) = AB/2
⇒ AB = 2 sin(60)
⇒ AB = 2 (√3)/2
AB = √3
What is the major difference between Grades 4 and 5 in terms of the teaching of probability?
Answer:
In Grade 4, students are introduced to the concept of chance and the idea that different situations have different probabilities of occurring. They learn that for many situations, there are a finite number of different possible outcomes. However, at this stage, students are not expected to calculate the probability of events occurring. In Grade 5, students continue to build on their understanding of probability and may begin to learn more advanced concepts and techniques for calculating probabilities.
Step-by-step explanation:
If FE =14 find the length of BC
Please give a very in-depth explanation and I will mark Brainliest!!
HI Your answer is 42
I have calculated it you can trust me
Well you have marked right in the pic
PLEASE MARK AS BRAINLIEST
Which expression is equivalent to 10f - 5f + 8 +6g +4?
The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.
To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:
10f - 5f + 8 + 6g + 4
Combining the terms with 'f', we have:
(10f - 5f) + 8 + 6g + 4
This simplifies to:
5f + 8 + 6g + 4
Next, we can combine the constant terms:
8 + 4 = 12
Thus, the simplified expression is:
5f + 12 + 6g
This expression is equivalent to 10f - 5f + 8 + 6g + 4.
In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.
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what is the value of f(x)=-1/3x-1/3 when x=-1/2
Answer:
f(-1/2) = -1/6
Step-by-step explanation:
To find the value of f(x) when x = -1/2, we substitute -1/2 for x in the expression for f(x) and simplify:
f(x) = (-1/3)x - 1/3
f(-1/2) = (-1/3)(-1/2) - 1/3
= 1/6 - 1/3
= -1/6
So, f(-1/2) = -1/6.
PLEASE HELP ITS HARD
Answer:
- 8a²
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m - n)}[/tex]
given
[tex]\frac{80a^9}{-10a^7}[/tex]
= [tex]\frac{80}{-10}[/tex] × [tex]a^{(9-7)}[/tex]
= - 8 × a²
= - 8a²
Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).
1. Start by calculating the distance between the vertices of the original triangle ABC:
- Distance between A(4, 3) and B(3, -2):
Δx = 3 - 4 = -1
Δy = -2 - 3 = -5
Distance = √((-[tex]1)^2[/tex] + (-[tex]5)^2[/tex]) = √26
- Distance between B(3, -2) and C(-3, 1):
Δx = -3 - 3 = -6
Δy = 1 - (-2) = 3
Distance = √((-6)² + 3²) = √45 = 3√5
- Distance between C(-3, 1) and A(4, 3):
Δx = 4 - (-3) = 7
Δy = 3 - 1 = 2
Distance = √(7² + 2²) = √53
2. Apply the scale factor of 1.5 to the distances calculated above:
- Distance between A' and B' = 1.5 * √26
- Distance between B' and C' = 1.5 * 3√5
- Distance between C' and A' = 1.5 * √53
3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):
- A' is located Δx units horizontally and Δy units vertically from A.
- Δx = 1.5 * (-1) = -1.5
- Δy = 1.5 * (-5) = -7.5
- Coordinates of A':
x-coordinate: 4 + (-1.5) = 2.5
y-coordinate: 3 + (-7.5) = -4.5
4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).
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what is five times five
Answer:
25
Step-by-step explanation:
5+5+5+5+5=25
Answer:25
Step-by-step explanation:
Question 4 a) Show that y₁= 1/t is a known solution of -t²y" + 3ty' + 5y = 0, where t > 0, and find the second solution.
y₁ = 1/t is indeed a known solution of the given differential equation.
The second solution can be found using reduction of order or other methods specific to the equation.
Let's find the first and second derivatives of y₁ with respect to t:
y₁ = 1/t
First derivative:
y'₁ = d/dt (1/t) = -1/t²
Second derivative:
y''₁ = d/dt (-1/t²) = 2/t³
Now, let's substitute y₁, y'₁, and y''₁ into the differential equation:
-t²y'' + 3ty' + 5y = 0
Substituting the values:
-t²(2/t³) + 3t(-1/t²) + 5(1/t) = 0
Simplifying the expression:
-2/t + (-3/t) + 5/t = 0
(-2 - 3 + 5)/t = 0
0/t = 0
We can see that the expression simplifies to 0/t, which is equal to 0.
Therefore, y₁ = 1/t is indeed a known solution of the given differential equation.
To find the second solution, we can use the method of reduction of order. Let's assume the second solution is of the form y₂ = v(t)y₁, where v(t) is a function to be determined.
Substituting this into the differential equation, we have:
-t²(y₂'' + v'y₁' + v''y₁) + 3t(y₂' + vy₁') + 5y₂ = 0
Expanding and rearranging the terms, we get:
-t²(v''y₁ + v'y₁' + v'y₁ + vy₁'') + 3t(vy₁' - v'y₁) + 5vy₁ = 0
Simplifying further:
(-t²v''y₁ - 2t²v'y₁' + 3tvy₁' + 5vy₁) + (-t²v'y₁ + 3tvy₁ - 5v'y₁) = 0
Combining like terms:
-t²v''y₁ - 2t²v'y₁' - t²v'y₁ - t²v'y₁ + 3tvy₁' + 3tvy₁ + 5vy₁ - 5v'y₁ = 0
Simplifying:
-t²v''y₁ - 3t²v'y₁' + 6tvy₁' + (5v - 5v')y₁ = 0
Since y₁ = 1/t, we have:
-t²v''(1/t) - 3t²v'(1/t²) + 6tv(1/t²) + (5v - 5v')(1/t) = 0
Simplifying further:
-v'' - 3v' + 6v(1/t) + (5v - 5v')(1/t) = 0
Reducing the equation:
-v'' - 3v' + 6v/t + (5v/t - 5v'/t) = 0
-v'' - 3v' + (6v + 5v - 5v')/t = 0
-v'' - 3v' + (11v - 5v')/t = 0
To simplify the equation, we can multiply through by t:
-tv'' - 3tv' + 11v - 5v' = 0
Now, we have a differential equation in terms of v(t) only. To solve this equation, we can apply appropriate techniques such as separation of variables, integrating factors, or other methods depending on the specific form of the equation. Solving for v(t) will give us the second solution to the original differential equation -t²y" + 3ty' + 5y = 0.
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3.
Your family is planning a road trip stretching from coast to coast for this summer. The route and the time frame are nearly set; now you need to plan out the finances. Your parents have decided that rental of an RV will be cheaper than staying in hotels, but they would like an estimate on the total cost. Can you help them?
a. To rent an RV, the following costs apply: $125 per day, plus 32 cents per mile. Additionally, to drop off the RV on the other side of the country, there is an extra fee of $2,500. Write an equation to describe the total cost of RV rental.
b. Your parents have two options for their road trip plans. The first option stretches over 3500 miles and includes fewer stops but more beautiful scenery. It will take about a week and a half (11 days). The second option stretches over just 3000 miles, but it includes more overnight stops and will therefore take two weeks (14 days). Which of these two options is cheaper?
c. Your little sister really wants to take the two-week trip, but your parents really want to keep the RV rental cost under $5,000. You can compromise by either taking a more direct route (lessening the miles) or by stopping for less overnight stays (lessening the days of the rental). What would the domains be for these two compromises? Justify why you think your domains are correct.
d. Write and solve equations to find how many miles or how many days you would have to eliminate in order to stay under the $5,000 budget. Explain each step as you solve your equations. Finally, make a recommendation to your parents about which compromise you think is best.
a. An equation to describe the total cost of RV rental:
Cost = (125 * d) + (0.32 * m) + 2500
b. Comparing the two costs will determine which option is cheaper.
c. For the more direct route: m ≤ 3500
For fewer overnight stays: d ≤ 14
These domains ensure that we don't exceed the original values for miles and days.
d. I recommend compromising by lessening the number of days of the rental. By reducing the rental period to 11 days, you can stay within the $5,000 budget while still allowing your little sister to take the two-week trip.
a. To write an equation for the total cost of RV rental, we can use the given information. The cost per day is $125, and there is an additional charge of 32 cents per mile. Let's denote the number of days as d and the number of miles as m. The equation for the total cost of RV rental can be written as:
Cost = (125 * d) + (0.32 * m) + 2500
b. To compare the costs of the two options, we need to calculate the total cost for each. Option 1 has 3500 miles and takes 11 days, while option 2 has 3000 miles and takes 14 days. We can substitute these values into the equation from part a to find the total costs for each option. Comparing the two costs will determine which option is cheaper.
c. To compromise and stay within a budget of $5,000, we can adjust either the number of miles or the number of days. For the more direct route, we can reduce the number of miles, and for fewer overnight stays, we can reduce the number of days. The domains for these compromises would be:
For the more direct route: m ≤ 3500
For fewer overnight stays: d ≤ 14
These domains ensure that we don't exceed the original values for miles and days.
d. To find the number of miles or days to eliminate in order to stay under the $5,000 budget, we can set up equations using the total cost equation from part a. Let's denote the reduced number of miles as m' and the reduced number of days as d'. We need to solve the following equation for each compromise:
(125 * d') + (0.32 * m') + 2500 ≤ 5000
By substituting the appropriate values into the equation and solving for m' or d', we can determine how many miles or days need to be eliminated.
Based on the given information, I recommend compromising by lessening the number of days of the rental. By reducing the rental period to 11 days, you can stay within the $5,000 budget while still allowing your little sister to take the two-week trip. This compromise ensures that you don't have to sacrifice too much scenic beauty or make drastic changes to the route.
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A circles radius is 1 1/3 yard whats the perimeter
Step-by-step explanation:
Perimeter = pi * diameter
radius = 1 1/3 yard then diameter = 2 2/3 yd
perimter = pi * 2 2/3 yds = 8.38 yds
Last year, Ali biked b miles. This year, he biked 358 miles. Using b, write an expression for the total number of miles he biked
B=(3,5,6,9) and C=(2,4,6,8) Find (A). A/B (B). B/C C. A/C (D). C/A
Answer:
The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.
5 In a Survery of 130 people 80 claimed to be CDO partisans and 60 claimed to be Anc partisan. If 30 of them are both ANC and CDO how many people are none of these two parties
Answer: there are 20 people who claimed to be neither CDO partisans nor ANC partisans.
Step-by-step explanation:
To determine the number of people who are none of these two parties, we need to subtract the total number of people who claimed to be CDO partisans, ANC partisans, and those who claimed to be both from the total number of people surveyed.
Total surveyed people = 130
Number claiming to be CDO partisans = 80
Number claiming to be ANC partisans = 60
Number claiming to be both ANC and CDO = 30
To find the number of people who are none of these two parties, we can calculate it as follows:
None of these two parties = Total surveyed people - (CDO partisans + ANC partisans - Both ANC and CDO)
None of these two parties = 130 - (80 + 60 - 30)
None of these two parties = 130 - 110
None of these two parties = 20
A graph has time driven (hours) on the x-axis, and Distance Driven (miles) on the y-axis. Points are grouped closely together an increase slightly. Points (2, 225) and (8, 75) are outside of the cluster.
The scatterplot shows the time driven on a trip compared to the distance driven. Inspect the scatterplot to determine if it has outliers.
How many outliers does the data set have?
The point
is an outlier in the data se
The data set has two outliers, namely the points (2, 225) and (8, 75).
Based on the given information about the scatterplot, we can observe that most of the points are grouped closely together and show a slight increase.
There are two points that lie outside of this cluster, specifically (2, 225) and (8, 75).
To determine if these points are outliers, we need to consider their deviation from the general pattern exhibited by the majority of the data points.
If these points deviate significantly from the overall trend, they can be considered outliers.
In this case, since (2, 225) and (8, 75) lie outside of the cluster of closely grouped points and do not follow the general pattern, they can be considered outliers.
These points are noticeably different from the majority of the data points and may have influenced the overall trend of the scatterplot.
The data set has two outliers, namely the points (2, 225) and (8, 75).
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Sampling based upon equal probability is called
Select one:
a. Cluster Sampling
b. Probability sampling
c. Stratified random sampling
d. Simple random sampling
e. Systematic sampling
Note: Answer E is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Sampling based upon equal probability is called d. Simple random sampling. The correct answer is d. Simple random sampling.
Simple random sampling is a sampling technique where each individual in the population has an equal probability of being selected for the sample. It is based on the principle of equal probability, ensuring that every element has the same chance of being chosen. This method involves randomly selecting samples without any specific grouping or stratification.
Cluster sampling involves dividing the population into clusters or groups and randomly selecting entire clusters for inclusion in the sample. It does not guarantee equal probability for individual units within each cluster.
Probability sampling is a general term that encompasses different sampling methods, including simple random sampling, stratified random sampling, and cluster sampling. It refers to sampling techniques that rely on random selection and allow for the calculation of probabilities associated with sample estimates.
Stratified random sampling involves dividing the population into distinct strata based on certain characteristics and then selecting samples from each stratum in proportion to their representation in the population. It does not guarantee equal probability of selection for all individuals.
Systematic sampling involves selecting every kth individual from a population list after randomly selecting a starting point. It does not guarantee equal probability of selection for all individuals.
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Find the volume of the solid obtained by rotating the region
bounded by the graphs y=(x-4)^3,the x-axis, x=0, and x=5
about the y-axis? (Express numbers in exact form. Use symbolic
notation and fractions where needed.)
Answer:
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis, we can use the method of cylindrical shells.
The formula for the volume of a solid obtained by rotating a region bounded by the graph of a function f(x), the x-axis, x = a, and x = b about the y-axis is given by:
V = 2π ∫[a, b] x * f(x) dx
In this case, the function f(x) = (x - 4)^3, and the bounds of integration are a = 0 and b = 5.
Substituting these values into the formula, we have:
V = 2π ∫[0, 5] x * (x - 4)^3 dx
To evaluate this integral, we can expand the cubic term and then integrate:
V = 2π ∫[0, 5] x * (x^3 - 12x^2 + 48x - 64) dx
V = 2π ∫[0, 5] (x^4 - 12x^3 + 48x^2 - 64x) dx
Integrating each term separately:
V = 2π [1/5 x^5 - 3x^4 + 16x^3 - 32x^2] evaluated from 0 to 5
Now we can substitute the bounds of integration:
V = 2π [(1/5 * 5^5 - 3 * 5^4 + 16 * 5^3 - 32 * 5^2) - (1/5 * 0^5 - 3 * 0^4 + 16 * 0^3 - 32 * 0^2)]
Simplifying:
V = 2π [(1/5 * 3125) - 0]
V = 2π * (625/5)
V = 2π * 125
V = 250π
Therefore, the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis is 250π cubic units.
PLEASE HELPP: 2.11.2 Project: Performance Task: The Parallax Problem (For San Francisco)
The Scenario: You’re looking for a sponsor to pay for you to participate in a sailboat race. Now that you’ve solved the parallax problem, use the same skills you used there to write a proposal that shows that you can win the race.
The Project: Use the information provided in the performance task to estimate your travel costs and to calculate your average speed and the speed of last year’s winner. Use the questions below to help you gather information to write your proposal
3. What is the distance between buoy A and B? (5 points)
4. What are the lengths of the other two triangle legs? (4 points: 2 points each)
Remember what you know about the shape of the Race Course.
5. What is the total length of the race course? (4 points: 3 for calculation, 1 for answer)
Part VIII: Calculate the winner’s speed. (10 points)
1. What was the winner’s speed during last year’s race? (5 points: 3 points for speed. 2 points for conversion to knots).
2. How does the winner’s speed compare with your average speed? How much faster or slower are you? (5 points)
Part IX: Write your proposal. (8 points)
Now it’s time to make your proposal to the sponsor. Your sponsor will have their logo on your boat, so they want to be sure it’s likely to do well. The sponsor also needs to know what the expenses and risks are, so they know how much their investment in you will cost.
1. Complete the table to summarize the results of your study. (4 points)
Category:
Race:
Risk Analysis:
Itemized Travel Cost
Safety hazards
Competitive Analysis:
My time and speed
Last year's winning time and speed
Reward Analysis:
My chances of winning
2. Write a summary paragraph explaining why the sponsor should accept your proposal. (4 points)
The proposal is as follows
Part III - The distance between buoys A and B is 12.8 kilometers.
Part IV - The length of the other two triangle legs are 10.2 kilometers and 8.4 kilometers.
Part V - The total length of the race course is 31.4 kilometers.
Part VIII - The winner's speed during last year's race was 10.8 knots.
See the proposal attached.
Why the sponsor should accept your proposalDear Sponsor,
I'm seeking sponsorship for the San Francisco sailboat race.
With a proven track record and the determination to win, your investment of $5,500 covers travel costs and potential hazards.
By associating your brand with a winning sailor, you'll gain significant exposure to thousands of spectators. Join me in this thrilling race for success.
Sincerely,
[Your Name]
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If � 1 = 4 a 1 =4 and � � = � � � − 1 + 4 a n =na n−1 +4 then find the value of � 5 a 5 .
The value of `a5 = λ5 = 824`.Therefore, the value of `a5` is 824.
Given the following values; `λ1 = 4` and `λn = na(n-1) + 4`.
We are required to calculate the value of `λ5` which is `a5`.
Solution We are given that;`λ1 = 4` which can also be expressed as `a1 = 4`. We are also given that `λn = na(n-1) + 4`. For `n=2`, `λ2 = 2a1 + 4 = 2(4) + 4 = 12`.
For `n=3`, `λ3 = 3a2 + 4 = 3(12) + 4 = 40`. For `n=4`, `λ4 = 4a3 + 4 = 4(40) + 4 = 164`. For `n=5`, `λ5 = 5a4 + 4 = 5(164) + 4 = 824`.
Hence, the value of `a5 = λ5 = 824`.Therefore, the value of `a5` is 824.
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What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS?
We would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.
To prove that triangles ΔXYZ and ΔFEG are congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence criteria, we need to show that they share certain corresponding angles and sides.
In ASA, we would need to show that both triangles have two congruent angles and the included side between those angles is congruent. In AAS, we would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.
Additional information that could be used to prove the congruence of ΔXYZ and ΔFEG using ASA or AAS includes:
1. Angle X = Angle F: If we can show that angle X in triangle ΔXYZ is congruent to angle F in triangle ΔFEG, we have one angle congruence.
2. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence.
3. Side XY = Side FE: If we can prove that side XY in triangle ΔXYZ is congruent to side FE in triangle ΔFEG, we have the included side congruence.
Alternatively:
4. Angle Z = Angle G: If we can show that angle Z in triangle ΔXYZ is congruent to angle G in triangle ΔFEG, we have the second angle congruence in AAS.
5. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence in AAS.
6. Side XZ = Side FG: If we can prove that side XZ in triangle ΔXYZ is congruent to side FG in triangle ΔFEG, we have a pair of non-included side congruence.
By establishing these angle and side congruences, we can use either the ASA or AAS congruence criteria to prove that triangles ΔXYZ and ΔFEG are congruent.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
B. Lenghts of the diagonals
Step-by-step explanation:
A parabola can be drawn given a focus of ... 100pts
Answer:
The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.
Step-by-step explanation:
The given directrix of the parabola is y = 2, which is a horizontal line.
This means that the parabola is vertical, with a vertical axis of symmetry.
The focus of a parabola is a fixed point located inside the curve. The y-coordinate of the given focus is y = -10. As this is below the directrix, it means that the parabola opens downwards.
The standard form of a vertical parabola is:
[tex]\boxed{(x-h)^2=4p(y-k)}[/tex]
where:
Vertex = (h, k)Focus = (h, k+p)Directrix: y = (k - p)Axis of symmetry: x = hAs the focus is (3, -10), then:
[tex](h, k+p)=(3,-10)[/tex]
[tex]\implies h = 3[/tex]
[tex]\implies k+p=-10[/tex]
As the directrix is y = 2, then:
[tex]k - p=2[/tex]
To find the value of k, sum the equations involved k and p to eliminate p:
[tex]\begin{array}{crcccr}&k &+& p& =& -10\\+&k& -& p& = &2\\\cline{2-6}&2k&&& =& -8\\\cline{2-6}\\\implies &k&&&=&-4\end{array}[/tex]
To find the value of p, substitute the found value of k into one of the equations:
[tex]-4-p=2[/tex]
[tex]p=-4-2[/tex]
[tex]p=-6[/tex]
Therefore, the values of h, k and p are:
h = 3k = -4p = -6The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.
The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.
How to determine the equation and vertex of a parabola?In Mathematics, the standard form of the equation of the directrix lines for any parabola is given by this mathematical equation:
(x - h)² = 4p(y - k).
Where:
h and k are the vertex.p is a point.Since the directrix is horizontal, the axis of symmetry would be vertical. This ultimately implies that, we would have the following parameters;
directrix is y = 2
Focus, (h, k + p) = (3, -10)
Next, we would determine the value of k as follows;
k + p = -10 .......equation 1
k - p = 2 .......equation 2
By solving the equations simultaneously, we have:
2k = -8
k = -4
For the value of p, we have the following from equation 2:
k - p = 2
-4 - p = 2
p = -4 - 2
p = -6
In conclusion, we can logically deduce that the parabola opens downward because the p-value is negative.
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When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 4 kg, the acceleration of the object is 9 m/s². When the same force acts upon another object, its acceleration is 6 m/s². What is the mass of this
object?
Step-by-step explanation:
a = k/m or ma = k
using 4 and 9 4* 9 = k = 36
then the equation becomes:
ma = 36
using a = 6
6 * m = 36 shows m = 6 kg
please answer i am stuck