Answer: False
Step-by-step explanation: It is false because the y-coordinate is the range.
the expression x^2-8x+6 can be written in the form (x-p)^2+q
Answer:(x-4)^2-10
Step-by-step explanation:
3. Jumal and Jabari are helping Jumal's father with a construction project. He needs to build a triangular frame as a piece to be used in the whole project, but he has not been given all the information he needs to cut and assemble the sides of the frame. He is even having a hard time envisioning the shape of the triangle from the information he has been given. Here is the information about the triangle that Jumal's father has been given.
Side a 10.00 meters
Side b= 15.00 meters
Angle A = 40.0°
Jumal's father has asked Jumal and Jabari to help him find the measure of the other two angles and the missing side of this triangle. Carry out each student's strategy as described below. Then draw a diagram showing the shape and dimensions of the triangle that Jumal's father should construct.
The triangles created using the law of sines and the law of cosines for Jumal's approach and Jabari's approach are attached
What is the Law of Sines?The Law of Sines states that the ratio of a sine of an angle to the length of the side facing the angle is the same for the three sides of the triangle.
Jumal's approach
a. The measure of the angle B can be found as follows;
sin(40)/10 = sin(B)/15
B = 15 × arcsine(sin(40)/10) ≈ 74.6°
b. The measure of angle C can be found using the angle sum property of a triangle as follows;
∠C = 180 - (40 + 74.6) = 65.4°
c. The length of the side c is therefore;
sin(40)/10 = sin(65.4)/c
c = sin(65.4) × 10/sin(40) ≈ 14.1
The length of the side c is about 14.1 meters
The triangle can be obtained by using the specified and obtained dimensions as shown in the attached drawing
Jabari's Approach
a. The Law of Cosines indicates; a² = b² + c² - 2·b·c·cos(A)
Therefore;
100 = 225 + c² - 2 × 15 × c × cos(40)
10² = 15² + c² - 23·c
c² - 23·c + 125 = 0
c = (23 ± √(29))/2
c = 14.2 and 8.8
c. Please find attached then possible drawings based on the calculated dimensions, created with MS Word
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A police unit has deployed a tracking system on a highway with a speed limit of 65 mph. A driver passes through one radar detector at 2pm and is traveling 60 mph at that moment. Then, the driver passes through a second radar detector 159 miles away at 4pm, again traveling 60 mph at that moment. However, a speeding ticket is being issued for this driver. When he asked for an explanation, the response was "Mean Value Theorem. " Explain. Your report should include:
i- Detailed explanation about the mean value theorem.
ii- Detailed calculation steps.
The Mean-Value-Theorem is being used to explain why the driver received a speeding ticket even though they were traveling at exactly 60 mph at both radar-detectors. It suggests that there must have been a moment during the trip where the driver's speed was above the speed limit.
The Mean-Value Theorem is a theorem from calculus that states that for a continuous function on a closed interval, there exists at least one point in the interval where the instantaneous rate of change (the derivative) of the function is equal to the average rate of change of the function over the interval.
In this case, the police unit used the two radar detectors to determine the average-speed of the driver between the two points. The distance between the two detectors is 159 miles, and the time it took for the driver to travel that distance was 2 hours (from 2pm to 4pm), so the average speed of the driver was 159/2 = 79.5 mph.
However, the speed-limit on the highway is 65 mph, so the driver was exceeding the speed limit and received a speeding-ticket.
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Solve for x, t, r and round to the nearest hundredth
Answer:
x = 14°
t = 12.367 ~ 12.4
r = 2.999 ~ 3
Step-by-step explanation:
1st we can find x by sum theory which is the sum of all side equal to 180° .
x + 90° + 76° = 180 °
x + 166° = 180°
x= 180° - 166°
x = 14° ... So the unknown angle is 14°
and we also can solve hypotenus t and adjecent r by using sin amd cos respectively by angle 76° .
sin(76) = 12/t
sin(76) t = 12 ....... criss cross it
t = 12 / sin(76) ....... divided both side by sin(76)
t = 12.367 ~ 12.4 ....... result
And
cos(76) = r / 12.4
r = cos(76) × 12.4 .......criss cross
r = 2.999 ~ 3 ....... amswer and i approximate it
Jamal winchester invested 75,000 in to a property. He expects his annual expenses to be 18,000. If Jamal wants to earn 8% annual income on his capital investment, what monthly rent must he charge?
Jamal must charge a monthly rent of 2,000 to earn an 8% annual income on his capital investment.
It is given that Jamal Winchester invested 75,000 in to a property and he expects his annual expenses to be 18,000. Jamal wants to earn 8% annual income on his capital investment. Hence, the monthly rent he must charge is determined as follows.
1. Calculate the desired annual income:
75,000 (capital investment) x 0.08 (8% annual income) = 6,000.
2. Add the annual expenses:
6,000 (desired annual income) + 18,000 (annual expenses) = 24,000.
3. Divide by 12 months to find the monthly rent: 24,000 ÷ 12 = 2,000.
Jamal must charge a monthly rent of 2,000.
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find the perimeter of the equilateral triangle whose area is 16root3/4
The perimeter of this equilateral triangle is equal to 12 units.
How to calculate the area of an equilateral triangle?In Mathematics and Geometry, the area of an equilateral triangle can be calculated by using this formula:
Area of an equilateral triangle, A = √3/4 × a²
Where:
a represent the side lengths of an equilateral triangle.
By substituting the given parameters or dimensions into the formula for the area of an equilateral triangle, we have the following;
16 √3/4 = √3/4 × a²
a² = 16
a = 4 units.
In Mathematics and Geometry, the perimeter of an equilateral triangle can be calculated by using this mathematical equation:
Perimeter of an equilateral triangle, P = 3a
Perimeter of an equilateral triangle, P = 3(4)
Perimeter of an equilateral triangle, P = 12 units.
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You are choosing between two different cheese wedges at the grocery store. Assume both
wedges are triangular prisms with bases that are isosceles triangles. The first wedge has a base
that is 2. 5 in. Wide and a height of 4. 5 in. , with the entire wedge being 3 in thick. The second
wedge has a base that is 3 in, wide and a height of 4 in. , with the entire wedge being 3. 5 in.
thick. Which wedge has a greater volume of cheese, and by how much?
The first wedge by 6. 375 cubic inches
The first wedge by 12. 75 cubic inches
The second wedge by 8. 25 cubic inches
The second wedge by 4. 125 cubic inches
The second wedge has a greater volume by 4.125 cubic inches. Therefore, the correct option is 4.
To determine which cheese wedge has a greater volume, you need to calculate the volume of each triangular prism using the given dimensions.
For the first wedge:
1. Calculate the area of the base (isosceles triangle):
(base x height) / 2 = (2.5 in x 4.5 in) / 2 = 5.625 square inches
2. Calculate the volume of the prism:
base area x thickness = 5.625 sq in x 3 in = 16.875 cubic inches
For the second wedge:
1. Calculate the area of the base (isosceles triangle):
(base x height) / 2 = (3 in x 4 in) / 2 = 6 square inches
2. Calculate the volume of the prism:
base area x thickness = 6 sq in x 3.5 in = 21 cubic inches
To find which wedge has a greater volume and by how much, subtract the smaller volume from the larger volume:
21 cu in - 16.875 cu in = 4.125 cu in.
Therefore, the correct answer is option 4: The second wedge has a greater volume by 4.125 cubic inches.
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Dagne measures and finds that she can do a vertical jump that is 27. 5% of her height. If Dagne is 48 inches tall, how high can she jump? Enter your answer in the box
If Dagne is 48 inches tall, then she can jump 13.2 inches high.
Given that Dagne can do a vertical jump that is 27.5% of her height, and she is 48 inches tall, we can find how high she can jump by multiplying her height by the percentage of her vertical jump as follows:
Jump height = 27.5% of height
Jump height = (27.5/100) x 48 inches
Jump height = 0.275 x 48 inches
Jump height = 13.2 inches
Therefore, Dagne can jump 13.2 inches high.
To explain this, we can say that the problem gives us information about the proportion of Dagne's height that she can jump vertically. The percentage of her height that she can jump is given as 27.5%, which we can convert to a decimal form (0.275) for calculation purposes. Multiplying this decimal by Dagne's height of 48 inches gives us the height that she can jump, which is 13.2 inches. So, Dagne can jump 13.2 inches high based on the given information.
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Customer: "Currently I am paying $60. 00 a month for my service. I would like to upgrade to the $80. 00 service package because my new employer offers a 20% discount with your company. What would be the cost difference compared to what I am paying now if I upgraded?" Employee: "With your discount you would only pay __________ a month more for the upgraded plan. "
"With your discount, you would only pay $4.00 a month more for the upgraded plan."
You are currently paying $60.00 a month for your service and you would like to upgrade to the $80.00 service package because your new employer offers a 20% discount with the company. Let's calculate the cost difference compared to what you are paying now if you upgraded.
Step 1: Calculate the discount on the $80.00 service package.
Your new employer offers a 20% discount, so to find the discount amount, multiply the original price by the discount percentage.
Discount = $80.00 * 20% = $80.00 * 0.20 = $16.00
Step 2: Subtract the discount from the original price to find the new monthly cost.
New price = Original price - Discount = $80.00 - $16.00 = $64.00
Step 3: Calculate the cost difference between your current plan and the upgraded plan.
Cost difference = New price - Current price = $64.00 - $60.00 = $4.00
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An instructor graded 200 papers and found 80 errors. If a paper is picked at
random, find the probability that it will have exactly 4 errors
The probability of a paper having exactly 4 errors can be calculated using the binomial probability formula, which is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
What is the probability of selecting a paper at random from 200 papers and instructor found 80 errors and the probability that a paper has exactly 4 errors?In binomial probability formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
n is the number of trials (in this case, the number of papers graded)
k is the number of successes (in this case, the number of papers with exactly 4 errors)
p is the probability of success (in this case, the probability that a paper has an error, which can be calculated by dividing the total number of errors by the total number of papers graded)
Calculate the probability of a paper having an errorp = 80/200 = 0.4
Calculate the probability of a paper having exactly 4 errorsP(X = 4) = (200 choose 4) * 0.4^4 * (1-0.4)^(200-4) ≈ 0.153
Therefore, the probability of picking a paper at random and finding exactly 4 errors is approximately 0.153 or 15.3%.
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PLEASE HELPPPPPPPP
PLEASE IMBEGGING
The area under the curve at the given points is 3.758 sq.units.
What is the area under the curve?The area under the curve at the given points is calculated as follows;
y = -3/x ; (-7, -2)
To find the area under the curve y = -3/x between x = -7 and x = -2, we need to integrate the function from x = -7 to x = -2.
∫[-7,-2] (-3/x) dx
= [-3 ln|x|]_(-7)^(-2)
= [-3 ln|-2| - (-3 ln|-7|)]
= [-3 ln(2) + 3 ln(7)]
= 3 ln(7/2)
= 3.758 sq.units
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Find the surface area of the regular pyramid 6 cm 4cm help
The surface area of the given regular pyramid is 84 cm^2.
To find the surface area of a regular pyramid, we need to calculate the area of each face and add them together. A regular pyramid has a base that is a regular polygon, and its lateral faces are triangles that meet at a common vertex. We can use the Pythagorean theorem to find the slant height of the pyramid, which is the height of each lateral face.
Let's assume that the base of the regular pyramid is a square with side length 6 cm, and the slant height is 4 cm.
First, we need to find the area of the base of the pyramid:
Area of the base = (side length)^2
= 6 cm x 6 cm
= 36 cm^2
Next, we need to find the area of each triangular lateral face. Since the pyramid is a regular pyramid, all the triangular faces are congruent.
We can find the area of each triangular face using the formula:
Area of a triangle = (1/2) x base x height
The base of each triangular face is equal to the side length of the square base, which is 6 cm. The height of each triangular face is equal to the slant height, which is 4 cm.
Area of each triangular face = (1/2) x 6 cm x 4 cm
= 12 cm^2
Since the pyramid has 4 triangular faces, we need to multiply the area of one triangular face by 4 to get the total area of all the triangular faces:
Total area of the triangular faces = 4 x 12 cm^2
= 48 cm^2
Finally, we can find the total surface area of the pyramid by adding the area of the base and the area of the triangular faces:
Total surface area = Area of the base + Total area of the triangular faces
= 36 cm^2 + 48 cm^2
= 84 cm^2
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A student lifts a 12 n textbook 1. 5 and carries the book 5 m across the room in 7s
The student does 18 J of work on the textbook. Their power output is 0.0228 W. Work is calculated by multiplying force and displacement, while power is the rate at which work is done and is calculated by dividing work by time.
To calculate the work done by the student on the textbook, we use the formula
work = force x distance x cos(theta)
where force is the weight of the textbook, distance is the height it is lifted, and theta is the angle between the force and distance vectors, which is 0 degrees since the force is acting vertically upward and the distance is upward as well. Thus, we have
work = 12 N x 1.5 m x cos(0) = 18 J
To calculate the power output of the student, we use the formula:
power = work / time
where work is the work done by the student on the textbook, and time is the total time it took to lift and carry the book. Thus, we have:
time = 1.5 s + 7 s = 8.5 s
power = 18 J / 8.5 s = 2.12 W
Therefore, the student did 18 J of work on the textbook, and had a power output of 2.12 W.
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--The given question is incomplete, the complete question is given
" a student lifts a 12 N textbook 1.5 m in 1.5 s and carries the books 5 m across the room in 7 s. how much work does the student do on the textbook? and what is the power output of the student."--
Lucy’s dog weighs nine and seventy-five hundredths kilograms. what is the weight, in kilograms, of lucy’s dog written in expanded notation?
The weight of Lucy's dog, written in expanded notation, is 9 kilograms and 0.75 kilograms.
Expanded notation is a way of writing a number as the sum of each digit multiplied by its place value. In this case, the number is 9.75. The digit 9 is in the tens place, so it represents 9 tens or 90. The digit 7 is in the ones place, so it represents 7 ones or 7.
The digit 5 is in the tenths place, so it represents 5 tenths or 0.5. The digit 7 is in the hundredths place, so it represents 7 hundredths or 0.07. Therefore, the weight of Lucy's dog in expanded notation is 90 kilograms plus 7 kilograms plus 0.5 kilograms plus 0.07 kilograms, which simplifies to 9 kilograms and 0.75 kilograms.
Mathematically, we can represent the given number as 9.75 = 9 x 10 + 7 x 1 + 5 x 0.1 + 7 x 0.01 = 90 + 7 + 0.5 + 0.07 = 9.57. Thus, the weight of Lucy's dog written in expanded notation is 9 kilograms and 0.75 kilograms.
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Whats 4x + 5 = 6 (x + 3) - 20 - 2x
To solve this equation, we first simplify both sides of the equation by using the distributive property to expand the right-hand side:
4x + 5 = 6(x + 3) - 20 - 2x
4x + 5 = 6x + 18 - 20 - 2x
Next, we can combine like terms on the right-hand side:
4x + 5 = 4x - 2
Now, we can subtract 4x from both sides to isolate the variable on one side of the equation:
4x - 4x + 5 = 4x - 4x - 2
5 = -2
This is a contradiction since 5 cannot be equal to -2. Therefore, there is no solution to this equation.
In other words, the equation is inconsistent and there is no value of x that can make it true.
75°(4x+7)° find x
(2x+10)°
(2x-10)° FIND X
The value of x using the assumptions of angle are 17 and 22.5
Finding the value of xFrom the question, we have the following parameters that can be used in our computation:
Angles: 75° and (4x + 7)°
Angles: (2x+10)° and (2x - 10)°
Assume 75° and (4x + 7)° are congruent angles, we have
4x + 7 = 75
So, we have
4x = 68
Divide by 4
x = 17
Assume (2x+10)° and (2x - 10)° are complementary angles, we have
2x + 10 + 2x - 10 = 90
So, we have
4x = 90
Divide by 4
x = 22.5
Hence, the values of x are 17 and 22.5
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The seventh-grade class is selling boxes of votive candles as a fundraiser. The first box purchased costs $14. 00, and each additional box costs $10. 0.
a. Is the relationship between the number of additional boxes of candles purchased and the total money spent linear?explain
b. An equation that relates the total money spent on boxes of candles, C, to the number of additional boxes purchased,b,is,
c. Using the equation from part (b), the total money spent by a person who bought 3 boxes of candles for the fundraiser would be $
No, the relationship between the number of additional boxes of candles purchased. C = 14.00 + 10.00b. The person would spend $34.00 on 3 boxes of candles.
a. No, the relationship between the number of additional boxes of candles purchased and the total money spent is not linear. This is because the cost of the first box is $14.00 and the cost of each additional box is $10.00.
A linear relationship implies that the change in the dependent variable (total money spent) is proportional to the change in the independent variable (number of additional boxes purchased), but in this case, the cost does not change at a constant rate.
b. The equation that relates the total money spent on boxes of candles, C, to the number of additional boxes purchased, b, is:
C = 14.00 + 10.00b
This equation takes into account the cost of the first box, which is $14.00, and the cost of each additional box, which is $10.00.
c. If someone buys 3 boxes of candles, they are purchasing 2 additional boxes (since the first box is already included in the $14.00). Using the equation from part (b), the total money spent by a person who bought 3 boxes of candles for the fundraiser would be:
C = 14.00 + 10.00(2) = $34.00
Therefore, the person would spend $34.00 on 3 boxes of candles.
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Can someone help me asap? It’s due today!!
Based on the information provided, James would have 20 different waffle options.
How many options will James have?Since each waffle cone can hold two scoops of ice cream and James must choose a different flavor for each scoop, we can approach this problem by using the multiplication principle of counting.
There are 5 different ice cream flavors to choose from for the first scoop, and 4 different flavors remaining for the second scoop. This is because James must choose a different flavor for each scoop.
Therefore, the number of different waffle cone options that James has is:
5 x 4 = 20
So, James has 20 different waffle cone options if he chooses a different flavor of ice cream for each scoop.
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Given the exponential model y= 200(.80)^x, tell whether the model represents exponential growth or decay. What is the growth/decay factor? A. Growth: (0.80) B. Decay: (200) C. Growth: (200) D. Growth: (0.80)
The growth/decay factor is the base of the exponent, which is 0.80 in this case. The factor is less than 1, indicating that the output (y) decreases as the input (x) increases.
what is exponent ?
In mathematics, an exponent (also known as a power or index) is a number that indicates how many times a given number (the base) must be multiplied by itself.
In the given question,
The given exponential model is:
y = 200(0.80)ˣ
where:
y is the output (dependent variable)
x is the input (independent variable)
To determine whether the model represents exponential growth or decay, we need to examine the base of the exponent, which is 0.80 in this case.
If the base is greater than 1, then the model represents exponential growth, and if the base is between 0 and 1, then the model represents exponential decay.
In this case, the base of the exponent is 0.80, which is between 0 and 1. Therefore, the model represents exponential decay.
The growth/decay factor is the base of the exponent, which is 0.80 in this case. The factor is less than 1, indicating that the output (y) decreases as the input (x) increases. The factor represents the rate of decay per unit of the independent variable, which in this case is 0.80.
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Please help me now Asapppp
So the angles that must be right angles are KER and ERI.
What is angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are usually denoted by the letters A and B, and the vertex is denoted by the letter V. The angle is denoted by the symbol ∠, followed by the letters of the rays with the vertex in between, such as ∠AVB. The measure of an angle is the amount of rotation needed to move one ray to coincide with the other ray, and is usually given in degrees or radians. Angles are used in many areas of mathematics and science, such as trigonometry, geometry, physics, and engineering. They are also used in everyday life, such as in navigation, construction, and design.
Here,
Since RE and RI are secants of the circle, we can use the Intersecting Secants Theorem to find the relationships between the angles in the diagram.
Angle ERK is half of the intercepted arc EIK, so we have m∠ERK = 1/2m(arc EIK).
Similarly, angle KRI is half of the intercepted arc KE, so we have m∠KRI = 1/2m(arc KE).
Angle REI is an exterior angle of triangle KIR, so we have m∠REI = m∠ERK + m∠KRI.
To determine which angles must be right angles, we need to look for cases where the intercepted arcs are semicircles, which have a measure of 180 degrees.
If arc EIK is a semicircle, then m(arc EIK) = 180 and m∠ERK = 1/2(180) = 90. Therefore, angle ERK is a right angle.
If arc KE is a semicircle, then m(arc KE) = 180 and m∠KRI = 1/2(180) = 90. Therefore, angle KRI is a right angle.
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The first is kept by the albatross, which first lands in our region. The second occurs every night in shooting, swimming, fighting, singing and others. Separately, they would reveal many to you. Together, they will reveal only one to you. And whose one is it?
Based on the information provided, it is not clear what "they" refer to. However, it seems that there are two distinct events or phenomena being described here.
The first involves the albatross, which is known to be a migratory bird that visits certain regions at certain times of the year. It is unclear what exactly is being "kept" by the albatross, but it could be some sort of information or knowledge that is unique to this bird.
The second event or phenomenon is described as happening every night and involving various activities such as shooting, swimming, fighting, and singing.
It is unclear what this refers to exactly, but it could be some sort of nightly ritual or tradition that takes place in a particular community or region.
The statement that "separately, they would reveal many to you" suggests that each of these phenomena has its own unique insights or knowledge to offer.
However, the statement that "together, they will reveal only one to you" implies that there is some sort of deeper connection or meaning between these two events that is not immediately apparent.
The question of "whose one is it?" suggests that there is some sort of ownership or responsibility associated with this revelation.
It is unclear who this refers to, but it could be interpreted as asking who is responsible for uncovering the deeper meaning or connection between these two phenomena.
In summary, the information provided is somewhat cryptic and open to interpretation. However, it seems that there are two distinct events or phenomena being described, and that there is some sort of deeper connection or meaning between them that is not immediately apparent.
The question of who is responsible for uncovering this connection remains unanswered.
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What kind of triangle is this?
A. Equilateral
B. Isosceles but not equilateral
C. Scalene
Answer:
C. Scalene
Step-by-step explanation:
Equilateral triangle has all sides equal.
Isosceles triangle has exactly 2 sides equal.
All side lengths in a Scalene triangle are distinct.
You rent an apartment that costs $1600$1600 per month during the first year, but the rent is set to go up 12.5% per year. What would be the rent of the apartment during the 10th year of living in the apartment? Round to the nearest tenth (if necessary).
The rent of the apartment during the 10th year of living in the apartment would be $4940.79
To solve the problem, we need to use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where:
A is the final amount
P is the initial principal
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the "principal" is the initial rent of $1600 per month, and the "interest rate" is the 12.5% increase per year. We want to find out the rent during the 10th year, so t = 10.
Let's plug in the values and solve for A:
A = 1600 * (1 + 0.125/12)^(12*10)
A = 1600 * (1.01042)^120
A = 1600 * 3.086
A = 4940.79
So the rent during the 10th year would be $4940.79 per month, rounded to the nearest tenth.
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RO Consider the convergent series (-1)" its sum s, and its partial sums n+1 84. That is, (-1)" and 8μ -Σ (-1)" n+1 RO NO 1. Is s - 85 going to be positive or negative? 2. Use the Alternating Series
The value of s - 85 cannot be determined based on the given information as we do not know the value of s.
Alternating Series Test states that if a series satisfies three conditions, namely the terms alternate in sign, the absolute value of the terms decreases as n increases, and the limit of the terms approaches zero as n approaches infinity, then the series converges.
The given series (-1)^n satisfies the first two conditions as the terms alternate in sign and the absolute value of the terms is decreasing. To check the third condition, we take the limit of the terms as n approaches infinity: lim n→∞ |(-1)^n+1/n+1| = lim n→∞ 1/(n+1) = 0.
Since all three conditions are satisfied, the series converges. We can also see from the given partial sums that the sum s lies between 83 and 85. Therefore, s - 85 is negative or zero.
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Use the equations to find ∂z/∂x and ∂z/∂y. ez = 5xyz
The partial derivative of z with respect to x is 5xy + 5xz, and the partial derivative of z with respect to y is 5xz + 5yz.
To find the partial derivatives of z with respect to x and y, we use the chain rule. The chain rule allows us to find the rate of change of a function with respect to one of its independent variables while holding all other independent variables constant.
Using the chain rule, we can find the partial derivatives of z with respect to x and y as follows:
∂z/∂x = 5(yz) + 5x(1)(z)
∂z/∂x = 5xy + 5xz
∂z/∂y = 5(xz) + 5y(1)(z)
∂z/∂y = 5xz + 5yz
Therefore, the partial derivative of z with respect to x is 5xy + 5xz, and the partial derivative of z with respect to y is 5xz + 5yz.
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An airplane flies at 500 mph with a direction of 135* relative to the air. The plane experiences a wind that blows 60 mph with a direction of 60*
The plane's new velocity is 421.4 mph with a direction of 63.43 degrees relative to the air.
To solve this problem, we need to use vector addition. Let's first draw a diagram to represent the situation.
First, we need to break down the velocity of the plane and the velocity of the wind into their horizontal and vertical components.
The velocity of the plane can be broken down into a horizontal component of 500*cos(135) mph and a vertical component of 500*sin(135) mph.
The velocity of the wind can be broken down into a horizontal component of 60*cos(60) mph and a vertical component of 60*sin(60) mph.
Now, we can add these components together to get the resultant velocity.
The horizontal component of the resultant velocity is 500*cos(135) + 60*cos(60) = -189.28 mph. The negative sign indicates that the velocity is in the opposite direction of the plane's original direction.
The vertical component of the resultant velocity is 500*sin(135) + 60*sin(60) = 374.28 mph.
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
|v| = sqrt((-189.28)^2 + (374.28)^2) = 421.4 mph.
Finally, we can find the direction of the resultant velocity using the inverse tangent function:
θ = tan^-1(374.28/-189.28) = -63.43 degrees.
So the plane's new velocity is 421.4 mph with a direction of 63.43 degrees relative to the air.
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Consider the following function f(x)=x^2+5
part a write a function in vertex form that shifts f(x) right 3 units
part b write a function in vertex form that shifts f(x) left 10 unites
Part a: f(x) = (x-3)^2 + 5
Part b: f(x) = (x+10)^2 + 5
Part a: To shift the function f(x) = x^2 + 5 right 3 units, we need to subtract 3 from the x-coordinate of the vertex. The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex. Thus, the function in vertex form that shifts f(x) right 3 units is:
f(x) = (x-3)^2 + 5
Part b: To shift the function f(x) = x^2 + 5 left 10 units, we need to add 10 to the x-coordinate of the vertex. Using the same vertex form as before, the function in vertex form that shifts f(x) left 10 units is:
f(x) = (x+10)^2 + 5
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How can I figure this out?
Answer:
Blue = 4
Red = 24
Green = 4
All = 32
Step-by-step explanation:
Area of a triangle: 1/2 * base * height, so for both blue and green:
1/2 * 2 * 4
1 * 4
4
Area of an object with 4 sides: length * width, so for red:
6 * 4
24
Area of everything: blue + red + green, so for all:
4 + 4 + 24
8 + 24
32
If two fair dice are rolled, what is the probability that the total showing is either even or less than five? 5.
these are the choices:
a. 5/9
b. 17/36
c. 19/36
d. 11/18
If two fair dice are rolled, the probability that the total showing is either even or less than five is 17/36. The correct answer is B.
There are 36 possible outcomes when rolling two dice, since each die has 6 possible outcomes.
To find the probability that the total showing is either even or less than five, we can first find the probability that the total showing is even, and then add to that the probability that the total showing is less than five, excluding the outcomes where the total showing is even.
To find the probability that the total showing is even, we can consider the following possibilities:
both dice show even numbers (probability 1/4)
both dice show odd numbers (probability 1/4)
So the probability of rolling an even total is 1/4 + 1/4 = 1/2.
To find the probability that the total showing is less than five, excluding the outcomes where the total showing is even, we can consider the following possibilities:
the two dice show 1 and 1 (probability 1/36)the two dice show 1 and 2 (probability 1/18)the two dice show 2 and 1 (probability 1/18)the two dice show 1 and 3 (probability 1/12)the two dice show 3 and 1 (probability 1/12)the two dice show 2 and 2 (probability 1/9)the two dice show 1 and 4 (probability 1/9)the two dice show 4 and 1 (probability 1/9)the two dice show 3 and 2 (probability 1/6)the two dice show 2 and 3 (probability 1/6)the two dice show 1 and 5 (probability 1/6)the two dice show 5 and 1 (probability 1/6)the two dice show 4 and 2 (probability 1/6)the two dice show 2 and 4 (probability 1/6)So the probability of rolling a total less than five, excluding the outcomes where the total showing is even, is 1/36 + 1/18 + 1/18 + 1/12 + 1/12 + 1/9 + 1/9 + 1/9 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 11/36.
Therefore, the probability that the total showing is either even or less than five is 1/2 + 11/36 = 17/36.
So the correct answer is (b) 17/36.
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Your friends, Fernando and Amelia, each own a video game designer company. They both want you to join their company. You currently have a part-time job making $8. 00 per hour. Fernando offers to pay you $15 per hour for the first month and then increase your hourly rate by $1. 00 each month. Amelia says she will start your pay at $8. 00 per hour but she will increase your hourly rate by 10% each month. In order to make the best decision, you decide to use the mathematics to choose the best offer based on the best hourly wage per month.
Write the equations to represent Fernando’s job offer and Amelia’s job offer. Let x = number of months, y = hourly wage.
Under what time period would you accept Fernando’s offer? Use mathematics to support your reasoning.
Under what time period would you prefer Amelia’s offer? Use mathematics to support your reasoning.
Now that we have looked at the different figures for Fernando and Amelia, which job would you take for the long run? Use mathematics to justify your answer
Answer:
The equation to represent Fernando's job offer is:
y = 15 + x
Where y is the hourly wage and x is the number of months worked.
The equation to represent Amelia's job offer is:
y = 8(1 + 0.1)^x
Where y is the hourly wage and x is the number of months worked.
To determine the time period for which Fernando's offer is better, we need to find the point where his hourly wage is greater than Amelia's. We can set the two equations equal to each other and solve for x:
15 + x = 8(1 + 0.1)^x
15 + x = 8(1.1)^x
x ≈ 20.44
Therefore, Fernando's offer is better for any time period greater than 20.44 months.
To determine the time period for which Amelia's offer is better, we need to find the point where her hourly wage is greater than Fernando's. We can set the two equations equal to each other and solve for x:
8(1 + 0.1)^x = 15 + x
8(1.1)^x = 15 + x
x ≈ 14.45
Therefore, Amelia's offer is better for any time period less than 14.45 months.
For the long run, we need to determine which offer has a higher hourly wage after a certain number of months. We can compare the two equations by finding their limits as x approaches infinity:
lim (y = 15 + x) as x → ∞ = ∞
lim (y = 8(1 + 0.1)^x) as x → ∞ = ∞
Therefore, both offers have the same long-term hourly wage of infinity. However, Fernando's offer has a faster rate of increase, so it may be more beneficial in the long run.
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