Antonio's weight after 5 weeks was 202.34 pounds, and it took him 19 weeks to weigh in at 161.05 pounds.
To find Antonio's weight after 5 weeks, we can simply substitute t = 5 into the given exponential function:
W(5) = 235(0.985)⁵
W(5) ≈ 209.88 pounds
So his weight after 5 weeks was approximately 209.88 pounds. To find how long it took him to weigh in at 161.05 pounds, we can set the function equal to 161.05 and solve for t:
161.05 = 235(0.985)ᵗ
0.685106383 ≈ 0.985ᵗ
t ≈ 25.5 weeks
So it took him approximately 25.5 weeks to weigh in at 161.05 pounds
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Complete question - Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)ᵗ where W is his weight in pounds and t is the time in weeks that he has been on the diet. What was his weight in pounds after 5 weeks? How long did it take(in weeks) him to weigh in at 161. 05 pounds?
At a noodles and company restaurant, the probability that a customer will order a nonalcoholic beverage is 48. Out of 12 customers 5 will order alcohol
The probability is that out of 12 customers, 7 will order a non-alcoholic beverage, and the remaining 5 will order an alcoholic beverage.
The likelihood that a client will arrange a non-alcoholic refreshment is given as 48%, which implies that the likelihood that a client will arrange an alcoholic refreshment is (100 - 48) = 52%.
Out of 12 customers, 5 will arrange liquor, which suggests that the remaining clients will arrange a non-alcoholic refreshment. We are able to calculate the number of clients who will arrange a non-alcoholic refreshment as takes after:
Number of clients who will arrange a non-alcoholic refreshment =
Add up to a number of clients - Number of clients who will arrange liquor
= 12 - 5
= 7
Subsequently, out of 12 clients, 7 will arrange a non-alcoholic refreshment, and the remaining 5 will arrange an alcoholic refreshment.
It is critical to note that these calculations are based on the presumption that each client will as it were arrange one refreshment.
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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."--
y = 49 - 4x y = 73 - 7x
The solution of the system of equation
x = 8 and y = 17
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's solve the system of equation by substitution method.
Therefore,
y = 49 - 4x
y = 73 - 7x
Hence, using substitution,
73 - 7x = 49 - 4x
73 - 49 = -4x + 7x
24 = 3x
divide both sides of the equation by 3
x = 24 / 3
x = 8
Therefore,
y = 73 - 7(8)
y = 73 - 56
y = 17
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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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A store sells a coat in three sizes: small, medium, and large. The coat comes in red, navy, and tan. Sales from a given day are displayed in the table
What is the experimental probability that the next coat sold is a medium, navy coat? Round your answer
to the nearest whole percent.
The probability of the next coat being sold as a medium navy coat is 11 / 95 when a store sells a coat in three sizes: small, medium, and large. The coat comes in red, navy, and tan.
We need to find the probability that the next coat sold as a medium navy coat. To find the probability we need to find the total number of coats and the number of medium navy coats,
Given data:
Medium navy coat = 22
Total Number of small coats = 18 + 24 +19 = 61
Total Number of medium coats = 21 + 22 + 25 = 68
Total Number of large coats = 19 + 20 + 22 = 61
From the given data the total number of coats is = 61 + 68 + 61 = 190
The probability that the next coat sold as a medium navy coat = a number of medium navy coats / total number of coats.
= 22 / 190
= 11 / 95
Therefore, the probability of the next coat being sold as a medium navy coat is 11 / 95
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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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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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The price of a calculator is decreased by
31
%
and now is
$
189. 6. Find the original price
Answer:
274.78
Step-by-step explanation:
Let's call the original price "x".
We know that the price decreased by 31%, so the new price is
100% - 31% = 69% of the original price:
0.69x = 189.6
To solve for x, we can divide both sides by 0.69:
x = 189.6 / 0.69
Simplifying this expression, we get:
x ≈ 274.78
Therefore, the original price was approximately $274.78.
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
In ΔLMN, m = 59 inches, n = 35 inches and ∠L=82°. Find ∠N, to the nearest degree
The answer is: ∠N ≈ 33°
To find ∠N in ΔLMN, we can use the Law of Cosines which states that c² = a² + b² - 2abcos(C), where c is the side opposite angle C.
In this case, side LM (m) is opposite angle ∠N, side LN (n) is opposite angle ∠L, and side MN (x) is opposite the unknown angle.
So, we can write:
m² = n² + x² - 2nxcos(82°)
Substituting the given values:
x² = 35² + 59² - 2(35)(59)cos(82°)
Solving for x, we get:
x ≈ 64.27
Now, using the Law of Sines which states that a/sin(A) = b/sin(B) = c/sin(C), we can find ∠N:
sin(∠N)/35 = sin(82°)/64.27
sin(∠N) ≈ 0.5392
∠N ≈ sin⁻¹(0.857) ≈ 32.6344°
Therefore, ∠N ≈ 33° to the nearest degree.
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Six friends are selling crafts at a flea market. they each need to pay $7. 20 to pay
for the table rental. they each sell 3 items. if every item is the same price, and the
6 friends make a total profit of $25. 20, what was the sale price of each item?
To find the sale price of each item, we need to use some basic algebra. Let's call the sale price of each item "x".
First, we need to find the total cost of the table rental for all six friends. Since each friend needs to pay $7.20, the total cost of the table rental is 6 * $7.20 = $43.20.
Next, we need to find the total revenue from selling the items. Each friend sells 3 items, so the total number of items sold is 6 * 3 = 18. The total revenue is the number of items sold multiplied by the sale price, so the total revenue is 18x.
We know that the total profit is $25.20, which is the total revenue minus the total cost of the table rental. So we can set up the equation:
18x - $43.20 = $25.20
Simplifying this equation, we get:
18x = $68.40
Dividing both sides by 18, we get:
x = $3.80
Therefore, the sale price of each item is $3.80.
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Peyton built a birdhouse in the shape of a pyramid with a square base.
The dimensions of the base were 16 in. By 16 in.
The slant height of the pyramid is 10 in.
What is the surface area of the birdhouse?
A. 262 in. 2
B. 576 in. 2
C. 640 in. 2
D. 1,280 in. 2
To find the surface area C of the birdhouse, we need to find the area of each face and add them together.
First, let's find the area of the square base:
Area of base = side^2 = 16^2 = 256 in^2
Next, let's find the area of each triangular face:
Area of each triangular face = 1/2 * base * height
Since the base is 16 in and the slant height is 10 in, the height can be found using the Pythagorean theorem:
height^2 = slant height^2 - base^2/4
height^2 = 10^2 - 16^2/4
height^2 = 100 - 64
height^2 = 36
height = 6
So the area of each triangular face is:
1/2 * 16 * 6 = 48 in^2
There are four triangular faces, so the total area of the triangular faces is:
4 * 48 = 192 in^2
Finally, we add the area of the base and the area of the triangular faces to find the total surface area:
256 + 192 = 448 in^2
Therefore, the surface area of the birdhouse is 448 square inches, which is closest to option A: 262 in^2.
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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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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
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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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.
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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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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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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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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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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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:
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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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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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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Hudson is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if he spins a spinner with
three equal-sized sections labeled Walk, Run, Stop and spins a spinner with 5 equal-
sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
There are 15 different possible outcomes when Hudson spins both spinners in his board game.
To determine the total number of possible outcomes when Hudson spins both spinners, you need to multiply the number of outcomes on the first spinner (Walk, Run, Stop) by the number of outcomes on the second spinner (Monday, Tuesday, Wednesday, Thursday, Friday).
Step 1: Determine the number of outcomes on the first spinner. There are 3 outcomes: Walk, Run, and Stop.
Step 2: Determine the number of outcomes on the second spinner. There are 5 outcomes: Monday, Tuesday, Wednesday, Thursday, and Friday.
Step 3: Multiply the number of outcomes from both spinners. 3 outcomes on the first spinner multiplied by 5 outcomes on the second spinner equals 15 total possible outcomes.
So, there are 15 different possible outcomes when Hudson spins both spinners in his board game.
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A school’s prom committee is composed of 10 students. Seven are girls: Kelly, Karri, Michela, Raquel, Rara, Nadya, and Neesa. Three are boys: Rio, Elke, and Kevin. If they choose a student at random, what is the probability the choose a student whose name begins with "K" P(K name)?
Question 1 options:
30%
70%
40%
50%
The probability of choosing a student whose name begins with "K" is 40%.
To find the probability of choosing a student whose name begins with "K," P(K name), we need to calculate the ratio of students with "K" names to the total number of students in the prom committee.
There are 10 students in the prom committee: 7 girls (Kelly, Karri, Michela, Raquel, Rara, Nadya, Neesa) and 3 boys (Rio, Elke, Kevin). Out of these, 4 students have names that start with "K": Kelly, Karri, Kevin, and Elke (note that Elke has been mistakenly included in the boys' list, but we'll consider it as a "K" name).
To find the probability, we'll use the formula:
P(K name) = (number of students with "K" names) / (total number of students)
P(K name) = 4 / 10 = 0.4 or 40%
So, the probability of choosing a student whose name begins with "K" is 40%.
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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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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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