a stone is dropped from the top of a cliff. it is observed to hit the ground 5.78 s later how high is the cliff?
Using the formula;
H= ut + 1/2 gt²
The initial velocity = 0
Hence H= 1/2 gt²
g= 10m/s t= 5.78 s
H = 1/2 x 10 x 5.78²
H = 167.042 m
H = 167 m approximately
How do you find theGreatest common factor for 15 and 40
Answer:
See Explanation
Step-by-step explanation:
\(15 = 3 \times \bold{ \red{ \boxed5}} \\ \\ 40 = 2 \times 2 \times 2 \times \bold{ \purple{ \boxed5}} \\ \\ common \: factor \: of \: 15 \: and \: 40= 5 \\ \\ \therefore \: gcf \: of \: 15 \: and \: 40 = 5\)
which of the following pairs of variables has an inverse relationship?
The pair of variables with an inverse relationship is y = 1/x. This relationship can be seen by graphing the two variables on a coordinate plane and observing the shape of the graph.
As x increases, y decreases and as x decreases, y increases. This is because the equation y = 1/x can be written as y = c/x, where c is a constant. Since c is a constant, as the value of x increases, the value of y decreases, and vice versa.
For example, if x = 4, then y = 1/4, or 0.25. If x increases to 8, then y decreases to 1/8, or 0.125. On the other hand, if x decreases to 2, then y increases to 1/2, or 0.5. As can be seen, as x increases, y decreases, and as x decreases, y increases, which shows the inverse relationship between the two variables.
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Find the missing dimension of the triangle.
A triangle with base labeled 1.5 inches and height labeled h. The area of the triangle is labeled 2 square inches.
In this case, the base is labelled as 1.5 inches, and the height is labelled as h. We also know that the area of the triangle is labelled as 2 square inches the missing dimension of the triangle is 2.67 inches.
What is the dimension of the triangle?The formula for the area of a triangle is:
\(Area = 1/2 \times base \times height\)
In this case, the base is labelled as 1.5 inches, and the height is labelled as h. We also know that the area of the triangle is labelled as 2 square inches. Therefore, we can plug in these values into the formula and solve for h:
\(2 = 1/2 \times 1.5 \times h\)
Multiplying both sides by 2:
\(4 = 1.5 \times h\)
Dividing both sides by 1.5:
\(h = 4/1.5 = 2.67 inches\)
Therefore, the missing dimension of the triangle is \(2.67 inches.\)
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The missing dimension of the triangle is 2.67 inches.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides. The sum of the three angles in a triangle is always 180 degrees.
The formula to find the area of a triangle is:
Area = 1/2 * base * height
We know that the base of the triangle is 1.5 inches and the area is 2 square inches. Plugging these values into the formula, we get:
2 = 1/2 * 1.5 * h
Multiplying both sides by 2, we get:
4 = 1.5 * h
Dividing both sides by 1.5, we get:
h = 2.67 inches
Therefore, the missing dimension of the triangle is 2.67 inches.
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Convert the rational number below to a decimal. Round to the nearest hundredth when necessary. 3/5
Answer: 0.6
Explanation: You need to divide 3 by 5 and it will give you the answer of 0.6
When converting a mixed number to improper you add a nominator and or number then multiply the sum with the numerator true or false
Answer:
the answer is false. you first multiply the number by the numerator then add it to the denominator
Beth says that the graph of g(x)=x-5+1 is a
Translation of 5 units to the left and 1 unit up of
F(x)=x
She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x) is Beths description of the transformation correct? Explain
Answer: No.
Step-by-step explanation:
The graph of g(x) = x - 5 + 1 is a Translation of 5 units to the right not to the left and 1 unit up of F(x) = x
the point (0,0) on the square root function would be translated at the same value which will be to the point (5,1) on the graph of g(x)
Beths description of the transformation is therefore incorrect.
Answer:
No, Beth is not correct. The function g(x) has an h value of 5 and a k value of 1. This would be a horizontal translation of the square root function of 5 units to the right, rather than the left. Beth was correct about the vertical translation of the square root function of 1 unit up. The point (0, 0) from the square root function would be translated to the point (5, 1) on the graph of g(x).
Step-by-step explanation:
This came right from Edg
Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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Is the function periodic? If so, find the period.See imagea) yes; 4b) yes; 5c) yes' 6d) no
Recall that a periodic function is a function that repeats itself at regular intervals, and the period is the distance between the repetitions.
Notice that the given graph repeats itself regularly, then it must be periodic.
From the given diagram we get that the period of the given graph is:
\(2-(-4)=2+4=6.\)Answer: Option C.
A baseball stadium reported the fraction of fans who bought hot dogs at each game throughout the season. The line plot displays hot dog sales data for each game. At what fraction of the games did more than of fans buy hot dogs?
Answer:
D
Step-by-step explanation:
Its D
Hope this helps :D
What's the answer and how do you find the baring??
when getting a bearing, we're referring to the angle from the North line moving clockwise, so of D from C? well, the "from" point gets the North line and we check the angle from that North line clockwise to the other point, Check the picture below.
I really need someone’s help I don’t remember how to do this
Answer:
3
Step-by-step explanation:
cubed root means _x_x_= the number
so in this case it would be _x_x_=27
and what times what times what equals 27?
3x3x3=27
What is the forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5? (all liberal arts colleges are private
The forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5 is $32935.
How to illustrate the cost?It should be noted that the forecasted cost is simply used to know the expected cost for a give data.
In this case, the forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5 is $32935.
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A nursery owner buys 5 panes of glass to fix some damage to her greenhouse. The 5 panes cost $12.2. she breaks 2 more panes while repairing the damage. What is the cost of another 2 panes of glass?
The cost of the other 2 panes of glass is $5.70. If this is wrong, I am sorry :( Have a great day!
Which properties justify the steps taken to solve the system? {2a 7b=03a−5b=31 Drag the answers into the boxes to match each step.
The equations can be solved in the following manner. As shown below.
Given to us10a + 35b = 021a - 35b = 217SolutionThe equations can be solved in the following manner. As shown below.
1. Multiplication Property of Equality
10a + 35b = 0, 21a - 35b = 217
2. Addition Property of Equality
31a = 217
3. Division Property of Equality
a = 7
4. Substitution Property of Equality
2(7) +7b = 0
5. Simplify
14 + 7b = 0
6. Subtraction Property of Equality
7b=-14
7.Division Property of Equality
b= -2
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There is a competition at the local movie theater for free movie tickets. You must guess all four employees' ages given a few clues. The first clue is when their ages are added together the sum is Kirk is 2 times the quantity of ten years less than the manager's age, Brian is 12 years younger than twice the manager's age, ,and Matt is 6 years older than ½ the manager's age. What are all four of their ages? Be sure to show set up equation work and answer
Complete question :
There is a competition at the local movie theater for free movie tickets. You must guess all four employees' ages given a few clues. The first clue is when their ages are added together the sum is 106. Kirk is 2 times the quantity of ten years less than the manager's age, Brian is 12 years younger than twice the manager's age, ,and Matt is 6 years older than ½ the manager's age. What are all four of their ages? Be sure to show set up equation work and answer
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following clue :
Let manager's age = m
Kirk's age = k
Brian's age = b
Matt's age = a
Sum of their ages = 106
k = 2(m - 10) = 2m - 20
b = 2m - 12
a = 0.5m + 6
k + b + a + m = 106
Express all their ages in terms of m
2m - 20 + 2m - 12 + 0.5m + 6 + m = 106
5.5m - 20 - 12 + 6 = 106
5.5m - 26 = 106
5.5m = 106 + 26
5.5m = 132
m = 132 / 5.5
m = 24
Manager's age = 24 years
kirk = 2(24 - 10) = 2(14) = 28 years
Brian = 2(24) - 12 = 48 - 12 = 36 years
Matt = 0.5(24) + 6 = 12 + 6 = 18 years
what is the answer to this equation ... 3 + 2c + 5c + 2 ??
Answer:
solution:7c+5
Solve: -5/6 + m = -3 1/6
m= -4
m= -2
m= -2 1/6
m= -2 1/3
Answer: -2 1/3
Step-by-step explanation:
Okay
which statement best describes the realationship between the numbers divisable by 6, 2 and 3
Thank yousunshinemadison101
What is the equation of the line parallel to the line with equation y=2/3x +1 and passing through the point (6,-2)?
Step-by-step explanation:
y= (-2/3) x-6 is parallel to y= (-2/3)x +4 goes through the point (3,-8)
work out an estimate for √4.92+3.18x7.31
Answer:
25.4639073013
Rounded is 25.4
Have a beautiful day! v(⌒o⌒)v♪
what is the page rank of node a after 1 iteration
The PageRank of node a after one iteration is 0.0425.
To determine the PageRank of node an after one iteration, we need to use the PageRank algorithm and the hyperlink matrix of the network.
Let H be the hyperlink matrix of the network, where each entry Hij represents the hyperlink from node i to node j, and let v be the initial probability distribution vector, where each entry vi represents the probability of starting at node i.
Assuming a damping factor of 0.85, the PageRank algorithm can be written as:
r = 0.85 * H * v + 0.15 * e
where r is the PageRank vector, and e is a vector of ones.
Using the hyperlink matrix and the initial probability distribution vector:
H = [[0, 1/2, 0, 0, 0],
[1/3, 0, 0, 0, 1/2],
[1/3, 0, 0, 1, 1/2],
[1/3, 1/2, 1, 0, 0],
[0, 0, 0, 0, 0]]
v = [1, 0, 0, 0, 0]
we can calculate the PageRank vector after one iteration:
r = 0.85 * H * v + 0.15 * e
= [0.0425, 0.1275, 0.4675, 0.2675, 0.095]
Therefore, the PageRank of node an after one iteration is 0.0425.
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what's the answer ?
\( \sqrt{72 \times 2} \)
Answer:
\( \sqrt{72 \times 2} \)=\( \sqrt{12²} \)=±12 is your answer
4y−14−8y=4 Please help
Help please!! This is super confusing for me :(
Answer:
Step-by-step explanation:
\(Perimeter \ of \ block =\dfrac{8}{20}\\\\\\\dfrac{3}{20}+w+\dfrac{3}{20}+w = \dfrac{8}{20}\\\\\\\dfrac{6}{20}+2w=\dfrac{8}{20}\\\\\\2w=\dfrac{8}{20}-\dfrac{6}{20}\\\\\\2w=\dfrac{2}{20}\\\\\\w=\dfrac{2}{20*2}\\\\\\w=\dfrac{1}{20} \ mi\)
Answer:
1/20 mile
Step-by-step explanation:
Let the Perimeter = P
20 (P) = 8 miles
P = 8/20 miles
Perimeter = 2 (Length) + 2 (width)
2 (3/20) + 2W = 8/20
2W = 8/20 - 6/20
2W = 2/20
W = 1/20
Of the students at Milton middle school 171 are girls if 45% of the students are girls how many total students are there at milton middle school
Answer:
380
Step-by-step explanation:
171:45=3,8
3,8*100=380
The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -9 < x < -4?
After answering the presented question, we can conclude that When we function simplify this expression, we get: rate of change = (f(-4) - f(-9)) / 5
what is function?Mathematicians study numbers and their permutations, equations and adjacent tissues, shapes and various positions, as well as potential locations for all of these things. The term "functioning" signifies the connection that exists between a set of inputs, each of which has its own output. A function is an input-output connection wherein every input results in a single, distinct return. Each function has a domain, codomain, or scope of its own. The letter f is frequently used to represent functions (x). An x denotes entering. The four main categories of accessible functions are on functions, one-to-one skills, so numerous skills, in capabilities, and on functions.
The formula for the average rate of change of a function f(x) across an interval [a,b] is:
(f(b) − f(a)) / average rate of change (b - a)
The spacing in this case is -9 x -4, therefore a=-9 and b=-4. As a result, the average rate of change of the function f(x) for this interval is as follows:
(f(-4) - f(-9)) / (-4 - (-9)) = average rate of change
When we simplify this expression, we get:
rate of change = (f(-4) - f(-9)) / 5
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The lowest temperature ever recorded is -89C. The highest temperature is 56.7C. What is the difference between the highest and the lowest temperature? Explain
Answer:
-89c+56.7=145.7is correct answer
a right circular cone is inscribed in a right circular cylinder. the volume of the cylinder is $72\pi$ cubic centimeters. what is the number of cubic centimeters in the space inside the cylinder but outside the cone? express your answer in terms of $\pi$.
The number of cubic centimeters in the space which is inside the cylinder but outside the cone for given volume is equal to 72 cubic centimeters.
As right circular cone inscribed in a right circular cylinder.
Let A be the apex of the cone and B be the center of the base of the cone.
Let r be the radius of the base of the cone,
and let h be the height of the cone.
Let R be the radius of the base of the cylinder,
and let H be the height of the cylinder.
Volume of the cylinder = 72π cubic centimeters.
⇒ πR^2H = 72π
⇒ R^2H = 72
Base of the cone is a circle with radius r.
⇒ area of the base of the cone is πr^2.
Height of the cone is h.
Volume of the cone = 1/3 × πr^2h
Volume of the space inside the cylinder but outside the cone.
= volume of the cylinder - volume of the cone.
= πR^2H - 1/3 × πr^2h
Substituting R^2H = 72, we get,
⇒ Required Volume = 72π - 1/3 × πr^2h
Find r and h in terms of R and H.
Using the concept of similar triangles .
For similar triangle sides are in proportion.
⇒r/R = h/H
Solving for r, we get,
r = R × ( h/H )
Substituting this into the equation for the volume,
Volume = 72π - 1/3 × π(R × ( h/H ))^2h
Simplifying, we get,
⇒ Volume = 72π - 1/3 × πh^3R^2/H^2
Value of h that maximizes the volume.
Take the derivative of the volume with respect to h and set it equal to zero,
dV/dh = -2/3 × πh^2R^2/H^2
⇒ -2/3 × πh^2R^2/H^2= 0
Solving for h, we get,
⇒h = 0
Substituting this value of h back into the equation for the volume, we get,
⇒ Required Volume = 72π - 0
⇒ Required Volume = 72π cubic centimeters.
Therefore, the number of cubic centimeters in the space inside the cylinder but outside the cone is 72π cubic centimeters.
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Here is a rectangle with length 5 units and width 2 units.
1. What is the area of the rectangle?
2. Dilate rectangle ABCD from point A by a scale factor of 2. Calculate the area of the image.
3. Dilate rectangle ABCD from point A by a scale factor of 3. Calculate the area of the image.
This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Solving for the area and scale factor we have:
L= 5 units
W = 2 units
The area of the rectangle =L * WA = (5 x 2)
A = 10 square units.
If the rectangle is dilated from point A by a scale factor of 2, the area of the image:A= (Scale factor of L * W)* L * W
= (2 x 2 x 5 x 2)
A = 40 square units.
If the rectangle is dilated from point A by a scale factor of 3, the area of the image is:A= (Scale factor of L * W)* L * W
= (3 x 3 x 5 x 2)
A= 90 square units
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