The value for x vector is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].
What is a vector?
A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.
Given a vector v ∈ R² let (x, y) be its standard coordinates, i.e., coordinates with respect to the standard basis [tex]e_1=\left[\begin{array}{ccc}5\\-1\end{array}\right][/tex] and [tex]e_1=\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex].
The desired coordinates x, y satisfy -
v = xe1 + ye1
So, the vector v is -
[tex]v=2\left[\begin{array}{ccc}5\\-1\end{array}\right] +5\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex]
[tex]v=\left[\begin{array}{ccc}10\\-2\end{array}\right] +\left[\begin{array}{ccc}-35\\-20\end{array}\right][/tex]
[tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex]
Therefore, the matrix is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].
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simplify a square minus b square + a upon a square + b square + b / a² + b square minus b Upon A minus A square minus b square
Tracie works for a salary of $2,666 per month. She has federal income tax withheld at the rate of 15percent, Social Security tax at the rate of 6.2 percent, Medicare tax at the rate of 1.45 percent, and health insurance premiums of $95 per month. Tracie’s net pay is $____________.
Tracie net pay is,
⇒ $1,967.1
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Tracie works for a salary of $2,666 per month.
Here, She has federal income tax withheld at the rate of 15%
Hence, The amount for federal income tax is,
⇒ 15% of $2666
⇒ 15/100 × 2,666
⇒ $399.9
And, Social Security tax at the rate of 6.2%
Hence, The amount for Social Security tax is,
⇒ 6.2% of 2,666
⇒6.2/100 × 2666
⇒ $165.3
And, Medicare tax at the rate of 1.45%.
Hence, The amount of Medicare is,
⇒ 1.45% of $2,666
⇒ 1.45/100 × 2,666
⇒ $38.7
And, She have health insurance premiums of $95 per month.
Thus, The net pay is,
⇒ $2,666 - ($95 + $38.7 + $165.3 + $399.9)
⇒ $1,967.1
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The U.S. per capita income for 2013 was $53143. If the average person operated like the federal government, how much money would the average person have spent in 2013?
Express your answer round to the nearest dollar.
Answer: divide $39857
Step-by-step explanation:
Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case. 50% syrup? 5% syrup? 75% syrup? 1.5% syrup?
DONT LEAVE OUT HOW MUCH LB OF SYRUP SHE WOULD HAVE IN EACH CASE
Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup
Calculatng lbs of syrupTo determine how much water Ella should add to make a specific concentration of syrup, you need to use the formula:
Syrup Concentration = (Mass of Sugar) / (Mass of Sugar + Mass of Water)
50% syrup: In this case, the syrup concentration is 0.50, so you can use the formula as follows:
0.50 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.5 - 0.5 lbs of sugar
Mass of Water = 0.5 lbs
The total amount of syrup will be 0.5 lbs of sugar + 0.5 lbs of water = 1.0 lbs
5% syrup: In this case, the syrup concentration is 0.05, so you can use the formula as follows:
0.05 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.05 - 0.5 lbs of sugar
Mass of Water = 9 lbs
The total amount of syrup will be 0.5 lbs of sugar + 9 lbs of water = 9.5 lbs
75% syrup: In this case, the syrup concentration is 0.75, so you can use the formula as follows:
0.75 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.75 - 0.5 lbs of sugar
Mass of Water = 0.33 lbs
The total amount of syrup will be 0.5 lbs of sugar + 0.33 lbs of water = 0.83 lbs
1.5% syrup: In this case, the syrup concentration is 0.015, so you can use the formula as follows:
0.015 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.015 - 0.5 lbs of sugar
Mass of Water = 33 lbs
The total amount of syrup will be 0.5 lbs of sugar + 33 lbs of water = 33.5 lbs
So, to summarize, Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup.
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Answer:
Step-by-step explanation:
Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup
Calculatng lbs of syrup
To determine how much water Ella should add to make a specific concentration of syrup, you need to use the formula:
Syrup Concentration = (Mass of Sugar) / (Mass of Sugar + Mass of Water)
50% syrup: In this case, the syrup concentration is 0.50, so you can use the formula as follows:
0.50 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.5 - 0.5 lbs of sugar
Mass of Water = 0.5 lbs
The total amount of syrup will be 0.5 lbs of sugar + 0.5 lbs of water = 1.0 lbs
5% syrup: In this case, the syrup concentration is 0.05, so you can use the formula as follows:
0.05 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.05 - 0.5 lbs of sugar
Mass of Water = 9 lbs
The total amount of syrup will be 0.5 lbs of sugar + 9 lbs of water = 9.5 lbs
75% syrup: In this case, the syrup concentration is 0.75, so you can use the formula as follows:
0.75 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.75 - 0.5 lbs of sugar
Mass of Water = 0.33 lbs
The total amount of syrup will be 0.5 lbs of sugar + 0.33 lbs of water = 0.83 lbs
1.5% syrup: In this case, the syrup concentration is 0.015, so you can use the formula as follows:
0.015 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.015 - 0.5 lbs of sugar
Mass of Water = 33 lbs
The total amount of syrup will be 0.5 lbs of sugar + 33 lbs of water = 33.5 lbs
So, to summarize, Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup.
1. Y is 200m North of X and Z is 200m East of Y. Find the bearing of Z from X
2. A man walks 800m on a bearing of 120°. calculate how far from east he is from his starting point
Answer:
see below
Step-by-step explanation:
1. XZ = √(200²+200²) =√2*200 = 282.8m
2. if the man started from 0,0 point & walks 120° meaning he's walking towards the northwest, so he'll be 400m west and 400√3 = 693m north from his starting point, because 120° -90° = 30° you are basically solving a problem of 3 sides length of a special straight triangle with an angle of 30. this type of triangle has a property of shorter side = 1/2 of the long side. 2nd shorter side = √3/2 of the long side. this, you should memorize. which will make lots of problems a piece of cake. good luck
Answer:
1. XZ = √(200²+200²) =√2*200 = 282.8m
2. Not sure
Step-by-step explanation:
i need help please!!
Derrick has been saving his earnings from his lemonade stand. Derrick has 90 dollars to spend. If he buys a new hat for 35 dollars, how many scarves can he buy with the remaining money if they cost 8 dollars each?
Answer:
6 scarves
Step-by-step explanation:
So he has $90 and spends $35 so: [tex]90-35=55[/tex]
The scarves cost 8 dollars each so we need to divide: [tex]55[/tex]÷[tex]8=6.875[/tex]
You can't buy have .875 of the scarves so he can only buy 6 scarves
Answer: 6
Step-by-step explanation: 90-35=55 55-8-8-8-8-8-8=7
Find the area of the sector of a circle with diameter 26 feet and an angle of 5π8 radians.
Round your answer to four decimal places.
The region has a 318.0863 square foot size, as stated in the sentence.
Diameter and girth are what?The diameter or extent of a circular is its circumference. A straight line connecting a spot on one length of the circular to a position at the other end, going through the middle, is the diameter.
Diameter of the circle is 26 feet , so radius of the circle is r
= 26/2
= 13 feet
Central angle of the sector is [tex]\frac{5 \pi}{8} \text { radians. }[/tex]
We know that area of a sector of circle of radius r and central angle θ is
[tex]A=\frac{1}{2} \theta r^2[/tex]
Therefore, area of the sector is
A = 1/2 × 5π/8 × 13² = 318.0863 square feet
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30 pts! Which could be the function of the following graph?
Answer:
It might be "C"
Step-by-step explanation:
Maximize Z= 3X1 + 4X2 Subject to: 5X1 + 4X2 ≤ 200 3X1+ 5X2 ≤ 150 8X1 + 4X2 ≥ 80 X1, X2 ≥ 0
In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
aX1 + bX2 ≤ c
where a, b, and c are constants.
The first constraint, 1.5X1 + 2.5X2 ≤ 80, is already in standard form.
The second constraint, 2X1 + 1.5X2 ≤ 70, can be rewritten in standard form as follows:
-2X1 - 1.5X2 ≤ -70
You can now write the problem in the following standard form:
Maximize Z = 5X1 + 4X2
Subject to:
1.5X1 + 2.5X2 ≤ 80
-2X1 - 1.5X2 ≤ -70
X1, X2 ≥ 0
In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.
This means that if you produce 40 units of X1 and 0 units of X2, you will achieve the highest possible value of Z.
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5.
If "x" and "y" are integers and 8^2x-y = 5^x-y+8, which of the
following is the value of x + y ?
A) 24
B) 22
C) 18
D) 12
For the equation [tex]8^{2x-y} = 5^{x-y+8}[/tex], the value for sum of integers x and y is option A: 24.
What is integer?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
The given equation is [tex]8^{2x-y} = 5^{x-y+8}[/tex].
The first step is to make the base same-
Multiply the left-hand side with 5 and right-hand side with 8.
[tex]5(8)^{2x-y} = 8(5)^{x-y+8}\\40^{2x-y} = 40^{x-y+8}[/tex]
Since, the bases are same, the power values can be taken into consideration -
2x - y = x - y + 8
Collect the like terms -
2x - x = - y + y + 8
x = 8
Substitute the value of x in any one side of the equation -
2x - y = 0
2(8) - y = 0
16 - y = 0
-y = -16
y = 16
So, now the value of expression x + y is -
8 + 16 = 24
Therefore, the final value is obtained as 24.
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If y = -5x + 3, determine the value of y when x = -4
Answer: Y = 23
Step-by-step explanation: -5 x -4 = positive 20 then add 3 which equals 23. 23 is the value of y
It is possible for two line segments to not intersect and also not be considered parallel.
true or false?
Oh yeah definitely, two lines don't have to be parallel or intersect. There are many examples. I'll give you one. Imagine two lines right now, one is flat horizontal, 180 degrees. Another line is above the horizontal line, at like 30 degrees. But they do not touch. So therefore, these lines are neither parallel or intersecting. The answer is true.
HELP ASAP QUESTION 1!
Answer:
The answer is 313° degrees.
Please solve this for me
The solutions to the equations are
a) The percentage of quokkas that weigh over 15.5 pounds is 2.1 %
b) The percentage of quokkas that weigh uncer 11.9 pounds is 75.9 %
c) Percentage of quokkas that weigh between 15.5 and 11.9 pounds 22.0 %
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
The weights of the quokkas are described by the normal model as
N ( 10 , 2.7 )
So , the mean μ = 10
And , the standard deviation σ = 2.7
a)
The percentage of quokkas that weigh over 15.5 pounds is given by the equation P ( x > 15.5 )
On simplifying the equation , we get
From the z-score formula ,
P ( z > ( 15.5 - 10 ) / 2.7 )
P ( z > 2.037 ) = 0.020825
0.020825 = 2.0825 %
Hence , the percentage of quokkas that weigh over 15.5 pounds is 2.1 %
b)
The percentage of quokkas that weigh uncer 11.9 pounds is given by the equation P ( x < 11.9 )
On simplifying the equation , we get
From the z-score formula ,
P ( z < ( 11.9 - 10 ) / 2.7 )
P ( z < 0.7037 ) = 0.020825
0.75919 = 75.919 %
Hence , the percentage of quokkas that weigh uncer 11.9 pounds is 75.9 %
c)
Percentage of quokkas that weigh between 15.5 and 11.9 pounds is
P ( 11.9 < x < 15.5 )
On simplifying the equation , we get
From the z-score formula ,
P ( 11.9 < x < 15.5 ) = 1 - P ( x < 11.9 ) - P ( x > 15.5 )
P ( 11.9 < x < 15.5 ) = 1 - 0.020825 - 0.75919
P ( 11.9 < x < 15.5 ) = 0.219985
P ( 11.9 < x < 15.5 ) = 22.0 %
Hence , the equations are solved using z-score
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Alexia and Tony went went for dinner and their meal cost $49.77. If they want to leave a 15% tip for their server, how much will the tip amount be? How much will their total bill be?
Answer:
Tip=7.47
Total bill=57.24
Step-by-step explanation:
tip=15/100×49.77=7.47(to nearest cent)
total bill=115/100×49.77=57.24(to nearest cent)
If a building acquired the beginning of the year at a cost of 2,200,000 has an estimated residual value of 400,000 and a estimated useful life of 20 years determine the following a. the depreciable cost b. The straight- line rate c.the annual straight-line depreciation
The depreciable cost,
$1,800,000
The straight-line rate,
5%
The annual straight-line depreciation,
90,000
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
If a building acquired the beginning of the year at a cost of 2,200,000 has an estimated residual value of 400,000 and an estimated useful life of 20 years.
The depreciable cost,
= cost - residual value
= 2,200,000 - 400,000
= $1,800,000
The straight-line rate,
=100/20
= 5%
The annual straight-line depreciation,
= 1,800,000 x 5/100
= 90,000
Therefore, all the required values are given above.
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If 6 is an element in the domain of f(x) = (8x-16)/2, what is the corresponding element in the range?
If 6 is an element in the domain of f(x) = (8x - 16)/2, the corresponding element in the range include the following: [16].
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Based on the information provided, we have the following function rule:
Function, f(x) = y = (8x - 16)/2
When the domain x = 6, the range (y) of this function is given by;
Range, y = (8(6) - 16)/2
Range, y = (48 - 16)/2
Range, y = 32/2
Range, y = 16.
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What is the common difference of the A.P. 11, - 1, - 13, - 25, . . . ?
Answer:
The common difference is -12
Step-by-step explanation:
Finding the common difference:
11, - 1, - 13, - 25, . . .
The difference between the first and second terms
-1 -11 = -12
The difference between the second and third terms
-13 - -1 = -13 + 1 = -12
The common difference is -12
The hypotenuse of a right triangle is on the line y = 3x + 2. The shorter leg of
the triangle is parallel to the x-axis and is 3 units long. Find the perimeter of the
triangle.
Answer:
The perimeter of the triangle is 30.5.
Step-by-step explanation:
To find the perimeter of the triangle, we need to find the length of the other leg.
We can use the equation of the line that defines the hypotenuse, y = 3x + 2, to find the coordinate of the endpoint of the shorter leg. The endpoint has x-coordinate equal to 3 (since the length of the leg is 3), and the y-coordinate can be found by substituting x = 3 into the equation:
y = 3x + 2
y = 3 * 3 + 2
y = 11
So the endpoint of the shorter leg is (3, 11).
Next, we can use the Pythagorean theorem to find the length of the other leg:
a^2 + b^2 = c^2
where a is the length of the shorter leg (which we know is 3), b is the length of the other leg, and c is the length of the hypotenuse (which is also on the line y = 3x + 2).
We can use the coordinates of the endpoint of the shorter leg to find the length of the hypotenuse:
c = √((3 - 0)^2 + (11 - 2)^2)
c = √(3^2 + 9^2)
c = √(9 + 81)
c = √90
So the length of the hypotenuse is √90.
Using the Pythagorean theorem, we can now find the length of the other leg:
3^2 + b^2 = (√90)^2
9 + b^2 = 90
b^2 = 81
b = 9
So the length of the other leg is 9.
Finally, the perimeter of the triangle is 3 + 9 + √90, which is approximately 12 + 9 + 9.5 = 30.5.
Need help!!!!!
Isiwjsiwkkw
Answer:
63, 69, 75, 81
Step-by-step explanation:
to find the first 4 terms substitute n = 1, 2, 3, 4 into the explicit rule.
a₁ = 63 + (1 - 1) × 6 = 63 + 0 × 6 = 63 + 0 = 63
a₂ = 63 + (2 - 1) × 6 = 63 + 1 × 6 = 63 + 6 = 69
a₃ = 63 + (3 - 1) × 6 = 63 + 2 × 6 = 63 + 12 = 75
a₄ = 63 + (4 - 1) × 6 = 63 + 3 × 6 = 63 + 18 = 81
the first four terms are 63, 69, 75, 81
Please help solve this equation "m+1P4 =mP5
Answer:
m+1p4 =mp5
1p4= mp5-m
m=p5
Find the length of the third side. If necessary, write in simplest radical form. 4 8
Answer: [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
We can use the pythagorean theorem to solve this.
We will call the length of the unknown side x for now.
Using the theorem, we will get to:
[tex]8^2-4^2=x^2[/tex]
[tex]64 - 16 = x^2[/tex]
[tex]48 = x^2[/tex]
[tex]x = \sqrt{48}[/tex]
In simplest radical form, it will be:
[tex]4\sqrt{3}[/tex]
Answer:
4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x represent the third side, then
x² + 4² = 8²
x² + 16 = 64 ( subtract 16 from both sides )
x² = 48 ( take square root of both sides )
x = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]
Sarah wants to install carpet to cover her rectangular dining room floor, which has a length of 12 feet and a width of 9 feet. The cost to install the carpet is $5 per square foot. Sarah predicts that the total cost to install the carpet will be $500. Which statement BEST explains why Sarah’s prediction is incorrect? PLS HELP TY
A. Sarah rounded the area of the floor to 110 square feet.
B. Sarah rounded the area of the floor to 100 square feet.
C. Sarah rounded the area of the floor to 98 square feet.
D. Sarah rounded the area of the floor to 108 square feet.
Answer:
B
Step-by-step explanation:
12 long 9 wide = 12*9 =108 sqft
$5/sqft
so she'll need 108*5 =540
but she rounded to 100 sqft
The following data includes the year, make, model, mileage (in thousands of miles) and asking price (in US dollars) for each of 13 used Honda Odyssey minivans. The data was collected from the Web site of the Seattle P-I on April 25, 2005.
year make model mileage price
2004 Honda Odyssey EXL 20 26900
2004 Honda Odyssey EX 21 23000
2002 Honda Odyssey 33 17500
2002 Honda Odyssey 41 18999
2001 Honda Odyssey EX 43 17200
2001 Honda Odyssey EX 67 18995
2000 Honda Odyssey LX 46 13900
2000 Honda Odyssey EX 72 15250
2000 Honda Odyssey EX 82 13200
2000 Honda Odyssey 99 11000
1999 Honda Odyssey 71 13900
1998 Honda Odyssey 85 8350
1995 Honda Odyssey EX 100 5800
Compute the correlation between age (in years) and price for these minivans. (Assume the correlation conditions have been satisfied and round your answer to the nearest 0.001.)
The correlation between age and price is -0.94. It indicates a strong negative correlation. Hence, as the age increases the price of the car decreases.
What is correlation?A procedure for determining the connections between two variables is referred to as correlation. You discovered that plotting two variables on a "scatter plot" can help you determine whether or not they are generally connected. Correlation is the most widely applied strategy even though there are other measures of association for variables measured at the ordinal or higher level of measurement.
The data was collected in 2005. So, to obtain the age we subtract the data collection year from the make year:
Age (x): 1,1, 3,3,4,4,5,5,5,5,6,7,10
Now, the array of price given is:
Price (y): 26900,23000,17500,18999,17200,18995,13900,15250,13200,11000,13900,8350,5800.
Using the correlation equation in excel sheet we see that the correlation coefficient between the age and the price is: - 0.94.
-0.94 indicates a strong negative correlation. Hence, as the age increases the price of the car decreases.
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If an ant can walk 7 inches per minute and the road is 28 feet wide, how many seconds will it take him to cross ?
Answer:
48 minutes
Step-by-step explanation:
Why did the ant cross the road?
Speed of ant = 7 inches per minute
Width of road = 28 feet
28 feet = 28 x 12 inches = 336 inches
At 7 inches per minute, to cross 336 inches , it would take 336/7 or 48 minutes
A) Which statement is not true?
A) When you add same signs, find the sum, keep the sign.
B) When you multiply or divide different signs the answer is always positive.
C) Subtraction means to add the reciprocal.
D) The product of a number and its reciprocal is 1
Answer:
B
Step-by-step explanation:
The statement isn't true because when you multiply or divide different signs the answer is always negative.
Both B and C are false.
A 80-kg base runner begins his slide into second base when he is moving at a speed of 4.7 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base.A) How much mechanical energy is lost due to friction acting on the runner?B) How far does he slide?
The runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.
What is the coefficient?
A coefficient is a number multiplied by a variable. Examples of coefficients: In the term 14 c 14c 14c, the coefficient is 14. In the term g, the coefficient is 1.
A) The mechanical energy lost due to friction can be calculated as follows:
Initial kinetic energy of the runner: KE = 0.5 * m * v² = 0.5 * 80 kg * (4.7 m/s)² = 140.29 J
The force of friction acting on the runner is given by:
[tex]friction_{force} = friction_{coefficient} * normal_{force}[/tex]
where,
[tex]friction_{coefficient} = 0.70[/tex]
[tex]and normal_{force} = m * g (g = 9.8 m/s^{2} )[/tex]
The normal force is given by:
[tex]normal_{force} = m * g = 80 kg * 9.8 m/s^{2} = 784 N[/tex]
Therefore, the force of friction acting on the runner is: [tex]friction_{force} = 0.70 * 784 N = 548.8 N[/tex]
The work done by friction is given by:
[tex]W = friction_{force} * distance[/tex]
Since the speed of the runner is reduced to zero, the work done by friction is equal to the change in kinetic energy:
[tex]W = KE_{final} - KE_{initial}[/tex]
= 0 - 140.29 J = -140.29 J
So, the mechanical energy lost due to friction is 140.29 J.
B) The distance the runner slides can be calculated using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.
The work done by friction is given by: W = friction_force * distance
Since the friction force is constant, the work done by friction is equal to the change in kinetic energy:
[tex]W = KE_{final} - KE_{initial}[/tex]
= 0 - 140.29 J = -140.29 J
Rearranging this equation and substituting in the known values, we get:
[tex]distance = -W / friction_{force}[/tex]
= -140.29 J / 548.8 N = 0.255 m or 25.5 cm
Hence, the runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.
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If you have a scoop that holds 2/5 cup, and a recipe calls for 3 3/5 cups of water, then how many scoops would you need to use?
36/25 scoops needed for the recipe if the we have a scoop that holds 2/5 cup, and a recipe calls for 3 3/5 cups of water.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have given that baker has 2/5 cup, and a recipe calls for 3 3/5 cups of water
3 3/5 = 18/5
we only has a 18/5 cup water.
Scoops we will need for the recipe = (18/5)/(2/5) = 36/25
Thus, we will need 36/25 scoops for the recipe.
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9 scoops would we need to use.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
2/5 cup of water can be hold by a scoop.
So, 1 cup of water hold 5/2 scoop
and, 18/5 cup of water can be hold by
=5/2 x 18/5
=18/2
= 9 scoops
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if a day of the week is randomly selected, what is the probability it is saturday, given that the day is on the weekend.
Probability that it is Saturday is 1/2 as it is on weekend. We can calculate this using Conditional Probability formula.
Given that a day of the week is randomly selected and that it is on the weekend, the probability of it being Saturday can be calculated as follows:
There are two days in a week that are on the weekend: Saturday and Sunday.
If we know that a day is on the weekend, the probability of it being Saturday is equal to the number of Saturdays on the weekend divided by the total number of weekend days. This is because there are two equally likely outcomes for the weekend (Saturday and Sunday), and we are interested in only one of them.
We can find this out by using formula:
P(A|B) = P(A and B) / P(B), where A and B are two events.
So, the probability of selecting Saturday, given that it is on the weekend, is 1/2. In other words, if we randomly select a day of the week and it is on the weekend, there is a 50% chance that it will be Saturday.
This can be written as P(Saturday|Weekend) = 1/2.
Therefore, probability = 1/2
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