If the drag force due to air resistance is 11 N acting backwards against Shaun. Shaun's acceleration is 4.64 m/s^2 down the slope.
To find Shaun's acceleration, we need to calculate the net force acting on him and his skateboard. The net force is the vector sum of all the forces acting on the object. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and its acceleration:
Net force = mass × acceleration
Let's break down the forces acting on Shaun and his skateboard:
The force of gravity, which acts vertically downwards with a magnitude of mg, where m is the total mass of Shaun and his skateboard and g is the acceleration due to gravity (9.8 m/s^2).
F₁ = m * g * sin(30°) = 75 kg * 9.8 m/s^2 * sin(30°) = 367.5 N
The force due to rolling friction between the skateboard wheels and the concrete, which acts backward against the skateboard.
F₂ = 9 N (given)
The drag force due to air resistance, which acts backward against Shaun.
F₃ = 11 N (given)
Now, let's add up the forces to get the net force:
Net force = F₁ - F₂ - F₃
= 367.5 N - 9 N - 11 N
= 347.5 N
Using Newton's second law of motion, we can now calculate Shaun's acceleration:
acceleration = Net force / mass
= 347.5 N / 75 kg
= 4.64 m/s^2 (down the slope)
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What is the volume 
The volume of the composite figure is 12 cubic in.
How to calculate the Volume of Composite Shapes?
Composite shapes have a volume that is made up of basic shapes. We can calculate the volume of the composite shapes using the steps listed below:
Step 1: Break down the compound shape into different components.
Step 2: Determine the volume of each basic shape.
Step 3: Combine the volumes of all the basic shapes.
Step 4: Write the solution in cubic units.
Firstly we can divide the figure into two rectangular prisms A and B. Then add these two to total volume the volumes of each prism.
The volume of prism A = length × width × height
V = 4 * 2 * 1
V = 8 cubic in.
The volume of prism B = length × width × height
V = 1 * 2 * 2
V = 4 cubic in.
Total volume = volume of prism A + volume of prism B
= 8 cubic in + 4 cubic in
= 12 cubic in
Hence, the volume of the composite figure is 12 cubic in.
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Z-score with the area of 0.0054if the area is halfway between two entry’s use the z score halfway between the corresponding z scores
Select the statement that correctly defines continuous and discrete quantitative variables. O A continuous variable has an infinite number of possible values, whereas a discrete variable always has a finite number of possible values. O A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units. O A continuous variable has a countable number of possible values, whereas a discrete variable has an uncountable number of possible values. O A continuous variable has numerical values, whereas a discrete variable serves to group items into categories.
The statement that correctly defines continuous and discrete quantitative variables is:
"A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units."
A variable is a quantity that may assume any one of a set of values.
This means that a continuous variable can take on any value within a certain range, which could be infinite, and that it can have decimal values. In contrast, a discrete variable has specific values that are separate and countable, such as integers or categories. For example, the height of individuals is a continuous variable, while the number of siblings someone has is a discrete variable.
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in a recent survey of 500 people,it was found that 2800 read Concord and 2300 read guardian while 400 read both papers. How many read neither
300 people read neither of the papers.
How to find how many read neither?Set theory is a branch of mathematical logic that studies sets, which are collections of objects. It is a fundamental theory in mathematics and can be used as a foundation for all other areas of mathematics.
Total population n(ξ) = 5000
Number of people reading Concord, n(C) = 2800
Number of people reading Guardian, n(G) = 2300
Number of people reading both = n(C ∩ G)] = 400
Number of people reading any of the newspaper = n(C ∪ G)] = n(C) + n(G) - n(C ∩ G) = 2800 + 2300 - 400 = 4700.
Number of people reading none of them is equal to = Total population - Number of people reading any of the newspaper = 5000 - 4700 = 300
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A mailer for posters is a triangular prism as shown. Determine the lateral surface area of the mailer. Draw a net if necessary.
The lateral surface area of the mailer is 234 In²
How to determine the lateral areaIt is important to note that the formula for the lateral area of a triangular prism is expressed as;
A = (a + b+ c) h
Given that the parameters are enumerated as;
A is the lateral area of the triangular prisma is the base sideb is the base sidec is the base sideNow, substitute the values into the equation, we have;
Lateral area, A = (4 + 4 + 5) 18
Add the values
Lateral area = (13)(18)
Multiply the values
Lateral area = 234 In²
Hence, the value is 234 In²
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NISSAN NP300 Special deal at 2007 price! R 221,180 (incl. VAT) Features • Dual airbags Power steering • Air-conditioning • Radio CD 3.3 Central locking Roof rack Roll bar and tonneau ber Side steps 3 year90 000km Service Plan • 3 year/100 000km Warranty NISSAN DataDot Anti theft Identification system NP300 Special Offers Months Interest Vehicle rate Price Deposit Click here to book your test drive *Residual Monthly instalments Total Payment R303 007 80 180 *Residual is an amount that must be paid at the end of the term after all the monthly payments have been made. 3.1 What is the cash price of the NISSAN NP 300? 3.2 If a person decide to pay for the vehicle in instalments, determine the number of years it will take to pay for the vehicle. Calculate the amount of the deposit needed. (2) (2) (3)
3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).
3.2. it would take approximately 6.67 years to pay off the vehicle through instalments.
A deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit
How The answer was obtained3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).
3.2 The given information does not explicitly state the number of years for the instalment plan, but it does provide the number of months (80) and the total payment amount (R303,007). Assuming a monthly payment plan, we can calculate the number of years as follows:
Number of years = Number of months / 12
Number of years = 80 / 12
Number of years ≈ 6.67 years
So it would take approximately 6.67 years to pay off the vehicle through instalments.
To calculate the deposit needed, we need to subtract the residual amount from the total cash price. From the given information, the total payment is R303,007 and the residual is R80,180, so:
Cash price = Total payment - Residual
Cash price = R303,007 - R80,180
Cash price = R222,827
So the cash price is slightly higher than the advertised price of R221,180, likely due to financing fees or interest. To determine the deposit needed, we can assume a specific percentage of the cash price that must be paid upfront. For example, if the deposit required is 10% of the cash price, then:
Deposit = 0.1 x Cash price
Deposit = 0.1 x R222,827
Deposit = R22,282.70
So a deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit.
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What is the completely factored form of 15a³bc³ – 6a²b²c³?
Answer:
The completely factored form of 15a³bc³ – 6a²b²c³ is 3a²bc³ × (5a - 2b).
Answer:
[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]
Step-by-step explanation:
[tex]15a^{3} bc^{3} - 6a^{2} b^{2} c^{3}[/tex]
[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]
Describe how you know whether an equation will be true for all values of x or true for no values of x
Answer:
Step-by-step explanation:
Generally an equation which will be true for all values of x have some statement which can be simplified into another state which will always be true.
So for example: [tex]x+4=x+4[/tex], is kind of a bit obvious to tell it's going to be true for all values as the two expressions have the same exact terms, but we can subtract "x" from both sides leading us to the statement: [tex]4=4[/tex] which is always true.
One important thing to note is you must be cautious at times, for example: [tex]\frac{x-2}{x-2}=\frac{x-2}{x-2}[/tex] may seem to be true for all values, and x-2 over x-2 is the same thing, so it simplifies to one and same thing on the right side: [tex]1=1[/tex] thus the statement should be true for all values right? Not completely, it's true for most values, except for x=2, and this is because 1=1 isn't exactly the same expression. In the original fraction the denominator has an x-2, and if we plug in x=2, we get 2-2 resulting in division by one, which of course isn't definable. So that's just one important thing to note as simplifying expressions may result in expressions that look equal, but are slightly different in a way.
a student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d= days, r= raffle tickets, and h= hours, what function can he use to calculate his earnings?
The function can be used to calculate his earnings, 15d + 0.25r + 2h
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
The function that the student can use to calculate his earnings is:
Earnings = 15d + 0.25r + 2h
where:
d = number of days worked
r = number of raffle tickets sold
h = number of hours worked at the game
The first term, 15d, represents the base pay of $15 per day worked.
The second term, 0.25r, represents the additional earnings of $0.25 per raffle ticket sold.
The third term, 2h, represents the additional earnings of $2 per hour worked at the game.
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determine an equation of the line drawn on the right. The shapes under the line are squares
Answer:57.6^3
thats t
help me pls and thank you :)
Explanation:
Spreadsheet software is strongly recommended. If you have excel, then it's best to use it since it's used practically everywhere. If you don't have excel, then there are tons of free alternatives such as OpenOffice or LibreOffice.
Enter the data as shown. Then form a third column labeled xy which represents multiplying each x and y pair for any given row. Eg: Tom = xy = 7*2 = 14. Use cell references to quickly compute this new column. I don't recommend manually multiplying each pair of items.
Once the xy column is formed, add up everything in it since [tex]\Sigma[/tex] represents summations. The command called "Sum" or "SUM" does this very quickly. In a cell off to the side type in [tex]=Sum(C2:C10)[/tex] which will add up the elements in cell C2, C3, ... all the way up to C10. Don't forget about the equal sign up front. That's needed to execute the command rather than print out text.
The result of the command should be 350
To verify you can manually add up the values to check the answer is correct.
Answer:
First you have to add :-X = 7+2+5+9+6+10+9+8+4
X= 50
Y = 2+5+7+4+2+9+9+4+10
Y = 52
Now ,
Σ(xy)= 50×52
= 2600
Hope it helpful to you
A verbal description of a linear function g is given. Express the function g in the form
g(x) = ax + b.
The linear function g has rate of change −12 and initial value 100.
g(x) =
G is a linear function with a rate of change of -12 and an initial value of 100. Its equation is: g = -12x + 100.
What is a linear function?Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.
What does the described linear function look like?As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.
Since f(x) = axe + b is the typical slope-intercept form of a linear function,
an is the slope (rate of change), and b is the y-intercept (initial value).
g = -12x + 100 is the necessary linear function, which is what has been presented.
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what’s the equation of the line graphed below i’ll give you brainlist pls help
y=3/2x+4
y=2/3x+4
y=2/3x-6
y=3/2x-6
Answer:
y = 2/3x + 4
Step-by-step explanation:
y-intercept (b) is 4
Use points (-6, 0) and (0, 4) to find the slope (m) = (4-0)/(0--6) = 4/6 = 2/3
y = mx + b = 2/3x + 4
The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest.) 865, 970, 985, 1005, 1015, 1035, 1055, 1080, 1095, 1095 Send data to calculator Suppose that one of the people moves. Her rent changes from $1095 to $1045. Answer the following.
The new list of rents, ordered from least to greatest, would be 865, 970, 985, 1005, 1015, 1035, 1055, 1080, 1045, 1095. The median rent would also be changed from $1095 to $1045.
Un capitalista tiene dos capitales que se diferencian en S/. 221 000, el mayor de ellos lo impone al 20% anual y el menor al 16% anual, así al cabo de 3 años, el monto producido por el mayor es el doble de lo que produce el menor. Hallar la suma de los capitales.
The sum of the capitals would be $530400.
What is the formula to calculate the simple interest?The formula to calculate the simple interest is -
I = PRT/100
Given is that a capitalist has two capitals that differ in $221,000. The largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces.
We can write the amount produced by largest as -
A = P(1 + rt)
A = 221000(1 + 0.2 x 3)
A = 221000 x 1.6
A = 353600
Amount generated by smallest -
a = 353600/2
a = 176800
Their sum would be -
A + a = 530400
Therefore, the sum of the capitals would be $530400.
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{Question in english -
A capitalist has two capitals that differ in S/. 221,000, the largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces. Find the sum of the capitals.}
Quadrilateral ABCD has the following angle measures:
m∠A = ?°, m∠B = 97°, m∠C = 47°, m∠D = 90°
What is m∠A?
306°
234°
126°
54°
PLEASE HELP!
Answer:
126
Step-by-step explanation:
360-97-47-90=126
so 126
Answer: C) 126
Step-by-step explanation: first, you need to use this equation...
m∠A + m∠B + m∠C + m∠D = 360°
=> m∠A + 97° + 47° + 90° = 360° add all of the numbers...
=> m∠A + 234° = 360° subtract both sides by 234
=> m∠A = 360°- 234°
=> m∠A = 126°
Hope you've understood...
My question is in the picture below
Answer:
j1gru3hek3n
Step-by-step explanation:
bso2jw4usk8
angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive
The grades that Angie need to receive in her next test so that her average is 92 is 91.
What is average?The average is defined as the mean value a given data set. The formula to calculate the mean of a given data set is:
Average = Sum of the observations / Total number of observations
Assume the marks that Angie needs in her next test is represented by x.
Given that Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. Therefore, the grades she need to receive in her next test so her average is 92 is:
Average = Sum of the grades of all test / Total Number of test
92 = (88+96+92+93+x)/5
460 = 369+x
460 - 369 = x
x = 91
Hence, she needs 91 grades in her next test.
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The complete question is:
Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive in her next test so that her average of all test is 92?
Which of the following graphs matches the equation y=-4x+3
The equation of line is y = -4x + 3 , where the slope is m = -4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -4x + 3 be equation (1)
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = -4
And , the y intercept is 3
The equation of line is plotted on the graph
Hence , the equation of line is y = -4x + 3
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The complete question is :
Which of the following graphs matches the equation y=-4x+3?
On a coordinate plane, a line goes through (0, 3)
On a coordinate plane, a line goes through (-2, 5) and (0, -3).
On a coordinate plane, a line goes through (0, 3) and (3, -1).
Janelle has set up bird feeders around the pond behind her house. Each feeder can hold 1/2 a cup of bird food. After measuring, Janelle finds that she has 3 cups of bird food. How many feeders can she fill?
Answer: Janelle can fill 6 feeders.
Step-by-step explanation:
To find the number of feeders Janelle can fill, we need to divide the total amount of bird food she has by the amount of bird food each feeder can hold.
First, let's convert the total amount of bird food from cups to half-cups:
3 cups / 2 = 6 half-cups
So, Janelle has 6 half-cups of bird food, and each feeder can hold 1 half-cup.
Therefore, she can fill:
6 half-cups / 1 half-cup per feeder = 6 feeders.
So, Janelle can fill 6 feeders.
2.63 divied by 0.5 standard way
Answer: 5.26
Step-by-step explanation:
Answer:
= 0.190
Solution:
Change the divisor 2.63 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
50 ÷ 263 = 0.190
and therefore:
0.5 ÷ 2.63 = 0.190
Both calculated to 3 decimal places.
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What is the value of x in l-16l = x
Answer: |-16| =x
- (-16)= x
x = 16
Step-by-step explanation:
thank you
Line A (y = 3x + 1) is transformed into
Line B (y=2x-7). Which best describes
the new slope and y-intercept?
The slope is[ ? ],
and the line is shifted[ ? ]
steeper
flatter
Answer:
The new slope is 2,
New y-intercept is - 7
Line is flatter since slope has reduced
Step-by-step explanation:
2. Determine the area of each composite figure below.
Answer:
[tex]6\pi[/tex]
Step-by-step explanation:
There's two things to note here, we're dealing with a semi-circle and also a semi-circle that has some area taken out of it.
Area of a Circle:The area of a circle can be calculated using the formula: [tex]A=\pi r^2[/tex] where "r" is the radius, equal to half the diameter.
Since we're dealing with the semi-circles, we can just divide this area by two to get: [tex]A=\frac{\pi r^2}{2}[/tex]
Now as noted, we have some of the area taken out, but fortunately it's just another semi-circle. We can simply calculate the area of the entire semi-circle, and then calculate the area of the semi-circle inside and subtract them.
So the diameter of the entire thing is just 8 ft, so the radius is half of this, equal to 8 ft. That means the area is: [tex]A=\frac{\pi (4)^2}{2}=A = \frac{\pi * 16}{2} = 8\pi[/tex]
One mistake that may be made here, is assuming the radius of the smaller semi-circle is just two, as provided in the image. It's actually the radius of the inner semi-circle plus two which gives us the radius of the outer circle, of 4 feet. Now luckily in this case, it actually still results in 2 ft (since 2 + 2 = 4), but in other examples, that may noe be the case.
So now let's calculate the area of the inner semi-circle: [tex]A=\frac{\pi (2)^2}{2}=2\pi[/tex]
Now let's just subtract the areas: [tex]8\pi - 2\pi = 6\pi[/tex], so the area is 6 pi
Help please! Which of the following tables represents a relation that is a function? Explained answer please
A
B
C
D
Answer:
Step-by-step explanation:
THE ANSWER TO YOUR QUESTION IS C.
The 8 red markers in a box account for 4% of all markers in the box. How many markers are in the box?.
Answer: 32
Step-by-step explanation: divide 8 into 4/100
Kcf
Keep change flip
Keep the 4/100 change the division sign to multiplication then flip the 8 to 8/1 then just multiply across.
Examine the figure below, solve for a, round to the nearest whole number.
T
37
A
46⁰
28
D
The measure of a from the triangle ATD is 27 units. Therefore, the option B is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
From the given triangle ADT, ∠A=46°, ∠D=84°, AT=37, AD=t and TD=a.
By angle sum property,
∠A+∠D+∠T=180°
46°+84°+∠T=180°
130°+∠T=180°
∠T=50°
sin46°/a=sin84°/37=sin50°/t
0.7193/a=0.9945/37=0.7660/t
0.7193/a=0.9945/37
0.9945a=0.7193×37
0.9945a=26.6141
a=26.6141/0.9945
a=26.76
≈27
0.9945/37=0.7660/t
0.9945t=0.7660×37
0.9945t=28.342
t=28.342/0.9945
t=28.5
Therefore, the option B is the correct answer.
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Please help fast!! What is the domain of the relation?
Please explain the answer!
The domain of the relation include the following: C. {-5, -2, 0, 1, 4}.
How to determine of this relation?In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:
Domain = {-5, -2, 0, 1, 4}.
In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {-5, -2, 0, 1, 4}.
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Which of the following angles is in the solution set of (see picture)
Angles are measured in degrees, with a full circle being 360°, and can be thought of as the amount of rotation that two straight lines or planes undergo.
What best define about angle?The class definition of angle changed from a collection of ambiguous expressions, such as “the measurement of all the sides,” “the place where lines meet,” and “the corner of a shape or anything,” to
The equation below can be set up to calculate this.
Tan(angle) = 80 ft / (200 ft – 4 ft)
Solving for the angle, we get:
angle = tan-1(80 ft / 196 ft (ca. 60 m))
angle = tan-1(0.408163265)
Angle = 36.87 degrees (to the nearest hundredth of a degree).
Therefore, The law of tangents indicates that the angle between the subject's eyes and the top of the structure is roughly 36.87 degrees.
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From the picture, find the value of the pawn in each of the following problems, and write the check
Answer:
6) x = 6
7) x = 4
8) x = 4
9) x = 6
10) x = 6
Step-by-step explanation:
This is based on Dr. Henry Borenson's method of using pawns to explain algebraic equations. Frankl I find using variables more intuitive
Let each pawn represent an x in the equations
6.
x + 8 = 10 + 4
x = 10 + 4 - 8
x = 14 - 8 = 6
7.
x + x = 4 + x
2x = 4 + x
2x - x = 4
x = 4
8.
x + x + x + 2 = 7 + 7
3x + 2 = 14
3x = 14 - 2
3x = 12
x = 12/3
x = 4
9.
2x + 4 = x + 10
2x - x = 10 - 4
x = 6
10
3x = x + 10 + 2
3x = x + 12
3x - x = 12
2x = 12
x = 6
