The force needed to hold the box in a stationary position on the inclined ramp is approximately 156.89 lb. This can be calculated by multiplying the weight of the box (424 lb) by the sine of the angle of inclination (22°).
When the box is at rest on the inclined ramp, the force of gravity acting on it can be resolved into two components: one perpendicular to the ramp (the normal force) and one parallel to the ramp (the force due to gravity along the incline).
The normal force counteracts the component of gravity perpendicular to the ramp and is equal in magnitude but opposite in direction. The force due to gravity along the incline can be determined by multiplying the weight of the box by the sine of the angle of inclination.
To prevent the box from sliding down the ramp, the force needed to hold it in place must exactly balance the force due to gravity along the incline. Therefore, the required force can be calculated by taking the weight of the box and multiplying it by the sine of the angle of inclination.
In this case, the weight of the box is 424 lb, and the angle of inclination is 22°. Thus, the force needed to hold the box in a stationary position is 424 lb sin(22°).
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2.
It cost Enica $9 75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was
Erica's total profit?
Answer:
$8.75
Step-by-step explanation:
Cost price= $9.75
Selling price= $1.00
profit= C.P-.SP
= 9.75-1.00
= $8.75
a circle has an arc of length 48π that is intercepted by a central angle of 120°. what is the radius of the circle? enter your answer in the box. 72 units
The radius of the circle is 144 units.
To find the radius of the circle, we can use the formula that relates the circumference of a circle to its radius and the central angle intercepted by an arc.
The formula is:
Arc length = 2πr * (θ/360)
Where:
Arc length is the length of the intercepted arc
r is the radius of the circle
θ is the central angle in degrees
In this case, we are given that the arc length is 48π and the central angle is 120°. Let's substitute these values into the formula and solve for r:
48π = 2πr * (120/360)
Simplifying the equation:
48 = 2r * (120/360)
48 = r * (1/3)
r = 48 * 3
r = 144
Therefore, the radius of the circle is 144 units.
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Answer!!!!! Help!!!
Answer:
The answer is postulate
What type of continuous distribution (normal, positively or negatively skewed, bimodal, exponential) would best represent the following situations? a) The age of people who have retired. b) The number of red Smarties in boxes of Smarties. c) The shoe sizes of Stouffvillians. d) The wait time between calls to Pizza Pizza.
If the continuous distribution is given then The age of people who have retired represents Normal distribution.
a) The age of people who have retired would likely follow a normal distribution, as it tends to have a symmetric bell-shaped curve.
b) The number of red Smarties in boxes of Smarties would have a discrete distribution, as it can only take on certain whole numbers and cannot be fractionally or continuously measured.
c) The shoe sizes of Stouffvillians may exhibit a bimodal distribution, as there might be two distinct peaks indicating two groups with different average shoe sizes.
d) The wait time between calls to Pizza Pizza could potentially follow an exponential distribution, as it is often used to model the time between events in a Poisson process, such as the arrival of phone calls. The distribution would have a long tail, representing longer wait times occurring less frequently.
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Which function matches the table?
Answer:
The A matches the table x+3
On a coordinate grid, a scale drawing of a banner is shaped like a parallelogram with verticals at (-15,10), (0,-5), (30,-5), and (15,10. Each square on the grid represents 1 square inch. What is the area of the banner?
The area of the banner is 562.5 square units.
To calculate the area of the banner, we can divide it into two triangles and then find the sum of their areas.
First, let's calculate the base and height of each triangle:
Triangle 1: Vertices (-15,10), (0,-5), and (30,-5)
The base of Triangle 1 is the distance between (-15,10) and (30,-5), which is 30 - (-15) = 45 units.
The height of Triangle 1 is the distance between (-15,10) and (0,-5), which is 10 - (-5) = 15 units.
Triangle 2: Vertices (0,-5), (30,-5), and (15,10)
The base of Triangle 2 is the distance between (0,-5) and (15,10), which is 15 units.
The height of Triangle 2 is the distance between (0,-5) and (30,-5), which is 30 - 0 = 30 units.
Now, let's calculate the area of each triangle using the formula for the area of a triangle: Area = (base * height) / 2.
Area of Triangle 1 = (45 units * 15 units) / 2 = 337.5 square units
Area of Triangle 2 = (15 units * 30 units) / 2 = 225 square units
Finally, to find the total area of the banner, we sum the areas of the two triangles:
Total Area = Area of Triangle 1 + Area of Triangle 2
Total Area = 337.5 square units + 225 square units
Total Area = 562.5 square units
Therefore, the area of the banner is 562.5 square units.
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Does anyone know this
Answer:
I belive the answer is A
Step-by-step explanation:
So any answer with 22t would make sense, so you have A and C. In C though, it is subtracting 22, but since 6195 is the total it would have to include the 22 so it is A.
Victoria ate 4\16 of a small pizza for lunch. How is this fraction written as a decimal?
Answer:
0.25
Step-by-step explanation:
4/16 --> 1/4 and 1/4 = 0.25
Find the GCF of the monomials: 18x² and 21x²y
A)3x
B)3x²
C)3xy
D)3x²y
PLEASE HELP MEEE
You guy's will get 40 points if you help me!
Answer:
mean = 5+9+9+6+6+11+8+4/7 = 8.29
median = 6
mode = 6
range = 11 - 4 = 7
Answer:
Step-by-step explanation:
5 , 9 , 6 , 6 , 11 , 8 , 4
Mean = sum of all data ÷ number of data
[tex]= \frac{5+9+6+6+11+8+4}{7}\\\\= \frac{49}{7}\\\\= 7[/tex]
Median: To find median, arrange in ascending order and medianis the middle term
4 , 5 , 6 , 6 , 8 , 9 , 11
Middle term = 4th term
Median = 6
Mode: a number that appears most often is mode
6 appears 2 times
Mode = 6
Range:
Range = maximum value - minimum value
= 11 - 4
= 7
Identify each scatterplot below with an appropriate value of r.
Answer:
A would be the answer
Step-by-step and
Hey guy pls help me with dis due today pls help no links pls
I did number one
pls explain answer
mode is 4 and the median is also 4
mode is the number that appears the most which is 4 and median is the number that is in the middle when you line up all the numbers in order (0,2,2,3,3,4,4,4,4,5,5,5,6,6,10)
4 people can dig a trench in 3 hours.
How long would it take 9 people?
Give your answer in minutes.
Answer:
80 minutes.
Step-by-step explanation:
do I need to explain? I hate explaining :(
Sophie has a box filled with trail mix the box has a length
Evaluate the expression for the given value of x.
3/4 x − 12 for x = 16
Answer:
if x is 16 then 3/4(16) - 12
when you simplify 4 by 16
3(4)-12
12-12=0
The roots of 3x2 + x = 14 are
1. imaginary
2. real,rational,equal
3.real,rational,unequal
4.real,irrational,unequal
Answer:
3
Step-by-step explanation:
3x2 +x −14 = 0 12 −4(3)(−14) = 1+168 =169 = 132
The roots of 3x² + x = 14 are real, irrational and unequal
What is Quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x, ax² + bx +c=0 with a ≠ 0 .
Given equation is :
3x² + x = 14
3x² + x - 14=0
we have, a=3, b=1 c=-14
D= b²-4ac
= 1²-4*3*(-14)
= 1+168
= 169
As, D>0
Hence, the roots are real.
Now,
x= -b±√b²-4ac/2a
= -1±√169/2*3
=-1±13/6
x= -1-13/6 and x= -1+13/6
x= -7/3 and x= 12/6=2
Hence, the roots are real, irrational and unequal.
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What is the description of angle 4 as it relates to the situation below?
angle 4 is the angle of elevation from the person to the radar tower.
angle 4 is the angle of depression from the radar tower to the person.
angle 4 is the angle of depression from the person to the radar tower.
angle 4 is the angle of elevation from the radar tower to the person.
In the given situation, "angle 4 is the angle of elevation from the radar tower to the person" is the description of angle 4.In trigonometry, an angle of elevation or inclination is the angle between the horizontal and the line of sight of an observer looking upwards. An angle of depression is the angle between the horizontal and the line of sight of an observer looking downwards.
In the given situation, angle 4 refers to the angle formed between the horizontal and the line of sight from the radar tower to the person. As the angle is formed while looking upwards from the radar tower to the person, it is called the angle of elevation. Hence, the correct description of angle 4 in this situation is "angle 4 is the angle of elevation from the radar tower to the person."
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How would I do this??
$12 with a 85% markup
12+85% is $22.20
80%x12=9.6
5%x12=0.6
9.6+0.6=10.2
12+10.2=22.20
Answer: $22.20
∑ = {C,A,G,T}, L = { w : w = CAjGnTmC, m = j + n }. For example, CAGTTC ∈ L; CTAGTC ∉ L because the symbols are not in the order specified by the characteristic function; CAGTT ∉ L because it does not end with C; and CAGGTTC ∉ L because the number of T's do not equal the number of A's plus the number of G's. Prove that L ∉ RLs using the RL pumping theorem.
If We consider the string w = [tex]CA^pG^pT^pC[/tex], then L ∉ RLs by pumping lemma.
To prove that L ∉ RLs using the RL pumping theorem, we assume L is a regular language and apply the pumping lemma for RLs. Let p be the pumping length of L.
We consider the string w = [tex]CA^pG^pT^pC[/tex], where |w| ≥ p. According to the pumping lemma, we can decompose w into uvxyz such that |vxy| ≤ p, |vy| > 0, and for all k ≥ 0, the string [tex]u(v^k)x(y^k)z[/tex] is also in L.
However, by examining the structure of L, we see that the number of A's and G's is dependent on each other and must match the number of T's.
Since pumping up or down would alter this balance, there is no way to satisfy the condition for all k, leading to a contradiction. Therefore, L cannot be a regular language, and we conclude that L ∉ RLs.
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Thomas walks 10 miles in 120 minutes. Select all of the unit rates below that
describe Thomas' walk. Show your work.
a) He can walk 1 mile in 12 minutes
b) He can walk 12 miles in 1 minute
c) He can walk of a mile in 1 minute
1
d) it takes him of a minute to walk 1 mile
12
12
Answer:
Hi! The answer to your question is B) He can walk 12 miles in 1 minute.
To find Unit rate divide the biggest number by the smallest; Example: [tex]120/10[/tex]
Step-by-step explanation:
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Hope this helps!!
- Brooklynn Deka
What is the area of the polygon given below
someone please help!
Answer:
12 units
Step-by-step explanation:
1st, I found the distance for the two parallel sides on the hexagon. I counted the lines to be 2 units each, which makes 4 units. And since all sides of a hexagon are equal. All the sides make 12 units, or centimeters. Therefore, the perimeter is 12 units
How much money would produce $70 as simple interest at 3.5% per
annum?
Answer:
$2000
Step-by-step explanation:
Simple Interest = $70
Rate = 3.5%
Time = 1
Principal = ?
Simple Interest = (Principal × Rate × Time)/100
Principal = (Simple Interest × 100)/(Rate × Time)
Principal = (70 × 100)/(3.5 × 1)
Principal = 7000/3.5
Principal = 14000/7
Principal = 2000
The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that 2 1 0 1 2 [AB] 0 -1 31 0 0 mln where m and n are real numbers. State all values of m and/or n such that the following statements are true. (a) Matrix A is invertible. (b) The system AX = B has no solutions. (c) The system AX = B has an infinite number of solutions. (d) Columns of the augmented matrix (AB) are linearly independent. (e) The system AX = 0 has a unique solution. (f) At least one eigenvalue of the matrix A is zero. (g) Columns of the matrix A form a basis in R3.
a. Matrix A is invertible when |A| = -m ≠ 0 then statement true.
b. The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.
c. The system AX = B has an infinite number of solutions when m = n = 0 then statement true.
d. Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.
e. The system AX = 0 has a unique solution when m ≠ 0 then statement true.
f. At least one eigenvalue of the matrix A is zero when m = 0 then statement true.
g. Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.
Given that,
The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that
[A|B] = [tex]\left[\begin{array}{ccc}2&1&0 \ | \ 2\\0&-1&3 \ | \ 1 \\0&0&m \ | \ n\end{array}\right][/tex]
Where m and n are real numbers.
We know that,
a. We have to prove matrix A is invertible.
For A to be invertible.
|A| ≠ 0
|A| is the determinant of the matrix A.
|A| = 2(-m) -1(0) + 0(0) = -m
Here, m is the real number.
So, |A| = -m ≠ 0
Therefore, Matrix A is invertible when |A| = -m ≠ 0 then statement true.
b. We have to prove the system AX = B has no solution.
When Rank[A|B] > Rank[A]
m = 0 and n ≠ 0 has a real number
Therefore, The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.
c. We have to prove the system AX = B has an infinite number of solutions.
When m = n = 0, and Rank[A] < 3
Therefore, The system AX = B has an infinite number of solutions when m = n = 0 then statement true.
d. We have to prove columns of the augmented matrix (AB) are linearly independent.
When m ≠ 0 and m∈R and n= 0
Therefore, Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.
e. We have to prove the system AX = 0 has a unique solution.
When [tex]\left[\begin{array}{ccc}2&1&0 \\0&-1&3 \\0&0&m \end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]
The equation are 2x + y = 0, -y + 3z = 0 and mz = 0
m ≠ 0 should be any real number except zero.
Therefore, The system AX = 0 has a unique solution when m ≠ 0 then statement true.
f. We have to prove at least one eigenvalue of the matrix A is zero.
When λ = 2, 1, m
m = 0 then eigen value is zero
Therefore, At least one eigenvalue of the matrix A is zero when m = 0 then statement true.
g. We have to prove columns of the matrix A form a basis in R³.
When m ≠ 0
Therefore, Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.
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regression analysis was applied and the least squares regression line was found to be ŷ = 400 3x. what would the residual be for an observed value of (2, 402)?
The Residual for an observed value of (2, 402) is -4.
The regression analysis and the least squares regression line was found to be ŷ = 400 3x.
The observed value is (2, 402).To find the residual for an observed value of (2, 402),
we need to use the formula for residual
Residual = Observed value - Predicted value
where Observed value = (2, 402) , Predicted value = ŷ = 400 + 3x , Putting x = 2 in the above equation
we get,
ŷ = 400 + 3(2) = 406
Now, Residual = Observed value - Predicted value= 402 - 406= -4
Therefore, the residual for an observed value of (2, 402) is -4.
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Ms. Clark spent $89.85 on sewing kits that cost $5 each plus $4.85 tax on the total bill. How many kits did she buy?
The sewing kits bought by Ms, Clark is 17 in number.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
As given in the question, Ms. Clark spent $89.85 on sewing kits that cost $5 each plus $4.85 tax on the total bill.
Let the number of sewing kits be x,
According to the question,
5x + 4.85 = 89.85
5x = 89.85 - 4.85
5x = 85
x = 17
Thus, the sewing kits bought by Ms, Clark is 17 in number.
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Determine a series of transformations that would map Figure C onto Figure D plz help asap
Answer:
Rotation about 180*
Translation about 7 units to the right and 8 down
Step-by-step explanation:
Solve: 4x^2 = 32 thanks
Answer:
D.Step-by-step explanation:
It is difficult to describe, but you just need to follow through the steps acorddingly.The answer 3h - 5 < 13?
Answer: h < 6
Step-by-step explanation:
3h - 5 < 13
3h < 18
h < 6
Answer:
h<6
Step-by-step explanation: