Charlie needs to apply a force in the opposite direction of the resultant vector sum of his brothers' forces. By converting the forces into Cartesian vectors based on the bearings, we can calculate the components of Charlie's required force to maintain equilibrium.
Explanation:Step 1: Break down the forces into their x and y components
The force exerted by Noah can be broken down into its x and y components using the following equations:
F_x_Noah = F_Noah × cos(θ_Noah) = 8 N × cos(023°) ≈ 7.13 N
F_y_Noah = F_Noah × sin(θ_Noah) = 8 N × sin(023°) ≈ 3.71 N
The force exerted by Jude can be broken down into its x and y components using the following equations:
F_x_Jude = F_Jude × cos(θ_Jude) = 5 N × cos(155°) ≈ -4.95 N
F_y_Jude = F_Jude × sin(θ_Jude) = 5 N × sin(155°) ≈ -0.58 N
Step 2: Sum the x and y components of the forces
To find the net force in the x-direction, we sum the x-components of the forces exerted by Noah and Jude:
F_x_net = F_x_Noah + F_x_Jude ≈ 7.13 N - 4.95 N ≈ 2.18 N
To find the net force in the y-direction, we sum the y-components of the forces exerted by Noah and Jude:
F_y_net = F_y_Noah + F_y_Jude ≈ 3.71 N - 0.58 N ≈ 3.13 N
Step 3: Calculate the magnitude of the net force
The magnitude of the net force can be calculated using the Pythagorean theorem:
F_net = √(F_x_net^2 + F_y_net^2) ≈ √(2.18 N^2 + 3.13 N^2) ≈ 3.74 N
Step 4: Find the angle of the net force
The angle of the net force can be calculated using the following equation:
θ_net = atan(F_y_net / F_x_net) ≈ atan(3.13 N / 2.18 N) ≈ 55.6°
Step 5: Calculate the force Charlie needs to exert
In order for Charlie to keep the toy fire truck in equilibrium, he needs to exert a force that is equal in magnitude and opposite in direction to the net force. Therefore, the force Charlie needs to exert is 3.74 N at an angle of 55.6° + 180° = 235.6° (since the net force is acting in the third quadrant).
The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution, with mean of 6.1 hours and standard deviation of 1.0 hour. Let x represents a random medical resedent selected at the hospital. Find P(x < 5.3).
You have five identical pieces of equipment. There is a 1 in 10 chance that each piece will fail in a year. What is the likelihood that NONE of the pieces fail during a year?
The probability that none of the five identical pieces of equipment will fail during a year is approximately 59.049%, calculated using the statistical independence of each piece's probability of not failing, which is 0.9, raised to the power of 5.
The question is asking for the probability that none of the five pieces of equipment fails within a year when there is a 1 in 10 chance of failure for each piece of equipment. To calculate this, we use the principle of statistical independence. If the chance that one piece of equipment does not fail is 9 in 10 (or 0.9), then the probability that all five do not fail is 0.9 raised to the power of 5.
Mathematically, this is calculated as:
[tex](0.9)^5[/tex]= 0.9 * 0.9 * 0.9 * 0.9 * 0.9
Performing the multiplication, the probability that none of the five pieces fail during a year is approximately 0.59049.
In conclusion, there is a 59.049% chance that none of the identical pieces of equipment will fail during a year, assuming that the failures are statistically independent events.
helppppppppppppppppppppppppppp
√9 = 3
3 is a real number , a whole number , a rational number , an integer and a natural number ,
So last option is correct
Set of all natural numbers , set of all whole numbers , set of all integers, set of all rational numbers , set of all real numbers.
five cards are drawn from a standard deck of cards. each card is replaced after being drawn. what is the probability of the following event: p(3 and 3 and 3 and 2 and 2)?
General Idea:
If A and B are independent, then the probability that events A and B both occur is:
[tex] p(A\; and\; B) = p(A) \times p(B). [/tex]
In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B
Applying the concept:
Five cards are drawn from a standard deck of cards. Each card is replaced after being drawn.
There are four 3's in a deck of card, four 2's in a deck of card. In a deck of card there are 52, so...
[tex] \\[tex] p(3\; and\; 3\; and\; 3 \; and \; 2 \; and\; 2)=\frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \\ \\ Multiply \; numerator \; with \; numerator \; and \; denominator \; with \; denominator\\ \\ \frac{4 \cdot 4 \cdot 4 \cdot 4 \cdot 4}{52 \cdot 52 \cdot 52 \cdot 52 \cdot 52} \\ \\ Cancel \; Common\; Factor\\ \\ \frac{1 \cdot 1 \cdot 1 \cdot 1 \cdot 1}{13 \cdot 13 \cdot 13 \cdot 13 \cdot 13} =\frac{1}{13^5} =\frac{1}{371293} [/tex] \; =\; p(3) \times \; p(3) \times \; p(3) \times \; p(2) \times p(2) [/tex]
Which graph represents the function?
The resulting graph of the rational function is the Graph at the top right graph 2.
To depict the rational function f(x) = 2/(x - 1) + 3, we must consider its characteristics. The function has a vertical asymptote at x = 1 because the function is undefined at that point, and it has a horizontal asymptote at y = 3 due to the behavior of the function as x approaches infinity. The graph will approach these asymptotes but never cross them.
For values of x greater than 1, the function will decrease towards the horizontal asymptote because the (x - 1) in the denominator increases, which causes the value of f(x) to decrease.
However, because of the '+3' term in the function, the curve will approach y = 3 as x goes to infinity.
To graph this function, plot several points where x is not equal to 1, then draw the curve that passes through these points while approaching the respective asymptotes.
The portions of the graph should fall above the horizontal line y = 3 for x < 1 and approach y = 3 from below for x > 1.
Therefore, the resulting graph of the rational function is the Graph at the top right graph 2.
The probable question may be:
Which graph represent the rational function f(x)=2/x-1+3
The average rate of change from x = 0 to x = 15 is about −4.667. How does the average rate of change from x = 0 to x = 20 compare to this number? The average rate of change from x = 0 to x = 20 is decreasing the average rate of change from x = 0 to x = 15.
Answer: The average rate of change from x = 0 to x = 20 is decreasing
✔ slower than
the average rate of change from x = 0 to x = 15.
Suppose that the height of the slide is 2 feet, when x = 20. What is the average rate of change over the entire slide?
-3.9
Step-by-step explanation:
So, the two answers are: Slower than, and -3.9
What is the solution of the square root of 3x+28-8=x (-8=x is not in the square root) any explanation and answer is appreciated!
Factor completely x^2 + 16.
(x + 4)(x + 4)
(x + 4)(x − 4)
Prime
(x − 4)(x − 4)
Answer: (x4-81) I searched it up..
Step-by-step explanation:
1. Sketch and/or explain the evidence you created for the Pythagorean Theorem. Be sure to explain how each part related to the Pythagorean Theorem.
Answer:
u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye
Step-by-step explanation:
what is the solution to the following system?
5x+2y+z=4
x+2z=4
2x+y-z=-1
A. x = 0, y = 1, z = 2
B. x = 1, y = –1, z = 2
C. x = 1, y = 0, z = –1
D. x = 2, y = 1, z = 0
Veronica bought a purse for 25 off its full price. what was the full price of the purse if Veronica paid $35.85 before sales tax? A) $59.75 B) $47.80 C) $ 60.85 D) $36.10
B- $47.80 for apex that's what i got.
The full price of the purse is C) $60.85.
Explanation:The price at which the purse is bought = $25
The price paid = $35.85
To find the full price of the purse, we need to add the discount amount to the price Veronica paid.
Since she got $25 off, the discount amount is $25.
Therefore, the full price of the purse is
= $35.85 + $25
= $60.85.
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The largest doll is 12 inches tall. The height of each of the other dolls is
7
10
710
the height of the next larger doll. Write an expression involving a power for the height of the smallest doll. Then evaluate the expression to find the height of the smallest doll to the nearest tenth of an inch.
Answer: with the problem you can see that
Smallest is 4.1 inches
Expression is 12 multiply by (7/10) to the power of 3
Answer:
Smallest is 4.1 inches
Expression is 12 multiply by (7/10) to the power of
Order the set of numbers from least to greatest.
The length of a rectangle is 3 m longer than its width.
The area of the rectangle is 154m^2
What is the width of the rectangle?
___m
Before you make any payments to the organization handling your DMP (debt management plan) what should you do?
Answer:
" A DMP allows you to deposit a set amount of money with a credit counseling organization each month, which is then strategically dispersed to your various creditors "
" DMPs are designed to help consumers work off their debt as quickly as possible by leaving these decisions largely to credit counseling professionals "
Before sending monthly payments to the organization handling your DMP, confirm with your creditors that they have in fact accepted the plan.
Before you make any payments to the organization handling your DMP (debt management plan) you should confirm with your creditors that they have accepted the plan.
What is Debt Management Plan?A Debt Management Plan is a laid-out framework for settling debts that is coordinated by a credit counseling organization. A certain amount of money is deposited with these organizations that help the debtor to offset his bills in a strategic manner.
So, before making any payments to the organization handling your DMP (debt management plan) you should confirm with your creditors that the plan for repayment is acceptable by them.
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Brainliest + 15 points. Help please? Who's up for the challenge?
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Use the domain {, 1, 2, 4, 8, 16} and plot the points on the graph that would best satisfy the equation y = log2x.
Which of the binomials below is a factor of this trinomial?
x2 - 3x - 10
A. x + 2
B. x - 2
C. x - 1
D. x + 1
The binomials below are a factor of this trinomial that will be x + 2. Option A is correct.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that, the expression is, x² - 3x - 10
Binomials in algebra are two-term expressions joined by a plus or minus sign, such as ax+b. While the second term might or might not, the first term always contains a variable.
A binomial can be solved or simplified for further work by factoring, which is the process of looking for simpler terms that, when multiplied together, produce the original binomial expression.
Thus, the binomials below are a factor of this trinomial that will be x + 2. Option A is correct.
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A bag contains 2 red marbles, 3 blue marbles, 4 yellow marbles, and 3 green marbles. In how many ways can choosing not yellow occur?
TANYA HAS A DOG LEASH THAT IS 4 YARDS LONG SHE SHOORTENS THE LEASH BY 6 FEET. WHAT IS THE LENGTH OF THE SHORTENED LEASH
Answer:
Its 6 feet
Step-by-step explanation:
A geometry teacher asked Charlene to define “acute triangle.” Charlene said that an acute triangle is a triangle whose three interior angles have measures less than 90°90°. Is Charlene’s definition valid?
A.Yes, because no right triangles fit this definition.
B.No, because some scalene triangles fit this definition.
C.Yes, because this definition fits all acute triangles and does not fit triangles that are not acute.
D.No, because not all acute triangles fit this definition.
Answer:
C.Yes, because this definition fits all acute triangles and does not fit triangles that are not acute.
Step-by-step explanation:
The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii
Answer:
Hence, the length of the chord joining two perpendicular radii is:
6√2 inches.
Step-by-step explanation:
Let r denote the radius of circle.
i.e. r=6 inches.
Let AB be the chord that connects two perpendicular radii i.e. OA and OB whose lengths are given to be 6 inches.
We can apply pythagorean theorem to find the length of the chord.
[tex]AB^2=OA^2+OB^2\\\\AB^2=6^2+6^2\\\\AB^2=36+36\\\\AB^2=72\\\\AB=\sqrt{72}\\\\AB=6\sqrt{2}[/tex].
Hence, the length of a chord connecting two perpendicular radii is:
6√2 inches.
help me with this and I will give you brainly
Find the slope of a parallel line to 5x+2y=6
Answer: [tex]\dfrac{-5}{2}[/tex]
Step-by-step explanation:
We know that equation in intercept form is given by :-
[tex]y=mx+c[/tex] , where m is the slope of the line {Coefficient of x}
The given equation of a line : [tex]5x+2y=6[/tex]
First rewrite the given equation in intercept form , we get
[tex]2y=6-5x\\\\\Rightarrow\ y=\dfrac{1}{2}(6-5x)\\\\\Rightarrow\ y=\dfrac{-5}{2}x+\dfrac{6}{2}\\\\\Rightarrow\ y=\dfrac{-5}{2}x+3[/tex]
Comparing to the general intercept form , we have , the slope of the line = [tex]\dfrac{-5}{2}[/tex]
Since the slopes of two parallel lines is equal.
Therefore, the slope of a parallel line to [tex]5x+2y=6[/tex] : [tex]\dfrac{-5}{2}[/tex]
HELP PLEASE! Are the two triangles similar? How do you know?
Answer:
The two triangles are similar by AAA
Step-by-step explanation:
we know that
If the two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
Remember that
The sum of the internal angles of a triangle must be equal to [tex]180\°[/tex]
so
In the triangle CDE
Find the measure of angle E
[tex]m<C+m<D+m<E=180\°[/tex]
substitute the values and solve for m<E
[tex]60\°+53\°+m<E=180\°[/tex]
[tex]m<E=180\°-(60\°+53\°)=67\°[/tex]
The measures of internal angles triangle CDE are [tex]60\°-53\°-67\°[/tex]
In the triangle FGH
Find the measure of angle G
[tex]m<F+m<G+m<H=180\°[/tex]
substitute the values and solve for m<G
[tex]60\°+m<G+67\°=180\°[/tex]
[tex]m<G=180\°-(60\°+67\°)=53\°[/tex]
The measures of internal angles triangle FGH are [tex]60\°-53\°-67\°[/tex]
therefore
The two triangles are similar by AAA
140% of a number is 364. Find the number
The number whose 140% is 364 is 260.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number = M
140% of M = 364.
140/100 x M = 364
Solve for M.
M = 364 x 100 / 140
M = 260
Thus,
140% of 260 is 509.6.
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Would be glad if you answer my question!
A rectangular auditorium seats 13201320 people. the number of seats in each row exceeds the number of rows by 1414. find the number of seats in each row.
The number of rows in the auditorium is 45, and each row has 59 seats.
Explanation:This problem can actually be solved using Algebra. If we let 'x' represent the number of rows in the auditorium, then the number of seats in each row would be x + 14 (since the number of seats in each row exceeds the number of rows by 14). Since the total number of seats is 1320, we can now set up and solve an equation: x(x + 14) = 1320.
Solving the equation, we get [tex]x^2[/tex] + 14x - 1320 = 0. This can be factored to (x - 45)(x + 29) = 0. The positive solution is x = 45. Therefore, there are 45 rows in the auditorium.
Substituting x = 45 back to our original equation x + 14, we find out that there are 45 + 14 = 59 seats in each row.
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If lines l and m are parallel, then ∠2 and ∠3 are _______ angles.
alternate interior
corresponding
alternate exterior
same-side-interior
Answer:
B) Corresponding
Step-by-step explanation:
Hello! The answer to this question is that <2 and <3 are corresponding angles. If you know the definition of corresponding angles and how they appear on a figure such as this, you should have no problem answering these problems in the future. Hope this comes to your help!
Given a collection of paired sample data, the ____________ algebraically describes the relationship between the two variables, x and y.
Final answer:
The linear equation describes the algebraic relationship between two variables in a paired sample data set, with the slope and y-intercept being key components of this equation.
Explanation:
Given a collection of paired sample data, the linear equation algebraically describes the relationship between the two variables, x and y. The most fundamental representation of a linear association is through a linear equation, which graphically manifests as a straight line in a scatter plot. Two commonly used forms of linear equations are y = mx + b and y = a + bx. The latter is frequently used in statistical contexts to differentiate from the algebraic context.
In these equations, m or b (when used as a coefficient) is known as the slope, indicating the rate of change or how much y changes as x changes. The y-intercept represented by a is the point at which the line crosses the y-axis, typically where x equals zero. A linear relationship between two variables is confirmed when a scatter plot of the pair shows points that approximate a straight line.