The resultant displacement is approximately 13.071m north and 8m east.
To find the resultant displacement, we need to combine the given displacements in a vector-like manner.
Let's break down the displacements into their components and then add them up.
The first displacement is 6m north.
Since it is purely in the north direction, its components would be 6m in the north direction (along the y-axis) and 0m in the east direction (along the x-axis).
The second displacement is 8m east.
As it is purely in the east direction, its components would be 0m in the north direction and 8m in the east direction.
The third displacement is 10m northwest.
To find its components, we can split it into two perpendicular directions: north and west.
The northwest direction can be thought of as the combination of north and west, each with a magnitude of 10m.
Since they are perpendicular, we can use the Pythagorean theorem to find the components.
The north component would be 10m multiplied by the cosine of 45 degrees (45 degrees because northwest is halfway between north and west).
Similarly, the west component would be 10m multiplied by the sine of 45 degrees.
Calculating the components:
North component = 10m [tex]\times[/tex] cos(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m
West component = 10m [tex]\times[/tex] sin(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m
Now, let's add up the components:
North component: 6m (from the first displacement) + 7.071m (from the third displacement) = 13.071m north
East component: 8m (from the second displacement).
For similar question on resultant displacement.
https://brainly.com/question/13309193
#SPJ8
2. A 30-foot tree broke from its base and fell against a house. If the tree touches the house at a height of 21
feet, how far is the base of the tree from the house? Leave your answer in the simplest radical form.
A. 51 square root 3
B. 9 square root 17
C. 3 square root 51
D. 21.42
Answer:
C
Step-by-step explanation:
Ms. Rathman has 5 nickels, 3 dimes, and 2 quarter. In how many ways can she make change
for 50¢? Make a systematic list to answer this question
Answer:
I guess 5
Step-by-step explanation:
2 q 0 n 0 d
1 q 1 n 2 d
1 q 3 n 1 d
1 q 5 n 0 d
0 q 3 d 4 n
help its pre- algebra
Answer:
bananas: 2480
plantains: 20
Step-by-step explanation:
equations:
b+p=2500
b=124p
just plug then in and solve
Answer:
20 plantains and 2480 bananas
Step-by-step explanation (b is bananas + p is plantains):
2500 = b+p
b=124*p
2500=(124*p)+p
2500=125p (divide by 125)
20=p
b=124(20)
b=2480.
20
2. Vernon practiced soccer 5 hours this week. He practiced 4 hours on weekdays and the rest over the weekend.
a. Write an equation that represents the situation. Define your variable.
b. What is the least common multiple of the denominators of 5 and 4 ? Show your work.
c. Solve the equation and interpret the solution. Show your work.
Answer:
a- Vernon practiced soccer 5 3/4hours this week. He practiced 4 1/3hours on weekdays and the rest over the weekend.
Step-by-step explanation:
Hope this helps
Solve x for -2x- 1 = -7
Answer:
x = 3
Step-by-step explanation:
Add 1 on both sides.
We get:
-2x = -6
Now divide -6 by -2...
-6/-2 = 3
-2x -1 = -7
add the "-1" on both sides, -2x -1 +1 = -7 +1
-2x = -6
divide "-2" on both sides, -2x/-2 = -6/-2
x = 3
how many four-character alpha-numeric codes are possible if repeated characters are not allowed?
Answer:
1,413,720
Step-by-step explanation:
Total number of characters = letters + numbers
= 26 + 10
= 36.
So total number of possible codes
= 36P4
= 36!/ (36-4)!
= 36*35*34*33
= 1413720
Please answer for instant brainliest.
Answer:
5 T-shirts
or
35 T-shirts
Step-by-step explanation:
Alright so this question is a bit tricky but I will explain to you the steps. What you want to do is take every possible answer and multiply it by $15 (The price of an adult t shirt) and see if the answer you get can be added onto with the price of small t shirts ($10).
In other words you need a multiple of $10 as your answer so you can add $10 onto to that number until you get your total of $2,375.
Lets start with 185 t-shirts.
If we do 185 shirts x $15 per shirt we get $2775
That is way above the total of $2,375 so we know that this cant be the answer.
Next we can do 110 t-shirts.
If we do 110 shirts x $15 this time we get $1650.
Now while this is less than the total this is not a multiple of 10.
To prove this lets take the total amount of money earned ($2,375) and subtract this $1650 from it to see how much in youth shirts they sold.
$2,375 - $1650 = $725
Now we can divide $725 by the rest of the $10 youth shirts and you will see we get 72.5 which is not a whole number so it cant be answer. Since you cant sell someone 25% of a shirt or they probably would be upset.
Moving onto 35 t shirts lets take the same steps.
35 x $15 (price of adult t-shirt)
We then get $525 from this. Lets subtract this total again from the grand total earnings they made from selling both shirts ($2,375)
$2,375 - $525 = $1850.
Now this is a multiple of 10. Meaning you can add 10 into it go get that number and you wont have more or less than it. It will be spot on.
So we can do $1850 divided by $10 to find the total amount of youth shirts sold. We get 185 from this, which is a possible answer.
Lets do the last one.
5 t shirts multiplied by $15
We get $75 from this and now lets subtract again from the grand total.
$2,375 - $75 = $2,300
Now this would work too which is what kind of stumps me but we will go with it. Going off this either 5 t-shirts or 35 t-shirts would work as an answer cause you can have an even number of youth shirts sold with either answer. So I could have done something wrong but I believe based off of this either would be correct but I could be missing something. Someone correct me if I made a mistake.
Anyways I hope this helps :)\
EDIT :
I see what I did wrong here and failed to take into account the total of 220 t-shirts sold. But I believe this can help solve the last 2 answers.
How much would you need to deposit in an account each month in order to have $40,000 in the account in 8 years? Assume the account earns 3% annual interest compounded monthly.
Answer:
$166666.67Step-by-step explanation:
$40000 = amount after 8 years time = 8 years interest = 3%principle amount = ?? ( p )$40000 = (( p ) × 3 × 8 )÷100p = (40000 × 100) ÷ ( 3 × 8 )p = $166666.67MARK ME AS BRAINLISTWhat is 50x60? Explain
Answer:
3000
Step-by-step explanation:
50 x 60 = 3000, because
5 x 6 = 30
then you add the 2 zeros making,
3000
Answer:
3000
Step-by-step explanation:
if we break it down, 5 x 6=30 but the numbers have zeros so you have to add one to that answer giving you 3000
need help with this, ASAP
What’s the value of DCB?
Pls help
Answer:
78
Step-by-step explanation:
angle ACD + angle DCB = 180 (Angles on straight line)
4x + 2 + 3x + 3 = 180
7x + 5 = 180
7x = 180-5
7x = 175
x = 175 / 7
x = 25
angle DCB = 3x +3 = 3*25 + 3 = 75 +3 = 78
7/8 − 1/3 =
i need help
Answer:
Step-by-step explanation:
7/8-1/3=13/24
Answer:
13/24
Step-by-step explanation:
7/8 = 21/24
1/3 = 8/24
21/24 - 8/24 = 13/24
A 26-year-old male buys 100/300/100 liability insurance, collision insurance with a $100 deductible, and comprehensive insurance with a $250 deductible What is his total annual premium? Liability Insurance Type Bodily injury Amount Premium 25/50 $220 50/100 $310 100/300 $450 25 $175 50 $245 100 $375 Property damage Collision & Comprehensive Premiums Deductible Collision Comprehensive $215 $129 $250 $185 $102 $500 $148 $85 $100 Rating Factor a Male 3.0 Female 1.45 Age 17-20 21-24 25-29 1.2 215 1.55 1.0 $1142.00 $1765.45 $1770.10 $1785.25
Answer: $1770.10
Step-by-step explanation:
Step 1.
450+ 375= 825
Step 2.
825+ 215+ 102= 1142
Step 3.
1142 × 1.55= 1770.1
a) Dati cinci exemple de numere intregi mai mici ca zero.
Answer:
Numerele întregi pozitive sunt toate numerele întregi mai mari decât zero: 1, 2, 3, 4, 5, .... Numere întregi negative sunt toate opusele acestor numere întregi: -1, -2, -3, -4, -5, .... Nu considerăm că zero este un număr pozitiv sau negativ. Pentru fiecare număr întreg pozitiv, există un număr întreg negativ, iar acești numere întregi se numesc opuse. De exemplu, -3 este opusul lui 3, -21 este opusul lui 21 și 8 este opusul lui -8. Dacă un număr întreg este mai mare decât zero, spunem că semnul său este pozitiv. Dacă un număr întreg este mai mic decât zero, spunem că semnul său este negativ.
Step-by-step explanation:
The volume of a cylinder is 84 pie inches cubed what can be concluded about the volume of the con
Answer:
that it has a radius of (84/(h×pi))^1/3
The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!
Part A: Answer the following questions about the cost function C(2) and the revenue function R(x).
1. What is the domain and range of C (x)?
2. What is the meaning of the slope and intercept of C(x)?
3. At what production level 2 will the company receive the most revenue?
Part B. Answer the following questions about the profit function P(x).
4. Assuming that the company sells all that it produces, what is the profit function?
5. Why is finding the range of P(x) important?
6. The company can choose to produce either 60 or 70 items. What is their profit for each case, and which level of production should they choose?
7. Can you explain, from our model, why the company makes less profit when producing 10 more units?
Solution :
a).
1. The domain of C(x)
[tex]$x \in [0, \infty)$[/tex]
Range of c(x) is [tex]$[0, \infty)$[/tex]
Since the negative value do not make any sense.
2. C(x) = Ax + b
Intercept here denotes the fixed cost (that is when x = 0)
The slope indicates the marginal cost (that is increase in cost per unit of quantity)
3. Revenue is maximum marginal revenue = 0
(that is when at the top of the parabola)
4. Profit = R(x) -C(x)
5. Range of P(x) is important so that we have the idea in mind about the maximum loss and the maximum profit for a particular quantity.
6 and 7 -- insufficient data.
During peak growing season, the kudzu vine can grow 6 inches in 12 hours. What is the growth
rate of kudzu in inches per hour?
А 0.25 inches
B
0.5 inches
С
2.0 inches
D
6.0 inches
Answer:
b
Step-by-step explanation:
Answer:
The answer is B. 0.5 inches.
Austin and Dale earn money by painting fences over the summer. Working alone, Austin takes 3 hours longer than Dale to paint a fence. Working together, the two of them can paint a fence in 2 hours. How many hours would it take each of them working alone?
Answer:
Austin will take 9 hours to paint a room and dale with take 3 hours to paint a room
Step-by-step explanation:
Suppose C1;C2;C3 are three didifferent biased coins, whose probability of heads equals 0.4, 0.5, and 0.2 respectively. Suppose coins are placed together in a box and you randomly picked a coin from the box. Flip the coin 10 times. Let A denote the event you randomly chose coin C1. Let B denote the event that you got exactly 4 heads out of the 10 coin flips.
Compute the following probabilities:
P(A∩B)
P(B)
P(A|B)
Solution :
[tex]$ P(A \cap B) = P(\text{coin}\ C_1 \text{ chosen and 4 heads in 10 trails})$[/tex]
[tex]$= \frac{1}{3} \times ^{10}C_4 \times 0.4^4 \times 0.6^6$[/tex]
= 0.0836
P(B)= P(coin [tex]$C_1$[/tex] chosen and 4 heads in 10 trails) + P(coin [tex]$C_2$[/tex] chosen and 4 heads in 10 trail) + P(coin [tex]$C_3$[/tex] chosen and 4 heads in 10 trail)
[tex]$=\frac{1}{3}\times ^{10}C_4 \times 0.4^4 \times 0.6^6 + \frac{1}{3}\times ^{10}C_4 \times 0.5^4 \times 0.5^6 + \frac{1}{3}\times ^{10}C_4 \times 0.2^4 \times 0.8^6$[/tex]
[tex]$=0.0836+0.0684+0.0294$[/tex]
[tex]$=0.1813$[/tex]
P(A|B) = [tex]$\frac{P(A \cap B)}{P(B)}$[/tex]
[tex]$=\frac{0.0836}{0.1813}$[/tex]
[tex]$=0.4611$[/tex]
d Problems
The enrolment of our school is 800. If 35 % are girls
a. What fraction are girls?
b. What fraction are boys?
Answer:
Step-by-step explanation:
g=800(0.35)=280
a. 280/800=7/25
b. 520/800=13/20
A cone has a radius of 3 units and a height of 4 units.
1. What is this volume of this cone?
2. Another cone has quadruple the radius, and the same height. How many times larger is the new cone’s volume?
Answer:
1. V = 37.7
2. V =603.19
Step-by-step explanation:
1. V = (3.14)×3^2 4/3
V =37.7
2. V=(3.14)×(3×4)^2 4/3
V = (3.14)×12^2 4/3
V = 603.19
2. In the figure, is an exterior angle to triangle .
(a) What is the angle measurement of Angle 3. Explain the angle relationship you used.
(b) What is the angle measurement of Angle 4. Explain the angle relationship you used.
(c) What is angle relationship between angles 3 & 4? What is the angle relationship between angles 1, 2, & 3? What do you notice that is similar between the two? What is different?
(d) The combination of which two angles in the triangle equal angle 4? Use your work from Part C to figure out why this is the case, and explain your conclusion.
Answer:
PLZ JUST SHOW YOUR WORK ON A PICE OF PAPER AND PLZ LABLE THEM A, B, C, D IF YOU DO U WILL BR MARKED BRAINLY'S.
Answer:a
Step-by-step explanation:
⇒ d + e + f = b + a + a + c + b + c
⇒ d +e + f = 2a + 2b + 2c
= 2(a + b + c)
But, according to triangle angle sum theorem,
a + b + c = 180 degrees
Therefore, ⇒ d +e + f = 2(180°)
= 360°
Answer:
I only know a and b so don't hate me...
Step-by-step explanation:
Part A)
Angle 3 is 103° because 77° + ∠3= 180° and ∠3 = 180° - 77° = 103°
Part B)
Angle 4 is 77° because ∠3 + ∠4 = 180° and ∠4 = 180° - 103° = 77°
find the value of 2xy+3yz-xyz, when x=2, y=-2, z=4
Step-by-step explanation:
[tex]x = 2[/tex]
[tex]y = - 2[/tex]
[tex]z = 4[/tex]
[tex] \: [/tex]
[tex] = 2xy + 3yz - xyz[/tex]
[tex] = y.(2x + 3z - xz)[/tex]
[tex] = y.(2x + z.(3 - x))[/tex]
[tex] = - 2.(2.2 + 4.(3 - 2))[/tex]
[tex] = - 2.(4 + 4.1)[/tex]
[tex] = - 2.(4 + 4)[/tex]
[tex] = - 2.8[/tex]
[tex] = - 16[/tex]
simplify 7/341 and give step by step explanation! I will mark you a brainliest.
Answer:
it can't be simplified
Step-by-step explanation:
Ulani is constructing a triangle that has sides measuring 12 cm and 28 cm. Which measurements could be the length of the third side? Select two options.
15 cm
24 cm
38 cm
41 cm
53 cm
Answer:
B and C
Step-by-step explanation:
Consider the game of rock-paper-scissors to be an experiment. In the long run, roommate A chooses rock 21% of the time, and roommate B chooses rock 61% of the time; roommate A selects paper 39% of the time, and roommate B selects paper 21% of the time; roommate A chooses scissors 40% of the time, and roommate B chooses scissors 18% of the time. (These choices are made randomly and independently of each other.) The probabilities were assigned using the . Define event A as the event that roommate A wins the game and thus does not have to wash the dishes.
Answer:
0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.
Step-by-step explanation:
Independent events:
If two events are independent, the probability of both happening is the multiplication of their probabilities.
Rock-paper-scissors rules:
A player that choose rocks beats one who chooses scissors.
A player that choose paper beats one who chooses rocks.
A player that choose scissors beats one who chooses paper.
Probability that roommate A wins the game and thus does not have to wash the dishes.
3 possible events:
Roommate A - Rocks(21% of the time) and Roommate B - Scissors(18% of the time)
So
[tex]p_R = 0.21*0.18 = 0.0378[/tex]
Roommate A - Paper(39% of the time) and Roommate B - Rocks(61% of the time).
So
[tex]p_P = 0.39*0.61 = 0.2379[/tex]
Roommate A - Scissors(40% of the time) and Roommate B - Paper(21% of the time).
So
[tex]p_S = 0.4*0.21 = 0.084[/tex]
Probability of roommate A winning:
[tex]p = p_R + p_P + p_S = 0.0378 + 0.2379 + 0.084 = 0.3597[/tex]
0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.
what is 48 *3/8 explain
Answer:
18
Step-by-step explanation:
=(
48
1
)(
3
8
)
=
(48)(3)
(1)(8)
=
144
8
=18
please help me , i need this like right noww pleaseeeeeeee !!!!!!!!
Answer: -9
Step-by-step explanation:
KH = x -1 and Eh =2x-12
2x-12 =10-1=9
Which of the following expressions represent a value greater than 4/5 ? A: 4/5 x 3/3. B: 4/5 x 1/2. C: 4/5 x 5/4 D: 4/5 x 4/5
Answer:
C = 1.
Step-by-step explanation:
A: 4/5 x 3/3 (1) = 4/5, Incase you didn't know, 3/3 means 1 whole because it is full. We can tell by just looking that this doesn't represent a value greater than 4/5, In fact, it's equal to 4/5.
B: 4/5 x 1/2 = 2/5 <--- By not using any calculator or math, we already know that 4/5 is greater than 2/5 and that 2/5 is less than 4/5. This is not the correct answer because it's less than 4/5.
C: 4/5 x 5/4 = 1. This could be a correct answer choice because one is greater than 4/5. If your confused, think of it like this, 5/5 is equal to one and then there's 4/5. Then you compare and contrast and see that 5/5 is greater than 4/5 so this is a correct answer choice.
D: 4/5 x 4/5 is equal to 16/25. In my opinion, I wouldn't choose this answer choice because though the numbers are bigger than 4/5, 4/5 IS equal to 16/25, so it wouldn't really be a correct answer choice.
Hope this helped!
The distance from Amy's house to Lake Ontario is 150 miles. On a map, it is 3 inches.
What is the scale used?
Answer:
50
Step-by-step explanation:
150 divided by 3 = 50