The displacement is 18.03 steps, and the direction is 47.25°
How to get the displacement?
We know that displacement is the difference between the final position and the initial position.
We assume the initial position (0, 0). Let's define the positive x-axis as the east and the positive y-axis as the north.
First, the student moves 8 steps east, so she is at:
(0 + 8, 0)
Then she moves 6 steps northeast, so the new position is:
(6*cos(45°) + 8, 6*cos(45°))
Finally, she moves 9 steps due north, so we have:
(6*cos(45°) + 8, 6*cos(45°) + 9)
Then the final position is:
(12.24, 13.24)
So the displacement is:
D = (12.24, 13.24) - (0, 0) = (12.24, 13.24)
The magnitude of the displacement is:
[tex]|D| = \sqrt{12.24^2 + 13.24^2} = 18.03[/tex]
So the magnitude is 18.03 steps.
And the direction is given by the arctangent of the quotient between the y-component and the x-component:
[tex]\theta = Arctg(13.24/12.24) = 47.25 \°[/tex]
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A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the
students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter
of his or her name, answer each of the following questions.
What is P(A), the probability that the first student is a girl?
What is P(B), the probability that the second student is a girl?
What is P(A and B), the probability that the first student is a girl and the second student is a girl?
Answer:
what is P(A), the probability that the first student is a boy? 3/5
what is P(B), the probability that the second student is a girl? 3/4
what is P(A and B), the probability that the first student is a boy and the second student is a girl? 1/2
No, évents A and B are not independent events
Step-by-step explanation:
The probability that the first student is a girl P(A)= 3/4.
The probability that the second student is a girl P(B)= 3/4.
The probability that the first student is a girl and the second student is a girl P(A and B)=9/16.
Given that there are three girls (Sandra, Marta, Jane) and one boy (Franklin), and the sample space of possible outcomes is:
{SA, SM, SJ, SF, MA, MS, MJ, MF, JA, JS, JM, JF, FA, FS, FM, FJ}
P(A): Probability that the first student is a girl (Sandra, Marta, or Jane).
Number of favorable outcomes where the first student is a girl: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(A) = Number of favorable outcomes / Total outcomes = 3 / 4
P(B):
Probability that the second student is a girl (Sandra, Marta, or Jane).
Number of favorable outcomes where the second student is a girl: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(B) = Number of favorable outcomes / Total outcomes = 3 / 4
P(A and B):
Probability that the first student is a girl and the second student is a girl.
Number of favorable outcomes where both students are girls: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(A and B) = P(A).P(B)
= 3/4 × 3/4
=9/16
Hence, P(A)=3/4
P(B)=3/4
P(A and B)=9/16
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help geometry ………ignore this i need 20 words
Answer:
The answer is 1
Step-by-step explanation:
What is the volume of a rectangular sandbox that is 3 feet by 4 feet by 1 foot?
13 ft 3
8 ft 3
12 ft 3
7 ft 3
Answer:
Volume = 12 ft^3
Step-by-step explanation:
Vol = length×width×height
= 3×4×1
= 12
The volume is 12 cubic feet.
The paddock in judy's ranch is 60 feet long and 20 feet wide. he also built a square corral adjacent to the paddock. if the side of the corral measures 16 feet, determine the total area of the paddock and corral.
Answer:
1456ft²
Step-by-step explanation:
A = lw
A = 60(20)
A = 1200ft²
A = 16(16)
A = 256ft²
1200 + 256 =
1456ft²
Find the area of a triangle whose sides are 35 cm, 45 cm and 50 cm.
Answer:To find out the Area of a scalene triangle whose three sides are given, first find out the half perimeter
s = (a+b+c)/2
where a, b, and c are the length of the three sides of a triangle
s = (35 + 45 + 50) / 2
= 130 / 2
= 65 cm
Area of scalene triangle is given by
A = sqrt (s (s - a) (s - b) (s - c))
= sqrt (65 * (65 - 35) ( 65 - 45) (65 - 50))
= sqrt (65 * 30 * 20 * 15)
= sqrt (585000)
= 764.853 sq cm
Step-by-step explanation:
#8 HELP IM STUCK ON THIS
Answer:
12 ft
Step-by-step explanation:
for the model is 1 and the actual is 5
conversion yards to feet
3 feet = 1 yard
20 * 3 = 60
60/5 = 12
your answers 12 ft
hope this helps:)
What is the factorization of the expression below?
x2-14x + 49
Answer:
The value of x = 7
Step-by-step explanation:
x²-14x + 49
=> x² - 7x - 7x + 49
=> x ( x - 7) - 7 ( x - 7 )
=> (x - 7) (x - 7)
=> x = 7
Help me i am on iready math
Answer:
14
Step-by-step explanation:
Because your total is 182 desserts and you want to arrange them into 13 rows you will divide the two numbers. So, 182/13 is 14. so 14 is your answer.
Hope that helped
Answer:
14 Tropical cupcakes per row
Hope this helped :)
Step-by-step explanation:
182 ÷ 13 = 14
Check:
14 × 13 = 182 ✓
Simplify this question
Step-by-step explanation:
9x²/3x + 12x/3x + 1
= 3x/1 + 4/1 + 1
= 3x + 5
I hope this is true..
The measurement of an angle is 40°, and the length of a line segment is 8 centimeters.
Answer:
I'm assuming it's a triangle of some sort. I'll assume it's a right triangle. All the angles and sides are there. I would need 2 angles and 1 side or 2 sides and 1 angle to get a specific triangle.
Step-by-step explanation:
sin(-17pi/6)
How do I solve this
Answer:
if you have a graphing calculator you can just plug the whole equasion in. the anser I got was -0.1547307191
Step-by-step explanation:
to get pie you have to hit second and then ^
How do you add these two consecutive triangular numbers?
TR(4)+TR(3)
The n-th trianglar number is given by
[tex]T_n = \dfrac{n(n+1)}2[/tex]
Then
[tex]T_4 + T_3 = \dfrac{4\times5}2 + \dfrac{3\times4}2 = \boxed{16}[/tex]
Alternatively, the triangular numbers are defined recursively by
[tex]\begin{cases}T_1 = 1 \\ T_n = T_{n-1} + n & \text{for } n>1\end{cases}[/tex]
This means
[tex]T_1=1[/tex]
[tex]T_2 = T_1 + 2 = 3[/tex]
[tex]T_3 = T_2 + 3 = 6[/tex]
[tex]T_4 = T_3 + 4 = 10[/tex]
so that
[tex]T_3+T_4=\boxed{16}[/tex]
i need some help with this
Answer:
x + y = 4
substitute (-A, 2B) in the equation.
-A + 2B = 4
substitute (3A-2, 3-B) in the equation
3A-2 + 3-B = 4
Use elimination method and hence multiply the first substituted equation by 3
-3A + 6B = 12
3A-2 + 3-B = 4
-2 + 3 + 5B = 16
5B = 15
B = 3
Substitute value of B in any of the equations
and hence A = 2
1. You and your friends receive a lunch bill for $22.50 before tax is included. The sales tax in your state
is 8%. What is the total cost when the tax is included?
Answer:
$24.30
Step-by-step explanation:
8% of 22.50 = $1.8
$22.50 + $1.8 = $24.30
Give brainliest, please!
Hope this helps :)
Can someone solve this please
Answer:
4x + 5x = 180
9x = 180
x = 180/9
x = 180 ÷ 9
x = 20
Construct a 90% confidence interval for the population mean, . assume the population has a normal distribution. a sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78
Answer:
[tex]CI=\{2.5053,3.2147\}[/tex]
Step-by-step explanation:
Assuming the conditions for constructing a t-confidence interval are true, we use the formula [tex]\displaystyle CI=\bar{x}\pm t^*\biggr(\frac{s}{\sqrt{n}}\biggr)[/tex] where our sample mean is [tex]\bar{x}=2.86[/tex], our sample standard deviation is [tex]s=0.78[/tex], our sample size is [tex]n=15[/tex], and a 90% confidence level is equivalent to a critical value of [tex]t^*=1.7613[/tex],
[tex]\displaystyle CI=\bar{x}\pm z^*\biggr(\frac{s}{\sqrt{n}}\biggr)\\\\CI=2.86\pm 1.761\biggr(\frac{0.78}{\sqrt{15}}\biggr)\\\\CI=2.86\pm0.3547\\\\CI=\{2.5053,3.2147\}[/tex]
Hence, we are 90% confident that the true population mean of a student's grade point average is between 2.5053 and 3.2147
John is weighing his jars of coins. his jar of pennies weighs 84.96 ounces, and his jar of nickels weighs 3.11 kilograms. there are 0.0283495 kilograms per ounce. which jar weighs more, and how many more pounds does it weigh? a. the jar of pennies weighs 8.41 pounds more than the jar of nickels. b. the jar of pennies weighs 0.089 pounds more than the jar of nickels. c. the jar of nickels weighs 2.06 pounds more than the jar of pennies. d. the jar of nickels weighs 1.55 pounds more than the jar of pennies.
The jar of nickels weighs 1.55 pounds more than the jar of pennies. The correct option is d
Calculating weightFrom the question, we are to determine the jar that weighs more
From the given information
His jar of pennies weighs 84.96 ounces
and his jar of nickels weighs 3.11 kilograms
First, we will 84.96 ounces to kilogram
From the given conversion,
There are 0.0283495 kilograms per ounce
That is, 0.0283495 kg = 1 ounce
If 1 ounce = 0.0283495 kg
Then,
84.96 ounces = 84.96 × 0.0283495 kg
∴ 84.96 ounces = 2.4086 kg
His jar of pennies weighs 2.4086 kg
Since the John's jar of nickels weighs 3.11 kg, his jar of nickels weigh more.
3.11 kg - 2.4086 kg = 0.7014 kg
Convert 0.7014 kg to pounds
1kg = 2.20462 pounds
∴ 0.7014 kg = 0.7014 × 2.20462 pounds
0.7014kg ≅ 1.55 pounds
Hence, the jar of nickels weighs 1.55 pounds more than the jar of pennies. The correct option is d.
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− 4 + 1 2 x = 8 is it true
Answer:
12 -4x = 8
So "Yes" it is true
Solve the following:
4x3 = 2x + 7
Answer:
If you meant 4x to the third power, than x = 1.34
Identify the terms, coefficients, and constants in the expression 20x+13.
Answer: coeficient is 20 and the constant which is 13
Step-by-step explanation:
Find the distance between y=7 and y=-1
Answer:
Er I think it’s 8 but not sure
Step-by-step explanation:
What is the quotient? startfraction 2 y squared minus 6 y minus 20 over 4 y 12 endfraction divided by startfraction y squared 5 y 6 over 3 y squared 18 y 27 endfraction startfraction 2 over 3 (y minus 5) endfraction startfraction 3 (y minus 5) over 2 endfraction startfraction (y minus 5) (y 2) squared over 6 (y 3) squared endfraction startfraction 3 (y 5) (y minus 2) over 2 (y 2) endfraction
The quotient of two fractions, (2y² - 6y - 20)/(4y + 12) and (y² + 5y + 6)/(3y² + 18y + 27), is: 3(y - 5)/2
What is a Quotient?Quotient can be described as the result you get from dividing a term by another term.
Let's find the quotient of (2y² - 6y - 20)/(4y + 12) and (y² + 5y + 6)/(3y² + 18y + 27)
Quotient = (2y² - 6y - 20)/(4y + 12) ÷ (y² + 5y + 6)/(3y² + 18y + 27)
Change the division sign to multiplication sign and turn the second fraction upside down
(2y² - 6y - 20)/(4y + 12) × (3y² + 18y + 27)/(y² + 5y + 6)
Bringing out the common terms, we would have:
2(y² - 3y - 10)/4(y + 3) × 3(y² + 6y + 9)/(y² + 5y + 6)
Factorize
2(y - 5)(y + 2)/4(y + 3) × 3(y + 3)(y + 3)/(y + 3)(y + 2)
Cancel out common factors
= 3(y - 5)/2
Quotient = 3(y - 5)/2
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Answer:b
Step-by-step explanation:
lol
I need help what is (4÷5×x) what I x
Answer:
0.8x
Step-by-step explanation:
According to BODMAS,
Step 1 :
4 ÷ 5
= 4 / 5
= 0.8
Step 2 : Multiply x.
0.8 * x = 0.8x
Answer:
Step one
4 ÷ 5
= 4/5
= 0.8
Step two = 0.8 * x
= 0.8x
its wrong someone help me with it
Answer:
the answer is π^8
Step-by-step explanation:
the math program has got some bugs in it. See your teacher and tell him or her about it
the points at which a quadratic equation intersects the x-axis
The points at which a quadratic equation intersects the x-axis are referred to as x intercepts or zeros or roots of quadratic equation
Given :
The points at which a quadratic equation intersects the x-axis
The points at which the any quadratic equation crosses or touches the x axis are called as x intercepts.
At x intercepts the value of y is 0.
So , the points at which a quadratic equation intersects the x-axis is also called as zeros or roots of the quadratic equation .
The points at which a quadratic equation intersects the x-axis are referred to as x intercepts or zeros or roots of quadratic equation
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The volume of this cylinder is 1,481,276.16 cubic inches. What is the radius? (will mark brainliest)
Answer:
radius = 72.00 in (nearest hundredth)
Step-by-step explanation:
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
Volume = 1,481,276.16 in³Height = 91 inπ ≈ 3.14Substituting the given values into the formula and solving for r:
[tex]\implies \sf 1481276.16=3.14 \cdot r^2 \cdot 91[/tex]
[tex]\implies \sf 1481276.16=285.74r^2[/tex]
[tex]\implies \sf r^2=\dfrac{1481276.16}{285.74}[/tex]
[tex]\implies \sf r^2=5184[/tex]
[tex]\implies \sf r=\sqrt{5184}[/tex]
[tex]\implies \sf r=72\:in[/tex]
Answer: radius : 72.00 inch
The following is a cylinder.
Volume of Cylinder: πr²h
Given following:
volume: 1,481,276.16height: 91 inchπ ≈ 3.14radius: rSolve for radius:
[tex]\rightarrow \sf \pi r^2h =V[/tex]
[tex]\rightarrow \sf (3.14) r^2(91) =1,481,276.16[/tex]
[tex]\rightarrow \sf r^2 =\dfrac{1,481,276.16 }{91(3.14)}[/tex]
[tex]\rightarrow \sf r^2 =5184[/tex]
[tex]\rightarrow \sf r=\sqrt{5184}[/tex]
[tex]\rightarrow \sf r=72[/tex]
John bought 4 pounds of hot dogs for his party.
How many ounces of hot dogs did John buy?
Answer:
64 Ounces
Step-by-step explanation:
64 Ounces of hot dogs
Answer:
64 oz
Step-by-step explanation:
1 lb = 16 oz
4 × 1 lb = 4 × 16 oz = 64 oz
evaluate the following expression. you should do this problem without a calculator e^In3
The relation between the exponential and the logarithm is used. Then the expression [tex]e^{\ln3}[/tex] is given as 3.
What is a logarithm?Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.
The expression is given below.
[tex]\rightarrow e^{\ln3}[/tex]
We know the formula
[tex]\rm e^{\ln x} = x[/tex]
Then the expression can be written as
[tex]e^{\ln3} = 3[/tex]
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Calculate the value of p in the diagram below
Answer:
40.5
Step-by-step explanation:
(n-2)*180
(7-2)*180=5*180=900
10p+135+149+121+90=900
10p=-495+900=405
p=40.5
Bob bikes to work 8 miles each day. The trip takes him 0.5 hours. If Bob bikes at a constant rate, what is his biking speed? A. 5 mph B. 8 mph C. 16 mph D. 40 mph
Given the distance covered and the time elapsed, if the bike is at a constant rate, the speed of Bob's bikes is 16 mph.
Option C) is the correct answer.
What is Speed?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Distance covered d = 8milesTime elapsed t = 0.5hrsSpeed of the bike S = ?Speed = Distance ÷ time
Speed = 8miles / 0.5hrs
Speed = 16 mph
Therefore, Given the distance covered and the time elapsed, if the bike is at a constant rate, the speed of Bob's bikes is 16 mph.
Option C) is the correct answer.
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