Running Bear ended up 29.204 miles from the village.
Running Bear left the village and traveled 30 miles in a direction of 30°. Then he went 50 miles in a direction of 220°. To find out how far he ended up from the village, we need to add up the distances he traveled in both directions.
Think of it like putting two arrows end to end on a piece of paper. The first arrow represents the 30 miles he traveled at 30°, and the second arrow represents the 50 miles he traveled at 220°. The total distance from the village to the final point is equal to the length of the combined arrow.
We can represent the two displacements as vectors in a rectangular coordinate system, with the x-axis as the East-West direction and the y-axis as the North-South direction.
The first displacement, 30 miles at 30°, can be written as a vector in the x and y directions using trigonometry:
x1 = 30 cos 30° = 15
y1 = 30 sin 30° = 15
The second displacement, 50 miles at 220°, can be written as a vector in the x and y directions using trigonometry:
x2 = 50 cos 220° = -25
y2 = 50 sin 220° = -43.301
The total displacement from the village to the final point is found by adding the components of the two vectors:
x = x1 + x2 = 15 - 25 = -10
y = y1 + y2 = 15 - 43.301 = -28.301
Finally, we can use the Pythagorean theorem to find the magnitude (distance) of the total displacement:
d = √(-10)^2 + (-28.301)^2 = √851.121 = 29.204 miles
So, Running Bear ended up 29.204 miles from the village.
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in each of the following scenarios, state what type of distribution should be used to model the response y: binomial, multinomial, poisson, or normal.
The total number of respondents and x would be the total number of respondents who rate the product a 5.
A survey asking respondents to rate a product on a scale of 1 to 5
In this scenario, a binomial distribution should be used to model the response y. A binomial distribution is a discrete probability distribution that is used to model the probability of a certain number of successes in a given number of trials. The formula for a binomial distribution is P(x) = nCx * p^x * (1-p)^(n-x) where n is the number of trials, x is the number of successes, and p is the probability of success in a single trial. In this case, n would be the total number of respondents and x would be the total number of respondents who rate the product a 5.
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find the horizontal and vertical asymptotes of the curve. y = 3 + x4 x2 − x4
The horizontal asymptote of the curve y = 3 + x^4 / x^2 - x^4 is y = 1 and the vertical asymptotes are x = +√(x^4) and x = -√(x^4).
How to find the horizontal and vertical asymptotes of the curve?To find the horizontal and vertical asymptotes of the curve y = 3 + x^4 / x^2 - x^4, we need to examine the behavior of the function as x approaches positive and negative infinity.
For the horizontal asymptote, we look at the behavior of the function as x approaches positive and negative infinity. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptotic.
According to question:In this case, the degree of the numerator (x^4) is equal to the degree of the denominator (x^4), and the leading coefficients are both 1. Therefore, the horizontal asymptotic is the ratio of the leading coefficients, which is y = 1.
For the vertical asymptote, we look for any x-values that make the denominator equal to zero, since the function is undefined for these values. In this case, x = +√(x^4) and x = -√(x^4) are the roots of the denominator, so they are the vertical asymptotes.
Therefore, the horizontal asymptote of the curve y = 3 + x^4 / x^2 - x^4 is y = 1 and the vertical asymptotes are x = +√(x^4) and x = -√(x^4).
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Which of the following functions are solutions of the differential equation y′′+2y′+1y=0 ?
A. y(x)=−x
B. y(x)=e^-x
C. y(x)=xe^x
D. y(x)=e^x
E. y(x)=xe^−x
F. y(x)=−e^x
G. y(x)=0
Option (B) and (E) functions are solutions of the differential equation y′′+2y′+1y=0.
What is differential equation?An equation known as a differential equation describes the derivative or derivatives of an unknown function. Because they are equations involving a function and its derivatives (where the variable is a function rather than a number) (the functions obtained by differentiating it). Save this response. Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.
Given that,
y′′+2y′+1y = 0
A.E = m² + 2m + 1 = 0
or, (m + 1)² = 0
or, m = ± 1
y = (c₁ + c₂x)e⁻ˣ
y = c₁e⁻ˣ + c₂xe⁻ˣ
Thus, option (B) and (E) are solutions of the differential equation:
y′′+2y +1y = 0.
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Kendra has been saving her earnings from mowing the neighborhood lawns. She has 80 dollars and wants to spend it all on games.
If each game costs 9 dollars, how many can Kendra buy?
What are the measures of angles AB and C show your work and explain your answers? I really only need the answer to C please :) this is my first post so giving as much as I can to people who answer. PLEASE ANSWER SOON
The measure of angles becomes:
∠a = 30°
∠b = 60°
∠c = 105°
What is triangle?Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
∠a and 30° are vertical angles and vertical angles are equal
∠a = 30°
We have a triangle with a, b and a right angle. Triangles have angles that add to 180°.
∠a + ∠b + 90° = 180°
30° + ∠b + 90° =180°
120° + ∠b = 180
∠b = 180° - 120°
∠b = 60°
Angle c and 70 form a straight line and straight lines are 180 degrees
∠c + 75° = 180°
∠c = 180° - 75°
∠c = 105°
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Arts and Crafts An arts and craft supply store has a large crate that
contains brass, silver, and copper beads. Several friends take turns
pushing their hands into the beads, grabbing one, recording the bead
type, and placing the bead back into the crate. They then repeat the
process. The table shows the count for each bead type. Write a
probability model for choosing a bead.
Dlhrann-
Enter your
The probability of p(copper)=0.28
Probability model for choosing a bead?Probability is a measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. Probability is a fundamental concept in mathematics, statistics, and science that is used to quantify uncertainty and forecast the likelihood of future events based on available data. Probability is a measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
Given
Total Beads =112+96+192=400
Placing the bead back to the crate
so the total beads are always 400
copper:112
p(copper)=112/400=0.28
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Write the equation of the line of best fit using the slope-intercept form of the line ?=??+? , show all your work , including the point used to determine the slope and how the equation was determined.
y = x is the linear regression equation for the given Dot plot.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, a graph of a linear regression that has points (60, 60) and (70, 70) as we can see in the graph.
From the general formula of the linear equation:
Y = mx + b
where m is the slope
b is the y-intercept
Slope m = (y₂ -y₁)/(x₂ - x₁)
In our case,
Slope = (70 - 60)/70 - 60
m = 10/10 = 1
Thus the equation of a line:
y = x + b
Since, the line goes from (60, 60)
60 = 60 + b
b = 0
Thus, the final equation of the line will be y = x
Therefore, the linear regression equation for the given Dot plot is y = x.
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what is 2 times 2 Thank you
Answer:
2 • 2 = 4 because you multiply numbers by adding groups of a number!
Answer:
Step-by-step explanation:
2x2=4
On January 22 in 1943, the town of Spearfish, South Dakota, set the record for the world’s fastest temperature change. At 7:30 a.m., the temperature was -4°F. By 7:32 a.m., the temperature was 45°F. By 9:00 a.m. the same day, the temperature was 54 °F. By 9:27 a.m., the temperature was -4 °F. How many degrees did the temperature change each minute from 9:00 to 9:27?
From 9:00 a.m. to 9:27 a.m., the temperature changed from 54°F to -4°F, a change of 58°F. This change took 27 minutes.
The temperature change per minute was 58°F / 27 minutes = 2.15°F per minute.
Find mqn
Please help me
70 degrees is the measure of MQN from the provided figure.
Solving angles in a line geometry.A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
From the given figure, we are to determine the measure of angle <MQN. Applying the sum of angles on a straight line:
<MQN + 80 +30 = 180
<MQN + 110 = 180
<MQN = 180 - 110
<MQN = 70 degrees
Hence the measure of <MQN from the given figure is 70 degrees.
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When multiplying an equation so that you can cancel one of the variables, be certain to multiply both sidesof the equation. For instance, multiplying the above equation incorrectly would yield
:--1.5x -1.5y = 40, which would give you very incorrect values when you tried to solve for x and y.
Part D Now, add the two equations and find the value of x.
Express your answer to three significant figures.
ANSWER
The two equations would be 1.5x + 2.5y = 30, 3x + 1.5y = 40, when we add both the equations we get, 4.5x + 4y = 70, and the value of x is 10.
How to solve the linear equation in two variables?To solve a system of linear equations in two variables using the substitution in two variables using the substitution method. First solve one of the equations for one variable. Substitute this in the other equation in terms of a single variable. Then solve it for the variable. Now, substitute it in any of the equations to get the value of another variable.
Given:
Add the two equations together:
1.5x + 2.5y = 30
3x + 1.5y = 40
(1.5x + 3x) + (2.5y + 1.5y) = (30 + 40)
4.5x + 4y = 70
Isolate the x-variable by subtracting 4y from both sides of the equation:
4.5x + 4y = 70
4.5x + 4y - 4y = 70 - 4y
4.5x = 70 - 4y
Divide both sides of the equation by 4.5 to solve for x:
4.5x = 70 - 4y
4.5x/ 4.5 = (70 - 4y)/4.5
x = (70 - 4y) / 4.5
Substitute the value of y from the first equation:
1.5x + 2.5y = 30
2.5y = 30 - 1.5x
y = (30 - 1.5x) / 2.5
Substitute the value of y into the equation for x and solve:
x = (70 - 4y) / 4.5
x = (70 - 4((30 - 1.5x) / 2.5)) / 4.5
x = 10
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Geometry 1 find the measure of the angle
Answer:
46
Step-by-step explanation:
draw a line at 96° & make it parallel to bottom line
which will slice 96° into 2 angles
lower half is 180-130=50
top half is 96-50=46
angle 4r equals to top half
In a game, Mateo earned 180 points for collecting stars. He earned 270 points for
lestroying ships. Plus, he earned 5 points for each prisoner he saved. If he finished
he game with 500 points, how many prisoners did he save?
A
50
B 10
C) 15
D 250
ht©Swun Math
6.EE.6
SWUN MATH
6.EE.7
Grade 6 Unit 5 Mid-Unit Assessment VB, Page 1
Answer:
B. 10
Step-by-step explanation:
We can solve this fast by adding the points from the stars and ships together, then subtracting that number from the total 500 points Mateo earnd.
So it would look like this:
180+270=450
500-450=50
So if Mateo scored 50 points from saving prisoners and save is worth 5 points each, we can do 50÷5=10.
100 POINTS!!!
Find the equation of the linear function represented by the table below in slope-intercept form.
x y
1 0
2 5
3 10
4 15
Percy thinks that since the data {5, 0, 4, 0, 0} has a mode of 0, the data has no mode.
Using 3-5 sentences, critique Percy's reasoning.
The reasoning of Percy is incorrect because there is one mode for the data set.
What is Mode?Mode of a data set is the value that occur most frequently in a data set.
There may be no mode, one mode or more than one mode for a data depending on the number of times values are repeating.
Given data is {5, 0, 4, 0, 0}.
Here the value 0 is repeating three times.
No other number has repeated three times.
So there is only one mode for the data set and is 0.
This does not mean that there is no mode for the set.
A data set has no mode if and only if all the numbers in the set are repeated same number of times.
Hence the reasoning of Percy is incorrect.
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Rabbits in a lab are to be kept on a strict daily diet that includes 34 grams of protein, 17 grams of fat, and 47 grams of carbohydrates. The scientist has only three food mixes available with the following grams of nutrients per unit.
Each rabbit needs 4 units of protein, 2 units of fats, and 3 units of carbohydrates for the dietary need.
Given that
Mix A: 6 protein, 4 fat, 2 carbs
Mix B: 4 protein, 2 fat, 6 carbs
Mix C: 5 protein, 2 fat, 8 carbs
Now convert these mixes into quadratic equations
6a + 4b + 5c = 47--------(1)
4a + 2b + 2c = 26--------(2)
2a + 6b + 8c = 44-------(3)
Now divide (2) and )3) equations by 2:
6a + 4b + 5c = 47
2a + b + c = 13------(4)
a + 3b + 4c = 22--(5)
Eliminates A:
Pairs equations #4 and #5
6a + 4b + 5c = 47
2a + b + c = 13
Now multiply -3 for Equation(4) and after add with Equation (1):
6a+4b+5c=47
-6a -3b-2c = 39
------------------------
b + 2c = 8
Pairs equations (4) and (5):
2a + b + c = 13
a + 3b + 4c = 22
multiply -2 for Equation(5) and after add with Equation (4):
2a + b + c = 13
-2a-6b -8c =44
-----------------------
-5b+-7c=-31
multiply everything by -1
5b+7c=31
2 by 2 system from equations above in bold:
b+2c=8
5b+7c=31
solves by substitution: b = 8 - 2c
5(8 - 2c) + 7c = 31
40 - 10c + 7c = 31
40 - 3c = 31
-3c = -9
c = 3
Then b = 8 - 2(3) = 8 - 6
b=2
Simplified second equation: 2a+b+c=13
2a+2+3=13
2a=8
a = 4
Therefore, A=4 B=2 C=3
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the first three terms of a sequence are given. round to the nearest thousandth (if necessary). 156,153,150,...156,153,150,... find the 46th term.find the 46th term.
The first term of the sequence is 156. Then the 46th term of the sequence is 156.
What are sequence and series?
A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after. In mathematics, a series can be generally described as the sum of an infinite sequence of values.
Given
The first three terms of a sequence are shown.
156,153,150 and so on.
The given sequence is repeating every three terms, and the repeating terms are 156, 153, 150.
So, to find the 46th term, we need to determine which set of repeating terms it belongs to.
Dividing 46 by 3 gives us a quotient of 15 with a remainder of 1, meaning the 46th term belongs to the 16th set of repeating terms and will be the first term in that set, which is 156.
So, the 46th term of the sequence is 156.
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The first term of the sequence is 156. Then the 46th term of the sequence is 156.
What are sequence and series?
A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after. In mathematics, a series can be generally described as the sum of an infinite sequence of values.
Given
The first three terms of a sequence are shown.
156,153,150 and so on.
The given sequence is repeating every three terms, and the repeating terms are 156, 153, 150.
So, to find the 46th term, we need to determine which set of repeating terms it belongs to.
Dividing 46 by 3 gives us a quotient of 15 with a remainder of 1, meaning the 46th term belongs to the 16th set of repeating terms and will be the first term in that set, which is 156.
So, the 46th term of the sequence is 156.
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This is the answer on the assignment question I think
Answer: you got it right
Step-by-step explanation:
Refer to the T-account below Work In Process 30,000 (12) Bal. 270,000 90,000 70,000 0,000 Entry (12) could represent which of the following? (9)110,000 Bal A) Direct labor cost incurred in production B) Purchases of raw materials C) The cost of goods manufactured transferred to Finished Goods D) The cost of indirect materials incurred in production
The correct option answer is C , that is Entry 12 represents The cost of goods manufactured transferred to Finished Goods
Given that, the T-account below Work In Process 30,000 (12) Bal. 270,000 90,000 70,000 110,000
We have, Total work in progress (WIP) before Transfer =
30,000 + 90,000 +70,000 + 110,000 = $300,000
And the ending work in progress (WIP) = 30,000
It clearly means that 270,000 (300,000 - 30,000) of goods has been transferred to finished goods inventory.
Therefore, the balance entry represents that the cost of goods manufactured transferred to Finished Goods.
The required question's table of T-account is attached below.
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Find the area if a triangular region whoe bae i 90m long and the correponding altitude i 40m long
The area of the triangular region is 1800 square meters.
The area of a triangular region can be calculated by multiplying its base by its corresponding altitude and dividing by 2.
Given a triangular region with a base of 90 m and a corresponding altitude of 40 m, the area of the region can be calculated as follows:
Area = (Base * Height) / 2
Area = (90 * 40) / 2
Area = 3600 / 2
Area = 1800 square meters
Therefore, the area of the triangular region is 1800 square meters.
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The area of the triangular region is 1800 square meters.
The area of a triangular region can be calculated by multiplying its base by its corresponding altitude and dividing by 2.
Given a triangular region with a base of 90 m and a corresponding altitude of 40 m, the area of the region can be calculated as follows:
Area = (Base * Height) / 2
Area = (90 * 40) / 2
Area = 3600 / 2
Area = 1800 square meters
Therefore, the area of the triangular region is 1800 square meters.
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For Halloween you bought a bag of 500 pieces of mixed candy. After just one hour you see that you only have 350 pieces left for the rest of the evening. What is the percentage change in candy after that first hour?a. -25%b. -35%c. -15%d. -30%
She has 480 pieces of candy left after Halloween (option a ) -25% percentage
to solve this problem we have to analyze the information given:
Candy available: six 100-piece bags
Number of children: 20
Pieces of candy for each child: 6
So, we have to calculate the total amount of candy available by multiplying the pieces of candy that each bag has (100) by the number of bags(6)
100 x 6 = 600
Then, we have to multiply the number of children (20) by the number of pieces of candy that each one receives (6) and then subtract that number to the number of pieces of candy available.
20x 6 = 120
600 -120 = 480
She has 480 pieces of candy left after Halloween (option a ) or -25 percentage
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Molly is building a model roller
coaster as part of a school project.
She chose the Millennium Force in
Cedar Point, which is 94 meterstall,
to model. If Molly uses a scale of
1 centimeter - 4 meters, what will
be the height of the model?
Your answer
The height of the model is 2350 cm or 23.5 m.
The concept used in this calculation is scale modeling. In scale modeling, the size of an object is reduced or increased proportionally to match a specified scale.
The height of the roller coaster is being reduced using a specific scale ratio of 1 centimeter to 4 meters. This allows Molly to build a model that represents the real-life roller coaster, but at a smaller size.
The height of the Millennium Force in meters is 94 meters. If Molly uses a scale of 1 centimeter to 4 meters, then 1 meter will be equal to 100/4 = 25 centimeters.
So, the height of the model will be 94 x 25 = 2350 centimeters.
Thus, the height of the model is 2350 cm or 23.5 m.
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The Millennium Force in Cedar Point, which is 94 meters tall. The height of the model will be 94 meters / 4 meters per centimeter = 23.5 centimeters.
Molly is building a model roller coaster that is based on the Millennium Force in Cedar Point, which is 94 meters tall. To create a model of the roller coaster, she is using a scale of 1 centimeter to 4 meters. This means that for every 1 centimeter on the model, it represents 4 meters in the actual height of the roller coaster.
To find the height of the model, we need to divide the actual height of the roller coaster by the ratio of meters per centimeter. That is:
Height of the model = 94 meters / (1 centimeter / 4 meters)
Height of the model = 94 meters * 4 meters / 1 centimeter
Height of the model = 376 meters / 1 centimeter
Height of the model = 376 centimeters
So, the height of the model is 376 centimeters.
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May you Please help me
The given coordinates make a right angled triangle.
What is scaling? How is it done?Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.
If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. Similarly, if the initial coordinates are (x, y) then after scaling the coordinates would be {Kx, Ky}.
Scale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities. In case of length scaling, we can write -
{K} = L{final}/L{initial}
Given are the coordinates of the triangle as -
P(-1, 3)
Q(9, - 1)
R(-3, - 2)
The distance formula is given as -
d² = (x₂ - x₁)² + (y₂ - y₁)²
PQ = 2√29
QR = √145
RP = √29
QR² = RP² + PQ²
145 = 29 x 4 + 29
145 = 145
Therefore, the given coordinates make a right angled triangle.
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A university student completed courses worth 3 credits and some courses worth 4
credits. The student earned a total of 54 credits after completing 15 courses. How
many courses worth 4 credits did the student complete?
Convert and round off to 3 decimal places a.1 235 m to km b.0,032 m to mm c.635 g to kg d.0,775 l to ml e.3,25kl to l f. 24,5 km to m g.63,8 ml to l h.2,3 tons to kg i.32 450 500 mg to kg j.7 623 cm to m
(−5/6x−7/12)−(−1/3x−1/4) . the slashes are fractions PLS ANSWER FAST
Answer:
That's what I got, not sure but I tried so I hope it helps.
Does someone mind helping me with this problem? Thank you!
Answer: the answer is 180 km.
Step-by-step explanation:
Answer:
180 km
Step-by-step explanation:
1 cm to 20 km
9cm=20 times 9
180 kilometers
what’s the square root of 50, 147,96 and -8 square root 16
The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.
How do you calculate the square root?The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value. It follows that a a = b if "a" is the square root of "b."
The square root of 50 is 7.07106781187.
The square root of 147 is 12.124355653
The square root of 96 is 9.79795897113
The square root of -8 is 2.82842712475i
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Parallelogram ABCD is plotted on a coordinate plane. The coordinates of point A are (-3, 5). Point B is at (1, 2), and point C is at (2, -4). What are the coordinates of the fourth vertex D
The coordinates of vertex D are (-3 + 1, 5 - 6) = (-2, -1).
What is parallelogram?
A parallelogram is a quadrilateral that has its opposite sides parallel and equal to each other. It has its interior opposite angles equal. Also, the angles on the same side of the transversal sum up to 180 degrees or are supplementary to each other.
To find the fourth vertex of a parallelogram given the coordinates of three vertices, we can use the property that opposite sides of a parallelogram are parallel and equal in length.
If we subtract the vector AB from the vector AC, we obtain the vector AD, which gives us the coordinates of the fourth vertex D.
AB = (1 - (-3), 2 - 5) = (4, -3)
AC = (2 - (-3), -4 - 5) = (5, -9)
AD = AC - AB = (5 - 4, -9 + 3) = (1, -6)
Therefore, the coordinates of vertex D are (-3 + 1, 5 - 6) = (-2, -1).
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Susie's mom is keeping track of how many pieces of candy Susie and her four brothers are eating. The information is graphed below. At what rate is the amount of candy changing? A. -75 pieces of candy per day B. 90 pieces of candy per day C. -90 pieces of candy per day D. 75 pieces of candy per day
The rate of change for a graph passing through (0, 0) and (2, -180) is -90 pieces of candy per day
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on
The slope intercept form of a linear equation is:
y = mx + b
where m is the rate of change and b is the y intercept
Let y represent the total pieces of candy remaining after x days. Let us assume that the graph passes through (0, 0) and (2, -180). Hence:
[tex]Slope(rate\ of\ change) = \frac{y_2-y_1}{x_2-x_1}\\ \\substituting:\\\\slope=\frac{-180-0}{2-0} =-90[/tex]
The rate of change is -90 pieces of candy per day
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