The angle formed between this vector and the positive x-axis measures around 61.26° and goes in a counterclockwise direction.
How to solveFirst, we calculate the components:
u = (80cos(30°), 80sin(30°)) ≈ (69.28, 40.00)
v = (60cos(60°), 60sin(60°)) ≈ (30.00, 51.96)
w = (50cos(120°), 50sin(120°)) ≈ (-25.00, 43.30)
Now, let's find the resultant vector (u+v+w):
u+v+w = (69.28 + 30.00 - 25.00, 40.00 + 51.96 + 43.30) ≈ (74.28, 135.26)
The magnitude of the resultant vector ||u+v+w|| can be found using the Pythagorean theorem:
||u+v+w|| = √(74.28² + 135.26²) ≈ 152.44
To find the direction, we calculate the angle θ:
θ = atan2(135.26, 74.28) ≈ 61.26°
The total size of the composite vector, obtained by adding u, v, and w, amounts to a value close to 152.44.
The angle formed between this vector and the positive x-axis measures around 61.26° and goes in a counterclockwise direction.
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The three vectors are in two-dimensional space and have the following components:
u = (80cos(30°), 80sin(30°))
v = (60cos(60°), 60sin(60°))
w = (50cos(120°), 50sin(120°))
What are the magnitude and direction is u+v+w? ||v|= 60 ||w||=50 ||u||= 80
I AM GIVING ALOT OF POINTS BECAUSE I NEED THIS RIGHT NOW I HAVE ONE MINUTE LEFT
Town A is 7 feet below sea level and Town B is 692 feet above sea level. What is the difference in elevation between Town A and Town B?
A. 685 feet
B. 692 feet
C. 695 feet
D. 699 feet
Answer:
D)699
Step-by-step explanation:
Since Town A is 7 feet below sea level, you will need to add that to 692 instead of subtract.
692+7=699
Answer: D
Step-by-step explanation: 692+7=699
Pls help me with this question
The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.
When two lines intersect, then their opposite angles are equal. Then the equation is given as,
m° + 66° + m° = 120°
Simplify the equation for m, then the value of 'm' is calculated as,
m° + 66° + m° = 120°
2m° = 120° - 66°
2m° = 54°
m° = 27°
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Complete the 2 column proof. mark all necessary immigration on the figure
ΔBCD and ΔDAB are congreuent by SAS.
We have,
Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included the angle of another triangle.
Now,
CB = AD (given)
CB || AD ( given )
∠CBD ≅ ∠ADB (alternate angles)
BD = BD ( Common )
ΔBCD ≅ ΔDAB ( By SAS )
Thus,
ΔBCD and ΔDAB are congreuent by SAS.
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Pls help me its due tommrow
PLSSS GUYSS I BEG U GUYS IM STRESSING ABOUT THIS PLSS HELPPPP
Answer:
Step-by-step explanation:
Volume of a pentagonal prism = 1/4√(5(5 + 2√5))·a²h
a = length of a base edge
h = height
Realistic dimensions would be 8" base edge and 11" height for a decent size birdhouse.
V = 1/4√((5(5+2√5))·(8)²(11) = 1211.22 in³
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Solve: 9x In x + x = 0
(Use calculator for x and round the answer to 3 decimal places)
Next
Don
The value of x in the equation 9x In x + x = 0 is x = 0.895
Calculating the value of x in the equationFrom the question, we have the following parameters that can be used in our computation:
9x In x + x = 0
To calculate the value of x, we start by dividing through the equation by x
So, we have the following representation
9 In x + 1 = 0
Subtract 1 from both sides of the equation
This gives
9 ln x = -1
Divide both sides by 9
ln x = -1/9
So, we have
x = e^(-1/9)
Evaluate the exponent
x = 0.895
Hence, the solution to the equation is x = 0.895
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Jake plays basketball. He kept track of the number of free throws he made per game. On your own paper, make a histogram or dot plot of Jake's data and then use that to describe the shape of the data.
9, 8, 15, 17, 18, 19, 10, 18, 17, 18, 18, 11, 12, 15, 16, 17, 17, 18, 17
Analysis of Jake's free-throw data shows that it is positively skewed, indicating that he most frequently scores around 17-18 points per game, with fewer games with lower scores.
Explanation:To visualize and understand Jake's free-throw data, we can create a histogram. First, we'll list the range of shots made per game. These are: 8, 9, 10, 11, 12, 15, 16, 17, 18, and 19. Then, for each number, count how many times it occurs in the data set. The distribution could look something like this:
8: •9: •10: •11: •12: •15: ••16: •17: •••••18: ••••19: •Based on this distribution, the shape of the data is positively skewed, with most of the data clustered around 17-18 points per game, and fewer games with lower scores.
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2.5.2 Test (CST): Transformations, Congruence, and Similarity, Part 1
Question 8 of 15
Which triangle makes this statement true?
ΔΑΒC =
B
16
90
T
34
AABC
28
The triangle that makes the statement true is Option A. ΔABC ≅ ΔRST
How is this so?For two triangle to be similar, they must have share the same angle size and sides that are related with a common ratio.
All the angles in Option A Δ RST are similar to those ΔABC.
Also note that
ST = 1/2 AB
SR = 1/2 BC and
RT = 1/2 AC
hence, the correct statement is:
ΔABC ≅ ΔRST
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Full Question:
See attached image.
4
A gasoline pump delivers 4 gallons of
gas per minute. How many minutes will
it take to fill a gas tank that holds
16 gallons?
2
min
14
If a gasoline pump delivers 4 gallons of gas per minute, proportionately, it will take it 4 minutes to fill a gas tank that holds 16 gallons.
What is proportion?Proportion refers to the ratio of one unit or quantity compared to another unit or quantity.
Proportions are represented as fractional values using decimals, fractions, and percentages.
The time it takes the gasoline pump to deliver 4 gallons = 1 minute
Proportionately, to deliver 16 gallons, the time = 4 minutes (16 ÷ 4)
Thus, using proportional relationships, to deliver 16 gallons, the gasoline pump will take 4 minutes.
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Resolver por sustitución 5x+2y=5 -3x+3y=5
Answer: x = - 5/19 , y = - 35/19
Please help me answer this question
What is the perimeter of a square that has an area of 595.36 square feet?
Answer :
97.6 feetStep-by-step explanation:
It's given that, Area of square is 595.36 square feet.
As we know that area of square is calculated by,
Area = side²Substituting the values,
595.36 = side
side =√595.36
side = 24.4 feet
Hence, the side of the square is 24.4 feet.
Now,
Perimeter (square) = 4 × side
Perimeter = 4 × 24.4
Perimeter = 97.6 feet
Therefore, The perimeter of the square is 97.6 feet
Answer:
97.6 ft
Step-by-step explanation:
we know a square has 4 equal sides.
Area of a square = side X side or side squared
Plug in the value of area
595.36 square feet = side squared
24.4 ft = side ( do square root in both sides)
Perimeter of an square= side + side + side + side or 4 X side
That’s 4 X 24.4 ft = 97.6 ft.
Tammy mad- $187 for 11 hours of work
At the same rate how much would she
make for 9 hours of work.
Use the box method to distribute and simplify ( − 1 − 3 � ) ( − 3 � 3 + 4 � + 5 + 5 � 2 ) . (−1−3x)(−3x 3 +4x+5+5x 2 ). Drag and drop the terms to the correct locations of the table. ( ( − − 1 1 − − 3 � 3x ) ) ( ( − − 3 � 3 3x 3 + + 4 � 4x + + 5 5 + + 5 � 2 5x 2 ) ) Rows: 0 Columns: 0 You must answer all questions above in order to submit.
The complete box table.
2x 6
4x² 8x³ 24x²
6x 12x² 36x
-3 -6x -18
We have,
(4x² + 6x - 3) (2x + 6)
There are two factors.
We distribute one factor with the other factor.
Now,
Distributing the expression.
4x² (2x + 6) + 6x (2x + 6) - 3 (2x + 6)
8x³ + 24x² + 12x² + 36x - 6x - 18
We can combine like terms if we want to simplify.
8x³ + 36x² + 30x - 18
Thus,
The complete box table.
2x 6
4x² 8x³ 24x²
6x 12x² 36x
-3 -6x -18
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I need help with this please
Answer:
a. 830.380
Step-by-step explanation:
3 × [tex]\frac{1}{10}[/tex] is [tex]\frac{3}{10}[/tex]. This is the same as .3 when it's written in decimal form.
The first place on the right side of the decimal is the 'tenths' place. The second spot on the right side of the decimal is the 'hundredths' place.
Like this:
hundreds tens ones . tenths hundredths thousandths
All of the answers have the 830 in them. The only difference between the answers is the .380, .308, .038, .083. Once you see you have 3/10 (which is said three-tenths, which is .3) you can eliminate the last two answers, c and d. Then check the hundredths place. You have 8/100 (which is said eight-hundredths, which is .08) then you can eliminate b and find your answer, a.
Ryan delivers flowers to two customers. He drives for 12 minutes at an average speed of 40 miles per hour to reach his first customer. He drives for 15 minutes at an average speed of 60 miles per hour second customer. during the 27 minutes, how many miles did he drive?
Ryan drove 23 miles during the 27 minutes.
To discover the total distance Ryan drove during the 27 mins, we want to first calculate the distance he drove to reach every consumer and then add the ones distances collectively.
For the first customer, Ryan drove for 12 minutes at an average pace of 40 miles per hour:
Distance = speed × timeDistance = 40 × (12/60) (changing minutes to hours)Distance = 8 milesFor the second customer, Ryan drove for 15 mins at an average velocity of 60 miles consistent with hour:
Distance = speed × timeDistance = 60 × (15/60) (converting mins to hours)Distance = 15 milestherefore, the entire distance Ryan drove in the course of the 27 mins is:
Total distance = distance to first customer + distance to 2nd consumerTotal distance = 8 + 15Total distance = 23 milesSo, Ryan drove 23 miles during the 27 minutes.
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what proportion of observation is greater than 7?
The proportion of observations greater than 7 is 0.25 or 25%.
How to solveFor this question, we need to identify the number of observations higher than 7.
After inspecting the dataset, 25 values can be seen that are greater than 7.
Then, the proportion of observations greater than 7 can be calculated as follows:
proportion = number of observations greater than 7 / total number of observations
proportion = 25 / 100
proportion = 0.25
Therefore, the proportion of observations greater than 7 is 0.25 or 25%.
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Suppose we have a dataset of 100 observations, where each observation is a continuous variable. What proportion of the observations in the dataset are greater than 7?
Angela walked 12 mile. She took a break for water and then walked some more. In all, she walked 1110 miles.
How far did Angela walk after her break?
Enter your answer in the box as a fraction in simplest form.
Which graph represents the solution to X>1/2
Answer:
The graph that represents the solution to X > 1/2 is the graph where the line is vertical, passing through x = 1/2, and all the points to the right of this line are shaded. This is because the inequality X > 1/2 means that X can take any value greater than 1/2, but not including 1/2.
Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 7 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.
A) H0: p > 0.0007 H1: p ? 0.0007
B) H0: p = 0.0007 H1: p > 0.0007
C) H0: p < 0.0007 H1: p ? 0.0007
D) H0: p = 0.0007 H1: p < 0.0007
The null hypothesis in symbolic form is H0: p ≥ 0.0007
The alternative hypothesis in symbolic form is Ha: p < 0.0007
We have,
The null hypothesis in symbolic form is H0: p ≥ 0.0007
This means that the true proportion of male fireflies unable to produce light is greater than or equal to 7 in ten thousand.
The alternative hypothesis in symbolic form is Ha: p < 0.0007
This means that the true proportion of male fireflies unable to produce light is less than 7 in ten thousand.
Thus,
The null hypothesis in symbolic form is H0: p ≥ 0.0007
The alternative hypothesis in symbolic form is Ha: p < 0.0007
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A certain circle can be represented by the following equation.
x^2+y^2-4x+12y-24=0
What is the center of the circle?
What is the radius of the circle?
I NEED HELP WITH THIS!!
The answers are GBACGFI and when put in backward alphabetical order it becomes IGFDCBA.
The code is IGFDCBA.
What is the code?The code is determined as follows:
1. 1/6 of students are trying out for a fall sport, then 5/6 are not.
The probability of selecting a student who is not trying out for a fall sport = 5/6.
Thus, the probability of students trying out for a spring sport = 5/6
To get 20 students who are trying out for a spring sport = 20 / (5/6)
To get 20 students who are trying out for a spring sport = 48 students.
Letter G
The smaller the mean absolute deviation the farther apart the data set is: False; Letter B
Every part of the population has an equal chance of being selected when dealing with random sampling: True; Letter A
Rolling a number larger than one on a regular six-sided dice;
Likely; Letter C
The probability of pulling out a green marble and keeping it = 7/12.
The probability of pulling out another green marble = 6/11
Therefore, the probability of pulling out two consecutive green marbles = 7/12 * 6/11
The probability of pulling out two consecutive green marbles = 31.8%; Letter G
If an event is most likely to not happen then the probability gets close to 0; Letter F
B has a probability of 1/4 of being landed on
If you spin the spinner 500 times, you can land B 500 x 1/4 = 125 times.; Letter I
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Simplify the expression 7a^-5b^3
Answer: To simplify the expression 7a^⁻⁵b^3, we can use the negative exponent property, which states that a^⁻ⁿ = 1/aⁿ. Applying this property to the variable a gives us:
7a^⁻⁵b^3 = 7(1/a⁵)b^3
We can also simplify b^3 to get the final answer:
7a^⁻⁵b^3 = 7b^3/a⁵
Therefore, the simplified expression is 7b^3/a⁵.
jenny wants to know what we mean when we say a tank is 284 cubic feet. how should we answer jenny?
When we say a tank is 284 cubic feet, we mean that the tank has a volume of 284 cubic feet.
We have,
When we say a tank is 284 cubic feet, we mean that the tank has a volume of 284 cubic feet.
When we measure the volume of a three-dimensional object like a tank, we typically use a unit of measures like cubic feet or cubic meters.
A cubic foot is the volume of a cube that measures 1 foot on each side.
So if we say a tank has a volume of 284 cubic feet, we mean that if we were to take a cube that measures 1 foot on each side and stack 284 of those cubes together, we would have a tank with the same volume as the resulting cube.
Thus,
When we say a tank is 284 cubic feet, we mean that the tank has a volume of 284 cubic feet.
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a man left his home and drove along a certain road at the rate of 48 km/h. one hour later, his son left the same house and drove along the same road in the same direction at 72 km/h. in how many hours does the son overtake the father?
Answer:
The son overtakes the father 3 hours after the father started driving which is 2 hours after the son started driving.
Step-by-step explanation:
Father:
speed = 48 km/h
distance = d
time = t
Son:
speed = 72 km/h
distance = d
time = t - 1
speed = distance/time
distance = speed × time
Father:
d = st
d = 48t
Son:
d = st
d = 72(t - 1)
d = 48t
d = 72(t - 1)
48t = 72(t - 1)
48t = 72t - 72
72 = 24t
t = 3
The son overtakes the father 3 hours after the father started driving which is 2 hours after the son started driving.
precalculus answer all the questions in the pictures part 3
The solution is:
Exponential model: ,horizontal asymptote
• Logarithmic model: ,vertical asymptote
Here, we have,
EXPLANATION
The exponential model has always a horizontal asymptote. In the parent function f(x) = aˣ, the asymptote is the x-axis because the function approaches 0 as x approaches infinity.
The logarithmic model has always a vertical asymptote. In the parent function f(x) = logₐ(x), the asymptote is the y-axis because the function approaches infinity as x approaches 0.
Hence, The solution is:
Exponential model: ,horizontal asymptote
• Logarithmic model: ,vertical asymptote
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What is the correct sequence for these steps in CADD, which describe how to draw a square whose diagonal length is provided?
enter the coordinates to specify the center of the square
define the number of sides
select the inscribed option
enter the radius value of the circle as half the length of the diagonal
select the Polygon command
enter the desired distance between the corners of the square
Which division problem is represented with this model?
Responses
15÷2
1 fifth divided by 2
15÷6
1 fifth divided by 6
16÷2
1 over 6 end fraction divided by 2
12÷5
1 half divided by 5
Answer:
C.
Step-by-step explanation:
We have five unshaded, 1 half of unshaded, and 1 shaded, Thus, It will be showed as [tex]\frac{1}{6}[/tex] ➗ [tex]2[/tex]
The table shows Henry's savings over several weeks. If the pattern continues, what will Henry's savings be in Week 10? Tell how you know. Week Savings
Check the picture below.
Will mark brainliest.
Applying the inscribed angle theorem, the missing measures are:
measure of arc TR = 106°
measure of arc TL = 74°
m∠L = 50°
m∠R = 37°
m∠RTV = 37°
Here, we have,
The Inscribed Angle Theorem
Measure of an inscribed angle = half the measure of the arc it intercepts
Central angle = measure of intercepted arc
We are given the following:
LR and TV are diameters of the circle O.
m∠TOR = 106° (central angle)
Find measure of arc TR:
measure of arc TR = m∠TOR
measure of arc TR = 106°
Find measure of arc TL:
measure of arc TL = 180° - m∠TOR
measure of arc TL = 180° - 106°
measure of arc TL = 74°
Find m∠L:
m∠L = ½(measure of arc TR)
m∠L = ½(106°)
m∠L = 50°
Find m∠R:
m∠R = ½(measure of arc TL)
m∠R = ½(74°)
m∠R = 37°
Find m∠RTV:
m∠RTV = ½(measure of arc RV)
m∠RTV = ½(180 - 106)
m∠RTV = ½(74)
m∠RTV = 37°
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complete question:
Find the measure of the following: m arcTR = m arcTL = m ∠L = m ∠R = m ∠RTV =
The city of Bangor, Maine has a scale model of Paul Bunyan nearly 30 feet tall. The model’s scale is 1:5. On the scale model, Paul Bunyan’s belt buckle is 12 feet from the ground. In real life, how far from the ground is Paul Bunyan’s belt buckle? The diameter of Paul Bunyan’s actual head is 9 inches. What is the diameter of the Paul Bunyan’s scale model head in feet?
The distance between of the belt buckle from the ground is 2.40 feet.
The diameter of the head is 3 3/4 inches.
What are the distance?A scale drawing is either an enlarged or reduced image of another image or object. A scale drawing is enlarged or reduced using a scale. A scale is a used to determine the ratio between the scale drawing and the original diagram.
The distance between of the belt buckle from the ground in real life would be greater than that of the scale drawing. Also, the diameter of the head would be larger in real life.
Distance between of the belt buckle from the ground = 12 / 5 = 2.40 feet
In order to determine the diameter of the scale head, first convert inches to feet.
1 inch = 1/12 feet
9/12 = 3/4 feet
Diameter of the scale head = 3/4 x 5 = 15/4 = 3 3/4 feet
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