The vector v can be expressed as v = -0.161 i + 0.618 j, where i and j are the unit vectors
To express a vector v in terms of i and j, we need to find its x and y components. The magnitude ||v|| of a vector is given by:
||v|| = √(v₁² + v₂²)
where v₁ and v₂ are the x and y components of v, respectively.
The direction angle θ of a vector with respect to the positive x-axis is given by:
θ = atan(v₂/v₁)
where atan denotes the arctangent function.
In this problem, we are given that the magnitude ||v|| of the vector v is 2/3, and its direction angle θ with respect to the positive x-axis is 116 degrees. Therefore, we can write:
||v|| = √(v₁² + v₂²) = 2/3
θ = atan(v₂/v₁) = 116°
Solving for the x and y components, we get:
v₁ = ||v|| cos(θ) = (2/3) cos(116°) ≈ -0.161
v₂ = ||v|| sin(θ) = (2/3) sin(116°) ≈ 0.618
Therefore, the vector v can be expressed as:
v = -0.161 i + 0.618 j
where i and j are the unit vectors in the x and y directions, respectively.
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I have 2 questions
1. my final for one of my classes is 150 points and I need to score at least a 53.16% on the final exam, how many points of the overall 150 would I need to get correct.
2. for my other final it is worth 200 points and I need to score at least a 44.45% on the final exam, how many points of the overall 200 would I need to get correct.
what is the measure of an angle if it is 590 less than six times its own supplement
This is a word problem involving supplementary angles. To solve it, we need to follow these steps:
Identify the given information and the unknown quantity. In this problem, we are given that an angle is 590 less than six times its own supplement. The unknown quantity is the measure of the angle.
Write an equation that relates the given information and the unknown quantity. We can use the fact that supplementary angles are two angles with a sum of 180°1. Let x be the measure of the angle. Then its supplement is 180 - x. The equation is:
x=6(180−x)−590
Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:
xx7xxx=6(180−x)−590=1080−6x−590=490=7490=70
Therefore, the measure of the angle is 70°.
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
The correct option regarding which bus has the least spread among the travel times is given as follows:
Bus 14, with an IQR of 6.
How to solveTo obtain measures of spread, we can use the dot plot to visualize the frequency of each observation in the data-set, and then calculate the interquartile range (IQR).
For a group of 15 students, we can find the quartiles as follows:
The first quartile (Q1) is the median of the first half of the data-set, which consists of the first seven students.
Looking at the dot plot, the fourth dot represents the median of the first half. For Bus 14, Q1 = 12. For Bus 18, Q1 = 9.
The third quartile (Q3) is the median of the second half of the data-set, which consists of the last seven students. Looking at the dot plot, the eleventh dot represents the median of the second half. For Bus 14, Q3 = 18.
For Bus 18, Q3 = 16.
We can then calculate the IQR as the difference between Q3 and Q1:
For Bus 14, IQR = Q3 - Q1 = 18 - 12 = 6.
For Bus 18, IQR = Q3 - Q1 = 16 - 9 = 7.
Based on the IQR values, we can conclude that Bus 14 is more consistent than Bus 18, as it has a lower IQR.
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PLEASE HELP! Showing all work, solve for x and why and round to nearest tenth
Answer:
x = 7.9 (nearest tenth)
y = 24.6° (nearest tenth)
Step-by-step explanation:
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:
[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, x = 7.9.
[tex]\hrulefill[/tex]
The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:
[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, y = 24.6°.
years from 1970 through 2010. X a mathematical model p+ 2 =44
Given the above model, we can state that it's predictions were accurate.
How is this so?The model uses the variable x which represents no. of years from 1970 to 2010
2010 -1970 = 40
P + (x/2) = 44
P + 40/2 = 44
P + 20 = 44
P = 44 - 20
p = 24
The model, it predicted 24% of the population would be smoking in this city in the year 2010. Whereas the data from the graph tell us that
28 % of the adults actually smoked in the city in 2010. Hence the model is accurate .
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Full Question:
The mathematical model
p+ x/2 =44
Describes the percentage, p, of adults who smoked cigarettes x years after 1970
Does the mathematical model underestimate or overestimate the percentage of adults who smoked cigarettes in 2010? By how much?
I just don’t know what you do here!? Please help!!
Solve the problem and show how you solved it.
Georgia is a long-distance swimmer. She swims 2 miles
every day. How many miles does she swim in 5 days?
Answer:
Step-by-step explanation:
chickennnnnnnnn
Find cordinates of point of inter section
7x+4y=23
8x-10y=19
Answer:
To find the coordinates of the point of intersection between the two lines, we can solve the system of equations by elimination or substitution. Here, we will use the elimination method.
First, we will multiply the first equation by 10 and the second equation by 4, in order to eliminate the y term:
- 70x + 40y = 230
- 32x - 40y = 76
Adding these two equations, we get:
- 102x = 306
Dividing both sides by 102, we get:
- x = 3
Now we can substitute this value of x into either equation to find the value of y. Using the first equation:
- 7(3) + 4y = 23
- 21 + 4y = 23
- 4y = 2
- y = 1/2
Therefore, the point of intersection is (3, 1/2).
Answer:
Step-by-step explanation:
OAB is a minor sector of the circle below.
Calculate the length of the minor arc AB in terms of pi
Not drawn accurately
AWARDING BRAINLIEST TO FIRST ANSWER
The Length of the arc in the circle shown is calculated to one decimal place, in terms of pi, as approximately 3.6π cm.
How to Calculate the Length of an Arc?The length of an arc in a given circle can be calculated by applying the formula as expressed below:
Length of arc (s) = ∅/360 * 2πr, where:
Reference angle = ∅
Radius of the circle = r.
Given the parameters:
Radius (r) = 16 cm
Reference angle (∅) = 40 degrees.
Plug in the values:
Length of the arc (s) = 40/360 * 2 * π * 16
Length of the arc (s) = 3.6π cm
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Answer:
To calculate the length of the minor arc AB in terms of pi, you need to know the measure of the central angle that intercepts the arc and the radius of the circle. Do you have that information?
Step-by-step explanation:
The cube root of the product of x and y, less twelve
The expression "the cube root of the product of x and y, less twelve" can be mathematically represented as ³√(xy) - 12.
To understand this expression, let's break it down step by step:
Product of x and y:
We multiply the values of x and y together to find their product, denoted as xy.
Cube root of the product:
We take the cube root of the product obtained in the previous step.
The cube root of a number x is the value that, when raised to the power of 3, equals x. In this case, we take the cube root of xy, represented as ³√(xy).
Subtract twelve:
Finally, we subtract twelve from the result obtained in the previous step, ³√(xy). This gives us the expression ³√(xy) - 12.
The expression ³√(xy) - 12 represents a mathematical operation involving the cube root of the product of x and y, followed by subtracting twelve from the result.
This can be useful in various mathematical contexts, such as solving equations or modeling real-world problems.
It's important to note that the expression is dependent on the values of x and y.
By substituting specific values for x and y, we can evaluate the expression to obtain a numerical result.
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What is the definition of perpendicular lines?
1.two lines that intersect in a way that forms right angles
2.two lines that intersect in a way that cuts both lines in half
3.two lines that intersect in a way that they share more than one common point
4.two lines that intersect in a way that forms two congruent angles
Answer:
Step-by-step explanation:
The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."
When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.
Therefore, option 1 is the correct definitation of perpendicular lines.
Answer: 1. Two lines that intersect in a way that forms right angles.
Step-by-step explanation:
Hope this helped! :)
Can someone help me with this
Answer:
x = 23°
Step-by-step explanation:
We Know
The 67° angle + the x must be equal to 90°
Find the x.
Let's solve
67° + x = 90°
x = 23°
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
-409-8
Click twice to plot each segment.
Click a segment to delete it.
Slope of the Line:
-3 -2 7
10
9
Submit Answer
5
4
7
9
10
The rise and run of the line is shown in the image below, where: slope of the line (m) = -3/4.
What is the Slope of a Line?The slope refers to how steep a line is. To find the slope of a line on coordinate plane, find the rise and the run of the line, then find their ratio.
Slope of a line (m) = change in y / change in x = rise / run
The red line in the image below represents the rise of the line while the blue line represents the run of the line.
The rise = 3 units
The run = 4 units
Therefore, we have:
Slope (m) = rise/run = -3 units / 4 units
Slope (m) = -3/4.
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A total of 480 black and red jerseys were produced in a factory. Each black Don jersey was sold at $56. Each red jersey was sold at $75. After all the jerseys were sold, the amount of money collected from the sale of the black jerseys was $18315 less than that of the red jerseys. (a) How many black jerseys were sold? (b) How much money was collected from the sale of the red jerseys?
Answer:
Step-by-step explanation:
The masses, in kilograms, of 25 pumpkins were
recorded and summarized in the histogram shown. No
pumpkin's mass was an integer number of kilograms.
How many pumpkins had a mass greater than
6 kilograms?
Observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.
What is a histogram?A histogram is a graph that displays the values of a numeric variable's distribution as a collection of bars.
The height of a bar represents the frequency of data points with values falling within the relevant bin; each bar typically spans a range of numerical values known as a bin or class.
Similar to a bar chart, a histogram is produced with bars of varying widths.
In a histogram, the frequency is revealed by the bar's area rather than its height.
We plot the frequency density rather than frequency on the y-axis. To figure this out, divide a group's frequency by its width.
So, the x-axis of the given histogram represents the mass of the pumpkins.
The y-axis of the histogram represents the number of pumpkins.
Then, the pumpkins with greater mass than 6 kilograms:
= 8 + 6 + 2
= 16
Therefore, observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.
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simplify (5^4)^2. 5^6. 5^8. 25^6. 25^8
Therefore here, (5⁴)². 5⁶. (5⁸)².(5⁶)². (5⁸)² simplifies to 5⁸².
The simplest version is what?The integer's basic form is represented by its smallest equivalent fraction. How to determine the simplest form: Look for shared components in the denominator and numerator.
By applying the exponentiation laws, let's us gradually simplify this an expression is:
[tex](5^4)^2 = 5^(4*2) = 5^85^6 * 5^8 = 5^(6+8) = 5^1425^6 = (5^2)^6 = 5^(2*6) = 5^1225^8 = (5^2)^8 = 5^(2*8) = 5^16[/tex]
When all of these simplifications are put back into the original statement, we get the following:
[tex](5^4)^2. 5^6. 5^8. 25^6. 25^8 = 5^8 * 5^14 * 5^12 * 5^16 * 5^16[/tex]
Using the rule that is [tex]a^b * a^c = a^(b+c)[/tex],
The first three terms can be combined to create:
[tex]5^8 * 5^14 * 5^12 * 5^16 * 5^16 = 5^(8+14+12) * 5^(16+16) = 5^50 * 5^32[/tex]
Using the same rule again, we can combine these two terms:
5⁵⁰* 5³²
= 5⁵⁰⁺³²
= 5⁸²
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Write a polynomial function in standard form with real coefficients whose zeros include 1,4i, and -4i
Answer:
f(x) = x^3 - x^2 + 16x - 16
Step-by-step explanation:
If a polynomial has the zeros 1, 4i, and -4i, then it must have the factors (x - 1), (x - 4i), and (x + 4i). This is because a factor of (x - a) produces a root of x = a.
To find the polynomial, we can multiply these factors together:
(x - 1)(x - 4i)(x + 4i)
= (x - 1)(x^2 - (4i)^2)
= (x - 1)(x^2 + 16)
= x^3 + 16x - x^2 - 16
So the polynomial function in standard form with real coefficients whose zeros include 1, 4i, and -4i is:
f(x) = x^3 - x^2 + 16x - 16
a baseball stadium keeps track of how many hot dogs each customer orders. the data is organized into the frequency table below. what os the relative frequency of customers ordering five hot dogs?
a.) about 5%
b.) about 7%
c.) about 8%
d.) about 14%
The relative frequency of customers ordering five hot dogs is 7%, option B is correct.
To find the relative frequency of customers ordering five hot dogs, we need to divide the frequency of customers who ordered five hot dogs by the total number of customers.
The total number of customers is the sum of the frequencies in the table:
Total frequency = 90 + 45 + 18 + 18 + 14 + 13 = 198
The frequency of customers ordering five hot dogs is 14, so the relative frequency is:
Relative frequency of customers ordering five hot dogs = (frequency of customers ordering five hot dogs) / (total frequency) = 14 / 198 = 0.0707
To express this as a percentage, we can multiply by 100:
Relative frequency of customers ordering five hot dogs = 0.0707 * 100% = 7.07%
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Pythagorean theorem - Missing sides
Pls help me I need your help to my homework
If you help me, I help you too I promise
4% is equivalent to what fraction
the value of 4% as a fraction is 1/25
4/100 is the fraction, but when 4 is divided into 100, it gives you 1/25 in simplest form.
A rainwater collection system uses a cylindrical storage tank with a diameter of 50 cm and a height of 80 cm what is the total volume of water in cubic centimeters that can be collected
Answer:
157,000
Step-by-step explanation:
π r² h
2 grams =
milligrams
There are 2000 milligrams in 2 grams of a substance, and it constitutes 40% of a 5-gram sample.
How to solveConvert grams to milligrams:
2 grams = 2 * 1000 milligrams
2 grams = 2000 milligrams
Calculate the percentage in a 5-gram sample:
Percentage = (2000 milligrams / 5000 milligrams) * 100
Percentage = (2 / 5) * 100
Percentage = 0.4 * 100
Percentage = 40%
Thus, there are 2000 milligrams in 2 grams of a substance, and it constitutes 40% of a 5-gram sample.
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2 grams = milligrams
How many milligrams are there in 2 grams of a substance, and what is the percentage of this amount in a 5-gram sample?
Find z
x+y=z
y-z=x
I will award brainlest
Answer:
To solve for z in terms of x and y using the given equations:
x + y = z ........(1)
y - z = x ........(2)
From equation (2), we get:
y - x = z (by adding z on both sides)
Substituting this value of z in equation (1), we get:
x + y = y - x
2x = 0
x = 0
Substituting x = 0 in equation (2), we get:
y - z = 0
y = z
Therefore, the solution is:
z = y
We cannot determine a specific value of z without knowing the values of x and y.
El área del hexágono regular cuyo lado mide 1 cm es?
Answer:
Respuesta: 2,25 cm cuadrados
Explicación paso a paso:
PERIMETRO: 6
APOTEMA: 0,75
AREA DEL HEXAGONO REGULAR: 6 X 0,75 / 2 = 2,25 CM CUADRADOS
Step-by-step explanation:
Select all equations that have infinitely many solutions
Answer:
2 and 4
Step-by-step explanation:
1)
14x+6=2(5x+3)
14x+6=10x+6
No Solutions
2)
3(x-5)+6=x-(9-2x)
3x-9=3x-9
Infinitely Many
3)
2+5x-9=3x+2(x-7)
5x-7=5x-14
No Solutions
4)
3(4x-6)+2=-4(4-3x)
12x-16=12x-16
Infinitely Many
Correct answer gets brainliest!!!!
Answer: 5
Step-by-step explanation:
They are the points
Keyboard A Keyboard B Keyboard C
Person
Person Totals (P) Overall
M = 1 M = 5 M = 6 A 6 N = 15
SS = 8 SS = 22 SS = 10 B 9 G = 60
C 18
D 12 k = 3
E 15
n = 5
Complete all calculations for the ANOVA Summary Table:
SS total, SS within, SS between treatments, SS between subjects, and SS error
df total, df within, df between treatments, df between subjects, and df error
MS between treatments and MS error
the F ratio
Then:
Find critical value for F based on df between treatments and df error, and decide if F ratio is significant or not.
Tukey's HSD is 2.0. Determine which keyboards are significantly different from one another in the number of errors people make and summarize the results.
Keyboards A and B are significantly different from one another
How to explain the informationThe F ratio has been found to be 4.30, equating to the MS between treatments divided by MS error resulting in a value of 2082/484. In order to seek out the critical value for F at an alpha level of 0.05 within degrees of freedom between treatments (2) and degrees of freedom error (3), we must consult the F-table, revealing it to be 5.14.
We reach the conclusion that rejecting the null hypothesis would not prove necessary as there appears to be no great significance when it comes down to the number of errors made with the three concerned keyboards.
Tukey's HSD signifies 2.0, indicating any distinction of means exceeding such scores is considered noteworthy. Calculating pairwise comparisons can enlighten us as to which keyboards are significant from one another:
Comparing Keyboard A versus Keyboard B: The difference was calculated using |25-6| / ✓(484/6*(1/6+1/6)) = 3.03, determining its significance surpassing Tukey's HSD (2.0).
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Smart Kitchen sells chocolate nonpareils in 8 oz. containers. Because the candy pieces are not uniform, the weight of each individual container varies slightly. A random sample of nine containers was weighed on a precision scale and the results are shown below:
8.09
8.20
8.03
7.86
7.87
8.06
8.43
7.99
8.08
Determine the interquartile range for this sample. Are there any outliers in this data set?
The interquartile range of the data will be 0.215.
How to calculate the valueThe lower half is:
7.86, 7.87, 7.99, 8.03
The median of the lower half is:
(Q1) = (7.87 + 7.99) / 2 = 7.93
The upper half is:
8.06, 8.08, 8.09, 8.20, 8.43
The median of the upper half is:
(Q3) = (8.09 + 8.20) / 2 = 8.145
The IQR is the difference between the third and first quartiles:
IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215
Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955
Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795
None of the data points fall outside these thresholds, so there are no outliers in this data set.
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A bank offers an investment account with an annual interest rate of 1.51% compounded quarterly. Charlie invests 4200 into the account for 5 years. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
After 5 years, there will be $4,528.73 in Charlie's account if no withdrawals are made.
How much money is in Charlie's account after 5 years?Compound interest means addition of interest to the principal sum of a loan or deposit. To get the amount, we will use the formula [tex]A=P(1+r/n)^{nt}[/tex] to get sum of money in the account.
Data:
P = 4,200, r = 1.51%, m = 4, t = 5
Plugging the values, we get:
[tex]A = 4200(1+0.0151/4)^{4*5}\\A = 4200* {1.003775}^{20}\\A = 4200*(1.07826994224)\\A = $4528.73375741\\A = $4528.73.[/tex]
Complete question "A bank offers an investment account with an annual interest rate of 1.51% compounded quarterly. Charlie invests 4200 into the account for 5 years. Answer the questions below. Assuming no withdrawals are made, how much money is in Greg's account after 5 years?"
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Please see the attached
The equation in slope-intercept form for the line that has slope of -2/5 and y-intercept of -4 is written as: y = -2/5x - 4.
How to Write the equation of a Line in the Slope-intercept Form?The slope-intercept form for any given straight line or linear relationship can be expressed as y = mx + b, where:
m = slope of the line
b = the y-intercept
Given the following:
slope (m) = -2/5.
y-intercept (b) = -4
To write the equation, substitute m = -2/5 and b = -4 into y = mx + b:
y = -2/5x - 4
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Jill's neighborhood has a mean of 3 children per household.
What happens to the mean if a family with 7 children moves away?
Responses
The mean remains the same.
The mean increases.
The mean decreases.
The correct option is the last one, the mean will decrease.
What happens to the mean if a family with 7 children moves away?For a set of N values {x₁, x₂, ..., xₙ} the mean is defined as the sum of the N values divided by N, this is:
mean = (x₁ + x₂ + ... + xₙ)/N
Now, here the mean is 3, and a family with 7 children (more than the mean) moves away.
That will cause a decrease in the mean, because we are removing one of the larger values.
The correct option is the last one.
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