Answer:
MAGNITUDE AND DIRECTION OF A VECTOR
Given a position vector →v=⟨a,b⟩,the magnitude is found by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found by tanθ=(ba)⇒θ=tan−1(ba)
Step-by-step explanation:
The population of town X was 220,000 in 2000, and 252,000 in 2010. Project the population in 2020.
Answer: To project the population in 2020, we can use the linear trend line equation.
First, we need to find the equation of the line. Let's use the two given points, (2000, 220,000) and (2010, 252,000), to find the slope of the line:
slope = (252,000 - 220,000) / (2010 - 2000) = 32,000
Next, we can use the slope-intercept form of the line equation: y = mx + b, where m is the slope and b is the y-intercept.
Plug in the first point: 220,000 = 32,000 * 2000 + b
Solve for b: b = 220,000 - 32,000 * 2000 = -44,000,000
The equation of the line is: y = 32,000x - 44,000,000
Finally, we can use the equation of the line to project the population in 2020:
y = 32,000 * 2020 - 44,000,000 = 264,000
So, the projected population in 2020 is 264,000.
Step-by-step explanation:
92÷3= solving the equation
32.66 repeated :>))))))))))))))
Answer:
30.6666666667
Step-by-step explanation:
92÷3 = 30.6666666667
An automobile dealership has found that for every 170 cars sold, 26 will be brought back to the dealer for major repairs. If the dealership sells 1360 cars this year, approximately how many cars will be brought back for major repairs?
Answer:
208 Cars will be brought back for major repairs.
Step-by-step explanation:
With the simple calculation of:
[tex]\frac{170}{1360}\frac{26}{x}[/tex]
We are solving for x.
We cross-multiply 1360 by 26.
35,360
Then divide that by 170.
which will get us the result of 208.
CAN SOMEONE HELP WITH THIS QUESTION✨
Answer:
m = √3 ≈ 1.7321b = 1 -π√3/6 ≈ 0.0931Step-by-step explanation:
You want the slope-intercept form equation for the tangent line at point (π/6, 1) on the curve y = 2·sin(x).
SlopeThe slope of the line at the point of tangency is the derivative of the curve at that point:
y' = 2cos(x) = 2·cos(π/6) = 2(√3/2)
m = √3 . . . . . approximately 1.7321
Y-interceptSolving the line's equation for b, we have ...
y = mx +b
b = y -mx = 1 -(√3)(π/6)
b = 1 -π√3/6 . . . . . approximately 0.0931
EquationThe equation of the line is ...
y = mx +b
y = (√3)x +1 -(π√3)/6
when the coefficients of polynomials are drawn from a finite field, the set of polynomials constitutes a
The set of polynomials over F is the set of all possible polynomials with coefficients from F, which includes all polynomials with degree up to the size of F.
A polynomial over a finite field is a mathematical expression of the form
[tex]P(x) = a_0 + a_1x + a_2x^2 + ... + a_nx^n[/tex],
where the coefficients a_i are elements of a finite field F. Therefore, the set of polynomials over a finite field F is the set of all possible polynomials with coefficients from F. For example, if F is the field with two elements {0, 1}, then the set of polynomials over F is [tex]{0, 1, x, x + 1, x^2, x^2 + 1, ...}[/tex]. As another example, if F is the field with three elements {0, 1, 2}, then the set of polynomials over F is [tex]{0, 1, 2, x, x + 1, x + 2, x^2, x^2 + 1, x^2 + 2, ...}[/tex]. In general, the set of polynomials over F is the set of all possible polynomials with coefficients from F, which includes all polynomials with degree up to the size of F.
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what statistical test would you do ? explain why you chose this test
The statistical test to be chosen depends on the nature of the data and the research question being answered. There are several statistical tests available, each with different assumptions and purposes.
Describe Statistical test?A statistical test is a method used to evaluate data and make inferences about a population based on a sample of the population. The purpose of a statistical test is to determine if the results of an experiment or survey are statistically significant, which means that they are unlikely to have occurred by chance. Statistical tests use mathematical models to determine the likelihood of an event occurring and provide a level of confidence in the results.
Here are some common statistical tests and when they might be used:
T-test: A t-test is used to compare the means of two groups to determine if there is a significant difference between them. This test is often used in experiments where one group is treated differently from another.
ANOVA: ANOVA (Analysis of Variance) is used to compare the means of three or more groups to determine if there is a significant difference between them.
Chi-square test: A chi-square test is used to determine if there is a significant relationship between two categorical variables.
Linear Regression: Linear regression is used to study the relationship between a dependent variable and one or more independent variables.
Logistic Regression: Logistic regression is used to predict a binary outcome based on one or more independent variables.
It is important to choose the right statistical test to ensure that the results are meaningful and accurate. The choice of the test depends on the research question, the nature of the data, and the assumptions of the test. It is advisable to consult with a statistician to determine the appropriate test for a given situation.
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A plumber uses an average of 20 meters of copper
pipe each week. Copper pipe costs $5 per meter. If
the plumber wants to reduce her weekly expenditure
on copper pipe by $4, what length of copper pipe
should she buy each week, in meters?
Answer:
$80
Step-by-step explanation:
If $a$ and $b$ are integers with $a > b$, what is the smallest possible positive value of $\frac{a+b}{a-b} + \frac{a-b}{a+b}$?
The smallest positive value for (a+b)/(a-b)+(a-b)/(a+b) where a and b are integers is 2.
What exactly are integers?In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.
Now
For given expression (a+b)/(a-b)+(a-b)/(a+b)
where a>b and both are integers.
solving the expression
((a+b)(a+b)+(a-b)(a-b))/((a+b)(a-b))
=2(a²+b²)/a²-b²
As (a+b)²=a²b²+2ab and a²-b²=(a+b)(a-b)
So for given expression negative and positive values for a,b gives same result then smallest values will be a=1, b=0
Then
=2*1/1
=2
Hence, The smallest positive value for (a+b)/(a-b)+(a-b)/(a+b) where a and b are integers is 2.
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What is the equation of a vertical line passing through the point (−5, −1)?
Answer:
x=-5
I think this is right
Step-by-step explanation:
Check the picture below.
15. ABC is
a. Congruent
b. Similar
c. Neither
to A'B'C'.
Answer:
Step-by-step explanation:
Similar
Titing Tunction Rune -3 -2 -1 3 2 1 7 ty A -2 1 2 3 g(x) X Determine the values of h and k in the equation of g(x). g(x)=√√x-h+k
The values of h and k are given as follows:
h = 1.k = -2.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]y = \sqrt[3]{x}[/tex]
Which makes the curve at the origin.
From the graph, the curve is made at point (1,-2), hence the translations are given as follows:
One unit right: h = 1.Two units down: k = -2.More can be learned about translations at brainly.com/question/28174785
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I need help
I don’t understand how to do it
Answer:
tan60 = [tex]\frac{x}{6}[/tex]
x = 6 x tan60
= 10.4 ( cor to 3 significant figures)
cos60 = [tex]\frac{6}{y}[/tex]
y = [tex]\frac{6}{cos60}[/tex]
= 12
Which equation would create a line perpendicular to y= 5x +10
Answer:
y=1/5x+10
Step-by-step explanation:
Consider the function below.
f(x)=8x−6
What would be the output if the input is 8?
Responses 2
an inattentive driver is traveling 16.0 m/s m / s when he notices a red light ahead. his car is capable of decelerating at a rate of 3.06 m/s2 m / s 2 .
It will take the inattentive driver 5.22 seconds to come to a complete stop, assuming the car's deceleration remains constant.
An inattentive driver traveling 16.0 m/s when he notices a red light ahead and his car is capable of decelerating at a rate of [tex]3.06 m/s^2[/tex]. To determine how much time it will take for the car to come to a complete stop, we can use the following equation of motion:
v = v0 + at
where v is the final velocity (in this case, 0 m/s), v0 is the initial velocity (16.0 m/s), a is the acceleration (negative, because the car is slowing down), and t is the time.
Rearranging and solving for t, we get:
t = -v0 / a
t = -16.0 / (-3.06)
t = 5.22 seconds
So, it will take the inattentive driver 5.22 seconds to come to a complete stop, assuming the car's deceleration remains constant. This time can be used to determine the minimum distance the driver needs to maintain between himself and the vehicle in front of him to avoid a collision.
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This graph shows the equations y= - 1/2x + 3 and y=2x-2.
A coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
a) Given that, the graph shows the equations y= - 1/2x+3 ------(i) and y=2x-2 ------(ii).
From the graph, the solution is (2, 2)
b) Put x=1 in equation (i), we get
y= -1/2(1)+3
y= 2.5
Put x=2 in equation (i), we get
y= -1/2(2)+3
y= 2
Put x=3 in equation (i), we get
y= -1/2(2)+3
y= -1/2 (3)+3
y= -1.5+3
y= 1.5
So, a coordinate that is a solution to the first equation is (3, 1.5)
Therefore, a coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).
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Order of Operations Consider the numerical expression: 3 + 6 × (5 + 4) ÷ 3 − 7.
Question 1
To evaluate the numerical expression, what is the first step in the order of operations?
A Perform any calculations inside parentheses.
B Perform all additions, working from left to right.
C Perform all multiplications, working from left to right.
D Perform all divisions, working from left to right.
Question 2
Evaluate the given numerical expression.
Responses
A 21
B 14
C 9
D 12
Answer:
Add 5 +4 × 6 ÷ 3 - 7 + 3and you will get 14 and that is your answer
Prove that
cos 75° = √2 (√3-1)÷4
Answer:
The Pythagorean Theorem states that, for a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Therefore, if we have a right triangle with angles A, B, and C, then:
$$A^2 + B^2 = C^2$$
Now, let's consider a triangle with angles of 75°, 45°, and 30°. We know that the sum of the angles must equal 180°, so these three angles add up to 180°.
We can now plug in the angles into the formula above and solve for the hypotenuse C:
$$(45^2) + (30^2) = C^2$$
$$2025 = C^2$$
$$\sqrt{2025} = C$$
Therefore, the length of the hypotenuse C is 45 units.
Now, let's look at the cosine of angle A, which is 75°. By definition, the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Therefore, for this triangle:
$$\cos 75° = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{\text{Adjacent side}}{45}$$
We can now find the length of the adjacent side by subtracting the length of the opposite side from the hypotenuse:
$$\text{Adjacent side} = 45 - \text{Opposite side}$$
The length of the opposite side is equal to the length of the other leg, which is 30 units in this case. Therefore, the length of the adjacent side is 15 units.
Putting this all together, we can now solve for the cosine of 75°:
$$\cos 75° = \frac{15}{45} = \frac{\sqrt{2} (\sqrt{3}-1)}{4}$$
Therefore, cos 75° = √2 (√3-1)÷4.
I need HELP please
Thank you
Answer:
x = 11
Step-by-step explanation:
both the petagons are similar so the sum of their sides will be same
i.e.
sum of ABCDE = sum of JKLMN
ABCDE = sum of all the five sides = 6+2+2+3+3 = 16
thus,
sum of JKLMN = 16
16 = x+1+1+1.5+1.5
16 = x+5
x = 16-5 = 11
2/3y + v = x solve for y
The variable y as the subject formula in the equation (2/3)y + v = x is y = (3/2)(x) - (3/2)(v)
What is y in the given equation?Given the equation in the question;
(2/3)y + v = x
y = ?
Solve for y, we make 'y' the subject of the formula.
(2/3)y + v = x
Subtract v from both sides
(2/3)y + v - v = x - v
(2/3)y = x - v
Multiply both sides by 3/2
(3/2)(2/3)y = (3/2)(x - v)
y = (3/2)(x - v)
Apply distributive property.
y = (3/2)(x) - (3/2)(v)
Therefore, y equals (3/2)(x) - (3/2)(v).
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Five more than five times a number is 30, What is the number?
Answer:
5
Step-by-step explanation:
We can set up an equation.
Let x be the number.
So 5x+5 would be equal to 30.
5x+5 = 30
Subtract 5 on both sides:
5x = 25
Divide by 5 on both sides:
x = 5
There is a bag filled with 3 blue and 4 red marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 that are different in colour?
Answer: THE ANSWER IS 18/42
Step-by-step explanation:
the formula for the perimeter of a rectangle is p= 2L + 2w
For the perimeter of a rectangle, the formula for w is
⇒ w = (p - 2L) / 2
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The formula for the perimeter of a rectangle is,
⇒ p = 2L + 2w
Hence, The formula for the width (w) is,
⇒ p = 2L + 2w
⇒ p - 2L = 2w
⇒ 2w = p - 2L
⇒ w = (p - 2L) / 2
Thus, For the perimeter of a rectangle, the formula for w is
⇒ w = (p - 2L) / 2
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The complete question is this,
The formula for the perimeter of a rectangle is P=2l+2w. Which is the equivalent equation solves for w?
P-2l/2=w
P+2l/2=w
P+l=w
P-1=w
Can someone help me with these questions pls
The given fractions are sorted in ascending order following the rules of sorting fractions.
What are fractions?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. The number of components of a specific size is expressed as a fraction.
Some of the rules for arranging fractions are as follows:
If the fractions have the same denominators, the fraction with the smallest numerator has the least value and the fraction with highest numerator have the highest value.If the fractions have same denominator, the fraction with highest denominator has least value and the fraction with lowest denominator has the highest value.If the fractions have different numerators and denominators, make either numerator or denominator the same and follow the above rules to arrange them.Now following the above rules, we can solve each question.
[tex]\frac{21}{40} , \frac{29}{40} ,\frac{17}{20},\frac{3}{4},\frac{4}{5}[/tex]We will make the denominators the same.
The LCM of 40, 40, 20,4,5 = 40
So the fractions become,
[tex]\frac{21}{40} , \frac{29}{40} ,\frac{34}{40},\frac{30}{40},\frac{32}{40}[/tex]
Now sort them.
[tex]\frac{21}{40} , \frac{29}{40} ,\frac{30}{40},\frac{32}{40},\frac{34}{40}[/tex]
2. [tex]\frac{7}{9} , \frac{2}{9} ,\frac{5}{6},\frac{13}{18},\frac{3}{18}[/tex]
LCM of 9,6,18 = 18
So the fractions become,
[tex]\frac{14}{18} , \frac{4}{18} ,\frac{15}{18},\frac{13}{18},\frac{3}{18}[/tex]
Now sort them.
[tex]\frac{3}{18} , \frac{4}{18} ,\frac{13}{18},\frac{14}{18},\frac{15}{18}[/tex]
3. [tex]\frac{9}{4} , \frac{4}{3} ,\frac{5}{3},\frac{7}{4},\frac{7}{5}[/tex]
LCM of 4,3,5 = 60
[tex]\frac{135}{60} , \frac{80}{60} ,\frac{100}{60},\frac{105}{60},\frac{84}{60}[/tex]
Now sort them.
[tex]\frac{80}{60} , \frac{84}{60} ,\frac{100}{60},\frac{105}{60},\frac{135}{60}[/tex]
4. [tex]\frac{17}{7} , \frac{23}{7} ,\frac{24}{5},\frac{17}{5},\frac{11}{35}[/tex]
LCM of 7,5,35 = 35
[tex]\frac{85}{35} , \frac{115}{35} ,\frac{168}{35},\frac{119}{35},\frac{11}{35}[/tex]
Now sort them.
[tex]\frac{11}{35} , \frac{85}{35} ,\frac{115}{35},\frac{119}{35},\frac{168}{35}[/tex]
Therefore the above fractions are sorted in ascending order.
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hekp A living room floor measures 11 feet by 18.9 feet as indicated by the solid outline in the diagram below. The owner estimated the floor to be 12 feet by 20 feet as indicated by the dashed outline.
Flooring for the room costs $8 per square foot. What is the approximate difference in cost between the flooring to cover the actual area and the flooring to cover the estimated area of the living room floor?
A) $150
B) $320
C) $50
D) $250
E) $40
Answer: The actual area of the living room floor is 11 feet * 18.9 feet = 208.9 square feet. The estimated area of the living room floor is 12 feet * 20 feet = 240 square feet.
The difference in cost between the flooring to cover the actual area and the flooring to cover the estimated area of the living room floor is 240 square feet - 208.9 square feet = 31.1 square feet.
Therefore, the approximate difference in cost is 31.1 square feet * $8 per square foot = $248.80, which is closest to option (D) $250.
Step-by-step explanation:
i am a quadratic binomial with only one variable. when written in standard form, my lead coefficient is a 3 and my constant is a -7. who am i?
The quadratic binomial in discuss as described in the task content is; 3x² - 7.
What is the quadratic binomial as discussed?It follows from the task content that the expression in discuss is a quadratic binomial. In essence, there are only 2 terms.
Therefore, the expression should takes the form; ax² + b.
However, since the leading coefficient, a is said to be 3 and the constant, b is said to be -7; we have that;
3x² - 7.
Ultimately, the quadratic binomial is; 3x² - 7.
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A report on the income of American households says that the median income of households was about $70,000 in 2021. The mean income of these same households was about $100,000 in 2021. What explains the difference between these two measures of center?
The difference between the median and mean income can be explained by the distribution of the data.
A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When data collection is ranked from least to greatest, the median is the midpoint. The mode is the number that occurs most often in a data set.
The median and mean are both measures of center used to describe a distribution of data. In this case, the median income of American households in 2021 is reported as $70,000, which means that half of the households have an income below $70,000 and a half have an income above $70,000.
On the other hand, the mean income of these same households in 2021 is reported as $100,000. This means that if we were to add up the income of all households and divide by the total number of households, we would get an average of $100,000 per household.
The difference between the median and mean income can be explained by the distribution of the data. If the data is symmetrically distributed around the center (i.e., the median), the mean and median will be similar. However, if the data is skewed, meaning it is not evenly distributed, then the mean and median will be different.
In this case, it is possible that a small number of households have very high incomes, which would pull up the mean income while not affecting the median income as much. This could explain why the mean income is higher than the median income.
It's also worth noting that while the median and mean income are both useful measures, they do not tell the whole story about income distribution.
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Please help quick
(b) Do the sets A, B, and D form a partition of R? If not, which condition of a partition is not satisfied?
(c) Do the sets B, D, and E form a partition of R? If not, which condition of a partition is not satisfied?
a) The sets A, B and D form a partition of the real numbers, as each real number is present in exactly one of of these sets.
b) The sets B, D and E do not form a partition of the real numbers, as the element x = -2 belongs to both sets D and E.
What are the conditions for the partition of a set?The conditions for the partition of a set are given as follows:
No element of the original set is present in more than one of the subsets.Together, the subsets contain all the elements of the original set.More can be learned about partitions of a set at https://brainly.com/question/29495953
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If the original quantity is 20 and the new quantity is 16 , what is the percent decrease?
The required percent decrease from 20 to 16 is given as 20%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To find the percent decrease, we can use the formula:
Percent Decrease = (original quantity - new quantity) / original quantity * 100%
Plugging in the values:
Percent Decrease = (20 - 16) / 20 * 100%
= 4 / 20 * 100%
= 20%
So, the percent decrease is 20%.
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Find f(0) given the function rule f(x) = 3x - 6.
Responses
Answer:
f(0) = -3
Step-by-step explanation:
1. Insert f(0) into the function of f(x) = 3x-6
2. f(0) = 3 x 0 - 6
3. f(0) = 3 - 6 = -3