(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13) are two vectors of norm 1 that are perpendicular to A = (3 , 2) .
What is perpendicular vectors ?In Cartesian coordinates, the given vector can be represented by the line y = -2x/3. The vector is the line segment that connects (0,0) and (3,-2).y = 3x/2 can be used to represent the normal.
If the vector is represented by a line connecting (0,0) to a point (p,q), then,p2 + q2 = 1 because the normal is one length, and q = 3p/2.
As a result,p² + 9p²/4 = 1, 13p²/4 = 1, p = ±√(4/13) = ±2/√13, q = ±3/√13.
After rationalization, one normal vector is (2√13/13 , 3√13/13) and the other is (-2√13/13 , -3√13/13).The two vectors of norm 1 perpendicular to A = (3 , 2) is :
(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13).
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Evaluation the expression -19-9-(11)
Then the final answer will be -17.
A medical experiment on tumor growth gives the following data table.
x y
61 48
95 76
97 82
101 95
115 118
The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 2640.8 and the sum of squares of regression (SSR) was 2429.8. Calculate R2, rounded to three decimal places.
Provide your answer below:
The calculation of the coefficient of determination, or R² rounded to three decimal places is 0.080.
What is the coefficient of determination (R²)?The coefficient of determination, R², is a statistical measurement that determines the proportion of variance in the dependent variable that the independent variable can explain.
In other words, R² shows how well the actual data is approximated by the regression line.
R-Squared (R²) is widely used to predict future outcomes and for hypothesis testing because it provides information about the goodness of fit of the statistical model.
x y
61 48
95 76
97 82
101 95
115 118
The total sum of squares (SST) = 2640.8
The sum of squares of regression (SSR) = 2429.8
R² = 1 - SSR/SST
R² = 1 - 2429.8/2640.8
R² = 1 - 0.92
R² = 0.080
R² = 8%
Thus, with R² = 8%, we can conclude that the y values are only accountable for 8% of the variation in x.
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A rectangle has an area ofx² + 9x + 14Find the expressions that represent the dimensions of the rectangle.O (x - 2) and (x - 7)O (x + 3) and (x + 6)(x + 2) and (x + 7)O (x + 1) and (x + 14)
x² + 9x + 14
The area of a rectangle is the product of the length and the width.
Factorizing the expression
x² + 9x + 14 = x² + 7x + 2x + 14
= x(x + 7) + 2(x + 7)
= (x + 7)(x + 2)
Hence the dimensions are (x + 2) and (x + 7)
Please help with this
Answer:
228
Step-by-step explanation:
Top 6x 6 = 36
4 sides 4(6x8)
4(48)
192
192 + 36 = 228
Answer:264
Step-by-step explanation: the surface area is every side added together and you calculate each side by multiplying the width height and length
Show that (3 * 8 * x)⁷ = 6⁷ * 4⁷ * x⁷
Answer:
Q.E.D.
Explanation:
Given the expression
[tex](3\times8\times x)^7[/tex]We want to show that it is equal to the right-hand side.
Now, we note that: 8 = 2 x 4
Substituting 8 = 2 x 4, we have:
[tex]=(3\times2\times4\times x)^7[/tex]We then go further to get:
[tex]=(6\times4\times x)^7[/tex]Distributing the exponent, we have:
[tex]=6^7\times4^7\times x^7[/tex]This is the given right-hand side of the equation as required.
Beginning in 1995,( 1995= 0 years) the Chicago Cubs decreased its ticket price by a constant amount each year until 2016 when they finally won the World Series. A ticket cost $77.50 in 2005, but only $49.50 in 2012. How much did a ticket cost in 2000?
The cost of the Chicago Cubs ticket in the year 2000 was $97.50.
What is defined as the constant rate of change?A rate of change is defined as the ratio of change in dependent values as well as outputs to change in independent variables or inputs. The change, also known as the function's slope, describes what numbers change between 2 points on the a coordinate plane.For the given question.
The price of the Chicago Cubs ticket in year 2005 is $77.50.
The price of the ticket reduced in year 2012 as $49.50.
There is a constant amount of decrease in the price.
Thus, difference in years;
= 2012 - 2005
= 7 years.
Difference in amount;
= 49.50 - 77.50
= -28
Price decreased in one year = 28/ 7 = -4 per year.
For the price of the ticket in the years 2000.
= 2005 - 2000
= 5 years.
Price decreased in 5 years is;
= -4 x 5
= -20
The price is 2000 is 77.50 + 20 = 97.50
Thus, the cost of the Chicago Cubs ticket in the year 2000 was $97.50.
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Painter charges $20 every hour that he paints let H represent the number of hours he paints & E represent his earnings select all statements that are trueA. The equation H equals 20 E shows the correct relationship between the earnings and hours worked B. With this hourly rate the painter must work more than 12 hours to earn 500C. With this hourly rate the painter earns 20h dollars for each hour worked.D. With this hourly rate if the painter works 10 hours he earns 20.E. Is the painter raises his hourly rate by two dollars the new equation is e=22h
Answer:
No.
Yes.
Yes.
No.
Yes...
How do you solve this?
Answer: B
Step-by-step explanation:
Answer: The answer is B
Step-by-step explanation:
Company operates stores under multiple banners in 13 states in the United States
Given:
Banners in 13 states in united states:
Total states in united state is 50.
(A)
Do not have store is:
[tex]\begin{gathered} =50-13 \\ =37 \end{gathered}[/tex]So in 37 states Company not operates any store.
(B)
Fraction do not have a store operates :
[tex]\begin{gathered} =\frac{37}{50} \\ =0.75 \end{gathered}[/tex]HELP HELP! PLEASE, MY MOM WANT ME TO BE DONE!
From least to greatest, we have:
2 to 3, 3:4, and 7/8
Explanation:Given the following:
7/8, 2 to 3, and 3:4
The least is 2 to 3, followed by 3:4, then 7/8
For each value of v, determine whether it is a solution to -96= -8(v +7)
Check off all of the equations that would give infinitely many solution
All of the equations that would give infinitely many solutions are given as follows:
[tex]\begin{gathered} 1)\text{ 3x + 12 = 3x + 12} \\ 2)\text{ 2\lparen3x - 4\rparen = 6x - 8} \end{gathered}[/tex]Thus the correct answer is option 3 and option 5.
Simplify the given expression into the form a+bi, where a and b are rational numbers?
Given:
2(-36- 3i )+ (5+2i)(12-2i)
Open the parenthesis
2(-36- 3i) + 5( 12 - 2i) + 2i ( 12 - 2i)
- 72 - 6i + 60 - 10i + 24i + 4 ( Note: i² = -1)
Re-arrange
-72+60 + 4 - 6i - 10i + 24i
= -8 + 8i
a can of juice is 5.5 inches high and its base has a diameter or 6 inches what is the volume of the can? round to the nearest hundredth
According to the problem, the can of juice has the form of a cylinder, so we have to use the following formula
[tex]V=\pi(r)^2h[/tex]Where the radius is half the diameter, r = 3 in, h = 5.5 in, and pi = 3.14. Replacing these values, we have
[tex]V=3.14\cdot(3in)^2\cdot5.5in=155.43in^3[/tex]Hence, the volume of the can is 155.43 cubic inches.Geometry ? What is the coordinate of G if triangle E’F’G’ is created by dilating EFG with a scale factor of 4 about the origin
In order to dilate the figure around the origin by a scale of 4, we need to multiply the coordinates of each point by 4. This is done below:
[tex]\begin{gathered} F^{\prime}=(4\cdot-1,4\cdot2)=(-4,8) \\ G^{\prime}=(4\cdot2,4\cdot-2)=(8,-8) \\ E^{\prime}^{}=(4\cdot-2,,4\cdot0)=(-8,0) \end{gathered}[/tex]The coordinates are: F'(-4, 8), G'(8,-8) and E'(-8,0).
Find the length of line segment MN. Round to the nearest hundredths place.
First, look th the graph and set the coordinate of the points:
M = (mx,my)= (-1,2)
N = (nx,ny)= (4,0)
Now, apply the distance formula:
[tex]\text{Distance =}\sqrt[]{(mx-nx)^2+(my-ny)^2}[/tex]Replace with the coordinates:
[tex]D\text{ =}\sqrt[]{(-1-4)^2+(2-0)^2}[/tex][tex]D=\sqrt[]{(-5)^2+2^2}=\sqrt[]{25+4}=\sqrt[]{29}\text{ =5.3}9[/tex]Distance: 5.39
A bag of marbles contains 6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble. What is the
probability of reaching into the bag and selecting a yellow marble?
73.
13
16
26
Answer:
2/13
Step-by-step explanation:
Out of a total 13 marbles , 2 are yellow 2 out of 13 = 2/13
Answer:
2/13
Step-by-step explanation:
6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble = 13 marbles
P( yellow) = number yellow / total
= 2/13
In a music class of 20 students, there are 12 who play the Guitar (G), 7 who play the Piano (P) and 4 who do not play any of these instruments.1)Represent this situation using a Venn diagram2)What is the probability no randomly selected student plays guitar and piano3)What is the probability that no randomly selected student plays either of these two instruments?4) How likely is it that no randomly selected student plays the piano
GIVEN:
Total number of students: 20
Number that plays the Guitar: 12
Number that plays the Piano: 7
Number that does not play any of the instruments: 4
Note that included in the number that plays either the guitar and the piano is the number that plays both instruments. Let's call this number x.
Number that play both instruments: To calculate this number, we have to get the number that plays each instrument alone and find the sum equated to the total number of students.
Number that plays the Guitar only: 12 - x
Number that plays the Piano only: 7 - x
Therefore, the total number of students will be:
[tex]\begin{gathered} 12-x+7-x+x+4=20 \\ 23-x=20 \\ \therefore \\ x=23-20 \\ x=3 \end{gathered}[/tex]Hence, there are 3 students that play both instruments.
Therefore, 9 students play the guitar only and 4 students play the piano only.
VENN DIAGRAM:
QUESTION 2:
The formula to calculate the probability of an event E is given to be:
[tex]P(E)=\frac{n(E)}{n(U)}[/tex]where
[tex]\begin{gathered} P(E)=\text{ Probability of event E happening} \\ n(E)=\text{ Number of times event E happened} \\ n(U)=\text{ Number of times all possible events occured} \end{gathered}[/tex]The number of students that play the guitar and piano is 3. This means that the number that does not play the guitar and piano is
[tex]\Rightarrow20-3=17\text{ students}[/tex]Therefore, the probability is given to be:
[tex]P=\frac{17}{20}[/tex]QUESTION 3:
This question requires us to find the probability of students that do not play any of the two instruments. This number is 4.
Therefore, the probability is given to be:
[tex]P=\frac{4}{20}=\frac{1}{5}[/tex]QUESTION 4:
The number of students that play the piano is 7. Hence, the number that doesn't play the piano will be:
[tex]\Rightarrow20-7=13[/tex]Therefore, the probability is:
[tex]P=\frac{13}{20}[/tex]Write an equation for the line through the point (x0,y0) with a slope of M in point slope form. Enter X0 and Y0 as y0. Use X and Y for variables names. Your equation should be of the form y=….
The equation of the line in point slope form is y = M(x - x₀) + y₀ .
The Point slope form of the line passing through the point (x₁,y₁) with slope m is given by the formula
(y - y₁) = m(x - x₁)
In the question ,
it is given that
the required line passes through the points (x₀ , y₀)
and the slope is M .
So, the point slope form equation of the line will be
( y - y₀) = M(x - x₀)
y - y₀ = M(x - x₀)
y = M(x - x₀) + y₀
Therefore , the equation of the line in point slope form is y = M(x - x₀) + y₀ .
The given question is incomplete , the complete question is
Write an equation for the line through the point (x₀,y₀) with a slope of M in point slope form. Your equation should be in the form of y = ... ?
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which question is best modeled with a division expression?
how many 3/8's are in 48
what is 3/8 of 48
what is the total of 3/8 and 48
how much more than 3/8 is 48
The question that can be best modeled as a division expression is how many 3/8's are in 48.
What is division?Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The other mathematical operations are addition, multiplication and division.
In order to determine the 3/8's in 48, divide 48 by 3/8.
In order to determine 3/8 of 48, multiply 48 by 3/8.
In order to determine the total of 3/8 and 48, add the numbers together.
In order to determine how much more than 3/8 is 48, subtract 3/8 from 48.
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Write a quadratic equationwith vertex (3,-6) and otherpoint (-7,14). Solve for a!
We have to find the parameter a of a quadratic equation knowing the following
• The vertex is (3,-6).
,• A random point is (-7,14).
Based on the given information, we have the following
[tex]\begin{gathered} h=3 \\ k=-6 \\ x=-7 \\ y=14 \end{gathered}[/tex]The vertex form of a quadratic equation is
[tex]y=a(x-h)^2+k[/tex]Replacing all the givens, we have
[tex]14=a(-7-3)^2-6[/tex]Now, we solve for a
[tex]\begin{gathered} 14=a(-10)^2-6 \\ 14=a(100)-6 \\ 14+6=100a \\ 100a=20 \\ a=\frac{20}{100}=\frac{1}{5} \end{gathered}[/tex]Therefore, a is equal to 1/5.I need help with this question! I tried to work the question out but the answer I got is not an answer choice.
Given:
The given expression is
[tex]2\times72-3\times8+6\times5+4[/tex]Required:
We have to find the value of the given expression.
Explanation:
[tex]\begin{gathered} 2\times72-3\times8+6\times5+4 \\ =144-24+30+4 \end{gathered}[/tex][tex]\begin{gathered} =120+30+4 \\ =150+4 \end{gathered}[/tex][tex]=154[/tex]Final answer:
Hence the final answer is
Which relation is a function? choose all the correct answers.[1] (1, 0), (3, 0), (1, 1), (3, 1) (1, 3) [2] (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)[3] (2, 7), (6, 5), (4, 4), (3, 3), (2, 1)[4] (9, −3), (9, 3), (4, −2), (4, 2), (0, 0)
A relation is a function if an input value has only one output value. This means that a value of x must have only one value of y. Looking at the options,
1) for x = 1, there are different values of y. They include y = 0, 1, 3
for x = 3, y = 0, 1
This means that it is not a function
2) No value of x has more than one value of y. Thus, no input has more than one output. This means that it is a function
3) for x = 2, there are different values of y. They include y = 7, 1
This means that it is not a function
4) for x = 9, there are different values of y. They include y = - 3, 3
for x = 2, there are different values of y. They include y = - 2, 2
This means that it is not a function
Thus, the correct option is
[2] (1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
express the quadratic function f(x)=3x^2 + 6x - 2 in the form a(x + h)^2 + k where a,h and k are constants
Answer:
Explanation:
Given:
[tex]f(x)=3x^2+6x-2[/tex]First, we do completing the square on the given function to express it into vertex form. So,
We write it in the form:
[tex]\begin{gathered} x^2+2ax+a^2 \\ \end{gathered}[/tex]And, factor out 3: So,
[tex]\begin{gathered} 3(x^2+2x-\frac{2}{3}) \\ \text{where:} \\ 2a=2\text{ or a=1} \\ \text{Hence} \\ 3(x^2-2x-\frac{2}{3}+1^2-1^2) \end{gathered}[/tex]Since:
[tex]\begin{gathered} x^2+2ax+a^2=(x+a)^2 \\ So, \\ x^2+2x+1^2=(x+1)^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3(x^2-2x-\frac{2}{3}+1^2-1^2) \\ =3((x+1)^2-\frac{2}{3}-1^2) \\ \text{Simplify} \\ f(x)=3(x+1)^2-2-3 \\ f(x)=3(x+1)^2-5 \end{gathered}[/tex]Therefore, the answer is:
[tex]f(x)=3(x+1)^2-5[/tex]in the figure below, when the sun angle of elevation is 50°, the tree casts a shadow 80 feet long which can be used to find the height of the tree?
We can use the tangent of 50º. The height is approximately 95.34 ft
1) We can trace a right triangle over that mark and calculate that height, using a trigonometric ratio.
2) As we have the adjacent leg to that 50º angle and the opposite leg, we can use the tangent of 50º to find that height out.
[tex]\begin{gathered} \tan (50)=\frac{x}{80} \\ x=80\cdot\tan (50) \\ x\approx\text{ 95.34} \end{gathered}[/tex]3) Hence the answer is
We can use the tangent of 50º. The height is approximately 95.34 ft
Real estate prices in a Denver neighborhood areNormally distributed with a mean price of $187,500 and astandard deviation of $12,500.ALDenver Neighborhood Real Estate Pricing
First, find the z-score of the two values $150,000 and $225,000
[tex]\begin{gathered} \text{z-score for }x_1 \\ z=\frac{x-\mu}{\sigma} \\ z=\frac{150000-187500}{12500} \\ z=\frac{-37500}{12500} \\ z_1=-3 \\ \; \\ \text{z-score for }x_2 \\ z=\frac{x-\mu}{\sigma} \\ z=\frac{225000-187500}{12500} \\ z=\frac{37500}{12500} \\ z_2=3 \end{gathered}[/tex]Since the z-scores are both 3 standard deviations away from the mean, by Emperical rule, we conclude that about 99.7% of the homes will be priced between $150,000 and $225,000.
3.615 x 4 regrouping
I need help with my homework pls be fast it’s 11pm for me and I couldn’t do this earlier because of family business
We have a linear function and we have to find the meaning of the slope.
The function is:
[tex]C=50h+35[/tex]In this function the slope is m=50, as it is the coefficient for h, the number of hours.
The slope usually represents the variation of the result variable (in this case, the cost in dollars) and the independent variable (in this case, h, the number of hours).
Then, we can think of the slope in this model as the marginal hourly rate he charges. This means that any additional hour of work will cost $50 more.
Then, from the options given, the correct one is: the charge per hour [Option D].
You start driving north for 5 miles, turn right, and drive east for another 12 miles. At the end of driving, what is your straight line dissonance from you r starting point?
You start driving north for 5 miles, turn right, and drive east for another 12 miles
The angle between north and east = 90
So, x is the hypotenuse of the triangle
[tex]x=\sqrt[]{5^2+12^2}=\sqrt[]{25+144}=\sqrt[]{169}=13[/tex]so, the length = 13 miles
Car Survey In a survey of 3,100 people who owned a certain type of car, 1,550 said they would buy that type of car again.
What percent of the people surveyed were satisfied with the car?
% of the people surveyed were satisfied with the car.
(Type a whole number.)
The percentage of people satisfied with car is 50.
What is percentage?
A number or ratio which can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it. There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of something, we mean that it is 50% of everything. As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any subject have been calculated in terms of percentages in academics. Ram, for instance, scored 78% on his exam.
To find the percentage We divide 1550 by 3100 and then multiply by 100
We get
[tex]\frac{1550}{3100}*100\\=50[/tex]
Hence the percentage of people satisfied with the car is 50%
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