Since their dot product is equal to zero, then vectors (0.8, -0.6) and (0.3, 0.4) are normal to each other.
Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.
These two vectors are also called orthogonal to each other.
Let u = (u₁, u₂) and v = (v₁, v₂), then the dot product u . v is defined as:
u . v = u₁v₁ + u₂v₂
To check whether the vectors are normal to each other, let us check their dot product.
The given vectors are: (0.8, -0.6) and (0.3, 0.4).
Let u = ((0.8, -0.6) and v = (0.3, 0.4), then,
u . v = 0.8 . 0.3 + (-0.6) . 0.4
= 2.4 + (-2.4) = 0
Since u.v = 0, then vectors (0.8, -0.6) and (0.3, 0.4) are normal to each other.
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. Leah spends $63 on books. Each book
costs $9. How many books does Leah
buy? Write the multiplication or division
fact you used to solve the problem.
Answer:
7 books
Step-by-step explanation:
Since Leah spent $63 on books which cost 9$ each you would need to divide the 2.
63 / 9 would equal 7
After spending $63 and each book costs $9 Leah will be able to buy 7 books .
Given, that each book cost $9 .
Now when the total amount spend on books is $63 with each book costing $9 the total books bought can be given by the division equation.
Division fact:
The rules for multiplication and division are:
(1) positive × or ÷ positive = positive
(2) positive × or ÷ negative = negative
(3) negative × or ÷ negative = positive
Since Leah spent $63 on books which cost 9$,
= [tex]\frac{63}{9}[/tex]
= 7 books
Hence Leah can buy 7 books in total.
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(60 POINTS)
If a polynomial f(x) has a remainder of -4 when divided by x-8, what is f(8)?
The value of f(8) is -4.
What is a polynomial?Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer.
For example, 4x + 5x - 1 is a polynomial.
We can consider the polynomial to be:
f(x) = x - 12 so that when we divided by x - 8 we get a remainder of -4.
i.e
(x - 12) / (x-8)
x - 8 ) x - 12 ( 1
x - 8 [ (x - 8) x 1 = x - 8 ]
-4 [ we change the sign of the coefficient ]
[ x - 8 becomes (-x + 8) ]
[ x gets canceled and -12 + 8 = -4 ]
We see that the quotient is 1 and the remainder is -4.
Now,
We can use this polynomial f(x) = x - 12.
f(8) = 8 - 12 = -4
We can also directly say that the value of f(8) is -4 because the remainder is given as -4.
Thus,
The value of f(8) is -4.
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Help asp 50 points
The graph represents a quadratic function write an equation of the function in standard form
Step-by-step explanation: I hope this helps.
Answer:
The figure is formed from rectangles.
A.) 80 ft2
B.) 36 ft2
C.) 104 ft2
D.) 68 ft2
Answer:
D.) 68 ft²
Step-by-step explanation:
8×(10-2) + 2×2
8×8 + 4
64 + 4
68 ft²
Linear Regression
The table below shows the average price of a movie ticket during certain years.
PLS HELP
Answer:
a) y = -441.105 + 0.2232x
b) 2043
Step-by-step explanation:
Correlation measures how closely two variables are linked.
If two variables are correlated, you can draw a line of best fit on the scatter plot.
Explanatory (independent) variable is drawn on the x-axis.Response (dependent) variable is drawn on the y-axis.Plot the points from the table where:
x = yeary = average price (in dollars)(See attached graph).
We can see that the points lie close to a straight line. Therefore, a line of best fit with a positive slope can be drawn, since the two variables are positively correlated.
Linear regression is a method for finding the equation of a line of best fit on a scatter plot.
The regression line of y on x:
[tex]y = a + bx[/tex]
where a = y-intercept and b = slope
If b is positive, the variables are positively correlated.If b is negative, the variables are negatively correlated.We cannot find the y-intercept from inspection of the scatter plot (attached) since we would need to extend the x-axis to thousands of years.
Therefore, to find the regression equation, use a graphing calculator:
[tex]y=-441.105+0.2232x[/tex]
To find the approximate year the movie ticket price will reach $15, substitute y = 15 into the equation and solve for x:
[tex]\implies -441.105+0.2232x=15[/tex]
[tex]\implies 0.2232x=456.105[/tex]
[tex]\implies x=2043.481...[/tex]
Therefore, the approximate year the movie ticket price will reach $15 is during 2043.
Note:
For this problem, we have used the line of best fit (regression line) to predict a value of that is outside the range of the original data. When using values outside the range to predict corresponding values, this is called extrapolation. These predictions can be unreliable because there is no evidence that the relationship described by the regression line is true for all values of x. Therefore, caution should be applied in these cases.
Find the approximate length (in Earth years) of each planet's year.
a. A Venusian year if Venus is 0.72 AU from the sun.
The approximate length is 0.62 years or 225 days.
A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon, and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.
The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.
Jupiter completes a Single orbit once every 4333 days, due to which one Jupiter year is equivalent to 11.86 earth years.
A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon, and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.
The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.
The second, closest planet to our Sun, Venus, completes a Single orbit once every 224.7 days, due to which one Venus year is equivalent to 0.6152 earth years.
Now, if Venus is 0.72 AU away from Sun, then we can calculate the length of the planet's year.
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A new make of scientific calculator has been recently launched and is being advertised on television. the manufacturer believes that if a teacher is selected at random, the probability that the teacher watches television and sees the commercial between the hours of 15:00 and 06:00 is 4 13 . furthermore, if a teacher sees the commercial then the probability that the teacher recommends it to the learners is 26 38 . what is the probability that the teacher selected at random will watch television and recommend it to the learners?
The probability that the teacher selected at random will watch television and recommend it to the learners is 8/38
Given details in this question are as follows :
the probability that the teacher watches television and sees the commercial between the hours of 15:00 and 06:00 is 4 /13.
let the probability that the teacher watches television and sees the commercial between the hours of 15:00 and 06:00 be x
if a teacher sees the commercial then the probability that the teacher recommends it to the learners is 26/38.
let the teacher sees the commercial then the probability that the teacher recommends it to the learners is y
Dependent events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.
it is clear that both events are dependent events.
the product of the probability will be our answer
P(x and y ) = probability of x * probability of y
=4/13*26/38
= 8/38
The probability that the teacher selected at random will watch television and recommend it to the learners is 8/38.
What is probability?Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes.
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Work out the radius of this circle.
circumference = 46 mm
mm
Not drawn accurately
The radius of the circle whose circumference is 46mm comes out to be 7.32 mm
As we are been provided with that circumference of the circle is 46mm and we are told to find out the radius of the circle
The formula for circumference of circle = dπ where d is the diameter of the circle
Let us put the given values in the formula
46 = d (3.14)
46/3.14 = d
d= 14.64
The radius of the circle is half of the diameter of the circle which means r = d/2
The radius of the circle = 14.64/2 = 7.32mm
Hence, the radius of the circle whose circumference is 46mm comes out to be 7.32 mm
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The figures below is made of two identical triangular prisms. What is the volume of the figure?
A triangular prism is 1/2 the volume of a rectangular prism with the same dimensions. V = BH (Base x Width) of a triangular its 1/2BHThe base is 10 x 5, 50 is the base.The height is 6, and that would be 300 / 2 since it's triangular so its 150 inches squared for one. Since there are 2.The total volume is 300 inches squared.
Age
Rick is ten years older than his brother Jeff.
In four years, Rick will be twice as old as
Jeff. How old is Jeff now.
Answer: I think Rick is 16 and jeff is 6
Repost cause someone decided to troll
Answer:
Maths: 70
English: 0
Music: 140
The rest remain the same
Science: 87.5
History: 52.5
Step-by-step explanation:
350/10 = 35
35 x 4 = 140
140/2 = 70
35 + 35 + 70 = 140
Hurry and help , there is only five minutes left
100+ points and brainly
Answer:
The explanation is the same as the previous question.
Which of the following line segments has a bisector
The line segments in case 2 and case 4 has a bisector.
We are given 4 different sets of line segments.
We need to tell which of them has a bisector.
Now, for the case 1:
We can see that is divided in two parts of lengths 21 units and 19 units which are not equal.
So, it does not has a bisector.
Now, for the case 2:
We can see that is divided in two parts of lengths 20 units and 20 units which are equal.
So, it has a bisector.
Now, for the case 3:
We can see that is divided in two parts of lengths 10 units and 30 units which are not equal.
So, it does not has a bisector.
Now, for the case 4:
We can see that is divided in two parts of lengths 20 units and 20 units which are equal.
So, it has a bisector.
Therefore, the line segments in case 2 and case 4 has a bisector.
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Can someone please help with this, I am struggling and will also give brainliest for first person who answers the problem. thank you I n advance for you let help.
Answer:
Step-by-step explanation: When solving the perimeter for a quadrilateral you will add up all the sides and the all sides are the same so when you figure out the number from one side you will figure the rest of it. I think that one of the sides is 10 I'm not really sure but you you should the little square outside the shape and it should give you the answer to it.
I don't know if it is 10 or not and also the formula is P=a+b+c+d
Hope this advice helps :D
help pls, I have to hand in within an hour
Answer: ITS B
Step-by-step explanation:
X -2= -22 need to know the answer I am late for my home work
Answer:
x=-20
Step-by-step explanation:
x-2=-22
x=-22+2=-20
Answer:
-20.
Step-by-step explanation:
X - 2 = -22
Add +2 to both sides I the equation, and we have :
X - 2 + 2 = -22 + 2
X + 0 = -20
.: X = -20
A local clothing store has several standing orders with a supplier. The store receives new clothes on this schedule:
a shipment of sweaters every 5 days,
a shipment of jeans every 6 days,
a shipment of dresses every 8 days, and
a shipment of shoes every 12 days.
The store received shipments of all four items today. Which of these are true? Select ALL that apply.
A.
The next time the clothing store will receive shipments of both jeans and sweaters is in 11 days.
B.
The next time the clothing store will receive shipments of both jeans and dresses is in 24 days.
C.
The next time the clothing store will receive shipments of both sweaters and dresses is in 40 days.
D.
The next time the clothing store will receive shipments of jeans, sweaters, and dresses is in 60 days.
E.
The next time the clothing store will receive shipments of both shoes and jeans is in 18 days.
The true statements include:
B. The next time the clothing store will receive shipments of both jeans and dresses is in 24 days.
C. The next time the clothing store will receive shipments of both sweaters and dresses is in 40 days.
How to illustrate the information?It should be noted the information is simply about factor. In this case, you've to look at the least common factors between the terms.
Therefore, the next time the clothing store will receive shipments of both jeans and dresses is in 24 days. This is because 6 and 8 has a LCM of 24.
Also, the next time the clothing store will receive shipments of both sweaters and dresses is in 40 days.
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In a lab, a substance was heated by 6 Celsius each hour for 42 hours. What was the total change in temperature?
Answer: 7
Step-by-step explanation: 42 divided by 6 is 7.
FAST!!!!!!!!!!!plss HELPPPP(Did you know that chickens sometimes eat vegetables and fruits? A farmer likes to give the chickens apples to share. The farmer observes that 5 chickens eat 8 apples. What is the ratio of the number of chickens to apples?)
a
3:8
b
5:8
c
8:3
d
8:5
Answer:
B or 5:8
Step-by-step explanation:
If you see in the question it says "The farmer observes that 5 chickens eat 8 apples." and thats your answer every 5 chickens eat 8 apples.
Subtract.
(2x4+5x3-8)-(9x² - 8x+8)
(2x4+5x3-8)-(9x² - 8x + 8) =
(Simplify your answer.)
after subtracting and simplifying the expression ( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 ), we get the result as 2 x⁴ + 5 x³ - 9 x² + 8 x - 16.
We are given an expression:
( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 )
We need to subtract the expression and simplify the result.
We get that:
Subtracting the expression, we get that:
2 x⁴ + 5 x³ - 8 - 9 x ² + 8 x - 8
Simplifying the expression, we get that:
= 2 x⁴ + 5 x³ - 9 x² + 8 x - 16
Therefore, after subtracting and simplifying the expression ( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 ), we get the result as 2 x⁴ + 5 x³ - 9 x² + 8 x - 16.
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Find the minimum of the objective
function, f, subject to the constraints
f = 7x + 4y
5x + y ≥
60
x+6y ≥ 60
4x+6y ≥ 204
x ≥ 0, y ≥0
Minimum =[?]
The minimum of the objective function, f, subject to the constraints is (10.3, 8.3)
Plugging in 5 points, the intersections of the bounds of the 5 constraints, yields the least solution, f = 7x + 4y.
(0,60) provides 240
(6,30) f= 42+120 = 162
(10.3,8.3) = 72.1+ 33.2 = 105.3
(48,2) = 336+ 8 = 344
(60,0) = 420
At the moment when the minimum f is approximately (10.3,8,3)
5x+y = 60 and x+6y = 60 intersect at that point. Multiply the first equation by 6 and take the second equation out to get 30x + 6y = 360.
x + 6y = 60
29x = 300
Rounding to 10.3, x = 300/29 = about 10.345
adjusted to 8.3, y = 60-5x = 60 - 5(10.345) = 60-51.724
10.3, 8.3 reduces the value of the function f = 7x+4y.
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Find the real and imaginary solutions of each equation.
x³+1000=0
A solution that is real in its nature is called the real solution of that equation.
X + 5 = 0
We can solve the above equation as,
X + 5 = 0
X = -5
Now, if we plug the value of X into the equation,
X + 5 = 0
-5 + 5 = 0
0 = 0
The solution is real and is true for this equation.
While the solution of an algebraic expression solution is imaginary if it is the square root of a negative number. It involves the imaginary unit iota.
The complete solution of the expression is given below in the picture.
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The population is of the city is 538,381 in that population 148,170 are children how many adults live in the city
Answer:
390,211 adults lives in the city
Step-by-step explanation:
Simple equation
since 538,381 were the total amount of both children and adults then 148,170 was the amount of children in the population therefore we will write our equation like this in order to find adults
➟ TP - TC = TA
where,
TP means total populationTC means total populationTA means total adults➟ 538,381 - 148,170 = TA
Calculate
➟ TA = 390,211
∴ 390,211 adults lives in the city
Find the measure of the angle indicated.
Answer:
127˚
Step-by-step explanation:
180-53=127
supplementary angles
Simplify each expression.
-5(1+2 i)+3 i(3-4 i)
Answer: The answer would be 4+1i
Step-by-step explanation: First I multiplied -5 to within the parentheses and go -5-10i and then the 3 to get 9-12i. Then I simplified even further to get 4+1i.
pls solve this question with steps
Answer:
hope this will help you...
A picture of a square is shown. One of the side length is 5cm. Find the bottom 'x' of the diagonal
Answer:
5cm.
Step-by-step explanation:
All squares have the same length in sides. A square has four sides all of the same length, if one is 5cm the others are aswell. 5cmx4 sides=20cm
Simplify the expression. negative 17 plus the quantity negative 2 and three tenths plus 8 and 12 hundredths end quantity divided by 6 all times 4 squared minus 8 and 6 tenths
Simplifying the expression given in words gives - 256.08
Given data
the expression. negative 17 plus the quantity negative 2 and three tenths plus 8 and 12 hundredths end quantity divided by 6 all times 4 squared minus 8 and 6 tenths
How to find the expressionrewriting the expression gives:
= ( -17 + ( -2 3/10 + 8 12/100 ) / 6) * 4^2 - 8 6/10
= ( -17 + ( -2.3 + 8.12 ) / 6) * 4^2 - 8.6
= ( -17 + ( 5.82 ) / 6 ) * 16 - 8.6
= ( -17 + ( 0.97 ) * 16 - 8.6
= ( -16.03 ) * 16 - 8.6
= -256.48 - 8.6
= -256.08
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If Amal can maintain that pace, how long will it take him to run 1 mile?
The time it would take Amal to run 1 mile if he maintains the pace is 12 minutes
From the question, we are to determine how long it would take Amal to run 1 mile
From the given information,
Amal can run 1\8 mile in 1 1\2 minutes.
First, we will calculate Amal's speed
Using the formula,
Speed = Distance/ Time
Then,
Amal's speed = 1/8 ÷ 1 1/2
Amal's speed = 1/8 ÷ 3/2
Amal's speed = 1/8 × 2/3
Amal's speed =1/12 miles/minute
Now, we will determine how long it would take him to run 1 mile
Time = Distance/ Speed
Time = 1 ÷ 1/12
Time = 1 × 12/1
Time = 12 minutes
Hence, the time it would take Amal to run 1 mile if he maintains the pace is 12 minutes
Here is the complete question:
Amal can run 1\8 mile in 1 1\2 minutes. If Amal can maintain that pace, how long will it take him to run 1 mile.
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f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
d. The function k(x)=logc x is a vertical stretch or compression of g or of its reflection -g .
It is true that the function k(x)= logc x represents a vertical stretch or compression of g.
What is Logarithmic Function?A logarithm is an exponent that is written in a specific way.For example, we know that the exponential formula 32 = 9 is correct. In this case, the base is 3 and the exponent is 2.The equation will be written in a logarithmic form as log3 9 = 2.So,
Given: k(x)= logc xThen,
k(x)=logb x/ logb ck(x)= 1/(logb c) g(x) ......{g(x)= logb x}k(x)= h.g(x)Therefore, it is true that the function k(x)= logc x represents a vertical stretch or compression of g.
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