Using Dot product
Two vectors x and y are said to be orthogonal if their dot product is zero
⇒ x.y = 0
This is because orthogonal vectors are make an angle of 90° with each other and therefore θ becomes 90°
Dot product is given by :
x.y = x*y*cosθ = xycos90°
∵cos90° is zero , x.y=0 for orthogonal vectors.
Let u,v,y be vectors in R
y is orthogonal to u and v
⇒ y.u = 0 and y.v=0
Now, we have to prove that y is orthogonal to (u+v)
The dot product of these vectors is given by:
y.(u+v) = y.u + y.v (Dot product is distributive) = 0 + 0 = 0
∵The dot product is zero , vector y and (u+v) are orthogonal
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there are twenty four hours in a day. jack worked for two-fourths of the day. how much time will jack spend working?
Answer: 12 hours
Step-by-step explanation: divided 24 by 4, which equals to 6, if Jack worked 2/4 of the day, he would have worked half the day, which is 12 hours.
ANSWER PLS AND FAST MY BROTHER NEED THE HELP
Answer:
$ 124,918
Step-by-step explanation:
Plus all of them toghether.
Also: I got yo back
Answer:
124,909
Step-by-step explanation:
Add them up.
38,219 + 57,623 + 29,067 = 12,909
graph the line y=-1/3+3
HELP NEED ANSWERS ASAP!''!!!!!!!!!!!!!!!
By using subtraction, Brenda needs an additional amount of $ 182.75 for the school trip.
How much money does Brenda need to save for her school trip?
In this question we notice that Brenda is aware of how much money she needs to make her school trip and besides we find a table with all the money saved during a 4-month period. Lastly, we must determine if the amount of money saved by Brenda is sufficient or not.
The money needed for the school trip is:
y = $ 197 + $ 230 + $ 85
y = $ 512
And the money saved by Brenda is:
x = $ 67 + $ 30.50 + $ 160 + $ 71.75
x = $ 329.25
Then, the additional money needed for Brenda is found by subtacting the second result from the first result:
z = y - x
z = $ 512 - $ 329.25
z = $ 182.75
Brenda needs an additional amount of $ 182.75 for the school trip.
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To pay for a home improvement project that totals $9,000, Genesis is choosing between taking out a simple interest bank loan at 9% for 3 years or paying with a credit card that compounds monthly at an annual rate of 18% for 7 years. Which plan would give Genesis the lowest monthly payment? The monthly credit card payment would be $295, which is lower than the monthly payment on the bank loan. The monthly payment on a bank loan would be $272.50, which is lower than the monthly credit card payment. The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment. The monthly credit card payment would be $374.21, which is lower than the monthly payment on the bank loan.
A plan which would give Genesis the lowest monthly payment is: C. The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
How to determine the plan with the lowest monthly payment?In order to determine the plan which would give Genesis the lowest monthly payment, we would calculate the simple interest earned over each of the time period.
Mathematically, the simple interest earned can be calculated by using this formula:
A = P(1 + rt)
Where:
A represents the future value.P represents the principal or original value.r represents the interest rate.t represents the time.Substituting the given parameters into the formula, we have;
A = 9000[1 + (0.09 × 3)]
A = 9000[1 + 0.27]
A = 9000 × 1.27
Future value, A = $11,430.
Next, we would calculate the monthly payment over a period of 36 months as follows:
Monthly payment = Future value/Time
Monthly payment = 11,430/36
Monthly payment = $317.50.
Similarly, we would calculate the compound interest earned on the credit card by using this formula:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
A = 9000[1 + (0.18/12)]⁽¹² ˣ ⁷⁾
A = 9000[1 + 0.015]⁸⁴
A = 9000 × 1.015⁸⁴
A = 9000 × 3.49258954
Future value, A = $31,433.31.
Next, we would calculate the monthly payment over a period of 84 months as follows:
Monthly payment = Future value/Time
Monthly payment = 31,433.31/84
Monthly payment = $372.21.
In this context, we can reasonably infer and logically deduce that the plan which would give Genesis the lowest monthly payment is the monthly payment on a bank loan.
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Answer:
C
Step-by-step explanation:
got 100% on exam
What steps would you take to approximate the total amount Gwinnett
County must pay teachers for the whole year?
The steps that you should take to approximate the total amount that Gwinnett County must pay teachers for the whole year are:
Find out the average wages paid to teachers in Gwinnett County.Find out the number of teachers in Gwinnett County.Multiply the number of teachers with the average wages paid. How to find the approximate amount paid to teachers?The approximate amount that is paid to teachers in will be based on the average wages that is paid to teachers in Gwinnett County. You can find this out by conducting an anonymous survey of different levels of teacher salaries in Gwinnett County or you can find it from the relevant Gwinnett County government department.
Then, look for records to show the number of teachers in Gwinnett County.
Multiply these two figures and you will then get the approximate the total amount that Gwinnett County needs to pay its teachers.
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The pressure, p (in lbs/ft2 ), in a pipe varies over time. five times an hour, the pressure oscillates from a low of 90 to a high of 230 and then back to a low 90. the pressure at t = 0 is 90.
The value of P(t) is p(t) = -70 cos(10xπ t) + 165.
What is pressure?Pressure in mathematics or physics is defined as force per unit area. The pressure exerted by a solid object which is resting on top of a solid surface is the weight divided by the area of the object . SI unit of force is Newton (N).
range of pressure = low of 90 to a high of 230
As, Pressure oscillating ten times every hour. So period n = .0.2 min.
Now, P = f(t) = Acos(Bt) + D
Amplitude = (HP - LP / 2
= (230- 90) / 2
= 140/ 2
= 70
Period B = 2xpi / 0.2 = 10xπ
and, D= (Ph + Pl) / 2
= (230+ 90) / 2
= 330/ 2
= 165
Hence, p(t) = -70 cos(10xπ t) + 165.
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Write an equation in standard form of a line that is parallel to y=4x-3 and passes through the point (7, 10).
The equation of a line that is parallel to y=4x-3 and passes through the point (7, 10) is 4x - y = 18.
What is the equation of a line that is parallel to y=4x-3 and passes through the point (7, 10)?Given that;
Equation of line: y = 4x - 3Point: ( 7,10 )First, we determine the slope of the line using the slope intercept form.
y = mx + b
m is slope and b is y-intercept.
y = 4x - 3
Comparing with the slope intercept form equation,
Slope m = 4
Now, to determine the the equation of line parallel, the slopes must equal.
We find the line using the point slope formula.
y - y₁ = m(x - x₁)
Plug in m = 4, x₁ = 7, y₁ = 10 and simplify.
y - 10 = 4(x - 7)
y - 10 = 4x - 28
-10 + 28 = 4x - y
4x - y = -10 + 28
4x - y = 18
Therefore, the equation of a line that is parallel to y=4x-3 and passes through the point (7, 10) is 4x - y = 18.
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Which choice shows 17+14+ 13 rewritten correctly using the commutative
property and then simplified correctly?
Answer:
Could I see the available choices?
Step-by-step explanation:
Answer:
didnt have the choices but any that would have it as the same problem different order
Step-by-step explanation:
17+14+13=13+14+17=14+13+17=14+17+13=17+13+14=13+17+14
a² + b²
______
a-b
if a = -3 and b = -5
Answer: -17
Step-by-step explanation:
-3^2 + -5^2/ -3 - (-5)
-34 / -3 - (-5)
-34/2
-17
8. A total of $36,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in
bonds is to exceed that in CDs by $5,000, how much will be invested in each type of investment?
The amount invested in CDs is $
The amount invested in bonds is $
Using a system of equations, it is found that:
The amount invested in CDs is $20,500.The amount invested in bonds is $15,500.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: amount invested in CDs.Variable y: amount invested in bonds.The total invested is of $36,000, hence:
x + y = 36000.
The amount invested in bonds is to to exceed that in CDs by $5,000, hence:
x = y + 5000.
Replacing in the first equation:
y + 5000 + y = 36000.
2y = 31000
y = 15,500.
x = y + 5000 = 20,500.
Hence:
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Find the equation of the line shown.
Answer:
The x is 2 and the y is 1. So, it's 1/2
Step-by-step explanation:
x = 2
y = 1
Slope goes y,x,
The midpoint of a line segment ab is (1, 2). point a coordinates are (3,-3)
and point b coordinates are (x, 7). find the value of x.
The value of x in (x,7) is -1
Mid Point of a line segment is defined as the point which divides the line segment in equal ratio that means divides in two equal parts.
Let one end point of line segment be A(a,b) and other end be B(c,d)
then its mid point X(x,y) will be given by [tex]x=\frac{a+c}{2} , y=\frac{b+d}{2}[/tex]...….(1)
Given the points A(3,-3) and B(x,7) and the midpoint X(1,2)
The mid point [tex](1,2)=(\frac{3+x}{2} ,\frac{-3+7}{2} )[/tex]...............using (1)
On comparing the x coordinate we get
[tex]1=\frac{3+x}{2}[/tex]
On cross multiplying we get
[tex]2=3+x[/tex]
On solving further
[tex]x=-1[/tex]
Therefore , the value of x in (x,7) is -1.
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is 9.02 x 10-8 larger than 9.02 x 10-6
Answer:Yes 90.2 x 10-8 is greater then 90.2 x 10-6
Step-by-step explanation:
The function f is defined by the following rule
f(x)=2x-1
Complete the function table
The value of the function at x = -3, -2, 0, 1, and 5 will be -7, -5, -1, 1, and 9, respectively.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The function is given below.
f(x) = 2x - 1
The value of the function at x = - 3 will be
f(-3) = 2(-3) - 1
f(-3) = - 6 - 1
f(-3) = - 7
The value of the function at x = - 2 will be
f(-2) = 2(-2) - 1
f(-2) = - 4 - 1
f(-2) = - 5
The value of the function at x = 0 will be
f(0) = 2(0) - 1
f(0) = 0 - 1
f(0) = - 1
The value of the function at x = 1 will be
f(1) = 2(1) - 1
f(1) = 2 - 1
f(1) = 1
The value of the function at x = 5 will be
f(5) = 2(5) - 1
f(5) = 10 - 1
f(5) = 9
The value of the function at x = -3, -2, 0, 1, and 5 will be -7, -5, -1, 1, and 9, respectively.
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Tiffany buys a circular mirror. She
wants to decorate the mirror by gluing
ribbon along the outer edge of the
mirror. How long is the ribbon if the
mirror has a 15 inch radius?
Area = 70,6.5 inch² long is the ribbon if the mirror has a 15 inch radius .
What area is a circle?
A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.
Describe Area -
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Tiffany buys a circular mirror.
r = 15 inch
long is the ribbon if the mirror has = πr²
= 3.14 × 15 × 15
= 70,6.5 inch²
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360 miles traveled on 12 gallons of gasoline? (write each rate as a unit rate)
The unit rate is 30 miles per gallon
How to calculate the unit rate ?The number of miles travelled is 360 miles
The number of gallons is 12 gallons
Therefore the unit rate can be calculated as follows
Unit rate= 360/12
= 30
Hence the unit rate is 30 miles per gallon
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Hassan's soccer team is trying to raise $688 to travel to a tournament in Florida, so they decided to host a pancake breakfast. Each person must pay $43 for the breakfast. How many people need to attend their breakfast in order to raise $688?
Answer: 182
Step-by-step explanation:
Current trends in math instruction are likely to lead to graduates who are able to?
Current trends in math instruction are likely to lead to graduates who are able to "find precise answers quickly by consulting texts and tables."
What is math instruction?A analysis of studies on mathematics instruction encompassing students with educational disabilities discovered a variety of behavioral, cognitive, & metacognitive approaches that have been shown to improve both mathematical computation & mathematical solving problems in students with LD.
Some key features regarding the math instruction are-
The majority of metacognitive instruction has indeed been combined with really explicit instructional strategies in which students are taught and then given ample practice opportunities.Metacognitive strategy training research has revealed the effectiveness of these training across a wide range of tasks and training types. Recent research on explicit solving problems, including the growth to higher-level math including algebra, and research on affectively oriented self-instruction, has piqued the interest of many.Some points regarding the importance of the math instruction are-
encourage students to learn the math facts, concepts, computational skills, as well as strategies needed to solve a variety of problemspromote the creation of efficient and adaptable problem-solving approaches; and instill adaptive arithmetical behaviors and beliefs in students.To know more about the computational skills, here
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A long year-end status report for work is 163 pages long. You need to print 16 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.75 each.
Answer:
19.56
Step-by-step explanation:
Number of pages x copies
164 x 16 = 2608
Divided by number of pages per ream
2608 ÷ 50 = 5.216
Total Reams by cost
5.216 x 3.75 = 19.56
a statistical procedure for analyzing the results of multiple studies to reach an overall conclusion.
A "meta-analysis" is a statistical procedure for combining the findings of multiple studies to reach a single conclusion.
What is meant by meta-analysis?Meta-analyses are more rigorous and quantitative than both kinds of reviews.
Some main points related to meta-analysis are-
These papers, in addition to providing an overview, provide a quantitative assessment of how effectively a treatment works or an evaluate of how significantly more likely a person is to grow a disease if they engage in a certain behavior.Meta-analyses are performed so that research from multiple studies with differing data can be combined to make more informed decisions about effectiveness of a medication on the a person's risk of developing a disease than a Magic 8-ball.The research question is defined first in meta-analyses. A well-defined research topic identifies the population impacted by the intervention as well as the potential treatment outcome(s).To know more about the meta-analysis, here
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What is the slope of the line that passes through the points (4, -6) and (-2, 3)?
Write your answer in simplest form.
Answer:
-3/2
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (3 - (-6))/(-2 - 4)
slope = (3 + 6)/(-6) = 9/(-6)
slope = -3/2
Answer:
Step-by-step explanation: 3/-2
Last year, 63 new houses were built in a neighborhood. So far this year,
Write your answer in simplest form
11
12
of them have been sold. How many new houses have been sold this year?
13
14
The total number of the houses sold this year are 54.
What is defined as the fraction?Fractions are identified as a numerical value representing a portion of a whole.
A fraction is a portion or segment of any quantity taken from the whole, which can be any number, a fixed number, or a thing.Every fraction has a numerator and even a denominator isolated by a horizontal bar recognized as the fractional bar.The denominator signifies the number of parts into which the whole has indeed been subdivided. It is positioned below the fractional bar in the lower part of the fraction.The numerator specifies how many fractional sections are recognized or selected. It is positioned above the fractional bar in the upper part of the fraction.So, 6/7 of the new houses are sold.
Total houses = 63
Multiply the values.
= 63×6/7
= 54
Therefore, the total number of the new houses sold this year is 54.
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The correct question is-
Last year, 63 new houses were built in a neighbourhood. So far this year, 6/7 of them have been sold. How many new houses have been sold this year?
Writing Numerical Expressions
A numerical expression is a mathematical phrase that contains only numbers and mathematical operations. For example, 6+2+1 is a numerical
expression.
Some numerical expressions contain multiplication. Multiplication can be represented in several ways, including a raised dot or parentheses. Here are
some ways to represent the product of 2 and 3.
2.3
2(3)
Think About It!
Identify the factors of the numerical expression 6(11).
(2)3 (2)(3)
MO
6(11) = 2 x 3 x 11
Its factors are =1 ,2 ,3 , 6, 11, 22, 33 66
2.3 = 2 x 3
Its factors are = 1, 2, 3, 6
2( 3) = 2 x 3
Its factors are = 1, 2,3, 6
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A diagram shows a 5 cm* 5 cm* 5 cm cube.Calculate the length of the diagonal AB. Give your answer correct to 1 decimal place
The length of the diagonal AB of the given square is 8.660
Given that a diagram of a cube having dimensions 5×5×5 and asked to find out the length of diagonal AB(which is a body diagonal of the cube).
To calculate the body diagonal 1st we need to calculate the face diagonal via the Pythagorean theorem
Let's assume the length of the face diagonal is x
By Pythagorean theorem
[tex]x^{2} =5^{2} + 5^{2}[/tex]
[tex]x^{2} =50[/tex]
[tex]x=5\sqrt{2}[/tex]
Therefore, the length of the face diagonal is [tex]5\sqrt{2}[/tex]
Let's assume the body diagonal is y
By Pythagorean theorem
[tex]y^{2} =5^{2} +(5\sqrt{2} )^{2}[/tex]
[tex]y=\sqrt{125}[/tex]
y=[tex]5\sqrt{3}[/tex]=8.660
Therefore, The length of the diagonal AB of the given square is 8.660
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What must the probability of a red light be on this road so that neither road would be preferred over the other on the basis of expected number of red lights?
The probability of a red light be on this road so that neither road would be preferred over the other on the basis of expected number of red lights is 0.3375.
What is Probability:
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math's to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.
Now,
PDF of a Binomial (n, x) distribution is
given as
p(X=x).[tex]C^n_x P^x (1-p)^(n-x)[/tex] x = 0,1,2,
Here n = 9, 2:4, p = 0.3
P(x-4)= 9^c_4(0.3)^4 (0.75)^5 = 0·1715 Ans
R Code
We will use the function pGnom() which gives the Cumulative probability of an
Probability of getting exactly 4 heads is
x <- pGnom (4,9, 0.3) - pGnom (3,9, 0.3)
(We substract 3 to get P(X = 4) since above we have P(X<4) - P(X ≤3)
b)
Expected number in a binomial distribution = np
We have to equate the Expected values
So
9x0.3 = 8xp
os, p = 0.3375.
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Math's Question. Please answer
Answer:
i think 15.84 is right
Step-by-step explanation:
bcz Ian all there is 99 4/5 paper towels and tere were 5 rolls. so, to calculate meters of each roll of paper towels we should divide the given value by 5
99 4/5 /5
Becky decorated 144 cakes in 6 days. How many cakes did she decorate in 1 day.
Answer:
24
Step-by-step explanation:
Answer:24
Step-by-step explanation:144/6=24
Find the measure of the missing angle.
Answer:
a = 52°Step-by-step explanation:
from the picture is a rigth angle (90°)
take off 38 from 90
90 - 38 = 52°
What is 1/2x+1/2x=x+1
Answer: 2x..?
Not 100% sure but here's my reasoning
(1/2 + 1/2 + 1)x
1/2 + 1/2 = 1
1 + 1 = 2
then you add the x, making it 2x
i could be wrong im literally half asleep eating chicken wings and finishing my own homework so forgive me if this is completely wrong lol