Answer:
[tex]\frac{11}{24}[/tex]
Step-by-step explanation:
3/8 + 1/4 + 1/2 - 2/3
- > 1/4 = 2/8
3/8 + 2/8 + 1/2 - 2/3
5/8 + 1/2 - 2/3
- > 1/2 = 4/8
5/8 + 4/8 - 2/3
9/8 - 2/3
- > LCM of 8,3: 24
- > 9/8 = 27/24
- > 2/3 = 16/24
27/24 - 16/24
11/24
Hope this helps you.
Factorize the following: cos²B + 5cosB - 6
Answer:
(cosB-1)(cosB+6)
Step-by-step explanation:
use u substitution . u = cosB
u^2+5u-6
factor
(u-1)(u+6)
put cosB back in for u
(cosB-1)(cosB+6)
using the unit circle what is the exact value of tanpi/6
Answer:
[tex] \frac{ \sqrt{3} }{3} [/tex]
Step-by-step explanation:
[tex]\frac{1}{3} \div \sqrt{3} [/tex]
What is one thousand minus on hundred and ten
Answer:
The answer is 890 . ...... :D
Suppose the volume of the cone is 324pi Find dy/dx when x=6 and y=27
Answer:
[tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle V = \frac{1}{3} \pi x^2y[/tex]
[tex]\displaystyle V = 324 \pi[/tex]
[tex]\displaystyle x = 6[/tex]
[tex]\displaystyle y = 27[/tex]
Step 2: Differentiate
Substitute in volume [Volume Formula]: [tex]\displaystyle 324 \pi = \frac{1}{3} \pi x^2y[/tex][Equality Properties] Rewrite: [tex]\displaystyle y = \frac{972}{x^2}[/tex]Quotient Rule: [tex]\displaystyle \frac{dy}{dx} = \frac{(972)'x^2 - (x^2)'972}{(x^2)^2}[/tex]Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = \frac{0x^2 - (2x)972}{(x^2)^2}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{-1944x}{x^4}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{-1944}{x^3}[/tex]Step 3: Evaluate
Substitute in variables [Derivative]: [tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = \frac{-1944}{6^3}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Plz answer asap question in picture
Answer:
-1 <x < 7
(-1,7)
Step-by-step explanation:
open circle on the left means the number is greater than
-1 <x
Open circle on the right means the number is less than
x < 7
Since both statements are true. we combine them
-1 <x < 7
open circles means parentheses, closed circles mean brackets
I need help please. Thank you
Answer:
0.0009765625
Step-by-step explanation:
This is what i got its probally incorrect
Two cars started from the same place at the same time but travelled in opposite directions. After 9 hours they were 910 kilometers apart. If the speed of one car is 10 kilometers per hour slower than the other what were their speeds per hour
Answer:
55.55 and 45.55
Step-by-step explanation:
Let the car 1 speed be x km/hr and car 2 speed be x-10 km/hr.
Their relative velocity is 2x-10.
Distance covered in 9 hrs=9(2x-10).
18x-90=910, x=55.55 km/hr, x-10=45.55km/hr
A group of 6 children and 6 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $14. How much will the zoo tickets cost in all?
Answer:
i believe it'll cost 200 dollars
Help me plz need the steps
In Figure 7 (open photo), GH is a diameter of the circle. What is
x² + y² ?
A)58
(B) 49
(C) 10
D) 9
(E) It cannot be determined from the information given.
Answer:
[tex]A)58[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ attachment]\\We\ are\ given:\\GH\ is\ the\ diameter\ of\ the\ circle.\\ Also,\\ GM=3\ units\ and\ MH=7\ units\\From\ the\ figure,\\GH\ subtends\ an\ angle\ at\ two\ points\ specifically\ M\ and\ N\ on\ the\\ arc.\\Now,\\We\ know\ that,\\'The\ Angle\ subtended\ by\ the\ diameter\ anywhere\ over\ the\ arc\ of\ the\\ circle\ is\ always\ 90\ degrees'.\\Hence,\\\angle GMH\ = \angle GNH=90\\[/tex]
[tex]Also,\\Pythagoras\ Theorem\ states\ that: 'In\ a\ right\ triangle,\ the\ sum\ of\ squares\\ \ of\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\ hypotenuse'\\In\ \triangle GMH,\\Since\ \angle GMH=90,\\GM^2+MH^2=GH^2[Through\ Pythagoras\ Theorem]\\Hence,\\Substituting\ GM=3,\ MH=7:\\3^2+7^2=GH^2\\GH^2=9+49=58[/tex]
[tex]Similarly,\\In\ \triangle GNH,\\Since\ \angle GNH=90,\\GN^2+NH^2=GH^2\\Hence,\\Substituting\ GN=x\ and\ NH=y:\\x^2+y^2=GH^2\\x^2+y^2=58[/tex]
Put the following equation of a line into slope-intercept form, simplifying all fractions 2x-2y=14
Answer: y = x - 7
Slope intercept form: y = mx + b
[tex]2x-2y=14\\\\-2y=-2x+14\\\\y=\frac{-2x+14}{-2} =\frac{-2(x-7)}{-2} =x-7[/tex]
Find the surface area of the figure below round your answer to the nearest tenth in necessary
Answer:
1548.3 [tex]m^{2}[/tex]
Step-by-step explanation:
Answer:
A = 1548.3 m²
Step-by-step explanation:
Which transformation maps the pre-image to the image?
dilation
reflection
rotation
translation
Answer:
Reflection
Step-by-step explanation:
Because reflecting yourself in a mirror means pre image to image
Answer:
Step-by-step explanation:
dilation
PLEASE HELP THIS IS DUE ASAP (answer in decimal!!!!)
what is the answer to 5- -8
Answer:
13
5 - -8
When you subtract a negative number it changes to an addition so 5- -8 becomes 5 + 8 which equals 13.
Given the formula A = 5h (B + b); solve for B.
2
Answer:
A=5h(B+b)
A/5h=B+b
A/5h - b= B
Blair & Rosen (B&R) plc is a U.K. based brokerage firm that specializes In building investment portfolios designed to meet the specific needs of its clients who are mostly private investors willing to invest their r savings in stocks and shares. One client who contacted B&R recently has a maximum of $500,000 to invest. The company`s investment advisor has decided to recommend the portfolio consisting of two investment funds: An internet fund where the companies are all active in internet businesses of one kind or another and the blue-chip fund which is more conservative and traditional. The internet fund has a projected annual return over the next few years of 12 %, while the blue-chip fund has a projected annual return of 9%. The investment advisor has decided that at most, $350,000 of the client`s funds should be invested in the internet fund. B&R services include risk rating for each investment alternative. The internet fund which is more risky of the two alternatives has a risk rating of 6 for every thousand dollar invested while the blue-chip fund has a risk rating of 4 per thousand dollar invested. So, for example, if $10000 is invested in each of the two investments funds, B&R risk rating for the portfolio would be 6(10) + 4(10)= 100. Finally B&R has developed a questionnaire to measure each client`s risk tolerance. Based on the responses, each client is classified as conservative, moderate or aggressive investor. The questionnaire results have classified the current client as a moderate investor. B&R recommends that a client who`s a moderate investor limit his or her portfolio to a maximum risk rating of 240. You have been asked to help the B&R investment advisor.
What is the recommended investment portfolio for this client?
What is the annual return for the portfolio?
a) The Investment portfolio consisting of the internet fund and Blue chip fund would be the recommended Portfolio for a moderate risk investor
b) The annual return for the portfolio is = $5100 ( Calculated using the excel formula sheet attached below )
The best/recommended investment portfolio for this client is the Investment portfolio consisting of the internet fund and Blue chip Fund because the Portfolio consists of a lower risk rating of 4 for every thousand which is conservative, and also an Internet fund which has a risk rating of 6 for every thousand ( aggressive ). The combination of a high and low risk investment fund in a portfolio results to an average/moderate risk portfolio.
Calculating the Annual return for the portfolio ( using the excel sheet below)
Model Internet fund Blue chip fund
Amount to invest 20 30
Total amount invested = 20 + 30 = 50
Total risk rating = 240
Total return = 5.1
hence: The recommended investment portfolio for this client is the Blue chip fund and the total return on the portfolio = $5100 applying the excel formulae attached below
Internet Fund = $20,000
Blue chip fund = $30,000
Learn more : https://brainly.com/question/7589262
what is the gcf of 10 and 62
What is the dimension of the vector space consisting of five-by-one column matrices where the rows sum to zero and the first row is equal to the second row?
a. 5
b. 4
c. 3
d. 2
Answer:
Option c.
Step-by-step explanation:
If we have a vector of N components (or variables), and we have K linear independent restrictions for these N components (such that K < N, we can't have more restrictions than components.)
The dimension of the vector will be given by N - K.
Here we know that we have a vector of 5 components, that can be written as:
[tex]v = \left[\begin{array}{ccc}v_1\\v_2\\v_3\\v_4\\v_5\end{array}\right][/tex]
And we have two restrictions, so we can expect that the dimension of the vector is:
5 - 2 = 3
But let's see it, the restrictions are:
"the first row is equal to the second row"
Then we can rewrite our vector as:
[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\v_5\end{array}\right][/tex]
Notice that now we have only 4 variables, v₁, v₃, v₄, and v₅
We also know that the sum of the rows is equal to zero, thus:
v₁ + v₂ + v₃ + v₄ + v₅ = 0
we know that v₂ = v₁, so we can replace that to get:
2*v₁ + v₃ + v₄ + v₅ = 0
Now we can isolate one of the variables, to write it in term of the others, for example, let's isolate v₅:
v₅ = -2*v₁ - v₃ - v₄
Now if we replace that in our vector, we have:
[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\-2*v_1 - v_3 - v_4\end{array}\right][/tex]
Notice that our vector depends on only 3 variables, v₁, v₃, and v₄, so we can define our vector in a 3-dimensional space.
Then the correct option is c, the dimension of the vector space is 3.
5 times a certain number plus 6 has the same value as two times the same number minus 3 what is the number
Let the number be x
ATQ
[tex]\\ \sf\longmapsto 5x+6=2x-3[/tex]
[tex]\\ \sf\longmapsto 5x-2x=-3-6[/tex]
[tex]\\ \sf\longmapsto 3x=-9[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-9}{3}[/tex]
[tex]\\ \sf\longmapsto x=-3[/tex]
if 2x + 1=7 what is the value of x
Answer:
x=3
Step-by-step explanation:
2x+1=7
2x=7-1
2x=6
x=6/2
x=3
Answer:
Solution,
2x + 1=7
or 2x = 7 - 1
or, 2x= 6
or, x = 6
2
or, x = 3
.:. x = 3
1. The curve y = (x - 1)(x – 5) cuts the x-axis at A and B and the y-axis at C.
(a) Find the coordinates of A and B.
(b) Hence, find the coordinates of the turning point, M.
Is M a maximum or a minimum point?
(c) Find the coordinates of C.
(d) Sketch the graph of y = (x - 1)(x - 5).
find the common ratio of the geometric sequence 4,3,9/4
Answer:
3/4
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
3/4
Check with the third and second terms
9/4 ÷3
9/4 *1/3= 3/4
The common ratio is 3/4
The sum of 'n' terms of an arithmetic sequence is 4n^2+3n. What is the first term, the common difference, and the sequence?
Answer:
The sequence has first term 7 and common difference is 8.
So the sequence is f(n)=7 + 8(n-1)
Step-by-step explanation:
Let a be the first term.
Let a+d be the second term where d is the common difference.
Then a+2d is the third....
And a+(n-1)d is the nth term.
Adding these terms we get:
an+(n-1)(n)/2×d
For the first term of this sum I seen we had n amount of a's and for the second term I used the well known identity sum of the first n positive integers is n(n+1)/2.
Let's simplify:
an+(n-1)(n)/2×d
Distribute:
an+(n^2d/2)-(nd/2)
Find common denominator:
(2an/2)+(n^2d/2)-(nd/2)
Combine terms into one:
(2an+n^2d-nd)/2
Reorder terms:
(n^2d+2an-nd)/2
Regroup terms:
(n^2d+(2a-d)n)/2
We want the following sum though:
4n^2+3n
This means d/2=4 (so d=8) and (2a-d)/2=3.
So plug d=8 into second equation to solve for a.
(2a-8)/2=3
2a-8=6
2a=14
a=7
The sequence has first term 7 and common difference is 8.
So the sequence is f(n)=7 + 8(n-1).
The number of basic trigonometric ratios is....
A.3
B.4
C.5
D.6
Answer:
There are three basic trigonometric ratios: sine , cosine , and tangent .
Step-by-step explanation:
HELP OR IM GONNA FAIL pleasee!!!! Last one
What is the solution to the system of equations graphed below?
10
X= - x+2
y = 5x + 28
-10
Answer:
(-4,8)
Step-by-step explanation:
The solution to the system is where the lines intersect
The lines intersect at x=-4 , y = 8
(-4,8)
____________ is/are when data is analyzed in order to make decisions about the population behind the data.
A. Experiments
B. Simulations
C. Surveys
D. Statistics
Answer:
statistics are when data analyzed in order to make decisions about the population behind the data.
The correct answer to the question is Statistics (Option D).
What is statistics?
Statistics is a field of study in mathematics which deals with raw data. It is a tool which refines the data to produce meaningful results and a pathway to better understanding of it.
Some examples of raw data can be population sample which loves to see a particular TV show or a sample of students getting so and so marks in Math test.
Data is analyzed mainly by three different measure of central tendency that is mean, median and mode.
Mean is the average value of given discrete data.Median is the middle value when the data is sorted in ascending or descending order.Mode is the value that has highest frequency.Therefore, Statistics the correct answer.
To know more about statistics refer:https://brainly.com/question/10734660
#SPJ2
HELP WHAT DOES THIS EVEN MEAN [CRY]
[tex]\\ \sf\longmapsto A=πr^2[/tex]
[tex]\\ \sf\longmapsto A=3.14(5)^2[/tex]
[tex]\\ \sf\longmapsto A=3.14(25)[/tex]
[tex]\\ \sf\longmapsto A=78.5cm^2[/tex]
help please i’ll give brainliest
Answer:
3rd option
..................[tex]A) \frac{4-2}{2-1} =2[/tex]
[tex]B)\frac{1-0.5}{4-2} =0.25[/tex]
[tex]C)>2[/tex]
[tex]D) 1[/tex]
~OAmalOHopeO
Answer:
The third one is your answer
Given: Measure of arc AB = measure of arc BC,
Measure of angle x = 60°, measure of angle y = 15°
Find: Measure of arc AC
9514 1404 393
Answer:
100°
Step-by-step explanation:
The relevant relation for angle x is ...
x = (AB +DE)/2
and for angle y, it is ...
y =(AC -DE)/2
Using the second relation to write an expression for DE, we have ...
DE = AC -2y
In the first equation, this lets us write ...
x = (AB +(AC -2y))/2 = (AB +(2AB -2y))/2
2x = 3AB-2y . . . . . . . . . . . . . . multiply by 2
(2x +2y)/3 = AB = AC/2 . . . . . add 2y; divide by 3
AC = (4/3)(x +y) = (4/3)(60° +15°) . . . . multiply by 2, substitute known values
AC = 100°
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!! Chapt 15 part 2a
Explain the process of matrix multiplication. What are the dimensions 9f of the resulting matrix? Use the following matrices for your explanation of the process. AB. Show your work.
We are given the matrices A and B
[tex]A = \left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right][/tex]
[tex]B = \left[\begin{array}{ccc}2\\1\\2\end{array}\right][/tex]
Multiplying these matrices:
We multiply matrices by taking the first column of the first matrix and the first row of the second matrix
we will multiply all the terms of the first column of the first matrix and multiply them by the terms of the first row of the second matrix, one by one
[tex]AB = \left[\begin{array}{ccc}2(2) + 3(1) + -1(2)\\0(2) + 2(1) + 5(2)\\2(2) + 4(1) + 0(2)\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{ccc}5\\12\\8\end{array}\right][/tex]
9514 1404 393
Explanation:
Two matrices with dimensions (numbers of (rows, columns)) of (a, b) and (c, d) can only be multiplied if the number of columns in the left matrix is equal to the number of rows in the right matrix. That is, b=c. The dimensions of the product matrix will be (a, d).
For row i of the left matrix and column j of the right matrix, element a(i,j) of the product matrix is the dot-product of row i with column j. (The dot-product of two vectors is the sum of the products of corresponding elements.)
__
The example matrices have (row, column) dimensions (3, 3) and (3, 1), so can be multiplied with a result having dimensions (3, 1).
It is useful to refer to an element of a matrix by specifying the row and column in which it resides. An element of matrix 'A' in row 2 and column 3 can be referred to as A(2,3). Often, subscripts are used, as in ...
[tex]A_{i,j}[/tex]
For matrix C = A·B, the element C(1,1) will be the sum ...
A(1,1)B(1,1) +A(1,2)B(2,1) +A(1,3)B(3,1)
Calculators, apps, spreadsheets, and web sites are available that will perform this arithmetic for you. It can be a bit tedious to do by hand.
Here the product is ...
[tex]A\cdot B=\left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right] \cdot\left[\begin{array}{c}2&1&2\end{array}\right] =\left[\begin{array}{c}2(2)+3(1)+(-1)(2)&0(2)+2(1)+5(2)&2(2)+4(1)+0(2)\end{array}\right] \\\\=\left[\begin{array}{c}5&12&8\end{array}\right][/tex]
