5/6 is the value of the expression.
To solve this expression, we need to find a common denominator for all the fractions:
1/4 + 1 + 3/4 - 2/3 - 1/2
= 1/4 + 3/4 + 1 - 2/3 - 1/2 (adding the fractions with common denominators)
= 4/4 + 1 - 8/12 - 6/12 (finding equivalent fractions with common denominators)
= 1 + 1/3 - 1/2 (simplifying)
To add 1/3 and -1/2, we need to find a common denominator of 6:
1 + 1/3 - 1/2
= 6/6 + 2/6 - 3/6 (finding equivalent fractions with common denominators)
= 5/6 (simplifying)
Therefore, the value of the expression is 5/6.
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ1
Y=5x+3 graph the line
Answer:
The graph is in the pic
Step-by-step explanation:
A person bets 1 dollar to b dollars that he can draw two cards from an ordinary deck of cards without replacement and that they will be of the same suit. Find b so that the bet is fair.
Answer:
$3.25
Step-by-step explanation:
In an ordinary deck of cards, we will notice that there are 52 cards.
However, we have 4 suits and 13 cards in each one making a total of 52, right?.
So, the probability that a person draws two cards and they will be of the same suit is:
\(P(X) =\dfrac{ \bigg (^4_1 \bigg) \times \bigg ( ^{13}_{2}\bigg) }{ \bigg ( ^{52}_{2} \bigg)}\)
\(P(X) =\dfrac{ \dfrac{4!}{1!(4-1)!} \times \dfrac{13!}{2!(13-2)!} }{ \dfrac{52!}{2!(52-2)!} }\)
\(P(X) =\dfrac{4}{17}\)
Given that; A person bets 1 dollar to b dollars;
To make the bet fair is;
\(\dfrac{4}{17}b - \dfrac{13}{17}(1) = 0\)
\(= \dfrac{4}{17}b = \dfrac{13}{17}\)
multiply both sides by 17
4b = 13
b = 13/4
b = 3.25
Therefore, to make the fair, the value of b need to be $3.25
Using the expected value formular, the value of b such that the game is fair is 3.25
Total number of cards in a deck = 52
Number of cards per suit = 13
Number of suits = 4
Selection without replacement :
Club = C ; Spade = S ; Heart = H ; Diamonds = D(C and C) or (H and H) or (S and S) or (D and D)
[(13/52 × 12/51) + (13/52 × 12/51) + (13/52 × 12/51) + (13/52 × 12/51)] = 0.2353
Probability of not selecting a card of the same suit :
1 - 0.2353 = 0.7647For game to be fair :
Σ[(X × P(X)] = 0X : ______ b _____ - 1
P(X): __ 0.2353__ 0.7647
[(0.2353b + (-1 × 0.7647)] = 0
0.2353b - 0.7647 = 0
0.2353b = 0.7647
Divide both sides by 0.2353
b = 0.7647 / 0.2353
b = 3.249
b = 3.25
Hence, the value of b is 3.25
Learn more : https://brainly.com/question/19755846
How many significant figures are in the number
43.6? 43.6 has [?] significant figures.
Answer:
43.6 has 3 significant figures.
(a) Show that if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^{T}\). Show with an example that the eigenvectors of A and \(A^{T}\) are not the same.
(b) Show that if λ is an eigenvalue of A, and A is invertible, then λ^-1 is an eigenvalue of A^-1.
If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.
What are eigenvalues and eigenvectors?The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.
The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.
Then, we have:
Av = λv
Taking transpose on both sides we have:
\(v^T A^T = \lambda v^T\)
The above equations thus relates transpose of vector and transpose of A to λ.
Now, consider a matrix:
\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)
Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.
The eigenvectors are:
\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)
Now, for transpose of A:
\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)
The eigen vectors are:
\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)
Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.
Learn more about eigenvalues here:
https://brainly.com/question/29749542
#SPJ1
transformed to create the graph of Y3x?
How is the graph of the parent function
O It is horizontally stretched by a factor of 3 and reflected over the y-axis.
It is translated 3 units down and reflected over the x-axis
It is horizontally compressed by a factor of 3 and reflected over the x-axis
It is translated 3 units down and reflected over the y-axis.
Answer:
The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.
What is 450 divided by 0.1?
Use the Factor Theorem to verify that the given binomial is a factor
of P(x). Then divide.
(x+5); P(x)=2x + 6x - 20
The Gauss-Markov theorem will not hold if__.
a. the error term has an expected value not equal to zero given any values of the independent variables
b. the regression model relies on the method of random sampling for collection of data
c. the independent variables have exact linear relationships among them
d. the error term has the same variance given any values of the explanatory variables
Solution is D the unbiased variables have specific linear relationships among them
The gauss-markov theorem will now not hold authentic if there is a linear relationship maximum of the impartial variable. this version will not paintings until there can be impartial variable and linear dating in between.
therefore, the Gauss–Markov theorem holds while we adhere to the four assumptions of OLS: linearity, no multicollinearity, strict exogeneity, and spherical errors. If we make these 4 assumptions, then β^ is BLUE, the best (minimum-variance) linear independent estimator.The Gauss-Markov theorem states that in case your linear regression version satisfies the primary six classical assumptions, then regular least squares (OLS) regression produces impartial estimates which have the smallest variance of all viable linear estimators.
To know more about Guass click here
brainly.com/question/30544041
#SPJ4
Given that ABCDEF, solve for x.
A. 3
B. 2
OC. 6
D. 4
The value of side length x (DF) in the triangle is 4.
What is the value of x?The figures in the image is that of two similar triangle.
Triangle ABC is similar to triangle DEF.
From the diagram:
Leg 1 of the smaller triangle DE = 5
Leg 2 of the smaller triangle DF = x
Leg 1 of the larger triangle AB = 30
Leg 2 of the larger triangle AC = 24
To find the value of x, we take the ratio of the sides of the two triangle since they similar:
Hence:
Leg DE : Leg DF = Leg AB : Leg AC
Plug in the values:
5 : x = 30 : 24
5/x = 30/24
Cross multiplying, we get:
30x = 5 × 24
30x = 120
x = 120/30
x = 4
Therefore, the value of x is 4.
Learn more about ratios and proportions at :brainly.com/question/29774220
#SPJ1
what is the solution of the set of the compound inequalities 3.5x-10>-3 and 8x-9<39
Answer:
Step-by-step explanation:
3.5x - 10 > -3
3.5x > 7
x > 2
8x - 9 < 39
8x < 48
x < 6
x > 2 and x < 6
Mr. Hooper has a tree in his front yard that grows every year. If the tree was 3 feet tall when he planted it 6 years ago , what is the current height of the tree in terms of f?
A. 3f + 6 feet
B. 6f + 3 feet
C. 3f + 18 feet
D. 6f + 18 feet
The height of the tree after 6 years can be expressed as "3 feet + 6f feet."
The correct answer is A. 3f + 6 feet.
To determine the current height of the tree in terms of "f,"
let's analyze the given information.
We know that the tree was initially 3 feet tall when it was planted 6 years ago.
Since the tree grows every year, we can assume that its growth rate is consistent.
Let's denote the current height of the tree as "h" (in feet).
After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").
Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."
For similar question on height.
https://brainly.com/question/28122539
#SPJ8
If triangles ABC and DEF are similar, what is y? Show your work.
The value of y is 18
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.
Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.
Therefore;
14/21 = 12/y
14y = 21 × 12
14y = 252
divide both sides by 14
y = 252/14
y = 18
Therefore the value of y is 18.
learn more about similar triangles from
https://brainly.com/question/14285697
#SPJ1
Between x = 0 and x = 1, which function has a greater average rate of change than y = 3x
?
Answer:
x=1
Step-by-step explanation:
y=3x so just add 1+3=4 then add veriable y=4x
3 2/5 x 6/9 what would it be help please
32
45
x6
Step-by-step explanation: 32
5
x6
9
=
32
45
x6
Oblicz ile wynosi niewiadoma (a+1)-(-8)= -9
Step-by-step explanation:
I don't understand your language but if it's the solution;
(a+1)-(-8)= -9
Remove the parentheses
a+1+8= -9
Collect the like terms
a= -9-8-1
a= -18
Ghana van company invested P45 700 for two years at a rate of 12%per annum compounded for quarter year. Work out the compound interest over the two years
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)
\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)
m.
x-intercept =
1/2
and y-intercept = 3
Write an equation for the line in point-slope form and in slope-intercept form
Answer:
slope intercept form: y= -6x+3
point slope form: y-0= -6(x -1/2)
Step-by-step explanation:
point slope form: y - y1 = m(x - x1)
substitute the values y-0=-6(x-1/2)
slope intercept form:
find the slope using two given points
m = (y2 - y1) / (x2 - x1)
= (3 - 0) / (0 - 1/2)
= 3 / (-1/2)
= -6
substitute into equation
y= -6x+3
1267.1 ml = L
pls help
Answer:
1.2671 L
Step-by-step explanation:
1 L (Liter) = 1000 mL (Milliliter)
So the unit multiplier used would be:
(\(\frac{1L}{1000mL}\)) OR (\(\frac{1000mL}{1L}\))
The initial unit is “mL” which has to be cancelled out (by the correct unit multiplier) so that the final answer is expressed in the desired units of “L”. Therefore the unit multiplier shown on the left will be used:
∴\((1267.1mL)\) × \((\frac{1L}{1000mL})\)
= \(\frac{1267.1}{1000}\) L
= 1.2671 L
which is a correct way to check that 4,358 divided by 7 is 622 remainder 4
Answer:
Ok, check your work one way is:
622x7 Then add 4 and you can see if its correct
622x7 = 4354
Now add 4.
4358. So it's correct.
Equation (622x7)+4= 4358
D
simplity
x3 + y 3
x+y
\(\displaystyle\bf\\\frac{x^3+y^3}{x+y}=?\\\\ ~~~~~~~~~~~We~use~the~formula:~~~~x^3+y^3=(x+y)(x^2-xy+y^2)\\\\\frac{x^3+y^3}{x+y}=\frac{(x+y)(x^2-xy+y^2)}{x+y}=\boxed{\bf x^2-xy+y^2}\\\\We~simplified~the~fraction~with~(x + y)\)
What’s the range of A and B and both
This is of Both
Range = Highest - Lowest data
Range = 45 - 10
Range = 35
Only A
Range = 45 - 10
Range = 35
Only B
Range = 40 - 15
Range = 25
Must click thanks and mark brainliest
Which ratios are less than 8 to 10?
Answer:
3:5 and 50:100
that should be the answer
Does (–1, 2) make the equation y = x + 9 true?
Answer:
(-1, 2) does not make the equation y=x+9 true.
Step-by-step explanation:
y=x+9
(-1, 2)=(x, y)
2=(-1)+9,
-1+9=8,
2 does not equal to 8.
Answer: No.
caculate the following multiplication
\(67 \times 12\)
Answer:
804
Step-by-step explanation:
Just use a calculator.
The cost of a bag of almonds is nine times the cost of an ear of corn. Also, the cost of a bag of almonds equals 40 more than the cost of 5 ears of corn. Find the cost of a bag of almonds.
Which of the following sets of ordered pairs represents a function? PLEASE HELP
The set of ordered pairs that represents a function is (D) {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.
A set of ordered pairs represents a function if each unique input (x-value) is associated with only one output (y-value).
{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}
In this set, both (-2, -1) and (-2, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.
{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3,0)}
In this set, all the ordered pairs have the same x-value (-5). Since (-5, -5), (-5, -4), (-5, -3), and (-5, -2) have the same x-value but different y-values, this set does not represent a function.
{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}
In this set, (-4, -5) and (-4, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.
{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}
In this set, each unique x-value is associated with a single y-value. There are no repeated x-values. Therefore, this set represents a function.
To learn more on Sets click:
https://brainly.com/question/30705181
#SPJ1
93,83,65,59,88,76,86,93,48,73,54,79
What is the percentage of these test scores that are less than 88?
Find the value of z that makes quadrilateral EFGH a parallelogram.2zz+10FEHGz=Submit
In a parallelogram opposite sides have the same length therefore, for figure EFGH to be a parallelogram we must have that:
\(GF=HE\)Substituting we get:
\(z+10=2z\)Now, we solve for "z". First, we subtract "z" from both sides:
\(\begin{gathered} z-z+10=2z-z \\ 10=z \end{gathered}\)Therefore, the value of "z" is 10.
Given that a+b = 10 and a square - b square = 40 find the value of a-b
Answer:
the value of a - b is 4.
Step-by-step explanation:
We have been given the following two equations:
a + b = 10 ------------(1)
a² - b² = 40 -------(2)
We can factor the left-hand side of equation (2) using the difference of squares identity:
(a + b)(a - b) = 40
Substituting equation (1) into this equation, we get:
10(a - b) = 40
Dividing both sides by 10, we get:
a - b = 4
Therefore, the value of a - b is 4.
Step-by-step explanation:
if I understand this correctly :
a + b = 10
a² - b² = 40
(a² - b²) = (a + b)(a - b) = 40
10(a - b) = 40
(a - b) = 4
First try was incorrect
Hall is baking a pie. The radius of the pie is 17 inches. What is the
area of the pie?
Use 3.14 for pi and round your answer to the nearest tenth.
label required
Answer:
907.5
Step-by-step explanation:
Formula to find the area of a circle: πr²
πr² = 3.14 x 17²
= 3.14 x 289
= 907.46
≈ 907.5
Hope this helps :)