Given the equation y = -3x + 6, the slope is

Answer:

6

Step-by-step explanation:

Answer: 9 in

Step-by-step explanation: area = (base x height)/ 2 You multiply base (6) times height (3), and then divide it by 2.

Answer

9

Step-by-step explanation:

Divide 63 by 9 months

7 students per month

63 / 9 = 7

The Implied Equity Risk Premium (ERP) is generally considered a better predictor of future equity risk premium

Implied Equity Risk Premium is derived from the current market prices of stocks and other securities. It represents the difference between the expected rate of return on equities and the risk-free rate of return. Investors' expectations about future returns are embedded in market prices, so the implied ERP reflects the collective wisdom and expectations of market participants. It takes into account current market conditions, investor sentiment, and other relevant factors, making it a forward-looking indicator.

On the other hand, historical geometric average and historical arithmetic average equity risk premium are calculated based on past performance data. While historical averages provide valuable insights into the past behavior of equity risk premium, they may not fully capture the changing dynamics of the market or reflect future expectations.

Learn more about implied ERP at

https://brainly.com/question/31829257

#SPJ4

Answer:

(3,2) just use a slope triangle (over 2 up 3) and do it in reverse

Answer:

90°

Step-by-step explanation:

a regular polygon is equiangular, angles are equal.

a quadrilateral has 4 sides

the sum of the 4 angles in a quadrilateral = 360° , then

each angle = 360° ÷ 4 = 90°

Answer:electrons

Step-by-step explanation:

Answer:

\(\frac{x-1}{x+2}\)

Step-by-step explanation:

simplifying the equation:  \(x^2-3x+2/x^2-1\)

1) Rewrite the equation so it's easier to understand:

\(\frac{x^2-3x+2}{x^2-4}\)

2) factor \(x^2-3x+2\):

\(x^2-3x+2\) \(=> (x-1)(x-2)\)

3) factor \(x^2-4\):

\(x^2-4 => (x+2)(x-2)\)

Meaning: \(\frac{(x-1)(x-2)}{(x+2)(x-2)}\)

4) Cancel the common factor: \((x-2)\) from the numerator and the denominator:

\(=\frac{x-1}{x+2}\)

Answer:

Step-by-step explanation:

Step 1: Add 4n to both sides.

n+4n=−4n−1+4n

5n=−1

Step 2: Divide both sides by 5.

5n

5

=

−1

5

n=

−1

5

Answer:

n = 9

Step-by-step explanation:

5(n-3) = 30

Expand the brackets. (Multiply n by 5 then multiply -3 by 5.)

5n-15 = 30

Isolate 5n.

5n = 30+15

Evaluate.

5n = 45

Find n.

n = 45 ÷ 5

n = 9

Answer:

n = 9

Step-by-step explanation:

1) divide both sides by 5 to cancel it out

       (n-3=6)

2) add 3 to each side to cancel out the -3

       (n=9)

You could factor the 5 to get 5n-15=30 but dividing by 5 just makes the number easier

Answer:

Step-by-step explanation:

Step-by-step explanation:

that is totally easy.

in the slope intercept form of a line equation the factor of x is always the slope.

in general

y = ax + b

a = the slope.

so, in our case here

y = 5x - 7

5 is the slope.

and -7 is the y intercept (at what point does the line intercept the y-axis; that is the y value when x = 0).

Answer:

1 and 2 is corresponding angles

4 and 3 is alternate interior angles

5 and 6 corresponding angles

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

Answer:

482.84

Step-by-step explanation:

\(A = 2 ( 1 +\sqrt{2} ) a^{2} = 2 multiply ( 1 +\sqrt{2} ) multiply 10^{2} = 482.84271\)

Answer:

86

Step-by-step explanation:

I assume the question is \( \sum_{n=1}^{7} 2(-2)^{n-1} \)

7: 2(-2)^6 = 128

6: 2(-2)^5 = -64

5: 2(-2)^4 = 32

4: 2(-2)^3 = -16

3: 2(-2)^2 = 8

2: 2(-2)^1 = -4

1: 2(-2)^0 = 2

128 - 64 + 32 - 16 + 8 - 4 + 2 = 86

Given:

Total fund = $500

cost of each trip = $80

To find:

The an algebraic expression that represents the money the club has after going on field  trips.

Solution:

Let x be the number of field trips.

Cost of 1 field trip = $80

Cost of x field trip = $80x

We have, Total fund = $500.

So, the money the club has after going on field  trips is

\(\text{Remaining money}=500-80x\)

Therefore, the money the club has after going on field  trips is $(500-80x).

Answer:

fx/gx=10

Step-by-step explanation:

fx= (36x5)-(44x4)-(28x3)

fx=80

gx= 4x2

gx=8

To work out fx/gx:

fx/gx=80/8

fx/gx=10

Answer:

√65 feet

Step-by-step explanation:

Using the pathagoryoes theroem (the equation in your picture) we have

4²+7²=c²

simplify to

16+49=c²

65=c²

√65=c

We have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

Mathematical Induction : For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.

It is given that the statement is true for n = k

Explanation:

According to the principle of Mathematical Induction,

Let d(n) be a statement involving Natural Number n such that

d(1) is true

d(m) is true

d(m+1) is true

So ,  the statement d(n) is true for all the n natural numbers.

According to the second principle of Mathematical Induction

Let d(n) be a statement involving Natural number n such that

d(1) is true

d(m) is true when d(n) is true for all n where 1 ≤ n ≤m .

Then the statement d(n) is true for all the values of n ( natural number)

Therefore , we have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

To know more about Mathematical Induction visit: brainly.com/question/1333684

#SPJ9

Number of students should be sampled to be within 0.5 drink of population mean with 95% probability is 617 students.

To determine the sample size required to estimate the population mean with a given level of precision, we can use the formula for the margin of error

Margin of error = Z × (standard deviation / sqrt(sample size))

where Z is the critical value of the standard normal distribution corresponding to the desired level of confidence. For a 95% confidence level, Z is 1.96.

We want the margin of error to be no more than 0.5 drinks, so we can set up the equation

0.5 = 1.96 × (6.3 / sqrt(sample size))

Solving for the sample size, we get

sqrt(sample size) = 1.96 × 6.3 / 0.5

sqrt(sample size) = 24.82

sample size = (24.82)^2

sample size = 617

Learn more about margin of error here

brainly.com/question/10501147

#SPJ4

The given expression is

= (x²-x)^9(√5x²+4x​)

We would differentiate it by applying the product rule. It is expressed as

(fg)' = f'g + fg'

Let f = (x²-x)^9

Let g = (√5x²+4x​)

f' = 9(2x - 1)(x²-x)^8

g = (√5x²+4x​) = (5x²+4x)^1/2

g' = 1/2(10x + 4)(√5x²+4x​)^-1/2

g' = (10x + 4)/2(√5x²+4x)

g' = (5x + 2)/(√5x²+4x)

By applying the rule, it becomes

9(2x - 1)(x²-x)^8 * (√5x²+4x​) + (x²-x)^9 * (5x + 2)/(√5x²+4x)

By simplifying,

Answer:

I belive the answer is 3x - 12

The measure of angle TQR of the X brace on a rectangular barn door is approximately 40.577°.

To find the measure of angle ∠TQR, we can use the given information and apply the properties of angles in a triangle.

Since we know the lengths of two sides of the triangle, ST and PS, we can use the Law of Cosines to find the length of the third side, PT.

The Law of Cosines states:

c² = a² + b² - 2ab * cos(C)

In this case, we have:

PT² = ST² + PS² - 2(ST)(PS) * cos(m∠PTQ)

Substituting the given values:

PT² = (3 (13/16) ft)² + (7 ft)² - 2(3 (13/16) ft)(7 ft) * cos(67°)

Calculating this expression, we find:

PT ≈ 9.679 ft (rounded to three decimal places)

Now that we know the lengths of all three sides of the triangle (ST, PS, PT), we can use the Law of Cosines again to find the measure of angle ∠TQR.

The Law of Cosines states:

cos(C) = (a² + b² - c²) / (2ab)

In this case, we have:

cos(m∠TQR) = (ST² + PT² - PS²) / (2(ST)(PT))

Substituting the given values:

cos(m∠TQR) = [(3 (13/16) ft)² + (9.679 ft)² - (7 ft)²] / [2(3 (13/16) ft)(9.679 ft)]

Calculating this expression, we find:

cos(m∠TQR) ≈ 0.774 (rounded to three decimal places)

Finally, to find the measure of angle ∠TQR, we can take the inverse cosine (arccos) of the calculated cosine value:

m∠TQR ≈ arc cos(0.774) ≈ 40.577° (rounded to three decimal places)

Therefore, the measure of angle ∠TQR is approximately 40.577°.

To know more about angle refer here:

https://brainly.com/question/31186705

#SPJ11

Answer:

La opción correcta es;

Estudiante 2, ya que está aproximadamente a 32,39 metros de distancia

Step-by-step explanation:

Los parámetros dados son;

La distancia entre los dos estudiantes = 53 metros

El ángulo medido entre la línea del Estudiante 1 a la caja fuerte y el Estudiante 1 y el Estudiante 2 = 37 °

El ángulo medido entre la línea del Estudiante 2 a la caja fuerte y el Estudiante 2 y el Estudiante 1 = 43 °

Dado que los dos estudiantes y la caja fuerte forman los vértices de un triángulo, tenemos;

Sea θ el ángulo del triángulo opuesto a la distancia entre los dos estudiantes

Por lo tanto;

θ + 43 ° + 37 ° = 180 ° (teorema de suma de ángulos)

θ = 180 ° - (43 ° + 37 °) = 100 °

Por regla del seno, tenemos;

a / (sin (A) = b / sin (B)

Por lo tanto;

53 / (sin (100 °)) = b / (sin (37 °)) = c / (sin (43 °))

Lo que da;

b = (sin (37 °)) × 53 / (sin (100 °)) = 32,39 metros

c = (sin (43 grados)) × 53 / (sin (100 grados)) = 36,7 metros

Por lo tanto, el Estudiante 2 está más cerca, ya que está aproximadamente a 32,39 metros de distancia.

To find the expected value of a discrete probability distribution, we multiply each possible outcome by its probability and then sum the products. In this case, we have:

E(X) = 0(3/16) + 1(3/16) + 2(1/8) + 3(1/2)

    = 0 + 3/16 + 1/4 + 3/2

    = 1.5

Therefore, the expected value of this distribution is 1.5.

In probability theory, the expected value (also known as the mean or average) of a discrete probability distribution is a measure of the central tendency of the distribution. It represents the theoretical long-term average of the values taken by a random variable over an infinite number of trials.

To find the expected value of a discrete probability distribution, we multiply each possible value of the random variable by its corresponding probability and add up the products. In other words, if X is a discrete random variable with possible values x1, x2, ..., xn and corresponding probabilities p1, p2, ..., pn, then the expected value E(X) is:

E(X) = x1 * p1 + x2 * p2 + ... + xn * pn

For example, consider the discrete probability distribution given in the table:

x     |  0  |  1  |  2  |  3  

pr(x) | 3/16| 3/16| 1/8 | 1/2

To find the expected value of this distribution, we multiply each possible value of X by its corresponding probability and add up the products:

E(X) = 0*(3/16) + 1*(3/16) + 2*(1/8) + 3*(1/2) = 0 + 0.1875 + 0.25 + 1.5 = 1.9375

Therefore, the expected value of this distribution is 1.9375.

To learn more about discrete probability distribution refer below

https://brainly.com/question/9602705

#SPJ11

Answer:

Line A is the right answer.

Answer:

a is right linear means straight line

Step-by-step explanation:

If y1 and y2 are continuous random variables with joint density function f (y1, y2) = ky1e−y2 , 0 ≤ y1 ≤ 1, y2 > 0 then,

a) k = 1 - e^(-1) ≈ 0.632,

b) fy1(y1) = ∫f(y1, y2)dy2 = ky1∫e^(-y2)dy2 = ky1(-e^(-y2))|y2=0 to y2=∞ = k*y1,

c) f(y2 | y1 < 1/2) = f(y1,y2)/fy1(y1) = e^(-y2)/(1 - e^(-1))*y1, for 0 ≤ y1 ≤ 1/2 and y2 > 0.

(a) To find k, we must integrate the joint density function over the entire range of y1 and y2, and set the result equal to 1, since the density function must integrate to 1 over its domain:

∫∫ f(y1,y2) dy1 dy2 = 1

∫0∞ ∫0¹ f(y1,y2) dy1 dy2 = 1

∫0∞ (k y1 e^-y2) dy2 ∫0¹ dy1 = 1

k ∫0∞ (y1 e^-y2) dy2 ∫0¹ dy1 = 1

k ∫0¹ y1 dy1 ∫0∞ e^-y2 dy2 = 1

k(1/2)(1) = 1

k = 2

Therefore, the joint density function is f(y1,y2) = 2y1e^-y2, 0 ≤ y1 ≤ 1, y2 > 0.

(b) To find fy1(y1), we must integrate the joint density function over all possible values of y2:

fy1(y1) = ∫0∞ f(y1,y2) dy2

fy1(y1) = 2y1 ∫0∞ e^-y2 dy2

fy1(y1) = 2y1(1) = 2y1

Therefore, fy1(y1) = 2y1, 0 ≤ y1 ≤ 1.

(c) To find f(y2 | y1 < 1/2), we need to use Bayes' rule:

f(y2 | y1 < 1/2) = f(y1 < 1/2 | y2) f(y2) / f(y1 < 1/2)

We know that f(y2) = 2y1e^-y2 and f(y1 < 1/2) = ∫0^(1/2) 2y1e^-y2 dy1.

First, we need to find f(y1 < 1/2 | y2):

f(y1 < 1/2 | y2) = f(y1 < 1/2, y2) / f(y2)

f(y1 < 1/2, y2) = ∫0^(1/2) ∫0^y2 2y1e^-y2 dy1 dy2

f(y2) = ∫0∞ ∫0^1 2y1e^-y2 dy1 dy2

Using these equations, we can find:

f(y1 < 1/2 | y2) = ∫0^(1/2) ∫0^y2 2y1e^-y2 dy1 dy2 / ∫0∞ ∫0^1 2y1e^-y2 dy1 dy2

f(y1 < 1/2 | y2) = 1 - e^(-y2/2)

f(y2) = 2y1e^-y2

f(y1 < 1/2) = ∫0^(1/2) 2y1e^-y2 dy1 = [2(1-e^(-y2/2))] / y2

Substituting these expressions back into Bayes' rule, we get:

f(y2 | y1 < 1/2) = (1 - e^(-y2/2)) * y1e^-y2 / (1-e^(-y2/2))

Simplifying this expression, we get:

f(y2 | y1 < 1/2) = y1 * e^(-y2/2), 0 < y2 < ∞

Therefore, the conditional density of y2 given that y1 < 1/2 is f(y2 | y1 < 1/2) = y1 * e^(-y2/2), 0 < y2 < ∞.

Learn more about continuous random variables:

https://brainly.com/question/12970235

#SPJ11

The locus of points three inches above the top of a table that measures four feet by eight feet is a rectangle parallel to the table's surface and located three inches above it. To construct the locus of points in a plane that are equidistant from the sides of a triangle A and at a distance d from point P, we can draw perpendicular bisectors from the sides of A and locate the points where these bisectors intersect. These points will form the locus of points equidistant from the sides of A and at a distance d from point P, labeled as X.

1. The locus of points three inches above the top of a table that measures four feet by eight feet is a rectangle with dimensions four feet by eight feet, parallel to the table's surface and located three inches above it.

2. To construct the locus of points in a plane that are equidistant from the sides of triangle A and at a distance d from point P, we can draw perpendicular bisectors from the sides of A.

3. The perpendicular bisectors will intersect at points that are equidistant from the sides of A and at a distance d from point P. These points form the locus of points and are labeled as X.

4. The locus of points X can be visualized as a set of points forming a shape in the plane.

To know more about bisectors intersect here: brainly.com/question/29548646

#SPJ11