suppose that f is an even function, g is odd, both are integrable on [-5,5]..

The ordered pair which s included in the solution to this system of inequality y ≥ 2/3x + 2, y < - 1/3x + 1 is (-6, -2) and (-6, 3).

The correct answer option is option B and C

y ≥ 2/3x + 2

y < - 1/3x + 1

Check all that applies:

(x, y) = (−6, −3)

(x, y) = (−6, −2)

(x, y) = (−6, 3)

(x, y) = (−6, 4)

y ≥ 2/3x + 2

substitute x = -6 into the inequality

y ≥ 2/3(-6) + 2

y ≥ -12/3 + 2

y ≥ - 4 + 2

y ≥ - 2

(x, y) = (-6, -2)

y < - 1/3x + 1

substitute x = -6 into the inequality

y < -1/3(-6) + 1

y < 6/3 + 1

y < 2 + 1

y < 3

(x, y) = (-6, 3)

So therefore, the solution to the system of inequality is (-6, -2) and (-6, 3).

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Expressions which represent the distance between the sandbag and the target is:

250-75 meters

i.e. 175 meters

Jonas's dropped a sandbag from a hot air balloon at a target that is 250 meters below the balloon.

At this moment, the sandbag is 75 meters below the balloon.

Then, distance between the sandbag and the target is:

250-75 meters

i.e. 175 meters

Hence, expressions which represent the distance between the sandbag and the target is:

250-75 meters

i.e. 175 meters

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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By using the Pythagorean theorem, we conclude that the length of the segment is 3.2 units.

We want to find the length of the graphed segment. In the grid, we can see that the horizontal displacement between the two ends measures one unit, and the vertical displacement measures 3 units.

So the length can be tought as the hypotenuse of a right triangle whose legs measure one unit and 3 units.

By using the Pythagorean theorem, we can find that lenght L by.

L^2 = 1^2 + 3^2

Now, if we apply the square root in both sides we will get:

L = √(1^2 + 3^2) = √(1 + 9) = √10 = 3.2

We conclude that the length of the segment is 3.2 units.

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Answer:

According to the proposed interrogate, as well as the graph provided, the correct answers to such are identified as B. Y = -2x + 5 and C. 2x + y = 4.

Step-by-step explanation:

To evaluate such, a comprehension of linear Cartesian data is required:

Slope = rise/run. If there is a negative rise, the direction of the line is proportional to the left-hand side as it exponentially grows or augments in units.

Y-intercept: The peculiar point in which the linear data observed intersects the y-axis.

X-intercept: The peculiar point in which the linear data observed intersects the x-axis.

Since this is a negative linear, all negative slopes apply.

The interrogate states, “Check all that apply.” Thus, there may be more than one correct answer, shall such be disseminated.

A. Cannot be the answer as the line should have been a horizontal line contained within quadrants I and II on the Cartesian Plane.

B. Contains a negative slope, thus is disclosed as a correct answer.

C. This configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

2x + y = 4

Y = -2x + 4 <== Slope-Intercept Form (Contains a negative slope, thus considered a correct answer.

D. Likewise, this configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

X - y = 9

-y = -x + 9

Y = x - 9 <== Slope-Intercept Form (Cannot be considered as the correct answer, given the positive slope configuration, thus is marked out).

Thus far, as evaluated, the correct answers to the proposed interrogate, as according to the linear data provided in the Cartesian Plane is acknowledged, and henceforth disseminated, as B. Y = -2x + 5 and C. 2x + y = 4.

*I hope this helps.

Answer:

28 degrees

Step-by-step explanation:

We know that (4x + 7) + (2x + 5) add up to a straight angle = 180 degrees, so we have the equation 4x + 7 + 2x + 5 = 180.

By combining like terms, we get 6x + 12 = 180.

Subtract 12 from both sides of the equation to get 6x = 168. Divide both sides by 6 and you get x = 28.

Answer: The height of the stone after time "t" is given by the function h(t) = 100t - 5t^2, where t is in seconds. To find the maximum height, we need to find the value of t for which the height is greatest.

To do this, we can take the derivative of h(t) with respect to t, which gives us the rate of change of height with respect to time. Then, we can set this derivative equal to 0 and solve for t. The value of t that satisfies this condition will be the time at which the height is at its maximum.

h'(t) = 100 - 10t

Setting h'(t) = 0, we get:

100 - 10t = 0

10t = 100

t = 10

So, the maximum height is h(10) = 100 * 10 - 5 * 10^2 = 100 - 500 = -400 meters.

Since the height cannot be negative, the maximum height the stone can reach is 100 meters.

Step-by-step explanation:

The area of the triangle is 52.32 square units

from the question, we have the following parameters that can be used in our computation:

The triangle (see attachment)

The base of the triangle is calculated as

base = 12 * tan(36)

The area of the triangle is then calculated as

Area = 1/2 * base * height

Where

height = 12

So, we have

Area = 1/2 * base * height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 12 * tan(36) * 12

Evaluate

Area = 52.32

Hence, the area of the triangle is 52.32 square units

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Answer:

B

Step-by-step explanation:

Angle 1 is an exterior angle, while angle 6 is an interior angle and so they are not congruent

Answer: A,B,D,F

A. Replace "a number with the variable, n

B. The two operations are multiplication and addition

C. NO

D. The constants are 6 and 9

E. NO

F. The expression is written as 6(9 + n)

Step-by-step explanation:

Proper way to complete this mathematical operation is A, B, D, F.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

The question is itself self-explanatory.

a. Replace "a number" with the variable, n.

b. The two operations are multiplication and addition.

d. The constants are 6 and 9.

f. The expression is written as 6(9 + n).

Therefore, expression is written as 6(9 + n).

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Complete question:

Write the expression. Then, check all that apply.

six times the sum of nine and a number

A 2-column table with 5 rows. Column 1 is labeled Key Words with entries six, times, the sum of, nine, a number. Column 2 is labeled Replace with entries 6, times, (+), 9, n.

Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

Given, a number 2,016

we have to find the place and face value of 6 in the given number 2,016.

So, the Place value of 6 in the given number is ones.

Ones is the place value of the digit 6 in the number 2,016

Also, the Face value of 6 in the given number is 6.

6 is the face value of the digit 6 in the number 2,016

Hence, Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

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Answer:

Thank youuuu!!

Applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers is GCD of that numbers .

Given :

You probably know the Fibonacci numbers 1 , 1 , 2 , 3 , 5 , 8 , ⋯ , where f n+2 = f n+1 + f n and we number as f 1 = 1,f 2 = 1 . Try applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers .

Euclidean algorithm :

The Euclidean Algorithm is a technique for quickly finding the GCD of two integers .

GCD ( 1 , 2 )

2 = 1 * 2 + 0

GCD ( 1 , 0 )

hence GCD ( 1 , 2 ) is 1 .

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Answer:

no

Step-by-step explanation:

Answer:

no its not

Step-by-step explanation:

cause they have the same denominator and 6 is more than 2 so there for 6/12 is not less than 2/12

The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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Answer:

Step-by-step explanation:

Given that

\(\alpha =2.5\) ,\(\beta =220\)

The weibull distribution with parameters \(\alpha \ \ and \ \ \beta\)

where \(\alpha =0 \ \ , \beta =0\)

\(F(x,\alpha ,\beta) \left|\begin{array}{cc}\frac{\alpha }{\beta } x^{\alpha-1e^-(x/\beta)^\alpha &x\geq 0\\0&x<0\end{array}\right\)

Then,

\(F(x,\alpha ,\beta )=\left|\begin{array}{cc}0&x<0\\1-e^-^{(x/\beta)}^\alpha &x\geq 0\end{array}\right\)

A) The probability that a specimen's lifetime is at most 250 is

\(P(X\leq 250)=F(250,2.7,220)\\\\=1-e^-^(250/220)^{2.7}\\\\=1-0.2436\\\\=0.7564\)

The probability that the specimen's life time is more than 300 is

\(P(X>300)=1-P(X\leq 300)\\\\=1-F(300;2.7,220)\\\\=1-(1-e^-^{(300/220)^{2.7}\)

\(=e^-^{(300/220)^{2.7}\)

= 0.0992

b)The probability of the specimen's lifetime is between 100 and 250

\(P(100<X<250)=P(X<250)-P(X<100)\\\\=F(250;2.7,220)-F(100;2.7,220)\\\\=(1-e^-^{(250/220)^2^.^7})-(1-e^-^{(100/220)^2^.^7})\\\\=(1-0.2436)-1(1-0.8878)\\\\=0.6442\)

c) The value such that exactly 50% of all specimens have lifetimes exceeding that value is

\(P(X>x)=0.50\\\\1-P(X<x)=0.50\\\\1-(1-e^-^{(x/220)^{2.7}}=0.50\\\\e^-^{(x/220)^{2.7}}=0.50\\\\-(x/220)^{2.7}=In(0.50)\\\\(x/220)^{2.7}=-In(0.50)\\\\(x/220)=[-In(0.50)]^{(\frac{1}{2.7})} \\\\x=220[-In(0.50)]^{(\frac{1}{2.7})}\)

x = 192.07

ANSWER

x = 20

EXPLANATION

The equation given can be express as

y = 0.25x + 50

y = 0.30x + 40

Since, both equations are functions

Equate the two functions together

0.25x + 50 = 0.30x + 40

Collect the like terms

0.25x - 0.30x = 40 - 50

x(0.25 - 0.30) =-10

x(-0.5) = -10

-0.5x = -10

Divide both sides by -0.5

-0.5x / -0.5 = -10/-0.5

x = 10/0.5

x = 20

When collecting the like terms, we isolate values with the same variables from values with a different variables.

If a positive sign crosses an equality sign it automatically becomes a negative sign and if a negative sign crosses an equality operator it automatically becomes a positive sign

Answer:

4, 7, 17

Step-by-step explanation:

4x4=16

7x7= 49

17x17= 289

I hope this helps!!

Answer:

-11

Step-by-step explanation:

Notice how

\(f(x)=x^{2} +8x+1\)

So when we have

\(f(-6)=(-6)^{2} +8(-6)+1= 36-48+1=-11\)

The answer is:

f(-6) = -11

Step-by-step explanation:

Plug in -6 for x:

\(\sf{f(x)=x^2+8x+1}\)

\(\sf{f(-6)=(-6)^2+8(-6)+1}\)

Simplify this:

\(\sf{f(-6)=36-48+1}\)

\(\sf{f(-6)=-12+1}\)

\(\sf{f(-6)=-11}\)

Step-by-step explanation:

16 - 10 × 1/5 + 13

16 - 5 + 13

11 + 13

24

Step-by-step explanation:

10/5=2

16-2+13=27.

d. 27

The total surface area of solid is,

S = 220 m²

And,  The volume of the prism is, 200 m³

We have to given that;

A solid prism is shown in figure.

Since, The surface area of a prism is,

S = (2 × Base Area) + (Base perimeter × height)

Where, "S" is the surface area of the prism.

Hence, We get;

base area = 5 x 10 = 50 m²

height = 4 m

Base Perimeter = 2 (5 + 10) = 30

Hence, We get;

S = (2 x 50) + (30 x 4)

S = 100 + 120

S = 220 m²

Since, A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;

V = base area × height.

Now, For given figure,

Volume of the prism = base area × height

base area = 5 x 10 = 50 m²

height = 4 m

Hence, Volume = 50 × 4 m³

= 200 m³

Thus, The volume of the prism is, 200 m³

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The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.

Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.

A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.

According to the given information:

The Capital Asset Pricing Model (CAPM) is expressed as:

R = Rf + beta*(Rm - Rf)

Where:

R = Required rate of return

Rf = Risk-free rate of return

beta = Beta coefficient (systematic risk)

Rm = Expected market return

Using the given values, we can compute the required rate of return for each stock:

Stock with beta of 0.5:

R = 5% + 0.5*(10% - 5%)

R = 7.5%

Stock with beta of 2:

R = 5% + 2*(10% - 5%)

R = 15%

Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.

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Answer:

A. down

Step-by-step explanation:

The parent graph is

f(x)=x

If this graph is transformed to obtain

g(x)=f(x)−4

The subtracttion means the graph will shift downward vertically

The graph of g(x) is obtained by shifting f(x) down by 4 unit.

Therefore the direction is down.

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Answer:

The constant of proportionality is the ratio between two directly proportional quantities. ... Two quantities are directly proportional when they increase and decrease at the same rate.

Step-by-step explanation:

by the Angle sum property of triangle,

55+75+(-6+7x) = 180

=> 130 +(-6+7x) = 180

=> (-6+7x) = 180-130

=> (-6+7x) = 50

=> 7x = 50+6

=> 7x = 56

=> x= 56/7

=> x = 8

Answer: first, second and fourth are primes, the third is not-prime.

Hope it helps :)

The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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