What values of a and b make f(x) = x3 + ax2 +bx have:
a) a local max at x = -1 and a local max at x = 3?
b) a local minimum at x = 4 and a point of inflection at x = 1?

Answer:

Step-by-step explanation:

the fewer jumps=the jumps Ronaldo did - the jumps Ahanu did

                          = 1080-1050

                          = 30

Answer:

1) by using a protractor

2) by finding a point

3) by extending the line of the angle until it reaches the other side of the field.

Step-by-step explanation:

There are different methods he can use to draw the angle on the other side of the yard, three of which are the following:

1) he can use a protractor to measure the angle he drew. That way he can go to the other side of the field and measure the same angle there. So then he can draw the angle in the new location.

2) He can draw a line on the given angle and find a point that passes through that line. Then he can draw a perpendicular line to the origin of the angle until it reaches the other side of the yard. This perpendicular line will cross the other side of the yard. This point where the line crosses the other side of the yard will be the new origin. With this new origin find the point again and draw a line that goes through the new origin and the new point he found.

3) Depending on the dimensions of the field, he can draw extend the line of the angle in such a way that it reaches the other side of the field. Then the angle will be on the other side. He can then use a square to move it around to where he wants it to be.

Answer:

x=75

Step-by-step explanation:

5x+5(x-10)=700

5x+5(x)+5(-10)=700

5x+5x-50=700

10x-50=700

    +50. +50

10x=750

/10. /10

x=75

Hopes this helps

Answer:

\( \sf \: x = 75\)

Step-by-step explanation:

Given equation,

→ 5x + 5(x - 10) = 700

Now the value of x will be,

→ 5x + 5(x - 10) = 700

→ 5x + 5x - 50 = 700

→ 10x = 700 + 50

→ x = 750/10

→ [ x = 75 ]

Hence, the value of x is 75.

The age of the artifact is 3523.77 years.

What is radioactive decay?

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Here,

The half-life of the reaction is defined as the time required by a substance to reach half its initial concentration. It is represented by t(1/2)

 All radioactive decay processes follow the first-order reaction.

The equation for the half-life for first-order reaction follows:

t(1/2) = 0.693/k....(1)

where,

k = rate constant of a first-order reaction

Given value:

t(1/2) = 5715 years

Put the value of t in equation (1), and we get

k = 0.693/5715

k = 1.21×10⁻⁴yr

The integrated rate law expression for first-order reaction follows:

t = 2.303/k×㏒(a/(a-x))

where,

t = time period

a = initial concentration of the reactant = 58.2 counts per minute

(a-x) = Concentration of reactant left after time t = 38.0 counts per minute

k = rate constant of a first-order reaction

Put the values in the equation and we get

t = 2.303/1.21×10⁻⁴㏒58.2/38

t = 3523.77 years.

Hence, the age of the artifact is 3523.77 years.

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Answer:

a) The coordinates of the missing vertex = (7, 8)

b) Area = 18 square units

   Perimeter = 18 units

Step-by-step explanation:

a) We know three of the four vertices:

A: (4, 2)           C ______ D(?)

B: (7, 2)               |             |

C: (4, 8)           A |______| B  

To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:

\( B_{x} - A_{x} = 7 - 4 = 3 \)                    

Hence, the distance of point D from point C in the x-direction is:

\( D_{x} = C_{x} + 3 = 4 + 3 = 7 \)

Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:

\( C_{y} - A_{y} = 8 - 2 = 6 \)  

Then, the distance of point D from point B in the y-direction is:

\( D_{y} = B_{y} + 6 = 2 + 6 = 8 \)

Therefore, the coordinates of the missing vertex (point D) are:

\( D = (D_{x}, D_{y}) = (7, 8) \)    

b) The area of the rectangle is:

\( a = (B_{x} - A_{x})*(C_{y} - A_{y}) = 3*6 = 18 units^{2} \)

The perimeter is given by:

\( p = 2*(3 + 6) = 18 units \)

I hope it helps you!          

The integral ∫ \(1/x^2 dx\) from 1 to infinity converges and its value is 1. The integral ∫ 1/x dx from 1 to infinity diverges. The integral ∫\(e^(-2) dx\) from 1 to infinity converges and its value is\(-e^(-2)\). The integral ∫ \(e^x\) dx from negative infinity to infinity diverges. The integral ∫\((1 + x^2) dx\) represents a convergent integral, but its exact value cannot be determined without specified bounds.

∫ \(1/(x^2) dx\) from 1 to infinity:

This integral converges. We can find its value by integrating the function and evaluating the limit as the upper bound approaches infinity:

∫ \(1/(x^2) dx = -1/x\) evaluated from 1 to infinity

= 0 - (-1)

= 1

∫ 1/x dx from 1 to infinity:

This integral diverges. As x approaches infinity, the function 1/x approaches 0, but it does not approach a finite value. Therefore, the integral diverges.

∫ \(e^(-2) dx\) from 1 to infinity:

This integral converges. Since e^(-2) is a constant, we can simply evaluate it over the interval:

∫\(e^(-2) dx = e^(-2) * x\) evaluated from 1 to infinity

=\((e^(-2) * infinity) - (e^(-2) * 1\))

\(= 0 - e^(-2)\\= -e^(-2)\\∫ e^x dx\\\)

This integral diverges. The function e^x grows exponentially as x approaches infinity or negative infinity, and it does not approach a finite value. Therefore, the integral diverges.

∫ \((1 + x^2) dx:\)

This integral converges. We can integrate the function to find its antiderivative:

∫ \((1 + x^2) dx = x + (1/3)x^3 + C\)

Since there are no specified bounds, we cannot determine the exact value of the integral. The antiderivative represents the general form of the integral.

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Answer:

\(-\frac{3}{2}\)

Step-by-step explanation:

You count up 3 units. Then you count to the left 2 units. It is negative because the line is slanted to the left.

Answer:

Step-by-step explanation:

The required area of the region bounded by the given graphs is 2 square units.

Given that area of the region bounded by the given graphs y= x-2 and

\(y^{2}\) = 2x - 4.

To find the area of the region bounded by the graph  y= x-2 and

\(y^{2}\) = 2x - 4 determine the points of intersection between two curves and solve the system of equation to find points.

Substitute y = x - 2 in the equation  \(y^{2}\) = 2x - 4 gives,

\((x-1)^{2}\) = 2x - 4.

On solving this quadratic equation gives,

x = 2 or x = 4.

Substitute these values of x in the equation y = x - 2, to find the corresponding values of y.

For x = 2, y = 2 - 2 = 0.

That implies, P1(2, 0)

For x = 4, y = 4 - 2 = 2.

That implies, P2(2, 2).

To find the area between the curves by using the following integral,

Area = \(\int\limits\)(y2 -y1) dx

Integrate above integral from x = 2 to x = 4 gives,

Area =  \(\int\limits^4_2\) (2x-4) - x-2 dx

On simplification gives,

Area =   \(\int\limits^4_2\) x- 2 dx

On integrating gives,

Area = \(x^{2}\)/2 - 2x \(|^{4} _2\)

Area = (\(4^{2}\)/2 -2×4) -  (\(2^{2}\)/2 - 2×2)

Area =  2 square units.

Hence, the required area of the region bounded by the given graphs is 2 square units.

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Answer: C

Step-by-step explanation: This is because there is no y - intercept. But since there is still a slope an x but be next to the 3/4. Which represents the rate of change.

Answer:

it depend on the question but if it is asking if they have the same answer then it is true

Step-by-step explanation:

Answer: false

Step-by-step explanation: 4+5=9 5+4=-9

a. The equilibrium interest rate,  is determined by the risk-free interest rate, the probability of repayment, and the cost of default.

b. The probability of the government repaying its loan can be calculated using the loan repayment threshold and the distribution of the output.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default.

a. To find the equilibrium interest rate,  we need to consider the risk-free interest rate, the probability of repayment, and the cost of default. The equilibrium interest rate is given by the formula: r = r + (c/p), where r is the risk-free interest rate, c is the cost of default, and p is the probability of repayment.

b. The probability that the government will repay its loan can be calculated by determining the percentage of the output distribution that exceeds the loan repayment threshold. Since 0.5 of the output is required to repay the loan, we need to calculate the probability that the output exceeds L/0.5.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default. This can be proven by comparing the repayment threshold (L/0.5) with the loan repayment amount (L + Lr). If the repayment threshold is greater than the loan repayment amount, the borrowing country would default.

Calculations and further details would be required to provide specific numerical answers for each part of the question.

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Considering the t-test applied, the number of degrees of freedom is given by:

d. 10.

For a sample of size n, the number of degrees of freedom is given by:

df = n - 1

When there are m samples, the amount of degrees of freedom is m multiplied by the sum of degrees of freedom of each sample.

In this problem, there are 2 samples with 6 - 1 = 5 df, hence:

2 x 5 = 10.

Option d is correct.

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Based on the graph given, the option that will show the same amplitude as function m is graph D.

The cosine function is seen as:

f(x) = A*cos(kx) + M

And the functions are:

When the function is m(x) = -2*cos(x+π).

The absolute value of the amplitude will be 2*|-2| = 4

Therefore, the option that can have the requirement above is graph D.

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In order to divide polynomials using synthetic division, you must be dividing by a linear expression and the leading coefficient (first number) must be a 1. For example, you can use synthetic division to divide by x + 3 or x – 6, but you cannot use synthetic division to divide by x2 + 2 or 3x2 – x + 7. If the leading coefficient is not a 1, then you must divide by the leading coefficient to turn the leading coefficient into a 1. For example, 3x – 1 would becomex minus 1/3 and 2x + 7 would becomex plus 7/2. If synthetic division will not work, then you must use long division.

Answer:

$368

Step-by-step explanation:

What is 50% of $736?

50% = \(\frac{50}{100}\) = \(\frac{1}{2}\)

We Take

736 x  \(\frac{1}{2}\) = $368

So, 50% of $736 is $368.

Answer:

option D

Step-by-step explanation:

According to Pascal's triangle

1

1 1

1 2 1

1 3 3 1

it is clear the second term will have an integer coefficient of 3

Therefore 3(x)²(-1)¹

3x²(-1)=-3x²

In a 3 x 3 between subjects factorial design, there are four sources of variance.

A 3 x 3 between subjects factorial design involves two independent variables, each with three levels, and participants are randomly assigned to different combinations of these levels. In this design, the four sources of variance are as follows:

Main Effect of Variable A: This source of variance represents the overall effect of the levels of the first independent variable. It assesses whether there are significant differences between the means of the three groups created by varying levels of Variable A.

Main Effect of Variable B: This source of variance represents the overall effect of the levels of the second independent variable. It examines whether there are significant differences between the means of the three groups created by varying levels of Variable B.

Interaction Effect: This source of variance assesses whether there is an interaction between the two independent variables. It examines whether the effect of one independent variable on the dependent variable differs across the levels of the other independent variable.

It evaluates whether the combined effect of the independent variables is greater (or lesser) than the sum of their individual effects.

Error Variance: This source of variance represents the variability in the dependent variable that cannot be accounted for by the independent variables. It includes random error, individual differences, and any other uncontrolled factors that may influence the outcome.

Therefore, in a 3 x 3 between subjects factorial design, there are four sources of variance: the main effects of Variable A and Variable B, the interaction effect between the two variables, and the error variance.

Each of these sources contributes to understanding the overall pattern of results and the relationships between the variables in the design.

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Answer:

1738

Step-by-step explanation:

Melissa has $11 remaining after purchasing 3.6 pounds of candy that cost $2.50 per pound.

Two or more expressions with an Equal sign is called as Equation.

Melissa had $20 to purchase candy for a party.

She purchased 3.6 pounds of candy that cost $2.50 per pound

Melissa spent 3.6 x $2.50

= 9 on candy.

Subtracting this amount from her initial $20, we get:

$20 - $9 = $11

Therefore, Melissa has $11 remaining after purchasing 3.6 pounds of candy that cost $2.50 per pound.

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Answer:

p=(-0.0125n) + 42.5

Step-by-step explanation:

Let p= price

n = number of shirts

m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

There are two points which are (1000, $30) and (3000, $5)

Our slope m = (p1-p2)/(n1-n2)

Filling in from our points m = (30-5)/(1000-3000)

m = 25/-2000

m = -0.0125

Since we have determined our slope, we can now find our equation

p-p1=m(n-n1)

p-30=(-0.0125)(n-1000)

p-30= (-0.0125n) + 12.5

p=(-0.0125n) + 42.5

Then, we can double check with the other point there:

p=(-0.0125n) + 42.5

5? (-0.0125x 3000) + 42.5

5= 5

Therefore,linear equation in the form p(n) is

p=(-0.0125n) + 42.5

Omitting the capital variable in a production function is likely to introduce a positive bias on the coefficient of labor, while omitting a variable measuring the probability of precipitation in an equation for concert attendance is likely to introduce a negative bias on the coefficient of the weekend dummy variable.

(c) In a production function for airplanes, if the capital variable is omitted, it is likely to introduce a positive bias on the coefficient of labor. The reason for this is that capital and labor are typically complementary inputs in production, and by omitting the capital variable, the model fails to account for the influence of capital on production. As a result, the estimated coefficient of labor will be higher than its true value, leading to a positive bias. The size of the bias will depend on the extent to which capital and labor are complements in the production process.

(d) In an equation for daily attendance at outdoor concerts, if the variable measuring the probability of precipitation is omitted, it is likely to introduce a negative bias on the coefficient of the weekend dummy variable. The reason for this is that the probability of precipitation at concert time is likely to affect attendance, and by omitting this variable, the model fails to capture its impact. As a result, the estimated coefficient of the weekend dummy variable will be lower than its true value, leading to a negative bias. The size of the bias will depend on the strength of the relationship between precipitation and attendance, as well as the proportion of concerts that are affected by precipitation.

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When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:

P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.

In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for

d.P = 0.433d + 14.7

Substitute P = 159 and solve for

d.159 = 0.433d + 14.7

Subtract 14.7 from both sides.

144.3 = 0.433d

Divide both sides by 0.433 to isolate d.

d ≈ 333.06

Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

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Therefore, the integral of |cos(s)| from 0 to π is 2.

To evaluate the integral of |cos(s)| from 0 to π, we first need to split the integral into two parts because the absolute value function affects the cosine function differently in the given interval.
1. Determine the intervals: From 0 to π/2, cos(s) is positive, so |cos(s)| = cos(s). From π/2 to π, cos(s) is negative, so |cos(s)| = -cos(s).
2. Split the integral: ∫₀ᵖᶦ |cos(s)| ds = ∫₀^(π/2) cos(s) ds + ∫(π/2)ᵖᶦ -cos(s) ds.
3. Integrate both parts: ∫₀^(π/2) cos(s) ds = [sin(s)]₀^(π/2), and ∫(π/2)ᵖᶦ -cos(s) ds = [-sin(s)](π/2)ᵖᶦ.
4. Evaluate the results: [sin(s)]₀^(π/2) = sin(π/2) - sin(0) = 1, and [-sin(s)](π/2)ᵖᶦ = -sin(π) + sin(π/2) = 1.
5. Add the two results: 1 + 1 = 2.

Therefore, the integral of |cos(s)| from 0 to π is 2.

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In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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Answer:

2:55 P.M

Step-by-step explanation:

After the movie: 10:26 A.M. + 2 hours and 51 minutes --> 1:17 P.M.

After the card game: 1:17 P.M. + 32 minutes --> 1:49 P.M.

After playing soccer: 1:49 P.M. + 1 hour and 6 minutes --> 2:55 P.M.

Answer:

The y-intercept of the function is 4

Step-by-step explanation:

The y-intercept is the point at which the graph crosses the y-axis.

Answer:

The independent variables in most cases is input variable. That is a value that does not depend on any other value and it can change independently.

Step-by-step explanation:

  All zeros of polynomial functions  -3/2 , 5i and -5i

Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively. Some of the methods used to find the zeros of polynomial are grouping, factorization, and using algebraic expressions.

2x^3+3x^2+50x+75 equal to 0

2x^3+3x^2+50x+75 = 0

⇒ x^2 (2x + 3) + 25 (2x + 3) = 0

⇒ (2x + 3) (x^2 + 25 ) = =

If any individual factor on the left side of the equation is equal to  0, the entire expression will be equal to 0

2x + 3 = 0

x^2 + 25 = 0

so, x = -3/2  and x = 5i and -5i

The final solution is all the values that make  2x^3+3x^2+50x+75 = 0

x = -3/2 , 5i and -5i

Hence, all zeros of polynomial functions  -3/2 , 5i and -5i

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Answer:

x=4

Step-by-step explanation:

4x+1=17

4x=16

x=4

6x-3=21

6x=24

x=4

because GL and GT are congruent.

LO and OT are congruent.