Question Solve the following equation for on the interval [0°, 360°). -6 sec (0) -3 = -15 Enter your answers in degrees. Provide your answer below: 9= and 8 =

The final output displays that the p-value is less than the significance level of 0.05, i.e. 0.01739 < 0.05. Therefore, the null hypothesis is rejected and the alternative hypothesis is accepted. We conclude that the GNP series is explosive.

The given R code represents the plotting of the GNP series, gnp and then test for a unit root against the alternative that the process is explosive.

The code is:

library(astsa)library(tseries)head(gnp)print(gnp)

GNP stands for Gross National Product and it is the total amount of goods and services that a country produces within a certain period of time.

The following is the R code for the same:

library(astsa)library(tseries)plot(gnp, main="GNP", xlab="Year", ylab="GNP")abline(h=mean(gnp), col="red")#

Testing for unit root test

adf.test(gnp, alternative = "explosive")

The output generated by the code is:GNP series, gnp is plotted in the above code using the plot() function.

Then, the abline() function is used to add a red horizontal line for the mean of the GNP series.

The final output displays that the p-value is less than the significance level of 0.05, i.e. 0.01739 < 0.05. Therefore, the null hypothesis is rejected and the alternative hypothesis is accepted.

Thus, we conclude that the GNP series is explosive.

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Answer:

30.8936

Step-by-step explanation:

Pressure guage reading is 8% lower than tbe actual pressure.

Therefore, for a tyre with guage pressure, 33.58 ;

The actual pressure of tyre would be :

Guage pressure - 8% of guage pressure

33.58 - (0.08 * 33.58)

33.58 - 2.6864

= 30.8936

Actual pressure = 30.8936

If the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

The mass of the object cannot be determined with the given information. Acceleration is related to force and mass through Newton's Second Law: F = ma. However, in this case, we are given the acceleration and force, but not the mass. To find the mass, we would need either the acceleration and the force, or the force and the mass.

However, if we assume that the force and acceleration are both in the same direction, we can use the formula F = ma to find the mass. Rearranging the formula, we get m = F/a.

Substituting the given values, we get:

m = 10 N / 12 m/s²

m = 0.83 kg

So, if the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

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Complete Question:

A moving train accelerates at a rate of 12 meters per second. What would your mass be if the applied force were 10N?

Answer:

D

Step-by-step explanation:

4C1*5C1*6C1*8C1

=960

An equation that can be used to determine how many months Ely will need to save money to reach his goal of a total of $1,550 in his savings account is 200 + 150x = 1,550.

An equation is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.

Equations use the equal symbol unlike mathematical or algebraic expressions, which combine variables with numbers, constants, and values using mathematical operands.

The intended monthly savings = $150

The amount already in Ely's account = $200

The total amount Ely needs = $1,550

Let the number of months required to reach $1,550 = x

200 + 150x = 1,550

150x = 1,550 - 200

150x = 1,350

x = 9 months.

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The measure of the angle can be found by solving the equation

x = 5(180 - x) - 660.

Let's assume the measure of the angle is x. The supplement of the angle is 180 - x since they are supplementary angles.

According to the given information, the measure of the angle is 660 less than five times its own supplement. Mathematically, we can represent this as

                                          x = 5(180 - x) - 660

To solve this equation, we first distribute 5 to 180 - x, resulting in

                                                      900 - 5x

Then we can simplify the equation as follows: x = 900 - 5x - 660. Combining like terms, we get 6x = 240. Dividing both sides by 6, we find that x = 40.

Therefore, the measure of the angle is 40 degrees.

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One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

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The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

The Cost of One Tomato Plant is $1.4 and the cost of one pepper plant is $1.25 .

Here are a pair of two linear equations in two variables.

Let assume ,

One tomato plant is x

one pepper plant is y

Pair of two linear equations in two variables :

         4x + 3y = 9.35     →  (i)

        2x + 11y = 16.55    →  (ii)

Multiplying equation (ii) by 2 , we have :

      4x + 3y = 9.35    (iii)

    4x + 22y = 33.10   (iv)

Subtracting equation (iv) from (iii)

     19y = 23.75

 ⇒    y = 1.25

substituting the value of y in any of the equation (i) & (ii), we have:

      4x +3(1.25) = 9.35

 ⇒    x = 1.4

therefore , x = 1.4 & y = 1.25 is the point where the given equations intersect.

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The Taylor polynomial T₅(x) is 0.99500416 and by use the Error Bound the maximum possible size of the error is 49943.1 × 10⁻⁷.

What is Taylor Series?

The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms represented in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equivalent for the majority of typical functions at this point.

Taylor series or Taylor expansion:

Infinity ∑ (n = 0) fⁿ(a)/n! (x - a)ⁿ

Where,

n! = factorial of n

a = real or complex number

fⁿ(a) = nth derivative of function f evaluated at the point a.

As given function is,

f(x) = cosx, a = 0, x = 0.1

Taylor polynomial of degree 'n' for f(x) center a,

Tₙ(x) = f(a) + f'(a)(x - a) + f''(a)/2 (x - a)² + f'''(a)/3 (x - a)³ + ......+ fⁿ⁻¹(a)/(n - 1)! (x - a)ⁿ⁻¹ + fⁿ(a)/n! (x - a)ⁿ

Evaluate values as follows:

f(x) = cosx ⇒ f(0) = 1

f'(x) = -sinx ⇒ f'(0) = 0

f''(x) = -cosx ⇒ f''(0) = -1

f'''(x) = sinx ⇒ f'''(0) = 0

f⁴(x) = cosx ⇒ f⁴(0) = 1

f⁵(x) = -sinx ⇒ f⁵(0) = 0

Substitute obtained values in Taylor series,

T₅(x) = 1 + (0) (x - 0) + (-1)/2 (x - 0)² + 0 + 1/24(x - 0)⁴ + 0

T₅(x) = 1 -1/2x² + 1/24x⁴

At x = 0.1

T₅(0.1) = 1 -1/2(0.1)² + 1/24(0.1)⁴

T₅(0.1) = 1 - 0.005 + 4.16 × 10⁻⁶

T₅(0.1) = 0.99500416

Hence, the Taylor polynomial T₅(x) is 0.99500416.

Evaluate the maximum possible size of the error:

cos(0.1) = 0.99999847

T₅(0.1) = 0.99500416

Icos(0.1) - T₅(0.1)I = 0.99999847 - 0.99500416

Icos(0.1) - T₅(0.1)I = 0.00499431

Icos(0.1) - T₅(0.1)I = 49943.1 × 10⁻⁷.

Hence, the Error Bound the maximum possible size of the error is 49943.1 × 10⁻⁷.

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$k = 3\sqrt{2}$.

We have:

\begin{align*}

\int^k_0 (2x^3 -kx^2 +2k)dx &= \left[\frac{1}{2}x^4 - \frac{k}{3}x^3 + 2kx \right]^k_0 \

&= \frac{1}{2}k^4 - \frac{k^4}{3} + 2k^2 \

&= \frac{3}{6}k^4 - \frac{2}{6}k^4 + \frac{12}{6}k^2 \

&= \frac{1}{6}k^4 + 2k^2

\end{align*}

Since we are given that this equals 12, we have:

\begin{align*}

\frac{1}{6}k^4 + 2k^2 &= 12 \

\frac{1}{6}k^4 &= 12 - 2k^2 \

k^4 &= 72 - 12k^2 \

k^4 + 12k^2 - 72 &= 0

\end{align*}

This is a quadratic in $k^2$, so we can solve for $k^2$ using the quadratic formula:

\begin{align*}

k^2 &= \frac{-12 \pm \sqrt{12^2 - 4(1)(-72)}}{2(1)} \

&= \frac{-12 \pm \sqrt{576}}{2} \

&= -6 \pm 12

\end{align*}

Since $k^2$ cannot be negative, we take the positive value:

�

2

=

6

+

12

=

18

k

2

=6+12=18

Thus, $k = \pm\sqrt{18}$. However, since $k$ represents the length of a side of the square, we must take the positive value:

�

=

18

=

3

2

k=

18

​

=3

2

​

Therefore, $k = 3\sqrt{2}$.

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According to Weber's law, two items must differ in weight by "5 percent"of weight in order to detect a difference.

We are given that Weber's law

For weight discrimination, Weber’s law states that the JND is proportional to the weight of the stimulus.

The JND is defined as the smallest difference between two weights that can be detected by an observer.

The proportionality constant is known as Weber’s fraction and varies depending on the type of stimulus and the sensory modality involved.

For weight discrimination, Weber’s fraction is typically around 2-3%.

This means that two items must differ in weight by approximately 2-3% of their weight in order to detect a difference.

The difference of weight in percent is 5%, the correct option is A.

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Answer:

-2

Step-by-step explanation:

G(x) = 3x -2

Let x = 0 to find the y intercept

G(0) = 3(0)-2

       =-2

Answer:

$21.25

Step-by-step explanation:

Multiplying 0.85 by 25 gives 21.25

The height of the flagpole is 12.9 feet to the nearest tenth.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

The boy is 5' 3" tall and his shadow is 4 feet.

The shadow of the flagpole is 17 feet.

The boy is 5.25 feet tall.

Let the height of the flagpole is h feet.

So,

17/h = 5.25/4

h = 68/5.25

h = 12.95

h = 12.9 to one decimal place.

Therefore, h = 12.9 to one decimal place.

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The circumference of circle of radius 70 cm is 440 \(cm^{2}\).

According to the question,

We have the following information:

Radius of the circle = 70 cm

(Diameter is twice that of its radius..)

We know that the following formula is used to find the circumference of circle:

Circumference of circle = 2πr

(More to know: the formula to find the area of circle is π\(r^{2}\).)

(More to know: there are two values of π. One is 3.14 and one is 22/7.)

Circumference of circle = 2*(22/7)*70

Circumference of circle = 440 \(cm^{2}\)

Hence, the circumference of the circle of radius 70 cm is 440 \(cm^{2}\).

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diamater:

\(d=2r \\\\d=2 \cdot 16 \\\\d=32\)

circumference:

\(C=2 \pi r \\\\C=2 \cdot \p \cdot 16 \\\\C=32 \cdot \pi \\\\C \approx 100.48\)

Hope that I helped you!

Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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a) The ratio of the distance Colton has traveled to the amount of time he has been traveling is; 14 mph which represents the average velocity

b) The value of d when travelling for 6 hours at the same velocity is; 84 miles

c) The value of h when he bikes 200 miles is; 14.3 hours

a) We are given;

Distance traveled = 49 miles

Time taken = 3.5 hours

Ratio of distance to time = 49/3.5 = 14 mph

This represents the average velocity

b) We are told that he traveled the same rate for 6 hours. Thus;

Distance is gotten from the formula;

d = velocity * time

d = 14 * 6

d = 84 miles

c) He wants to bike 200 miles. When h is the number of hours taken, then; h = d/v

h = 200/14

h = 14.3 hours

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Answer:

1. to c.

2. to d.

3. to a.

4. to b.

Step-by-step explanation:

These answers should be right.

Hope this helps!

The matching of the polynomials to their correct names are:

a. h(x) = 15x+2 is a linear binomial

b. j(x)=x²-3x³ + 9x²  is a  Quartic trinomial

c. f(x)= 3x² - 5x+7 is a Quadratic trinomial

d. 8(x)=-5x³ is a Cubic monomial

A polynomial is an expression having more than one algebraic terms.

1) A quadratic trinomial is a polynomial that is defined as a quadratic expression with all three terms in the form of ax² + bx + c, where a, b, and c are numbers and not a 0.

2) A cubic monomial is defined as a a monomial that has a degree of 3.

3) Linear binomial is defined as a polynomial with two terms whose variable has degree 1. For example, 4x − 5 or 3x + 12 are both linear binomials.

4) A quartic trinomial is defined as a polynomial with three terms having the highest degree 4

Thus:

a. h(x) = 15x+2 is a linear binomial

b. j(x)=x²-3x³ + 9x²  is a  Quartic trinomial

c. f(x)= 3x² - 5x+7 is a Quadratic trinomial

d. 8(x)=-5x³ is a Cubic monomial

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Answer:

Step-by-step explanation:

Given equations

This system has one solution since the two lines represented by the equations have different slopes.

Solution:

And y is:

The point is:

Answer:

m=-5

Step-by-step explanation:

distribute -3: -3m+6=21

subtract 6 from both sides: -3m=15

divide by negative three: m=-5

Answer:

m = -5

Step-by-step explanation:

-3(m-2)=21

-3m + 6 = 21

-3m = 15

         15

m = --------

         -3

m = -5

Answer:

y= -2x-2

Step-by-step explanation:

firstly find the gradient

m=y2-y1/x2-x1

m= -10-2/4-(-2)

m= -12/6

m= -2

then calculate for the equation by using

y-y1=m(x-x1)

y-2= -2(x-(-2)

y-2= -2x-4

y= -2x-2

Answer:

Step-by-step explanation:

Answer:

wait didn't you answer the question sir I'm confused

Step-by-step explanation:

Answer:

y = 6/5x - 2 (or y = 1.2x - 2)

Step-by-step explanation:

To find the slope-intercept form ( = mx + b) you need to rearrange the equation of the line:

Step 1 - Add 18x to both sides

15y = 18x - 30

Step 2 - Divide both sides by 15.

y = 6/5x - 2

The like radicals are 3x√x²y, –12x√x²y, x√yx² and 2√x²y.

A radical expression is an expression containing a square root.

Given are some expressions,

Like radicals are those whose entities in the square root are the same.

So, from the given options, like radicals are:

3x√x²y = This is like radical with the entity x²y  inside the square root.

–12x√x²y = This is like radical with the entity x²y  inside the square root.

x√yx² = This is like radical with the entity x²y  inside the square root.

2√x²y = This is like radical with the entity x²y  inside the square root.

Hence, The like radicals are 3x√x²y, –12x√x²y, x√yx² and 2√x²y.

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