Find the value of K
(x+5) is a factor of the Polynomial p(x)
if p(x)=2x³ +7x²+Kx + 20

Adrian run in one hour is 5.698 km.

How to calculate speed, Distance and Time ?

Given,

Adrian ran in 1.5 hours = 8.547 km

We know, in 1.5 hours there is 90 minutes

so, in 1 min adrian ran = 8.547 / 90

                                    =  0.09496 km

We need to find the km in one hour means in 60 minutes

So, Adrian ran in 60 min = 60 * 0.09496

                                         =  5.6979 km or 5.698 km per hour

Hence, Adrian run in one hour is 5.698 km.

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Answer:

y = (-6)*x - 16

Step-by-step explanation:

The slope-intercept form of a line is given by the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

In this case, the line passes through the point (-4,8) and has a slope of -6, so we can plug these values into the equation to find the y-intercept:

y = (-6)*x + b

We know that the line passes through the point (-4,8), so we can substitute these values into the equation to solve for b:

8 = (-6)*(-4) + b

8 = 24 + b

b = -16

Therefore, the equation of the line in slope-intercept form is:

y = (-6)*x - 16

Details scalcets,

a) If u is unit vector , then, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2 where v and w also unit vectors.

b) Exact value of angle between the vectors is 34.3803442 and Approximation value, 34.4..

c) Exact value of the angle between the vectors, a = 71 - 2j + k, b = 3i - k is 30.60889766 ~ 30.61 (approximation value).

In mathematics, a unit vector is defined as a normed vector space is a vector of length one.

a) If u is a unit vector , we have to calculate ⃗u.⃗v and ⃗u.⃗w where v and w are also unit vectors.

We know that, Angle between two vectors θ is

Cosθ = u⃗ .⃗v/|u| |v|

=> cos 60° |u| |v| = ⃗u.⃗v

=> ⃗u.⃗v = 1/2(1)(1) = 1/2

Also, Cosθ = ⃗u.⃗v/|u| |w|

=> Cosθ |u| |w| = ⃗u.⃗w

=> ⃗u.⃗w = cos 120° (1)(1)

=> ⃗u.⃗w = -1/2

So, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2

b) We have, a = (7,2), b = (3,-1)

Cosθ = a.b/|a| |b|

|a| = √(7)²+ (2)² = √49+4 = √53

|b| = √(3)²+ (-1)²= √9+1 = √10

a.b = 7×3 - 2×1 = 21 - 2 = 19

so, Cos θ = 19/√10 (√53) = 19/√530

=> θ = Cos⁻¹( 19/√530)

=> θ = 34.3803442 ~ 34.4

c) We have, a = 7i - 2j + k, b = 3i - k

Cos θ = a.b/|a| |b|

|a| = √(7)² + (-2)² +(1)² = √49+4+1 = √54

|b| = √(3)²+ 0 +(-1)² = √9+1 = √10

a.b = (7i - 2j + k).(3i - k) = 21 -0 - 1 = 20

Cosθ = 20/√10√54 = 20/√540

θ = cos⁻¹(20/√540) = 30.60889766 ~ 30.61

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cupcakes are shared

equally among four of her children, 4 Cupcakes  will each child get

what do you mean by share?

An equity ownership stake in a corporation is represented by a share. Dividends from any earnings the company makes are owed to the shareholders. They also bear the brunt of any losses the business may sustain.

Ordinary shares.

Non-voting shares.

Preference shares.

Redeemable shares.

There are a number of different types of shares including equity shares, preference shares, right shares, bonus shares, sweat equity shares (where companies issue shares at a discount or for consideration) and employees stock options plans.

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The measure of ∠CDE is 54°

What is measure ?

When attributes of an item or event are quantified, they can be compared to other objects or events and utilized as a basis for comparison. Determining how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind is the process of measurement, in other words.

A measure is a piece of mathematics that expresses the size of sets in numerical terms. A different method of determining how large a set is is embodied by each unique measure. Initially, it could seem as though a set's cardinality is the only natural way to determine its size.

<CDE = far arc - near arc / 2

i.e

<CDE = arcCBE - arcCE / 2

arcCE = 126°

arcCBE = 360° - 126° = 234°

<CDE = (234° - 126°)/ 2

<CDE = 108 / 2

<CDE = 54°

Therefore the measure of < CDE is 54°

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Situation which illustrates best the concept of absolute advantage is: Option A - A German factory can build more sports cars than foreign factories.

Absolute advantage is the potential of an individual,  a company, or a  country to produce a higher quantity of output than its competitors while using the same inputs. It means an institution with absolute advantage has more efficiency in producing a particular commodity than its rivals. It utilizes lower marginal cost (materials and labor), making its output much cheaper than others.

A factory in German has an absolute advantage because it can produce more sports car  than foreign countries. Absolute advantage makes the factory more competitive in the market than its rivals.

Therefore, the correct answer is option A.

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With the Application of probability The expression is [ x^r] = C ( r - 1, r - 8 ).

What is probability?

There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event. It is possible to claim that probability is the likelihood that a specific event will occur as the two words are equivalent.

solution:

G(x) = ( x^1 + x^2 + x^3 .....)^8

G(x) =  (x( x^1 + x^2 + x^3 .....) )^8

Then using infinite geometric series,

       = x^8 ( 1 / ( 1 - x )) ^8

Then using negative binomial series:

So [ x^r] = 0 if r = 0, 1, 2, 3...7 and [ x^r] = C ( r - 1, r - 8 ) if r > 7

Therefore, The expression is [ x^r] = C ( r - 1, r - 8 )

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The value of x is $53.34 but cannot exceed $115, while the value of y can be as low as $160 but cannot exceed $345.

Relationships that compare two numbers or other mathematical expressions in an unequal manner are known in mathematics as inequalities. The most common use is to compare the magnitude of two numbers on a number line.

The answer to the query is

Diane will make a charitable donation "up to $460," which indicates it can be less than or equal to 460 but not more. Then,

$460 donated to charity (max)

plus $160 for educational (160 being the minimum)

Education is also stated to be three times (or greater) than City.

If x represents the city and y represents education, then

x + y = 460 . And we are aware that y 3x.

x + 3x = 4x = 460

x = 115.

This implies that she will contribute $345 to Educational when she donates 3 times (or $115) to City. The maximum value is these.

She won't provide more than $460.

Earlier, Educational had a minimal need.

When y = 160,

x equals y/3,

=> x = 160/3 = $53.34. She so gave 213.34 dollars, which is still less than $460.

As a result, x (which is City) might be anywhere between $53.34 and $115.

x, which stands for educational, might be as little as $160 or as high as $345.

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Answer:

7

Step-by-step explanation:

The percent of error for the given measured value and the absolute error is equal to 0.392%

As given in the question,

Measurement value is equal to 12.8 inches

Absolute error in the measurement is equal to 0.05

True value is equal to ( Measurement value - absolute error )

= ( 12.8 + 0.05 )

= 12.75

Percent of error is given by

= |True value - Measured value |/ (true value) × 100

= [ | 12.75 - 12.8 |/ 12.75 ] × 100

= 0.392%

Therefore, the percent of error for the given measured value and the absolute error is equal to 0.392%

The given question is incomplete, I answer the question in general according to my knowledge:

A measurement is taken to be 12.8 in. and the absolute error is 0.05 in. What is the percent of error? Round off your answer to 3 decimal places.

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Answer:

y = -x + 8

Step-by-step explanation:

First find the slope (m):

m = (0-2) / (8-6) = -1

Next put one of the points (I pick (8,0)) into the point-slope formula:

y-y1 = m(x-x1)

y-0 = -1(x-8)

Now write it in slope-intercept form:

y = -x + 8

For the regression equation, ŷ = b₀ + b₁x where b₁ is slope of this line and it is equals to (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and b₀ is y-intercept which is equals to (∑y - b₁ ∑x)/n .

A regression line indicates the linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis. Correlation is determined by analyzing the data pattern formed by the variables.

The regression line is plotted closest to the data points in the regression plot. We use the ordinary least squares estimation method (O.L.S.E), to find the formulas to calculate the slope and intercept of the regression line, which minimizes the sum of squares due to the error. A simple linear regression model is given by y = b₀ + b₁x --(*)

where y : dependent variable

x: independent variable

b₁ --> slope of regression line

b₀ --> y-intercept

We have , regression line is ,

ŷ = (slope )x+ (y intercept)

ŷ represet the predicted value.

The formulas to compute slope(b₁) value and y-intercept (bo) value of regression line are following:

b₁ = (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and

b₀ = ŷ - b₁x = (∑y - b₁ ∑x)/n

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The value of the expression is x

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

x + y = x - y

x - 2y = ?

Recall that. we have

x + y = x - y

Add y to both sides of the equation

So, we have the following representation

x + 2y = x

Add -2y to both sides of the equation

So, we have the following representation

x = x - 2y

Rewrite as

x - 2y = x

Hence, the solution of x - 2y is x

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The probability that an account in state 4 will be in bad debt be 0.3

Given, accounts receivable have been grouped into the following states:

State 1: Paid

State 2: Bad debt

State 3: 0–30 days old

State 4: 31–60 days old

Sixty percent of all new bills are paid before they are 30 days old.

The remainder go to state 4.

Seventy percent of all 30-day-old bills are paid before they become 60 days old.

If not paid, they are permanently classified as bad debts.

P(State 1 and State 3) = 0.6

P(State 4) = 0.40

We have to find the P(State 4 and State 2)

P(State 4 and State 2) = P(State 4) + P(State 2) - P(State 4 or State 2)

P(State 4 and State 2) = 0.4 + 0.6 - 0.7

P(State 4 and State 2) = 0.3

So, the required probability be, 0.3

Hence, the required probability be, 0.3

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The point of interaction of two circles:

(x-a)²+(y-b)² = ro²

(x-c)²+(y-d)² = r1²

The e point of interaction of the two circles is given by the formulas given below:

       D = √(c-a)²+(d-b)²

        б = √(D+r0+r2)(D+r0-r2)(D-r0+r2)(-D+r0+r2)

        X1,2 = a + c/2 + (c-a)(r0² - r1²)/2D² ± 2 b-d/D²

        X1,2 = b + d/2 + (d-b)(r0² - r1²)/2D² ± 2 a-c/D²

r0 = 935.62 ft

r1 = 959.630 ft

a = 553.7

b = 1147.86

c = 1162.93

d = 269.83

First we calculate,

                            D = √(c-a)²+(d-b)²

                               = 1980.95 ft

Lets check whether these circles intersect or not:

D<r0+r1 and D> r0-r1

r0+r1 = 2166.57 ft and D = 1980.95 ft -192.51 = 192.51 which is less than D

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a group with at least n k 1 people such that no two members of the group are friends,We will prove this statement by inductive hypothesis.

Base Case: If n=k+1, then we can easily find a group with nk1 people such that no two members of the group are friends. We simply select the k+1 people in the room, excluding Alex. Since Alex has k friends, and no other person in the room has more than k friends, it follows that none of these k+1 people are friends.

Inductive Step: Assume that the statement is true for n=k+1. Now we must show that it is true for n=k+2.

We can select a group of k+1 people from the room, again excluding Alex. By the inductive hypothesis, we know that no two members of this group are friends. Now, we select the remaining person in the room, and add them to the group. This person cannot be friends with any of the members of the group, since Alex has k friends and no other person in the room has more than k friends. Therefore, the group we have formed has at least nk1 people, and no two members of the group are friends.

Therefore, by induction, we have proved that we can find a group with at least nk1 people such that no two members of the group are friends.

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The number of miles Carlos drove the rental car is 88 miles.

Carlos paid a total of $64 to rent a car. The rental company charges a one-time fee of $20, with an additional charge of $0.50 per mile driven.

Therefore, the number of miles Carlos drive the rental car can be calculated as follows:

Using equation,

let

x = number of miles driven

64 = 20 + 0.50x

subtract 20 from both sides of the equation'

64  - 20 = 20 - 20 + 0.50x

44 = 0.50x

divide both sides by 0.50

Therefore,

44 / 0.50 = 0.50x / 0.50

x = 88

Therefore, the number of miles is 88 miles.

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The normal curve that corresponds to P (X > 37) is C, as the shaded area corresponds to the probability of 0.4207.

The normal curve is a bell-shaped curve which is used to represent a continuous probability distribution. It is used to represent the probability of a random variable X, which is normally distributed with mean μ and standard deviation σ. In this case, we have X with mean μ = 50 and standard deviation σ = 7. To compute the probability P(X > 37), we first draw a normal curve with the area corresponding to the probability shaded. Then, we can look up the area from the table of areas under the normal curve. The area corresponds to 0.4207, and the normal curve that corresponds to this probability is C, as the shaded area corresponds to the probability of 0.4207. This normal curve has the mean of 50 and the standard deviation of 7, with the area beyond 37 shaded.

P(X > 37)

= 1 - P(X ≤ 37)

= 1 - 0.4207

= 0.5793

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The power series representation for the given function is:

1+ 9x + (9x)² + (9x)³ + .... (9x)ⁿ (where 0 ≤ n ≤ ∞).

What is the power series?

Power series is a sum of terms of the general form aₙ(x-a)ⁿ. Whether the series converges or diverges, and the value it converges to, depends on the chosen x-value, which makes power series a function.

Let u = 9x.

Return to the series above and replace each u with a 9x directly:

Where 0 n , 1 + 9x + (9x) 2 + (9x) 3 +.... (9x) n

Here, the interval of convergence is easily found. It follows that

|9x| 1 -1/9 x 1/9 because we know that geometric series must have | u | = 1

Finally, we may leverage the fact that geometric series have a sum to get the sum: S = a / (1 - u).

Here, u = 9x and a = 1

Therefore, the total is simply S = 1 /(1 - 9x).

Any sum can be calculated provided x is between -1/9 and x and less than 1/9.

Hence, The power series representation for the given function is:

1+ 9x + (9x)² + (9x)³ + .... (9x)ⁿ (where 0 ≤ n ≤ ∞).

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2f(3,1)

To use the midpoint rule to estimate the value of the double integral of a function f(x,y) over the region R=[0,6]x[0,6], we need to divide the region R into a grid of subintervals, with m subintervals in the x-direction and n subintervals in the y-direction. In this case, m=n=3, so we divide each side of the region R into 3 subintervals of equal length.

The midpoint rule states that the approximation of the integral is given by the sum of the areas of the rectangles formed by the subintervals, where the height of each rectangle is given by the value of the function at the midpoint of the subinterval.

To implement the midpoint rule, we first need to determine the width and height of each subinterval. The width of the subintervals in the x-direction is given by (6-0)÷3 = 2, and the width of the subintervals in the y-direction is also given by 2. The height of each rectangle is given by the value of the function f at the midpoint of the subinterval.

We can then evaluate the double integral by summing the areas of the rectangles formed by the subintervals. For example, the first rectangle would have a height equal to the value of the function at (0+2)÷2=1 and a width of 2, so its area would be 2f(1,1). The second rectangle would have a height equal to the value of the function at (2+4)÷2=3 and a width of 2, so its area would be 2f(3,1)

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The rate at which the distance between the buses is changing when they are 13 miles apart is -85.25 mph.

Given, two buses are driving along parallel freeways that are 12 miles apart, one heading east and the other heading west.

Assuming that each bus drives a constant 58 mph.

Now, we have to find the rate at which the distance between the buses is changing when they are 13 miles apart and heading towards each other.

Considering distance as a function of time,

D = f(t) = √((12)² + (13 - 116t)²)

f'(t) = (13 - 116t)(-116)/√((12)² + (13 - 116t)²)

f'(0) = (13 - 116(0))(-116)/√((12)² + (13 - 116(0))²)

f'(0) = -1508/√(144 + 169)

f'(0) = -1508/√313

f'(0) = -85.25

So, the rate of distance is decreasing at the rate of 85.25

Hence, the rate of distance is decreasing at the rate of 85.25

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The function of the line and parabola shown in the graph is x + 6 ≤ 1 and x² + 3 > 1 respectively, so, option A is correct.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The graph of the function,

Calculate the equation of the line which is passing through (-6, 0) and (0, 5) as shown below,

y - 5 = 5 - 0 / 0 - (-6) (x - 0)

y - 5 = 5 / 6 x

6y - 30 = 5x

And the equation of the parabola can be written as,

x² + 3 = 0

From the graph, it can be seen that the solution of the line is where the line graph and parabola graph can meet,

Thus, the line will be x + 6 ≤ 1 and x² + 3 > 1.

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Answer:

$15,510.00

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] x [tex]\frac{41360}{1}[/tex] = [tex]\frac{124080}{8}[/tex]= 15510

The area of the shaded region is 425 cm².

Let us find the area of the entire figure first and subtract the unshaded region area to find the area of the shaded region.

The given figure is of a square of side 25 cm.

Total area = 25²

=> 625 cm²

The shaded figure inserted is a rhombus.

Apart from this , we can observe four unshaded triangles of equal area.

Area of each individual triangle :

=> ½ × 5 × 20

=> 50 cm²

Area of 4 triangles ;

=> 200 cm²

Remaining area of the shaded figure :

=> 625 - 200

=> 425 cm² .

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If  a customer buys 2 cantaloupes and p pounds of potatoes on friday from the local farmers' market, the total cost equation would be A. C = 0.63p + 7.

Equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation also often contain an algebra. Algebra is used in maths when you do not know the exact number in a calculation.

Based from the question above, we don't know the exact number of potato that the customer bought. We only know that the customer buys p pounds of potatoes.

Potato price = $0.90

on Friday, the potato price is (30% discount)

= 0.90 - (0.90 * 30%)

= $0.63

Since the customer buys for p pounds of potatoes, therefore the total cost of potatoes

= $0.63 * p

= 0.63p

From the question above, we know that the customer buys 2 cantaloupes.

cantaloupes price = $3.50 each

The total cost for cantaloupes

= 2 * $3.50

= $7

Now, let's put it into the total cost equation to find the answer from the multiple choice.

Total cost (c) = 0.63p + 7

Therefore, the answer is A.

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Answer:

$16.50

Step-by-step explanation:

$110 * 15% =

$110 * 15/100 =   ==> percent value is 100 times greater than the fraction

$1650/100 =  ==> multiply 110 and 15

$16.50

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Answer:

Tip=[tex]16.50[/tex]

Step-by-step explanation:

Tip%=15

Bill=$110

Tip=[tex]\frac{15}{100}[/tex]x[tex]110[/tex]

Tip=[tex]16.50[/tex]

Hope this helps u

Answer:

A

Step-by-step explanation:

A. This is true and occurred during the industrial revolution

B. The government had not started managing the economy (yet)

C. This was happening even in the 1700s

D. This was also more apparent in the 1700s with the 13 colonies, especially with cash crops such as tobacco.