The function f(x)=lnx has a Taylor series at a=6. Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms.

The slope of both functions remains the same, there is no effect of the value of k on a slope.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.

The given functions are :

f(x) = 2x + 5

g(x) = ( 2x + 5) -3

From the graph of both functions,

Let us consider two pairs of coordinates to find the slope,

For f(x)

(0,5) and ( -2, 1)

The slope of f(x)

m= ( 1- 5) / (-2 -0)

m= 2

For g(x) at (0,2) and (-1, 0) slope of g(x),

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

m = 2

The slope remains unaffected.

y-intercept of f(x) , put x = 0

⇒ y = 5

y-intercept of g(x) , put x = 0

y =(0+ 5) -3

y = 2

Change in the value of y-intercept due to the value of k = -3.

Therefore, for the given function f(x) = 2x + 5 and g(x) = ( 2x + 5) -3, the effects of the value of k on slope and y-intercept are as follows:

The slope of both functions remains the same, there is no effect of the value of k on a slope.

Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.

The graph is attached.

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Answer:

Step-by-step explanation:

y=4x+2

For a point to be perpendicular to a line

then the product of the two gradients must be negative one (I.e, m1×m2=-1)

where m1= 4

m2=-(1/m1)

m2=-1/4

point (7,-6)

x1=7 y1=-6

from the general equation of a line

y-y1=m(x-x1)

y-(-6)=-1/4(x-7)

y+6=-1/4(x-7)

y+6=-1/4x+7/4

y+1/4x=(7/4)-6

y+1/4x=-17/4

y+1/4x+17/4=0

4y+x+17=0

A) The data models a geometric sequence

B) Using a recursive formula, the time she will complete station 5 is; 2

C) Using a explicit formula, the time she will complete station 9 is; 512

A)  From the given coordinates (1, 3), (2, 6), (3, 12), (4, 24), we can say that when x increases by 1, y is multiplied by 2. Thus, as the quotient between consecutive terms is the same, the data depicts a geometric sequence.

B) The recursive formula for a geometric sequence with common ratio r and first term a₁ is given by the formula:

f(n) = a₁(r)ⁿ⁻¹

Since a₁ = 2 and r = 1, then we have;

f(1) = 2(1)¹⁻¹

f(1) = 2

f(5) = 2

C) The explicit formula from the calculations above will be;

aₙ = 2ⁿ

Thus;

a₉ = 2⁹

a₉ = 512

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The estimate value of the standard deviation of the population ( manufacturing process) is 0.125..

The standard deviations is estimated to be one fourth of the sample range (as most of data values are within two standard deviations of the mean).

We have given that,

A sample of manufacturing process.

Sample size, n = 5

Mean of sample ranges = 0.50

we have to calculate the estimate of standard deviations of population.

thus , we estimate the standard deviations as fourth of the mean of the sample ranges is

S = Mean of sample ranges/4

=> S = 0.50/4

=> S = 0.125

Hence, the standard deviation of the population is estimated as 0.125..

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Answer: A. 10

Step-by-step explanation:

Plug in x which is 5 to equation 1

15-5=10

Plug in x which is 5 to equation 2

5-10= -5

The total amount of infection needed to develop symptoms of measles is 7840

Consider the model,

N(t)= f(t)=-t(t-21)(t+1).

The area of the graph of N(t) from t=0 to t = 12 is,

N(t)dt

Use six subintervals and their midpoints to estimate the above as follows:

Here, a=0,b=12, n=6

The length of each subinterval is,

h= b-a/n = 12-0/6

=2

So, the midpoints of each subinterval are 1, 3, 5, 7, 9, and 11.

Use Midpoint Rule,

A = [N(t)dt]

= At[ƒ (1) + ƒ (3) + ƒ (5) +ƒ(7)+ƒ(9)+ƒ(11)] =2[40+216+480+784+1080+1320]

= 7840

Thus, the total amount of infection needed to develop symptoms of measles is 7840.

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The equation of the circle centered at (−5, 8) and having a radius of 7 is (x + 5)² + (y - 8)² = 49.

The standard form of the equation of a circle is expressed as;

x² + y² = r²

The horizontal (h) and vertical (k) translations represents the center of the circle.

Hence;

(x - h)² + (y - k)² = r²

Given the data in the question;

Center of the circle: (−5, 8)

Now, plug the values of h, k and r into the equation above and simplify,

(x - h)² + (y - k)² = r²

( x - (-5) )² + ( y - 8 )² = 7²

(x + 5)² + (y - 8)² = 49

Therefore, the equation of the circle is (x + 5)² + (y - 8)² = 49.

Hence, option A is the correct answer.

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Answer: 40%

Step-by-step explanation: 18/45 = x/100

divide 100 by 45 and you get 2.22 repeating.

multiply 2.22 by 18 and you get 40%

the polynomial that represents the volume of the box is is 6x^3 +5x^2 -3x-2

V=lwh

l=x+1

w=2x+1

h=3x-2

V=(x+1)(2x+1)(3x-2)

V=(x*2x+x*1+1*2x+1*1)(3x-2)

V=(2x²+x+2x+1)(3x-2)

V=(2x²+3x+1)(3x-2)

V=2x²*3x+2x²*(-2)+3x*3x+3x*(-2)+1*3x+1*(-2)

V=6x³-4x²+9x²-6x+3x-2

V=6x³+5x²-3x-2

complete question is

Find the volume of the box. Use the formula V = lwh.

Rectangular box with sides x plus 1, 2x plus 1, and 3x minus 2.

6x3 – 2

6x3+ x – 2

6x3 – 13x2 – 3x – 2

6x3 + 5x2 – 3x – 2

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The solutions of the absolute value inequality.

|-2c-3| > -4

are all the real numbers.

Here we have a really trivial inequality, which is:

|-2c - 3| > -4

Notice that we have an absolute value there, and the absolute value is defined as:

|x| = x   if x ≥ 0

|x| = -x if   x < 0

Then the absolute value |x| is always equal to or larger than zero, so:

|x| > -4

Is true for any value of x.

Then our inequality:

|-2c - 3| > -4

Is true for any value of c, because the left side is always equal to or larger than 0, and 0 > -4

So c can be any real number.

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1 is the greatest common factor of 8 and 15 .

GCF stand for greatest common factor.It is a set of numbers is the largest factor that each and all the number share. GCF is also often used to find the common denominator.

First we need to write common factor of each number.

The common factors of 8 = ( 1,2,4,8)

The common factor of  15= (1,3,5,15)

1 is the  only one common factor here which is divides both 8 and 15.

So 1 is the only and GCF of 8 and 15.

Thus, 1 is the right answer.

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Answer:

6 sides

Step-by-step explanation:

since the measure of an interior angle of a polygon can be found with the formula 180(n-2) / n where n is the number of sides we can substitute 120 to the answer and cross multiply to find that

120n = 180(n-2)

120n = 180n-360

360 = 60n

n = 6

Answer:

Step-by-step explanation:

The largest number of the five positive integers is 146.

Mean:

The mean is the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of mean that can be calculated. The formula for calculating the arithmetic mean is to add up the numbers in a set and divide by the total quantity of numbers in the set.

Median:

The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median.

Here we have to find the largest integer.

Data given:

Four of the five integers are 8, 18, 36, and 62.

It is given that mean of five numbers 1.5 times their median.

mean = (8+18+36+62 + x)/5

median = 36

mean = 1.5 × median

(124 + x) / 5 = 1.5 × 36

124 + x = 5 × 54

x = 270 - 124

  = 146

Therefore we get the largest number as 146.

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Answer:

42

Step-by-step explanation:

because the distance between 42 and zero is 42

Answer: x-18

Step-by-step explanation:

Answer: 5[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

19=(x+(2x+2))
Subtract 2 from each side
17=x+2x
17=3x
Divide each side by 3
[tex]\frac{17}{3}[/tex] = x
5 [tex]\frac{2}{3}[/tex] = x

Answer: C

Step-by-step explanation:

-2 and 2 add up to 0

Answer:

c

Step-by-step explanation:

-2 + 2 =0

Answer:

60

Step-by-step explanation:

50+70=120

180-20=60

Answer:

120°

Step-by-step explanation:

Your question didn't include an image or angle names, so it was pretty confusing to get what you were asking for. If you were asking for the exterior angle of the missing angle, then here's your answer:

The 3 angle measures of a triangle will always equal 180.

Since we've already got two angles, all we need to do is a simple equation to get our missing angle:

180-(50+70)=60

Now that we've got the missing angle, we need to calculate the exterior angle, the thing we're here for. We know (hopefully at this point) that an exterior angle and its interior angle are a linear pair, meaning that the two add up to 180. Knowing this, we can do this equation to finish off the question:

180-60=120

And there's your answer, 120°

There's also a shorter way of doing this, let me know if you'd like to see it. But for now, hope I helped!

To check whether the true average is 59k or not, A sample mean T-Test needs to be conducted.

What is an Average?

In the field of statistics, average means that the ratio of the sum of the numbers of a given set, to the total number of characters in a given set. It is also called as the Arithmetic mean.

It is given that the student center has published the data that the average salary of the college graduates is 59k. Accordingly, the sample of 49 college students were verified and the sample average salary came out to be 44k.

When we analyze the  given question, we find that,

The total number of students were 49,

The true average was found to be 59k,

and the Sample average is found to be 44k.

Thus, in  the present question we will use the One- sample T-test.

We used this test, as the statistical hypothesis test is used to find if the unrecognized population mean is different from the specific value.

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the total distance around Pennsylvania is not shoreline will be 892 miles.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Pennsylvania has 51 miles of coast along Lake Erie and a 57-mile shoreline along the Delaware Estuary.

The total distance around Pennsylvania is about 1000 miles.

So the distance around Pennsylvania is not shoreline will be 1000-(57+51) = 892miles

Hence, the total distance around Pennsylvania is not shoreline will be 892 miles.

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Answer: x ∈ {-0.5, -5, -12.5}

Step-by-step explanation: To solve the inequality 2x³ + 21x² + 60x + 25 > 0, we first need to find the values of x that make the inequality true. We can do this by setting the expression equal to 0 and solving for x.

We can start by factoring the expression to make it easier to solve. Notice that 2x³ + 21x² + 60x + 25 is a polynomial with a leading coefficient of 2 and a constant term of 25. This means that it has the form (x + a)(x + b)(x + c), where a, b, and c are constants.

We can start by factoring out the common factor of 2x from the first two terms: 2x³ + 21x² + 60x + 25 = 2x(x² + 10.5x + 12.5). Now we can see that the expression has the form (x + a)(x + b)(x + c), where a = 0.5, b = 5, and c = 12.5.

So, we can rewrite the expression as (x + 0.5)(x + 5)(x + 12.5) = 0. Now we can solve for x by setting each factor equal to 0 and solving for x:

x + 0.5 = 0 => x = -0.5

x + 5 = 0 => x = -5

x + 12.5 = 0 => x = -12.5

Therefore, the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5.

Now we need to determine which of these values make the inequality 2x³ + 21x² + 60x + 25 > 0 true. To do this, we can substitute each of the values of x into the inequality and see which ones make the inequality true.

When x = -0.5, the inequality becomes 2(-0.5)³ + 21(-0.5)² + 60(-0.5) + 25 > 0, which simplifies to -0.5 + 5.25 - 15 + 25 > 0. This is true, because the left-hand side is 29 > 0.

When x = -5, the inequality becomes 2(-5)³ + 21(-5)² + 60(-5) + 25 > 0, which simplifies to -125 + 525 - 300 + 25 > 0. This is also true, because the left-hand side is 225 > 0.

When x = -12.5, the inequality becomes 2(-12.5)³ + 21(-12.5)² + 60(-12.5) + 25 > 0, which simplifies to -391.25 + 1181.25 - 750 + 25 > 0. This is also true, because the left-hand side is 1147.5 > 0.

Therefore, the solution to the inequality is x ∈ {-0.5, -5, -12.5}. This means that the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5. The inequality is satisfied when x is any of these values.

Answer:

y=-3x+2 y=-x-4

Step-by-step explanation:

It will take 51.9 seconds to return to sea level.

The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Using the speed - distance relationship, the time taken for the scientist to travel back to sea level would be 51.9 seconds

Distance = Speed × time

First travel :

Distance covered = 90 × 3.5 = 315 feet

Second travel :

Distance covered = 30 × 2.2 = 66 feet

Net change in position from sea level :

(315 - 66) feet = 249 feet

Maximum speed = 4.8 feet per second

Time taken = Distance / speed

Time taken = 249 ÷ 4.8 = 51.875 seconds

Hence, it will take 51.9 seconds to return to sea level.

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Both the pairs of opposite sides in a parallelogram are parallel and congruent.

According to the question,

We've proved that one pair of sides in parallelogram must be congruent

Let ABCD is a parallelogram ,

We know that AB // CD

Here, AC is transversal for the parallel lines AB and CD

So, ∠BAC = ∠DCA    (Using interior angle property) --------(1)

Similarly , We also know that BC // AD

=> ∠BCA = ∠DAC -----------(2)

Now , In ΔABC and ΔADC,

Therefore , ΔABC ≅ ΔADC    (as per ASA congruence rule)

Therefore , AB = CD and BC=AD   (Corresponding sides of congruent triangles are equal)

Hence , Both the pairs of opposite sides in a parallelogram are parallel and congruent.

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An equation that can be used to determine the tree's height is 22.5/8.25 = x/5.5.

The height of this tree is equal to 15 feet.

The distance of this person from the tree is equal to 14.25 feet.

In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Additionally, two (2) geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Now, we can write an equation that can be used to determine the tree's height. Since the ratio of the corresponding sides of similar triangles are equal in magnitude, we have the following mathematical expression (equation):

22.5/8.25 = x/5.5

Where:

x represents the height of the tree.

22.5/8.25 = x/5.5

Cross-multiplying, we have:

8.25x = 22.5 × 5.5

8.25x = 123.75

x = 123.75/8.25

x = 15 feet.

The distance of this person from the tree can be calculated as follows;

Distance = Length of tree's shadow - Length of person's shadow

Distance = 22.5 - 8.25

Distance = 14.25 feet.

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Answer:

510

Step-by-step explanation:

Answer: The answer is 510

Step-by-step explanation:

35.7/0.07 = 510

False. Because a 95% confidence interval is two standard errors on either side of the mean.

What is a 95% confidence interval?

If 100 separate samples were taken and a 95% confidence interval was calculated for each sample, then around 95 of the 100 confidence intervals would contain the actual mean value (), according to the definition of a 95% confidence interval.

For a 95% confidence interval, the value lies within 2 standard deviations of the normal distribution.

For upper and lower bounds one standard error on either side of the mean is 68%.

So, the 95% confidence interval is two standard errors on either side of the mean.

Hence, the given statement is False.

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Answer:

3,31

Step-by-step explanation:

i dont got steps for this but i think thats the right answer