Find the Taylor polynomial of degree 5 near x = 3 for the following function. y = 5sin(5x) Answer 2 Points 5sin(5x) – P5(x) = Find the Taylor polynomial of degree 3 near x = 0 for the following function. 3 y = V2x + 1 Answer 2 Points V2x + 1 = P3(x) =

find dy/dx

x= t sin(t); (Given in the question)

y= t²+8t; (Given in the question)

then, x= t sin(t)

dx/dt = sin t + t cos t ;

y= t²+8t

dy/dt = 2t + 8;

then, dy/dx = dy/dt x dx/dt

dy/dx = (2t+8)/(sin t + t cos t)

dy/dx = 2(t+4)/(sin t + t cos t)

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Answer:

Step-by-step explanation:

Let Jason's money be x and Jeff's money be y

Substitute x in the second equation

Then

The probability that an individual resulting from a cross between a true-breeding tall pea plant and a true-breeding dwarf plant will be true-breeding is 50%, while the probability that it will be a true-breeding tall plant is 25%.

When a true-breeding tall pea plant is crossed with a true-breeding dwarf plant, all the offspring in the first generation, or F1 generation, will be heterozygous and have one allele for tallness and one allele for dwarfness. Since the allele for tallness is dominant over the allele for dwarfness, all the F1 plants will be tall. However, none of the F1 plants will be true-breeding because they all carry one allele for tallness and one allele for dwarfness.

When two F1 plants are crossed with each other, the resulting offspring in the F2 generation will have a 3:1 ratio of tall to dwarf plants. However, only one-third of the tall F2 plants will be true-breeding, meaning they will have two alleles for tallness and will always produce tall offspring when self-fertilized.

Therefore, the probability that an individual resulting from this cross will be true-breeding is 50%, while the probability that it will be a true-breeding tall plant is 0%.

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The image is formed behind the mirror, and the image is upright.

Given data: Object height, h = 3.0 cm Image distance, v = ? Object distance, u = -20.0 cmFocal length, f = -60.0 cmUsing the lens formula, the image distance is given by;1/f = 1/v - 1/u

Putting the values in the above equation, we get;1/-60 = 1/v - 1/-20

Simplifying the above equation, we get;v = -40 cm

This negative sign indicates that the image is formed behind the mirror, as the object is placed in front of the mirror.

Hence, the image is virtual and erect. Using magnification formula;M = -v/uWe get;M = -(-40) / -20M = 2Hence, the height of the image is twice the height of the object.

The height of the image is given by;h' = M × hh' = 2 × 3h' = 6 cm Now, let's draw the ray diagram:

Thus, the position of the image is -40.0 cm and the height of the image is 6 cm.

The image is formed behind the mirror, and the image is upright.

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The length of the segment with the variable x is as follows:

EF = 9 units.

A trapezium is a quadrilateral. The midsegment of a trapezoid is a line that goes across from the middle of one leg to the middle of the other leg.

Therefore, the side EF is the mid segment of the trapezium.

Hence, let's find the variable x as follows:

Therefore,

EF = x - 5 + 2x - 4 / 2

combine like terms

EF = x + 2x - 5 -4 / 2

EF = 3x - 9 / 2

x = 3x - 9 / 2

cross multiply

2x = 3x - 9

2x - 3x = -9

-x = -9

x = 9

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Answer:

\(\boxed{-\frac{7}{12} }\)

Step-by-step explanation:

\(-1\frac{1}{3} +\frac{3}{4}\)

→ Make both denominators the same

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}\)

→ Convert mixed number into improper fraction

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}=-\frac{16}{12} +\frac{9}{12}\)

→ Do the -16 + 9 and leave 12 as the denominator

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}=-\frac{16}{12} +\frac{9}{12}=-\frac{7}{12}\)

The required simplification o f\(-1\frac{1}{3} +\frac{3}{4}\) into fraction form  is -1 / 12

To simplify -1 1 / 3 plus 3 / 4 into fraction form.

The process in mathematics to operate and interpret the function to make the function simple or more understandable called simplifying and the process is called simplification.

Fraction is defined as the number of compositions constituting the Whole. And it is represented as a / b, where a = numerator and b = denominator.

Since the given problem is
\(-1\frac{1}{3} +\frac{3}{4}\)

We need to simplified it into fraction form like a / b.

\(=-1\frac{1}{3}+\frac{3}{4} \\= -2/3 + 3/4\)
=  ( -8 + 9 ) / 12
= -1 / 12

Thus, The required simplification of  \(-1\frac{1}{3} +\frac{3}{4}\)  into fraction form is -1 / 12.

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Answer:

-(n -1)(n^2 + n + 1)(n + 1)(n^2 - n + 1).

Step-by-step explanation:

1 - n^6 = (1 - n^3)(1 + n^3)

1 - n^3 = -(n -1)(n^2 + n + 1)  and

1 + n^3 = (n + 1)(n^2 - n + 1)

So Substituting we have:

-(n -1)(n^2 + n + 1)(n + 1)(n^2 - n + 1)

Answer:

Plugged this into my calculator and got this

cos 75 = 0.2588190451

Answer:

The price elasticity of demand, when using the midpoint​ formula, would be B.1.29.

How to find the price elasticity of demand ?

Price elasticity of demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

where:

Q1 = initial quantity demanded = 20 units

Q2 = final quantity demanded = 15 units

P1 = initial price = $8

P2 = final price = $10

Substituting the values:

Price elasticity of demand = ((15 - 20) / ((15 + 20) / 2)) / (($10 - $8) / (($10 + $8) / 2))

= (-5 / 17.5) / (2 / 9)

= (-0.2857) / (0.2222)

= -1.2857

= 1. 29

The ellis weight is heavier and by 7.23 lbs.

We are given that;

Weight= 5pounds

Now,

To convert Ed’s weight from kilograms to pounds, we can multiply by the conversion factor of 2.20462262185. We get:

Ed’s weight in pounds = 50 kg * 2.20462262185 lbs/kg Ed’s weight in pounds = 110.2311310925 lbs

To convert Ellis’s weight from stones and pounds to pounds, we can multiply the number of stones by 14 and add the number of pounds. We get:

Ellis’s weight in pounds = 7 stones * 14 lbs/stone + 5 lbs Ellis’s weight in pounds = 98 + 5 Ellis’s weight in pounds = 103 lbs

To compare the weights, we can subtract them and see which one is larger. We get:

Ed’s weight - Ellis’s weight = 110.2311310925 lbs - 103 lbs Ed’s weight - Ellis’s weight = 7.2311310925 lbs

Therefore, by unitary method the answer will be 7.23 lbs.

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Step-by-step explanation:

y=|x| is a vee graph starting at (0,0)

y=|x| - 3 is a vee graph starting (0,-3)

see attachment

As I understand, we need to evaluate the given rational expression, we will get that the evaluated expression is equal to - 1/10

Evaluating an expression just means that we need to replace the variable in the expression for a given value, here we have the expression:

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

And we want to evaluate it in:

\(k = -\frac{2}{5}\)

So we just need to replace k by that value in the above expression, we will get:

\(\frac{3}{2} + (-(-\frac{2}{5} )) + (-2)\)

Now we can just solve this:

\(\frac{3}{2} + (-(-\frac{2}{5} )) + (-2)\\\\\frac{3}{2} + \frac{2}{5} + (-2)\\\\\frac{15}{10} + \frac{4}{10} + (-2) = \frac{19}{10} - \frac{20}{10}= -\frac{1}{10}\)

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Answer:

-1/10

Step-by-step explanation:

it corect i did it in khan acadmy

Given that the salesperson sells insurance policies to 2 out of 40 customers, we can determine the probability using the binomial distribution formula.

The probability of a salesperson selling a car to exactly three out of the next three customers can be calculated using binomial probability.

To calculate the probability, we use the binomial distribution formula: P(X = k) = C(n, k) * \(p^k * (1 - p)^{n - k}\), where P(X = k) is the probability of selling exactly k cars, n is the number of trials (in this case, 3 customers), p is the probability of selling a car to a single customer (2/40), and C(n, k) is the binomial coefficient.

For this scenario, we need to find the probability of selling exactly 3 cars out of the next 3 customers. Substituting the values into the formula, we have P(X = 3) = C(3, 3) *\((2/40)^3 * (1 - 2/40)^{3 - 3}\). Since C(3, 3) equals 1, the calculation becomes 1 * \((2/40)^3 * (1 - 2/40)^{3 - 3}\).

Simplifying further, we have P(X = 3) = \((2/40)^3 * (1 - 2/40)^0\). Evaluating the equation, we get P(X = 3) = (\(1/20)^3 * (1 - 1/20)^0\) = (1/8000) * 1 = 1/8000.

Therefore, the probability that the salesperson will sell a car to exactly three out of the next three customers is 1/8000.

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The function according to the rigid transformation g(k + 3) = - 4 · f(k + 3), where f(x) = x² - x - 1, is equal to the quadratic equation g(k + 3) = - 4 · k² - 20 · k - 44.

In this problem we find the definition of a quadratic equation and besides we are asked to find the result of horizontal translation, a reflection about the x-axis and a dilation, all of them rigid transformations. In other words, we must look for the resulting expression according to this definition:

g(k + 3) = - 4 · f(k + 3)

g(k + 3) = - 4 · [(k + 3)² - (k + 3) - 1]

g(k + 3) = - 4 · [(k² + 6 · k + 9) - (k + 3) - 1]

g(k + 3) = - 4 · (k² + 5 · k + 11)

g(k + 3) = - 4 · k² - 20 · k - 44

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Answer:

1: below its initial height.

2: if Jimmy has 20 balls and Chris take 15,how many balls does Jimmy have?

3: I would want Mrbeast to be the President because he would help everyone.

Answer:

x = -2

Step-by-step explanation:

3x - 1 × 3 = 5 × x + 1

3x - 3 = 5x + 1

3x - 5x = 1 + 3

-2x = 4

-2x/-2 = 4/-2

x = -2

Answer:

? = 16

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan ? = opp side / adj

tan ? = 13 / 46

Taking the inverse tan of each side

tan ^ -1 ( tan ? ) = tan ^-1 ( 13/46)

? = 15.78075

To the nearest degree

? = 16

According to the above information the solution would be choice a. y=x, x-axis, y=x, y-axis.

The total of all six interior angles in a hexagon is 720°. The formula (n-2) 180°, wherein 'n' is the numbers of sides in the polygon, is used to determine the sum of internal angles. Given that a hexagon has six sides, we can take n to be six. (6-2) divided by 180 results in 720°.

1) Choose a generic point with measurements (a,b)

2) The result is the same if you reflect it across the line y = x. (b,a)

3) The result of reflection (b,a) over the x-axis is (b,-a)

4) By applying (b,-a) to y = x, it becomes (-a,b)

5) When (-a,b) is reflected across the y-axis, it becomes (a,b)

The hexagon ABCDEF is carried onto itself by that collection of reflections since they have transferred (a,b) into a single location (a,b).

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Answer:

22.2 cm

Step-by-step explanation:

First, find the area of the larger circle.

50.2 x 2.5 = 125.5

Now, we need to find the diameter of the larger circle. We have the area, so we can plug this value into the formula of the area of the circle to find the diameter.

A = pi • r^2

125.5 =3.14 •r^2

122.36 = r^2

r = 11.1

Since radius is half the diameter, multiply r by 2.

11.1 x 2 = 22.2 centimeters

a). The probability of counter of each color is  

(b).There are 7 red counters are in the bag.

Probability is a branch of mathematics that deals with the occurrence of a random event.

a. Probability of event to happen is calculated by using below formula,

P(E) = Number of favorable outcomes / Total Number of outcomes.

Total number of counters = n

Number of blue counters = 1

Number of red counters = n - 1

If, two counters are taken at random from the bag.

Then, Probability of the both counter are of different color is;

1/n × n-1/n- 1 = 1/n

b. Since, The probability that a counter of each color is taken is 0.125

1/n = 0.125

so, n = 8

Number of red counters = n - 1 = 8- 1 = 7        

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Answer:

x = -3

y = 7

Step-by-step explanation:

y = -2x + 1

7 = -2x + 1

-1           -1

6 = -2x

divide by -2

x = -3

Answer:

x = -3

Step-by-step explanation:

y = 7

y = -2x+1

substitute for y

7 = -2x+1

subtract 1 from each side

6 = -2x

divide both sides by -2

6/-2 = x

x = -3

The diameter of the cups used for a slushy stand uses dome shaped lids is 4 inches.

A slushy stand uses dome shaped lids

Lids resemble the shape of a hemisphere

Volume of lid as 16/3 pi cubic inches

Therefore, volume of hemisphere is 16/3 pi cubic inches as lid resemble shape of hemisphere,

Volume of hemisphere is 2/3πr³

V =  2/3πr³

16/3π = 2/3πr³

8 = r³

r = 2

So the radius of the lids is 2

Diameter  = 2r

d = 2x2

D = 4 inches.

Therefore, the diameter of the cups used of lids is 4 inches.

The area that a hemisphere takes up is referred to as its volume. The volume of a thing determines how much space it takes up. A hemisphere is a half-sphere in three dimensions, such as bowls, headphones, an igloo, domes in buildings, etc.

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The correct answer when writing 4,050,000 in scientific notation is 4.05 x 10^6.

When a number is too big or too tiny to be comfortably represented in decimal form, scientific notation is used to avoid having to write out an exceptionally long string of digits.

When writing 4,050,000 in scientific notation, certain commonly occurring errors can lead to incorrect results. These include forgetting to shift the decimal point leftwards until only one non-zero digit exists to its left; an elongated six-place movement is necessary here. '

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Answer:

\( log_{2}(9x) - log_{2}(3) = 3 \\ 3 = log_{2}(8) or log_{2}( {2}^{3} ) \\ log_{2}( \frac{9x}{3} ) = log_{2}(8) \\ \frac{9x}{3} = 8 \\ 9x = 8 \times 3 \\ 9x = 24 \\ x = \frac{24}{9} \\ x = \frac{8}{3} \\ x = 2 \times \frac{2}{3} \)

Answer:

\(\log _2\left(9x\right)-\log _2\left(3\right)=3 : x = \frac{8}{3}\)

Decimal:

\(x = 2.66666...\)

Step-by-step explanation:

\(\log _2\left(9x\right)-\log _2\left(3\right)=3\)

Add \(log _2\left(3)\) to both sides:

\(\log _2\left(9x\right)-\log _2\left(3\right)+\log _2\left(3\right)=3+\log _2\left(3\right)\)

Simplify:

\(\log _2\left(9x\right)=3+\log _2\left(3\right)\)

Use the logarithmic definition: If \(\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c\)

\(\log _2\left(9x\right)=3+\log _2\left(3\right)\quad \Rightarrow \quad \:9x=2^{3+\log _2\left(3\right)}\)

\(9x=2^{3+\log _2\left(3\right)}\)

Expand \(2^{3+\log _2\left(3\right)} : 24\)

\(9x=24\)

Solve: \(9x=24 : x = \frac{8}{3}\)

\(x = \frac{8}{3}\)

Verify solutions: \(x = \frac{8}{3}\)  : True

The solution is:

\(x=\frac{8}{3}\)

Hope I helped. If so, may I get brainliest and a thanks?

Thank you, have a good day! =)

Compound interest is an effective way to save money and increase returns on investments over time, with the longer the time period and the higher the rate of interest, resulting in higher returns.

Compound interest is a type of interest paid on a loan or other form of debt that is calculated both on the original principal and the accumulated interest from prior periods. In other words, compound interest is earned on the interest that was previously earned.

Formula for compound interest: \(A = P(1+r/n)^nt\)

A = Total Accumulated Amount (principal + interest)

P = Principal Amount

r = Rate of Interest

n = Number of times the interest is compounded per unit t

t = Time Period

For example, 100 invested at 5% compound interest for 3 years will be calculated as follows:

A = \(100(1+0.05/1)^1*3\)

A = 115.76

This means that after 3 years, the total amount accumulated will be 115.76, which is the principal amount plus the interest earned.

To calculate the total interest earned, subtract the principal amount from the total accumulated amount (115.76 - 100 = 15.76). This means that the total interest earned was 15.76.

Compound interest can be a great way to save money and earn a higher return on your investment over time. The longer the time period and the higher the rate of interest, the higher the return will be.

Compound interest is an effective way to save money and increase returns on investments over time, with the longer the time period and the higher the rate of interest, resulting in higher returns.

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S is not a basis for R3 because it is linearly dependent and does not span R3.

To explain why S is not a basis for R3, we need to consider the properties of a basis, which are linear independence and spanning the entire space.

S = {(1, 1, 1), (0,1,1), (1,0,1), (0, 0, 0)}

Step 1: Check for linear independence
A set of vectors is linearly independent if none of the vectors can be written as a linear combination of the other vectors in the set. In this case, S is linearly dependent because the fourth vector (0, 0, 0) can be represented as a linear combination of the other vectors:

0 * (1, 1, 1) + 0 * (0, 1, 1) + 0 * (1, 0, 1) = (0, 0, 0)

Step 2: Check if S spans R3
A set of vectors spans R3 if every vector in R3 can be written as a linear combination of the vectors in S. Since S contains the zero vector (0, 0, 0), it does not contribute to the span of S, and the remaining three vectors are not enough to span R3.

In conclusion, S is not a basis for R3 because it is linearly dependent and does not span R3.

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Answer:

speed=24km/h or 6.67m/s

Step-by-step explanation:

Given data:

time taken = t =43 hours

distance covered = d = 1032 km

to find:

speed of the ship = v =?

solution:

as we know that speed is defined as the distance covered by an object in unit time.Formula

speed = distance covered /time taken

speed = 1032km/43hours

speed =24km/h or in international system of units the answer is 6.67m/s

Answer:

w = 4 or w=-3.5

Step-by-step explanation:

This likely factors into

(2w  + 7)(w - 4) = 0

in which case there are 2 factors.

2w + 7 = 0

w = - 3.5      or

w - 4 = 0

w = 4

Answer:

Let the actual pressure = x

The reading is x + 8 % , so the reading is 108% of the actual.

Divide the reading by 108% for the actual

39.42/1.08 = x

X = 36.5 psi

The actual pressure is 36.5 psi