Evaluation the expression

Answer: D

Step-by-step explanation:

First, remember two things about translations.

For a function f(x).

A horizontal translation to the right of N units is written as:

f(x - N)

A vertical translation up of N units is written as:

f(x) + N.

Now let's look at the graph.

You can see that:

g(x) is: 4 units at the right of f(x) and 3 units bellow f(x).

Then we have:

g(x) = f(x - 4) - 3.

and f(x) = ∛x

then g(x) = ∛(x - 4) - 3

The correct option is D.

The function g(x) is transformed from the function f(x) by translating function f(x) by 4 units in the right direction and then by translating that graph 3 units in a downward direction.

Given :

Function --   \(\rm f(x) = \sqrt[3]{x}\)

The following steps can be used to determine the unknown function g(x):

Step 1 - According to the given graph, translate function f(x) 4 units in the positive x-axis that is in the right direction.

Step 2 - Now, again according to the given graph, translate function f(x) 3 units in the downward direction that is in the negative y-axis.

Step 3 - The resulting graph is the graph of the function g(x). Whose equation is written as:

\(\rm g(x) = \sqrt[3]{x-4} - 3\)

So, the correct option is D).

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This can be calculated by adding up the total number of passengers on all five flights (41+39+40+39+33 = 192) and dividing it by the total number of available seats on those flights (69 x 5 = 345). So, 192 divided by 345 equals 0.774 or 77.4%. The load factor for Jim Bob Airlines' last five flights was 55.65%.

To find the load factor for Jim Bob Airlines' last five flights, follow these steps:

1. Add the number of passengers on each flight:
  41 (MSY to DFW) + 39 (DFW to OKL) + 40 (OKL to TUL) + 39 (TUL to FWB) + 33 (FWB to MSY) = 192 passengers

2. Calculate the total number of available seats for the five flights:
  69 seats per flight × 5 flights = 345 available seats

3. Calculate the load factor by dividing the total passengers by the total available seats:
  Load factor = (192 passengers) / (345 available seats) = 0.5565 (rounded to four decimal places)

4. Convert the load factor to a percentage:
  Load factor percentage = 0.5565 × 100 = 55.65%

The load factor for Jim Bob Airlines' last five flights was 55.65%.

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Answer:

1.3

Step-by-step explanation:

BC is the distance between B and C.

BC = x − (-0.4)

BC = x + 0.4

AB is the distance between A and B.

AB = -0.4 − (-1.25)

AB = -0.4 + 1.25

AB = 0.85

Substitute into the equation.

BC = 2AB

x + 0.4 = 2(0.85)

x + 0.4 = 1.7

x = 1.3

Answer:

x=1.3

Step-by-step explanation:

AB=(-0.4-(-1.25))=1.25-0.40=0.85

BC=2AB=2×0.85=1.70

x=-0.4+1.7=1.3

Ans of your question . in which class do u read?

The differentiation of the function is f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

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

f(x) = 2x³ + 6x - 1/x + 3eˣ - sin(x)

The derivative of the functions can be calculated using the first principle which states that

if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹

Using the above as a guide, we have the following:

f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

Hence, the differentiation of the function is f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

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Answer:

The answer is below

Step-by-step explanation:

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $19 monthly fee and charges an additional $0.13 for each minute of calls. The second plan has a $24 monthly fee and charges an additional $0.08 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal

Answer: Let the number of minutes of calls that will cost the two plans to be equal be x. The first plan has a $19 monthly fee and charges an additional $0.13 for each minute of calls, therefore the total cost in x minutes = $19 + $0.13x

The second plan has a $24 monthly fee and charges an additional $0.08 for each minute of calls, therefore the total cost in x minutes = $24 + $0.08x

For the two plans to be equal, the cost of the first plan should be equal to the cost of the second plan. i.e.:

$19 + $0.13x =  $24 + $0.08x

Solving for x:

\($19 + $0.13x = $24 + $0.08x\\0.13-0.08=24-19\\0.05x=5\\x=5/0.05=100\\x=100\ minutes\)

It would take 100 minutes of calls for the costs of the two plans to be equal

Regular hexagon ABCDEF is inscribed in a circle with center H, the image of segment BC after 120 degree clockwise rotation about point H is the segment joining the points B' and C', which has endpoints (-0.5r\(\sqrt{3\), -0.5r) and (-0.5r, -0.5r).

Since the hexagon is inscribed in a circle with center H, we can conclude that H is also the center of the circle passing through vertices B, C, and D. Therefore, the circle passing through B, C, and D is also a 120 degree clockwise rotation of the circle passing through A, B, and C.

To find the image of segment BC after a 120 degree clockwise rotation about point H, we need to find the coordinates of B and C relative to H, and then apply a 120 degree rotation matrix to these coordinates.

Let the radius of the circle be r, and let the coordinates of H be (0,0). Then the coordinates of B and C are:

B: (r cos(60), r sin(60))

C: (r cos(0), r sin(0)) = (r, 0)

To apply a 120 degree clockwise rotation matrix, we can use the following matrix:

[ cos(-120) -sin(-120) ]

[ sin(-120) cos(-120) ]

Simplifying, we get:

[ cos(120) sin(120) ]

[ -sin(120) cos(120) ]

Applying this matrix to the coordinates of B and C, we get:

B': [ cos(120) sin(120) ][ r cos(60) ] = [ -0.5r \(\sqrt{3}\)]

[ -sin(120) cos(120) ][ r sin(60) ] [ -0.5r ]

C': [ cos(120) sin(120) ][ r ] = [ -0.5r ]

[ -sin(120) cos(120) ][ 0 ] [ -0.5r ]

Therefore, the image of segment BC after a 120 degree clockwise rotation about point H is the segment joining points B' and C', which has endpoints (-0.5r\(\sqrt{3}\), -0.5r) and (-0.5r, -0.5r), respectively.

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Answer:

6n-5

Step-by-step explanation:

Some different types of sequences

To find sequence patterns, often the sequences are arithmetic (adding by a constant amount) or geometric (multiplying by a constant amount).  

To test if something is a geometric sequence, find the quotient of (divide) adjacent terms.

To test if something is an arithmetic sequence, find the difference of (subtract) adjacent terms.

Finding the type of our sequence

Note the following:

19-13=6

13-7=6

7-1=6

So, to get each next term, add 6.  However, what is the nth term?

Finding an expression for our sequence

You'll be adding up "n" sixes to get there (expressed with multiplication, because multiplication is shorthand for repeated addition), but we need a starting point so that when n=1, the expression equals 1, and when n=2, the expression equals 7... and so on.  This starting point shifts the "6n" piece of our expression so that it lines up on the sequence.  I'm going to call this starting point "b" for the base that is supporting this sequence.

So the expression will look something like \(6n+b\)

Knowing that the expression needs to equal 1 when n=1, we can set up an equation and solve for "b".

\(6n+b=n^{\text{th}} \text{ term}\\6(1)+b=(1)\\6+b=1\\(6+b)-6=(1)-6\\b=-5\)

So, the expression for the nth term of the sequence is \(6n-5\)

Verifying

To verify that the expression we found is right, we can test our expression for each of the terms we do know:

The first term (n=1) is 1

\(6n+b=n^{\text{th}} \text{ term}\\\)

\(6(1)-5 \overset{?}{=} (1)\)

\(6-5 \overset{?}{=} 1\)

\(1 \overset{\checkmark}{=} 1\)

The second term (n=2) is 7

\(6n+b=n^{\text{th}} \text{ term}\\\)

\(6(2)-5 \overset{?}{=} (7)\)

\(12-5 \overset{?}{=} 7\)

\(7 \overset{\checkmark}{=} 7\)

The third term (n=3) is 13

\(6n+b=n^{\text{th}} \text{ term}\\\)

\(6(3)-5 \overset{?}{=} (13)\)

\(18-5 \overset{?}{=} 13\)

\(13 \overset{\checkmark}{=} 13\)

The fourth term (n=4) is 19

\(6n+b=n^{\text{th}} \text{ term}\\\)

\(6(4)-5 \overset{?}{=} (19)\)

\(24-5 \overset{?}{=} 19\)

\(19 \overset{\checkmark}{=} 19\)

Answer: I believe it is the 2nd one

Step-by-step explanation: You are adding ZA and AY together and you would get ZY because you are not going to add both a's in there

Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Answer:

m=0 and m=3

Step-by-step explanation:

there are two solutions

Answer:

Neither game A or B is fair

Step-by-step explanation:

statement accurately describes whether these games are fair is neither game A nor game B.

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

For, game A:

Not fair

For game B,

Again,  unfair.

P (odd, odd)= 1/4

P(even, even)=1/4

P(odd, even)=1/2

Hence, none of the game is fair.

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Answer:

8 is the answer

hope this helps you.

Answer:

(Go with the melon, tomato, or pumpkin)

Step-by-step explanation:

MELON: I chose the melon. The target is 40ft away, so the maximum height of the launch has to be 12 feet.

TOMATO: I chose the tomato (because the numbers are round and easy to manipulate) The target is 60ft away, so the maximum height of the launch has to be 45 feet.

PUMPKIN: I chose the pumpkin. The target is 50 ft away, so the maximum height is 62 feet.

Answer:

According to sources on googIe, the average price of a hot dog would be $5.22.

If a shopper needs 48 hot dogs, they would need a total of $250.56 dollars to pay.

Step-by-step explanation:

48 x 5.22 = 250.56

Answer:

yes it is i think don't sew meh if im wrong

Step-by-step explanation:

Cam can run 9.3205 miles when she finishes.

mile, any of several distance measurements, such as the statute mile of 5,280 feet (1.609 km). It was derived from the Roman mille passus, or "thousand paces," which was equivalent to 5,000 Roman feet.

The term "mile" is derived from the Latin "mille passus," which means "one thousand paces," and a mile was 1,000 Roman strides, with a stride equaling two steps. In 1592, the English Parliament standardised the Mile measurement at eight furlongs (660 feet).

Cam signed up to run a 15-kilometre running race.

So, here, we will convert kilometers to miles-

I kilometer is =0.621371 miles

And, I mile =1.609344 kilometres.

Thus, converting kilometres to miles.

Simply multiply the Number of kilometres by 0.62137.

Therefore, 1 kilometre =0.621371 miles

1.5 kilometer=15*0.621371 miles =9.32057 miles

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Answer:

4

Step-by-step explanation: d d x ( x 2 + 4 y 2 ) = d d x ( 4 )

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The term that describes the sample in this scenario is "biased."A sample is considered biased when it is not representative of the target population.

In this case, the fact that 33% of the sample consists of teachers despite the fact that the target population contains far fewer than 33% teachers indicates that the sample is not representative of the target population.

There are many reasons why a sample might be biased. For example, if the method of selecting participants is flawed or if the sample size is too small, it can result in a biased sample. In this case, it's possible that the method used to select participants led to an overrepresentation of teachers in the sample. Therefore, the sample is biased, and any conclusions drawn from it may not be generalizable to the target population.

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Answer: 5 terms.

Step-by-step explanation:

We know that the n-th term of a sequence is:

Aₙ = n² + 20

Where n can be any natural number, then n ∈ {1, 2, 3, ...}

We want to find how many terms are smaller than 50.

Then we could find the first value of n such that Aₙ is equal or larger than 50.

Then we can solve:

Aₙ = n² + 20 = 50

then:

n² = 50 - 20 = 30

n = √30 = 5.48

This is not a natural number, so we need to round to the next one that is n = 6

This means that the first natural number n such that Aₙ is equal or larger than 50 is n = 6, then for the values:

n = 1, 2, 3, 4, 5

Aₙ is smaller than 50

This means that there are 5 terms of the sequence that are smaller than 50.

Answer:

704 pi in ^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

V = pi ( 8)^2 * 11

V = pi (704)

V = 704 pi in ^3

Answer:

Step-by-step explanation:

Solution,

Radius(R)= 8 in.

Height (h)= 11 in.

Volume of cylinder=?

Now,

Volume of cylinder:

\(\pi {r}^{2} h\)

\(\pi \: {(8)}^{2} \times 11 \)

\(\pi \times 64 \times 11\)

\(704\pi \: {inches}^{3} \)

Hope this helps...

Good luck on your assignment..

Given:

Consider the complete question is "Which expression is equivalent to \(8\sqrt{6}\)? A. \(\sqrt{14}\)  B.  \(\sqrt{748}\) C. \(\sqrt{196}\) D. \(\sqrt{384}\)".

To find:

The equivalent expression.

Solution:

We have,

\(8\sqrt{6}\)

It can be written as

\(=(\sqrt{8})^2\sqrt{6}\)

\(=\sqrt{8}\cdot \sqrt{8}\codt \sqrt{6}\)

\(=\sqrt{8\cdot 8\cdot 6}\)          \([\because \sqrt{a}\sqrt{b}=\sqrt{ab}]\)

\(=\sqrt{384}\)

So, \(\sqrt{384}\) is equivalent to \(8\sqrt{6}\).

Therefore, the correct option is D.

Answer:

175

Step-by-step explanation:

To find a proportion, you need to put both parts over the total.  You would put the part of silver (14) over the total (80) and the part you are trying to find (X) over the total number of students (1,000). Then you cross multiply 14 x 1,000 and divide by 80 giving you 175 silver cars.

True. Even with an infinite population, it is still possible to construct a frame consisting of all the elements.

The key is to use a well-defined and systematic sampling method that allows us to make inferences about the population based on a representative subset of its elements.

For example, in a hypothetical scenario where we are studying the properties of all real numbers between 0 and 1, which is an infinite population, we can still construct a frame by using a systematic sampling method such as selecting every nth decimal point.

This allows us to construct a representative subset of the population and make inferences about the entire population based on that subset.

The infinity of a population does not preclude the construction of a frame consisting of all its elements, as long as a systematic and well-defined sampling method is used.

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a. the linear approximating polynomial L(x) is 1+x

b. the quadratic approximating polynomial Q(x) is 1 + x + x^2

a. The linear approximating polynomial for a function f(x) centered at the point a can be found using the formula:

L(x) = f(a) + f'(a)(x - a)

where f'(a) is the derivative of the function evaluated at the point a.

b. The quadratic approximating polynomial for a function f(x) centered at the point a can be found using the formula:

Q(x) = f(a) + f'(a)(x - a) + (1/2)f''(a)(x - a)^2

where f''(a) is the second derivative of the function evaluated at the point a.

c. To approximate the quantity 1/(1-x) using the linear and quadratic approximating polynomials obtained in parts a. and b., we need to first find the values of f(a), f'(a), f''(a) at the given point a.

Let's assume a = 0 for simplicity.

a. Linear Approximation:
To find the linear approximating polynomial, we need to evaluate f(0) and f'(0).

f(x) = 1/(1-x)

f(0) = 1/(1-0) = 1

To find f'(0), we need to take the derivative of f(x) and evaluate it at x = 0.

f'(x) = 1/(1-x)^2

f'(0) = 1/(1-0)^2 = 1

Using the linear approximation formula, we can now find the linear approximating polynomial L(x):

L(x) = f(0) + f'(0)(x - 0) = 1 + 1(x - 0) = 1 + x

b. Quadratic Approximation:
To find the quadratic approximating polynomial, we need to evaluate f''(0).

f''(x) = 2/(1-x)^3

f''(0) = 2/(1-0)^3 = 2

Using the quadratic approximation formula, we can now find the quadratic approximating polynomial Q(x):

Q(x) = f(0) + f'(0)(x - 0) + (1/2)f''(0)(x - 0)^2 = 1 + 1(x - 0) + (1/2)2(x - 0)^2 = 1 + x + x^2

Now, we can use these linear and quadratic approximating polynomials to approximate the given quantity 1/(1-x). For example, if we want to approximate the value of 1/(1-x) at x = 0.1, we can substitute x = 0.1 into both L(x) and Q(x) to get the approximate values.

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At x=6 the function f(x) is discontinuous.

Given,

\(f(x)=\frac{x^2-x-42}{x+6}\)

Factorizing numerator of f(x),

\(f(x)=\frac{x^2-x-42}{x+6}\\\\f(x)=\frac{x^2-x-42}{x+6}\\\\f(x)=\frac{x^2+6x-7x-42}{x+6}\\\\f(x)=\frac{x(x+6)-7(x+6)}{x+6}\\\\f(x)=\frac{(x+6)(x-7)}{x+6}\)

So, when x=6, both the numerator and denominator becomes zero.

Therefore, discontinuity occurs when x=6.

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Answer:

Write the dividend under the bar and the divisor to the left. Each is written in descending order of powers of

x

. If any power of

x

is missing, then include it with a

0

coefficient. For example, if you were dividing by

x

2

−

1

, then you would express the divisor as

x

2

+

0

x

−

1

.

Choose the first term of the quotient to cause leading terms to match. In our example, we choose

x

2

, since

(

x

−

1

)

⋅

x

2

=

x

3

−

x

2

matches the leading

x

3

term of the dividend.

Write the product of this term and the divisor below the dividend and subtract to give a remainder (

2

x

2

).

Bring down the next term (

−

x

) from the divisor alongside it.

Choose the next term (

2

x

) of the quotient to match the leading term of this remainder, etc.

Stop when there is nothing more to bring down from the dividend and the running remainder has lower degree than the divisor.

In our example, the division is exact. We are left with no remainder.

Step-by-step explanation:

i did the test

Based on the given information, the correct answer would be, b) yes; the distance between points f and g was used to create circle h.

In the given scenario, the construction demonstrates how to copy an angle correctly using technology. Specifically, it states that circle h was created using the distance between points f and g. This means that a compass was likely used to measure the distance between these two points. By setting the compass to this distance, a circle can be drawn with point f as the center.

Copying an angle involves creating a circle with a center at one of the vertex points of the angle and using the distance between points on the rays of the angle to determine the radius of the circle. In this case, the distance between points f and g was used to create circle h, which corresponds to copying the angle. Option b accurately describes the process used to copy the angle.

Therefore, option b ("yes; the distance between points f and g was used to create circle h") accurately describes the process of copying an angle using technology in this given construction.

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The correct answer is option

A) "Yes; the distance between points A and F was used to create circle H."

Option A is the correct answer because the distance between points A and F is indeed used to create circle H in this construction.

To copy an angle correctly using technology, you need to follow specific steps.

One of these steps involves using the distance between two points to create a circle. In this construction, the distance between points A and F is used to create circle H.

By placing the compass on point A and adjusting its width to reach point F, a circle can be drawn around point A.

Copying an angle correctly also involves drawing a ray from the vertex of the angle. In this construction, the ray is drawn from point F, which is a common endpoint of the angle being copied.

By intersecting the circle with this ray, a new point G is obtained. Finally, a line can be drawn connecting point A and point G to complete the construction of the copied angle.

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Answer:

(x, y) ≈ (-2.17, ±sqrt(95)) or (x, y) ≈ (-1.03, ±sqrt(21))

Step-by-step explanation:

To solve this system of equations, we can use the method of substitution. We can start by isolating one of the variables in one of the equations and substituting it into the other equation. Let's solve for x in the first equation:

5y² + 24x - 77 = 0

24x = 77 - 5y²

x = (77 - 5y²)/24

Now we can substitute this expression for x into the second equation:

14x² + 5y² + 150x + 119 = 0

14((77-5y²)/24)² + 5y² + 150((77-5y²)/24) + 119 = 0

Simplifying this expression gives:

49y^4 - 5390y² - 108090y - 404271 = 0

We can solve for y using the quadratic formula:

y² = (5390 ± sqrt(5390² - 4(49)(-404271)))/(2(49))

y² = (5390 ± sqrt(16946804))/98

y² = (5390 ± 4118)/98

y² = 95 or y² = 21

Substituting each value of y into the expression we found for x earlier gives:

x = (77 - 5(±sqrt(95))²)/24 ≈ -2.17 or x = (77 - 5(±sqrt(21))²)/24 ≈ -1.03

Therefore, the solution to the system of equations is:

(x, y) ≈ (-2.17, ±sqrt(95)) or (x, y) ≈ (-1.03, ±sqrt(21))