Given g(x)=−x−4, find g(5)

Answer:

B=1 C=4 D=6 A=9

Step-by-step explanation:

Its a clock

Answer:

A = 9

B = 1

C = 4

D = 6

Step-by-step explanation:

Answer:

I believe the answer is 330 pennies.

Step-by-step explanation:

since the pattern is adding 22 each time, do 22 x 15 and you get 330.

Answer:

The first three nonzero terms in the Maclaurin series is

\(\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }\)

Step-by-step explanation:

GIven that:

\(f(x) = 5e^{-x^2} cos (4x)\)

The Maclaurin series of cos x can be expressed as :

\(\mathtt{cos \ x = \sum \limits ^{\infty}_{n =0} (-1)^n \dfrac{x^{2n}}{2!} = 1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+... \ \ \ (1)}\)

\(\mathtt{e^{-2^x} = \sum \limits^{\infty}_{n=0} \ \dfrac{(-x^2)^n}{n!} = \sum \limits ^{\infty}_{n=0} (-1)^n \ \dfrac{x^{2n} }{x!} = 1 -x^2+ \dfrac{x^4}{2!} -\dfrac{x^6}{3!}+... \ \ \ (2)}\)

From equation(1), substituting x with (4x), Then:

\(\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}- \dfrac{(4x)^6}{6!}+...}\)

The first three terms of cos (4x) is:

\(\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}-...}\)

\(\mathtt{cos (4x) = 1 - \dfrac{16x^2}{2}+ \dfrac{256x^4}{24}-...}\)

\(\mathtt{cos (4x) = 1 - 8x^2+ \dfrac{32x^4}{3}-... \ \ \ (3)}\)

Multiplying equation (2) with (3); we have :

\(\mathtt{ e^{-x^2} cos (4x) = ( 1- x^2 + \dfrac{x^4}{2!} ) \times ( 1 - 8x^2 + \dfrac{32 \ x^4}{3} ) }\)

\(\mathtt{ e^{-x^2} cos (4x) = ( 1+ (-8-1)x^2 + (\dfrac{32}{3} + \dfrac{1}{2}+8)x^4 + ...) }\)

\(\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + (\dfrac{64+3+48}{6})x^4+ ...) }\)

\(\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }\)

Finally , multiplying 5 with \(\mathtt{ e^{-x^2} cos (4x) }\) ; we have:

The first three nonzero terms in the Maclaurin series is

\(\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }\)

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Answer:

3x^{2} -16x-19

Step-by-step explanation:

If we are going to be simplying this problem, then we need to take it step by step.

Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.

Answer:

(3x - 19) • (x + 1)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((3•((x-5)2))+14•(x-5))-24

STEP

2

:

Equation at the end of step 2

(3 • (x - 5)2 + 14 • (x - 5)) - 24

STEP

3

:

Trying to factor by splitting the middle term

Factoring 3x2-16x-19

The first term is, 3x2 its coefficient is 3 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is -19

Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57

Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .

-57 + 1 = -56

-19 + 3 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3

3x2 - 19x + 3x - 19

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (3x-19)

Add up the last 2 terms, pulling out common factors :

1 • (3x-19)

Step-5 : Add up the four terms of step 4 :

(x+1) • (3x-19)

Which is the desired factorization

Given that

Federal income tax =4594.84

Social security tax withheld = 2397.52.

Medicare tax withheld =479.14.

Recall that The Federal Insurance Contributions Act (FICA) is a U.S. law that mandates a payroll tax on the paychecks of employees, as well as contributions from employers, to fund the Social Security and Medicare programs.

The money was paid in FICA tax =Federal income tax +Social security tax + Medicare tax

Hence the money was paid in FICA tax is $7471.50.

Answer: 2876.66

Step-by-step explanation:

FICA taxes= Social security tax+ Medicare tax

2397.52 + 479.14=2876.66

The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°

Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.

From the diagram shown:

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

20 + 105 + ∠Z = 180

∠Z = 55°

Since triangle XYZ and triangle GHI are similar, hence:

∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°

The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°

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Answer:

see explanation

Step-by-step explanation:

2

4x² + 64 ← factor out the common factor of 4 from each term

= 4(x² + 16)

3

(a - 10)² = 121 ( take square root of both sides )

a - 10 = ± \(\sqrt{121}\) = ± 11 ( add 10 to both sides )

a = 10 ± 11

then

a = 10 - 11 = - 1

a = 10 + 11 = 21

Answer:

54 Joules

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

correct on edge

Answer:

The distance between the man and woman is changing at the rate of 1.5 m/sec.

Step-by-step explanation:

Speed = \(\frac{distance}{time}\)

⇒ distance = speed x time

After 35 minutes (2100 seconds) ,

the man has walked a distance = 1.3 x 2100

                                                   = 2730 m

After 35 minutes, the woman has walked a distance = 1.6 x 2100

                                                    = 3360 m

The sketch of the displacement of the man and woman forms a triangle with an included angle. Applying the cosine rule, we have:

\(c^{2}\) = \(a^{2}\) + \(b^{2}\) - 2abCos θ

   = \(3360^{2}\) + \(2730^{2}\) - 2 x 3360 x 2730 x Cos \(60^{o}\)

   = 11289600 + 7452900 - 18345600(0.5)

   = 18742500 - 9172800

  = 9569700

c = \(\sqrt{9569700}\)

  = 3093.5 m

The distance between the man and woman at 35 minutes is 3093.5 m.

The distance between the man and woman is changing at the rate = \(\frac{3093.5}{2100}\)

                              = 1.4731

                              = 1.5 m/sec

The distance between the man and woman is changing at the rate of 1.5 m/sec.

Answer:

hey i hope this helps u !!!

Step-by-step explanation:

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

The value is attached in the image file please find it.

In point a:

First, we calculate the find the mean,

Formula:

\(\to Mean (\bar{x}) = \frac{( \sum x)}{n}\)

                   \(=\frac{540}{13}\\\\ = 41.54\)

To calculate the standard deviation, subtract the mean value from all observations then square its value:

\(SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\\)   \(= \sqrt{ \frac{339.2308}{13-1}}\)

                             \(= \sqrt{ \frac{339.2308}{12}}\\\\= \sqrt{28.269}\\\\=5.31\)

please find attached file

In point b:

New \(x_i = 1 x_i + 0.05 x_i = 1.05 x_i\)

Calculate new mean:

\(\to \bar{x} = \frac{\sum x}{n} \\\)

       \(=\frac{567}{13} \\\\= 43.62\)

calculating the standard deviation:

\(SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\\)   \(= \sqrt{ \frac{374.0022}{13-1}}\)

                             \(= \sqrt{ \frac{374.0022}{12}}\\\\= \sqrt{31.16}\\\\=5.58\)

please find attached file

In point C:

Calculate new mean:

\(\to \bar{x} = \frac{\sum x}{n} \\\)

       \(=\frac{47.25}{13} \\\\= 3.46\)

calculating the standard deviation:

\(SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\\)   \(= \sqrt{ \frac{2.5975}{13-1}}\)

                             \(= \sqrt{ \frac{2.5975}{12}}\\\\= \sqrt{0.216}\\\\=0.46\)

please find attached file

In point d:

for b,

New \(\bar{x}= 1.05 \bar{x}= 1.05(41.54) =43.62\)

New\(s= 1.05s= 1.05(5.31)=5.57\)

for c,

New\(\bar{x}= \frac{ \bar{x}}{12}= \frac{41.54}{12} = 3.46\)

New \(s = \frac{s}{ 12} = \frac{5.31}{12}= 0.44\)

Answer:

third city

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

The time required for a radioactive isotope to decay to a certain percentage of its initial amount can be found using the following formula:

t = (t1/2 / ln(2)) * ln(N0/N1)

where:

t is the time elapsed since the release of the radioactive material

t1/2 is the half-life of the radioactive isotope (6 days in this case)

N0 is the initial amount of the radioactive isotope

N1 is the remaining amount of the radioactive isotope (14% of N0 in this case)

ln is the natural logarithm

We can solve for t by plugging in the given values:

t = (6 / ln(2)) * ln(1 / 0.14)

t ≈ 22.4 days

Therefore, the farmers needed to wait about 22.4 days to use the hay safely.

The answer is C, because there are two different numbers correlated to the same number on the Y side. The table does not represent a function.

The table is not a function because: A. one x-value corresponds to two different y-values.

If each x-value on a table of values is assigned to only one y-value, that table represents a function. If an x-value corresponds to more than one y-value, the table is not a function.

Thus, the x-value, 5, corresponds to two y-values, 2 and 5. Therefore the table does not represent a function.

The answer is: A.

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Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

Answer:

below

Step-by-step explanation:

3(x-9)

3(x+1)

divide by a gcf and place it outside the parenthesis.

Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

Answer:

yes

Step-by-step explanation:

\(\text {Hi! Let's Solve this Equation!}\)

\(\text {\underline {The First Step is to Flip the Equation}}\)

\(\text {Before: 16-x=-2}\\\text {After: x+16=-2}\)

\(\text {\underline {The Next Step is to Subtract 16}}\)

\(\text {x+16-16=-2-16}\)

\(\text {Your New Problem Is: x=-18}\)

\(\text {\underline {The Final Step is to Divide -1}}\)

\(\text {x/-1=-18/-1}\)

\(\text {Your Answer Would Be:}\)

\(\fbox {x=18}\)

\(\text {Best of Luck!}\)

Answer:

18

Step-by-step explanation:

16 - x = -2

-x = -2 - 16

-x = -18

x = 18

Hopefully this answer helps you :)

Answer:

5

Step-by-step explanation:

Answer:

t= 0.4933

t ≥ t ( 0.025 ,8 ) = 2.306

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

Step-by-step explanation:

We state our null and alternative hypotheses as

H0: ud= 0 Ha: ud≠0

The significance level is set at ∝= 0.05

The test statistic under H0 is

t= d`/ sd/√n

which has t distribution with n-1 degrees of freedom

The critical region is t ≥ t ( 0.025 ,8 ) = 2.306

Computations

Student       Scores before      Scores after    Difference           d²

                        reading book                    ( after minus before)

1                          720                   740             20                       400

2                        860                   860              0                           0

3                        850                   840             -10                       100

4                        880                   920             40                       1600

5                        860                   890             30                        900

6                        710                    720              10                         100

7                       850                    840              -10                       100

8                      1200                  1240             40                        1600

9                      950                    970              20                           40

∑                    6930                  8020           140                         4840

d`= ∑d/n= 140/9= 15.566

sd²= 1/8( 4840- 140²/9) = 1/8 (4840 - 2177.778) = 2662.22/8= 332.775

sd= 18.2422

t= 3/ 18.2422/ √9

t= 0.4933

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

Observe that

\(\dfrac{(n!)^2}{(2n+1)!} = \dfrac{n!(2n-n)!}{(2n+1)(2n)!} = \dfrac1{(2n+1)\binom{2n}n}\)

Starting with a well-known series

\(\displaystyle 2\arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}\)

we take some (anti)derivatives to find a sum that more closely resembles ours.

Let \(f(x)=2\arcsin^2(x)\). Then

\(\displaystyle f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{n \binom{2n}n}\)

\(\displaystyle x f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{n \binom{2n}n}\)

\(\displaystyle x f''(x) + f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{\binom{2n}n}\)

\(\displaystyle x^2 f''(x) + x f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{\binom{2n}n}\)

Noting that both sides go to zero as \(x\to0\), by the fundamental theorem of calculus we have

\(\displaystyle \sum_{n=1}^\infty \frac{2^{2n} x^{2n+1}}{(2n+1)\binom{2n}n} = \frac14 \int_0^x (t^2 f''(t) + t{}f'(t)) \, dt\)

so that when \(x=\frac12\), and rearranging some factors and introducing a constant, we recover a useful sum.

\(\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac12 \int_0^{1/2} (x^2 f''(x) + x f'(x)) \, dt\)

Integrate by parts.

\(\displaystyle \int_0^{1/2} x^2 f''(x) \, dx = \frac14 f'\left(\frac12\right) - 2 \int_0^{1/2} x f'(x) \, dx\)

\(\displaystyle \int_0^{1/2} x f'(x) \, dx = \frac12 f\left(\frac12\right) - \int_0^{1/2} f(x) \, dx\)

Then our sum is equivalent to

\(\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac18 f'\left(\frac12\right) - \frac14 f\left(\frac12\right) + \int_0^{1/2} \arcsin^2(x) \, dx\)

The remaining integral is fairly simple. Substitute and integrate by parts.

\(\displaystyle \int_0^{1/2} \arcsin^2(x) \, dx = \int_0^{\pi/6} u^2 \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} - 2 \int_0^{\pi/6} u \sin(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 2 \int_0^{\pi/6} \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1\)

Together with

\(f\left(\dfrac12\right) = 2 \arcsin^2\left(\dfrac12\right) = \dfrac{\pi^2}{18}\)

\(f'\left(\dfrac12\right) = \dfrac{4\arcsin\left(\frac12\right)}{\sqrt{1-\frac1{2^2}}} = \dfrac{4\pi}{3\sqrt3}\)

we conclude that

\(\displaystyle \sum_{n=0}^\infty \frac{(n!)^2}{(2n+1)!} = \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} \\\\ ~~~~~~~~~~~~~~~~~~ = 1 + \left(\frac18\cdot\frac{4\pi}{3\sqrt3}\right) - \left(\frac14\cdot\frac{\pi^2}{18}\right) + \left(\frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \boxed{\frac{2\pi}{3\sqrt3}}\)

Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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The original price was $105.04 and the discount is 10%.

Calculate the discount:

10 * 105.04 / 100 = 10.50

The discount is $10.50

The final (sale) price is:

$105.04 - $10.50 = $94.54

Answer:

1) B

2) B

Step-by-step explanation:

1) funtion 1 slope is 4

function 2 we use y2-y1/x2-x1

10-6/3-1

4/2

2 is the slope of function 2

so function 1 is bigger

1) only b is correct because it lands on the same line of y=x

hopes this helps please mark brainliest

Answer:

no more  Fortnight gift cards

Step-by-step explanation: