Find the common ratio: 64, -16, 4, -1, ...

Answer:  0

Step-by-step explanation:

Answer:

center:

(-0.25, 5)

foci :

(-0.25, 0.158771) | (-0.25, 9.84123)

vertices :

(-0.25, -0.59017) | (-0.25, 10.5902)

wolframramalpha

Answer:

  14(cos(125°) +i·sin(125°))

Step-by-step explanation:

The product of two complex numbers is the product of their magnitudes at an angle equal to the sum of their angles.

For A = a·cis(α) and B = b·cis(β), the product AB is ...

  AB = (a·cis(α))·(b·cis(β)) = ab·cis(α+β)

where "cis(x)" stands for the sum (cos(x) +i·sin(x)).

The product of interest is ...

  Z1·Z2 = (7cis(15°))·(2cis(110°)) = (7·2)cis(15°+110°)

  Z1·Z2 = 14cis(125°) = 14(cos(125°) +i·sin(125°))

We conclude that the exponential function is:

f(x) = -1*(2)ˣ

Here we know that we have an exponential function of the form:

f(x) = a*b^x

And we know two points on the function, that are:

f(1) = -2 = a*b^1 = a*b

f(2) = -4 = a*b^2

Then we have a system of equations to solve, which is:

-2 = a*b

-4 = a*b^2

From the first equation we can solve:

-2/a = b

Replacing that in the other equation we can get:

-4 = a*(-2/a)^2 = 4/a

a = 4/-4 = -1

Now that we know the value of a, we can get the value of b:

-2/a = b

-2/-1 = 2 = b

In this way, we conclude that the exponential function is:

[tex]f(x) = -1*(2)^x[/tex]

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Answer:

x = 185 grams

Step-by-step explanation:

let 100% of the recommended daily amount = x

148 = 80%x

148 = 0.8x

divide by 0.8 both sides

x = 185

Answer:

slope is 4

Step-by-step explanation:

Slope is rise/run

for every 4 units it rises it runs 1 unit

4/1=4

The probability of occurrence for the events A, B and C is; 1/4.

For the first event A in which case, there's no odd number on the first two rolls, the possible events are; EEE and EEO. Consequently, the required probability is;

Event A = 2/8 = 1/4.

For the event B in which case, there's an even number on both the first and last rolls; the possible events are; EEE and EOE. Consequently, the required probability is;

Event B = 2/8 = 1/4.

For the event C in which case, there's an odd number on each of the first two rolls; the possible events are; OOO and OOE. Consequently, the required probability is;

Event C = 2/8 = 1/4.

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Answer:

h = -14

Step-by-step explanation:

-7πh = 98π

⇔ -7h = 98   (Just Divide both sides by π)

⇔ h = 98 ÷ (-7) = -14

Hi :)

We should find h. All it takes is some algebra skills ^•^

First off, you can see than we have π on both sides. So, why not divide both sides by π and get it out of the way?

We end up with

[tex]\boldsymbol{-7h=98}[/tex]

Super! Now all we have to do is divide both sides by -7

We end up with

[tex]\boldsymbol{h=-14}[/tex]

[tex]\tt{Learn~More;Work~Harder}[/tex]

:)

The probability that the candidate will win is P = 0.357

We know that the odds against the particular candidate are 9 to 5.

The the odds for the candidate are 5 to 9, this means that in 5 cases the candidate will win, and in 9 cases the candidate will lose.

Then the candidate wins in 5 out of 14 cases, then the probability that the particular candidate wins the elections is given by the quotient:

P = 5/14 = 0.357

The probability that the candidate will win is P = 0.357

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Answer:

32 seconds

Step-by-step explanation:

first 8 secknds gives us the value of set 2.5l

2.5L to make 10 =

10÷2.5=4

That said 2.5L fills 1pL by 4 giving us;

4×2.5= 10L

The possible values of y are 9n where n is an integer greater than 0 equal to 0

The statement is given as;

y is a multiple of 9

The above means that

The number y can be divided by 9 without remainder

The numbers in this category are:

Numbers = 9, 18, 27, 36, 45......

This can be rewritten as:

Numbers = 9n where n is an integer greater than 0 equal to 0

Hence, the possible values of y are 9n where n is an integer greater than 0 equal to 0

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Using a trigonometric identity, and considering that the angle is in the fourth quadrant, the tangent of the angle is given as follows:

tan(theta) = -1/4

The following identity is used to relate the measures, considering an angle [tex]\theta[/tex]:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

For this problem, the sine is given as follows:

[tex]\sin{\theta} = -\frac{1}{\sqrt{17}}[/tex]

Then the cosine, which we need to find the tangent, is found as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

[tex]\left(-\frac{1}{\sqrt{17}}\right)^2 + \cos^2{\theta} = 1[/tex]

[tex]\frac{1}{17} + \cos^2{\theta} = 1[/tex]

[tex]\cos^2{\theta} = \frac{16}{17}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{16}{17}}[/tex]

Since the angle is in the fourth quadrant, the cosine is positive, hence:

[tex]\cos{\theta} = \frac{4}{\sqrt{17}}[/tex]

It is the sine of the angle divided by the cosine of the angle, hence:

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{-\frac{1}{\sqrt{17}}}{\frac{4}{\sqrt{17}}} = -\frac{1}{4}[/tex]

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[tex]\bold{Answer:} \small\boxed{21e-42}[/tex]

Step-by-step explanation:

 [tex]To\ solve\ : \ 9e-6(-2e+7)[/tex]

we first must use the distributive property. You can think about solving this like this:

[tex]=9e-(6)(-2e+7)[/tex]

Notice how we are not distributing -6, but only 6. Now we can solve normally:

[tex]=9e-(-12e+42)[/tex]

Now we distribute the '-' sign to the terms in parenthesis.

[tex]=9e+12e-42[/tex]

[tex]\longrightarrow \large\boxed{21e-42}[/tex]

The decimal form is 15.08 rounded.

Answer:4 1/12.

Step-by-step explanation: First, you add 3 and a half with a quarter. A half equals two quarters so it equals 3 and 3/4.  Then, you add 3 3/4 with 1/3. A common denominator here is 12. 3/4 times 3/3 = 9/12. 1/3 times 4/4 = 4/12. 9+4 = 13. The answer is more than one so we carry and get 4 and 1/12.

Answer:

Step-by-step explanation:

Let the function be (3x+15)/(6-x) then the value of x exists at -5.

Given: Rational Expression (3x+15)/(6-x)

To find the value of x when given a rational expression equivalent to 0.

To estimate the value of x, convey the variable to the left side and convey all the remaining values to the right side. Simplify the values to estimate the result.

Consider, (3x+15)/(6-x) = 0

3x + 15 = 0(6-x)

3x + 15 = 0

Subtract 15 from both sides of the equation, e get

3x + 15 - 15 = 0 - 15

simplifying the above equation, we get

3x = 0 - 15

3x = -15

Divide both sides by 3, then we get

x/3 = -15/3

x = -5

Therefore, the value of x exists at -5.

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Answer:

0.6 km/hr

Step-by-step explanation:

Speed downstream: 13/5= 2.6 km/hr

Speed upstream: 7/5= 1.4 km/hr

Therefore, Velocity of current is: 1/2 (2.6-1.4) km/hr = 1/2(1.2) km/hr

The value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14

The equation is given as:

(43/7 ÷ x + 32/9) ÷ 25/6 = 4/3

Rewrite as a product

(43/7 ÷ x + 32/9) x 6/25 = 4/3

Multiply both sides of the equation by 25/6

(43/7 ÷ x + 32/9)= 4/3 x 25/6

Evaluate the product

(43/7 ÷ x + 32/9)= 50/9

Rewrite the equation as:

43/7x + 32/9= 50/9

Subtract 32/9 from both sides

43/7x = 2

Multiply both sides by 7x

14x = 43

Divide by 14

x =43/14

Hence, the value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14

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Answer:  10

Step-by-step explanation: 800/80 = 10

The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.

A geometric sequence is a special series where every term is the product of the previous term and a common ratio.

The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.

In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........

The first term of the sequence, a = 9.

The second term of the sequence, a₂ = -6.

By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:

a₂ = a.r²⁻¹.

Substituting the values, we get:

-6 = 9(r²⁻¹),

or, r²⁻¹ = -6/9,

or, r = -2/3.

Thus, the common ratio of the given geometric sequence is -2/3.

The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:

a₄ = a.r⁴⁻¹ = a.r³.

Substituting the values, we get:

a₄ = 9(-2/3)³,

or, a₄ = 9.(-8/27),

or, a₄ = -8/3.

Thus, the 4th term of the given geometric sequence is -8/3.

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The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

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The factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2

The polynomial is given as:

2x^3 - 3x^2 - 5x + 6

Next, we test the factors

Option A. x + 6

Set the factor to 0

x + 6 = 0

Solve for x

x = -6

So, we set up the division as follows:

-6  l   2    - 3     -5      6

Bring down the leading coefficient

-6  l   2    - 3     -5      6

        2

Multiply 2 and -6

-6  l   2    - 3     -5      6

                -12

        2

Add -3 and -12

-6  l   2    - 3     -5      6

                -12

        2      -15

Repeat this process

-6  l   2    - 3     -5      6

                -12    72    -402

        2      -15    67    -396

-396 is the remainder of the above division.

This means that x + 6 is not a factor of the polynomial

Option B. x - 2

Set the factor to 0

x - 2 = 0

Solve for x

x = 2

So, we set up the division as follows:

2  l   2    - 3     -5      6

Bring down the leading coefficient

2  l   2    - 3     -5      6

        2

Multiply 2 and 2

2  l   2    - 3     -5      6

                4

        2

Add -3 and -12

2  l   2    - 3     -5      6

                4

        2      1

Repeat this process

2  l   2    - 3     -5      6

                4      2      -6

        2      1       -3     0

0 is the remainder of the above division.

This means that x - 2 is a factor of the polynomial

There is no need to check for the remaining options

Hence, the factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2

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Answer:

2400

Step-by-step explanation:

40 = 2^3 * 5

120 = 2^5 * 5

150 = 2 * 3 * 5^2

LCM = 2^5 * 3 * 5^2

If four books are 100%, then 3 books are how much percent of total books?

[tex]\frac{3}{4}[/tex] × 100 = 3 × 25 = 75%

Hope it helps!

The answer is 75%.

To find the percentage, divide the number of given books by total books and multiply by 100%.

The total number of eggs needed for b batches is n = 3b

The total number of eggs needed for 6 batches is 18.

Multiplication is one of the basic mathematical operation that is used to determine the product of two or more numbers. The sign used to denote multiplication is x. Other mathematical operations include addition, subtraction and division.

In order to determine the total number of eggs needed, multiply the number of eggs needed for one batch by the total number of batches.

Total eggs needed = eggs needed for one batch x total number of batches

n = 3 x b

n = 3b

6 x 3 = 18

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Answer:

[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]

[tex]\lim_{x\rightarrow 0 } x-1+\frac{1+ln^{2}x}{x} = + \infty[/tex]

Step-by-step explanation:

[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]

[tex]= [\lim_{x\rightarrow +\infty } (x-1)]+[ \lim_{x\rightarrow +\infty } (\frac{1+ln^{2}x}{x})][/tex]

=          +∞             +          0

= +∞

[tex]\lim_{x\rightarrow +\infty } x-1+\frac{1+ln^{2}x}{x}[/tex]

[tex]= [\lim_{x\rightarrow 0 } (x-1)]+[ \lim_{x\rightarrow 0 } (\frac{1+ln^{2}x}{x})][/tex]

=            -1             +      +∞  

= +∞  

It should be noted that a trial balance is a report which lists the balances of the ledger accounts of a company.

It should be noted that the information is incomplete. Therefore, an overview will be given. It should be noted that the accounts that are reflected on a trial balance are related to the accounting items.

The adjusted trial balance simply lists the general ledger account balances after the adjustments have been made. In such a case, these adjustments typically include prepaid and accrued expenses, and non-cash expenses such as depreciation.

Furthermore, a trial balance is a list of the closing balances of ledger account while adjusted balance is a list of general account. An adjusted trial balance is typically prepared by creating a series of journal entries which are designed to account for any transactions that haven't been completed.

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40+1 in dollars per hour

Answer: -6

Step-by-step explanation:

[tex]x+3y=-5\\\\3y=-x-5\\\\y=-\frac{1}{3}x-\frac{5}{3}[/tex]

So, since parallel lines have the same slope, the slope of the line we need to find is -1/3.

Substituting into point-slope form, the equation is

[tex]y-2=-\frac{1}{3}(x+7)\\[/tex]

Converting to the required form,

[tex]y-2=-\frac{1}[3}x-\frac{7}{3}\\\\\frac{1}{3}x+y=-\frac{1}{3}\\\\-3x-9y=3[/tex]

So, B-A is equal to -6.

After half of the men go away, the provisions will last for another 16 days.

First, we know that the garrison has provisions for 10 days.

2 days after that, the garrison has provisions for another 8 days. Here we know that the number of men on the garrison is reduced to its half. Then, the time that the provisions in the garrison will last is multiplied by 2.

So we just need to solve the product:

2*8 days = 16 days.

After half of the men go away, the provisions will last for another 16 days.

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