Find the measure of XY

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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Using the z-distribution, it is found that a sample size of n = 18,805 is required.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]z = 2.81, \sigma = 24.4, M = 0.5[/tex].

Hence we solve for n to find the needed sample size.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = 2.81\frac{24.4}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 24.4 \times 2.81[/tex]

[tex]\sqrt{n} = 48.8 \times 2.81[/tex]

[tex](\sqrt{n})^2 = (48.8 \times 2.81)^2[/tex]

n = 18,805.

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Answer:

Step-by-step explanation:

What if the estimate is within 1 of the population mean?

Answer:

[tex]3x^2[/tex]

Step-by-step explanation:

First main thing to know is the product and quotient rule of exponents.

Product Rule:

  [tex]x^a*x^b = x^{a+b}[/tex]

  And if this doesn't make sense, you can think of the exponent like this:

  [tex]x^a*x^b = (x*x*x*x...\text{ a amount of times}) * (x * x * x \text{ b amount of times})[/tex]

  and since multiplication is commutative, we can just combine all these x's, and since the total amount on the left is "a", and the right is "b", the total combined x's should be a+b, which can be expressed as:
   [tex]x*x*x... \text{ a+b amount of times}[/tex]

   which can be expressed as an exponent (x^(a+b))

Quotient Rule:

   [tex]\frac{x^a}{x^b} = x^{a-b}[/tex]

  You can use similar reasoning for this, since if you write it out you get

   [tex]\frac{x*x*x...\text{ a amount of times}}{x*x*x\text{ b amount of times}}[/tex]

  and since you have an x in the numerator and the denominator, you can simply cancel the x's out. In doing this you want to remove the denominator, so you cancel out "b" x's. So there will be (a-b) x's left in the numerator, and a 1 in the denominator, so it's just x^(a-b)

Ok so now let's apply these to solve your question

[tex]\frac{(15x^{-4})*x^{15}}{(5x^4)*x^5}\\[/tex]

So let's combine the exponents in the numerator and denominator using the product rule

[tex]\frac{15x^{11}}{5x^9}\\[/tex]

Now we can divide the 15 by 5, and divide the x^11 by the x^9 using the quotient rule

[tex]3x^2[/tex]

The expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of the exponent can be written as - (1/27).

Exponents are of the form aˣ, read as " a to the power x", function as a multiplied by itself x number of times, and are used in a numerical and algebraic expression.

To simplify these expressions, we use the following laws of the exponents:

[tex]1. a^m.a^n = a^{m + n}\\2.\frac{a^m}{a^n} = a^{m-n}\\ 3. (a^m)^n = a^{mn}\\4. a^{-m} = \frac{1}{a^m}\\5. a^0 = 1[/tex]

In the question, we are asked to simplify the expression, [tex](-243)^{-3/5}[/tex].

The expression can be solved using the laws of exponent as follows:

[tex](-243)^{-3/5}\\[/tex]

= [tex]((-3)^5)^{-3/5}[/tex]

= [tex](-3)^{-3}[/tex] {Using the law of exponent: [tex](a^m)^n = a^{mn}[/tex]}

= [tex]\frac{1}{-3^3}[/tex] {Using the law of exponent: [tex]a^{-m} = \frac{1}{a^m}[/tex]}

= 1/(-27)

= - (1/27).

Thus, the expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of exponent can be written as - (1/27).

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The odds against selecting a red marble is =2/11

The number of marbles which were red = 9

The number of marbles which were blue = 2

The total amount of marbles in the Box = 11

When one marble is picked at random from the box, the odds against selecting a red marble can be gotten through the blue marble.

That is, the number of blue marble/ total marble

= 2/11

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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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13) 120 + 1.5 + 0.25 = 121.75 pounds

14) 4 - 1.5 = 2.5 pints

15) (2.25)(32)= $72

As per the unitary method, Mrs. Smith's current weight is 121 pounds and 3 ounces.

To find Mrs. Smith's current weight, we need to add the weight she gained over the last two months to her initial weight. First, we will convert the mixed fractions to improper fractions for easier calculations.

1½ pounds can be written as (2 * 1) + 1/2 = 3/2 pounds.

1/4 pound remains as it is.

Now, let's add the weight gained in the last two months:

3/2 pounds + 1/4 pound = (3/2) + (1/4) = (6/4) + (1/4) = 7/4 pounds.

Next, we add the total weight gained to Mrs. Smith's initial weight:

120 pounds + 7/4 pounds = (120 * 4/4) + (7/4) = (480/4) + (7/4) = 487/4 pounds.

To express the answer in pounds, we convert the improper fraction back to a mixed fraction:

487/4 pounds can be written as (4 * 121) + 3 pounds.

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The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.

Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;

D = 6371 + (343)×2

Hence, we have; diameter, D = 7057 km.

Hence, the distance travelled after 8 revolutions is;

C = 8 × πd

C = 8 × 3.14 × 7057

C = 177,271.8 km.

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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 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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Answer:

80 cups

Step-by-step explanation:

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°))

The value of surface integral using the Divergence Theorem is [tex]729\pi[/tex] .

Divergence Theorem states that the surface integral of a vector field over a closed surface, is equal to the volume integral of the divergence over the region inside the surface. Mathematically the it can be calculated using the formula:[tex]\int\int\int\limit{ }_V(\delta \cdot F)=\int\int(F \cdot n)dS[/tex]

The divergence of F is

[tex]div F=\frac{d}{dx}(2x^{3}+y^{3})+\frac{d}{dy}( y^{3} +z^{3})+\frac{d}{dz}3y^{3} z[/tex]

[tex]div F=6x^{2}+3y^{2}+3y^{2}[/tex]

Let E be the region [tex]{(x,y,z):0\leq z\leq 9-x^{2} -y^{2}[/tex] then by divergence theorem we have [tex]\int \int\limits^{}_s {F\cdot n\times dS} =\int\int\int\limits^{}_E divFdV=\int\int\int\limits^{}_E(6x^2+6y^2)dV[/tex]

Now we find the value of the integral:

[tex]=\int\limits^{2\pi}_0\int\limits^3_0\int\limits^{9-r^2}_0(6r^2)rdzdrd{\theta}\\=\int\limits^{2\pi}_0 \int\limits^3_0(9-r^2)6r^3drd{\theta}\\=2\pi\int\limits^3_0 {(54r^3-6r^5)} dr\\[/tex]

[tex]=2\pi\times \frac{729}{2}\\=729\pi[/tex]

Thus we can say that the value of the integral for the surface around the paraboloid is given by [tex]729\pi[/tex].

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Answer:

9 Sahil has a fish tank in the shape of a cuboid, as shown in the diagram-- Diagram is NOT accurately drawn The tank is

55 cm long

28cm wide

cm 33 high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the tank. What is the greatest number of neon tetra fish Sahil can put in his tank?

Step-by-step explanation:

When a set of given numbers or items is to be arranged in a definite way or pattern, permutation can be used to determine the number of ways in which this can be done. Thus the required answer to the question is 990.

When a set of given numbers or items is to be arranged in a definite way or pattern, permutation can be used to determine the number of ways in which this can be done. The applicable formula is:

[tex]_{n} P_{r}[/tex] = [tex]\frac{n!}{(n - r)!}[/tex]

where: n is the total number of items given, and r is the number of items selected.

Thus the given question can be solved as :

[tex]_{11} P_{3}[/tex] = [tex]\frac{11!}{(11-3)!}[/tex]

       = [tex]\frac{11!}{8!}[/tex]

       = [tex]\frac{11 * 10 * 9 * 8!}{8!}[/tex]

       = 11 x 10 x 9

       = 990

[tex]_{11} P_{3}[/tex] = 990

Therefore, the required answer is 990.

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Answer: 1308m

Step-by-step explanation:

Top and Bottom: 19 x 16 x 2 = 608

Sides: 16 x 10 x 2 = 320

Front and Back: 19 x 10 x 2 = 380

608 + 320 + 380 = 1308

Answer:  10

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

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:

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

Answer: 1:52 PM

Step-by-step explanation:

PAULA: 2:14PM FINISHED THE RACE

BEATRICE: FINISHED 22 MINUTES EARLIER THEN PAULA

YOU TAKE 2:14PM AND SUBTRACT THE 22 MINS BEATRICE RAN TO GET YOU ANSWER.

SO 2:14 -14 MINS=2:00PM 14+8=22 (THE MINS BETRICE FINISHED)

2:00-8 MINS ( REMAINING FROM THE 22 ) THEN 2:00-8 MINS =1:52

ANSWER:1:52PM

Answer:

[tex]x=2^{\frac{2}{3}}[/tex]

Step-by-step explanation:

1) Add 8 to both sides.

[tex]2x^3=8[/tex]

2) Divide both sides by 2.

[tex]x^3=\frac{8}{2}[/tex]

3) Simplify [tex]\frac{8}{2}[/tex] to 4.

[tex]x^3=4[/tex]

4) Take the cube root of both sides.

[tex]x=\sqrt[3]{4}[/tex]

5) Rewrite 4 as 2².

[tex]x=\sqrt[3]{2^2}[/tex]

6) Use this rule: [tex]{({x}^{a})}^{b}={x}^{ab}[/tex].

[tex]x=2^{\frac{2}{3}}[/tex]

Decimal Form: 1.587401

__________________________________________

Check the answer:

[tex]2x^3-8=0[/tex]

1) Let [tex]x=2^\frac{2}{3}[/tex].

[tex]2(2^{\frac{2}{3} })-8=0[/tex]

2) Use this rule: [tex](x^a)^b=x^{ab}[/tex].

[tex]2\times2^{\frac{2\times3}{3} } -8=0[/tex]

3) Simplify 2 * 3 to 6.

[tex]2\times2^{\frac{6}{3} } - 8 =0[/tex]

4) Simplify 6/3 to 2.

[tex]2\times2^2-8=0[/tex]

5) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]2^3-8=0[/tex]

6) Simplify 2^3 to 8.

8 - 8 = 0

7) Simplify 8 - 8 to 0.

0 = 0

Thank you,

Eddie

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

The inference is that the sum of the PPV and the false discovery rate for any test is always 100% because they complement each other.

When we add together the PPV and the false discovery rate for any test, the sum is always 100%.

It should be noted that the false discovery rate is the complement of the positive predicate value. The addition of their probability gives 100%.

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Answer:

6 * (5 + n)

Explanation:

Sum = addition

Difference = subtraction

Product = multiplication

Quotient = division

Answer:

center:

(-0.25, 5)

foci :

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

vertices :

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

wolframramalpha

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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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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Answer:

-13

Step-by-step explanation:

-2x6 = -12

-9+8= -1

-1+-12=-13

Hope this helps