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3 years ago

Use synthetic division and the Remainder Theorem to find f(4) if f(x) = – 2x3 + 9x2

Mathematics

1 answer:

Elis [28]3 years ago

6 0

Step-by-step explanation:

Let's see. f(4) makes the divisor x-4

4|-2 9 -6 7

| 8 -68 296

-2 17 -74 2072

The quotient is -2x²+17x-74 with a remainder of 2072

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BRAINLEIST ANSWER TO WHOEVER GIVES ME CORRECT ANSWER FIRST

vova2212 [387]

The second answer is correct

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3 years ago

Keisha, Scott, and Ryan have a total of $101 in their wallets. Keisha has $6 more than Scott. Ryan has 3 times what Scott has. H

Yuri [45]

Answer:

Keisha =$25

Scott =$19

Ryan = $57

Step-by-step explanation:

Let the amount each have be represented by A, B and C

Keisha = A

Scott = B

Ryan = C

Keisha , Scott and Ryan have a total of $101.

That’s

A + B + C = $101

Keisha has $6 more than Scott

A = 6 + B

Ryan has 3 times Scott

C = 3B

Substitute 6+B for A and 3B for C in the first equation.

That’s

A + B + C = 101

6 + B + B + 3B = 101

6 + 5B = 101

Subtract 6 from both sides

6 - 6 + 5B = 101 - 6

5B = 95

Divide both sides by 5

B = 95/5

B = 19

Scott has $19

Recall Keisha has $6 more than Scott B.

That’s A = 6 + B

A = $6 + $19

A = $25

Keisha has $25

Also, Ryan C has 3 times what Scott B has .

That’s

C = 3 x B

C = 3 x 19

C = $57

Therefore, Keisha has $25, Scott has $19 and Ryan has $57

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3 years ago

What is the measure of 0 in radians?

Allushta [10]

Answer:

Thus, the expression to find the measure of θ in radians is θ = π÷3

Step-by-step explanation:

Given that the radius of the circle is 3 units.

The arc length is π.

The central angle is θ.

We need to determine the expression to find the measure of θ in radians.

Expression to find the measure of θ in radians:

The expression can be determined using the formula,

where S is the arc length, r is the radius and θ is the central angle in radians.

Substituting S = π and r = 3, we get;

Dividing both sides of the equation by 3, we get;

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3 years ago

7.2 Given a test that is normally distributed with a mean of 100 and a standard deviation of 10, find: (a) the probability that

kompoz [17]

Answer:

The probability that a single score drawn at random will be greater than 110

P( X > 110) = 0.1587

b)

The probability that a sample of 25 scores will have a mean greater than 105

P( x> 105) = 0.0062

c)

The probability that a sample of 64 scores will have a mean greater than 105

P( x⁻> 105) = 0.002

d)

The probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105

P( 95 ≤ X≤ 105) = 0.9544

Step-by-step explanation:

a)

Given mean of the Normal distribution 'μ' = 100

Given standard deviation of the Normal distribution 'σ' = 10

Let 'X' be the random variable of the Normal distribution

let 'X' = 110

$Z = \frac{x-mean}{S.D} = \frac{110-100}{10} =1$

The probability that a single score drawn at random will be greater than 110

P( X > 110) = P( Z >1)

= 1 - P( Z < 1)

= 1 - ( 0.5 +A(1))

= 0.5 - A(1)

= 0.5 -0.3413

= 0.1587

let 'X' = 105

$Z = \frac{x-mean}{\frac{S.D}{\sqrt{n} } } = \frac{105-100}{\frac{10}{\sqrt{25} } } = 2.5$

The probability that a single score drawn at random will be greater than 110

P( x> 105) = P( z > 2.5)

= 1 - P( Z< 2.5)

= 1 - ( 0.5 + A( 2.5))

= 0.5 - A ( 2.5)

= 0.5 - 0.4938

= 0.0062

The probability that a single score drawn at random will be greater than 105

P( x> 105) = 0.0062

c)

let 'X' = 105

$Z = \frac{x-mean}{\frac{S.D}{\sqrt{n} } } = \frac{105-100}{\frac{10}{\sqrt{64} } } = 4$

The probability that a single score drawn at random will have a mean greater than 105

P( x> 105) = P( z > 4)

= 1 - P( Z< 4)

= 1 - ( 0.5 + A( 4))

= 0.5 - A ( 4)

= 0.5 - 0.498

= 0.002

The probability that a sample of 64 scores will have a mean greater than 105

P( x⁻> 105) = 0.002

d)

Let x₁ = 95

$Z = \frac{x_{1} -mean}{\frac{S.D}{\sqrt{n} } } = \frac{95-100}{\frac{10}{\sqrt{16} } } = -2$

Let x₂ = 105

$Z = \frac{x_{1} -mean}{\frac{S.D}{\sqrt{n} } } = \frac{105-100}{\frac{10}{\sqrt{16} } } = 2$

The probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105

P( 95 ≤ X≤ 105) = P( -2≤z≤2)

= P(z≤2) - P(z≤-2)

= 0.5 + A( 2) - ( 0.5 - A( -2))

= A( 2) + A(-2) (∵A(-2) =A(2)

= A( 2) + A(2)

= 2 × A(2)

= 2×0.4772

= 0.9544

The probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105

P( 95 ≤ X≤ 105) = 0.9544

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3 years ago

Adam has created a triangular table, as shown. Because his table will have only one pedestal leg, he needs to find the balance p

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