Please solve the following polynomial functions for the variable as defined.

[tex]1. \ \ x^2 - 5x + 6[/tex]

[tex]2. \ \ 4x^3 - 3x^2 + 2[/tex]

Answer:

See answers below

Step-by-step explanation:

Given the following functions:

r(x) = x - 6

s(x) = 2x²

r(s(x)) = r(2x²)

Replacing x with 2x² in r(x) will give;

r(2x²) = 2x² - 6

r(s(x)) = 2x² - 6

(r-s)(x) = r(x) - s(x)

(r-s)(x) = x - 6 - 2x²

Rearrange

(r-s)(x) = - 2x²+x-6

(r+s)(x) = r(x) + s(x)

(r-s)(x) = x - 6 + 2x²

Rearrange

(r-s)(x) = 2x²+x-6

The question is incomplete. The complete question is :

In a​ poll, 1100 adults in a region were asked about their online vs.​ in-store clothes shopping. One finding was that 43​% of respondents never​ clothes-shop online. Find and interpret a ​95% confidence interval for the proportion of all adults in the region who never​ clothes-shop online.

Solution :

95% confidence interval for p is :

[tex]$\hat p - Z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}} < p < \hat p + Z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}$[/tex]

[tex]$0.43 - 1.96\times \sqrt{\frac{0.43(1-0.43)}{1100}} < p < 0.43 + 1.96\times \sqrt{\frac{0.43(1-0.43)}{1100}}$[/tex]

0.401 < p < 0.459

Therefore, 95% confidence interval is from 0.401 to 0.459

Answer:

See explanation.

General Formulas and Concepts:

Algebra I

Algebra II

Pre-Calculus

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Parametric Differentiation:                                                                                     [tex]\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle x = 2t - \frac{1}{t}[/tex]

[tex]\displaystyle y = t + \frac{4}{t}[/tex]

Step 2: Find Derivative

Here we see that if we increase our values for t, our derivative would get closer and closer to 0.5 but never actually reaching it. Another way to approach it is to take the limit of the derivative as t approaches to infinity. Hence  [tex]\displaystyle \frac{dy}{dx} < \frac{1}{2}[/tex].

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametrics

Book: College Calculus 10e

9514 1404 393

Answer:

Step-by-step explanation:

To find the initial amount, put 0 where t is in the formula and do the arithmetic.

  A(0) = 523(1/2)^0 = 523(1) = 523

The initial amount is 523 grams.

__

To find the amount remaining after 100 years, put 100 where t is in the formula and do the arithmetic.

  A(100) = 523(1/2)^(100/30) ≈ 523(0.0992123) ≈ 52

About 52 grams will remain after 100 years.

Answer:

0.000000073

Step-by-step explanation:

Given number is,

7.3E - 8

In scientific notation number will be,

7.3 × 10⁻⁸

In standard form the number will be,

0.000000073

Let f(x) = ax³ + 9x² + 4x – 10

g(x) = 0⇒x - 3 = 0

⇒ x = 0 + 3

⇒ x = 3

On dividing f(x) by x - 3, it leaves a remainder 5.

Now keeping, f(3) = 5

⇒a(3)³ + 9(3)² + 4(3) - 10 = 5

⇒ a × 27 + 9 × 9 + 4 × 3 - 10 = 5

⇒ 27a + 81 + 12 - 10 = 5

⇒ 81 + 12 - 10 - 5 = 27a

⇒ 81 + 12 - 15 = 27a

⇒ 93 - 15 = 27a

⇒ 78 = 27a

⇒ a = 27/78

⇒ a = 0.3461

Answer:

I think the answer is 5/6

Step-by-step explanation:

There are three even numbers and two uneven numbers less than four. Therefore, on a standard die, the.probability of Rollin a number that is even or less than for is 5/6.

Answer:

0.9113

Step-by-step explanation:

Given :

Sample standard deviation of Stock X = 4.665

Sample standard deviation of Stock Y = 8.427

Sample Covariance = 35.826

The Correlation Coefficient, R is related to sample covariance and standard deviation using the formular :

R = Covariance(X, Y) / (SD(X) * (SD(Y))

R = 35.826 / (4.665 * 8.427)

R = 35.826 / 39.311955

R = 0.9113

Hence, correlation Coefficient, R = 0.9113 which depicts a strong positive relationship.

Answer:

u = 2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj side / hypotenuse

cos 45 = sqrt(2) / u

u cos 45 = sqrt(2)

u = sqrt(2) / cos 45

u = sqrt(2) / 1/ sqrt(2)

u = sqrt(2) * sqrt(2)

u =2

u=2

Answer:

Solution given:

Cos 45°=base/hypotenuse

[tex]\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{u}[/tex]

doing crisscrossed multiplication

[tex]\sqrt{2}*\sqrt{2}=1*u[/tex]

u=2

Answer:

(3x+2) by (2x+1)

Step-by-step explanation:

A cardboard is a rectangle, and has two dimensions. Given a quadratic equation, you should find a way to split it in two.

The easiest way to do so is through factoring. (There are many ways to do this, take a look at the plethora of sources offered on the internet.)

When the expression 6x^2 + 7x + 2 is factored, it is (3x+2)(2x+1). Hence, these are your dimensions.

Answer:

Step-by-step explanation :

Let % increase in administrative secretary be = x

Let % increase in new faculty receive be = y

Administrative secretary salary = 28,000

New faculty receive Salary = 40,000

(8)*(x/100)* (28000) + (7)*(y/100)*(40000) = 5,000

2240x +2800 y = 5,000

224x +280 y = 500

56x +70y = 125

Therefore, x and y should be chosen such that it satisfy the above equation.

Answer:

[tex]7x {}^{2} + 5x[/tex]

Step-by-step explanation:

[tex]9x {}^{2} + 8x - (2x {}^{2} + 3x) \\ \\ = 9x {}^{2} + 8x - 2x {}^{2} - 3x (remove \: brackets) \\\ \\ = 7x {}^{2} - 5x [/tex]

Answer:

X = 101.48

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Average of 62 seconds with a standard deviation of 24.5 seconds.

This means that [tex]\mu = 62, \sigma = 24.5[/tex]

If the manager wants to advertize that 95% of the time, they serve customers within X seconds, what is the value of X?

This is the 95th percentile of times, which is X when Z has a p-value of 0.95, so X when Z = 1.645.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 62}{24.5}[/tex]

[tex]X - 62 = 1.645*24[/tex]

[tex]X = 101.48[/tex]

9514 1404 393

Answer:

  B. a = plus-or-minus 4

Step-by-step explanation:

  3a² -21 = 27 . . . . . . . given

  3a² = 48 . . . . . . . . . . add 21 to both sides (desired form)

  a² = 16 . . . . . . . . . . .  divide both sides by 3

  a = ±4 . . . . . . . take the square root

There are several ways to solve a quadratic equation. I'll complete the square:

z ² - (3 - 2i ) z + 5 - 5i = 0

(z - (3 - 2i )/2)² - ((3 - 2i )/2)² + 5 - 5i = 0

(z - (3 - 2i )/2)² - (3 - 2i )²/4 + 5 - 5i = 0

(z - (3 - 2i )/2)² = (3 - 2i )²/4 - 5 + 5i

(z - (3 - 2i )/2)² = (3² - 2×3×(-2i ) + (-2i )²)/4 - 5 + 5i

(z - (3 - 2i )/2)² = (5 - 12i )/4 - 5 + 5i

(z - (3 - 2i )/2)² = (5 - 12i - 20 + 20i )/4

(z - (3 - 2i )/2)² = (-15 + 8i )/4

Let w = (-15 + 8i )/4. Then write w = |w| exp(i arg(w)), where

|w| = √((-15/4)² + 2²) = 17/4

arg(w) = π - arctan(8/15)

The square roots of w are then

√w = √(|w|) exp(i (arg(w) + 2nπ)/2)

where n in the set {0, 1}.

Taking the square root of both sides gives

z - (3 - 2i )/2 = √w

z = (3 - 2i )/2 + √w

and the two solutions can be simplified to

z = √17/4 + √17 i

z = -√17/4 - √17 i

Answer:

The total number of ways is 252.

Step-by-step explanation:

Number of girls = 18

number of boys = 14

Commitee of one girl and a boy

(18 C 1)(14 C 1)

= 252

Answer:

Step-by-step explanation:

This is nice and simple. I'm going to walk through it like I do when teaching this concept to my class for the first time. This is a good problem for that.

We are given a square and we are looking for the rate at which the area is increasing when a certain set of specifics are given. That means that the main equation for this problem is the area of a square, which is:

[tex]A=s^2[/tex] where s is a side.

Since we are looking for the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], we need to take the derivative of area formula implicitly:

[tex]\frac{dA}{dt}=2s\frac{ds}{dt}[/tex] that means that if [tex]\frac{dA}{dt}[/tex] is our unknown, we need values for everything else. We are given that the initial area for the square is 49. That will help us determine what the "s" in our derivative is. We plug in 49 for A and solve:

[tex]49=s^2[/tex] so

s = 7

We are also given at the start that the sides of this square are increasing at a rate of 8cm/s. That is [tex]\frac{ds}{dt}[/tex]. Filling it all in:

[tex]\frac{dA}{dt}=2(7)(8)[/tex] and

[tex]\frac{dA}{dt}=112\frac{cm^2}{s}[/tex]

The surface area of a square of side L is given by

[tex]A = L^2[/tex]

The rate of change of the area per unit time is

[tex]\dfrac{dA}{dt} = 2L\dfrac{dL}{dt}[/tex]

We can express the length L on the right hand side in terms of the area A [tex](L = \sqrt{A})[/tex]:

[tex]\dfrac{dA}{dt} = 2\sqrt{A}\dfrac{dL}{dt}[/tex]

[tex]\:\:\:\:\:\:\:=2(\sqrt{49\:\text{cm}^2})(8\:\text{cm/s})[/tex]

[tex]\:\:\:\:\:\:\:=112\:\text{cm}^2\text{/s}[/tex]

Answer:

didn't get the question did u forget to put the sequence ???????

pls write the question fully so that I can help you

9514 1404 393

Explanation:

There are several ways you can go at this. Here are a couple. All proofs will start with the given relations being repeated as part of the proof. Here are the next steps.

∠AED ≅ ∠BAE . . . . alternate interior angles are congruent

∠AED +∠AEB = 90° . . . . angle sum theorem

∠BAE +∠AEB = 90° . . . . substitution property of equality

∠CEF ≅ ∠BCE . . . . alternate interior angles are congruent

∠CEF +∠CEB = 90° . . . . angle sum theorem

∠BCE +∠CEB = 90° . . . . substitution property of equality

∠BAE +∠AEB = ∠BCE +∠CEB . . . . substitution property of equality

∠BAE +∠AEB = ∠BCE +∠AEB . . . . substitution property of equality

∠BAE = ∠BCE . . . . addition property of equality

∠ABE = ∠CBE = 90° . . . . BE ⊥ AC

BE ≅ BE . . . . reflexive property of congruence

ΔBEA ≅ ΔBEC . . . . ASA congruence theorem

∠BAE ≅ ∠BCE . . . . CPCTC

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

Technician __Shutdown

Taylor, T___4

Rousche, R _ 3

Hurley, H__ 3

Huang, Hu___2

Gupta, ___ 5

The Numbe of samples of 2 possible from the 5 technicians :

We use combination :

nCr = n! ÷ (n-r)!r!

5C2 = 5!(3!)2!

5C2 = (5*4)/2 = 10

POSSIBLE COMBINATIONS :

TR, TH, THu, TG, RH, RHu, RG , HHu, HG, HuG

Sample means :

TR = (4+3)/2 = 3.5

TH = (4+3)/2 = 3.5

THu = (4+2) = 6/2 = 3

TG = (4 + 5) = 9/2 = 4.5

RH = (3+3) = 6/2 = 3

RHu = (3+2) /2 = 2.5

RG = (3 + 5) = 8/2 = 4

HHu = (3+2) = 2.5

HG = (3+5) = 8/2 = 4

HuG = (2+5) / 2 = 3.5

Mean of sample mean (3.5+3.5+3+4.5+3+2.5+4+2.5+4+3.5) / 10 = 3.4

Population mean :

(4 + 3 + 3 + 2 + 5) / 5 = 17 /5 = 3.4

Population Mean and mean of sample means are the same.

This distribution should be approximately normal.

9514 1404 393

Answer:

  30°

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°.

  230° +C +50° +50° = 360°

  C = 360° -330° = 30°

  m∠C = 30 degrees

Answer:

21

Step-by-step explanation:

5/3=35/x

3 x 35=105

5 x x= 5x

105=5x

105/5=5x/5

21=x

The number of people who bought the more expensive ticket is 21.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

Let the number of people be X so we can form the following expression given below:-

5/3=35/x

3 x 35=105

5 x x= 5x

105=5x

105/5=5x/5

21=x

Therefore the number of people who bought the more expensive ticket is 21.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ2

Answer:

False

Step-by-step explanation:

The absolute value shows the distance a value is from 0, which is always positive.

Answer:

0.6

Step-by-step explanation:

In this question, the | symbol means "given", so we can phrase the question as "Find the probability that a student watches more than one hour of TV given that they are in the 6th period class"

Next, because there is a 100% chance that the student is in the 6th period class, we can disregard the results of the 3rd period class.

Given that the student is in the 6th period class, there are 15 total students (as 9+6=15 = the sum of the yes and no answers for 6th period) and 9 students that said yes. Therefore, there is a 9/15 = 3/5 = 0.6 probability that a student watches more than 1 hour of TV given that they are in the 6th period class