What are the zeros of the polynomial function f(x)=x3-7x2+8x+16

Answer:

(0.2, -1.2)

Step-by-step explanation:

When solving a system of equations by graphing, we first plot the two equations on a graph, then the point of intersection of the two graphs is the solution to the system of equations.

Therefore giving the equations y = - x - 1; and y = 14x - 4, we have to first plot the both linear equations using online geogebra graphing tool. The intersection of both linear graphs is the solution to the problem.

We can see that the point of intersection is A(0.2, -1.2)

Step-by-step explanation:

2 x y + x + 2 y is equal to 3 x y + 2 y final answer is 5xy

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

Website 1 : 10357, 10537, 10767, 10561, 10544, 10581, 10602, 10665, 10335, 10419, 10737, 10410, 10485, 10601, 10458, 10472, 10435, 10375, 10436, 10510, 10345, 10559, 10520, 10425, 10351, 10465, 10491, 10671, 10366, 10440, 10618, 10606, 10406, 10538, 10449, 10462

Mean, xbar = ΣX/ n ; n = sample size = 36

Xbar = 377999 / 36 = 10499.9722

Standard deviation, s = √[(x - xbar)² / (n-1]

Using calculator :

Standard deviation (Website 1 :), s = 110.239865

Website 2 : 11067, 11029, 10888, 10789, 10914, 10663, 10787, 11140, 11042, 11074, 10868, 10853, 10900, 11088, 10991, 10928, 10959, 11126, 11033, 11114, 11150, 11155, 11027, 10900, 11015, 11123, 10953, 11181, 10855, 10731, 10971, 10770, 11070, 11122, 11018, 10903

Mean, xbar = ΣX/ n ; n = sample size = 36

Xbar = 395197 / 36 = 10977.6944

Standard deviation, s = √[(x - xbar)² / (n-1]

Using calculator :

Standard deviation (Website 2), s = 132.617995

2.)

Yes, the viewership between the two websites are different with the second website has a higher mean viewership with a mean of 10977.6944.

3.)

The probability of 12000 views per month on each website :

Probability = Mean viewership per month / required viewership

Website 1 :

P(12000) = 10499.9722 / 12000 = 0.8749

Website 2 :

P(12000) = 10977.6944 / 12000 = 0.9148

4.)

More consistent website :

We use the standard deviation value, the higher the standard deviation, the higher the variability :

Website 1 should be more consistent has it has a Lower standard deviation score, hence, should show lower variability than website 2.

5.)

Website suitable for advertisement should be one with higher viewership per month in other to reach a larger audience. Hence, website 2 should be recommended for advertisement.

Complete Question

Four spinners are spun. Spinner 1 has outcomes {1,2,3,4,5,6,7,8} Spinner 2 has outcomes {1,2,3,4,5,6} Spinner 3 has outcomes {1,2,3,4,5,6} Spinner 4 has outcomes {1,2,3,4,5} The outcomes for each spinner are equally likely. S is the sum of the numbers that come up on the spinners. What is the expected value of S?

Answer:

[tex]E(s)=14.5[/tex]

Step-by-step explanation:

From the question we are told that:

Spinner 1 ={1,2,3,4,5,6,7,8}

Spinner 2=  {1,2,3,4,5,6}

Spinner 3 = {1,2,3,4,5,6}

Spinner 4  {1,2,3,4,5}

Generally the equation for expected outcome is mathematically given by

[tex]E(s)=\sum P(x).x[/tex]

Where

[tex]x=\frac{n(n+1)}{2}[/tex]

For Spinner 1

[tex]E(s_1)=\sum \frac{1}{8}*\frac{8(8+1)}{2}[/tex]

[tex]E(s_1)=4.5[/tex]

For Spinner 2

[tex]E(s_2)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]

[tex]E(s_2)=3.5[/tex]

For Spinner 3

[tex]E(s_2)=E(s_3)[/tex]

For Spinner 3

[tex]E(s_4)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]

[tex]E(s_4)=3[/tex]

Therefore The Expected Value

[tex]E(s)=\sum E(s 1..4)[/tex]

[tex]E(s)=4.5+2(3.5)+3[/tex]

[tex]E(s)=14.5[/tex]

Answer:

y=x216–6x16+4116

Step-by-step explanation:

plato :)

The equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

The equation of a parabola that has a vertical axis, passes through the point (–1, 3)

The vertex of the parabola is at (3, 2)

As we know, in the standard form of the parabola (h, k) represents the vertex of the parabola.

h = 3

k = 2

Plug the above point in the equation:

[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]

x = 3

y = 2

[tex]\rm 2\ =\ \dfrac{3^{2}}{16}-\dfrac{6(3)}{16}+\dfrac{41}{16}[/tex]

= 9/16 - 18/16 + 41/16

= (9-18+41)/16

= 32/16

2 = 2 ( true)

The equation of the parabola is:

[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]

Thus, the equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.

Learn more about the parabola here:

brainly.com/question/8708520

#SPJ2

Answer:

Each kids weight in a chart

Step-by-step explanation:

I chose this because its the most organized way of doing that

Answer:

I think you mean this :

[tex] \sqrt{x - 5} = 6 \\ = > {( \sqrt{x - 5} })^{2} = {6}^{2} \\ = > x - 5 = 36 \\ = > x = 36 + 5 \\ = > x = 41[/tex]

Or,

Square root of x-5=6 is :

[tex] \sqrt{x - 5} \:=\:\sqrt{6} [/tex]

Hello there!

Previously, we learnt that to solve the equation, we have to isolate the sin, cos, tan, etc first.

First Question

The first question has sin both sides. Notice that if we move sin(theta) to left. We get:-

[tex] \displaystyle \large{2 {sin}^{2} \theta - sin \theta = 0}[/tex]

We can common factor out the expression.

[tex] \displaystyle \large{sin \theta(2sin \theta - 1) = 0}[/tex]

It is a trigonometric equation in quadraric pattern.

We consider both equations:-

First Equation

[tex] \displaystyle \large{sin \theta = 0}[/tex]

Remind that sin = y. When sin theta = 0. It means that it lies on the positive x-axis.

We know that 0 satisfies the equation, because sin(0) is 0.

Same goes for π as well, but 2π does not count because the interval is from 0 ≤ theta < 2π.

Hence:-

[tex] \displaystyle \large { \theta = 0,\pi}[/tex]

Second Equation

[tex] \displaystyle \large{2sin \theta - 1 = 0}[/tex]

First, as we learnt. We isolate sin.

[tex] \displaystyle \large{sin \theta = \frac{1}{2} }[/tex]

We know that, sin is positive in Quadrant 1 and 2.

As we learnt from previous question, we use π - (ref. angle) to find Q2 angle.

We know that sin(π/6) is 1/2. Hence π/6 is our reference angle. Since π/6 is in Q1, we only have to find Q2.

Find Quadrant 2

[tex] \displaystyle \large{\pi - \frac{\pi}{6} = \frac{6\pi}{6} - \frac{\pi}{6} } \\ \displaystyle \large{ \frac{5\pi}{6} }[/tex]

Hence:-

[tex] \displaystyle \large{ \theta = \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]

Since both first and second equations are apart of same equation. Therefore, mix both theta from first and second.

Therefore, the solutions to the first question:-

[tex] \displaystyle \large \boxed{ \theta = 0,\pi, \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]

Second Question

This one is a reciprocal of tan, also known as cot.

[tex] \displaystyle \large{cot3 \theta = 1}[/tex]

For this, I will turn cot to 1/tan.

[tex] \displaystyle \large{ \frac{1}{tan3 \theta} = 1}[/tex]

Multiply whole equation by tan3 theta, to get rid of the denominator.

[tex] \displaystyle \large{ \frac{1}{tan3 \theta} \times tan3 \theta = 1 \times tan3 \theta } \\ \displaystyle \large{ 1= tan3 \theta }[/tex]

We also learnt about how to deal with number beside theta.

We increase the interval, by multiplying with the number.

Since our interval is:-

[tex] \displaystyle \large{0 \leqslant \theta < 2\pi}[/tex]

Multiply the whole interval by 3.

[tex] \displaystyle \large{0 \times 3 \leqslant \theta \times 3 < 2\pi \times 3} \\ \displaystyle \large{0 \leqslant 3 \theta < 6\pi }[/tex]

We also know that tan is positive in Quadrant 1 and Quadrant 3.

and tan(π/4) is 1. Therefore, π/4 is our reference angle and our first theta value.

When we want to find Quadrant 3, we use π + (ref. angle).

Find Q3

[tex] \displaystyle \large{\pi + \frac{\pi}{4} } = \frac{5\pi}{4} [/tex]

Hence, our theta values are π/4 and 5π/4. But that is for [0,2π) interval. We want to find theta values over [0,6π) interval.

As we learnt previously, that we use theta + 2πk to find values that are in interval greater than 2π.

As for tangent, we use:-

[tex] \displaystyle \large{ \theta + \pi k = \theta}[/tex]

Because tan is basically a slope or line proportional graph. So it gives the same value every π period.

Now imagine a unit circle, and make sure to have some basic geometry knowledge. Know that when values addition by 180° or π would give a straight angle.

We aren't using k = 1 for this because we've already found Q3 angle.

Since we know Q1 and Q3 angle in [0,2π).

We can also use theta + 2πk if you want.

First Value or π/4

[tex] \displaystyle \large{ \frac{\pi}{4} + 2\pi = \frac{9\pi}{4} } \\ \displaystyle \large{ \frac{\pi}{4} + 4\pi = \frac{17\pi}{4} }[/tex]

Second Value or 5π/4

[tex] \displaystyle \large{ \frac{5\pi}{4} + 2\pi = \frac{13\pi}{4} } \\ \displaystyle \large{ \frac{5\pi}{4} + 4\pi = \frac{21\pi}{4} }[/tex]

Yes, I use theta + 2πk for finding other values.

Therefore:-

[tex] \displaystyle \large{3 \theta = \frac{\pi}{4} , \frac{5\pi}{4} , \frac{9\pi}{4}, \frac{17\pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} }[/tex]

Then we divide every values by 3.

[tex] \displaystyle \large \boxed{\theta = \frac{\pi}{12} , \frac{5\pi}{12} , \frac{9\pi}{12}, \frac{17\pi}{12} , \frac{13\pi}{12} , \frac{21\pi}{12} }[/tex]

Let me know if you have any questions!

Answer:

[tex]4x^2+4x+5[/tex]

Step-by-step explanation:

[tex]f(x)=5x^2-3\\g(x)=x^2-4x-8[/tex]

Set up an expression.

[tex]5x^2-3-(x^2-4x-8)[/tex]

Distribute the negative (-1)

[tex]5x^2-3-x^2+4x+8[/tex]

Solve / Simplify

[tex]4x^2+4x+5[/tex]

I'm late, but I hope this helps!

Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

2x^2 - 3x = 12

2x^2 - 3x - 12 = 0

a = 2

b = -3

c = -12

(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)

3 +/- sqrt( 9 + 96 ) / 4

3 +/- sqrt(105) / 4

Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]

Hope this helps!

Answer:

dv = attached below

dr = 0.05 cm

dh = 0.2 cm

Approximate volume of metal = 2.8 * π  cm^3

Step-by-step explanation:

height of can ( h ) = 10 cm

diameter = 4 cm ;  r = 4/2 = 2cm

thickness of metal in top and bottom = 0.1 cm

thickness of metal in sides = 0.05 cm

attached below is the detailed solution

Answer:

There are 666 numbers multiple of 3 in the interval.

Step-by-step explanation:

Multiples of 3:

A number is a multiple of 3 if the sum of it's digits is a multiple of 3.

Range [2,2000]:

First multiple of 3 in the interval: 3

Last: 1998

How many:

[tex]1 + \frac{1998 - 3}{3} = 1 + 665 = 666[/tex]

There are 666 numbers multiple of 3 in the interval.

Answer:

Step-by-step explanation:

Interior angle opposite to each side of the polygon is:

Since the circle is unit circle, its radius is 1 unit.

Let the side is a, then as per definition of sine we have:

The perimeter is:

Answer:

Paul is 2 and Kennedy is 6

Step-by-step explanation:

6 × 1/3 = 2

2 + 4 =6

Answer:

0.127

Step-by-step explanation:

Answer:

BD = 4.1

Step-by-step explanation:

DA is an angle bisector which also divides the opposite side of the angle it bisects in a way that it is proportional to tye other two sides.

By implication, we would have the following:

AB/BD = AC/DC

AB = 5.3

AC = 5.5

DC = 4.3

BD = ?

Plug in the values

5.3/BD = 5.5/4.3

Cross multiply

BD*5.5 = 4.3*5.3

BD*5.5 = 22.79

Divide both sides by 5.5

BD = 22.79/5.5

BD = 4.1 (to 1 decimal place)

9514 1404 393

Answer:

  (2x -11)(x -1)

Step-by-step explanation:

The middle term can be rewritten as a sum using the coefficients of the first and last terms. Then the expression can be factored by pairs of terms.

  2x^2 -13x +11 = 2x^2 -2x -11x +11 = 2x(x -1) -11(x -1)

  = (2x -11)(x -1)

Answer:

d

Step-by-step explanation:

h

Answer:

The answer is "28"

Step-by-step explanation:

[tex](LTPD) = 52\%\\\\(AQL) = 20\%\\\\\to \frac{LTPD}{AQL} = \frac{52\%}{20\%}= 2.6\\\\[/tex]

The value of [tex]\frac{LTPD}{AQL} = 2.6[/tex] that value of [tex]\frac{LTPD}{AQL} = 2.618[/tex]

Acceptance number, [tex]c = 9[/tex]

Value of [tex]n\times AQL = 5.426[/tex]

Sample size [tex]n = n\times \frac{AQL}{AQL} =\frac{5.426}{20\%} = 27.13=28[/tex]  

9514 1404 393

Answer:

  Tn = -4n² +40n +36

Step-by-step explanation:

A graphing calculator readily performs the quadratic regression, yielding the formula ...

  Tn = -4n² +40n +36

__

The first and second differences of the given sequence terms are ...

  28, 20, 12 and -8, -8

The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:

  -4, -16, -36, -64

Subtracting these values from the original sequence gives the linear sequence ...

  76, 116, 156, 196

which has first term 76 and common difference 40. The equation for the n-th term of this is ...

  an = 76 +40(n -1) = 36 +40n

Adding this linear sequence to the sequence of squared terms, we get ...

  Tn = -4n² +40n +36

Using the hypergeometric distribution, it is found that there is a 0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.

The containers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that exactly one of the containers is from the Florida supplier is P(X = 1), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,18,3,11) = \frac{C_{11,1}C_{7,2}}{C_{18,3}} = 0.2831[/tex]

0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.

A similar problem is given at https://brainly.com/question/24826394

Answer:

$28000

Step-by-step explanation:

12×1000 + 12×1500 = 12000 + 18000 = $30000

the shortfall is the difference between $58000 and $30000

58000 - 30000 = $28000

Answer:

The point slope form of the equation is,

[tex]y + 10 = - \frac{19(x + 6)}{5} [/tex]

m = (y2-y1)/(x2-x1) = (9-(-10))/((-6)-(-1)) = -19/5

b = y1-mx1 = -69/5

Answered by GAUTHMATH

Answer:

No.

Step-by-step explanation:

3x+2y<11 doesn't have a y-intercept of 6 and doesn't have a x-intercept of 4.

2x-y<9 is not the same direction as 3x+2y<11.

Answer:

9 is. ................m.m..mk

A sample of size n taken from a normally distributed population with mean µ and standard deviation σ has a sample mean of µ and standard deviation of σ/√n.

So the sample mean would still be 180.1, while the sample standard deviation would be 100/√94 ≈ 10.31.

Answer:

(483.981 ; 504.019)

Step-by-step explanation:

Given :

σ = 100

Sample size, n = 661

xbar = 494

We use the Z distribution since we are working with the population standard deviation ;

C.I = xbar ± (Zcritical * σ/√n)

Zcritical at 99% = 2.576

C.I = 494 ± (2.576 * 100/√661)

C.I = 494 ± 10.019

Lower boundary = (494−10.019) = 483.981

Upper boundary = (494+10.019) = 504.019

C.I = (483.981 ; 504.019)