450 x 670 - 80 x 500 = ?

Answer

The polynomial is

P(x) = 2x⁴ - 5x³ + 3x²

Explanation

We are told to write a polynomial of degree 4 with zeros (roots)

x = 1

x = (3/2) = 1.5

x = 0

x = 0 (multiplicity of 2 means it appears twice)

So, we can piece together the polynomial

P(x) = (x - 1) (x - 1.5) (x) (x)

We can write this as

P(x) = x² (x - 1) (x - 1.5)

= (x³ - x²) (x - 1.5)

We can multiply through by 2 to turn the 1.5 into a whole number

P(x) = (x³ - x²) (2x - 3)

= x³ (2x - 3) - x² (2x - 3)

= 2x⁴ - 3³ - 2³ + 3x²

= 2x⁴ - 5x³ + 3x²

Hope this Helps!!!

Filling in the blanks, I assume you're talking about a random variable [tex]X[/tex] distributed uniformly over the integers [tex]a\le x\le b[/tex]. Let both [tex]a,b>0[/tex] so we can write the support of [tex]X[/tex] as the set

[tex]S = \{-a, -a+1, -a+2, \ldots, -1, 0, 1, \ldots, b-2, b-1, b\}[/tex]

Note that [tex]|S| = a+b+1[/tex], so the PMF of [tex]X[/tex] is

[tex]\mathrm{Pr}(X=x) = \begin{cases}\frac1{a+b+1} & \text{if } x\in S \\ 0 & \text{otherwise}\end{cases}[/tex]

Let [tex]Y=\max\{0,X\}[/tex]. Then

[tex]Y = \max\{0,X\} = \begin{cases}0 & \text{if } X\le0 \\ X & \text{if } X>0 \end{cases}[/tex]

which tells us

[tex]\displaystyle \mathrm{Pr}(Y=0) = \mathrm{Pr}(X\le0) = \sum_{x=-a}^0 \mathrm{Pr}(X=x) = \frac{a+1}{a+b+1}[/tex]

and

[tex]\displaystyle \mathrm{Pr}(Y\neq0) = \mathrm{Pr}(X>0) = \sum_{x=1}^b \mathrm{Pr}(X=x) = \frac b{a+b+1}[/tex]

Hence the PMF of [tex]Y[/tex] is

[tex]\mathrm{Pr}(Y=y) = \begin{cases}\frac{a+1}{a+b+1} & \text{if } y=0 \\\\ \frac b{a+b+1} & \text{otherwise}\end{cases}[/tex]

Let [tex]Z=\min\{0,X\}[/tex]. The same reasoning applies, but this time

[tex]Z = \min\{0,X\} = \begin{cases} 0 & \text{if } X \ge 0 \\ X & \text{if } X < 0 \end{cases}[/tex]

Now

[tex]\displaystyle \mathrm{Pr}(Z=0) = \mathrm{Pr}(X\ge0) = \sum_{x=0}^b \mathrm{Pr}(X=x) = \frac{b+1}{a+b+1}[/tex]

and

[tex]\displaystyle \mathrm{Pr}(Z\neq0) = \mathrm{Pr}(X<0) = \sum_{x=-a}^{-1} \mathrm{Pr}(X=x) = \frac a{a+b+1}[/tex]

so that

[tex]\mathrm{Pr}(Z=z) = \begin{cases}\frac{b+1}{a+b+1} &\text{if }z=0 \\\\ \frac a{a+b+1} & \text{otherwise}\end{cases}[/tex]

Answer:

x = 8

Step-by-step explanation:

17x-5 = 16x + 3

Step 1: Subtract 16x from both sides.

17x−5−16x=16x+3−16x

x−5=3

Step 2: Add 5 to both sides.

x−5+5=3+5

x=8

The solution to the equation is x = 8.

To solve the equation 17x - 5 = 16x + 3 and find the value of x, we can follow these steps:

Start by simplifying both sides of the equation by combining like terms. Add 5 to both sides to move the constant term to the right side of the equation:

17x - 5 + 5 = 16x + 3 + 5

17x = 16x + 8

Next, we want to isolate the x term on one side of the equation.

Subtract 16x from both sides:

17x - 16x = 16x - 16x + 8

x = 8

Therefore, the solution to the equation is x = 8.

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The equation for Kilberly's running or walking will be R+4w ≤ 6.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that For Kimberly's P.E final she must either walk or run at least 5 miles this week. She knows it would take her 15 minutes to run a mile and 40 minutes to walk a mile, Kimberly only has 6 hours in which she must accomplish this final.

Let the running is represented by 'R' and walking by 'w". The equation will be written as below:-

R + 4W ≤ 6

Put the running and walking times in the equation above.

15 + ( 4 x 40 ) ≤ 6

175 minute ≤ 6 x 60

175 minutes ≤ 360 minutes.

Therefore, Kimberly covers the distance in less than 6 hours.

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The population of rabbits by the year 2023  is 13985.

We have to use the following exponential function. This will be:

y = a b^t

In 2008 means, t=0

So we have 7100 = a b^0

a = 7100

y = 7100b^t

In 2013 means t = 2013-2008 =5

8900 = 7100 b⁵

b⁵ = 89/71

b = 1.046

So the equation will be

y = 7100 (1.046)^t

For 2023, t=2023-2008= 15

y = 7100(1.046)¹⁵

= 13985

The population is 13985.

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Answer:

13/20 is the greatest because it is equal to 65% of 100%.

Step-by-step explanation:

5/8 = to 12.5x5=62.5%. 3/5= 20x3=60%. 3/10 = 10x3=30%. So 13/20 is the greatest.

Answer:

x=10

Step-by-step explanation:

Given: =The exterior angles of an octagon are x°,2x°,3x°,4x°,5x°,6x°,7x°,8x°.

Then, x°+2x°+3x°+4x°+5x°+6x°+7x°+8x° =360°

⇒ 36x = 360

⇒ x= 10

1. The cheapest meat is Ms barker free Ronge whole chicken in $6 per kilo.

2. The cost of 200 grams of honey leg ham is $3.4.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cost of all meat is shown in figure.

Now,

By the figure, we get;

The cheapest meat is Ms barker free Ronge whole chicken which is in

$6 per kilo.

And, The cost of honey leg ham = $17 per kilo

Since, 1 kilograms = 1,000 grams

The cost of 1 gram of honey leg ham = $17/1000

So, The cost of 200 grams of honey leg ham = 200 × 17 / 1000

                                                                      = $3.4

Thus,

1. The cheapest meat is Ms barker free Ronge whole chicken in $6 per kilo.

2. The cost of 200 grams of honey leg ham is $3.4.

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Answer:

divide both sides by the coefficient of v which is 12

-24/-12=-12v/-12

-2=v

Answer:

Find the Inverse f(x)=3x-1/4. f(x)=3x−14 f ( x ) = 3 x - 1 4. Step 1. Write f(x)=3x−14 f ( x ) = 3 x - 1 4 as an equation. y=3x−14 y = 3 x - 1 4.

Step-by-step explanation:

The numerical values of a in the points Q(-1, a) and P(3, -2) with a distance of 4√5 are  6 and -10.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point Q( -1, a )

Point P( 3, -2 )

To find the numerical value of a, plug the given coordinates into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

Square both sides

( 4√5 )² = ( 3 - (-1) )² + ( -2 - a )²

( 4√5 )² = ( 3 + 1 )² + ( -2 - a )²

( 4√5 )² = ( 4 )² + ( -2 - a )²

80 = 16 + ( -2 - a )²

80 - 16 = ( -2 - a )²

64 = ( -2 - a )²

( -2 - a )² = 64

Expand the parenthesis

( -2 - a )( -2 - a ) = 64

a² + 4a + 4 = 64

a² + 4a + 4 - 64 = 0

a² + 4a - 60 = 0

solve for a

( a - 6 )( a + 10 ) = 0

a - 6 = 0, a + 10 = 0

a = 6, a = -10

Therefore, the values of a are 6 and -10.

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After finding the probability we find that 0.04 students are left-handed from the 209 students randomly selected from the campus.

11 % of the population is left-handed so here we have to find the probability of left-handed students if 209 random students are selected from 5225 students on campus here Favorable outcome is 209 and the total outcome is 5225, so the favorable outcome upon the total number of the outcome.

According to the probability formula :

Probability = [tex]\frac{favorable outcome}{Total number of outcome}[/tex]

Probability = 209 / 5225

After diving the above equation we find that 0.04 students are left-handed from the 209 students randomly selected from the campus.

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Step-by-step explanation:

(f○g)(x) means f(g(x))

(g○f)(x) means g(f(x))

f(g(x)) means to use the expression of g(x) as input to f(x). so, we replace all simple x in f(x) by g(x) = x².

f(g(x)) = x²/(x² + 2)

using the same principle we get for

g(f(x)) = (x/(x + 2))² = x²/(x + 2)²

now we need to solve

x²/(x² + 2) = x²/(x + 2)²

let's multiply both sides with both denominators :

x²(x + 2)² = x²(x² + 2)

x²(x² + 4x + 4) = x²(x² + 2)

so, one solution is clear : x = 0.

because then we have 0 = 0.

for x <> 0 we can divide both sides by x² and get

x² + 4x + 4 = x² + 2

4x + 4 = 2

4x = -2

x = -2/4 = -1/2

both expressions are equal for x = 0 and x = -1/2

Answer:

  (a)  y < 3(x +2)² +2

Step-by-step explanation:

You want to know the inequality representing the region less than the quadratic with vertex (-2, 2) and containing the point (-4, 14).

The vertex form equation for a quadratic with vertex (h, k) and some scale factor 'a' is ...

  y = a(x -h)² +k

For the given vertex (-2, 2), the boundary line equation is ...

  y = a(x -(-2))² +2 = a(x +2)² +2

The value of 'a' is positive when the curve opens upward.

Here, the point (-4, 14) has a y-value greater than that of the vertex, so we know the curve opens upward (a > 0).

The only reasonable answer choice is ...

  y < 3(x +2)² +2

Answer:

2000 pounds is 1 ton

6 tons is 12,000

7 tons is 14,000

16,000 pounds is 8 tons

Answer:

y-21 = 4(x+9)

Answer:

See below

Step-by-step explanation:

y-0=2/3(x-6)         (expand L side)

What is the equation in slope-intercept form?

y = 2/3 x - 4

The length of the side is 11.79cm

The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.

On a sheet of paper, draw a square with a pencil.

It is a two-dimensional figure.

The area of a shape on paper is the area it occupies.

Area of a square i= 139cm^2

a^2 = 139

The length of the side (a) = [tex]\sqrt{139}[/tex] = 11.79cm

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Answer:

x=65

Step-by-step explanation:

47+68+x=180

x=65

:]

Answer: 65 = x

Step-by-step explanation:

1) First find the mini triangles, left and right angles

We will be calling the left one A and the right one B.

2) Next use triangle sum to find B.

62 + 50 + b = 180

b=68

3) Use triangle sum again to find A.

53 + 80 + a = 180

a = 47

4) Use triangle sum to find the top mini angle.

47 + 68 + c = 180

c = 65

5) Since x is in the vertical angle of c, they are equal

c = x

65 = x

Answer:

B and c

Step-by-step explanation:

182/7=26

168/6=28

Answer:

I need you to be more specific and answer options. That is the only way anyone can answer this question.

Step-by-step explanation:

among all rectangles that have a perimeter of 48 Then the  dimensions of the one whose area is largest is 12 by 12

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2(L + W)

L is the length of the rectangle

W is the width

Given that the perimeter is 156, hence;

2(L + W) = 48

2L + 2W = 48

L + W = 24

W = 24 - L

The area of the rectangle is expressed as:

A = LW

A = L(24-L)

A = 24L - L^2

To get the dimensions of the one whose area is largest, dA/dL = 0

dA/dL = 24 - 2L

0 = 24 - 2L

2L = 24

L = 24/2

L = 12

Recall that 2(L+W) = 48

2(12 + W) = 48

12 + W = 24

W = 24 - 12

W = 12

Hence the dimensions of the one whose area is largest is 12 by 12

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Answer:

they washed 55 cars

Step-by-step explanation:

I did the math good luck

The percentage increase when the price of an item increased is 30%.

From the information, the price of an item yesterday was $130 and today, the price rose to $169.

The increase in the price will be:

= $169 - $130

= $39

Therefore, the percentage increase will be:

= Increase in price / Original price × 100

= 39 / 130 × 100

= 30%

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The new length of the building will be 110 feet.

Volume of Cuboid:

                              Volume of cuboid is

                        V =  length x breadth x height cubic unit

Given,

The building was going to be 100 feet long, 75 feet deep, and 30 feet high.

Therefore, the volume will be:

               = 75 × 100 × 30 ft³

               = 225000 ft³

Now owner decided increase the volume of the building by 10% without changing the dimensions of the depth and the height.

There was an increase by 10%,

New volume will be,

V' = 225000 + (10% × 225000)

  = 247500 ft³

Therefore, the new length will be:

as,

        Volume =  length x breadth x height

        length  =  Volume/ (breadth x height)

New length will be

                      = 247500/(30 × 75)

= 110 feet

Thus the new length of the building will be 110 feet.

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The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7

Given,

The binomials; (2x² + 4x - 7) (3x - 1)

We can use FOIL method to solve this;

FOIL method;

Binomials are multiplied using the FOIL Method. An acronym is FOIL FOIL. First, Outside, Inside, and Last are the letters that stand for the order of multiplying terms. To get your answer, multiply the first term, then the outside term, then the inside term, then the last term, and then combine terms that are similar.

Here,

(2x² + 4x - 7) (3x - 1)

= (3x × 2x²) + (3x × 4x) - (3x × 7) - 2x² + 4x - 7

= 6x³ + 12x² - 21x - 2x² + 4x - 7

= 6x³ + 10x² - 17x - 7

That is,

The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7

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Answer:

Hope this helps!!

Ok, so

We know that, at West Elementary school, there are 438 students and 22 full-time teachers. We want to know the number of students per teacher. This is:

mean = 27

standard deviation = 4

n = 17

z = ?

Result :

z = 2.5

Answer:

-18

Step-by-step explanation:

first subtract ten from both sides now you're left with -2y=36 ,lastly divide both sides by -2 and you're left with y= -18