What is the factored form of 27 - 530?
(2 - 10 ) ( - 590) (9 - 510)
( 20 + 1820م + 18 ) ( 10 - 2) -
O
O
0
(2 - 10) ( 9 + 9 10 + 510)
(2 - 10 ) ( 18 + 2 510 + 20 )

The probability of drawing two blue marbles if the first marble is not replaced is 1/5

The probability of tossing a head and drawing a red marble

The given parameters are:

White = 1

Blue =3

Red = 2

Total = 6

The probability of a head is

P(Head)= 1/2

The probability of drawing a red marble is

P(Red)= 2/6 = 1/3

The required probability is

P = P(Head) * P(Red)

This gives

P = 1/2 * 1/3

P =1/6

The probability of drawing two blue marbles if the first marble is not replaced.

Here, we have:

P(B1) = 3/6 = 1/2

P(B2) = 2/5

The required probability is

P = P(B1) * P(B2)

This gives

P = 1/2 * 2/5

P =1/5

Hence, the probability of drawing two blue marbles if the first marble is not replaced is 1/5

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The system has:

A system of two linear equations is given by:

y = a*x + b

y = c*x + d

1) The system has no solutions when both lines are parallel lines, this happens when both lines have the same slope and different y-intercept.

y = a*x + b

y = a*x + d

2) The system has one solution when the lines have different slopes:

y = a*x + b

y = c*x + d

3) The system has infinite solutions when both equations describe the same line:

y = a*x + b

y = a*x + b

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Answer:

D

Step-by-step explanation:

We will use the order of operations to evaluate the expression.

From left to right , Multiplication/Division followed by Addition/Subtraction.

21 / 3 + 8 - 4

= 7 + 8 - 4

= 15 - 4

= 11

Therefore, the answer is D

Answer:

D) 11

Step-by-step explanation:

Division and multiplication always comes first in an equation. Since there is no multiplication in the expression, we can divde first.

21 / 3 = 7

Our new expression will be: 7 + 8 - 4

Now we can just add (7) , (8), and (-4) not caring about the order, since they are all addition or subtraction.

I'll do the addition first, but order does not matter.

7 + 8 = 15

15 - 4 = 11

So 11 is our final answer.

Looking at the answer choices, D has 11, so D is our answer for this question.

4.44 is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company given that pure beeswax has a density of 0.555 ounce per cubic inch and an online company sells pure beeswax at a price of $8.00 per ounce. This can be obtained by multiplying the values.

Given that,

Density of pure beeswax = 0.555 ounce per cubic inch

Cost of beeswax per ounce = $8.00 per ounce

Selling price in dollars per cubic inch will be,

⇒0.555×$8.00 = $4.44

Hence 4.44 is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company given that pure beeswax has a density of 0.555 ounce per cubic inch and an online company sells pure beeswax at a price of $8.00 per ounce.

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To test the value of the mean in a population when only sample mean and sample deviation are known to perform the test then it is appropriate to use z-test procedure.

What is a Z-test?

A statistical method of testing a hypothesis is the z-test where either:

Additional prerequisites for using the z-test include the following:

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The quotient of the polynomials [tex]2x^{3} +3x^{2} -5x-6[/tex] divided by (x+1) is [tex]2x^{2} -x-6[/tex].

Given two polynomials [tex]2x^{3}+3x^{2} -5x-6[/tex] and (x+1).

We have to determine whether [tex]2x^{3}+3x^{2} -5x-6[/tex] is divisible by (x+1).

Factors are the numbers which are multiplied to get the number whose factors are given. The factor theorem is a theorem which links factors and zeroes of a polynomial.

Polynomial is an expression of more than two algebraic terms may be in addition or subtraction.

We have to first find the factors of polynomial [tex]2x^{3}+3x^{2} -5x-6[/tex].

[tex]2x^{3}+3x^{2} -5x-6[/tex]=[tex]2x^{3}+3x^{2} -4x-x-6[/tex]

=[tex]x^{2}[/tex](2x+3)-2(2x+3)-x

=[tex](x^{2} -x-2)[/tex](2x+3)

=([tex]x^{2}[/tex]-x-2)(2x+3)

=[[tex]x^{2}[/tex]-2x+x-2](2x+3)

=[x(x-2)+1(x-2)](2x+3)

=(x+1)(x-2)(2x+3)

Because (x+1) is a factor of [tex]2x^{3}+3x^{2} -4x-x-6[/tex],so it is divisible by (x+1).

Hence using factor theorem we can say that [tex]2x^{3}+3x^{2} -4x-x-6[/tex]is divisible by (x+1).

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The total surface area of a regular square pyramid having slant height of 10units and base length of 6 units is 168 square inches which is fifth option.

Given that slant height is 10 units and base lengths of 6 units.

We are required to calculate total surface area of regular square pyramid.

We know that total surface area of regular square based pyramid is equal to [tex]s^{2} +s\sqrt{s^{2} +4h^{2} }[/tex] in which s is side of base length and h is slant height of regular square pyramid.

Total surface area=[tex]6^{2} +6\sqrt{6^{2} +4*10^{2} }[/tex]

=36+6[tex]\sqrt{36+400}[/tex]

=36+6[tex]\sqrt{436}[/tex]

=36+6*20.88

=36+125.28

=161.28

Nearest option is 168 square inches.

Hence the total surface are of regular square based pyramid is option 5 which is 168 square inches.

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Answer:

1st option

Step-by-step explanation:

let y = h(x) and rearrange making x the subject , that is

y = 6x - 6 ( add 6 to both sides )

y + 6 = 6x ( divide both sides by 6 )

[tex]\frac{y+6}{6}[/tex] = x

change y back into terms of x with x = [tex]h^{-1}[/tex] (x)

[tex]h^{-1}[/tex] (x) = [tex]\frac{x+6}{6}[/tex]

I think its (B)

V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed

Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:

a. The mean is of: 3.3

b. The standard deviation is of: 1.23.

c. They would have a mean of 3.3 and a standard deviation of 0.55.

For this problem, the mean is given by:

M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3

The standard deviation is:

[tex]S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23[/tex]

It states that for distribution of sample means of size n:

Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.

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Answer:

1) (x-6)^2=49

2) C

Step-by-step explanation:

Subtract 12 x and you get

-x^2-12x+13=0

You will be left with, after making a perfect square

(x-6)^2=49

To get rid of the squared/2nd power, add plus or minus to the opposite side and square root both sides. You will be left with

x-6=plus or minus 7

Your answer comes out to the to problem. Setting both to 0, you get -13, and 1. -6 plus 7 is 1, and -6 plus a -7 is -13.

The dimensions of the rectangle are: length= 18 in and width =1 in.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : l*w, where b = length and w =width. The question gives that the area is 18 in².

For this question, the length exceeds its width by 17 inches - l=w+17. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=l*w

18=(w+17)*w

18=w²+17w

w²+17w-18=0

Next step will be solve the previous equation ( W²+17W-18=0)

[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]

Therefore,

[tex]w_1=\frac{-17+19}{2\cdot \:1}=1\\ \\ \\ w_2=\frac{-17-19}{2\cdot \:1}=-18[/tex]

For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², you have.

18=l*w

18=l*1

l=18 in

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The probability that the schools in Los Angeles will be closed for four days next year is 0.1680.

In order to comprehend separate events that happen at a steady pace over the course of a specified amount of time, Poisson's distributions are frequently utilized.

Formula for Poisson's distribution:

f(x) = ((λ^x)/x!).(e^(-λ))

x = Event to be calculated for

λ = Expected number of occurrences

P(X = x) = ((λ^x)/x!).(e^(-λ))

Here λ = 3 and x = 4

P(X = 4) = (81 / 4!).(e^(-3))

P(X = 4) = (81 * e^(-3))/24

P(X = 4) = (81 * 0.049)/24

P(X = 4) = 0.1680

Hence, the probability that schools in Los Angeles will be closed for four days next year is 0.1680.

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The equation of the line is y = 3/2x - 3

The points are given as:

(0, -3), (2, 0), and (4, 3).

Start by calculating the slope (m) using:

m = (y2-y1)/(x2 -x1)

This gives

m = (3 + 3)(4 - 0)

Evaluate

m = 3/2

The equation is the calculated as:

y = m(x - x1) + y1

This gives

y = 3/2(x - 0) - 3

y = 3/2x - 3

Hence, the equation of the line is y = 3/2x - 3

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Answer:   y = -x + 2

Step-by-step explanation:

Point slope form is y - y = m(x - x)

m = the slope of the line

Slope-intercept form is y = mx + b

m = the slope of the line

b = y-intercept

So because the - is in the m spot in the point-slope form, that means that is the slope of the line meaning it will also be in the m spot in slope-intercept form. The y-intercept of the line is found when x is 0.  When we look at the two coordinates provided you can see that one of them shows when x is 0.  We see that when x is 0, y is 2  which means that the y-intercept is 2.

So when you put the 2 in place of b,  you get   y = -x + 2

Let X be the number of times you win.

The total number of ways to select 2 balls (order does not matter) =>

The number of ways so that two balls are white:

= 3/55

The number of ways so that two balls are red:

= 3/55

The number of ways so that one ball is red, one is white:

= 9

The number of ways so that two balls are blue:

= 10

i.e. p = 10+9/55 = 19/55

The number of ways so that one ball is blue, one is white:

p = 15/55 = 3/11

The number of ways so that one ball is blue, one is red:

15/55 = 3/11

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The value of w(u(4)) is 73.

u( x ) = - 2*x + 2

w( x ) = 2*x^2 + 1

w( u( x ) ) = w( - 2*x + 2  )

⇒ w( u( x ) ) = 2*( - 2*x + 2  )^2 + 1

⇒ w( u( x ) ) = 2*[ 2^2 + ( 2*x )^2 - 2*2*( 2*x ) ] + 1

⇒ w( u( x ) ) = 2*[ 4 + 4*x^2 - 8*x ] + 1

⇒ w( u( x ) ) = 8 + 8*x^2 - 16*x + 1

⇒ w( u( x ) ) = 8*x^2 - 16*x + 9

⇒ w( u( 4 ) ) = 8*4^2 - 16*4 + 9

⇒ w( u( 4 ) ) = 8*16 - 16*4 + 9

⇒ w( u( 4 ) ) = 128 - 64 + 9

⇒ w( u( 4 ) ) = 73

In mathematics, a feature from a set X to a fixed Y assigns to each detail of X exactly one detail of Y. The set X is called the domain of the function and the set Y is referred to as the codomain of the function. features were firstly the idealization of how various quantity relies upon any other quantity.

These elementary functions include

A function is defined as a relation between a set of inputs having one output each. In simple phrases, a function is a courting among inputs wherein every entry is associated with exactly one output. every function has a site and codomain or range. A characteristic is normally denoted through f(x) in which x is the input.

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Answer: $92.30

Step-by-step explanation:

Finding the area of one of the triangles formed by the diagonal,[tex]s=\frac{9+12+19}{2}=20\\\\A=\sqrt{(20)(20-9)(20-12)(20-19)}=4\sqrt{110}[/tex]

Therefore, the area of the entire parallelogram is [tex]8\sqrt{110}[/tex].

Therefore, the cost is [tex](8\sqrt{110})(1.1) \approx 92.30[/tex]

Answer:

$92.30   i got it right.

Step-by-step explanation:

edg 2023 its right.

The amount of packing material is 1506 cubic inches

The given parameters are:

Can

Radius, r = 7 inches

Height, h = 18 inches

Box

Base dimension, l = 15 inches

Height, h = 19 inches

The volume of the can is:

[tex]V = \pi r^2h[/tex]

So, we have:

[tex]V_1 = 3.14 * 7^2 * 18[/tex]

[tex]V_1 = 2769[/tex]

The volume of the box is

[tex]V =l^2h[/tex]

So, we have:

[tex]V_2 =15^2 * 19[/tex]

[tex]V_2 =4275[/tex]

The amount of packing material is;

Amount = V2 - V1

This gives

Amount = 4275 - 2769

Evaluate

Amount = 1506

Hence, the amount of packing material is 1506 cubic inches

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Answer:

x=m/9

Steps:

m=9x

m/9=x

x=m/9

Answer:

1000xm

Step-by-step explanation:

1 meter = 3.2808 feet, hence. 9.8424 x 10^8 feet in 1 second. 1 foot in x seconds. hence it takes 1 / (9.8424 x 10^8) = 0.10168 x 10^(-8) seconds. ➡️1km = 1000xm⬅️

It will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

To find out how long it will take light to travel one meter, we need to convert the given distance of 10,000 km to meters and the time of 3.0 x 10² seconds to seconds.

Given:

Distance traveled by light = 10,000 km

Time taken by light = 3.0 x 10² seconds

To convert km to meters, we know that 1 km = 1 x 10³ m, so:

10,000 km = 10,000 x 1 x 10³ m = 1 x 10⁷ m

Now, we can find the time taken to travel one meter by dividing the total time by the total distance:

Time taken to travel one meter = Total time / Total distance

Time taken to travel one meter = (3.0 x 10² seconds) / (1 x 10⁷ m)

To simplify the expression, we can cancel out one factor of 10 from the numerator and denominator:

Time taken to travel one meter = (3.0 x 10) / (1 x 10⁶ m)

Now, we get the final answer:

Time taken to travel one meter = 3.0 x 10⁻⁵ seconds

So, it will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

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Based on the number of years till maturity and the required rate of return, the price of the zero-coupon bond is $852.22.

When a bond's par value is not given, assume it is $1,000.

the price of a zero coupon bond is:

= par value / (1 + rate) ^ number of years till maturity

solving gives:

= 1,000 / (1 + 3.25%)⁵

= 1,000 / 1.17341139582939453125

= $852.22

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The factorise form of the two expression are as follows:

b. (x - 3)(2 / 3 x - 6) = 0

Therefore, let's open the brackets

2 / 3 x² - 6x -2x + 18 = 0

2 / 3 x²  - 8x + 18 = 0

multiply through by 3

2x² - 24x + 54 = 0

Hence,

 2 (x - 3)  (x - 9)

c.

(-3x - 15)(x + 7)  = 0

Therefore,

-3x² - 21x - 15x - 105 = 0

-3x² - 36x - 105 = 0

-3(x + 5)(x + 7)

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Answer:

x > - 3

Step-by-step explanation:

6(x + 2) > x - 3 ← distribute parenthesis on left side

6x + 12 > x - 3 ( subtract x from both sides )

5x + 12 > - 3 ( subtract 12 from both sides )

5x > - 15 ( divide both sides by 5 )

x > - 3

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏

✏[tex]\bigstar\textsf{Solution \quad Steps:-}[/tex] ✏

use the distributive property

[tex]\sf{\longmapsto 6x+12 < x-3}[/tex]

subtract both sides by x and 12

[tex]\sf{\longmapsto{5x < -15}[/tex]

divide both sides by 5

[tex]\sf{\longmapsto x < -3}}[/tex]

`hope it's helpful to u ~

Answer:

69%

Step-by-step explanation:

Overall grade = 0.35*minor grade + 0.65*major grade

major grade: 0.65*61 = 39.65

minor grade: 0.35*84 = 29.4

total: 39.65+29.4 = 69.05

Rounded = 69%

The missing data item for the given set of data if the median is 14 is 18.

The Median is the "middle" of a sorted list of numbers.

Therefore, the missing data item for the given set of data if the median is 14 can be calculated as follows:

10 10, 11, 11, 12, 12, 14, 15, 16, 18, 19, 19,

Therefore, if you add 18 the middle number of the sorted numbers will be 14.

10 10, 11, 11, 12, 12, 14, 15, 16, 18, 18, 19, 19,

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Answer:

[tex]x=6[/tex]

Step-by-step explanation:

Given equation:

[tex]x-\left(2x-\dfrac{3x-4}{7}\right)=\dfrac{4x-27}{3}-3[/tex]

Expand the left side:

[tex]\implies x-2x+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Let all terms on the left side have the same denominator of 7:

[tex]\implies \dfrac{7x}{7}-\dfrac{14x}{7}+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Join the terms on the left side:

[tex]\implies \dfrac{7x-14x+3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Let all the terms on the right side have the same denominator of 3:

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-\dfrac{9}{3}[/tex]

Join the terms on the right side:

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27-9}{3}[/tex]

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-36}{3}[/tex]

Cross multiply:

[tex]\implies 3(-4x-4)=7(4x-36)[/tex]

Expand:

[tex]\implies -12x-12=28x-252[/tex]

Add 12x to both sides:

[tex]\implies -12=40x-252[/tex]

Add 252 to both sides:

[tex]\implies 240=40x[/tex]

Divide both sides by 40:

[tex]\implies 6=x[/tex]

[tex]\implies x=6[/tex]

Profit function : p(x) = 53 x - 12

Cost is the total cost of producing the output.

The cost function consists of two different types of costs:

- Variable costs

- Fixed costs.

Variable costs vary with output (number of units produced). Total variable costs can be

expressed as the product of variable costs per unit and the number of units produced. If there are multiple items

manufactured costs are higher.

Fixed costs usually do not vary with performance.

Revenue is the total payment received from the sale of goods or the provision of a service.

The revenue function R() reflects the revenue from selling “” quantity of output items at price

"p" after item.

() =

Profit functions

The profit function P() is the difference between the revenue function R(x) and the total cost function C()

So P() = R() – C()

=−

Now, Profit = Revenue - Cost

= 60 x - ( 12 + 7 x)

= 60 x -12 -7 x

Profit = 53 x - 12

Hence, Profit function : p(x) = 53 x - 12

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If the factors of the polynomial were (x-5) and (x-6), the values of x that would make the polynomial equal to zero would be 5 and 6.

5 - 5 = 0

6 - 6 = 0

Assuming the polynomial is (x-5)(x-6), if one factor is 0 then anything multiplied by 0 is still 0.

Hope this helps!