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The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

According to the question,

We have the following information:

[tex]64x^{3} +8[/tex]

The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.

So, we have the following expression:

[tex](4x)^{3} + 2^{3}[/tex]

Now, we can use the following identity to factor the given expression:

[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]

We have a = 8x and b = 2:

(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}

(8x+2) (16[tex]x^{2}[/tex]-16x+4)

Taking 4 as the common factor from the second bracket:

4(8x+2) (4[tex]x^{2}[/tex]-4x+1)

Now, finding the factors of second bracket:

4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)

4(8x+2) {2x(2x-1)-1(2x-1)}

4(8x+2) (2x-1) (2x-1)

4[tex](2x-1)^{2}[/tex] (8x+2)

Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

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The probability of getting watermelon is 3/58.

The given values are

A pineapple chew was selected 53 Times

A lemon chew was selected 2 times

A watermelon chew was selected 3 times

The probability that you Bella remove from the bag is pineapple chew.

probability is which we can't predict actual it is usually about the prediction

As we know

probability - expected outcome/total outcome

The question Bela perform experiment 58 times then the total outcome will be 58 if you pineapple was selected 53 times the probability of the chew Bella pick of pineapple is 53/58

The probability of Bella pick chew of lemon -2/58

The probability of Bella pick watermelon is - 3/58

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Answer:

30 divided by 0.08 will get you 375

Step-by-step explanation:

Answer:  x + 8

Step-by-step explanation:

[tex]f(g(x))=f(\frac{1}{2}x+2) = 4+2(\frac{1}{2}x+2) = 4+x+4 =x +8[/tex]

(5-√5)² in the form a + b√5 can be written as 30 - 10√5 where, the integers a and b are 30 and -10 respectively.

What is integer?

Positive, negative, and zero are all examples of integers. The Latin word "integer" means to "whole" or "intact." Therefore, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.

We know that,

[tex](a-b)^2= a^2 + b^2 - 2ab[/tex]

Using this mathematical identity, putting the values from question,

(5-√5)² = 5² + √5² - 2(5)(√5)

(5-√5)² = 25 + 5 - 10√5

(5-√5)² = 30 - 10√5

This is in the form a + b√5 where, the integers a and b are 30 and -10 respectively.

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Answer:

x = 5

Step-by-step explanation:

2(x+5) =20  Distribute the 2

2(x) + 2(5) = 20

2x + 10 = 20  Subtract 10 from both sides of the equation

2x = 10  Divide both sides by 2

x = 5

Answer:

5

Step-by-step explanation:

2(x + 5) = 20 Divide both sides by 2

x + 5 = 10

x = 10 - 5

x = 5

Answer:

521 mm2

Step-by-step explanation:

Formulas:

area of circle= 3.14 x radius x radius

area of semicircle = 0.5 x 3.14 x radius x radius

diameter of circle= 20mm

radius=0.5x20mm=10mm

area of trapezium= 0.5 x (base+base) x height

Working:

area of semicircle= 0.5 x 3.14 x 10mm x 10mm = 157mm2

area of trapezium = 0.5 x (20mm+32mm) x 14mm = 364mm2

total area of figure= 157mm2 + 364mm2 =521mm2

The margin of error tells you how many percentage points your results differ from the true population value.

The margin of error is a close guess at a given level of probability about the confidence interval. It is denoted as a tiny percentage that is allowed for in the event of an error.

The amount of uncertainty associated with a survey result is referred to as the margin of error. It indicates how confident you can be in the outcome's accuracy. A smaller margin of error indicates that your survey is more precise. A confidence level is the probability that a survey will yield the same results if repeated.

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Considering the right angle triangle given the values of the variables are

Information from the question

right angle triangle

The values of the variables is worked using SOH CAH TOA

The right angle triangle of sides as described below

hypotenuse = k

opposite = n

adjacent = 6

The variable n is solved using tan, TOA, the angle is 30

tan 30 = Opposite / Adjacent

tan 30 = n / 6

tan 30 * 6 = n

n = 2√3

The variable k is solved using cos, CAH, the angle is 30

cos 30 = Adjacent / Hypotenuse

cos 30 = 6 / k

k = 6 / cos 30

k = 4√3

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Answer:

96, $ 144

Step-by-step explanation:

After simplification, the equivalent expression is 18(p-2). So the option D is correct.

In the given question,

We have to find factor 18p-36 equivalent expressions.

The given option is

A. 3(9p-12)

B. 9(2p-4p)

C. 2(9p-18)

D. 18(p-2)

The given expression is 18p-36.

We simplify the given expression to find their equivalent expression.

To simplify the expression we take out the common term from both terms.

We can see that 18 is a common multiply of both number 18 and 36. SO we take out 18 from both terms.

Taking common 18

18p-36 = 18(p-2)

Hence, the equivalent expression is 18(p-2). SO the option D is correct.

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The value of each term is

The length of the line ED = 45 units

The length of the line DF = 27 units

The length of the line EF = 36 units

Here we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

Substitute the value in the equation

sin D = Opposite side / Hypotenuse

= 36/45

= 4/5

sin E = Opposite side / Hypotenuse  

= 27/45

= 3/5

cos D = Adjacent side / Hypotenuse

= 27/45

= 3/5

cos E = Adjacent side / Hypotenuse

= 36/45

= 4/5

Hence, the value of each term is  

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The solution of the equation 2(x + 1) = 6(x – 1), is the value of x = 2.

To solve an equation means to find what the value of the variable of the equation would be that would make the equation true if the value of the variable is plugged into the equation.

The necessary steps taken to find the value of x in the equation, 2(x + 1) = 6(x – 1) are explained below:

2(x + 1) = 6(x – 1) [given]

Apply the distributive property

2x + 2 = 6x - 6

Combine like terms

2x - 6x = -2 - 6

-4x = -8

Divide both sides by -4

-4x/-4 = -8/-4

x = 2

The value of x is 2. To check the solution, plug in the value of x back into the equation:

2(2 + 1) = 6(2 – 1)

2(3) = 6(1)

6 = 6 [true]

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The remainder is the amount "leftover" after performing some computation.

Hence,

(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.

(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.

What is a remainder?

The remainder is the amount "leftover" after performing some computation. In arithmetic, the remainder is the integer "leftover" after dividing one integer by another to produce an integer quotient.

Here given that,

The strength of boys is [tex]121[/tex]

The strength of girls is [tex]116[/tex]

So, the total number of students are

[tex]121+116=337[/tex]

The leader first makes groups of [tex]9[/tex] students and then assigns any remaining students to make some of the groups have [tex]10[/tex] students.

So we divide by [tex]9[/tex] to find out the remainder and the total number of groups are:-

[tex]\frac{337}{9}=37[/tex]

and the remainder value is [tex]4[/tex].

Therefore, there are [tex]37[/tex] groups in the total out of which [tex]4[/tex] are out of [tex]10[/tex]students.

So,

[tex]\frac{37}{4}=33[/tex] groups are of [tex]9[/tex] students.

Hence,

(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.

(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.

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Solution of the given inequality -18 + x < 16 is equal to x < 34.

As given in the question,

Given inequality is equal to :

-18 + x < 16

Get the value of the variable x by adding 18 both the side of the inequality we get,

-18 + x + 18 < 16 + 18

Collect all like terms together we get,

⇒ x + (-18 + 18 ) < 34

⇒ x + 0 < 34

Solution of the inequality -18 + x < 16 is given by

⇒ x < 34

For the given inequality -18 + x < 16 the value of variable x is less than 34.

Therefore, solution of the given inequality -18 + x < 16 is  x < 34.

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Answer:

321 is the next number that comes in the calculator.

Answer:

Step-by-step explanation:

the answer is "downward". If you say "why", it is because of the degree coefficient.

in the equation, the latest degree is 2 (which is quadratic equation) so from the degree its coefficient is -3. If it is negative, it should be downward like -3. But if it is positive it should be upward like 3, 1, 44.

Answer: [tex]5^{2} + 4[/tex]

Step-by-step explanation:

[tex]2 + 3^3[/tex] =?

2 + 27 = 29

10 * 2 - 9 = 20 - 9 = 11

[tex]5^2 + 4[/tex] = 25 + 4 = 29

[tex]5^3\\[/tex] = 5 * 5*5 = 125

3+ 4 * 3 = 3 + 12 = 15

There are 255 students who prefer Movie C.

In the given case, the total number of students in the campus = 900

Number of students in the random sample :

= 31 + 27 + 34 + 28

= 120

Number of students who prefer to watch movie C in the chosen sample:

= 34

To get number of students who would prefer to watch the movies C in the total population of 900, we can extrapolate the data from the chosen sample to the entire population.

Thus, number of students expected to prefer movie C in the campus =

34/120 × 900

= 255

Hence the expected number of students are 255.

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The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.

From the given figure, we need to identify the corresponding angles.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

From the figure, ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7 are the corresponding angles.

The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.

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Lucas will be using the shipping box D as it is the box with the greatest volume of 27ft³

The volume of a rectangular box is calculated by multiplying its three dimensions which are the length, width, and height . That is Length × Width × Height in the same units.

volume of box A = 5ft × 3ft × 1ft

volume of box A = 15ft³

volume of box B = 4ft × 2ft × 3ft

volume of box B = 24ft³

volume of box C = 7ft × 1ft × 2ft

volume of box C = 14ft³

volume of box D = 3ft × 3ft × 3ft

volume of box D = 27ft³

Therefore, the shipping box with the largest volume is box D with 27ft³

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Answer:

Step-by-step explanation:

FEEL ME ITS D

ITS D

THE ONE WITH THE 333

if we take 25 to be the 100%, what is 100 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 100& x \end{array} \implies \cfrac{25}{100}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{1}{4}=\cfrac{100}{x}\implies x=400[/tex]

Answer:

25

Step-by-step explanation:

25/100=.25x100=25

The given expression has a value of 2.5.

The BODMAS rule is named after the letters in the acronym: B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication. A stands for addition, and S stands for subtraction. According to the BODMAS rule, mathematical statements having several operations must be solved from left to right in the BODMAS order.

Given expression 6 x (2/3 divided by 2) + 0.5

To solve this expression, we must employ the BODMAS rule.

First 2/3 divided by 2

(2/3)/2

= 1/3

Now multiply 1/3 with 6

= 1/3 x 6

= 2

Now add both 2 and 0.5

= 2 + 0.5

= 2.5

Therefore the value of the given expression is 2.5

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The product of two numbers exists done by multiplying a number with the other. The product of a number x and 7 exists 7x.

The result of multiplying two or more numbers together is known as a product in mathematics. A number that is obtained by multiplying two or more other numbers together is referred to in mathematics as a product.

The outcome of one or more multiplications is referred to as a "product." For instance, the mathematical statement "times equals" would be written with the multiplier, the multiplicand, and their product as the variables.

Let the variable be x

x be a number

So, the product of x and 7 exists calculated as:

Product = 7 × x

Product = 7x

Therefore, the product of a number (x) and 7 exists 7x.

The complete question is:

The product of a number and 7

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4- (+) (-4) is similar to 4+4 by the rule of addition in integers that is if Negative + Negative then Add the number and put the sign of greater number.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples. Three categories of integers exist: Zero (0) (0) Good integers (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers).

The rules of addition in integers says,

- + -  = +

by this,

4-(-4)=8

by concept of addition,

4+4=8

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By using unitary method it is obtained that -

Scale used my Colton = 1 : 500

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here unitary method is used

18 mm long field in the drawing is equivalent to 9000 mm long field in real

1 mm long field in the drawing is equivalent to [tex]\frac{9000}{18}[/tex] mm long field in real

1 mm long field in the drawing is equivalent to 500 mm long field in real

Scale used by Colton 1 : 500

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Answer:

f(2) = 0

Step-by-step explanation:

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x).

Therefore, applying the factor theorem, if (x - 2) is a factor of a polynomial f(x) then f(2) = 0.