What is the value of sin(A)?

If we use a × b, then it means that a is b times more than a and if we use a/b it means that we are making parts of a by the factors of b.

A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. The other operations are multiplication, addition, and subtraction. When two natural numbers are divided with a remainder, or in the Euclidean method, the result is an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains after computing the quotient.

Rule of Division and Multiplication of Integers

Multiplication:

Rule 1: A positive integer and a negative integer cannot be added together.

Rule 2: A positive number is the result of two positive integers.

Rule 3: It states that the sum of two negative integers is positive.

Examples:

Rule 1: 1. (+4) x (-2) = -8 2. (-2) x (+5) = -10

Rule 2: 1. (+6) x (+8) = +48 2. (+6) x (+2) = +12

Rule 3: 1. (-6) x (-8) Equals +48 2. (-2) x (-4) = +8

Division:

Rule 1: A positive integer and a negative integer cannot be multiplied together.

Rule 2: A positive number is the quotient of two positive integers.

Rule 3: A positive number is the quotient of two negative integers.

Examples:

Rule 1: 1. (-8) / (+4) = -2 2. (-12) / (+6) = -2

Rule 2: 1. (+6) / (-3) = -2 2. (+24) / (-6) = -4

Rule 3. 1. (+9) / (+3) = +3 2. (+16) / (+4) = +4

Rule 4: 1. (-6) / (-2) = +3 2. (-42) / (-7) = +6

This is the summary of multiplication and division rules.

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The probability P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

For the probability,

The sample space of a die is, S = {1,2,3,4,5,6}

The probability of getting a number less than 2 is P(x < 2) = 1/6

The probability of getting an odd number is P(Odd) = 3/6

The required probability is calculated as:

P = 1/6 * 3/6

P = 1/12

Hence, the value of P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.

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The total area of the shaded regions is 72 unit sq.

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = side x side

Given that square has an area of 196.

The region contains two overlapping squares that is the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1.

We can come up with equations as;

Since the area of their overlap is 1 then the side length is 1 unit.

Let the length of the smaller square is x.

The length of the larger square is 2x.

Therefore,

x + 2x - 1 = 3x - 1

Thus, 3x - 1 = 14

x = 5

The area of larger square = 100

The smaller one is 25

The area of shaded region;

196 - 124 = 72.

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We have that the data is: (x₁ = 2, y₁ = 2) and (x₂ = 6, y₂ = 3).

The formula to calculate the slope of the line is:

m = y₂ - y₁/x₂-x₁

m = 3 - 2/6 - 2 = 1/4

Answer:

9a-b-2a-10b=7a-11b

Step-by-step explanation:

collect the like terms, meaning add or subtract the numbers from the ones with the same variable(in this case a and b are the different variables)

9a-2a=7a

-b-10b=-11b

therefore, the correct answer is D

Step-by-step explanation:

Well , all you have to do is to collect the like terms bringing those with the same unknown together.

=9a-2a-b-10b

=7a-11b

The 80 % confidence interval for the mean repair cost for the TVs will be [87.873,101.266] and the critical value that should be used in constructing the confidence interval is ±1.337 for 80% interval.

An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.

Here,

df = 17-1=16

critical value = ±1.337 for 80% interval

lower end value,

-1.337=(x-94.57)/[20.65/√17]

x = 87.87

higher end value,

1.337=(x-94.57)/[20.65/√17]

x = 101.27

hence, 80% interval:[87.87 101.27]

The range of values within which the mean repair cost for TVs falls within an 80% confidence interval is [87.873,101.266], and a critical value of ±1.337 should be used to construct the confidence interval.

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The expression [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in simplified radical form obtained by using the laws of indices is presented as follows;

[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]

The laws of indices are a set of rules that can be used to simplify expressions of variables and numbers that consists of powers that have the same base.

The expression is; [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex]

The laws of indices which can be used to evaluate the expression includes;

Expressing the index in terms of 5, we get;

[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]

[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]

The expression, [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in the simplified form is [tex]2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]

A second method evaluating the expression is presented as follows;

[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]

[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2^\frac{5}{5} \cdot t^\frac{5}{5} \times t\cdot w^{\frac{15}{3} } \times w^\frac{2}{5}[/tex]

[tex]2^\frac{5}{5} \cdot t^\frac{5}{5} \times t^{\frac{1}{5} }\cdot w^{\frac{15}{3} } \times w^\frac{2}{5} = 2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5}[/tex]

[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]

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Answer:

LCD is 18

Step-by-step explanation:

1/6 = 3/18

11/9 = 22/18

The percentage of increase in rate is 25%  

The percentage is a value that is expressed as a fraction of 100. In simple words, the percentage means, a part per hundred. To calculate the percent of a number, divide the number by the whole and multiply by 100. It is denoted by the symbol “%”.    

Here we have

The rate of petrol was Rs. 120  

After three months the rate of petrol was Rs.150

The increased rate = Rs.150 - Rs. 120 = 30

The percentage of increase = ( Increased rate/ initial rate) × 100

=  [tex]\frac{30}{120} \times 100[/tex]  = 25%      

Therefore,

The percentage of increase in rate is 25%

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Answer:

My teacher uses:

Please Excuse My Dear Aunt Sally : PEMDAS

Parenthesis, exponents, multiplication, division, addition, subtraction

Step-by-step explanation:

Answer:

parenthesis, exponents, multiplication, division, addition, subtraction

Step-by-step explanation:

The constant of proportionality is: k = 0.45

The equation is: p = 0.45w.

The equation that models the proportional relationship between two variables, x and y, can be expressed in slope-intercept form as y = kx, here, the value of k is the constant of proportionality between the two variables x and y.

Thus, constant of proportionality, k = y/x.

In the table given, we can use the coordinates of one point, (3, 1.35), to find the constant of proportionality, k:

Constant of proportionality, k = 1.35/3

Constant of proportionality, k = 0.45

To write the equation of the relationship between weight (w) and price (p), substitute k = 0.45 into p = kw.

p = 0.45w

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The values of the variables t and k are 33 and 21, respectively.

We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.

t - k = 12

3t + 2k = 141

We will substitute the value of t from the first equation into the second equation.

t = 12 + k

3t + 2k = 141

3(12 + k) + 2k = 141

36 + 3k + 2k = 141

5k = 105

k = 21

We will substitute the value of k into the first equation to find the value of t.

t = 12 + k

t = 12 + 21

t = 33

Hence, the values of t and k are 33 and 21, respectively.

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It take the speed of 299 m to travel 30 cm .

What is speed?

Speed is what it means. the speed at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.

Let us convert cm to m for distances

C = 2.998× 10^8 ms

The relationship between distance, speed, and time is

T =1 ×10^6/8

Because in this case you are being asked how long or time it takes, make it the subject.

Rounding the quotient produces.

Adjust it again to fit the scientific notation.

The result is -

d= c×t

d=2.998×10^8 m/s 10^6 m/s

d=2.998

As a mathematical expression, the time taken for light is 2.998

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The Indefinite integral of the function [tex]\int \tan \left(x\right)\sec ^2\left(x\right)dx[/tex] = [tex]\frac{\tan ^2\left(x\right)}{2}[/tex]

Given;

To get the Indefinite integral of the function [tex]\int \tan \left(x\right)\sec ^2\left(x\right)dx[/tex] ;

Let;

⇒ [tex]\int \tan \left(x\right)\sec ^2\left(x\right)dx[/tex]

Assume tan(x) as 'u', then sec²(x)dx = du;

⇒ [tex]\int \:udu[/tex]

⇒  [tex]\frac{u^2}{2}[/tex]

⇒ [tex]\frac{\tan ^2\left(x\right)}{2}[/tex]

By adding a constant C;

⇒ [tex]\frac{\tan ^2\left(x\right)}{2}[/tex] + C

Hence, the Indefinite integral of the function [tex]\int \tan \left(x\right)\sec ^2\left(x\right)dx[/tex] = [tex]\frac{\tan ^2\left(x\right)}{2}[/tex]

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Answer:

-27

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

Since the problem says that you are subtracting -5 you have to turn everything that is on the right to a positive number like so:

-32 - (-5) ---> -32 + 5

So now all you have to do is add 5 to -32

Therefore equaling -27

So your final answer is C. -27

The total number of hours that Laurie worked for the week is; 35 hours

The parameters given are;

Total number of hours worked for the week = 4s + 3 hours

Rate of earning = 2s + 4 dollars per hour

Gross Amount earned = $700

Thus;

(4s + 3)(2s + 4) = 700

8s² + 6s + 16s + 12 = 700

8s² + 22s + 12 = 700

8s² + 22s - 688 = 0

Solving this with an online quadratic calculator gives;

s = 8

Thus;

Total hours worked = 4(8) + 3 = 35 hours

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1001 many times will the digit 9 occur in the final product.

First of all,

13×7 × 11 =1001

The result is 4 digit number and hence when multiplied by 3 digit number, it is resulting in the number repetition.

             123× 1001 = 123123

             445 × 1001 = 445445

Based on this logic we can assume that,

             99 × 101 = 9999

             85× 101 = 8585

             20 × 101 = 2020.

2.  Any 3 digit number multiplied with 1001 will result in same pattern. for example:

              123 × 1001 = 123123

              997 × 1001 = 997997

              500× 1001 = 500500

Ans so on.

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The number of outfits that Gianna can buy given her budget is 8.

The first step is to determine the total cost of the items bought so far

Total cost = price of the bicycle + cost of the bicycle reflectors + cost of the bike gloves

Cost of the bicycle reflectors = cost of one reflector x 2

Cost of the bicycle reflectors = $10.01 x 2 = $20.02

Total cost = $20.02 + $356.46 + $20.72 = $397.20

Amount that is left to buy the outfits = amount Gianna has - total cost

$760 - $397.20 = $362.80

Number of outfits she can buy = amount left / cost of one outfit

Number of outfits she can buy =  $362.80 /  $45.35

Number of outfits she can buy = 8

Here is the complete question:

Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax. she buys a new bicycle for $356.46. she buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72. she plans to spend some of all of the money she has left to buy new biking outfits for $45.35 each. How many outfits can she buy ?

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The probability that at most 10% of the items in a given batch will be defective = 0.31333

We are aware that the item is broken.

Rate it 17.15 if X is either less than 16.85 or is.

Therefore, we simply found the area of one tail and multiplied it by two as we have seen their identical distance from the Min.

Therefore, let's choose 16.85.

We'll calculate a Z score for that.

Therefore, let's go on to the X value less the mean more than the standard deviation

This may be 16.85 -70, which will be 0.15 divided by.1 negative.

You will have a result of -1.5.

As a result, the Z distribution's region to the left of negative 1.5 will have a value of 0.0668. Divide that amount by two.

Z-score=0.0668/2=0.31333

You will also receive 0.31333.

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Answer:

The two lines are parallel!

Step-by-step explanation:

:)

Answer:

30%

Step-by-step explanation:

60/200 = 3/10 = 30%

Answer:

$7,686.77744

Step-by-step explanation:

19000-14%=16340

16340-14%=14052.4

14052.4-14%=12085.064

12085.064-14%=10393.155

10393.155-14%=8938.1133

8938.1133-14%=7686.77744

For the given expressions , the equivalent expressions are as follow:

As given in the question,

Given expressions are given below:

Simplify and find the equivalent expression from the following given expressions:

=9⁴

= 9 × 9 × 9 × 9

= 6561

36 = 6²

    ≠ 6561

=9⁴

= 9 × 9 × 9 × 9

= 6561

= 4⁹

= 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4

=262144

≠6561

= 9⁴

= 9 × 9 × 9 × 9

= 6561

Therefore, for the given expressions , the equivalent expressions are as follow:

The complete question is :

Which expressions are equivalent? Choose ALL that apply.

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Using PEDMAS, the expression is 188.75

BODMAS is an acronym and it stands for parentheses, exponents, division, multiplication, addition, subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS.

To solve this problem, we just need to apply PEDMAS rule here and evaluate the expression.

210 ÷ 5.2 * 9 3/4 - 205 = 755 / 4 = 188.75

The expression has a value of 188.75

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Sandeep picked up 4.5 pounds of fresh apples from the field

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the standard form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

Pounds of pre-picked apples picked up by Sandeep = 3 pounds

Charges per pound = $4

The total amount paid by Sandeep = $30

Let x be the pounds of fresh apples picked up by Sandeep

In the formulation of the equation we get the following:

Pounds of pre-picked apples*Charges per pound + Pounds of fresh apple picked*Charges per pound = Total amount paid by Sandeep

= 3*4 + x*4 = 30

12 +4x = 30

4x = 18

x = 4.5

So, fresh apples = 4.5 pounds

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The ratio 12/19 means 12 students prefer free time at the beginning of the class and 19 students prefer free time at the end of the class. (option C)

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.

For example if the ratio of boys to girls in a school is 5:4, this means in the school 5boys to 4 girls , and 10boys to 8girls. It can also be expressed as 5/4

Therefore if 12/1,9 is the ratio of students that prefer free time at the beginning to students that prefer free time at the end of a class, then , 12 students prefer free time at the beginning and 19 prefer at the end of the class.

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Answer:

c

Step-by-step explanation:

pls

Answer:

The solution is A. 183

Step-by-step explanation:

112-38×14÷14+109

= 74×1+109

= 74+109

= 183