prove that cos x = sin x cot x.

Value of c is determined 61 unit.

What is right-angled triangle?

Triangle that has one angle 90 degree is called right-angled. In case of a right triangle the square of the largest side length is equal of the sum of the square of the other two side length.

SA triangle has three side length 11-unit, 60 unit and 61 unit respectively.

The triangle is verified as a right-angled triangle by Pythagorean theorem.

And as the properties of a Pythagorean theorem the sum of the square of two side length is equal to the square of the largest side length.

if we say, one side length, a = 11 unit

             second side length, b = 60 unit

    the largest side length, c

now we will check,  

√(11²+60²) = c² =√3721 = 61

the value of c = 61 unit.

hence, the SA is right-angled triangle.

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The triangle with side lengths given in the question can be classified as a scalene triangle.

A scalene triangle is a type of triangle in which none of its three given length of sides are equal. It can be differentiated from other types with respect to  this property.

A triangle is a plane shape which can be described by three sides and three measure of internal angles. Some other types of triangle are: equilateral, obtuse, isosceles etc. The sum of all internal angles of a triangle is 180^o

Considering the given length of sides in the question, it can be proven the the only type of triangle that can be formed is a scalene triangle. Therefore, the triangle can be classified as a scalene triangle.

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Carlos needs a total of 400 Euros for buying 500 Euros.

The total amount available with Carlos for his holiday to Germany = 515 Euros

Amount spent to obtain these 515 Euros = £ 412

As it is clear that for buying 515 Euros he spent 412 Euros.

So, we will first find the Euros spent on buying 1 Euro.

For that, we will use Unitary Method:

So, the total Euros spent for buying 1 Euro will be = (412/515) = 0.8

So, for finding the total Euros spent for obtaining 500 Euros we will simply multiply the total Euros needed by the Euro spent for buying 1 Euro.

Thar will be equal to (0.8 * 500) = 400 Euros.

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Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards

Multiplication is an arithmetic operation in which a number (known as a multiplicand) is multiplied by another number (known as a multiplier) to produce a product.

In this problem, we will need to use of some mathematical operators to solve the problem

1.

He currently has 216 cards, but he needs 15 sets of cards.

1 set of card = 72 cards

Let's calculate the number of sets he currently has.

1 set of card = 72 cards

x set = 216 cards

cross multiply both sides and solve for x.

x * 72 = 216 * 1

x = 216 / 72

x = 3 sets

He currently has 3 sets of cards.

Since he wants 15 sets of cards, we will need 12 more set of cards.

The number of cards can be calculated by multiplying 12 by 72

Number of cards = 12 * 72 = 864

He needs 864 more cards.

2.

1 set of card = $27

1 set = 72 cards

But she's bringing $9 to join, we can calculate the ratio of cards she will get.

1 / 27 = x / 9

x = 9 / 27

x = 1/3

She will get 1/3 of the cards bought which will be

72 * 1/3 = 24 cards

She will get 24 cards

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The short explanation of the effects of the above operations will not affect the inequality.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9, then we have

4 x 3 x 2 x 4 x 9 < 7 x 3 x 2 x 4 x 9

864 < 1512

2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)

11 + 3 + (-4) > - 2 + 3 + (-4)

10 > - 3

3. -2 ≤ -2 Subtract 6 from both sides, then 8, and then 2

-2 - 6 - 8 - 2 ≤ -2 - 6 - 8 - 2

- 18 ≤ - 18

4. -4 < 8 Divide both sides by -4, then by -2

- 4 / (-4) > 8 / (-4)

1 / (-2) > - 2 / (-2)

- 1/2 < 1

The short explanation of the effects of the above operations will not affect the inequality.

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The probability of the two cards being D and D, P(D, D), is 4/9. The correct option is: 4/9.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.

Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.

Calculating probability of selecting a card:

From the question, we are to determine the probability of selecting two cards with D and D

From the formula for probability, we have that

P(D) = Number of favorable outcomes to D / Total number of possible outcomes

From the given information,

Number of favorable outcomes to D = 2

Number of possible outcomes = 3

Thus,

P(D) = 2/3

Then,

The probability of selecting two cards that have D and D with replacement is

P(D, D) = P(D) × P(D)

P(D, D) = 2/3 × 2/3

P(D, D) = 4/9

Hence, the probability is 4/9.

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Using sine and cosine rule, the length of d in the triangle is equal to 4.5cm

The sine rule is a mathematical formula used to calculate the lengths of the sides and angles of any triangle when given two angles and one side or two sides and one angle. It is also known as the law of sines.

To find the length of d, we have to find the length of E.

Using sine rule;

f / sin F = e / sin E

5 / sin 75 = e / sin 79

e = 5sin79 / sin 75

e = 5.7cm

To find the length of d, we have to find the angle D by using the sum of angle theorem.

m∠ E + m∠ F + m∠ D = 180°

79 + 75 + m∠ D = 180

m∠ D = 180 - 154

m∠ D = 26°

Using cosine rule

d² = e² + f² - 2efCosD

d² = 5.7² + 5² - 2(5.7)(5)cos26

d² = 20.615598

d = √20.615598

d = 4.5cm

The length of side d is 4.5cm

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According to the exponential function,

a) The function that models the given situation is f(rabbits) = 65000(√500/13)ˣ

b) The number of rabbits in 1870 is 6.5

c) According to your model, the first pair of rabbits introduced into Australia is 19th century

Here we have given that during the 19th century, here rabbits were brought to Australia.

And here we also know that the rabbits had no natural enemies on that continent, their population increased rapidly.

And we have given that there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.

Then according to the exponential function that could be used to model the rabbit population y in Australia in terms of x, the number of years since 1865 is to be determined.

Then the exponential function can be written as,

=> f(rabbits) = 65000(√500/13)ˣ

When we plot these on the graph then we get the graph like the following.

Through the graph we have identified that the value of rabbits in 1870 is 6.5

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No, one mole is not equal to one gram. For an object, the mole and gram numerical values differ.

1 gram, what is it?

One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.

The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.

A mole's relationship to a gram is

The product of the number of Moles of an object to its atomic weight equals one gram.

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The value of  Avogadro's number is 6.02214076 × 10²³. The ratio of the actual mass of an element to its atomic mass is always constant which is known as  Avogadro's number.

What is one mole?

One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.

The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.

The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of  6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.

It shows how many atoms or molecules make up one gram of an element's or compound's molecular weight. The value is "6.022 × 10²³" when the atomic mass of an element is divided by the actual mass of its atom.

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The exponential function that represents the population is y = a*3^x.

What is exponential function?

The formula for exponential functions is y = ab^x, where b is the constant ratio and a  is the starting point. Observe that as the value of x increases by a constant amount, the value of y increases by a common ratio by looking at a table of ordered pairs. All exponential functions share this trait.

We have to find the exponential function for the given table.

Since,

Exponential function = ab^x

where,

a is the starting point

b is the common ratio.

Here,

Common ratio = 24/8 = 72/24 = 216/72 = 648/216 = 3

So, the function becomes,

Exponential function = y = a*3^x

Hence, the exponential function that represents the population is

y = a*3^x.

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The bicycle tire needs an amount of 115 pumps to be fully inflated. (Correct choice: B)

In this problem we need to determine the number of pumps needed to inflate the bicycle tire at maximum pressure, this number (n) is equal to the maximum capacity of the tire (V), in ounces, and the mass added by a single pump (p), in ounces:

n = V / p

If we know that V = 640 oz and p = 5.6 oz (1 lb = 16 oz), then the number of pumps is:

n = 640 oz / 5.6 oz

n = 114.286

n = 115

An amount of 115 pumps are needed to inflate the bicycle tire to maximum pressure.

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The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 as calculated from the given data is 5.20 and 7.60.

The confidence interval for the difference of the population mean is calculated as,

CI = ( x1 - x2 ) +- z x √SD1²/n1 + SD2²/n2

= ( 82.9 - 76.5) +- 1.96 x √7.97²/293+ 6.66²/n2.82

=6.4 ± 1.199

=(v5.201 , 7.599)

therefore , approximately 5.20 , 7.60 .

Therefore , the confidence interval between them is found to be as , ( 5.20 , 7.60 ) answer.

The confidence interval is a calculation based on the statistics of the observed data that estimates the amount of uncertainty associated with a sample.

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Answer:

-1.256165295×10×10×10×10×10×10×10×10×10×10×10

Step-by-step explanation:

negative changes everything

Apply arithmetic operations on both sides of the equation to move the variable to one side and all other values to the opposite side.

Let's begin with a basic equation: x + 2 = 7.

How may x be obtained on its own?

x + 2 - 2 = 7 - 2 x = 5 after deducting 2 from both sides.

Put the solution, x = 5, back into the equation to confirm it. We get 5 + 2= 7.

Since LHS = RHS

In the triangle, find x.

Use triangle properties or the Pythagorean theorem to find the value of x, the unknown side or angle in a triangle.

Let's use an example to better understand how to solve for x in a triangle.

Using the Pythagorean theorem, we obtain AC2 = AB2 + BC2 where x2 = 72 + 242 x = 49 + 576 x = 625 x = 25 units.

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Answer:

12

Step-by-step explanation:

3 + 4 + 5 = 12

Answer: 347

Step-by-step explanation:

Answer:

Given that ,

738 students wore red while 162 students wore green.

Therefore , total number of students ,

[tex]\dashrightarrow \: 738 + 162 \\ \dashrightarrow \: 900[/tex]

Now , 738 students out of 900 wore red.

So , percentage of students who wore red ,

[tex]\dashrightarrow \: \frac{738}{9\cancel{00}} \times \cancel{100} \\ \\ \dashrightarrow \: \cancel\frac{738}{9} \\ \\ \dashrightarrow \: 82\%[/tex]

hope helpful :-;

Answer:

not sure if I understand but I believe you are talking about writing it down

In any version of Microsoft Word, type m2, then highlight the 2. Now press and hold Ctrl and Shift, then press the + key and it will be changed to superscript and will look like this: m2

Example of perfect square trinomial is: x² + 6x + 9 it is expressed as

(x + 3)²

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Example:

  x² + 6x + 9

= x² + 3x + 3x + 9

= (x +3) (x + 3)

= (x + 3)²

so, this is a perfect square trinomial.

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The degree of the polynomial x4 x3 5x 3 is 4, since it is the highest degree of the polynomial.

A polynomial is an expression that consists of variables, coefficients, and operators such as addition, subtraction, multiplication, and division. It is used to represent a mathematical relationship between variables. The degree of a polynomial is the highest power that appears in the expression, and it indicates the number of terms that make up the polynomial. Polynomials are usually written in descending order of powers, and the highest power is the leading term.

The highest degree of any polynomial is considered its degree. It is also referred to as the degree of the polynomial's leading term, since it is the highest power of x. In this case, the leading term is x4.

The degree of a polynomial can be used to classify the type of polynomial it is. For example, if the degree of a polynomial is 2, it is a quadratic polynomial. Similarly, if the degree of a polynomial is 3, it is a cubic polynomial.

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3 and -3 are additive inverses because 3 + (-3) = 0.

Therefore, -3 is the additive inverse of 3.

Additive Inverse:

The additive reciprocal/ Inverse of a number is its inverse. When a number is added to the additive reciprocal, both numbers sum to zero. A simple rule is to change positive numbers to negative numbers and vice versa. We know that 3+ (-3) =0. So -3 is the additive reciprocal of 3, and 3 is the additive reciprocal of -3.

If the sum of two real numbers is 0, each real number is said to be the additive reciprocal of the other real number. Therefore, R + (-R) = 0. where R is a real number. R and -R are the additive reciprocals of each other. Example: 3/4 + (-3/4) = 0. where 3/4 is the additive reciprocal of -3/4 and vice versa. This is an example of the additive reciprocal of a fraction.

We have room temperature water in a bucket. Adding 1 liter of hot water raises the temperature of the entire bucket by a certain amount. Then add another liter of cold water. Opposite temperature water in the bucket will cancel out, resulting in a bucket of room temperature water. The same rules apply when taking the additive reciprocal of a number. The additive inverse property applies to both real and complex numbers.

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The sum of 2.3 and 1.94, that is 2.3 + 1.94 is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.

Therefore the answer is 4.24.

The first number, 2.3, can be broken down into 2 wholes and 3 tenths.

The second number, 1.94, can be broken down into 1 whole, 9 tenths and 4 hundredths.

To add the two numbers together, we first add the wholes: 2 + 1 = 3.

Next, we add the tenths: 3 + 9 = 12

Since we cannot have more than 9 tenths in a whole, we must regroup 12 tenths as 1 whole and 2 tenths.

We add the regrouped tenths to the number of wholes: 3 + 1 = 4

After regrouping, we have 4 whole and 2 tenths.

Now we add the hundredths: 0 + 4 = 4

Thus the sum is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.

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On solving the provided question, we can say that - the valuye os the complementary angle is 83.0000000004.

When two angles add up to 90 degrees, they are said to be complimentary. When two angles add up to 180 degrees, they are said to be subservient. . When the sum of two angles equals 90 degrees, they are called complementary angles. For example, 30 and 60 degrees are supplementary angles. A supplementary angle is two angles that add up to 180 degrees, and a supplementary angle is two angles that add up to 90 degrees. of 30 and 60 degrees are supplementary. A supplementary angle is two angles combined to make a 180 degree angle, while a supplemental angle is two angles combined to make a 90 degree angle. Two angles are referred to as complimentary if their total is 90 degrees. Alternatively said, a right angle is created by the complementary angles (90 degrees).

here we have

(12x + 7) = 90

12x = 83

x= 6.9166666667

12x = 83.0000000004

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The division technique can be used to evaluate the given expression

12.75÷1. 5

The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are  (÷) and (/).

“p divided by q” can be written as: (p÷q) or (p/q).

The method of verification can be expressed as:

Dividend = (Divisor × Quotient) + Remainder.

The given equation is:12.75÷1.5

We'll first write the above decimal numbers in fractional form.

12.75÷1.5

1275/100÷15/10

2. Now we'll divide it further.

⇒1275/100÷15/10

⇒1275/100×15/10

⇒1275/10×15

⇒225/10×3

⇒88/10

3. And finally, we'll write our quotient in decimal form.

⇒88/10

⇒8.8

ㅤ

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The percent of the variance in the dependent variable unexplained by the independent variable is 81%

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.

9 percent of the variance is explained by the independent variable if the correlation coefficient is 0.3.

The correlation coefficient is therefore represented as follows:

[tex]r = 0.3[/tex]

The explained variance is found using the following formula:

[tex]R^{2} = r^{2} \\R^{2} = (0.3)^{2} \\R^{2} = (0.3)*(0.3)\\R^{2} = 0.9[/tex]

Thus, 81% of the variance remains unexplained by variations in the independent variable.

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As per the given percentage of tax and discount, the final cost of the milk is $3.8186

The term percentage in math is known as a relative value indicating hundredth parts of any quantity.

Here we have given that You buy a gallon of milk that costs $3. 50.

And here we also know that the milk is discounted for 10% off.

Here we have also have to pay tax of 6. 25% on the discounted price.

First we have to calculate the discounted prices, that can be obtained by the following calculation,

=> 3.50 - [3.50 x 10/100]

=> 3.50 - [3.50 x 0.1]

=> 3.50 - 0.35

=> 3.15.

Now, we have to calculated the tax for the price of the milk,

=> 3.50 + [3.50 x 6.25/100]

=> 3.50 + [3.50 x 0.0625]

=> 3.50 + 0.2186

=> 3.8186.

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[tex]8x+5y=-17[/tex] when y is -5

Substitute for y with given value:

[tex]8x+5(-5)=-17[/tex]

[tex]8x-25=-17[/tex]

Add 25 to both sides:

[tex]8x-25+25=-17+25[/tex]

[tex]8x=8[/tex]

Divide both sides by 8:

[tex]\dfrac{8x}{8} =\dfrac{8}{8}[/tex]

[tex]\fbox{x = 1}[/tex]

Answer: Hypotenuse

Step-by-step explanation:

The Hypotenuse is known as the longest side of a triangle.

The graph of tan(x/4) < 1/5 over the interval 0<= x<=2pi radians is attached. An approximate solution to the trigonometric inequality tan(x/4)<1/5 over the interval 0<= x<=2pi radians is 0 <= x < 0.7896.

y = 1/5 is a horizontal straight line parallel to x-axis.

Plot of tan(x/4)<1/5 over the interval 0<= x<=2pi radians is attached. The shaded region is the solution.

tan(x/4) < 1/5

Taking tan inverse on both sides

tan⁻¹(tan(x/4)) < tan⁻¹(1/5)

x/ 4 <  tan⁻¹(1/5)

Multiplying by 4 on both sides

x < 4tan⁻¹(1/5)

x < 0.7896

Applying the limits of intervals

0 <= x <= 2pi ≈ 6.28

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