Find the value of the indicated trigonometric ratio.

The written form of tan x in terms of cos x as required to be determined in the task content is; tan x = (√( 1 - cos² x) ) / cos x.

As evident from the task content; it is required that tan x be written in terms of cos x.

Hence, recall from trigonometric identities that;

tan x = sin x / cos x

However, since sin² x = 1 - cos² x from ( sin²x + cos²x = 1)

It follows that; sin x = √( 1 - cos² x)

Hence, it can be written that;

tan x = (√( 1 - cos² x ) ) / cos x.

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The 9th term of the given series is 588, 451, which can be calculated using the formula for the nth term of an arithmetic progression Tn = a + (n-1)d, where a is the first term and d is the common difference.

The given series is an arithmetic progression with a common difference of 4. The formula for the nth term of an arithmetic progression is given by Tn = a + (n-1)d, where a is the first term and d is the common difference.

Therefore, for the given series, a = 1 and d = 4.

Substituting these values in the above formula, we get

T9 = 1 + (9-1)4

 = 1 + 32

 = 33

Now, adding 33 to each of the terms of the given series, we get

1 + 33 = 34

5 + 33 = 38

25 + 33 = 58

125 + 33 = 158

Therefore, the required 9th term of the series is 588, 451.

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The probability of all the defendants being found guilty is 1/16. Answer: 1/16.

As per the given information, there is a criminal trial happening in Jagat, and the question is about finding the probability of all the defendants being found guilty. Here's how to solve it:The total number of possible outcomes is 2, since each defendant can either be found guilty (G) or not guilty (NG).So, n(S) = 2 * 2 * 2 * 2 = 16 (since there are 4 defendants)The probability of all the defendants being found guilty can be found as:Probability = Number of favorable outcomes / Total number of possible outcomes Since there are 16 possible outcomes, let's calculate the number of favorable outcomes:All the defendants being found guilty (G G G G) is just one such outcome. Hence, the number of favorable outcomes is 1.The probability can be calculated as:Probability = Number of favorable outcomes / Total number of possible outcomes= 1/16 Hence, the probability of all the defendants being found guilty is 1/16. Answer: 1/16.

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Answer:

The first five natural number are 1, 2, 3, 4 and 5. Hence, the mean of the five natural numbers is 3.

Answer:

3

Step-by-step explanation:

[tex]\frac{1+2+3+4+5}{5}[/tex] =  [tex]\frac{15}{5}[/tex] = 3

The natural numbers are also called the counting numbers.  They are the set of numbers: 1, 2, 3, ....

Helping in the name of Jesus.

Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in the ratio of 2:3.

To solve this problem, we need to use the concept of ratio and proportion.

Let's first find the total amount of money contributed by Sam and Terry. Since the ratio of their contributions is 2:3, we can write:

Total contribution = Sam's contribution + Terry's contribution

Let's assume that Sam contributed $2x and Terry contributed $3x. Then, we have:

Total contribution = $2x + $3x = $5x

Now, we know that the total contribution is equal to the price of the juice, which is not given in the problem. So, let's assume that the price of the 2-litre tub of juice is $10. Then, we have:

Total contribution = Price of juice = $10

Therefore,

$5x = $10

Solving for x, we get:

x = $2

So, Sam contributed $4 and Terry contributed $6.

Now, to find the amount of juice each one received, we need to share the 2-litre tub in a ratio of 2:3.

The total ratio is 2+3 = 5.

So, Sam will receive 2/5 of the juice and Terry will receive 3/5 of the juice.

Therefore, Sam will receive (2/5) × 2 litres = 0.8 litres of juice, and Terry will receive (3/5) × 2 litres = 1.2 litres of juice.

In conclusion, Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in a ratio of 2:3.

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Answer:

4c + 2d + 10

Step-by-step explanation:

The expression given is mostly already simplified, and the like terms that have variables are already combined.

As for 7 and 3, they are like terms because neither of them are attached to a variable.

Combining these like terms:

The equivalent expression is now 4c + 2d + 10.

Answer:

P(odd or at most 14)

Answer: (a) 7/27, 0.2593, 25.93%

P(king)

Answer: (d) 13/52

P(spade or heart)

Answer: (b) 1/2

Answer:

Step-by-step explanation:

[tex]a)\quad AB[/tex]

[tex]b)\quad AB[/tex]

[tex]c)\quad AC[/tex]

[tex]d)\quad BC[/tex]

[tex]e)\quad BC[/tex]

[tex]f)\quad AC[/tex]

Answer:

    m∠4 = 133°

Step-by-step explanation:

Given m∠7 = 37°

Since m∠7 ≅ m∠6 [Vertically opposite angles]

and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]

Therefore, 47°+ m∠4 = 180°

m∠4 = 180 - 47

       = 133°

The correct statement is a=b implies that ac=bc.

If the real numbers a and b are such that a=b, then their values are equal.

The result of adding c to both sides of the formula a=b is:

a+c = b+c

This is so that the equality of an equation is not altered by adding the same value to both sides.

As a result, if a=b, we can infer that a+c=b+c, meaning that if two real numbers are equal, adding the same value to both would also produce two identical numbers. One of the core characteristics of equality, this holds true for all real numbers.

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The volume of the stone is 1032 cm³.

The volume of the stone can be calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 2.7 cm. Therefore, the volume of the stone is V = 10 x 24 x 2.7 = 648 cm³.

The volume of the water in the container is calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 7 cm. Therefore, the volume of the water in the container is V = 10 x 24 x 7 = 1680 cm³.

The difference between the volume of the water and the volume of the stone is the volume of the water displaced by the stone, which is V = 1680 - 648 = 1032 cm³. Therefore, the volume of the stone is 1032 cm³.

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The answer will be as follows after answering the supplied question As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is the location of one of the points and m is the line's slope.

We may use the slope formula to calculate the slope:

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

where the coordinates of the two points are (x1, y1) and (x2, y2).

m = (5 - (-3)) / (3 - (-1)) = 8 / 4 = 2

As a result, the slope of the line is 2. We can now use one of the two locations to get the equation of the line. Let's take (-1, -3) as an example:

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

y + 3 = 2(x + 1)

y + 3 = 2x + 2

y = 2x - 1

As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.

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a) The basic formula is [tex]y=v_0t-gt^2/2[/tex]

[tex]9.81m/sec^2 x \ t^2 - (14 m/sec x t) - 60m = 0[/tex]

quadratic equation t= -b+/- √b^2-4ac /2a

t= 14+- √(-14)^2 -4(4.905)(-60)/ 2(4.905) = 5.20 sec

b) [tex]y=v_0t-gt^2/2[/tex]

At max height H, [tex]V_y = 0[/tex]

[tex]Vy^2 = V^2_{0y} - 2g(y-y_0)[/tex]

[tex]0=(14)^2 -2(9.81)(H-60)[/tex]

[tex]H=70m[/tex]

The ball would fall 10m from max height of 70m. set y=0 and H=10m

[tex]y=gt^2/2+H, t = 1.42 \ sec[/tex].

[tex]\bold{Therefore, 5.2 - 1.42 = 3.77 \ sec}[/tex]

Matthew who started an annuity on his 25th birthday by depositing $630 monthly into an account earning 8% annual interest compounded monthly will become 55 years old when the retirement account will be $1,000,000.

An annuity involves a series of payments made periodically.

The annuity attracts an interest rate compounded periodically.

Compounding involves charging interest on accumulated interest and the principal for each compounding period.

I/Y (Interest per year) = 8%

PV (Present Value) = $0

PMT (Periodic Payment) = $630

FV (Future Value) = $1,000,000

Results:

N = 368.641 months

= 30 years and 9 months

Sum of all periodic payments = $232,470

Total Interest = $767,530

Matthew's current age = 25 years

55 years old (25 + 30)

Thus, Matthew will be 55 years old when his retirement (annuity) account grows to $1,000,000.

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Answer : There are 84 different ways that six letters can be grouped from nine letters total.

Now that we have determined that the problem deals with combinations, we can use the formula for combinations to calculate the number of ways that six letters can be grouped from nine letters total. The formula for combinations is:

C(n,k) = n! / (k! * (n-k)!)

Where n is the total number of items, and k is the number of items being chosen. In this case, n = 9 and k = 6. Plugging these values into the formula gives us:

C(9,6) = 9! / (6! * (9-6)!)

C(9,6) = 9! / (6! * 3!)

C(9,6) = 362880 / (720 * 6)

C(9,6) = 362880 / 4320

C(9,6) = 84

Therefore, there are 84 different ways that six letters can be grouped from nine letters total.

Answer: 84.

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On answering the provided question, we have got that 3.3 is the average  equation result after rolling the dice ten times.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

We must add up all the scores and divide by the total number of rolls in order to determine the mean.

The total of every score is:

1 + 1 + 2 + 2 + 3 + 1 + 4 + 2 + 5 + 4 + 6 + 2 = 33

There are ten rolls in total.

The mean is as a result:

mean = total scores / total rolls = 33 / 10 = 3.3

3.3 is the average result after rolling the dice ten times.

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Answer:

£10,000

Step-by-step explanation:

100%-20%= 80% --> 0.8

£8000 divided by 0.8 = £10,000

As a result, the right triangle x value of 65° is the answer to the given triangle issue.

Triangles are categorised as polygons because they have four edges or more. Its shape is simple and symmetrical. The characters ABC make a square angle that is a triangle. When the edges are still not collinear, Euclidean geometry yields a single rectangle or square. Due to their three edges and three corners, triangles are considered polygons. The corners of a triangle are where its three edges meet. Angles in a trapezoid add up to 360 °.

Here,

Given:

Triangle is 90 degrees because of its right orientation.

The total of the triangle's angles is 180 degrees.

Thus,

=> x + 25° + 90° = 180°

=> x + 115° = 180°

=> x = 180° -115°

=> x = 65°

Thus, the value of x is 65°.

As a result, the answer to the provided triangle problem is

Right triangle's x number is 65 degrees.

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a) The total cost, c, in dollars, of Theo's order based on the number of

bagels, b, he buys is: c = 0.75b + 3.5

b) The statement c(6) = 8 represents that the number of bagels bought was 6 which resulted in a total cost of $8

The general expression for a linear equation in slope intercept form is:

y = mx + b

Where:

m is slope

b is y-intercept

a) Let the number of bagels bought be b

Cost of each bagel = $0.75

Cost of chocolate = $3.50

Thus:

Total cost is:

c = 0.75b + 3.5

b) c(6)=8

This means the number of bagels bought was 6 which resulted in a total cost of $8

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The real cube root of 64 is 4.

The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.

the prime factorization using the exponent found in the previous step. We can write the number 64 as:

64 = 2^2 * 2^2 * 2^2

Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:

∛2 = 1.259921...

Step 5: Multiply the factors together to get the final result:

∛64 = ∛(2^2 * 2^2 * 2^2) = ∛2^6 = (∛2)^2 = 1.259921...^2 = 4

Therefore, the real cube root of 64 is 4.

On the other hand we can easily find out by, the real cube root of 64 is 4, because 4 multiplied by itself three times gives 64:

4 * 4 * 4 = 64

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The real cube root of 64 is 4.

What is a Real cube root?

The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.

the prime factorization using the exponent found in the previous step. We can write the number 64 as:

64 = 2² * 2² * 2²

Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:

∛2 = 1.259921...

Step 5: Multiply the factors together to get the final result:

∛64 = ∛(2² * 2² * 2²) = ∛2⁶ = (∛2)² = (1.259921...)² = 4

Therefore, the real cube root of 64 is 4.

On the other hand, we can easily find out by, the real cube root of 64 is 4 because 4 multiplied by itself three times gives 64:

4 * 4 * 4 = 64

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The answer is in the attachment given below ...

Thank you :)

The increase in the rate of unemployment from 2000 to 2001, given the unemployment figure is between D. 0. 46 % and 0. 49 %.

First, find the rate of unemployment in 2000 to be :

= Unemployment number / Total labor force x 100 %

= 3, 503, 917 / 25, 554, 417  x 100 %

= 13.71  %

The rate of unemployment in 2001 was :

= 3, 745, 300 / 26, 416, 800 x 100 %

= 14. 18 %

The increase in the rate of unemployment is:

= 14. 18 - 13. 71

= 0. 47 %

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The equivalent unit of production- Weighted Average Method is given in the attached image.

The equivalent units of production (EUP) in the weighted average method refer to the units of output that have been partially completed during a period, and are expressed in terms of fully completed units.

In the weighted average method, the costs incurred during the period are combined with the costs of beginning work in process (BWIP) to determine the cost per equivalent unit. This cost per equivalent unit is then used to assign costs to the units completed and transferred out and to the units still in process at the end of the period.

The EUP in the weighted average method is calculated by adding together the units completed during the period with the equivalent units of work done on the units that are still in process at the end of the period.

The equivalent units are calculated by multiplying the number of partially completed units by the percentage of completion for the period.

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Answer:

(3h+4)(2h+3)

Step-by-step explanation:

6h^2 + 8h + 9h + 12h

(6h^2+8h) + (9h+12h)

2h(3h+4) + 3(3h+4)

(3h+4)(2h+3)

Answer:

(3h+4) (2h+3)

Step-by-step explanation:

i hope this helps

Liam saved $192.05 from his summer jobs.

It is based on the probability that something will happen. The fundamental underpinning of theoretical probability is the justification for probability. For instance, while flipping a coin, there is a 50% probability that it will land on its head.

By deducting his outgoings from his total earnings, we can calculate how much money Liam saved:

m = 328.65 - 136.60

Condensing the phrase:

m = 192.05

Liam was able to save $192.05 as a result of his summer jobs.

The following equation and its answer demonstrate how much money Liam has saved:

m = 328.65 - 136.60

m = 192.05

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Step-by-step explanation:

16.41 ft / 5 m = 'unit rate' (or conversion factor) = 3.282 ft/ m

then    # ft = 3.282 ft / m   *  # meter     (approximately )

Answer: Answers below

Step-by-step explanation:

1. $15.64

2. 5370.28 Yen

3. 13425.70 Yen

4. $100

5. 67128.51 Yen

6.$782.08

Answer: 1: 15 2: 5370 3:13400 4: 160 5: 67100 6: 780

Step-by-step explanation: These are rounded to the nearest 100th

By answering the above question, we may state that Multiplying these equation prime factorizations together, we get:

[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]

A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.

then multiply the prime factors together using the laws of exponents.

[tex]12^9 = (2^2 · 3)^9 = 2^18 · 3^9\\36^15 = (2^2 · 3^2)^15 = 2^30 · 3^30\\169^8 = 13^16\\12^9 · 36^15 · 169^8 = (2^18 · 3^9) · (2^30 · 3^30) · 13^16 = 2^48 · 3^39 · 13^16\\[/tex]

(b)

[tex]16^13 = 2^52\\10^7 = 2^7 · 5^7\\81^18 = (3^4)^18 = 3^72\\[/tex]

Multiplying these prime factorizations together, we get:

[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]

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Answer:

B. [tex]\sqrt[3]{-x-9}[/tex]

Step-by-step explanation:

Switch x and y, and then solve for y.

[tex]y = -x^3-9\\x=-y^3-9\\x+9=-y^3\\-x-9=y^3\\\sqrt[3]{-x-9} =y[/tex]