What number should come next in the sequence? 0.8, 0.35, -0.1, -0.55, ... FASTTTTT

From all the steps below, we have been able to prove that; 1 - cot23° = 2/(1 - cot22°).

We want to prove that  1 - cot23° = 2/(1 - cot22°).

We will prove it using the trigonometric expression

cot(22° + 23°) = cot45°

Using trigonometric identities, we can rewrite as;

(cot22° cot23° - 1)/(cot22° + cot23°) = 1

Cross multiply to get;

cot22° cot23° - 1 = cot22° + cot23°

Rearrange to get;

cot22° cot23° - 1 - cot22° - cot23° =0

⇒ cot22° cot23° - 1 - cot22° - cot23° + 2 =2

⇒ cot22° cot23° + 1 - cot22° - cot23° =2

⇒ cot22° cot23° - cot22° - cot23° + 1 = 2

⇒ cot22° (cot23° - 1) - 1 (cot23° - 1) = 2

⇒ (cot22° - 1) (cot23° - 1) = 2

Divide both sides by  (cot23° - 1) to get;

cot23° - 1 = 2/(cot22° - 1)

⇒ 1 - cot23° = 2/(1 - cot22°).

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Answer:

D

Step-by-step explanation:

When f(x) is equal to 0, x=4.

Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²

Transformation is a techniques use to change the position of an object on an xy-plane.

Given the parent function f(x) = x² and the function g(x) = x²-12x +36

Factorize g(x);

g(x) = x²-6x-6x+36

g(x)=x(x-6)-6(x-6)

Group the terms to have;

g(x) = (x-6)²

Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²

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Answer:

transitive property

Step-by-step explanation:

This is the answer by definition.

The substitution property is demonstrated in the case of m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so, m∠AZF=m∠SZW+m∠LZF.

In order to find the value of the unknown, the substitution property is a concept in algebra that is used to substitute the value of a given variable or quantity into an expression.

According to the substitution property of equality, "If two variables x and y are equal, then x can be substituted for y in any equation or expression, and y can be substituted for x in any equation or expression."

According to the question, m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so by the substitution property, on substituting the value of  m∠AZL+m∠LZF in the first expression, we get, m∠AZF=m∠SZW+m∠LZF.

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Answer:

84

Step-by-step explanation:

Let the number of hamburgers be h and the number of cheeseburgers be c.

This means that:

Substituting c=3h into the first equation, it follows that 4h=336, and thus h=84.

Combining the terms into one fraction, we have

[tex]kx + b - \dfrac{x^3+1}{x^2+1} = \dfrac{(k-1)x^3 + bx^2 + kx + b - 1}{x^2+1}[/tex]

If this converges to 0 as [tex]x\to\infty[/tex], then the degree of the numerator must be smaller than the degree of the denominator.

To ensure this, take [tex]k=1[/tex] and [tex]b=0[/tex]. This eliminates the cubic and quadratic terms in the numerator, and we do have

[tex]\displaystyle \lim_{x\to\infty} \frac{x - 1}{x^2 + 1} = \lim_{x\to\infty} \frac{\frac1x - \frac1{x^2}}{1 + \frac1{x^2}} = 0[/tex]

Alternatively, we can compute the quotient and remainder of the rational expression.

[tex]\dfrac{x^3+1}{x^2+1} = x - \dfrac{x-1}{x^2+1}[/tex]

Then in the limit, we have

[tex]\displaystyle \lim_{x\to\infty} \left(kx + b - x + \frac{x-1}{x^2+1}\right) = (k-1) \lim_{x\to\infty} x + b = 0[/tex]

Both terms on the left vanish if [tex]k=1[/tex] and [tex]b=0[/tex].

Answer: 2

Step-by-step explanation: 66-52 is 14 and 14/7=2

Answer:

5

Step-by-step explanation:

where there is the decimal point,you count the numbers after the decimal point

Answer:

xy-49

Step-by-step explanation:

x x y is xy and -7x7 is 49 so the answer is xy- 49

The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given the polynomial:

-2x³ - 7x² + 3x - 4

Simplifying:

= -(2x² - x + 1)(x + 4)

Hence:

-2x³ - 7x² + 3x - 4 = (-2x² + x - 1)(x + 4)

(x + 4)(ax² + bx + c) = −2x³ − 7x² + 3x − 4

The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.

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792 different sets of 7 colors can be chosen.

Remember that if we have a set of N elements, the number of different sets of K elements that we can make out of these N elements is given by:

C(N, K) = N!/(N - K)!*K!

In this case, we have 12 distinct colors and we want to select 7, so we have:

N = 12

K = 7

Replacing that we get:

C(12, 7) = 12!/(12 - 7)!*7! = 12*11*10*9*8/(5*4*3*2*1) = 792

792 different sets of 7 colors can be chosen.

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Answer:

piex

Step-by-step explanation:

the circumference of a circle is pie times the diameter of the circle.

1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t

2. the distance travelled at time t = 3.5 h is 18 Km

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

From the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.

Thus, we shall determine the distance travel in time t as follow

Speed = distance / time

12 = distance / t

Cross multiply

Distance = 12 × t

Distance in time t = 12t

But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:

s = 60 - 12t

Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t

The distance at t = 3.5 hours can be obtained as illustrated below:

s = 60 - 12t

s = 60 - (12 × 3.5)

s = 60 - 42

s = 18 Km

Thus, the distance travelled at t = 3.5 hours is 18 km

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If the points of the vertices are (-3,1_,(4,2),(9,-3),(2,-4) then the perimeter of the figure is 28.28 units.

Given points of the vertices of the figure having four sides be (-3,1),(4,2),(9,-3),(2,-4).

We have to find the perimeter of the figure.

Perimeter is the sum of lengths of all the sides of a figure.

First give some name to the points so that it will be easy to understand the sides like A(-3,1),B(4,2),C(9,-3),D(2,-4).

Perimeter of the figure =AB+BC+CD+DA

AB=[tex]\sqrt{(2-1)^{2} +(4+3)^{2} }[/tex]

=[tex]\sqrt{1+49}[/tex]

=[tex]\sqrt{50}[/tex] units

BC=[tex]\sqrt{(9-4)^{2} +(-3-2)^{2} }[/tex]

=[tex]\sqrt{25+25}[/tex]

=[tex]\sqrt{50}[/tex]units

CD=[tex]\sqrt{(2-9)^{2} +(-4+3)^{2} }[/tex]

=[tex]\sqrt{49+1}[/tex]

=[tex]\sqrt{50}[/tex] units

DA=[tex]\sqrt{(2+3)^{2} +(-4-1)^{2} }[/tex]

=[tex]\sqrt{25+25}[/tex]

=[tex]\sqrt{50}[/tex] units

Perimeter=[tex]\sqrt{50} +\sqrt{50} +\sqrt{50} +\sqrt{50}[/tex]

=4[tex]\sqrt{50}[/tex]

=4*5*[tex]\sqrt{2}[/tex]

=20[tex]\sqrt{2}[/tex]

=20*1.411

=28.284

After rounding off we will get 28.28 units.

Hence if the points of the vertices are (-3,1_,(4,2),(9,-3),(2,-4) then the perimeter of the figure is 28.28 units.

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The required sales in dollars needed to achieve managements target is $607,5000.

Net income is total revenue less total cost. Total cost is the sum of fixed cost and variable cost. Fixed cost is the cost that remains constant regardless of the level of output. e.g. rent. Variable cost is the cost that varies with output e.g. wages.

Net income = sales - total cost

Net income = sales - (fixed cost + variable cost)

$67,500 = sales - ($175,500 + 0.6sales)

$67,500 = sales - $175,500 - 0.6sales

$67,500 + $175,500 = sales - 0.6sales

243,000 = 0.4sales

sales = 243,000 / 0.4

sales = $607,500

Here is the complete question:

For Pharaoh Company, variable costs are 60% of sales, the fixed costs are $175,500. Managements net income goal is $67,500.Compute the required sales in dollars needed to achieve managements target net income of $67.500.

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Answer:

2 Inches or ~1.43 Inches

Step-by-step explanation:

2 Inches if it's not including the spacing before the first "E" and after the "S", ~1.43 Inches if it's including the spacing.

You would get 2 Inches since if each letter is 10 inches (total 6 letters), that would be 60 inches. There are 5 total spaces in between all the letters. 70 Inches(Banner size) - 60 Inches (total letter size) = 10 Inches, divided equally within the 5 spaces. That would equal 2 :)

You also get ~1.43 Inches by doing the same process as the one shown above^ (that is if you're including the spacing before and after the word)

:)

The value of Quotient from the given terms is 9.6* 10^8

According to the statement

we have given that the two terms and we have to find the quotient of the these terms.

So, we know that the

Quotient is a the number resulting from the division of one number by another.

And for find the quotient we have to divide the terms with each other.

So, The given terms are [tex]7.536*10^7[/tex]and [tex]7.85*10^2[/tex]

divide both terms with each other.

Quotient = [tex]\frac{7.536*10^7}{7.85*10^2}[/tex]

Then

The value of quotient becomes

Quotient = [tex]0.96 * 10^9[/tex]

After removing the decimal from the answer it will become

Quotient = [tex]9.6* 10^8[/tex].

So, The value of Quotient from the given terms is 9.6* 10^8

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Answer: its 7.85x10^-9

Step-by-step explanation:

Step-by-step explanation:

It is just where it crosses the x axis

6) -3, -4

7) 1, -6

8) -5, -6

9) 3, -2.5

6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.

How long should she keep the remaining amount to get a total interest of Rs 6,800 from the beginning:

The rate of 8% p.a. in her saving account.

20,000 at 8% interest for 2 years:

= 20,000*2*8/100

= 3200

5000 was withdrawn after 2 years and earned interest.

After 2 years, the new principal:

= 20000- 5000

=15000

She needs to get interested of 6800–3200 =3600 for the next N years.

N= 100* I /PR

= 100*3600/(15000*8)

=3

6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.

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Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.

For the principal [tex]P[/tex] and the rate of interest [tex]r\%[/tex] per annum, the total interest after [tex]t[/tex] years is given by the formula: [tex]I=\dfrac{Prt}{100}[/tex].

Given that Sajina deposited Rs 20,000 at the rate of 8% p.a. in her savings account.

So, [tex]P=20,000[/tex] and [tex]r=8[/tex].

Thus, after t=2 years the total interest would be

[tex]I=\dfrac{Prt}{100}\\\Longrightarrow I=\dfrac{20000\times 8\times 2}{100}\\\therefore I=3200[/tex]

So, the total interest after 2 years would be Rs 3,200.

Given that Sajina withdrew Rs 5,000 and the total interest of 2 years.

So, the new principal will be [tex]P'=20,000-5,000=\test{Rs}\hspace{1mm}15,000[/tex].

The total interest she wanted to gain is Rs 6,800. She had already gained Rs 3,200.

so, the remaining interest [tex]I'=6,800-3,200=\text{Rs}\hspace{1mm}3,600[/tex].

Let the required time be [tex]t'[/tex] years after how many years she got a total interest of Rs 6,800 from the beginning.

For principal [tex]P'=15,000[/tex], rate of interest [tex]r=8\%[/tex]; the total interest after [tex]t'[/tex] years would be [tex]I'=\dfrac{P'rt'}{100}=\dfrac{15000\times 8\times t'}{100}=1200t'[/tex]. But given that [tex]I'=3600[/tex].

So, we must have

[tex]1200t'=3600\\\Longrightarrow t'=\dfrac{3600}{1200}\\\therefore t'=3[/tex]

Therefore, Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.

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The correct answer is  If x + 1 is odd, then x is even.

The converses of the conditional statement:

"If q then p" provides the converse statement to the conditional expression "If p then q."

The converse of the conditional statement is  If x + 1 is odd, then x is even.

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Answer

B

explanation

3480ones = 3480x1=3480

Answer:

40

Step-by-step explanation:

19*2 = 38 + 2 = 40

Answer:

Step-by-step explanation:

we have to get k by itself on one side of the equal sign. To do that we have to get rid of 3. To get rid of 3 we have to do the opposite. The opposite of +3 is -3 so we -3 on both sides. 19 - 3 = 16. So k = 16

k+3=19

 -3  -3

   k=16

Answer:

It could be 105, 112 or 133.

Step-by-step explanation:

Having 7 as a factor means it is a multiple of 7.

The first 3 digit multiple of 7: 100 ÷ 7 = 14 2/7 → first 3 digit multiple of 7 is 15 × 7 = 105

Last 3 digit multiple of 7 less than 140: 140 ÷ 7 = 20 → last 3 digit multiple of 7 less than 140 is 19 × 7 = 133

→ The possible multiples of 7 to consider are [15..19] × 7 which gives 105, 112, 119, 126 and 133.

The sum of the digits of these number is:

105 → 1 + 0 + 5 = 6

112 → 1 + 1 + 2 = 4

119 → 1 + 1 + 9 = 11

126 → 1 + 2 + 6 = 9

133 → 1 + 3 + 3 = 7

Of these sums only 6, 4 and 7 are less than 9, thus the possible numbers are 105, 112 or 113.

Answer: d = 1/3

Step-by-step explanation: 48y = 48/4 = 12. So, 2d(18) is equal to 12. 12/18 is 2/3 so 2d has to equal 2/3. That means d = 1/3.

The perimeter of the minor segment is 77. 4m

The formula for determining the perimeter of the minor segment is given as;

Perimeter = θ/360 × 2πr + 2r sin θ/2

where;

Substitute into the formula;

Perimeter = (72/360 × 2 × 3. 142 × 24. 5) +( 2 × 24. 5 × sin 72)

Perimeter = 30. 79 + 46. 60

Perimeter = 77. 4 m

Thus, the perimeter of the minor segment is 77. 4m

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The combination shows that the numbers of possible live card hands drawn without replacement from a standard deck of 52 playing cards is 2,598,960.

A permutation is the act of arranging the objects or numbers in order while combinations are the way of selecting the objects from a group of objects or collection such that the order of the objects does not matter.

Since the order does not matter, it means that each hand is a combination of five cards from a total of 52.

We use the formula for combinations and see that there are a total number of C( 52, 5 ) = 2,598,960 possible hands.

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Answer:

l = 2.25 cm

Step-by-step explanation:

given l is inversely proportional to w² then the equation relating them is

l = [tex]\frac{k}{w^2}[/tex] ← k is the constant of proportion

(i)

to find k use the condition w = 1.5 , l = 16 , then

16 = [tex]\frac{k}{1.5^2}[/tex] = [tex]\frac{k}{2.25}[/tex] ( multiply both sides by 2.25 )

36 = k

l = [tex]\frac{36}{w^2}[/tex] ← equation of proportion

(ii)

when w = 4 , then

l = [tex]\frac{36}{4^2}[/tex] = [tex]\frac{36}{16}[/tex] = 2.25 cm

The value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2. This can be obtained by using Pythagoras' theorem.

This question can be solved using Pythagoras' theorem,

If in a right angled triangle, hypotenuse is the longest side of the triangle and always opposite to the angle 90°, height and base are the two shorter sides which are adjacent to the angle 90°.

If hypotenuse = c, height = a and base = b then,

⇒ hypotenuse² = height² + base²

⇒ c² = a² + b²

Here in the question it is given that,

By using the Pythagoras' theorem we can write that,

⇒ hypotenuse² = height² + base²

⇒  6² =  a² + a²

⇒  36 =  2a²

By dividing both sides of the equation by 2,

⇒  18 =  a²

⇒  a² = 18

By taking square on both side of the equation,

⇒ a = 3√2 inches

Hence the value of a is 3√2 inches if it is given that the hypotenuse is        c = a√2 and 6 = a√2.

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Using the z-distribution, it is found that since the p-value is less than 0.02, we reject the null hypothesis.

At the null hypothesis, it is tested if the proportion is of at most 59%, that is:

[tex]H_0: p \leq 0.59[/tex]

At the alternative hypothesis, it is tested if the proportion is greater than 59%, hence:

[tex]H_1: p > 0.59[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]p = 0.59, n = 900, \overline{p} = 0.63[/tex]

Hence the value of the test statistic is found as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.63 - 0.59}{\sqrt{\frac{0.59(0.41)}{900}}}[/tex]

z = 2.44.

Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is higher than a value, with z = 2.44, the p-value is of 0.0073.

Since the p-value is less than 0.02, we reject the null hypothesis.

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The number of copies sold (x) to date is 463043

The given parameters are:

Copies sold = 42,600

Proportion sold = 9.2% of the number of copies sold to date.

The number of copies sold (x) to date is calculated as:

Copies sold = Proportion * number of copies sold to date

Substitute the known values in the above equation

9.2% * x = 42,600

Divide both sides by 9.2%

x = 463043

Hence, the number of copies sold (x) to date is 463043

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