If 2x and 4x are complementary angles,find them

The recursive formula for the given problem is W(n) = W(n-1) + 2 * W(n-1), with the base case W(0) = 1. This formula calculates the number of n-letter "words" that can be created from an unlimited supply of 'a's, 'b's, and 'c's,

To derive the recursive formula, we consider two cases for the first letter of the word: either it is an 'a' or it is not. If the first letter is 'a', we need to ensure that the remaining (n-1) letters form a word with an even number of 'a's. Therefore, the number of words in this case is equal to W(n-1), as we are recursively solving for the remaining letters.

If the first letter is not 'a', we have the freedom to ch

oose from 'b' or 'c'. In this case, we have two options for each of the remaining (n-1) letters, resulting in 2 * W(n-1) possibilities. By summing these two cases, we obtain the recursive formula W(n) = W(n-1) + 2 * W(n-1), which calculates the total number of n-letter words satisfying the given criteria.

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The function that best represents the value of the computer in months is V(t) = 1,300(.61^(t/12)).Where t is the number of months since the computer was purchased

The given function V(t) = 1,300(.61), models the value of a computer in terms of the number of years since it was purchased. The value of the computer is represented by the function V(t) which is directly proportional to (0.61) raised to the power of t. Divide the t by 12, because there are 12 months in a year, to get the value in months.

As a consequence, the calculation V(t) = 1,300(.61(t/12)) displays the computer's value in terms of months from purchase. It demonstrates the decline in the value of the computer over time.

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Answer:

16

Step-by-step explanation:

The figure shown is a trapezoid

Area of a trapezoid = 1/2(bottom base length + top base length) × height

Bottom base length = 7 units

Top base length = 1 unit

Height = 4 units

So area = 1/2 ( 7 + 1 ) × 4

==> add 7 and 1

Area = 1/2 (8) × 4

==> multiply 1/2 and 8

Area = 4 × 4

==> multiply 4 and 4

Area = 16

Answer:

vertex is (6, -11)

Step-by-step explanation:

Given equation
f(x) = x² - 12x + 25

is that of an upward-facing parabola(since the coefficient of x² is positive).

The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x

f'(x) = d/dx(x² - 12x + 25)

= 2x - 12

f'(x) = 0 ==> 2x - 12 = 0

2x = 12

x = 6

Substitute x = 6 in f(x) to get

f(6) = 6² - 12(6) + 25

= 36 - 72 + 25

= -11

So the vertex is at (6, -11)

The probability that fewer than 3 of them use their smartphones in meetings or classes is 0.0366.

The binomial probability distribution is a discrete probability law with two parameters: trial number (n) and success probability (p) (p). When there are two mutually exclusive outcomes of finite trials, the binomial distribution is utilised.

The probability that a specific 3 people all use their smartphones in meetings or class is 0.53³.

Probability that remaining 7 people do not use their phone is 0.47⁷

¹⁰C₃ = 10*9*8/(3*2*1) = 120.

Thus, the probability of exactly 3 people using their smartphones in meetings or in class is 10C3*0.533*0.477, or 0.0905.

So, adding up the 3 possibilities (that 0 of them, 1 of them, or 2 of them use their smartphones in meetings or class) we get

¹⁰C₀*0.530*0.4710 + ¹⁰C₁*0.531*0.479 + ¹⁰C₂*0.532*0.478 = 0.0366.

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Complete question:

Assume that when adults with smartphones are randomly​ selected, 53​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

Answer:

5/3*1/5= 1/3

Step-by-step explanation:

change the mixed fraction into improper fraction which is 1*3+2=5

then multiply

Answer:

Step-by-step explanation:

The pattern of this sequence is : From a term, we minus 6 to get to the next term

107 - 6 = 101
101 - 6 = 95
So on and so on.

The difference between 107 and -61 is : 107 - (-61) = 168

Everytime we go to the next term, we get 6 units closer to -61

So, -61 will be the 168 : 6 = 28th term of this arithmetic sequence.

The answer of the given question based on the saving bank account  , the equation will be Savings = 120 + 30x.

A bank savings account is one simplest type of bank account. It allows you to keep your money safely while earning through interest per month. Money in a savings account is useful for emergencies since they are insured. You also get a card which enables you to withdraw or deposit money into your account. Parent's usually take this type of account for their children for future purposes.

Let x represent the number of weeks that has passed since Hannah opened the bank account.

Therefore, the equation that represents her savings is:

Savings = (amount of money deposited initially) + (amount of money added per week x number of weeks)

In this case, the amount of money deposited initially is $120, and

the amount of money added per week is $30.

Therefore, the equation is:

Savings = 120 + 30x

Note that "x" represents the number of weeks that have passed since Hannah opened the account.

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For the linear equations provided by the coordinates in the table;

The first equation of this system is y = -2x.

The second equation of this system is y = x - 3.

The solution to the system is (1, -2).

We have four points (-5,10), (-1,2), (0,0), and (11,-22) for first equation, and four points (-8,-11), (-2,-5), (1,-2), and (7,4) the second equation.

The slope (m) is given by the formula (y2 - y1) / (x2 - x1).

For the first line, we can use the points (-5,10) and (-1,2)

m1 = (2 - 10) / (-1 - (-5)) = -8/4 = -2.

the first equation is y = -2x

the second line, we can use the points (-8,-11) and (-2,-5)

m2 = (-5 - -11) / (-2 - -8) = 6/6 = 1.

the second line has a slope of 1,

the equation should have the form y = x + c.

To find c, we can use one of the points, for instance (-2,-5):

-5 = -2 + c => c = -5 + 2 = -3.

So, the second equation is y = x - 3.

the solution to the system, we need to find where the two lines intersect.

y = -2x

y = x - 3

Setting both equation equally

-2x = x - 3

=> 3x = 3

=> x = 1.

Substituting x = 1 into the first equation

y = -2(1) = -2.

the solution to the system of linear equation would be (1, -2).

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Step-by-step explanation:

8) all real numbers.

10)

\(y = a {b}^{x} \\ 12 \div 4 = 3 \\ b = 3 \\ a = 4 \\ y = 4 \times {3}^{x} \)

Answer:

c approx= 3.46

Step-by-step explanation:

30°-60°-90° triangle is a Special Right Triangle. There's a great short cut to find the sides if you know any one side. No trig or Pythagorean Theorem necessary (but that is where the short cut comes from)

The hypotenuse is double the short leg OR the short leg is half the hypotenuse. The long leg is the short leg times the sqroot3. In your question we know the long leg is 3.

3÷ sqroot3 = sqroot3

The short leg is sqroot3. The hypotenuse is double that, 2sqroot3.

c = 2sqroot3 is the exact value.

c ~= 3.46

Answer:

(8,0)

and infinite number of ordered pairs make the equation

true 4,4 ... 5,3 ... 9,-1 ....

the solution can be said to be the loation where the graph crosses the x axis that point is (8,0)

Step-by-step explanation:

The age of the artifact is 3523.77 years.

What is radioactive decay?

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Here,

The half-life of the reaction is defined as the time required by a substance to reach half its initial concentration. It is represented by t(1/2)

 All radioactive decay processes follow the first-order reaction.

The equation for the half-life for first-order reaction follows:

t(1/2) = 0.693/k....(1)

where,

k = rate constant of a first-order reaction

Given value:

t(1/2) = 5715 years

Put the value of t in equation (1), and we get

k = 0.693/5715

k = 1.21×10⁻⁴yr

The integrated rate law expression for first-order reaction follows:

t = 2.303/k×㏒(a/(a-x))

where,

t = time period

a = initial concentration of the reactant = 58.2 counts per minute

(a-x) = Concentration of reactant left after time t = 38.0 counts per minute

k = rate constant of a first-order reaction

Put the values in the equation and we get

t = 2.303/1.21×10⁻⁴㏒58.2/38

t = 3523.77 years.

Hence, the age of the artifact is 3523.77 years.

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Answer:

Step-by-step explanation:

We can use the interest equation (mind you it is the same thing as said in the problem) to solve this:

\(A=P(1+\frac{r}{n})^{nt}\)

Where A is the resulting amount, r is the interest rate, n is the number of times compounded per year and t is the time.

\(A=1209(1+\frac{.082}{12} )^{12*26}\)

A = $10,120.29

Answer:

20

Step-by-step explanation:

8*50=400 /4*5=20

400/20=20

Answer:  -20

Step-by-step explanation:

-8 by 50   ÷   4 by 5

-8 × 50     ÷    4 × 5

\(\dfrac{-8\times 50}{4\times 5}\\\\\\=\dfrac{-2\times 10}{1\times 1}\\\\\\=\large\boxed{-20}\)

Answer:

Option d: 6x +1

Step-by-step explanation:

Answer:

x=4.75

Step-by-step explanation:

16(4x-3)=8(2x+4)

16*4x-3=8*2x+4

    -2x       -2x

16*2x-3=8*4

multiply 8*4=32

16*4x-3=32

-16         -16

4x-3=16

   +3 +3

4x=19

divide 4 by both sides

x=4.75

Answer:

42,857 hours

Step-by-step explanation:

Saturn is about 1.2 billion miles away from earth. If the space shuttle is traveling 28,000 kmph then it would take about 42,857 hours.

Answer:

C

Step-by-step explanation:

After rotation the hexagon 180° you will have the same image that you started with.

The required graph is attached below that represents the solution to the system of inequalities.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

For the first inequality, x + y > 1, we can rewrite it as y > -x + 1 and graph the boundary line y = -x + 1. Since the inequality is strictly greater than, we should shade the region above the line.

For the second inequality, -x + y ≤ 3, we can graph the boundary line -x + y = 3, which is the same as y = x + 3. Since the inequality is less than or equal to, we should shade the region below the line.

Point (0, 2) is in the shaded region. Plugging in x = 0 and y = 2 into the inequalities gives:

x + y > 1: 0 + 2 > 1, which is true

-x + y ≤ 3: -0 + 2 ≤ 3, which is true

Therefore, (0, 2) is a solution to the system.

Any point in the shaded region will be a solution to the system, and any point outside the shaded region will not be a solution.

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Answer:

650

Step-by-step explanation:

\(7/10s = 455\\7s = 4550\\s = 650\)

Answer:

650

Step-by-step explanation:

\(\frac{70}{100} =\frac{455}{y}\)

First, to answer this you cross multiply. This means:

\(45,500=70y\)

Now you divide each side by 70, and you get 650

The fraction of a day that can be attributed to 8 hours 20 minutes is   25/72 of a day.

In math, a fraction is a way of representing a part of a whole or a ratio between two numbers. It is written as a numerator and a denominator separated by a horizontal line called a fraction bar.

One hour is equal to 60 minutes, then we can say that 8 hours is equivalent to( 8*60) minutes. Then we can say that (480 minutes + 20 minutes) = 500 minutes.

since we know that 1 day is 24 hours = 24(60), then we can form this inform of a ratio as ;

500:( 24(60))

= 500: 1440

= 50/ 144

= 25/72 of a day.

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In the equation y = $7.20x + $790, "y" represents the total cost. An equation is a mathematical statement that shows the relationship between two or more variables. In this equation, there are two variables - "x" and "y". The variable "x" represents the number of units produced or sold, while "y" represents the total cost.

The coefficient of "x" in the equation, which is 7.20, represents the variable cost per unit. This means that for each unit produced or sold, there is an additional cost of $7.20. The constant term, which is $790, represents the total fixed costs. Fixed costs are those costs that do not vary with the number of units produced or sold.To find the total cost of producing or selling a certain number of units, we can plug in the value of "x" into the equation and solve for "y". For example, if we want to find the total cost of producing 100 units, we can substitute x=100 into the equation:
y = $7.20(100) + $790
y = $720 + $790
y = $1510
Therefore, the total cost of producing 100 units is $1510. In summary, "y" represents the total cost in the given equation, which is determined by both fixed and variable costs.
In the equation y = $7.20x + $790, "y" represents option C: total costs. This equation has two components: "$7.20x" represents the variable costs per unit, where x is the number of units, and "$790" represents the total fixed costs. By adding these two components together, you get the total costs (y) for producing x units.

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Answer:

The second one...the answer for n is +ive not -ive so it cant be a fraction

Sulfhuric acid, boric acid and vinegar have 7 atoms present in them

To find the compounds with equal number of atoms, we must take each individual atoms and find how many atoms are present in them.

In the first compound, we have sulfuric acid.

\(H_2SO_4 = 7 atoms\\\)

Second compound, we have phosphoric acid

\(H_3PO_4 = 8 atoms\)

Third compound, we have vinegar

\(C_2H_3O_2 = 7 atoms\)

Fourth compound, we have boric acid

\(H_3BO_3 = 7 atoms\)

From the above, only sulfuric acid, vinegar and boric acid have equal number of atoms present in them.

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Answer:

tan 58° = 11/x

Step-by-step explanation:

The two legs form the right angle of the triangle.

One leg is x, and the other leg is 11.

Look at the 58° angle. The leg with length x is next to the 58° angle, so the leg with length x is the "adjacent" leg. The leg with length 11 is opposite the 58° angle, so that leg is the "opposite" leg. For the 58° angle, adj = x, and opp = 11.

Now you need to remember the definitions of the sine, cosine, and tangent ratios for a right triangle.

sin A = opp/hyp

cos A = adj/hyp

tan A = opp/adj

The only ratio that involves the adjacent and opposite legs is the tangent.

Answer:

tan 58° = 11/x

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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Answer:

49.85%

Step-by-step explanation:

Streaming is defined as sending and receiving an video or an audio content in continuous flow over any network. It allows one to begin the playback and while it sends the rest of the data.

In the context, the percentage of the videos on a streaming site that is between 264 and 489 seconds is 49.85% which is found by a graph where the distribution of the lengths of the videos in seconds on a popular video streaming sites.

The statement is true. The value p = 2 is a solution to the inequality p - 5 < 20.

To determine if a given value is a solution to an inequality, we substitute that value into the inequality and check if it holds true. In this case, we substitute p = 2 into the inequality p - 5 < 20:

2 - 5 < 20

-3 < 20

Since -3 is indeed less than 20, the inequality holds true when p = 2. Therefore, p = 2 is a valid solution to the inequality p - 5 < 20.

It is important to note that there may be other values of p that also satisfy the inequality. However, the question specifically asks if p = 2 is a solution, and based on the substitution and evaluation, it is true that p = 2 satisfies the inequality.

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