Can mutually exclusive events have an intersection of events? Explain your answer

The geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...

There are three parameters which differentiate between which geometric sequence we're talking about.

The first parameter is the initial value of the sequence.

The second parameter is the quantity by which we multiply previous term to get the next term.

The third parameter is the length of the sequence. It can be finite or infinite.

Suppose the initial term of a geometric sequence is 'a'

and the term by which we multiply the previous term to get the next term is 'r' (also called the common ratio)

Then the sequence would look like

[tex]a, \: ar, \: ar^2, \: ar^3, \: \cdots[/tex]

(till the terms to which it is defined)

If the initial term is 'a', then the geometric sequence with common ratio = 2 would look like:

[tex]a, \: a(2), \: a(2)^2, \: a(2)^3, \: \cdots\\\\a, \: a(2), \: a(4), \: a(8), \: \cdots[/tex]

Checking all the options to see which one has got common ratio 2:

Initial term a = 14,

The geometric sequence with a = 14, and r = 2 would be:

[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]

The sequence  14, 16, 18, 20, ... doesn't match with it, so its not correct option.

Initial term a = 64,

The geometric sequence with a = 14, and r = 2 would be:

[tex]64, 64(2), 64(4), 64(8), \cdots\\\\64, 128, 256, 512, \cdots\\[/tex]

The sequence 64, 32, 16, 8, ... doesn't match with it, so its not correct option.

Initial term a = 64,

The geometric sequence with a = 14, and r = 2 would be:

[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]

The sequence  14, 28, 56, 112, ... matches with it, so its correct option.

Initial term a = 87,

The geometric sequence with a = 87, and r = 2 would be:

[tex]87, 87(2), 87(4), 87(8), \cdots\\\\87, 174, 348, 696, \cdots\\[/tex]

The sequence 87, 85, 83, 81, ... doesn't match with it, so its not correct option.

Thus, the geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...

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Answer:

Option B) The variable Y will cancel out first.

Step-by-step explanation:

we have

5x-y=-21 ----> equation A

x+y=-3 ----> equation B

Solve by elimination

Adds equation A and equation B

5x-y=-21

x+y=-3

--------------

5x+x=-21-3 ----->variable y will be eliminated first

6x=-24

x=-4

To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we can use the substitution method. By setting up a system of equations and solving for the variables, we find that the cost of one bag of windflower bulbs is $45 and the cost of one package of crocus bulbs is $7.50.

To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we can set up a system of equations. Let's use the substitution method.

Let x represent the cost of one bag of windflower bulbs and let y represent the cost of one package of crocus bulbs.

We can set up two equations:

2x + 5y = 105

9x + 5y = 164.50

From the first equation, we can rewrite it as: 2x = 105 - 5y. We can substitute this expression for 2x in the second equation:

9(105 - 5y) + 5y = 164.50

Solving for y, we get y = 7.50. Substituting this value back into the first equation, we can solve for x: 2x + 5(7.50) = 105. Solving for x, we get x = 45.

Therefore, the cost of one bag of windflower bulbs is $45 and the cost of one package of crocus bulbs is $7.50.

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Follow below steps:

Mark and Julio are selling flower bulbs for a school fundraiser. To find the cost of one bag of windflower bulbs and one package of crocus bulbs, we set up two equations based on the information given, and then solve them using the substitution method.

Let x be the cost of one bag of windflower bulbs and y be the cost of one package of crocus bulbs. According to Mark's sales, the equation is:

2x + 5y = 105 ...(1)

According to Julio's sales, the equation is:

9x + 5y = 164.50 ...(2)

To use the substitution method, we first isolate y in equation (1):

y = (105 - 2x) / 5 ...(3)

Next, we substitute equation (3) into equation (2):

9x + 5((105 - 2x) / 5) = 164.50

9x + 105 - 2x = 164.50

7x = 59.50

x = 8.50

Now that we have the value for x, we can use it to find y by substituting x back into equation (3):

y = (105 - 2(8.50)) / 5

y = (105 - 17) / 5

y = 88 / 5

y = 17.60

Therefore, the cost of one bag of windflower bulbs is $8.50 and the cost of one package of crocus bulbs is $17.60.

The range for this situation represents all possible values of the cost of filling the gas tank in dollars.

The range for this situation represents the set of all possible outputs of the function, which in this case is the cost of filling the gas tank.

Since the equation given is p(g) = 3.5g, the range would be all possible values of p, the cost of filling the gas tank.

The range would depend on the values of g, the amount of gas in gallons, that you input into the equation.

For example, if you fill the tank with 1 gallon of gas, the cost would be p(1) = 3.5 * 1 = $3.50.

If you fill the tank with 3 gallons of gas, the cost would be p(3) = 3.5 * 3 = $10.50.

Therefore, the range for this situation would be all values of p, the cost, that can be obtained by inputting different values of g, the amount of gas in gallons, into the equation p(g) = 3.5g.

The range for this situation is from $0 (empty tank) to $42 (full tank). The cost can be any value in this range depending on the number of gallons pumped into the tank.

In this context, the function [tex]\( p(g) = 3.5g \)[/tex] represents the cost  p  of filling the gas tank with  g  gallons of gas. The range of the function is the set of all possible values for the cost.

Since the cost is directly proportional to the number of gallons, we can evaluate the function for the minimum and maximum values of  g . The minimum value of  g  is 0 gallons (empty tank), and the maximum value is 12 gallons (full tank).

1. For g = 0 , [tex]\( p(0) = 3.5 \times 0 = 0 \)[/tex]. So, the minimum cost is $0.

2. For  g = 12 , [tex]\( p(12) = 3.5 \times 12 = 42 \)[/tex]. So, the maximum cost is $42.

Therefore, the range for this situation is from $0 (empty tank) to $42 (full tank). The cost can be any value in this range depending on the number of gallons pumped into the tank.

Answer:

x=ysq2-2

Step-by-step explanation:

because you get the x alone and subtract the variable

Answer:

Graph A

Step-by-step explanation:

because the function given is y= (x+3)(x+3) the vertex is (-3,0)

Answer:

googles explanation is below

Step-by-step explanation:

Rule 3: Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. Basically, - (-4) becomes +4, and then you add the numbers. For example, say we have the problem -2 - –4.

Answer:

  x = 3, x = -1/6 are the zeros

Step-by-step explanation:

I find graphing the equation using a graphing calculator to be about the fastest way to find the zeros.

__

For this equation, you can look for factors of 6·(-3) = -18 that have a sum of -17. Those are -18 and +1, so the factorization of the equation is ...

  y = (1/6)(6x -18)(6x +1) = (x -3)(6x +1)

The roots are the values of x that make the factors be zero, so x=3 and x=-1/6.

__

You can also use the quadratic formula to find the zeros. That tells you the solution to ...

  ax² +bx +c = 0

is

  x = (-b ±√(b²-4ac))/(2a)

Comparing your equation to the standard form, you can identify the coefficients as ...

  a = 6, b = -17, c = -3

so the zeros are ...

  x = (-(-17) ±√((-17)² -4(6)(-3)))/(2(6))

  x = (17 ±√369)/12 = (17 ±19)/12 = {-2, 36}/12 = {-1/6, 3}

The zeros are x = -1/6 and x = 3.

To find zeros of a quadratic equation, you use the quadratic formula. Applying this formula to the equation y = 6x^2 - 17x - 3 yields two solutions, representing the two points where the function intersects the x-axis.

The subject of this question concerns finding the zeros of a given quadratic equation, y = 6x^2 - 17x - 3. Zeros are the x-values that make the equation equal to zero or to point where the function intersects the x-axis.

To find the zeros, we'll use the quadratic formula, which is derived from an equation of the form ax² + bx + c = 0: x = [ -b ± sqrt(b^2 - 4ac) ] / (2a).

Applying the quadratic formula to your equation, with a = 6, b = -17, and c = -3, we get the two solutions, which are the zeros of the equation: x = [ 17 ± sqrt((-17)^2 - 4*6*-3) ] / (2*6). Computing this, we get two solutions, or two zeros, which are the points where your function y = 6x^2 - 17x -3 crosses the x-axis.

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Answer:

x=1 if I understood correctly.

Step-by-step explanation:

[tex] \sqrt{x} + 5 + x - 3 = 4[/tex]

[tex] \sqrt{x} + 2 + x = 4[/tex]

[tex] \sqrt{x} + x = 2[/tex]

At this point if you try all the integers, you will find that only 1 is the solution to this equation, because:

[tex] \sqrt{1} + 1 = 2[/tex]

[tex]1 + 1 = 2[/tex]

[tex]2 = 2[/tex]

Hope I helped!

For this case we must solve the following equation:

[tex]\sqrt {x + 5} -3 = 4[/tex]

We add 3 to both sides of the equation:

[tex]\sqrt {x + 5} = 4 + 3\\\sqrt {x + 5} = 7[/tex]

We raise the square to eliminate the root:

[tex]x + 5 = 7 ^ 2\\x + 5 = 49[/tex]

We subtract 5 on both sides of the equation:

[tex]x = 49-5\\x = 44[/tex]

Answer:

[tex]x = 44[/tex]

The equation used to solve for x in the given diagram is 7x + 11x = 90, representing the total sum as 90 degrees.

In the diagram, you have an angle formed by two given lines. To find the value of x, you can use the fact that the total sum is 90 degrees.

1. The first angle of the diagram is labeled as 7x.

2. The second angle of the diagram is labeled as 11x.

So, the equation for the sum of these angles should equal 90 degrees:

7x + 11x = 90

Now, you can simplify the equation:

18x = 90

To isolate x, divide both sides by 18:

18x / 18 = 90/ 18

x = 5

So, the equation used to solve for x is indeed 7x + 11x = 90, which simplifies to 18x = 90 when considering the angles around the point.

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The given question pertains to different aspects of probability in Mathematics, such as combinations, proportions and matched pairs. Each concept is used to determine the likelihood of an event occurring and they all play integral roles in statistical analysis.

The details indicate that this question pertains to probability in Mathematics especially applied to situations like combinatorics, proportions and matched pairs. So let's explore each of those concepts with the details given:

In probability, the concept of combinations is important because it helps to determine the likelihood of a particular event occurring. For instance, P(choosing all five numbers correctly) relates to the probability of choosing numbers correctly in a given set. It's determined by P(choosing 1st number correctly) * P(choosing 2nd number correctly) * P(choosing 5th number correctly).

The term 'two proportions' perhaps refers to odds ratio or probability comparison between two events.

This is a statistical technique often used in studies where each individual or item has a unique match - for example, a study comparing the math scores of twins. Here, it seems like an insight into statistical analysis where outcomes are compared within matched pairs. Therefore, these different concepts are all part of probability and statistics.

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Answer: n = g/5

Step-by-step explanation:

Answer:

The answer is 8, so 8^1

Step-by-step explanation:

You add and subtract exponents when multiplying and dividing.

Answer:

  C)  65,535

Step-by-step explanation:

You can add up the 8 terms ...

  3, 12, 48, 192, 768, 3072, 12288, 49152

to find their sum is 65535.

_____

Estimating

Knowing the last term (49152) allows you to make the correct choice, since the sum will be more than that and less than double that.

_____

Using the formula

You know the formula for the sum of a geometric sequence is ...

  S = a1(r^n -1)/(r -1)

where a1 is the first term (3), r is the common ratio (4), and n is the number of terms (8).

Filling in the values, you find the sum is ...

  S = 3(4^8 -1)/(4-1) = 4^8 -1 = 65535

The sum of the geometric sequence 3, 12, 48, ... with 8 terms is 65,535. We use the geometric sum formula and identify a common ratio of 4 to compute the answer, which is option C.

To find the sum of a geometric sequence, we use the formula S = a * (1 - r^n) / (1 - r), where S is the sum of the sequence, a is the first term, r is the common ratio, and n is the number of terms. In this sequence, the first term a is 3, and we can find the common ratio r by dividing the second term by the first term: r = 12 / 3 = 4. With 8 terms in the sequence, we can calculate the sum.

S = 3 * (1 - 4^8) / (1 - 4) = 3 * (1 - 65536) / (1 - 4) = 3 * (-65535) / (-3) = 65535.

Therefore, the sum of the sequence is 65,535, which corresponds to option C.

Answer:

A. 3(t+2)

Step-by-step explanation:

We can easily solve your question by using any computational tool or calculator

Please see attached images for a full analysis of your problem

The result is

A. 3(t+2)

[tex]\bf \cfrac{~~\frac{4t^2-16}{8}~~}{\frac{t-2}{6}}\implies \cfrac{4(t^2-4)}{8}\cdot\cfrac{6}{t-2}\implies \cfrac{4\stackrel{\stackrel{difference}{of~squares}}{(t^2-2^2)}}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot\cfrac{\stackrel{3}{\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}~~}{t-2}[/tex]

[tex]\bf \cfrac{\begin{matrix} 4 (t-2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(t+2)}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{3}{~~\begin{matrix} t-2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 3(t+2)[/tex]

Every letter is either red or blue. So the probability is 0.

[tex]|\Omega|=7\\|A|=0\\\\P(A)=\dfrac{0}{7}=0[/tex]

Answer:

(d-5)x2

Step-by-step explanation:

you said a number d is subtracted by 5 then doubled so lets make an example. d=6

(6-5)x2

(6-5)=6-5=1

(1)x2=1x2=2

If a number d is decreased by 5 and then doubled, then we can represent that event with an algebraic expression as:

[tex]2\times (d-5)[/tex]

The number d decreased by 5 is written as: [tex]d - 5[/tex]

When we double a thing, we multiply by 2.

Thus we have the algebraic form of given condition as:

[tex]2\times(d-5)[/tex]

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Answer:

C. [tex]52\sqrt{3}\ ft^2[/tex]

Step-by-step explanation:

Use formula for the area of trapezoid

[tex]A=\dfrac{a+b}{2}\cdot h,[/tex]

where a is the smaller base, b is the larger base and h is the height.

From the diagram,

[tex]a=11\ ft\\ \\b=15\ ft\\ \\h=4\sqrt{3}\ ft[/tex]

So, the area of trapezoid is

[tex]A=\dfrac{11+15}{2}\cdot 4\sqrt{3}=13\cdot 4\sqrt{3}=52\sqrt{3}\ ft^2[/tex]

Answer:

  $37 3/8

Step-by-step explanation:

Add the rise to the opening price to find the closing price.

  33 1/8 + 4 1/4 = (33 +4) + (1/8 +2/8) = 37 3/8 . . . . . . dollars per share

Final answer:

The closing price of Nagasaki Corporation's stock, after adding the increase of [tex]\$4 \frac{1}{4}[/tex]to the opening price of [tex]\$33\frac{1}{8}[/tex], was  [tex]\$37\frac{3}{8}[/tex] per share.

Explanation:

The student asked: On the morning of June 4, the stock of Nagasaki Corporation opened at a price of  [tex]$33\frac{1}{8}[/tex]per share. At the end of the day, the price had risen [tex]$4 \frac{1}{4}[/tex] per share. What was the price at the end of the day?

To find the closing price of the stock, we need to add the increase to the opening price:

Convert the mixed numbers to improper fractions: [tex]\$33\frac{1}{8} = \frac{265}{8} \ and\ \$4\frac{1}{4} = \frac{17}{4}[/tex]

Find a common denominator to add the fractions: Since 8 and 4 are both multiples of 4, we will convert [tex]\frac{17}{4} to \frac{34}{8}.[/tex]

Add the fractions [tex]: \frac{265}{8} + \frac{34}{8} = \frac{299}{8}[/tex]

Convert the improper fraction back to a mixed number: [tex]\frac{299}{8} = $37\frac{3}{8}[/tex]

Therefore, the closing price of the stock was  [tex]$37\frac{3}{8}[/tex]per share.

Answer:

  11,184,808

Step-by-step explanation:

The n-th term of a geometric series is ...

  an = a1·r^(n-1)

To fill in the formula, we need a1·r^n, so need to multiply the last term shown by r.

The value of r is 32/8 = 4, and the other terms of interest are a1 = 8, a1·r^(n-1) = 8388608. So, the sum is ...

  [tex]S_n=\dfrac{ra_1r^{n-1}-a_1}{r-1}=\dfrac{4\cdot 8,388,608-8}{4-1}=11,184,808[/tex]

Answer:

  (g◦f)(-6) = -9

Step-by-step explanation:

(g◦f)(-6) means g(f(-6))

Put the number where the variable is and evaluate.

  f(-6) = 3/2(-6) +5 = -9 +5 = -4

  g(f(-6)) = g(-4) = 7 -(-4)² = 7 -16 = -9

Then ...

  (g◦f)(-6) = -9

The given geometric sequence is 4, 16, 64, 256.

Given: Geometric Sequences

Among the given sequences, geometric sequence will be identified if the ration between two adjacent numbers is constant for the given sequence.

Option (A): 5, 12, 17, 29, 46

Common ratio (r) is:

r = 12/5 = 2.4

r = 17/12 = 1.4

r = 29/17 = 1.7

r = 46/29 = 1.6

Here, common ratio is not constant.

Hence, option (A) is incorrect.

Option (B): 3, 7, 11, 15, 19

Common ratio (r) is:

r = 7/3 = 2.3

r = 11/7 = 1.5

r = 15/11 = 1.3

r = 19/15 = 1.3

Here, common ratio is not constant.

Hence, option (B) is incorrect.

Option (C): 4, 6, 10, 16, 26

Common ratio (r) is:

r = 6/4 = 1.5

r = 10/6 = 1.66

r = 16/10 = 1.6

r = 26/16 = 1.62

Here, common ratio is not constant.

Hence, option (C) is incorrect.

Option (D): 4, 16, 64, 256

Common ratio (r) is:

r = 16/4 = 4

r = 64/16 = 4

r = 256/64 = 4

Here, common ratio is constant.

Hence, option (D) is correct.

Therefore, the geometric sequence is 4, 16, 64, 256.

Correct option is (D).

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Let's say x is J because it's Lemon Juice.

It's said that the pH of J is less than 4 so: pH(J) < 4 and pH(J) is greater than 1.5 so: pH(J) > 1.5

Now we can construct:

[tex]1.5 < pH(J) \wedge pH(J) < 4[/tex]

Or simply:

[tex]1.5 < pH(J) < 4[/tex]

We can also write this with an interval:

[tex]pH(J)\in(1.5, 4)[/tex]

Hope this helps.

r3t40

Inequalities are used  to relate unequal expressions.

The compound inequality that represents the normal range of pH values of lemon juice: (b) 1.5 < x < 4

Let the pH of lemon juice be represented with x.

x less than 4 means: x < 4

x greater than 1.5 means x > 1.5

So, we have:

x < 4 and x > 1.5

Rewrite as:

x > 1.5 and x < 4

Express x > 1.5 as 1.5 < x

1.5 < x and x < 4

Combine the inequalities

1.5 < x < 4

Hence, the required compound inequality is: (b) 1.5 < x < 4

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Answer:

  $2248.75

Step-by-step explanation:

Susan's monthly payment is ...

  total payment = loan payment + insurance payment

  = $2128.00 + (483,000×0.30/100)/12

  = $2128.00 + 1449/12

  = $2128.00 + 120.75

  = $2248.75

Answer:

Step-by-step explanation:

485'228.3

Answer:

Both 3:1

Step-by-step explanation:

30:10 Divide by 10

3:1

45:15 Divided by 15

3 : 1

Answer:

the same

Step-by-step explanation:

Answer:

  irrational

Step-by-step explanation:

Pi is irrational.

-1 is rational.

Their sum is irrational.

_____

In general, the sum of a rational number and an irrational number is irrational.

The number 'pi' is an irrational number. When we subtract 1 from 'pi', we still obtain an irrational number, therefore 'pi-1' is irrational.

The number pi is a well-known irrational number. An irrational number cannot be expressed as a ratio of two integers, and its decimal expansion never ends or repeats. When we subtract 1 from pi, we get another number. Since we are creating a new number by subtracting an integer from an irrational number, that number remains irrational. Therefore, pi-1 is also an irrational number.

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Answer:

D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32} ⇒ answer D

Step-by-step explanation:

* Lets talk about the domain and the range of a function

- The domain is the input values

- The range is the output values

- f(x) = y,  x is the input then x is the domain of the function and y is the

  output then y is the range of the function

- Example:

# If x = {2 , 3 , 5) and f(x) = 2x

- The input is x to find f(x) substitute the values of x in f(x)

- f(2) = 2(2) = 4 , f(3) = 2(3) = 6 , f(5) = 2(5) = 10

- The output is f(x) = {4 , 6 , 10}

- From all steps above the domain of f(x) is {2 , 3 , 5) and the range

 is {4 , 6 , 10}

* Lets solve the problem

- There are 32 teams participating  in a single-elimination soccer

 tournament

- x is the number of rounds

- f(x) is the number of teams

- only the winning teams from each round progress to the next

 round of the tournament

* Lets look to the graph and find the domain and the range

- The domain the the values of x and the range is the values of f(x)

∵ At x = 0 then f(0) = 32 ⇒ 32 teams inter the 1st round

∵ At x = 1 then f(1) = 16 ⇒ 16 teams inter the 2nd round

∵ At x = 2 then f(2) = 8 ⇒ 8 teams inter the 3rd round

∵ At x = 3 then f(3) = 4 ⇒ 4 teams inter the 4th round

∵ At x = 4 then f(4) = 2 ⇒ 2 teams inter the 5th round

∵ At x = 5 then f(5) = 1 ⇒ 1 team in win

- From all above:

∴ The domain is {0 , 1 , 2 , 3 , 4 , 5} and the range is {1 , 2 , 4 , 8 , 16 , 32}

* D = {0 , 1 , 2 , 3 , 4 , 5} and R = {1 , 2 , 4 , 8 , 16 , 32}

Answer:

The correct answer is option A.  23 in

Step-by-step explanation:

It us given that, the length of a rectangle is 5 more than 3 times its width. The perimeter of the rectangle is 58 in.

To find the length of rectangle

Let 'x' be the width of rectangle.

Length = 3x + 5

Perimeter of rectangle = 2(length + width)

58 = 2(3x + 5 + x)

58 = 2(4x + 5)

29 = 4x + 5

4x = 29 - 5

4x = 24

x = 24/4 = 6

Therefore length of rectangle = 3x + 5

 = 3*6 + 5 = 23 in

The correct answer is option A.  23 in

Answer:

The correct answer option is B. [tex] S _ n = a _ 1 [ \frac { 1 - r ^ n } { 1 - r } ] [/tex].

Step-by-step explanation:

The following is the formula that is used to find the sum of a geometric progession:

[tex] S _ n = a _ 1 [ \frac { 1 - r ^ n } { 1 - r } ] [/tex]

where [tex]S_n[/tex] is the sum, [tex]a_1[/tex] is the first term, [tex]r[/tex] is the common ratio while [tex]n[/tex] is the number of terms.

The formula which can be used to find the sum of the first n terms of a geometric sequence is:

          [tex]S_n=a_1(\dfrac{1-r^n}{1-r})[/tex]

Geometric sequence--

A sequence is said to be a geometric sequence if each of the term of a sequence is a constant multiple of the preceding term of the sequence.

This constant multiple is known as a common ratio and is denoted by r.

Also, if the first term of the sequence is: [tex]a_1[/tex]

Then the sequence is given by:

[tex]a_1,\ a_2=a_1r,\ a_3=a_1r^2,\ a_4=a_1r^3,\ .............a_n=a_1r^{n-1},\ .....[/tex]

The sum of the first n terms of the sequence is given by:

[tex]S_n=a_1(\dfrac{1-r^n}{1-r})[/tex]

Answer:

sin(x°) = 11/s

Step-by-step explanation:

The tangent is the ratio of sine to cosine, so ...

tan(x°) = sin(x°)/cos(x°)

Multiplying by cos(x°) gives ...

sin(x°) = cos(x°)·tan(x°) = (r/s)·(11/r)

sin(x°) = 11/s

Answer:

sin x° = 11 divided by s

Step-by-step explanation:

Given,

tan x° = 11 divided by r

[tex]\implies tan x^{\circ}=\frac{11}{r}[/tex]

Also, cos x° = r divided by s

[tex]\implies cos x^{\circ}=\frac{r}{s}[/tex]

We know that,

[tex]\frac{sinx^{\circ}}{cos x^{\circ}}=tan x^{\circ}[/tex]

[tex]\implies sinx^{\circ}= tan x^{\circ}\times cos x^{\circ}[/tex]  ( by cross multiplication )

By substituting the values,

[tex]sin x^{\circ}=\frac{11}{r}\times \frac{r}{s}=\frac{11r}{rs}=\frac{11}{s}[/tex]

⇒ sin x° = 11 divided by s

We know that, Final Amount in Compound Interest is given by :

[tex]\bigstar\;\;\boxed{\mathsf{Amount = Principal\left(1 + \dfrac{Rate\;of\;interest}{100}\right)^{Number\;of\;Years}}}[/tex]

Given :

●  Principal = $5000

●  Rate of interest = 1.25

●  Number of Years = 10

Substituting the values in the Formula, We get :

[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{1.25}{100}\right)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{0.25}{20}\right)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5000\left(1 + \dfrac{0.05}{4}\right)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5000\left(\dfrac{4.05}{4}\right)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5000\times (1.0125)^{10}}[/tex]

[tex]\implies \mathsf{Amount = 5661.354}[/tex]

Answer : $5661.354 money will be in the account 10 years later

Answer: $5,661.35

Step-by-step explanation:

I used the exponential growth formula to get my answer.

Latest time he can leave to be home by a quarter before 5 is 4:13

Step-by-step explanation:

Given Max's trip home takes 32 minutes. we have to find the time at which he can leave to be home by a quarter before 5.

quarter before 5 means 4:45

Max's takes 32 min to come to home so he has to leave 32 minutes before the given time.

Hence, latest time he can leave to be home by a quarter before 5 is 4:45-32 = 4:13

Answer:

Max must leave home at 4:58 to get their before half past 5.

Step-by-step explanation: