sine rule find the length of ac

The correct option D. $98,636.72; is the amount in Merle's account after six years.

The formula for the compound interest is-

A = P * (1 + r/nt)^nt

In which,

From the beginning to end of the third year:

A = P(1 + 0.05 )^6

A = 40,000 × 1.05^6

A = $53,603.83

Now, add $20,000 to the amount obtained.

A = $53,603.83 + $20,000

A = $73,603.83

Thus, at the end of sixth year:

A = 73,603.83 x 1.05^6

A = $98,636.16

Therefore, the balance in Merle's account after six years is  $98,636.16.

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An arithmetic logic unit (ALU) performs all arithmetic operations (for example, addition and subtraction) and all logic operations.

An arithmetic logic unit (ALU) is a digital circuit used to perform arithmetic and logic operations. It represents the fundamental building block of the central processing unit (CPU) of a computer. Modern CPUs contain very powerful and complex ALUs. In addition to ALUs, modern CPUs contain a control unit (CU).

Basic arithmetic and logical operations are carried out using an ALU. Addition, subtraction, multiplication, and division are a few examples of arithmetic operations.

Binary numbers, or 0 and 1, are used to store and modify every piece of data in computers. Since a switch has just two possible states—open or closed—transistor switches are used to alter binary numbers. An open transistor, through which no current flows, is equivalent to a 0. A closed transistor with a current flowing through it symbolizes a 1.

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Answer:

[tex]120^{\circ}[/tex]

Step-by-step explanation:

Using the exterior angle theorem, [tex]x=50^{\circ}+70^{\circ}=120^{\circ}[/tex].

Answer:

Step-by-step explanation:

we know the inside total angles for triangle is 180 degrees.

We are given the two internal angles as 70 and 50 degrees.

So the equation can be written as

70+50+y = 180

y= 60

Also, we know that straight line is 180 degrees.  Now we can write the second equation as follow:

60+x = 180

x = 120 degrees

The amount of commission the agent receives if the bonus amount is Rs. 1,500, is Rs. 24,000.

To find the commission received by the agent, we first determine the excess sales using the bonus rate and bonus amount.

The excess sales are added to Rs. 900,000 to determine the total sales for the year.

The commission rate is applied to the total sales to ascertain the amount of the commission the agent received.

Commission on the total annual sales = 2%

Bonus on the excess of sales over Rs. 900,000 = 0.5%

Bonus amount = Rs. 1,500

Excess sales over Rs. 900,000 = Rs. 300,000 (Rs. 1,500/0.5%)

Total sales = Rs. 1,200,000 (Rs. 900,000 + Rs. 300,000)

Commission amount = Rs. 24,000 (Rs 1,200,000 x 2%)

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Answer:  B 9:21

Step-by-step explanation:

9 reduces to three and 21 reduced to 7

The amount of red paint used is 3/4 gallons

The amount of blue paint used is 1 1/2 gallons.

The amount of red paint used is 3/8 gallons

The amount of blue paint used is 3/4 gallons

The amount of white paint used is 3 /8 gallons

In order to determine the quantity of each type of paint needed, multiply the fraction of each type of paint used by the total gallons of purple paint.

Amount of red paint used = 1/4 x 3 = 3/4 gallons

Amount of blue paint used = 1/2 x 3 = 3/2 = 1 1/2 gallons

The quantity of each type of paint used to make the lighter purple shade:

Amount of red paint used = 1/4 x 1 1/2

1/4 x 3/2 = 3/8 gallons

Amount of blue paint used = 1/2 x 3/2 = 3/4 gallons

Amount of white paint used = 1/4 x 1 1/2

1/4 x 3/2 = 3 /8 gallons

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Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.

Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.

Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.

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Correct Question:

Match the plot with a possible description of the sample.

60 70 80 90 100

Choose the correct answer below

A. Wait time (in minutes) for a sample of doctors offices

B. Ages (in years) of a sample of residents of a retirement home.

C. Highest yearly temperatures (F) for a sample of deserts.

D. Time (in hours_ spent watching TV in a day for a sample of teenagers.

Answer:

Step-by-step explanation:

In  linear equation, 5  batches of slime can Mr. Lincoln make.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                 Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Based on the given conditions, formulate = 3 ÷ 2/3

                                             = 3 * 3/2

                                          = 3 * 3/2

                                            = 9/2

the smallest integer greater than or equal to = 9/2 : 5

                                                                         = 5

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The  probability that between 78% and 86% were non-teacher workers from private schools is 0.7689

Eighty-four percent of non-teacher workers were employed in private schools.

p = 0.84

q = 1 - p = 1 - 0.84 = 0.16

if a random sample of 200 non-teacher workers from private schools was selected

We need to find the  probability that between 78% and 86% were non-teacher workers from private schools.

n = 200

μρ = 0.84

αp = √(p(1 - p)/n) = √(0.84(0.16)/200) = 0.026

P(0.78 < P < 0.86) = P((0.78 - 0.84)/0.026 < (p - μp)/σp < (0.86 - 0.84)/0.026)

= P(-2.31 < z < 0.77)

= P(z < 0.77) - P(z < -2.31)

using z table

0.7794 - 0.0103

= 0.7689

Therefore, the  probability that between 78% and 86% were non-teacher workers from private schools is 0.7689.

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Answer:

x = 40°

y = 35°

Step-by-step explanation:

Let us take two triangles ∆ABC and ∆ADE

We know that, in a triangle the sum of all angles is equal to 180°

So,

For the traingle ABC

Now,

m∠A + m∠B + m∠C = 180°

80° + 60° + x° = 180°

140° + x° = 180°

x° + 140° - 140° = 180° - 140°

x = 40°

For the triangle ADE

Now,

m∠A + m∠D + m∠E = 180°

80° + 65° + y° = 180°

145° + y° = 180°

y° + 145° - 145° = 180° - 145°

y = 35°

Thus, The value of x and y is 40° and 35° respectively

Answer: [tex]\frac{n^{2} }{n+1}[/tex]

Step-by-step explanation:

The numerator (top digit) are squares. For example,

1 is [tex]1^{2}[/tex]

4 is [tex]2^{2}[/tex]

9 is [tex]3^{2}[/tex]

and so on.

The bottom digit increases by one.

Therefore, the Nth term would be that number (N) squared on the numerator, and n+1 on the denominator.

The solution to the equality of the functions f(x) and g(x) are;

At x = 0 and x = 1

We are given the functions as;

f(x) = 3ˣ and g(x) = 2x + 1

Now, we want to find the point at which the functions f(x) and g(x) are equal. This is;

f(x) = g(x)

Thus, from the graph, we can see that;

When x = 0, f(x) = 1 and g(x) = 1

Similarly, when x = 1, f(x) = 3 and g(x) = 3

Thus, these are the points where f(x) is equal to g(x)

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The leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp in 364 ways.

The number of members in the campfire girls troop

= 14

The number of members the leader of the campfire girls troop can appoint at a time = 3

The number of ways to appoint r members out of n members

= nCr = n!/(r)!×(n-r)!

Therefore, the number of ways in which the leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp

= 14C3 = 14!/(3)!×(14-3)! = 364 ways

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Answer:

1 hour

Step-by-step explanation:

Answer: 1hour

Step-by-step explanation: lol

The value of the iterated integral is equal to 24. In general, when evaluating iterated integrals, it is important to remember to integrate with respect to the outer variable first, and then with respect to the inner variable. This will ensure that the resulting value of the integral is correct.

To evaluate this iterated integral, we need to integrate with respect to the outer variable first, and then with respect to the inner variable. In this case, the outer variable is x and the inner variable is y.

We can write the iterated integral as:

∫₀² ∫₂³ xy² dx dy

To find the value of this integral, we first need to evaluate the inner integral with respect to x. We can do this by taking the integral of xy² with respect to x from 0 to 2, which gives us:

∫₀² xy² dx = [x³y² / 3]₀² = (2³ * 3²) / 3 = 24/3

Now that we have found the value of the inner integral, we can evaluate the outer integral with respect to y. We can do this by taking the integral of 24/3 with respect to y from 2 to 3, which gives us:

∫₂³ (24/3) dy = [24y / 3]₂³ = (24 * 3) / 3 = 24

Therefore, the value of the iterated integral is equal to 24.

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Data that are left-skewed would include values that are unusually high.

A data is symmetric when it has a mirror image on both sides of the mean. For a symmetric data the mean = mode = median.

If the data is asymmetric, it can either be left-skewed or right-skewed. A left-skewed data has mots of its values greater than the mean. In this case the mean < median < mode. Left-skewed data mostly contains very less amount of values with smaller magnitudes.

Hence, data that are left-skewed would include values that are unusually high.

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The null hypothesis is R = 0

In this question we have been given a hypothesis that the fraction of people with severe depression is higher in country a than in country b.

We need to test the hypothesis.

Suppose that we have chosen the statistic of interest to be PAPB.

Let the ratio R be the fraction of depressed people in country a divided by fraction in country b

We need to find the null hypothesis.

We know that the null hypothesis as statement says that  there is no relationship between two measured variables/phenommena.

In this case, for null hypothesis the ratio must be zero.

Therefore, for given situation the null hypothesis is R = 0

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The complete question is:

We want to test the hypothesis: the fraction of people with severe depression is higher in country A than in country B.

We have chosen the statistic of interest to be PAPB (fraction of depressed people in country A divided by fraction in country B). We call this ratio R.

What is the null hypothesis?

Group of answer choices

1 R=0

2 R=1

Answer:

10

Step-by-step explanation:

the answer is 10 because of everything I did

It will take about 39 years for a principal of $4600 to grow to $29900 continuously compounded

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula to calculate compound interest is given as

A = P(1 + r/n)^nt

A = Pe^rt (Continuously compounded)

Let's substitute the values into the formula and solve

29900 = 4600e^(0.048 * t)

t = 39 years

The time it takes to compound the principal to $29900 is approximately 39 years

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Possible distinction between  the center of the sphere and  surface of the sphere is

The sphere is one of the most significant mathematical figures. Spheres and nearly-spherical objects can be seen in both nature and industry.

Soap bubbles and other bubbles have a spherical shape when they are in an equilibrium state. The celestial sphere is a fundamental concept in astronomy, and the Earth is usually represented as spherical in geography.

The majority of pressure vessels, curved mirrors and lenses, and other manufactured items are based on spheres. Because spheres roll effortlessly in all directions, the majority of balls used in sports and toys are spherical, just like ball bearings.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{50}~,~\stackrel{y_1}{45})\qquad (\stackrel{x_2}{70}~,~\stackrel{y_2}{61}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{61}-\stackrel{y1}{45}}}{\underset{run} {\underset{x_2}{70}-\underset{x_1}{50}}} \implies \cfrac{ 16 }{ 20 } \implies {\Large \begin{array}{llll} \cfrac{4 }{ 5 } \end{array}}[/tex]

Nothing further can be done with simplifying the given expression.

13+16 are the numbers that equals to 19.

The equal sign in the  mathematics describes by  equality between the values,. Of the  equations, or expressions are the  written on both sides. There symbol for equal to is two be the  small horizontal lines placed to parallelly. We place the to the  'equal to' sign is between two things that are to the same or equal.

As we know,

If two things are equal or if one thing is equal to the  another, they are the same or  in the size, number, standard, or values .

As per the question we have to find equal number of 19.

So 13+6 are the equal number that equals to 19.

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Answer: 2x + 2

Step-by-step explanation:

The composition of two functions f and g, denoted g(f(x)), is a new function that is obtained by substituting the function f(x) into the function g(x) in place of x.

In this case, f(x) = x + 1 and g(x) = 2x. Substituting f(x) into g(x) in place of x gives us g(f(x)) = 2(x + 1) = 2x + 2.

Therefore, the final expression for g(f(x)) is 2x + 2. The coefficient of x is 2, and the constant term is 2.

The formula for an exponential function is y = 45/8x + 57/8.

Here we have to find the formula for an exponential function that passes through the points.

Given data:

The two points are (-1, 3/2) and (3, 24).

We need to find the slope of the line. So,

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

m = (24 - 3/2) / ( 3+ 1)

   = 45/ 8

The general equation of a line:

y = mx + c

Now putting the value of x and y as -1 and 3/2 and m = 45/8.

3/2 = -1 × 45/8 + c

c = 57/8

Now we get the equation:

y = 45/8x + 57/8

Therefore the equation is y = 45/8x + 57/8.

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You would start at points (0, 40) and then move to (1, 32), (2, 24), (3, 16), (4, 8), and (5, 0) because he gives out 8 bags per hour.

What is a line graph?

An informational shift over time is graphically represented by a line graph. It is a graph that was created by connecting points with line segments.

Michael starts with 40 bags of cucumbers and gives out 8 bags per hour until there are none left.

Michael starts giving them away until he has no bags left.

To create the graph we need coordinate points to locate on the graph.

So initially he has 40 bags and gives away 8 bags for every 1 hour.

The number of bags will be represented on the y-axis, and the number of hours will be represented on the x-axis.

The coordinates are:

x-axis           y-axis

  0                 40

  1                  32

  2                 24

  3                  16

  4                   8

  5                   0

Hence, you would start at points (0, 40) and then move to (1, 32), (2, 24), (3, 16), (4, 8), and (5, 0) because he gives out 8 bags per hour.

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The residual for each of the coordinate pairs, (x, y) are-

a) -3.1; b) -0.2; c)  0.32; d) 0; e) -0.1; f) -6.96.

For the stated question;

Data is given by the line of best fit as;

y = 1.1x + 3.4

Then, the residual for the given coordinates are found as;

Residual = y - (1.1x + 3.4)

a. (5,8.8)

Residual = 5.8 - (1.1(5) + 3.4)

Residual = -3.1

b. (2.5,5.95)

Residual = 5.95 - (1.1(2.5) + 3.4)

Residual = -0.2

c. ((0,3.72)

Residual = 3.72 - (1.1(0) + 3.4)

Residual = 0.32

d. (1.5,5.05)

Residual = 5.05 - (1.1(1.5) + 3.4)

Residual = 0

e. (-3,0)

Residual = 0 - (1.1(-3) + 3.4)

Residual = -0.1

f. (-5,-4.86)

Residual = -4.86 - (1.1(-5) + 3.4)

Residual =  -6.96

Thus, the residual for each of the coordinate pairs, (x, y) are found.

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The probability is it that she actually uses performance-enhancing drugs is 0.5975.

Given that,

The national flufferball association makes the decision to put in place a drug testing programme to check its athletes for the use of illicit performance-enhancing substances. In reality, 3% of professional flufferball players abuse performance-enhancing substances. A drug test has a 2% false positive rate and a 4% false negative rate. Alternatively, a person who abstains from drug use has a 0.02 percent chance of testing positive. With a 0.04 probability, a person who uses the medications will test negative. A player is tested at random, and the results are positive.

We have to find how probable is it that she actually uses performance-enhancing drugs.

We know that,

The provided data is

P(D)=0.03

P(D')=1-0.03=0.97

P(T|D')= 0.02

P(T'|D)=0.04

P(T|D)=1-P(T'|D)=1-0.04=0.96

The probability that she really takes the drugs is,

P(D|T)=P(D)P(T|D)/P(D)P(T|D)+P(D')P(T|D')

P(D|T)=(0.03×0.96)/(0.03×0.96)+(0.02×0.97)

P(D|T)=0.5975

Therefore, The probability is it that she actually uses performance-enhancing drugs is 0.5975.

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