Discuss the coordinates of a point P(x, y) on a coordinate plane, and how these can be
described by its distance, r, from the origin and the angle made with the positive x-axis.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}\)

\(A = 2000\left(1+\frac{0.03}{12}\right)^{12\cdot 20}\implies A=2000(1.0025)^{240} \implies \boxed{A \approx 3641.51} \\\\\\ 3641.51~~ - ~~2000~~ \approx~~ \stackrel{earned~interest}{\boxed{1641.51}}\)

We will have the following:

His speed on the return (r) trio was 4mph faster than his speed in the first trip (o), so:

Then, we have that speed times distance equals time, and distance is equal to time over speed. Thus:

Then, we have:

So, the initial speed was of 8mph.

Then we deternine the distance:

So, the two cities are 48 miles apart.

Answer:

never skew

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

4 * 2 + 3 - 2 =

= 8 + 1 =

= 9

The measures of the three intercepted arcs from least to greatest are;

AC < BC < AB

We have,

We are given that

Angle ACB = 63 degrees

Arc BC is 118 degrees.

Now, from the Triangle angle sum theorem, we know that the sum of all interior angles of any triangle is always equal to 180 degrees.

Thus, the sum of the interior angles of the inscribed triangle given to us id also 180 degrees.

Now, since Angle ACB = 63 degrees

Then Arc AB = 63 * 2 = 126

Arc AC = 360 - (Arc BC + Arc AB)

We are given BC = 118 degrees

Thus;

Arc AC = 360 - (118 + 126)

Arc AC = 116°

Thus, the least arc angle is Arc AC while the greatest is Arc AB

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complete question:

Triangle ABC is inscribed in a circle centered at point O.

The figure shows triangle ABC is inscribed in a circle centered at point O and has an angle ACB is 63 degrees and arc BC is 118 degrees.

Order the measures of the three intercepted arcs from least to greatest.

Answer:

m<wzx = 71

Step-by-step explanation:

Assuming these are interior angles of a triangle.

The sum of all three interior angles of a triangle is always 180 degrees, therefore:

m<xyz + m<wxz + m<wzx = 180

Substitute our values:

58 + 51 + m<wzx = 180

m<wzx = 180 - 58 - 51

m<wzx = 71

Answer:

a) 120

b) 10

c) 1/12

Step-by-step explanation:

The number of ways that a sample of r can be selected from a population of n is:

nCr = n! / (r! (n−r)!)

a) 3 people selected from a group of 10

₁₀C₃ = 120

b) 3 women selected from a group of 5

₅C₃ = 10

c) Of the 120 committees that can be chose, 10 are all women.  So the probability is 10/120 = 1/12.

Answer:

12.5

Step-by-step explanation:

Answer:

37.5

Step-by-step explanation:

Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

-4 ≤ x ≤ 0

Step-by-step explanation:

Given

x ≤ 0 or x ≥ -4

Required

Write using Interval notation

x ≤ 0 or x ≥ -4

This can be rewritten as

x ≤ 0 or -4 ≤ x

Reorder the above inequality to give:

-4 ≤ x or x ≤ 0

The above inequality can then be combined to give

-4 ≤ x ≤ 0

Hence, the interval notation of x ≤ 0 or x ≥ -4 is -4 ≤ x ≤ 0

Answer:

$|-7000|

Step-by-step explanation:

divide 84000 by 12 = 7000

Answer:

7,000.00

Step-by-step explanation:

if you have 84,000 and divide it by 12 you would get 7,000.

Answer:

59.02%

Step-by-step explanation:

SO SORRY THAT THIS IS LATE anyway what you is minus the biggest number by the smallest number which would be 3,529 - 2,806 = 723

BECAUSE 3,529 is the original number you would do 723 / 3,529 = 0.5902521

then you would times that number by 100

0.5902521 x 100 = 59.02%

hope this helps

Answer:

Initially, national security was defined as the government's ability to protect its citizens from military attacks. Today, this definition also includes other non-military areas such as defense against crime and terrorism, economic security, environmental security, food security, energy security and cyber security.

Answer:

8.25

= root under (8-0)^2+(2-0)^2

= root under (8)^2+(2)^2

=root under 64+4

= root under 68

8.25 units

I hope this will help you and plz mark me as brainest answer

Answer:

I would say about 7 feet and 1 inch

Step-by-step explanation:

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

y=2/3x-2

Explanation:

The equation of a line can be written as y=mx+c

m=slope and c = y-intercept

The point at the x−intercept has coordinates (-3,0)

In y=mx+c

0=2/3(3)+c

0=2+c

-2=c

The equation is y=2/3x-2

Answer:

\( y = \frac{2}{3} x - 3\)

Step-by-step explanation:

Slope (m) = 2/3

y-intercept (b) = - 3

Equation of line in slope intercept form is given as:

\( y = mx + b\)

Plug the values of m and b in the above equation, we find:

\(y = \frac{2}{3} x + ( - 3) \\ \\ y = \frac{2}{3} x - 3\)

Answer:

Chris sells 5 tickets and Mary sells 16 tickets

Step-by-step explanation:

System of Equations

To solve the problem we call:

x = number of tickets sold by Chris

y = number of tickets sold by Mary

They sold a total of 21 tickets, thus:

x + y = 21            [1]

Mary sold adult tickets for $6.50 each and Chris sold student tickets for $4.00 each. The total income was:

4x + 6.5y = 124       [2]

Multiplying [1] by -4:

-4x - 4y = -84            [3]

Adding [2] and [3]:

2.5y = 40

Dividing by 2.5:

y = 40/2.5

y = 16

From [1]

x = 21 - 16 = 5

x = 5

Chris sells 5 tickets and Mary sells 16 tickets

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

base = 12 ft²

The base could be 3 ft x 4 ft, 6 ft x 2 ft, etc.    (any numbers multiplied together = 12)

Step-by-step explanation:

volume = 1/3bh

8 = 1/3b(2)

multiply both sides of the equation by 3:

24 = 2b

b = 12 ft²

Answer:

5(x + 3)

Step-by-step explanation:

the sum of x and 3 is x + 3, then multiply by 5 to obtain

5(x + 3)

Answer:

Step-by-step explanation:

The correlation coefficient that could represent the relationship in the scatterplot is B. -.098.

A correlation coefficient is a number between -1 and 1 that is meant to show the strength of the relationship between two variables.

When the relationship between the variables is negative - one variable increases while the other variable decreases - then the correlation coefficient will be negative.

As we can see in the graph, the relationship between time spent practicing and number of notes played incorrectly is negative. The correlation coefficient will therefore be negative.

-0.098 is therefore the best answer because it is negative. -1.43 is beyond the range of -1 to 1 so cannot be a correlation coefficient.

Options for this question:
A) 0.34 B) -.098 C) -1.43 D) 0.99

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Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

The average distance from the mean is 0.09.

The mean is also known as the average and is calculated by adding up all the values in the set and then dividing the sum by the total number of values.

So, for the given set of data: 24.49, 24.68, 24.77, 24.83, 24.73, the mean would be calculated as follows:

Mean = (24.49 + 24.68 + 24.77 + 24.83 + 24.73) / 5

= 24.70

It tells us what the typical value is within the data set. In this case, the mean value of the data set is 24.70.

Next, let's find the median of the set of data. The median is the middle value of a data set when it is arranged in numerical order. In this case, the data set is already arranged in numerical order, so we can easily find the median.

The median value of the data set is the middle value, which is 24.77.

Now, we will calculate the deviation from the mean for each data point within the set. The deviation from the mean tells us how far each value is from the mean value. This is calculated by subtracting the mean from each value in the set.

Deviation from the mean for each data point:

-0.21, -0.02, 0.07, 0.13, 0.03

As you can see, some values are above the mean, and some are below the mean. The deviation from the mean can be used to determine how spread out the data is from the mean value.

Finally, we will calculate the mean deviation for the set. The mean deviation is the average of the absolute values of the deviation from the mean.

Mean deviation = (|(-0.21)| + |(-0.02)| + |0.07| + |0.13| + |0.03|) / 5

= 0.09

The mean deviation tells us the average distance from the mean value.

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Answer:

Variance = 0.1645

Standard deviation = 0.4056

Step-by-step explanation:

Kindly check attached picture for detailed explanation

a) Option a) 9 - 1/2 is equal to 17/2.

b) Option b) 27 - 2/3 is equal to 79/3.

a) The expression 9 - 1/2 can be simplified by finding a common denominator for the terms. The common denominator for 9 and 1/2 is 2.

Multiplying 9 by 2/2, we get:

9 * (2/2) = 18/2

So, the expression 9 - 1/2 can be simplified to:

18/2 - 1/2 = 17/2

Therefore, option a) 9 - 1/2 is equal to 17/2.

b) The expression 27 - 2/3 can be simplified in a similar manner by finding a common denominator for the terms. The common denominator for 27 and 2/3 is 3.

Multiplying 27 by 3/3, we get:

27 * (3/3) = 81/3

So, the expression 27 - 2/3 can be simplified to:

81/3 - 2/3 = 79/3

Therefore, option b) 27 - 2/3 is equal to 79/3.

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Answer:

The zeroes of f(x) = (x-7)(x+8) are 7 and -8.

Step-by-step explanation:

You have to figure out what makes each of the equal to zero.

Step 1 : Make the 2 equations both equal 0.

x-7 = 0

x+8 = 0

Step 2: Solve for x

x-7 = 0

x=7

x+8 = 0

x=-8

So 7 and -8 are both zeroes of this function.

Answer:

$638.4

Step-by-step explanation:

Randy's gross salary (salary without any deduction) = $760

taxed rate =16%

Amount tax paid =tax% of gross income

=16/100 * $760

=$16*760/100

=$12160/100

=$121.6

net salary = gross salary - tax paid

=$760 - $ 121.6

=$638.4

Randy's net salary is $638.40

Randy's gross salary = $760 per week.

Tax paid on his salary = 16%

Net salary is the difference between the salary earned and the amount paid as tax. This will be:

= Salary - Tax

= $760 - (16% × $760)

= $760 - (0.16 × $760)

= $760 - $121.60

= $638.40

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Answer:

c(3a) = 2(3a)^2 - 4(3a) + 3 = 18a^2 - 12a + 3.

Step-by-step explanation:

c(3a) = 18a^2 - 12a + 3

Note: this is the simplified form of the expression.