How much of the circle is shaded? Write your answer as a fraction in simplest form.

The solution to the expression in this problem is given as follows:

x = -1/3 + 1.7i and x = -1/3 - 1.7i.

The rational expression for this problem is defined as follows:

[tex]\frac{2x}{3x - 5} - \frac{x + 1}{3x + 5} = -\frac{4}{9x^2 - 25}[/tex]

Applying the least common factor at the left side, we have that:

[tex]\frac{2x(3x + 5) - (x + 1)(3x - 5)}{9x² - 25} = -\frac{4}{9x^2 - 25}[/tex]

[tex]\frac{6x^2 + 10x - 3x^2 + 5x - 3x + 5}{9x^2 - 25} = -\frac{4}{9x^2 - 25}[/tex]

As the denominators are equal, the solution is obtained equaling the denominators, hence:

3x² + 2x + 5 = -4

3x² + 2x + 9 = 0.

Which is a quadratic function with coefficients given as follows:

a = 3, b = 2, c = 9.

Inserting these coefficients into a calculator, the solutions are given as follows:

x = -1/3 + 1.7i and x = -1/3 - 1.7i.

The rational expression is given by the image presented at the end of the answer.

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Question 1:

[tex]\frac{2}{3} n-16=-\frac{5}{6}n+2[/tex], solve for n.

[tex]\frac{2}{3} n-16=-\frac{5}{6}n+2[/tex]

=> [tex]\frac{2}{3} n=-\frac{5}{6}n+18[/tex]

=> [tex]\frac{2}{3} n+\frac{5}{6}n=18[/tex] =>[tex]\frac{4}{6} n+\frac{5}{6}n=18[/tex]

=> [tex]\frac{9}{6} n=18[/tex] => [tex]\frac{3}{2} n=18[/tex]

=> [tex]n=18(\frac{2}{3})[/tex]

=> [tex]n=6(2)[/tex]

Sol: n=12

Question 2:

[tex]5-\frac{1}{3}p=\frac{4}{9}p+12[/tex], solve for p.

[tex]5-\frac{1}{3}p=\frac{4}{9}p+12[/tex]

=>[tex]5=\frac{4}{9}p+\frac{1}{3}p+12[/tex]

=> [tex]5=\frac{4}{9}p+\frac{3}{9}p+12[/tex]

=>[tex]5=\frac{7}{9}p+12[/tex]

=> [tex]-7=\frac{7}{9}p[/tex]

=> [tex]-7(\frac{9}{7}) =p[/tex]

=> [tex]-(9)=p[/tex]

Sol: p=-9

Question 3:

The relationship between ∠2 and ∠7 is that they are alternate interior angles.

Question 4:

The relationship between ∠1 and ∠3 is that they are corresponding angles.

Question 5:

The relationship between ∠4 and ∠5 is that they are alternate exterior angles.

eeeeeAnswer:

Step-by-step explanation:

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 for Function A.

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{(-8)}}} \implies \cfrac{4 +5}{10 +8} \implies \cfrac{ 9 }{ 18 } \implies \cfrac{1 }{ 2 }\impliedby \stackrel{\textit{slope of}}{A} \\\\[-0.35em] ~\dotfill[/tex]

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{5}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \stackrel{\textit{slope of}}{B} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{A}{\cfrac{1}{2}} ~~ < ~~ \stackrel{B}{5} \end{array}}~\hfill[/tex]

At 11.5 hours, the red turtle pass the blue turtle. The red turtle won the race. The solution has been obtained by studying graph of the functions.

What is graph of the function?

The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. The graph of f is also known as the graph of

y = f(x).

In the graph, it is seen that from 6 to 13 hours, the blue turtle is at the same place whereas the red turtle is moving.

Therefore, at 11.5 hours the red turtle passes the blue turtle.

The red turtle won the race in 16 hours because in the graph it is observed that the blue turtle did not complete the entire km. The graph of blue turtle is a little less than that of red turtle.

Hence, at 11.5 hours, the red turtle pass the blue turtle and wins the race.

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Since there are multiple questions, so the question answered above is attached below.

Answer:

3

Step-by-step explanation:

Take the x-intercept (1,0) and y-intercept (0,-3) to find the slope/gradient:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-3)}{1-0}=3[/tex]

The missing angle measure for the following letters are:

a - 65°

b - 115°

c - 115°

d - 65°

e - 65°

Corresponding angles are generated when two parallel lines are crossed by a transversal.

Opening and closing a lunchbox, completing a Rubik's cube, and endless parallel railway tracks are all examples of equivalent angles.

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Answer:

the answer is A

I hope I help you in this ans and tq.

The function of x giving the length of each of the original sides would be  [tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex].

What is Function of x?

A function is a formula that expresses one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) states that y changes depending on the value of x.

The original length of each side of the lawn can be represented by the function x + 100, and the original width can be represented by the function x + 60.

To find the area of the original lawn, we can multiply the length and width functions.

So, the function for the area of the original lawn is:

         [tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex]

This is a quadratic function in x, whose leading coefficient is 1, and the value of x is the same amount of length added to each side of the lawn.

Hence, The function of x giving the length of each of the original sides would be  [tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex].

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The time in years for which the values are the same is given as follows:

7.25 years.

A decaying exponential model is given as follows:

y = a(1 - r)^t.

For which:

The parameters for this problem are given as follows:

a = 56000, r = 0.12.

Hence the exponential model is given as follows:

y = 56000(0.88)^x.

The linear model is given as follows:

y = b - mx.

In which:

The parameter values for this problem are given as follows:

b = 56000, m = 56000/12 = 4666.67.

Hence the linear model is:

y = 56000 - 4666.67.

The point of intersection of the two graphs is at a time of 7.25 years.

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According to economists, her opportunity cost of consuming caramel-coated popcorn would be the forgone peanut butter pretzels.

Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them.

Better choices can be made by being aware of the opportunities that might be lost when a company or person chooses one investment over another. It is necessary to weigh the advantages and disadvantages of each choice offered in order to correctly assess opportunity costs.

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Answer: 70/13

Step-by-step explanation:

Slope = rise/run

(r-5)/(6-r) = 5/8

30-5r = 8r-40

70 = 13r

70/13 = r

Answer:

  0.4247

Step-by-step explanation:

You want to know the proportion of heights less than 103.1 cm if the population is normal with a mean of 105 cm and a standard deviation of 10 cm.

The proportion can be found using a suitable probability calculator. The one shown in the attachment tells us ...

  the proportion of heights less than 103.1 cm is about 0.4247.

__

Additional comment

The height of interest is less than the mean by approximately 0.2 times the standard deviation. This suggests the proportion will be close to, but less than, 0.5000.

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For the relation of times of money , Francine and Tommy start with the amount of money equals to $18 and $3 respectively.

Let 'x' represents the amount of money with Francine .

And 'y' represents the amount of money with Tommy.

In the first condition:

x = 6y __(1)

To purchase baseball cap Francine gave $33 then the given relation is :

y - 33 = 2( x - 33 )

⇒ y - 33 = 2x - 66

⇒y = 2x -66 + 33

⇒ y = 2x -33 __(2)

Substitute the value of 'x' from (1) in (2) we get,

y = 2(6y) - 33

⇒y = 12y - 33

⇒ 12y - y = 33

⇒ 11y = 33

⇒ y = $3

⇒ x = 6(3)

⇒ x = $18

Therefore, the amount of money Francine and Tommy start with is equal to $18 and $3 respectively.

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Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of different sizes.

Frequency distributions can show the actual number of observations falling in each range or the percentage of observations. In the latter sample, the distribution is called a relative frequency distribution.

Frequency distribution tables can be utilised for both categorical and numeric variables. Continuous variables should only be used with class intervals, which will be described shortly.

A relative frequency distribution displays the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.

--This question is incomplete; the complete question is

"Relative frequency distributions are generally more useful than frequency distributions when _____."--

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Area swept by minute hand of a clock is 66cm².

Given that length of the minute hand of clock is 6cm.

We know that, total angle covered by the minute hand of clock is 360° in 60 minutes.

Total time interval = 7:45 PM – 7:05 PM = 35 minutes

In 60 minutes 360° angle covered

Then, in 1 minute 360/60 angle covered

So, in 35 minutes

total angle covered = 360/60 * 35 = 210°

Total area covered = sectional area of circle with radius 6cm

Total area covered = Ф/360 * πr²

= 210/360 * 22/7 * 6² = 66 cm²

Therefore, total area swept by minute hand of a clock is 66cm².

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The Interquartile range of the given set is 1.5.

What is Interquartile range ?

The variation between the third and first quartiles is defined by the interquartile range. The numbers that partition the entire series into four equal sections are known as quartiles. There are therefore 3 quartiles. The lower quartile is represented by the letter Q₁, the higher quartile by the letters Q₁, and the middle quartile by the letter Q₃.

Given set : 81, 82, 83, 83, 84, 84, 84, 85

Here, It is already in increasing order but the number of values is 8 which is even.

So, Q₁ part = 81, 82, 83, 83

Q₁ will be the median of 82 and 83.

So, Q₁ = (82+83)/2

          = 82.5

Similarly, Q₃ part =84, 84, 84, 85

So, Q₃ will be the median of 84 and 84.

hence, Q₃ = (84+84)/2

                 = 84

We know that, Interquartile range = Q₃ - Q₁

                                                          =  84 - 82.5

                                                          = 1.5

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The value of the function f(0) + f(-4) is -12

From the question, we have the following equation that can be used to solve the question

f(x) = 3 - |2x - 5|

Also, we have the function values to be

f(0) and f(-4)

When these values are calculated, we have

f(0) = 3 - |2(0) - 5| = -2

f(-4) = 3 - |2(-4) - 5| = -10

substitute the known values in the above equation, so, we have the following representation

f(0) + f(-4) = -2 - 10

Evaluate

f(0) + f(-4) = -12

Hence, the solution is -12

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The value of k is -2

Now, According to the question:

The given equation is:

20 - 6 + 4k = 2 - 2k

We have to solve for the value of k.

Now,

20 - 6 + 4k = 2 - 2k

Combine the like terms;

20 - 6 - 2 = -2k - 4k

Calculate the sum or difference:

20 - 8 = -6k

12 = -6k

Calculate the product or quotient:

k = -12/6

k = -2

Hence, The value of k is -2

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To find the smallest even consecutive numbers whose sum is at most 90, we can start with the smallest even number, which is 2. Then, we can add 2 to it to get the next even number, which is 4. We can keep adding 2 to get the next even numbers, and keep track of their sum. We can stop as soon as the sum exceeds 90.

The smallest even consecutive numbers whose sum is at most 90 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90

The first 20 even consecutive numbers sum 90.

Answer:

$8,600 - $31,100

Step-by-step explanation:

Hope this helps :)

So, the probability that a randomly selected cell phone that has been recalled came from site 3 is 2.5 or 25%.

We can use Bayes' theorem to calculate the probability that a phone that has been recalled came from site 3. Bayes' theorem states that:

P(A|B) = P(B|A) * P(A) / P(B)

where:

P(A|B) is the probability of event A occurring given that event B has occurred (in this case, the probability that a phone came from site 3 given that it has been recalled)

P(B|A) is the probability of event B occurring given that event A has occurred (in this case, the probability that a phone has been recalled given that it came from site 3)

P(A) is the prior probability of event A occurring (in this case, the probability that a phone came from site 3)

P(B) is the prior probability of event B occurring (in this case, the probability that a phone has been recalled)

So, in this case, we have:

P(site 3 | recalled) = P(recalled | site 3) * P(site 3) / P(recalled)

We know that:

P(recalled | site 3) = 9%,

P(site 3) = 10%

We also know that:

P(recalled) = P(recalled | site 1) * P(site 1) + P(recalled | site 2) * P(site 2) + P(recalled | site 3) * P(site 3)

= (5% * 60%) + (7% * 30%) + (9% * 10%) = 3% + 2.1% + 0.9% = 6%

So, we can now calculate the probability that a phone that has been recalled came from site 3 as:

P(site 3 | recalled) = (9% * 10%) / 6% = 0.15 / 0.06 = 2.5

So the probability that a randomly selected cell phone that has been recalled came from site 3 is 2.5 or 25%.

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Answer:

X ≤ -1

How do we know this?

Well, if x = the value of any number in the graph, we can see that it can be equal to negative one, or less than -1, meaning we use the symbol ≤.

The inequality describes the mile marker she would be at this point is:

325 + 2y ≤ 475

Now, According to the question:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

The fastest driving speed of Willow is 75 miles per hour,

There is a bit of traffic on her route that might slow her speed down,

So, the inequality which represents the speed of the willow is:

y ≤ 75

Hence, the inequality which represents the speed of the driving of willow is y ≤ 75.

Now, the expression 361 + 2y represents what mile marker he is at after 2 hours. We know that the fastest he will drive is 75, so we could replace y=75 in the last expression to know what mile marker he would be seeing at that point. This is:

325 + 2(75) => 325 + 150 = 475

Now, we know that the inequality would be:

325 + 2y ≤ 475

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The area of the roof is 157.5 .

It is given that the roof of a clock tower is a pentagonal pyramid.

Each side of the base is 7 ft long.

The slant height is 9 ft.

we know that, to find area we have,

Area=1/2 × 7 × 9 × 5

= 315/2

= 157.5

Hence, 157.5 square feet is the area of the roof.

Pentagonal pyramid

A pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point.

It is a three  dimensional figure, it is a solid figure or an object or shape that has three dimensions—length, width, and height.

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The smallest equivalent fraction of the number is considered to be its simplest form.The answer is  7/3 : 21/5 = 5 : 9.

Values should now be entire numbers.By removing the denominators, convert fractions to integers.

Since the denominators of our two fractions are different, we must identify the least common denominator and rewrite our fractions using the common denominator as necessary.

LCD(7/3, 21/5) = 15

Now we have:

7/3 : 21/5 = 35/15 : 63/15

Now that the denominators of our two fractions are similar, we may multiply them both by 15 to get rid of the denominators.

Then, we have:

7/3 : 21/5 = 35 : 63

With the highest common factor, attempt to further reduce the ratio (GCF).

GCF is 7 for 35 and 63.

Divide both terms by GCF 7, then:

35 ÷ 7 = 5

63 ÷ 7 = 9

By multiplying both components by the GCF = 7, it is possible to reduce the ratio 35: 63 to its simplest terms.

35 : 63 = 5 : 9

Therefore:

7/3 : 21/5 = 5 : 9

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The number 868 represents the final balance of the acount, then we conclude that the correct option is C.

"The value 868 represents the final balance in the account, which means the account ended with $868."

Weknow that the equation 868 = 700(1 + 0.04t) represents the amount of money earned on a savings acount.

We want to see what does 868 represent in this situation.

Where the form of the equation is:

money earned = function that depends on t.

So the value at the left, 868, just represents the final balance of the account, this is the amount of money that there is in the account at the end.

Thus, the correct option is C.

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After the increment in the function the value of x is -2.25

In math the term function is denoted as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we know that the function g(x)=6cos(7x+22), x increase by for 7x+22 to increase by 2π.

In order to calculate the value of x in the function, we have to equate the value of function with 2π.

Then we get,

=> 7x + 22 = 2π

When we solve the equation for x then we get,

=> 7x = 2π - 22

=> x = (2π - 22)/7

When we simplify this one then we get the value of x as,

=> x = 0.285π - 3.14

=> x = 0.89 - 3.14

=> x = -2.25

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