a fire station is to be located along a road of length a, where a is a fixed positive real number. if fires will occur at points uniformly chosen on (0, a), where should the station be located so as to minimize the expected distance from the fire?

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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Jade's mother is the sun of Jade because she motivated Jade against race and gender, class and privilege, and fear and courage. Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, Jade's mother is the sun. So the option 3 is correct.

While expressing the complicated emotions of an aspirational, devoted girl, Jade's narrative voice offers riveting insights on the intricacies of race and gender, class and privilege, and fear and courage. Watson's story, which brims with empathy and wisdom, extols the ability of creative expression to reimagine and transform the world.

The many individuals who find themselves in the world looking for themselves are addressed in Watson's exquisitely written book. Piecing Me Together is a novel about how young people deal with the struggles and pain of daily life while remaining entire and true to themselves. It is both timely and timeless.

The reason why Jade's mother is said to as the sun of Jade is because she inspired Jade to overcome prejudices related to class, privilege, and fear.

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The complete question is:

Consider this excerpt from chapter 39:

Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, who is the sun?

1. The tour guide

2. Maxine

3. Jade's mother

4. The symphony members

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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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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For the given statement, the domain and range are - Domain : x ,Range : f(x)  40.

In mathematical notation, symbols are used in expressions and formulas to represent operations, unnamed numbers, relations, and any other mathematical objects. In mathematics, science, and engineering, mathematical notation is frequently used to communicate complicated ideas and properties in a clear, unambiguous manner.

A notation is a set of clear guidelines for using symbols to describe numbers and actions.

The sum of numerous linked terms is frequently represented by the sign (capital sigma) in shorthand notation. In statistics, sigma notation is frequently employed.

For each dividend number, the extended notation division method merely repeats the division, multiplication, and subtraction operations.

Given data :

x is the mass of the chicken (in kg)

f(x) : the cooking time ( in minutes )

Domain : x

Range : f(x)  40

f(x) = 15x + 40 - 15 minutes per kg (x) plus 40 more minutes

f (1) = 15 x 1 + 40 = 55

A 1 kg chicken needs 15 min + 40 min = 55 min

f (2) = 15 x 2 + 40 = 70

A 2 kg chicken needs 30min + 40 min = 70 min

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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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A per the measurement, there is only form exactly 1 unique triangle.

The term triangle in math is known as a two-dimensional shape with three sides, three interior angles, and three vertices.

Here we have know that a rope 10 units in length, if side lengths must be in whole units.

And we need to find the number of different triangles can be made.

Here we know that length is 10 units, and the side length are whole units.

Which means that here we have 3 distinct value.

So as we all know that all of the triangles you make are the same triangle. Which means that if your three side lengths can form a triangle, then they can only form exactly 1 unique triangle.

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The simplified form of the expression (3x² - 4xy + y²)(4x + 3y) is 12x³ - 7x²y + 8xy²  + 3y³.

Given the expression in the question;

(3x² - 4xy + y²)(4x + 3y)

To simplify, apply distributive property by multiplying each term in the first expression by each term in the second expression.

(4x + 3y)(3x² - 4xy + y²)

4x (3x² - 4xy + y²) + 3y(3x² - 4xy + y²)

3x² × 4x - 4xy × 4x  + y² × 4x  + 3x² × 3y - 4xy × 3y  + y² × 3y

12x³ - 16x²y + 4xy²  + 9x²y - 12xy²  + 3y³

Collect like terms

12x³ - 16x²y + 9x²y + 4xy²  - 12xy²  + 3y³

Add -16x²y and 9x²y

12x³ - 7x²y + 4xy² - 12xy²  + 3y³

Add 4xy²  and -12xy²

12x³ - 7x²y + 8xy²  + 3y³

Therefore, the simplified form is 12x³ - 7x²y + 8xy²  + 3y³.

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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]

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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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.

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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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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eeeeeAnswer:

Step-by-step explanation:

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 equation is 2m + 3.10 = 21.10

And, the number of miles in the taxi ride is m = 9.

Now, According to the question:

Joseph took a taxi from his house to the airport. The taxi company charged a pick-up fee $3.10 plus $2 per mile. The total fare was $21.10.

Now,

The equation is written as,

2m + 3.10 = 21.10

Subtract 3.10 from both sides

2m = 18

Divide 2 from both sides

m = 9

Hence, The equation is 2m + 3.10 = 21.10

And, the number of miles in the taxi ride is m = 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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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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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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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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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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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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Lateral Area = 108 square km

Surface Area = 120 square km

Think of the triangles as the floor and ceiling of this 3D room. The walls are three rectangular sides.

We have a 9 by 4 wall with an area of 9*4 = 36 square km

We have a 9 by 3 wall with an area of 9*3 = 27 square km

We have a 9 by 5 wall with an area of 9*5 = 45 square km

The lateral area is 36+27+45 = 108

The two triangles form the base faces of this prism.

Let's find the area of one of the triangles

area=0.5*base*height = 0.5*3*4 =6

One triangle has an area of 6, so both triangles in total have an area of 2*6 = 12 square km.

The total surface area is therefore 108+12 = 120 square km.

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Answer:

$8,600 - $31,100

Step-by-step explanation:

Hope this helps :)

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:

  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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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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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