Select the correct answer from each drop-down menu.

The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side

of the playground. The length of the playground is /and its width is w. The length of each side of the flower beds is a. Which two equivalent

expressions represent the total fencing material required to surround the playground and flower beds? Assume that the playground and beds

do not overlap

Answer: Children = 108

Adult = 52

Step-by-step explanation:

Let x = number of children

Let y = number of adult

Based on the information given, we can form an equation which will be:

x + y = 160 ........ i

2x + 5y = 476 ........ ii

Multiply equation i by 2

Multiply equation ii by 1

2x + 2y = 320 ....... iii

2x + 5y = 476 ........ iv

Subtract iii from iv

3y = 156

y = 52

Number of adults = 52

Since x + y = 160

x + 52 =160

x = 160 - 52

x = 108

Number of children = 108

Answer:

(y-5)^2=14(x+7/2)

Step-by-step explanation:

The equation for a parabola with a focus at (0,5) and a directrix at x = -7 is (y - 5)² = 14 (x + 3.5).

A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.

Given,

Focus of the parabola at (0, 5).

Directrix is x = -7.

The parabola is horizontal parabola since the directrix is a vertical line.

Equation of the parabola is of the form,

(y - k)² = 4p (x - h)

Here (h, k) is the vertex.

Vertex of the parabola is the mid point of focus (0, 5) and the point (-7, 5).

(h, k) = ([tex]\frac{0 + -7}{2}[/tex], 5) = (-7/2, 5)

Now, p is the distance from vertex to focus.

p = 0 - -7/2 = 7/2 = 3.5

So the equation is,

(y - 5)² = 4× 3.5 (x - -3.5)

(y - 5)² = 14 (x + 3.5)

Hence the equation is (y - 5)² = 14 (x + 3.5).

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Answer:

Slope = 1/5

Step-by-step explanation:

After plotting the points you do rise over run. 1/5 or 1 over 5 meaning you rise 1 and run across 5 to get to the next point

Answer:

$720

Step-by-step explanation:

The formula is:

A = P(1 + rt)

We know

P = $6000

r = 3% = 0.03

t = 4 years

A = 6000( 1 + 0.03 x 4) = $6720

Now we have to find the interest by taking

$6720 - $6000 = $720

So, he earns $720 in interest in 4 years.

The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x) = log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x)=log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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In the spring of 2012, 2300 student athletes participated in a sport.

The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

In 2014, there were 2277 student athletes participating in spring sports.

Suppose there were x contestants in 2013.

The answer was 2277, which was 110 percent more pupils competing in 2014 than in 2013. So,

[tex]$110 \%$ of $\mathrm{x}=2277$$\frac{110}{100} \times \mathrm{x}=2277$$\mathrm{x}=\frac{2277 \times 100}{110}$$\mathrm{x}=2070$[/tex]

2070 pupils therefore competed in 2013.

Let y be the student who will be vying in 2012.

Now, the number of pupils competing in 2070 was 90% that of the year 2012's.

So,

[tex]$90 \%$ of $y=2070$$$\begin{aligned}& \frac{90}{100} \times y=2070 \\& y=\frac{2070 \times 100}{90} \\& y=2300\end{aligned}$$[/tex]

As a result, 2300 students competed in the 2012 competition.

Therefore, the answer is 2300.

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Answer:

(9, -5)

Step-by-step explanation:

The vector AC has coordinates (27, -18), because:

21 - (-6) = 27

-13 - 5 = -18

If the ratio of AB to BC is 5 to 4, it means that

AB = [5/(5+4)]AC = (5/9)AC

Therefore, we have

AB = (5/9)AC = (5/9) (27, -18) = (15, -10)

Which means that:

xB - xA = 15 <=> xB - (-6) = 15 <=> xB + 6 = 15 <=> xB = 9

yB - yA = -10 <=> yB - 5 = -10 <=> yB = -10 + 5 <=> yB = -5

So B has coordinates (9, -5).

Answer:1

Step-by-step explanation:;

Answer: 4y (4y^2-2y-5)

Step-by-step explanation:

24 cars lacked power steering but did have air conditioning and an automatic gearbox.

According to the question,

No. of cars with Air conditioning = 88

No. of cars with Automatic transmission = 96

No. of cars with power steering = 76

All three = 4

None of these extras = 19

Only air conditioning = 23

Only automatic transmissions = 61

Only power steering = 28

Power steering and automatic transmission both = 11

The calculation for missing values:

11 - 4 = 7

96-61-4-7 = 24

88-24-4-23=37

It is obvious that 24 cars lacked power steering but did have air conditioning and an automatic gearbox.

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The domain and range of f(x) = |x| is

Domain: all real numbers

range: positive real numbers

The distance of a number from a number line's origin is referred to as the absolute value of that number. Its representation is |x|, which establishes the size of any integer 'x'.

Any integer's absolute value, regardless of its sign, will be one of the real numbers, whether it is positive or negative. The modulus of x, which is represented by two vertical lines |x|, is a mathematical concept.

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value.

Since absolute value can be zero the range is all positive numbers

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Answer: 2.4

Step-by-step explanation:

we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.

hope that helps...

The number of phones sold is 26 and the number of accessories sold is 30.

An equation is said to be linear if the maximum power of the variable is usually 1.  A linear equation with one variable has the standard form Ax + B = 0. In this case, x is the variable and A is the coefficient of x, and B is a constant.

In mathematical problems, 'x' stands for unknown value or quantity. Here we use the Linear equation concept to solve the problem.

Given that

Cameron earns an $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells.

On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold. ​

Let x and y be the number of phones and accessories

Given that

Cameron made a total of $361 in commission

=> 11x + 2.5y = 361  ----- (1)

Total number of phones and accessories sold

=> x + y = 56

Multiply by 11

=> 11x + 11y = 616 ----- (2)

Do (2) - (1)

=> 11x + 11y - ( 11x + 2.5y) = 616 - 361

=> 11x + 11y - 11x - 2.5y = 255

=> 8.5y = 255

=> y = 255/8.5

=> y = 30  

Substitute y = 30 in x + y = 56  

=> x + 30 = 56

=> x = 26

Therefore,

The number of phones sold is 26 and the number of accessories sold is 30.

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a. The exponential function that is good model for the country population is:

Pₙ = 8100000(1.02)ⁿ ,

b. It will take 5.27 years to reach 9 million.

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Exponential Function Formula

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent.

a. Given,  initial population P₀ = 8100000, Rate of increase R = 2%.

If a constant rate of growth be R% per annum,

then function for population after n years

Pₙ = P₀ x (1+R/100)ⁿ

Population Pₙ = 8100000 × (1+2/100)ⁿ

Pₙ = 8100000(1.02)ⁿ

b. Let after x years population will be 9 million.

then,

9000000 = 8100000 (1 + 2/100)ˣ

(1 + 2/100)ˣ = 9000000/8100000

(1.02)ˣ = 90/81

(1.02)ˣ = 1.11

Taking log on both sides

ln (1.02)ˣ = ln (1.11)

ln(a)ⁿ = n ln(a)

x ln(1.02) = ln (1.11)

x = ln(1.11)/ln(1.02)

x = 5.27 years

Hence, the population will reach 9 million in 5.27 years.

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Given:

The quadratic equation is:

[tex]12a^2+9a+7=0[/tex]

To find:

The solution of the given equation in simplest form by using the quadratic formula.

Solution:

If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have,

[tex]12a^2+9a+7=0[/tex]

Here, [tex]a=12,b=9,c=7[/tex]. Using the quadratic formula, we get

[tex]x=\dfrac{-(9)\pm \sqrt{(9)^2-4(12)(7)}}{2(12)}[/tex]

[tex]x=\dfrac{-9\pm \sqrt{81-336}}{24}[/tex]

[tex]x=\dfrac{-9\pm \sqrt{-255}}{24}[/tex]

[tex]x=\dfrac{-9\pm i\sqrt{255}}{24}[/tex]              [tex][\because \sqrt{-a}=i\sqrt{a}][/tex]

The solutions of the given equations are [tex]x=\dfrac{-9-i\sqrt{255}}{24}[/tex] and [tex]x=\dfrac{-9+i\sqrt{255}}{24}[/tex].

Therefore, the correct option is B.

Answer:

y = 8/5x - 3

Step-by-step explanation:

First, find the slope using rise over run (y2 - y1) / (x2 - x1)

(y2 - y1) / (x2 - x1)

(-19 - 5) / (-10 - 5)

-24 / -15

= 8/5

Plug in the slope and a given point into y = mx + b, and solve for b

y = mx + b

5 = 8/5(5) + b

5 = 8 + b

-3 = b

Plug in the slope and b into y = mx + b

y = 8/5x - 3

So, the equation is y = 8/5x - 3

The equation is

log ( milligrams of drug A ) =3 - 0.0737 ( Time)

As per the details  stated above,

Curved relationship between the number of milligrams of drug A is  (x) still in the body and the number of hours since drug A was delivered (y)

The co-efficient of the constant is 3.00

the co-efficient of the time is -0.0737

the SE  co-efficient of the constant is 0.4017

the SE co-efficient of the time is 0.005

the t-ratio of the constant is 7.481

the t-ratio of the time is -14.74

now the equation formed is

logarithm of drug A in milligrams is  (The co-efficient of the constant - the co-efficient of the time )

that is log ( milligrams of drug A ) =3 - 0.0737 ( Time).

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Answer:

the distance would be 13 units

Answer:

Ot would be 13 units but I saw somone already posted But hope this helps

Answer:

2. one angle is 108, and other is 72

3. x is 12

Step-by-step explanation:

the ratio is 3:2.

3x + 2x = 180

5x = 180

x = 36

36 x 3 = 108

36x 2 = 72

so that is why the two angles re 108and 72.

for the last question, 37 plus 41 plus x = 90

37 plus 41 is 78

90 - 78 = 12

so that is why x is 12.    

Answer:

1. 360

2. Yes because in a regular hexagon all angles are congruent so the exterior angles are as well

3. (i) 60 (ii) 120

4.

(i) 1. 360 2. Yes because in a regular octagon all angles are congruent so the exterior angles are as well 3. (i) 45 (ii) 135

(ii) 1. 360 2. Yes because in a regular 20-gon all angles are congruent so the exterior angles are as well 3. (i) 18 (ii) 162

Step-by-step explanation:

Works for each polygon

1. First take the number of sides and subtract it by 2 then multibly that by 180

6-2=4x180=720

Then divide by the number of angles and subrtact that number by 180 to find the measure of one exterior angle

720/6=120

180-120=60

Then multiply by the number of exterior angles

60x6=360

2. Regular polygons always have equal angles so the exterior angles are as well

3. Put in your numbers from earlier

(i) 60 (ii)120

Hope this helps! :)

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Thus, complete scale is: 1 inch = 57.7 miles

This can be solved by the concept of cross-multiplication method.

A centimeter is smaller than an inch. On the other side of the centimeter ruler, inches are denoted by the large, continuous hash marks that are inscribed above the digits. On a ruler, the inch is the largest unit and is denoted by the longest line. There is a number next to each 1-inch line on the ruler that designates.

Since the international yard was adopted in the 1950s and 1960s, standards for the precise length of an inch have fluctuated, but the inch is now based on the metric system and is defined as precisely 25.4 mm.

Correct order is:

d. 27 / 1557 = 1/d

e. 27 . d = 1 . 1557

a. 27d = 1557

f. 27d / 27 = 1557 / 27

b. d = 57.7

c. scale: 1 inch = 57.7 miles

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Answer:

m=3n

Step-by-step explanation:

3 movies per month. So 3 n per m.

Answer:

n=3m

Step-by-step explanation:

n is number of movies

3 is the 3 movies per month

m is each month

so it's n=3m

Answer:

A= 4pi r

C = 2pi r

Step-by-step explanation:

A plot point example contains a point in a story that defines the turning point in the story.

A story's plot point is a crucial turning moment that occurs during the narrative. The tale and the characters may be developed and advanced using these ideas.

Plot points offer your tale movement by advancing the plot and dragging the reader along. 'A particularly crucial portion of a storyline of a work of fiction,' according to the definition of a plot point. Never undervalue the significance of your framework, even if your book is contemplative or literary.

An example of plot point is :

In a story about a young girl who is trying to save her village from an impending monster attack, the plot point may occur when the girl discovers an ancient artifact that gives her the power to defeat the monster. This event marks a significant turning point in the story, as it sets the stage for the girl to take on the monster and potentially save her village.

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Answer:

8 + 56d

Step-by-step explanation:

We will open the parentheses, multiplying the stuff outside by the stuff inside. So, we get:

8*1 + 8*7d

Then, we can simplify by giving us:

8 + 56d

Hope this helped!

Answer:

slope is zero

Step-by-step explanation:

slope is the difference of the y-values over the difference of the x-values

(-3-(-3)) ÷ (5-2)

0/3