How many flowers spaced every 4 inches are needed to surround a circular garden with a 15-foot radius? Round all circumference and area calculations to the nearest whole number.

9514 1404 393

Answer:

  -1/3x

Step-by-step explanation:

We want to find the term 'a' such that ...

  (5/6x -4) + a = (1/2x -4)

Add 4-1/2x to both sides.

  (5/6 -1/2)x -4 +4 +a = 0

  (5/6 -3/6)x + a = 0 . . . . . . express the fractions using a common denominator

  1/3x + a = 0 . . . . . . . . . . simplify the difference

  a = -1/3x . . . . . . . . . . .subtract 1/3x

The term you can add to make the desired equivalent is -1/3x.

9514 1404 393

Answer:

  a) yes

  b) see attached

  c) see discussion

  d) neither

  e) increasing (2,5); decreasing (-2, 2)

Step-by-step explanation:

a) The graph passes the vertical line test, so is the graph of a function.

__

b) A table of values is attached

__

c) Generally, this sort of function would be defined piecewise:

  [tex]\displaystyle f(x)=\begin{cases}-\dfrac{1}{2}x+1&\text{for }-2\le x<2\\2x-4&\text{for }2\le x \le5\end{cases}[/tex]

In the attachment, we have shown the use of the "maximum" function to define it. The effect is the same.

__

d) The function has no symmetry about the origin or the y-axis, so is neither odd nor even.

__

e) The function is increasing where the line has positive slope, on the interval (2, 5). The function is decreasing where the line has negative slope, on the interval (-2, 2).

Answer:

[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}][/tex]

when:

[tex]|x|<\frac{1}{2}[/tex]

Step-by-step explanation:

In order to solve this problem, we must begin by splitting the function into its partial fractions, so we must first factor the denominator.

[tex]\frac{x+6}{2x^2-9x+5}=\frac{x+6}{(2x+1)(x-5)}[/tex]

Next, we can build our partial fractions, like this:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]

we can then add the two fraction on the right to get:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A(x-5)+B(2x+1)}{(2x+1)(x-5)}[/tex]

Since we need this equation to be equivalent, we can get rid of the denominators and set the numerators equal to each other, so we get:

[tex]x+6=A(x-5)+B(2x+1)[/tex]

and expand:

[tex]x+6=Ax-5A+2Bx+B[/tex]

we can now group the terms so we get:

[tex]x+6=Ax+2Bx-5A+B[/tex]

[tex]x+6=(Ax+2Bx)+(-5A+B)[/tex]

and factor:

[tex]x+6=(A+2B)x+(-5A+B)[/tex]

so we can now build a system of equations:

A+2B=1

-5A+B=6

and solve simultaneously, this one can be solved by substitution, so we get>

A=1-2B

-5(1-2B)+B=6

-5+10B+B=6

11B=11

B=1

A=1-2(1)

A=-1

So we can use these values to build our partial fractions:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]

[tex]\frac{x+6}{(2x+1)(x-5)}=-\frac{1}{2x+1}+\frac{1}{x-5}[/tex]

and we can now use the partial fractions to build our series. Let's start with the first fraction:

[tex]-\frac{1}{2x+1}[/tex]

We can rewrite this fraction as:

[tex]-\frac{1}{1-(-2x)}[/tex]

We can now use the following rule to build our power fraction:

[tex]\sum_{n=0}^{\infty} ar^{n} = \frac{a}{1-r}[/tex]

when |r|<1

in this case a=1 and r=-2x so:

[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2x)^n[/tex]

or

[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2)^{n} x^{n}[/tex]

for: |-2x|<1

or: [tex] |x|<\frac{1}{2} [/tex]

Next, we can work with the second fraction:

[tex]\frac{1}{x-5}[/tex]

On which we can factor a -5 out so we get:

[tex]-\frac{1}{5(1-\frac{x}{5})}[/tex]

In this case: a=-1/5 and r=x/5

so our series will look like this:

[tex]-\frac{1}{5(1-\frac{x}{5})}=-\frac{1}{5}\sum_{n=0}^{\infty} (\frac{x}{5})^n[/tex]

Which can be simplified to:

[tex]-\frac{1}{5(1-\frac{x}{5})}=-\sum_{n=0}^{\infty} \frac{x^n}{5^(n+1)}[/tex]

when:

[tex]|\frac{x}{5}|<1[/tex]

or

|x|<5

So we can now put all the series together to get:

[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}}[/tex]

when:

[tex]|x|<\frac{1}{2}[/tex]

We use the smallest interval of convergence for x since that's the one the whole series will be defined for.

Answer:

Area: 360 cm

Perimeter: 44 cm

Step-by-step explanation:

To calculate the area, you must multiply the length x width.

If you need help calculating the perimeter too, just add all your lengths and widths together twice.

Answer:

Step-by-step explanation:

[tex]\frac{3x + 5}{2x + 7}[/tex] = 5

do cross multiplication

3x + 5 = 5(2x + 7)

3x + 5 = 10x + 35

5 - 35 = 10x - 3x

-30 = 7x

-30/7 = x

20 A

since there are 7 angles given it means that the polygon is heptagon as heptagon has 7 sides.

sum of interior angle of heptagon = (n-2)*180

(7-2)*180

5*180

900

Now ,

110 + 90 + 150 + 102 + 110 + 170 + x = 900

732 + x = 900

x = 900 - 732

x = 168 degree

20 B

since 5 angles are given it means that the polygon is pentagon as pentagon has 5 sides.

sum of interior angles of a pentagon = (n-2)*180

(5-2)*180

3*180

540 degree

Now ,

110 + 95 + 120 + 114 + x = 540

465 + x = 540

x = 540 - 465

x = 75 degree

21

let one rational number be x

according to the question,

1/7 * x = 2

x/7 = 2

do cross multiplication

x = 14

Answer:

1822

Step-by-step explanation:

The fraction 1822 is equal to 911 when reduced to lowest terms.

18

22

is equivalent to 9

11

because 9 x 2 = 18 and 11 x 2 = 22

27

33

is equivalent to 9

11

because 9 x 3 = 27 and 11 x 3 = 33

36

44

is equivalent to 9

11

because 9 x 4 = 36 and 11 x 4 = 44

Answer:

18/22

Step-by-step explanation:

You can choose any number and if you multiply the top number (numerator) and the bottom number (denominator) by that same number, the fractions are equivalent.

If you choose the number 2, then multiply 9 x 2 = 18, and 11 x 2 = 22

Or multiply by 7. Then you would get an equivalent fraction of 63/77  

Answer:

(-6,-12)

Step-by-step explanation:

A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.

[tex] - 2 \times 3 = - 6[/tex]

[tex] - 4 \times 3 = - 12[/tex]

So our new coordinates is

(-6,-12)

Answer:

(-6,-12)

Step-by-step explanation:

A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.

So our new coordinates is

(-6,-12)

Step-by-step explanation:

Answer:

T = 2.215

df = 7

Critical value = 2.364

Fail to reject the null

Step-by-step explanation:

Swimmer __Spandex __Speedo Fastskin__ d

1 __________31.1 _______29.1 __ 2

2_________ 28.9 ______30.4 __ -1.5

3_________ 31.4 ______ 32.0 __ - 0.6

4_________ 34.9 ______31.7 __ 3.2

5 _________27.7 ______28.2 __ - 0.5

6_________ 36.7 _____ 32.9 ___ 3.8

7 _________ 33.3 _____28.6 ___ 4.7

8_________ 30.8 _____26.2 ___ 4.6

The mean difference = Σd / n

2, - 1.5, - 0.6, 3.2, - 0.5, 3.8, 4.7, 4.6

μd = Σd / n = 15.7 / 8 = 1.9625

Sd = standard deviation of difference = 2.5065 (using calculator)

H0 : μd = 0

H1 : μd ≠ 0

The test statistic:

T = μd / (Sd/√n)

T = 1.9625 / (2.5065/√8)

T = 2.2145574

The degree of freedom, df = n - 1 = 8 - 1 = 7

Using a Pvalue calculator :

α = 0.05

Critical value, Tcritical = 2.364 (T distribution table)

Since Test statistic < Critical value

we fail to reject H0 ;

Answer:

what r u answers picks

Step-by-step explanation:

cant answer with out of t

Answer:

1200

Explanation:

Order does not matter, if we said xyz order, it would still not make a difference if it was zyx or yzx hence we use the combination formula:

nCr = n! / r! * (n - r)!

where n= total number of items

r= number of items chosen at a time

Combinations are used when the order of events do not matter in calculating the outcome.

We calculate using the formula:

(30×20×12)÷3!=1200

There are therefore 1200 ways for the three distinct items to not be in same row or column

Answer:

Second term of this sequence: [tex]10[/tex].

Third term of this sequence: [tex]20[/tex].

Step-by-step explanation:

The first step is to find the common ratio of this sequence.

In a geometric sequence, multiply one term by the common ratio to find an expression for the next term. Let [tex]r[/tex] denote the common ratio of this sequence. For this sequence:

However, the question states that the value of the fourth term is [tex]40[/tex]. In other words, [tex]5\, r^{3} = 40[/tex].

Solve this equation for [tex]r[/tex]:

[tex]r^{3} = 8[/tex].

[tex]r = 2[/tex].

(Since the power of [tex]r[/tex] is non-even in the equation, there's no need to consider the sign of [tex]r\![/tex] when taking the cube root.)

Substitute [tex]r = 2[/tex] into the expression for the second term and the third term to find their values:

Answer:

this is the answer I got! i don't know if it helps, but I hope it does

Answer:

The answer is below

Step-by-step explanation:

The bar chart to the question is attached below.

The distance traveled by Paolo = 210 m, The distance traveled by Lucas = 150 m, The distance traveled by Jashua = 175 m, The distance traveled by Topher = 190 m

1) The farther distance walk by Paolo = The distance traveled by Paolo - The distance traveled by Topher = 210 m - 190 m = 20 m

2) The farther distance walk by Jasha = The distance traveled by Jashua - The distance traveled by Lucas = 175 m - 150 m = 25 m

3) The farther distance walk by Topher = The distance traveled by Topher - The distance traveled by Lucas = 190 m - 150 m = 40 m

4) Combined distance of Paolo's and Lucas = 210 m + 150 m = 360 m

Combined distance of Jashua and Topher = 175 m + 190 m = 365 m

Therefore the Combined distance of Jashua and Topher is more

5) Average distance = (210 + 150 + 175 + 190)/4 = 181.25 m

Answer:

 B and D are polynomial

Step-by-step explanation:

An algebraic expression with non-zero coefficients and variables having non-negative integers as exponents is called a polynomial.

A)

If it is [tex]1 -\frac{5x^{2}}{x }=1-5x[/tex]   , then it is a polynomial.

But if it is [tex]\frac{1-5x^{2}}{x}[/tex] then it is not a polynomial

Answer: Tis 0

Step-by-step explanation:

Answer:

There are 2 x intercepts

9514 1404 393

Answer:

  A.  yes

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other.

The diagonals of a parallelogram bisect each other. If they are also congruent, then the parallelogram is a rectangle.

Answer:

Yes.

Step-by-step explanation:

Press option yes

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

[tex]\angle A+40+100=180[/tex]

[tex]\angle A+140=180[/tex]

[tex]\angle A=180-140[/tex]

[tex]\angle A=40[/tex] degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

[tex]\implies BC=AC [/tex]

Now, Sine law

[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]

Using the sine law

[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]

[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]

[tex]BC=\frac{8\times sin40}{sin 100}[/tex]

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

Answer:

C

Step-by-step explanation:

[tex] ({8}^{ { - 9})^{ \frac{ - x}{9} } } [/tex]

when putting a power to another power, then these two powers are multiplied.

so, -9 × (-x/9) = (-9 × -x) / 9 = 9x/9 = x

so, this reduces to the original

[tex] {8}^{x} [/tex]

and therefore C is the right answer.

Answer:

B. -21.012÷ -3.4

its yr correct ans.

hope it helps

Answer:

52nd percentile

Step-by-step explanation:

The sorted data :

36.0, 37.0, 39.5, 40.0, 40.5, 43.0, 44.0, 45.5, 45.5, 46.5, 48.0, 48.00, 49.0, 50.0, 51.5, 52.5, 53.0, 53.5, 54.0, 57.3, 57.5, 58.0, 58.5, 59.0, 59.5, 60.0, 61.0, 61.0, 61.0, 61.5, 62.0, 62.5, 63.0, 63.0, 63.5, 64.0, 64.0, 64.0, 64.5, 65.0, 66.0, 67.5, 67.5, 68.5, 70.0, 70.5, 71.5, 72.0, 72.5, 72.5, 72.5, 73.5, 74.5, 77.5

The total size of the data = 54

The value 61.0 occurs in position ; 27th, 28th and 29th

Taking the position average :

(27+28+29)/3 = 84/3 = 28th position

This means the percentile score of 61 is :

(Position average / total size) * 100%

(28/54) * 100%

0.5185185 * 100%

= 51.85%

This means that 61 inch length falls in the 52nd percentile

Answer:

0.33

Step-by-step explanation:

See comment for complete question

Given

[tex]H = 60\%[/tex]

[tex]W=25\%[/tex]

[tex]HW = 20\%[/tex] --- at-home wins

Required

The proportion of at-home games that were wins

This proportion is represented as:

[tex]Pr = HW : H[/tex]

Substitute values for HW and H

[tex]Pr = 20\% : 60\%[/tex]

Divide by 20%

[tex]Pr = 1 : 3[/tex]

Express as fraction

[tex]Pr = 1 /3[/tex]

[tex]Pr = 0.33[/tex]

Answer:

three

P A R

A R A D

A D I S E 

P Q R

A B C D

A B C D E

There are three such pairs of letters. 

Answer:

hey what's

Step-by-step explanation:

a question wow okay the answer is

total area =A1+A2+A3

A1=1/2b*h

A1=1/2*8mm*6mm

A1=24mmsquare

A2=1/2b*h

A2=1/2*8mm*6mm

A2=24mmsquare

A3=b*h

A3=8mm*6mm

A3=48mmsquare

Atotal=24mmsquare+24mmsquare+48mmsquare

Atotal=96mmsquare

Answer:

72 red

45 blue

63 yellow

Step-by-step explanation:

8+5+7= 20

180÷20= 9

red = 9*8

blue = 9*5

yellow = 9*7

Answer:

4

Step-by-step explanation:

Since this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees.

We can see that this is a 30-60-90 degree triangle.

The rules of 30-60-90 degree triangles are that the side opposite the 90 degree angle, or the hypotenuse can be measured with the variable [tex]2a[/tex]. The side opposite the 30 degree angle can be measured with [tex]a[/tex], and the side opposite the 60 degree angle will be measured with [tex]a\sqrt{3}[/tex].

We can see that 8 represents [tex]2a[/tex] because it is the hypotenuse. Since the side marked [tex]x[/tex] is separated by the hypotenuse by an angle of 60 degrees, we note that side marked [tex]x[/tex] is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked [tex]a[/tex], and since we already know that 8 is equal to [tex]2a[/tex], we realize that the side marked x is equal to [tex]a[/tex], or 4.

The value of x in the triangle is 4.

What is the Pythagorean theorem ?

The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

It is given this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees. By the sum of all the three interior angles of a triangle is 180 degrees

The side opposite the 90 degree angle, or the hypotenuse can be measured with the variable '2a' . The side opposite the 30 degree angle can be measured with 'a' , and the side opposite the 60 degree angle will be measured with 'a√3'.

8 represents '2a' because it is the hypotenuse. Since the side marked x is separated by the hypotenuse by an angle of 60 degrees, we note that side marked x is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked 'a', and since we already know that 8 is equal to '2a', we realize that the side marked x is equal to

'a' , or 4.

2a=8

a=4

x=a=4

so, the the value of x in the triangle is 4.

Learn more about the  Pythagorean theorem here:

https://brainly.com/question/24154260

#SPJ5

Answer:

I don't know the answer to ur question. LOL

Answer:

stop being desperate

nobody is gonna fall in love with some desperate weirdo