A pond has been created in a remembrance garden. It has an approximate diameter of 10 metres. A person walks around the
pond four times a day. How far have they travelled per day to the nearest metre?
(Circumference of a circle is 2T or C=Td, where te=3.14)​

Answer:

5

Step-by-step explanation:

6 nickles,3 dimes ,1 quarter +1 nickel, 2 dimes 2 nickles, 1 dime 4 nickles,

Answer:

yhat=1.36+0.74x

when x=7 then yhat=6.54

Step-by-step explanation:

Th regression equation is

yhat=a+bx

where slope b is

[tex]b=\frac{nsumxy-(sumx)(sumy)}{nsumx^{2}-(sumx)^{2} }[/tex]

and intercept a is

a=ybar-bxbar

x   4   5   2   6    9

y   4   6   2   7    7

xy 16 30  4  42  63

x² 16 25  4  36  81

n=5.

sumx=26.

sumy=26.

sumx²=162.

sumxy=155.

[tex]b=\frac{5*155-(26)(26)}{5*162-(26)^{2} }[/tex]

[tex]b=\frac{99}{134 }[/tex]

b=0.7388

b=0.74 (rounded to 2 decimal places)

xbar=sumx/n=26/5=5.2

ybar=sumy/n=26/5=5.2

a=ybar-b*xbar

a=5.2-0.7388*5.2

a=5.2-3.8418

a=1.3582

a=1.36 (rounded to 2 decimal places)

Thus, the required regression equation is

yhat=1.36+0.74x

When x is 7 this gives yhat

yhat=1.36+0.74*7

yhat=1.36+5.18

yhat=6.54

Answer:

x=1    x = -1

Step-by-step explanation:

2|5x|= 10

Divide each side by 2

2/2|5x|= 10/2

|5x|= 5

Absolute values have 2 solutions, one positive and one negative

5x = 5      5x = -5

Divide each side by 5

5x/5 = 5/5      5x/5 = -5/5

x = 1                 x = -1

Answer:

Step-by-step explanation:

● 2|5x| = 10

● 2 × |5| ×x = 10

5 is positive so |5| = 5

● 2×5× |x| = 10

● 10×|x| = 10

● |x| = 10

● x = 1 or x = -1

Answer:

you look at the third decimal place which will affect the second decimal place.

in this case: 2 affects 4 -- leaves it as 4

so the number rounded to two decimal places is 7.14

Answer:

It's 16, i did the unit test already.

Step-by-step explanation:

Answer:

Hey there!

The correct answer would be f(x)=(x-3)^2

Let me know if this helps :)

Answer:

d.  x = -3

Step-by-step explanation:

[tex]\sqrt{(x + 3)}[/tex]÷ (x+8)(x-2) = 0

f(x) / g(x) = 0

Variable x cannot be equal to any of the values −8,2 since division by zero is not defined. Multiply both sides of the equation by (x−2)(x+8).

[tex]\sqrt{(x + 3)}[/tex] = 0 ------ square both sides

x + 3 = 0

solve for x:

x = -3

Answer: y=2x+2

Step-by-step explanation:

slope-intercept form: y=ax+b

----------------------------------------

#1 Find the slope

- Use rise/run to find the slope: 8/4=2

- Use slope formula: (2-(-6))/(0-(-4))=8/4=2

#2 Find the y-intercept

- Given the point (2, 0) it is already the y-intercept which is 2

----------------------------------------

a=2

b=2

y=2x+2

Answer:

definite integral I = 0.001591  to six decimal places

Step-by-step explanation:

The definite integral is given as:

[tex]\int ^{0.1}_{0} \ x \ arctan (5x) \ dx[/tex]

For arctanx , the power series is in the order [tex]x - \dfrac{x^3}{3}+ \dfrac{x^5}{5}-\dfrac{x^7}{7}+...[/tex]

[tex]arc tan \ x = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ x ^{2n+1}}{2n +1}[/tex]

The next step is to substitute the value of 5x for x in the above equation;

So,

[tex]arc tan \ (5x) = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ (5x) ^{2n+1}}{2n +1}[/tex]

To  multiply both sides by (x); we have

[tex]x\ arc tan \ (5x) = x \ \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5 ^{2n+1} \times x^{2n+1}}{2n +1}[/tex]

[tex]x\ arc tan \ (5x) = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5 ^{2n+1} \times x^{2n+2}}{2n +1}[/tex]

Taking the integral on both sides with respect to x;

[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5^{2n +1}}{2n+1} \ \int ^{0.1}_0 x^{2n+2} \ dx[/tex]

[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5^{2n +1}}{2n+1} \ [(0.1)^{2n+3}][/tex]

[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = \sum \limits ^{\infty}_{n=0} \dfrac{(-1)^n \ 5^{2n +1} \times (0.1)^{2n+3} }{(2n+1)(2n+3)}[/tex]

[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = [\dfrac{5 \times (0.1)^3}{1.3}-\dfrac{5^3(0.1)^3}{3.5}+\dfrac{5^5(0.1)^7}{5.7}-\dfrac{5^7(0.1)^9}{7.9}+ ...][/tex]

[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx = [\dfrac{1}{600}-\dfrac{1}{1200}+\dfrac{1}{112000}-\dfrac{1}{806400}+ ...][/tex]

[tex]\int^{0.1}_{0} \ x \ arctan (5x) \ dx =1.591 \times 10^{-3}[/tex]

[tex]\mathbf{\int^{0.1}_{0} \ x \ arctan (5x) \ dx =0.001591}[/tex] to six decimal places

Answer:

Step-by-step explanation:

[tex] \mathsf{ \frac{ { - 3}^{5} }{ { - 3}^{6} } }[/tex]

To divide two terms with the same base , the power of divisor is subtracted from the power of the dividend and the same base is taken

⇒[tex] \mathsf{ { - 3}^{5 - 6} }[/tex]

⇒[tex] \mathsf{ { - 3}^{ - 1} }[/tex]

Applying law of negative index

⇒[tex] \frac{1}{3} [/tex]

Hope I helped!

Best regards!!

Answer:

The equivalent expression for x+9=10 is x=1.

Step-by-step explanation:

We have a statement i.e. x+9=10

We need to find an equivalent statement for the above statement.

If we subtract 9 on both sides of the above statement,

x+9-9=10-9

We know that, 9-9=0 and 10-9 =1

x+0=1

x=1

So, the equivalent expression for x+9=10 is x=1.

Answer:

The given graph shows the relationship between the f(x) and g(x).

Since the problem is to find the points where f(x) becomes equal to g(x) then we will be focusing only to the x-axis and ignore the points of y-axis.

Out of the four choices, the correct answer for the given functions of x will be f(2) = g(2) and f(0) = g(0), f(0) and g(0) is located at the origin. So the points where the curve and line are intersecting is at f(2) and g(2) and the other point is at f(0) and g(0), neglecting the y-axis.

Step-by-step explanation:

Answer:

Hey there!

The letters B, C, D, H, K, M, T, V, W, and X have at least one line of symmetry.

A, E, I, O, U and Y are the vowels.

So we have a total of 21 consonants, and 10 are symmetrical.

Thus, the probability is 10/21.

Let me know if this helps :)

Answer:

C'(-3, -1)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a new position. Types of transformation are reflection, rotation, dilation and translation.

If a point A(x, y) is rotated 180 degrees counterclockwise about the origin the new coordinates is A'(-x, -y)

Since C(4, 4) is rotated about point (1, 3), we have to make point (1, 3) the origin. This means the new origin O' is at (1, 3). The horizontal and vertical distance between the new origin and point C gives the new coordinate of point C. Point C x coordinate is 3 units from the new origin and y coordinate is  1 unit from the new origin, hence the new coordinate of point C is (3, 1).

A 180⁰ counter clock wise rotation of point C would give a new point at C'(-3, -1)

The solution is Option A.

The amount of income left over after paying the federal income tax is given by the equation A = $ 24,490.00

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of income left over be represented as A

Now , the equation will be

The amount of taxable income is $31,850.00

And , the taxable income is in the range $ 8,350 - $ 33,950

So , the fixed tax for the amount is $ 835.00

The percentage of tax is 15 % of the amount over

So , the amount over = $ 8,350

Substituting the values in the equation , we get

The amount over = $31,850.00 - $ 8,350.00

The amount over = $ 23,500.00

Now , 15 % of amount over = 23,500 x ( 15/100 )

15 % of amount over = $ 3,525.00

And , Total tax = 15 % of amount over + fixed tax for the amount

Total tax = $ 3,525.00 + $ 835.00

Total tax = $ 4,360.00

Now , the amount of income left over A = amount of taxable income - Total tax

Amount of income left over A = $31,850.00 - $ 4,360.00

Amount of income left over A = $ 27,490.00

Therefore , the value of A is $ 27,490.00

Hence , the amount left over is $ 27,490.00

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Answer:

A) mea culpa

Step-by-step explanation:

Answer:

107

Step-by-step explanation:

Hello, Let's note n the odd number that we are looking for.

If n is odd, n+1 is even but n+2 is odd again and so on and so forth.

So, the 16 consecutive odd numbers are

n, n+2, n+4, ... n+2k, ,,,, ,n+30

It means that the average is:

[tex]\displaystyle \dfrac{1}{16}(n+(n+2)+...+(n+2k)+...+(n+2*15))\\\\=\dfrac{1}{16}\sum_{k=0}^{k=15} {(n+2k)}\\\\=\dfrac{1}{16}\left(n * 16 + 2 \sum_{k=1}^{k=15} {k} \right)\\\\=\dfrac{1}{16}\left(n * 16 + 2 (\dfrac{15*16}{2}) \right)\\[/tex]

And it must be equal to 122, so we can write.

[tex]\dfrac{1}{16}\left(n * 16 + 2 (\dfrac{15*16}{2}) \right)=122\\\\n+15=122\\\\n = 122-15=107[/tex]

Thank you.

The quantity of tomatoes that are left is equal to 1.875 pounds.

Given the following data:

To determine the quantity of tomatoes that are left:

In order to determine the quantity left from the tomatoes Glenn bought, we would use the following mathematical expression:

[tex]Quantity\;left = Fraction\; used \times Total\;quantity[/tex]

Substituting the given parameters into the formula, we have;

[tex]Quantity\;left = \frac{5}{8} \times 3\\\\Quantity\;left = \frac{15}{8}[/tex]

Quantity left = 1.875 pounds

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Answer:

72°

Step-by-step explanation:

From the information given:

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.

We are also told that there is a  Trapezoid EFGH with EH as the Pine avenue and EF as the Elm street.

However, side FG and EH are parallel.

∠G = 108°

From the property of parallel lines :

since FG || EH

Then  ∠G = ∠H  = 108°  (i.e corresponding angle will also be equal)

The required angle between Elm Street and Pine Avenue would be interior angles +  180°  given that  alternate angles are also equal.

The required angle between Elm Street and Pine Avenue = 180° - 108°

The required angle between Elm Street and Pine Avenue = 72°

Answer:

B. 72

Step-by-step explanation:

Answer:

a. for positive odd integers starting 1 and increaments by 2:

     ( first odd number ) + 2 ∈ S

b. for positive integer powers of 3 :

      3( integer ) ∈ S

c. for integer coefficient of the given polynomial :

      s. t ∈  S     ,      s - t ∈ S      and      s +  t  ∈  S

Step-by-step explanation:

the odd number starts with 1 and increases by two, and the set of that would range from 1 to infinity.

Answer:

5

Step-by-step explanation:

y=mx+b

B is always the y intercept.

Answer: |PQ| =3 units ,  |QR| = 3√5 units,  |RP| = 6 units.

Step-by-step explanation:

Distance between two points (a,b,c) and (x,y,z) is given by :-

[tex]D=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}[/tex]

Given: P(6, 6, 1), Q(4, 4, 2), R(4, 10, 5)

Then,

[tex]|PQ|=\sqrt{(6-4)^2+(6-4)^2+(1-2)^2}=\sqrt{2^2+2^2+(-1)^2}\\\\=\sqrt{4+4+1}=\sqrt{9}=3[/tex]

[tex]|QR|=\sqrt{(4-4)^2+(10-4)^2+(5-2)^2}=\sqrt{0+6^2+3^2}\\\\=\sqrt{36+9}=\sqrt{45}=3\sqrt{5}[/tex]

[tex]|RP|=\sqrt{(6-4)^2+(6-10)^2+(1-5)^2}=\sqrt{2^2+(-4)^2+(-4)^2}\\\\=\sqrt{4+16+16}=\sqrt{36}=6[/tex]

So, |PQ| =3 units ,  |QR| = 3√5 units,  |RP| = 6 units.

Answer:

Step-by-step explanation:

[tex]Amount=P(1+r)^t\\=4800(1+0.1)^{\frac{3}{2}}\\=4800(1.1)^{\frac{3}{2}}\\\approx 5537.72 ~Rs[/tex]

Answer:

n = -8

Step-by-step explanation:

-0n - 2n = 16

- 2n = 16

n = 16/-2

n = -8

Answer:

x = -8/b

Step-by-step explanation:

2bx-bx= -8

bx = -8

Divide by b since b is nonzero

x = -8/b

Work Shown:

The set {A,B,C,1,2} has five items. There are four slots to fill.

So we have 5^4 = 5*5*5*5 = 625 different possible passwords where the characters can be repeated.

625 four-character passwords can be formed.

----------------------------

Each character of the password is independent of previous characters, which means that the fundamental counting principle is used to solve this question.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

----------------------------

Thus, the number of passwords is:

[tex]5 \times 5 \times 5 \times 5 = 5^4 = 625[/tex]

625 four-character passwords can be formed.

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Answer:

407 falls between whole numbers 406 and 408.

Step-by-step explanation:

whole numbers set of numbers which begins with 0 add has sequence of number differing by one unit.

set of whole numbers will be 0,1,2,3,4,5...........................till infinity.

Given whole number = 407

No. before 407 will be one less than 407 i.e 407 -1 = 406

No. after 407 will be one more than 407 i.e 407 + 1 = 408

Thus, 407 falls between 406 and 408 which are part of whole numbers.

Step-by-step explanation:

5/2f or 2.5f I think

..................

Total seats: 52 x 7 + 8 x 12 = 364 + 96 = 460

Total cost for total seats = 460 x 23 = 10,580

Cost for buses: 150 x 7 + 80 x 8 = 1050 + 640 = 1690

Total cost = 10,580 + 1,690 = $12,270

Answer: Continuous Data

Quantitative data

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