Find the approximate circumference of a circle with a diameter of 6 inches. Use 3.14
as an estimate of 77 that is correct to two decimal places.
O A. C = 18.84 in
OB. C≈ 20.46 in
C. C 18.84 in
OD. C≈ 18.84954 in

Answer:

a: 57.3

b: 3.8

Step-by-step explanation:

a: The formula to solve a triangle is a=height*base/2

that makes a= 9.96*11.5/2

a=57.27~=57.3

b: because there is 15 balls take 57.27 and divide it by 15

57.27/15=3.8

Answer:

Just multiply each by 5

Step-by-step explanation:

5x125= 625

explanation:

multiply the previous term by 5

So we are given with three different equations,

[tex]$$\begin{aligned}&x-2 y+3 z=12 \rightarrow(1) \\&2 x-y-2 z=5 \rightarrow(2) \\&2 x+2 y-z=4 \rightarrow(3)\end{aligned}$$[/tex]

We will convert the individual equations into matrices,

[tex]$$\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\2 & -1 & -2 & 5 \\2 & 2 & -1 & 4\end{array}\right]$$[/tex]

   [tex]\begin{aligned}&R_2 \leftarrow R_2-2 \times R_1 \\&=\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\0 & 3 & -8 & -19 \\2 & 2 & -1 & 4\end{array}\right]\end{aligned}[/tex]

[tex]\begin{aligned}&R_3 \leftarrow R_3-2 \times R_1 \\&=\left[\begin{array}{rrr|c}1 & -2 & 3 & 12 \\0 & 3 & -8 & -19 \\0 & 6 & -7 & -20\end{array}\right] \\&R_2 \leftarrow R_2 \div 3 \\&=\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\0 & 1 & -2.6667 & -6.3333 \\0 & 6 & -7 & -20\end{array}\right]\end{aligned}[/tex]

[tex]\begin{aligned}&R_1 \leftarrow R_1+2 \times R_2 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 6 & -7 & -20\end{array}\right] \\&R_3 \leftarrow R_3-6 \times R_2 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 9 & 18\end{array}\right]\end{aligned}[/tex][tex]\begin{aligned}&R_3 \leftarrow R_3 \div 9 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 1 & 2\end{array}\right] \\&R_1 \leftarrow R_1+2.3333 \times R_3 \\&=\left[\begin{array}{ccc|c}1 & 0 & 0 & 4 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 1 & 2\end{array}\right]\end{aligned}[/tex]

[tex]\begin{aligned}&R_2 \leftarrow R_2+2.6667 \times R_3 \\&=\left[\begin{array}{ccc|c}1 & 0 & 0 & 4 \\0 & 1 & 0 & -1 \\0 & 0 & 1 & 2\end{array}\right]\end{aligned}[/tex]

[tex]i. e.$$\begin{aligned}&x=4 \\&y=-1 \\&z=2\end{aligned}$$[/tex]

Solution By Gauss elimination method is,

[tex]$x=4, y=-1$ and $z=2$[/tex]

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Simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]  is equal to 3/(x-6).

As given in the question,

Given complex fraction is [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]

Simplify the denominator by taking least common multiple,

[tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }\\\\\\= \frac{3}{\frac{x-4}{\frac{x-4-2}{x-4} } }\\\\\\= \frac{3(x-4)}{(x-6)(x-4)} \\\\\\=\frac{3}{x-6}[/tex]

Therefore, simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]  is equal to 3/(x-6).

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Answer:

27.25 feet long

Explanation and Check part below

Hope this helps :)

Step-by-step explanation:

The area is 599.5 square feet and it is 22 feet wide. So in order to find the area we have to multiply the width (22 feet wide) and the legth (unknow number which will stand for "x"). Since we area multiplying the width and legth we need to do the inverse operation which is dividing. We didvide the area 599.5 by the width 22 to get 27.25 feet long.

22x = 599.5

----- -------- <------ Fraction bar/divide

22 22

x = 27.25

Check:

When a number is next to parenthesis it means to multiply the 2 numbers.

22 (27.25) = 599.5

599.5 = 599.5

True statement.

Answer:

95

Step-by-step explanation:

Because they are opposite angle. Since TRV and SRV is opposite that means they are equal each other

Answer:

a30= -15

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

2 out of 3 can be expressed as 2/3. Since we are looking at the 1 out of 3 people, we can use the expression 1/3 x 171 or 171/3, which equals 57

Answer:

x=7, y=11

Step-by-step explanation:

Using simultaneous equations we can sub y in equation 1 into equation 2.

Equation 1. y=2x-3

Equation 2. x+y=18

Since y=2x-3 we can replace it so that

2'. x+2x-3=18

Now simplify

= 3x-3=18

Add 3 onto both sides to undo the subtraction of 3 so that,

3x=21

Now divide both sides by three to undo the multiplication of 3 so that,

x=7

Now sub in x (which is 7) into one of the equations to find y

7+y=18

To undo the five, subtract 7 from both sides so that

y=11

The equation of the circle with radius 8 and center at (5 , -2) is (x - 5)^2 + (y + 2)^2 = 64.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius 8 and center at (5 , -2), substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (5 , -2)

r = 8

(x - 5)^2 + (y - -2)^2 = 8^2

(x - 5)^2 + (y + 2)^2 = 64

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Step-by-step explanation:

Let radius of circle is r=18 units

Perimeter of full circle is given by 2πr

Thus, perimeter of three quarters circle is given by,

( ¾ × 2πr) + (2 × r)

The perimeter of this "circle" would be:

( ¾ × 2 × π × 18) + (2 × 18) = 27π + 36 ≈ 120.78 m

The equivalent expression of (5 ^3/4)^2/3 is √5

Expressions are mathematical statements that are represented by variables, coefficients and operators

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The expression is given as

(5 ^3/4)^2/3

Evaluate the product of the exponents

So, we have

(5 ^3/4)^2/3 = 5^(3/4 x 2/3)

Evaluate the product of the exponents

So, we have

(5 ^3/4)^2/3 = 5^(2/4)

Evaluate the quotient

So, we have

(5 ^3/4)^2/3 = 5^(1/2)

Express as square roots

So, we have

(5 ^3/4)^2/3 = √5

Hence, the equivalent expression of (5 ^3/4)^2/3 is √5

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   The equation of the parabola that has vertex at (1,4) and focus (1,6) is

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

(x - h)² = 4p(y - k)

(y - k)² = 4p(x - h)

  This will depend on its aperture

  Since the vertex and the focal axis are on the same axis, we analyze that:

(x - 1)² = 4p(y - 4)

f = (1, 4 + p)

4 + p = 6

p = 6 - 4

p= 2

(x - 1)² = 4*2(y - 4)

(x - 1)² = 8(y - 4)

x² - 2x + 1 - 8y + 32 = 0

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Answer:yes b

Step-by-step explanation:

because you subtract it

The variables that

x + y = 2100  

5 x + 7 y = 11700  

Let x = total dollar amount of sales of phone;

      y = total dollar amount of sales of computer

for total sales of phones anna earns 5% commission

So anna 's commission = 5% of x

                                       = 0.05x

for total sales of computer anna earns 7% commission

So anna 's commission = 7% of y

                                       = 0.07y

Given the total sales; x + y = 2100

And commission; 0.05x + 0.07y = 117; or 5x + 7y = 11700

Therefore the system of equations are

x + y = 2100   …….equation (1)

5 x + 7 y = 11700  ……equation (2)

In mathematics, a variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.

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The total change is 82.5 (or 82 and 2/5) bushels remaining and has sold 82.25 (or 81 and 2/5) bushels

He has sold (16+3/5) bushels/day x 6 days

=(16 x 6 ) + (3 / 5 * 6)

= 96 + 6/5

= 97 + 1/2

= 97.5

The change in the number of bushels is 180 – 97.5 = 82.5 or 82 and 2/5 bushels. A measure of capacity equal to 8 gallons (equivalent to 36.4 litres), used for corn, fruit, liquids, etc. A measure of capacity equal to 64 US pints (equivalent to 35.2 litres), used for dry goods.

Hence , the total change in  82.5 (or 82 and 2/5) bushels remaining and has sold 82.25 (or 81 and 2/5) bushels.

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The value of term a9 is 9k+32.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the term of arithmetic sequence and common difference,

a1 = 4 and d = K+4.

now find the value of term a9.

a(n) = a1 + (n - 1)d

now, substitute a(n) = a9, a1 = k, d = k+4.

a9 = k + (9 - 1)(k+4)

a9 = k + 8(k+4)

a9 = k + 8k + 32

a9 = 9k +32

Hence,The value of term a9 is 9k+32.

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Answer: 1

Step-by-step explanation:

s = 5, t = 2

10/5*2

= 10/10

=1

The total surface area of the pyramid 806.12 [tex]m^{2}[/tex].

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

Side (s) = 12

Altitude (h) = 6

Area = 3√3/2*s² + 3*s*√(h²+3s²/4)

Area = 3√3/2*(12)² + 3*(12)*√[6²+3(12)²/4]

Area = 806.12 [tex]m^{2}[/tex]

A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it.  

Area of a square is equal to the sum of the lengths of its sides, where an is a square side.

The surface area of a three-dimensional shape refers to the amount of open space that it occupies. A solid shape's volume is the amount of space it takes up.

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Answer:

Step-by-step explanation:

OK, so you see how its like 4/10 right? (not four tenths but ya know four on top and ten underneath)

Look how for your Y axis it goes: 2, 4. 6, 8, 10

what comes after ten by counting by twos? 12!

Also the correct equation is; Y = K X ( Y =_ x) ( blank is whatever your constant of proportionality is.

Thank you Pre-Algebra\

Signed~ Earl

The cost of the toothbrush will be equal to $14.40. The correct option is A.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that an electric toothbrush costs $72, including a 20% price markup.

The price of the toothbrush will be calculated as,

P = ( 72 x 20 ) / 100

P = 1440 / 100

P = $14.40

Therefore, the cost of the toothbrush will be equal to $14.40. The correct option is A.

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Answer: 60.00

i did the test.

Answer:

384

Step-by-step explanation:

8x4=32 32x 12 cans=384 sq centimeters

Answer:

(Some textbooks describe a proportional relationship by saying that " y varies proportionally with x " or that " y is directly proportional to x .") This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.

10:4 = 5:2

6:2 = 3:1      

Not equal.

The expected value of chi-square statistics is not significantly different from the observed value.

What is chi-square statistics?

Chi-square statistics is defined as a measure that is used to denote the difference between the expected frequencies and the observed frequencies of an event. It is illustrated using the symbol, 'χ2'.

Deciding for the goodness of a fit

The assigned value of chi-square is 1.273 while the critical value is 13.388

The hypotheses for the goodness of fit test are given below:

Null Hypothesis: the expected value is not significantly different from the observed values

Alternate Hypothesis: the expected value is significantly different from the observed values

We know that the chi-square test is right-tailed.

Further, the value of test statistics is 1.273, which is less than the critical value, 13.388

Thus we fail to reject the null hypothesis and we accept it.

Hence, we can conclude that the expected value is not significantly different from the observed value.

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Answer:

6 pack of t shirts for 15 :3

Step-by-step explanation:

The solutions for each of the equations provided in the reference picture is as follows:

(1) [x = (-3)]

(2) [y = (-10)]

(3) (m=3/4)

(4) (b = 0)

(5) (r = 7)

(6) (v = -60)

As per question statement and reference picture, we are provided with 6 different equations which are

(1) [(4 x+1)=(2 x-5)]

(2)[(y-3)=(-3 y-43)]

(3) [(7-14 m)=(2 m-5)]

(4)[(-10 b+5)=(7 b+5)]

(5)[(r+15)=(4 r-6)]

(6)[(10-2 v)=(-5 v-50)]

We are required to find the solution of all the equations mentioned above.

Considering equation (1), we get,

{[(4 x+1)=(2 x-5)] }

or,(4 x-2 x)=[(-1)-5]

or, 2 x=-(1+5)

or, 2 x=-6

or, x={-6}/{2}=(-3)

Considering equation (2), we get,

{[(y-3)=(-3 y-43)] }

or, (y+3 y)=(3-43)

or, 4 y=(-40)

or, y=(-10)

Simplifying equation (3), we get,

{[(7-14 m)=(2 m-5)] }

or, (7+5)=(2 m+14 m)

or, 12=16 m

or, m={12}/{16}={3}/{4}

Simplifying equation (4), we get,

{[(-10 b+5)=(7 b+5)] }

or, (5-5)=(7 b+10 b)

or, 17 b=0

or, b=0

Simplifying equation (5), we get,

{[(r+15)=(4 r-6)] }

or, (15+6)=(4 r-r)

or, 3 r=21

or, r=7

Finally, Simplifying equation (6), we get,

{[(10-2 v)=(-5 v-50)] }

or, (5 v-2 v)=[(-10)-50]

or, 3 v=-(10+50)

or, 3 v=-60

or, v=(-20)

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The required answers are-

Part a: The equation that represents the total cost C is C = 250 + 7x.

Part b: The equation that represents the average cost A per person is A = 250 + 7 = 257.

Part c: The estimate number of people who must attend before the average cost drops to $15 per meal is 25.

Part d: The average cost keeps on decreasing exponentially and then becomes straight.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now it is given that,

Rental of banquet hall = $250

One time charge for meal = $7 per plate

x = the number of people who attend.

Part a: The equation that represents the total cost C

Since there are x people in the banquet

So, number of plates = x

Thus, Total One time charge for meal = 7x

So Total Cost = Rental of banquet hall + Total One time charge for meal

⇒ C = 250 + 7x

this is the equation that represents the total cost C

Part b: The equation that represents the average cost A per person

Putting x = 1 in the above equation of total cost we get,

A = 250 + 7 = 257

this is the equation that represents the average cost A per person

Part c: The estimate number of people who must attend before the average cost drops to $15 per meal

From the graph it is seen that there are 25 people who must attend before the average cost drops to $15 per meal.

Part d: what happens to the average cost as the number of people who attend increases.

The average cost keeps on decreasing exponentially and then becomes straight.

The required answers are-

Part a: The equation that represents the total cost C is C = 250 + 7x.

Part b: The equation that represents the average cost A per person is A = 250 + 7 = 257.

Part c: The estimate number of people who must attend before the average cost drops to $15 per meal is 25.

Part d: The average cost keeps on decreasing exponentially and then becomes straight.

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For the area of triangle, the constant of variation is 1/2.

The link between the independent (x) and dependent (y) variables is shown by a constant of variation. A continuous relationship between the variables indicates to the user that there is one; it does not alter regardless of how the scenario changes.

It can be employed to ascertain how the dependent variable will alter in response to changes in the independent variable. For instance, if a person drives continuously at the same pace, they may calculate their distance by multiplying the number of hours they spent driving by the speed they were moving at. In this instance, the speed is the constant since it remained constant regardless of how long or how far they travelled during the journey.

A triangle's area is equal to (1/2) * (base) * (height).

It fluctuates in tandem with both the base length and the height.

The (1/2) represents the variational constant.

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Applying the midpoint formula, the coordinates of B are: (-7, 4).

The midpoint formula is:

M(x, y) = [(x2 + x1)/2, (y2 + y1)/2]

Given:

M(x, y) = (-3, 0)

A(x1, y1) = (1, -4)

B(x2, y2) = (?, ?)

Plug in the values into the midpoint formula:

M(-3, 0) = [(x2 + 1)/2, (y2 + (-4))/2]

Isolate each coordinate

-3 = (x2 + 1)/2

-6 = x2 + 1

-6 - 1 = x2

x2 = -7

0 = (y2 - 4)/2

0 = y2 - 4

y2 = 4

Therefore, applying the midpoint formula, the coordinates of B are: (-7, 4).

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