A state seal, which is round, hangs in the capitol building. it has a radius of 2 feet. what is the seal's circumference?

I hope this photo will help you.

Answer:

about 8.2 cm

Step-by-step explanation:

The key is to realize that the volume never changes.
The formula for the volume of a sphere is (4/3)*pi*radius^3
22/7 is being substituted in place of pi in this problem
The volume of one of the small spheres is
(4/3)*(22/7)*2^3 is about 33.524 cm^3
64 of those spheres would have a volume of 33.524*64, or about 2145 cm^3
Now, the problem is to find a sphere with a volume of 2145 cm^3
Volume = (4/3)*(22/7)*radius^3
plug in and solve
2145 = 4.1905*r^3
r^3=511.87
r is about equal to 8.2 centimeters

The property for the missing justification is: A. addition property of equality.

If b - a = c, based on the addition property of equality, we can isolate b by adding a to both sides, i.e. b - a + a = c + a, to give us b = c + a.

Using the addition property of equality, 7 was added to both sides of the equation as shown in step 3.

Therefore, the missing justification is: A. addition property of equality.

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Iota, also known as the symbol , is denoted as being the square root of -1. Since square roots of negative numbers do not exist, there is a variable that represents it complexly. In fact, every real number (a) can be represented using the form (a) + (0).

On occasion, variables can also use and it does not have to be talking about the square root of -1. However, this rarely ever happens to avoid confusion. Check instructions in questions to see how is defined.

The true statement is David's calculations are incorrect, he used the circumference and the height to find the volume.

Correct calculation:

C = 2πr

8.6 = 2 × 3.14 × r

8.6 = 6.28r

r = 8.6/6.28

r = 1.36942675159235 inches

convert 1.36942675159235 inches to cm

= 3.478343949044569 cm

Approximately,

r = 3.5 cm

Volume = πr²h

= 3.14 × 3.5² × 15.2

= 3.14 × 12.25 × 15.2

= 584.668 cm³

Approximately,

volume = 584.7 cm³

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The number of times I would expect to roll a number that is not a 5 is 300 times.

A standard die has 6 faces. There are 5 numbers that are not 5 on a standard die. They are 1, 2, 3, 4, 6.

The number of times a 5 won't be rolled = (5/6) x 360

5 x 60 = 300 times

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Answer:

Step-by-step explanation:

Since 20 is 4/3 * 15, the answer must be 4/3 * 18

4/3 * 18 = 24, so the answer is 24

Answer:

Hello! The answer is 19.25 m²

Step-by-step explanation:

A = 1/2(4 + 7)3.5

A = 1/2(11)3.5

A = (5.5)3.5

A = 19.25 m²

Answer:

19.25 m²

Step-by-step explanation:

A = (1/2)(b1 + b2)h

A = (1/2)(7 m + 4 m)(3.5 m)

A = 19.25 m²

Answer: 9

Step-by-step explanation:

By CPCTC,

[tex]32=5x-13\\\\45=5x\\ \\ x=9[/tex]

The length of arc FD with a radius of 15 and angle of 120° is 10π units.

An equation is an expression that shows the relationship between two or more numbers and variables.

The length of an arc is given by:

arc length = (Ф/360) * 2π*radius

Let us assume that the angle is 120°

arc FD = (135/360) * 2π(15) = 10π

The length of arc FD with a radius of 15 and angle of 120° is 10π units.

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Answer:

the angle = ~56.3 degrees

Step-by-step explanation:

1. y=3/2(x) and y=0
2. say x is equal to 4. the length along the x axis is 4. you would plug x=4 into y=3/2x to get the length along the y axis (which would be 6). then you would use these lengths to find the angles value with tan. tan^-1(6/4), so the answer would be ~56.3 degrees

The simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x  + 3

The side lengths are given as:

2x^2 + 5x + 3, 2 + 2x and 3x - 2

Add these lengths to determine the perimeter (P)

P = 2x^2 + 5x + 3 + 2 + 2x + 3x - 2

Collect like terms

P = 2x^2 + 5x + 2x + 3x  + 3 + 2 - 2

Evaluate the like terms

P = 2x^2 + 10x  + 3

Hence, the simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x  + 3

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The expression for the area of the base of Prism is   x2 – 2x – 9

The volume of a rectangular prism is this

Volume = Area x Height

Substituting the given expressions

x3 + 2x2 - 17x - 36 = Area x (x + 4)

Area = (x3 + 2x2 - 17x - 36) / (x + 4)

Now, let's use synthetic division

-4 |    1    2    -17   -36

----    __-4___8___36

        1    -2     -9     0

The expression for the area is

Area = x2 - 2x - 9

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Answer:

48.375

Step-by-step explanation:

Area of square- area of circle

Side^2 - pieR^2

(15)^2 - 3.14*7.5*7.5

225 - 176.625

= 48.375

Hope this helps

The area of the square is 56.25 m².

The area of the square is:

Area = Side²

Area = (7.5 m)²

Area = 56.25 m²

The second degree polynomial with leading coefficient of -2 and root 4 with multiplicity of 2 is:

[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]

A polynomial of degree N, with the N roots {x₁, ..., xₙ} and a leading coefficient a is written as:

[tex]p(x) = a*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]

Here we know that the degree is 2, the only root is 4 (with a multiplicity of 2, this is equivalent to say that we have two roots at x = 4) and a leading coefficient equal to -2.

Then this polynomial is equal to:

[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]

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Answer:

Step-by-step explanation:

Answer:

1.89753

Step-by-step explanation:

22/11,594

         [tex]\frac{22}{11.594} * 1000 = \frac{22000}{11594}[/tex]

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Can't answer 1-6 cause I have no idea what you need

7) A triangle with two congruent sides is isosceles.

8) [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex]

9) [tex]\angle C[/tex]

10) [tex]\overline{AB}[/tex]

11) [tex]\angle A, \angle B[/tex]

12) isosceles triangle

The single dilation of the shape is a dilation by a scale factor of 1.5 with center R

From the graph, we have the center of dilation to be point R.

This is so because R = R'

Also, we have:

R = (-1, -4)

S = (2, 0)

S' = (3.5, 2)

Calculate the distance RS and RS' using

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

This gives

[tex]RS = \sqrt{(0 + 4)^2 + (2+ 1)^2} = 5[/tex]

[tex]RS' = \sqrt{(2 + 4)^2 + (3.5+ 1)^2} = 7.5[/tex]

Divide RS' by RS to determine the scale factor (k)

k = 7.5/5

k = 1.5

Hence, the single dilation of the shape is a dilation by a scale factor of 1.5 across point R

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Answer:

29 years

Step-by-step explanation:

In 29 years the grandson will be 40 and the grandfather will be 80. 80 is twice as much as 40.

Answer: 29 years

Step-by-step explanation: if the grandfather is 51 when the grandson is 11 then the grandfather was 40 when his grandson was born. This mean the grandfather will be 80 when the grandson is 40. 40-11=29

Answer:

Central Angle (Radians)=

1.0482

Central Angle (Degrees)=

6.0058e+1

Sector Area Equals

0.477

Step-by-step explanation:

a) By the alternate segment theorem, [tex]x=53^{\circ}[/tex]

b) Alternate angles are equal

The population in 20 years is 719 people.

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

According to the question

[tex]\frac{dP}{dt} = kP[/tex]   where P is population at any time

solving equation,

[tex]\int[/tex][tex]\frac{dP}{dt} =\\[/tex] [tex]\int kP[/tex]

[tex]lnP=kt+C[/tex]                                 -(1)

Applying the conditions,

at t=0, P = 500

[tex]ln500=C[/tex]                                      -(2)

at t=10, P= 600

putting it in equation gives

[tex]ln(600) = k(10)+ln(500)[/tex]

ln(6/5) = k(10)

[tex]k = \frac{ln(6/5)}{10}[/tex]

at t=20 , P= ?

[tex]lnP=(\frac{ln(6/5)}{10})20 + ln500[/tex]

[tex]lnP=({ln(6/5)}{2 + ln500[/tex]

On putting the values of ln(6/5) , ln(500)

[tex]lnP=0.182(2) + 6.214[/tex]

[tex]P = e^{6.578}[/tex]

P = 719.099

On rounding off

P ≈ 719 people

Thus the population in 20 years is 719 people.

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Answer:

1/5

Step-by-step explanation:

In the circle equation shown, the 1/25 all by itself on the right side of the equation is r^2.

r^2 = 1/25

Squareroot both sides.

r = 1/5

Additional wire of  26 7/20 feet, in the form of a mixed fraction, is required to complete the job.

A mixed fraction is represented by both its quotient and remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Max has total 6*9 2/5feet of wire, that is, 282/5 feet of wire.

Fred has total 7*16 3/4 feet of wire, that is, 469/4 feet of wire.

The total amount of wire required=200 feet

The total amount of wire available=282/5+469/4

                                                         =3473/20

An additional amount of wire is required=200-3473/20

                                                                   =(4000-3473)/20

                                                                   =527/20

Thus, the additional amount of wire required is expressed as a mixed fraction= 26 7/20 of feet.

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If the measure of angle θ is 3π/4, the true statements are:

In Trigonometry, an angle with a magnitude of 3π/4 (radians) is equivalent to 135° (degrees) and it's found in the second quarter. Thus, we would calculate the reference angle for θ in second quarter as follows:

Reference angle = 180 - θ

Reference angle = 180 - 135

Reference angle = 45°.

Also, a terminal point for this angle θ is given by (-√2/2, √2/2) which corresponds to cosine and sine respectively. This ultimately implies that sin(θ) = √2/2.

tan(θ) = cos(θ)/sin(θ)

tan(θ) = [(-√2/2)/(√2/2)]

tan(θ) = -1

In conclusion, we can logically deduce that only options A and B are true statements.

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Complete Question:

If the measure of angle θ is 3π/4, which statements are true. Select all the correct answers.

A. sin(θ)=sqrt2/2

B. The measure of the reference angle is 45

C. The measure of the reference angle is 30

D. The measure of the reference angle is 60

E. cos(θ)=sqrt2/2

F. tan(θ)=1

Answer: V≈1642 cm³.

Step-by-step explanation:

D=20 cm      d=12 cm      h=8 cm       V=?

[tex]R=\frac{D}{2}=\frac{20}{2} =10 \ (cm).\\ r=\frac{d}{2}=\frac{12}{2}=6 \ (cm).\\ \boxed {V=\frac{1}{3} *\pi *h*(R^2+R*r+r^2)} \ \ \ \ \ \Rightarrow\\V=\frac{1}{3}*\pi *8*(10^2+10*6+6^2)\\V=\frac{1}{3}*\pi *8*(100+60+36)\\ V=\frac{8}{3} *\pi *196\\V=\frac{8*196*\pi }{3} \\V\approx1642\ cm^3.[/tex]

Answer:

the answer is c ASA

Step-by-step explanation:

i think I. not sure

After he withdraws $50.00 in cash the bank reconciliation shows that Ryan would have: $1 501.98 in bank balance.

Add all the deposits

Total = $338.82

Add the checks

654.24 + 100.00 + 458.92

= $1,213.16

Total amount deposited is:  Cash + Check

1,213.16 + 338.82

Total Deposit = $1,551.98

Less withdrawal of $50

$1,551.98 - $50

Balance left = 1 501.98

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Full Question:

Ryan Massey wants to deposit the following into his savings account: 28 ten-dollar bills, 9 five-dollar bills, 20 quarters, 85 dimes, 32 pennies, and three checks for $654.24, $100.00, and $458.92. He wants to receive $50.00 in cash.

How much cash would he lave left after he withdraws $50.00 in cash?