A stadium has a seating capacity of 8,000. Suppose it is divided into 20 equal sections. How many seats are in each section?

Final answer:

The volume of a cone with a diameter of 6 inches and a height of 6 inches is approximately 56.5 cubic inches when rounded to the nearest tenth, using the volume formula for a cone.

Explanation:

To calculate the volume of a cone, we can use the formula

V = [tex]\(\frac{1}{3}\)\pi r^2 h[/tex]

First, find the radius (r) by dividing the diameter by 2.

The cone's diameter is 6 inches, thus the radius[tex]\(r = \frac{6}{2} = 3\) inches.[/tex]

Next, apply the values to the cone volume formula:

V =[tex]\(\frac{1}{3}\)\pi (3)^2 \times 6\)[/tex]

Now perform the calculations

V = [tex]\(\frac{1}{3}\)\times 3.14 \times 9 \times 6[/tex]

V = 56.52 cubic inches

Therefore, the volume of the cone is approximately 56.5 cubic inches to the nearest tenth.

Answer:

A∩B={[tex]25, 45, 65[/tex]}

B is a proper subset of A:

B⊂A

Step-by-step explanation:

A∩B means the intersection of the set A and the set B. In other words, is the set of elements contained in these both sets.

Given the set A and the set B:

[tex]A =[/tex]{[tex]15, 25, 35, 45, 55, 65[/tex]}

[tex]B =[/tex]{[tex]25, 45, 65[/tex]}

You can indentify that the numbers common in both sets are: 25,45 and 65.

Therefore you get:

A∩B={[tex]25, 45, 65[/tex]}

Since all elements of B are in A, and A contains elements that are not in B, then B is a proper subset of A:

B⊂A

Answer:1/2(2)(4.4)(5) + 1/3(1/2)(2)(4.4)(3.9)

The product of [tex](8.8 \times 10^{6} )(5 \times 10^{2})[/tex] is [tex]4.4 \times 10^{9}[/tex]. The correct option is B,  4.4 × 109

From the question,

We are to determine the product of (8.8 × 106)(5 × 102)

First, we will write the expressions properly

The given expression written properly is

[tex](8.8 \times 10^{6} )(5 \times 10^{2})[/tex]

Now, the product of the expression can be determined as shown below

[tex](8.8 \times 10^{6} )(5 \times 10^{2})[/tex]

This becomes

[tex]8.8 \times 10^{6} \times 5 \times 10^{2}[/tex]

= [tex]8.8 \times 5 \times 10^{2}\times 10^{6}[/tex]

= [tex]44 \times 10^{2}\times 10^{6}[/tex]

= [tex]44 \times 10^{2+6}[/tex]

= [tex]44 \times 10^{8}[/tex]

= [tex]4.4 \times 10^{9}[/tex]

Hence, the product of [tex](8.8 \times 10^{6} )(5 \times 10^{2})[/tex] is [tex]4.4 \times 10^{9}[/tex]. The correct option is B,  4.4 × 109

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Answer:

452.39

Step-by-step explanation:

A=(pi)r^2

A=3.14(12)^2

A=452.39

Answer: The area of the circle is 452.16 square units.

Step-by-step explanation:

To find the area of a circle you need to use the area of a circle formula. The formula is A= π x r^2.

π= 3.14

r= 12

The r is radius which is half of the diameter. When you apply the formula you get :

A = 3.14 x 12^2

A= 3.14 x 144

A= 452.16

For this case we must simplify the following expression:

[tex](x ^ {\frac {3} {8}}) ^ {\frac {3} {4}}[/tex]

By definition of power properties we have to:

[tex](a ^ m) ^ n = a ^ {m * n}[/tex]

So, rewriting the expression we have:

[tex](x ^ {\frac {3} {8}}) ^ {\frac {3} {4}} = x ^ {\frac {9} {32}}[/tex]

ANswer:

[tex]x ^ {\frac {9} {32}}[/tex]

The simplified value of the expression [tex]\((\frac{x^3}{8})^\frac{3}{4}\)[/tex] is [tex]\(\frac{x^\frac{9}{4}}{2^\frac{9}{4}}\).[/tex]

To simplify the expression [tex]\((\frac{x^3}{8})^\frac{3}{4}\)[/tex] using the laws of exponents,

combine the exponents and simplify the fraction.

So, [tex]\((\frac{x^3}{8})^\frac{3}{4}\)[/tex] can be written as [tex]\(\frac{x^{3 \cdot \frac{3}{4}}}{8^\frac{3}{4}}\)[/tex].

Next, simplify the exponents:

[tex]\(3 \cdot \frac{3}{4} = \frac{9}{4}\).[/tex]

So, the expression [tex]\(\frac{x^{3 \cdot \frac{3}{4}}}{8^\frac{3}{4}}\)[/tex]can be written as [tex]\(\frac{x^\frac{9}{4}}{8^\frac{3}{4}}\)[/tex].

To further simplify, express 8 as  [tex]\(2^3\)[/tex]:

So, [tex]\(\dfrac{x^\dfrac{9}{4}}{8^\dfrac{3}{4}} = \dfrac{x^\dfrac{9}{4}}{(2^3)^\dfrac{3}{4}}\).[/tex]

Now, applying the property [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:

[tex]\(\dfrac{x^\dfrac{9}{4}}{(2^3)^\dfrac{3}{4}} = \dfrac{x^\dfrac{9}{4}}{2^{3 \cdot \frac{3}{4}}}\).[/tex]

Simplifying the exponent [tex]\(3 \cdot \frac{3}{4} = \frac{9}{4}\)[/tex]:

[tex]\(\frac{x^\frac{9}{4}}{2^{3 \cdot \frac{3}{4}}} = \frac{x^\frac{9}{4}}{2^\frac{9}{4}}\).[/tex]

Therefore, the simplified value is  [tex]\(\frac{x^\frac{9}{4}}{2^\frac{9}{4}}\).[/tex]

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Answer:

The volume ratio of Prism A to Prism B is [tex]\frac{729}{8}[/tex]

Step-by-step explanation:

Step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> scale factor

x/y----> ratio of the surface area of Prism A to Prism B

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]\frac{x}{y}=\frac{81}{4}[/tex]

substitute

[tex]z^{2}=\frac{81}{4}[/tex]

[tex]z=\frac{9}{2}[/tex]

step 3

Find the volume ratio of Prism A to Prism B.

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> scale factor

x/y----> volume ratio of Prism A to Prism B

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{9}{2}[/tex]

substitute

[tex](\frac{9}{2})^{3}=\frac{x}{y}[/tex]

[tex](\frac{729}{8})=\frac{x}{y}[/tex]

The volume ratio of two similar prisms with a surface area ratio of 81:4 is obtained by cubing the square root of the surface area ratio, resulting in a volume ratio of 729:8.

The question involves finding the volume ratio of two similar prisms when the surface area ratio is given.

Since the surface areas are in a ratio of 81:4, the corresponding linear dimensions will be in the square root ratio, which is 9:2. For two similar three-dimensional shapes, if the ratio of their corresponding lengths is a:b, then the ratio of their surface areas is a^2:b^2, and the ratio of their volumes is a^3:b^3.

Therefore, the volume ratio of Prism A to Prism B can be found by cubing the linear dimension ratio: (9:2)^3 which equals 729:8. Hence, the volume ratio of Prism A to Prism B is 729:8.

Answer:

Length = 17 inches, Width = 14 inches

Step-by-step explanation:

Let the width(W) of the rectangle be x inches

The length(L) of the rectangle will be x + 3 inches

Perimeter(P) of the rectangle is 62 inches

i.e

P = 2L + 2W

2(x + 3) + 2x = 62

2x + 6 + 2x = 62

4x = 62 - 6 = 56

x = [tex]\frac{56}{4}[/tex] = 14 inches

So the width is 14 inches and;

The length is 14 + 3 = 17 inches

The width of the rectangle is 14 inches, and the length is 17 inches.

To find the length and width of a rectangle, we can use the information given in the problem and set up an equation. Let's say the width of the rectangle is x inches. The length would then be x + 3 inches. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Plugging in the given values for the perimeter, we get:

62 = 2(x + 3) + 2x

Simplifying the equation:

62 = 2x + 6 + 2x

Combine like terms:

62 = 4x + 6

Subtract 6 from both sides:

56 = 4x

Divide both sides by 4:

x = 14

So the width of the rectangle is 14 inches. Substituting this value back into the equation for the length, we get:

Length = 14 + 3 = 17 inches

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18/40 = 9/20 =

Simplified

Answer:

9/20 is the simplified 18/40

Answer:

y=2x

Step-by-step explanation:

2 up, 1 over. put rise over run so that concludes the 2x.

The line starts at 0 so there is no y-intercept

y=2x The "formula" would be y=mx+b where m is the slope and b is the y-intercept. in this case, the slope is 2 and the y-intercept is 0 therefore the equation is y=2x (no zero because we can atoumtucally assume that its a zero)

Answer:i will help!!

Step-by-step explanation:

Answer:

Answer is line and ray.

Step-by-step explanation:

Ray -  A ray starts from a point and ends to the infinity.

Therefore, ray is one dimensional and has infinite length.

Point - It is one dimensional but has no length.

Plane - It may be three/two dimensional.

Segment - It is one dimensional but has a limited length.

Line - It's one  dimensional with infinite length.

Angle - It's two dimensional structure.

Answer is line and ray.

One-dimensional objects with infinite length are infinite straight wires. An example is a transmission line used for electricity distribution.

The one-dimensional objects that have infinite length are infinite straight wires. An infinite straight wire is a wire that has a length much greater than its other dimensions. In the limit  L→ ∞, the field of an infinite straight wire is obtained.

An example of a one-dimensional object with infinite length is the transmission line used for electricity distribution. These lines can stretch for many kilometers and are considered one-dimensional because their length is much greater than their width and height.

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The circle has circumference [tex]18\pi\,\mathrm{in}[/tex]. If [tex]m\angle POQ=\theta[/tex], then

[tex]\dfrac{6\pi\,\rm in}{18\pi\,\rm in}=\dfrac\theta{2\pi\,\rm rad}\implies\theta=\dfrac{2\pi}3\,\mathrm{rad}[/tex]

Answer: [tex]\dfrac{2\pi}{3}\text{ radians}[/tex]

Step-by-step explanation:

We know that the formula to calculate the length of arc having central angle 'x' is given by :-

[tex]l=x r[/tex], where r is radius of the circle.

Given : In circle O, radius OQ = [tex]l=9\text{ inches}[/tex]

The measure of arc PQ =[tex]6\pi\text{ inches.}[/tex]

The measure of central angle POQ ( in radians ) is given by :-

[tex]x=\dfrac{l}{r}\\\\\Rightarrow\ x=\dfrac{6\pi}{9}}\\\\\Rightarrow\ x=\dfrac{2\pi}{3}[/tex]

Hence, the measure of central angle POQ =[tex]\dfrac{2\pi}{3}\text{ radians}[/tex]

Answer:

3.4 x 10 ^-3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

The scientific or the exponential form of the number is A = 3.4 × 10⁻³

Given data ,

To express 0.0034 in scientific notation, we need to represent it as a number between 1 and 10 multiplied by a power of 10.

First, we move the decimal point to the right until we have a number between 1 and 10. In this case, we move the decimal point three places to the right, resulting in 3.4.

Next, we determine the power of 10 by counting the number of places we moved the decimal point.

Since we moved it three places to the right, the power of 10 is -3

So , the exponential form is

Putting it all together, 0.0034 in scientific notation is 3.4 × 10⁻³

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Answer:

x = [tex]\frac{5}{26}[/tex]

Step-by-step explanation:

Given equation:

[tex]\frac{3}{4}x + \frac{5}{8} = 4x[/tex]

[tex]\frac{3(2)x + 5}{8} = 4x[/tex]            ∵taking GCF 8

[tex]\frac{8 (6x + 5) }{8}[/tex]  = 4x × 8

6x + 5 = 32x    ⇒   5 = 32x - 6x   ⇒  5 = 26x   ⇒  x = [tex]\frac{5}{26}[/tex]

Answer:

Option B. 767

Step-by-step explanation:

we know that

75%=75/100=0.75

To find the school’s students who attended the last home

football game, multiply 0.75 by the total students of Central High School

so

0.75*(1,023)=767.25

Round to the nearest whole number

767.25=767 students

Answer:

20 harnesses

36 leashes

Step-by-step explanation:

h = number of harnesses

l = number of leashes

set up two equations based on the information provided:

h + l = 56; since the number of harnesses and leashes made up the total item sold, which is 56

7.5h + 3.25l = 267; the same concept as the last step

h = 56 - l; let one of the variable stand by itself

7.5(56 - l) + 3.25l = 267; substitute the variable h into the other equation

420 - 7.5l + 3.25l = 267; solve

420 - 4.25l = 267; add common variables, remember you take the sign in front of the number when doing math

-4.25l = -153; subtract 420 from both side

l = 36; divide both side by -4.25

36 leashes were sold last month; 56 - 36 = 20, which means 20 harnesses were sold.

Answer:

g(x)=(x+7)^2-3

Step-by-step explanation:

Given:

f(x)= x^2

Now we have to translate f(x) 7 units to the left and 3 units down to form the function g(x).

As per the rules of translation

when any parent function, in given case f(x)=x^2, is translated to 'a' units to the left then 'a' is added to the value of x. thus making f(x+a)

Also when the parent function is translated any 'a' units down then 'a' is subtracted from the value of function. thus making f(x)-a

Translating f(x), 7 units to the left

f(x+7)= (x+7)^2

Translating f(x+7), 3 units down

f(x+7)-3 = (x+7)^2-3

Hence new function g(x)=(x+7)^2-3!

Answer: p+(q÷r) this is because you divide a and r and add p to it

Should be “p+q/r”.

Using English grammar, one can group the terms using “sum of...”, “product of...”, and “quotient of x and y.” (Where ... can be “x and y”)

Subtracting in English is slightly different using “x subtracted from y” meaning “y-x”.

All of these terms can be used in tandem to create expressions like the given answer.

5 gallons, 24 quarts (6 gallons), 10.6 gallons

To arrange 5 gallons, 10.6 gallons, and 24 quarts from smallest to largest, first convert all measurements into the same unit (quarts). The arrangement from smallest to largest is 5 gallons, 24 quarts, and 10.6 gallons.

To arrange the given measurements of 10.6 gallons, 5 gallons, and 24 quarts from smallest to largest, we first need to convert them into the same unit for an accurate comparison. Given the conversion factor of 1 gallon equals 4 quarts, we can start the comparison process.

In quarts, the order from smallest to largest is as follows: 20 quarts (5 gallons), 24 quarts, and 42.4 quarts (10.6 gallons). Therefore, when we arrange the original units from smallest to largest, it will be 5 gallons, 24 quarts, and then 10.6 gallons.

8 & 4 when you add them together it’s 12 and when you multiply then it’s 32. When you see sum in a problem it means add. When you see product in a problem it means multiply.

Step-by-step explanation:

We can do this either by looking at:

the bonds of 12, (of which there are 7 pairs)

(which pairs of numbers add up to 12?)

or the factors of 32 (of which there are 3 pairs)

Using the factors seems quicker.

Write the factors and in each find their sum.

As 12 is quite small in comparison to 32, I would expect that the middle factors will be the ones we want - they have the smallest sum and the smallest difference of all the pairs:

1×32

=32

1+32

=33

2×16

=32

2+16

=18

4×8

=32

4+8

=12

these are the ones we want.

The equivalent of the given expression 3 × 7.2 will be 21.6.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The result of 3 times 7.2 can be found by simply multiplying 3 and 7.2 together:

3 × 7.2 = 21.6

Therefore, the equivalent of 3 times 7.2 is 21.6.

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To determine what is equivalent to 3×7.2, simply multiply 3 by 7.2 to get 21.6.

Raul used the model to calculate 3×7.2. To find what is equivalent to 3×7.2, we can multiply the two numbers directly. Multiplying 3 by 7.2 gives us 21.6, so 3×7.2 is equivalent to 21.6.

The question seems to be asking for a calculation based on a model, but without the specifics of the model, the best we can do is a straightforward multiplication. Remember, when multiplying by a whole number and a decimal, you multiply as if they were both whole numbers and then place the decimal in the product based on the number of decimal places in the original numbers.

your 2nd answer is true. since your measure of the two bottom angles which are angles KML and MLk has to equal the measure of the angle outside the triangle. to the 2nd answer choice is true

Answer: Third option

[tex]-x + 2 = 3x - 4.[/tex]

Step-by-step explanation:

One of the ways of solving a system of equations is by equating the equations and solving for one of the variables.

In this case we have the system:

[tex]y = -x + 2\\\\y = 3x - 4[/tex]

Note that if [tex]y[/tex] is equal [tex]-x + 2[/tex] and also [tex]y[/tex] equals [tex]3x - 4[/tex]

Then logically [tex]-x + 2[/tex] must be equal to [tex]3x - 4[/tex].

We write equality.

[tex]-x + 2 = 3x - 4.[/tex]

Then the correct answer is the third option.

We can also solve for the variable x

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

Answer:

She'll have to pay $46.75

Step-by-step explanation:

42.50 divided by 10% is 425 which equals $4.25. 42.50 + 4.25 = 46.75

42.50 + 10% = 46.75. So therefore you can check your answer twice and it will be the same answer.

ANSWER

D.

[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]

EXPLANATION

We want to find the expression which is a square of a binomial.

In other words, we want to identify the expression which is a perfect square trinomial.

[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]

This expression can be rewritten as,

[tex] {(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} [/tex]

This is a perfect square trinomial that can be factored as:

[tex] {(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} = (4x + 3y) ^{2} [/tex]

This is the square of a binomial.

The correct answer is D

The answer is:

D) [tex]16x^{2} +24xy+9y^{2}[/tex]

We are looking for an expression that satisfies the perfect square trinomial form, which can be defined by the following notable product:

[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]

From the given options, we can see that the only option that matches with the perfect square trinomial form is:

[tex]16x^{2} +24xy+9y^{2}[/tex]

We can rewrite the expression by the following way:

[tex](4x+3y)^{2}[/tex]

If we square the binomial, we will have the perfect square binomial expression given from the options.

So, squaring, we have:

[tex](4x+3y)^{2}=(4x)^{2}+2*(4x*3y)+(3y)^{2}\\\\(4x+3y)^{2}=16x^{2} +24xy+9y^{2}[/tex]

Hence, the answer is:

D) [tex]16x^{2} +24xy+9y^{2}[/tex]

Have a nice day!

Answer:

From the information provided we have:

PD ≅ RD (= 11)

∠CPD ≅ ∠CRD (= 90°)

They both have CD as the hypotenuse.

=> ΔCPD ≅ ΔCRD

=> ∠PCD ≅ ∠RCD

Now we know that:

∠RCP = ∠PCD + ∠RCD

∠RCP = 2 · ∠RCD

∠RCP = 2 · 33° = 66°

So the answer is B

Answer: B. 66°

Step-by-step explanation:

In then figure figure , we consider two triangle ΔPCD and Δ RCD in which

∠P ≅ ∠R = 90°

PD≅RD =11

CD≅CD   [Reflexive Property]

Hence, By HL theorem we have

ΔPCD ≅ Δ RCD

[ HL theorem says that if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of other right triangle, then the triangles are said to be congruent.]

Now , By CPCTC we have

∠PCD≅∠RCD

Then , ∠RCP = 33°+33°=66°

The expression [tex]\frac{7\sqrt{x^2}}{5\sqrt{y^3}}[/tex] can be simplified to  [tex]\frac{7\sqrt{x^2}}{5y\sqrt{y}}[/tex].

Let's simplify the expression [tex]\frac{7\sqrt{x^2}}{5\sqrt{y^3}}[/tex]:

First, simplify the square root terms:

[tex]\frac{7|x|}{5\sqrt{y^3}}[/tex]

Now, combine the constants:

[tex]\frac{7}{5} \cdot \frac{|x|}{\sqrt{y^3}}[/tex]

To simplify further, you can rewrite [tex]\sqrt{y^3}[/tex] as [tex]\sqrt{y^2 \cdot y}[/tex] and then cancel out one of the y terms:

[tex]\frac{7}{5} \cdot \frac{|x|}{y\sqrt{y}}[/tex]

So, the simplified expression is [tex]\frac{7|x|}{5y\sqrt{y}}[/tex], or equivalently, [tex]\frac{7\sqrt{x^2}}{5y\sqrt{y}}[/tex].

Answer:

Because some applicants volunteer and meet the GPA requirements the events are NOT MUTUALLY exclusive. Thus, the probability is 65%

The probability that an applicant meets the GPA requirements or volunteers is 65%.

To find the probability that an applicant meets the GPA requirements or volunteers, we need to determine the number of applicants who meet either requirement. From the given information, there are 950 applicants who meet the GPA requirements and 600 applicants who volunteer for community service. However, there are 250 applicants who meet both requirements, so we count them only once.

To find the total number of applicants who meet either requirement, we add the number of applicants who meet the GPA requirements and the number of applicants who volunteer and subtract the number of applicants who meet both requirements:

Total number of applicants who meet either requirement = 950 + 600 - 250 = 1300

The probability that an applicant meets the GPA requirements or volunteers is the number of applicants who meet either requirement divided by the total number of applicants:

Probability = Number of applicants who meet either requirement / Total number of applicants = 1300 / 2000 = 0.65 = 65%

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The possible dimensions of the rectangle are

4 and 1

3 and 2

Its the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).



We are given that rectangle has a perimeter of 10 meters.

Since we know that the perimeter of the rectangle is twice the sum of the length and width of rectangle.

Thus, perimeter of the rectangle = 2 (L + W)

10 = 2 (L + W)

L +w = 10/2 = 5

Some basic dimensions could be ;

4 and 1

3 and 2

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Answer:

it is the surface of the 3d shape spread out like an blue print

Step-by-step explanation:

Answer:

A pattern which you can cut and fold to make a model of a solid shape.