1. The football team at Vindale College is having a new stadium built that
will accommodate 49,697 people. According to one fan's calculations,
that is 67% more people than their old stadium could seat. How many
seats did the old stadium have? Round to the nearest whole number.

Answer:

Step-by-step explanation:

The ratio of the volume of the pyramid to the volume of the prism is 1.so, the option A. is correct.

Let the base of  the base of a prism is b and the height of the prism is h.

so, the volume of the prism-

                                    V= [tex]b^{2}[/tex] h

also, given that base of the given pyramid is also b and the height of the pyramid is three times the height of the prism.

                                     h'=3h

so, the volume of the square pyramid-

                                    V'=[tex]\frac{1}{3}[/tex][tex]b^{2}[/tex]h'

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

                                    V'=[tex]b^{2}[/tex]h

so, now-

                                  [tex]\frac{V'}{V}[/tex]=[tex]\frac{b^{2}h }{b^{2}h }[/tex]

                                   [tex]\frac{V'}{V}[/tex]= 1

  so. the ratio of the volume of the pyramid to the volume of the prism is 1.                                

9514 1404 393

Answer:

  60 meters

Step-by-step explanation:

The area of Square B is the difference of the areas of squares C and A, so is 225 square meters. The side length is √225 = 15 meters, so the sum of the lengths of the four sides is 4·15 = 60 meters.

The perimeter of square B is 60 meters.

Answer:

D

Step-by-step explanation:

6 days is 60%

Hello there!

Answer:

[tex]V = 18432\pi[/tex] or approximately 57876.48

Step-by-step explanation:

[tex]V = \frac{4}{3} \pi R^{3}[/tex]

R = 24

[tex]V = \frac{4}{3} \pi *24^{3} = 18432\pi[/tex]

if [tex]\pi =3.14[/tex] then:

[tex]V = 57 876.48[/tex]

Answer:

50.26548246 or 50.3 mm^2 (rounded to the tenth)

Step-by-step explanation:

[tex]\pi 8^{2} = 201.0619298[/tex]

just divide that # by 4 and you get the answer! Hope this helps!

The formula to calculate the distance:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute and solve:

d = √(-5(-2))² + (-4-1)²

d = √7² + (-5)² = √49 + 25

d = √74 ====> Alternative "A"

Answer:

1.8

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

Answer:

about 2

Step-by-step explanation:

you see there is a chance you might not get 10 but i belive its 2 times you will

roll a ten bc its all just random

Answer:

[tex]80^{\circ}[/tex]

Step-by-step explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

Answer: 700 yards of fencing (assumed).

Step-by-step explanation:

To be able to calculate the number of yards that Farmer Johnson needs, you will have to know the dimensions of the field.

I will therefore assume certain figures and you can use it as a reference.

Assume that the field is a rectangular field that measures 200 yards in length and 150 yards in breath.

This means that the amount of yards needed will be the perimeter of the yard:

Perimeter = (Length * 2) + (Width * 2)

= (200 * 2) + ( 150 * 2)

= 400 + 300

= 700 yards of fencing.

The slope of the line is 20.

The slope represents the rate of change in the price per hour is $20.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Two coordinates from the graph.

(1, 60) and (3, 100)

Slope.

= (100 - 60) / (3 - 1)

= 40 / 2

= 20

The slope represents the rate of change in the price per hour.

Thus,

The value of the slope is 20.

The slope denotes that the rate of charge per hour is $20.

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Answer:

$3.50

Step-by-step explanation:

1.10 / 2 = 0.65

1.10 + 0.65 = 1.75

2.20 / 2 = 1.10

1.10 / 2 = 0.65

1.10 + 0.65 = 1.75

1.75 + 1.75 = 3.50

therefor the answer is $3.50

let me know if you would like me to explain in more detail

Answer:

Step-by-step explanation: The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed (a cylinder and two cones). The silo is made up of a cylinder (with height 10 feet and base radius 5 feet) and two cones (each with height 5 ft and base radius 5 ft). The formulas given at the beginning of the SAT Math section:

Volume of a Cone:

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

Volume of a Cylinder:

[tex]V=\pi r^2h[/tex]

can be used to determine the total volume of the silo. Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is given by

[tex]V_{silo} =\pi (5^2)(10)+(2)(\frac{1}{3})\pi (5^2)(5)=(\frac{4}{3})(250)\pi[/tex]

which is approximately equal to 1,047.2 cubic feet.

The final answer is D.

The fraction after solving and simplifying the mixed fraction 5 3/4 ÷ 1 1/2​ is 23 / 6.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. For instance, 8 1 / 2 is a mixed fraction if 8 is a whole number and 1/2 is a fraction.

Given:

5 3/4 ÷ 1 1/2​

Solve the mixed fraction into improper fractions as shown below,

5 × 4 + 3 / 4 ÷ 1 × 2 + 1 / 2

20 + 3 / 4 ÷ 2 + 1 / 2

23 / 4 ÷ 3 / 2

23 / 4 × 2 / 3

23 × 2 / 4 × 3

On simplifying,  

23 × 1 / 2 × 3

23 / 6

Thus, the value is 23 / 6.

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Answer:

b is correct answer

Step-by-step explanation:

that is correct answer

Answer:

The sequence diverges

Step-by-step explanation:

Answer: -14

Step-by-step explanation:   When you have a problem like this all you do in multiply the answer and the number your given.

 7x-2 that would by -14

You want to check your answer by changing X for -14 and you solve from there. Plus 2 negatives equal a positive.

Hope this helps!

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{x}{-2} = 7}[/tex]

[tex]\text{Multiply } \rm{ -2}\text{ to both sides}[/tex]

[tex]\mathsf{\dfrac{x}{-2}\times -2 = 7\times -2}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x = 7\times -2}[/tex]

[tex]\mathsf{x = -14}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = -14}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

  1/2log₂(a-1) -log₂(9)

Step-by-step explanation:

You want the expanded form of log₂(√(a-1)/9).

The relevant rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

The rules are applicable for any base.

  [tex]\log_2{\dfrac{\sqrt{a-1}}{9}}=\log_2{(\sqrt{a-1})}-\log_2{(9)}=\boxed{\dfrac{1}{2}\log_2{(a-1)}-\log_2{(9)}}[/tex]

Answer:

B. Few energy sources

Step-by-step explanation:

Answer:

1409.28

Step-by-step explanation:

hope this helps :)

Answer:

17) (4,7) (4,5)

18) (-4,7), (-4,5) , (4,7. ) ,( 4,5) is a rectangle solve for area

19) quadrant 2

Step-by-step explanation:

ok i know the answer 1+1=2

Answer:

[tex]x \approx 55.8[/tex]

Step-by-step explanation:

In order to solve this problem, one must use the trigonometric ratios. These ratios are the following,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)= \frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Remember, each side is named relative to the angle, thus sides will attain different names depending on the angle which one sues to calculate with.

In this case, one is given the measure of the angle, and the measure of the side opposite to the angle. One is asked to find the measure of the side adjacent to the angle. Use the trigonometric ratio ([tex]tan[/tex]) to solve for the unknown. Substitute in the given values,

[tex]tan(25)=\frac{26}{x}[/tex]

Manipulate the equation such that it is solved for the parameter(x),

[tex]x=\frac{26}{tan(25)}[/tex]

Solve,

[tex]x \approx 55.8[/tex]

The coordinate of 3 4 indicates a point on a cartesian plane.

In mathematics, the coordinate system refers to the method in which a location of a point is identified in the plane or space.

There are two coordinate system, one is cartesian coordinate system and the other is polar coordinate system.

Each coordinate system has some reference lines called reference axis or reference direction or point called reference direction and point.

As per the definition of a cartesian coordinate system, a location of a point is identified by a pair of numerical terms. The first one indicates the X coordinate and the second one indicates the Y coordinate.

So, the above coordinate 3 4 refers to a point on the XY coordinate system where 3 is the X coordinate and the distance from Y axis and 4 is the Y coordinate and distance from the X axis.

ordinate refers to y point in (x, y)

in (3,4)

ordinate = 4

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Use the coordinate plane to graph points, lines, and geometric forms in the different quadrants, and then use the absolute value to determine the distances between them.

What does ordinate math entail?

An exact position of a point in the coordinate plane can be demonstrated using a collection of values called coordinates. Meaning of a Coordinate Plane. The intersection of the x-axis and y-axis, two perpendicular lines that form a 2D plane known as a coordinate plane.

Which three coordinate systems are there?

Cartesian, cylindrical, and spherical are the three most often used coordinate systems. We'll discuss a cylinder-based coordinate system as well as a cartesian-based one in this chapter.

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Those are vertical angles so both sides need to be equal.

2x+15 = 145

Subtract 15 from both sides:

2x = 130

Divide both sides by 2:

x = 65

Answer:

145 = 2x + 15

2x = 130

x = 65

145 and 2x + 15 are vertical angles and therefore congruent.

Answer:

-5

Step-by-step explanation:

-9 - ( -4 )

= -9 + 4

= -5

Step-by-step explanation:

-9-(-4) ( when there is a- in front of an expresion in parentheses, change the sign of each term in the expression )

-9+4 (Calculate the sum)

- 5

Answer:

55cm^2

Step-by-step explanation:

Split into 2 parts, the rectangle on the left, and triangle on the right.

Rectangle:

8 cm x 5 cm = 40 cm^2

Triangle

14 cm - 8 cm = 6cm (Height)

(5cm(base) x 6cm)/2 = 15cm ^2

15cm^2 + 40cm^2 = 55cm^2