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Q:

Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is \( 180 ^ { \circ } \) . In a triangle, the measures of the three angles are \( x , x - 28 \) , and \( x + 37 \) . What is the measure of each angle? The measure of the first angle, \( x \) , is \( \square ^ { \circ } \) . 

Q:

Two boats leave a port at the same time. One travels at \( 25 mi / hr \) in a direction \( N 32 ^ { \circ } E \) , and the other travels at \( 30 mi / hr \) in a direction \( S 32 ^ { \circ } E \) . 

a. Sketch the navigation direction of the boats. 

b. Find the distance between them after \( 1 \) hour. 

Q:

A rectangular building is to be placed on a lot that measures \( 30 m \) by \( 40 m \) . The building must be placed in the lot so that the width of the lawn is the same on all four sides of the building. Local restrictions state that the building cannot occupy any more than \( 50 \% \) of the property. What are the dimensions of the largest building that can be built on the property? 

Q:

If a baseball is a sphere with a radius of \( 3.75 cm , \) what is the surface area of the baseball? Use 

\( \pi = 3.14 . \) 

A. \( 60.5 cm ^ { 2 } \) 

B. \( 181.46 cm ^ { 2 } \) 

C. \( 176.6 cm ^ { 2 } \) 

D. \( 725.8 cm ^ { 2 } \) 

Q:

What is the radius of a circle whose equation is \( ( x + 5 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 4 ^ { 2 } ? \) 

\( 2 \) units 

\( 4 \) units 

\( 8 \) units 

\( 16 \) units 

Q:

The line through \( A \) and \( B \) is \( \over leftrightarrow { A B } \) . The length of segment \( \overline { A B } \) is \( A B \) . The ray starting at \( A \) and passing through \( B \) is \( A \vec { B } \) . These descriptions are of

a. undefined terms 

b. defined terms 

c. postulates 

d. theorems 

Q:

If \( A \) is the area of the circle, then \( A _ { s } = A \frac { \theta } { 2 \pi } \) represents the area of the sector, because \( \frac { \theta } { 2 \pi } \) gives the fraction of the area covered by the sector. 

Find the area of the sector formed by central angle \( \theta \) in a circle of radius \( r \) if \( \theta = \frac { \pi } { 4 } ; r = 8 m\) .        \(m ^ { 2 } \)

 

Q:

For the problem below, \( \theta \) is a central angle in a circle of radius \( r \) . Find the length of arc \( s \) cut off by \( \theta \) . Enter exact answers, do not round. 

\( \theta = 60 ^ { \circ } ; r = 12 \) inches 

\( s = \square \) inches 

Q:

A rancher has \( 800 \) feet of fencing to put around a rectangular field and then subdivide the field into \( 3 \) identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms. 

Q:

Roy drove his boat from a dock due north for \(6\) miles. He then turned and drove the boat due west for about \(8\) miles and dropped anchor. Approximately how many miles from the dock did Roy drop anchor? 

\(2\)

\(5.3\) 

\(10\) 

\(14\) 

Q:

A rancher has \( 800 \) feet of fencing to put around a rectangular field and then subdivide the field into \( 3 \) identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.

Q:

In a scalene triangle, the longest side is opposite the angle with the smallest measure.

 A. True 

B. False 

Q:

What is the greatest number of obtuse angles a triangle can contain? 

A. 0

B. 3

C. 2

D. 1 

Q:

Sketch two triangles, \( \triangle D E F \sim \triangle G H F \) . If \( D E = 6 \) when \( G H = 8 \) 

and \( E F = 39 , \) what is the length of side of \( H F ? \) Remember to draw two triangles and label their vertices correctly, with corresponding parts labeled. 

Q:

Use the following similar triangles \( ( \triangle A B C \sim \triangle D E F ) \) . 

If \( B C = 30 \) when \( E F = 25 \) and \( D F = 11 \) , what is the length of the corresponding side to \( D F ? \) Solve mathematically (drawings not to scale.)

Round your answer to the nearest tenth. 

\( A C = \) 

Q:

If \( \triangle A B C \) is similar to \( \triangle D E F \) , the sides of \( \triangle A B C \) must be congruent to the corresponding sides of \( \triangle D E F \) .

A. True 

B. False 

Q:

Write and solve an equation for the situation. 

The perimeter of a parallelogram is 76 meters. The width of the parallelogram is 2 meters less than its length. Find the length and the width of the parallelogram. 

 

The length of the parallelogram is __

The width of the parallelogram is __

Q:

The side of a square is \( 2 m n \) . Find the area of the square. 

\( 2 m ^ { 2 } n ^ { 2 } \) 

\( 4 m ^ { 2 } n \) 

\( 8 m ^ { 2 } \) 

\( 4 m ^ { 2 } n ^ { 2 } \) 

Q:

What is the value of \( x \) ? 

A: 20

B: 40

C: 50

D: 60 

Q:

Sketch the following to help answer the question. Kite \( Q R S T \) has a short diagonal of \( Q S \) and a long diagonal of \( R T \) . The diagonals intersect at point \( P \) . Side \( Q R = 10 m \) and diagonal \( Q S = 12 m \) . Find the length of segment RP. 

\( 6 m \) 

\( 8 m \) 

\( 10 m \) 

\( 12 m\) 

Q:

Jen is on the platform of her boat. She sights the top of a lighthouse at an angle of \( 30 ^ { \circ } \) as shown below. She knows that the height of the lighthouse is \( 50 \) meters. 

How far is Jen from the base of the lighthouse, in meters? 

\( 25 \) 

\( 25 \sqrt { 3 } \) 

\( 50 \sqrt { 3 } \) 

Q:

Fill in the blank to correctly complete the following sentence. 

The vertex of the graph of \( f ( x ) = x ^ { 2 } + 8 x + 7 \) has \( x \) -coordinate (Type an integer or a simplified fraction.) 

Q:

Calculate the area of this shaded region. 

Q:

In \( \triangle T U V , \angle T \) is a right angle, \( T U = 10 , U V = 26 \) , and \( V T = 24 \) . If \( \triangle T U V \sim \triangle W X Y \) and \( W Y = 72 \) , what is the area of \( \triangle W X Y \) ? 

Q:

Find the surface area of the figure when \( s = 2 m \) and \( I = 8 m \) . 

\( \square m ^ { 2 } \) 

Q:

A rectangular solid has a length of \( 6.7 m \) , a width of \( 2.3 m \) , and a height of \( 7 m . \) 

Find the volume of the solid. (Round your answer to one decimal place.) 

Q:

A pyramid has a volume of \( 20 \) cubic inches and the area of the base is \( 15 \) square inches. What is the height of the pyramid? 

Q:

Quadrilateral \( A B C D \) has the coordinates \( A ( - 3,2 ) , B ( 2,5 ) , \) and 

\( D ( 0 , - 3 ) \) . If Quadrilateral \( A B C D \) is a square, what are the coordinates of vertex \( C ? \) 

\( ( 5,0 ) \) 

\( ( 0,5 ) \) 

\(( 0 , - 2 ) \) 

\( ( 2,0 ) \) 

Q:

Lucinda wants to build a square sandbox, but she has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length. 

a. Arrange four equal-length sides so the diagonals bisect each other. 

b. Arrange four equal-length sides so the diagonals are equal lengths also. 

c. Make each diagonal the same length as four equal-length sides. 

d. Not possible; Lucinda has to be able to measure a right angle. 

A (a) 

B (b)

C (c) 

D (d) 

Q:

 

\(\overline { L M } \) is the midsegment of \(\square A B C D . A B = 46\) and \(D C = 125 .\) What is \(L M ?\) 

a. \( 171 \)   b. \( 85.5 \)  c. \( 79 \)   d. \( 95.5\) 

\(A ( a ) \)

\( B ( b ) \) 

\( C ( c ) \) 

\( D ( d ) \) 

Q:

A cube has SIX (6) faces and EIGHT (8) VERTICES. Using Euler's Theorem (F + V = E + 2), find the number of edges. 

Q:

If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar. 

Q:

 What type of quadrilateral has diagonals that are perpendicular, opposite angles that are congruent, adjacent angles that are not congruent, and four congruent sides?

 A Trapezoid B Square C Rectangle D Rhombus 

Q:

The radius of a spherical balloon is increasing at a rate of \( 3 \) centimeters per minute. How fast is the surface area changing when the radius is \( 12 \) centimeters? Hint: The surface area is \( S = 4 \pi r ^ { 2 } \) . Rate of change of surface area 

Q:

You are building a rectangular pen with two parallel partitions, as shown below. I

 

f you have \( 1,100 \) meters, what will be the total length of the longest side of the pen that gives the maximum area? 

Q:

A community pool that is shaped like a regular pentagon needs a new cover for the winter months. The radius of the pool is \( 20.10 ft \) . The pool is \( 23.62 ft \) on each side. 

To the nearest square foot, what is the area of the pool that needs to be covered? 

Q:

The square pyramid below has a height of \( 12 \) centimeters and a slant height of \( 20 \) centimeters. The square base of the pyramid has side lengths of \( 32 \) centimeters. 

Q:

Write the equation for the ellipse centered at the origin with \( y \) -intercepts at 

\( 26 \) and \( - 26 \) and foci located at \( ( 0,10 ) \) and \( ( 0 , - 10 ) \) . 

\( \frac { y ^ { 2 } } { 676 } + \frac { x ^ { 2 } } { 576 } = 1 \) 

\( \frac { y ^ { 2 } } { 26 } + \frac { x ^ { 2 } } { 24 } = 1 \) 

\( \frac { y ^ { 2 } } { 576 } + \frac { x ^ { 2 } } { 676 } = 1 \) 

\( \frac { y ^ { 2 } } { 24 } + \frac { x ^ { 2 } } { 26 } = 1\) 

Q:

Cube A has an edge length of \( 2 \) and cube \( B \) has an edge length of \( 6 \) . How many times greater is the volume of cube B than cube \( A \) ? 

A. \( 16 \) times     B. \( 24 \) times     C. \( 3 \) times     D. \( 27 \) times 

Q:

What is the length of the arc that subtends a central angle of \( 139 ^ { \circ } \) , for a circle with a radius of \( 7.5 \) centimeters? Use \( 3.14 \) . for \( \pi \) when necessary. 

A. \( 18.19 cm \) 

B. \( 14.86 cm \) 

C. \( 16.14 cm \) 

D. \( 12.36 cm\) 

Q:

The perimeter of a square with a side length of \( s \) is equal to the circumference of a circle of radius \( r \) . What is the ratio of \( s \) to \( r \) ? 

A. \( \frac { \pi } { 2 } \)     B. \( \frac { \pi } { 4 } \)     C. \( 2 \pi \)     D. \( \sqrt { \pi } \) 

Q:

The base of a triangle is shrinking at a rate of \( 7 \frac { cm } { hr } \) and the height of the triangle is increasing at a rate of \( 4 \frac { cm } { hr } \) . Find the rate at which the area of the triangle changes when the height is \( 18 cm \) and the base is \( 9 cm \) . Provide your answer below: 

Q:

Find the area of the sector of a circle with radius \( r = 19 \) in and angle \( \theta = \frac { \pi } { 3 } \) 

A. \( \frac { 19 \pi } { 6 } \) square inches B. \( 10830 \) square inches C. \( \frac { 19 \pi } { 3 } \) square inches D. \( \frac { 361 \pi } { 6 } \) square inches 

Q:

The area of a square with a side length of \( s \) is equal to the area of a circle of radius \( r \) . What is the ratio of s to \( r \) ? 

A. \( \frac { \pi } { 2 } \)      B. \( 2 \sqrt { \pi } \)     C. \( \frac { \pi } { 4 } \)     D. \( \sqrt { \pi } \) 

Q:

8. Line \( \overline { A B } \) has the endpoints \( A ( 8,7 ) \) and \( B ( 15,14 ) \) 

What are the \( x \) - and \( y \) -coordinates of point C that partitions \( \overline { A B } \) at a \( 2 : 5 \) ratio. Where is point \( C ?\) 

Q:

Cameron is creating a garden. He designs a rectangular garden with a length of \( ( x + 5 ) \) feet and a width of \( ( x + 3 ) \) feet. When \( x = 6 , \) what is the area of the garden? 

Q:

A tennis court is surrounded by a fence so that the distance from each boundary of the tennis court to the fence is the same. If the tennis court is \( 76 \) feet long and \( 34 \) feet wide, what is the area of the entire surface inside the fence? 

Q:

Consider the circle with equation \( ( x + 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 37 \) 

Find all points on the circle with \( x \) -coordinate \( 2 \) . Enter only the \( y \) -coordinate(s). If there are more than one solutions, separate them with a comma. If there is no solution, enter DNE. 

Q:

Sylvia has just discovered that the valve on her cement truck failed during the night and that all the contents ran out to form a giant cone of hardened cement. To make an insurance claim, she needs to figure out how much cement is in the cone. The circumference of its base is \( 44 \) feet, and it is \( 4 \) feet high. Calculate the volume to nearest cubic foot. 

\( 205 ft ^ { 3 } \) 

\( 445 ft ^ { 3 } \) 

\( 615 ft ^ { 3 } \) 

\( 149 ft ^ { 3 } \) 

Q:

Lashonda has \( 360 \) meters of fencing and wishes to enclose a rectangular field. Suppose that a side length (in meters) of the field is \( x \) , as shown below. 

(a) Find a function that gives the area \( A ( x ) \) of the field (in square meters) in terms of \( x \) . 

(b) What side length \( x \) gives the maximum area that the field can have? 

(c) What is the maximum area that the field can have? 

Q:

Izny is making homemade clay pendants in the shape of a solid hemisphere, as modeled below. Each pendant has a radius of \( 2.8 cm \) . 

How much clay, to the nearest cubic centimeter, does Izzy need to make \(100\) pendants? 

Q:

The Leaning Tower of Pisa in Italy is known for its slant, which occurred after its construction began. The angle of the slant is \( 86.03 ^ { \circ } \) from the ground. The low side of the tower reaches a height of \( 183.27 \) feet from the ground. 

Determine and state the slant height, \( x \) , of the low side of the tower, to the nearest hundredth of a foot. 

Q:

In the diagram below, parallelogram \( E F G H \) is mapped onto parallelogram \( I J K H \) after a reflection over line \( \ell \) . 

Use the properties of rigid motions to explain why parallelogram \( E F G H \) is congruent to parallelogram \( I J K H \) . 

 

Q:

 

Determine and state the coordinates of the center and the length of the radius of the circle whose equation is \( x ^ { 2 } + y ^ { 2 } + 6 x = 6 y + 63 \) . 

Q:

The side lengths of \( \triangle ABC \) are given by \( 2,4 \) , and \( 5 \) , respectively. What is the length of the shortest leg of a triangle \( \triangle DEF \) that is similar to \( \triangle ABC \) and whose longest leg measures \( 22 \) ? 

\( 6.6 \) 

\( 11.4 \) 

\( 8.8 \) 

\( 12.1 \) 

\( 14.5\) 

Q:

Find the distance between the points \( ( 10,1 ) \) and \( ( 1,10 ) \) . Round decimals to the nearest tenth. units 

Q:

What is the mass, rounded to the nearest gram, of the figure below given \( r = 6 cm \) and a density of 

\( p = 6 \frac { g } { cm ^ { 3 } } ? \) 

\( 3714 g \) 

\( 4524 g \) 

\( 3619 g\) 

Q:

Find the distance d(A,B) between points A and \( B \) . 

\( A ( 1 , - 6 ) ; B ( 1,2 ) \) 

Q:

Ivy is running errands for her mother. She bikes along straight paths to the supermarket, the bank, and then back home. 

- ivy starts from her house at point A. 

- First, she goes to the supermarket at point B.

 - Next, she goes to the bank at point C.

 - Last, she heads back to her house at point A. 

Find the distance between ivy's house and the supermarket and the distance between the supermarket and the bank. Each distance is rounded to the nearest meter. 

Q:

On a number line, point \( F \) is at \( 4 \) , and point \( G \) is at \( - 2 \) . Point \( H \) lies between point \( F \) and point \( G \) . If the ratio of \( F H \) to \( H G \) is \( 3 : 9 \) , where does point H lie on the number line? Point \( H \) is at 

Q:

Suppose there is a triangle with sides \( a , b , \) and \( c \) and angles \( A , B \) , and \( C \) . Using the known given information below and the law of cosines, what is the measure of side \( c \) ? Round your answer to the nearest whole number, if necessary. 

\( a = 29 cm \) 

\( b = 28 cm \) 

\( C = 52 ^ { \circ } \) 

Q:

What is the sum of the interior angles of a regular heptagon? 

A. \( 900 ^ { \circ } \) 

B. \( 1260 ^ { \circ } \) 

C. \( 1080 ^ { \circ } \) 

D. \( 360 ^ { \circ } \) 

Q:

Chili is made in a cylindrical stock pot with diameter \( 14.0 \) in. and height \( 15.0 \) in. If the pot is \( \frac { 3 } { 4 } \) full, how many \( 1 \frac { 1 } { 2 } \) cup bowls can be served? Round to the nearest whole bowl that can be completely filled. 

\( ( 1 \) cup \( = 14.4 in ^ { 3 } ) \) 

Q:

A sphere fits perfectly into the cylinder as shown, touching the top and bottom of the cylinder. If the height of the cylinder is \( 32 \) inches, what is the approximate volume of the sphere? 

\( 2,731 \pi cu \) in. 

\( 4,096 \pi cu \) in. 

\( 8,192 \pi cu \) in. 

\( 5,461 \pi cu \) in. 

Q:

Points \( R , S \) , and \( T \) have the coordinates \( R ( - 8 , - 4 ) , S ( 2 , - 16 ) \) , and 

\( T ( 0,2 ) \) . Together the points make a triangle. If the triangle was translated so that point \( R \) ended up at the coordinates \( ( - 20 , - 10 ) \) 

what would be the new coordinates of point \( S ? \) 

\( ( - 9 , - 16 ) \) 

\( ( - 4 , - 31 ) \) 

\( ( - 19 , - 21 ) \) 

\( ( - 10 , - 22 ) \) 

Q:

 A circle has the center-point \( R \) at coordinates \( ( 6 , - 5 ) \) 

with the diameter \( \overline { K L } \) where \( K \) has coordinates \( ( 4 , - 10 ) \) . Find the coordinates of \( L \) . 

 

Q:

How much leather will be needed to cover a ball with a diameter of \( 6 \) inches? 

\( 150.72 in ^ { 2 } \) 

\( 28.26 in ^ { 2 } \) 

\( 37.68 in ^ { 2 } \) 

\( 113.04 in ^ { 2 } \) 

Q:

In rectangle \( P Q R S , P Q = 18 , P S = 14 \) , and \( P R = 22.8 \) . Diagonals \( \overline { P R } \) and \( \overline { Q S i n t e r s e c t } \) at point \( T \) . What is the length of \( \overline { T Q } \) ? 

A. \( 7 \) 

B. \( 9 \)

C. \( 11.4 \) 

D. \( 22.8\) 

Q:

Use numerals instead of words. In parallelogram DEFG, DE \( = 6 \) inches and \( D F = 6.4 \) inches. Diagonals \( \overline { G E } \) and \( \overline { D F } \) intersect at point H. If \( G H = 4 \) inches, what is the length of \( \overline { G E } \) ? 

\( G E = \square \) inches 

Q:

4. If a cone of height \( 12 \) meters is to have a volume of \( 48 \pi \) 

cubic meters, what does the radius of the circular base need to be? 

\( r = \sqrt { \times } m\) 

Q:

Calculate the volume of the regular triangular pyramid with the base edges of length \( 16 \) inches and a height of length \( 16 \) inches. (Hint: Remember that the base of a regular triangular pyramid must be an equilateral triangle, not necessarily congruent to the sides of the pyramid.) Volume \( = \) 

Q:

9. If a sphere has a surface area of \( 18496 \pi \) inches, what is the volume of the sphere? 

\( V = \) 

Q:

What is the approximate surface area of a square pyramid with a height of \( 6 \) inches and side length of \( 10 \) inches? A \( 600 \) in \( ^ { 2 } \) 

\( 136 in ^ { 2 } \) 

\( 200 in ^ { 2 } \) 

\( 256 in ^ { 2 } \) 

Q:

\(x ^ { 2 } + y ^ { 2 } - 12 x + 6 y - 36 = 0 \) is the equation of a circle with center \( ( h , k ) \) and radius \( r \) for: 

\( h = \) 

\( k = \) 

Q:

Find the length of the median \(C F\) of the \(\triangle A B C\) whose vertices are \(A ( 18,7 ) , B ( 12,9 ) \) and 

\(C ( 18,11 ) .\) 

a. \(5.24\) units b. \(7.24\) units c. \(4.24\) units d. \(6.24\) units 

Q:

Match the concept to its definition. 

Perpendicular bisectors 

Midsegment 

Altitude

 Angle bisectors 

Median 

 

Perpendicular segment, ray or line, through one triangle side to the opposite vertex 

Segment connecting midpoints of two segments in a triangle 

Perpendicular segment, ray, or line to on€ triangle side through the midpoint of that side 

Segment, ray, or line from midpoint of side to opposite vertex 

Segment, ray or line that bisects angle 

Q:

If \(m \angle M K L = 83 , m \angle J L = 127 ,\) and 

\(m \angle M M = ( 9 x - 10 ) ^ { \circ } \) . Find the value of \(x .\) 

Q:

Graph the image of \(\triangle W X Y\) after the following sequence of transformations: Rotation \(180 ^ { \circ } \) counterclockwise around the origin Reflection across the \(X\) -axis 

Q:

Cole found \(BC\) in \(\triangle A B C\) . His work is shown below. Identify the first step in which his work shows an error. Step 1: \(9 ^ { 2 } + 15 ^ { 2 } = c ^ { 2 } \) 

Step 2: \(81 + 225 = c ^ { 2 } \) 

Step 3: \(306 = c ^ { 2 } \) 

Step 4: \(\sqrt { 306 } = c\) 

Step 5: \(c \approx 17 ,\) so BCis about \(17\) in. 

Q:

This object is made from \(7\) centimetre cubes. Determine its surface area. 

Q:

Find the area of the triangle given \(a = 13 , c = 21\) , and \(B = 87\) degrees. Round your answer to the nearest tenth, and enter the number only. Note: The figure shown is not drawn to scale. 

Q:

A parallelogram has the dimensions shown below. What is the area of the varalleloeram? 

Q:

Find the surface area and volume of a square based pyramid if the edge of the base is \(8\) inches and the slant height is \(20\) inches. Round your answer to the nearest WHOLE number. What is the Surface Area? What is the Volume to the nearest whole number? 

Q:

Using the origin as the center of dilation and a scale factor of \(2\) , what are the new coordinates of point \(B\) ? 

Q:

In the Similarity in Right Triangles Gizmo, you can explore a right triangle and the triangles created by the altitude to its hypotenuse. 

Q:

Find the center of the ellipse. 

\(25 x ^ { 2 } + y ^ { 2 } - 100 x - 2 y + 76 = 0\) 

\(( [ ? ] , [ ] ] \) 

 

Q:

WebMD.com reports that the average amount of bacteria on a bathroom countertop is \( 452 \) bacteria per square inch. How many bacteria would you expect to find on a rectangular bathroom countertop that measures \( 1.5 \) feet by \( 2 \) feet? Round your answer to the highest place value. 

Q:

Under a certain transformation, \( \triangle A B C \rightarrow \triangle A ^ { \prime } B ^ { \prime } C ^ { \prime } \) . The perimeter of \( \triangle A ^ { \prime } B ^ { \prime } C ^ { \prime } \) is twice the perimeter of \( \triangle A B C \) . 

A. translation B. reduction C. enlargement D. rotation 

Q:

Find the diameter of a circle that has an area of \( 4.5 yd ^ { 2 } \) . 

\( 2.39 yd \) 

\( 2.25 yd \) 

\( 1.43 yd \) 

\( 1.20 yd\) 

Q:

A customer at a specialty coffee shop observed the amount of time, in minutes, that each of \( 20 \) customers spent waiting to receive an order. The results are recorded in the table below. 

Find the mean and sample standard deviation of these data. Round to the nearest hundredth. 

Q:

A company is going to make a water tank in the shape of a cylinder. As shown below, the tank will have a height of \( 4 ft \) and a diameter of \( 10 ft \) . The tank will be made from metal (including its top and bottom). If the metal costs \( \$ 23 \) for each square foot, how much will the metal cost in total? Use \( 3.14 \) for \( \pi \) , and do not round your answer. 

Q:

A regular octagon has an apothem of approximately \( 7.0 cm \) and a perimeter of approximately \( 46.4 cm . \) Find the area of the octagon. 

Q:

A company makes concrete bricks shaped like rectangular prisms. Each brick is \( 10 \) inches long, \( 6 \) inches wide, and \( 4 \) inches tall. If they used \( 13,200 \) in \( { } ^ { 3 } \) of concrete, how many bricks did they make? 

Q:

A company makes wax candles in the shape of a cylinder. Each candle has a radius of \( 2 \) inches and a height of \( 6 \) inches. If the company used \( 3165.12 \) in \( { } ^ { 3 } \) of wax, how many candles did it make? 

Use \( 3.14 \) for \( \pi \) , and do not round your answer. 

Q:

Determine the surface area of the figure

 

Q:

An animal sanctuary houses a variety of animals. To understand the workload of the sanctuary's veterinarians, the director looked at which types of animals are treated or not treated by various doctors. The Venn diagram shows this information for three of the doctors. 

(a) Select all the doctors who treat elks. 

\( \square \) Dr. Turner \( \square \) Dr. Rogers \( \square \) Dr. Long 

(b) How many types of animals are treated only by Dr. Rogers? 

\( \square \) 

(c) Which types of animals are treated by all three doctors (Dr. Turner, Dr. Rogers, and Dr. Long)? Choose all that apply. 

Q:

Suppose a water tank in the shower or a tight circular cylinder is right feet long and thirty feet in diameter. How much water does the tank hold? Round to the nearest cubic foot

 

Q:

A swimming pool has to be drained for out of the pool at a rate of \( 15 m ^ { 3 } \) per Use the value \( 3.14 \) for \( \pi \) , and round you hour(s) 

Q:

A real number between \( 1 \) and \( 11 \) will be picked according to the probability distribution shown in the figure. Regions under the curve are labeled with \( A , B , \) and \( C \) . The area of each region is shown in the table. 

Use the figure and the table to answer the parts below. 

(a) Find the probability that a real number between \( 1 \) and \( 5 \) is picked.

 (b) Find the probability that a real number between \( 1 \) and \( 8 \) is picked. 

Q:

If Lisa were to paint her living room alone, it would take \( 2 \) hours. Her sister Naomi could do the job in \( 5 \) hours. How long would it take them to work together? If needed, submit your answer as a fraction reduced to the lowest terms.