Part A
Which of the following expressions could be used to find
the volume of the sheet cake? Select all that apply.

Sheet cake has length of 12 in., height of 3 in. and width of 5 in.
A. 60 × 3
B. 12 + 5 + 3
C. 3 × 5 × 12
D. 12 × 5
E. (3 × 5) × 12
Part B
The baker adds another 1-inch-thick layer to the bottom of the sheet cake. The height of the sheet cake is now 4 inches. What is the volume of the sheet cake?
A. 200 in.3
B. 240 in.3
C. 180 in.3
D. 220 in.3

Answer:

AB=8cm⇒AE=4cmCD=6m⇒CF=3cmIn△AEDAE=4cm,AO=5cmOE=(AO)2−(AE)2=52−42=3cmIn△OFCCF=3cm,CO=5cmOF=OC2−CF2=52−32=4cm

∴ Distance between the chords=4cm−3cm=1cm

Answer:

I) 1 cm

II) 7 cm

Step-by-step explanation:

We are given a circle with a radius of 5 cm. AB and CD are two parallel chords of length 8cm and 6cm respectively. And we want to calculate the length of the chords if they are:

I) On the same side of the center.

Please refer to the first figure.

In it, O is the center, AB measures 8 and CD measures 6.

To find the distance between the two chords, we essentially need to find KJ, which is OJ - OK.

We will construct a segment from O to K and from K to J. This is perpendicular to the chords. Therefore, by the Perpendicular Bisector Theorem, it also bisects the chords.

ΔAOK is a right triangle. Therefore:

[tex]AO^2=OK^2+KA^2[/tex]

AO is simply the radius.

KA is half the length of AB since OK perpendicularly bisects the chord.

Therefore:

[tex](5)^2=OK^2+(4)^2[/tex]

So:

[tex]25=OK^2+16\Rightarrow OK^2=9\Rightarrow OK=3[/tex]

Likewise, ΔCOJ is also a right triangle. Therefore:

[tex]CO^2=OJ^2+JC^2[/tex]

CO is the radius, and JC will be half the length of CD. Thus:

[tex](5)^2=OJ^2+(3)^2\Rightarrow OJ^2=16\Rightarrow OJ=4[/tex]

Therefore, the distance KJ between the two chords are:

[tex]KJ= OJ-OK=4-3=1\text{ cm}[/tex]

II) On opposite sides of the center.

Please refer to the second figure.

Again, O is the center, AB measures 8, and CD measures 6.

Likewise, segments OK and OJ are perpendicular bisectors of AB and CD, respectively.

And to find the distance, we essentially need to find JK or OJ + OK.

ΔKOB is a right triangle. Thus:

[tex]OB^2=OK^2+KB^2[/tex]

OB is the radius, and KB is half of AB:

[tex](5)^2=OK^2+(4)^2\Rightarrow OK=3[/tex]

ΔJOD is also a right triangle. Thus:

[tex]OD^2=OJ^2+JD^2[/tex]

OD is the radius and JD is half of CD:

[tex](5)^2=OJ^2+(3)^2\Rightarrow OJ=4[/tex]

Therefore, the distance between the two chords are:

[tex]JK=OJ+OK=4+3=7\text{ cm}[/tex]

Answer:

5

Step-by-step explanation:

thanks for the points

Answer:

positive slope is shown by the graph

Answer:

360° 2π rad 6.283185 rad

Answer:

i got 15.1

Step-by-step explanation:

Answer:

v = 87

Step-by-step explanation:

the angle v+39 lies on a straight line. so substract v+39 from 180 to get the interior angle for that side.

afterwards, knowing that the sum of interior angles of a triangle = 180, form an equation with all the angles and solve for v

Answer:

Let E denote the event of choosing a jury with 10 men and 2 women.

The sample space for selecting 12 members from the pool contains 55C12 elements.

The number of ways of selecting 10 men and 2 women is 26C10  29C2.

The probability of event E =  

The probability of selecting a jury with 10 men and 2 women is 0.005 (0.5%).

Step-by-step explanation:

see the image :

Answer:

The probability of selecting a jury with 10 men and 2 women out of out of 29 men and 26 women  is 0.005 (0.5%)

Step-by-step explanation:

Let P(E) denote the probability of choosing a jury with 10 men and 2 women out of 29 men and 26 women.

The sample space for selecting 12 members from the total no of member will be 55c12

The number of ways of selecting 10 men and 2 women is 26c10  29c2.

The probability of event E =  [tex]$=P(E)=\frac{{ }_{20} C_{10} \times{ }_{20} C_{2}}{-C_{12}}$[/tex]

                                                [tex]$=\frac{5,311,735 \times 406}{438,729,741,450}$[/tex] [tex]$=0.005$.[/tex]

The probability of selecting a jury with 10 men and 2 women is 0.005 (0.5%).

Click here to know more about the probability .

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Answer:

number c

Step-by-step explanation:

.............. just for filling 20 characters

the cosine of angle B

C. 0.767

the cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse: Also, cos A = sin B = b/c.

The cosine formula to find the side of the triangle is given by: c = √[a2 + b2 – 2ab cos C] Where a,b and c are the sides of the triangle.

Pythagoras Theorem is a generalization of the Law of Cosine.

The law of cosine can be applied in any triangle.

Learn more about the cosine of a triangle here

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Answer:

5.6

Step-by-step explanation:

Given :

Quality rating for 8 movies :

5.6, 7.9, 7.0, 5.9, 7.8, 6.2, 6.4, 5.2

Let rating for the 9th movie = x

Average quality rating olfor the 9 movies = 6.4

To find x :

Sum of all ratings / number of ratings = 6.4

(5.6 + 7.9 + 7.0 + 5.9 + 7.8 + 6.2 + 6.4 + 5.2 + x) / 9 = 6.4

(52 + x) / 9 = 6.4

52 + x = 57.6

x = 57.6 - 52

x = 5.6

Answer:

Solution given:

radius [r]=40ft

length of arc=70/360×2πr=70/360×2×π×40

=48.86=49ft is your answer

Answer:

49ft is the answer. hope it helps

Answer:

80 Degrees

Step-by-step explanation:

just flip and overlap the figure (in your mind)

Answer:

The home is worth $424,528 today

Step-by-step explanation:

To get the worth of the home today, we are going to use the exponential formula

We have this as follows;

A = P(1 + r)^t

where A is the value of the house after some time t

P is the initial value the home was worth which is $160,000

r is the rate of increase in the price of the home which is 5% = 5/100 = 0.05

t is the number of years which is 20

substituting these values;

A = 160,000(1 + 0.05)^20

A = $424,528

Answer:

Your answer will be A. positive correlation

Step-by-step explanation:

hope this helps :)

Answer:

x= - 3

Step-by-step explanation:

2x - 3= 4x + 3

2x = - 6

x = - 3

Answer:

y= -3x + 10

Step-by-step explanation:

we can answer this question thanks to this formula:

y-y1 = m(x-x1) where y1 and x1 indicate the coordinates of the given point and m indicates the slope

y-4 = -3(x-2)

y = -3x+6+4

y= -3x + 10

Answer:

Honestly it looks like a rectangular prism.

Step-by-step explanation:

Picture that you're folding it. the dark lines are the crevaces that you fold on.

Answer:

There was a %5 increase

Step-by-step explanation:

You just have to substract 65-60 and you get 5

Answer:

for the first photo the answer is 5x + 6(-x + 4) = 13

Step-by-step explanation:

if y equals to -x +4

then replace the y in this equation: 5x + 6y = 13  with this ( -x +4 ) its simple.

I cannot answer the other 2 photos at the moment but ill see if I can whenever else I have time.

Answer:

16

Step-by-step explanation:

By intersecting secants theorem:

[tex]9(2x - 17 + 9) = 8(8 + 10) \\ \\ 9(2x - 8) = 8 \times 18 \\ \\ 2x - 8 = \frac{144}{9} \\ \\ 2x - 8 = 16 \\ \\ 2x = 16 + 8 \\ \\ 2x = 24 \\ \\ x = \frac{24}{2} \\ \\ x = 12[/tex]

CE = 9 + (2x - 17)

CE = 9 + (2*12 - 17)

CE = 9 + (24 - 17)

CE = 33 - 17

CE =16

Answer:

20700

Step-by-step explanation:

3 times 3 times 2300 = 20700

Answer:

V = 432 m³

Step-by-step explanation:

The volume (V) of a prism is calculated as

V = Ah ( A is the area of the base and h the height )

A = [tex]\frac{1}{2}[/tex] bh ( area of triangular base, with b the base, h the perpendicular height)

Here b = 16 and h = 6 , then

A = [tex]\frac{1}{2}[/tex] × 16 × 6 = 8 × 6 = 48 m²

Then

V = 48 × 9 = 432 m³

Answer:

1.5x + 2

Step-by-step explanation:

(3x + 4)/2 = 1.5x + 2

Answer:

KitKat

Step-by-step explanationKitKat

Answer:

ZWXY

Step-by-step explanation:

The other shape is the same but you want to name it the same way that they named the first one

Step-by-step explanation:

there are 7 decimal places from between 2 and 3 to the very end. so the answer is 7

Answer: 2.36x^10

Step-by-step explanation:

Answer:

Reduced fee for each additional round will be $5.

Step-by-step explanation:

Let the reduced fee for each additional round played = $x

Charges for one round = $13

If Tom played for 6 rounds, total charges for the 6 rounds = 13 + 6x

Since, Tom paid $43 for 6 rounds,

13 + 6x = 43

6x = 43 - 13

6x = 30

x = 5

Therefore, reduced fee for each round will be $5.