Mr. Walker asked his students to use the associative property to find an expression that is equivalent to (13 + 15 + 20) + (20 + 47 + 18). The expressions that four students created are shown in the table below.

Expressions Generated by Students
Student
Expression
Jeremy
(20 + 13 + 15) + (20 + 47 + 18)
Layla
(20 + 47 + 18) + (13 + 15 + 20)
Keith
(13 + 20) + (20 + 47 + 18) + 15
Melinda
(13 + 15 + 20 + 20) + (47 + 18)

How many of the students correctly applied only the associative property to rewrite the expression?
one
two
three
four
Mark this and return

Answer:

Surface of[tex]35,875.86 cm^2[/tex]

Voliume of [tex]234,671.58 cm^3[/tex]

Long and painful calculations

Ok, this is going to take some time. The volume is the sum of all the solids, minus the half cylinder that makes the "tunnel" beneath it. That said, we can split the item into 3 main shapes, and the cylinder: The pyramid in the top left, the square based prism below the pyramid, and the trapezoid prism to the right. I edited a bit the image with paint to add measurements. It's paint so quality is what it is and deal with comic sans as a font.

Let's find the total surface first. We have the surface of the four faces of the pyramid, which are triangles of base 54 and height (red line)[tex]\sqrt{36^2+(\frac{54}2)^2} =\sqrt{2025}=45cm[/tex], givins us a total area of [tex]4\times \frac{bh}2 = 2\times 45\times 54 = 4860 cm^2[/tex]

We add the two lateral faces of the left prism: they are two rectangles of side length 70 and 54, for a total area of [tex]2(70)(54) = 7580 cm^2[/tex]

Take the rectangle to the side of the prism, of sides 54 and 70-34 = 36, giving an area of [tex]54\times 36 = 1944 cm^2[/tex]

Pick the inclined "roof" of the right prism, again a rectangles, sides 54 and 61: surface is [tex]3294 cm^2[/tex]

Two side faces of the right building: first pick the height (magenta line), with pythagorean theorem again, equal to [tex]\sqrt{ 61^2-11^2} = \sqrt{3600} = 60 cm[/tex]. The surface becomes [tex]2 \frac{(B+b)h}2 = (34+45)(60)= 4740 cm^2[/tex]

Missing the short sides and the half cylinder making the gallery. The sides - if you imagine un-hinging one and attaching to the bottom of the other - will make a rectangle of sides (45+70) cm and 54 cm with a circular hole in the middle. surface is [tex](45+70)\times54 - \pi(54/2)^2 =[/tex][tex]3920.94 cm^2[/tex].

Finally, the half cylinder. It's a "rectangle) tall (60+54) cm - the length of the whole contraption, and long half the circle, or [tex]27\pi[/tex]. It's surface is  [tex](60+54)\times\27\pi = 9664.92 cm^2[/tex]

Done with surfaces. At this point we just add everything together. Grab a calculator and start adding up, if I didn't miss anything the total surface will be [tex]35875.86 cm^2[/tex]

Volumes now. You wished this was over? I totally did.

Bulk of the calculations are done luckly. It's just to cut and paste here and there.

Pyramid first. We know the side length, we know the height, volume is the usual formula

[tex]\frac 13l^2h = \frac 13 54^2\times 36= 33,048 cm^3[/tex]

Cube beneath. This one is also easy Sides are 54cm, 54cm and 70cm, volume is their product:

[tex]54*54*70= 204,120 cm^3[/tex]

Side prism now: again base surface times height, let's use the trapezoid as a base since we already have the area from above:

[tex]A_th = 2370\times54 = 127,980 cm^3[/tex]

From this we take half a cylinder of radius 27 tall as the whole structure is long. [tex]\frac12 \pi r^2h = \frac12 \pi (27)^2(60+54) = 130,476.42 cm^3[/tex]

We're done. Let's add the volume of the first 3 solids and subtract the last one - hope you have your calculator handy, to get in total a volume of [tex]234,671.58 cm^3[/tex]

Double and triple check numbers, even if I rand them with excel.

Step-by-step explanation:

x - 1 + 5x = 23

6x - 1 = 23

6x = 23 + 1 = 24

6x = 24

x = 24/6

x = 4 ans.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE.

Answer:

The answer is actually 31.6 m (3 s.f.). The correct process will be use the sine rule to find out BC and CD. Then find out the length of AC by adding AB (which is 5.8 m) and BC (16.9 m after working out). Then work out the angle of CAD, which will be 46 degrees. Then use the cosine rule on triangle ACD to dine out AD.

Step-by-step explanation:

pls subs to my yt

Answer:

Step-by-step explanation:

Convert the exponential equation to a logarithmic equation using the logarithm base  

( 5 )  of the left side  ( 25 )  equals the exponent  ( 2 ) .   log 5 ( 25 ) = 2

Use the definition of a logarithm,  

log b ( x ) = y  ⟹  b y = x , to convert from the logarithmic form to the exponential form.

32  4/ 5 = 16

Answer: 35.113

Hope this helps!

Answer:

on what...like brush how do we help u if u don't have a question

Step-by-step explanation:

Given points,

( -2 , 3) and (4,3)

we know,

slope = y_2 - y_1 / x_2 - x_1

so according to it we got,

→ (3 - 3)/4 - (-2)

→ 0/6

hope this answer helps you dear! take care.

Hello!

To find the slope when we have 2 points, we use the following formula:

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

m=[tex]\frac{3-3}{4-(-2)} \\\frac{0}{6} \\0[/tex]

Here's something for you to remember:

Hope it helps!

~Just a determined gal

#CarryOnLearning

[tex]MysteriousNature[/tex]

190=110+70+95−(30+25+40)+x190=110+70+95−(30+25+40)+x

Simplifying, we get that x=10x=10.

its 10

Answer:

4 8/10

Step-by-step explanation:

4x1+4x1/10+4x1/10=4+4/10+4/10=4 8/10

Adding 4 ones, 4 tenths and 4 tenths gives 4.8

To add 4 ones, 4 tenths and 4 tenths, we can combine the whole numbers and the decimal parts separately.

4 ones = 4 x 1

4 tenths = 4 x 1/10

So, 4 ones + 4 tenths + 4 tenths

= 4 x 1 + 4 x 1/10 + 4 x 1/10

= 4 + 0.4 + 0.4

= 4+ 0.8

= 4.8

Therefore, when you add 4 ones, 4 tenths and 4 tenths, the result is 4.4.

Learn more about Place value here:

https://brainly.com/question/27734142

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Answer:

-7.2, -6.3, [5], [-6.3], 8

Answer:

A=2, B=28

Step-by-step explanation:

A:6:7

8:24:B

A=8÷4

 =2

B=7×4

 =28

Answer:A=2

B=28

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

move 4 to right, then its in vertext form where where -h = 1 and k = 4. the vertext is (h,k), so just swap thr sign in h andnout it into the coordinate and get (-1,4)

Answer:

114 degrees

Step-by-step explanation:

6x+12=3x+63

-3x -12 -3x  -12

3x=51

x=17

6(17) +12 = 114

Answer:

yes its B................

The decimal approximation for cot(235°36') is approximately -0.9503.

To find the decimal approximation for cot(235°36'), we first need to convert the angle to degrees.

The given angle is 235°36'. We can convert this to decimal degrees by adding the fraction of minutes to the degree value. There are 60 minutes in a degree, so we divide 36 by 60 to convert it to a fraction of a degree:

36 / 60 = 0.6 degrees

Now, we can add this fraction to the degree value:

235 + 0.6 = 235.6 degrees

The cotangent function is the reciprocal of the tangent function. To find the cotangent of an angle, we can use the following formula:

cot(x) = 1 / tan(x)

Since we want to find cot(235.6°), we can find tan(235.6°) first and then take the reciprocal.

Using a scientific calculator or software, we can find

tan(235.6°) ≈ -1.0529

Now, we can take the reciprocal to find cot(235.6°):

cot(235.6°) ≈ 1 / (-1.0529) ≈ -0.9503

Therefore, the decimal approximation for cot(235°36') is approximately -0.9503.

for such more question on fraction

https://brainly.com/question/28372533

#SPJ8

Step-by-step explanation:

V = Volume of cube

a = edge of cube

Formula of volume of cube:

V = a³

[tex]V = { (\frac{1}{4}) }^{3} \\ V = \frac{1}{64} [/tex]

Volume of the cube = [tex] \frac{1}{64} [/tex]

Answer:

30m + 75

$255

Step-by-step explanation:

Since John  has to pay a monthly fee of 0, you can let m represent the number of months and then add the one time membership fee of $75.

30 multiplied by 6 is 180 and 180 plus 75 is 255.

Answer:

3

Step-by-step explanation:

Answer:

Answer 2

Step-by-step explanation:

Answer:

- 5 ≤ x < 3

Step-by-step explanation:

The lower limit has a solid circle at - 5

This means that x can equal - 5

The upper limit has an open circle at 3

This means that x cannot be equal to 3

The inequality represented by the diagram is then

- 5 ≤ x < 3

Answer:

Type of variation

1) Direct variation

Simple equation y=Kx

Y varies directly with x

Practical example-

Radius of the circle lit by a car's

Light decreases (y) as the distance away from the garage decreases (c)

2) Inverse variation

Simple equation y=k/x

Y inversely with c

Example- the brightness of a car's light increase (y) as the distance away from the garage decreases (x)

3) Joint variation

Simple equation y=kxz

Y varies jointly with x and z

Example-The heat lose through a glass window (y) varies jointly with the area of the window (x) and the temperature differences between inside and outside

Step-by-step explanation:

Answer:

hope this helps :)

Answer:

m=98

Step-by-step explanation:

-6/7m=-84 - Divide both sides by -6/7

-84/(-6/7)=84*7/6=98

Answer:

m = 98

Step-by-step explanation:

First multiply the fraction's denominator, which is 7, on both sides to get -6m = -588. Then divide both sides by -6 to get m = 98.

Hope this helps you :)

Answer:

The bottom right

*you won't see it yourself that the answer is correct because you are working on and iReady test friend*

Step-by-step explanation:

If you map out the shape in your head and slowly fold up the flaps, then you get a rectanglular prism.

Answer:84

Step-by-step explanation:

hope this helps :))

for every 13 dogs, there are 25 cats. is the answer.

Answer:

Below in bold.

Step-by-step explanation:

Using the quadratic formula :

roots =  [-16 +/-√(16^2 - 4*16*5)] / (2*16)

= -0.5 +/- √(-64) /32

= -0.5 +/- 8i/32

= -0.5 + 0.25i and -0.5 - 0.25i

[tex]\sf\longmapsto 16x^2+16x+5=0[/tex]

[tex]\sf\longmapsto x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\sf\longmapsto x=\dfrac{-16\pm\sqrt{16^2-4(16)(5)}}{2(16)}[/tex]

[tex]\sf\longmapsto x=\dfrac{-16\pm√256-320}{32}[/tex]

[tex]\sf\longmapsto x=\dfrac{-16\pm√-64}{32}[/tex]

[tex]\sf\longmapsto x=\dfrac{-16\pm8i}{32}[/tex]

[tex]\sf\longmapsto x=\dfrac{-2\pm i}{4}[/tex]

[tex]\sf\longmapsto x=\dfrac{-1}{2}\pm\dfrac{1}{4}i [/tex]