Fill in the blanks for each box

A total of 200 video game players take a survey on their favorite game. Unknown Kingdom

zepelin [54]

Answer:

Could you explain it another way?

Step-by-step explanation:

4 0

2 years ago

Your parents decide to build a rectangular pool in your backyard. They determine that the length of the pool should be 15 feet l

damaskus [11]

Width = X

Length = X + 15

Perimeter of a Rectangle = 2W + 2L

2(X) + 2(X + 15)

2X + 2X + 30

4X + 30

Answer = 4X + 30

Hope this helps! :)

4 0

2 years ago

A punch glass is in the shape of a hemisphere with a radius of 5 cm. If the punch is being poured into the glass so that the cha

Galina-37 [17]

Answer:

28.27 cm/s

Step-by-step explanation:

Though Process:

The punch glass (call it bowl to have a shape in mind) is in the shape of a hemisphere
the radius $r=5cm$
Punch is being poured into the bowl
The height at which the punch is increasing in the bowl is $\frac{dh}{dt} = 1.5$
the exposed area is a circle, (since the bowl is a hemisphere)
the radius of this circle can be written as $'a'$

what is being asked is the rate of change of the exposed area when the height $h = 2 cm$
the rate of change of exposed area can be written as $\frac{dA}{dt}$ .
since the exposed area is changing with respect to the height of punch. We can use the chain rule: $\frac{dA}{dt} = \frac{dA}{dh} . \frac{dh}{dt}$

and since $A = \pi a^2$ the chain rule above can simplified to $\frac{da}{dt} = \frac{da}{dh} . \frac{dh}{dt}$ -- we can call this Eq(1)

Solution:

the area of the exposed circle is

$A =\pi a^2$

the rate of change of this area can be, (using chain rule)

$\frac{dA}{dt} = 2 \pi a \frac{da}{dt}$ we can call this Eq(2)

what we are really concerned about is how $a$ changes as the punch is being poured into the bowl i.e $\frac{da}{dh}$

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

$r = \frac{a^2 + h^2}{2h}$

and rearrage the formula so that a is the subject:

$a^2 = 2rh - h^2$

now we can derivate a with respect to h to get $\frac{da}{dh}$

$2a \frac{da}{dh} = 2r - 2h$

simplify

$\frac{da}{dh} = \frac{r-h}{a}$

we can put this in Eq(1) in place of $\frac{da}{dh}$

$\frac{da}{dt} = \frac{r-h}{a} . \frac{dh}{dt}$

and since we know $\frac{dh}{dt} = 1.5$

$\frac{da}{dt} = \frac{(r-h)(1.5)}{a}$

and now we use substitute this $\frac{da}{dt}$ . in Eq(2)

$\frac{dA}{dt} = 2 \pi a \frac{(r-h)(1.5)}{a}$

simplify,

$\frac{dA}{dt} = 3 \pi (r-h)$

This is the rate of change of area, this is being asked in the quesiton!

Finally, we can put our known values:

$r = 5cm$

$h = 2cm$ from the question

$\frac{dA}{dt} = 3 \pi (5-2)$

$\frac{dA}{dt} = 9 \pi cm/s// or//\frac{dA}{dt} = 28.27 cm/s$

5 0

2 years ago

will give brainliest!!!!! will give brainliest!!!!! will give brainliest!!!!! will give brainliest!!!!! will give brainliest!!!!

Marrrta [24]

Answer:

849.24 cm²

Step-by-step explanation:

we know it is a cube so to find the surface area of each square you do

12x12=144 and there are 5 sides so 144x5=720

We know sides of the squares are 12 cm so half of that (6) would be the bottom of the triangle

Now using pythagorus you would do a²+b²=c²

15²+6²=c²

225+36=c²

√261=√c²

16.15=c this only half of one of the sides of the pyramid so you would times 16.15 by 8 to equal 129.24

now add 720+129.24=849.24 cm²

6 0

2 years ago

Read 2 more answers

A plastic sack contains 20 green and yellow, 14 red and yellow, and 16 orange and yellow gummy treats. How much greater is the p

noname [10]

Answer:

Probability of choosing green and yellow treat is higher than Probability of choosing an orange and yellow treat by 0.08

Step-by-step explanation:

Given -

Green and yellow gummy treats = 20

Red and yellow gummy treats = 14

Orange and yellow gummy treats = 16

Total gummy treat = 20+14+16 = 50

Probability of choosing green and yellow treat = 20/50 = 0.4

Probability of choosing an orange and yellow treat = 16/50 = 0.32

Probability of choosing green and yellow treat is higher than Probability of choosing an orange and yellow treat by 0.08

4 0

2 years ago