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3 years ago

8

The P.E. teacher at Sunshine Middle School wants to know which sports are popular among students in her school. Since it would t

ake so long to ask all of the students, she will survey a group of students. The school has 288 6th graders, 256 7th graders, and 280 8th graders. The P.E. teacher surveys 36 6th graders and 32 7th graders. How many 8th graders should she survey in order for the group to be a representative sample?

1 answer:

sineoko [7]3 years ago

5 0

28 BECAUSE IT CONTINUES THE PATTERN OF SUBTRACTING 4 FROMTHE AMOUNT PULLED PER GRADE

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Applying the Procedure

Verizon [17]

Answer:

15 Square Inches

Step-by-step explanation:

Volume of the cone=40 cubic inches

Height of the cone=8 Inches

<u>Step 1:</u> Applying the formula for the volume of a cone

Volume of a Cone $=\frac{1}{3}\pi r^2 h=\frac{1}{3} X $Base Area X Height$

<u>Step 2:</u> Substituting values for the variables

$40=\frac{1}{3} X $Base Area X 8$

<u>Step 3:</u> Simplifying the right side

$40=\frac{8}{3} X $Base Area$

<u>Step 4:</u> Multiplying by the reciprocal

$40X\frac{3}{8}=\frac{8}{3} X\frac{3}{8} X $Base Area\\$

<u>Therefore, Base Area of the Cone=15 Square Inches</u>

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8 0

2 years ago

14,494 ten thousand round to

SVETLANKA909090 [29]

"14,494 rounded to the nearest ten-thousands" would be 10,000.

Because the value of the digit before the ten thousands place (4) is less than the value of 5, the digit in the ten-thousands position does not change.

3 0

3 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

How do you solve this please help

coldgirl [10]

Answer:

thanks

Step-by-step explanation:

I have been patient trying to get a job

6 0

2 years ago

Subtract: 8 3/8 - 3 1/4<br><br> Answers: <br> A: 5 1/8<br> B: 5 5/8<br> C: 5 1/4<br> D: 5 1/2

Flura [38]

I believe the answer is D

6 0

2 years ago