As a member of the student council at your school, you want to determine if the seventh-grade students prefer to
have an after-school soccer program or an after-school movie club. There are 110 seventh-grade students at your
school, and you decide to take a sample of 20 students.
Describe in detail how you can randomly select 20 seventh-grade students for your sample.

Answer:

i measures of the third angle is 18degrees

The speed when the power is 2000watts is 22.5m/s

If the power, P (watts), of a car engine is proportional to the square of its

speed, s(m/s), this is expressed as:

P = k/s

When s=25, P=1800 then;

1800 = k/25
k = 25 * 1800
k = 4500

In order to calculate the speed when the power is 2000;

s = k/p
s= 4500/2000
s = 22.5m/s

Hence the speed when the power is 2000watts is 22.5 m/s

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Answer: D

On April 26, 1986, the Number Four RBMK reactor at the nuclear power plant at Chernobyl, Ukraine, went out of control during a test at low-power, leading to an explosion and fire that demolished the reactor building and released large amounts of radiation into the atmosphere. When the core of a reactor overheated, what happened at Chernoby Though it overheated, no negative impacts occurred

Step-by-step explanation:

Answer:

x € R

Step-by-step explanation:

In mathematics, every expression

divided by itself is equal to one

For this expression For every value that will be replaced by x will be equal to one

5/9

you can use a common denominator of 36, and multiply the numerators of each fraction by whatever number the denominator had to be multiplied by to get to 36

14/36+15/36-9/36

then you add and subtract

20/36=

5/9

Answer: D)

Step-by-step explanation: using a matrix calculator for each equation, the last one was the only one that was possible which came out to be ( 0,4,0,-4)

The radius of the circular garden whose circumference is 122.46 feet is: 19.5 feet.

Circumference = 2πr, where r is the radius of the circle.

Given the following:

122.46 = 2(3.14)(r)

122.46/2(3.14) = r

r = 19.5 feet.

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Answer:

  (b)  Subtract the total deductions from the gross pay

Step-by-step explanation:

The term "net pay" is applied to the pay after deductions are subtracted. It is also called "take-home pay."

The pay computed based on earnings, commissions, credits, and bonuses, before any deductions, is called the "gross pay."

  net pay = gross pay - deductions

Net pay is calculated by subtracting total deductions from gross pay.

Answer: Sugar = 3 cartons, Flour = 5 cartons, Rice = 6 cartons

Step-by-step explanation:

Sugar = 10 packets/carton

Flour = 6 packets/carton

Rice = 5 packets/carton

10, 20 30... sugar

6, 12, 18, 24, 30... flour

5, 10, 15, 20, 25, 30... rice

30/10 = 3 cartons of sugar

30/6 = 5 cartons of flour

30/5 = 6 cartons of rice

For all the number of packets to be equal.

Answer:

20

Step-by-step explanation:

85% of 24 is 20

Answer:

See below

Step-by-step explanation:

Not sure what they are looking for here....unless there is more info

[tex]\sqrt[14]{y}[/tex]  =  [tex]y^{1/14}[/tex]     perhaps?

Answer:

Angle ACD = 54° ( Angle standing on same arc at the circumference are equal )

Based on the longitudes of Quito and Singapore, the shortest distance between the two areas is 19,702.5 km .

Because both cities are close to the equator, you use the longitudinal difference method to find the shortest distance.

First find the difference in longitudes:

= Singapore - Quito

= 104 - (-78.5) because Quito is west

= 104 + 78.5

= 182.5°

Then subtract this from 360°:
= 360 - 182.5

= 177.5°

Every 1° longitude along the Equator is 111 km so the shortest distance is:

= 177.5 x 111

= 19,702.5 km

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Answer:

Step-by-step explanation:

Answer:

12/13

Step-by-step explanation:

36/39

Divide by 3

12/13

Given 3x and 5x --------------- (i)

(3x+10)/(5x+10) = 5/7

21x + 70 = 25x + 50

4x = 20

x = 5

Answer:

15%

Step-by-step explanation:

Percent increase in the original price of jacket = 15%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Original price of jacket = $110

Increased price of jacket = $126.5

Increased amount = $126.5 - $110

                               = $16.5

Increased amount in percentage = ($16.5/$110) × 100

                                                       = 0.15 × 100

                                                       = 15%

Hence, 15% is increase in the original price of jacket.

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The two coterminal angles in radian measure (one positive and one negative) for each angle for figure 1 and 2 are,[(13π/4),(-π/4) and [(7π/4),(-17π/4) rad] respectively.

Angles having the same terminal side at standard position are called coterminal angles.

Although the magnitudes of coterminal angles varies, they all have the same sides and vertices.

Positive or negative coterminal angles are possible. The positive coterminal is obtained by adding 2 rad or 360° to the negative coterminal, while the negative coterminal is obtained by removing 2 rad or 360°.

For figure 1;

The positive coterminal angle is found as;

[tex]\rm \rightarrow \theta + 2 \pi \\\\ \rightarrow \frac{5 \pi}{4} + 2 \pi \\\\ \rightarrow\frac{13 \pi}{4} \ rad[/tex]

The negative coterminal angle is found as;

[tex]\rm \rightarrow \theta - 2 \pi \\\\ \rightarrow \frac{5 \pi}{4} - 2 \pi \\\\ \rightarrow\frac{-3 \pi}{4} \ rad[/tex]

For figure 2;

The positive coterminal angle is found as;

[tex]\rm \rightarrow \theta + 2 \pi \\\\ \rightarrow \frac{-9\pi}{4} + 2 \pi \\\\ \rightarrow\frac{7 \pi}{4} \ rad[/tex]

The negative coterminal angle is found as;

[tex]\rm \rightarrow \theta - 2 \pi \\\\ \rightarrow \frac{-9 \pi}{4} - 2 \pi \\\\ \rightarrow\frac{-17 \pi}{4} \ rad[/tex]

Hence,the two coterminal angles in radian measure (one positive and one negative) for each angle for figure 1 and 2 are,[(13π/4),(-π/4) and [(7π/4),(-17π/4)] respectively.

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The unfilled volume inside the cylinder is 640π cubic units

Volume of a cylinder = πr²h

= π × 8² × 15

= π × 64 × 15

= 960π cubic unit

Volume of a cone = 1/3πr²√l² × r²

= 1/3 × π × 8² √17² × 8²

= 1/3 × π × 64 √289 × 64

= 1/3 × π × 64 √353

= 320π cubic unit

Unfilled volume = 960π cubic unit - 320π cubic unit

= 640 cubic unit

The complete question:

A solid oblique cone with a slant length of 17 units is inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. What is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units

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Answer:

640pi

Step-by-step explanation:

Answer:

192 yd³

Step-by-step explanation:

The volume of a rectangular pyramid is given by the formula:

[tex]V=\frac{1}{3} lwh\text{ where } l \text{ is the base length, }w \text{ is the base width, and }h \text{ is the pyramid height}[/tex]

In this case: [tex]l = 9, w=8, h = 8[/tex]

[tex]\therefore V=\frac{1}{3}(9\text{ yd})(8\text{ yd})(8\text{ yd})=192\text{ yd}^3[/tex]

Answer:

Down below

Step-by-step explanation:

First one:  Sixth root of B.  Second one:  Fourth root of X to the Z power.  Third one:  Square root of nine to the third power.  Fourth one:  M root of M to the P power.  Fifth one:  Square root of J to the two plus x power.

Sorry if this is wrong.  I'm almost positive this is correct.  The only one I'm not sure about is the third one and maybe the last one.  Since there's no two there I'm not sure if it would still be called the square root.

Answer:

418

Step-by-step explanation:

Step-by-step explanation:

7km/hr and 13km/hr

Because in this case we divide the total time taken will be 10km/hr but according to the question we have to subtract 3km/hr and also have to add 3km/hr. There for there for there average speed of friends with wind was 7km/hr and friends without wind will be 13km/hr.

Answer:

10.8 km/h to the nearest tenth.

Step-by-step explanation:

Let x be the average with no wind.

Speed = distance / time

With the wind:

x + 3 = 15 / t           A        where t = time in hours for the first half of journey

Against the wind:

x - 3 = 15/(3 - t)       B

Subtract A - B:

6 = 15/t - 15(3 - t)

6t(3 - t) = 15(3 - t) - 15t

18t - 6t^2 = 45  - 30t

6t^2 - 48t + 45 = 0

2t^2 - 16t + 15 = 0

t = - 1.085

So average speed (from equation B)

x = 15/ (3 - 1.085) + 3

  = 10.8 km/h to the nearest tenth.

Answer:

3y = -2x + 1

Step-by-step explanation:

Equation of given line is 2y = 3x + 2

==> y = (2/2)x + 1

Slope = 3/2

Slope of perpendicular line is negative of reciprocal of given line ie slope = -2/3

So equation of perpendicular line is of the form

y = (-2/3)x + c where c is a constant

Given that this passes thru x= -1, y =1 we can substitute these values in the above to get

1  =  (-2/3)(-1) + c
This yields 1 = (2/3) + c or c = 1-2/3 = 1/3

So the equation of the perpendicular line is

y = (-2/3)x + 1/3

3y = -2x + 1

Answer:

  406.3 cm²

Step-by-step explanation:

The total surface area is the sum of the base area and the lateral area. The lateral area is the sum of the areas of the 6 congruent triangular faces.

__

Each triangular face has a base of 8 cm and a slant height of 10 cm. Its area is ...

  A = 1/2bh

  A = 1/2(8 cm)(10 cm) = 40 cm²

Then the area of 6 faces is 6×40 cm² = 240 cm².

The base area is given.

The total area is the sum of the lateral area and the base area:

  total area = 240 cm² +166.3 cm² = 406.3 cm²

The surface area is about 406.3 cm².

Answer:

a:

1. ABC = 60°

2. BCA = 90°

3. CAB = 30°

b:

XVR = WVS = 125°

RVS = 55°

RST = VSU = 110°

RSV = UST= 70°

TUS = 39°

Step-by-step explanation:

a:

According this is a Right Triangle ( BCA = 90°) and the sum angles of a triangle is 180° :

90+5x+9x+6=180

14x=84

x=6

Then we have : ABC = 9(6)+6 =60

CBA = 5(6)=30

b :

Given that the size of the opposite angles to a vertex are equal and the sum of the interior angles of a triangle is 180 degrees, the size of all angles can be easily found.

The data recorded by Ben shows the attendance log of his classmates over a given period of time.

This refers to a simple chart that resembles a histogram that is used to represent small data.

Hence, we can see that because Ben tracked the attendance of the class over a given time period with the frequency on a frequency table, a sample of a dot plot has been provided below,

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Answer:

b = 4.4 feet

Step-by-step explanation:

To find the value of "b", all you need to do is plug the values for "a" and "c" into the pythagorean Theorem and isolate "b".

a² + b² = c²            <------ Phythagorean Theorem

9² + b² = 10²         <------- Plug in a = 9 and c = 10

81 + b² = 100        <-------- Square both values

b² = 19                  <-------- Subtract 81 from both sides

[tex]\sqrt{b^{2} } = \sqrt{19}[/tex]            <-------- Square root both sides to remove exponent

b = 4.358...

b = 4.4 feet

Answer:

C

Step-by-step explanation:

Anything less than 5 rounds down while 5 and anything more rounds up. Therefore...

15.3 rounds to 15

7.9 rounds to 8

7.4 rounds to 7

So, his answer is reasonable.