A hollow crystal ball is made of glass that is 3 centimeters thick. The ball has a radius to the outside surface of 8 centimeters. What is the approximate volume of glass used to make the ball? Use 3.14 for pi.

The volume of the recycling bin will be 429 m³.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The bin is 12 meters long, 5 1/2 meters wide, and 6 1/2 meters tall.

Now,

Since, We know that;

The volume of right rectangular = Length x Width x Height

Hence, The volume of right rectangular prism = 12 x 5 1/2 x 6 1/2

                                                                       = 12 x 11/2 x 13/2

                                                                       = 3 x 11 x 13

                                                                       = 429 m³

Thus, The volume of the recycling bin will be 429 m³.

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The range of boys and girls is 12 hours.

The median for boys is 12.5 hours

The median for girls is 6.5 hours.

The range is the difference between the highest value and the lowest value of a given set of data.

We have,

From the line plot,

Boys:

Hours      Number of boys      

1

2

3

4

5

6

7

8        x

9

10        x x x

11

12     x
13     x

14     x

15      xx

16

17

18

19

20     x

Girls:

Hours      Number of girls

1

2
3   x

4    xxx

5

6    x

7    x

8    x

9

10  xx

11

12

13

14

15   x

Now,

Range:

Boys:

= Longest time - Shortest time

= 20 - 8

= 12 hours

Girls:

= 15 - 3

= 12 hours

Median:

Boys:

= 8, 10, 10, 10, 12, 13, 14, 15, 15, 20

= 12.5

Girls:

= 3, 4, 4, 4, 6, 7, 8, 10, 10, 15

= 6.5

Thus,

The range is the same for both boys and girls.

The median for boys is 12.5.

The median for girls is 6.5.

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The complete question:

Find the range and median for both boys and girls.

The student's question pertains to the mathematical analysis of motion, specifically through the interpretation of velocity versus time and position versus time graphs related to cycling activities and races.

The question involves interpreting graphs that represent the velocity versus time and position versus time of two individuals riding bicycles and a race between friends. Students in middle school are often introduced to concepts of speed, velocity, and displacement and are tasked with analyzing graphs to understand these concepts in a practical scenario. The problem sets mentioned, including the velocity-time graphs, position-time graphs, and measurements of motion through various activities such as biking or collision events, are all connected to the mathematical analysis of motion in physics. By understanding how to read these graphs, students can determine factors such as constant velocity, average speeds, displacement, and the outcomes of simple collisions. These skills are essential in developing an understanding of kinematics, which is a branch of classical mechanics that describes the motion of points, objects, and systems of bodies without considering the causes of motion.

The smallest number is 90.63

We have three different two digit numbers total is 286.

We have to determine the smallest of the three numbers.

The two digit numbers can be in only in range of 1 to 99.

While a three digit number can be in range from 100 to 1000.

Hence, the two-digit number is smallest.

According to the question -

Let's assume that the three numbers are -   x, y and z.

Now -

x + y + z = 286

If we assume three equal two digit numbers will together make 286, than each two digit number will be = [tex]\frac{286}{3}[/tex] = 95.33.

In this case -   x = 95.33     y = 95.33       z = 95.33

Now, subtract 95.33 from 100 = 100 - 95.33 = 4.7

Assume, that we take 4.7 out from x, then x will be equal to -

x = 95.33 - 4.70 = 90.63

And divide 4.7 equally to both y and z -

y = z = 97.6

However, you can divide the 4.7 in any ratio among the numbers y and z for getting different numbers. Since we are focused on finding the smallest number of three we will not do it here.

Hence, the smallest number is x = 90.63

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The actual distance between the two towns, considering that they are 7cm apart on a map with a scale of 1:500000, is 35 kilometers.

In the given scenario, you're being asked to find the actual distance between two towns based on their distance on a map, using the map's scale, which is 1:500000. This means 1 cm on the map is equivalent to 500000 cm on the ground.

Since the towns are 7 cm apart on the map, the actual distance on the ground will be 7 (distance on the map) multiplied by 500000 (scale of the map), i.e., 3500000 cm. Since there is 100000 cm in 1 km, you convert the distance to kilometers by dividing by 100000. Hence, the actual distance is 3500000/100000 = 35 km.

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Answer:

√(100² + 60²) = √(10,000 + 3,600) = √13,600 = 20√34 = about 116.6 m

116.6 goes into the box.

From the pythagoras theorem AB² = AX² + BX²

14² = 13² + BX²

196 = 169 + BX²

27 = BX²-----  > BX=√27

BX  = 5.20

The four triangles formed by construction of the diagonals are all congruent since the diagonals are perpendicular bisectors.

Total area of the rhombus is 4 times of ABX  triangle

It would take 1.8 years to to get $992 with a 6% simple interest annually.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

Given that man deposited $800 in his account at a bank which offers 6% simple interest per annum.

Principal =  $800

Rate = 6%

Time = 9

Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = (800× 6× 9) / 100

Simple Interest = 432 dollar

Also, Simple Interest = (Principal × Rate × Time) / 100

$992 = (800 × 6× Time) / 100

992 = 48× Time

Time= 20.6

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To find the number of feet in 7/11 of a mile, you multiply 5280 (the number of feet in a mile) by 7/11. The answer is 3360 feet.

To calculate how many feet are in 7/11 of a mile, you first have to understand that there are 5280 feet in one mile. If you need to find out the feet in a fraction of a mile, you can multiply this number of feet in one mile by that fraction. In this case, the fraction is 7/11. So, the calculation would go as follows:

5280 feet/mile * 7/11 mile = 3360 feet.

Therefore, 7/11 of a mile is equivalent to 3360 feet.

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The value of expression at m=-1 is 100, so there were 100 visitors 1 months before the number of visitors was measured

All figures are in 3-D form. But the base of each polygonal prism is different.

One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.

A prism is a solid form that is enclosed by plane faces on all of its sides. A prism has two different kinds of faces. Bases refer to identical top and bottom faces. The name "prism" refers to the form of these bases.

All figures are in 3-D form. And all the figures are polygonal prism.

But the base of each polygonal prism is different.

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If you take a 10-minute shower each day, you would use approximately 25 gallons of water.

The average person in the U.S. uses approximately 100 gallons of water per day, which includes daily activities such as cooking, washing dishes and clothes, flushing the toilet, and bathing. If you take a 10-minute shower each day, you would use a certain amount of water.

To calculate the amount of water used during a 10-minute shower, you would need to know the flow rate of your showerhead. On average, a showerhead has a flow rate of 2.5 gallons per minute. So, multiplying the flow rate by the duration of the shower gives us:

2.5 gallons/minute * 10 minutes = 25 gallons

Therefore, if you take one 10-minute shower a day, you would use approximately 25 gallons of water.

Answer:

The height of small can need to be 12.8 cm to hold all the paint

Step-by-step explanation:

- Jamil had a 1/4 can of paint left

- The radius of the can is 8 cm and its height is 20 cm

- He wants to put the remaining paint into a smaller can with a

 radius of 5 cm

- We need to find the height of the smaller can

- The volume of the paint in the larger can is the same volume of paint

  will put in the smaller can

- Lets find the volume of the paint in the larger can

∵ The volume of the paint in the larger can = 1/4 its volume

∵ The can is shaped a cylinder

∵ Volume the cylinder = πr²h, where r is the radius of it and h its height

∵ r = 8 cm and h = 20 cm

∴ The volume of the paint = [tex]\frac{1}{4}\pi (8)^{2}(20)=320\pi[/tex] cm³

- Same amount of paint will put in the smaller can

∵ r = 5 cm and V = 320π cm³

∴ 320π = π(5)²h

- Divide both sides by π

∴ 320 = 25 h

- divide both sides by 25

∴ h = 12.8 cm

* The height of small can need to be 12.8 cm to hold all the paint

The height of the smaller can need to be to hold all the paint will be 12.8 cm.The term height is frequently used to describe someone's or something's height.

Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.

From the given conditions;

The volume of the paint in the larger can is,[tex]\rm V_L[/tex]

The volume of the paint in the smaller can is,[tex]\rm V_S[/tex]

The volume of the cylinder is, V

The radius of the can is,r= 8 cm

The height is,h=20 cm

The volume of the paint in the larger can is found as;

[tex]\rm V_L = \frac{1}{4} V \\\\ V=\pi r^2 h \\\\ V_L= \frac{1}{4} \pi (8)^2 (20) \\\\ V_L = 320 \pi \ cm^3[/tex]

The volume of the larger can is equal to the volume of the smaller can;

[tex]\rm V_S = V_L \\\\ 320 \ \pi \ cm^3=\pi r^2 h \\\\ \pi \ cm^3=\pi (5)^2 h \\\\ 320=25h \\\\ h =12.8 \ cm[/tex]

Hence the height of the smaller can need to be to hold all the paint will be 12.8 cm.

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Answer:

21

Step-by-step explanation:

Answer:

0.24w+0.5y

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Final answer:

The approximate monthly percent decrease in value is 0.67%.

Explanation:

To find the approximate monthly percent decrease in value, we need to first calculate the annual percent decrease. We know that the boat loses 8% of its value every year. So, the annual percent decrease is 8%.

To find the monthly percent decrease, we need to divide the annual percent decrease by 12 (since there are 12 months in a year).

Therefore, the approximate monthly percent decrease in value is 0.67%.

Final answer:

The approximate monthly percent decrease in value of the boat that depreciates at 8% annually is 0.65% when rounded to the nearest hundredth of a percent.

Explanation:

To find the monthly percent decrease in value of a boat that costs $23,400 and depreciates 8% annually, we need to calculate the equivalent monthly rate. The formula for monthly depreciation is (1 - (1 - annual depreciation rate)^(1/12)). In this case, the annual depreciation rate is 0.08 for 8%. Applying the formula, we get:

Monthly depreciation = 1 - (1 - 0.08)^(1/12) = 1 - (0.92)^(1/12)
= 1 - (0.92)^(0.08333...)
= 1 - 0.99347... (value calculated using a calculator)
= 0.00653... or 0.653% (after converting to a percentage).

To round to the nearest hundredth of a percent, we get approximately 0.65% monthly depreciation. This is the approximate monthly percent decrease in the boat's value.

If she made $192 at work. Then the amount of money she puts in her savings account will be $80.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Elena always puts 5/12 of the money she makes at work in her savings account. If she made $192 at work.

Then the amount of money she puts in her savings account will be

→ 5/12 x 192

→ 80

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Answer:

D

Step-by-step explanation:

Answer: $2875

Step-by-step explanation:

The formula to calculate the simple interest is given by :-

[tex]S.I.=P\times r\times t[/tex], where P is the principal amount , r is the rate of interest and t is the time period.

Given: Principal amount = $2500

Rate of interest = 15%=0.15

Time period = 1 year

Now, the simple interest gained by Darrel after 1 year will be :-

[tex]S.I.=2500\times 0.15\times 1=\$375[/tex]

Now, the total amount his friend owed altogether= [tex]P+I=2500+375=\$2875[/tex]

Broderick initially has $420, adds $213 from deposits, and needs $1,243 for checks, resulting in him needing to add $610 to cover his checks.

To calculate how much money Broderick needs to add to his account to cover his checks, we must first figure out his total deposits and then subtract the total amount he needs for the checks.

Broderick starts with $420 in his account and makes 6 deposits of $35.50 each. To find the total amount deposited, we multiply the number of deposits by the amount of each deposit:

Adding this total to his initial amount gives us:

Next, Broderick needs to write 4 checks for $310.75 each. The total amount for the checks is:

To determine how much additional money is needed, we subtract Broderick's available money from the total amount needed for the checks:

Therefore, Broderick needs to add $610 to his account to cover the checks.