Tim tried to use Cavalieri's principle to show that the two figures have the same volume.
"The base areas are the same. Therefore, corresponding cross-sections have the same area. So the volumes must be the same."
What is the first mistake Tim made?

Amount earned per week=400-380=$20

Price of one shoe=70$

Total weeks

Minimum 4 weeks

Answer:

4 weeks

Step-by-step explanation:

Given:

Therefore,

Weekly surplus = weekly net income - weekly expenses

                          = $400 - $380

                          = $20

Given:

Number of weeks = cost of new shoes ÷ weekly surplus

                              = $70 ÷ $20

                              = 3.5

                              = 4 weeks (rounded to nearest week)

Therefore, it will take 4 weeks to save enough to buy the shoes.

Answer:

Mean = 1.8 in

Step-by-step explanation:

The Median is the middle value when all data values are placed in order of size.

Ordered data values:  0, 0, 0, 1, 1, 1, 2, 3, 4, 6

As there is an even number of data values, the middle value is the mean of the middle two data values.  Therefore, the Median = 1 in

The Mean is the sum of all data values divided by the total number of data values.

[tex]\implies \textsf{Mean}=\dfrac{0+0+0+1+1+1+2+3+4+6}{10}=1.8[/tex]

Therefore, the Mean = 1.8 in

The Median is a better measure of central tendency when the data includes outliers (data values that are far away from the majority), as it is not affected by those outliers.  As there does not appear to be any outliers in this data set, the mean can be used to best describe the center of the data.

Therefore, the Mean = 1.8 in

Step-by-step explanation:

4(5x²) + 16 = 400

5x² + 4 = 100

5x² = 96

x² = 19.5

x = ±sqrt(19.5) = ±4.415880433...

Answer:

20 cookies - $ 12

Step-by-step explanation:

6 cookies - $3.60

20 cookies - X

X = (20 · 3,60) : 6

X = $ 12

Answer:

$12

Step-by-step explanation:

let the cost of 20 cookies= y

ok!!!

since 6 cookies ---------------$3.60

20 cookies will cost--------- y

making y subject

y= 3.60×20/6

y= 72/6=$12

therefore, 6 cookies will cost $ 12

Answer:

radius r = 1.41047396 m

base circumference C = 8.86226925 m

volume V = 5.87697483 m^3

curved surface area A = 12.5 m^2

base surface area B = 6.25 m^2

total surface area K = 18.75 m^2

base circumference C = 2.82094792 π m

volume V = 1.87069919 π m3

curved surface area A = 3.97887358 π m^2

base surface area B = 1.98943679 π m^2

total surface area K = 5.96831037 π m

Step-by-step explanation:

V = (2/3)πr^3

C = 2πr

A = 2πr^2

B = πr^2

K = (2πr^2) + (πr^2) = 3πr^2

Answer:

Approximately 6.4 ft³

Step-by-step explanation:

A *hemisphere* is half of a sphere. As far as surface area goes, we not only need to account for the curved area, but also the area of the circular disc at the bottom. The area of the curved region is going to be half the area of the whole sphere. Since a sphere with radius r has a surface area of 4πr², the curved part of the hemisphere must have half that, or 2πr². Add in the area of the circular disc, πr², and we have a total area of 3πr². Setting this equal to the given area of 12.5 ft², we can solve for r:

[tex]3\pi r^2=12.5\\r^2=12.5/3\pi\\\\r=\sqrt{12.5/3\pi}[/tex]

Now, using the formula for the volume of a sphere, [tex]V=(4/3)\pi r^3[/tex], we can substitute our new value for r and solve:

[tex]V=(4/3)\pi r^3\\=(4/3)\pi(\sqrt{12.5/3\pi})^3\\\approx 6.4[/tex]

Answer:

5/12 = 0.416666....   also in percentage 29,41 % of the plant are beans and 70.59 % are tomato plants.

Answer:

x = 3

Step-by-step explanation:

Equating the secants :

Answer:

3

Step-by-step explanation:

Theorem:

If two secants intersect outside a circle, then the product of the length of the exterior segment of one secant and the length of that secant equals the product of the corresponding parts of the other secant.

In this case:

10 × (10 + 5x + 2) = 9 × (9 + 7x)

10(5x + 12) = 9(7x + 9)

50x + 120 = 63x + 81

-13x = -39

x = 3

Answer:

  53,157

Step-by-step explanation:

The population growth of a bacterial colony can be modeled by an exponential function of the form ...

  p(t) = a·b^t

where a is the initial population and b is the growth factor. The growth factor is ...

  b = 1 +r

where r is the growth rate.

__

In this problem we have ...

  a = 29,600

  b = 1 +5% = 1.05

  t = 12

So, the population after 12 hours is

  p(12) = 29600×1.05^12 ≈ 53,157

The colony will contain 53,157 bacteria in 12 hours.

Answer:

B

Step-by-step explanation:

essentially the plan that increases the price the most per week reaches the goal of $12 fastest.

plan A is $0.10 per week.

plan B it is not clear, if it means 10% of the original price every week, or every week 10% of the price of the previous week. I assume the first and simplest.

that means 10% of $8 = $0.80 per week.

plan C : the same amount every week until reaching $12. we need to increase in total by $4 (from $8 to $12). to reach these $4 in 8 weeks, we need to increase the price every week by 4/8 = $0.50.

plan D : $0.25 per week.

so, the plan with the highest increase every week and therefore the fastest one reaching $12 is plan B.

The correct answer is option B which is the pool must have been the same depth at the start of the interval as it was at the end of the interval.

The rate of change is defined as the changes that occur in any data with respect to time like changing of level of water respect to time. Changing of the position of any object with respect to time that is speed.

Here in the question, it is given that Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. The meaning of this statement is that the level of the water in the pool is the same as that of the level two weeks ago.

Therefore the correct answer is option B which is the pool must have been the same depth at the start of the interval as it was at the end of the interval.

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Answer:

2.32

Step-by-step explanation:

Answer:

x = 3, y = -1.

Step-by-step explanation:

4x + 5y = 7

y = 3x - 10

Substitute for  y = 3x - 10 in the first equation:

4x + 5(3x - 10) = 7

4x + 15x - 50 = 7

19x = 7 + 50 = 57

x = 57/19 = 3.

Now plug x = 3 in the second equation

y = 3(3) - 10

y = 9 -10

y = -1.

Answer:

m∡ABC=140º

Step-by-step explanation:

Answer:

8 Edges.

Imagine a cardboard box. The top has four edges and the bottom of it has another four.

Answer:

8

Step-by-step explanation:

count top edges then multiply by 2

In order to revise the second sentence for a presentation, the best thing to do would be to break it up into two sentences.

The second sentence is quite long and so would not be the best fit for a presentation.

We can solve this by breaking it into two sentences such as:

This makes the presentation more readable and ensures that the information is better passed on.

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Answer:

B - Breaking into two sentences

Step-by-step explanation:

Edge 2023

The perimeter of the triangle ΔWXY is P = 14.50 cm

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔXYZ

Now , the measure of sides of the inscribed triangle ΔQRS is

QR = 2.93 cm

RS = 2.04 cm

QS = 2.28 cm

where the points Q , R and S are the midpoints of the sides of the triangle ΔXYZ

So , the measure of sides of the triangle are twice the lengths of the sides of triangle ΔQRS

And , the perimeter P = 2 ( 2.93 + 2.04 + 2.28 )

On simplifying , we get

P = 2 ( 7.25 )

P = 14.50 cm

Hence , the perimeter is P = 14.50 cm

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The complete question is attached below :

What is the perimeter of ΔWXY?

a) 11.57 cm

b) 12.22 cm

c) 12.46 cm

d) 14.50 cm

Answer:

15t

Step-by-step explanation:

if you do the sqrt of 25 you get five than multiply that by 3 to get 15 then do the sqrt of t to get t

Hope this helps! ;-)

Answer:10 squared plus 9 squared equals 15 squared

Step-by-step explanation:

take the square root of your answer

The volume of the cylinder when its radius is tripled is 405π unit³.

The volume of the cylinder when its radius is tripled is calculated by applying the formula for volume of a cylinder as follows;

V = πr²h

where;

V₁/r₁² = V₂/r₂²

where;

V₁ is the initial volume = 45π unit³

r₁ = 3 units

when the radius is tripled, r₂ = 3r₁

V₁/r₁² = V₂/r₂²

V₂ = (V₁/r₁²) x r₂²

V₂ = (V₁/r₁²) x (3r₁)²

V₂ = 9V₁

V₂ = 9 x 45π unit³

V₂ = 405π unit³

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Answer:

Part B:3/6 should be your answer answer:)!

Part C:The side length is 4 feet 6 inches, it is a rational number because both numbers can be showed as a fraction.

Step-by-step explanation:

Answer: Heyaa!

If you mean medicine treatment the definition is...

If you mean just basic treatment the definition is...

Hopefully this helps you:

- Matthew

Answer:

x = 74 degrees

Answer:

74 degrees

Step-by-step explanation:

Remember that CO interior angles equal to 180 degrees so what you need to simply do is do 180 minus 106 degrees giving you 74 degrees as your answer

Answer:

3.1 hrs  painting together

Step-by-step explanation:

Lucia rate = 1 room/ 5 hr

Marie rate = 1 room/8hr

now combine the rates

1 room / ( 1/5 + 1/8) = 3.077 hrs

The fractional expression 18/48 is greater than 14/48 or 6/16 is greater than 7/24. Then the correct option is A.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The expressions are 6/16 and 7/24.

Then the LCM of the 16 and 24 will be 48.

Then the expressions will be 18/48 and 14/48.

The fractional expression 18/48 is greater than 14/48 or 6/16 is greater than 7/24.

Thus, the correct option is A.

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The actual weight of the mobile in grams is 194 grams.

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

As broken scale shows a false weight that is always higher than the actual weight by the same number of grams.

When a mobile phone is put on the scale, the real weight will be  'x'

but it shows,

x+a= 202

When an headphone is put on the scale, the real weight will be  'y'

but it shows,

y+a=221

When the mobile phone and the headphone are put on the scale together, the weight is

x+y+a= 415

So,

x+221=415   [Since y+a= 221 grams]

x= 194 grams

The actual weight of the mobile phone in grams is 194 grams.

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Answer:

A = 120 cm²

Step-by-step explanation:

The 4 part of the ratio relates to the height of triangle A , then

16 ÷ 4 = 4 cm ← value of 1 part of the ratio, then

5 parts = 5 × 4 cm = 20 cm

The area (A) of triangle B is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 12 and h = 20 , then

A = [tex]\frac{1}{2}[/tex] × 12 × 20 = 6 × 20 = 120 cm²