State fundamental theorems

Let's see

For initial cone

Volume

For new cone

Volume

So

Answer:

16 times

Step-by-step explanation:

[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.

[tex]\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h[/tex]

Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so 16 times greater than the smaller cone.

Given:

Substituting the given values into the formula:

[tex]\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units[/tex]

If the radius is quadrupled:

Substituting the new given values into the formula:

[tex]\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units[/tex]

To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:

[tex]\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16[/tex]

So the volume of the larger cone is 16 times greater than the volume of the smaller cone.

Answer:

Step-by-step explanation:

5 in.

a.

(6.257 25) in.

-

b. (6.25π – 12.5√2)in.²

d.

Find the value of x and y rounded to the nearest tenth.

C.

(6.25π- 12.5) in.2

Answer:

The number is 8

Step-by-step explanation:

Let x be the number

3x+4 = 28

Subtract4 from each side

3x+4-4 = 28-4

3x= 24

Divide by 3

3x/3 =24/3

x = 8

Answer:

1

Step-by-step explanation:

this is becasue the slope is positive

Answer:

Step-by-step explanation:

2/3 - 5/4 + 7/3

=8/12 - 15/12 + 28/12 (LCM=12)

(8 - 15 + 28)/12

=21/12

=7/4

The situation which can be defined using an exponential function is "The number of bacteria decreases by 7% each hour".

An exponential function is used to represent a situation in which values of an event do not increase at a constant or linear rate.

From the above,

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Answer:229.1

Step-by-step explanation: to much work I thought to hard that’s the answer your welcome buddy

Answer:

4045.43

Step-by-step explanation:

Answer:

I think the answer is c -2

Step-by-step explanation:

but don't quote me on that and if it's wrong i truly am sorry

Answer:

Step-by-step explanation:

Answer:

125 minus 81 will give me 34°

Answer:

x = 44°

Step-by-step explanation:

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Answer:

Step-by-step explanation:

45000+7544644555=x

x=7544689555

Answer:

x = 7544599555

Step-by-step explanation:

First let's make an equation :

7544644555 - x = 45000

Now to make x the subject and positive :

We add x to both sides :

7544644555 = 45000 + x

Now we subtract 45000 from both sides :

7544644555 - 45000 = x

x = 7544599555

Hope this helped and brainliest please

The frame can hold a mirror with an area of 78.5 in².

The area for a circle of diameter D is given by the formula:

[tex]A = pi*(D/2)^2[/tex]

Where pi = 3.14

Here we know that the diameter is 10 inches, replacing that in the area equation we can get:

[tex]A = 3.14*(10in/2)^2 = 3.14(5in)^2 = 78.5 in^2[/tex]

So the frame can hold a mirror with an area of 78.5 in².

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The first incorrect step is step 2 because this step did not take the two signs positive and negative.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a linear equation in a mod function;

|2x - 3| - 1 = 2

Step 1:

|2x - 3| = 3

Step 2:

2x - 3 = 3 or 2x - 3 = -3

(after removing mod, we get two same values but opposite in sign)

The first incorrect step is step 2 in which did not take the two sign,

2x - 3= 3 or 2x + 3 = 3   (wrong)

Thus, the first incorrect step is step 2 because this step did not take the two signs positive and negative.

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Answer:

5a−3ai+30i+18

Step-by-step explanation:

i just did this

If the surface area of the cylinder is 12π square meters. Then the radius of the sphere will be 1.7 meters.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A cylinder has a height of 4 meters and a radius of 1.5 meters.

Then the approximate radius of a sphere that has the same surface area as the cylinder.

We know that the Surface area of the cylinder will be is given as

Surface area = 2πrh

Surface area = 2 x π x 1.5 x 4

Surface area = 12π square meters

Then we have

Surface area of sphere = surface area of cylinder

                              4πr² = 12π

                                  r² = 3

                                   r = 1.7 meters

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Answer:

2.0 m

Step-by-step explanation:

A. 2.0 m

Answer:

Step-by-step explanation:

2x+6 ≤ 10  or  2x + 8 > 20

⇔ 2x ≤ 4  or  2x > 12

⇔ x ≤ 2  or  x > 6

Answer:

24 ft sq

Step-by-step explanation:

find area of triangles

6×4=24

24/2=12

add areas together

12+12=24

Answer:

48

Step-by-step explanation:

when you multiply a negative times a negative (or divide a negative by a negative), it equals a positive!

-6 times -8 will equal 48!

let me know if you have any questions :)

Answer:

25.13cm

Step-by-step explanation:

formula for circumference of a circle is (2r)π with r being the radius

since the problem gave us the diameter already we can change the formula to 8π (2r is equal to the diameter since diameter is twice as long as the radius)

this gives us the circumference of 25.13

The number of days that Sydney can afford to rent while staying within her budget is 3 days.

Total budget  ≤ (total number of days x cost per day) + (cost per mile x total mile)

$260 ≤ $77.50xx + ($0.10 x 275)

$260 ≤ $77.50xx + 27.50

$260 - 27.50  ≤ $77.50xx

232.50  ≤ $77.50xx

xx  ≤  232.50 / $77.50

xx  ≤ 3

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The number of years in 1000 days is = 2 . 74 years .

Division is the arithmetic operation that is used to determine the quotient of a number. Division parts a number into equal parts with another number.

Number of years in 100 days = 1000 / 365

= 2 . 74 years

Here is the complete question:

how many Years are in 1,000 days

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The probability that Jake will earn at least 30 points on a throw is 0.335

The attached image represents the missing part of the question.

From the attached image, we can see that:

For Jake to earn at least point, he must hit the three circles (starting from the inner circle)

The radius of the yellow circle is:

Radius = 3

While the width of the other circles is:

Width = 4

The total area of the sections that give a point of at least 30 is:

A₁ = π * (3 + 4 + 4)² = 121π

The total area of all the sections is:

A₂ = π * (3 + 4 + 4 + 4 + 4)² = 361π

The probability of getting at least 30 points is:

P(At least 30) = 121π/361π

Evaluate

P(At least 30) = 0.335

Hence, the probability that Jake will earn at least 30 points on a throw is 0.335

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Answer:

The solution for the compound inequality is x \in(2,6)

Step-by-step explanation:

To find the solution set for these compound inequalities, we need to solve the inequality.

First, we shall solve the inequality

Adding both sides of the equation by 10, we have,

Dividing both sides by 3.5, we get,

Now, we shall solve the inequality ,

Adding both sides of the equation by 9, we have,

Dividing both sides by 8, we get,

The solution inequality for the given set of compound inequality 3.5x - 10 > - 3 & 8x - 9 < 39 is 2 < x < 6.

The general equation of a straight line inequalities are -

[y] < [m]x + [c]

[y] > [m]x + [c]

[y] ≥ [m]x + [c]

[y] ≤ [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following compound inequality -

3.5x - 10 > - 3

8x - 9 < 39

We have -

3.5x - 10 > - 3

8x - 9 < 39

3.5x - 10 > - 3

3.5x > 7

x > 2

AND

8x - 9 < 39

8x < 48

x < 6

Solution inequality -

2 < x < 6

Therefore, the solution inequality for the given set of compound inequality 3.5x - 10 > - 3 & 8x - 9 < 39 is 2 < x < 6.

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Considering the side length, the area of the complete square flag will be of 256 inches squared.

The area of a square of side length l is given by l squared, that is:

A(l) = l².

In this problem, we have that l = 16 inches, hence the area in square inches is given by:

A(16) = 16² = 256.

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Answer:

The answer is 4188.79 ft^3.

Step-by-step explanation:

The formula is V=4/3πr^3. The radius is 10, turning that into V=4/3π10^3. 10^3 is 1000, and 1000 times 4/3 is 1333.33. 1333.33 times 3.14 (or π) is equal to 4188.79 ft ^3 rounded to the nearest 100th. I hope this helps! :)

Answer:

3840

Step-by-step explanation:

Given expression:

4(x+5)(x+1)(x+3)(x - 3)

To:

Evaluate the expression ; for x = 5.

Solution:

Evaluate x = 5 :

Simplify using PEMDAS rule:

P : Parentheses

E : Exponents

M : Multiplication

D : Division

A : Addition

S : Subtraction

Hence, after evaluating the given expression for x = 5 , the answer'll be 3840.

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to evaluate

[tex]\large\pmb{4(x+5)(x+1)(x+3)(x-3)}[/tex] for x=5.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's what PEMDAS stands for:

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

So, let's start computing...

///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\//\\\///\\\///\\\///\\\\///\\\\///\\\///\\\///\

                                   Evaluating the expression

First, substitute 5 for x:

[tex]\star~\large\pmb{4(5+5)(5+1)(5+3)(5-3)}[/tex]

Now, use the Order of Operations.

The first operation here is:

[tex]\dag[/tex] P=Parentheses

So we need to perform the operations inside the parentheses first:

[tex]\star~\large\pmb{4(10)(6)(8)(2)}[/tex]

The next operation is multiplication, since we don't have any exponents here:

[tex]\star~\large\pmb{40\times6\times8\times2}[/tex]

Multiply!

[tex]\star~\Large\pmb{3840}~~\square\!\!\!\!\!\checkmark[/tex]

That's the value of the expression 4(x+5)(x+1)(x+3)(x-3) for x=5.

Hope it helps you out! :D

Ask in comments if any queries arise.

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Answer:

8.3 minutes

Step-by-step explanation:

93,000,000 m/186,000 m/s = 500 s

500/60 = 8.333333

1. Mean of the data: 8

2. Median: 8

3. IQR = 4

4. Members that use the facility 10 days a month is: 2.

See reasons below.

Mean = sum of all values ÷ number of data values (easily solved using a dot plot

Median = middle value (easily found using a box plot).

Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).

1. Mean of the data: use the dot plot.

Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8

2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.

Median = 8

3. IQR = Q3 - Q1 = 10 - 6

IQR = 4

4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.

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Answer:

Step-by-step explanation:

First one- x=0

Second=All real numbers