Using Cavalieri's Principle, what is the general formula for the volume of a cone?

Answer:

A) 60

B) Common ratio, r, = 2/3

The first term, a, = 13.5

Step-by-step explanation:

A)

The formula for  the nth term of a linear sequence is an+b. So we can say:

30=5a+b

75=20a+b

which means

b=30-5a

b=75-20a

30-5a=75-20a

15a=45

a=3

30=5(3)+b

b=30-15=15

So our formula is 3n+15. Sub in 15 for n to find the 15th term: 3(15)+15=45+15=69

B)

The formula for  the nth term of an exponential sequence is arⁿ⁻¹, where a is the first term of the sequence and r is the common ratio. Therefore we can say: 9=ar, and 4=ar³, which means a=9/r and a=4/r³

9/r=4/r³

9r³=4r

9r²=4

r=√(4/9)=2/3

9=a(2/3)

a=27/2=13.5

Answer:

1/2 of an answer is zero answer.

Step-by-step explanation:

yeah :)

Answer:

- 3

Step-by-step explanation:

[tex]f(x) = \sqrt{x + 1} \\ plug \: x = 0 \\\therefore f(0) = \sqrt{0 + 1} \\\therefore f(0) = \sqrt{1} \\ \therefore f(0) =1 \\ \\ g(x) = 2x - 5 \\ plug \: x = f(0) \\ \therefore g( f(0)) = 2 f(0)- 5 \\ \therefore g( f(0)) = 2 (1) - 5 \\\therefore g( f(0)) = 2 - 5 \\ \\ \huge \red {g( f(0)) = \boxed {- 3} }[/tex]

Step-by-step explanation:

Starting from the upper left in the clockwise direction:

congruent: no

similar: no

upper right side:

congruent: yes

similar: yes

lower right side:

congruent: no

similar: yes

lower left side:

congruent: yes

similar: yes

Answer:

27

Step-by-step explanation:

14/2+5 x 4

7+20

27

Answer:

27

Step-by-step explanation:

14 divided by 2 + 5 x 4

5 x 4 first (pemdas)

5 x 4 is 20

14 / 2 = 7

7 + 20 = 27

if you don’t know pemdas it’s:

p arenthases

e xponents

m ultiply

d ivide

a dd

s ubtract

Answer:

B. 3/9 = 4/12 = 1/3

Step-by-step explanation:

I calculated it logically

Answer:

10.4 cm

Step-by-step explanation:

Since the area is half of the base multiplied by the height A = 1/2 * b * h, the height can be found from h = 2A/b

h = (2 * 83.72 )/16.1 = 10.4

Answer:26.02

Step-by-step explanation:83.72-(16.1x2)/2=26.02 (sry I know it’s confusing but that’s how I do math lol) brainlyest plz plz I need it for my rank

Answer: 0<8xp<8

Step-by-step explanation:

Answer:

8xp < 8 > 0

Step-by-step explanation:

Is your algebra expression i'm pretty sure.

[tex]\displaystyle\bf\\x^2+x^2=10^2\\\\2x^2=19^2\\\\x^2=\frac{10^2}{2}\\\\ \sqrt{x^2}=\sqrt{\frac{10^2}{2}}\\\\x=\frac{10\sqrt{2}}{\sqrt{2}\times\sqrt{2}}\\\\x=\frac{10\sqrt{2}}{2}\\\\\boxed{\bf x=5\sqrt{2}~~~~~~Correct~ansver:~~D)}[/tex]

Answer:

1. a = 14

2. m = 8

3. N/A

4. m = 2

5. N/A

6. n = 0, [tex]\frac{9}{25}[/tex], 0.36

7. x = 27

8. x = 65

Step-by-step explanation:

Answer:

The answer is [tex]15.00[/tex] %

Step-by-step explanation:

Let's start defining the random variable. We have the following variable :

[tex]X:[/tex] '' The amount spent per year on reading and entertainment among adults in the 25- to 34- year age group ''

We assume that [tex]X[/tex] follows the normal distribution. We can write :

[tex]X[/tex] ~ N ( μ , σ )

Where μ is the mean of the distribution and σ is the standard deviation (both are parameters from the normal distribution). Using the data from the question :

[tex]X[/tex] ~ [tex]N(2060;495)[/tex]

In order to answer the question, we first must calculate the probability :

[tex]P(X>2575)[/tex] (I)

We are going to calculate this probability by making a substitution. If we substract the mean to the variable [tex]X[/tex] and then divide by the standard deviation, we obtain a new variable [tex]Z[/tex] which can be modeled as a [tex]N(0;1)[/tex]. This is convenient because the cumulative distribution from [tex]Z[/tex] is tabulated and can be found on any book or either in Internet.This process is called standardizing the variable :

[ ([tex]X[/tex]-μ) / σ ] = [tex]Z[/tex] ~ [tex]N(0;1)[/tex] ⇒ If we apply this to the equation (I) ⇒

[tex]P(X>2575)=P(Z>\frac{2575-2060}{495})=P(Z>1.04)[/tex]

Then,

[tex]P(Z>1.04)=1-P(Z\leq 1.04)[/tex] (II)

Looking in any cumulative distribution table of [tex]Z[/tex] ⇒ [tex]P(Z\leq 1.04)=0.85[/tex]

If we replace this value in (II) ⇒

[tex]P(Z>1.04)=1-P(Z\leq 1.04)=1-0.85=0.15[/tex]

Using percent we obtain [tex]15.00[/tex] %

Answer:

80.54

Step-by-step explanation:

height- 30

base- 5

tan-1(30/5)

tan-1(6)

= 80.54

Answer: y <= x^(2) - 3x - 1

How to: Graph the inequality by finding the boundary line, then shading the appropriate area.

Have a great day and stay safe !

Answer:

Step-by-step explanation:

k

Answer:Yes

Step-by-step explanation:Because if u use the antropy system you'll know i hope i helped

Answer:

600

Step-by-step explanation:

V=(LxWxH)/3

Multiply 10x15x12/3 and get 600

Answer:

120

Step-by-step explanation:

multiply 10 times 24

then divide 240 by 2

Answer:

remy would be correct

Step-by-step explanation:

Answer:

62.8ft

Step-by-step explanation:

circumference= pie x diameter

pie=3.14

diameter=20ft

c=3.14 x 20ft

=62.8ft

Answer:

Tens

Step-by-step explanation:

it’s really easy if you know your place values just go ones,tens,hundreds,thousands and keep going but the answer is tens place.

Answer:

$11,640

Step-by-step explanation:

Answer: the second option (1/2)

Step-by-step explanation:

numbers greater than 3: 4, 5, and 6

3 numbers

so 3/6 or 1/2

1/2 or 50% so the second option

Answer:

13

Step-by-step explanation:

The perimeter is all of the sides added together. Because this is a rectangle, the length and width are the same on both sides. They gave you the length and width, so just add them:

4 + 4 + 2.5 + 2.5 = 13.

So the perimeter of the shape is 13.

Answer:

13 m

Step-by-step explanation:

2.5 + 4 + 2.5 + 4

2.5 + 2.5 + 8

5 + 8

13

Answer: 11.70

Step-by-step explanation:

Answer:

x=64

Step-by-step explanation:

[tex]x^{2} =A\\x^{2} = 4,096[/tex]

Answer:

Hello! answer: 64

Step-by-step explanation:

Each side length of the square is the same therefore we just have to find the square root of 4096 64 × 64 = 4096 therefore the side length of the square is 64 HOPE THAT HELPS!

Answer

5 hair bands

Step-by-step explanation:

$38-$27(Sunglasses)=11

11/2=5.5

you can't buy 5.5 hairbands so you round the number to the nearest whole number.

so the answer is 5 hairbands.

Answer:

36 miles

Step-by-step explanation:

Since there are 60 minutes in a hour, you can see that 20 minutes is a third of that time. To find the answer, you multiply the values by 3 to equal on hour. 20x3 = 60 and 12x3 = 36, meaning he drove 36 miles in a hour.

Answer:

70 amps

Step-by-step explanation:

The current I is inversely proportional to the resistance R

I=k/R   (k is the constant of proportionality)

A)   I=210 amperes

     R=4 ohms

I=k/R

k=I×R

k=210×4=840

B)    R=12 ohms

     k=840

    I=k/R

   I=840/12=70 amperes

The current will be 40 mA when the resistance is 15 ohms.​

Ohms law says that the current running through the conductor is directly proportional to the potential difference across its extremities as long as the temperature and other physical conditions are constant.

Ohms law formula is -

V=IR, Where

Voltage is V and is measured in Volts,

The current flowing through the conductor is I and it represented in amperes and the resistance is R and is measured in ohms.

Given that, the voltage, V, in an electric circuit is held constant, If the current is 120mA when resistance is 5 ohms,

120 mA = 0.12 A

Therefore,

V = IR

V = 0.12 × 5

V = 0.6 volts

Now, when the resistance is 15 ohms, the current will be =

0.6 = I × 15

I = 0.6 / 15

I = 0.04 A

I = 40 mA

Hence, the current will be 40 mA when the resistance is 15 ohms.​

Learn more about Ohms law, click;

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