What is the approximate surface area of the sphere?

Answer:

[tex]96\ basketballs[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylinder (hollow drum)

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=48\ in[/tex]

[tex]r=24\ in[/tex]

substitute

[tex]V=\pi (24)^{2} (48)[/tex]

[tex]V=27,648\pi\ in^{3}[/tex]

step 2

Find the volume of one basketball

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=6\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ in^{3}[/tex]

step 3

Find the maximum number of basketballs that the cylindrical drum contains

so

Divide the volume of the cylinder by the volume of one basketball

[tex]27,648\pi/288\pi=96\ basketballs[/tex]

Answer:

Option B f(x) = x + 1

Step-by-step explanation:

The given points are

x        y        Relationship (x & y)

-2      -1        -2 + 1 = -1      

0        1         0 + 1 = 1    

1        2          1 + 1 = 2    

3       4          3 + 1 = 4    

5       6          5 + 1 = 6

As we can see the difference in x and y values of each ordered pairs is one

Therefore, relationship between x & y that can be represented by y = x + 1

Option B f(x) = x + 1 is the answer.

Answer:

The variation equation is

[tex] f = \frac{k.m_1.m_2}{ {r}^{2} } [/tex]

step-by-step explanation:

From the question, the two masses are

[tex]m_1 \: and \: m_2[/tex]

This implies that the product of the two masses

[tex] = m_1 \times m_2 = m_1.m_2[/tex]

Moreover, the force,f varies directly with the products of the two masses

[tex] \implies \: f\propto m_1.m_2....eqn.1[/tex]

Also, the force varies inversely with the square of the distance,r

[tex] \implies \: f\propto \frac{1}{ {r}^{2} }.......eqn.2[/tex]

Joining equation 1 and 2, we got

[tex] \implies \: f\propto \frac{1}{ {r}^{2}} \times m_1.m_2[/tex]

[tex] \implies \: f \propto\frac{m_1.m_2}{ {r}^{2}}[/tex]

But the constant of variation is k

Multiplying the right hand side of the equation by k, we got

[tex] \implies \:f=\frac{k.m_1.m_2}{ {r}^{2}}[/tex]

Answer:

B

Step-by-step explanation:

Corresponding angles are not always congruent

Corresponding angles are congruent.

Answer is B.

r1 = -12 and r2 = 12

[tex]\bf 40\pi =\cfrac{5}{18}\pi r^2\implies 40\pi =\cfrac{5\pi r^2}{18}\implies 720\pi =5\pi r^2\implies \cfrac{720\pi }{5\pi }=r^2 \\\\\\ 144=r^2\implies \sqrt{144}=r\implies 12=r[/tex]

Answer:

The amplitude  of the given sinusoidal function is 3.5

Step-by-step explanation:

The given sinusoidal function is

[tex]m(x)=-3.5\cos x[/tex]

This function is of the form:

[tex]m(x)=a\cos bx[/tex]

where

a=|-3.5|=3.5 is the amplitude.

Therefore the amplitude of the given sinusoidal function is 3.5

I believe I did this correctly. Comment to tell me if I didn't.

__________________________________

I got infinite solutions.

For the second problem, I subtracted 9 from both sides. Then I divided them all by -1. They are the same equations.

ANSWER

b) infinite solutions

EXPLANATION

The given system is:

x=3y+9 ...(1)

9-x=-3y...(2)

Put equation (1) into equation (2)

This implies that,

9-(3y+9)=-3y

Expand the parenthesis,

9-3y-9=-3y

-3y=-3y

1=1

This implies that, that the system has infinitely many solutions.

Answer:

Step-by-step explanation:

[tex]\text{De}\text{finition of logarithm:}\\\\\log_ab=c\iff a^c=b\\\\\text{where}\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\ \wedge\ c\in\mathbb{R}\\===========================\\\\\log_2n=4\iff n=2^4\\\\n=16[/tex]

Answer:

I don't know what answers you were given to your problem but I think the answer is

D) log n =4log2

Sorry if I got it wrong.

Answer:

C. 9P6

Step-by-step explanation:

Given choices are :

A. 8P5

B. 9P1

C. 9P6

D.8P1

Now we need to find about which below is largest when evaluated.

So let's evaluate them using formula:

[tex]nPr=\frac{n!}{\left(n-r\right)!}[/tex]

[tex]8P5=\frac{8!}{\left(8-5\right)!}=\frac{8!}{\left(3\right)!}=6720[/tex]

[tex]9P1=\frac{9!}{\left(9-1\right)!}=\frac{9!}{\left(8\right)!}=9[/tex]

[tex]9P6=\frac{9!}{\left(9-6\right)!}=\frac{9!}{\left(3\right)!}=60480[/tex]

[tex]8P1=\frac{8!}{\left(8-1\right)!}=\frac{8!}{\left(7\right)!}=8[/tex]

Largest value among those numbers is 60480.

Hence correct choice is C. 9P6

None.

Distribute the 3 to the (x + 4) to get 3x + 12.

Subtract 3x from both sides to get 12 = 4.

This is not true, so there are no solutions.

T o find the median if there are two numbers in between find the mean or the average. To do that add up the 2 middle numbers then divide by 2 that's your median

Answer:

36

Step-by-step explanation:

If s is the side length, then the area of the square is

A = s^ = (6)^2 = 36

This is how you were expected to answer this question.  However, the actual correct answer is 36 cm^2.

Answer:

36

Step-by-step explanation:

Answer:

113.09733552923 in2

Step-by-step explanation:

The leash is basically the radius. If the radius is 6...

If you find the area of the circle using the formula πr square. π=3.14. you can do the rest.

Answer:

C

Step-by-step explanation:

[tex] \frac{ - 1}{3} \times a = -1[/tex]

then

[tex]a = 3 \: where \: a \: is \: our \: line \: slope[/tex]

Answer:

[tex]\boxed{\text{C. } y - 2 = 3(x - 6)}[/tex]

Step-by-step explanation:

The slope of the perpendicular line m₂ must  be the negative reciprocal of the slope m₁ of the first line.

[tex]m_{2} = -\dfrac{1}{m_{1}} = -\dfrac{1}{-\frac{1}{3}} = 3[/tex]

The only equation with m = 3 is  

[tex]\boxed{\textbf{C. } y - 2 = 3(x - 6)}[/tex]

This is the point slope form of the equation for a straight line through (6, 2) with slope = 3.

Answer:

A. 6

Step-by-step explanation:

f(x) = x² − 12x + 7

To complete the square, we first factor the leading coefficient to make it 1 (which it already is).

Then, we take half the second coefficient, square it, and then add to both sides.  So (-12/2)² = (-6)² = 36.

f(x) + 36 = x² − 12x + 36  + 7

Then we factor the perfect square:

f(x) + 36 = (x − 6)² + 7

Then solve for f(x) by subtracting and simplifying:

f(x) = (x − 6)² + 7 − 36

f(x) = (x − 6)² − 29

So the value of a is 6.

Answer:

[tex](-7x^2+3)(x-3)[/tex]

Step-by-step explanation:

We can take "common" from first 2 terms and common from next 2 terms. Shown below:

[tex]-7x^3+21x^2+3x-9\\-7x^2(x-3)+3(x-3)\\(-7x^2+3)(x-3)[/tex]

That's how we do it. We can't simplify, or factor, any further.

All triangles equal 180 degrees.

The answer is 180 degrees.

Answer:

No correlation

Step-by-step explanation:

With the information provided, we have to conclude there is no correlation, since there is no apparent link between the two information.

It would be a positive correlation for example if we knew that the more apples Juan eats, the more he sleeps (or vice-versa).

It could be a negative correlation if we found that the more apples he eats, the less hours of sleep he has (or vice-versa).

But in this instance, we don't have any data indicating there is any form of correlation between those two numbers.

Where is 'the following'?

(I'll Answer in comments just give detail)

Answer:

range

Step-by-step explanation:

this is because it is asking the not central which is range.

Answer: Second option.

Step-by-step explanation:

The square root of a number "x" is a number "b" that multiplied by itself is "x":

[tex]b*b=x[/tex]

We know that the square root of 16 is 4 ([tex]\sqrt{16}=4[/tex]) because:

[tex]4*4=16[/tex]

Then [tex]\sqrt{13}[/tex] should be less than 4.

We know that the square root of 9 is 3 ([tex]\sqrt{9}=3[/tex]) because:

[tex]3*3=9[/tex]

Then [tex]\sqrt{13}[/tex] should be greater than 3.

Therefore, the value of  [tex]\sqrt{13}[/tex] is between 3 and 4.

This matches with the second option.

Hello Brainly Student! Your answer is 3 and 4! Hope this helped!!

Answer:

3n+21

Step-by-step explanation:

3 × n =3n

3 × (+7) = +21

Answer:

Use distributive property.

3(n+7),

3*n + 3*7=

3n + 21

Hope this helps and have a great day!

Answer:

A) −13

Step-by-step explanation:

(x + 6)^2 = 49

Take the square root of each side

sqrt((x + 6)^2) = ±sqrt(49)

x+6 = ±7

Subtract 6 from each side

x+6-6 = -6  ±7

x =-6  ±7

Separating into 2 parts

x = -6+7          x = -6-7

x = 1               x = -13

Answer:

the answer is 2.9 x 10^0 and 3.2 x 10^-2

Step-by-step explanation:

10^0 is equal to 1 so 2.9 x 10^0 is really 2.9 times 1 which is less than 3

if i could get brainliest answer that would be great!

10^-2 is a exponential that makes a number go down so 3.2 going down is less than 3

Answer:

C and D

Step-by-step explanation:

A.   2.9 × 10¹ = 2.9 × 10     = 29

B.  3.2 × 10³ = 3.2 × 1000 = 3000

C.  2.9 × 10⁰ = 2.9  × 1      = 2.9

D. 3.2 × 10⁻² = 3.2 × 0.01 = 0.032

Both C and D have values less than 3.

Answer:

n = 4, m = 1

Step-by-step explanation:

Given the 2 equations

3m + n = 7 → (1)

m + 2n = 9 → (2)

Rearrange (2) expressing m in terms of n, by subtracting 2n from both sides

m = 9 - 2n → (3)

Substitute m = 9 - 2n into (1)

3(9 - 2n) + n = 7 ← distribute left side

27 - 6n + n = 7 ← simplify left side

27 - 5n = 7 ( subtract 27 from both sides )

- 5n = - 20 ( divide both sides by - 5 )

n = 4

Substitute n = 4 into (3) for corresponding value of m

m = 9 - (2 × 4) = 9 - 8 = 1

Thus m = 1 and n = 4

Answer:

$36.75

Step-by-step explanation:

Answer: the sales tax alone is $36.75

the above ground pool with the sales tax is 561.75

Step-by-step explanation:

525x.07 =36.75

525x1.07=561.75 or another way you could do it is 525+36.75=561.75

Answer: Option B

2 is NOT in the domain of f ° g

Step-by-step explanation:

First we must perform the composition of both functions:

If [tex]g(x) = \sqrt{x-9}[/tex] and not [tex]\sqrt{x} -9[/tex]

[tex]f (x) = 4x + 3\\\\g (x) = \sqrt{x-9}\\\\f (g (x)) = 4 (\sqrt{x-9}) + 3[/tex]

The domain of the composite function will be all real numbers for which the term that is inside the root is greater than zero. When x equals 2, the expression within the root is less than zero

[tex]f (g (x)) = 4 (\sqrt{2-9}) + 3\\\\f (g (x)) = 4 (\sqrt{-7}) + 3[/tex]

The root of -7 does not exist in real numbers, therefore 2 does not belong to the domain of f ° g

The answer is Option B.

Note. If   [tex]g(x) = \sqrt{x}-9[/tex]

So

[tex]f(g(x)) = 4(\sqrt{x})-36 + 3[/tex]   And  2 belongs to the domain of the function

The area of the square is 36 squared inches, because it is a square with a side of 6 inches.

The two semicircles have a radius of 3 inches. If we subtract their areas from the area of the square, we have

[tex]36-2\left(\dfrac{\pi\cdot 3^2}{2}\right) = 36-9\pi[/tex]

The shaded region is half of this area, so the answer is

[tex]\dfrac{36-9\pi}{2} \approx 7.7[/tex]

36 minus 9 multiplied by Pi . Then divide that answer by 2 to get 7.7

Answer:wazz up

Step-by-step explanation:

yooo what’s up dude

The value of the expression for 121 is 11

Answer:

[tex]4 \times 3^{3}\\\\4\times3 \times3\times3\\\\108[/tex]

Step-by-step explanation:

Four times three cubed

Given the statement, times means multiplication.

four times three

4        x         3

It says three cubed, where cubed means raised to 3. So that means we right an exponent, and the exponent is 3.

4 x 3³

When we have an exponent, that tells you how many times you will multiply it by itself. So since the exponent is 3, we multiply 3 by itself 3 times.

3³ = 3 x 3 x 3

So 4 x 3³ = 4 x 3 x 3 x 3

Lastly, if we get the product your result will be 108.

4 x 3 x 3 x 3

=4 x 27

= 108

The expression is 4 times 3 cubed. The value equivalent to 4 times 3 cubed is 108.

The expression is 4 times 3 cubed.

To find the value equivalent to 4 times 3 cubed, we need to calculate it.

3 cubed means 3 raised to the power of 3, which is 3 x 3 x 3 = 27.

So, the value equivalent to 4 times 3 cubed is 4 x 27 = 108.

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