The volumes of two spheres are in a ratio of 1:8. what is the ratio of their radii?

Answer:

C) 2 tan θ

E) [tex]\frac{sin2[theta]}{cos^2[theta]}[/tex] (it wouldn't let me do the actual θ symbol)

Step-by-step explanation:

This is essentially what the other person said, but in a better format.

Answer with explanation:

The given cosine function is

   y= - cos 3 (theta)= -3 cos A, where , theta =A.

→→Domain of Cos A

          = All Real number

    = Period is from (-π , π)

Range of Cos A=[-1, 1]

→Domain of Cos 3 A,will be also, all real number.

Period is from,

         [tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]

But range of Cos 3A,will be same as ,Cos A which is equal to ,[-1,1].

→Plotted the graph of ,y=-cos 3 A, having cycle ,

  [tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]

Answer:

3x+6

Step-by-step explanation:

you have to distribute the negative to get the parentheses away and simplify

Mean: 12.545454545455

Median: 12

Range: 8

Mode: 15, appeared 3 times

Largest: 17

Smallest: 9

Sum: 138

Count: 11

Answer:

3/4 ÷ 4/5 = .75 ÷ .80

Step-by-step explanation:

3/4 ÷ 4/5

= .75 ÷ .80

= 0.9375

The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.

so

the answer is the option

A. the remote interior angles

The value of x is 7 for the given equation.

Logarithm,  a mathematical concept involving multiplication. It is the exponent or power to which a base must be raised to yield a given number.

For the given situation,

The equation is 5log(x+3)=5.

On solving this equation, we can get value of x.

⇒ [tex]5log(x+3)=5[/tex]

⇒ [tex]log(x+3)=1[/tex]

We know that, log 10 = 1

Then,

⇒ [tex]log(x+3)=log10[/tex]

⇒ [tex]x+3=10[/tex]

⇒ [tex]x=7[/tex]

Hence we can conclude that the value of x is 7 and the graph fro the logarithmic equation is shown below.

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Answer:

D edge

Step-by-step explanation:

Final answer:

Using the Remainder Theorem, after substituting 5 into the polynomial p(x), we find that the remainder when p(x) is divided by (x - 5) is 240.

Explanation:

To find the remainder of p(x) divided by (x - 5), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial p(x) divided by (x - a) is p(a). Thus, we need to evaluate p(5).

Let's substitute x with 5 in the polynomial p(x):

p(5) = 2(5)^3 - 3(5) + 5
= 2(125) - 15 + 5
= 250 - 15 + 5
= 240.

Therefore, the remainder when p(x) is divided by (x - 5) is 240.

Answer:

a.[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]

b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]

Step-by-step explanation:

We have to complete each equation

We are given that

[tex]((12)^2)^3\cdot (12)^{-4}[/tex]

[tex](12)^6\cdot (12)^{-4}[/tex]

Using identity

[tex](a^x)^y=a^{xy}[/tex]

[tex](12)^{6-4}=(12)^2[/tex]

Using identity: [tex]a^x\cdot a^y=a^{x+y}[/tex]

[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]

b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}[/tex]

[tex]\frac{(12)^2}{(12)^2}[/tex]

[tex](12)^{2-2}=(12)^0=1[/tex]

Using identity: [tex]\frac{a^x}{a^y}=a^{x-y},a^0=1[/tex]

[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]

The probability of losing the game is 3/10 or 0.3 when the probability of winning is 7/10, because the total probability must always equal 1.

If the probability of winning the game is 7/10, then the probability of losing the game is the complement of the probability of winning. This means we subtract the probability of winning from 1. Therefore, the probability of losing the game is 1 - 7/10 = 3/10 or 0.3. This is because the sum of the probabilities of all possible outcomes in a probability distribution must equal 1.

The correct statement is A;If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89

The EMI formula is :

[tex]\dfrac{pr(1 + r)^n}{(1 + r)^n - 1}[/tex]

Where r = 5.5/12/100 = 0.00425

p = 37,796.89

and n = 20 x 12 = 240

Putting the values in formula we get'

= (37,796.89x 0.00425 x 2.767)/1.767

= $350

Hence,

The correct statement is A; If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89

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Answer:If Karen's monthly payment were $240, the amount of the loan that she is considering taking out would be less than $37,796.89.

Step-by-step explanation:

[tex]\\ \text{Let the speed of the car is x km/h}\\ \text{Then, the speed of the train is x+5 km/hr}\\ \text{Now, 4 hr is the time of the car}\\ \text{and 7 hour is the time of the train}\\ \text{We know the formula}\\ \text{Distance }= \text{Velocity }\times \text{ time}\\ \text{Distance travelled by car is 4x}\\ \text{Distance travelled by train is }7(x+5)\\ \text{The total distance is given by 255 km. Hence, we have}\\ 4x+7(x+5)=255\\ 4x+7x+35=255\\ 11x=220\\ x=20[/tex]

The speed of the car is 20 km/hr and hence the speed of the train is 2+5=25 km/hr.

The speed of the train is given by 25 km/hr.

The value of the expression ∛27x⁹ is 9x³.

The given expression is ∛27x⁹.

Cube root of twenty seven times of x power nine.

We can split the terms inside the cube root.

27=3×3×3

∛x⁹ = x³

Now let us plug in the above expression.

= 3√3³ × x⁹

= 3√3³ × √ x⁹

= 3 × 3 × x³

= 9x³.

Hence, the value of the expression ∛27x⁹ is 9x³.

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Answer:

the answer is option d y+1 =3 (x-4)

A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)

Solution:

We have 48 [tex] \frac{miles}{hour}  [/tex]

To convert, miles to centimeters.

Let us convert miles to feet and then inches and then centimeters.

1miles=5280feet

And, 1 foot=12inches

So, 5280 feet or 1 miles =12*5280inches

So, 1miles=63360inches

Now, Let us convert inches to centimeters

1centimeter=0.39inches

Or, 1 inch= [tex] \frac{1}{0.39}  [/tex] centimeter

So, 63360inches (or 1 mile)= [tex] \frac{63360}{0.39}  [/tex] centimeter

1mile or 63360inches=162461.54centimeter

1mile=162461.54 centimeter

We have, 48 [tex] \frac{miles}{hour}  [/tex]

We have, 48 *[tex] \frac{162461.54 centimeter}{60minutes}  [/tex]

We have, 48* [tex] \frac{162461.54 centimeter}{60*60seconds}  [/tex]

So,  We have, 48* [tex] \frac{162461.54 centimeter}{3600seconds}  [/tex]

=48*[tex] \frac{162461.54}{3600}  [/tex][tex] \frac{centimeters}{second}  [/tex]

=48*45.13[tex] \frac{centimeters}{second}  [/tex]

=2166.15[tex] \frac{centimeters}{second}  [/tex]

Answer:= Speed of the car in centimeters per second is 2166.15 centimeters/second

The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

Since the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°

So, substituting the value of θ into the positions, we have

(20cos75°, 20sin75°)

20cos75° = 20cos(45 + 30)

Using the compound angle formula

cos(A + B) = cosAcosB - sinAsinB

With A = 45 and B = 30

cos(45 + 30) = cos45cos30 - sin45sin30

= 1/√2 × √3/2 - 1/√2 × 1/2

= 1/2√2(√3 - 1)

= 1/2√2(√3 - 1) × √2/√2

= √2(√3 - 1)/4

= (√6 - √2)/4

= (-√2 + √6)/4

So, 20cos75° = 20 × (-√2 + √6)/4

= 5 (-√2 + √6)

20sin75° = sin(45 + 30)

Using the compound angle formula

sin(A + B) = sinAcosB + cosAsinB

With A = 45 and B = 30

sin(45 + 30) = sin45cos30 + cos45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= 1/2√2(√3 + 1)

= 1/2√2(√3 + 1) × √2/√2

= √2(√3 + 1)/4

= (√6 + √2)/4

= (√2 + √6)/4

So, 20sin75° = 20 × (√2 + √6)/4

= 5(√2 + √6)

Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).

So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

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