Two spheres have volumes of 87pi cm³ and 64pi cm³. If the surface area of the smaller sphere is 16pi cm², what is the
surface area of the larger sphere?
O 64pi cm²
O 96pi cm²
O 128pi cm²
O 256pi cm²

The solutions of the system of inequalities are:

(0, 3)

(6, 2)

Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).

And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.

Then the points that are solutions are:

(0, 3)

(6, 2)

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Answer:

48

Step-by-step explanation:

Start by dividing both sides of the equation by 1/8.

9 divided by 1/8 is equivalent to 9 times 8, so we are left with

(p+24)= 72

Now subtract 24 from both sides to get p by itself.

72-24= 48

P= 48

Step-by-step explanation: In order to factor an integer, which is 8, we'll need to repeatedly divide it by ascending sequence of primes. (2, 3, 5). The number of times that each prime divides the original integer becomes Its exoponent.

In the example 1/8 (p + 24) = 9, Prime number 2 to the 3rd power equals 8.

\(\frac{1}{2^3} (p +24)=9\)

We now need to perform a multiplication. We can use this rule: \(\frac{A}{B} C=\frac{AC}{B}\)

In the example, the factors are in the new numerator are: 1, (p + 24), notice that all non-fraction factors are placed in the numerator. The factors in the denominator are: \(2^3\)

\(\frac{p + 24}{2^3} =9\)

Therefore, our answer is: 48.

p = 48.

Answer:

k = 4

Step-by-step explanation:

(-2)k+1 × (-2)3  = (-2)7​

-2k + -6 = -14

- 2k = -14 + 6

- 2k = - 8

k = -8 / -2

k = 4

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Answer:

A = 2184 cm²

Step-by-step explanation:

the area (A) of the figure is calculated as

A = \(\frac{1}{2}\) h(b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

here h = 42 , b₁ = 52 , b₂ = 52 , then

A = \(\frac{1}{2}\) × 42 × (52 + 52) = 21 × 104 = 2184 cm²

Answer:

A = 2184 cm2

Step-by-step explanation:

Area of a parallelogram:

\(A = b*h\)

\(b=52,h=42\)

\(A=(42)(52)=2184cm^{2}\)

Hope this helps.

Answer:

x- intercept = - 8 , y- intercept = 4

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

x - 2(0) = - 8

x - 0 = - 8

x = - 8 ← y- intercept

to find the y- intercept let x = 0 in the equation and solve for y

0 - 2y = - 8

- 2y = - 8 ( divide both sides by - 2 )

y = 4 ← y- intercept

The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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The equivalent expression is 8^x/16

Exponential equations are inverse of logarithmic equations. Given the expression below;

2^3x-4

This can also be expressed as;

2^(3x-4) = 2^3x/2^4

2^3x-4 =8^x/2^4

2^3x-4 = 8^x/16

Hence the equivalent expression is 8^x/16

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Answer:

x = 7

Step-by-step explanation:

yeah

Answer:

x = 7

Step-by-step explanation:

-4x - 3 = -3x - 10\\ \\

      +3           +3

-4x = -3x + 7

+3x    +3x

-x = 7

/-1  /-1

x = 7

Answer:

  True

Step-by-step explanation:

Substitute for T and evaluate:

  10 -3 ≥ 2

  7 ≥ 2 . . . . . . . true; T=10 is a member of the solution set

Answer:

10%×200=20

Step-by-step explanation:

25%×200=50

35%×200=70

Answer:

Parameter estimates

The coefficient for Px (-5) suggests that there is an inverse relationship between the price of the fruit drink and the quantity demanded. In other words, as the price of the drink increases, the quantity demanded decreases.

The coefficient for M (0.001) suggests that there is a positive relationship between the median annual family income and the quantity demanded. In other words, as the median income increases, the quantity demanded also increases.

The coefficient for Py (10) suggests that there is a positive relationship between the price of the competing brand of fruit drink and the quantity demanded for this brand. In other words, as the price of the competing brand increases, the quantity demanded for this brand also increases.

Step-by-step explanation:

To calculate the monthly consumption of the fruit drink, we plug in the given values into the demand equation,

Qx = 10 - 5(2) + 0.001(20,000) + 10(2.5)

Qx = 10 - 10 + 20 + 25

Qx = 45 liters per family per month.

Therefore, the monthly consumption of the fruit drink per family is 45 liters.

If the median annual family income increased to $30,000, then the new monthly consumption of the fruit drink per family can be calculated as follows,

Qx = 10 - 5(2) + 0.001(30,000) + 10(2.5)

Qx = 10 - 10 + 30 + 25

Qx = 55 liters per family per month.

Therefore, the monthly consumption of the fruit drink per family would increase from 45 liters to 55 liters per family per month.

To determine the demand function, we need to solve for Qx in terms of the other variables,

Qx = 10 - 5Px + 0.001M + 10Py

Qx - 10Py = 10 - 5Px + 0.001M

Qx = (10 - 5Px + 0.001M) / 10Py

Therefore, the demand function is:

Qx = (10 - 5Px + 0.001M) / 10Py

To find the inverse demand function, we need to solve for Px in terms of Qx.

Qx = 10 - 5Px + 0.001M + 10Py

5Px = 10 - Qx - 0.001M - 10Py

Px = (10 - Qx - 0.001M - 10Py) / 5

Therefore, the inverse demand function is,

Px = (10 - Qx - 0.001M - 10Py) / 5

The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Answer:

C) 7 units

Step-by-step explanation:

Count the lines in between

Answer:

Coordinates of the starting point ( -50 ; 0 )

Coordinates 4 seconds later Q ( - 25*√3  ;  25 )

Coordinates 32 seconds later R ( 25  ;  - 25*√3 )

Step-by-step explanation:

a) If Jeremy takes 48 seconds fr a lap then

The length of the lap ( length of the circle ) is:

L =  2*π*r    ⇒   L = 100*π

If the time for one lap was 48 seconds at a constant speed, the speed was

v = 100*π / 48   [m/s]

v = 6,54 m/s

12 seconds  is  1/4 0f 48  in that time he (she) reach the northernmost point, then he(she) necessarily started on the negative side of the       x-axis the coordinates at this point are

( -50 ; 0 )

b) 4 seconds later, at v = 6,54 m/s by rule of three

In 12 seconds                         90⁰

In  4  seconds  (the third part )       x ??

x = 30⁰

sin 30⁰  = 1/2

cos 30⁰ = (√3)/2

And coordinates for the point are

sin 30⁰ =  1/2  = y/50     ⇒  y =  25

cos 30⁰ = (√3)/2  = x / 50   ⇒ x = 25*√3

coordinates of the point 4 seconds later

Q ( - 25*√3  ;  25 )    she (he) is in the negative part of x-axis

c) 32 seconds later

32  is    12   +   12    +    8

Then she (he) is 8 seconds below the positive side of x-axis

8 is 2/3 of 12   ( negative 60⁰ )

sin 60⁰ = (√3)/2   = y/50       y  =  25*√3    negative

cos  60⁰ = 1/2 * 50   =  X/50  x  = 25

Coordinates of the point R

R ( 25  ;  - 25*√3 )

Answer:

I can't see could you take a picture or something

Step-by-step explanation:

Step-by-step explanation:

Simplify: \(9x^2 -4x-3=\) [?] when x= -2

Substitute in -2 for x:

\(9(-2)^2 -4(-2)-3\\= 9(-2)^2 -4(-2)-3\\=9(4) +8 -3\\= 36 + 8 - 3\\\)

x = 41

Answer: = 41

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

Helping in the name of Jesus.

Answer:

50,000

Step-by-step explanation:

The product would be 654,100. Replace the other numbers to find the value of 5. The value of 5 is 050,000 or 50,000.

I hope this helps!

Answer:

First you should know every Liter is 1000ml

so now we know we have a 1000ml bottle of milk

now you should divide 1000 by 300

and the answer is 3 glasses and one third glass

Step-by-step explanation:

mili = 10^-3

liter = dm³

deci = 10^-1

dm³ = (10^-1)³ =10^-3 m³

miliLiter = 10^-3 × 10^-3 = 10^-6m³

300 ml = 3×10² × 10^-6 = 3 × 10^-4

10^-3 ÷ (3× 10^-4)= 3.3333

Answer:

Step-by-step explanation:

1L = 1000 ml

1000 : 300 = 3.33

3 glasses (with the remainder of 0.3333 ml)

If x = -2 is a zero with a multiplicity of one, x = 3 is a zero with a multiplicity of two, and x = 1 is a zero with a multiplicity of one, then the polynomial can be written in factored form as:

\(f(x) = (x + 2)(x - 3)^2(x - 1)\)

To find the polynomial in expanded form, we can use the distributive property and the rules of exponents:

\(f(x) = (x + 2)(x - 3)(x - 3)(x - 1)\\= (x^2 - x - 6)(x - 3)(x - 1)\\= (x^3 - 4x^2 + 3x + 18)(x - 1)\\= x^4 - 5x^3 + 6x^2 + 4x + 18\)

Therefore, the polynomial that has a lead coefficient of one and exactly three distinct zeros, with x = -2 as a zero with multiplicity of one, x = 3 as a zero with multiplicity of two, and x = 1 as a zero with multiplicity of one, is:

\(f(x) = x^4 - 5x^3 + 6x^2 + 4x + 18\)

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Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

The area of a circle can be found using either of the following formulas:

\(\pi r^2\), where π (pi) is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.

\(A = (d/2)^2π,\) where d is the diameter of the circle. This formula can also be written as \($A = r^2\pi$\), where r is the radius of the circle and A is the area.

Both formulas are equivalent and can be used interchangeably, depending on the given information about the circle.

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

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There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

n has no value.

There is no solution to this equation

Step-by-step explanation:

let n be the number

In pieces:

sum of the number and 1: (n + 1)

8 times the sum: 8(n + 1)

-7 times a number: -7n

sum of -7 times and...: -7n + 8(n + 1)

number minus 7: n - 7

the same as: =

All together:

-7n + 8(n + 1) = n - 7

-7n + 8(n+1)=n-7

-7n + 8n+8=n-7

0=-15

Answer:

It would be c.................

Answer:

The correct answer will be 18

Step-by-step explanation:

First mutiply your object of the question which is 9 times 16 then make sure you have the right answer then divide it by 8 and 144 the answer you got, and you get 18

Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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Answer:

A

Step-by-step explanation:

Answer:

£0.50

Step-by-step explanation:

t = one cup of tea

c = one piece of cake

t + c = £1.10

2t + c = £1.70

the cost increases by £0.60 (£1.70 - £1.10) when you order one more cup of tea which means that one cup of tea costs £0.60

substitute £0.60 into t + c = £1.10

£0.60 + c = £1.10

rearrange to get c = £1.10 - £0.60 = £0.50

so one piece of cake costs £0.50

The product of the rational expressions given is; (7x²-7x)/(x²-4)

The given rational expressions are;

Hence, the product of the two Rational Expressions can be evaluated as follows;

The product of the rational expressions given is therefore; (7x²-7x)/(x²-4)

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