32 slices from 4 cakes = slices from 5 cakes

Answer:

[Tex]A(t)=5000(0.7)^t[/tex]

Step-by-step explanation:

The problem presented is one in which the population of the bacteria  depreciates by a decay factor r every year.

Since it is a decay problem, we use the model:

[Tex]A(t)=P(1-r)^t[/tex]

Initial Population, P=5000

Decay Rate,r=30%=0.3

t=time interval

Therefore, the equation that represents this situation is:

[Tex]A(t)=5000(1-0.3)^t[/tex]

[Tex]A(t)=5000(0.7)^t[/tex]

The equation that represents this situation is y = 5000(0.7)ˣ

An exponential decay is given by:

y = abˣ

where a is the initial value of y, b is the rate of decay and y, x are variables.

Since the culture begins with 5000 cells, hence a = 5000. The cells die by 30% each year, hence b = 100% - 30% = 0.7

The equation is: y = 5000(0.7)ˣ

Therefore the equation that represents this situation is y = 5000(0.7)ˣ

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Answer:

34

8

Step-by-step explanation:

1/2bc - 6ac + 2ab

(1/2)(-1)(-3) - (6)(2)(-3) + (2)(2)(-1)

(1/2)(4) - (-36) + (-4)

2 + 36 - 4

34

1/4(ac)² + 1/6ac

(1/4)[(2)(-3)]² + (1/6)(2)(-3)

(1/4)(-6)² + (1/6)(-6)

(1/4)(36) + (-1)

9 - 1

8

Answer:

it's 90%

Step-by-step explanation:

1. Divide 18 by 20 and you will get a decimal form answer

2. Then you multiple it by 100 and you will get your answer which is 90.00%

18 out of 20 is 90 percent.

To find the percentage of 18 out of 20, you can follow these steps:

1. Divide the given number (18) by the total number (20).

18 ÷ 20 = 0.9

2. Multiply the result by 100 to get the percentage.

0.9 × 100 = 90

Therefore, 18 out of 20 is 90 percent.

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Answer:

95%

Step-by-step explanation:

Step 1: 38/40= 0.95

Step 2: multiply 0.95x100= 95

You have

[tex]\dfrac{x}{20}=\dfrac{4}{5}[/tex]

Multiply both sides by 20:

[tex]20\cdot\dfrac{x}{20}=\dfrac{4}{5}\cdot 20[/tex]

The equation becomes

[tex]x=16[/tex]

Hi

X/20 = 4/5 ⇒  X =   20*4 /5  =   5*4*4 /5 = 16/1 =16

16/20 = 4/5

Answer:

Step-by-step explanation:

(0,2)  (1,0)

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{0-2}{1-0}\\\\=\frac{-2}{1}\\\\=-2[/tex]

Answer: 10 + 1/2 spoons of vanilla.

Step-by-step explanation:

This question says:

For 1kg of cake, we need 1/3 kg of flour and 3 spoons of vanilla.

How much vanilla do we need if we want to make a cake of 3 + 1/2 kg?

Ok, if for 1kg we need 3 spoons, then for (3 + 1/2)kg we need (3 + 1/2) times 3 spoons, this is:

(3 + 1/2)*3 spoons

=3*3 + 3/2 = 9 + 3/2 = 9 + 2/2 + 1/2 = 10 + 1/2

We need 10 + 1/2 spoons of vanilla.

Answer:

42 - 24n

Step-by-step explanation:

(7-4n)  6

Distribute

7*6 - 4n*6

42 - 24n

Answer:

42 x - 24 x n - i = 0

Step-by-step explanation:

Expand the following:

6 x (7 - 4 n) = i

6 x (7 - 4 n) = 6 x×7 + 6 x (-4 n):

6×7 x - 4×6 x n = i

6×7 = 42:

42 x - 4×6 x n = i

6 (-4) = -24:

42 x + -24 x n = i

Subtract i from both sides of 42 x - 24 x n = i:

42 x - 24 x n - i = i - i

-i + i = 0:

Answer:  42 x - 24 x n - i = 0

The inverse of the function f(x) = 1/5x is found by switching the roles of y and x, then solving for y. This results in the inverse function f^-1(x) = 5x, which undoes the effect of the original function.

The inverse of a function, in this case f(x) = 1/5x, is the function that will reverse the effect of the original function. In this case, to find the inverse function of f(x), you swap the roles of y and x in the original function and solve for y.

So, f(x) = 1/5x becomes x = 1/5y. Multiply both sides by 5 to get rid of the denominator on the y-side, which results in 5x = y. Thus, the inverse function is f^-1(x) = 5x.

It's indeed an inverse function as it reverses the effect of the initial function f(x).

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Answer:

0.72

Step-by-step explanation:

[tex] \cos \: 44 \degree = 0.7193398003 \\ \cos \: 44 \degree =0.72[/tex]

Answer:

i am very sorry but i am trying to solve it so wait a few minutes please

Step-by-step explanation:

Answer: D

x+3/x-3

Step-by-step explanation:

Answer:

18 and 38

Step-by-step explanation:

Data set is given:

The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

Lower half of the data:

Lower quartile:

Upper half of the data:

Upper quartile:

Answer:

Upper: 38

Lower: 19

Step-by-step explanation:

~I hope this helps~

Answer:

Step-by-step explanation:

Given

x times by 9

Required

Write out an algebraic expression for the above.

Follow the instructions below to get the algebraic expression of the above.

1. First, write out the variable: x

2. Then write out an expression for "times by 9". This means multiply x by 9.

So, this gives x * 9.

x * 9 = 9x.

Hence, the expression for the above question is 9x

Answer:

170 degrees

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary, meaning that they add up to 180 degrees. This means that x+10=180, or that x=170 degrees. Hope this helps!

Answer:

C =  144*pi  cubic units  (cylinder)

V  =  27*pi cubic units (cone)

Step-by-step explanation:

Cylinder r=3 H=16

cone d=6 H=9​

I know what you mean.

You want volume.

C = (pi)*r^2 * h

V = (1/3)*(pi) *r^2 * h   for a cone

---------------------------

C = (pi) * (3)^2 * 16 =  144*pi  cubic units  (cylinder)

V = (1/3)*(pi)*(3^2) * 9 =  27*pi cubic units (cone)

Answer:

the area of the circle is [tex]2.25\pi\ cm^2[/tex].

Step-by-step explanation:

We have,

Circumference of a circle is 3π cm

Formula of circumference of a circle is given by :

[tex]C=2\pi r[/tex]

r is radius of circle

[tex]r=\dfrac{C}{2\pi}\\\\r=\dfrac{3\pi }{2\pi}\\\\r=1.5\ cm[/tex]

Area of a circle is given by :

[tex]A=\pi r^2\\\\A=\pi (1.5)^2\\\\A=2.25\pi\ cm^2[/tex]

So, the area of the circle is [tex]2.25\pi\ cm^2[/tex].

Answer:

(-3+5)+(3n-n) = 2+2n

Step-by-step explanation:

Answer:

Step-by-step explanation:

To calculate the interest paid by ethan on the borrowed bike using the formula.

Simple Interest = Principal * rate * time/100

Principal =  $2,190, rate = 2.5%, time = 3years

On substitution

SI = [tex]\frac{2190*3*2.5}{100}[/tex]

[tex]SI = \frac{16,425}{100}\\ SI= $164.25[/tex]

The interest ethan will pay is $164.25

Ethan will pay $164.25 in interest for the loan he took for a new dirt bike, calculated using the formula for simple interest (I = PRT) with P as the principal ($2,190), R as the rate (2.5% or 0.025), and T as the time (3 years).

To calculate simple interest, you can use the following formula: I = PRT, where I is the Interest, P is the principal amount (original amount borrowed), R is the interest rate (in decimal form), and T is the time in years. In this case, the principal amount is $2,190, the interest rate is 2.5% or 0.025 as a decimal, and the time is 3 years.

You would then plug these values into the formula to get:

I = 2190 * 0.025 * 3

After calculating that, we would find that Ethan will pay $164.25 in interest.

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The area of the base of the triangular prism-shaped pencil holder is 18 square centimeters, calculated by dividing the given volume of 216 cm³ by the height of 12 cm.

The question asks for the area of the base of a pencil holder with a given volume and height, shaped like a triangular prism. To find the area of the base of the pencil holder, we can use the formula for the volume of a prism: Volume = Base Area  imes Height. Since the volume and height are given, we can rearrange the formula to solve for the Base Area as follows:

Base Area = Volume / Height

Plugging in the values given:

Base Area = 216 cm³ / 12 cm

Base Area = 18 cm²

Therefore, the area of the base of the pencil holder is 18 square centimeters.

Answer:

5 steps.

Step-by-step explanation:

hope it helps!

Final answer:

The diameter of a circle with a radius of 1 foot is 2 feet.

Explanation:

The radius of a circle is half the diameter. So, if the radius (r) of a circle is given as 1 foot, the diameter (d) is simply twice the radius. Therefore, the diameter is:

d = 2 × r

d = 2 × 1 ft

d = 2 ft

Hence, the diameter of the circle is 2 feet.

The percentage decrease in price from $90 to $63 is 30%.

To find the percentage decrease in price, we need to calculate the difference between the old price ($90) and the new price ($63), and then divide that difference by the old price. Finally, we multiply the result by 100 to get the percentage.

Step 1: Calculate the difference: $90 - $63 = $27

Step 2: Divide the difference by the old price: $27 / $90 = 0.3

Step 3: Multiply the result by 100 to get the percentage: 0.3 * 100 = 30%

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Answer:

3n - 6 = 38

3n -6 + 6 = 38 + 6

3n = 44

3n/3 = 44/3

n = 44/3

Step-by-step explanation:

1. set up the equation (the - affect the 6 not the 3)

2. add 6 to both sides

3. divide both sides by 3 to get n

Answer:

its 5760ins

Step-by-step explanation:

80 inches * 36 inches * 2 inches = 5760 inches3

good day, and be safe

∵∴∵∴∵∴∵∴∵      

⊕ΘΞΠΤ⊕      

∵∴∵∴∵∴∵∴∵

Answer:

1/12

Step-by-step explanation:

If the Captain hits the pirate ship, it won't affect whether she's also hit by the pirate's cannons (and vice-versa), because they both fired at the same time. So, these events are independent.

Since they are independent, in order to get the probability that both the pirate and the Captain hit each other's ships, we just need to multiply together the probability that the captain hits and the probability that the pirate hits.

The probability that the Captain hits is 1/2

The probability that the pirate hits is 1/6

So, the probability that both the pirate and the Captain hit each other's ships is 1/2 * 1/6 = 1/12

Final answer:

The probability that Captain Jessica and the pirate Michael hit each other's ships simultaneously is 0.0835 or 8.35%, calculated by multiplying the individual probabilities of each hitting the other's ship (0.5 for Captain Jessica and approximately 0.167 for the pirate).

Explanation:

To calculate the probability that both Captain Jessica and the pirate Michael hit each other's ships when they fire their cannons at the same time, we must consider each event independently and then multiply the probabilities of the two events since they are independent. Le'ts calculate the combined probability step-by-step.

First, we know that Captain Jessica has a probability of hitting the pirate ship which is ½ or 0.5.

Second, the dread pirate Michael has a probability of hitting the Captain's ship which is ⅙ or approximately 0.167 (1 divided by 6).

Since these are independent events, we multiply the two probabilities to find the combined probability of both events occurring together: 0.5 * 0.167 = 0.0835.

Therefore, the probability that both Captain Jessica and the pirate Michael hit each other's ships simultaneously is 0.0835 or 8.35%.

Answer:

The width is 5 and the length is 11

Step-by-step explanation:

The formula for perimeter is

P = 2(l+w)

We know the perimeter is 32

32 = 2 (l+w)

Divide each side by 2

32/2 = 2(l+w)

16 = l+w

We know the length is 6 longer than the width

l = w+6

16 = w+6+w

Combine like terms

16 = 2w+6

Subtract 6 from each side

16-6 = 2w+6-6

10 = 2w

Divide by 2

10/2 = 2w/2

5 =w

The length  is

l = w+6

   5+6 = 11

Answer:

V = 24 mi^3

Step-by-step explanation:

The volume is given by

V = l*w*h

V = 4*3*2

V = 24 mi^3

Answer:

The answer is %33,33.

Step-by-step explanation:

Depending on the information given in the question, we can see that Judith received a score of 85 or higher in one of her three tests.

So we can calculate her probability of receiving 85 or higher as 100/3 = %33,33.

I hope this answer helps.

Answer: the answer is 12