40 POINTS. WILL AMRK BRAINLIEST!!! NEED ASAP
Dave's sister baked 3 dozen pies of which a third contained chocolate, a quarter contained marshmallows, a sixth contained cayenne, and one twelfth contained salted soy nuts. What is the smallest possible number of pies that had none of these ingredients?

Answer:

First problem: 89.07 grams

Second problem: 3910.15 days

Step-by-step explanation:

We can solve these problems with the exponencial equation:

P = Po * (1+r)^t

Where P is the final value, Po is the inicial value, r is the rate and t is the time.

In the first problem, the half-life is 119.77 days and Po = 100, so we have that:

P = 100 * (1-0.5)^(t/119.77)

So after 20 days, we will have:

P = 100 * (1-0.5)^(20/119.77) = 89.07 grams

For the second problem, we have the half-life of 5730 days, and the final value over the inicial value is 62.31%, so:

P/Po = (1-0.5)^(t/5730)

0.6231 = 0.5^(t/5730)

log(0.6231) = log(0.5^(t/5730))

-0.4730 = (t/5730)*log(0.5)

-0.4730 = (t/5730)*(-0.6931)

(t/5730) = 0.6824

t = 0.6824 * 5730 = 3910.15 days

Using the formula for half-life calculation, approximately 82.57 milligrams of Selenium left after 20 days. Based on the amount of Carbon-14 left, the last eruption of the volcano occurred approximately 3896 years ago.

The calculation of remaining amount of a given isotope relies on the understanding of what is called a half-life. In the case of selenium, with a half-life of 119.77 days, we are looking at 20 days had passed. This would be a fraction of the half-life (20/119.77 = 0.167). The amount left can be calculated by the formula N = N0 * (1/2)^(t/T), where N is the final amount, N0 is the initial amount, t is the elapsed time, and T is the half-life. This becomes 100 * (1/2)^(0.167) which results in approximately 82.57 milligrams of Selenium left.

For the interval of carbon-14 relating to the volcano eruption using a half-life of 5730 years, we know from the sample that 62.31% of the original amount remains. This relates to 0.623 as the fraction of half life that has passed. Using the formula log2(1/0.623) we get approximately 0.68 half-lives. From this, we can find the time passed, which is half-life times the number of half-lives. This results in 5730 * 0.68 = approximately 3896 years ago for the last eruption.

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Answer:

9.09 %

Step-by-step explanation:

1). 6000 / 3 = 2000 $ interest per year

2). 2000 / 22 000 = 9.09 %

Answer:

Base = 8 feet

Step-by-step explanation:

[tex]area \: of \: \triangle = \frac{1}{2} \times base \times height \\ 16 = \frac{1}{2} \times base \times 4 \\ 16 = base \times 2 \\ base = \frac{16}{2} \\ base = 8 \: feet[/tex]

The shapes don't really play a role in this story, do they.  Both points are on the horizontal line y=5 so the distance between them is the absolute difference of the x coordinates, 5- -3 = 8

Answer: 8

The distance between the centers of the circle and triangle is 8.

The distance between two points of a line is given as:

Distance = [tex]\sqrt{(c - a)^2 + (d - b)^2}[/tex]

Where (a, b) and (c, d) are the two points.

We have,

The centre of a circle = (5, 5)

The centre of a triangle = (-3, 5)

Consider (a, b) = (5, 5) and (c, d) = (-3, 5)

The distance between the centre of a circle and the centre of the triangle.

= √(-3 - 5)² + (5 - 5)²

= √(64 + 0

= √64

= 8

Thus,

The distance between the centres is 64.

Learn more about the distance of a line here:

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Answer:

x = 3, y = 0

Step-by-step explanation:

2x - 2y = 6

x - y = 3

x = 3 + y

3(3 + y) + 2y = 9

9 + 3y + 2y = 9

5y = 0

y = 0

x = 3 + 0

x = 3

Answer:

A:(2m^4n^3)^3(5m^4n^3)^2

Step-by-step explanation:

Answer:

The area is approximately 453 ft²

Step-by-step explanation:

Area of a circle = [tex]\pi r^{2}[/tex]

If [tex]\pi[/tex] = 22/7, and  r = 12 ft

Area = (22/7)×12²

= 3.143*144

= 452.592 ft²

≈ 453 ft²

Answer:

2 * 2 * 2 * 2 * 5

Step-by-step explanation:

Answer:

2^4*5 OR 2*2*2*2*5

Step-by-step explanation:

using prime factorization

factors of 80 are 10*8 then factor 8 and 10 and so on until you are left with all prime numbers.

Hope this helps!

Answer:

D 1/11 m/s

Step-by-step explanation:

Method 1:

d=11s

the unit is m/s which is d/s

meter is 1 here, and time is 11

so, 1/11 meter per second.

Method 2:

First remove A and C, which is obviously not related

B is obviously too fast for a rabit, and thus the answer is D.

Answer: B. d - 0.2

Step-by-step explanation: 20%= 20/100= 0.2

Which means = d-0.2

Hope this helped.

Answer:

B: d- 0.2

Step-by-step explanation:

Answer:

Here we can see they are vertically opposite angles so x = 35°

x=35

bcoz they are vertically opposite angles.

As we know vertically opposite angles are equal.

Answer:

540 degrees

Step-by-step explanation:

Answer:

the correct answer is C 540 degrees

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Each year, the population of the town increases by a rate of 4%, or 0.04.

In order to find the answer, you need to multiply the population of that year by 1.04. 1.04 is used in order to add the 4% to the overall total.

At the end of the first year, the population is 3250. (3125 x 1.04)

At the end of the second year, the population is 3380. (3250 x 1.04)

Answer:

7/21

Step-by-step explanation:

Answer:

1/729

Step-by-step explanation:

Just multiply 3 for the amount of rounds there are (6) so 3^6 is equal to 729

Answer:

The distance in miles that the cities are apart is 40 miles

Step-by-step explanation:

To get from 1 inch to 8 inches, you multiply by 8. This means you multiply 5 miles by 8 to get 40 miles.

Answer:40 miles

Step-by-step explanation:

because 1 inch is 5 miles and the cities are 8 miles apart so 8x5=40.

An employee at a cell phone store sold 40 phones for $450 each, totaling $18,000 in sales. Based on her commission rate of 2.5%, she earns $450 in commission for the week.

The subject of this question is how to calculate the employee's commission based on her sales. First, we need to calculate the total sales the employee made. She sold 40 phones at $450 each, so her total sales would be 40 * $450 = $18,000.

Next, we need to figure out what 2.5% of her total sales is because this is her commission rate. The calculation would be $18,000 * 2.5/100 = $450.

So, the employee's commission for this week is $450.

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Answer: 128

Step-by-step explanation:

[tex]width: 2x^2-3\\height:7\\S=7(2x^2-3)\\S=14x^2-21[/tex]

Answer:

The total number of combinations is 2,358,720,000

Step-by-step explanation:

For the letter part of the ID we have 3 letters out of a space of 26 possible letters (a-z), and they can't repeat. For the number part we want to group 5 numbers out of 10 possible algarisms (0-9).So we can make an arrangement for the letters and one for the numbers and multiply them. The arrangment can be done using the following formula:

A(n,k) = (n!)/(n-k)!

Where n is the total number of possibilities and k is the size of the group.

For the letters:

A(26,3) = (26!)/(26-3)! = (26!)/(23!) = (26*25*24*23!)/(23!) = 26*25*24 = 15600

For the numbers:

A(10,5) = (10!)/(10 - 5)! = 10!/5! = (10*9*8*7*6*5!)/(5!) = 10*9*8*7*6*5 = 151200

The total number of combinations is the product of both, so:

combinations = 15600*151200 = 2,358,720,000

Divide the perimeter by 2:

6x + 4 / 2 = 3x+2

This is one length plus one width.

Now subtract the width to find the length:

3x +2 - x-1 = 2x+ 3

Length is 2x+ 3

Answer:

2x+3 or C

edge2021

Answer:

The answer is A, 14 inches.

Answer:

13

Step-by-step explanation:

f(x) = 10/2 + 8 = 5 + 8 = 13

Look at the attached picture⤴

Hope it will help u...

I think that the answer would be 0.52 if you round it

Answer:

The image will be congruent to the pre-image because n = 1.

Answer:

Awsner number 2

Step-by-step explanation:

There are 3 red out of 7 total so red will be 3/7

There are 4 blue out of 7 total so blue will be 4/7

After he picks one he puts it back so every red will be 3/7 and every blue will be 4/7

B) multiply the probability of picking a red one by the probability of picking a red one again:

3/7 x 3/7 = 9/49 probability of picking 2 red ones.

Answer:

6; solution is not extraneous

Step-by-step explanation:

[tex]\sqrt{3x-2} =4[/tex]

[tex](\sqrt{3x-2})^{2} = (4)^2[/tex]

[tex]3x-2= 16[/tex]

[tex]3x = 18[/tex]

[tex]x =6[/tex]

[tex]\sqrt{3(6)-2}=4[/tex]

[tex]\sqrt{18-2}=4[/tex]

[tex]\sqrt{16} =4[/tex]

[tex]4=4[/tex]

6; solution is not extraneous

because 4 is equal to 4, an extraneous answer would be the correct answer given, however when you plug it into the equation it is not equal

Answer:

y - 1 = -4(x+3)

Step-by-step explanation:

We will use the point slope form of a line

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is the point

y - 1 = -4(x--3)

y - 1 = -4(x+3)