A barrel contains 50 gallons of water water leaked out of the barrel at a rate of 5 gallons every 4 days at this rate how many days did it take for all 50 gallons of water to leak out of the barrel

Answer:

It will take 26 years

Step-by-step explanation:

In this question, we are tasked with calculating the time it will take for an amount of money earned to be tripled if compounded continuously.

To calculate this amount of time, we are going to use the formula for compound interest.  Mathematically, for an interest compounded, the amount is as follows;

[tex]A = P(1 + r/n)^{nt}[/tex]

Where;

A is the amount at the end of compounding; which is 3 times the original amount = 3 × $200 = $600

P is the initial amount = $200

r is the rate of compounding = 4.25% = 4.25/100 = 0.0425

n is the number of times in which the amount is compounded annually, we take this as 1

t is the time taken to reach the amount

We substitute these values in the equation;

600 = 200(1 + 0.0425/1)^t

Divide through by 200

3 = (1.0425)^t

Take the logarithm of both sides

log 3 = log(1.0425)^t

log 3 = tlog 1.0425

t = log 3/log1.0425

t = 26.4 which is approximately 26 years

Answer:

A. electrons will fill orbitals of lower energy first, paring up only after each orbital of the same energy already has one electron

Step-by-step explanation:

The rule states that for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs.

Answer:

x =2 or x=7

Step-by-step explanation:

x^2-9x+14= 0

Now splitting the middle term we get,

x^2-7x -2x +14 =0

x(x-7) - 2(x-7) =0

(x-2) (x-7) =0

x-2=0 or x-7 =0

x =2 or x=7

The factors of [tex]x^2-9x+14[/tex] are (x - 7) and (x - 2)

"It is a mathematical statement which consists of variables and constants, and some algebraic operations."

For given question,

We have been given a quadratic expression [tex]x^2-9x+14[/tex]

We need to factorize given quadratic expression.

[tex]\Rightarrow x^2-9x+14\\\\= x^2-7x-2x+14~~~~~~~~...........(-9x=-2x-7x~~and~14=(-9)\times (-2))\\\\=x(x-7)-2(x-7)\\\\=(x-7)(x-2) ~~~~~~~~~~~~............(Seperate~out~common~terms)[/tex]

Therefore, the factors of [tex]x^2-9x+14[/tex] are (x - 7) and (x - 2)

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Answer: Total Surface Area

Step-by-step explanation:

Hi, to calculate the amount of cardboard needed to create a cereal box we have to calculate the total surface area.

The volume is used to calculate the amount of cereal that the box can contain, and the lateral surface area will not include all the cardboard needed for the complete box.

Feel free to ask for more if needed or if you did not understand something.

To calculate the amount of cardboard needed to create a cereal box, we would be solving for the Total Surface Area. This is the sum of the areas of all the faces (or sides) of the box.

When we talk about the amount of cardboard needed to create a cereal box, we are interested in determining the

Total Surface Area

of the box. The surface area is the measure of the total amount of material needed to cover the surface of an object. If we're considering a cereal box, which is a three-dimensional rectangular prism, its total surface area is calculated by summing up the areas of all its six faces (top and bottom, front and back, left and right). Specifically, the formula for the total surface area of a box or rectangular prism is 2lw + 2lh + 2wh where l is the length, w is the width, and h is the height.

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Answer:

[tex]\dfrac{24}{31}[/tex]

Step-by-step explanation:

Given information:

Total number of girls = 14

Total number of boys = 17

Total number of peoples = 14 + 17 = 31

6 girls and 7 boys brought balloons.

Let A and B are two events, such that

A = Choosing a girl

B = Choosing someone who did not bring a balloon.

[tex]A\cup B[/tex] = Choosing girl or someone who did not bring a balloon.

[tex]n(S)=31,n(A)=14,n(B)=18,n(A\cup B)=14+10=24[/tex]

The probability of randomly choosing a girl or someone who did not bring a balloon is

[tex]P=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]P=\dfrac{24}{31}[/tex]

Therefore, the required probability is [tex]\dfrac{24}{31}[/tex].

The probability of randomly choosing a girl or someone who did not bring a balloon at a party is 24 out of 31, which simplifies to the fraction 24/31.

To solve this problem, we can use the concept of probability and the addition rule since the events are not mutually exclusive.

First, let's define the total number of people at the party: 14 girls + 17 boys = 31 people.

Next, we look at the number of girls who brought balloons, which is 6, meaning there are 14 - 6 = 8 girls who did not bring balloons.

Similarly, 17 boys - 7 boys who brought balloons = 10 boys who did not bring balloons.

Now, let's calculate the number of ways to choose a girl or someone who did not bring a balloon. For the girls, it's simply the total number of girls, 14. For those who did not bring balloons, we need to add the number of girls who did not bring balloons to the number of boys who did not bring balloons: 8 girls + 10 boys = 18 people who did not bring a balloon.

Combining these, the event of choosing a girl overlaps with the event of choosing someone who did not bring a balloon, so we have to subtract the number of girls who did not bring a balloon once to avoid double-counting: 14 + 18 - 8 = 24.

Thus, the probability is: 24 out of 31, which we can write as 24/31.

Gummy Bear = 16

Lollipop = 16

Lime = 0

Ring pop = 4

Question mark (total) = 36

Answer:

Arc AB = 80°

Arc AD= 100°

Step-by-step explanation:

Arc AB

Since AC is the diameter, it would be 180°, and since arc BC is given (100°), arc AB would be 80°

Arc AD

Since BD is a diameter, it would also be 180°. Arc ED is given and previously you found arc AB. So subtract 50 and 80 from 180 and you'll get 50° for arc AE. Add that with arc ED and you'll get 100°

Answer:

1. 24      2. 12       3. it is a very easy concept

Step-by-step explanation:easy

Answer:

1x^2

Step-by-step explanation:

Answer:

Density

Step-by-step explanation:

Density is the number of items per unit area. It is gotten by dividing the number of items by the area it occupies. It measures the compactness of an item in a given area. The higher the density, the more compact items are per unit area and the lesser the density, the less compact items are per unit area. It is measured in items/m²

Answer:

a:

[tex]sin(\theta)=\frac{opposite}{hypotenus}[/tex]

[tex]sin(60)= \frac{a}{4\sqrt3}[/tex]

[tex](4\sqrt3)sin(60)= a[/tex]

[tex](4\sqrt3)(\frac{\sqrt3}{2})= a[/tex]

[tex]6= a[/tex]

b:

the answer choices all have the same value for b, so I dont have to solve for b at all.

[tex]b=6\sqrt2[/tex]

c:

[tex]cos(\theta)=\frac{adjacent}{hypotenus}[/tex]

[tex]cos(60)= \frac{c}{4\sqrt3}[/tex]

[tex](4\sqrt3)cos(60)= c[/tex]

[tex](4\sqrt3)(1/2)= c[/tex]

[tex]2\sqrt3= c[/tex]

d:

d is inside a 45-45-90 triangle. Therefore, side a and d must be of the same length.

[tex]d=a[/tex]

[tex]d=6[/tex]

Answer:

3.2 miles

Step-by-step explanation:

Initial fee plus state tax first because they are static:

3.25 + 0.5 = 3.75

Remove the initial charge plus tip from total cost:

14.75 - 3 - 3.75 = 8

Divide by 0.5 to get how many 1/5 of a mile he went:

8 / 0.5 = 16

Divide 16 by 5 to get miles:

16 / 5 = 3.2 miles

Answer:

3.2 miles

Step-by-step explanation:

Initial fee plus state tax first because they are static:

3.25 + 0.5 = 3.75

Remove the initial charge plus tip from total cost:

14.75 - 3 - 3.75 = 8

Divide by 0.5 to get how many 1/5 of a mile he went:

8 / 0.5 = 16

Divide 16 by 5 to get miles:

16 / 5 = 3.2 miles

Answer:

x = -11

Step-by-step explanation:

3x - 4 + 2(x - 5) = 9x + 8 - 2x

3x - 4 + 2x - 10 = 9x + 8 - 2x

3x + 2x - 9x + 2x = 8 + 10 + 4

- 2x = 22

- x = 22/2

- x = 11

x = - 11

The equation 3x - 4+2(x-5)= 9x + 8- 2x can be solved by first simplifying to 5x - 4 = 7x + 8. After re-arranging, it simplifies to -12 = 2x, and therefore, x = -6.

To solve this equation, first simplify and combine like terms on each side of the equation. That gives us: 5x - 4 = 7x + 8. Next, let’s get all the x terms on one side. To do that, we subtract 5x from both sides, which gives us -4 = 2x + 8. Then, subtract 8 from both sides to isolate the 'x', resulting in -12 = 2x. Finally, divide both sides by 2 to find the value of x, which is -6.

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The expression equivalent to the given expression is [tex]\left[\dfrac{1}{(36a^{4}b^{10})}\right][/tex] and this can be determined by using the arithmetic operations.

Given :

Expression  ---   [tex]\left[\dfrac{(2a^{-3}b^4)^{2}}{(3a^5b)^{-2}}\right]^{-1}[/tex]

The following steps can be used in order to evaluate the given expression:

Step 1 - The arithmetic operations can be used in order to evaluate the given expression.

Step 2 - Write the given expression.

[tex]\left[\dfrac{(2a^{-3}b^4)^{2}}{(3a^5b)^{-2}}\right]^{-1}[/tex]

Step 3 - Simplify the above expression.

[tex]\left[\dfrac{1}{(3a^5b)^{2}(2a^{-3}b^4)^{2}}\right][/tex]

Step 4 - Open the brackets and square the given terms in the denominator.

[tex]\left[\dfrac{1}{(9a^{10}b^2)\times (4a^{-6}b^8)}\right][/tex]

Step 5 - Multiply the terms present in the denominator.

[tex]\left[\dfrac{1}{(36a^{4}b^{10})}\right][/tex]

Therefore, the correct option is C).

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Answer:

the answer should be as follows:

-2(q-3)

the closest answer would be A

Answer:

C

Step-by-step explanation:

I just guessed and got it right

Answer:

C. taking the square root of both sides of the equation

Answer:

Accoridng to your question we have to find the square root of 0.0025

However students face some problem in finding square roots of number in decimal but it is too easy to find .

√0.0025

0.05 is the square root of 0.0025

after decimal there are two zero and by square root there will be one zero and 25 is the square root of 5 .

so thus we find the square root amd the correct answer is 0.05

The square root of 0.0025 is 0.05, which follows the rule that the square root of a decimal results in half the number of decimal places in the square root, compared to the original number.

The student has asked to find the square root of 0.0025. When expressed as a square root, the number 0.0025 is equal to 0.05 because (0.05 * 0.05 = 0.0025). This can be understood by recognizing that the decimal places need to be managed correctly when finding the square root of a decimal. For instance, the square root of 25 is 5, and since 0.0025 has four decimal places, the square root will have half as many decimal places, resulting in 0.05. This concept is further emphasized by using fractional powers, such as re-expressing a number squared (x²) as the square root ( √x ), where x to the power of 2 is the same as x to the power of 1/2.

Answer:

c:

Step-by-step explanation:

Answer:

complementary angles are angles that sum up to 90 degrees. that is all I can say because I can't see any diagram

Answer:

complementary angles are angles that sum up to 90°

i can't see any diagram

Answer:

It’s 14

Step-by-step explanation:

Just add

Answer:

1200 apples.

Step-by-step explanation:

The way I thought about this was, you need to figure out how many apples per percent. Thus, I divided 420 by 35, which gave me 12.

We have deduced that every percent = 12 apples.

Multiply 12 by 100 (apples per percent x total percentage)

12 x 100 = 1200

Answer:

The answer is 288 pages are filled with hockey cards

Step-by-step explanation:

First, you need to figure out what percentage of the album is full which is 32% So, with that 32% you figure out how many pages that is. So you would find 32% of 900 which is 288 therefor, that would be your answer.

I hope this helped <3

Answer:

Let's suppose that the ideal blood pressure is 100 (the ideal values are between 90 and 110, i am taking the middle value)

If 125 is the 100%, and we want to go to 100, then we need to decrease by:

125 - 100 = 25

now, to calculate the percentage that represents the 25, we need to calculate:

(25/125)*100% = 20%

So to reduce his blood pressure to normal, he must reduce it by 20%

To find out by what percentage Cory must reduce his blood pressure to normal, subtract the normal from Cory's blood pressure, divide the result by Cory's initial blood pressure, and then multiply by 100. For instance, if normal blood pressure is 120, Cory must reduce his blood pressure by approximately 4%.

To calculate the percentage that Cory needs to reduce his blood pressure, we first need to know the normal blood pressure level. For example, if the normal blood pressure is considered to be 120, then we can proceed as follows:

So, Cory would need to reduce his blood pressure by approximately 4% to return to a normal level, assuming normal blood pressure is 120.

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Answers:

Across->

Housing: Fixed, $950, $11,400, ?

Food: Variable, $650, $7,800,?

Clothing: Variable, $75, $900,?

Transportation: Fixed, $500, $6,000,?

Insurance&medical: Variable, $1,200, $14,400,?

Entertainment: Variable, $100, $1,200,?

Emergency fund: Fixed, $50, $600,?

Saving for C: Fixed, $50, $600,?

Saving for R: Fixed, $100, $1,200,?

Step-by-step explanation:If it is the cost monthly you are looking for, divide the yearly cost by 12. If you are looking for yearly cost, multiply the monthly cost by 12.

And if you would like to know what a variable and fixed expense is, the variable expense is the expense that can change, so say for instance, food isn’t gonna cost at two different places, so it’s variable. A fixed expense is an expense that is regularly paid and always the same cost.

Answer:

Housing: Fixed, $950, $11,400, 23.3%

Food: Variable, $650, $7,800, 16%

Clothing: Variable, $75, $900, 1.8%

Transportation: Fixed, $500, $6,000, 12.3%

Insurance&medical: Variable, $1,200, $14,400, 29.5%

Entertainment: Variable, $100, $1,200, 2.5%

Emergency fund: Fixed, $50, $600, 1.2%

Saving for C: Fixed, $50, $600, 1.2%

Saving for R: Fixed, $100, $1,200, 2.5%

Step-by-step explanation: Added correct percentages...

Answer:

The length of BC is needed because it is the side opposite ∠A.

Step-by-step explanation:

Given the right angles triangle as shown in the attachment, we can get sin(A) without using Pythagoras theorem. Instead we will use SOH CAH TOA trigonometry identity.

According to SOH:

Sin(A) = Opposite/Hypotenuse

Sin(A) = |BC|/|AB|

Opposite side of the triangle is the  side facing ∠A.

Based on the formula, we will need to get the opposite side of the triangle which is length BC for us to be able to determine sinA since the hypotenuse is given.

Answer:

Bc is needed because it is opposite of A

Step-by-step explanation:

Answer:

15 - 3(8³) = 3y³

Step-by-step explanation:

5 – 8³ = y³

3(5 - 8³) = 3(y³)

15 - 3(8³) = 3y³

Answer:

15-8=y

Step-by-step explanation:

Answers: A fraction is a perfect square if it's reduced version (of an improper fraction if the number is greater than 1) has both numerator and denominator numbers that are perfect squares. IE: 25/36 is a perfect square because both 25 and 36 are perfect squares.

Step-by-step explanation:

So for example 5/25 is a perfect square but 2/5 wouldn't be a perfect square.

Tell me if this helped you

If a fraction can be expressed as the product of two equal fractions, it may also be expressed in its simplest form as a perfect square.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

A fraction is a perfect square if both the numerator and the denominator of its reduced version, which is an improper fraction if the integer is greater than 1, are perfect squares. To put it another way, 25/36 is a perfect square as 25 and 36 are both perfect squares.

Thus, if a fraction can be expressed as the product of two equal fractions, it may also be expressed in its simplest form as a perfect square.

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Answer:

848 ft³

Step-by-step explanation:

The volume of a cylinder is given as:

V = pi * r² * h

Where r = radius of the cylinder

h = length of the cylinder.

The diameter of the cylindrical pipe, d = 6 ft

The radius of the cylindrical pipe, r = d/2 = 6 / 2 = 3 ft

The length of the cylindrical pipe, h = 30 ft

The volume of the cylindrical pipe is:

V = 3.14 * 3² * 30

V = 847.8 ft³ = 848 ft³ (to the nearest whole number)

The volume of the cylindrical pipe is 848 ft³.

The volume of a cylindrical construction pipe with a diameter of 6 ft and length of 30 ft can be calculated using the formula for the volume of a cylinder (V = πr²h). Given the specifics, the volume of the pipe is approximately 848 cubic feet.

The subject of this question is determining the volume of a cylinder, in this case, a construction pipe. The formula used to calculate the volume of a cylinder is V = πr²h. Here, the diameter of the cylindrical pipe is 6 ft, therefore radius (r) is half of diameter which is 6/2 = 3 ft and the length of the pipe, h, is 30 ft. Substituting r and h into the equation, we have V = 3.14 * (3ft)² * 30ft = 3.14 * 9ft² * 30ft = 847.8 cubic feet. Rounding to the nearest whole number, the volume of the pipe is approximately 848 cubic feet. The unit of volume in this instance is cubic feet, which is a measure of space occupied by a three-dimensional object.

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Answer:

4 m/s downwards

Step-by-step explanation:

Velocity is given by dividing the distance by time taken to cover the diatance. Therefore, expressed as v=d/t

The distance is given as 24 m but the time given covers only half the distance. Therefore, the distance is 0.5*21=12 m

Time taken is given as 3 s

Substituting 12 m for d and 3 s for t then

V=12/3= 4 m/s

Velocity must have direction component hence velocity is 4 m/s downwards