A water tank holds 18,000. How long will it take for the water level to reach 6000 gallons if the water used at an average rate of 450 gallons per day?

Answer:

52.5

Step-by-step explanation:

You would use the Pythagorean theorem to solve this. Using the formula,

a^2 + b^2 = ^2

You would have an equation of 50^2 + 16^2 = c ^2.

50^2 is 2500, and 16^2 is 256.

There, you have 2500+256 = c^2

add those together, and you have 2756.

Now, you have to find the square root of 2756 (to solve 2756 = c^2)

which leaves you with 52.4976189936 . Rounded to the nearest tenth, you end up with 52.5.

Answer:

Option C

Step-by-step explanation:

Answer:

B.

You need to subtract 1 term because you don't include the starting 5

4^10 - 1 =  4^9

You multiply 5 by 4 each time for 9 times so it is 5 x 4^9

Hope this helps

Step-by-step explanation:

Sarah earns $120 per week from her part-time job. To complete the table, we need to list her expenses.  Sarah's expenses may vary, but here are some common examples she might have:

1. Transportation: Sarah may spend money on bus fare or gas if she drives. This expense depends on her mode of transportation and how far she travels.
2. Food: Sarah needs to eat, so she may spend money on groceries or meals outside. The amount spent on food will depend on her eating habits and whether she eats out frequently or cooks at home.
3. Utilities: Sarah may have to pay for utilities like electricity, water, and internet. The cost of utilities can vary depending on the region and the size of her living space.

4. Rent/ Mortgage: If Sarah lives independently or contributes to household expenses, she may have to pay rent or contribute to a mortgage payment.
5. Entertainment: Sarah may have expenses related to leisure activities such as going to the movies, concerts, or other entertainment events.
These are just a few examples, and Sarah's actual expenses may differ. It's important for her to track her spending to understand where her money goes. By doing so, she can budget effectively and make informed financial decisions.

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Answer: Numeric is anything of, relating to, or containing numbers. The numbering system consists of ten different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If a value is an alphanumeric, it contains letters and numbers.

Step-by-step explanation:

A drug administered 50 mg every three hours and the drug decays 12% per hour, the limiting value is approximately 416.67 mg.

To find the limiting value, we need to determine the amount of the drug remaining after each administration and observe how it approaches a stable value over time.

First, let's calculate the decay factor per hour. The drug decays by 12% per hour, which means it retains 88% of its previous value after each hour.

Decay factor = 1 - 0.12 = 0.88

Now, let's calculate the amount of drug remaining after each administration:

After 1st administration: 50 mg

After 2nd administration: 50 mg * 0.88 = 44 mg

After 3rd administration: 44 mg * 0.88 = 38.72 mg

After 4th administration: 38.72 mg * 0.88 = 34.04 mg

After 5th administration: 34.04 mg * 0.88 = 29.92 mg

As we can see, the amount of drug remaining decreases with each administration, approaching a limiting value. To find this limiting value, we can continue the pattern or use a formula.

The formula for the limiting value of a drug administered every three hours is:

Limiting value = dosage / (1 - decay factor)

In this case, the dosage is 50 mg, and the decay factor is 0.88.

Limiting value = 50 mg / (1 - 0.88) = 50 mg / 0.12 ≈ 416.67 mg (rounded to two decimal places)

Therefore, the limiting value is approximately 416.67 mg.

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Answer:

D) Angle angle angle

Answer:

This number is neither repeating or irrational.

Step-by-step explanation:

An irrational number is a number with a never-ending decimal that does NOT repeat. This number would be considered rational.

(a) The equation of motion is x'' - 0.0971x = 0.

(b) The amplitude is 0.667 ft and the period is 11.53 s.

(c) The mass completes 0 complete cycles at the end of 3π seconds.

(d) The mass passes through the equilibrium position heading downward for the second time at 0.669 seconds after it is released.

(a) To find the equation of motion for this system, we can use the formula:

mx'' + kx = 0

Where m is the mass, k is the spring constant, and x is the displacement from equilibrium.

First, we need to find the spring constant, k.

We can use Hooke's Law, which states that the force exerted by a spring is proportional to its displacement from equilibrium:

F = -kx

Where F is the force exerted by the spring, and x is the displacement from equilibrium.

We know that when the mass weighs 64 pounds,

The spring stretches 0.32 feet.

Converting pounds to force using the formula F = mg,

Where g is the acceleration due to gravity (32.2 ft/s²), we get:

F = 64 lb (1/32.2 ft/s²)

  = 1.9888 lb ft/s²

We also know that the displacement from equilibrium is 0.32 feet. Substituting these values into Hooke's Law, we get:

1.9888 lbft/s² = -k 0.32 ft

Solving for k, we get:

k = -6.215 lb/s²

Now we can substitute m and k into the equation of motion and simplify:

mx'' + kx = 0 64 lb

x'' - 6.215 lb/s² x = 0

x'' - 0.0971x = 0

This is a second-order linear homogeneous differential equation with constant coefficients. The general solution is:

x(t) = c1 cos(√(0.0971)t) + c2sin(√(0.0971)t)

Where c1 and c2 are constants determined by the initial conditions.

(b) The amplitude and period of motion can be found from the general solution. The amplitude is the maximum displacement from equilibrium, which is equal to the initial displacement of the mass:

A = 8 in

  = 0.667 ft

The period is the time it takes for one complete cycle of motion, which is given by:

T = 2π /Ω

Where Ω is the angular frequency, which is equal to √(k/m):

Ω = √(6.215 lb/s² / 64 lb)

   = 0.544 rad/s

Substituting this value into the formula for the period, we get:

T = 2π/0.544 s

  = 11.53 s

(c) To find the number of complete cycles completed by the mass in 3π seconds, we can divide the time by the period:

n = (3πs) / (11.53 s/cycle)

  = 0.817 cycles

Since the mass cannot complete a fraction of a cycle, we can say that the mass completes 0 complete cycles at the end of 3πseconds.

(d) To find the time at which the mass passes through the equilibrium position heading downward for the second time,

We first need to find the phase shift, ∅, of the motion. The phase shift is the amount by which the motion is shifted to the right or left from the equilibrium position.

In this case, the motion is shifted to the right by π/2 radians, since the mass is released from a point 8 inches above the equilibrium position.

The general solution for x(t) can be rewritten as:

x(t) = A cos(√(0.0971)t - ∅)

Where A is the amplitude and phi is the phase shift.

Since we know that the mass is heading downward at this point,

we can set x'(t) = -5 ft/s and solve for t:

x'(t) = -A √(0.0971) sin(√(0.0971)t - ∅)

      = -5 ft/s

Solving for t, we get:

t = ∅/√(0.0971) + arcsin(5/(A√(0.0971)))

Substituting in the values for A, ∅, and solving, we get:

t = 0.669 s

Therefore, the mass passes through the equilibrium position heading downward for the second time at 0.669 seconds after it is released.

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Answer:

243m²

Step-by-step explanation:

work out 18x18=324

work out 9x9=81.

324-81= 243

Answer:

4 * 50 = 200

Step-by-step explanation:

Because he is descending at a rate of 4 feet every minute, after 50 minutes he is 200 feet down.

Answer:

Don’t really know what the question is, but these are the answers for x

Answer:

A=105.84

Step-by-step explanation:

Explanation is in the file. This is real. I just typed it up and took a screenshot. If you don't trust me, then don't look.  

Please brainliest! I worked so hard!

The explicit formula for geometric sequence calculator is  n = a 1 + r^(n-1) (n-1)

We can easily determine the value of any term in the sequence using the formula once you have those values.

where:

The sequence's nth word is a n.

The first term in the series is a 1.

The frequency of successive terms is expressed as r.

The sequence's length, n, is given.

The values of a 1, r, and n must be known in order to use this algorithm as a geometric sequence calculator. You can easily determine the value of any term in the sequence using the formula once you have those values.

Therefore, the explicit formula for geometric sequence calculator is  n = a 1 + r^(n-1) (n-1).

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She needs to deposit of amount  $92,421.48 today to do this.

We need to find out the present value of $1,000 per month for the next 10 years by considering the interest rate and compounding period given. We are given,Anita wants to withdraw $1,000 per month for the next 10 years.The bank pays interest at 6% compounded monthly.We can calculate the present value of $1,000 per month for the next 10 years by using the formula for Present Value of Annuity. The formula for Present Value of Annuity is given by:PVA= A((1- (1+r)^-n)/r), wherePVA = Present Value of AnnuityA = Amountn = Number of Periodsr = Interest Rate per PeriodFirst, we calculate the interest rate per period as follows:r = 6% per annum/ 12 monthsr = 0.5% per monthNumber of periods (n) = 10 years x 12 months per year = 120 months Amount of Annuity (A) = $1,000Using the above values, we can calculate the present value of the annuity as follows:PVA = 1000 * ((1- (1+0.5%)^-120)/(0.5%))PVA = $92,421.48Therefore, she needs to deposit $92,421.48 today to do this. Therefore, the correct option is $92,421.48.

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Answer:

64 students drink coke only

34 students drink pepsi only

Step-by-step explanation:

Here, we want to know the number of students that drink coke only and number of students that drink pepsi only.

Let the number of students that drink both be x

Mathematically,

n(μ) = 119 where μ represents the universal set

n(P) = 39

n(C) = 69

n(C n P) = x

n(C n P)’ = 16

n(P) only = 39 - x

n( C) only = 69 - x

Mathematically;

119 = (69-x) + (39-x) + x + 16

119 = 69 + 39 + 16 -2x + x

119 = 124 - x

x = 124 - 119

x = 5

So the number of students drinking pepsi only = 39 -5 = 34

The number of students drinking coke only = 69-5 = 64

Answer:

If you want to derive an equation from the question, you answer is:

3*x+4<-62

If you want the solved equation for x, your answer is:

x<-22

(Depending on what your question is)

Step-by-step explanation:

For the first answer, you can represent the unknown number as x. Three times is equivalent to 3 multiply, so it will look like 3*x, or just 3x. Increased by four is just adding four, so your equation will now look like 3x+4. Less than -62 is just 3x+4<-62. To solve future problems, just carefully look at the words. Does it mention divided by? Maybe decreased? Carefully look and analyze the question and plug in the operators, variables, and numbers.

For the second solution, since we've already translated the question to an equation from above, we can solve the equation we've derived, which is 3x+4<-62. Subtract four on both sides. The equation will look like this: 3x+4-4<-62-4. Simplifying, we get 3x<-66. Next, we divide both sides of the equation by 3, and we will get x<-22.

Good luck on your studies!

(I may be young but I know stuff so you can trust me :) )

Answer:

x-intercept (3 ,0)

y-intercept ( 0, –4)

12x-9y=36 —> 12x-9(0)=36 —> 12x=36

x=36/12 —> x=3 —> So (x,y)=(3,0)

12(0)-9y=36 —> -9y=36 —> y=36/-9

y= –4 —> So (x,y) =(0,–4)

I hope I helped you ^_^

The following are crucial factors in hypothesis testing:

In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.

Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.

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Using the percentage formula it is obtained that there are 40 number of pages in the book.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

Let's use "x" to represent the total number of pages in the book.

According to the problem, Daniel has read 80 percentage of the book, which means he has read -

8/100 = 0.8x pages

He still has 8 pages left to finish, so we can set up an equation -

0.8x + 8 = x

Solving for x, we can subtract 0.8x from both sides -

0.8x + 8 - 0.8x = x - 0.8x

8 = 0.2x

Then, we can divide both sides by 0.2 to get -

x = 40

Therefore, there are 40 pages in the book.

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Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.

The length of the missing side (hypothenuse) is equal to 5

"Information available from the question"

Opposite side of the triangle(y) = 3

Adjacent side of the triangle (z)= 4

Hypothenuse side of the triangle = x

Pythagorean Theorem

This formula is used to find the missing side of a right angle triangle if two sides are given.

\(x^{2} =y^2+z^2\)

Let's substitute the values into the formula and solve for the hypothenuse

\(x^{2} =3^2+4^2\)

\(x^{2}\) = 9 + 16

\(x^{2}\) = 25

\(x=\sqrt{25}\)

x = 5

The length of the missing side (hypothenuse) is equal to 5.

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The nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

Given the 13th unit requires 87 minutes and 26th unit requires 64 minutes.To find the estimated time required by the 50th unit, we need to use the equation of the linear equation of the line.Let's find the value of m (slope).`m = (64 - 87)/(26 - 13)m = -23/13`Let's find the value of b (y-intercept).`b = 87 - (-23/13) × 13b = 87 + 23b = 110`

Therefore, the equation of the line can be written as:y = -23/13 x + 110Let's substitute the value of x as 50 and find the value of y (time required by the 50th unit).`y = -23/13 × 50 + 110y = 47.31`Rounded to the nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

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9 students made at least 3 picture frames.

An illustration of variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data on the same graph.

Given:

The plot shows picture frames made by students last week.

Number of Frames     Number of students

              0                               6

              1                                4

              2                               1

              3                               2

              4                               7

So, the students made at least 3 picture frames

= 2+ 7

= 9

Hence, 9 students made at least 3 picture frames.

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At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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Answer:

15 cartons

Step-by-step explanation:

18 eggs and u have 3 of them. 18*3 is 54 144-54 is 90 90/6 is 15 15 cartons.

Hope this helps plz hit the crown :D

The set g={2,4,6,8} in Z10 under the operation * is a group.

To determine whether the set g={2,4,6,8} in Z10 is a group under the operation *, we need to verify four properties: closure, associativity, identity element, and inverse element.

Closure: For any two elements a and b in g, the product ab should also be in g. In this case, multiplying any two elements in g (mod 10) will result in another element in g, satisfying closure.

Associativity: For any three elements a, b, and c in g, the operation * should be associative. Since multiplication in Z10 is associative, the operation * on g is also associative.

Identity Element: An identity element e exists in g such that for any element a in g, ae = ea = a. The element 2 serves as the identity element in g since 2a = a2 = a for all elements a in g.

Inverse Element: For every element a in g, there exists an inverse element b in g such that ab = ba = e. In this case, each element in g has an inverse within g. For example, 28 = 82 = 6, 46 = 64 = 4, 64 = 46 = 6, and 82 = 28 = 2.

Since the set g={2,4,6,8} in Z10 satisfies all four group properties, it is indeed a group under the operation *.

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Answer:

x=9 y=12.7

Step-by-step explanation:

Side A= 9

Side B= 9

Side C= 12.7

Answer: 9/2 this answer was on my exam.