find the inverse of the function y equals x squared minus 12 ​

The water pressure on the submerged object is given by d = P ÷ 64

Pressure is the force applied perpendicularly to an object's surface in relation to the area across which it is applied (symbol: p or P).  

a. The given formula is is P=64d

or , d = P ÷ 64

b. at a pressure of 672

d = 672  ÷ 64

or, d = 10.5 feet

Hence the pressure is 672 pounds per square foot at a depth of 10.5 feet.

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The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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Answer: 28.25%

Step-by-step explanation:

113/400=0.2825=28.25%

The mass of the drug in the organ at time t depends on the concentration of the drug in the blood entering the organ and the rate at which the blood is entering and leaving the organ. This can be calculated by multiplying the volume of the organ by the concentration of the drug in the blood.

At time t, since the rate at which the blood is entering and leaving the organ is 3 cm^3/sec, the amount of drug in the organ is equal to the amount of drug entering the organ plus the amount of drug that was initially in the organ. As there was no trace of the drug initially, the mass of the drug in the organ at time t is 3 cm^3/sec multiplied by the concentration of the drug in the blood (1/3 gm/cm3) multiplied by the volume of the organ (150 cm^3).

Therefore, the mass of the drug in the organ at time t is 150 gm.

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Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

0.375

Step-by-step explanation:

Convert the fraction to a decimal by dividing the numerator by the denominator.

3/8 = 0.375

Answer:

D. 3x(x-5)

Step-by-step explanation:

3x^2 - 15x

factor out 3 x from the expression

3x x (x-5)

therefore, ur answer is 3x(x-5) or D

The transformation of f(x) to g(x) is :

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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Answer:

x=5.24-9+180n,174.75+180n

Step-by-step explanation:

Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

Answer:

5 toppings

Step-by-step explanation:

The formula is y=2x+14 with x being the number of toppings and y the total price.

Plug in 25 as y to see how much x would be at that price.

25=2x+14

11=2x

x=5.5

You can't get half of a topping so you would have to round down to 5 toppings.

Answer:

you can order 4 toppings but if you wanted a specific answer, it would be 5.5

Step-by-step explanation:

you have 25, subtract 14, you have 11, divide 11 by 2, you get 5.5 but you cant get half so you have 4 if you round it

Answer:

In English -

The legs are the sides opposite the acute angles of a right triangle. The legs are the lesser sides of the right triangle. The hypotenuse is the longest side of the right triangle.

In Spanish -

Los catetos son los lados opuestos a los ángulos agudos de un triángulo rectángulo. Los catetos son los lados menores del triángulo rectángulo. La hipotenusa es lado mayor del triángulo rectángulo.

The equation that represent the number of penguins is (6 ×  4) + (3 × 6) + (3 × 6) = p.

A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.

Therefore, the equation that can be used to find the total number of penguins living in the building is as follows:

Hence,

(6 ×  4) + (3 × 6) + (3 × 6) = p

where

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Answer:

Step-by-step explanation:

To find the highest point we use t = -b/2a (because that's the equation used to find the maximum of the function which is the maximum height the rocket reaches before heading back down ( aka highest point of the parabola at the turning point)

f(t)  = -4.9t^2 +15 +10

A = -4.9

B  = 15

C=10

Plug it in

-15/2(-4.9)   = 1.53 seconds

(In case you get confused 15 turns negative because b in the equation has a - symbol in front. If you had -15 as B you would put -(-15) making it positive)

Hope this is helpful

1.53seconds after launch, will the rocket reach its highest point.

In mathematics, height is defined as the vertical distance from the top of an object to the bottom. Sometimes it is labeled as "height".

The term height in geometry refers to the measurement of an object along the y-axis in coordinate geometry.

Height is a way of measuring someone or something from the bottom to the top or from the head to the feet. In other words, height indicates how tall someone or something is. We can compare how tall we will be when we grow up. We often compare the average height of men and women in different countries.

Given:

f(t)=−4.9t2+15t+10

The vertex is the highest point of the function

when t= \(\frac{-b}{2a}\)

          =\(\frac{-15}{2(-4.9)}\)

          ≈ 1.53

f(t) is the maximum value

1.53seconds after launch, will the rocket reach its highest point.

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Answer:

C, the third answer choice should be it.

Step-by-step explanation:

The annual percentage rate for this credit card account is 15.75%.

The annual percentage rate (APR) is the actual annual cost of borrowing money.

Before applying the APR on the account balance, we determine the monthly percentage rate (MPR) by dividing the APR by 12.

Given the interest in dollars and the principal or account balance, the APR can be computed by dividing the interest by the account balance and multiplying it by 12.

Principal        $1,565.89       $1,026.44

Interest                20.55               13.47

Payment           560.00

End of the month balance 1,026.44

Interest rate (MPR) = 1.31235% ($20.55/$1,565.89 x 100)

Annual percentage rate = 15.75% (1.31235% x 12)

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What is the annual percentage rate?

Answer:

10

Step-by-step explanation:

The polar coordinates of (1, -9) are (9.06, -1.47 radians).

To convert from rectangular coordinates to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:

r = √(1² + (-9)²) = √82 ≈ 9.06

θ = tan⁻¹((-9)/1) ≈ -1.47 radians

Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).

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Answer:

The Pythagorean Triplet that has 5 is 3-4-5

Step-by-step explanation:

We can prove this using Pythagorean Theorem: a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

x=16/3

10=3x-6

10+6=3x-6+6

10+6=3x-6+6

16=3x-6+6

16=3x-6+6

16=3x

16/3 3x/3

16/3 3x/3

16/3

Answer:

$13.05

Step-by-step explanation:

The prize will be $13.05 after the discount.

29x45%=13.05

        OR

29x0.45=13.05

Answer:

Rewrite the equation using the logarithmic property loga(b) = loga(c) if and only if b = c:

x2 - 15 = 2x

Move all the terms to one side of the equation:

x2 - 2x - 15 = 0

Use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 1, b = -2, and c = -15

x = (-(-2) ± sqrt((-2)^2 - 4(1)(-15))) / 2(1)

x = (2 ± sqrt(64)) / 2

x = 1 ± 4

Potential solutions are x = 5 and x = -3.

Check each potential solution in the original equation to see if it is valid. The logarithm of a negative number is undefined, so x = -3 is an extraneous solution. Therefore, the only valid solution is x = 5.

Plug x = 5 into the original equation to check:

log(5^2 - 15) = log(2(5))

log(10) = log(10)

Both sides are equal, so x = 5 is the correct solution.

Step-by-step explanation:

Answer:

a. 5.53

b. 1.078

c. 0.126

d. 0.109

e. 0.549

f. 0.834

g.  0.451

Step-by-step explanation:

The percentage of the flights that arrive on time, P(x) = 79%

The number of flights in the sample, n = 7 flights

a. The mean of the probability distribution, μ = ∑x·P(x)

Therefore, we have; μₓ = n·p

μₓ = 7 × 79/100 = 5.53

b. The standard deviation, σₓ = √(n·p·(1 - p))

∴ σₓ = √(7 × 0.79 × (1 - 0.79)) ≈ 1.078

c. We have;

p = 0.79

q = 1 - p = 1 - 0.79 = 0.21

By binomial probability distribution formula, we have;

The probability of exactly four, P(Exactly 4) = ₇C₄·p⁴·q³

P(Exactly 4) = 35 × 0.79⁴×0.21³ ≈ 0.12625

d. The probability of less than 4 is given as follows;

P(Less than 4) = ₇C₀·p⁰·q⁷ + ₇C₁·p¹·q⁶ + ₇C₂·p²·q⁵ + ₇C₃·p³·q⁴

∴ P(Less than 4) = 1×0.79^0 * 0.21^7 + 7 * 0.79^1 × 0.21^6 + 21*0.79^2*0.29^5+ 85×0.79^3*0.21^4 ≈ 0.109

The probability of less than 4 is ≈ 0.109

e. The probability that more than 5 is given as follows;

P(More than 5) = ₇C₆·p⁶·q¹ + ₇C₇·p⁷·q⁰

7×0.79^6 * 0.21 + 1 * 0.79^7 × 0.21^0 ≈ 0.549

f. The probability that at least 5 of the flight were on time is given as follows;

P(At least 5) = ₇C₅·p⁵·q² + ₇C₆·p⁶·q¹ + ₇C₇·p⁷·q⁰

∴ P(At least 5) = 21×0.79^5 * 0.21^2 + 7×0.79^6 * 0.21 + 1 * 0.79^7 × 0.21^0 ≈ 0.834

g.  For the probability that no more than 5 of the flights were on time, e have;

P(At most 5) = 1 - P(More than 5)

∴ P(At most 5) = 1 - 0.549 ≈ 0.451.

The 99.5% confidence interval for a sample of size 353 with a mean of 75.7 and a standard deviation of 6.8 is: (74.94, 76.46)

To calculate the confidence interval, we can use the following formula:

CI = x ± tα/2 * s / √n

In this case, the critical value of the t-distribution for a confidence level of 99.5% is 2.776. Plugging in the other values, we get the following confidence interval:

CI = 75.7 ± 2.776 * 6.8 / √353

CI = (74.94, 76.46)

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We are aware that (\(1^2\) + a1 + b) = 15 represents the sequence's initial term. The second term is determined by the formula (\(2^2\) + a2 + b) = 22. These equations can be expressed as a set of linear equations:

a + b = 14 ...(1)

a + b = 14 ...(1)

The results of the simultaneous solving of these equations are a = -3 b = 17.

Thus, \((n-3)^2 + 17\) is the nth term in the series in the form of (n+a)2 + b.

An Arithmetic Progression (AP) is a sequence of numbers in which each term is obtained by adding a fixed value to the previous term. This fixed value is called the common difference of progression.

For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic progression with a common difference of 3. To find the next term, we add 3 to the previous term:

2 + 3 = 5

5 + 3 = 8

8 + 3 = 11

11 + 3 = 14

And so on.

In general, the nth term of an arithmetic progression can be calculated using the formula:

an = a1 + (n - 1)d

where:

an is the nth term of the sequence

a1 is the first term of the sequence

the common difference between terms

n is the number of the term you want to find

So, if we wanted to find the 10th term of the sequence 2, 5, 8, 11, 14, ..., we would use the formula:

a10 = 2 + (10 - 1)3

a10 = 2 + 27

a10 = 29

Therefore, the 10th term of the sequence is 29.

To find the nth term of the sequence in the form of (n+a)² + b, we need to first find the values of a and b.

Let's begin by finding the difference between consecutive terms in the sequence:

The difference between the first and second terms is 22 - 15 = 7.

The difference between the second and third terms is 31 - 22 = 9.

We can observe that the difference between consecutive terms is not constant, which means that the sequence is not arithmetic. However, we can check if the second differences are constant:

The second difference is 2.

Since the second differences are constant, we can conclude that the sequence can be represented by a quadratic equation of the form (n² + an + b). Now, we need to solve for the values of a and b.

We know that the first term of the sequence is given by (1² + a1 + b) = 15. Similarly, the second term is given by (2² + a2 + b) = 22. We can write these equations as a system of linear equations:

a + b = 14 ...(1)

4a + b = 11 ...(2)

Solving these equations simultaneously, we get:

a = -3

b = 17

Therefore, the nth term of the sequence in the form of (n+a)² + b is:

(n-3)² + 17

So, for example:

The 1st term is (1-3)² + 17 = 9 + 17 = 26

The 2nd term is (2-3)² + 17 = 1 + 17 = 18

The 3rd term is (3-3)² + 17 = 0 + 17 = 17

The 4th term is (4-3)² + 17 = 1 + 17 = 18

The 5th term is (5-3)² + 17 = 4 + 17 = 21

and so on.

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Answer:

107 and 108.

Step-by-step explanation:

Based on the information given about the combination, the number of different parts of fruits that can be selected from the bowl will be 6.

Since the bowl contains an apple, a plum, a pear, and a banana, the different pairs of fruit that can be selected from the bowl will be 4C2.

We can solve this further which will be:

= 4C2

= 4! /2! (4 - 2)!

= 4! / 2!2!

= (4 × 3 × 2)/ 2 × 2

= 24/4

= 6

Therefore, 6 different pairs of fruit can be selected.

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Given:

Pure acid is to be added to a 20% acid solution to obtain 40 L of a 40% acid solution.

To find:

The amount of each solution.

Explanation:

Let x be the amount of liter of pure acid solution.

Let 40-x be the amount of liter of 20% acid solution.

So, the equation can be written as,

Solving we get,

Since x = 10,

Therefore,

Final answer:

The pure solution is 10 liter.

20% acid solution is 30 liter.

Answer:

16.0%

Explanation:

Initial Population = 3827 thousand

Final Population = 3214 thousand

The percent decrease is approximately 16.0% (to the nearest tenth).