The exponential function g, whose graph is given below, can be written as g(x)=a*b^x


Complete the equation for g(x)

PLEASE HELP!!!!

A) The equation of the linear model that relates pressure P (in pounds per square inch) to depth d (in feet) is: P = 0.45d + 14.7. B) Integral of the slope of the model = P = 0.45d + 14.7. C) The pressure at a depth of 80 feet is 50.7 pounds per square inch. D) The depth at which the pressure is 3 atm is 65.333 feet.

Given information:

At sea level, the weight of the atmosphere exerts a pressure of 14.7 pounds per square inch, commonly referred to as 1 atmosphere of pressure. as an object descends in water pressure P and depth d are Linearly relaind.

In h nit water, the preseute at a depth of 33 it is 2 - atms, ot 29.4 pounds per square inch.

(A) Linear model that relates pressure P (in pounds per square inch) to depth d (in feet):Pressure exerted by a fluid is given by the formula P = ρgh, where P is pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column above the point at which pressure is being calculated.

As per the given information, At a depth of 33 feet, pressure is 29.4 pounds per square inch.

When the depth is 0 feet, pressure is 14.7 pounds per square inch.

The difference between the depths = 33 - 0 = 33

The difference between the pressures = 29.4 - 14.7 = 14.7

Let us calculate the slope of the model; Slope = (y2 - y1)/(x2 - x1)

Slope = (29.4 - 14.7)/(33 - 0)Slope = 14.7/33

Slope = 0.45

The equation of the linear model that relates pressure P (in pounds per square inch) to depth d (in feet) is:

P = 0.45d + 14.7

(B) Integral of the slope of the model:

Integral of the slope of the model gives the pressure exerted by a fluid on a surface at a certain depth from the surface.

Integral of the slope of the model = P = 0.45d + 14.7

C) Pressure at a depth of 80 feet:

We know, the equation of the linear model is: P = 0.45d + 14.7

By substituting the value of d in the above equation, we get: P = 0.45(80) + 14.7P = 36 + 14.7P = 50.7

Therefore, the pressure at a depth of 80 feet is 50.7 pounds per square inch.

D) Depth at which the pressure is 3 atms:

The pressure at 3 atmospheres of pressure is: P = 3 × 14.7P = 44.1

Let d be the depth at which the pressure is 3 atm. We can use the equation of the linear model and substitute 44.1 for P.P = 0.45d + 14.744.1 = 0.45d + 14.7Now we can solve for d:44.1 - 14.7 = 0.45d29.4 = 0.45dd = 65.333 feet

Therefore, the depth at which the pressure is 3 atm is 65.333 feet.

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Answer:

1. 8 units downwards and 2 units left

2.7 units right and 4 units upwards

3. 5 units right and 4 units downwards

Step-by-step explanation:

That how it goes

Answer:

Step-by-step explanation:

(52 divided by 80) multiplied by 100
that will give you the answer

The substance's half-life is approximately 4.67 days.

To find the substance's half-life, we need to determine the time it takes for the mass of the substance to decrease to half of its initial mass (\(\[ N_0 \]\)).

In the exponential decay model \(\[ N = N_0 \cdot e^{-kt} \]\), we can substitute \(N = \frac{N_0}{2}\)to represent half of the initial mass.

\(\[ \frac{N_0}{2} = N_0 \cdot e^{-kt} \]\)

Dividing both sides of the equation by \(\[ N_0 \]\) yields:

\(\[ \frac{1}{2} = e^{-kt} \]\)

To solve for the half-life, we need to find the value of t that satisfies the equation above. Taking the natural logarithm (ln) of both sides, we get:

\(\[ \ln\left(\frac{1}{2}\right) = -kt \]\)

Simplifying further:

\(\[ \ln\left(\frac{1}{2}\right) = -k \cdot t \]\)

Now we can solve for t:

\(\[ t = -\frac{{\ln\left(\frac{1}{2}\right)}}{k} \]\)

Given that k = 0.1483, we can substitute it into the equation to find the half-life in days:

\(\[ t = -\frac{{\ln\left(\frac{1}{2}\right)}}{0.1483} \]\)

Using a calculator, the value of ln(1/2) is approximately -0.6931. Substituting this value into the equation:

\(\[ t = -\frac{{-0.6931}}{{0.1483}} \]\)

t ≈ 4.67 days

To effectively solve the problem, consider the given variables: N represents mass at time t, \(\[ N_0 \]\) is the initial mass at t = 0, k is the positive constant (decay constant), and t represents time in days. Apply the formula \(\[ N = N_0 \cdot e^{-kt} \]\) by substituting the given values. Ensure consistency in units and double-check the results for accuracy and adherence to exponential decay principles.

Therefore, the substance's half-life is approximately 4.67 days.

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We can rewrite \(e^(2y + C) as K * e^(2y),\) where K = \(e^C\) Let's solve the given differential equations one by one:

To solve the equation dy/dx = x^3 + 2y^2, we can rearrange it as dy/(x^3 + 2y^2) = dx. Then integrate both sides:

∫(1/(x^3 + 2y^2)) dy = ∫dx.

Integrating the left-hand side requires some manipulation. Let's substitute y^2 with u to simplify the integral:

∫(1/(x^3 + 2u)) dy = ∫dx.

Taking the derivative of u with respect to x, we get:

du/dx = 2y * dy/dx.

Substituting dy/dx from the original equation, we have:

du/dx = 2y * (x^3 + 2y^2).

Now, rewrite the equation as:

du/(x^3 + 2u) = 2y * dx.

Integrating both sides gives us:

∫(1/(x^3 + 2u)) du = ∫(2y) dx.

The integral on the left-hand side can be solved using partial fractions. Let A and B be constants such that:

1/(x^3 + 2u) = A/(x + √2u) + B/(x - √2u).

By equating the numerators, we get:

1 = A(x - √2u) + B(x + √2u).

Expanding and simplifying:

1 = (A + B)x + (A√2 - B√2)u.

Matching the coefficients of x and u, we have:

A + B = 0 ... (1)

A√2 - B√2 = 1 ... (2).

From equation (1), we have B = -A. Substituting it into equation (2), we get:

A√2 + A√2 = 1,

2A√2 = 1,

A = 1/(2√2) = √2/4.

Thus, B = -A = -√2/4.

The integral becomes:

∫(1/(x^3 + 2u)) du = (√2/4)∫(1/(x + √2u)) du - (√2/4)∫(1/(x - √2u)) du.

Using u = y^2, we can rewrite it as:

(1/√2)∫(1/(x + √2y^2)) du - (1/√2)∫(1/(x - √2y^2)) du.

Now, we integrate each term separately:

(1/√2)ln|x + √2y^2| - (1/√2)ln|x - √2y^2| = √2y + C.

Simplifying further:

ln|x + √2y^2| - ln|x - √2y^2| = 2y + C.

Applying the logarithmic property ln(a) - ln(b) = ln(a/b), we have:

ln((x + √2y^2)/(x - √2y^2)) = 2y + C.

Exponentiating both sides:

(x + √2y^2)/(x - √2y^2) = e^(2y + C).

We can rewrite e^(2y + C) as K * e^(2y), where K = e^C

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Answer:

(16, 11) or ( 16, 10 )

Step-by-step explanation:

The solution to each equation is:

1. a = 5

2. x = 3

3. y = -1

4. z = 5

5. b = 6

To find the solution, we have to isolate the variable in each equation to one side.

1. 3(2a +5) +4(3a +1) = 109

Expand the brackets:

6a + 15 + 12a + 4 = 109

Collect like terms:

18a + 19 = 109

Subtract 19 from both sides:

18a = 90

Divide both sides by 18:

a = 5

2. 5(2x +3) +3(5x -2) = 84

Expand the brackets:

10x + 15 + 15x - 6 = 84

Collect like terms:

25x + 9 = 84

Subtract 9 from both sides:

25x = 75

Divide both sides of the equation by 25:

x = 3

3. 4(5y +3) -5(3y +1) = 2

Expand the brackets:

20y + 12 - 15y - 5 = 2

Collect like terms:

5y + 7 = 2

Subtract 7 from both sides:

5y = -5

Divide both sides by 5:

y = -1

4. 6(3z -2) +4(z -5)= 78

18z - 12 + 4z - 20 = 78

Collect like terms:

22z - 32 = 78

22z = 110

z = 5

5. 3(6b -1) -7(2b +3)=0​

18b - 3 - 14b - 21 = 0

4b - 24 = 0

4b = 24

Divide both sides by 4:

b = 6

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Answer:

78 adult tickets were sold that day

Step-by-step explanation:

Answer:

Inequality: \(3b+1+2\leq 18\)

Toni can carry up to 5 books.

Step-by-step explanation:

"Up to" means you cannot exceed over the amount, meaning everything in her backpack has to be less than or equal to 18 lbs.

Add 1 and 2, to get 3 and subtract from both sides, which gets you \(3b\leq 15\)

Finally, divide both sides by 3, which gets you 5.

Answer:

£140 increased by 5% is £147.00

Answer:

it should be 147.00 , I'm so sorry if I'm wrong!

There are 11 prime dates in it.

The prime numbers between 1 and 30 are 1, 2,3,5,7,11,13,17,19,23,29

Relative prime:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Hence There are 11 prime dates in the month of June.

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Answer: 10

Step-by-step explanation:

Since exactly 1 in every $n$ consecutive dates is divisible by $n$, the month with the fewest relatively prime days is the month with the greatest number of distinct small prime divisors. This reasoning gives us June ($6=2\cdot3$) and December ($12=2^2\cdot3$). December, however, has one more relatively prime day, namely December 31, than does June, which has only 30 days. Therefore, June has the fewest relatively prime days. To count how many relatively prime days June has, we must count the number of days that are divisible neither by 2 nor by 3. Out of its 30 days, $\frac{30}{2}=15$ are divisible by 2 and $\frac{30}{3}=10$ are divisible by 3. We are double counting the number of days that are divisible by 6, $\frac{30}{6}=5$ days. Thus, June has $30-(15+10-5)=30-20=\boxed{10}$ relatively prime days.

Answer:

90 I think coz its a right angle

Answer:

$305.9022863 or $305.90 (rounded to 2 decimal places)

Step-by-step explanation:

It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula  

A= P(1+R)^n

A= the total amount P=Initial amount       R= rate  n=time period

P=$100 R=15% or 0.15(decimal)  n=8 (years)  

A= 100 (1.15)^8

A= 100(3.059022863)

A=305.9022863

The amount you will have after 8 years is $220

The formula for calculating simple interest is expressed as:

SI =PRT

P is the principal = $100

T is the time = 8 years

R is the rate. = 15%

SI = 100 * 8 * 0.15
SI = $120

Amount after 8years = $100 + $120
Amount after 8years = $220

Hence the amount you will have after 8 years is $220

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The common ratio of the associated geometric sequence 3, 15, 75, 375, 1875 ... is 5.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a sequence shown in the table:

3, 15, 75, 375, 1875 ...

The sequence represents the geometric progression.

As we know,

The common ratio is the ratio of two successive terms:

Common ratio r = second term/first term

r = 15/3 = 75/15 = 5

Thus, the common ratio of the associated geometric sequence 3, 15, 75, 375, 1875 ... is 5.

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Answer:

the answer is 1

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

for y²=4ax

directrix is x=-a

for y²=4x ,directrix is x=-1

for y²=4(x-2), shift directrix 2 units right.

so directrix is x=-1+2=1

so for (y+4)²=4(x-2) directrix is x=1

Answer:

484 meters squared

Step-by-step explanation:

Area is Length times Width.

You're dealing with a square meaning all sides are equal.

You simply need to do 22m x 22m = 484m squared

The plane travels 2500 miles in 5 hours. The solution has been obtained by using unitary method.

What is the unitary method?

Using the unitary technique, the value of each individual unit is first calculated, and then the value of the necessary number of units is determined.

We are given that an airplane travels 125 miles in 1/4 hour. It travels the same number of miles each hour.

Using unitary method,

The miles traveled in 1 hour = 125 * 4 = 500 miles

So, the miles traveled in 5 hours = 500 * 5 = 2500 miles

Hence, the plane travels 2500 miles in 5 hours.

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Question:  An airplane travels 125 miles in 1/4 hour. It travels the same number of miles each hour. How many miles does the plane travel in 5 hours?

The given function is f(x)= 9−x². The average value of the function over the interval [0, 3] is 6.

Given function is f(x) = 9 - x²Average value of the function f(x) over the interval [0, 3] is given by:  

$ \frac{1}{b-a}\int_a^b f(x)dx = \frac{1}{3-0}\int_0^3(9-x^2)dx$  $ = \frac{1}{3}\left(9x-\frac{x^3}{3}\right)\bigg|_0^3 $  $ = \frac{1}{3}\left[27-\frac{27}{3}\right]$  $ = \frac{1}{3}(18)$  $ = 6$

Hence, the average value of f(x) = 9 - x² over the interval [0, 3] is 6.

Rounding this to two decimal places, we get the average value to be 6.00.

The average value of a function can be interpreted as the average height of the graph of the function over a certain interval. It is calculated by taking the integral of the function over that interval, and dividing by the length of the interval.

To find the average value of the given function f(x) = 9 - x² over the interval [0, 3],

we use the formula $ \frac{1}{b-a}\int_a^b f(x)dx $ , where a = 0, b = 3 and f(x) = 9 - x².  

$ \frac{1}{b-a}\int_a^b f(x)dx = \frac{1}{3-0}\int_0^3(9-x^2)dx$  $ = \frac{1}{3}\left(9x-\frac{x^3}{3}\right)\bigg|_0^3 $  $ = \frac{1}{3}\left[27-\frac{27}{3}\right]$  $ = \frac{1}{3}(18)$  $ = 6$

Therefore, the average value of the function f(x) = 9 - x² over the interval [0, 3] is 6.

This means that the average height of the graph of the function over this interval is 6. We can tell whether this average value is more or less than 1.5 without doing any calculations, because we can compare it to the value of 1.5 that we get by finding the equation of the line that passes through the points (0,9) and (3,0).

Since the graph of f(x) lies above this line, we know that its average value must be greater than 1.5.

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In the 7th year, you would be making $24,000 more than your starting salary from the job offer.

To calculate how much more than your starting salary you would be making in the 7th year after receiving a $4,000 raise for each of the next 6 years, follow these steps:
1. Determine the total raises you will receive in 6 years: $4,000 raise per year * 6 years = $24,000 total raise.
2. Subtract your starting salary from your 7th-year salary to get  the difference: (starting salary + $24,000) - starting salary = $24,000.
In the 7th year, you would be making $24,000 more than your starting salary from the job offer.

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Answer:

1020

Step-by-step explanation:

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.

The amplitude of the canonical function is determined by the Pythagorean theorem:

A' = √(2² + 5²)

A' = √ 29

The angular frequency C  is the constant within the trigonometric functions from the non-canonical formula:

C = 4π

Then, we find the initial position of the weight in time: (t = 0)

y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)

y(0) = 5

And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)

5 = √ 29 · sin (4π · 0 + D)

5 / √ 29 = sin D

D ≈ 0.379π rad

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

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Answer:

C. producer

Step-by-step explanation:

producers are plants and they provide food and shelter for small animals and stuff.

The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.

The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.

There are three types of equilibrium: stable, unstable, and neutral.

Examples of equilibrium in everyday life:

A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.

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Answer:

132 cm squared

Step-by-step explanation:

6x5=30

6x5=30

6x8=48

1/2(8x3)=12

1/2(8x3)=12

Total added together is 132 cm squared

Answer:

x=26°, y=26°, z=26°

Step-by-step explanation:

x+74=100 (the sum of linear pair)

x=100-74

x=26

x=y=26 (alternate angle)

y=z=26 (vertically opposite angle V.O.A)

Answer: \(3x^3+6x^2-5x-10\)

Step-by-step explanation:

\(\left(x+2\right)\left(3x^2-5\right)\)

\(x\cdot \:3x^2+x\left(-5\right)+2\cdot \:3x^2+2\left(-5\right)\)

\(=3x^3+6x^2-5x-10\)