Find f(g(2)) if f(x) = 2x-1 g(x) = -3x Find f(g(2)) if f(x) = 2x-1 g(x) = -3x -6 -9 3 -13Let Q (in grams) represent the mass of a quantity of carbon-14, which has a half-life of 5730 years. The quantity present after t years is Q(t)=10\cdot\left(\frac12\right)^{\left(\frac t{5730}\right)}Q(t)=10⋅(
2
1
​
)
(
5730
t
​
)
.

Determine the quantity present after 2000 years.


Let Q (in grams) represent the mass of a quantity of carbon-14, which has a half-life of 5730 years. The quantity present after t years is Q(t)=10\cdot\left(\frac12\right)^{\left(\frac t{5730}\right)}Q(t)=10⋅(
2
1
​
)
(
5730
t
​
)
.

Determine the quantity present after 2000 years.


7.851 grams

1.117 grams

0.785 grams

1.745 grams

Answer:

Step-by-step explanation:

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

To determine the line symmetry of your figure (C), examine the shape and try to identify if it can be divided into mirror-image halves using any of these lines. If so, that will be the type of line symmetry it has. If not, choose "none of the above."

1. Vertical line symmetry: A figure has vertical line symmetry when it can be divided into two equal halves by a vertical line, and the halves are mirror images of each other.

2. Horizontal line symmetry: A figure has horizontal line symmetry when it can be divided into two equal halves by a horizontal line, and the halves are mirror images of each other.

3. Diagonal line symmetry: A figure has diagonal line symmetry when it can be divided into two equal halves by a diagonal line, and the halves are mirror images of each other.

4. None of the above: If the figure cannot be divided into equal halves by any line (vertical, horizontal, or diagonal) and have mirror-image halves, then it does not have any line symmetry.

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Step-by-step explanation:

\(10500 = 3 \times 5 \times 5 \times 5 \times 7 \times 2 \times 2 \\ \\ 10500 = 2 \times 2 \times 3 \times 5 \times 5 \times 5 \times 7 \\ 10500 = {2}^{2} \times 3 \times {5}^{3} \times 7\)

We need to calculate the total daily dosage based on the patient's weight and divide it into three equal doses. Each dose of gentamicin should be approximately 114 mg.


To determine the amount of gentamicin to be administered for each dose, we need to calculate the total daily dosage based on the patient's weight and divide it into three equal doses.

First, we convert the patient's weight from pounds to kilograms: 188 lb ≈ 85.27 kg.

Next, we calculate the total daily dosage of gentamicin based on the weight: 4 mg/kg/day × 85.27 kg = 341.08 mg/day.

Since the total daily dosage should be divided into three equal doses, we divide 341.08 mg by 3: 341.08 mg ÷ 3 = 113.693 mg.

Rounding to the nearest whole number, each dose should be approximately 114 mg of gentamicin.


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Answer:

it goes in once  the finished solution is 75/16 = 75/16

Step-by-step explanation:

Answer:

4 11/16

Step-by-step explanation:

Step 1 - Find Whole Number

Calculate out how many times the denominator goes into the numerator. To do that, divide 75 by 16 and keep only what is to the left of the decimal point:

75 / 16 = 4.6875 = 4

Step 2 - Find New Numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

75 - (16 x 4) = 11

Step 3 - Get Solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 75/16 as a mixed number is:

4 11/16

❏\( \huge \boxed {\mathfrak{ \pink{Answer}}}\)❒

▶ \( \tt \red{see \: \: attachement \: \: for \: \: ploted \: \: points}\)

Answer:

See included figure.

Step-by-step explanation:

I assume you are given a grid to plot on, but I've just quickly made one myself to show how to do it.

First off: remember that in a point with two coordinates it's always (x,y).
This means the first number is the x coordinate and the second number is the y coordinate.

So all you have to do then is make some lines through those coordinates, then the point is the point where those two lines intersect.

To find the length of QR in triangle PQR, we can use the trigonometric ratio known as the sine function.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Given that angle P = 26° and the length of PQ = 8.5 feet, we can use the sine function to find the length of QR.

sin(P) = Opposite / Hypotenuse

sin(26°) = QR / 8.5

To solve for QR, we can rearrange the equation:

QR = sin(26°) * 8.5

Using a calculator, we find:

QR ≈ 3.6761 * 8.5

QR ≈ 31.2449

Rounding to the nearest tenth, the length of QR is approximately 31.2 feet.

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Answer:

980377,802343,374430

Step-by-step explanation:

Pls follow

Answer:

The son is 10, and the father is 50.

Step-by-step explanation:

10 times 5 would be 50, and 50+10 is 60.

Answer:

Father: 50

Son: 10

Step-by-step explanation:

Son's age: S

Father's age: F

F=5S

F+S=60.

Substitute.

5S+S=60

6S=60

S=10

F=50. As a check, 10+50=60 and 50/5=10.

Hope this was helpful.

~cloud

The statement " a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint" is true because  shadow prices provide valuable information about the marginal value of resources and constraints in linear programming problems

A shadow price represents the marginal value of a resource or constraint in a linear programming problem. It indicates how much the optimal value of the objective function will increase if the right-hand side of a constraint is increased by one unit, while keeping all other constraints and variables fixed. The shadow price of a constraint is calculated by adding one unit to the right-hand side of the constraint and re-solving the linear programming problem.

The resulting increase in the objective function value is the shadow price of that constraint. Shadow prices are useful in making decisions about resource allocation, pricing, and capacity planning in a variety of industries such as manufacturing, transportation, and energy.

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Answer:

First, we know that he spent rs500 plus rs60 in the whole process, then the total cost is:

C = rs500 + rs60 = rs560

Now he sells the oranges in packs of 12, then if he has 120 oranges, the total number of packs that he can sell is:

120/12 = 10

So he has 10 packs of 12 oranges.

And he sells each one for rs58.8

Then if he sells the 10 packs, the total revenue is:

R = 10*(rs58.8) = rs588

The profit is the difference between the revenue and the cost, here the profit is:

P = R - C = rs588 - rs560 = rs28

And the profit percentage is calculated as follows:

(P/C)*100%

Where P = profit and C = cost, then we have:

(rs28/rs560)*100% = 5%

This means that Dr. Hart result may be not true for the entire population.

Heart disease is a condition when the heart is disturbed. Several types of heart disease, including:

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Answer:

-3+0i

Step-by-step explanation:

have a good day :)

Answer:

He used 20 ounces of the 10% alloy.

Step-by-step explanation:

Let x represent the number of ounces of alloy containing 10%

silver that was used.

Let y represent the number of ounces of alloy containing 40%

silver that was used.

The weight of the alloy made is 60 ounces. It means that

x + y = 60

The amount of silver contained in the first alloy is 10/100 × x = 0.1x

The amount of silver contained in the second alloy is 40/100 × x = 0.4x

The amount of silver contained in the mixture is 30/100 × 60 = 18

Therefore,

0.1x + 0.4y = 18- - - - - - - - - - - - -1

Substituting x = 60 - y into equation 1, it becomes

0.1(60 - y) + 0.4y = 18

6 - 0.1y + 0.4y = 18

- 0.1y + 0.4y = 18 - 6

0.3y = 12

y = 12/0.3

y = 40

x = 60 - 40

x = 20

The first three nonzero terms in the Taylor polynomial approximation for the given initial value problems are:

Here are the solutions to the three given initial value problems, including the first three nonzero terms in the Taylor polynomial approximation:

y' = 5x² + 2y²; y(0) = 1

To find the Taylor polynomial approximation for this initial value problem, we need to first find the derivatives of y with respect to x. Taking the first few derivatives, we get:

y'(x) = 5x² + 2y²

y''(x) = 20xy + 4yy'

y'''(x) = 20y + 4y'y'' + 20xy''

Next, we evaluate these derivatives at x = 0 and y = 1, which gives:

y(0) = 1

y'(0) = 2

y''(0) = 4

Using the formula for the Taylor polynomial approximation, we get:

y(x) ≈ y(0) + y'(0)x + (1/2)y''(0)x²

y(x) ≈ 1 + 2x + 2x²

Therefore, the first three nonzero terms in the Taylor polynomial approximation for this initial value problem are 1, 2x, and 2x².

y' = 2sin(y) + e\(^(3x)\); y(0) = 0

To find the Taylor polynomial approximation for this initial value problem, we need to first find the derivatives of y with respect to x. Taking the first few derivatives, we get:

y'(x) = 2sin(y) + e

y''(x) = 2cos(y)y' + 3e\(^(3x)\)

y'''(x) = -2sin(y)y'² + 2cos(y)y'' + 9e\(^(3x)\)

Next, we evaluate these derivatives at x = 0 and y = 0, which gives:

y(0) = 0

y'(0) = 2

y''(0) = 7

Using the formula for the Taylor polynomial approximation, we get:

y(x) ≈ y(0) + y'(0)x + (1/2)y''(0)x²

y(x) ≈ 2x + 3.5x²

Therefore, the first three nonzero terms in the Taylor polynomial approximation for this initial value problem are 2x, 3.5x² .

4x''' + 7tx = 0; x(0) = 1, x'(0) = 0

To find the Taylor polynomial approximation for this initial value problem, we need to first find the derivatives of x with respect to t. Taking the first few derivatives, we get:

x'(t) = x'(0) = 0

x''(t) = x''(0) = 0

x'''(t) = 7tx/4 = 7t/4

Next, we evaluate these derivatives at t = 0 and x(0) = 1, which gives:

x(0) = 1

x'(0) = 0

x''(0) = 0

x'''(0) = 0

Using the formula for the Taylor polynomial approximation, we get:

x(t) ≈ x(0) + x'(0)t + (1/2)x''(0)t² + (1/6)x'''(0)t³

x(t) ≈ 1 + (7t⁴)/96

Therefore, the first three nonzero terms in the Taylor polynomial approximation for the given initial value problems are:

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Answer:

a) decimal 7.222

fraction: 65/9

percentage: 722.22

b) Fraction: 37/5

decimal: 7.4

Percentage: 740

Step-by-step explanation:

The two column proof is completed as follows

Statement                                     Reason

1  DE bisects /BDC                       Given

DE bisects angle BEC                Given

2. angle BDE ≅ angle CDE         An angle bisector divides an angle into

                                                     two  congruent angles                                

3.  angle BED ≅ angle CED        An angle bisector divides an angle into                                                        

                                                     two  congruent angles                      

4. line DE ≅ line DE                    Reflexive Property

5. Δ BDE ≅ Δ CDE                     ASA

6. line BE  ≅ line CE                   Corresponding Parts of Congruent                  

                                                   Triangles are Congruent (CPCTC)

7. line AE ≅ line AE                   Reflexive Property

8. Δ AEB ≅ Δ AEC                     SAS

9. ∠ ABE ≅ ∠ ACE                     Corresponding Parts of Congruent

                                                   Triangles are Congruent (CPCTC)

In geometry, ASA stands for "angle-side-angle" and refers to a method of proving that two triangles are congruent.

To prove that two triangles are congruent using the ASA postulate, you need to show that:

In the problem the included side is line DE

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Distance from Detroit to columbus is 220 miles

It is given in the question,

The average speed Mrs. smith drove = 60 mph.

Returning, her average speed was 55 mph.

Time taken =  1/3 of an hour longer on the return trip

We have to Find total distance between Detroit and Columbus

So, Let the distance between Detroit and Columbus be "x" miles

Average speed = 60

So, time taken by her to cover distance of x miles with speed of 60 mph

Time = Distance / speed

=> t = x / 60

She Took x/60 hours to reach Columbus

While returning her speed was 55 mph.

So, time taken by her to cover the same distance but at a speed of 55 mph :

=> t = x / 55

Now we are given that she took 1/3 of hour more while returning .

So, \(\frac{x}{55} - \frac{x}{60} = \frac{1}{3}\)

⇒ x/660 = 1/3

=> x = 660/3

=> x = 220 miles

Hence ,  Detroit is 220 miles far from Columbus

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The car will travel a distance of 33.34 meter in 2 sec.

The definition of velocity is a vector estimate of the rate & direction of motion.

Some features abut the velocity are-

Now according to the question-

A car is driving at 60 kilometers per hour.

That means car is travelling 60 km in 1 hour.

Velocity of the car = 60km/hr

convert the velocity in m/s

1 km = 1000 m

1 hour = 3600 second.

velocity = (60×1000m)/3600s

velocity = 100/6  m/s

Now, the distance covered by the car in 2 seconds

Distance = velocity×time

Distance = (100/6)×2

Distance = 100/3

Distance = 33.24 (approx)

Therefore, distance covered by the car in 2 second is 33.34 meters.

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Answer:

67.5 kg

Step-by-step explanation:

To determine the weight of 45 books, we need to determine the weight of one book, using the equation (30 books = 45 kg). This can be done by dividing 30 to both sides of the equation. Therefore,

We obtained the following equation;

Now, multiply both sides by 45 to determine the weight of 45 books.

Therefore, the weight of 45 books is 67.5 kg.

Answer:

\(\huge\boxed{\bf{45books = 67.5kg}} \)

Step-by-step explanation:

Given:-

To find:-

Ans:-

30books = 45kg

45books = y kg

Let's find 45 books (y)

\(\sf \to \frac{30}{45} = \frac{45}{y}\)

\(\sf \to 45*45 = 30*y\)

\(\sf \to 2,025 = 30*y\)

\(\sf \to y = \frac{2,025}{30}\)

\(\sf \to y = 67.5kg\)

~therefore 45books = 67.5kg

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\(\huge\colorbox{red}{BlackPain}\)

Step-by-step explanation:

4: Triangle area = b*h/2 = 8*10.5/2 = 42

5: b*h/2 = area

285 = 15*b/2

b = 38

Answer:

I think you mistype the question?

Step-by-step explanation:

8×3×4 is not 24

It should be 2(3 4)

1. c

2. b

twenty characters

The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

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Answer:

8800 yards

Step-by-step explanation:

All you have to do is 5 * 1760 = 8800 yards

Answer:

8800 yards

Step-by-step explanation:

1760 yards x 5 miles = 8800

cause 1 mile is 1760 but u need five miles so you times it

Answer:

--------------------------

As I understand you would like percent increase if number is increased from 80 to 100.

The difference in numbers is:

What percent of 80 is 20?

Hence this change is represented as 25% increase.

Answer:

x = 1

Step-by-step explanation:

From the table shown in the picture,

For input value x = 1, output values of y = 2, 4, 6, 8, 10

Similarly, from the graph shown,

For input value x = 1, output values of y = 2, 4, 6, 8, 10

Therefore, both will represent the same relationship.

From the graph attached, straight line parallel to y-axis is x = 1.

Therefore, x = 1 will be the correct option.

Answer:

460

Step-by-step explanation:

8x220=1760

5x200=1000

(2760+x)/14=230

2760+x=230x14

2760+x=3220

x=3220-2760

x=460

Answer: y-intercept of the function is (0,-2).

Answer:

A

Step-by-step explanation: