if k(x) = 3x, then f'(x)=? A. x³Ln3 B. 3xLn3 C. 3x/Lnx D. 3/3xLn3​

Answer:

Correct

Step-by-step explanation:

Yes that is correct

Answer:

56 minutes

Step-by-step explanation:

We can use proportions to solve.

6 miles            8 miles

------------     = ------------------

42 minutes        x minutes

Using cross products.

6x = 42 *8

Divide each side by 6

x = 42/6 * 8

x = 7*8

x = 56

9514 1404 393

Answer:

  y = 3 -x

Step-by-step explanation:

Subtract x from both sides of the equation.

  x -x +y = 3 -x

  y = 3 - x

Answer:

y=3-x

explanation

its that

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

\(y(x)=-\frac{6}{7}e^{-4x}+\frac{1}{7}e^{3x}\) (See attached graph)

Step-by-step explanation:

Given Second-Order Homogeneous Differential Equation

\(y''+7y'+12y=0,y(0)=-1,y'(0)=0\)

Use Auxiliary Equation

\(m^2+7m+12=0\\\\(m+4)(m+3)=0\\\\m=-4,\: m=3\)

General Solution for Distinct Real Roots

\(y(x)=C_1e^{m_1x}+C_2e^{m_2x}\\\\y(x)=C_1e^{-4x}+C_2e^{3x}\)

Take the derivative of y(x)

\(y'(x)=-4C_1e^{-4x}+3C_2e^{3x}\)

Create a system of equations given initial conditions

\(y(x)=C_1e^{-4x}+C_2e^{3x}\\\\y(0)=C_1e^{-4(0)}+C_2e^{3(0)}=-1\\\\C_1+C_2=-1\)

\(y'(x)=-4C_1e^{-4x}+3C_2e^{3x}\\\\y'(0)=-4C_1e^{-4(0)}+3C_2e^{3(0)}=0\\\\-4C_1+3C_2=0\)

Solve the system of equations

\(\left \{ {{C_1+C_2=-1} \atop {-4C_1+3C_2=0}} \right.\\\\\left \{ {{4C_1+4C_2=-1} \atop {-4C_1+3C_2=0}} \right.\\\\7C_2=-1\\\\C_2=-\frac{1}{7}\)

\(C_1+C_2=-1\\\\C_1-\frac{1}{7}=-1\\ \\C_1=-\frac{6}{7}\)

Final Solution

\(y(x)=C_1e^{-4x}+C_2e^{3x}\\\\y(x)=-\frac{6}{7}e^{-4x}+\frac{1}{7}e^{3x}\)

The function is solved and f(x) represents the total number of hours; x represents the number of weeks he exercises this summer

Given data ,

Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week.

So , the function is given by

The function to keep track of his exercise is f(x) = 7x + 15

On simplifying the equation , we get

f(x) represents the total number of hours; x represents the number of weeks he exercises this summer

Hence , the function is f(x) = 7x + 15

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ1

The measure of segment AB from the given question is 25

In line geometry, a line is the distance between two points while an angle is the point where two lines intersect.

Given the following parameters

AC = 31

BC = 6

Required

AB

Using the addition postulate

AB + BC = AC

Substitute

AB = AC - BC

AB =  31 - 6

AB = 25

Hence the measure of segment AB from the given question is 25

Learn more on addition postulate here: https://brainly.com/question/2134445

#SPJ1

The total number of significant figures ( numerically as an integer ) in the given measurement 6.07 m is equal to 3.

Here in the measurement 6.07 m

Zero is in between two non zero digit 6 and 7.

Zero is countable.

Total number of significant figure in 6.07 m is 3.

Therefore, the number of significant figure in the 6.07 m is equal to 3.

Learn more about significant figure here

brainly.com/question/29153641

#SPJ4

Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

At 0 degree celsius of temperature, Sales will be $-159.474 which is meaningless to interpret.

The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b. The line's slope is represented by the m. A straight line's slope is a measure of how steep it is. The gradient is another name for it. The slope equations. The ratio of a line's "change in y" to its "change in x" is known as the slope. You can get the slope of a line by dividing the distance between two points (x1,y1) and (x2,y2) by the distance between the two locations.

From the given information,

By using calculator,

A. Putting Temperature=20 in the given regression equation,

Predicted sales= 442.284

B. Slope=$ 30.0879

If temperature increases by 1 degree celsius then Sales increases by $30.0879, on average.

C. y-intercept= -159.474

At 0 degree celsius of temperature, Sales will be $-159.474 which is meaningless to interpret.

To know more about slope visit :-

https://brainly.com/question/3605446

#SPJ1

The slope of the line passing through the points (-6, 1) and (8, -7) is -4/7.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Point A: ( -6,1 )

x₁ = -6

y₁ = 1

Point B: ( 8,-7 )

x₂ = 8

y₂ = -7

Now, plug the given x and y values into the slope formula above and simplify:

\(Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{-7 - 1}{8 - (-6)} \\\\Slope\ m = \frac{-7 - 1}{8 + 6} \\\\Slope\ m = \frac{-8}{14} \\\\Slope\ m = -\frac{4}{7}\)

Therefore, the slope of the line is -4/7.

Learn more about slope formula here: brainly.com/question/24578307

#SPJ1

The set of real numbers strictly contains the set of integers.

Every integer is a real number.

But pi is a real number and is not an integer

Hence choice A is correct

Answer:

Male-19&Female-13

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

The amount invested at 10% by $568.65 and investment rate is -

amount invested at 13%. is $5275

amount invested at 10%.  is $1171

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

here, we have,

Let x represent the amount invested at 13%.

Let y represent the amount invested at 10%.

$6,446 is invested, part at 13 % and the rest at 11%.

This means that

x + y = 6,446

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the amount invested at 13%,

P = x

R = 13%

T =1 year

I = (x × 13 × 1)/100 = 0.13x

Considering the amount invested at 10%,

P = y

R =10%

T = 1 year

I = (x × 10 × 1)/100 = 0.10y

If the interest earned from the amount invested at

13% exceeds the interest earned from the amount invested at

10% 10 % by $568.65, it means that

0.13x - 0.10y = 568.65,- - -- - - - - -1

Substituting x = 6,446 - y into equation 1, it becomes

0.13(6,446- y) - 0.10y =568.65

i.e. y= 1171

solving, we get,

x=5275

y= 1171

amount invested at 13%. is $5275

amount invested at 11%.  is $1171

To learn more about invested  visit ,

brainly.com/question/14807003

#SPJ1

Answer:

0.03

Step-by-step explanation:

calculator calculator calculator

Answer:

$608

Step-by-step explanation:

Turn the percentage into a decimal

$800(0.24) = 1$92

So you need to subtract 192 of 800

800 - 192 = $608

Hope this helps dude

Answer:

Direct variation is modeled by

... y = k·x

Then the value of k can be found by finding the ratio of any corresponding pair of numbers from your table. I find it convenient to choose the one where x=10, so the math is easy to do mentally.

... y/x = k

... 16/10 = k = 1.6

Then the equation is

... y = 1.6x

_____

Checking the other values in the table, we find that this equation fits all of them, so you do have direct variation.Step-by-step explanation:

Answer:

420 km

Step-by-step explanation:

75 times 5 = 375

75/10 = 7.5 times 6 = 45

375 + 45 = 420

The two tanks differ in terms of Filling rates and initial volumes.

We can work with the equation for tank A, which represents a linear relationship between the volume of liquid in the tank (y) and the time it has been filling (x).

The equation y = 75x + 110 tells us that the tank A is filling at a constant rate of 75 units per minute, starting with an initial volume of 110 units.

To analyze the data for tank B, we would need to know the volumes of the tank at different times as it is being filled.

If the relationship for tank B is also linear, we could find the equation that represents it by using two points from the table and the slope-intercept form of a linear equation (y = mx + b). Once we have both equations, we can compare them to see how the two tanks differ in terms of filling rates and initial volumes.

To know more about initial volumes .

https://brainly.com/question/30013901

#SPJ11

Answer:

Thx

Step-by-step explanation:

Merry Christmas

9514 1404 393

Answer:

  y = (1/3)√x

Step-by-step explanation:

Vertical scaling of a function is accomplished by multiplying the function by the scale factor. If you want to scale the square root function by a factor of 1/3, then the scaled function is ...

  y = (1/3)√x

By substitution; x = 4 and y = -31

An equation is a mathematical statement that shows that two mathematical expressions are equal. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity.

y=-6x-7 --- 1

7x+y=-3 --- 2

Substituting y as 6x - 7 in equation 2

7x + (-6x - 7) = -3

7x - 6x - 7 = -3

x - 7 = -3

x = -3 + 7

x = 4

Substitute x as 4 in equation 1

y = -6x - 7

y = -6(4) - 7

y = -24 - 7

y = -31

Learn more about equations here: https://brainly.com/question/22688504

#SPJ1

Angle J is equal to 90°.Hence, the measure of Angle J is 90°.

Kayla can see that the measure of Angle I and Angle J form a straight line. Since Kayla knows that a straight line has an angle measure of 180°, what is the measure (in degrees) of Angle J

Given,The angle formed by angle I and J is a straight line which measures 180°.We need to find the measure of angle J.To find the measure of angle J, we need to find out the angle measure of angle I.

From the above information, we know that the angle formed by angle I and J is a straight line that measures 180°.So,Angle I + Angle J = 180°Substitute Angle I in terms of Angle J. We know that the angles are supplementary and they add up to 180 degrees.

If we know the measure of one of the angles, we can find the measure of the other angle as well.So ,Angle I = 180° - Angle JNow, substitute the value of Angle I in the above equation.Angle I + Angle J = 180°(180° - Angle J) + Angle J = 180°180° - Angle J + Angle J = 180°

Thus, Angle J is equal to 90°.Hence, the measure of Angle J is 90°.

For more questions on Angle .

https://brainly.com/question/28394984

#SPJ8

Answer:

Step-by-step explanation:

uhh

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

For similar question on amount invested.

https://brainly.com/question/2720767  

#SPJ8

Answer:

243 ft^3

Step-by-step explanation:

The volume of a triangular prism is the triangular base times the height.

To get the area of the triangle, multiply the base time height and divide by 2.

9*6/2=27

Now multiply by the height

27*9=243

Answer: 243 ft^3

Answer:

243ft^3

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

It would take a total of 20 days to produce the batch of pens.

Let's calculate the work done by the 3 machines for the first 8 days:

Work done by 3 machines in 8 days = (3/12) * 8 = 2 days' worth of work

The remaining work that needs to be done by all 12 machines is:

Remaining work = 1 - (2/20) = 0.9

Now, we can use the work formula to find the total number of days needed to complete the remaining work with 12 machines:

Total work = 0.9

Work done by 12 machines in one day = 12/20 = 0.6

Total number of days needed = 0.9/0.6 = 1.5

Therefore, the total number of days needed to produce the batch of pens is:

8 (days with 3 machines) + 1.5 (days with 12 machines) = 9.5 days

However, we also need to add the 10.5 days it would take for all 12 machines to complete the batch from the beginning:

10.5 + 9.5 = 20 days

To learn more about pens follow the link:

https://brainly.com/question/1968583

#SPJ1