Find the derivative of the following functions:
a. f(x) = e^x-1 + ln(3x–1)
b. g(x) = (2x – 1)^2 (x^2 – 1)
c. H(x) = f(x)/g(x) using f(x) and g(x) in parts (a) and (b).

Answer:

2

Step-by-step explanation

-7p = -3p -8

Move variable to left-hand side

-7p + 3p= -8

Collect like terms

-4p = -8

Divide both sides by 4

p = 2

The given triangle is a right angled triangle having the follwoing sides;

Hypotenuse = x (longest side)

Opposite = 14 (side facing the given acute angle)

Theta = 15 degrees

Using the SOH trigonometry identity;

sin 15 = opposite/hypotenuse

sin15 = 14/x

x = 14/sin15

x = 14/0.2588

x = 54.09

x is approximately equal to 54.1. Option B is coorect

Here is it graphed in Desmos, hope it helps!

To find the Laplace transform of f(t), we use the formula:

L{f(t)} = ∫[0,∞) \(e^(-st)\) f(t) dt

where L{f(t)} denotes the Laplace transform of f(t) and u(t) is the unit step function.

Using the linearity of the Laplace transform, we can find the Laplace transform of each term separately and add them up.

L{6u(t-2)} = \(6e^(-2s)\) / s (applying the time-shift property)

L{3u(t-5)} = \(3e^(-5s)\) / s (applying the time-shift property)

L{-4u(t-6)} = -\(4e^(-6s\)) / s (applying the time-shift property)

Therefore, the Laplace transform of f(t) is:

F(s) = L{f(t)} = 6\(e^(-2s)\) / s + \(3e^(-5s)\) / s - \(4e^(-6s)\)/ s

= \((6e^(-2s) + 3e^(-5s) - 4e^(-6s)) / s\)

Hence, the Laplace transform of f(t) is F(s) = \((6e^(-2s) + 3e^(-5s) - 4e^(-6s)) / s.\)

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Answer:

x=28

Step-by-step explanation:

-2(3x-9)+5x =-10

now we times -2 to to the inside of the parenthese

giving us

-6x+18 +5x= -10

add like terms

add -6x and 5x

-1x+18=-10

now we add like terms of the constants

minus 18 on  both sides

-1x=-28

now divide by -1

x = 28

Answer:

x = 28

Step-by-step explanation:

First, remove the parentheses by distributing -2.

-6x + 18 + 5x = 10

Next, collect the like terms.

-x + 18 = -10

Next, move the constant to the right-hand side and change its sign.

-x = -10 - 18

Next, calculate the difference

-x = -28

Lastly, change the signs on both sides of the equation.

x = 28

These are the steps to answer this equation.

Answer:

\(700 - 100 = 7 \\ \)

2000 +4600 _3800 _1 +40000 ,_500-35+421000 (200_a+34

In this case, for every 1 unit volume of coal extracted, approximately 116.88 units of overburden need to be removed.T

o calculate the overall stripping ratio, we need to determine the volume of overburden removed in relation to the volume of coal extracted.

The volume of overburden can be calculated by multiplying the area of the strip by the thickness of the overburden. Given the strike length of the coal seam (152 m) and the overburden thickness (108 m), we can calculate the area of the strip as follows:

Strip Area = Strike Length x Overburden Thickness

= 152 m x 108 m

= 16,416 m²

Next, we need to calculate the volume of coal by multiplying the area of the coal seam by its thickness. Given that the seam thickness is 10 m, we can calculate the area of the coal seam as follows:

Coal Seam Area = Strike Length x Seam Thickness

= 152 m x 10 m

= 1,520 m²

Now, we can calculate the overall stripping ratio by dividing the volume of overburden by the volume of coal:

Stripping Ratio = Volume of Overburden / Volume of Coal

= (Strip Area x Overburden Thickness) / (Coal Seam Area x Seam Thickness)

= (16,416 m² x 108 m) / (1,520 m² x 10 m)

= 1,775,488 m³ / 15,200 m³

= 116.88

Therefore, the overall stripping ratio is approximately 116.88.

The stripping ratio is a measure of the amount of overburden that needs to be removed to extract a unit volume of coal. A high stripping ratio indicates that a significant amount of overburden needs to be removed, which can have implications for the cost and efficiency of coal extraction operations.

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Based on the profit model provided, there are two break-even points for the product "sleeping bags." The x-coordinate of either one of these break-even points should be provided, rounded to three decimal places.

To determine the break-even points, we need to identify the x-coordinate where the profit is equal to zero. The break-even point represents the level of sales at which the company neither makes a profit nor incurs a loss.

The profit model should provide the necessary information to calculate the break-even points. However, the profit model or any specific details related to it were not provided in the question. Without the profit model or additional information, it is not possible to calculate the break-even points for the sleeping bags or provide the x-coordinate of either break-even point.

To determine the break-even points accurately, it is essential to have information such as fixed costs, variable costs, selling price per unit, and any other relevant factors that impact the profit of the sleeping bags. With this information, it is possible to calculate the break-even points using mathematical formulas and determine the corresponding x-coordinates.

In summary, without the profit model or any additional information, it is not possible to provide the x-coordinate of either break-even point for the sleeping bags.

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Complete Question:

Use the additional information and the profit model above to answer this question. there are two break-even points. give the -coordinate of either one. round to 3 decimal places. sleeping bags.

Option a. W is a subspace of R² because it satisfies the three conditions required for a subset to be a subspace. The set W contains all vectors in R2 whose components are rational numbers.

The set W is a subspace of R² because it satisfies the three conditions required for a subset to be a subspace:

The zero vector is in W because the components of the zero vector are rational numbers.

W is closed under vector addition because the sum of two rational numbers is also a rational number.

W is closed under scalar multiplication because the product of a rational number and a rational number is also a rational number.

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Answer:

85%

Easy explanation:

First, make a fraction.

   Favorite Color Red                      323

-----------------------------------     =      -------------

Total Students Surveyed                380

Next, divide the number of students who's favorite color is red (numerator) by the total number of students surveyed (denominator).

323 / 380 = .85

Finally, convert the decimal to a percentage.

.85 = 85%

85% of the total number of students surveyed said that their favorite color is red.

Answer:

82.555

Step-by-step explanation:

I used a calculator

Answer:

16

Step-by-step explanation:

28 - 12 = 16  

16/2=8

8+8=16

Answer:

16

Step-by-step explanation:

Answer:

We are given the initial price of a car and we are also told that the car sold for a 15% profit which means that the price that the car was sold for is 15% more than it's initial price.  This is just a simple multiplication problem which we multiply the initial price by the total percentage plus 0.15

\(Sold\ Price = Initial\ Price *(Total\ Percentage+Profit\ Percentage)\)

\(Sold\ Price = \$5200*(1+0.15)\)

\(Sold\ Price = \$5200*(1.15)\)

\(Sold\ Price = \$5980\)

Therefore, our final answer is that the selling price was $5980

Hope this helps!

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

In (a), as education level increases, so does income, showing a positive correlation. In (b), as class size decreases, the belief that students are receiving a quality education increases, showing a negative correlation. In (c), as testosterone levels increase, so does aggression, indicating a positive correlation. In (d), as the price of apples rises, the sale of apples decreases, indicating a negative correlation

(a) is an example of a positive correlation, as higher education level and larger annual income are positively associated with each other.

(b) is an example of a negative correlation, as smaller class sizes are negatively associated with the belief that students are receiving a quality education.

(c) is an example of a positive correlation, as increased testosterone levels are positively associated with increased aggression.

(d) is an example of a negative correlation, as rising prices of apples are negatively associated with the sale of apples.

In a positive correlation, the two variables move in the same direction, so an increase in one variable is associated with an increase in the other variable. In a negative correlation, the two variables move in opposite directions, so an increase in one variable is associated with a decrease in the other variable.

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Answer:

(5,2) i believe

Step-by-step explanation:

if T1 and T2 are unbiased estimators of μ(0) and independent of each other, the variance of the estimator aT1 + (1-α)T2 can be expressed as \(a^2 Var(T1) + (1-\alpha )^2 Var(T2)\).

Let's calculate the variance of the estimator aT1 + (1-α)T2, where T1 and T2 are unbiased estimators of μ(0) in R, and α is a constant.

First, we know that the variance of a linear combination of random variables can be expressed as follows:

\(Var(aT1 + (1-\alpha )T2) \\= a^2 Var(T1) + (1-\alpha )^2 Var(T2) + 2a(1-\alpha ) Cov(T1, T2)\),

where Var(T1) and Var(T2) represent the variances of T1 and T2, respectively, and Cov(T1, T2) represents their covariance.

Since T1 and T2 are unbiased estimators, we have E(T1) = E(T2) = μ(0). Therefore, Cov(T1, T2) = E(T1T2) - E(T1)E(T2) = μ(0) - μ(0) = 0, as the estimators are independent.

Substituting the values into the variance formula, we get:

Var(aT1 + (1-α)T2) =

\(\\a^2 Var(T1) + (1-\alpha )^2 Var(T2) + 2a(1-\alpha ) Cov(T1, T2)\)

\(= a^2 Var(T1) + (1-\alpha )^2 Var(T2).\)

Therefore, if T1 and T2 are unbiased estimators of μ(0) and independent of each other, the variance of the estimator aT1 + (1-α)T2 can be expressed as \(a^2 Var(T1) + (1-\alpha )^2 Var(T2)\).

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Answer:

x=0

Step-by-step explanation:

1) x-6/6= -1 is the equation

2) To get rid of the denominator, multiply both sides by 6 to get x-6= -6

3) Add 6 on both sides to get x=0

Step-by-step explanation:

(i) Use law of cosine:

c² = a² + b² − 2ab cos C

c² = (√3 − 1)² + (√3 + 1)² − 2(√3 − 1)(√3 + 1) cos 60°

c² = 3 − 2√3 + 1 + 3 + 2√3 + 1 − 2(3 − 1) (½)

c² = 6

c = √6

(ii) Use law of sines:

a / sin A = c / sin C

(√3 − 1) / sin A = √6 / (½√3)

(√3 − 1) / sin A = 2√2

½ (√3 − 1) = √2 sin A

½ (√6 − √2) = 2 sin A

¼ (√6 − √2) = sin A

Use a calculator:

A = 15°

(iii) Use SAS area:

A = ½ ab sin C

A = ½ (√3 − 1) (√3 + 1) sin 60°

A = ½ (3 − 1) (½√3)

A = ½√3

Answer:

4/6

Step-by-step explanation:

Answer:

Use a factor tree. For example, 625 = 5 x 125 = 5 x 5 x 25 = 5 x 5 x 5 x 5. Because there are 4 fives, and we are looking for the square root, (5 x 5) (5 x 5) = 625. Therefore the square root of 625 is 25.

Answer:

a. 8

b. 10

c. 14

d. 6

a. 8

b. 2

c. 14

d. 6

Answer:

a) x=12

b) s=10

c) y=34

d) t=12

Subtraction:

a) x=8

b) s=2

c) y=14

d) t=6

Multiplication:

a) x=20

b) s=32

c) t=18

d) y=100

Division:

a) x=8

b) x=3

c) x=5

d) x=10

Mixed Practice:

a) x=3

b) y=-11

c) s=8

d) m=60

e) z=0

f) x=1

g) s=92

h) x=16

i) x=1/8

j) x=250

k) y=99

l) t=4

m) t=28

n) q=16

o) t=2

Step-by-step explanation:

Here you go, brainliest would be much appreciated. :)

Answer:

-9

Step-by-step explanation:

The cash flow identity is a useful tool for understanding the financial health of a company.

Cash flow from assets = Net income + Depreciation - Increase in net working capital - Capital expenditures

Net income = Sales revenue - Cost of goods sold - Selling, general, and administrative expenses - Depreciation

Using the data from the financial statements, we can calculate the cash flow from assets as follows:

Cash flow from assets = $238,900 + $46,200 - $1,900 - $120,000 = $102,100

Cash flow to creditors = $17,800 - $4,900 = $12,900

Cash flow to owners = $0 + $82,200 = $82,200

Cash flow from assets = Cash flow to creditors + Cash flow to owners

$102,100 = $12,900 + $82,200

The cash flow identity is verified.

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Answer:

c. 5cm

Step-by-step explanation:

25=½(3+7)*h

25*2=10*h

50/10=h

5cm =h

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Answer:

2 - 30ft²

3 - 57yd²

Step-by-step explanation:

Hey There!

The first step in solving this problem is finding the formula for area of a trapezoid

\(A = \frac{a+b}{2} h\)

a = base 1

b = base 2

h = height

For the first one the dimensions are

a = 6

b = 9

h = 4

now we just plug in the values

\(A=\frac{6+9}{2} 4\\6+9=15\\\frac{15}{2}=7.5\\7.5*4=30\)

so the area of the first trapezoid is 30 ft²

For the second one the given dimensions are

a = 8

b = 11

h = 6

now we just plug in the values

\(A=\frac{8+11}{2} 6\\8+11=19\\\frac{19}{2} =9.5\\9.5*6=57\)

so the area of the second trapezoid is 57 yd²