The area of the four walls of a room is 156 m2. The breadth and height of the room are 8 m and 6 m
respectively. Find the length of the room.​

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:

a is the coefficient of the x^2 term, which is -3 in this case.

b is the coefficient of the x term, which is -5 in this case.

c is the constant term, which is 9 in this case.

Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:

a = -3

b = -5

c = 9

Answer:

b. 9.2 minutes

Step-by-step explanation:

To find the expected waiting time for a random call from the sampie given by using the formula:

\(\sum (f(X)) = \dfrac{\sum f (x) \times x}{\sum x}\)

number of calls (x)           waiting time f(x) in minutes         f(x) *(x)

0                                                     0                                         0            

2                                                     3                                         6

4                                                     10                                       40

6                                                     15                                       90  

8                                                     10                                       80

10                                                     6                                       60  

\(\sum x = 30\)                                                                          \(\sum f(x) *x = 276\)

Therefore:

\(\sum (f(X)) = \dfrac{276}{30}\)

\(\sum (f(X)) = 9.2\)

The area of the enclosed region is  16√2 - 8 squared units

The region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π consists of two parts, one above the x-axis and one below the x-axis. We can find the area of each part separately and then add them to get the total area.

First, let's find the x-coordinates of the points where the curves intersect. These are the points where 4 sin(x) = 4 cos(x), or sin(x) = cos(x), which occurs when x = π/4 + kπ/2 for any integer k. Since we are only interested in the intersection points between x = 0 and x = 0.9π, we only need to consider the case k = 0. So the intersection point is x = π/4.

Now, let's consider the part of the region above the x-axis. We need to find the area between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = π/4. This is given by the integral:

A1 = ∫[0, π/4] (4 sin(x) - 4 cos(x)) dx

Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:

A1 = ∫[0, π/4] (4 sin(x) - 4 sin(x + π/2)) dx

  = ∫[0, π/4] (4 sin(x) + 4 sin(x)) dx   (since sin(x + π/2) = sin(x))

  = 8 ∫[0, π/4] sin(x) dx

  = 8 [-cos(x)] [0, π/4]

  = 8 (1 - 1/√2)

  = 8√2 - 8

Next, let's consider the part of the region below the x-axis. We need to find the area between the curves y = 4 cos(x) and y = 4 sin(x) from x = π/4 to x = 0.9π. This is given by the integral:

A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 sin(x)) dx

Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:

A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 cos(x - π/2)) dx

  = ∫[π/4, 0.9π] (4 cos(x) + 4 sin(x)) dx   (since cos(x - π/2) = sin(x))

  = 4 ∫[π/4, 0.9π] (2 cos(x) + 2 sin(x)) dx

  = 4 [2 sin(x) - 2 cos(x)] [π/4, 0.9π]

  = 4 (2/√2 + 2) - 4 (1 - 1/√2)

  = 8√2

So the total area of the region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π is:

A = A1 + A2

A = 8√2 - 8 + 8√2

A = 16√2 - 8 squared units

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Answer:

d=23in

circumference= πd

= 23×3.14

=72.22 probably

A sample size of at least 275 mice must be weighed in order to estimate the mean weight with a 95% confidence interval with a margin of error of 0.4 grams is used.

We may use the formula to determine the minimal sample size n required to estimate the mean weight of mice with a 95% confidence interval and a margin of error of 0.4 grams:

\(n = (\frac{ z * 6}{E} )^{2}\)

where z is the required degree of confidence (in this case, 95% equates to a z-score of 1.96), б is the standard deviation (3 grams), and E is the maximum permissible error (0.4 grams).

When we enter the given values into the formula, we get:

\(n = [(1.96*3)/0.4]^2\\n = 274.576...\)

We round up to the nearest integer because we can't have a fraction of a mouse and get:

n = 275 (rounded near to 100th)

As a result, a sample size of at least 275 mice must be weighed in order to estimate the mean weight with a 95% confidence interval with a margin of error of 0.4 grams is used.

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Answer:

demos los fdeoms

Step-by-step explanation:

14

Answer: A

Step-by-step explanation:

The set of ordered pairs that does NOT represent a function is option A because it contains two ordered pairs with the same first element (2), but different second elements (2 and 7), violating the definition of a function, which requires that each input (first element) is associated with only one output (second element).

Thank You For Reading! Spread the knowledge.

Answer:

You see that 73 degrees and angle 'a' must add up to be = to 180 degrees since both angles form that straaight line on the left. So 180 degrees - 73 = 107 degrees which is measure of angle 'a'

Step-by-step explanation:

Answer:

107°

Step-by-step explanation:

The two angles below form a linear pair.

They are characterized by forming a sum of 180°, which is the standard angle measure of any line.

⇒ a + 73° = 180°

⇒ a = 107°

Answer:

0.5p < 6.50

p < 13

Step-by-step explanation:

The inequality would be p < 13. Since Madison can't spend more than 6.50, the cost of potatoes would need to be less than 6.50. To solve the inequality, you would have to divide both sides by 0.5, giving you p < 13.

Answer:

Madison can buy 13 pounds of patatoes.

Step-by-step explanation:

You have to divide 6.50 by 0.50, but in order to do that you have to move the decimal on both sides two times to the right then you can divide. Then to double check you muliply 13 by 50.

Answer:28

Step-by-step explanation:

hope this helpes

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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Answer:

9

Step-by-step explanation:

221/13=17

So $17 for one hour

153/17=9

I dunno if this is right :)

Answer:

Carmen has to work 9 hours to make $153.

Step-by-step explanation:

Well first we would need to find out how much she makes an hour, so to do that we would divide the 221 by 13 hours and get 17. Then you just keep multiplying until you have the right number.

17x4=68

17x5=85

17x6=102

17x7=119

17x8=136

17x9=153

Answer:

If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater). You may prove this theorem by taking a point P on BC such that CA = CP.

Step-by-step explanation:

That's how you can prove which side is bigger

Answer:

D. If I do not listen to this song, then it will not get stuck in my head.

Step-by-step explanation:

Answer:

"If I don't listen to this song, then it won't get stuck in my head."

The volume of a cuboid or box is the multiplication of length, width, and height by that expression the width of the given cuboid box is 10 inches.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

The volume of cuboid = length × height × width.

Given that,

Height (H) = 9 inches.

The length is three inches more than the width.

So,

L = 3 + W

Now,

Volume of box = 1170 inches³

Now,

The volume of the cuboid is given as

V = L×W×H

1170 = (3 + W) × W×9

W² + 3W - 130 = 0

W² + 13W - 10W - 130 = 0

W(W + 13) - 10(W + 13) = 0

(W + 13)(W - 10) = 0

W = 10,-13 since the length can never be negative so 10 inches will be right.

Hence "The width of the given cuboid box is 10 inches".

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the final result of the double integral is `(4/3)*a. we have to Integrate the inner integral with respect to z.

what is inner integral ?

An inner integral is a mathematical term that refers to the integral function that is evaluated first in a double integral.

In the given question,

To solve this double integral, we will use the following steps:

Integrate the inner integral with respect to z.

Evaluate the result of the inner integral at  upper and lower limits of z.

Substitute the result of the inner integral into the outer integral and integrate with respect to y.

Evaluate the result of the outer integral at the upper and lower limits of y.

Simplify the expression.

Now, let's apply these steps to solve the given double integral:

Integrate the inner integral with respect to z:

∫(x²*z + y²*z + z³) dz = x²/2*z² + y²/2*z² + z^4/4 + C

where C is the constant of integration.

Evaluate the result of the inner integral at the upper and lower limits of z:

(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)

Substitute the result of the inner integral into the outer integral and integrate with respect to y:

markdown

∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

Evaluate the result of the outer integral at the upper and lower limits of y:

= ∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

from y = -sqrt(a²-x²) to y = sqrt(a²-x²)

= (2/3)*x²*(a²-x²)¹⁵ + (2/3)*(a²-x²)²⁵

- (2/3)*x²*(-a²+x²)¹⁵ + (2/3)*(-a²+x²)²⁵

Simplify the expression:

= (4/3)*a³ - (4/3)*a*x²

Therefore, the final result of the double integral is `(4/3)*a

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Answer:

Step-by-step explanation:

1/3 is greater.

The weighted average length of a nail from the carpenter's box whose distribution is give in image is: 3.5cm.

What is weighted average ?

Weighted average is a type of average that takes into account the relative importance or weight of each data point. In a weighted average, each data point is multiplied by a corresponding weight, which reflects its relative importance, and the products are then summed and divided by the sum of the weights.

To find the weighted average length of a nail, we need to multiply each nail length by its percent abundance, then add up all the products and divide by the total percent abundance.

Let's start by calculating the product of each nail length and its percent abundance:

Short nail: (2.5 cm) x (70.5%) = 1.7625 cm

Medium nail: (5.0 cm) x (19%) = 0.95 cm

Long nail: (7.5 cm) x (10.5%) = 0.7875 cm

Now, we add up all the products:

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

Finally, we divide by the total percent abundance:

70.5% + 19.0% + 10.5% = 100%

Therefore, the weighted average length of a nail from the carpenter's box is: 3.5 cm ÷ 100% = 3.5cm

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The Solution:

The correct answer is 16 square in.

Given the net in the picture on the Question section, we are asked to find the surface area of the pyramid that can form using the given net.

The pyramid (or the net) has a total of 5 surfaces, these are:

4 similar triangles, each with a base of 2 inches and a height of 3 inches; and a square of side 2 inches.

So,

The required surface area is the total area of all 5 surfaces.

By formula, the area of a triangle is

While the area of a square is

So, the required area of the pyramid is

In this case,

Substituting these values in the above formula, we get

Therefore, the correct answer is 16 square in.

Answer: See the attached image below

==========================================================

Explanation:

Part A

The rule for a 180 degree rotation about the origin is

\((x,y) \to (-x,-y)\\\\\)

The x and y values flip in sign from positive to negative, or vice versa.

A point like P(1,-1) will move to P ' (-1, 1) as shown in the first diagram. Points Q and R follow the same idea.

Side note: It doesn't matter if we rotate clockwise or counterclockwise. We'll end up at the same result. This only works for 180 degree rotations.

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

Part B

When we apply an x-axis reflection, we apply this rule

\((x,y) \to (x,-y)\\\\\)

This rule is nearly the same as the previous rule, but this time the x coordinate stays the same.

For example, the point P(1,-1) moves to P ' (1, 1)

The same applies to points Q and R as shown in the second diagram.

The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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Answer: \(x^4-x^3-16x^2+16x\)

Step-by-step explanation:

Factor theorem : If x=a is a zero of a polynomial p(x) then (x-a) is a factor of p(x).

Given: Zeroes of polynomial : -4,0, 1, and 4.

Then Factors = \((x-(-4)), (x-0), (x-1) and (x-4)\)   [By factor theorem ]

\(=(x+4), (x-0), (x-1) and (x-4)\)

Multiplying these factors to get polynomial in standard form.

\((x+4)\times(x-0)\times(x-1)\times(x-4) \\\\= x(x+4)(x-4)(x-1)\\\\= x(x^2-4^2)(x-1)\\\\= x(x^2-16)(x-1)\\\\= x(x^2-16)(x-1)\\\\=x(x^2x+x^2\left(-1\right)+\left(-16\right)x+\left(-16\right)\left(-1\right))\\\\= x(x^3-x^2-16x+16)\\\\=x^4-x^3-16x^2+16x\)

Hence, B is the correct option.

The system of equations that allows finding the cost of each bag of tulip bulbs (t) and each bag of daffodil bulbs (d) are:

A system of equations refers to simultaneous equations, which are two or more equations that must be solved together.

                           Tulip      Daffodil     Total Sales

Lisa's sales             4              8               $176

Mark's sales           8              6               $192

Lisa's sales, L = 4t + 8d = 176 ... equation 1

Mark's sales, M = 8t + 6d = 192 ... equation 2

Multiply equation 1 by 2:

8t + 16d = 352 ... equation 3

Subtract equation 2 from equation 3:

8t + 16d = 352

- 8t + 6d = 192

= 10d = 160 (352 - 192)

d = 16 (160/10)

Substitute d in either equation 1 or 2, to get t:

8t + 6d = 192

8t + 6(16) = 192

8t + 96 = 192

8t = 96

t = 12 (96/8)

4t + 8d = 176

= 4(12) + 8(16) = 176

= 48 + 128 = 176

176 = 176

Thus, the cost of each bag of tulip bulbs (t) is $12, while the cost of one bag of daffodil bulbs (d) is $16 based on the system of equations above.

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Answer:

12/5

Step-by-step explanation:

Find the y-intercept form of the line by isolating y:

x + 5y = 12

5y = -x + 12

5         5

y = (-1/5)x + 12/5

y = mx + b

In this form, 12/5 is b, which is the line's y-intercept.

The correct range of f(x) is 4.5 and f(x) is positive for negative interval.

In mathematics, a function is a relation between two sets of numbers, called the domain and the range, that assigns to each element in the domain a unique element in the range. In other words, a function is a rule that takes an input value (or values) and produces a corresponding output value (or values), where the output value is determined by applying a specific set of instructions to the input value. A function can be represented symbolically by an equation, formula, or graph, and it is typically denoted by a letter such as f(x), g(x), or h(x). The input values of a function are often referred to as the independent variable or argument, while the output values are referred to as the dependent variable.

According to the question;

\(f(x)= -\frac{1}{2} |x-4|\)

The Range of f(x) = -0.5-(-5)

f(x) = 4.5

Therefore the correct range of f(x) is 4.5 and f(x) is positive for negative interval.

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Answer:

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Answer:

\( \frac{3}{2} \)

Answer: The area is going to be 0.8

Step-by-step explanation:  The diameter is 1

You need the radius of the circle which is half the diameter. So the Radius(R) is 0.5.

After you find the radius of the circle to find the area of the circle you use the formula pie (R)^2. You are using 3.14

3.14(0.5)^2= 0.785

you then want to round your answer to the nearest tenth so the 8 turns the 7 into an 8.

So, the Area is 0.785 but after rounding it is 0.8.

Hope that helped :)

The point has an x-coordinate of -4 and a y-coorindate of -1, and it is on the third quadrant.

First, remember that for a point (x, y):

For the point that is 4 units to the lefft and 1 unit down (of the origin) it is written as:

(-4, -1)

Then we can see that this point is on the quadrant III.

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