Simplify and write your answer in exponential form : 32 ×3−5×36=

The trapezoid's area can be understood as triangle a + triangle b. So, we write these triangles as an expression, and, since we cannot solve with no values, we simplify to prove the area of the trapezoid.

A triangle's area is 1/2bh. In their case, b is represented as b or a depending on the triangle.

t = 1/2ah + 1/2bh

Now, since both expressions use the terms 1/2 and h, distributed onto a second variable, it can be rewritten as a single expression where both are distributed onto both variables at the same time. This is because both terms being multiplied by something separately is the same as combining both terms and multiplying them both at the same time.

t = 1/2(a)h + 1/2(b)h
t = 1/2(a + b)h

Step-by-step explanation:

come on ! for sure you have worked with a thermometer before in your life ?

please don't switch off the brain just because it is math. keep it and your common sense active also for math problems.

you would be surprised how many you can solve just by logical thinking and applying your own life experiences. math is actually everywhere.

how many degrees from 3 to 0 ? 3

how many degrees from 0 to -5 ? 5 !

so, in total 3 + 5 = 8 degrees.

formally it is

|-5 - 3| = |-8| = 8 degrees difference.

you know the "absolute value" function that returns always the positive value of the argument, no matter if it is negative or already positive ?

Answer:

She is 11, turning 12. She was born in 2009.

Step-by-step explanation:

Answer:

Im not sure what im solving here so can you tell me what?

Step-by-step explanation: Some of them already have and X meaning

Hello there!

3.14 is rational. Hope this helps!

Why? Because pi is irrational, pi squared and the square root of pi is irratonal as well. Hope this helps you!

~Just an emotional teen

\(SilentNature\)

Find partial derivatives, evaluate them at the point, use point-normal form, simplify to get equation of the tangent plane: -8(x + 2) + (y - 2) - (z - 14) = 0 for z = 2x^2 - y^2 + 5y at (-2, 2, 14).

To find the equation of the tangent plane to the surface given by z = 2x^2 - y^2 + 5y at the point (-2, 2, 14), follow these steps: Compute the partial derivatives, . Evaluate the partial derivatives ,  Plug in the normal vector components, Simplify the equation.
1. Compute the partial derivatives of the function with respect to x and y. This will give you the normal vector to the tangent plane.
∂z/∂x = 4x
∂z/∂y = -2y + 5
2. Evaluate the partial derivatives at the given point (-2, 2, 14):
∂z/∂x(-2, 2) = 4(-2) = -8
∂z/∂y(-2, 2) = -2(2) + 5 = 1
3. Now you have the normal vector to the tangent plane: (-8, 1, -1)
4. Use the point-normal form of the equation of a plane:
(ax - a0x) + (by - b0y) + (cz - c0z) = 0
5. Plug in the normal vector components and the point coordinates:
-8(x - (-2)) + 1(y - 2) - 1(z - 14) = 0
6. Simplify the equation to get the final equation of the tangent plane:
-8(x + 2) + (y - 2) - (z - 14) = 0
The equation of the tangent plane to the surface z = 2x^2 - y^2 + 5y at the point (-2, 2, 14) is -8(x + 2) + (y - 2) - (z - 14) = 0.

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By using the L'Hospital's Rule, we have shown that the limit of x^(3/x) as x approaches infinity is equal to 1.

To find the limit of the function \(x^{3/x}\) as x approaches infinity, we can use L'Hopital's Rule, which states that if we have an indeterminate form of a fraction such as 0/0 or infinity/infinity, we can take the derivative of the numerator and the denominator separately until we no longer have an indeterminate form.

First, we can rewrite the function as e^(ln(\(x^{3/x}\))). Then, we can use the properties of logarithms to simplify it further as e^((3ln(x))/x). Now, we have an indeterminate form of infinity/infinity, and we can apply L'Hopital's Rule.

Taking the derivative of the numerator and denominator, we get:

lim x→∞ \(x^{3/x}\) = lim x→∞ e^((3ln(x))/x)

= e^(lim x→∞ (3ln(x))/x)

Using L'Hopital's Rule on the exponent, we get:

= e^(lim x→∞ (3/x²))

Since the denominator is approaching infinity faster than the numerator, the limit of 3/x² as x approaches infinity is zero, and we are left with:

= e^(0)

= 1

Therefore, the limit of \(x^{3/x}\) as x approaches infinity is 1.

Alternatively, we can use some algebraic manipulation and the squeeze theorem to find the limit without using L'Hopital's Rule. We can rewrite the function as \(x^{3/x}\) = (x^(1/x))³, and notice that as x approaches infinity, 1/x approaches zero, and so x^(1/x) approaches 1 (as the exponential function with base e^(1/x) approaches 1). Therefore, we have:

lim x→∞ \(x^{3/x}\)= lim x→∞ (x^(1/x))³

= 1³

= 1

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Complete Question:

Find the limit. Use L'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.

lim x→∞ \(x^{3/x}\)

Answer:

a: 2 cm; b: 34 cm; c: 46 cm^2

Step-by-step explanation:

the missing side length is 2

9 - (4 + 3) = 2

when you add them all together you get

5 + 4 + 2 + 2 + 3 + 3 + 6 + 9 = 34

the perimeter is 34

you can split the shape up in multiple ways

you can split it into three rectangles

(5 * 4) + (2 * 4) + (3 * 6)

20 + 8 + 18 = 46

Answer:

a) 2 cm

b) 34 cm

c) 44 cm²

Step-by-step explanation:

a) 9 cm - 4 cm - 3 cm = 2 cm

b) 9 cm + 5 cm + 4 cm + 2 cm + 2 cm + 3 cm + 3 cm + 6 cm = 34 cm

c) 5 cm × 4 cm + 2 cm × 3 cm + 3 cm × 6 cm = 44 cm²

Given \(n=18\), \(\bar{x}=39\), and \(s=3\), the margin of error at a 99% confidence level is approximately 1.819 (using the critical value of 2.576).



To find the margin of error at a 99% confidence level, we need to use the formula:

\[ \text{{Margin of Error}} = \text{{Critical Value}} \times \left( \frac{s}{\sqrt{n}} \right) \]

Where:

- \( n \) is the sample size,

- \( \bar{x} \) is the sample mean,

- \( s \) is the sample standard deviation, and

- The critical value corresponds to the desired confidence level.

Given:

- \( n = 18 \)

- \( \bar{x} = 39 \)

- \( s = 3 \)

- Confidence level: 99% (which means \( \alpha = 0.01 \))

First, we need to find the critical value associated with a 99% confidence level. This value can be obtained from the standard normal distribution table or calculated using statistical software. For a two-tailed test and a confidence level of 99%, the critical value is approximately 2.576.

Now we can calculate the margin of error:

\[ \text{{Margin of Error}} = 2.576 \times \left( \frac{3}{\sqrt{18}} \right) \]

Performing the calculations:

\[ \text{{Margin of Error}} \approx 2.576 \times \left( \frac{3}{\sqrt{18}} \right) \approx 2.576 \times 0.707 \approx 1.819 \]

Therefore, the margin of error at a 99% confidence level is approximately 1.819 (rounded to three decimal places).

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Answer:

2 1/3 ; 9 1/3

Step-by-step explanation:

Given that:

Outside temperature increases by 3 1/2 degrees every 1 1/2 hours

The rate per hour of temperature increase will be :

Let rate per hour = x

3 1/2 = 1 1/2

x = 1

Cross multiply :

1 1/2 * x = 3 1/2 * 1

3x/2= 7/2

Multiply both sides by 2/3

3x/2 * 2/3 = 7/2 * 2/3

x = 14/ 6

x = 2 2/6

x = 2 1/3

Hence, outside temperature increases at the rate of 2 1/3 degrees per hour.

2.) Temperature increase after 4 hours :

(Temperature rate per hour * number of hours)

(2 1/3) * 4

(7/3) * 4

28 / 3

= 9 1/3

Hence, temperature increase after 4 hours = 9 1/3

2 1/3 ; 9 1/3

Step-by-step explanation:

Given that:

Outside temperature increases by 3 1/2 degrees every 1 1/2 hours

The rate per hour of temperature increase will be :

Let rate per hour = x

3 1/2 = 1 1/2

x = 1

Cross multiply :

1 1/2 * x = 3 1/2 * 1

3x/2= 7/2

Multiply both sides by 2/3

3x/2 * 2/3 = 7/2 * 2/3

x = 14/ 6

x = 2 2/6

x = 2 1/3

Hence, outside temperature increases at the rate of 2 1/3 degrees per hour.

2.) Temperature increase after 4 hours :

(Temperature rate per hour * number of hours)

(2 1/3) * 4

(7/3) * 4

28 / 3

= 9 1/3

Hence, temperature increase after 4 hours = 9 1/3

I know because i am in the future

Using the formula of number of theortical plates in column,

the column have 702437.485 , theoretical plates.

We have given that,

A peak elutes from a column at 27.4 min

with width at half height of 14.6 sec

we have to calculate the theoretical plates in the column .

Using the formula,

N = 55.4 ( tₙ /w₀.₅)²

where,। N ---> number of therotical plates

tₙ--> peak elutes time in second

w₀.₅ ---> width at half height

we have, tn = 27.4 min = 27.4 ×60 sec = 1644 sec w₀.₅ = 14.6 sec

putting all values in above formula we get,

N = 55.4 ( 1644/14.6)² = 702437.485

Hence, 702437.485, number of theortical plates in this column have.

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Answer:

the measurement of a is 60°............

Answer:

A=60

Step-by-step explanation:

it adds up to 180 so subtract 30 and 90 for the right angle and you got 60

The angles in a triangle always add up to 180°, regardless of the type of geometry. This holds true for flat, spherical, and saddle-shaped geometries. The sum of the angles in any triangle is a fundamental property of Euclidean geometry.

This is known as the Triangle Sum Theorem.In spherical geometry, which is the geometry on the surface of a sphere, the sum of the angles in a spherical triangle also adds up to 180 degrees. However, the angles in a spherical triangle are measured in spherical degrees instead of regular degrees.

In hyperbolic geometry, which is a non-Euclidean geometry with a saddle-shaped curvature, the sum of the angles in a hyperbolic triangle is still 180 degrees, but the individual angles can have negative values or be greater than 180 degrees in terms of regular degrees.

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The probability there is at least one pair is therefore 1−p.

acc to our question-

hence,The probability there is at least one pair is therefore 1−p.

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UIF stands for Unemployment Insurance Fund.

Thus this is the full form of UIF.

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The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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Based on the given information "all other things being equal," we can estimate that the traffic will be higher for a dealership in a suburban location compared to a rural location. Therefore, we would estimate a positive number, indicating that the traffic in the suburban location is expected to be higher than in the rural location.

In general, a dealership in a suburban location tends to experience higher traffic compared to a rural location. This estimation is based on several factors. Suburban areas are typically more densely populated and have a higher concentration of residential and commercial activities, leading to increased overall traffic volume.

Additionally, suburban locations often have better transportation infrastructure, including highways, main roads, and public transportation options, which attract more commuters and potential customers to the area.

On the other hand, rural areas are characterized by lower population densities and fewer amenities, resulting in lower levels of traffic. Therefore, the estimate of a positive difference in traffic between a suburban and rural dealership is reasonable.

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Answer:

g = \(\frac{p^2-V^2}{2h}\)

Step-by-step explanation:

assuming I have your statement correctly interpreted.

V = \(\sqrt{p^2-2gh}\) ( square both sides to clear the radical )

V² = p² - 2gh ( subtract p² from both sides )

V² - p² = - 2gh ( isolate g by dividing both sides by - 2h )

\(\frac{V^2-p^2}{-2h}\) = g

multiply numerator/ denominator of left side by - 1

g = \(\frac{p^2-V^2}{2h}\)

Answer: 15 antique houses

Step-by-step explanation:

New houses : Antique houses

                  4 : 5

                 12 : ?

12 ÷ 4 = 3

Multiply 5 by 3

5 × 3 = 15

12 : 15

There are 15 antique houses.

Answer:

25 = 10 + w

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Plz mark as brainliest!!!

Answer: 64

Step-by-step explanation: 4160/65                                                                     64

Answer:

hufduydtuyrdfuotfuftiutfiytdytdutrdurteuyrcytidty7 vdtiduyrduyrdtrd gursugrs7trddutrs

Answer:

The value of x = 0    

Step-by-step explanation:

Given

To determine

The value of x = ?

If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).

i.e. y → 5×4 =20

It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.

Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.

i.e. x → 4×0 = 0

Thus, the rule of dilation is:

P(x, y) = P'(4x, 4y)

Hence,

B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)

Thus,

The value of x = 0           ∵ 0×4 = 0

To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.

To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.

The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.

By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.

Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.

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Answer:

everything that adds up to 18

Step-by-step explanation:

Answer:

I believe the answer is $18. He will spend at most $30 and he has already spent $12. The possible additional amounts he can spend is $18 since:

30 - 12 = 18

Step-by-step explanation:

(Maybe I got confused with the question, so im not confident that its correct.

I hope it helps!)

Answer:

\(m=\frac{5}{2}\)  

If I am wrong its   \(m=\frac{-5}{-2}\)

Step-by-step explanation:

Finding the slope of \((-4,5)(-8,-5)\) we use the slope formula

\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

\(m=\frac{5}{2}\)

Simplify the answer if needed

\(m=\frac{-10}{-4} =\frac{5}{2} =2.5\)

The function f(x) = 6(x - ex) reaches its highest possible value at x=0, where f(0) equals 6 multiplied by the result of subtracting e to the power of 0 from 0, which simplifies to -6.

To find the absolute maximum value of the function f(x) = 6(x - ex), we need to take the derivative of the function and set it equal to zero.

f'(x) = 6(1 - e^x)

Setting f'(x) = 0, we get:

6(1 - e^x) = 0

e^x = 1

x = ln(1) = 0

Now we need to check if this critical point is a maximum or a minimum. We can do this by taking the second derivative of the function:

f''(x) = -6e^x

Plugging in x = 0, we get:

f''(0) = -6e^0 = -6 < 0

Since the second derivative is negative, we know that the critical point at x = 0 is a maximum.

Therefore, the absolute maximum value of the function f(x) = 6(x - ex) is f(0) = 6(0 - e^0) = -6.

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