Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 6, (4,1) 4 Vf(4, 1) =

An expression that represents the given calculation is (450 + 348) × 7

The correct answer is an option (B)

"It is a combination of numbers, variables and some mathematical operations."

It is an acronym and it stands for Bracket , Order , Division , Multiplication , Addition and Subtraction .

In this question ,

its been said to first add then multiply

First add 450 to 348

(450 + 348)

now multiply the result with 7

(450 + 348  ) × 7

Therefore, an expression that represents the given calculation is (450 + 348) × 7

The correct answer is an option (B)

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12 is the equivalent value of x from the diagram.

The given diagram is a line geometry. We are to determine the value of x from the diagram.

From the given diagram, we can see that the line m is parallel to line n. Hence the equation below will fit to determine the value of 'x'

132 + 3x + 12 = 180 (Sum of angle on a straight line)

3x + 144 = 180

3x = 180 - 144

3x = 36

x = 36/3

x = 12

Hence the value of x from the line diagram is 12.

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Answer:

x=68°

Step-by-step explanation:

In quadrant 3 the FULL  value is 90°

90°-22°

=68°

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

Hope this helped!!

Answer:

68 degrees

Step-by-step explanation:

The probability of reaching into a box and randomly drawing a specific chip, such as chip 107, is calculated as the number of favorable outcomes (in this case, one chip) divided by the total number of possible outcomes (the total number of chips in the box).

If only one chip numbered 107 in the box, then the probability of randomly drawing that chip would be 1/N, where N is the total number of chips in the box. If there are multiple chips numbered 107, the probability would be the number of chips numbered 107 divided by the total number of chips in the box.

So, if there is only one chip numbered 107 in the box, and the total number of chips in the box is N, the probability of randomly drawing that chip would be 1/N. If we don't know the value of N, we can't calculate the probability exactly.

It's worth noting that probabilities are always between 0 and 1, inclusive, where 0 means an impossible event, and 1 means a certain event.

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Answer:

Just be yourself

Step-by-step explanation:

Answer:

B- hope this helps:)

Step-by-step explanation:

The total cost to paint 864.5 square feet of wall is $2,048.87.

It is given that the cost to paint one square foot of wall is $2.37.

We are asked to find the total cost to paint 864.5 square feet of wall.

If we have a number that has a decimal point then we have two parts.

The whole number part and the fractional part.

After the decimal point, we will count the place value as tenths, hundredths, thousandths, and so on.

You can also see the given figure below.

We know that,

One square foot = $2.37.

Remember that Feet is the plural form of the foot.

We can write,

864.5 square feet = 864.5 x  one square foot

Because in 864.5 square feet we have 864.5 one square foot.

And since one square foot cost $2.37.

864.5 square feet will cost 864.5 x 2.37 dollars.

Now,

864.5 x 2.37 = $2048.865.

Rounding to the nearest hundredth.

6 is in the hundredth place so we will round 86 to 87 since the number in the thousandth place is greater than 4.

Thus the total cost to paint a wall of 864.5 square feet is $2,048.87.

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Answer:

the scale factor is 3 ......

The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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Answer

search how they got the answer

Step-by-step explanation:

Answer:

√63

Step-by-step explanation:

a² + b² = c²

1²=1

8²= 64

now think what + 1 = 64

√63  

Answer:

b= √63

b ≈ 7.94

Step-by-step explanation:

Pythagorean theorem:

a² + b² = c²

b² = c² - a²

b=√c²﹣a²

b= √ (8)² - (1)²

b=√ 64 - 1

b= √63

b ≈ 7.94

The number of spanning trees of a connected graph can be proven to be the product of the number of spanning trees of each of its blocks.

Here are the steps-

1. Consider a connected graph G with blocks B1, B2, ..., Bk. Each block is a maximal connected subgraph with no cut-vertex.

2. The number of spanning trees of G can be denoted as T(G), and the number of spanning trees of each block Bi can be denoted as T(Bi).

3. To prove the given statement, we need to show that\(T(G) = T(B1) * T(B2) * ... * T(Bk).\)

4. We can start by considering a single block B1. Since B1 is a maximal connected subgraph with no cut-vertex, it is a connected graph on its own.

5. The number of spanning trees of B1, T(B1), can be calculated using any method such as Kirchhoff's theorem or counting the number of spanning trees directly.

6. Now, consider the original graph G. We can remove block B1 from G, which leaves us with a graph G' that consists of the remaining blocks B2, B3, ..., Bk.

7. G' is still a connected graph, but it may have cut-vertices. However, the removal of B1 does not affect the connectivity between the other blocks, as each block is a maximal connected subgraph.

8. The number of spanning trees of G', denoted as T(G'), can be calculated using the same method as step 5.

9. Since G' is the remaining part of G after removing B1, the number of spanning trees of G can be expressed as T(G) = T(B1) * T(G').

10. We can repeat this process for the remaining blocks B2, B3, ..., Bk. For each block Bi, we remove it from G and calculate the number of spanning trees of the remaining graph.

11. By repeating steps 6-10 for all blocks, we can express the number of spanning trees of G as-

\(T(G) = T(B1) * T(G')\)

\(= T(B1) * T(B2) * T(G'')\)

= ...

\(= T(B1) * T(B2) * ... * T(Bk).\)

12. Therefore, we have proved that the number of spanning trees of a connected graph G is the product of the number of spanning trees of each of its blocks.

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Answer:

It will be 29.39

Step-by-step explanation:

Hope this Helped

\( \sin ^{ - 1} ( \frac{4}{9}) = 26.39\)

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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The derivative of \(f(x) = ln(sin^−1(e^(x^2)))\) using chain rule is \(f'(x) = 2x * e^(x^2) / √(1-e^(2x^2)).\)

To find the derivative of the function\(f(x) = ln(sin^−1(e^(x^2)))\), we can use the chain rule and the properties of logarithmic and trigonometric functions.

Let's break down the problem step by step:

The inner function is \(sin^−1(e^(x^2))\). The derivative of \(sin^−1(u) is 1/√(1-u^2).\)

Therefore, the derivative of \(sin^−1(e^(x^2))\) with respect to \(x is 1/√(1-(e^(x^2))^2) * d/dx(e^(x^2))\).

The derivative of \(e^(x^2) with respect to x is 2x * e^(x^2).\)

The derivative of \(f(x) = ln(sin^−1(e^(x^2)))\) can be written as:

\(f'(x) = 1/√(1-(e^(x^2))^2) * 2x * e^(x^2).\)

Simplifying the expression further, we have:

\(f'(x) = 2x * e^(x^2) / √(1-e^(2x^2)).\)

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9514 1404 393

Answer:

Step-by-step explanation:

Let t represent the number of touchdowns scored. Then 35-t is the number of field goals, and the total score is ...

  7t +3(35 -t) = 193

  4t = 88 . . . . . . . . . . simplify, subtract 105

  t = 22

  35 -t = 13

The team scored 22 touchdowns and 13 field goals.

Answer:

to find parallel;

first of all, parallel equations should have the same slope and a different y-intercept!

when were given a point (x,y), we write our equation in the y = mx + b form, then substitute the given point for (x,y) and solve for B!

However, to find the slope of the perpendicular equation, you need to get the negative reciprocal of the slope!

For example, if the slope is 3 in the original equation, it would be - 1/3 in perpendicular equation.

We then substitute the given point for (x,y)!

hope this helps :)

Leave a comment if you need further explanation

Step-by-step explanation:

If the shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches then, the perimeter of the shape is 91.4 inches.

To find the perimeter of the shape, we need to know the length of the curved boundary (the circumference of the half-circle) and the length of the straight boundary (the perimeter of the equilateral triangle).

The radius of the half-circle is half the length of the side of the equilateral triangle, which is 10 inches. Therefore, the circumference of the half-circle is:

C = πr = π(10) = 31.4 inches.

The perimeter of the equilateral triangle is 3 times the length of one side, which is 20 inches. Therefore, the perimeter of the triangle is:

P = 3s = 3(20) = 60 inches

Finally, the perimeter of the entire shape is the sum of the lengths of the curved and straight boundaries:

Perimeter = C + P = 31.4 + 60 = 91.4 inches.

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Complete Question

This shape is made up of one half-circle attached to a square with side lengths 11 inches. Find the perimeter of the shape.

You can use 3.14 as an approximation for π. help i don't know it.

We are given log ( 10^3)

We can use one of the properties of logs

log u^n = n log u

Rewriting log ( 10^3) using this property

log ( 10^3) = 3 log 10

log has an implied base of 10

log 10 = 1

3 log 10 = 3 *1 =3

The two correct choices are

A. 3 * log 10

D. 3

Answer:

Step-by-step explanation:

In statistical analysis, a hypothesis refers to a tentative explanation or prediction that is based on limited evidence and is subject to further investigation and testing. It is a statement that can be either true or false, and is typically formulated in such a way that it can be tested using statistical methods.

The hypothesis is often used to guide the research process, to help identify potential patterns or relationships in the data, and to evaluate the significance of the results.

Overall, the hypothesis plays a critical role in statistical analysis, as it provides a framework for understanding and interpreting data, and helps to ensure that research findings are reliable and valid.

A hypothesis in the context of statistical analysis is a tentative explanation or prediction about the relationship between two or more variables, which is subject to testing and empirical evaluation using statistical methods.

It is a statement that can be either true or false, and it is usually formulated in terms of the expected direction and strength of the relationship between the variables of interest.

The hypothesis is typically derived from existing theory, prior research, or common sense, and it serves as a guide for the collection, analysis, and interpretation of data in a scientific study.

The process of testing a hypothesis involves setting up null and alternative hypotheses, selecting an appropriate statistical test, collecting and analyzing data, and drawing conclusions based on the results of the analysis.

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Answer:

It is 660.4 millimeters.

Step-by-step explanation:

All you have to do is multiply 25.4 by 26.

There are no extreme values of the function ƒ(x, y, z) = xy z^2 on the given intersection.

To find the extreme values of the function ƒ(x, y, z) = xy z^2 on the given intersection, we need to find the critical points.

First, let's substitute y = x into the equation of the sphere:

x^2 (x^2) z^2 = 4

Simplifying the equation, we have:

x^4 z^2 = 4

Taking the square root of both sides, we get:

x^2 z = ±2

Now, we can substitute y = x into the equation of the function:

ƒ(x, y, z) = x(x)(z^2) = x^2 z^2

Since we have x^2 z^2 in both the function and the equation of the sphere, we can substitute x^2 z^2 = 4:

ƒ(x, y, z) = 4

The function ƒ(x, y, z) = 4 is a constant function, which means it has no critical points.

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Answer:

The correct answers are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours.  This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour.  He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles.  This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours

Step-by-step explanation:

When an individual places their phone number on the Do Not Call (DNC) Registry, it remains there permanently, and telemarketers are prohibited from making unsolicited calls to that number until the individual requests to be removed from the list.

When an individual places their phone number on the Do Not Call (DNC) Registry, it remains there permanently, and telemarketers are prohibited from making unsolicited calls to that number until the individual requests to be removed from the list. This list is managed by the Federal Trade Commission (FTC), which enforces the Telephone Consumer Protection Act (TCPA) in the United States. If someone's phone number is on the DNC registry, the registry rules apply indefinitely. This means that even if the individual's phone number is still listed after a period of time, telemarketers are prohibited from calling that number. If the individual wishes to receive telemarketing calls again, they must remove their phone number from the list by dialing the DNC registry's phone number, which is 1-888-382-1222. The process of removing a phone number from the list is a simple one. Dial the number on your phone, and then follow the instructions that the voice prompt gives you. Furthermore, it is important to know that calls from organizations that you have given permission to call you are still allowed even if your number is on the DNC registry.

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The system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a total of 35 pounds of apples and strawberries.

Suppose the number of pounds of apples and strawberries is x and y respectively.

If the total of 35 pounds of apples and strawberries as a result,

x + y = 35-------(1)

If each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 then,

2x + 3y = 80---------(2)

Multiply equation 1 by 2 and subtract from equation 2 as

2x + 3y -2(x+y) = 80 - 2(35)

y = 10

Substitute the value of y we get x = 25

As a result, there are 25 pounds of apples and 10 pounds of strawberries in all.

Thus, the system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

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To calculate the standard error (SE) for the percentage of young adults who favor gay marriage, we need to consider the sample size and the proportion of individuals in the sample who favor gay marriage.

The formula for calculating the standard error (SE) of a sample proportion is SE = sqrt((p * (1 - p)) / n), where p is the sample proportion and n is the sample size.

In this case, the sample proportion is given as 73% or 0.73, and the sample size is 321 young adults. Substituting these values into the SE formula, we get SE = sqrt((0.73 * (1 - 0.73)) / 321).

To calculate the SE, we first calculate (0.73 * (1 - 0.73)) to get 0.1979. Dividing this value by the sample size of 321 and taking the square root, we find that the SE for the percentage of young adults who favor gay marriage is approximately 0.0211.

Therefore, the standard error (SE) for the percentage of young adults who favor gay marriage, based on the CBS news poll data, is approximately 0.0211 or 2.11%. The SE provides an estimate of the variability or margin of error associated with the sample proportion.

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(a) A/x + Bx + \(C/(1 + x) + Dx^2 + Ex/(1 - x) + Fx^2\)

(b)A/x + \(B/x^2 + C/x^3\) + D/(x - 2) + \(E/(x^2\)+ 2x + 4) + F/(x + 2) + \(G/(x^2\) - 2x + 4)

(a) To perform partial fraction decomposition on the function:

\((x^4 (x^3 + x)) / (x^2 - x^4)\)

we first factor the denominator:

\(x^2 - x^4 = x^2(1 - x^2) = x^2(1 + x)(1 - x)\)

The partial fraction decomposition of the function is:

\((x^4 (x^3 + x)) / (x^2 - x^4) = A/x + Bx + C/(1 + x) + Dx^2 + Ex/(1 - x) + Fx^2\)

where A, B, C, D, E, and F are constants to be determined.

(b) To perform partial fraction decomposition on the function:

\(4 / (x^6 - 8x^3)\)

we first factor the denominator:

\(x^6 - 8x^3 = x^3(x^3 - 8) = x^3(x - 2)(x^2 + 2x + 4)(x + 2)(x^2 - 2x + 4)\)

The partial fraction decomposition of the function is:

\(4 / (x^6 - 8x^3)\) = \(A/x + B/x^2 + C/x^3\) + D/(x - 2) + \(E/(x^2 + 2x + 4) + F/(x + 2)\) + \(G/(x^2 - 2x + 4)\)

where A, B, C, D, E, F, and G are constants to be determined.

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