If f(x) = 7x2 ? 5x, find f?'(2) and use it to find an equation of the tangent line to the parabola y = 7x2 ? 5x at the point (2, 18).f ' (2)=y (x)=

There are 3 balanced strings in set T.

To count the number of balanced strings in the set T={0, 1, 2}, we can establish a bijection between the set of balanced strings and T itself. A balanced string is defined as a string in which the sum of its digits is a multiple of 3.

We can define a function f: T" -> T that maps each string in T" to T by preserving the balanced property. If a string in T" is already balanced, f returns the string itself. If the string is not balanced, f replaces the last digit with digit that makes the sum a multiple of 3.

By showing that this function is both injective (one-to-one) and surjective (onto), we establish a bijection. The bijection rule states that if two sets have a bijection between them, they have the same cardinality. Therefore, the number of balanced strings is equal to the number of elements in T, which is 3.

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After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

To find the area of the surface of the part of the plane x + 2y + 3z = 1 that lies inside the cylinder x^2 + y^2 = 3, we can use a parametric representation for the plane and cylinder intersection.

Let x = r * cos(θ) and y = r * sin(θ), where r^2 = 3 (from the cylinder equation). Now, we can find z in terms of r and θ using the plane equation:

z = (1 - x - 2y) / 3
z = (1 - r * cos(θ) - 2r * sin(θ)) / 3

Now, we have the parametric representation of the intersection: (r * cos(θ), r * sin(θ), (1 - r * cos(θ) - 2r * sin(θ)) / 3). To find the surface area, we need to calculate the partial derivatives with respect to r and θ and then find the magnitude of the cross product.

After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

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Answer:

33.45

16x+19

20

She bought 70 books at the thrift store.

15+x=85

Answer:

Judy bought 70 books at the thrift store.

Step-by-step explanation:

I got 70 by adding 15+70=a and a= 85

The difference between 3/7 and 1/14 is 5/14

Difference can be described as subtracting one number from the other.

The first step is to write out the fractions and subtract 1/14 from 3/7

3/7 - 1/14

= 6-1/14

= 5/14

Hence the difference between 3/7 and 1/14 is 5/14

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Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.

P(A) = f / N.

probability = 2%/100=0.0002

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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Answer:

452.389

Step-by-step explanation:

Answer:

Step-by-step explanation:

first you would want to flip the equation then multiply 9 on both sides to get

5(F-32)=9C

Then you would want to divide both sides by 5 which crosses out the 5 from the equation and is moved to the other side which then were you simplify getting

F-32=9C/5

Lastly you want to add 32 to both sides causing - 32 to cross out getting

F=9C/5 +32

making F=9C/5 + 32 our answer

Answer:

Each team needs two people for a 3-legged race.

Therefore, the number of orders (combinations) of 2 people at a time from 8 is

₈C₂ = 8!/(2!6!)

     = (8*7*6!)/(2*6!)

     = (8*7)/2

     = 56/2

     = 28

Answer: 28

Each team needs two people for a 3-legged race.

Therefore, the number of orders of 2 people at a time from 8 is

₈C₂ = 8!/(2!6!)

    = (8*7*6!)/(2*6!)

    = (8*7)/2

    = 56/2

    = 28

After solving, you will be able to know that your answer is 28

Answer:

r=f-(gm)

Step-by-step explanation:

Benz wagon has f gallons of gas

We are now told that Benz Wagon uses (g) gallons of gas for every mile traveled

Thus, amount of gas used after "m" miles is; gm

We are given r as the amount of gas remaining.

Thus;

r=f-(gm)

The graph of function g(x) = f(x - 5) on the same coordinate plane as f(x) = x is obtained by shifting f(x) five units to the right.

To graph the function g(x) = f(x - 5) on the same coordinate plane as f(x) = x, we need to apply the transformation to each point on the graph of f(x).

Let's start by understanding the function f(x) = x. This is a simple linear function where the value of y (or f(x)) is equal to the value of x. It passes through the origin (0, 0) and has a slope of 1, meaning that for every increase of 1 in x, y also increases by 1.

Now, let's consider the transformation g(x) = f(x - 5). This transformation involves shifting the graph of f(x) to the right by 5 units. This means that every point (x, y) on the graph of f(x) will be shifted horizontally by 5 units to the right to obtain the corresponding point on the graph of g(x).

To graph g(x), we can apply this transformation to a few key points on the graph of f(x). Let's choose some x-values and find their corresponding y-values for both f(x) and g(x).

For f(x) = x:

When x = 0, y = 0

When x = 1, y = 1

When x = 2, y = 2

Now, to obtain the corresponding points for g(x), we need to subtract 5 from each x-value:

For g(x) = f(x - 5):

When x = 0, x - 5 = -5, y = -5

When x = 1, x - 5 = -4, y = -4

When x = 2, x - 5 = -3, y = -3

Now, let's plot these points on the coordinate plane and connect them to visualize the graph of g(x):

The graph of f(x) = x:

The graph of g(x) = f(x - 5):

As you can see, the graph of g(x) = f(x - 5) is a shifted version of the graph of f(x) = x. It has the same slope of 1, but all the points are shifted horizontally to the right by 5 units. The point (0, 0) on the graph of f(x) becomes (-5, -5) on the graph of g(x), and so on.

This transformation is useful for shifting functions horizontally, allowing us to study how changes in the input affect the output.

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Answer:

The correct answer is B

Step-by-step explanation:

zzzz

Answer:

30 cubes

Step-by-step explanation:

10 x 4 x 6 = 240 in³

2 x 2 x 2 = 8 in³

240/8 = 30 cubes

Answer:

I believe 240

Step-by-step explanation:

Since ur multtiplying

10 times 4 times 6 you get 240

Answer:

8/75

Step-by-step explanation:

Ratio:

32:300

Fraction:

32/300

Simplest form(divide the numerator and the denominator by 4)

Answer: 8/75

Answer:

C is not a function but D is

Step-by-step explanation:

For one input, you can only have one output for this to be a function. For table C, the input of 4 has 4 different outputs, so it cannot be a function.

D is a function however, because each input has only one output, even if the output is the same number.

Vertically compressing the exponential parent function f(x) = 2^x by a factor of 3 means multiplying every function value by 1/3, resulting in a steeper and narrower curve closer to the x-axis.

If we vertically compress the exponential parent function f(x) = 2^x by a factor of 3, it means that every point on the graph of the function will be compressed closer to the x-axis. In other words, the function values will be multiplied by 1/3.

Let's consider a point on the original exponential function, (x, f(x)). After the vertical compression, this point will have the coordinates (x, (1/3)f(x)). For example, if f(x) = 8 for some x, after compression, the corresponding point will be (x, (1/3)(8)) = (x, 8/3).

This vertical compression affects all points on the graph uniformly, resulting in a steeper and narrower curve compared to the original exponential function.

The y-values of the compressed function will be one-third of the y-values of the original function for each x-value. Therefore, the graph will be squeezed vertically, with the y-values closer to the x-axis.

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If the \(z\)-score is \(z_1 < 0\), find the area under the curve to the right of \(-z_1\) and subtract that from 1.

If the z-score is z<0 , find the area under the curve to the right of -z  and subtract that from 1.

what is z-score?

z-score is a statistical measurement that describes a value's relationship to the mean of a group of values and the formula for the z-score is

z = (x - μ)/σ

x = data point

μ = mean

σ = standard deviation

Mean:- The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

Now,

As we know the area is just the space according to given condition

and if we find the area to the right of -z and substract it from 1 (as for z-score whole area is 1 square unit) then we get the area for z<0.

Hence,

             If the z-score is z<0 , find the area under the curve to the right of -z  and subtract that from 1.

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The measurement of angle b is 523 degree.

We know that,

Lines are divided into numerous categories in geometry, including parallel, perpendicular, intersecting, and non-intersecting lines, among others. We may draw a particular line called a transversal that meets non-intersecting lines at different locations.

Since

Corresponding angles are one of the types of angles created when the transversal intersects two parallel lines. These are produced in the transversal's matching or equivalent corners.

Now from figure we can see that,

Angle a and Angle c are corresponding angles

And it is given that,

angle a = 127 degree

Therefore,

Angle c = 127 degree

Since we know that angle of line  = 180 degree

So,

Angle b = 180 - 127

             = 53 degree

Thus,

∠b = 53 degree

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The complete question is attached below:

Answer:

1:6.

Step-by-step explanation:

210/35 = 6

so the ratio 35:210 simplifies to 1:6.

Answer:

1

Step-by-step explanation:

Substitute 3 for x and 2 for y:

3^2 - 2(3)(2) + 2^2

= 9 - 12 + 4

= 1

3^2−(2)(3)(2)+2^2

3^2−(2)(3)(2)+2^2

= 1

Ratio analysis can be made more meaningful in all the following ways except by focusing more on long-term solvency than on short-term solvency.

Ratio analysis is a mathematical technique for analyzing a company's financial documents, such as the balance sheet and income statement, to gather knowledge about its liquidity, operational effectiveness, and profitability. Fundamental equity research is built on ratio analysis.

In order to get insights into profitability, liquidity, operational effectiveness, and solvency, ratio analysis examines line-item data from a company's financial statements.

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The full question:

ratio analysis can be made more meaningful in all the following ways except by?

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The greatest common factor being 60 , the difference between these two values is 10 .

The greatest common divisor (GCD) from mathematics is the largest positive integer that splits each of two or more non-zero integers. The symbol gcd stands for the greatest common divisor of the two integers x and y. (x,y). For instance, gcd(8,12)=4 is the GCD of the numbers 8 and 12.

It is given that the GCD between 60 , z and another number is 10. We know that z lies between 35 and 55.

Now there are only two numbers between 35 and 55 which has a factor of 10.

The numbers are 40 and 50.

Hence the difference between these two numbers is 50-40 = 10

Therefore the required value is 10.

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Answer:

i think the answer is D

but it doesn't presence in the choice

Solution

Step 1

A)The domain refers to all real values of x for which the function is defined. The values of x for which the function is undefined are not a part of the domain. If you are given the equation then you can find the domain of that function by solving/ factorizing the denominator of the equation to find the zero(s) of the equation in the denominator. These values gotten are the values of x that will make the function undefined and hence are not part of the domain. Every other real value of x apart from these zero(s) obtained is part of the domain.

B)

Step 1

Factorize the denominator of the equation to find the zeroes of the equation

Step 2

Find the required factors to replace 13x and is equal to -90x²

Step3

Replace 13x with these factors

Step 4

Factorize the equation and find the values of x

Hence, the domain of the function is all real values of x except -3 and 5/6

Answer:

4

Step-by-step explanation: