Janice has 400g of sugar and 2 kg of flour. She says that the ratio of sugar to flour simplifies to 200:1. Explain why she is incorrect and give the correct answer.

The slope and derivative of a vertical tangent are both undefined due to the vertical nature of the tangent line.

The slope/derivative of a vertical tangent.
A vertical tangent occurs when a curve has a point where its tangent line is vertical.

In terms of the slope and derivative, the following is true about the vertical tangent:
Slope:

The slope of a vertical tangent is undefined because the vertical line has no run (change in x). Slope is calculated as the rise (change in y) divided by the run (change in x), and division by zero is not possible.
Derivative:

The derivative of a function at a point represents the slope of the tangent line to the curve at that point.

When the tangent is vertical, the derivative is also undefined because the slope is undefined.

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Answer:

34/45+90

Step-by-step explanation:

474\88

88*78/67

55-66/34*34

= 75

Answer:

I will not give you an answer, but I will give you how too get the equation started.

Step-by-step explanation:

set up an equation using:

x= amount invested at 3%

7800 - x = amount invested at 12%

.03(x) + .12(7800 - x) = 504

.03x +936 - .12x = 504

-.09x = -432

x = 4800

Answer:

20 P 9 means selecting 9 objects (order matters) out of 20 objects.

So in this case, the eight choice of a line up of 9 has 13 options.

For example, think about it this way. The first choice has 20 options, 2nd has 19, and so on...

So the answer is 13

Let me know if this helps!

The value of "x" is the unknown number that, when multiplied by 12, gives a result of 72. By solving the equation, we find that the unknown number is 6.

Let's call the unknown number "x". The statement "When 12 is multiplied by a number, the result is 72" can be represented mathematically as:

12 * x = 72

This equation states that when we multiply 12 by the unknown number "x", we obtain a product of 72. To find the value of "x", we need to solve this equation.

To solve for "x", we can divide both sides of the equation by 12:

(12 * x) / 12 = 72 / 12

Simplifying, we have:

x = 6

Therefore, the equation that fits the given statement is:

12 * x = 72

Where "x" is equal to 6.

In this equation, the value of "x" is the unknown number that, when multiplied by 12, gives a result of 72. By solving the equation, we find that the unknown number is 6.

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To draw the digital circuit corresponding to the expression x(yz' + z), we can break it down into logical operations.

The given expression involves the logical operations of NOT, AND, and OR. In the circuit diagram, we would have three inputs: x, y, and z. Firstly, we need to calculate the complement of z (represented as z') using a NOT gate. The output of the NOT gate would then be connected to one input of the AND gate. The other input of the AND gate would be connected directly to the input y.

The output of the AND gate would be connected to one input of the OR gate. Finally, the input x would be directly connected to the other input of the OR gate. The output of the OR gate would be the result of the expression x(yz' + z).

The circuit would consist of an input x connected directly to an OR gate, while an input y would be connected to one input of an AND gate along with the complement of input z (z') obtained through a NOT gate. The output of the AND gate would be connected to the other input of the OR gate, and the output of the OR gate would represent the result of the given expression x(yz' + z).

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Answer:

The perimeter of the tabletop is 152 inches

Step-by-step explanation:

So if P = 2L + 2W we have to do

(2*48) + (2*28)

So

96 + 56 = 152

Answer:

14

Step-by-step explanation:

27-13

Step-by-step explanation:

Let A be Alvin's age and E be Elga's age

A + E = 27

also A + 13 = E

Substitute for A in the first equation

E -13 + E = 27

2E = 40

E = 20, so Elga is 20 years old and Alvin is 7.

Answer:

try your best

Step-by-step explanation:

Answer:

14.

Step-by-step explanation:

-67 - (-81)=14

y= 3/8 OR 0.375

Step-by-step explanation:

yes

Answer:

y = - 4.5

Step-by-step explanation:

2y - 3 = 4y + 6 ( subtract 4y from both sides )

- 2y - 3 = 6 ( add 3 to both sides )

- 2y = 9 ( divide both sides by - 2 )

y = - 4.5

Factorizing this expression p² - 36 = (p+6 )(p − 6)

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

The expression is given as p² - 36. This will be:

= p² - 6²

= (p - 6) (p + 6)

In conclusion, the expression is (p - 6) (p + 6)

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The width of the rectangle is (x-8).

Given that, the area of a rectangle is x²-10x+16 and the length is x-2,

So, we know that the area of a rectangle is the product of its dimension,

we will factories the given polynomial and the factors obtained will be the dimensions of the rectangle,

Factorizing the polynomial,

= x²-10x+16

= x² - 8x - 2x + 16

= x(x-8) - 2(x-8)

= (x-2)(x-8)

We can say the (x-2) and (x-8) are the dimension of the rectangle.

Since, the area of a rectangle is the product of length and the width.

Hence, the width of the rectangle is (x-8).

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The work done by force f in moving a particle counterclockwise around the given curve is zero.

The given force \(f = (x-5y)i + (5x-y)j\) is a conservative force. A conservative force is characterized by having a curl of zero, indicating that it can be derived from a potential function. For conservative forces, the work done over a closed path is always zero.

In this case, the particle moves counterclockwise around the circle defined by \((x-4)^2 + (y-4)^2 = 16\). Since the force f is conservative, the work done by f on the particle is independent of the path taken and depends only on the initial and final positions of the particle.

As the particle completes one counterclockwise revolution around the circle, it returns to its initial position. Therefore, the work done by force f is zero, indicating that the force does not transfer any energy to or from the particle.

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The recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2. (Correct choice: A)

A recursive formula is a formula to find the value of an element in terms of previous elements of the same series. According to the statement, a sequence is defined by f(n) = - 4 + 2 · n. To derive the recursive definition, we must use algebra properties on the following difference:

Δf = - 4 + 2 · (n + 1) - (- 4 + 2 · n)

Δf = 2

n = 1

f(1) = - 4 + 2 · 1

f(1) = - 2

Then, the recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2.

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Micah's best long jump will be 3 meters as per the given data.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

Lets Avi's best jump = A

Micah's best jump = M

Now,

Avi's best long jump is 1 1/6 times as long as Micah's.

So,

A = 1 1/6 M = 7/6 M

And,

Avi's best long jump is 3 1/2 meters.

A = 3 1/2 = 7/2

By substituting,

7/2 = 7/6 M ⇒ M = 3 meter.

Hence "Micah's best long jump will be 3 meters as per the given data".

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Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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Answer:

You would DIVIDE to solve this problem.

each runner will

get 1/6 gallon of apple juice

Step-by-step explanation:

Answer:

  f'(x) = -2/√(x³)

Step-by-step explanation:

You want the derivative of f(x) = 4/√x.

The power rule for derivatives is ...

  \(\dfrac{d}{dx}(x^n)=nx^{(n-1)}\)

Applied to the given function, we have ...

  \(f(x)=\dfrac{4}{\sqrt{x}}=4x^{-\frac{1}{2}}\\\\f'(x)=4(-\frac{1}{2}x^{-\frac{3}{2}})\\\\\boxed{f'(x)=-\dfrac{2}{\sqrt{x^3}}}\)

__

Additional comment

The first attachment shows a calculator gives the same result.

The second attachment shows the derivative curve matches the one described by the function we found.

This is because

This is found through trial and error.

This is for problem 1 only. Problems 2 through 6 will follow a similar structure.

The sampling Distribution of the sample proportion of people who answer yes to the question is normal with mean p = 0.6 and standard deviation σp = 0.049.

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading. We will take a random sample of 100 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is binomial.

The binomial distribution is appropriate since there are two possible outcomes: either a person believes that Martha Stewart is guilty of obstruction of justice and fraud related to insider trading or does not believe so. The sample size is n = 100.

The probability of a person believing that Martha Stewart is guilty is p = 0.6 and the probability of a person not believing is q = 1 - p = 0.4.

The mean of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:μp = p = 0.6

The variance of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:σ²p = pq/n = (0.6)(0.4)/100 = 0.0024

The standard deviation of the sample proportion of people who believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading is given by:σp = sqrt(σ²p) = sqrt(0.0024) = 0.049

This standard deviation measures how much the sample proportion is likely to vary from one sample to another. The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal by the Central Limit Theorem (CLT) if the sample size is sufficiently large, which is the case here since np and nq are both greater than or equal to 10: np = (100)(0.6) = 60 and nq = (100)(0.4) = 40.

Therefore, the sampling distribution of the sample proportion of people who answer yes to the question is normal with mean p = 0.6 and standard deviation σp = 0.049.

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Answer:

The common ratio is 5

Step-by-step explanation:

We know this because the first term times 5 equals the second term and the second term times five equals the third term and so forth.

Answer: 30-4=x  4+x=30 x=26

Step-by-step explanation: So he has 30 tickets and he gives 2 to each of his friends which means that lee has 26 friends with 4 tickets left over.

Answer:

20.40

Step-by-step explanation:

Answer:

10 dollars. I think.

Step-by-step explanation:

Answer:

hi i think the answer shouldbe 34/43 as its out of 43 and there is 34 people on the internet. I think this should be write but it may  be wrong. if this is right please vote for brainliest. i hope my answer is right and this helps bye.

The 95% confidence interval for the true mean weight of all packages received by the parcel service is: 17.17 to 18.63 pounds.

The formula to find the 95% confidence interval for the true mean weight of all packages received by the parcel service is:

Confidence Interval = sample mean ± (critical value * standard error)

The standard error (SE) is calculated using the formula:

SE = standard deviation/√sample size

The parameters are given as:

Sample mean weight: x' = 17.9 pounds

Standard deviation: σ = 2.1 pounds

Sample size: n = 32

Thus:

SE = 2.1/√32

SE ≈ 0.3717

The critical value for a 95% confidence level with a sample size of 32 is: z = 1.96

Thus:

Confidence Interval = 17.9 ± (1.96 * 0.3717)

Lower bound = 17.9 - (1.96 * 0.3717) = 17.17

Upper bound = 17.9 + (1.96 * 0.3717) = 18.63

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Complete question is:

32 packages are randomly selected from packages received by parcel service. the sample has a mean weight of 17.9 pounds and a standard deviation of 2.1 pounds. What is

Answer:

see below (I hope this helps!)

Step-by-step explanation:

Alternate exterior angles are congruent so we know that ∠2 ≅ ∠ 7. Vertical angles are also congruent so ∠7 ≅ ∠6. Consecutive interior angles are supplementary so we know that ∠6 and ∠4 are supplementary. Now, we can use the Transitive Property (this states that if a = b and b = c then a = c) to compare ∠2 and ∠4. In this case, a = ∠2, b = ∠7 and c = ∠6 so we know that ∠2 ≅ ∠6 and since ∠6 is supplementary to ∠4, we can use the Transitive Property again to conclude that ∠2 and ∠4 are supplementary.