Let y = 3x^2 Find the change in y, Δy when x = 5 and Δx = 0.4 _____
Find the differential dy when x = 5 and dx = 0.4 _____

Answer: (4, 0) and (0, -18)

Step-by-step explanation:

The formula for area of a triangle is 1/2 x base x height.

Let the height = x

Then the base (length) = 2x ( twice the height)

You know have 16 = 1/2 * 2x * x

Multiply both sides by 2 to remove the 1/2:

32 = 2x * x

Simplify the right side:

32 = 2x^2

Divide both sides by 2:

16 = x^2

Take the square root of both sides:

X = 4

The height is 4 units and the length is 8 Units

A certain plane is described by 2x+3y+4z=16. Find the unit vector normal to the surface in the direction away from the origin.Firstly, we will obtain the coefficients of the x, y and z variables from the equation of the plane:2x + 3y + 4z = 16The coefficients are 2, 3, and 4 respectively.

Now, we will calculate the magnitude of the normal vector, ||N||, using the formula:||N|| = √(a² + b² + c²)where a, b, and c are the coefficients of the x, y, and z variables respectively.||N|| = √(2² + 3² + 4²)= √(4 + 9 + 16)= √29Therefore, the unit normal vector in the direction away from the origin is given by:N = (2/√29) i + (3/√29) j + (4/√29) k. Given the equation of a plane as 2x + 3y + 4z = 16, we have to find the unit vector normal to the surface in the direction away from the origin. Here's how we can do it:To find the unit vector normal to the surface, we first need to find the coefficients of the x, y, and z variables from the equation of the plane. In this case, the coefficients are 2, 3, and 4 respectively.Next, we can use the formula ||N|| = √(a² + b² + c²) to calculate the magnitude of the normal vector, where a, b, and c are the coefficients of the x, y, and z variables respectively. In this case, ||N|| = √(2² + 3² + 4²) = √29.Finally, we can find the unit normal vector in the direction away from the origin by dividing each coefficient by the magnitude of the normal vector, ||N||. Thus, the unit normal vector is:N = (2/√29) i + (3/√29) j + (4/√29) k

Therefore, the unit vector normal to the surface in the direction away from the origin is (2/√29) i + (3/√29) j + (4/√29) k.

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Answer:

2/5

Step-by-step explanation:

C is at the second tick of 6 segements, so C = 2/6 = 1/3.

If we convert all fractions to /60, you can easily see the answer:

1/3 = 20/60

2/5 = 24/60

1/4 = 15/60

1/5 = 12/60

So we're looking for an answer larger than 20/60, which is only 24/60, a.k.a. 2/5.

Answer:

2 is greater than C on the number line

Step-by-step explanation:

Answer:

congruent

Step-by-step explanation:

Answer:

18 units^2

Step-by-step explanation:

Formula for Area of trapezoid:    ( base 1 + base 2 / 2) * height

(3 + 9 / 2) * 3 = (12 / 2) * 3 = 6 * 3 = 18 units^2

I hope this helps

Answer:

18²

Step-by-step explanation:

Formula for a trapezium:

Area = base1 + base2/2 × height

3 + 9/2 × 3

= 12/2 × 3

18²

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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9514 1404 393

Answer:

  2y

Step-by-step explanation:

Eliminating parentheses, we have ...

  30x +30y -30x -28y

Grouping like terms gives ...

  (30x -30x) +(30y -28y)

Simplifying leaves ...

  0x +2y

  2y

Answer: 240 seconds OR 4 minutes

Step-by-step explanation:

Length of the train = 1 km

Length of the tunnel = 1 km

Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km

= 2000 m

Speed of the train = 30 km/hr = 8.333 metres per second

Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.

= 240 seconds = 4 minutes

To calculate the value of the observed z-score for a group of 25 seniors, we need to compare their average score to the known population mean and standard deviation.

The z-score measures the number of standard deviations a data point or sample average is away from the population mean. It is calculated using the formula:

z = (x - μ) / σ,

where x is the sample average, μ is the population mean, and σ is the population standard deviation.

In this case, the sample average is 160, the known population mean is 150, and the standard deviation is 10. Plugging these values into the formula, we get:

z = (160 - 150) / 10 = 1.00.

Therefore, the value of the observed z-score is 1.00, which corresponds to option (c).

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The system of equations we have is

Now, to find the aumented matrix, we have to have all of the variables in each equation on one side, for this in the first equation we add 1 to both sides of the equation:

And for the second equation we need to add 8y to both sides and substract 2 from both sides (this is to have variables on the left and independent number on the right):

Now, the system is left as follows

We represent this a matrix with the following form:

The first line will represent the first equation

The second line will represent the second equation

And the first column will be the x values, and the second column the y values:

I will expand on the meaning of this in the following diagram:

That last one is the aumented matrix of the system.

Answer:

6A+2C=60

Step-by-step explanation:

It mean 6 of A added to 2 of C is equivalent to a total of 60

Answer:

581 square centimeters

Step-by-step explanation:

Answer:

11 classes will have 8 students, 1 class will have 7 students

Step-by-step explanation:

Take the total number of students and divide by the number of classes

95 / 12 =7.916666

Most classes will have 8 students, 1 class will have 7 students

Answer:

C) 6870.00

Step-by-step explanation:

1 liter is equal to 1,000 mililiters.

So you must multiply 6.87 by 1,000.

You can easily do this by moving 6.87 to the left by 3 units (number of 0's in 100)

so you get

6870.00

A point is the solution of the inequality expression given as: -2x + 3y > 1 - 5x + 6y is (0, -2/3)

The inequality expression is given as:

-2x + 3y > 1 - 5x + 6y

Collect the like terms in the above expression

So, we have:

3y - 6y > 1 + 2x - 5x

Evaluate the like terms in the above expression

So, we have:

-3y > 1 - 3x

Divide both sides by -3

y < -1/3 + x

Let x = 0

So, we have

y < -1/3

This means that a point in the solution is

(x, y) = (0, < -1/3)

-2/3 < -1/3

So, we have

(x, y) = (0, -2/3)

Hence, a point is the solution of the inequality expression given as: -2x + 3y > 1 - 5x + 6y is (0, -2/3)

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Answer:

In this question, we can use the Pythagorean theorem to solve for x.

11^2 + x^2 =24^2

x^2 = 24^2 -11^2

x is about 21.3

Let me know if this helps!

The value of the triple integral is 72π.

To evaluate this triple integral in cylindrical coordinates, we first need to express the region E using cylindrical coordinates.

The cylinder x² + y² = 16 can be expressed in cylindrical coordinates as r² = 16, or r = 4. The planes z = -5 and z = 4 define a region of height 9.

So, the region E can be expressed in cylindrical coordinates as:

4 ≤ r ≤ 4

-5 ≤ z ≤ 4

0 ≤ θ ≤ 2π

The integrand √(x² + y²) can be expressed in cylindrical coordinates as r, so the integral becomes:

∭E√x²+y²dV = ∫0²π ∫4⁴ ∫-5⁴ r dz dr dθ

Note that the limits of integration for r are from 0 to 4, which means we are only integrating over the positive x-axis. Since the integrand is an even function of x and y, we can multiply the result by 2 to get the total volume.

The integral with respect to z is easy to evaluate:

∫₋₅⁴ r dz = r(4 - (-5))

= 9r

So the triple integral becomes:

∭E√x²+y²dV = 2 ∫0^2π ∫4⁴ 9r dr dθ

= 2(9) ∫0^²π 4 dθ

= 72π

Therefore, the value of the triple integral is 72π.

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a. If the claim is true, the probability of a sample mean lifetime of 36.7 hours is virtually zero.

b. Yes, a sample mean lifetime of 36.7 hours would be unusually short if the claim is true.

c. If the sample mean lifetime of 36.7 hours is observed, the manufacturer's claim becomes less plausible.

d. If the claim is true, the probability of a sample mean lifetime of 39.8 hours is approximately 0.3446.

e. No, a sample mean lifetime of 39.8 hours would not be considered unusually short if the claim is true.

Let us discuss each section separately:

a. The probability of a sample mean lifetime of 36.7 hours, given that the claim is true, can be calculated using the Z-score formula. The Z-score represents the number of standard deviations a given value is from the population mean. In this case, we can calculate the Z-score as follows:

Z = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

Plugging in the values:

Z = (36.7 - 40) / (5 / √100)

Z = -3.3 / 0.5

Z = -6.6

Using a standard normal distribution table or a calculator, we can find the probability corresponding to a Z-score of -6.6, which is virtually zero.

Therefore, P(X < 36.7) ≈ 0.

b. If the claim is true, a sample mean lifetime of 36.7 hours would be unusually short. The probability of observing a sample mean of 36.7 hours, given that the claim is true, is nearly zero. This suggests that obtaining such a low sample mean is highly unlikely if the manufacturer's claim of a population mean of 40 hours is accurate.

c. If the sample mean lifetime of the 100 batteries were 36.7 hours, it would cast doubt on the manufacturer's claim. The calculated probability of P(X < 36.7) ≈ 0 implies that the observed sample mean is extremely unlikely to occur if the manufacturer's claim is true. Thus, the claim becomes less plausible in light of the obtained sample mean.

d. Using the same formula as in part (a), we can calculate the probability of a sample mean lifetime of 39.8 hours, given that the claim is true:

Z = (39.8 - 40) / (5 / √100)

Z = -0.2 / 0.5

Z = -0.4

Using the standard normal distribution table or a calculator, we find the probability corresponding to a Z-score of -0.4 to be approximately 0.3446.

Therefore, P(X < 39.8) ≈ 0.3446.

e. If the claim is true, a sample mean lifetime of 39.8 hours would not be considered unusually short. The calculated probability of P(X < 39.8) ≈ 0.3446 indicates that obtaining a sample mean of 39.8 hours is reasonably likely if the manufacturer's claim of a population mean of 40 hours is accurate.

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Answer:

D is the correct answer

Step-by-step explanation:

your welcome

Answer:

nine and six hundred two thousandthsStep-by-step explanation:

Answer:

-5/4

Step-by-step explanation:

To find the slope, we have to use this formula:

\(\frac{y2-y1}{x2-x1}\)

in this case -2 is your first x

5 would be your first y

2 would be your second x

and 0 is your second y

so:

0 - 5

-------    = -5/4

2 - (-2)

Answer:

A = 2(7) + (1/2)(4)(4 + 9) = 14 + 26 = 40 m²

Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.

Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.

Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.

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The best mathematical model that fits the scatterplot is the logarithmic model. So, correct option is D.

To determine the best mathematical model that fits the scatterplot, we look at the coefficient of determination (R²) values for each regression model. The coefficient of determination indicates the goodness of fit of the regression model, with values closer to 1 indicating a better fit.

Given:

Linear regression R² value: 0.883

Quadratic regression R² value: 0.537

Exponential regression R² value: 0.492

Logarithmic regression R² value: 0.912

Comparing the R² values, we observe that the logarithmic regression model has the highest value of 0.912. This indicates that the logarithmic regression model provides the best fit to the scatterplot among the given options.

Therefore, correct option is D.

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540 and 5760 sandwiches can the sandwich shop create

10 fillings, 9 bread, 6 condiments

= 10 possibilities × 9 possibilities × 6 possibilities

=540

10 fillings, 9 bread, 6 condiments

= 10 possibilities × 9 possibilities × 64 possibilities

=5760

sandwich can have any no.of condiments,

let say A,B,C are condiment  then possibilities are

A,B,C,AB,BC,AC,ABC , no condiment

i.e, \(2^{6}\) = 64 possibilities.

A likelihood that something will or won't occur or exist: the condition or reality of being possible There is a chance of rain today. A potential event or object that might exist It's possible that life exists on other worlds. More about potential from Merriam-Webster.

An example of a probability that you will attend a party is if there is a 50/50 chance that you might do so. The green dress is an example of a potential option you may select from when given the choice between wearing a red dress or a green dress.

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Answer:

Rhoda

Step-by-step explanation:

sub same values of x into both expressions. The expressions are equivalent if the values of the expressions are equal