For the following functions f: R^3 rightarrow R and g: R rightarrow R^3, find nabla f and g' and evaluate (f compositefunction g)' (1).f(x, y, z) = xz + yz + xy, g(t) = (et, cos(t), sin(t))

Rose walks 3.2 miles every day. How many miles will she have walked in 5 days?

3.2*5 = 16 miles

Christie was on a road trip. She travelled 320.95 miles on day one, 231.45 miles on day two, and 120.32 miles on day three. How many miles did she travel during her three-day trip?

320.95 + 231.45 + 120.32 = 672.72 miles

Hugh drove 774.4 miles. His car averaged 24.2 miles per gallon of gas. How many gallons of gas did the car use?

774.4/24.2 = 32 gallons

The alternative hypothesis is two-sided if it states that a parameter is different from the null hypothesis value (i.e., it can be larger or smaller). In other words, a two-sided alternative hypothesis allows for the possibility of the parameter being either larger or smaller than the null value.

On the other hand, the alternative hypothesis is one-sided if it specifically states that the parameter is either larger than the null hypothesis value or smaller than the null value. A one-sided alternative hypothesis focuses on only one direction of the parameter's deviation from the null value.

To summarize:

- Two-sided alternative hypothesis: Allows for the parameter to be larger or smaller than the null value.

- One-sided alternative hypothesis: Focuses on either the parameter being larger or smaller than the null value.

If you would like to represent this explanation using LaTeX code, you can use the following snippet:

The alternative hypothesis is \(\textbf{two-sided}\) if it states that a parameter is \(\textbf{different}\) from the null hypothesis value. It is \(\textbf{one-sided}\) if it specifically states that the parameter is \(\textbf{larger}\) or \(\textbf{smaller}\) than the null value.

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Step-by-step explanation:

To determine the future value for the 401(k), we need to determine the amount contributed annually. It is stated that the amount the employee contributes to the fund is 9% of $45,624. $45,624(0.09) = $4,106.16 The employer contributes a maximum of 3% of the employee contribution. Therefore: $45,624(0.03) = $1368.72.  Therefore, the total annual contribution is $5,474.88, giving a future value of $196,302.40. For the Roth IRA, the monthly contributions are $352.45 giving a future value of $152,636.09. Therefore, the 401(k) has a greater future value by $43,666.31.

The value of mSW is -63.75 by using the information given about the angles mSW, mTV, and mTUV and substituting the value of x.

Given:
mSW = (12x – 5)
mTV = (2x + 7)
mTUV = (6x - 19)

To find mSW, we need to substitute the value of mSW into the equation for mTUV, since mTUV is the angle between mSW and mTV.

mTUV = mSW + mTV

Substituting the given values:
(6x - 19) = (12x – 5) + (2x + 7)
Now, let's solve the equation step by step.

First, we can simplify the equation by combining like terms:
6x - 19 = 12x - 5 + 2x + 7
Next, let's simplify the equation further by combining like terms on the right side:
6x - 19 = 14x + 2
To isolate the variable, let's move the constant terms to one side and the variable terms to the other side:
6x - 14x = 2 + 19

Simplifying:
-8x = 21
Now, we can solve for x by dividing both sides of the equation by -8:
x = -21/8
Finally, to find the value of mSW, we substitute the value of x into the equation for mSW:
mSW = 12x - 5
mSW = 12(-21/8) - 5
Evaluating this expression:
mSW = -63.75
Therefore, the value of mSW is -63.75.

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Answer:

6i

Step-by-step explanation:

sqrt(-121) - sqrt(-25)

11i - 5i

6i

Answer: 6+x or x+6

Step-by-step explanation:

You are adding 6 to a number, in this case, we'll use x.

Answer:

A. 72

Step-by-step explanation:

Determinant of a 2x2 matrix: ad - bc

In that case,

24(18) - 30(12)

432 - 360

72

And we have our answer.

Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

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The most predictable effect of Earth's axis being perpendicular to the line between the Sun and Earth would be the absence of seasonal variations.

The tilt of Earth's axis is what causes the change in seasons as different parts of the planet receive varying amounts of sunlight throughout the year. If Earth's axis were to become perpendicular to the line between the Sun and Earth, the planet would no longer experience these seasonal variations. This means that the climate would become more consistent throughout the year, with less temperature variation between different regions. Without the tilt, the equator would receive the same amount of sunlight year-round, leading to a relatively stable climate with minimal temperature fluctuations. The regions closer to the poles, which currently experience more pronounced seasons, would see a reduction in temperature extremes.

Additionally, the absence of a tilted axis would also affect the length of daylight hours. Currently, as Earth orbits the Sun, different parts of the planet experience longer or shorter days. However, with a perpendicular axis, there would be equal amounts of daylight and darkness across all latitudes throughout the year. This would have significant implications for ecosystems, as organisms rely on daylight and darkness cues for various biological processes such as migration, reproduction, and growth.

Overall, the most predictable effect of Earth's axis being perpendicular to the line between the Sun and Earth would be the loss of seasonal variations and the establishment of a more consistent climate throughout the year, with equal daylight hours across all latitudes.

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Answer:

Angle 2 = 45 degrees

Step-by-step explanation:

Angle 1 = Angle D because they are alternate interior angles.

Angle 3 = Angle A because they are alternate exterior angles.

Angle 1 = 135 degrees

Therefore, Angle D = 135 degrees

180 - Angle D = Angle 2

Angle 2 = 180 - 135

Angle 2 = 45 degrees

Based on the points on the line, the equation that represents a parallel line is B. y = -2x + 13.

The slope of the points given is:

= (Y2 - Y1) / (X2 - X1)

= (-17 - 9) / (7 - (-6))

= -26 / 13

= -2

The slope of lines that are parallel to each other is the same.

The means that the equation to a line that is parallel to a line that runs through points (-6, 9) and (7, -17) is y = -2x + 13.

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Answer:

the coordinates are-

(3,3)

(0,5)

(0,3)

thenks and mark me brainliestt :))

Answer:

the answer is A prime that is a set containing all the numbers in the universal set that can't be found in A

it is like removing A from the universal set

The resulting sets are not found in the set  {4, 5, 7, 8, 10, 13, 14, 16, 17, 19), therefore the choice that describes the set of numbers is (A U B)'

Sets is a collection of numbers of elements

Given the following sets

A = {1, 3, 6, 9, 12, 15, 18} and

B = {2, 9, 11, 20).

U = {integers from1 to20}

From the given sets:

A U B ={1,2,3, 6, 9, 11, 12,25, 18, 20}

The resulting sets are not found in the set  {4, 5, 7, 8, 10, 13, 14, 16, 17, 19), therefore the choice that describes the set of numbers is (A U B)'

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The distance from the chin to the forehead is 1.5 times the distance between the ears.

The average person's chin-to-forehead distance is 9 inches, and the distance between human ears is 6 inches. You are asked to compare the distance from a person's chin to their forehead to the distance between their ears.

Calculation:-

We can express the given information as:9/6

9/6 = 1.5.

Average speed is calculated by dividing the total distance something has traveled by the total time it took to travel that distance. Velocity is how fast something is going at a given moment.

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The margin of error if we want a 90% confidence interval for the true population mean age is calculated to be 1.62 years, therefore option (a) is correct.

We can use the formula for the margin of error:

Margin of error = z × (σ / √(n))

where z is the z-score for the desired level of confidence, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the z-score is 1.645. Substituting the given values, we get:

Margin of error = 1.645 × (9.84 / √(100)) = 1.62

Therefore, the margin of error is 1.62 years, which is option (a).

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The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows

                                  y = 2 (1/5)^x - 5             y = 4^x

Initial value:               2                                    1

base function:        1/5 = decay function       4 = growth function

Translation:             5 units down                    no transformation

A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.

It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.

Decay function are exponential functions with the base function as

This is the opposite of growth function which has values greater than 1

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ANSWER: dA/dt=0.17A A(0)=950

The correct differential equation and initial condition for the continuous compounding of a sum of 950$ at 17% interest are given by dA/dt = 0.17A and A(0) = 950. This represents the rate of change of the amount A(t) with respect to time and the initial investment value, respectively.

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Using the binomial distribution, it is found that there is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that at least one commits an error is given by:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{30,0}.(0.3)^{0}.(0.7)^{30} = 0.000023\)

Then:

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.000023 = 0.999977\)

There is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.

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The gravitational potential energy of the vacationers will decrease as they approach the end of the pier.

As the vacationers approach the end of the pier, their gravitational potential energy will decrease.

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It depends on the height of the object and the acceleration due to gravity.

In this scenario, as the vacationers walk out on the horizontal pier, their height above the ground remains constant. Since the height does not change, the gravitational potential energy also remains constant.

However, as they approach the end of the pier, their distance from the center of the Earth decreases. As a result, the gravitational potential energy decreases because it is directly proportional to the distance from the center of the Earth.

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Answer:

4

Step-by-step explanation:

7h-15h+40=-72

-8h=-32

h=4

To divide a number into a number with an exponent

So, factor the number then put it to the power of (how many will appear)

for example :

8 = 2 * 2 * 2

so, there are 3 of the number 2

So,

8 = 2^3

Answer:

2.25$

Step-by-step explanation:

54 divided by 24 is 2.25$

could i get a heart and branliest please?

Answer:

$2.24 per pound of cat food

Step-by-step explanation:

You just divide the price from the amount of pounds of cat food.

It is important to carefully evaluate the results of any study before drawing conclusions about the effectiveness of a treatment.

Yes, the result of a study can indicate whether the treatment is effective. However, without knowing the specific study and treatment being referred to, it is impossible to provide a confidence interval. A confidence interval is a range of values that we can be reasonably confident contains the true population parameter based on the data collected from a sample.

It is typically expressed as a range of values with a certain level of confidence, such as 95% or 99%.To determine if a treatment is effective, researchers will typically conduct a study with a treatment group and a control group.

The treatment group receives the treatment being tested, while the control group receives a placebo or another standard treatment.

The researchers then compare the outcomes of the two groups to determine if there is a significant difference that can be attributed to the treatment being tested.

If the results show a significant difference, then the treatment is considered effective.

However, it is important to note that there are many factors that can affect the outcome of a study, such as sample size, study design, and the characteristics of the participants.

Therefore, it is important to carefully evaluate the results of any study before drawing conclusions about the effectiveness of a treatment.

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Answer: 6:15 > 30:80

Step-by-step explanation:

Answer:

Step-by-step explanation:

 >

A bin of 50 parts contains 5 that are defective and a sample of 10 parts is selected without replacement, then total 40,753,713 samples contain at least 4 defective parts.

A bin of 50 parts contains 5 that are defective.

A sample of 10 parts is selected without replacement.

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = Samples with precisely 4 defectives + samples with precisely 5 defects

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(^{5}C_{4}\cdot ^{45}C_{6}+ ^{5}C_{5}\cdot^{45}C_{5}\)

Using the formula \(^nC_{r} = \frac{n!}{r!(n-r)!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5!}{4!(5-4)!}\cdot\frac{45!}{6!(45-6)!}+\frac{5!}{5!(5-5)!}\cdot\frac{45!}{5!(45-5)!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5!}{4!1!}\cdot\frac{45!}{6!39!}+\frac{5!}{5!0!}\cdot\frac{45!}{5!40!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5\times4!}{4!\times1}\cdot\frac{45\times44\times43\times42\times41\times40\times39!}{6\times5\times4\times3\times2\times1\times39!}+1\cdot\frac{45\times44\times43\times42\times41\times40!}{5\times4\times3\times2\times1\times40!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 5 × 15 × 44 × 43 × 7 × 41 + 1 × 9 × 11 × 7 × 41

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 40,753,713

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Answer:

B) <

Step-by-step explanation:

b is the answer because -1 is bigger than 0 so, the answer is b.

The interest generated in Pauls savings account is $4.68

The amount generated in Larissa's savings account is $5015.80

Compound interest is interest that builds up over a certain length of time on both principal and interest. The principle is also used to account for the interest that has accrued on a principal over time. Furthermore, the cumulative principal value is used to calculate interest for the subsequent time period. The new way of calculating interest now utilized in all international financial and commercial operations is known as compound interest. When we look at the compound interest values that have built over various time periods, the power of compounding is clearly apparent.

The interest that is paid on both principle and interest and is compounded on a regular basis is known as compound interest. The interest is calculated for the new principal at regular intervals when the accumulated interest and the current principal are combined. The initial principal plus the interest that has already accrued make up the new principal.

The initial principal(p) of Paul is $1000

rate(r) is 5.5%

Number of days(t) = 20th March to 20th April = 31 days = 31/365 years

So the Amount generated =\(p * (1 + \frac{r}{365})\x^{365*t}\)

⇒ A = \(1000* (1 + \frac{5.5}{100*365})\x^{31} = 1000*1.00468 = 1004.68\)

The interest generated = 1004.68 - 1000 = $4.68

Similarly for Larissa

time = 24th Feb to 17th March = 21 days = 21/365 years

So the Amount generated =\(p * (1 + \frac{r}{365})\x^{365*t}\)

⇒ A = \(5000* (1 + \frac{5.5}{100*365})\x^{21} = 5000*1.00317 = 5015.80\)

The amount generated is $5015.80

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