Find the directional derivative of f(x, y, z) = xy + z' at the point P = (5.-5.-1) in the direction pointing to the origin. (Give an exact answer. Use symbolic notation and fractions where needed.) D(P) =

Answer:

x = 3

Step-by-step explanation:

The 2 lines intersect at (3, - 2 ) with x = 3

To calculate the volume of the air inside the garage, we need to multiply the area of the garage floor by its height.

First, let's convert the dimensions from meters to centimeters:

Length of the garage floor = 8 m = 800 cm

Width of the garage floor = 8 m = 800 cm

Height of the garage = 3 m = 300 cm

Now, we can calculate the volume:

Volume = Length × Width × Height

      = 800 cm × 800 cm × 300 cm

      = 192,000,000 cm³

Therefore, the volume of the air inside the garage is 192,000,000 cm³.

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Answer:

250 students

Step-by-step explanation:

Let the number of sixth grade students be represented by = x

We were told that:

At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. 100 sixth-grade students prefer hip hop music.

Hence:

40% of x = 100

40/100 × x = 100

40x/100 = 100

Cross Multiply

40x = 100 × 100

x = 10000/40

x = 250

The number is sixth-grade students is 250 students

The Michelson-Morley experiment was conducted in 1887 to detect the existence of the luminiferous ether, which was thought to be the medium through which light traveled.

Here is the procedure for the Michelson-Morley experiment:

1. Set up a light source, a half-silvered mirror, two mirrors, and two detectors in a square configuration.

2. Split the light beam using the half-silvered mirror so that one beam goes to one mirror and the other beam goes to the other mirror.

3. Reflect the beams back to the half-silvered mirror and combine them to produce an interference pattern.

4. Rotate the entire apparatus by 90 degrees and repeat the measurement.

5. Compare the interference patterns from the two orientations.

If there is a luminiferous ether, the speed of light should be faster in the direction of the ether flow and slower in the perpendicular direction. This should produce a difference in the interference patterns.

However, the Michelson-Morley experiment showed that there was no difference in the interference patterns, indicating that the luminiferous ether did not exist.

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Using the test statistic, at the 0.05 level of significance, we do not find sufficient evidence to support the political scientist's claim and hence reject the null hypothesis.

To determine whether there is enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65%, we can perform a hypothesis test using the given data.

Let's set up the null and alternative hypotheses:

H₀: p ≤ 0.65 (Null hypothesis: The proportion of college students interested in election results is 65% or less)

Ha: p > 0.65 (Alternative hypothesis: The proportion of college students interested in election results is more than 65%)

We are given that the sample size is 265 college students, and out of this sample, 180 students say they're interested in their district's election results.

To perform the hypothesis test, we'll calculate the test statistic, which is the z-statistic in this case, using the formula:

z = (p - p₀) / √(p₀(1-p₀)/n)

Where p is the sample proportion, p₀ is the hypothesized proportion under the null hypothesis, and n is the sample size.

Let's calculate the sample proportion:

p = 180 / 265 ≈ 0.679

Now, we can calculate the test statistic:

z = (0.679 - 0.65) / √(0.65(1-0.65)/265) ≈ 1.295

Next, we'll compare the test statistic with the critical z-value at a 0.05 level of significance (α = 0.05) for a one-tailed test.

Using a standard normal distribution table or a statistical calculator, the critical z-value at α = 0.05 is approximately 1.645.

Since the test statistic (1.295) does not exceed the critical z-value (1.645), we fail to reject the null hypothesis. In other words, we do not have enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65% based on this sample.

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Step-by-step explanation:

Area of the large trapezoid :

   height * average of bases

     area = 8 * (6+11)/2 = 68 cm^2

  MINUS the area of the parallelogram   4x3 =12 cm^2

68 - 12 = 56 cm^2 = shaded region

Answer:

Both of them.

Step-by-step explanation:

Gina says the cost is 8t, which means you can easily find out the cost of each t-shirt if you know the the total cost too. Bindi says the total cost was 192, which is completely useless on its own, but paired with Gina's info, you can get the answer. Divide 192 by 8, and you get the cost of each t-shirt.

Complete question :

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:

a. More than 20 minutes? b. For 20 minutes or less

Answer: 0.0764 ; 0.9236

Step-by-step explanation:

Mean (m) = 15 minutes

Standard deviation (sd) = 3.5

Z - score :

Z = (x - m) / sd

A) more than 20 minutes

P(X > 20) ; x = 20

Z > (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z > 1.429) = 0.5 - P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 - 0.4236 = 0.0764

2) 20 minutes or less :

P(X <= 20) ; x = 20

Z < (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z < 1.429) = 0.5 + P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 + 0.4236 = 0.9236

Answer:

-x^2+12x+3

Step-by-step explanation:

remove parenthesis

collect the terms

and simplify

Answer:

A: 6

B: 16

C: 2

D: -12

Step-by-step explanation:

They are asking you to multiply the equations:

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

Distribute and you should get:

6x^3 + 16x^2 + 2x - 12

The Coefficients A,B,C, and D are 6, 16, 2, and -12.

Answer: Triangle A'B'C is a 180° rotation of triangle ABC about the origin

Answer:

Carla ran 0.1 miles per minute.

Step-by-step explanation:

To solve this, we need to use the distance formula.

The formula is d=rt, where d is the distance traveled, r is the rate in which the distance is traveled, and t is the amount of time it took to go that distance. So lets plug it all in.

d=rt

3=(r)(30)

Now, we need to do the inverse of multiplying 30 to both sides, which would be the same as dividing by 30 on both sides.

3/30=(r)(30/30)

0.1=r

The rate is 0.1. Carla ran 0.1 miles per minute.

Answer:

3/6

Step-by-step explanation:

2/3  1/2  

x2    x3

4/6  -  3/6

he ate 3/6 of the pizza

Answer: First question for the slope that passes through (-7, -2) and (6,-2) is m = 0. For the line that passes through (5, 3) and 5, -7) is m = 1/0.

I hope this helps!

Step-by-step explanation:

(−7,−2) and (6,−2)

(x₁,y₁) = (−7,−2)

(x₂,y₂) = (6,−2)

y₂ − y₁ / x₂−x₁

= −2 − −2 / 6 − −7

= 0/13

m = 0

m = y₂ − y₁ / x₂ − x₁

= −7 − 3 / 5 - 5

= −100

m = 1/0

Answer:

5 minutes

Step-by-step explanation:

\(from \: the \: above \: quetion \: we \: are \: expected \: to \: find \: time \\ time = \frac{ volume}{rate} \\ calculating \: volume \\ volume = area \: \times lenght \\ area \: of \: the \: tank = \pi \: r {}^{2} \\ area \: ofthe \: tank = 3.14 \times \frac{1.6}{2} \\ area \: of \: the \: tank = 3.14 \times 0.8 {2}^{2} = 2.0096 {}^{} \\ volume = 2.0096 \times 4 = 8.0384cm {}^{3} \\ time = \frac{8.0384}{1.7} \\ time = 4.728470588\\ time = 5 \: mins \: ( to \: nearest \: minutes) \)

Answer:

480 Pennies.

Step-by-step explanation:

25% (1980) + 35% (1980-2000) = 60%

40% (2000+) Percent of 1200 is 480 Pennies.

This equation is always true, which means that it is an identity. In other words, any value of x will satisfy the equation. Therefore, the equation has infinitely many solutions.

In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equals sign ("="). The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation, respectively. The purpose of an equation is to describe a relationship between two or more variables or quantities, such as x + 3 = 7 or y = 2x - 5. Equations can be used to solve problems and answer questions in various fields of study, such as algebra, geometry, physics, chemistry, and engineering. Solving an equation typically involves finding the value or values of the variable(s) that make the equation true. Some equations may have a unique solution, while others may have multiple solutions or no solutions at all. The study of equations and their properties is a fundamental topic in mathematics.

Here,

To solve the equation 8x + 6 = 14 - 4(2 - 2x), we can first simplify the right-hand side:

8x + 6 = 14 - 8 + 8x

Simplifying further, we get:

8x + 6 = 6 + 8x

Subtracting 8x from both sides, we get:

6 = 6

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After answering the given query, we can state that Consequently, the equation fruit tray weighs 3.21 pounds.

A mathematical equation links two statements and employs the equals sign (=) to indicate equality. In mathematics, an equation is a mathematical assertion that proves the equality of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal symbol separates the numbers by a gap. A mathematical algorithm can be used to determine how the two lines on either side of a letter relate to one another. The emblem and the particular piece of software are frequently identical. like, for instance, 2x - 4 = 2.

Let's use "b" to indicate the weight of the fruit container.

We are aware that both containers carry a combined 5.55 pounds. So that we can create an equation:

Apple basket weight of 2.34 plus banana basket weight of b equals 5.55 (total weight of both baskets)

When we simplify this solution, we obtain:

b = 5.55 - 2.34

b = 3.21 lbs.

Consequently, the fruit tray weighs 3.21 pounds.

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Jackie use the rule y = 3x+4.

Given that there is table giving the values of x and y,

The equation of a line is linear in the variables x and y which represents the relation between the coordinates of every point (x, y) on the line. i.e., the equation of line is satisfied by all points on it.

The equation of a line can be formed with the help of the slope of the line and a point on the line.

The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis.

The point refers to a point on the with the x coordinate and the y coordinate.

Considering the two points, (0, 4) and (1, 7),

By using these points, we will find the line by which the points are passing,

So, we know that equation of a line passing through two points is given by,

y - y₁ = y₂ - y₁ / x₂ - x₁ (x - x₁)

y - 4 = 7-4 / 1-0 (x - 0)

y - 4 = 3x

y = 3x+4

Hence Jackie use the rule y = 3x+4.

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Alejandro reads roughly 2/3 pages per minute as a result.

The adjective moment (my-NOOT), which means something is extremely tiny, and the object minute (MIN-it), which means 60 seconds of time, are both derived from the Latin word minutus, which means "small." Despite having distinct pronunciations, both words allude to tiny dimensions.

We need to divide the number of pages he read by the time it took him to read them.

The unit rate is:

40 pages ÷ 60 minutes = 2/3 pages per minute

So, Alejandro's reading 2/3 pages per minute.

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Answer:

\(y=-\frac{1}{2}x+5\)

Step-by-step explanation:

\(\frac{y-5}{x-0}=\frac{3-5}{4-0} \\\frac{y-5}{x}=-\frac{2}{4}\\2y-10=-x\\2y=-x+10\\y=-\frac{1}{2}x+5\)

The forward Fourier Transform formula for a signal is X(jω) = F{x(t)}. The inverse Fourier Transform formula is x(t) = F^(-1){X(jω)}. The two formulas are related by the Fourier Transform property called duality or symmetry.

1. The forward Fourier Transform formula is given by:

  X(jω) = ∫[x(t) * e^(-jωt)] dt

  This formula calculates the complex spectrum X(jω) of a signal x(t) by integrating the product of the signal and a complex exponential function.

2. The inverse Fourier Transform formula is given by:

  x(t) = (1/2π) ∫[X(jω) * e^(jωt)] dω

  This formula reconstructs the original signal x(t) from its complex spectrum X(jω) by integrating the product of the spectrum and a complex exponential function.

  The similarity between these two formulas is known as the Fourier Transform property of duality or symmetry. It states that the Fourier Transform pair (X(jω), x(t)) has a symmetric relationship in the frequency and time domains. The forward transform calculates the spectrum, while the inverse transform recovers the original signal. The duality property indicates that if the spectrum is known, the inverse transform can reconstruct the original signal, and vice versa.

3. To determine the Fourier Transform of the given signal x(t) = [-1, 1, 0, -1], we apply the defining integral:

  X(jω) = ∫[-1 * e^(-jωt1) + 1 * e^(-jωt2) + 0 * e^(-jωt3) - 1 * e^(-jωt4)] dt

  Here, t1, t2, t3, t4 represent the respective time instants for each element of the signal.

  Substituting the time values and performing the integration, we can obtain the Fourier Transform of x(t).

Note: Please note that without specific values for t1, t2, t3, and t4, we cannot provide the numerical result of the Fourier Transform for the given signal. The final answer will depend on these time instants.

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Answer:

nothing

Step-by-step explanation:

The ones digit will not change.....only the 'tens' digit will change...

Answer:

\(\left \{ {{x=2} \atop {y=2}} \right.\)

Step-by-step explanation:

Substitute the second equation into the first one:

\(4x+(2x-2)=10\\6x-2=10\\6x=12\\x=2\)

Substitute \(x=2\) into the second equation:

\(y=2\times 2-2\\y=4-2\\y=2\)

\(\therefore \left \{ {{x=2} \atop {y=2}} \right.\)

Answer:

no solution

Step-by-step explanation:

if you solve for x then you get x-x which leads you to -6=0 that is no true and undefined

x-6=x

answer

x=6

why? pag nilipag mo yung negative 6 sa kanan . magiging positive sign na sya

As we know that, in basic mathematics and algebra, 0 is additive identity and 1 is multiplicative identity, while the multiplicative inverse of any number is reciprocal of the number (say we have a number x, then it's multiplicative inverse will be 1/x) and additive inverse is the same number but with opposite sign (say we have a number x, then it's additive inverse will be -x), sum of additive inverse of a number and the number gives us 0 (i.e additive identity) and the product of Multiplicative inverse of a number and the number always gives us 1 (i.e multiplicative identity)

Hence, the required answer is A) additive identity

The volume of a square pyramid with base side length "s" and height "h" is (1/3) * s^2 * h.

To find the volume of a square pyramid, we can use the formula (1/3) * \(s^{2}\) * h, where "s" represents the side length of the square base and "h" represents the height of the pyramid.

The formula is derived from the concept of integration. Imagine dividing the pyramid into infinitesimally thin horizontal layers. Each layer can be considered as a thin disk with radius s and thickness dx. The volume of each disk is given by dV = \(\pi\) * \(r^{2}\) * dx, where r is the radius and dx is the thickness.

Integrating this volume expression from 0 to h (the height of the pyramid) will sum up all the infinitesimally thin disks, resulting in the total volume of the pyramid. Therefore, we have:

V = ∫[0, h] \(\pi\) * \((s/h*x)^{2}\)  * dx,

where s/h * x represents the radius of each disk at a particular height x.

Simplifying the integral, we get V = (1/3) * \(\pi\) *\((s/h*x)^{2}\)  * x^3 evaluated from 0 to h, which simplifies to (1/3) * \(s^{2}\) * h.

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Answer:

I'm going to say 87.0

Step-by-step explanation:

Sorry if wrong i'm D-U-M-B also