1. Find An Equation Of The Tangent Plane (In The Variables X, Y And Z) To The Parametric Surface R(U,V)=〈5u,−2u2+2v,V2〉 At The Point (15,−20,1). 2. Find A Vector Parametric Equation For The Part Of The Plane Z=100−(4x+5y) That Lies Above[0,5]×[0,4]. R⃗ (U,V)=R→(U,V)= For 0≤U≤50≤U≤5 And 0≤V≤40≤V≤4. (B) DA→=∂R⃗ ∂U×∂R⃗ ∂V=DA→=∂R→∂U×∂R→∂V= (C)
1. Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface r(u,v)=〈5u,−2u2+2v,v2〉 at the point (15,−20,1).
2. Find a vector parametric equation for the part of the plane z=100−(4x+5y) that lies above[0,5]×[0,4]. r⃗ (u,v)=r→(u,v)=
for 0≤u≤50≤u≤5 and 0≤v≤40≤v≤4. (b) dA→=∂r⃗ ∂u×∂r⃗ ∂v=dA→=∂r→∂u×∂r→∂v= (c) dA=∥dA→∥=∥∥∥∂r⃗ ∂u×∂r⃗ ∂v∥∥∥=dA=‖dA→‖=‖∂r→∂u×∂r→∂v‖= (d) Set up and evaluate a double integral for the surface area of the part of the plane z=100−(4x+5y) that lies above the square [0,5]×[0,4]. Surface area = (e) A region RR in the xyxy-plane has area 3.33.3. What is the area of the part of the plane z=100−(4x+5y) that lies above and / or below the region R? Surface area = (f) Would the method you used to answer part (e) work for a function that is not a plane?

A nurse would encourage the following foods for a client with a red blood cell count of 3.2 million cells/cm3:

Iron is essential for the production of hemoglobin, which is responsible for carrying oxygen in the blood. Vitamin C aids in the absorption of iron from plant-based sources.

A diet high in these nutrients can help maintain or improve red blood cell count. In addition to iron and vitamin C, a balanced diet that includes plenty of fruits and vegetables, lean protein, and whole grains is recommended for overall health.

The nurse may also encourage hydration and physical activity as both are important factors in maintaining healthy blood cells.

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Answer:

Step-by-step explanation:

6\(\sqrt{5\\\)

\(\sqrt{5*36}\)

\(\sqrt{180}\)

If you think about it logically, how can you take 6 out? So there was a number 36 under the root, and because of that there is a possibility to take it out, because 6 squared is 36

Answer:

The answer is TRUE

Step-by-step explanation:

It will forever be important for researchers to account for attrition or loss of participants. This helps them trace back steps.

True. It is important for researchers to account for attrition or loss of participants during follow-up as it may introduce bias and affect the validity and generalizability of the study results.

Researchers should try to minimize attrition by implementing strategies such as frequent communication with participants, offering incentives, and using follow-up methods that are less burdensome for participants. When reporting study results, researchers should also provide information on the reasons for attrition and the characteristics of those who dropped out compared to those who completed the study.

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Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.

A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.

Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and

m∠2 = 9x+12, and x = 10.

Putting the value of x, we get,

m∠1 = 6x + 18 = 6*10 + 18 = 78°

m∠2 = 9x+12 = 9*10 + 12 = 102°

m∠1 + m∠2 = 180°

Therefore, ∠1 and ∠2 are consecutive angles pairs.

We can prove that oars are parallel by converse of consecutive angles theorem.

Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel

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Given the volume of the sphere as 26667 cm³, we calculated the radius to be approximately 17.7 cm using the formula for the volume of a sphere. By multiplying the radius by 2, we found that the diameter of the sphere is approximately 35.4 cm.

To calculate the diameter of a sphere when given its volume, we can use the formula for the volume of a sphere:

V = (4/3) * π * r³

Where V is the volume and r is the radius of the sphere. Since we are given the volume, we can rearrange the formula to solve for the radius:

r = (\(\sqrt[3]{(3V / (4\pi )}\)))

Substituting the given volume V = 26667 cm³ into the formula, we have:

r = (\(\sqrt[3]{(3 * 26667 / (4\pi )))}\)

Calculating this expression, we find:

r ≈ (\(\sqrt[3]{80001 / \pi ))}\) ≈ 17.7 cm

Now that we have the radius, we can calculate the diameter by multiplying the radius by 2:

d = 2 * r ≈ 2 * 17.7 ≈ 35.4 cm

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Answer:

A

Step-by-step explanation:

Answer:

= - 7x - 25.

Step-by-step explanation:

\( \frac{ - 1}{2} (14x \ + 50) \\ \\ = - 0.5(14x + 50) \\ \\ = - 7x + - 25 \\ = - 7x - 25\)

The coordinates of A' is (-12,18) which is option c so option c is correct.

Given that:

Quadrilateral math has vertices m = (1,3), A= (-4,6|), T= (-2,7), and H=(5,9). Quadrilateral M'A'T'H' is the image after dilating MATH by scale factor of 3 about the origin.

Let take x and y coordinates

scale factor = 3

(x ,y) = (3x,3y)

So A(-4,6) = A'(3*(-4),3*(6)

=A'(-12,18)

Therefore option c (-12,18) is correct.

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Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

6/(2)+4

3+4

7(BODMAS)

But if you use calculator it we give you

5

The statistical decision based on the reported results of the hypothesis test is that the null hypothesis was rejected at the α = .05 significance level.

The t-value reported is 2.38, and the degrees of freedom are 21. This suggests that the test was likely a t-test with an independent samples design, where the sample size was n = 22 (since df = n - 1).

The p-value reported is less than .05, which indicates that the probability of obtaining the observed results, or results more extreme, under the assumption that the null hypothesis is true, is less than .05. Therefore, the null hypothesis is rejected at the .05 significance level in favor of the alternative hypothesis.

In conclusion, the statistical decision is that there is sufficient evidence to suggest that the population means are not equal, and the sample size was 22. However, we do not have information about the direction of the effect (i.e., whether the difference was positive or negative).

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Answer:

£3575

Step-by-step explanation:

If Trevor bought the car for £5000, he wants to make a 10% profit on it.

His profit will be 10% of £5000 which is (10/100) x 5000 = £500.

So, his total cost for the car and profit will be £5000 + £500 = £5500.

Since Trevor is holding a sale, he is offering a 35% discount on the car. Therefore, the discounted price of the car will be:

Discount = 35/100 x £5500 = £1925

The price at which Trevor should advertise the car is the original price minus the discount:

Advertised price = £5500 - £1925 = £3575

Therefore, Trevor should advertise the car for £3575.

The required equation of motion y(t) = Asin(wt + d) can be written by using the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b):

y(t) = 0.35sin(3.415t + 1.847)

To find the equation of motion for the given mass-spring system, we first need to find the angular frequency (w) and the amplitude (A) of the system.

The angular frequency can be found using the formula:

w = \(\sqrt{\frac{k}{m} }\)

where k is the spring constant and m is the mass attached to the spring. Given that the spring constant is 120 N/m and the mass attached is 19 kg, we have:

w = \(\sqrt{\frac{120}{19} }\) = 3.415 rad/s

The amplitude can be found using the initial displacement of the mass. The mass is displaced 0.35 meters above equilibrium, so the amplitude is:

A = 0.35 meters

Now we can write the equation of motion in the form:

y(t) = Acos(wt + d)

where d is the phase angle. To find the phase angle, we need to find the initial displacement and velocity of the mass.

The initial displacement is 0.35 meters above equilibrium, so:

y(0) = A = 0.35 meters

The initial velocity is given as 1 meter/second, which is the velocity at t = 0. Therefore:

y'(0) = -Awsin(d) = 1

We can solve for the phase angle by dividing the second equation by the first:

-sin(d) / cos(d) = 1 / (Aw)

tan(d) = -1 / (Aw)

tan(d) = -1 / (0.35 * 3.415) = -0.906

d = arctan(-0.906) = -41.427 ° = -0.724 radians (rounded to 3 decimal places)

Therefore, the equation of motion is:

y(t) = 0.35cos(3.415t - 0.724)

We can rewrite this in the form y(t) = Asin(wt + d) by using the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b):

y(t) = 0.35sin(3.415t + 1.847)

Therefore, A = 0.35 and d = 1.847 radians (rounded to 3 decimal places).

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In a valid syllogism, the conclusion follows logically from the two premises.

A syllogism contains information that is compatible with the facts, it is said to make truthful assertions.  A syllogism can, however, be true without being valid or valid without being true. When a syllogism's conclusion flows naturally from its premises, it is considered legitimate or logical. When a syllogism contains information that is compatible with the facts, it is said to make truthful assertions.

Here is a good categorical syllogism illustration: The majority of mammals have warm-blooded systems. Minor: Black dogs are all animals. Consequently, all black dogs have heated blood.

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Answer:

Point slope form is the best form to use for this particular question.

We reflect point slope form as:  \(y-y_{1} =m(x-x_1)\)

M reflects the slope, and the X and Y values are the coordinates given.

M = -2, X = 4, Y = 2

This should result in an equation that looks like this:

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

Now, if we want to turn this equation into slope-intercept form, we have to do some calculations. First of all, we have to multiply -2 with (x-4) to get

\(y-2=-2x+8\)

Next, we add two on both sides to isolate the Y variable.

Therefore, the slope-intercept equation would be: \(y=-2x+10\)

Answer:

The first choice

Step-by-step explanation:

You are setting up as you read it.  The left side has 5 x and 6 units, so you would set up 5 positive x times and 6 positive unit tiles.  On the the right you are setting up 4 positive x tiles and 3 negative unit tiles.  It is not asking you to solve with the algebra tiles, just to set it up.

Answer:

we don't have a temperature so it would be difficult to figure this out

Step-by-step explanation:

a) The  scatter diagram is shown below.

b) The estimated regression equation for the given data is given as \(y = 5.47 + 1.18x\).

c) When x = 6, the estimated value of y is approximately 12.65.

d) T

e) The sample correlation coefficient is approximately 0.8107.

f) In this case, the standard error of the estimate is approximately 5.10.

g) Without these details, it is not possible to conduct the t-test.

Scatter diagram is a visual representation of data points plotted on a Cartesian coordinate system. It is used to display the relationship between two variables.

a) To develop a scatter diagram, plot the given data points (xi, yi) on a graph, where xi represents the values of the independent variable and yi represents the values of the dependent variable. The  scatter diagram is shown below.

b) To develop the estimated regression equation, we need to find the equation of the line that best fits the data points. This line represents the relationship between the independent variable (x) and the dependent variable (y). The estimated regression equation is given by:

y = a + bx

where "a" represents the y-intercept and "b" represents the slope of the line.

Using statistical methods such as least squares regression, the estimated regression equation can be calculated. In this case, the estimated regression equation is:

y = 5.47 + 1.18x

c) To predict the value of y when x = 6, substitute x = 6 into the estimated regression equation:

y = 5.47 + 1.18(6)

y = 12.65

Therefore, when x = 6, the estimated value of y is approximately 12.65.

d) The percentage of the total sum of squares accounted for by the estimated regression equation is given by the coefficient of determination (R-squared). It represents the proportion of the total variation in the dependent variable (y) that can be explained by the independent variable (x) through the estimated regression equation.

In this case, the coefficient of determination (R-squared) is 0.6563, or approximately 65.63%. This means that the estimated regression equation can account for about 65.63% of the total variation in the dependent variable.

e) The sample correlation coefficient (r) measures the strength and direction of the linear relationship between the two variables. In this case, the sample correlation coefficient is approximately 0.8107, indicating a strong positive linear relationship between the variables.

f) The standard error of the estimate measures the average distance between the observed data points and the predicted values from the regression equation. In this case, the standard error of the estimate is approximately 5.10.

g) To test for a significant relationship using the t-test, you would need additional information such as the sample size and the significance level (α) specified in the question. Without these details, it is not possible to conduct the t-test.

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...........................

Answer:

B,C,D

Step-by-step explanation:

\( log_{5}(5) + log_{5}(125) = \\ = log_{5}(5 \times 125) = \\ = log_{5}(625) \\ = log_{5}( {5}^{4} ) \\ = 4\)

Answer:

     y

-------------

  x²¹ z⁵

Step-by-step explanation:

 (x⁻⁹ y³ z⁻²)²

-------------------

   x³ y⁵ z

   x⁻¹⁸ y⁶ z⁻⁴

-------------------

   x³ y⁵ z

        y⁶

-------------------

 x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴

      y

-------------------

     x²¹ z⁵

I hope this helps!

After simplification by rule of exponent solution is,

⇒ y /  x²¹ z⁵

We have to given that;

The expression is,

⇒ (x⁻⁹ y³ z⁻²)² /  x³ y⁵ z

Now, We can simplify by rule of exponent as;

⇒ (x⁻⁹ y³ z⁻²)² /  x³ y⁵ z

⇒  x⁻¹⁸ y⁶ z⁻⁴ / x³ y⁵ z

⇒ y⁶ / x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴

⇒ y /  x²¹ z⁵

Thus, After simplification by rule of exponent solution is,

⇒ y /  x²¹ z⁵

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Answer:

530.66

Step-by-step explanation:

to find the area you need to do pi times the radius square and to find the radius squared you just times it by its self so 13 times 13 which is 169 and pi is 3.14

so now you just do 3.14x169=530.66

Answer

$40

Explanation

Because the perfume is on sale (70% off), it only costs 30% of its original price.

So we divide the sale price of the perfume ($12) by 30%

12 ÷ 30 = 0.4

Then, we multiply 0.4 by 100

0.4 × 100 = $40

I hope it's correct

Answer:

120.

Step-by-step explanation:

It is given that a car rental sells accident insurance to 28% of its customers.

Total number of customers = 430

We need to find the number of customers that are predicted to purchase insurance.

Required no. of customers = 28% of 430

\(n=430\times \dfrac{28}{100}\)

\(n=430\times 0.28\)

\(n=120.4\)

Round to the nearest integer.

\(n\approx 120\)

Therefore, the required no. of customers is 120.