A skateboard ramp has a slope of 4/9. What is the measure of the angle the ramp forms with the ground

The second-order Taylor approximation to f(x, y) = 17 cos(x) sin(y) at the point (phi, phi/2) is given by g(x, y) = 17 cos(phi) sin(phi/2) -17(x-phi)sin(phi) sin(phi/2) + 8.5(y-phi/2)cos(phi) cos(phi/2) -17(x-phi)^2 cos(phi) sin(phi/2)/2 -4.25(y-phi/2)^2 sin(phi) sin(phi/2)/2 -8.5(x-phi)(y-phi/2)sin(phi) cos(phi/2).

g(x, y) = f(phi, phi/2) + (x-phi)f_x(phi, phi/2) + (y-phi/2)f_y(phi, phi/2) + (x-phi)^2f_xx(phi, phi/2)/2 + (y-phi/2)^2f_yy(phi, phi/2)/2 + (x-phi)(y-phi/2)f_xy(phi, phi/2).

In this case, f(phi, phi/2) = 17 cos(phi) sin(phi/2), f_x(phi, phi/2) = -17 sin(phi) sin(phi/2), f_y(phi, phi/2) = 8.5 cos(phi) cos(phi/2), f_xx(phi, phi/2) = -17 cos(phi) sin(phi/2), f_yy(phi, phi/2) = -4.25 sin(phi) sin(phi/2), and f_xy(phi, phi/2) = -8.5 sin(phi) cos(phi/2). Therefore, g(x, y) = 17 cos(phi) sin(phi/2) -17(x-phi)sin(phi) sin(phi/2) + 8.5(y-phi/2)cos(phi) cos(phi/2) -17(x-phi)^2 cos(phi) sin(phi/2)/2 -4.25(y-phi/2)^2 sin(phi) sin(phi/2)/2 -8.5(x-phi)(y-phi/2)sin(phi) cos(phi/2).

The second-order Taylor approximation to f(x, y) = 17 cos(x) sin(y) at the point (phi, phi/2) is given by g(x, y) = 17 cos(phi) sin(phi/2) -17(x-phi)sin(phi) sin(phi/2) + 8.5(y-phi/2)cos(phi) cos(phi/2) -17(x-phi)^2 cos(phi) sin(phi/2)/2 -4.25(y-phi/2)^2 sin(phi) sin(phi/2)/2 -8.5(x-phi)(y-phi/2)sin(phi) cos(phi/2).

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Step-by-step explanation:

x = Moe's money

y = Loki's money

z = Nick's money

1/5 x = 1/4 y = 1/3 z (Moe gave 1/5, Loki 1/4, Nick 1/3, but all donations to Ott are the same amount of money).

that also means

y = 4/5 x

z = 3/5 x

in total the group has

x + 4/5 x + 3/5 x = 5/5 x + 4/5 x + 3/5 x = 12/5 x

Ott got 3× 1/5 x (since everybody gave the same amount of money, so it is in sum 3 times of what Moe gave).

so, Ott now has 3/5 x , out of a total of 12/5 x.

his fractional part is therefore

3/5 / 12/5 = 3/5 × 5/12 = 3/12 = 1/4.

he has 1/4 of the group's total money.

Answer:

4

Step-by-step explanation:

By finding the probability, we can expect that 2 out of the 30 students will win the prize.

First, we should get the probability of winning this game.

Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.

Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:

p = 1/6

The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:

q = 1/5

The joint probability is then:

P = 2*(1/6)*(1/5) = 1/15.

Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.

Then the expected number of students that will win is equal to the probability times the total number of students:

(1/15)*30 = 2

So out of the 30 students, we can expect that 2 will win.

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The associated z score for filling to 10.98 oz. is -1.16.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

where x is the raw score, μ is the mean and σ is the standard deviation.

Given that μ = 12.01, σ = 0.89, hence:

For x = 10.98:

z = (10.98 - 12.01)/0.89 = -1.16

The associated z score for filling to 10.98 oz. is -1.16.

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Answer:

y<1

Step-by-step explanation:

-8y+3>-5

-8y>-8

y<1

Step-by-step explanation:

\(5x + 3x - 4 = 10 + 8x \\ 8x - 4 = 10 + 8x \\ 8x - 8x = 10 + 4 \\ = 14\)

Since x has been eliminated (8x-8x = 0), there are no solutions in this equation.

Answer:

x = -3, -1, 1, 3.

Step-by-step explanation:

x^4 - 10x^2 + 9 = 0

Step 1

Let t = x^2

So , we have the quadratic

t^2 - 10t + 9 = 0

Step 2

Factorise:

(t - 1)(t - 9) = 0

Step 3

So, t - 1 = 0 or t - 9 = 0

t = 1, 9.

But t = x^2

So, we have x^2 = 1 or x^2 = 9

So, x = ±1, ±3.

x = -3, -1, 1, 3.

The slope or gradient of the blue line from the given graph is -3.3.

The equation of line is shown in the graph.

The slope or gradient of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope or gradient = Rise/Run

From the given graph, the gradient of a line is

Slope = rise/run

= -4/1.2

= -3.3

Hence, the slope or gradient of the blue line from the given graph is -3.3.

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Answer:

with my own opinion the answer is b

Using the z-distribution, it is found that the margin of error is of 0.059.

We are given the standard deviation for the population, hence the z-distribution is used.

It is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which:

In this problem, the parameters are:

Then:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(M = 1.645\frac{0.25}{\sqrt{49}}\)

\(M = 0.059\)

The margin of error is of 0.059.

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Answer:

the answer is 14.13 in³ for the volume

Answer:

5

Step-by-step explanation:

Maximum: the value of y where the height of the function is greater than (or equal to) the height anywhere else in that interval.

From inspection of the graph, the maximum is 5

This is a graph of \(f(x)=2\sin(x)+3\)

Range: \(1\leq f(x)\leq 5\)

Answer:

maximum: 5, minimum: 1

Explanation:

check out the image for better visualisation:

The maximum number of deliveries the appliance company can make in one month is 53

What does the monthly of $4,000 for delivery service mean?

The monthly budget of $4,000 for delivery service means that the company cannot afford to spend more $4,000 on delivery service each month, in essence, the maximum number of deliveries per month is a function of the cost per delivery and total budgeted delivery cost per month

Total budgeted cost=cost per delivery*number of deliveries per month

Total budgeted cost=$4,000

cost per delivery=$75

number of deliveries per month=unknown(assume it is X)

$4,000=$75*X

X=$4,000/$75

X=53( rounded to the nearest whole number)

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In part (a), we are asked to sketch the graph of the function f based on the inequality given. In part (b), we need to use the definition of a derivative to determine if the function is differentiable

(a) To sketch the graph of the function f based on the inequality -r² + 2x ≤ 1, we can rewrite the inequality as 2x ≥ r² - 1. This equation represents the region above the curve of the function f. The graph will depend on the range of x and r values specified.

(b) To determine if the function is differentiable at r = L, we need to check if the derivative of the function exists at that point. Using the definition of a derivative, we calculate the limit as Δr approaches 0 of (f(L + Δr) - f(L))/Δr. If the limit exists, the function is differentiable at r = L.

(c) To determine if the function is continuous at r = 1, we need to check if the function is defined and the limit as r approaches 1 exists and is equal to the value of the function at r = 1. If the function is defined at r = 1 and the limit exists, and the two are equal, then the function is continuous at r = 1.

In conclusion, in part (a), we sketch the graph of the function f based on the given inequality. In part (b), we use the definition of a derivative to determine differentiability at r = L. In part (c), we determine continuity at r = 1 by checking the function's definition and the limit as r approaches 1.

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The estimate for the sum of the numbers is 230, and the actual sum of the numbers is 209.

To estimate the sum of the numbers, we can round each number to the nearest ten and then add them together. When rounding off to the nearest tens, we look at the number at the tenth position. If it is five and above, we round it off to the next nearest tens number and if it is below five, we round it off to the previous nearest tens number.

76 rounds to 80   since 6 is above 5
6 rounds to 10 since 6 is above 5
25 rounds to 30 since 5 is located at 5 and above interval
5 rounds to 10 since 5 is located at 5 and above interval
10 rounds to 10 since 0 is below 5
87 rounds to 90 since 7 is above 5

So, the estimate for the sum of the numbers is: 80 + 10 + 30 + 10 + 10 + 90 = 230

To find the actual sum of the numbers, we simply add them together without rounding:

76 + 6 + 25 + 5 + 10 + 87 = 209

The complete question is: 76. 6 25. 5 10. 87 =

What was Sela's estimate and what is the actual sum of the number?

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Answer and Step-by-step explanation:

This graph is linear. The graph would look like this:

#teamtrees #WAP (Water And Plant) #PAW (Plant And Water)

#PAWG (Plant And Water Gang)

First, let´s calculate the length of the sides of the triangle, by calculating the distance between the given points.

Use the following formula:

where (x1,y1) and (x2,y2) are the limits of a segment with length d.

Then, the ditance between points X and Y is;

The distance between points Y and Z is:

and the distance between points Z and X is:

Then, you have two sides with the same length, which are sides XY and YZ and another side with a different length.

When a triangle has two sides with the same length, such a triangle is isosceles.

The equation of the line perpendicular to y = 3x + 5 and passing through the point (3, -1) is y = (-1/3)x.

To find the equation of a line that is perpendicular to y = 3x + 5 and passes through the point (3, -1), we need to consider the slope of the given line.

The given line has a slope of 3, as it is in the form y = mx + b, where m represents the slope.

For a line to be perpendicular to y = 3x + 5, its slope must be the negative reciprocal of 3. The negative reciprocal of 3 is -1/3.

Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values of the point (3, -1) and the slope -1/3 to get:

y - (-1) = (-1/3)(x - 3)

Simplifying:

y + 1 = (-1/3)x + 1

Rearranging the equation:

y = (-1/3)x + 1 - 1

y = (-1/3)x

Therefore, the equation of the line perpendicular to y = 3x + 5 and passing through the point (3, -1) is y = (-1/3)x.

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Answer:

BD = 21 units

Step-by-step explanation:

By applying mean ratio theorem in the given triangle ABC,

\(\frac{AD}{BD}=\frac{BD}{CD}\)

AD × CD = BD²

21 × 21 = BD²

BD² = (21)²

BD = 21

Therefore, measure of segment BD is 21 units.

Answer:

A contractor bought 10.8 ft2 of sheet metal. has used 3.5 ft2 so far and has 146$ worth of sheet metal remaining. The equation 10.8x-3.5x=146 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?

The volume of the triangular prism = base area x height

Since its base is a right triangle, then

From the figure leg1 = 6 ft and leg2 = 8 ft

Now multiply it by the height of the prism

Since its height = 12 ft, then

The answer is A

The set can be written as: {6a + 2b | a, b ∈ Z} which means that the elements of the set are all possible values of 6a + 2b where a and b are integers. Written with braces, the set would look like this: { ..., -14, -8, -2, 4, 10, 16, ... }.

This set is defined as the set of all possible values obtained by multiplying any integer 'a' by 6 and any integer 'b' by 2 and then adding the results. Therefore, the set contains all the integers that can be expressed as 6a + 2b, where 'a' and 'b' are integers.

To list the elements of this set between braces, we need to find all possible combinations of values of 'a' and 'b' that belong to the set of integers 'Z' and substitute them into the expression 6a + 2b. This gives us the set of all possible values that can be obtained by multiplying an integer by 6 and another integer by 2 and then adding the results.

The resulting set includes all even integers since 6a is even for all integer values of a, and the sum of two even integers is always even. Therefore, we can write the set as follows:

{..., -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, ...}

Understanding how to define and list the elements of sets is essential in various fields, including mathematics, statistics, and computer science. It allows us to organize data, study relationships between variables, and make predictions or decisions based on the properties of the set.

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Answer:

x = 3

Step-by-step explanation:

7x-8=13

Add 8 to each side

7x-8+8=13+8

7x = 21

Divide each side by 7

7x/7 = 21/7

x = 3

Diagonal of rectangle is changing by the rate of 4.373 in. /sec.

Rate of change (ROC) is the rate at which a variable changes over a particular period of time

To find the average rate of change, divide the change in the y-values ​​by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values ​​such as average speed or average velocity.

A ratio is a special ratio in which the two terms have different units.

the calculation part is shown in the below picture attached .

so after seeing the solution we come to an answer of = 4.373 in./sec

therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec

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Answer:

There would be 10 more Girls.

The probability that neither fire engine is available when needed is 0.0025. The probability that a fire engine is available when needed is 0.9975.

(a) The probability that neither fire engine is available when needed can be calculated by multiplying the probabilities of both engines not being available. Since the two fire engines operate independently, their availability is assumed to be independent events.

Let's denote the event "Engine 1 is not available" as A and the event "Engine 2 is not available" as B. The probability of neither engine being available is equal to the probability of both events A and B occurring.

P(A) = 1 - 0.95 = 0.05 (probability of Engine 1 not being available)

P(B) = 1 - 0.95 = 0.05 (probability of Engine 2 not being available)

Since A and B are independent events, the probability of both occurring is given by:

P(A and B) = P(A) * P(B) = 0.05 * 0.05 = 0.0025

Therefore, the probability that neither fire engine is available when needed is 0.0025.

(b) The probability that a fire engine is available when needed can be calculated by taking the complement of the probability that neither engine is available. In other words, it is equal to 1 minus the probability that neither engine is available.

P(A and B) = 0.0025 (probability that neither engine is available)

P(at least one engine available) = 1 - P(A and B) = 1 - 0.0025 = 0.9975

Therefore, the probability that a fire engine is available when needed is 0.9975.

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