a) Convert the point (5, -4,-5) to cylindrical coordinates. Give answer for radius and angle as positive values. Round to decimal place if needed. b) Find an equation in polar coordinates that has the same graph as the equation y4 = -5X4 - 3 in rectangular coordinates. Give your answer in form r = f(θ) c) Draw the polar curve by equation r = 4 + 4 cos θ

The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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Answer:

The LCD of 1/6 and 1/3 is 6.

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/6, 1/3

For the denominators (6, 3) the least common multiple (LCM) is 6.

LCM(6, 3)

Therefore, the least common denominator (LCD) is 6.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/6 = 1/6 × 1/1 = 1/6

1/3 = 1/3 × 2/2 = 2/6

False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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Answer:

35

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

m=2

3m²- 2m- 7

3(2)² -2(2) -7

3(4)- 4- 7

12- 4- 7= 1

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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Let his original bill be x.

0.06x = 4.89

x = $81.5

A) On Monday a driver purchased 18 gallons of gas for $61.38, then the price of gas per gallon on Monday was $3.41.

B) The next day the price of gas was $3.29 per gallon, the driver would have saved $2.82 if he waited until Tuesday to buy gas.

Part A: To find the price of gas per gallon on Monday, we need to determine the cost per unit of gas. To do this, we divide the total cost by the number of gallons. The formula is:

Price per gallon = Total cost ÷ Number of gallons

Plug in the given values:

Price per gallon = $61.38 ÷ 18 gallons

Perform the division:

Price per gallon = $3.41 per gallon

So the price of gas per gallon on Monday was $3.41.

Part B: To find the amount of money the driver would have saved if he waited until Tuesday to buy gas, we need to find the difference in price per gallon and then multiply that by the number of gallons purchased. The formula is:

Savings = (Price per gallon on Monday - Price per gallon on Tuesday) × Number of gallons

Plug in the given values:

Savings = ($3.41 per gallon - $3.29 per gallon) × 18 gallons

Perform the calculation:

Savings = $2.82

So the driver would have saved $2.82 if he waited until Tuesday to buy gas.

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The average speed of the driver based on the distance travelled and the time is  99 km / hr.

Average speed is the total distance travelled per time. Average speed can be determined by dividing total distance by total time.

Average speed = total distance / total time

Total time = 11 - 9 = 2 hours

Average speed = 198 / 2 = 99 km / hr

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Answer:

Part A

The addition equation that gives Amber's total running time is presented as follows;

Amber's total running time = 1/6 hr + (1/6 + 1/12) hr  + 5/12 hr

Part B

Amber's total running time = 5/6 hr = 50 minutes

Step-by-step explanation:

Part A

The given parameters are;

The time duration Amber first ran = 10 min = 1/6 hr

The time duration Amber walks in between = 5 min = 1/12 hr

The increase in the number of minutes Amber runs in subsequent times = 5 min = 1/12 hr

Therefore, the Amber's total time is given as follows;

1/6 hr + 1/12 hr + (1/6 + 1/12) hr + 1/12 hr + x hr = 1 hr

7/12 hr + x hr = 1 hr

x hr = 1 hr - 7/12 hr  = 5/12 hr

x = 5/12

Therefore, her total running time is given by the following addition equation;

Amber's total running time = 1/6 hr + (1/6 + 1/12) hr  + 5/12 hr

Part B

Therefore her total running time is given as follows;

Amber's total running time = 1/6 hr + (1/6 + 1/12) hr  + 5/12 hr = 5/6 hr = 50 minutes

Answer:cube root 381.7

Then half it too find the radius.

Step-by-step explanation:

The expression sin(e^37) does not have a well-defined limit as x approaches 0 from the left side since the argument e^37 is not an angle and is a constant.

To find the limit of the function sin(e^37) as x approaches 0 from the left side, we need to evaluate the limit and analyze the behavior of the function near 0.

The expression sin(e^37) represents the sine of a very large number, approximately equal to 5.32048241 × 10^16. The sine function oscillates between -1 and 1 as the input increases, but it does so in a periodic manner.

As x approaches 0 from the left side (x < 0), the function sin(e^37x) will oscillate rapidly between -1 and 1. However, since the argument of the sine function (e^37) is an extremely large constant, the oscillations will occur at a much higher frequency.

To calculate the limit, we can directly evaluate the function at x = 0 from the left side.

sin(e^37 * 0) = sin(0) = 0.

Therefore, the limit of sin(e^37) as x approaches 0 from the left side is equal to 0.

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The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

Answer:

-17/5

Step-by-step explanation:

Multiply ten to everything to get

6x-1= x+2-20

Simplify to 5x= -17

Solve to get x = -17/5

The value of IVP by use of Laplace transforms is y(t) = 3 - 2t + 20e^{-3t}(t+1) - 15e^{-3t}.

As per data IVP is:

4y′′ + 12y′ + 9y = 60, δ(t−2), y(0) = −4, y′(0) = 24.

In order to solve this differential equation, we'll need to use the Laplace transform method.

The formula for Laplace Transform is:

L{f(t)} = ∫0∞f(t)e−st dt

Where s is a complex variable and f(t) is a function of t.

So, Applying Laplace transform to given differential equation, we get:

L{4y′′+12y′+9y} = L{60δ(t − 2)}4L{y′′} + 12L{y′} + 9L{y}

                        = 60L{δ(t − 2)}

Using the property of Laplace transform L{δ(t-a)} = e^{-as}

So, we have

4[s²Y(s) - s.y(0) - y′(0)] + 12[sY(s) - y(0)] + 9Y(s) = 60e^{-2s}.

Now, we will substitute the initial values in the equation.

After substituting the values, we get:

4[s²Y(s) + 24s + 4] + 12[sY(s) + 4] + 9Y(s) = 60e^{-2s}

Now, we can find Y(s).

Simplifying the above equation, we get:

Y(s) = 3/s - 2/s² + 20/(s+3)² - 15/(s+3)

Now, applying the inverse Laplace transform to Y(s), we get:

y(t) = 3 - 2t + 20e^{-3t}(t+1) - 15e^{-3t}

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Part (a)

BC = opposite side (furthest leg from the reference angle)

AB = adjacent side (closest leg from the reference angle)

AC = hypotenuse (always opposite the 90 degree angle)

=============================================

Part (b)

i. False. Angle B is 90 degrees as shown by the square angle marker.

ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.

iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.

iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.

==============================================

Part (c)

cos(theta) = adjacent/hypotenuse = AB/AC

tan(theta) = opposite/adjacent = BC/AB

Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.

==============================================

Part (d)

The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.

sin(C) = opposite/hypotenuse = AB/AC

cos(C) = adjacent/hypotenuse = BC/AC

tan(C) = opposite/adjacent = AB/BC

Note the tangent ratio is the reciprocal of what we found back in part (c).

Answer & Step-by-step explanation:

(a)

The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))

The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)

The opposite is on the line CB (this is opposite the given angle)

(b)

i.   false (b is a right angle)

ii.  false (the side opposite C is BA)

iii. true

iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)

(c)

cosine ratio: \(cos=\frac{adjacent}{hypotenuse}\)

tangent ratio: \(tan=\frac{opposite}{adjacent}\)

The cosine and tangent ratios of the given angle:

\(cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}\)

(d)

Remember SOH-CAH-TOA:

Sine=Opposite/Hypotenuse

Cosine=Adjacent/Hypotenuse

Tangent=Opposite/Adjacent

Using the angle C, plug in the appropriate sides:

\(sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}\)

:Done

To verify the zeros of the function f(x) = -x^3 - 7x^2 - 7x + 15 at x = -5, -3, and 1, we need to substitute these values into the function and check if the result is zero.

1. For x = -5: f(-5) = -(-5)^3 - 7(-5)^2 - 7(-5) + 15 = 0
2. For x = -3: f(-3) = -(-3)^3 - 7(-3)^2 - 7(-3) + 15 = 0
3. For x = 1: f(1) = -(1)^3 - 7(1)^2 - 7(1) + 15 = 0

As f(x) evaluates to zero for all three values, we can confirm that -5, -3, and 1 are indeed the zeros of the function.

To describe the end behavior of the function, we can look at the leading term, which is -x^3. Since the exponent is odd and the coefficient is negative, the end behavior is as follows:

- As x approaches positive infinity, f(x) approaches negative infinity
- As x approaches negative infinity, f(x) approaches positive infinity

This means that the graph of the function starts in the top left quadrant (when x is very negative) and ends in the bottom right quadrant (when x is very positive).

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(a) shows that every pair of opposite sides in the hexagon a′b′c′d′e′f′ are parallel and equal in length. On the other hand, (b) demonstrates that the triangles a′c′e′ and b′d′f′ have equal areas.

(a) To show that every pair of opposite sides in hexagon a'b'c'd'e'f' are parallel and equal in length, we can use the fact that the centroids of triangles divide the medians into segments of equal length.

Let's consider a'b' and d'e'. The centroid of triangle fab, a', divides the median fb into two segments, a'f and a'b', such that a'f = 2/3 * fb. Similarly, the centroid of triangle def, e', divides the median de into two segments, e'd and e'f', such that e'd = 2/3 * de.

Since fb = de (opposite sides of hexagon abcdef), we have a'f = e'd. Now, we can consider the triangles a'f'd' and e'df'. By the properties of triangles, we know that if two sides of a triangle are equal, and the included angles are equal, then the triangles are congruent.

In this case, a'f' = e'd' (as shown above) and angle a'f'd' = angle e'df' (corresponding angles). Therefore, triangle a'f'd' is congruent to triangle e'df'.

By congruence, the corresponding sides a'd' and e'f' are equal in length.

By similar reasoning, we can show that b'c' and e'f', as well as c'd' and f'a', are parallel and equal in length.

(b) To show that triangles a'c'e' and b'd'f' have equal areas, we can use the fact that the area of a triangle is one-half the product of its base and height.

In triangle a'c'e', the base is c'e' and the height is the perpendicular distance from a' to c'e'. Similarly, in triangle b'd'f', the base is d'f' and the height is the perpendicular distance from b' to d'f'.

Since opposite sides in hexagon a'b'c'd'e'f' are parallel (as shown in part (a)), the perpendicular distance from a' to c'e' is equal to the perpendicular distance from b' to d'f'.

Therefore, the heights of triangles a'c'e' and b'd'f' are equal. Additionally, the bases c'e' and d'f' are equal (as shown in part (a)).

Using the area formula, area = 1/2 * base * height, we can see that the areas of triangles a'c'e' and b'd'f' are equal.

Hence, we have shown that triangles a'c'e' and b'd'f' have equal areas.

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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The slant height of the square pyramid that has a surface area of 304 sq. in. is: 16 inches.

Surface area (SA) = a² + 2al

Given the following parameters:

Plug in the values into (SA) = a² + 2al:

304 = 8² + 2(8)l

304 = 64 + 16l

304 - 64 = 16l

240 = 16l

240/16 = l

15 = l

l = 16

Therefore, the slant height of the square pyramid that has a surface area of 304 sq. in. is: 16 inches.

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Answer:

The profit decreases by $ 375 for every $ 1 increase in the selling price.

Step-by-step explanation:

From the definition of the secant line we get that the average rate of change of \(P(x) = -0.015\cdot x^{2}+1.2\cdot x -11.5\), where \(x\) is the selling price of the product, measured in dollars per unit, is:

\(r = \frac{P(55)-P(50)}{55-50}\) (1)

Now we evaluate the function at each bound:

x = 50

\(P(50) = -0.015\cdot (50)^{2}+1.2\cdot (50)-11.5\)

\(P(50) = 11\)

x = 55

\(P(55) = -0.015\cdot (55)^{2}+1.2\cdot (55)-11.5\)

\(P(55) = 9.125\)

Then, the average rate of change is:

\(r = \frac{9.125-11}{55-50}\)

\(r = -0.375\)

Hence, the profit decreases by $ 375 for every $ 1 increase in the selling price.

The statements that best interprets the average rate of change from x = 50 to x = 55 is (b) The profit decreases by $375 for every $1 increase in the selling price.

The profit function is given as:

\(P(x) = -0.015x^2 + 1.2x - 11.5\)

Calculate P(x), when x = 50.

So, we have:

\(P(50) = -0.015(50)^2 + 1.2(50) - 11.5\)

\(P(50) = 11\)

Calculate P(x), when x = 55.

So, we have:

\(P(55) = -0.015(55)^2 + 1.2(55) - 11.5\)

\(P(55) = 9.125\)

The average rate of change from x = 50, to 55 is then calculated using:

\(m = \frac{P(55) - P(50)}{55-50}\)

So, we have:

\(m = \frac{9.125 - 11}{55-50}\)

\(m = \frac{-1.875}{5}\)

Divide

\(m = -0.375\)

The function is in 1000 units.

So, we have:

\(m = -0.375\times 1000\)

\(m = -375\)

-375 implies a decrease of $375 for every $1 increase in sales

Hence, the correct statement is (b)

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Double ids refers to a system where there are two separate intrusion detection systems, in this case, system a and system b. The given probabilities indicate the likelihood of each system sounding an alarm in the presence or absence of an intruder.

a. Let P(Ai) and P(Bi) represent the probabilities of system a and system b sounding an alarm in the presence of an intruder, respectively. Let P and P(Bf) represent the probabilities of system a and system b sounding an alarm in the absence of an intruder, respectively. Therefore, P(Ai) = 0.9, P(Bi) = 0.95, P = 0.2, and P(Bf) = 0.1.

b. To find the probability that both systems sound an alarm in the presence of an intruder, we multiply the probabilities of system a and system b sounding an alarm: P(Ai and Bi) = P(Ai) x P(Bi) = 0.9 x 0.95 = 0.855.

c. To find the probability that both systems sound an alarm in the absence of an intruder, we multiply the probabilities of system a and system b sounding an alarm when there is no intruder: P(and Bf) = P x P(Bf) = 0.2 x 0.1 = 0.02.

d. Given that there is an intruder, the probability of both systems sounding an alarm is already calculated in part b as 0.855.

In conclusion, the probabilities of the double IDS (Intrusion Detection System) are represented by P(Ai), P(Bi), P, and P(Bf). The probability that both systems sound an alarm in the presence of an intruder is 0.855, while the probability that both systems sound an alarm in the absence of an intruder is 0.02. Therefore, the given information allows us to calculate the probabilities of the double IDS accurately in different scenarios.

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QUESTION

Solve for m in the the formula:

Solution

To solve for m

we will first multiply both-side of the equation by m

That is:

On the left-hand side of the equation m at the numerator will cancel-out m at the denominator, leaving us with just r

Next, is to divide both-side of the equation by C

At the right-hand side of the equation, c at the numerator will cancel-out c at the denominator, leaving us with just m

This implies that:

Answer:

This is geometric sequence and the common ratio is equal to ⅓.

Step-by-step explanation:

A geometric sequence has a common ratio which is gotten when we divide a term by the subsequent term in a sequence. The common difference would be the same for every two consecutive terms we divide by each other.

Thus:

8/64 = ⅛

1/8 = ⅛

Common ratio = ⅛

Answer:

the answer is 1,792!

Step-by-step explanation:

7x (3x+x)

7(8) (3(8)+8)

56 (24+8)

56 (32)

1,792

I hope this helps! :)

Answer:

1792

Step-by-step explanation:

Answer:

If I give you a nickel, what am I wanting you to tickle? my ____

Step-by-step explanation:

Answer:

297

Step-by-step explanation:

calculator

Answer: 363

Step-by-step explanation: calculator

Answer:

see explanation

Step-by-step explanation:

Median -

To find the median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.

Answer: 34

Mode -

The most frequent number—that is, the number that occurs the highest number of times.

Answer: 34

Answer:

I think

Mode = 34

Median = 34

Step-by-step explanation:

yes

im not sure though try it!