1. The Cartesian equation of the polar curve r-2sine+2cost is
a. (-1)(y-1²-2 (8) ²²2
b. X2 + y2=2
c. X + y =2
d. X2+ y2 =4
e. Y2-x2 =2

From the given information, the probability of getting at least one head in two coin tosses is 3/4 or 0.75.

A coin toss is a random event in which a coin is flipped and the outcome is either heads or tails. The outcome of a coin toss is not dependent on any previous tosses, and each toss is considered to be independent of the others.

The probability of getting at least one head in two coin tosses can be calculated as follows:

There are four possible outcomes when tossing two coins: HH, HT, TH, and TT, where H represents heads and T represents tails. Out of these four outcomes, three have at least one head (HH, HT, TH), and only one has no heads (TT).

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The Maclaurin series expansion of f(x) = cos(x⁴) is f(x) = 1 - (x⁸)/2! + (x¹⁶)/4! - (x²⁴)/6! + ... . This expansion provides an approximation of the original function in the form of an infinite sum of powers of x.

The Maclaurin series expansion of f(x) = cos(x⁴) can be found by substituting the series expansion of cosine function into the given function. The series expansion of cosine function is cos(x) = 1 - (x²)/2! + (x⁴)/4! - (x⁶)/6! + ... .

To find the Maclaurin series of f(x) = cos(x⁴), we substitute x^4 in place of x in the cosine series expansion. Thus, f(x) = cos(x⁴) = 1 - [(x⁴)²]/2! + [(x⁴)⁴]/4! - [(x⁴)⁶]/6! + ... .

Simplifying further, we get f(x) = 1 - (x⁸)/2! + (x¹⁶)/4! - (x²⁴)/6! + ... .

In summary, the Maclaurin series expansion of f(x) = cos(x⁴) is f(x) = 1 - (x⁸)/2! + (x¹⁶)/4! - (x²⁴)/6! + ... .

This expansion provides an approximation of the original function in the form of an infinite sum of powers of x. The more terms we include in the series, the more accurate the approximation becomes within a certain range of x values.

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Answer:

none. it's 1104

Step-by-step explanation:

none of the above

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of the expression is 1104.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

92 x (9 - 3) x 2

92 x 6 x 2

92 x 12

1104

Thus,

The value of the expression is 1104.

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Answer:

its 3.3 x 10 with 8 squared

Step-by-step explanation:

The sum of the areas of the enclosed regions is 2.004 , and -3.811 the rate at which h changes with respect to x when x = 1.8 .

Given : f(x) = 1 + x + e^x^2 - 2x and g(x) = x^4 - 6.5x^2 + 6x + 2

The graphs of y = f(x) and y = g(x) intersect in the first quadrant at the points (0, 2), (2, 4), and (A, B) = (1.032832, 2.401108).

(a)  the sum of the areas of the enclosed regions is given by

Area =

\(\int\limits^A_0[[g(x) - f (x)] dx +\int\limits^2_A [f(x) - g(x)] dx\)

= 0.997427 +1.006919

= 2.004

(b)  the sum of the volumes of the enclosed regions is given by

Volume = [[ƒ(x) − g(x)]² dx = 1.283

(c) the rate at which h changes with respect to x when x = 1.8

h(x) = f(x) = g(x)

h'(x) = f'(x) - g'(x)

h'(1.8) = f'(1.8) g'(1.8)

          =-3.812 (or -3.811)

Hence , the sum of the areas of the enclosed regions is 2.004 , and -3.811 the rate at which h changes with respect to x when x = 1.8 .

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1. The cost per zinnia plant is: A. $0.04

2. The linear equation is D. C = 0.04z + 15

3. The cost of purchasing 700 zinnia plants is: C. $43.

Part 1: To find the cost per zinnia plant, derive two points from the info given which are:

(200, 23) and (500, 35)

The slope = cost per zinnia plant = 35 - 23 / 500 - 200

= 12/300

= $0.04.

Therefore, the correct answer: A.$0.04

Part 2: To derive a linear equation to represent the cost, C, to purchase z number of zinnia plants, substitute (z, C) = (200, 23) and m = 0.04 into C = mz + b to find the y-intercept (b):

23 = 0.04(200) + b

23 = 8 + b

23 - 8 = b

b = 15

Substitute m = 0.04 and b = 15 into C = mz + b:

C = 0.04z + 15

Therefore, the correct answer is D. C = 0.04z + 15

Part 3:

Using the equation C = 0.04z + 15, we can find the cost of purchasing 700 zinnia plants:

C = 0.04(700) + 15

C = 43

Therefore, the correct answer is: C. $43.

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The statement that is not true is

B. Perpendicular lines never intersect at right angles.

The definition of perpendicular lines is that they will intersect each other at 90 degree angles.

Answer:

B. Perpendicular lines never intersect at right angles.

Step-by-step explanation:

The perpendicular lines are lines that intersect at a right (90 degrees) angle. So, the option (B) is wrong and not true.

A new homeowner must choose between two financing options while buying a $2,590 living room set.

Part A: The price of Offer 1 as a whole is $5,251.14.

Part B: The entire price of offer 2 is $5,304.32.

Part C: The superior financing option for the prospective homeowner is Offer 1.

Part A: To calculate the total cost of offer 1, we can use the formula for compound interest:

A = \(P (1 + r/n)^{(nt)}\)

where A represents the total amount paid, P represents the principal (amount borrowed), r represents the annual interest rate, n represents the number of times the interest is compounded annually, and t is the length of time in years.

Plugging in the values for offer 1, we get:

A = \(2590 (1 + 0.249/12)^{(12*3)}\)

= \(2590 (1.02075)^{36}\)

= 2590 (2.026)

= $5,251.14

Therefore, the total cost of offer 1 is $5,251.14.

Part B: Using the same formula, we can calculate the total cost of offer 2:

A = \(2590 (1 + 0.229/12)^{(12*4)}\)

= \(2590 (1.01908)^{48}\)

= 2590 (2.048)

= $5,304.32

Therefore, the total cost of offer 2 is $5,304.32.

Part C: Comparing the two offers, we can see that offer 1 has a higher interest rate but a shorter time period, while offer 2 has a lower interest rate but a longer time period. To determine which offer is better, we can calculate the total amount of interest paid for each offer.

For offer 1, the total interest paid is:

$5,251.14 - $2,590 = $2,661.14

For offer 2, the total interest paid is:

$5,304.32 - $2,590 = $2,714.32

Therefore, offer 1 has a lower total amount of interest paid and is the better financing offer for the new homeowner.

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The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

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Answer:

D.  (0,-8)

Step-by-step explanation:

Put the equation into slope/y-intercept format:

4x - 8y = 64

-8y = -4x + 64

y = (1/2)x - 8   [The y-intercept is -8; the value of y when x = 0]

D.  (0,-8)

Answer:

Step-by-step explanation:

Length = 5 * 3 = 15 feet

Width = 3.5 * 3 = 10.5

Area: 15 * 10.5 = 157.5 square feet

Answer:

See below

Step-by-step explanation:

The measure of all the arcs can be obtained by using 'Central angle and its corresponding arc theorem'.

1. The measure of arc AD is \( \boxed {105}\degree \)

2. The measure of arc ABC is \( \boxed {205}\degree \)

3. The measure of arc ADB is \( \boxed {190}\degree \)

4. The measure of arc BD is \( \boxed {85}\degree \)

Answer:

$4.18

Step-by-step explanation:

You take $3.80 and multiply by it .1 (turn 10% into a decimal by moving the decimal to the right two places).

This gives you .38

Then you add .38 to $3.80 which gives you $4.18.

With a dilation factor of 1 / 4, Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) would be: A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1). Second option

The solution to the problem would be the solution that is gotten when we divide these points by 1/4. This is the dilation factor

we would have:

A(−4, 6), B(−2, 2), C(4, −2), D(4, 4)

= (-4 * 1/4, 6 * 1/4) , B(-2 * 1/4, 2 * 1/4), C(4 * 1/4, -2 * 1/4), D(4 * 1/4, 4 * 1/4)

= A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1)

Hence the second option is correct.

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Answer:A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).

Step-by-step explanation:

To dilate a point using a scale factor, you multiply both the x-coordinate and the y-coordinate of the original point by the scale factor.

Given the original vertices of the polygon ABCD and a scale factor of one fourth (1/4), we can find the coordinates of the dilated vertices A', B', C', and D':

Original vertex A(-4, 6):

x-coordinate of A': -4 * 1/4 = -1

y-coordinate of A': 6 * 1/4 = 1.5

So, vertex A' is (-1, 1.5).

Original vertex B(-2, 2):

x-coordinate of B': -2 * 1/4 = -0.5

y-coordinate of B': 2 * 1/4 = 0.5

So, vertex B' is (-0.5, 0.5).

Original vertex C(4, -2):

x-coordinate of C': 4 * 1/4 = 1

y-coordinate of C': -2 * 1/4 = -0.5

So, vertex C' is (1, -0.5).

Original vertex D(4, 4):

x-coordinate of D': 4 * 1/4 = 1

y-coordinate of D': 4 * 1/4 = 1

So, vertex D' is (1, 1).

Comparing the calculated coordinates with the options given:

A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)

Among the given options, the correct vertices of polygon A′B′C′D′ are A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).

Hey There!

\(3954 \times 54534 - (64563 \div 5435) \\ = 215627436 - 11.88 \\ = 215627424.120\)

Hope it helps

The ratio is 3:5 .

The problem we are dealing with is related to the term ratio, where the ratio is characterized as the comparison of two quantities of the same units that shows how much of one amount is present within the other amount. Ratios can be classified into two sorts. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio indicates how two distinct entities or groups are related. whereas, the part-to-whole proportion indicates the relationship between a particular group to an entirety.The situation we are given is that the player attempted 15 baskets in a game and out of  9 was the number of times he made the attempted baskets.We just need to find the ratio of the number of baskets made to the number of  baskets attempted,

= 9:15

Here we divide each by 3

= 9/3: 15/3

=3:5

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Let's simplify step-by-step.

−7x2−6x+9−7x2−6x+9

=−7x2+−6x+9+−7x2+−6x+9

Combine Like Terms:

=−7x2+−6x+9+−7x2+−6x+9

=(−7x2+−7x2)+(−6x+−6x)+(9+9)

=−14x2+−12x+18

Answer:

=−14x2−12x+18

Let's simplify step-by-step.

−3x2−x+7−3x2−x+7

=−3x2+−x+7+−3x2+−x+7

Combine Like Terms:

=−3x2+−x+7+−3x2+−x+7

=(−3x2+−3x2)+(−x+−x)+(7+7)

=−6x2+−2x+14

Answer:

=−6x2−2x+14

Answer: -10x^2-7x+16

Step-by-step explanation: (-7x^2-6x+9)+(-3x^2-x+7)  

-7x^2-6x+9-3x^2-x+7

Nothing to distribute.

Combine like terms:

Final Answer: -10x^2-7x+16

Answer:

RM 600

Step-by-step explanation:

1 unit -> bought for RM 2.50

             sold for RM 3.10

Selling price is higher than buying price, hence a profit is made.

Profit (for 1 unit) = Selling price - Buying Price

                           = RM 3.10 - RM 2.50

                           = RM 0.60

Since Deeni bought 1000 units of stock,

Profit Obtained = 1000 x RM 0.60

                           = RM 600

The correct answer is, P(X > 18) is the same as P(X < 18). Option b is correct. The probability P(X > 18) is related to P(X < 18) in such a way that: P(X > 18) is the same as 1 − P(X < 18).

Explanation:

The mean length of a certain product X is μ = 18 inches.

As we know that the length of a certain product X is normally distributed.

So, we can conclude that: Z = (X - μ) / σ, where Z is the standard normal random variable.

Let's find the probability of X > 18 using the standard normal distribution table:

P(X > 18) = P(Z > (18 - μ) / σ)P(Z > (18 - 18) / σ) = P(Z > 0) = 0.5

Therefore, P(X > 18) = 0.5

Using the complement rule, the probability of X < 18 can be obtained:

P(X < 18) = 1 - P(X > 18)P(X < 18) = 1 - 0.5P(X < 18) = 0.5

Therefore, the probability P(X > 18) is the same as P(X < 18).

Hence, the correct answer is, P(X > 18) is the same as P(X < 18). Option b is correct.

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Step-by-step explanation:

in my opinion

2(4x-5)-2=-4

=2×4x-2×5-2=-4

8x-10-2=-4

8x=-4+10+2

8x=-4+12

8x=-16(divide both sides by 8)

×=2

Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

We can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

A 95% confidence interval for the population mean can be constructed using the t-distribution when the sample size is small (<30) or the population standard deviation is unknown.

In this case, we have a random sample of 46 people with a mean body mass index (BMI) of 27.2 and a standard deviation of 6.0.

Thus, we need to use the t-distribution to construct the confidence interval.

The formula for the confidence interval is as follows:

Upper limit of the confidence interval:27.2 + (2.013) (6.0/√46) = 29.032Lower limit of the confidence interval:27.2 - (2.013) (6.0/√46) = 25.368

Therefore, the 95% confidence interval for the population mean BMI is (25.368, 29.032).

This means that we can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

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Answer:

Im pretty sure ur answers would be

x= -32/27 and X=  -46/27

Step-by-step explanation:

So srry if im wrong tho

The trigonometric ratio of the angle in radical and decimal form are:

cos 210° = -(√3)/2

sin 210° = -1/2

cos 210° = -0.87

sin 210° = -0.50

There are different trigonometric ratios such as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We are given the angle as  θ = 210°. Thus:

cos 210° = -(√3)/2

Negative because it is in the third quadrant.

sin 210° = -1/2

Negative because it is in the third quadrant.

Similarly, those angles in decimals to the nearest hundredth are:

cos 210° = -0.87

sin 210° = -0.50

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Answer:

For statement 1 :

INPUT UNIT OF ITEM : Time of the year on Serengeti Desert

OUTPUT UNIT OF ITEM : Simba washes his clothes

For statement 2

INPUT UNIT OF ITEM : 1 capful of detergent

OUTPUT UNIT OF ITEM : each load of wash

Step-by-step explanation:

For statement 1 :

INPUT UNIT OF ITEM : Time of the year on Serengeti Desert

OUTPUT UNIT OF ITEM : Simba washes his clothes

For statement 2

INPUT UNIT OF ITEM : 1 capful of detergent

OUTPUT UNIT OF ITEM : each load of wash

From answers provided above the basis for the answers is that an input unit of item will have to result to a reaction which is an output unit of item hence the answers above

The period of the Markov chain is 2.

The period of this Markov chain is determined by the number of times you have to go through the probability transition matrix before you return to the same state. The period for this Markov chain is 2, as you can see from the probability transition matrix below:

 P(i,j)   State 0   State 1    State 0   0.5   0.5    State 1   0.3   0.7  


Starting from State 0, the probability of transitioning to State 0 is 0.5, and the probability of transitioning to State 1 is 0.5. If we start from State 1, the probability of transitioning back to State 0 is 0.3, and the probability of transitioning back to State 1 is 0.7.

Therefore, it takes two steps for the chain to return to its original state and the period of this Markov chain is 2.

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