In δmno, m = 540 inches, n = 330 inches and o=600 inches. find the measure of ∠o to the nearest 10th of a degree

The slope of the tangent line to the given polar curve at the specified point is √3.

What is polar equation?

Cartesian coordinates, which may be found by moving across an x-axis and up and down the y-axis in a rectangular pattern, are complemented by polar coordinates. Polar coordinates are written as (r,) as opposed to the (x, y) used for Cartesian coordinates.

A point's location in polar coordinates is determined by its r from the origin and the angle θ (measured in radians) between the line leading to the point and the x-axis.

As given,

For the polar equation r = 4 sin θ, we have

x = r cosθ

x = 4 sinθ cosθ

x = 2sin2θ

y = r sinθ

y = 4 sin²θ

Differentiate obtained values of x and y with respect to θ respectively,

dx/dθ = d(2sin2θ)/dθ

dx/dθ = 2cos2θ (2)

dx/dθ = 4cos2θ

Similarly,

dy/dθ = d(4sin²θ)/dθ

dy/dθ = 4sin2θ

Evaluate the slope (dy/dx) as follows:

dy/dx = (dy/dθ) / (dx/dθ )

dy/dx = (4 sin2θ) / (4 cos2θ)

dy/dx = (sin2θ) / (cos2θ)

dy/dx = (tan2θ)

At θ = π/6

slope = dy/dx

Substitute values,

slope = tan2( π/6)

slope = tan( π/3)

slope = √3.

Hence, the slope of the tangent line to the given polar curve at the specified point is √3.

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The possible 4-digit numbers are 1,680.

Probability that 4-digit number ends up being an odd number greater than or equal to 6000 is 57.14%.

a) The number of possible 4-digit numbers that can be formed using the given digits without repetition is given by the permutation formula:

P(8,4) = 8! / (8 - 4)! = 8 x 7 x 6 x 5 = 1,680

Therefore, there are 1,680 possible 4-digit numbers using the given digits.

b) The total number of 4-digit numbers that can be formed from the given digits is 1,680, as calculated in part a).

To find the probability that the 4-digit number is odd and greater than or equal to 6000, we need to calculate the number of odd 4-digit numbers in the range [6000, 6999] and the number of odd 4-digit numbers greater than or equal to 7000, and divide each by the total number of 4-digit numbers.

Number of odd 4-digit numbers in [6000, 6999]:

The last digit must be 1, 3, 5, or 7 (4 choices). The first three digits can be any of the remaining 7 digits (7 choices for the first digit, 6 choices for the second digit, and 5 choices for the third digit). Therefore, the number of odd 4-digit numbers in [6000, 6999] is:

4 x 7 x 6 x 5 = 840

Number of odd 4-digit numbers greater than or equal to 7000:

The first digit must be 7 (1 choice). The last digit must be 1, 3, 5, or 7 (4 choices). The second and third digits can be any of the remaining 6 digits (6 choices for the second digit and 5 choices for the third digit). Therefore, the number of odd 4-digit numbers greater than or equal to 7000 is:

1 x 4 x 6 x 5 = 120

The total number of odd 4-digit numbers is 840 + 120 = 960.

Therefore, the probability that the 4-digit number is odd and greater than or equal to 6000 is: 960 / 1,680 = 0.5714 or approximately 57.14%.

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The power series represented by the given expression is centered at 7.

The power series given is of the form ∑ [infinity] (−1)n(x − 7)3n (3n)! n = 0. Here, the term (x - 7) indicates that the series is centered at 7. The center of a power series is the point around which the terms are being expanded. In this case, the series is being expanded around x = 7. The power series representation of a function is useful in many areas of mathematics, including calculus and differential equations. Knowing the center of a power series is important because it allows us to use the series to approximate the value of the function at any point in its domain.

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Answer:

x=3

I did my work I promise!  TRUST ME!!! this was easy.

The value of the variable b in the second triangle is 4

To solve for the value of the variables in each right triangle, we need to use the Pythagorean theorem which states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (legs).

This theorem can be expressed mathematically as:

a² + b² = c²,

where c is the hypotenuse and a and b are the legs.

1. In the first triangle, we have two sides a and c and need to find the length of the third side b.

Using the Pythagorean theorem, we have:

a² + b² = c²

\(9 + b^2 = 25$$\)

\($$b^2 = 25 - 9$$\)

\($$b^2 = 16$$\)

\($$b = \sqrt{16}$$\)

b = 4

Therefore, the value of the variable b in the first triangle is 4.

2. In the second triangle, we have one side a and the hypotenuse c, and need to find the length of the other leg b.

Using the Pythagorean theorem, we have:

a² + b² = c²

\($$3^2 + b^2 = 5^2$$\)

\(9 + b^2 = 25$$\)

\($$b^2 = 25 - 9$$\)

\($$b^2 = 16$$\)

\($$b = \sqrt{16}$$\)

b = 4

Therefore, the value of the variable b in the second triangle is 4.

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Step-by-step explanation:

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The likelihood that a green marble from jar A will be drawn out of it is 0.105.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.

Here,

For jar A,

Total Marbles=10

Number of green marbles=7

Number of blue of marbles=3

For jar B,

Total Marbles=10

Number of green marbles=3

Number of blue of marbles=7

Probability of choosing jar A=15/100

Probability of choosing jar B=85/100

Probability that a marble is drawn out of it is the marble is green that came from jar a= 15/100*7/10

=105/1000

=0.105

Probability that a marble is drawn out of it is the marble is green that came from jar A is 0.105.

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Waiting time representing 8th percentile = 299.09 days.

Find values on the left of the mean in this negative Z score table. Table entries for z represent the area under the bell curve to the left of z.

Negative scores in the z-table correspond to the values which are less than the mean.

Let X be the random variable representing the waiting time.

Here the mean(\mu) = 203 days

Standard deviation (\sigma) = 25.7 days

For calculating the 8th percentile, we need to find the z- score having an area of 0.08.

By the Z-score table, we have Z= -3.7

Now, Using the formula X=Z\sigma +\mu

X = (-3.7)*(25.7)+204

X = 299.09 days

Therefore, Waiting time representing the 8th percentile = 299.09 days.

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Answer:

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Step-by-step explanation:

Given;

Total Months = 14

Total Words = 1920

Required

Find the time spent in Portugal and time spent in Brazil

Let P represent Portugal and B represent Brazil; This implies that

\(P + B = 14\) ---- Equation 1

Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that

\(130P + 150B = 1920\) --- Equation 2

Make P the subject of formula in equation 1

\(P = 14 - B\)

Substitute 14 - B for P in equation 2

\(130(14 - B) + 150B = 1920\)

Open Bracket

\(1820 - 130B + 150B = 1920\)

\(1820 + 20B = 1920\)

Subtract 1820 from both sides

\(1820 - 1820 + 20B = 1920 - 1820\)

\(20B = 100\)

Divide both sides by 20

\(\frac{20B}{20} = \frac{100}{20}\)

\(B = 5\)

Substitute 5 for B in \(P = 14 - B\)

\(P = 14 - 5\)

\(P = 9\)

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.

Given log 630 ≈ 1.898 and log 62 ≈ 0.387,

We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387

And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086

So, log 615 ≈ 2.086

In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.

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Answer:

Related

A triangle has sides with lengths of 9 km, 11 km, and 15 km. Is it a right angle?

A triangle has sides with lengths of 9 km, 11 km, and 15 km. Is it a right triangle?

a^2 +b^2 = c^2

9^2 + 11^2 =? 15^2

81 + 121 =202 < 225

The triangle is not right, it is obtuse because the sum of the squares of the two shorter sides is less than the square of the largest sides.

Step-by-step explanation:

The right triangle calculator will help you find the lengths of the sides of a right-angled triangle. This triangle solver will also teach Pythagorean theorem calculator helps you find out the length of a missing leg or hypotenuse of a right triangle.

Answer:

y=x-5

Step-by-step explanation:

The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

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Answer:

he will take the same time as its the same flow of water so he will spend 9 min and 2 sec

The standard deviation of this binomial distribution is 4

The given parameters are:

The standard deviation is calculated using:

\(\sigma = \sqrt{np(1 - p)\)

So, we have:

\(\sigma = \sqrt{100 * 20\% * (1 - 20\%)\)

Evaluate

\(\sigma = 4\)

Hence, the standard deviation of this binomial distribution is 4

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Answer:

$198.75

Step-by-step explanation:

total amount spent = cost of groceries + cost of flowers

total cost of groceries = initial cost - coupon value

coupon value = 0.10 x 150 = $15

Total cost = $135

total cost of flowers = cost of flowers + tax value

tax value = 0.0625 x $60 = $3.75

total cost of flowers = $3.75 + $60 = $63.75

total amount spent = $135 + $63.75 = $198.75

On solving the given problem, The value of the median of the distribution is closest to 5.

In order to visualize data, a histogram is used. The width and area of each rectangle in the histogram are proportional to the class interval and data frequency, respectively.

When a dataset is sorted in either ascending or descending order, the median is the value that appears in the middle of the dataset.

Ascending numbers are listed in the following order:

2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9

Median is -  5

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The correct option is A, equilibrium price increases from $6 to $8.

In economics, equilibrium is a state in which the supply and demand for a product or service are balanced, resulting in a stable price. This can occur in a free market, where the price of a good or service is determined by the interaction of buyers and sellers.

Overall, equilibrium is a fundamental concept in many different fields, representing a state of balance or stability in a system or situation.

If the demand schedule changes from D2 to D1, then the demand curve shifts to the left. As a result, the new equilibrium point will be where the new demand curve (D1) intersects with the supply curve (S1).

From the table, we can see that the new equilibrium point is at a price of $8 and a quantity of 15. Therefore, the equilibrium price increases from $6 to $8, but the equilibrium quantity decreases from 15 to 13.

So the correct answer is: equilibrium price increases from $6 to $8.

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Answer:

D

Step-by-step explanation:

the line isn’t dotted so we take also the points that lies on the line

the shaded part is right the line so we take the points >

Answer:

A

Step-by-step explanation:

Put '0' in for 's' and solve :

0 = -p^2 + 75 p + 1200

 Use Quadratic Formula with a = -1      b=75      c = -1200

      to find p = ~ 24  OR  52       THE LEAST NUMBER WOULD BE 24

Answer:

y= 6/5x +0

Step-by-step explanation:

That just be how it is

Answer: y= 3/2 x

Step-by-step explanation:

use y = mx + b

Answer:

from left to right

-8

-9

-10

-11

Total Seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

If you're fortunate enough to have a rectangular lawn, determining the size is straightforward. Multiply the length and breadth measurements together to get the total. You now have your region/area.

So, Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.

Grass seed is sold in 2 kg boxes,

Maisie wants to make a rectangular lawn 10 m by 14 m,

She has 5 boxes of grass seed

To Find, Has Maisie got enough grass seed to make a lawn 10m by 14 m

Solution:

3 kg of grass seed to make a rectangular lawn 5 m by 9m.

=> 3 kg  of grass seed  needed for 5 x 9 = 45 m²

=>  1 m² required  = 3/45  kg seed

a rectangular lawn 10 m by 14 m,

area = 10 x 14 = 140 m²

Hence 140 m² required = 140 x  3/45  =  9.33 kg

Grass seed is sold in 2 kg boxes,

She has 5 boxes of grass seed

Hence total seeds = 5 x 2 = 10 kg

Therefore, total seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

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The number of  ways that he can make the fruit salad if it must contain watermelon is 35.

Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.

The salad contains water melon, now we have to select 4 more fruits out of 7.

Using combination

\(^{n{C}_r\) = n! / r! (n-r)!

\(^{7}C_4\) = 7!/ 4! (7-4)!

      = 7*6*5*4! / 4! * 3*2

      = 35

Hence,  number of ways that he can make the fruit salad if it must contain watermelon is 35.

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Answer: 35 on edge got it right

Step-by-step explanation: