The following problems refer to triangle ABC. Round your answer to the nearest tenth. If a = 6.1.c = 6.2. B = 113º , find b. b

Answer:

841 kmh-1

Step-by-step explanation:

speed = distance / time

time = 810 x 24 = 19440

16,340,000 km / 19440 = 840.535

To find the probability that a participant selected at random found the products favorable, we can calculate the weighted average of the favorable responses from both the industry-sponsored and non-industry-funded studies.

For the industry-sponsored studies, 65% of participants found the products favorable, and for the non-industry-funded studies, 47% found the products favorable. Since there were 65 industry-sponsored studies and 35 non-industry-funded studies, the overall probability is:

(65/100) * 0.65 + (35/100) * 0.47 = 0.4225 + 0.1645 = 0.587 or 58.7%

If a randomly selected participant found the product favorable, we can use Bayes' theorem to calculate the probability that the study was sponsored by the food industry given this favorable response. The calculation is:

P(Industry-sponsored | Favorable) = (P(Favorable | Industry-sponsored) * P(Industry-sponsored)) / P(Favorable)

P(Favorable | Industry-sponsored) = 0.65

P(Industry-sponsored) = 65/100

P(Favorable) = 0.587

P(Industry-sponsored | Favorable) = (0.65 * (65/100)) / 0.587 ≈ 0.719 or 71.9%

Similarly, if a randomly selected participant found the product unfavorable, we can use Bayes' theorem to calculate the probability that the study had no industry funding given this unfavorable response. The calculation is:

P(No industry funding | Unfavorable) = (P(Unfavorable | No industry funding) * P(No industry funding)) / P(Unfavorable)

P(Unfavorable | No industry funding) = 0.36

P(No industry funding) = 35/100

P(Unfavorable) = 1 - P(Favorable) = 1 - 0.587 = 0.413

P(No industry funding | Unfavorable) = (0.36 * (35/100)) / 0.413 ≈ 0.305 or 30.5%

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The multifactor productivity measure for each of the weeks shown for the production of chocolate bars assuming a 40-hour week and an hourly wage of $16 and overhead costs 1.5 times labor cost is 0.127.

Multifactor productivity is an economic metric that calculates the ratio of an organization's total outputs to its total inputs used for production over a given period. It determines how efficiently the organization uses its resources in the production process, and it is calculated using the formula :

MFP = Total output / ( Labor cost + Material cost + Overhead cost)Where MFP stands for multifactor productivity. Overhead costs, labor costs, and material costs are the inputs used for production.

The data provided is shown in the table below:| Week | Output | Labor | Materials | Overhead | |------|--------|-------|-----------|----------| | 1 | 3000 | 100 | 6000 | 150 | | 2 | 4500 | 150 | 9000 | 225 | | 3 | 6000 | 200 | 12000 | 300 |For each week, we must first calculate the labor, material, and overhead costs.

Labor cost per week = number of hours worked x hourly wage

Labor cost per week = 40 x $16 = $640

Material cost per week is given.

Overhead cost per week = 1.5 x labor cost

Overhead cost per week = 1.5 x $640 = $960

Now that we have all of the necessary input data, we can use the MFP formula to calculate multifactor productivity for each week.MFP for Week 1 = 3000 / (100 x $16 + $6000 + $150 + $960)MFP for Week 1 = 0.127MFP for Week 2 = 4500 / (150 x $16 + $9000 + $225 + $960)MFP for Week 2 = 0.127MFP for Week 3 = 6000 / (200 x $16 + $12000 + $300 + $960)MFP for Week 3 = 0.127

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The domain of all six trigonometric functions is all real numbers, and the range of the sine and cosine functions is between -1 and 1, while the range of the tangent, cosecant, secant, and cotangent functions is all real numbers except for certain values where the denominator is equal to zero.

Using the properties of the unit circle, we can define the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) based on the coordinates of points on the unit circle.

The domain of all six trigonometric functions is the set of all real numbers, since the input angle can take any value in radians or degrees.

The range of the sine and cosine functions is the set of all real numbers between -1 and 1, inclusive. This is because the y-coordinate (sine) and x-coordinate (cosine) of any point on the unit circle can range from -1 to 1.

The range of the tangent, cosecant, secant, and cotangent functions is the set of all real numbers except for values where the denominator (sine, cosine) is equal to zero. For example, the range of the tangent function is all real numbers except for the values of x where cos(x) = 0, which occur at multiples of pi/2.

So, in summary, the domain of all six trigonometric functions is all real numbers, and the range of the sine and cosine functions is between -1 and 1, while the range of the tangent, cosecant, secant, and cotangent functions is all real numbers except for certain values where the denominator is equal to zero.

Using properties of the unit circle, the domain and range of the six trigonometric functions are as follows:

1. Sine (sin): Domain is all real numbers, Range is [-1, 1].
2. Cosine (cos): Domain is all real numbers, Range is [-1, 1].
3. Tangent (tan): Domain is all real numbers except odd multiples of π/2, Range is all real numbers.
4. Cosecant (csc): Domain is all real numbers except integer multiples of π, Range is (-∞, -1] and [1, ∞).
5. Secant (sec): Domain is all real numbers except odd multiples of π/2, Range is (-∞, -1] and [1, ∞).
6. Cotangent (cot): Domain is all real numbers except integer multiples of π, Range is all real numbers.

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Answer:

x^2 - 13x + 36

Step-by-step explanation:

Use the so-called FOIL method:  multiply First terms, Outer terms, Inner terms, Last terms.

First terms:  (x)(x) = x^2

Outer terms:  (x)(-9) = -9x

Inner terms:  (-4)(x) = -4x

Last terms:  (-9)(-4) = 36

Combining the x terms, we get

x^2 - 13x + 36

Answer:

x = 6.3 ft

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, reduction to original.

scale factor = \(\frac{5.2}{10.4}\) = \(\frac{1}{2}\)

Then

x = 12.6 × \(\frac{1}{2}\) = 6.3 ft

Answer:

The answer is 6.3

Step-by-step explanation:

Could you mark me brainiest.

Answer:

0.21

Step-by-step explanation:

i cant do a number line but to check these all you need to do is compare the digits untill you see one is bigger. once you find that you can tell which one is the biggest number. hope this helps!

The "data view" of a dataset with two groups that each contain 40 people will have 80 rows.

A data set is a collection of data that is organized and processed to provide useful information. In a data set, each row represents a single observation or record. In the case where a data set contains two groups, each group represents a separate set of observations or records.

If each group has 40 people, this means that there are 40 separate observations or records in each group. Therefore, the total number of rows in the "data view" of the data set will be equal to the sum of the number of rows in each group, which is 40 + 40 = 80.So, the "data view" of a data set with two groups that each have 40 people will have 80 rows, with each row representing a single observation or record from one of the two groups.

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The given system of equation is,

consider the equation (2),

consider the quation (3) and mulitply with 2,

then subract them,

Thus, the system of equation are, infinitely many solution.

The answer is (x,y) = (oo,oo).

Answer:

enlargement ; 2

Step-by-step explanation:

dilation is change in the size of the figure.

in the given scenario, figure's size is increasing so dilation is called enlargement and scale factor must be greater than 1.

scale factor = dimension of new shape / dimension of original shape

let's calculate the difference in terms of boxes of both figures to calculate the scale factor,

scale factor = 6/3

thus, in the given dilation we have enlargement of 2

Answer:

E - (28, 25)

Hope this helps!

Answer:

.25 miles is your answer.

Philip should receive $68.50 in quarterly dividends and the annual yield on this stock is about 2.81%.

To calculate the quarterly dividend that Philip need to acquire, we need to first calculate the quarterly dividend per share:

Quarterly dividend in step with share = Annual dividend per percentage / 4

In this situation, the once a year dividend in line with proportion is $2.74, so the quarterly dividend per proportion is:

Quarterly dividend per proportion = $2.74 / 4 = $0.685

For the reason that Philip owns 100 shares, his quarterly dividend should be:

Quarterly dividend = Quarterly dividend per share * number of stocks

Quarterly dividend = $0.685 * 100 = $68.50

Therefore, Philip should receive $68.50 in quarterly dividends.

To calculate the once a year yield on this inventory, we want to divide the yearly dividend in line with proportion by the present day stock price, after which multiply by way of 100 to specific the result as a percentage:

Annual yield = (Annual dividend per share / inventory price) * 100

In this case, the annual dividend per percentage is $2.74, and the inventory charge is $97.55. Plugging those values into the components, we get:

Annual yield = ($2.74 / $97.55) * 100

Annual yield ≈ 2.81%

Therefore, the annual yield on this stock is about 2.81%.

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The function f is increasing for x > 3/2.

To determine the values of x for which the function f is increasing, we need to find the critical points of f, which are the values of x where the function changes from increasing to decreasing or vice versa.

The first step is to find the derivative of f:

f'(x) = (2x - 3)e-x

Next, we need to find the critical points by setting f'(x) = 0 and solving for x:

(2x - 3)e-x = 0

2x - 3 = 0

x = 3/2

This is the only critical point of f. To determine the behavior of f near this critical point, we need to find the second derivative of f:

f''(x) = (2 - 3e-x)

For x < 3/2, f''(x) < 0, which means f is concave down and f'(x) is decreasing. This means that f is decreasing for x < 3/2.

For x > 3/2, f''(x) > 0, which means f is concave up and f'(x) is increasing. This means that f is increasing for x > 3/2.

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Answer:

\(m = \frac{2 - ( - 4)}{1 - ( - 1)} = \frac{6}{2} = \frac{3}{1} = 3\)

Answer:

B

Step-by-step explanation:

Remark

If we draw a line from F to T, we can make a couple of statements.

Call the center of the circle O

1. <FTE = 1/2 the central angle of <FOE. The size of <FOE is the same size as the minor arc. Since The minor arc = 60 degrees, then FTE = 30 degrees.

2. <GTF = 1/2 78 by the same reasoning used above.  GTF = 39 because that is 1/2 of 78.

So the answer to the size of <T = 39 + 30 = 69 which is B

There is a much simpler way of doing this.

The central angle of the two arcs is 78 + 60 = 138

The <GTE is 1/2 the central angle

<GTE = 1/2 * 138 = 69

Let the price of the hot dogs be x and drink be y.

It is given that you can get 6 hotdogsand 2 drinks for $18.00 so it follows:

Simplify to get:

It is also given that you can get 7 hotdogs and 8 drinks for $46.50 so it follows:

Multiply (i) by 8 to get:

Subtract (ii) from (iii) to get:

Substitute x=1.5 in (i) to get:

Hence the cost are:

1.5$ per hotdog.

4.5$ per drink.

Part A:What is the probability of getting a red jellybean on the first draw?

Given information: Red jellybeans = 12  Yellow jellybeans = 8  Green jellybeans = 4   Total jellybeans = 24                           The probability of getting a red jellybean on the first draw is:

Probability of getting a red jellybean=Number of red jellybeans/Total jellybeans=12/24=1/2=0.5

Decimal: P(1st Red)=0.5 Percent: P(1 st Red )=50%

Part B: Let's say you did get a red jellybean on the first draw.

What is the probability that you will then get a green on the second draw?

Now, the total number of jellybeans is 23, since one red jellybean has been taken out. The probability of getting a green jellybean is: Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174 Decimal: P(2nd Green | 1st Red )=0.174 Percent: P(2nd Green | 1st Red )=17%

Part C: If you had gotten a yellow on the first draw, would your answer to Part B be different?

Yes, because there is only 1 rotten egg yellow jellybean and if it were chosen in the first draw, it would not be returned back to the container. Therefore, the total number of jellybeans would be 23 for the second draw, and the probability of getting a green jellybean would be:

Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174

Thus, the answer would be the same as Part B.

Part D: What is the conditional probability of the dependent event "red then green?"

Given that one red jellybean and one green jellybean are selected: Probability of the first jellybean being red is 1/2

Probability of the second jellybean being green given that the first jellybean is red is 4/23

Probability of "red then green" is calculated as follows: Probability of red then green=P(Red) × P(Green|Red)= 1/2 × 4/23 = 2/23  Decimal: P(1st Red and 2nd Green )=2/23  Percent: P(1st Red and 2nd Green )=8.70%

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Answer:

the average of data is which is found by subtracting third and fourth term

Answer:

A

Step-by-step explanation:

the median of a set of data is the middle NUMBER arrange in ascending order

The coordinate of F is (3, 3).

What is the formula to find the midpoints?

Diagonals of a parallelogram bisect each other, meaning they divide each other into equal parts.

The formula is used to find the midpoints are as follows;

(x1 + x2)/2, (y1+y2)/2

DF and EG are diagonals of parallelogram DEFG, therefore:

The midpoint of DF = midpoint of E

Then,

The midpoint of D(0, 2) and F(x, y) is:

(0 + x)/2 , (2 + y)/2

The midpoint of E(-1, 5) and G(4, 0) is;

(-1 + 4)/2, (5 + 0)/2

Comparing the equation;

x/2 = 3/2

x = 3

2+y/2= 5/2

y = 3

Hence, the coordinate of F is (3, 3).

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Answer:

4(n-8)

Step-by-step explanation:

4(n-8)

I think it'd be written like this

Answer:

y = 1.44x⁴

Step-by-step explanation:

From the question,

Y∝d²

To remove the proportionality sign we introduce a constant.

Y = kd²............... Equation 1

make k the subject of the equation

k = Y/d²............. Equation 2

Given: Y = 4, d = 10

Substitute these values into equation 2

k = 4/10²

k = 4/100

k = 0.04

Substitute these value of k in equation 1

Y = 0.04d²................ Equation 3

Similarly,

d∝x²,

d = Cx²

make C the subject of the equation

C = d/x²................... Equation 4

Given:  d = 24, x = 2

Substitute into equation 4

C = 24/2²

C = 24/4

C = 6

Hence,

d = 6x²................... Equation 5

Substitute the value of d in equation 5 into equation 3

y = 0.04(6x²)²

y = 0.04(36x⁴)

y = 1.44x⁴

Hence the formula for y in terms of x is y = 1.44x⁴

Answer:

C

Step-by-step explanation:

The line of symmetry is a line that splits the figure into 2 halves where each half is a mirror image of the other. In the third figure, if a line is drawn through x = -1, the halves mirror each other. If a line is drawn through y = -2, the top and bottom halves mirror each other.

For a polygon, both are x= -1 and y= -2 lines of symmetry would be a figure of option C.

Consider a plane. Consider a design or shape on that plane. Now consider an axis.

If we think of that axis as a mirror, and on the opposite side of that axis create the image of the considered shape,

then if the shape's image looks exactly as the shape itself, then that shape is called to have reflectional symmetry.

We need to find for which polygon both are x= -1 and y= -2 lines of symmetry.

The line of symmetry is a line that splits the figure into 2 equal halves where each half is a mirror image of the other.

In the third figure, if a line is drawn through x = -1, the halves mirror each other.

If a line is drawn through y = -2, the top and bottom halves mirror each other.

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9514 1404 393

Answer:

  8 in

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

Solving for h, we find ...

  h = 2A/b

Filling in the given values tells us the height of the triangle.

  h = 2(24 in^2)/(6 in) = 8 in

The height of the triangle is 8 inches.

Answer:

100000000

Solution:

9^4=6561

3^0=1

3^1=3

3^2=9

3^3=27

3^4=81

3^5=243

3^6=729

3^7=2187

3^8=6561

6561=(1×3^8)+(0+3^7)+(0×3^6)+(0^3^5)+(0×3^4)+(0×3^3)+(0×3^2)+(0×3^1)+(0×3^0)

100000000 with the base of 3

Answer: 14.73091

Step-by-step explanation:

The square root of 217, (or root 217), is the number which when multiplied by itself gives the product as 217. Therefore, the square root of 217 = √217 = 14.730919862656235.

20 is the possible outputs for the function defined by c(x)=20x for all of the students that would pay for the field trip

The function that is known to represent what would be the cost of the trip of these students is given as C(x)=20x.

The cost of the trip for one of the students is put at 20 dollars each.

We would have x as the total number of those that would be attending this trip. In order to get the output that would show us the cost of the trip.

We take X to be a whole number.

then x = 1

such that that  c(1) = 20(1) = 20

Then the total is 20 per student

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the cost for an upcoming field trip is 20 dollars the cost of the feild trip c is a function of the number of students x select all the possible outputs for the function defined by c(x)=20x

A 20 B 30 c 50

The approximate value of the given expression is 4.7946 when rounded to four decimal places.

To approximate the value of the given expression, we can use logarithmic properties and the provided logarithmic values.

The expression is:

\(log_4(20) + log_2(3)\)

Using logarithmic properties, we can rewrite the expression as:

log(20) / log(4) + log(3) / log(2)

Now, substituting the given logarithmic values:

log(20) = 1.3010 (rounded to four decimal places)

log(4) = 0.6021 (rounded to four decimal places)

log(3) = 0.7925 (given)

log(2) = 0.3010 (given)

Plugging in these values into the expression:

1.3010 / 0.6021 + 0.7925 / 0.3010

Performing the calculations:

= 2.1620 + 2.6326

= 4.7946 (rounded to four decimal places)

Therefore, the approximate value of the given expression is 4.7946 when rounded to four decimal places.

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