what is the correct order of the numbers from least to greatest 1\2, 0.6,6%,6\5

If sin (α) =(5)/(13) in Quadrant I and cos(β) = (-12)/(13) in Quadrant II, then sin(α + β ) = -120/169 .So, the answer is option 1).

To evaluate sin(α + β), we can use the trigonometric identity:

sin(α + β) = sin α cos β + cos α sin β

First, we need to find cos α. Since sin α is positive and in Quadrant I, we can use the Pythagorean identity to find cos α:

cos α = √(1 - sin² α) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13

Next, we need to find sin β. Since cos β is negative and in Quadrant II, we can use the Pythagorean identity to find sin β:

sin β = -√(1 - cos² β) = -√(1 - (-12/13)²) = -√(1 - 144/169) = -√(25/169) = -5/13

Now we have all the values we need to evaluate sin(α + β):

sin(α + β) = sin α cos β + cos α sin β

= (5/13)(-12/13) + (12/13)(-5/13)

= -60/169 - 60/169

= -120/169

Therefore, the answer is option 1) -120/169.

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The Standard Normal Table is a tool that is used to calculate probabilities associated with the standard normal distribution.

When using the Standard Normal Table, we can find the area to the left of z < -2.34 by first locating the value -2.3 in the left-hand column of the table and the value -0.04 in the top row of the table.

Then, we find the intersection of the row and column to locate the corresponding value of 0.0099. This value represents the area to the left of -2.3 on the standard normal distribution.

To find the area to the left of -2.34, we need to adjust the value by subtracting the area to the left of -2.34 from the area to the left of -2.3.

The standard normal distribution is symmetric around the mean of 0. It means the area to the right of -2.3 is the same as the area to the left of 2.3.

Therefore, the area to the left of z < -2.34 is the area to the left of -2.3 (0.0099) minus the area between -2.34 and -2.3 (0.0040), which equals 0.0059. So, the area to the left of z < -2.34 is 0.0059.

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The mean number of states will be 6.

The percentage of students who visited more than 7 states will be 20%.

The mean number of states will be:

= 120 / 20

= 6.

The percentage of students who visited more than 7 states will be:

= 4/20 × 100

= 20%

The number of students who visited 7 or 8 states compare to the number of students who visited 5 states or less as they're both 7 each. This implies that they're equal.

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Answer:

The equation for the alternating current can be described by: y = 155 sin(120πt)

Where y is the voltage in volts (V) and t is the time in seconds (s).

To find the value of y when t = 1/90 s:

y = 155 sin(120π(1/90))

y ≈ 30.8 V

To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:

100 = 155 sin(120πt)

sin(120πt) = 100/155

t = arcsin(100/155)/(120π)

t ≈ 0.001 s

Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds

a. The correlation coefficient: ≈ -0.184

b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'

To find the line of best fit using a linear regression algorithm, we need to find the slope (m) and y-intercept (b) of the equation in the form y = mx + b.

We will start by calculating some statistics from the given data.

First, let's find the means of x and y:

x_mean = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 9 = 45 / 9 = 5

y_mean = (8 + 4.037 + 7.200 + 4.180 + 4.763 + 1 + 1.047 + 2.436 + 1.844) / 9 ≈ 34.507 / 9 ≈ 3.834

Next, we need to find the sum of the product of the differences between each point and the mean for both x and y:

Σ((x - x_mean) * (y - y_mean)) = (1 - 5) * (8 - 3.834) + (2 - 5) * (4.037 - 3.834) + ... + (9 - 5) * (1.844 - 3.834) ≈ -8.311

We also need to find the sum of the squared differences between each x and the mean of x:

Σ((x - x_mean)^2) = (1 - 5)^2 + (2 - 5)^2 + ... + (9 - 5)^2 = 60

Now, we can calculate the slope (m):

m = Σ((x - x_mean) * (y - y_mean)) / Σ((x - x_mean)^2) ≈ -8.311 / 60 ≈ -0.1385

To find the y-intercept (b), use the formula:

b = y_mean - m * x_mean ≈ 3.834 - (-0.1385) * 5 ≈ 4.525

Now we have the line of best fit equation:

y = -0.1385x + 4.525

a. To find the correlation coefficient (r), we need to divide the covariance of x and y by the product of the standard deviations of x and y.

First, let's find the covariance:

cov(x, y) = Σ((x - x_mean) * (y - y_mean)) / (n - 1) ≈ -8.311 / 8 ≈ -1.039

Next, find the standard deviations of x and y:

sd_x = sqrt(Σ((x - x_mean)^2) / (n - 1)) = sqrt(60 / 8) ≈ 2.738

sd_y = sqrt(Σ((y - y_mean)^2) / (n - 1))

sd_y = sqrt((8 - 3.834)^2 + (4.037 - 3.834)^2 + ... + (1.844 - 3.834)^2) / 8 ≈ sqrt(33.904) / 8 ≈ sqrt(4.238) ≈ 2.058

Now we can calculate the correlation coefficient:

r = cov(x, y) / (sd_x * sd_y) ≈ -1.039 / (2.738 * 2.058) ≈ -0.184

b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'

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Answer:

C. DEFG and VWXY

Step-by-step explanation:

It is the better answer choice here

Using the height formula of the trapezoid, we know that the height is 5000m respectively.

In geometry, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English or a trapezium in British and other forms of English.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.

The bases of the trapezoid are the parallel sides.

There are four sides to a trapezoid.

A trapezium is another name for a trapezoid.

It features two parallel sides that are not equal and two nonparallel sides.

So, find the height of the trapezoid as follows:

Formula: h = 2A/a+b

a = 8mm, b = 6 mm

A = 35 mm²

Unit conversion:

a = 8*10⁻³mm

b = 6*10⁻³mm

Using the formula:

h = 2A/a+b

h = 2*35/8*10⁻³+6*10⁻³

h = 5000m

Therefore, using the height formula of the trapezoid, we know that the height is 5000m respectively.

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Answer:

[tex]\frac{12}{5}[/tex] = 12 ÷ 5

[tex]\frac{1}{4}[/tex] = 1 ÷ 4

[tex]\frac{3}{8}[/tex] = 3 ÷ 8

[tex]\frac{9}{2}[/tex] = 9 ÷ 2

The length of JL is 20.572.

An angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians, and they are used to describe the relationships between lines and shapes in geometry.

The size of an angle is determined by the amount of rotation needed to bring one of the rays into coincidence with the other. A full rotation around the vertex is equivalent to 360 degrees or 2π radians. A right angle, which is formed by one ray perpendicular to another, has a measure of 90 degrees or π/2 radians.

Angles can be classified according to their measures as acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (between 90 and 180 degrees), straight angles (exactly 180 degrees), and reflex angles (between 180 and 360 degrees).

Angles also have a number of important properties and relationships, such as vertical angles (formed by two intersecting lines and are congruent), complementary angles (two angles whose measures sum up to 90 degrees), and supplementary angles (two angles whose measures sum up to 180 degrees).

cos  A= (leg adjacent to ∠A)/hypotenuse: cos(∠KLM)= [tex]\frac{LM}{KL}[/tex]

Substitute, LM= 7, KL= 12 : cos(∠KLM)= [tex]\frac{7}{12}[/tex]

Calculate cos(∠KLM)= [tex]\frac{7}{12}[/tex] : ∠KLM= 54.315°

Representing same angles: ∠JLK= ∠KLM

Substitute ∠KLM= 54.315° into ∠JLK= ∠KLM ⇒∠JLK= 54.315°

cos  A= (leg adjacent to ∠A)/hypotenuse: cos(∠JLK)=[tex]\frac{KL}{JL}[/tex]

Substitute, KL= 12, ∠JLK= 54.315°  ⇒ cos(∠JLK)= [tex]\frac{12}{JL}[/tex]

Calculate cos(54.315°)=[tex]\frac{12}{JL}[/tex] ⇒ JL= 20.572

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The complete question is:

Answer:

351-7 cm³

Step-by-step explanation:

Volume a cylinder = π r² h

π = 3.14

r = radius = 4cm

h = height = 7cm

Then:

Volume = 3.14 * 4² * 7

volume = 3.14 * 16 * 7

volume = 351.7 cm³

Answer:

Step-by-step explanation:

The correct answer is option D, 1078[tex]\pi[/tex] [tex]cm^{3}[/tex].

The volume of the cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h.

Radius = 7cm Height = 22cm.

Substituting the value in the formula, we get

[tex]\pi[/tex]*[tex]7^{2}[/tex]*22 = 1078[tex]\pi[/tex].

Hence the Answer is 1078[tex]\pi[/tex].

Answer:

3386.64 cm3

Step-by-step explanation:

i use this formula    π r² h

Every point on the graph of g(x) is 1 unit higher than the corresponding point on the graph of f(x).

Given that

f(x) = 4(0.5)^x and g(x) = 4(0.5)^x + 1

The graphs of the functions f(x) = 4(0.5)^x and g(x) = 4(0.5)^x + 1 are both exponential functions with a base of 0.5.

The only difference between these two functions is the addition of a constant term of 1 to the second function.

This constant term shifts the graph of g(x) vertically upward by 1 unit compared to the graph of f(x).

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Complete question

Describe how the graph of f(x) = 4(0.5)^x compares to the graph of g(x) = 4(0.5)^x +1

The completed table is attached accordingly. The standard deviation is given as 11.69

To derive the missing values, in the (x -μ) colume we need to first find the mean of the values.

This is writen as .....

μ = (2 + 8+14+19+20+21+26+  33+36+41  )  / 10 = 22.0

Now we can calculate the missing value as

(x-μ)

-20

-14

-8

-3.0

-2.0

-1.0

4.0

11.0

14.0

19.0

To find the missing values in the (x-μ)² column, we can simply square the values we just found

(x-μ)²

400

196

64

9.0

4.0

1.0

16.0

121.0

196.0

361.0

Next, we can find the sum of the (x-μ)² column

Σ(x-μ) ² = 1368

To find the variance, we divide the sum by the number of values and round to the nearest hundredth:

s² = Σ(x-μ)² / n = 1368 / 10 = 136.8

To find the standard deviation, we take the square root of the variance and round to the nearest hundredth:

s = √ (s²)

 = √(136.8)

≈ 11.69

Hence, the standard deviation of the elephant ages is approximately 11.69.

See the attached table.

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The majority of students have a body mass between 46.7 and 79.1 kg, and there are 36 students with a body mass of 61.7 kg or greater.

Assuming a normal distribution of body mass among the students, we can use the concept of standard deviation to answer the question. Let's assume that the mean body mass of the students is 60 kg, and the standard deviation is 5 kg.

To find the range of body mass where the majority of students fall, we can use the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Therefore, the range of body mass where the majority of students fall is between 55 kg (60 kg - 5 kg) and 65 kg (60 kg + 5 kg).

To find the number of students with a body mass equal to or greater than 61.7 kg, we need to find the z-score of 61.7 kg, which is

(61.7 - 60) / 5 = 0.34.

We can then use a standard normal distribution table to find the proportion of the area to the right of this z-score, which is 0.3665. This means that approximately 36.65% of the students have a body mass equal to or greater than 61.7 kg.

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--The given question is incomplete, the complete question is given

" entre que valores varia la masa corporal (MC) de la mayoría de estudiantes y que cantidad tiene corporal (MC) igual o mayor que 61,7 kg"--

The best prediction about the number of cookies the college will need is that they will have about 480 students who prefer cookies. Option A is the correct answer.

According to the table, out of 225 students, 27 students prefer cookies. To find an estimate of the number of cookies the college will need for its 4,000 students, we can set up a proportion:

27/225 = x/4000

Solving for x, we get:

x = (27/225) * 4000

x = 480

Therefore, the best prediction about the number of cookies the college will need is that they will have about 480 students who prefer cookies. Option A is the correct answer.

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So the measure of angle HLK is 45 degrees.

In geometry, an arc is a part of a curve that is typically a segment of a circle. It is defined by any two points on the curve, which are called its endpoints, and by all the points that lie along the curve between those two endpoints. An arc can be measured by its degree measure, which is the measure of the central angle that intercepts the arc, or by its length, which is the distance between its endpoints along the curve. In the context of a circle, an arc is also called a circular arc.

Here,

Since the measure of minor arc HK is 90°, we know that angle HJK is also 90°, since it is an inscribed angle that intercepts the same arc.

By the inscribed angle theorem, the measure of angle HLK is half the measure of arc HK. Therefore,

measure of angle HLK = 1/2 * measure of arc HK

= 1/2 * 90°

= 45°

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Answer: Look below:

Step-by-step explanation:

when n = 1:

a1 = 4 x 3^(1-1) = 4 x 3^0 = 4 x 1 = 4

so a1 = 4

similarly working:

a2 = 4 x 3^1 = 12

a3 = 36

a4 = 108

a5 = 324
a6 = 972

We need to round up to the nearest integer, the required sample size is 76 households.

To estimate the required sample size, we can use the formula:

[tex]n = (z^2 * s^2) / E^2[/tex]

Where:

z is the z-score corresponding to the confidence level (90% = 1.645)

s is the standard deviation of the population (square root of the variance, so s = sqrt(3.61) = 1.898)

E is the maximum error allowed (0.15 gallons)

Plugging in the values, we get:

[tex]n = (1.645^2 * 1.898^2) / 0.15^2[/tex]

n = 75.57

Since we need to round up to the nearest integer, the required sample size is 76 households.

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Answer:

81

Step-by-step explanation:

for the volume you just multiple length, height, and depth

Answer: 81.

Step-by-step explanation:

9 x 3 x 3 . LxWxH  brother!

We got x = 149.53 by using Pythagorean theorem.

angle of semicircle is always be 90°.

[tex]172^2=85^2+x^2[/tex]

[tex]29584=7225+x^2[/tex]

[tex]x^2=29584-7225[/tex]

[tex]=22359[/tex]

[tex]x=\sqrt{22359}[/tex]

[tex]\boxed{\bold{x=149.53}}[/tex]

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Answer:

20 miles

Step-by-step explanation:

1 hr= 2.8 miles

7hrs=2.8×7

2.8×7= 19.6

19.6 to 1dp is 20

Answer:

12312

Step-by-step explanation:

add the 11485 to 827 to figure out how many times did the red team do

According to the equation, the monthly fee that Sara paid was $60.

Let's start by assigning some variables. Let x be the monthly fee that Sara paid and let y be the number of months that Sara was a member of the gym. We know that Sara paid $15.95 to become a member, so her total cost can be represented by the equation:

Total Cost = Initial Cost + Monthly Fee x Number of Months

$735.95 = $15.95 + x x y

Now we have an equation with two variables. To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting $15.95 from both sides of the equation:

$720 = x x y

Next, we need to solve for x. Since we don't know the value of y, we can't solve for x directly. However, we do know that Sara was a member for 12 months, so we can substitute y = 12 into the equation:

$720 = x x 12

Now we can solve for x by dividing both sides by 12:

$60 = x

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Hi

1/5 is mint  : so  30*1/5 = 6

1/2 of what remain is chocolate :  which mean  (30-6) /2 = 24/2 = 12

So vanilla will be :  30-6-12 =  30-18 = 12

recap :  6 mint, 12 chocolate and 12 vanilla.

If the cabinets are 34 inches tall, 24 inches deep, and 16 inches wide, the volume of the kitchen cabinets is 16,384 cubic inches.

To find the volume of the rectangular prisms-shaped kitchen cabinets, we need to multiply the three dimensions: height, depth, and width. We are given the following measurements:

Height = 34 inches

Depth = 24 inches

Width = 16 inches

So the formula for the volume is:

Volume = Height x Depth x Width

Substituting the given values, we get:

Volume = 34 x 24 x 16

Volume = 16,384 cubic inches

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Answer:

Step-by-step explanation:

In the equation h=6d, the independent variable is d, which represents the number of days. The dependent variable is h, which represents the height of the plant that depends on the number of days it has been growing.