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Given statement "If we project the area of a hip roof onto a horizontal plane, it will appear as two triangles and two trapezoids"

Given statement is True.
Because, A hip roof has four sloping sides that meet at the top ridge, forming a pyramid-like shape. When projected onto a horizontal plane, the following shapes will appear:

Two triangles:

These are formed by the two ends of the roof, where the sloping sides meet the ridge.
Two trapezoids:

These are formed by the two sides of the roof, where the eave edges meet the ridge.
So, when projecting the area of a hip roof onto a horizontal plane, it will indeed appear as two triangles and two trapezoids.

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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:

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.

Answer: there should be 80 blacks

Step-by-step explanation:

i promise

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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Answer:

95 is the sequence

Step-by-step explanation:

The given sequence appears to follow the pattern where each term is obtained by multiplying the previous term by 2 and then adding 1. Using this pattern, we can derive a formula for the nth term of the sequence as a(n) = 3 * 2^(n-1) - 1, where a(n) represents the nth term of the sequence and n is a positive integer.

For example, to find the 6th term of the sequence, we can substitute n = 6 into the formula to get a(6) = 3 * 2^(6-1) - 1 = 3 * 2^5 - 1 = 95. So, the 6th term of the sequence is 95.

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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To find the missing value in the equivalent ratio 12:18 = 16:___, you can use cross-multiplication.

First, you multiply the first term of the first ratio by the second term of the second ratio, and then you set it equal to the product of the second term of the first ratio and the missing value in the second ratio.

So, you get:

12 x ___ = 18 x 16

To solve for the missing value, you can divide both sides of the equation by 12:

___ = (18 x 16)/12

Simplifying the right-hand side, you get:

___ = 24

Therefore, the missing value in the equivalent ratio 12:18 = 16:___ is 24

Answer:24

Step-by-step explanation:

12:18

= 6:9

= 2:3

=16:24

First, you simplify it as much as you can and then scale it up to the number necessary.

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:

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

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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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:

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

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:

Circle with center C and point D. Triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

What is construction?

In the context of geometry, construction refers to the process of creating geometric figures or shapes using only a compass and straightedge (also called a ruler). The goal of construction is to create accurate and precise geometric figures using only these two tools and a given set of instructions.

To construct an equilateral triangle DEF with points E and F on circle C, we will follow the following steps:

Step 1: Draw a circle with center C and point D on it.

Step 2: Draw a line through points C and D. This line will be the base of our equilateral triangle DEF.

Step 3: Construct the perpendicular bisector of line CD. This can be done by drawing two circles with centers at C and D, both with radius greater than half the length of CD. The two circles will intersect at two points, and the line passing through these two points will be the perpendicular bisector of CD.

Step 4: Let G be the intersection point of the perpendicular bisector and circle C that is closest to point D. Draw lines from G to points C and D. These lines will intersect circle C at points E and F, respectively.

Step 5: Check that the length of CE is equal to the length of CF. This can be done using a compass and ruler.

Step 6: Finally, draw lines from points E and F to point D. The resulting triangle DEF will be equilateral.

To prove that triangle DEF is equilateral, we can show that DE = EF = FD. We already know that CE = CF from step 5. Since C is the center of the circle, CE = CF = CD. By construction, angle ECD and angle FCD are both 60 degrees, since they are inscribed angles that intercept the same arc.

Therefore, triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

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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

A Reflect triangle over the line x = -1 will take ABC to A"B"C".

What is triangle reflection theorem?

The outcome is the same as rotating the initial triangle 180 degrees around the origin, just as the theorem predicts, when we reflect the triangle over the y-axis and then cross the x and y axes while reflecting the outcome across the x axis.

The single transformation that takes ABC to A"B"C" is a reflection over the line x = -1.

The new triangle A'B'C' is formed by reflecting ABC across the line x = -2, where each point in A', B', and C' is the reflection of the corresponding point in ABC. As a result, A', B', and C''s x-coordinates are all 4 units to the left of A', B', and C''s x-coordinates.

The final triangle A"B"C is formed by reflecting A'B'C' over the line x = 0, where each point in A", B", and C" is a reflection of the corresponding point in A'B'C' over the line x = 0. Accordingly, the x-coordinates of A, B, and C" are all located two units to the right of the x-coordinates of A', B', and C'.

If we combine these two reflections into a single transformation, we can think of it as reflecting ABC over a line that is 2 units to the right of x = -2, which means it has an equation of x = -2 + 2 = -1. This line is the perpendicular bisector of the segment connecting the points (-2, 0) and (0, 0), which is the line that connects the two reflection lines x = -2 and x = 0.

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Answer:

12312

Step-by-step explanation:

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

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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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

Answer:

?

Step-by-step explanation:

It would be a bit helpful if you uploaded a picture, since I don't see one.

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"--

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

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.

The probability of winning the game is the same in both instances, so I will pick a card and put it back before picking the second card.

The probability of an event is a number that indicates how likely the event is to occur and is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%.

The  card has  total of 10 possible pairs:

(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), and (4,5).

we have that only (3,5) n adds up to 8,  .

In conclusion, the probability of winning the game is 1/10 or 10%.

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