B

E

3

3

A

4

с

D

F

4

Enter the length of curve DE given that the curve is 5% longer than line

segment AB.

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

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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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.

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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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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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:

  (a)  $1350.46

  (b)  $50.46

Step-by-step explanation:

You want to know the future value of a $1300 CD earning 1.27% compounded monthly for 3 years, along with the amount of interest earned.

The compound interest formula tells you the future value is ...

  FV = P(1 +r/12)^(12·t)

where r is the annual interest rate and t is the number of years.

Using the given values, we have ...

  FV = $1300(1 +0.0127/12)^(12·3) ≈ $1350.46

(a) The value after 3 years is $1350.46.

The interest earned is the difference between the final value and the amount of the original investment:

  Interest = $1350.46 - 1300.00 = $50.46

(b) The interest earned by the CD is $50.46.

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It would take the bowling ball approximately 3.1 seconds to fall 150 feet.

What is distance?

Distance is the total movement of an object, regardless of direction. We can define distance as how much ground an object has covered, regardless of its starting or ending point.

Distance is defined as the size or amount of displacement between two positions. Note that the distance between two locations is not the same as the distance between them. The distance traveled is the total length of the path traveled between two positions.

Here given equation,

d = 16t², where t is the time in seconds and d is the distance in feet and distance is 150 feet.

We want to find the value of t.

Now,

[tex]d = 16 {t}^{2} \\ {t}^{2} = \frac{d}{16} \\ {t}^{2} = \frac{150}{16} \\ t = \sqrt{( \frac{150}{16}) } \\ t = \sqrt{9.375} \\ t = 3.0619[/tex]

So, t = 3.1 (rounded to one decimal place)

Therefore, it would take the bowling ball approximately 3.1 seconds to fall 150 feet.

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Correct question is "How long would it take the bowling ball to fall 150 feet where equation of distance is d = 16t² ?(Estimate your answer to one decimal place). "

Answer:

?

Step-by-step explanation:

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

Given statement "3-6 You can determine the slope of a roof using a flat board, a bubble level and a ruler,or a sight card can be used." is true. Because flat board, a bubble level and a ruler,or a sight card methods are commonly used to determine the slope of a roof, and both are effective.

Determining the slope of a roof is an important task for many construction and roofing projects.

One method to determine the slope of a roof is to use a flat board, a bubble level, and a ruler.

First, place the flat board horizontally on the roof surface, and use the bubble level to make sure it is level.

Then, measure the distance between the bottom of the board and the roof surface at the point where the board intersects with the roof using the ruler. This distance is the rise.

Next, measure the distance from the point where the board intersects with the roof to the end of the board using the ruler. This distance is the run. Finally, divide the rise by the run to get the slope.

Another method to determine the slope of a roof is to use a sight card. A sight card is a specially designed tool that can help to measure the angle of a slope or pitch. The sight card is held at the bottom of the roof and lined up with a known vertical or horizontal line, such as the edge of a building.

Statement is true.

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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.

The complete chart here is

|---Simplify the Polynomial---|--Degree--|--Leading Coefficient--|--Constant--|

|------7a^4 - 3a^3 - 2a + 2------|------4-------|---------------7----------------|--------2-------|

Explain polynomial

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and exponentiation. Polynomials can have one or more terms and are commonly used to model relationships in science and engineering.

What is meant by coefficient?

The coefficient is a numerical factor that is multiplied by a variable or a product of variables in an algebraic expression or equation.

According to the given information

To add the two polynomials, we combine like terms. That is, we add the coefficients of terms that have the same degree.

(7a⁴ - 6a³ + 1) + (3a³ - 2a + 1)

= 7a⁴ + (-6a³ + 3a³) + (-2a) + (1 + 1)

= 7a⁴ - 3a³ - 2a + 2

So, the simplified polynomial is `7a⁴ - 3a³ - 2a + 2`.

The degree of this polynomial is `4` since the term with the highest degree is `7a⁴`.

The leading coefficient of this polynomial is `7` since it is the coefficient of the term with the highest degree.

The constant term of this polynomial is `2` since it is the term with a degree of `0`.

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Answer: there should be 80 blacks

Step-by-step explanation:

i promise

The calculated height of the trapezoid is 5 ft.

The formula for the area of a trapezoid is:

A = (b1 + b2)h/2

where A is the area, b1 and b2 are the lengths of the parallel sides, and h is the height.

We are given that the area of the trapezoid is 25.5 ft^2, and the lengths of the parallel sides are 3.2 ft and 7 ft.

Substituting the given values into the formula, we get:

25.5 = (3.2 + 7)h/2

Simplifying the expression on the right side, we get:

25.5 = 5.1h

Dividing both sides by 5.1, we get:

h = 25.5/5.1

h = 5

Therefore, the height of the trapezoid is 5 ft.

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The statement that correctly compares the two functions on the interval [-1, 2] is A. Both functions are increasing, but function g increases at a faster average rate.

For function f, as x increases from -2 to 2, we can see that the corresponding values of f(x) also increase, but at a decreasing rate. This is because the function is exponential and approaching a horizontal asymptote as x goes to infinity. Therefore, f(x) is increasing, but at a decreasing rate.

For function g, we don't have enough information to determine if it's increasing or not, since only its equation is given. The correct option is A.

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The proportion of cherry tomatoes that are rejected based on their diameter is 0.0033. (option a).

To use the CDF, we need to standardize the diameter values using the z-score formula:

z = (x - μ) / σ

where z is the z-score, x is the diameter value, μ is the mean diameter, and σ is the standard deviation.

For tomatoes with a diameter of at most 15 mm, we have:

z = (15 - 22) / 2.5 = -2.8

For tomatoes with a diameter of at least 30 mm, we have:

z = (30 - 22) / 2.5 = 3.2

Next, we use the z-table to find the area under the Normal distribution curve that corresponds to these z-scores. For a z-score of -2.8, the area is 0.0026. For a z-score of 3.2, the area is 0.9993.

Finally, we add these two areas together to get the total proportion of rejected tomatoes:

proportion = 0.0026 + (1 - 0.9993) = 0.0033

Hence the correct option is (a).

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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 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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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:

The regular triangle, regular hexagon, and regular dodecagon have special triangles formed by their radius and apothem, which are congruent right triangles with legs equal to half the length of one side and hypotenuse equal to the radius or apothem, and are 30-60-90 triangles.

Regular polygons with three special triangles formed by their radius and apothem are,

Regular triangle

The radius and apothem of an equilateral triangle are equal. Therefore, the special triangles formed by the radius and apothem are congruent right triangles with legs equal to half the length of one side of the equilateral triangle and hypotenuse equal to the radius or apothem. In other words, the special triangles are 30-60-90 triangles.

Regular hexagon

The radius of a regular hexagon is equal to the length of one side, and the apothem is equal to the height of an equilateral triangle with side length equal to the length of one side of the hexagon.

Regular dodecagon

The radius of a regular dodecagon is equal to the length of one side multiplied by the square root of 2 plus the square root of 2 times the square root of 3. The apothem is equal to the height of an isosceles triangle with base equal to one side of the dodecagon and legs equal to the radius of the dodecagon.

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For the hexagon, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the longer leg.

The three regular polygons that have special triangles formed by their radius and apothem are the triangle, square, and hexagon.

For the triangle, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the shorter leg.

For the square, the special triangle formed by its radius and apothem is a 45-45-90 right triangle, where the radius is the hypotenuse and the apothem is one of the legs.

For the hexagon, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the longer leg.

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Let's say that the store starts with a coupon value of x.  On the first day, the probability of  drawing the pink tag is 1/n, where n is the total number of tags in the box.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probabilities can be expressed as fractions, decimals, or percentages.

A Coupon refers to a discount or a voucher that can be redeemed for a specified value or product at a store or business.

If the tag is not drawn, the probability of drawing it on the second day is 1/(n-1), since there is one less tag in the box. If the tag is not drawn on the second day, the probability of drawing it on the third day is 1/(n-2), and so on.

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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

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

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.