Kyla brought pies to a picnic. After the picnic, Kyla noticed 16/8 of the pies were eaten.

How many of the pies that Kyla brought to the picnic were eaten?


A. 16

B. 8

C. 2

D. 1

Answer:47

7•7

Step-by-step explanation:

The results of the balls in Phillip's bag are:

The mean = 8.

The median = 7.

The mode = blue

The range = 12

The mean (or the average) is the sum of all the values divided by the total number of values. Let's calculate the mean for the given data:

Total number of balls = 8 + 3 + 6 + 3 + 13 + 15 = 48

Mean = (8 + 3 + 6 + 3 + 13 + 15) / 6 = 48 / 6 = 8

Mean = 8.

The median is the middle value when a set of values is arranged in ascending or descending order.

Let's arrange the given data in ascending:

3, 3, 6, 8, 13, 15

As the total number of values is even, the median will be the average of the two middle values, which are 6 and 8.

Median = (6 + 8) / 2 = 7

The median = 7.

The mode is the value that appears most frequently in a set of values. Let's find the mode of the given data:

Red balls: 8

Green balls: 3

Yellow balls: 6

Orange balls: 3

Black balls: 13

Blue balls: 15

Blue balls have the highest frequency (i.e., 15) among all the colors.

The range is the difference between the highest and lowest values in a set of values. Let's find the range of the given data:

Highest value = 15 (blue balls)

Lowest value = 3 (green balls and orange balls)

Range = Highest value - Lowest value = 15 - 3 = 12

Range = 12.

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The sample space are:

{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}

The favorable outcomes care:

{RS, RT, SR, ST, TR, TS}

The probability is  0.3 or 30%

Part A:

The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.

The sample space can be represented as follows:

{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}

Part B:

The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.

The favorable outcomes can be represented as follows:

{RS, RT, SR, ST, TR, TS}

Part C:

To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.

The number of favorable outcomes is 6, and the size of the sample space is 20.

Therefore, the probability of selecting 2 cards that are consonants is:

P(consonants) = favorable outcomes / sample space

P(consonants) = 6 / 20

P(consonants) = 0.3 or 30%

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A congruence transformation that maps triangle RST to triangle UVW is a reflection along the line y = 1, followed by a translation 2 units right and down by 1 units.

A congruence transformation that maps triangle RST to triangle UVW is a rotation of 180°, followed by a translation 2 units left and down by 5 units.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-image underwent a sequence of congruence transformation to produce the image.

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We can see that they are similar because the ratio of the corresponding sides of the triangle are the same = 5/3.

A triangle is a polygon with three sides and three angles. It is one of the most basic shapes in geometry and is formed when three non-collinear points are connected by straight lines. The three sides of a triangle can have different lengths, and the three angles can have different measures. Triangles can be classified based on their sides and angles.

BC/DE = AD/AB

15/9 = AB/6

AB = (15 × 6)/9 = 90/9 = 10.

15/9 = 10/6 = 5/3.

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the surface area of the cylinder represented by the given net is approximately 166.306 square feet.

To calculate the surface area of a cylinder using its net, we need to identify the different components of the net and their measurements.

Without the specific net provided, I will assume a standard net of a cylinder, consisting of two circles for the top and bottom faces, and a rectangle for the lateral (side) surface.

Given that the measurements provided are 10 ft and 16 ft, we can assume that the height of the cylinder is 10 ft and the circumference of the circular bases is 16 ft.

The surface area of a cylinder is given by the formula:

Surface Area [tex]= 2 \times \pi \times r \times (r + h)[/tex]

where r is the radius of the circular base and h is the height of the cylinder.

Since the circumference of the circular base is given as 16 ft, we can calculate the radius (r) using the formula:

Circumference [tex]= 2 \times π times r[/tex]

[tex]16 = 2 \times π \times r[/tex]

[tex]r = 16 / (2 \times \pi)[/tex]

[tex]r v\ approx 2.546 ft[/tex] (rounded to three decimal places)

Now that we know the radius (r) and the height (h) of the cylinder, we can substitute these values into the formula for surface area:

Surface Area  [tex]= 2 \times π \times 2.546 \times (2.546 + 10)[/tex]

Surface Area  [tex]\approx 166.306 ft^2[/tex] (rounded to three decimal places)

Therefore, the surface area of the cylinder represented by the given net is approximately  [tex]166.306[/tex] square feet.

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If the shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, the percentage of the circle is shaded is: 31.83% .

We can start by finding the area of the entire circle. The formula for the area of a circle is:

A = πr^2

where A is the area and r is the radius. Since the diameter of the circle is 10 cm, the radius is half of that, or 5 cm. Therefore, the area of the entire circle is:

A = π(5 cm)^2 = 25π cm^2

Next, we can find what percentage of the circle is shaded by dividing the shaded area by the total area of the circle and multiplying by 100:

Percentage shaded = (shaded area / total area) x 100

Percentage shaded = (25 cm^2 / 25π cm^2) x 100

Percentage shaded = 100 / π ≈ 31.83%

Therefore, approximately 31.83% of the circle is shaded.

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To ensure that smooth curves have no cusps, we need to require that z'(t) never vanishes. This condition ensures that the tangent line to the curve changes smoothly and continuously as we move along the curve, without any abrupt changes in direction that would create cusps.

To understand why the condition that z'(t) never vanishes is necessary to ensure that smooth curves have no cusps, we first need to understand what a cusp is. A cusp is a point on a curve where the tangent line changes direction abruptly, creating a sharp point or corner in the curve.

Now, let's consider the curve traced by the parametrization z(t) = t^2it^3 with -1 ≤ t ≤ 1. To determine whether this curve has any cusps, we need to calculate the derivative of z(t) with respect to t:

z'(t) = 2it^3 + 3t^2i

If we set z'(t) equal to zero and solve for t, we get:

2it^3 + 3t^2i = 0
t^2(2i t + 3i) = 0

This equation has two solutions: t = 0 and t = -3/2i. These are the points on the curve where z'(t) vanishes.

At t = 0, the curve passes through the origin, which is a smooth point. However, at t = -3/2i, the curve has a cusp. To see why, we can look at the behavior of z(t) near this point.

As t approaches -3/2i from either side, the magnitude of t^2 increases without bound, while the magnitude of t^3 remains constant. This means that z(t) approaches infinity along a straight line with slope -3/2i. In other words, the curve has a sharp corner or cusp at this point.

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The volume of the prism is gotten as 312 cm³.

Volume is described as a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units.

The basic formula for volume is length × width × height.

The formula for the volume of triangular prism = area of triangle x length

area of triangle = 1/2 x base x height

⇒ area of triangle = 1/2 x 8 x 6 = 24 cm²

Therefore, volume of the prism = 24 x 13 = 312 cm³

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The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 250 ft-lb.

The work done in lifting the lower end of the chain to the ceiling can be calculated using the formula for work, which is given by:

Work = force x distance

In this case, the force is the weight of the chain, which is 25 lb, and the distance is the length of the chain, which is 10 ft.

So, the work done in lifting the lower end of the chain to the ceiling is:

Work = 25 lb x 10 ft

Work = 250 ft-lb

Therefore, the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 250 ft-lb.

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The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.

The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.

To find the work done in lifting the lower end of the chain to the ceiling, we need to consider the average weight of the chain as it is being lifted.

1. First, find the weight per foot of the chain:Weight of chain = 25 lbLength of chain = 10 ftWeight per foot = (25 lb) / (10 ft) = 2.5 lb/ft2.

Determine the average weight being lifted:Since you're lifting the chain from one end, the average weight you're lifting is half of the chain's total weight.

Average weight = (25 lb) / 2 = 12.5 lb3. Calculate the work done:Work done = Force x DistanceForce = Average weight = 12.5 lbDistance = Length of chain = 10 ftWork done = (12.5 lb) x (10 ft) = 125 ft-lb

So, the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.

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We'd need a sample size of at least 659 to estimate the population proportion with a periphery of error of 0.03.

To find the sample size demanded a confidence interval with a periphery of error of 0.03, we need to use the following formula

n = ( zσ/ E) * ( zσ/ E) * pq

where

z is the z- score corresponding to the asked position of confidence( let's assume 95 confidence, which corresponds to a z- score of 1.96)

σ is the population standard deviation( which is unknown in this case, so we'll use a conservative estimate of0.5)

E is the periphery of error( which is0.03)

p is the estimated proportion( which is0.41)

q = 1- p

Plugging in the values, we get

n = (1.960.5/0.03) * (1.960.5/0.03*0.41( 1-0.41) ≈658.72

Rounding up, we get a sample size of 659. thus, we'd need a sample size of at least 659 to estimate the population proportion with a periphery of error of 0.03, assuming a 95 confidence position and a population proportion estimate of 0.41.

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The first statement which says that the day is cloudy, cold, and windy represents the part of the biosphere respectively.

The term "biosphere" (from the Greek "o" for "life" and "sharia" for "sphere"), also referred to as "ecosphere" (from "o" for "environment" and "sphaira"), refers to the whole of all ecosystems on Earth.

It is also known as the Earth's life zone. In terms of matter, the biosphere—which is technically a spherical shell—is a closed system with few inputs and outputs.

It is an open system in terms of energy, with photosynthesis absorbing solar energy at a rate of about 130 terawatts annually.

According to the broadest definition of physiology, the biosphere is the entire ecological system that includes all living things and their interactions, including those with the lithosphere, cryosphere, hydrosphere, and atmosphere.

Therefore, the first statement which says that the day is cloudy, cold, and windy represents the part of the biosphere respectively.

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The scouts are using quantitative analysis.

Answer:

Surface area of prism A is approximately 12.4 square units.

Step-by-step explanation:

Since prism A and prism B are similar, their corresponding side lengths are proportional. Let's use the scale factor k to represent the ratio of the side lengths of prism B to those of prism A. Then, the volume of prism B is (k³)(27) = 27k³ cubic units. Similarly, the surface area of prism B is (k²)(surface area of prism A).

We are given that the volume of prism B is approximately 512 cubic units. Therefore, we can solve for k:

27k³ = 512

k³ = 512/27

k ≈ 3.62

Now, we can use k to find the surface area of prism A:

surface area of prism B = (k²)(surface area of prism A)

128 = (3.62²)(surface area of prism A)

surface area of prism A ≈ 12.4 square units

Therefore, the surface area of prism A is approximately 12.4 square units.

Answer:

To calculate the minimum sample size required for a given margin of error and confidence level, we can use the following formula:

n = (z^2 * p * (1-p)) / E^2

where:

Substituting the values, we get:

n = (2.576^2 * 0.5 * (1-0.5)) / 0.05^2

n = 664.3

Rounding up to the nearest whole number, the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level is 665.

the sequence of transformations that produces R'S'T' from RST is translation 2 units to the right and 3 units down, followed by a rotation of 90 degrees clockwise, and finally a reflection across the x-axis.

A triangle is a polygon since it has a total of three faces along with three vertices. It belongs to the fundamental geometric shapes. Triangles having vertex positions alternating between A and B are referred to as triangles ABC. A unique plane and a triangle in Euclidean geometry appear when the three vertices are not collinear. Due to its three sides and three corners, triangles are considered polygons. The corners of a triangle are defined as the locations where its three sides meet. Three triangle angles are multiplied to get 180 degrees.

To transform triangle RST to R'S'T', we can use the following sequence of transformations:

Translation: Move the triangle 2 units to the right and 3 units down. This will result in triangle R''S''T'' with vertices (2, -3), (-2, 0), (-3, -2).

Rotation: Rotate triangle R''S''T'' 90 degrees clockwise about the origin. This will result in triangle R'''S'''T''' with vertices (3, 2), (0, 2), (2, 3).

Reflection: Reflect triangle R'''S'''T''' across the x-axis. This will result in triangle R'S'T' with vertices (3, -2), (0, -2), (2, -3).

Therefore, the sequence of transformations that produces R'S'T' from RST is translation 2 units to the right and 3 units down, followed by a rotation of 90 degrees clockwise, and finally a reflection across the x-axis.

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The average distance of electric cars is 275.

The range of the data set is 300.

Given:

To find: Average distance of electric cars

Solution:

The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:

250, 250, 250, 400, 300, 300, 350, 100

To find the average distance of electric cars, we can use the formula:

Average = (Sum of all the data points) / (Number of data points)

Substituting the given values, we get:

Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8

Average = 2200 / 8

Average = 275

Therefore, the average distance of electric cars is 275.

Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.

Range = Maximum value - Minimum value

Range = 400 - 100

Range = 300

Therefore, the range of the data set is 300.

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Step-by-step explanation: Solve for y by simplifying both sides of the equation, then isolating the variable. y = 0

Hope it helped :D

Answer: Circumference = 18 π cm

Step-by-step explanation:

We can use this formula to find the circumference of a circle:

➜ r is equal to the radius, also known as half the width of a circle.

      C = 2πr

We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 18.

      C = 2πr

      C = 2π(9)

      C = 18 π cm

Answer: 18π

Step-by-step explanation:

The circumference of a circle is equal to 2πr, with r being equal to the radius. The radius of a circle is defined as the length from any point on the circle to its middlemost point. In this case, we are given the value of the radius as defined by the line. The radius equals 9, which we can plug into the equation.

C= 2πr

C = 2π(9)

C = 18π = 56.55

Hope this helps!

The rate at which the base of the triangle is changing when the altitude is 20 cm and the area is 120 cm^2 is 0 cm/s.

To solve this problem, we need to use the formula for the area of a triangle, which is:

A = (1/2)bh

Where A is the area, b is the base, and h is the altitude.

We know that the area is 120 cm^2 and the altitude is 20 cm. So we can plug in these values and solve for the base:

120 = (1/2)b(20)

240 = 20b

b = 12 cm

Now we need to differentiate both sides of the equation with respect to time (t):

dA/dt = (1/2)(db/dt)h

We are given the value of dh/dt (which represents the rate at which the altitude is changing) is 3 cm/s. We need to find db/dt (which represents the rate at which the base is changing).

Plugging in the values we know, we get:

dA/dt = (1/2)(db/dt)(20)

Solving for db/dt, we get:

db/dt = (2dA/dt)/h

Plugging in the values we know, we get:

db/dt = (2)(0)/20

db/dt = 0 cm/s
Since the area is constant (120 cm²) and the altitude is constant (20 cm), the base of the triangle is not changing. Therefore, the rate at which the base is changing is: 0 cm/s

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If x is a non-negative real number, then the expression √ x is called the Principal square root. The answer is Principal Square Root.

What is Principal Square Root?

The positive square root of a non-negative real integer is the principal square root. It is the one and only non-negative real number that, when squared, yields the given non-negative real number. The principal square root of 9 is 3, for example, because 3 multiplied by itself equals 9.

The radical sign (√) is frequently used to represent the principal square root. The term √x denotes Principal square root of x. The sign can be used to indicate the negative square root of x in some settings, but this is less frequent.

The principal square root notion is significant in mathematics, including algebra, geometry, and calculus. It's used to solve equations, simplify expressions, and calculate lengths and distances. It's also used in a wide range of scientific and engineering applications.

Therefore, if x is a non-negative real number, then the expression √ x is called the Principal square root.

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If x is a nonnegative real number, then the expression √ x is called the square root of x. The square root of a nonnegative real number is a value that, when multiplied by itself, equals the original number.

If x is a nonnegative real number, then the expression √x is called the "principal square root" of x. The principal square root of a nonnegative real number x is the nonnegative real number that, when multiplied by itself, equals x. In other words, if y = √x, then y * y = x. This ensures that the result is also a nonnegative real number.

For example, the square root of 4 is 2 because 2 multiplied by 2 equals 4. The square root function is denoted by the symbol √ and is used to find the positive number that, when squared, gives the input value.

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Therefore (t) can  be written as **(2 - 3Q) / (Q + 4)**.

Within the given equation, Q is a variable. It stands for an unknowable amount or value that can be ascertained by equation-solving.

A quantity that can take on any one of a number of values is referred to as a variable. A variable in mathematics is a symbol or letter that denotes an unknowable amount or value. The variable Q in the given equation stands for an unknowable quantity or value that can be ascertained by resolving the equation.

The equation is as follows:

Q = (2 - 4t) / (t + 3)

When we divide both sides by (t + 3), we obtain:

Q(t + 3) = 2 - 4t

When we increase the left side of the equation, we obtain:

Qt + 3Q = 2 - 4t

The result of adding 4t to both sides of the equation is:

Qt + 3Q + 4t = 2

Combining related concepts gives us:

t(Q + 4) = 2 - 3Q

The result of dividing both sides by (Q + 4) is:

t = (2 - 3Q) / (Q + 4)

t can therefore be written as **(2 - 3Q) / (Q + 4)**.

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The equation with the new substitutions and conversion factor is a'B'T' = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)*a^6/6 where k is (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2) The intercept value of the log-log graph would have been -1.108.

Starting with Equation 4: T = ka^6/6, we can substitute a = (d/k)^(1/6) and b = (2/3)^(1/2) * (d/k)^(1/3) to get

T = k[(d/k)^(1/6)]^6/6

T = k(d/k)^(1/2)/6

T = (k^(1/2)/6) * d^(1/2)

Now we can rearrange the equation so that a, b, and t are on the left side

a'B'T' = ka^6/6

(a/d)^(1/6) * b^(2/3) * T' = k[(a/d)^(1/6)]^6/6 * T'

(a/d)^(1/6) * (2/3)^(1/2) * (d/k)^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'

(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'

(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) = k^(1/2)/6

k = [(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3)]^2/6

k = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)

With this new conversion factor, the intercept of the log-log graph would have changed. The intercept represents the value of T when a = 1 (since log(1) = 0). Using the new conversion factor, we have

T = (1/6) * (2/3)^(1/3) * d^(1/2) * a^(1/3)

T = (1/6) * (2/3)^(1/3) * d^(1/2)

log(T) = log[(1/6) * (2/3)^(1/3) * d^(1/2)]

log(T) = log(1/6) + log[(2/3)^(1/3)] + log(d^(1/2))

log(T) = log(1/6) + (1/3) * log(2/3) + (1/2) * log(d)

So the intercept of the log-log graph would be log(1/6) + (1/3) * log(2/3) = -1.108, assuming that d is held constant. This intercept represents the value of log(T) when log(a) = 0, or when a = 1. In other words, when a = 1, the predicted value of T would be 0.162 (or 16.2% of its maximum value).

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

" Plug the two substitutions into Equation 4 (T = ka^6/6)). Rearrange the equation so that a, b,t are on the left side of the equation and d remains on the right side, e.g. a'B'T' = ka^6/6 you will figure out what the "k" if you used this version of the equation (including your new conversion factor, how would this have changed the intercept of your log-log graph? what would its value have been?"--

According the question given you jogged around the distance of 26[tex]\frac{2}{3}[/tex] miles.

What is an improper fraction?

When the numerator value exceeds the denominator value, the fraction is incorrect. Incorrect fractions can also be expressed in the form of a whole number and a proper number, where the numerator is the remainder and the denominator is left unchanged.

Here, we have

Given: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week.

We have to find out how many miles did you jog.

The total jogging distance will be

= 4(6 2/3) miles

= 4 × 20/3 miles

= 80/3 miles

= 26[tex]\frac{2}{3}[/tex] miles.

Hence, you jog 26[tex]\frac{2}{3}[/tex] miles.

Question: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week, how many miles did you jog?

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Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

∠A = ∠C in trapezoid ABCD with arcAB = arcCD, can be proven with the property of isosceles triangles.

Since arcAB = arcCD, the lengths of the two arcs are equal. This implies that the lengths of the segments subtended by these arcs, AB and CD, are also equal.

Let E and F be the midpoints of the non-parallel sides AD and BC, respectively. Connect E and F with a line segment EF.

Since E and F are midpoints, DE = EA and BF = FC. In addition, since AB = CD = L, we can say that:

DE + EA = BF + FC

EA = FC

So, by the Hypotenuse-Leg (HL) theorem of congruence, triangles AEF and CFE are congruent:

ΔAEF ≅ ΔCFE

Now, since the triangles are congruent, their corresponding angles are equal:

∠A = ∠C

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Answer: Trapezoid

Step-by-step explanation:

Answer:

it's also called a quadrilateral with 1 right angle

The scale factor of the dilation must be greater than 1. if the image A'B'C' is bigger than the preimage ABC

If the image A'B'C' is bigger than the preimage ABC, then the scale factor of the dilation must be greater than 1.

In other words, the length of any segment in the image is larger than the corresponding segment in the preimage by the same factor.

Since D is the center of the dilation, we can use the ratio of the corresponding side lengths of the image and preimage triangles to find the scale factor.

For example, if we want to find the scale factor for A', we can use:

scale factor = B'C'/BC

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Thus, the appropriate measure of variability found for the given data is 10.

The difference here between maximum and smallest values in a data set is known as the range. Utilizing the exact same units as the data, it measures variability. More variability is shown by larger values.

Given length of ribbons:

3, 6, 9, 11, 12, 13

Minimum value = 3

Maximum value = 13

Actually, the range, which is determined by deducting the lowest value from the greatest value in the dataset, would be the proper measure of variability for this data.

Range = Maximum value - Minimum value

Range = 13 - 3

Range = 10

Thus, the appropriate measure of variability found for the given data is 10.

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9. The volume of the triangular pyramid is given by:

V = (1/3)Bh

Here, B is the base area.

The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:

h = sqrt(26.7² - 11.7²) = 23.274 km

The area if the base is:

B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km

Now, the volume is:

V = (1/3)(136.89)(15) = 2053.35 cubic km

Hence, the volume of the triangular pyramid is 2053.35 cubic km.

9. The volume of the triangular pyramid is 2053.35 cubic km. 11. The area of the shaded portion is 348.19 cubic in 13. The slant height of the cone is 8.53 meters.

A fundamental conclusion in geometry relating to the lengths of a right triangle's sides is known as Pythagoras' theorem. According to the theorem, the square of the length of the hypotenuse, the side that faces the right angle, in any right triangle, equals the sum of the squares of the lengths of the other two sides, known as the legs.

9. The volume of the triangular pyramid is given by:

V = (1/3)Bh

Here, B is the base area.

The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:

h = √(26.7² - 11.7²) = 23.274 km

The area if the base is:

B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km

Now, the volume is:

V = (1/3)(136.89)(15) = 2053.35 cubic km

Hence, the volume of the triangular pyramid is 2053.35 cubic km.

11. The volume of a cone is given by:

V = (1/3)πr²h

The dimension of the bigger cone is radius is 9 in, and height 15 in:

V1 = (1/3)π(9 in)²(15 in) = 381.7 cubic in

The dimension of the smaller cone is radius is 4 in, and height 10 in:

V2 = (1/3)π(4 in)²(10 in) = 33.51 cubic in

Now, the area of the shaded portion is:

V1 - V2 = 381.7 - 33.51  = 348.19

13. The volume of a cone is given by:

V = (1/3)πr²h

Substituting the values we have:

542.87 = (1/3)π(6 m)²h

h = 542.87 / [(1/3)π(6 m)²] = 6.05 m

Now, using the Pythagoras Theorem for the slant height we have:

s² = r² + h²

s² = (6 m)² + (6.05 m)²

s² = 72.9

s = √(72.9) = 8.53 m

The slant height of the cone is 8.53 meters.

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