can a triangle be formed with three sides of equal length? Explain using the model above.

The area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 is estimated to be 4/3.

Ram's Rule is a numerical integration method used to estimate the area under a curve by dividing it into trapezoids. The formula for calculating the area under the curve is given by A = (1/2) x (b - a) x (f(a) + f(b)), where A is the area, b and a are the limits of the integration and f(a) and f(b) are the values of the function at the limits a and b respectively.

In this case, the area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 can be estimated using Ram's Rule as follows:

A = (1/2) x (3 - 1) x (1/1 + 1/3)

 = (1/2) x (2) x (4/3)

 = 4/3.

Therefore, the area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 is estimated to be 4/3.

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Answer: 12 11/26 laps

Step-by-step explanation:

9 3/13= 9 6/26

9 6/26+ 3 5/26=12 11/26.

The value of in x° is sin x = 3/z

The ratio of an angle's opposing side to its adjacent side, or its tan

tan x = 3/y

cos x = y/z

We choose 3 and y to represent the opposite and adjacent sides, respectively, because this ratio is 3:y.

Technically, we ought to write 3t and yt, but we'll take a chance since y appears in the second ratio as well!

Since y is already used to represent the adjacent side, z is used to represent the length of the hypotenuse.

The right triangle's sides are now finished.

Because tan x = sin(x)/cos(x), therefore

sin x = tan(x)*cos(x)

        = (3/y)*(y/z)

        = 3/z

Answer: a) sin x = 3/z

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It is not possible to describe the standard deviations of salary, hourly rate, years worked, education, and age without having the data.

Standard deviation is a measure of the spread or dispersion of a set of data. It is calculated as the square root of the variance and is used to give an idea of how far the individual values in a data set are from the mean or average.

In order to describe the standard deviations of salary, hourly rate, years worked, education, and age, we would need to have the actual data for those variables. Without the data, it is not possible to calculate the standard deviations and describe what they tell us about the variables.

It is important to note that the standard deviation can give us information about the distribution of the data and the variability of the values. For example, if the standard deviation is small, this means that the majority of the values are close to the mean, while a larger standard deviation indicates that the values are more spread out. This information can be useful in making inferences about the variables and in making predictions about future values.

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Answer: The answer is 1/4.

Step-by-step explanation:

The area of the logo is 6 square feet.

We start wit a logo of 4 inches by 6 inches, and we want to make it 6 times larger, so the new dimensions are:

6*(4 inches) = 24 inches.

6*(6 inches) = 36 inches.

Remember that:

1ft = 12 in

Writting that in feet, we will get:

24 inches = (24/12) ft = 2ft

36 inches = (36/12) ft = 3ft

Then the area of the logo is:

A = 2ft*3ft = 6 ft²

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The average rate of change over for the interval 1 < x < 5 k(x) greater than the average rate of change over of g(x)

A function is a relationship between inputs where each input is related to exactly one output.

We have,

g(x) = 1.8 [tex]x^{2}[/tex]

The average rate of change of g(x) over the interval 1 < x < 5:

= [tex]$\frac{g(5)-g(1)}{5-1}[/tex]

= [tex]$\frac{1.8 \times (5)^{2} -1.8 \times(1)^{2} }{5-1}[/tex]

= [tex]$\frac{43.2}{4}[/tex]

= 10.8..............(1)

The average rate of change of f(x) = [tex]x^2[/tex] in the interval 1 < x < 5:

= [tex]$\frac{25-1}{4}[/tex]

= [tex]$\frac{24}{4}[/tex]

= 6..............(2)

The average rate of change of g(x) = 1.2 [tex]x^2[/tex] in the interval 1 < x < 5:

= [tex]$\frac{28.8}{4}[/tex]

= 7.2.................(3)

The average rate of change of h(x) =1.5 [tex]x^2[/tex] in the interval 1 < x < 5:

= [tex]$\frac{36}{4}[/tex]

= 9...........(4)

The average rate of change of k(x) = 2 [tex]x^{2}[/tex] in the interval 1 < x < 5:

= [tex]$\frac{48}{4}[/tex]

= 12.........(5)

From (1), (2), (3), (4), and (5) we see that,

The average rate of change of [tex]$\mathbf{k}(x)=2 x^2$[/tex] is larger than the average rate of change of [tex]$g(x)=1.8 x^2$[/tex].

12 > 10.8

Thus,

Option D is the correct answer.

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[tex]\cfrac{PQ}{XY}=\cfrac{QR}{YZ}\implies \cfrac{5}{30}=\cfrac{6}{YZ}\implies 5YZ=180\implies YZ=\cfrac{180}{5}\implies YZ=36 \\\\\\ \cfrac{PQ}{XY}=\cfrac{PR}{XZ}\implies\cfrac{5}{30}=\cfrac{10}{XZ}\implies 5XZ=300\implies XZ=\cfrac{300}{5}\implies XZ=60 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Perimeter of }XYZ}{30~~ + ~~36~~ + ~~60}\implies \text{\LARGE 126}[/tex]

Length of major axis using formula of eccentricity is √2,2

Given that foci of the ellipse is at (0,2) & (0,−2)

⇒Major axis of ellipse is along y-axis.

So, equation of ellipse can be taken as: x²/a² +y/b² = 1 where a<b

Length of minor axis, 2a=4   (Given)

⇒a=2    ....(1)

and  b=2   ....(2)

e = √(1-a²/b²)

⇒a²=b²-b²e²

b²=8

Therefore b=2√2  .....3

Find equation of ellipse using above result

x²/4 + y²/8 = 1

Checking options, we have ( 2,2) satisfying the equation of ellipse above.

Hence the length of the is √2,2

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The shortest distance between planet Q and planet R is  1.64 × 10⁷ .

RP = 1.6 * 10⁷

most compact distance

The Pythagoras theorem x₂ = R * P² + Q * P² is then used to determine the shortest distance (x).

This results in x = (3.6 * 10⁶) + (1.6 * 10⁷) = 2.

x² = 12.96 * 10¹²  + 2.56 * 10¹⁴ should be evaluated.

Write the equation as: x²= 12.96 * 10¹² + 256 * 10¹²

Sums x² = 268.96*10¹² should be evaluated.

multiply both sides' square roots.

x = 16.4 * 10⁶

Replace with: x = 1.64 * 10⁷

In light of this, the distance between planet Q and planet R is 1.64 * 10⁷ km.

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The complete  question is

The distances between some planets are given below.

Planet Q is 3.6 x 10⁷ to the power of 6 km from planet P.

Planet R is 1.6 x 10⁷ to the power of 7 km from planet P.

Work out the shortest distance between planet Q and planet R. Give your answer in standard form.

The equation of a radical function can be determined by using the transformation rules for x- and y- shifts, stretches/compressions, reflections, and rotations.

The equation of a radical function can be determined by applying various transformation rules. The most common transformations are shifts, stretches/ compressions, reflections, and rotations. For example, a radical function that is shifted left two units would have an equation of y = sqrt(x + 2). This is because the function is shifted two units to the left of the origin, so the equation must include an x + 2 term. Similarly, if the function is reflected in the x-axis, the equation would be y = -sqrt(x). This is because the reflection inverts the sign of the y-coordinate, so the equation must include a negative sign in the radical. For stretches and compressions, the equation must include a coefficient in front of the radical. For example, if the function is stretched horizontally by a factor of 3, then the equation would be y = 3 sqrt(x). This is because the function is stretched by a factor of three, so the equation must include a coefficient of 3 in front of the radical. Finally, for rotations, the equation must include a term for the angle of rotation. For example, if the function is rotated counterclockwise by 45 degrees, then the equation would be y = sqrt(x + y/tan45). This is because the angle of rotation is 45 degrees, so the equation must include a tan45 term.

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When rotated about its center, a regular heptagon has 7 rotational symmetries. In addition to rotational symmetry, a regular heptagon has 1 line of reflectional symmetry.

Rotation symmetry, also known as radial symmetry or circular symmetry, is a fundamental concept in geometry that refers to the property of a shape to remain unchanged after rotating it about a fixed point. This point is typically the center of the shape, although it can be any point within the shape.

The amount of rotation required for the shape to become congruent to its original form is called the "angle of rotation." If a shape can be rotated multiple times and still remain unchanged, it is said to have multiple rotational symmetries.

For example, a circle has an infinite order of rotational symmetry, as it can be rotated 360 degrees and still look exactly the same. On the other hand, a square has 4 rotational symmetries, as it can be rotated 90 degrees and still look the same 4 times.

Rotational symmetry is a useful concept in mathematics and science as it provides a way to describe the symmetry of objects and shapes in the real world. It also helps us understand how objects and shapes change when they are rotated, and it provides a way to classify objects based on their symmetrical properties.

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Answer:

Multiply by the inverse.

Answer: 45

Step-by-step explanation:

(15)/(1/3) is the same thing as multiplying the top (numerator), by the inverse of the bottom (denominator).

So we have the following: [tex]\frac{15/1}{1/3}[/tex]

Taking the inverse means flipping the fraction. The inverse of [tex]\frac{1}{3}[/tex] is [tex]\frac{3}{1}[/tex]. So we can keep the top, and multiply by the inverse.

[tex]\frac{15}{1}[/tex] X [tex]\frac{3}{1}[/tex] = 15 x 3 = 45.

Does this make sense?

The failure of direct democracy most directly led to the Roman Republic's demise and its transition to an empire. That is option D.

Democracy is defined as the government by the people for the people and based of the will of these people.

In the first part of ancient Rome (509-27 BC), the people were governed by elected officials. This is democracy as we understand it today.

But things began to change, people became less interested in the affairs of government, and the failure of democracy led directly to the rise of one-man empires. The Roman Empire lasted from 27 BC to 476 BC.

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The location of the second bus stop is given as follows:

(10, 8).

The relationship is described as follows:

When x increases by 4, y increases by 2.

The four translation rules are defined as follows:

The change in x is given as follows:

7 - 3 = 4.

The change in y is given as follows:

6 - 4 = 2.

Hence, starting from the first bus stop, the coordinates of the second bus stop are given as follows:

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True. The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They cannot be used to calculate the dispersion around the median or mode, or any other center-of-mass metric.

The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They can therefore be used to calculate the difference between the highest and lowest values in a data set. The standard deviation, which is the square root of the variance, is used to calculate how far away from the mean each result is on average. The average of the squared deviations between each data point and the mean is the variance. The variance and standard deviation cannot be used to quantify the dispersion of data around other measures of center, such as the median or mode, because they only measure the dispersion of data around the mean.

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The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.

In this case, the ratio of the corresponding sides of the two triangles are:

AB/DE = 3/18 = 1/6

BC/EF = 7/42 = 1/6

Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.

The transaction should be recorded as an Accounts Payable (A/P) liability in Sanford’s financial accounting system.

Accounts Payable is a liability account that records the amount of money a company owes to its suppliers for goods and services that have been received, but not yet paid for. In this case, Sanford is responsible for paying the supplier $15,000 for the helmets that have been delivered to its warehouse.

This payment should be recorded in the Accounts Payable account as a debit of $15,000 and a credit to the Cash account of $15,000. By doing this, Sanford’s Accounts Payable balance will be reduced to reflect that the invoice has been paid, and the Cash account will be increased to reflect the payment made. This will keep the company’s financial records up to date and accurate.

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To solve we need to calculate the z-score, but since we are given the sample size then we shall begin as follows:

The z-score is calculated as (320 - 300)/(50/6) = 2.4, which means that the value of 320 is 2.4 standard deviations above the population mean of 300. Using a standard normal table or calculator, we can find the probability that a standard normal random variable is less than 2.4, which is approximately 0.9918.

This means that the probability that the sample mean is greater than 320 is approximately 0.9918. In other words, there is a 99.18% chance that a randomly selected sample of 36 U.S. Marines will have a mean number of pushups greater than 320.

μ=300, σ=50, n=36, x=320

So,

σ/√n

= 50/√36

= 8.33333

z=(320-300)/8.33333

z=2.4

Therefore,

P(x>320)=P(z<2.4)=0.9918.

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First, we can find the total number of calendars sold by Rosie and Suzy combined:

19 (calendars sold by Rosie) + 26 (calendars sold by Suzy) = 45 calendars

Next, we can find the number of calendars sold by Juan:

Juan sold 4 times as many calendars as Rosie and Suzy combined, so Juan sold 4 * 45 = 180 calendars.

The area of the shaded region is 17.4 rounded up to the nearest tenth.

The unshaded region forms a circle with a radius of 9/2, so to get the area of the shaded region, we subtract the area of the circle from the area of the square as follows:

area of square = 9 m × 9 m = 81 m²

area of the circle = 22/7 × 9/2 × 9/2

area of the circle = 891/14 m²

area of the shaded region = 81 m² - 891/14 m²

area of the shaded region = (1134 - 891)/14

area of the shaded region = 243/14

area of the shaded region = 17.3571

Therefore, the area of the shaded region is 17.4 rounded up to the nearest tenth.

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Answer:

Step-by-step explanation:

it is the pink one

The value of your investment at maturity is $16,800. The interest is $9,800.

What is the meaning of initial investment?

The initial sum of money required to open an account or start a buy-in relationship is known as an initial investment. The two distinct but related industries of banking and long-term investment brokering are the main uses of the term "initial investment."

Given that the initial investment is $7,000. The rate of interest is 10% = 0.10. The number of years of investment is 14 years.

The formula of simple interest is

I = Prt

I = interest, P = principal, r = rate of interest, t = time.

Putting P = 7000, r = 0.10, t = 14 in I = Prt:

I = 7000 × 0.10 × 14

I = 9,800

The amount will be interest + principal = 9800+ 7000 = 16,800.

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The length d for the angle of depression 3° and altitude 1m is equal to 19 m to the nearest metre using the trigonometric ratio of cosine for the angle 87°

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the length d and the altitude of 1 m, we shall derive a complementary angle as:

90° - 3° = 87°

such that;

cos 87° = 1/d {adjacent/hypotenuse}

d = 1/cos 87°

d = 19.1073.

Therefore, the length d for the angle of depression 3° and altitude 1m is equal to 19 m to the nearest metre using the trigonometric ratio of cosine for the angle 87°.

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Answer:

The answer is a = -11/3.

The table should be completed as follows;

Object                         Radius                  Circumference

ceiling fan                    2.8 ft                         17.584 ft.

water bottle cap          13 mm                       81.64 mm.

bowl                             9.0 cm                       56.5 cm.

drum                             12.0 in                       75.4 in.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr

Where:

For the ceiling fan, the circumference is given by:

C = 2πr

C = 2 × 3.14 × 2.8

C = 17.584 ft.

For the water bottle cap, the circumference is given by:

C = 2πr

C = 2 × 3.14 × 13

C = 81.64 mm.

For the bowl, the radius is given by:

C = 2πr

56.5 = 2 × 3.14 × r

56.5 = 6.28r.

Radius, r = 56.5/6.28 = 8.9968 ≈ 9.0 cm.

For the drum, the radius is given by:

C = 2πr

75.4 = 2 × 3.14 × r

75.4 = 6.28r.

Radius, r = 75.4/6.28 = 12.0 in.

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The probability of odd or less than 6 is 0.75 which is 75%

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

From the question, there are 4 numbers

These include: 5,6,7,8

Pr(odd) 2/4

Pr(x<6) 1/4

Adding the fractions we have

1/2  + 1/4  = 3/4  = 0.75

Converted to percentage = 75%

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Answer:To calculate the length and width of the original figure with a scale factor of 50%, you need to reverse the scaling by multiplying the new dimensions by 100% / 50% = 2.

So if the new length is L, the original length would be L * 2 = 2L. Similarly, if the new width is W, the original width would be W * 2 = 2W.

Step-by-step explanation:here's a step-by-step explanation:

Identify the new length (L) and new width (W) of the figure.

Multiply the new length by a factor of 2 to find the original length: 2L = L * 2

Multiply the new width by a factor of 2 to find the original width: 2W = W * 2

The original length is 2L and the original width is 2W.

Note: This process works for any scale factor, not just 50%. To find the original dimensions, simply multiply the new dimensions by 100% / the scale factor.

Answer:

Step-by-step explanation:

You're right; it's 97 degrees. The angles of a triangle add up to 180, so to solve for each triangle's unknown angle value, subtract the known angles from 180. For the left triangle, that's 33 and for the right triangle it's 50. Those missing angles plus the one the question is asking for should add up to 180 degrees as well. Hence, 180 - 33 - 50 = 97.