A 6 inch by 10 inch rectangle is dilated by a factor of 2. What is the area of the dilated rectangle?

The answer of the given figure is ∠B = 72° and ∠C = 108°

In geometry, corresponding angles are pairs of angles that have the same relative position and the same degree of rotation, in two different geometric figures that are being compared.

More specifically, when two lines are crossed by another line, the angles on one side of the crossing line that are in the same relative position to each other (i.e., they are on the same side of the crossing line and are either both interior angles or both exterior angles), are corresponding angles.

According to question

∠CFE = 72°

In given diagram

DC ║ EF ║ AB and CB is transversal

∴ ∠CFE + ∠BFE = 180° ( Linear pair )

72° + ∠BFE = 180°

∠BFE = 180 - 72

∠BFE = 108°

∵∠DCF = ∠BFE ( Corresponding equal angle )

∠DCF = 108°

∠C = 108°

∠CFE = ∠B (  Corresponding equal angle )

72° = ∠B

∴∠B = 72°

Hence, the ∠B = 72° and ∠C = 108°

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The solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero

The values of the parameter s

for which the system has a unique solution are s ≠ -45/8. Let's understand how to find the solution and the values of s:

Given equation of the system is,5x1s + 9x2 = -3 ...(1)

5x1 + sx2 = 4 ...(2)

Now, let's solve the given system of equations using the elimination method:

Multiply equation (2) by 5, we get:25x1 + 5sx2 = 20 ...(3)

Now, we'll subtract equation (1) from equation (3) as:

25x1 + 5sx2 = 20- (5x1s + 9x2 = -3)20x1 + 5sx2 = 23 ... (4)

Let's divide equation (4) by 5s, we get:

4x1 + x2/s = 23/5s ... (5)

Multiply equation (2) by 9 and subtract equation (1) from it. We get:40x2 + 9sx2 = 39

Simplifying the above equation, we get:(49s+360)x2 = 39 ... (6)

Now, we have two equations:(5) 4x1 + x2/s = 23/5s(6) (49s+360)

x2 = 39The given system of equations will have a unique solution only if x2 ≠ 0. So, let's consider the value of x2.If x2 ≠ 0, then from equation (6)

we get,49s+360 ≠ 0 or s ≠ -360/49

This means that s ≠ -360/49 is necessary for the given system to have a unique solution.

Now, let's solve the equation (5):4x1 + x2/s = 23/5s

If we multiply both sides of the equation (5)

by s, we get:

4sx1 + x2 = 23/5If x2 ≠ 0, then we can solve this equation for x1 as:

x1 = (23/5s - x2)/4s

Therefore, the solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero value.

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we can solve the given equation by taking log to get answer as x = log₈(25)

what is  an equation ?

An equation is a mathematical statement that contains an equal sign, indicating that two expressions have the same value. It is a way of expressing the relationship between different variables or quantities.

In the given question,

Taking the logarithm of both sides with base 8, we get:

log₈(8ˣ) = log₈(25)

Using the logarithmic property that logₐ(b^c) = c logₐ(b), we can simplify the left-hand side to:

x log₈(8) = log₈(25)

Since log₈(8) = 1, we have:

x = log₈(25)

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Answer:

?=45 degrees

Step-by-step explanation:

All of the angles are congruent.

So the equation is:45+90+?=180

?=45 degrees

Answer: 45 degrees

Step-by-step explanation:

The value of angle V which is ∠V is calculated as:  64.01°

The trigonometric ratios are used to find the angles and lengths of a right angle triangle.

Some of the trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

The parameters given are:

∠W = 90°

UW = 39

WV = 80

VU = 89

Thus, using trigonometric ratios, we have:

∠V = tan⁻¹(80/39)

∠V = 64.01°

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So the formula for the nth term of the arithmetic sequence with the third term 7 and the common difference -2 is aₙ = 13 - 2n.

An arithmetic sequence's nth term is represented by the formula:

aₙ = a₁ + (n-1)d

In this case, we are given that the third term is 7, so we can use this information to find a₁:

a₃ = a₁ + (3-1)(-2)

7 = a₁ - 4

a₁ = 11

Now we have a₁ and d, so we can write the formula for the nth term:

aₙ = 11 + (n-1)(-2)

Simplifying this expression, we get:

aₙ = 13 - 2n

So the formula for the nth term of the arithmetic sequence with the third term 7 and the common difference is

-2 is aₙ = 13 - 2n.

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The ability of a study to detect a difference if one actually exists is called option (d) power

Power in statistics is the probability of correctly rejecting a false null hypothesis. In other words, it is the ability of a statistical test to detect a difference or effect if one actually exists in the population being studied. A study with high power has a low probability of a Type II error (failing to reject a false null hypothesis) and a high probability of correctly detecting a true difference or effect.

Power is affected by several factors, including sample size, effect size, level of significance (alpha), and variability of the data. Researchers often aim for a power of at least 80% to ensure that their study has a reasonable chance of detecting a meaningful effect.

Therefore, the correct option is (d) power

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The equation representing the area of the rectangle with width w is A = w² + 2w.

We have a rectangle with a length that is 2 units longer than the width w. Let's refer to the rectangle's length as L. Then we have:

[tex]L = w + 2[/tex]

The product of a rectangle's length and breadth determines its area A. So, to find an equation representing the area of the rectangle, we need to multiply the length L by the width w. Substituting L with the expression we got from the problem statement, we get:

A = L × w

A = (w + 2) × w

A = w² + 2w

This is the final equation representing the area of the rectangle in terms of its width w

This is a quadratic equation in standard form, where the coefficient of the squared term is 1, the coefficient of the linear term is 2, and the constant term is 0. We can use this equation to find the area of the rectangle for any given width w.

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Answer:

No solution

Step-by-step explanation:

Solve for x

[tex]|x-13|+18=-4[/tex]

Subtract 18 on both sides

[tex]|x-13|=-22[/tex]

There is no solution to this problem. Absolute value cannot be less then 0.

Thus, the  arc length of DC for the given central angle of circle is found as: 16.74 units.

Arc Length Formula: Assume a circle with radius r. If a circle's arc of length s subtends a central angle theta (measured in radians), the formula is as follows: r X theta = s.

For the given circle:

Thus,

∠APD + ∠DPC = 180° (angle sum property of triangle)

60 + ∠DPC = 180°

∠DPC = 180° - 60°

∠DPC = 120°

Using the formula for the arc length:

Arc length = Ф/360 * 2*π*r

Arc length DC = 120/360 * 2*3.14*8

Arc length DC = 16.74 units

Thus, the  arc length of DC for the given central angle of circle is found as: 16.74 units.

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Complete question:

In the figure below DB and AC are diameters of circle P. The length of PB is 8 units . What is the arc length of DC.

The figure is attached.

The ratios that would create the same orange color as Maia's ratio of  [tex]2:3[/tex] are  [tex]2[/tex] red to [tex]3[/tex] yellow,  [tex]44[/tex] red to  [tex]66[/tex] yellow, and [tex]28[/tex] red to [tex]42[/tex] yellow.

The ratio of 4 drops of red food coloring to 6 drops of yellow food coloring can be simplified to 2:3 by dividing both numbers by 2. This means that for every 2 drops of red food coloring, Maia used 3 drops of yellow food coloring to create orange icing.

Let's evaluate each of the given ratios:

2 red to 3 yellow: This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.

40 yellow to 100 red: We can simplify this ratio by dividing both numbers by 20, giving us 2 yellow to 5 red. This ratio is not equivalent to Maia's ratio of 2:3, so it would not create the same orange color.

44 red to 66 yellow: We can simplify this ratio by dividing both numbers by 22, giving us 2 red to 3 yellow. This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.

24 red to 26 yellow: We can simplify this ratio by dividing both numbers by 2, giving us 12 red to 13 yellow. This ratio is not equivalent to Maia's ratio of 2:3, so it would not create the same orange color.

28 red to 42 yellow: We can simplify this ratio by dividing both numbers by 14, giving us 2 red to 3 yellow. This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.

Therefore, the ratios that would create the same orange color as Maia's ratio of  [tex]2:3[/tex] are  [tex]2[/tex] red to [tex]3[/tex] yellow,  [tex]44[/tex] red to  [tex]66[/tex] yellow, and [tex]28[/tex] red to [tex]42[/tex] yellow.

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Answer: A (0.5)

Step-by-step explanation:

Determine by dividing total number of popcorn sold by the attendance. Use the plotted points to help you.

The sample size required to estimate a population proportion with a desired level of confidence and margin of error depends on the size of the population and the confidence level desired. In this case, the population proportion is unknown and the desired confidence level is 99.5% with a margin of error of 4%.

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

n = (Z² * p * q) / E²

where n is the sample size, Z is the Z-score corresponding to the desired level of confidence (which for a 99.5% confidence level is 2.81), p is the estimated population proportion (which is 0.5 as we have no reasonable estimate), q is 1-p, and E is the margin of error (which is 0.04).

Plugging in these values, we get:

n = (2.81² * 0.5 * 0.5) / 0.04² ≈ 1381

Therefore, a sample size of at least 1381 is required to estimate the population proportion with 99.5% confidence and a margin of error of 4%.

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17,600 citizens chose Fish or Snakes.

What is circle graph?

A circle graph, also known as a pie chart, is a type of data visualization used to represent data in a circular format. It is called a pie chart because the graph resembles a pie, which is divided into slices or sectors, where each sector represents a portion of the whole data set. The size of each slice is proportional to the corresponding value it represents in the data set. The circle graph is often used to show relative sizes of different categories or portions of a whole. It is a popular way to display data in business, statistics, and other fields.

According to the given information, the percentage of citizens who chose Fish or Snakes is 12% + 10% = 22%.

It is also given total number of citizens are 80,000.

To find the number of citizens who chose Fish or Snakes, we can first calculate 22% of 80,000,

[tex]22\% \: of \: 80000 \\ = \frac{22}{100} \times 80000 \\ = 0.22 \times 80,000 \\ = 17,600[/tex]

Therefore, 17,600 citizens chose Fish or Snakes.

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Answer: 586.20

Step-by-step explanation:

you add the balance on june 5th with the amount withdrawed to get the past balance

The circumference of the bottle cap is nothing but the circumference of a circle and it is 9.42 cm.

The circumference of a circle or other curved geometric form refers to the space encircling it. It is a boundary's one-dimensional linear measurement.

The diameter of the circle is given, D = 3cm

Therefore the radius of the circle, r = D/2 = 3/2 cm

Circumference of circle = 2[tex]\pi[/tex]r

                                         = 2 * 3.14 * 3/2

                                         = 3.14 * 3

                                         = 9.42 cm

Therefore the circumference of the bottle cap is 9.42 cm.

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To prove Triangle ACE is congruent to Triangle BDE using the ASA postulate, we need either ∠A ≅ ∠B or ∠C ≅ ∠D.

To prove two triangle congruent by angle side angle postulate, these triangle must have two sides equal or one angle from these two must be equal and identical to each other.

What are congruent triangle?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is’ ≅’.

The meaning of congruence in Maths is when two figures are similar to each other based on their shape and size. There are basically four congruence rules that proves if two triangles are congruent.

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a.(Constant of proportionality: 5)

b.(Constant of proportionality: 5)

Hi! I'm happy to help you with your question. Let's analyze each table and fill in the missing parts.

a.
X | 2
Y | 10

To find the constant of proportionality, divide Y by X:
10 / 2 = 5 (Constant of proportionality)

Now, let's fill in the missing parts for X=7 and X=1 using the constant of proportionality:
For X=7:
Y = 5 * 7 = 35

For X=1:
Y = 5 * 1 = 5

So, the completed table for (a) is:
X | 2  | 7  | 1
Y | 10 | 35 | 5
(Constant of proportionality: 5)

b.
X | 1
Y | 15

To find the constant of proportionality, divide Y by X:
15 / 1 = 15 (Constant of proportionality)

As there are no other values in table (b), we can't fill in any more parts. The constant of proportionality is 15.

Your answer:
a.
X | 2  | 7  | 1
Y | 10 | 35 | 5


b.
X | 1
Y | 15
(Constant of proportionality: 15)

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The correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient.

To calculate the correlation coefficient between x and f(x), we need to calculate several quantities first:

mean of x:

[tex]$\overline{x}[/tex] = {50+35+60+65+70+75+80}{7} = {435}/{7}

= 62.14

mean of f(x):

[tex]$\overline{f(x)}[/tex]= {1,272 + 1,884.5 + 2,322 + 2,584.5 + 2,672 + 2,584.5 + 2,322}/{7}

= 2,112.86

and, standard deviation of x:

[tex]$s_x[/tex]=[tex]\sqrt{\frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n-1}}[/tex]

= [tex]= \sqrt{\frac{(50-62.14)^2 + (35-62.14)^2 + (60-62.14)^2 + (65-62.14)^2 + (70-62.14)^2 + (75-62.14)^2 + (80-62.14)^2}{6}} \\\approx 17.27$[/tex]

and, standard deviation of f(x):

[tex]$s_{f(x)} = \sqrt{\frac{\sum_{i=1}^n (f(x_i) - \overline{f(x)})^2}{n-1}}[/tex]

= (1,272-2,112.86)² + (1,884.5-2,112.86)² + (2,322-2,112.86)² + (2,584.5-2,112.86)² + (2,672-2,112.86)²+  (2,584.5-2,112.86)² + (2,322-2,112.86)²}/ 6

= 385.09

Now, covariance of x and f(x):

[tex]$cov(x,f(x)) = \frac{\sum_{i=1}^n (x_i - \overline{x})(f(x_i) - \overline{f(x)})}{n-1}[/tex]

= {(50-62.14)(1,272-2,112.86) + (35-62.14)(1,884.5-2,112.86) + (60-62.14)(2,322-2,112.86) + (65-62.14)(2,584.5-2,112.86) + (70-62.14)(2,672-2,112.86) + (75-62.14)(2,584.5-2,112.86) + (80-62.14)(2,322-2,112.86)} / 6

= 762.36

Using these values, we can calculate the correlation coefficient:

[tex]$r = \frac{cov(x,f(x))}{s_x s_{f(x)}} = \frac{762.36}{17.27 \cdot 385.09} \approx 0.39$[/tex]

Therefore, the correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.

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The translation vector is (5, 5). Now we can find the image of point (-3, -2) under the same translation: (-3+5, -2+5) = (2, 3)

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

Let's denote the translation vector as (a, b), then the image of point (x, y) under the translation is given by (x+a, y+b).

We know that the image of point (6, -9) under the translation is (11, -4), so we can write:

(6+a, -9+b) = (11, -4)

Solving this system of equations for a and b, we get:

a = 5 and b = 5

Therefore, the translation vector is (5, 5). Now we can find the image of point (-3, -2) under the same translation:

(-3+5, -2+5) = (2, 3)

So the image of point (-3, -2) under the given translation is (2, 3).

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the height of the trapezoid is 8.4 kilometers. To find the height, h, of a trapezoid when given the area, A, we need to use the formula:

A = ([tex]b_{1} + b_{2}[/tex])h/2

where b1 and b2 are the lengths of the two parallel bases of the trapezoid.

Given that the area of the trapezoid is 42 square kilometers, we can write:

42 = ([tex]b_{1} + b_{2}[/tex])h/2

We can simplify this equation by multiplying both sides by 2:

84 = ([tex]b_{1} + b_{2}[/tex]) h

Now we need to find the values of b1 and b2. Unfortunately, the problem does not provide us with these values. Without them, we cannot find the exact value of h. However, we can provide an example to show how to solve the problem if we have the values of b1 and b2.

Let's say that b1 = 4 km and b2 = 6 km. We can substitute these values into the equation:

84 = (4 + 6)h

Simplifying:

84 = 10h

Dividing both sides by 10:

h = 8.4 km

So, in this example, the height of the trapezoid is 8.4 kilometers.

In general, to find the height of a trapezoid when given the area, we need to know the values of both bases. Once we have those values, we can use the formula above to solve for the height. If we are not given the values of the bases, we cannot find the exact value of the height.

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The probability that the individual waits more than 7 minutes is 0.3 or 30%. The probability that the individual waits between 2 and 7 minutes is 0.5 or 50%.

Let X be the waiting time for a particular individual at the bus stop. As per the given information, X follows a continuous uniform distribution with parameters a=0 and b=10 (as the bus arrives every 10 minutes).

The probability that the individual waits more than 7 minutes can be calculated as follows:

P(X > 7) = (b-7)/(b-a) = (10-7)/(10-0) = 3/10 = 0.3

Similarly, the probability that the individual waits between 2 and 7 minutes can be calculated as follows:

P(2 < X < 7) = (7-2)/(10-0) = 5/10 = 0.5

In summary, the probability that the individual waits more than 7 minutes is 0.3 and the probability that the individual waits between 2 and 7 minutes is 0.5. This means that there is a higher chance that the individual waits between 2 and 7 minutes than waiting for more than 7 minutes.

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Therefore , the solution of the given problem of function comes out to be Oy=-0.5z²+z+4.

On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

We must make use of the data provided in the challenge in order to identify the quadratic function.

=>  f(z) = a(z + 4)(z - 2)

where an is a constant we need to figure out.

We can use the position (-6, -8), which is where the function passes through, to determine the value of a:

=>  -8 = a(-6 + 4)(-6 - 2)

=>  -8 = a(-2)(-8)

=>  -8 = 16a

=>  a = -1/2

Inputting this number of an into the quadratic function equation yields the following results:

=>  f(z) = -1/2(z + 4)(z - 2)

By extending this phrase, we get:

=> f(z) = -1/2(z² - 2z - 8)

Further simplification results in:

=>  f(z) = -0.5z² + z + 4

The quadratic function's corresponding equation is thus:

=>  Oy=-0.5z²+z+4

The following is the appropriate decision from the options provided:

=> Oy=-0.5z²+z+4

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Answer:

A line graph, because it would show the association or relationship between two variables

Step-by-step explanation:

English please I don't unless

Therefore , the solution of the given problem of surface area comes out to be scale factor of the dilation is 15.0, rounded to one decimal point.

By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.

Here,

By dividing the volume of the dilated figure by the volume of the initial figure, we can determine the scale factor of the dilation:

volume of dilated figure / volume of initial figure is the scale factor.

Scale factor:

=>  25,500/1700 cm3

=> 15 scale factor

The approximate scale factor of the dilation is 15.0, rounded to one decimal point.

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Answer:

use long divison  ike this

      16

  -------

8 | 132

    8

  -----

    52

    48

  -----

     4

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                         132/8 = 16 with 4 leftover

                                             32 divided by 8 is 4, 96 divided by 8 is 12, the                                                                  

                                                  extra 4 left over

the tower leans 5.6° from the vertical, so we can draw a line perpendicular to the ground from the top of the tower to find the height. Let's call the height "h". the length of the tower is approximately  [tex]57 meters[/tex] (rounded to the nearest meter).

We know that the angle of elevation from the tourist to the top of the tower is [tex]29.2^\circ[/tex]  , so we can label that angle as 29.2°. We also know that the angle between the perpendicular line and the ground is 5.6°, so we can label that angle as 5.6°.

Using trigonometry, we can find the value of h:

[tex]tan(29.2^\circ) = h/105[/tex]

[tex]h = 105^\circ tan(29.2^\circ)[/tex]

[tex]h \approx 55.05[/tex]

So the height of the tower is approximately   [tex]55.05[/tex] meters.

To find the length of the tower, we can use the Pythagorean theorem:

[tex]h^2 + x^2 = (105/cos(5.6^\circ))^2[/tex]

[tex]x^2 = (105/cos(5.6^\circ))^2 - h^2[/tex]

[tex]x \approx 56.67[/tex]

So the length of the tower is approximately [tex]56.67[/tex] meters.

Therefore, the length of the tower is approximately [tex]57[/tex] meters (rounded to the nearest meter).

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The margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.

To find the margin of error for a 95% confidence interval, we need to determine the standard error of the mean. The  standard error of the mean formula can be written as:

SE = σ/√n

where:

SE = standard error of the mean,

σ = the standard deviation of the population

n = the sample size.

the standard deviation of the laboratory = 0.005

sample size = 4.

calculating the standard error of the mean:

SE = 0.005/√4

= 0.0025

Next, we need to find the critical value for a 95% confidence interval. the sample size is small (n < 30), then we need to use a t-distribution.

Critical value = 3.182.

The formula for calculating the margin of error is:

ME = t*SE

where :

ME = margin of error

t = critical value = 3.182.

SE = standard error of the mean = 0.0025

By substuting the values, we get:

ME = t*SE

= 3.182*0.0025

= 0.008 grams

Therefore, the margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.

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