Unit 7 polygons and quadrilaterals
Homework 7 trapezoids
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Directions: if each quadrilateral below is a trapezoid, find the missing measures

This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.

Tangent is a line or plane that touches a curve or surface at a single point. It is a measure of the steepness of a curve or surface at a particular point. It is equal to the ratio of the change in the y-coordinate to the change in the x-coordinate of a point on the curve. Tangent is used in many areas of mathematics and physics, including calculus, geometry, and mechanics. It is also used to describe the rate of change in a function, as well as to define the angle between two intersecting lines.

The tangent line equation for a line with a slope of 50 degrees is y = tan(50°)x.
To solve for x, you must rearrange the equation to isolate x on one side of the equation.
To do this, divide both sides of the equation by tan(50°), giving the equation x = y/tan(50°). This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.

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The angle E is 50.21°

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

Given, the right angle triangle at ∠F = 90°

According to the figure, base = 16cm, hypotenuse = 25cm

Apply Cosine rule;

Cos x = 16/25

x = Cos⁻¹ (16/25)

x = 50.21°

Therefore, the angle E is 50.21°

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Triangle: According to the question the measure of angle E is 50.21°

A triangle is a three-sided polygon which has three angles and three vertices. It is one of the basic shapes in geometry and is a fundamental shape in many mathematical and engineering fields. A triangle can be classified according to its angles or sides. Right triangles have one angle that is a right angle (90°) and two acute angles, obtuse triangles have one obtuse angle (greater than 90°) and two acute angles, and equilateral triangles have three equal angles and three equal sides.

Given, the right angle triangle at ∠F = 90°
According to the figure, base = 16cm, hypotenuse = 25cm
Apply Cosine rule;
Cos x = 16/25
x = Cos⁻¹ (16/25)
x = 50.21°
Therefore, the angle E is 50.21°

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The following points are matched:

Thus, the definitions are matched to their respective terms.

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The area of the triangle is 5x² + 11x -12 whose base is 5x - 4 and height is 2x + 6.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

The formula for calculating a triangle's area is:

Area = 1/2 x Base x Height

Plugging in the given values, we get:

Area = 1/2 x (5x - 4) x (2x + 6)

Simplifying, we get:

Area = 1/2 x (10x² + 22x - 24)

Distributing the 1/2, we get:

Area = 5x² + 11x - 12

Therefore, the area of the triangle is 5x² + 11x - 12.

The three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

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Answer:

To increase 80g by 25%, you need to find 25% of 80 and then add that to 80.

25% of 80 is (25/100) x 80 = 20

So, to increase 80g by 25%, you add 20g to 80g:

80g + 20g = 100g

Therefore, an increase of 25% on 80g is 100g.

Step-by-step explanation:

Higher z-scores imply more severe or unusual observations in the data set since they are indicative of values that are further from the mean en terms of standard deviations.

With the use of Z-scores, you are able to scale up data points from populations with various means and standard deviations. The comparison of observations for various sorts of variables, which would otherwise be challenging, is now possible thanks to the use of a common scale.

The relationship between a value and a group of values' mean is described statistically by the Z-score. Standard deviations from of the mean serve as the unit of measurement for Z-score. The score for a data point is equal to a mean score if the Z-score is 0.

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We have that, The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is 0.709

1. The shape, center, and spread of the M-W distribution are:Shape: NormalCenter: 4.8 inches (69.3 - 64.5)Spread: The standard deviation of the difference between two normally distributed variables is given by the formula:

[tex]\sigma (M-W) = \sqrt{(\sigma_1^2 + \sigma_2^2)} = \sqrt{(2.8^2 + 2.5^2)} \approx 3.64[/tex]

Let us define [tex]Z = (M - W - 2)/3.64[/tex]. So the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is:

[tex]P(M > W + 2) = P((M - W - 2)/\sigma(M-W) > (- 2)/\sigma (M-W)) = P(Z > -0.55) = 1 - P(Z \leq  - 0.55)[/tex]

Using a standard normal table or a calculator, we find that [tex]P(Z \leq  -0.55) \approx 0.291[/tex]. Therefore, the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is: [tex]P(M > W + 2) \approx  1 - 0.291 = 0.709[/tex].

The shape, center, and spread of the M-W distribution are:

Shape: Regular Center: 4.8 inches (69.3 - 64.5)

Dispersion: The standard deviation of the difference between two normally distributed variables is given by the formula:

[tex]\sigma (M-W) = \sqrt{(\sigma_1^2 + \sigma_2^2)} = \sqrt{(2.8^2 + 2.5^2)} \approx 3.64[/tex]

The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is: [tex]P(M > W + 2) \approx 0.709[/tex].

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If A = [tex]PDP^{-1}[/tex], Then [tex]A^{k}[/tex] = [tex](PDP^{-1}) ^{k}[/tex] = [tex]PDP^{-1}[/tex][tex]PDP^{-1}[/tex] .....[tex]PDP^{-1}[/tex] = [tex]PD^{k} P^{-1}[/tex]since [tex]P^{-1}[/tex] P = I, the identity matrix.

Further, the representation can be made as in the following attachment.

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"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter."

A histogram is a type of graph used in statistics to represent the distribution of a set of continuous data. It consists of a set of adjacent bars, where the area of each bar represents the frequency or relative frequency of observations within a specific interval or "bin" of the data.

The x-axis of a histogram shows the range of values for the variable being measured, divided into intervals or bins. The y-axis shows the frequency or relative frequency of observations within each interval or bin. Histograms are commonly used to show the shape, center, and spread of a distribution of data, as well as any potential outliers or gaps in the data.

In the given question, the histogram shows a skewed distribution, where the majority of book sales occurred in the lower intervals (1-3, 2-3, and 5-6) and the frequency decreases as the number of books sold increases. The maximum range of the data is 14 (from the interval 10-11 to the interval 2-3), which suggests a wide spread of book sales across different intervals.

"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter." comes the closest to describing the spread and distribution of the data shown in the histogram.

The other options do not accurately describe the shape or spread of the data shown in the histogram.

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Answer:

C: The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.

Step-by-step explanation:

Answer:

To find the area of the given figure, we can divide it into two separate shapes, a rectangle and a triangle, and then add their areas together.

First, we can find the area of the rectangle by multiplying its length and width. From the diagram, we can see that the length of the rectangle is 12 cm and the width is 5 cm.

Area of rectangle = length x width

Area of rectangle = 12 cm x 5 cm

Area of rectangle = 60 cm^2

Next, we can find the area of the triangle by using the formula for the area of a triangle, which is:

Area of triangle = 1/2 x base x height

From the diagram, we can see that the base of the triangle is 5 cm and the height is 8 cm.

Area of triangle = 1/2 x base x height

Area of triangle = 1/2 x 5 cm x 8 cm

Area of triangle = 20 cm^2

Finally, we can find the total area of the figure by adding the area of the rectangle and the area of the triangle:

Total area = area of rectangle + area of triangle

Total area = 60 cm^2 + 20 cm^2

Total area = 80 cm^2

Therefore, the area of the given figure is 80 square centimeters.

Step-by-step explanation:

Therefore, the probability of selecting a defective battery followed by another defective battery is about 12/145 or 8.28%.

The probability of selecting a defective battery on the first draw is 9/30, or 3/10, since there are 3 defective batteries out of 30 total.

Since one battery has already been drawn, there are now 29 batteries left in the box, and 8 defective batteries remaining. The probability of selecting another defective battery on the second draw, without replacement, is 8/29.

To find the probability of both events happening (selecting a defective battery followed by another defective battery), we multiply the probabilities of each event:

P(defective battery and then another defective battery) = P(defective battery on first draw) × P(defective battery on second draw)

P(defective battery and then another defective battery) = (3/10) × (8/29)

P(defective battery and then another defective battery) = 24/290 = 0.0828 or 8.28%

Therefore, the probability of selecting a defective battery followed by another defective battery out of 30 AAA batteries in a box where 9 are defective and two batteries are selected without replacement is 0.0828 or 8.28%.

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All of the measures of central tendency and spread for these data will need to be changed from the original computations in order to reflect the correct values.

In this case, the initial set of scores was 4, 5, 8, 9, 11, 13, 15, 18, 18, 18, and 20. The teacher initially computed the mean, median, standard deviation, and IQR and then discovered that one of the 18s should have been a 16.The mean is affected by any change in the data, so this measure will need to be changed to reflect the correct values. The new mean is 73.The median is also affected by any change in the data, so this measure must be recalculated to reflect the correct values.

The new median is 15.5.The standard deviation measures the spread of data from the mean, so this measure must also be changed to reflect the correct values. The new standard deviation is 1.4.Finally, the IQR measures the spread of the middle 50% of the data, so this measure must also be changed to reflect the correct values. The new IQR is 6. All of the measures of central tendency will need to be changed.

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The 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 is [15.8, 20.8].

The 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 can be calculated using a two-sample t-test.

First, calculate the sample difference in means. Subtract the mean for method 1 (50.3) from the mean for method 2 (68.6) to get 18.3.

Next, calculate the pooled standard deviation, which is the weighted average of the standard deviations for each sample:

Pooled standard deviation = [tex]√(((n1-1)×s12 + (n2-1)×s22)/ (n1+n2-2))[/tex]

n1=116, s12=15.62, n2=151, s22=17.21

Pooled standard deviation = [tex]√(((116-1)×15.62 + (151-1)×17.21)/ (116+151-2))[/tex]
Pooled standard deviation = [tex]√(1422.3788/265)[/tex]

Pooled standard deviation = 4.89

Finally, calculate the 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2:

99% Confidence Interval = Sample Difference in Means ± (Critical Value) × (Pooled Standard Deviation/√(n1+n2))

99% Confidence Interval =[tex]18.3 ± (2.58) × (4.89/√(116+151))[/tex]

99% Confidence Interval = 18.3 ± 2.50

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Answer:

What is the measure of angle F?

Step-by-step explanation:

You're welcome.

Answer:

A

Step-by-step explanation:

a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water.

a) Rotational speed at which the water just touches the bottom of the cylinder:

                  We will use the formula for centripetal force for a liquid with the volume of a cylinder to obtain the rotational speed at which the water just touches the bottom of the cylinder.

         The formula for centripetal force for a liquid with the volume of a cylinder is as follows:

                   F = (ρr²πh)ω²WhereF:

   Centripetal forceρ: Densityr: Radiush : Heightω: Rotational speed Substituting the given values,

we get: F = (1000 kg/m³ × (0.1m)² × π × 0.12m)ω²F

                = 377 Nω

                = √(F/m)ω

                = √(377 N/ 10 kg)ω

                = √37.7ω = 6.14 rad/sb)

      Pressure at points A and B:

                                We will use the formula for hydrostatic pressure for a liquid to calculate the pressure at points A and B. The formula for hydrostatic pressure for a liquid is as follows:

                         P = ρgh

  Where,

           P: Pressureρ: Densityg: Acceleration due to gravity: DepthSubstituting the given values for point A,

we get P = 1000 kg/m³ × 9.8 m/s² × 0.1 mP

                = 980 Pa

        Substituting the given values for point B,

we get P = 1000 kg/m³ × 9.8 m/s² × 0.22 mP

                = 2156 Pa

      The resulting pressure at point A is 980 Pa and the resulting pressure at point B is 2156 Pa.

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Para calcular la diferencia en los saldos de la cuenta de jubilación, necesitamos calcular los saldos en ambos casos y luego restarlos.

Para el primer caso, donde la persona comienza a hacer contribuciones anuales a los 40 años, tenemos:

Número de años hasta la jubilación: 60 - 40 = 20 años

Contribución anual: $6,000

Tasa de interés anual: 5%

Usando la fórmula para el valor futuro de una serie de pagos (anualidades) ordinarias, tenemos:

VF = Pmt x [(1 + r)^n - 1] / r

Donde VF es el valor futuro (saldo de la cuenta), Pmt es la contribución anual, r es la tasa de interés anual y n es el número de períodos (en este caso, el número de años hasta la jubilación).

Entonces, para este caso, el saldo de la cuenta sería:

VF = $6,000 x [(1 + 0.05)^20 - 1] / 0.05 = $198,395.72

Para el segundo caso, donde la persona comienza a hacer contribuciones anuales a los 30 años, tenemos:

Número de años hasta la jubilación: 60 - 30 = 30 años

Contribución anual: $6,000

Tasa de interés anual: 5%

Usando la misma fórmula que antes, el saldo de la cuenta sería:

VF = $6,000 x [(1 + 0.05)^30 - 1] / 0.05 = $398,633.09

Entonces, la diferencia en los saldos de la cuenta sería:

$398,633.09 - $198,395.72 = $200,237.37

Por lo tanto, la respuesta es la opción B) $200,237.36.

Answer: B- $200,237.36

Step-by-step explanation: Got it right on the test! And also the person above helped me out a lot!!

Answer:

Step-by-step explanation:

To find the average rate of change of the function f(x) from -5 to -2, we need to calculate:

(f(-2) - f(-5))/(-2 - (-5))

First, let's find f(-2) and f(-5):

f(-2) = (-2)^2 - 4 = 0

f(-5) = (-5)^2 - 4 = 21

Substituting these values in the above formula, we get:

(0 - 21)/(-2 + 5) = -21/3 = -7

Therefore, the average rate of change of f(x) from -5 to -2 is -7.

So the answer is (C) -7.

Answer:

567 is the correct number.

Step-by-step explanation:

[tex]5 + 6 + 7 = 18[/tex]

[tex]1 + 8 = 9[/tex]

So 567 is divisible by 9 since

[tex]567 \div 9 = 63[/tex]

The value of Pi to four decimal places is 3.1416.

There are 8 vertices on a cube.

The prime number closest to 100 is 97.

The sum of the internal angles of a hexagon is 720 degrees.

The number represented in binary as 100 is 4 in decimal notation.

Answer:

Answer:

(-2,9)

Step-by-step explanation:

when moving it 5 units left on the x axis it would be 5-7

So in turn you would be given (-2,9)

Because the y stays the same you would still have (?,9)

At the end of the 13-week mosquito season, we would expect to find around 558 mosquitoes in the trap.

It would be unreasonable to continue counting individual mosquitoes after about 13 weeks, since that is usually the end of the mosquito season. This is because, after the 13th week, the number of mosquitoes captured in the trap is likely to decrease significantly, making it pointless to count them individually. At the end of the 13-week mosquito season, the expected number of mosquitoes in the trap can be estimated using a simple exponential decay function.

Assuming the initial number of mosquitoes in the trap is N0 and the rate of decay is k, the number of mosquitoes after t weeks (Nt) can be calculated using the following equation: [tex]Nt = N0 * e-kt.[/tex]

For example, if the initial number of mosquitoes in the trap is 1000 and the rate of decay is 0.2, then the number of mosquitoes after 13 weeks can be estimated as follows:[tex]N13 = 1000 * e-0.2*13 = 558[/tex]

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Answer:

they bought 62 item from noodles and 51 items from hot chips

Answer:

Another order pair could be (30,10).

Every y value is "one-third of" every x value.

Answer: $3.64

Step-by-step explanation:

At the store, you buy four toys for $1.5, which means you pay $1.5 * 4, or $6.

Then, you calculate the sales tax, which is 6%, which means you multiply $6 by (100% + 6%), or $6*(1.06) which is $6.36.

Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.

Answer:

1

Step-by-step explanation:

LOL

Answer:

1+1-1=1

Step-by-step explanation:

1+1=2

2-1=1

your answer is 1

Answer:

A

Step-by-step explanation:

a) ✔️

This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.

b) ❌

There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.

c) ❌

This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.

d) ❌

This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.

The scale factor of the blueprint of the deck is 1.5 inches = 4 feet

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given that, Scott has a blueprint of the new deck he is building with dimensions 7.5 inches by 4.5 inches. The actual deck will have dimensions 20 feet by 12 feet.

We need to find the scale factor,

7.5 / 20 = 1.5 / 4

Therefore,

There are 1.5 inches in 4 feet

Hence, the scale factor of the blueprint of the deck is 1.5 inches = 4 feet

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Answer:

hi

Step-by-step explanation:

guvuvugjdhddiebeidgddb

The length of the other leg is 38 yards

Right Triangle is a triangle in which one of the interior angles measures 90 degrees. It is also a figure where one of the three angles measures 90° and the other two angles are acute that sums to 90°.

Using Pythagoras theorem to the Right Triangle,

C^2 = A^2 + B^2

Where C = Hypotenuse = 45 yards

A = One of the leg = 24 yards

To get the value of B,

C^2 = A^2 + B^2

B^2 = C^2 - A^2

B^2 = (45^2) - (24^2)

B^2 = 2025 - 576

B^2 = 1449

B = √1449

B = 38 yards

Therefore, the length of other leg is 38  yards

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Answer: -2.0

Step-by-step explanation: