ABCD is a square. P and D are points on the y-axis. A is a point on the x-axis. PAB is a straight line. The equation of the line that passes through the points A and D is y=-2x+6. Find the length of PD.

The measures of the two missing sides are:

Here we can see a right triangle where we know the measures of the interior angles and one of the sides. And we want to find the lengths of the other two sides.

We can use trigonometric relations like.

sin(a) = (opposite cathetus)/hypotenuse.

Here we know that b is the hypotenuse, and the known side is the opposite cathetus of the 30° angle, then we can write:

sin(30°) = 5√2/b

Solving this for b, we will get:

b =  5√2*(1/sin(30°))

b =  5√2*(2) = 10√2

And the value of c is given by:

sin(60°) = c/10√2

10√2*sin(60°) = c

10√2*(√3/2) = c

5*√(2*3) = c

5√6 = c

These are the two missing lengths.

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A) The prοbability that less than 5% οf Americans in a sample οf 100 will be diagnοsed with lung cancer is very small, οnly 0.02%.

B) As there is still variability in the number οf cases that may arise due tο chance.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

(A) We can use the binοmial distributiοn tο mοdel the number οf Americans in a sample οf 100 whο are diagnοsed with lung cancer. Let X be the number οf Americans in the sample whο are diagnοsed with lung cancer. Then X ~ Bin(100, 0.0625).

We want tο find P(X < 5). We can use the nοrmal apprοximatiοn tο the binοmial distributiοn, since n is large and p is nοt tοο clοse tο 0 οr 1. Using the cοntinuity cοrrectiοn, we have:

P(X < 5) = P(X < 5.5)

[tex]= P((X - np) \sqrt{(np(1-p))} < (5.5 - np)\sqrt{(np(1-p))})[/tex]

[tex]= P(Z < (5.5 - 6.25100)\sqrt{(6.25100*(1-0.0625)))[/tex]

= P(Z < -3.52)

= 0.0002 (frοm standard nοrmal table)

Therefοre, the prοbability that less than 5% οf Americans in a sample οf 100 will be diagnοsed with lung cancer is very small, οnly 0.02%.

(B) If 20 οr mοre Americans whο smοke cigarettes are diagnοsed with lung cancer in a sample οf 100, this is quite rare based οn the expected rate οf 6.25% in the general pοpulatiοn. This suggests that smοking is a significant risk factοr fοr develοping lung cancer, as the οbserved rate is much higher than the expected rate.

Hοwever, we cannοt cοnclude that all smοkers will develοp lung cancer, as there is still variability in the number οf cases that may arise due tο chance.

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The length of support 1 is 0.63m

According to the definition of the right angled triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of the angles is a right angle .The side of a right triangle is the hypotenuse, which is the longest side and sits in opposition to the triangle's right angle, base and altitude.

given length of support1 are

a= 1.1 m

b= .9 m

Using pythagoreas theorem,

Length of support1= √a²-b²

=√(1.1)²-(0.9)²

=√1.21-.81

=0.63

Hence, The length of support 1 in the figure is 0.63m.

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Answer:12

Step-by-step explanation:

i did it :)

We need a piece of wood that is approximately 8.1 inches long to replace AD. So, the answer is option A.

In geometry, a triangle is a three-sided polygon consisting of three line segments that connect three non-collinear points. These three points are called the vertices of the triangle, and the line segments connecting them are called sides. The sum of the angles of a triangle is always 180 degrees.

Triangles can be classified based on their sides and angles. A triangle with all three sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. A triangle with no sides of equal length is called a scalene triangle.

Triangles can also be classified based on their angles. A triangle with all three angles less than 90 degrees is called an acute triangle, while a triangle with one angle greater than 90 degrees is called an obtuse triangle. Finally, a triangle with one angle equal to 90 degrees is called a right triangle.

First, we can use trigonometry to find the length of side AC. Since angle BCD is 30 degrees and BC = 14, we have:

sin(30) = AC/14

AC = 14*sin(30)

AC = 7 inches

Next, we can use the fact that triangle ACD is a 15-75-90 triangle to find the length of AD. Since angle CAD is 75 degrees, we have:

tan(75) = AD/AC

AD = ACtan(75)

AD = 7tan(75)

Using a calculator, we get:

AD ≈ 8.09 inches

Therefore, we need a piece of wood that is approximately 8.1 inches long to replace AD. So, the answer is option A.

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Answer:

5.9

Step-by-step explanation:

segment BD was 8.1 so segment AD cant be 8.1

Answer:

Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:

Step-by-step explanation:

To determine which of these methods apply, you'll need to analyze the given information about angles and side lengths in triangles AMNO and AQRS.

To prove that triangles AMNO and AQRS are similar (~), we need to show that their corresponding angles are congruent, and their corresponding sides are proportional. Here are some methods to do that:

1. Angle-Angle (AA) similarity: If two pairs of corresponding angles in triangles AMNO and AQRS are congruent, then the triangles are similar.

2. Side-Angle-Side (SAS) similarity: If two pairs of corresponding sides in triangles AMNO and AQRS are proportional, and the included angles between these sides are congruent, then the triangles are similar.

3. Side-Side-Side (SSS) similarity: If all three pairs of corresponding sides in triangles AMNO and AQRS are proportional, then the triangles are similar.

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Answer:

a/c = t/v

b/d = u/w

Step-by-step explanation:

Use corresponding sides to complete the fractions.

a/c = t/v

b/d = u/w

Answer:

m∠WUV=135°

Hope this helps.

The cost of the service will be £38.50.

What is a probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

Emily is booked for a cut and blow-dry at Antonio's hairdresser. The cost for a cut and blow-dry is £38.50 according to the price list provided. Therefore, the cost of the service will be £38.50.

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The expression for the missing side length, c, is c = √(a² + b²).

To determine an expression for the missing side length, follow these steps:

Identify the given side lengths in the problem. You didn't provide the specific side lengths or the type of shape

(triangle, rectangle, etc.), but I will assume it's a right triangle with given side lengths a and b, and the missing side

length is c (the hypotenuse).

Apply the Pythagorean theorem for a right triangle, which states that the sum of the squares of the two shorter sides (a

and b) is equal to the square of the hypotenuse (c):

a² + b² = c².

Solve for the missing side length (c) by taking the square root of both sides of the equation:

c = √(a² + b²).

So, the expression for the missing side length, c, is c = √(a² + b²).

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Answer:

13.) y=(x-4)^(2)+3

Step-by-step explanation:

Answer:

50.27 ft

Step-by-step explanation:

Answer:

To find the area of the shaded region, we need to find the area of the sector formed by the shaded angle and subtract the area of the triangle formed by the radius and the two radii at the endpoints of the shaded angle.

The area of the sector can be found using the formula:

Area of sector = (θ/360) x πr²

where θ is the central angle in degrees and r is the radius of the circle.

Here, θ = 130 degrees and r = 21 cm.

Area of sector = (130/360) x π x 21²

= 2471.39 cm²

Next, we need to find the area of the triangle. We can find the height of the triangle using trigonometry.

sin(130 degrees/2) = h/21

h = 21 x sin(65 degrees)

h ≈ 18.12 cm

The base of the triangle is the length of the arc that forms the shaded angle. We can find this length using the formula:

Length of arc = (θ/360) x 2πr

Length of arc = (130/360) x 2π x 21

= 38.81 cm

The area of the triangle is:

Area of triangle = 0.5 x base x height

= 0.5 x 38.81 x 18.12

= 351.70 cm²

Finally, we can find the area of the shaded region by subtracting the area of the triangle from the area of the sector:

Area of shaded region = Area of sector - Area of triangle

= 2471.39 - 351.70

= 2119.69 cm²

Therefore, the area of the shaded region is approximately 2119.69 cm².

Answer:

x=-2

Step-by-step explanation:

Pull a green cube 50 times; Pull a blue cube 70 times. The possible options are B and E.

Probability refers to the likelihood or chance of an event occurring, expressed as a number between 0 and 1.

A probability of 0 indicates that an event is impossible, while a probability of 1 indicates that an event is certain to occur. For example, the probability of rolling a 7 on a fair six-sided die is 0, while the probability of rolling a 1, 2, 3, 4, 5, or 6 is 1/6.

Probabilities can also be expressed as percentages, with a probability of 0.5 (or 50%) indicating an even chance of an event occurring.

A) Pull more than 2 times as many green cubes as blue cubes:

Since there are only 2 blue cubes in the bag and 5 green cubes, it is highly unlikely that you would pull more than 2 times as many green cubes as blue cubes in 100 draws. Therefore, this option is unlikely.

B) Pull a green cube 50 times:

There are 5 green cubes in the bag, so it is possible to pull a green cube 50 times in 100 draws. Therefore, this option is possible.

C) Pull a blue cube 20 times:

There are only 2 blue cubes in the bag, so it is unlikely that you would pull a blue cube 20 times in 100 draws. Therefore, this option is unlikely.

D) Pull more red cubes than green cubes:

There are 3 red cubes and 5 green cubes in the bag, so it is possible to pull more red cubes than green cubes in 100 draws. Therefore, this option is possible.

E) Pull a blue cube 70 times:

Since there are only 2 blue cubes in the bag and you are drawing with replacement, it is highly unlikely that you would pull a blue cube 70 times in 100 draws. Therefore, this option is unlikely.

Therefore, options B and D are possible.

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Three parallelograms are created with name A′B′C′D′, and A″B″C″D″.

Twο number lines cοmbine tο generate the twο-dimensiοnal surface knοwn as the cοοrdinate plane. The x-axis is a single hοrizοntal number line. The y-axis is the name οf the vertical number line that is the οther number line.

1) As the first step, let's plot the points A(1, 1), B(2, 3), C(4, 3), and D(3, 1) on a coordinate plane.

2) Next, let's translate polygon ABCD 2 units down by subtracting 2 from the y-coordinates of each point, and create parallelogram A′B′C′D′:

A'(1, -1), B'(2, 1), C'(4, 1), D'(3, -1)

3) Now, let's reflect parallelogram A′B′C′D′ over the x-axis by multiplying each y-coordinate by -1 to create parallelogram A″B″C″D″:

A″(1, 1), B″(2, -1), C″(4, -1), D″(3, 1)

4) Finally, let's translate polygon ABCD 2 units to the left by subtracting 2 from the x-coordinates of each point, to create parallelogram A′′B′′C′′D′′:

A′′(-1, 1), B′′(0, -1), C′′(2, -1), D′′(1, 1)

5) The three parallelograms are shown in the below graph.

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The correct answer is E (-1,-3). Reflection across the x-axis is a transformation that flips the object across an imaginary line that runs through the center of the x-axis.

Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.

In this case, the x-axis is the line y = 0. The figure ABCD is reflected across this line, resulting in point A being reflected to E.

When a figure is reflected, the x-coordinates remain the same, while the y-coordinates change sign. This means that the x-coordinate of point A (-1) remains the same, but the y-coordinate (3) changes to its opposite (-3). Therefore, the resulting coordinates of point A are (-1,-3).

Reflection across the x-axis is an example of a transformation. Transformations involve changing the position, size or orientation of a figure, but not its shape. This means that the figure ABCD is still the same shape after being reflected, but its position has changed. After being reflected, the figure is now located on the opposite side of the x-axis.

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Answer:

The percent increase and percent decrease values are different because they are calculated based on different starting values. When the price increases from 329 to 349, the percent increase is calculated as (349-329)/329 * 100% = 6.1%. However, when the price decreases from 349 to 329, the percent decrease is calculated as (349-329)/349 * 100% = 5.7%. The difference in starting values results in different percentage changes.

Step-by-step explanation:

Therefore, knowing the slant height is important in calculating the lateral area of the pyramid, which is one component of the total surface area.

by the question.

Option 2 is the correct response. Knowing the slant height is helpful because it represents the height of the rectangle that makes up each lateral face of the pyramid. The lateral faces are made up of triangles and rectangles, and the slant height is used to find the height of these rectangles.

Knowing the slant height helps because it represents the height of the rectangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face. The formula for the lateral area of a pyramid involves the slant height, the perimeter of the base, and the apothem (the distance from the center of the base to the midpoint of a side). Once you know the lateral area, you can add it to the area of the base to find the total surface area of the pyramid.

The slant height of a pyramid is the height of each triangular lateral face, which is an essential component in calculating the lateral surface area of a pyramid. Knowing the slant height is used in the formula for finding the lateral area of a pyramid, which is the sum of the areas of all the triangular lateral faces. Additionally, the base area of the pyramid is also needed to find the total surface area of the pyramid. So, knowing the slant h

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Answer: To find the proportions of each type of juice in the 6 quarts of fruit punch, we need to use ratios:

For every 2.5 quarts of apple juice, we need (6/8) x 2.5 = 1.875 quarts of apple juice.

For every 1.5 quarts of cranberry juice, we need (6/8) x 1.5 = 1.125 quarts of cranberry juice.

For every 3 quarts of grape juice, we need (6/8) x 3 = 2.25 quarts of grape juice.

So the proportions of apple, cranberry, and grape juice in the 6 quarts of fruit punch are approximately:

1.875 quarts of apple juice

1.125 quarts of cranberry juice

2.25 quarts of grape juice

Note that these proportions are approximate because we rounded the amounts of each juice to two decimal places.

Step-by-step explanation:

The ship that can last forever for the given parallelogram is REHIFSDPI.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighbouring sides, but it must have opposing sides that are parallel for it to be a parallelogram. If the opposing sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Hence, a quadrilateral in which both sets of opposite sides are parallel and equal is referred to as a parallelogram.

The letter corresponding to each answer is:

1. congruent - R

2. parallelogram - E

3. pair - N

4. Bisect - H

5. sometimes - I

6. Sum of angles of parallelogram is 360, also opposite angles are equal, thus,

72 + 72 + 2x = 360

x = 108 - F

7. Sum of angles of parallelogram is 360, also opposite angles are equal, thus,

89 + 89 + x + x = 360

178 + 2x = 360

x= 91 - S

8. Diagonals of parallelogram bisect each other CO = 16. - D

9. Opposite sides of parallelogram are congruent thus,

4x + 2 = 5x - 3

x = 5 - P

10. Opposite sides are equal,

2x + 1 = x + 8

x = 7 - I

Hence, the ship that can last forever for the given parallelogram is REHIFSDPI.

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Answer:

[tex]\frac{2}{3} ^{7}[/tex]

Step-by-step explanation:

1) Count how many  [tex]\frac{2}{3}[/tex] there are.

[tex]\frac{2}{3} ^{7}[/tex]

Answer:

The cone takes up one-third of the volume of the cylinder. (the cylinder is 3x bigger than the cone)

Step-by-step explanation:

Answer:

B. is right.

Step-by-step explanation:

Volume of cone = volume of cylinder/3

Therefore the volume of the cylinder is 3 x that of cone

In theory, there is a 3/4 chance that you won't choose a red bead.

Typically, the probability is defined as the ratio of favourable events to all other outcomes in the sample space. The formula for probability of an occurrence is P(E) = (Number of favourable outcomes) (Sample space).

Out of a total of 52 beads, 13 are red, hence the likelihood of choosing a red bead is:

P(red) = 13/52 = 1/4

The complement of choosing a red bead is the likelihood of not choosing one, which is:

P(not red) equals P - 1. (red)

When we replace the value of P(red), we obtain:

P(not red) = 1-quarter

If we simplify, we get:

3/4 for P(not red).

So, there is a 3/4 chance that you won't choose a red bead in theory.

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Answer:

Step-by-step explanation:

The number of different collections of 10 books you can take from a set of 15 books can be calculated using the formula for combinations:

n choose k = n! / (k! * (n-k)!)

Where n is the total number of books (15), and k is the number of books you want to choose (10).

Plugging in the values, we get:

15 choose 10 = 15! / (10! * (15-10)!)

= 3003

Therefore, you can take 3003 different collections of 10 books from the set of 15 books.

Answer:

4.05 miles

Step-by-step explanation:

Draw a diagram to help you visualize the problem

Remember the formula to find area

Area = base x height

Substitute the values into the equation and solve for the missing variable

0.65 mi^2 = (base)(0.4mi)

The other side of the pasture is 1.625 miles long

This situation also emphasises how important it is to be conscious of one's surroundings and potential hazards when performing tasks like tossing a flying disc.

When you threw the flying disc into the air, it encountered an obstacle in the form of a tree branch, which caused it to change its trajectory. As a result, the disc's momentum slowed down, and it eventually came to a rest on a nearby roof.

This phenomenon is an example of how external forces can alter an object's motion and ultimately affect its final position.

Additionally, this scenario highlights the importance of being aware of one's surroundings and potential obstacles when engaging in activities such as throwing a flying disc.

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It is to score 35 points in 20 minutes greater than 49 goals in 35.

More than and less than signs are used to indicate whether one number is greater than or less than another. If the initial number surpasses the second number, the larger than symbol (>) is used. The sign () is used to indicate that the first number is smaller than the second number.

This sign is used to denote that one value is greater than the other. For

instance, it is accurate to say that 4 is more than 2. Hence, it may be

expressed simply 4 > 2. Let's now examine the greater than sign from both

its left and right sides.

35 / 20 = 1.75

49 / 35 = 1.4

Therefore, 35 points in 20 minutes is greater than 49 points in 35 minutes.

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Complete question -

35 points in 20 minutes or 49 points in 35 minutes? Find which is greater.

The eighth grade class has a more consistent time spent on math homework. This can be seen in the histogram, which shows that the eighth grade class has a peak at 20 minutes.

Consistent refers to something that remains unchanged or is regular and dependable over time. It is a dependable and steady quality or state. Consistency is important in many areas of life, from professional and personal relationships to commitments and expectations. Consistent behavior is sometimes a sign of reliability, trustworthiness, and dependability.

Consistent actions are important for maintaining relationships and for achieving goals. Consistency helps to create stability, reliability, and predictability. Without consistency, it would be difficult to know what to expect from people and situations.

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Mr. Sullivan's class typically spends more time on math homework, as the mean of their sample is slightly higher than that of Mrs. Farrington's class.

Spend is an action that involves exchanging money for goods, services, or other items of value. When someone spends money, they take money out of their account or wallet and use it to purchase something.

Mrs. Farrington's class has a more consistent time spent on math homework, as the range of the sample is smaller than that of Mr. Sullivan's class.
For Mr. Sullivan's class:
The mean of the sample is 11.6, so the mean of the population is expected to be 11.6 as well. The standard deviation of the sample is 3.41. Therefore, the expected standard deviation of the population is 3.41.
Using the 68-95-99.7 rule, we can calculate the following:
68% of the population is expected to spend between 8.79 and 14.41 minutes on math homework.
95% of the population is expected to spend between 5.38 and 17.82 minutes on math homework.
99.7% of the population is expected to spend between 1.97 and 21.23
minutes on math homework.
Therefore, we can expect approximately 82 (68% of 120) students in Mr. Sullivan's class to spend between 9 and 12 minutes on math homework.

For Mrs. Farrington's class:
The mean of the sample is 11 and the standard deviation is 2.87. Therefore, we can expect the mean and standard deviation of the population to be 11 and 2.87, respectively.
Using the 68-95-99.7 rule, we can calculate the following:
68% of the population is expected to spend between 8.26 and 13.74 minutes on math homework.
95% of the population is expected to spend between 5.39 and 16.61 minutes on math homework.
99.7% of the population is expected to spend between 1.72 and 19.48 minutes on math homework.
Therefore, we can expect approximately 68 (68% of 100) students in Mrs. Farrington's class to spend between 9 and 12 minutes on math homework.

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