An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 29 feet up. The ladder makes an angle of 71 degrees with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

Answer:

50.27 ft

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:

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:

Answer:

Step-by-step explanation:

To find the price that maximizes the country's revenue, we need to consider the relationship between price, sales, and revenue.

Let's start by calculating the current revenue for the country:

Revenue = Price × Sales

Revenue = $80/barrel × 7 million barrels/day

Revenue = $560 million/day

Now let's consider the effect of a price increase on sales. According to the problem, a $1 increase in price will result in a decrease of 100,000 barrels/day in sales. This means that the new sales rate at a price of $81/barrel will be:

New sales = 7 million barrels/day - 100,000 barrels/day per $1 increase × (81 - 80)

New sales = 6.9 million barrels/day

The new revenue at a price of $81/barrel will be:

New revenue = $81/barrel × 6.9 million barrels/day

New revenue = $559.9 million/day

We can repeat this process for a range of prices to see how revenue changes:

Price Sales (million barrels/day) Revenue (million $/day)

 80                            7.0                             560.0

 81                            6.9                             559.9

 82                            6.8                             544.0

 83                            6.7                             534.1

 84                            6.6                             528.0

 85                            6.5                             520.0

From this table, we can see that the price that maximizes revenue is $84/barrel. At this price, the country will sell 6.6 million barrels/day, and generate revenue of $528 million/day.

Therefore, the price that will maximize the country's revenue is $84/barrel, and it will sell 6.6 million barrels/day at that price.

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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Therefore , the solution of the given problem of angles comes out to be  the engraved angle ACB is 16 degrees in size.

Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.

Here,

A circle's inscribed angle has a measure that is half that of the interrupted arc. As a result, the inscribed angle ACB intersecting arc AB with a measure of 32 degrees will have a measure of:

=> Angle ACB = 32 / (1/2)

=> ACB = 16 degree angle

As a result, the engraved angle ACB is 16 degrees in size.

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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:12

Step-by-step explanation:

i did it :)

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:

1.986 x 10 to the tenth power

Step-by-step explanation:

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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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:

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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Answer:

x=-2

Step-by-step explanation:

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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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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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

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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The area of Desert 1 is 28,000,000 square miles and the area of Desert 2 is 4,000,000 square miles.

Let's assume that the area of Desert 2 is x square miles.

According to the problem statement, the area of Desert 1 is seven times that, or 7x square miles.

We are also given that the sum of their areas is 32,000,000 square miles:

x + 7x = 32,000,000

Simplifying the left side of the equation:

8x = 32,000,000

Dividing both sides by 8:

x = 4,000,000

Now that we know the area of Desert 2 is x = 4,000,000 square miles, we can find the area of Desert 1 by multiplying by 7:

7x = 7(4,000,000) = 28,000,000

Therefore, the area of Desert 1 is 28,000,000 square miles and the area of Desert 2 is 4,000,000 square miles.

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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:

m∠WUV=135°

Hope this helps.

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:

I'm stuck too like is so aggravating

As a result, the cylinder's capacity is roughly 11,088 cubic metres.

The diameter of a circular is the distance measured through its middle. The radius of a circle is the distance to the middle to any spot on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d .

First, we need to find the radius of the cylinder. We know that the diameter is 28 meters, so the radius is half of that, which is 14 meters.

Using the formula for the volume of a cylinder, V = πr²h, we can now substitute the given values:

V = (22/7) x 14² x 4.5

Simplifying this expression:

V = (22/7) x 196 x 4.5

V = 11,088 cubic meters

Therefore, the volume of the cylinder is approximately 11,088 cubic meters.

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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:

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:

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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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

Mr. Oppong's chargeable income for the year of assessment 2022 is GH¢109,100.

Taxes must generally be paid on all types of income, even those derived from a business or profession. Employment. Dividends.

We must take into account Mr. Kwesi Oppong's salary, benefits, and any deductions when determining his chargeable income for the assessment year of 2022.

Let's start by figuring out his gross revenue for 2022. The annual wage scale for Mr. Oppong is GH85,000 X GH5,000 - GH130,000, which denotes a salary range of GH85,000 to GH130,000. To make things easier, we might suppose that his pay is the midpoint of the range, or GH107,500.

His annual acting allowance is GHC 5,000, so the following would be his total income from salary and allowances:

GH107,500 plus GH5,000 plus (GH300 x 12) plus (GH250 x 12) equals GH114,500.

Next, we must look at his advantages. Mr. Oppong is given a vehicle with a designated driver and free fuel, as well as a furnished place to stay. They are taxable benefits, but in order to estimate their worth, we need more details.

Mr. Oppong also holds a life insurance policy with a GHC 70,000 capital and GHC 8,000 yearly premium. This is not a necessary component of his chargeable income.

Let's now explore the inferences made by Mr. Oppong. 5.5% of his income is put into Social Security by him. Since the Social Security rate is set at GH450 every month, Mr. Oppong can only contribute a maximum of GH5,400 (GH450 x 12) in a given year.

As a result, the following would be Mr. Oppong's chargeable income for the year of assessment 2022:

GH114,500 minus GH5,400 equals GH109,100.

Thus, GH 109,100 will be Mr. Oppong's chargeable income for the assessment year 2022.

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