An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 31 feet up. The ladder makes an angle of 78 degrees with the ground. Find the length of the ladder

Answer:

The value of A is 62

Step-by-step explanation:

since it is parallel to C

The length of AD is approximately 9.2 units.

A triangle is a geometric figure that is formed by three line segments joining three non-collinear points in a plane. It is a three-sided polygon and the most basic two-dimensional shape. A triangle has three interior angles and three vertices. The sum of the interior angles of a triangle is always 180 degrees, and each angle is measured in degrees. Triangles can be classified based on the length of their sides and the measures of their angles. There are several types of triangles such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are used in various fields such as engineering, architecture, mathematics, and physics, and they are an essential part of many geometric calculations and constructions.

To solve this problem, we can use the angle bisector theorem which states that if a line bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the adjacent sides.

Let AD = x. Then we can set up the following proportion:

AC/CD = AB/BD

Substituting the given values, we get:

24/x = 15/(18 - x)

Simplifying this equation, we get:

360 - 15x = 24x

39x = 360

x = 9.23 (rounded to the nearest tenth)

Therefore, the length of AD is approximately 9.2 units.

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After solving the given fraction 2 3/7+4 6/7, the resultant answer is 51/7.

Fractions represent any number of parts of a whole, or more generally equal parts.

In everyday English, fractions represent how many parts of a particular size there are. 8, 3/4.

Fractions represent a whole object or part of a collection.

A fraction consists of two parts. The number at the top of the line is called the counter. Indicates how many equal parts of the whole or collection are taken.

The number below the line is called the denominator.  

So, solve the fractions as follows:

= 2 3/7+4 6/7

= 14+3/7 + 28+6/7

= 17/7 + 34/7

= 17+34/7

= 51/7

Therefore, after solving the given fraction 2 3/7+4 6/7, the resultant answer is 51/7.

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Complete question:

Solve the fractions: 2 3/7+4 6/7

To find the total value of the investment after 8 years with monthly compounding, we can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Plugging in the given values, we get:

A = 5000(1 + 0.025/12)^(12*8)

A ≈ $6,105.74

Therefore, the total value of the investment after 8 years is approximately $6,105.74.

So, the correct option is (a) $6,105.74.

By using subtraction of polynomial, The polynomial 5x2y2 - 18xy2 - 10x2y is bigger by 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2 than -5x2 + 6x2y - 7xy.

To find the difference between 5x^2y^2 - 18xy^2 - 10x^2y and -5x^2 + 6x^2y - 7xy, we simply subtraction of polynomial the second expression from the first expression:

(5x^2y^2 - 18xy^2 - 10x^2y) - (-5x^2 + 6x^2y - 7xy)

= 5x^2y^2 - 18xy^2 - 10x^2y + 5x^2 - 6x^2y + 7xy (distributing the negative sign)

= 5x^2y^2 - 10x^2y + 5x^2 - 18xy^2 - 6x^2y + 7xy (rearranging terms)

= 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2 (combining like terms)

Therefore, the expression 5x^2y^2 - 18xy^2 - 10x^2y is bigger than -5x^2 + 6x^2y - 7xy by 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2.

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Answer:

3 Pounds

Step-by-step explanation:

If 1 slice of pie = 8 ounces that means that 6 slices would be 48 ounces because of 6 slices * 8 ounces. Now we have to take the 48 ounces and divide them by 16 because 16 ounces = 1 pound. And in doing so, 6 slices would = 3 Pounds.

Answer:

Each black pentagon in the soccer ball is surrounded by five white hexagons. Each white hexagon is, in turn, surrounded by three black pentagons and three other white hexagons. This pattern is repeated throughout the soccer ball.

To find the measures of the angles of the shapes that make the soccer ball, we need to first consider the angles of a regular pentagon and a regular hexagon.

A regular pentagon has five sides and five angles that are equal in measure. The formula for finding the measure of each angle in a regular pentagon is:

(angle measure) = (180(n-2))/n, where n is the number of sides.

In the case of a regular pentagon, n=5. Therefore, the measure of each angle in a regular pentagon is:

(angle measure) = (180(5-2))/5 = 108 degrees.

A regular hexagon has six sides and six angles that are equal in measure. The formula for finding the measure of each angle in a regular hexagon is:

(angle measure) = (180(n-2))/n, where n is the number of sides.

In the case of a regular hexagon, n=6. Therefore, the measure of each angle in a regular hexagon is:

(angle measure) = (180(6-2))/6 = 120 degrees.

Now, let's consider the angles of the shapes that make up the soccer ball.

Each black pentagon has five angles that are equal in measure. Therefore, each angle in a black pentagon measures:

(angle measure) = (180(5-2))/5 = 108 degrees.

Each white hexagon has six angles that are equal in measure. Therefore, each angle in a white hexagon measures:

(angle measure) = (180(6-2))/6 = 120 degrees.

Answer:

just do what the guy above me did

Step-by-step explanation:

i checked its correct

Paisley would have about $48147 in her account when Jayden's money has tripled using compounding.

What is compounding ?

In mathematics, compounding refers to the process of adding interest to an investment or loan, such that the interest is earned on both the principal amount and any previously accumulated interest.

First, let's find out how many years it will take for Jayden's money to triple in value. We can use the formula for compound interest:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where:

A = final amount

P = principal (starting amount)

r = interest rate (as a decimal)

n = number of times compounded per year

t = number of years

For Jayden, P = $16,000, r = 8.625% = 0.08625, n = 1 (compounded annually), and we want to find t when A = 3P = $48,000. Plugging in these values, we get:

[tex]\$48,000 = \$16,000(1 + 0.08625/1)^{(1t)[/tex]

[tex]3 = 1.08625^t[/tex]

[tex]ln(3) = t*ln(1.08625)[/tex]

[tex]t = ln(3) / ln(1.08625)[/tex]

t ≈ 13.2 years

So it will take about 13.2 years for Jayden's money to triple in value.

Next, let's find out how much Paisley will have in her account after the same amount of time, using the formula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

For Paisley, P = $16,000, r = 8.375% = 0.08375, and n = 12 (compounded monthly). Plugging in t = 13.2 years, we get:

[tex]A = \$16000*(1 + 0.08375/12)^{(12*13.2)[/tex]

A ≈ $48147

Therefore, Paisley would have about $48147 in her account when Jayden's money has tripled in value, to the nearest dollar.

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Answer:

a. 58/99

b. 53/90

c. 29/50

Step-by-step explanation:

The sampling variability can be reduced by increasing the sample size. Hence, it is essential to ensure that a large enough sample size is used to obtain reliable estimates of population parameters.

Parameter and statistic: Parameter is a value that describes the population, while statistic is a value that describes a sample.

Parameters are usually represented using Greek letters, while statistics are usually represented using Roman letters. In other words, a parameter is a population characteristic, whereas a statistic is a sample characteristic.

P and p hat: P represents the true proportion of a population with a particular attribute, while p hat represents the proportion of a sample with that attribute. P hat is an estimate of the true proportion p, which may differ from the actual proportion due to sampling error.

Sampling variability: Sampling variability is the variation in sample statistics that occurs from sample to sample. It is the result of the fact that different samples of the same size drawn from the same population will produce different estimates of the population parameter due to random sampling error. The sampling variability can be reduced by increasing the sample size. Hence, it is essential to ensure that a large enough sample size is used to obtain reliable estimates of population parameters.

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The statement that must be true is: Carter withdrew or spent $150 during the month.

Deposit is money held in a bank account or with another financial institution that requires a transfer from one party to another.

If Carter had a total of $50 in his bank account at the start of the month and made deposits totaling $150 during the month, then he had a total of $200 in his account during the month.

Since he still had a total of $50 in his account at the end of the month, it means that he must have spent or withdrawn $150 during the month, which is equal to the total amount of deposits he made.

Therefore, the statement that must be true is: Carter withdrew or spent $150 during the month.

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Answer:

Mode = 25

Median = 29

Mean = 30.3

Range = 36

Step-by-step explanation:

To find the mode, order the numbers lowest to highest and see which number appears the most often.

To find the median, calculate the mean by adding together the middle values and dividing them by two.

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.

the answer will be 3675.0 m (rounded to one decimal place)

What is rounded off?

Rounding off is a process of approximating a number to a certain degree of accuracy. When we round off a number, we usually need to specify the number of digits we want to keep or the position to which we want to round.

For example, if we want to round off 3.14159 to two decimal places, we would look at the third decimal place (which is 1) and see that it is less than 5, so we would keep the first two decimal places and round off the rest. Thus, rounding off 3.14159 to two decimal places would give us 3.14.

Rounding off is often used to simplify numbers or make them easier to work with, especially in situations where exact values are not necessary or practical.

To round 3675 m to the nearest tenth of a meter, we need to look at the hundredth digit, which is 7. Since 7 is greater than or equal to 5, we need to round up the last digit (tenth digit). Therefore, rounding 3675 m to the nearest tenth of a meter gives us:

Hence the answer will be 3675.0 m (rounded to one decimal place).

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Answer: present age of father=42

               present age of son=14

Step-by-step explanation:

let x=present age of father

56-x=present age of son

10 yrs ago:

x-10=age of father

56-x-10=46-x=age of son
age of father=8 times age of son

x-10=8(46-x)

x-10=368-8x

9x=378

x=42

56-x=14

present age of father=42

present age of son=14

Answer:

Step-by-step explanation

wow, never seen this before

The contrapositive of the given statement is: She will not hang out with her friends If she did not get off work early

Given that we have the following statement:

"If she gets off work early, she will hang out with her friends."

The contrapositive of a statement is defined as:

The above means that we have the contrapositive of the given statement to be:

She will not hang out with her friends If she did not get off work early,

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A violation of substantive due process (B)A new law fines book publishers for printing content that is considered unpatriotic. A drug dealer with several prior convictions is sent to prison without a trail.

The procedural rights guaranteed by the United States Constitution ensure that all citizens are treated equally before the law. For example, all citizens have the right to a lawyer, to a public and speedy trial, to have their case judged by a jury of their peers, etc.

In Scenario B, the drug dealer's rights are violated by law enforcement. Even if he has a criminal record, law enforcement has no right to immediately throw him in jail.

Due process is the application of all legal rules and principles relating to a case by the state to uphold all legal rights of individuals. Due process balances the power of the laws of the land and protects individuals against the laws. When the government harms a person without following the exact procedure of the law, it is a violation of due process and violates the rule of law.

It is the constitutional process in which the federal government before denying a citizen the right to life, liberty, or freedom, must give proper notice to the person, the opportunity of being heard, and the decision is taken without any discrimination. The act which violates the Procedural due process is giving a driver a traffic ticket without telling him, his right, i.e, can appeal in court against it.

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Yes, there difference between the RHS Congruence Rule and Hypotenuse-Leg Theorem.

The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side. In order to prove any two right triangles congruent, we apply the HL (Hypotenuse Leg) Theorem or the RHS (Right angle-Hypotenuse-Side) congruence rule.

The value of the angle a is 49 degrees and angle b is 139 degrees in the given triangle.

External angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle. For each vertex, there are two equivalent exterior angles.

Each vertex typically displays a single external angle. The exterior angles of a triangle are those that are formed outside of it. The exterior angle of a triangle is defined as the angle formed between one of a triangle's sides and its neighboring extended side. As a result, the exterior angle of a triangle is the angle formed by any extended side of a triangle and its neighboring side.

Given that the measure of angle y = 49 degrees.

We observe from the figure that angle a is vertically opposite angle of y thus,

angle y = angle a = 49 degrees.

Now, angle b is exterior angle and,

angle b = angle a + 90

angle b = 49 + 90

angle b = 139 degrees.

Hence, the value of the angle a is 49 degrees and angle b is 139 degrees in the given triangle.

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The probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI is approximately 0.304.

This problem can be solved using the binomial distribution, which models the probability of a certain number of successes in a fixed number of independent trials, each with the same probability of success.

Let X be the number of Indianapolis residents in a sample of 30 who wanted the Giants to beat the Patriots. Then X follows a binomial distribution with n = 30 and p = 0.97, since the probability of success (rooting for the Giants) is 0.97 for each resident.

We want to find the probability that fewer than 95% of the sample wanted the Giants to win. That is, we want to find P(X < 0.95*30) = P(X < 28.5), where X has the binomial distribution with parameters n = 30 and p = 0.97.

We can use a continuity correction and approximate this probability by the cumulative distribution function of a normal distribution with mean np and variance np(1-p). That is,

P(X < 28.5) ≈ P(Z < (28.5 - np) / sqrt(np(1-p)))

where Z is a standard normal random variable. Substituting the values of n and p, we get

P(X < 28.5) ≈ P(Z < (28.5 - 300.97) / sqrt(300.97*0.03))

≈ P(Z < -0.51)

Using a standard normal table or calculator, we find that P(Z < -0.51) ≈ 0.304. Therefore, the probability that fewer than 95% of the sample wanted the Giants to win is approximately 0.304.

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The given question is incomplete, the complete question is:

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city’s own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 97% of Indianapolis residents wanted the Giants to beat the Patriots.

What is the probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLIV?

Answer: 9

Step-by-step explanation:

Let's first represent the given information in the form of an equation. We know that the long sleeve t-shirts (x) cost $27 each, and the short sleeve t-shirts (y) cost $20 each. Elijah collected $543 in total. So we can write the equation as:

27x + 20y = 543

We also know that Elijah sold 15 short sleeve t-shirts (y), so we can plug that value into the equation:

27x + 20(15) = 543

Now, we solve for x:

27x + 300 = 543

Subtract 300 from both sides of the equation:

27x = 243

Now, divide by 27:

x = 9

So Elijah sold 9 long sleeve t-shirts.

Number of long sleeve t shirts that Elijah sell is 9 long sleeve t shirts.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given that,

The long sleeve t-shirts cost $27 each and the short sleeve t-shirts cost $20 each.

He collected a total of $543.

So, we get an equation,

27x + 20y = 543

Also, given that, Elijah sold 15 short sleeve t-shirts.

Substitute y = 15.

27x + (20 × 15) = 543

27x + 300 = 543

27x = 543 - 300

27x = 243

x = 9

Hence Elijah sold 9 long sleeve t shirts.

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The volume of the sphere is option (d) 904.32 cm³

Volume is a measure of the amount of three-dimensional space occupied by a substance, object, or region of space

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

Substituting r = 6 cm and π ≈ 3.14 into the formula, we get:

V = (4/3) × 3.14 × 6³

Find the cube of the number

V = (4/3) × 3.14 × 216

Multiply the numbers

V ≈ 904.32

Rounding the answer to the nearest hundredth, we get approximately 904.32 cm³.

Therefore, the correct option is (d) 904.32 cm³.

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The given question is incomplete, the complete question is:

What is the approximate volume of the sphere when the radius is 6 cm?

Use 3.14 to approximate pi and round the answer to the nearest hundredth if necessary.

a) 48 cm³

b) 150.72 cm³

c) 288.00 cm³

d) 904.32 cm³

Answer:

(5 + 9) + 3 = 17

Step-by-step explanation:

The Associative Property of Addition states that no matter how you group the numbers to be added, the results will still be the same. In this case:

Original:

5 + (9 + 3) = 17

5 + 12 = 17

17 = 17 (True)

Associative Property of Addition:

(5 + 9) + 3 = 17

(14) + 3 = 17

17 = 17 (True)

As you can see, the grouping does not matter as the outcome is still the same.

~

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The coordinates of B is (2, -4).

The coordinates of C is (-2, 4).

The coordinates of D is (5, 8).

The coordinates of E is (-2, -4).

In Mathematics and Geometry, a reflection over the x-axis is represented by this transformation rule (x, y) → (x, -y). Therefore, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

For a reflection over the x-axis, the new coordinates of A is given by:

(x, y)            →      (x, -y)

A (2, 4)      →      (2, -(4)) = B (2, -4)

For a reflection over the y-axis, the new coordinates of A is given by:

(x, y)            →      (-x, y)

A (2, 4)      →      (-(2), 4) = C (-2, 4)

By applying a translation, the new coordinates of A is given by:

(x, y)            →      (x + 3, y + 4)

A (2, 4)      →      (2 + 3, 4 + 4) = D (5, 8)

By applying a rotation 180° clockwise, the new coordinates of A is given by:

(x, y)            →      (-x, -y)

A (2, 4)      →      (-(2), -(4)) = E (-2, -4)

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Using the interquartile range (IQR) method, the value 2 is considered an outlier in the given data.

To determine if there is an outlier in the given data, we need to calculate the lower and upper bounds using the interquartile range (IQR) method.

First, we need to calculate the first quartile (Q1), second quartile (Q2 or median), and third quartile (Q3) of the data.

Arranging the data in ascending order

2, 9, 13, 17, 18, 20, 23, 24, 33, 34, 43, 45, 53, 53

Q1 = 17

Q2 = 24

Q3 = 43

Next, we can calculate the IQR by subtracting Q1 from Q3

IQR = Q3 - Q1 = 43 - 17 = 26

Now we can calculate the lower and upper bounds

Lower bound = Q1 - 1.5 × IQR = 17 - 1.5 × 26 = -8

Upper bound = Q3 + 1.5 × IQR = 43 + 1.5 × 26 = 79

Any values outside the lower and upper bounds are considered outliers.

In this case, we have a value of 2 that is outside the lower bound of -8. Therefore, 2 is considered an outlier in the given data.

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Answer:

85.6 square units.

Step-by-step explanation:

The surface area of a rectangular prism is the sum of the areas of all six faces. To find the surface area of the given rectangular prism, we can use the formula:

Surface Area = 2lw + 2lh + 2wh

where "l" is the length, "w" is the width, and "h" is the height.

Substituting the given values, we get:

Surface Area = 2(6.8)(1.6) + 2(6.8)(3.8) + 2(1.6)(3.8)

= 21.76 + 51.68 + 12.16

= 85.6

the surface area of the rectangular prism is 85.6 square units.

An equation that best models the situation include the following: A. y = 34x² - 334x + 1075.

In order to determine an equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the number of months would be plotted on the x-axis of the scatter plot while the units would be plotted on the y-axis of the scatter plot.

Based on the scatter plot (see attachment) which models the relationship between the number of months and units, an equation for the line of best fit is given by:

y = 34x² - 334x + 1075

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Answer:

A.

Step-by-step explanation:

the solution to a relation (like an equation, but also inequalities and so on) is the set of values that make the whole thing true (or consistent).

every other value is not a solution.

Answer:

-1

Step-by-step explanation: