Question 19
By age 65 the number of Americans who experience hearing loss sufficient to affect communication is:
a. 1 in 2
b. 1 in 3
c. 1 in 4
d. 1 in 5

Box plot, as the median can be easily ascertained from the substantial amount of data. The answer is option (a).

The middle value in a given set of figures or statistics is referred to as the median. The average value for a given collection of integers can be calculated using one of three main methods in mathematics. The mean, the median, and the mode are the three. Central tendency measurements refer to these three factors. The average value of the supplied data is calculated using mean. The midpoint value of the given data is defined by a median. The input data's repeating value is defined by the mode.

A box plot is a very visual way to show a brief summary of one or more sets of data. It is particularly useful for quickly comparing and summing multiple sets of findings from distinct trials. A box plot provides a visual picture of the distribution of results as well as clues regarding data symmetry at a look.

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Answer:

There are 775 - 91 + 1 = 685 integers.

In the given range, the smallest multiple of 14 is 98, and the largest multiple of 14 is 770. ((770-98)/14) + 1 = 49 multiples of 14.

So the probability of choosing a multiple of 14 from this range is 49/685.

The femur length for someone with a height of 187 cm is; 55 cm

The formula for the equation of a line formed by 2 coordinates is;

(y2 - y1)/(x2 - x1) = (y - y1)/(x - x1)

Using the coordinates (30, 127) and (35, 139), we have;

(139 - 127)/(35 - 30) = (y - 127)/(x - 30)

12/5 = (y - 127)/(x - 30)

12(x - 30) = 5(y - 127)

12x - 360 = 5y - 635

5y = 12x + 275

Thus, when the height is y = 187 cm, we have;

5(187) = 12x + 275

935 = 12x + 275

12x = 935 - 275

12x = 660

x = 660/12

x = 55 cm

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The square root of the number 23 is 5 after using the division method the answer is 25.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The number is 23 which is a real number and positive number.

As we know we can find the square root of a positive numbers only, the square root of a negative number cannot exist

The square root of the number 23 = [tex]\sqrt{23}[/tex]

The sign √ is a radical sign.

After using the division method:

[tex]\sqrt{23} = 4.7958[/tex]

After reducing the number up to two decimal places:

[tex]= 4.79[/tex]

Rounding the above number to the whole:

[tex]= 4.79 \thickapprox 5[/tex]

[tex]5\times5 = 25[/tex]

Thus, the square root of the number 23 is 5 after using the division method the answer is 25.

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The solutions to the equation [tex]tan^2(x) = (sec^2(x) - 1)[/tex]are:

x = 2nπ or x = (2n+1) π/2, where n is an integer.

The power reducing formula for the tangent function is:

[tex]tan^2(x) = (sec^2(x) - 1)[/tex]

Therefore, we can rewrite the equation as:

[tex](sec^2(x) - 1) = 0[/tex]

Simplifying further, we get:

[tex]sec^2(x) = 1[/tex]

Taking the square root of both sides, we get:

sec(x) = ±1

Recall that secant is the reciprocal of cosine, so we can write:

cos(x) = ±1

The cosine function can only take values between -1 and 1, so the only possible solutions are:

cos(x) = 1, which implies x = 2nπ (where n is an integer)

or

cos(x) = -1, which implies x = (2n+1)π/2 (where n is an integer).

The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.

It is most commonly used for reducing the power of the sine and cosine functions.

The power reducing formula for cosine is:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

The power reducing formula for sine is:

[tex]sin^2(x) = (1 - cos(2x))/2[/tex]

These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]

By solving for either[tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine[tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex] we can arrive at the power reducing formulas.

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Answer:

12

Step-by-step explanation:

to divide by a fraction use the acronym K.C.F or keep change flip to re-arrange the problem.

[tex]\frac{3}{\frac{1}{4} }[/tex] can be re-written as

[tex]\frac{3}{1} *\frac{4}{1}[/tex]

or 3*4 which equals 12

The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.

However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:

Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6

So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

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The sequences that appear to be converging are:

2/7, 11/16, 26/37, 47/65, 74/101, 107/144, 146/197...

8/7, 64/49, 512/343, 4096/2401, 37768/16807, 262144/117649...

32.45, 31.80, 31.655, 31.654, 31.653, 31.652,...

converging refers to a sequence or series of numbers approaching a limit as more terms are added. It indicates that the values of the sequence or series are getting closer and closer to a specific value or point without ever reaching it.

a sequence is a list of numbers or objects arranged in a specific order. Each element in the sequence is called a term, and the position of the term in the sequence is called its index.

According to the given information:

The first two sequences are examples of converging sequences. In the first sequence, the numerators and denominators increase by a fixed amount for each term, but the ratio of the terms approaches a limit as the sequence progresses. Similarly, in the second sequence, each term is the previous term multiplied by a fixed factor, and the terms approach a limit as the sequence progresses.

The fifth sequence is also an example of a converging sequence, where the terms are decreasing and getting closer to a specific value as the sequence progresses.

The third sequence is not converging since the terms are increasing without bound, and the fourth sequence is oscillating between two values and not getting closer to any specific value.

The sixth sequence starts with a fixed value and increases by a fixed percentage for each term, so the terms are also increasing without bound and not converging to a specific value.

In summary, converging sequences have terms that approach a specific value as the sequence progresses, while non-converging sequences either increase or oscillate without getting closer to any specific value.

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Answer:  B.

200,237.36

Step-by-step explanation: just got it right on the quiz

The area of figures are calculated a follows:

1. 78.5 m²    2. 66.5 m²    3. 35 m²    4. 153.86 m²    5. 70 m²

1. The area of the circle = πr²

= 3.14 * 5²

= 78.5 m²

2. The figure is a trapezoid, therefore:

Area of the trapezoid = 1/2 * (a + b) * h

= 7(5 + 14)/2

= 66.5 m²

3. Area of triangle = 1/2 * base * height = 1/2 * 14 * 5 = 35 m²

4. The area of the circle = πr²

= 3.14 * 7²

= 153.86 m²

5. Area of parallelogram = base * height = 14 * 5 = 70 m²

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Answer:

Subtract 12 from both sides of the equation

Step-by-step explanation:

Solve for x:

12+x=15

-12       -12

x = 3

Brainlist please.

Answer:

D) Subtract 12 from both sides of the equation.

To solve for x in the equation 12 + x = 15, we need to isolate the variable x on one side of the equation. We can do this by subtracting 12 from both sides of the equation, which gives:

12 + x - 12 = 15 - 12

x = 3

Therefore, the solution for x is 3.

Your answer is option b)

The time at which a star rises shifts approximately 4 minutes earlier each day, due to Earth's orbit around the Sun. Since there are roughly 30 days in a month, we can calculate the change in the rise time of Aldebaran over the course of a month.

Step 1: Calculate the time change over one month
30 days * 4 minutes per day = 120 minutes

Step 2: Convert minutes to hours
120 minutes ÷ 60 minutes per hour = 2 hours

Step 3: Subtract the time change from the current rise time
2:00 am - 2 hours = 12:00 am (midnight)

Therefore, you can expect Aldebaran to rise next month at midnight. The correct answer is b) midnight.

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Answer:

the two-digit number is 65.

Step-by-step explanation:

Let's assume that the tens and units digits of the two-digit number are x and y, respectively.

According to the given condition,

10x + y < 6(x + y) - 1 (less than 6 times the sum of its digits by 1)

Simplifying the above equation, we get:

4x - 5y < -1 (dividing both sides by 2)

Also, it is given that the difference between the digits is 1, so we can write:

x - y = 1 (difference between the digits is 1)

Now, we need to solve these two equations to find the values of x and y.

Multiplying the second equation by 4, we get:

4x - 4y = 4

Adding this equation to the first equation, we get:

4x - 5y + 4x - 4y = 3

Simplifying the above equation, we get:

8x - 9y = 3

Now, we can solve these two equations simultaneously to find the values of x and y.

Multiplying the second equation by 8, we get:

8x - 8y = 8

Subtracting this equation from the previous equation, we get:

y = 5

Substituting this value of y in the equation x - y = 1, we get:

x - 5 = 1

x = 6

Therefore, the two-digit number is 65.

The solution is, 5.4 × 10⁻³ is the number in scientific notation.

Given:

The signal from a certain satellite takes approximately 0.0054 seconds to reach earth.

we will write the number in a scientific notation

The scientific notation is the number that is between 1 and 9 multiplied by 10 raised to an exponent

So, the given number will be:

0.0054

=54/10000

=54/10 * 1/1000

=5.4 × 10⁻³

Hence, The solution is, 5.4 × 10⁻³ is the number in scientific notation.

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Answer:

The best example of a defined benefits plan is: "a set amount an employee will receive at retirement".

In a defined benefits plan, the employer promises to pay employees a specific, predetermined amount of money upon retirement. This amount is typically based on factors such as the employee's salary and years of service. The employer is responsible for contributing to and managing the retirement fund, and the employee receives a guaranteed amount of money upon retirement, regardless of how the fund performs.

The other options listed are not examples of defined benefits plans. The wages and benefits an employee receives at a job are part of their compensation package and may include retirement benefits, but they do not guarantee a specific amount of money at retirement. The amount of pay an employee receives each hour is their hourly wage and is not related to retirement benefits. The money an employer puts into a retirement fund for each employee may be part of a defined benefits plan, but it is not a complete plan in and of itself.

Line JN = line AE = 22ft

Line DC = Line LM = 17ft

Line KL = line BC = 12 ft

< D = <M = 158°

< K = <B = 135°

Two shapes are said to be congruent when they both have the same length size and same angle measurements.

From the given shapes, polygon ABCDE = JKLMN.

Therefore the corresponding angles and lengths is as follows:

Line JN = line AE = 22ft

Line DC = Line LM = 17ft

Line KL = line BC = 12 ft

< D = <M = 158°

< K = <B = 135°

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The Central Limit Theorem (CLT) is an important theorem in statistics because it serves as the foundation for various statistical techniques and analyses.

The CLT states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's original distribution, provided that the population has finite mean and variance.
Normality:

The CLT establishes the concept of normality, which is a critical assumption in numerous statistical tests such as the t-test, z-test, and ANOVA. By knowing that the sample means are normally distributed, we can apply these tests to make inferences about population parameters.
Simplification:

Due to the CLT, we can simplify complex statistical problems by using normal distributions instead of dealing with the original population distribution.

Calculations more manageable and allows us to utilize the standard normal distribution table.
Confidence intervals:

The CLT enables us to construct confidence intervals for population parameters such as the mean.

Essential in estimating unknown population parameters based on sample data and understanding the associated uncertainty.
Margin of error:

The theorem helps in determining the margin of error for estimates, allowing us to quantify the accuracy of our estimates and make better decisions based on data.
Large sample sizes:

The CLT is particularly relevant when dealing with large sample sizes, as the distribution of sample means becomes more normal, and we can apply various statistical techniques with greater confidence.
The Central Limit Theorem is important in statistics because it enables us to assume normality, simplify problems, construct confidence intervals, determine the margin of error, and apply various statistical techniques with greater confidence, especially when dealing with large sample sizes.

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Answer: sin x= 20/24 x = 34

Step-by-step explanation:

The value of k is 20.

An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables and may involve arithmetic operations such as addition, subtraction, multiplication, division, or exponents. The goal of solving an equation is to determine the value of the variable that makes the equation true. Equations are commonly used in algebra and other mathematical fields to model real-world situations and solve problems. They can be written in various forms, including standard form, slope-intercept form, point-slope form, and general form, among others.

Since the sum of two angles on a straight line is always 180 degrees, we can set up an equation:

First angle + Second angle = 180

112 + 3k + 8 = 180

Simplifying the equation, we get:

3k + 120 = 180

Subtracting 120 from both sides, we get:

3k = 60

Dividing both sides by 3, we get:

k = 20

Therefore, the value of k is 20.

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The coordinates of point P are (6.4, 18, -12).

A coordinate of a point refers to a set of values that specify the position of that point in a particular reference system or coordinate system. Coordinates are used to uniquely identify the location of a point in a geometric space, such as a plane or a three-dimensional space.

According to the given information:

To find the coordinates of point P, we can use the concept of vector comparison. We are given that the ratio of vector AB to vector AP is 6:4.

Let's denote the coordinates of point P as (x, y, z).

Given:

AB vector = (10, 2, -6)

B coordinates = (4, 6, -8)

AB:AP = 6:4

We can calculate the coordinates of point P as follows:

Since AB:AP = 6:4, we can express this as a vector equation:

(10, 2, -6) / (x - 4, y - 6, z + 8) = 6/4

Now we can cross-multiply to get:

10 / (x - 4) = 6/4

2 / (y - 6) = 6/4

-6 / (z + 8) = 6/4

Simplifying further, we have:

10(x - 4) = 6 * 4

2(y - 6) = 6 * 4

-6(z + 8) = 6 * 4

Expanding the equations, we get:

10x - 40 = 24

2y - 12 = 24

-6z - 48 = 24

Solving these equations, we get:

10x = 64

2y = 36

-6z = 72

Dividing by the respective coefficients, we get:

x = 6.4

y = 18

z = -12

So, the coordinates of point P are (6.4, 18, -12).

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The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.

The total number of combinations of selecting 5 cards from a deck of 52 cards is 52C5 = 5251504948/120 = 2598960.

The probability of exactly 4 of the 5 cards being Aces is 48*100/2598960 = 0.0018%.

The probability of all 5 of the cards being Spades is 1287*100/2598960 = 0.0495%.

The probability of exactly 4 of the 5 cards being face cards is 49540100/2598960 = 0.7618%.

The probability of exactly 2 Aces and exactly 2 Kings being selected is 1584*100/2598960 = 0.0609%.

The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.

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The probability that a lightbulb will last between 1,950 and 2,050 hours is 0.84, or 84%.

To solve this problem, we need to find the probability that the lifespan of a lightbulb will fall between 1,950 and 2,050 hours.

First, we need to standardize the distribution using the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For x = 1,950 hours:

z = (1,950 - 1,975) / 25 = -1

For x = 2,050 hours:

z = (2,050 - 1,975) / 25 = 3

Now, we need to find the area under the standard normal distribution curve between z = -1 and z = 3. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = 3 is 0.9987. Therefore, the area between z = -1 and z = 3 is:

0.9987 - 0.1587 = 0.84

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Answer:

P(heads) = 1/2

There are 4 prime numbers less than 10: 2, 3, 5, 7.

P(prime number) = 4/10 = 2/5

1/2 × 2/5 = 1/5

The domain of the data set {(-10,-6),(-4,-10),(3,8),(9,-2)} are  {-10, -4, 3, 9} and the range are  {-6, -10, 8, -2}.

The domain of a function is the set of all possible inputs for the function. In other words, the domain of a function is the independent value of a function. The domain are usually the x values.

The range of a function refers to all the possible values y could be. Therefore, the range is the dependent values. The range are usually the y values.

Hence,

The domain of the data set are {-10, -4, 3, 9}

The range of the data sets are {-6, -10, 8, -2}

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Angle m1 has a value of 113 degrees.

Angles that are vertical (opposite in a vertical direction) Vertical angles, also known as vertically opposite angles, are the opposing angles formed when two lines converge. Angles that are vertically opposite one another are always equal to one another.

Alternate interior angles are made when a transversal joins two coplanar lines. They can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two coplanar lines at two separate points.

According to the statement, it is creating a pair of linear angles whose sum is 180.

m1 + 67° = 180°

m1 = 113°

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The side length of the second cube is 3.8 in.

Cube is a solid shape that has all its sides equal.

To calculate the side length of the second cube, we use the formula below

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the length is 3.8 in

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Answer: Oy = 15.5x

Step-by-step explanation: Gas mileage refers to the quantity of miles driven per unit volume of gasoline, typically expressed as "miles per gallon." In the context of the present inquiry, the vehicle in question exhibited a capacity to traverse a distance of 310 miles subsequent to the utilization of 20 gallons of gasoline. Thus, it is possible to calculate the gas mileage through the division of the quantity of gas consumed by the distance elapsed, resulting in:

The fuel efficiency of a vehicle, represented by the metric of gas mileage, is typically calculated by the ratio of distance traveled in miles to the amount of fuel consumed in gallons. In the present case, the gas mileage is equivalent to the quotient of 310 miles by 20 gallons, resulting in an efficiency rating of 15.5 miles per gallon.