Suppose the heights (in inches) of adult males in a country are normally distributed with a mean of 68 and a standard deviation of 2. Find the percent of men who are no more than 64 inches tall. What is the % of the men in the country are no more than 64 inches tall.​

Answer:

Step-by-step explanation:

x = 24

A matrix such that T(x) =Ax is [tex]Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

The matrix is [tex]x = \left[\begin{array}{ccc}x_1\\x_2\end{array}\right][/tex], [tex]v_1= \left[\begin{array}{ccc}-3\\5\end{array}\right][/tex] and [tex]v_2 = \left[\begin{array}{ccc}7\\-2\end{array}\right][/tex].

The linear transformation is R² → R².

T is defined by the vector equation -

T(x) = x1v1 + x2v2

Substitute the values in the equation -

T(x) = [tex]x_1 \left[\begin{array}{ccc}-3\\5\end{array}\right] + x_2 \left[\begin{array}{ccc}7\\-2\end{array}\right][/tex]

A vector equation like this can be rewritten as a matrix equation Ax where the columns of A are just v1 and v2 -

[tex]Ax = \left[\begin{array}{ccc}v_1&v_2\end{array}\right][/tex]

Substitute the values in the matrix -

[tex]Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right][/tex]

Therefore, the matrix obtained is [tex]Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right][/tex].

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The unit rate for the speed of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is faster.

A unit rate means a rate for one of something.

Given that, Two runners are training for their next competitions. Each runner is able to run a certain distance in proportion to the time. The table displays the distance Runner A can run in relation to the time. Meanwhile, the graph on the right displays the distance Runner B can run in relation to time. We need to find the unit rates for both runners,

Runner A =

Unit rate = distance / time

= 54 / 4.5

= 12 ft / sec

Therefore, unit rate for the speed of Runner A is 12 ft / sec

Runner B =

According to graph, the Runner B can run 75 ft in seconds

Unit rate = distance / time

= 75 / 5

= 15 ft / sec

Therefore, unit rate for the speed of Runner B is 15 ft / sec

Since, the speed of Runner B is greater than Runner A therefore, Rubber B is faster.

Hence, the unit rate for the speed of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is faster.

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Answer:

2.15 * 10⁶

Step-by-step explanation:

1,000,000= 1 * 10⁶

2,150,000= 2.15 * 10⁶

Answer:

The required equation of the line passing through (4,2) and parallel to y = 1/2x - 3 is y = 1/2x.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope of the given line,
y = 1/2x - 3
m = 1/2

The slope of the parallel lines is always equal

Now, the Equation of the parallel line passing through the point (4, 2) is given as
y - y₁ = m (x - x₁)
y -2 = 1/2(x - 4)
y = 1/2x

Thus, the required equation of the line passing through (4,2) and parallel to y = 1/2x - 3 is y = 1/2x.

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Answer:

y=-7/2x-9/2

Step-by-step explanation:

Answer:

15.11

Step-by-step explanation:

first you have to change 182% to a decimal (1.82) then multiply it by the number of hours (8.3) then you get your answer 15.106. last round it to the nearest tenth (15.106) and you get 15.11

Answer: The answer should be 0.207%

Step-by-step explanation:

540.54/261040.5

54054/26104050

429/207175

0.00207 X 100/100

0.207/100

0.207%

Answer: If the service rate is 6 customers per hour, the mean service time can be calculated as 1/6 = 0.1 hours or 6 minutes. The negative exponential distribution is commonly used to model the service time distribution in queuing theory. The cumulative distribution function (CDF) of the negative exponential distribution is given by:

F(x) = 1 - e^(-λx)

where λ = 1/μ, where μ is the mean service time (in this case, μ = 0.1 hours or 6 minutes).

So, the probability that the service time will be less than or equal to 6 minutes can be calculated as:

F(6) = 1 - e^(-0.1 * 6) = 1 - e^(-0.6) ≈ 0.5488

So, the answer is approximately 0.549, which is closest to option (b).

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Volume of a cylinder = area of end X height =  pi r^2 * h

  r = 4 in    h = 10 in

volume = pi (4)^2 * 10 =    160 pi in^3      or    ~  503 in^3

Answer:

160π in.³

Step-by-step explanation:

Get the circle area then multiply for the height. In the end, devide the result by 3,14 (π).

π* . r²                                  50,24 . 10*
π* . 4²                                 502,40 in.³ (cylinder volume)
50,24 (circle area)            

obs: 502,4 leads you to a non-comma π result, considering π as 3,14. If you round, the correct way will be transforming into 502. But 502/3,14 is equal to 159,87..., infinite non-repetitive numbers.

Result in π = 160π* in.³

r - circle radius

10* - height

π* - 3,14 (Used that way)

No, the product of 7/8 multiplied by 2/9 will not be greater than either of the two factors.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Here,
To find the product, we can multiply the two fractions,

(7/8) × (2/9) = (7 × 2) / (8 × 9)
                = 14/72 = 1/6

Since 1/6 is less than both 7/8 and 2/9, the product is not greater than either of the two factors.

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According to the Centers for Disease Control

and Prevention, kids should get C) at least 60 minutes of exercise each day.

Exercise is a movement activity that has an important role for health. With exercise, one's body becomes healthier and stronger. Not only maintaining physical health, exercise also affects spiritual health.

The aim of exercise is to improve one's health. In addition to improving physical fitness, exercise can also improve and improve the performance of the human brain so that it can work more optimally. Therefore, exercise is considered to be able to increase one's self-confidence.

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C) 2.5 kHz, C) 15, A) 101010, D) CA35, A) (A), A) XOR, B) Exclusive OR, A)True, A) (A + B)C, B) Variable complements can be eliminated by using Karnaugh maps.

K-maps, commonly referred to as Karnaugh maps, are visual tools for simplifying digital circuits and Boolean algebraic formulas. In order to make Boolean functions simpler for use in digital electronics, Maurice Karnaugh first presented them in 1953. K-maps are used to consolidate terms with similar values and get rid of extraneous terms in the truth table of a Boolean function. With a grid of cells corresponding to all conceivable combinations of binary input values, the map is a two-dimensional representation of a truth table. Depending on the truth value of the relevant word in the truth table, the cells in the grid are either filled with 0s or 1s.

The fundamental benefit of employing Karnaugh maps is that they give the Boolean expression a visual representation, making it simpler to spot patterns and understand the expression. They can also be used to check the accuracy of the final expression and find flaws in digital circuits. Karnaugh maps can be used to quickly and effectively simplify complicated digital circuits, which cuts down on the time and effort needed for circuit design.

Karnaugh maps are perfect for designing and optimizing digital circuits because they may be used to simplify big or complex Boolean statements. For more effective and efficient results, they can be combined with other digital design tools, such as logic gates.

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The equation that represents each change is given as follows:

a) y = 2^x-  6.

b) y = 2^(x + 1).

c) y = -2^x.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

Additionally, when a function is reflected over the x-axis, we have that the function's definition is multiplied by -1.

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Answer:

Step-by-step explanation:

14

The ratio of Kenny's weight to Melvin's weight is 6/7.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Kenny’s weight is 6/7 times Melvin's weight.

Let x be the weight of Melvin.

Then, Kenny's weight = 6/7 x, as per the information given.

Ratio of Kenny’s weight to Melvin's weight = (6/7 x) / x = 6/7

Hence the required ratio of Kenny's weight to Melvin's weight is 6/7.

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Therefore , the solution of the given problem of standard deviation comes out to be the typical distance between the observed and predicted foot lengths is 1.61 centimeters.

Variance is a measure of difference used in statistics. The average variance between the data and indeed the mean is calculated using the mathematical formula of that figure. By comparing each data point's value to the mean, it incorporates all data points into its computations, unlike some other number measures of variability.

Here,

D. The typical distance between the observed and predicted foot lengths is 1.61 centimeters.

The standard deviation of the residuals measures the typical distance between the observed values and the predicted values (based on the regression line).

In this case, the regression analysis is for foot length and arm span, and the standard deviation of the residuals tells us about the typical distance between the observed foot lengths and the predicted foot lengths based on the regression line.

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The grouped frequency distribution for the data is shown below.

A grouped frequency distribution is a way of summarizing and organizing raw data into a more manageable and meaningful form. The data is divided into intervals or "classes", and the number of data points that fall into each class is counted and recorded as the frequency of that class. This allows for easier interpretation and comparison of the data, as well as identifying patterns or trends. The grouped frequency distribution is commonly displayed in a table or a histogram.

Given that,

79, 85, 71, 83, 78, 67, 70, 87, 81, 86, 74, 67, 68, 76, 66, 72, 76, 80

Now, arranging the given data in ascending order,

66, 67, 67, 68, 70, 71, 72, 74, 76, 76, 78, 79, 80, 81, 83, 85, 86, 87

The grouped frequency distribution for the data:

Test Scores                   Frequency

65.5 - 71.5                        6

71.5 - 77.5                         4

77.5 - 83.5                        5

83.5 - 89.5                        3

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The perimeter of the square is 40m

The formula for calculating the area of a square is given as;

A =  a²

Given that;

Substitute the value

100 = a²

Find the square root of both sides

a = 10m

The formula for the perimeter of a square is expressed as;

Perimeter = 4a

Substitute the value into the formula;

Perimeter = 4(10)

expand the bracket

Perimeter = 40 m

Hence, the value is  40 m

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Using Hamilton's method of apportioning, 21 salespeople can be assigned in the table in the following order:

2, 5, 6, 8.

The approach that now bears his name was first proposed by Alexander Hamilton. Congress endorsed his approach in 1791, but President Washington rejected it. Later, in 1852, it became widely used until 1911. He starts by calculating the precise number of items that each group needs.

Since in the interested question it's about salesperson assigned, we’ll use the language of shift and hours, so we can determine how many salespersons each shift should get.

Now total no. of customers given = 125 + 305 + 439 + 515

                                                        = 1375

Now total no of salesperson available = 21.

So, the divisor = 1375/21

                        = 65.47

Now using Hamilton's method when we divide the average customers per shift by the divisor, we get the no. of salesperson assigned.

So, the salesperson assigned are:

Morning = 125/65.47

              = 2

Midday = 305/65.47

             = 5

Afternoon = 430/65.47

                 = 6

Evening = 515/65.47

               = 8 (Decimals rounded according to Hamilton's principle)

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The number of children who ordered hamburgers from class A = ( 5/6 )A , where A is the total number of students in the class A

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of students in class A = A

Let the number of students in class B = B

Let the number of students in class C = C

Now , the equation will be

The number of students who ordered hamburgers is = ( 5/6 )A

The number of students who ordered hot dogs is = ( 2/4 )B

The number of students who ordered hot dogs is = ( 1/2 )B

The number of students who ordered chicken wings is = ( 1/2 )C

Hence , the number of students who ordered hamburgers , hot dogs and chicken wings are ( 5/6 )A , ( 1/2 )B and ( 1/2 )C respectively

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The HCF of the numbers is 1078

From the question, we have the following parameters that can be used in our computation:

183260 and 2900898

Next, we factorize each number

This is represented as

183260 = 1078 * 170

2900898 = 1078 * 2691

The common factor above is

Comon factor = 1078

Hence. the HCF is 1078

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The probability that the thread length of a randomly selected bolt is farther than 2. 5 standard deviations from its mean value is 0.62%.

If the thread length of bolts is normally distributed, then we can use the concept of probability to determine the probability that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value.

This can be calculated using the area under the normal curve.

Specifically, the area to the right of 2.5 standard deviations is 0.0062, meaning that there is only a 0.0062 probability (or 0.62%) that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value

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Answer:

21-68+5$567798876545

a) The measure of side PN of the triangle is PN = 18 cm

b) The measure of ∠CDA = 45°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the first triangle be represented as ΔOMP

Let the second triangle be represented as ΔOPN

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Now , the measure of OP = √ ( OM² - MP² )

Substituting the values in the equation , we get

The measure of OP = √ ( 25 )² - ( 7 )²

The measure of OP = √ ( 625 - 49 ) = √ ( 576 )

The measure of OP = 24 cm

And , the triangle OPN is a right triangle ,

So , the measure of PN = √ ( ON )² - ( OP )²

Substituting the values in the equation , we get

The measure of PN = √ ( 30 )² - ( 24 )²

The measure of PN = √ ( 900 - 576 ) = √ ( 324 )

The measure of PN = 18 cm

Therefore , the measure of PN of the triangle is 18 cm

b)

The two parallel lines are l₁ and l₂ where line t is the transversal

The measure of ∠FAE = 55°

The measure of ∠GAF = 80°

Now , the measures of angles in a straight line is 180°

So , the measure of ∠GAB = 180° - ( 55° + 80° )

The measure of ∠GAB = 45°

And , measure of ∠GAB = measure of ∠DAE ( alternate angles are equal )

So , the measure of ∠DAE = 45°

And , the measure of ∠DAE = the measure of ∠CDA ( alternate interior angles of a transversal line are equal )

Therefore , the measure of ∠CDA = 45°

Hence , the side PN of triangle is 18 cm and angle ∠CDA = 45°

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Answer:

2

Step-by-step explanation:

4/2 = 2 therefore 2 women will be in two committies.