Suppose heights of 20-year-old men are approximately normally distributed with a mean of 71 in. and a population standard deviation of 5 in. a random sample of twenty 20-year-old men is selected and measured. find the probability that the sample mean x lies between 68 and 74 inches.

Answer:

the answer is V≈19.68cm³

V=a3

a

Edge

cm

Step-by-step explanation:

The row of 9 bolts laid end to end would be 7 7/8 inches long.

To find the total length of 9 bolts laid end to end, we multiply the length of one bolt by the number of bolts.

Given:

- Length of one bolt: [tex]\( \frac{7}{8} \)[/tex] inch

- Number of bolts: 9

Total length:

[tex]\[ \text{Total length} = \text{Length of one bolt} \times \text{Number of bolts} \][/tex]

[tex]\[ \text{Total length} = \frac{7}{8} \times 9 \][/tex]

Now, multiply:

[tex]\[ \text{Total length} = \frac{7 \times 9}{8} \][/tex]

[tex]\[ \text{Total length} = \frac{63}{8} \][/tex]

To express this in mixed number form:

[tex]\[ \frac{63}{8} = 7 \frac{7}{8} \][/tex]

Therefore, the row of 9 bolts laid end to end would be [tex]\( 7 \frac{7}{8} \)[/tex] inches long.

The equation to represent the relationship between the time Sabar walks, denoted by [tex]x[/tex] , and the number of calories he burns, denoted by [tex]y[/tex], can be written as [tex]\( y = mx \),[/tex] where [tex]\( m \)[/tex] is the rate at which calories are burned per unit time.

To establish a relationship between the time Sabar spends walking and the number of calories he burns, we can use a simple linear equation. In this context, the independent variable [tex]x[/tex] represents the time spent walking, and the dependent variable [tex]\( y \)[/tex] represents the number of calories burned.

The rate at which calories are burned is typically constant for a given activity if the intensity remains consistent. This rate is represented by the coefficient [tex]\( m \)[/tex] in the equation [tex]\( y = mx \)[/tex]. The value of [tex]\( m \)[/tex] would be determined by how many calories Sabar burns per minute, hour, or any other time unit chosen for [tex]x.[/tex]

For example, if Sabar burns 5 calories per minute, then [tex]\( m = 5 \)[/tex]calories/minute, and the equation would be [tex]\( y = 5x \)[/tex]. If we measure time in hours and Sabar burns 300 calories per hour, then [tex]\( m = 300 \)[/tex]calories/hour, and the equation would be [tex]\( y = 300x \).[/tex]

This linear equation assumes that the relationship between time and calories burned is directly proportional, meaning that the number of calories burned increases at a constant rate as the time spent walking increases. This is a common assumption for steady-state aerobic activities like walking at a consistent pace.

Sum of two monomials is not necessarily always a monomial.

For example:

Suppose we have two monomials as 2x and 5x.

Adding 2x+5x , we get 7x.

So if two monomials are both like terms then their sum will be a monomial.

Suppose we have two monomials as 3y and 4x

Now these are both monomials but unlike, so we cannot add them together and sum would be 3y + 4x , which is a binomial.

So if we have like terms then the sum is monomial but if we have unlike terms sum is binomial.

Product of monomials:

suppose we have 2x and 5y,

Product : 2x*5y = 10xy ( which is a monomial)

So yes product of two monomials is always a monomial.

The sum of two monomials is not always a monomial and the product of two monomials is always a monomial.

Further explanation:

Explanation:

Consider the two monomials as [tex]5y{\text{ and }}7y.[/tex]

The sum of the two polynomials can be obtained as follows,

[tex]\begin{aligned}{\text{Sum}} &= 5y + 7y\\&= 12y\\\end{aligned}[/tex]

The sum of the two monomials is monomial.

Consider the two monomials as [tex]5y{\text{ and }}7x.[/tex]

The sum of the two polynomials can be obtained as follows,

[tex]{\text{Sum}} = 5y + 7x[/tex]

The sum of the two monomials is not monomial.

Consider the two monomials as [tex]4y{\text{ and }}6x.[/tex]

The product of the two polynomials can be obtained as follows,

[tex]\begin{aligned}{\text{Product}} &= 4y \times 6x\\&= 24xy\\\end{aligned}[/tex]

The product of the two monomials is monomial.

The sum of two monomials is not always a monomial and the product of two monomials is always a monomial.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: sum, two monomial, monomials, always monomial, product, always, monomial, factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.

Area of a triangle = [tex]\frac{1}{2} base*height[/tex]

In a right angle triangle the two legs are the base and height of the triangle.

One angle of the triangle is 23 degree  and one adjacent leg is 27.6 cm.Let the other leg opposite to 23 degree angle by x.Sine of an angle is ratio of opposite and hypotenuse. Hypotenuse is given as 30 cm.

[tex]Sin 23=\frac{x}{30}[/tex]

x= 30 sin23.

x=11.72cm.

The legs of the triangle are 11.72 cm and 27.6 cm.

Area of triangle =[tex]\frac{1}{2} x11.72 x27.6 =161.7cm^{2}.[/tex]

Given is the damage index equation, [tex] y=\frac{-2}{3} x+14 [/tex]

where y represents damage index, and x represents ambient temperature.

It is similar to slope-intercept form of linear equation given by y = mx + b.

Where m is said to be the slope of line and b is the y-intercept of the line. When x = 0, y = b.

Similarly, if plug x = 0 in the damage index equation, [tex] y=\frac{-2}{3} (0)+14=14 [/tex]

So, If ambient temperature, x = 0. Then damage index, y = 14.

Hence, option D is correct i.e. " If the ambient temperature is 0 then the damage index would be 14".

Answer:

The answer is D because 14 is the y-intercepts, which means that the x-value is 0. So the correct meaning is If the ambient temperature is 0 then the damage index would be 14. .

Step-by-step explanation:

The solution for the system of equations is incorrect because line [1] should have a y-intercept at (0, 2) and not at (0, 1).

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is the system of equations of straight lines -

y = -1/3x + 2

y = 2x - 5

plotted on the graph.

The error Emma made is that while plotting Equation [1] -

y = -1/3x + 2

The line should have passed from point (0, 2) on y - axis and not from (0, 1)

Therefore, the solution for the system of equations is incorrect because

Line [1] should have a y-intercept at (0, 2) and not at (0, 1).

To solve more questions on straight lines, visit the link below-

brainly.com/question/29030795

#SPJ6

[Refer to the image attached for full question]

Final answer:

To find out how much more was cut from the skirt than the pants, convert fractions to have a common denominator and subtract: 3/4 inch minus 1/6 inch equals 7/12 inch.

Explanation:

To determine how much more the tailor cut off the skirt than the pants, we need to subtract the length cut from the pants from the length cut from the skirt. The tailor cut 3/4 of an inch off the skirt and 1/6 of an inch off the pants. To perform the subtraction, we need a common denominator, in this case, 12 is suitable. So we convert 3/4 to 9/12 and 1/6 to 2/12.

Now, we subtract the smaller fraction from the larger one:

9/12 - 2/12 = 7/12 of an inch.

Therefore, the tailor cut 7/12 of an inch more off the skirt than the pants.