In a survey of men in a certain country (ages 20 - 29), the mean height was 63.7 inches with a standard deviation of 2.8 inches.
What height represents the 85th percentile?
What height represents the first quartile?

To change the base of a logarithm, for example from base a to base c, we use the formula [tex]log_{a} (b)[/tex] = [tex]log_{c} (b)[/tex] / [tex]log_{c} (a)[/tex].

In order to change the base of a logarithm the following basic formula is used,

[tex]log_{a} (b)[/tex] = [tex]log_{c} (b)[/tex] / [tex]log_{c} (a)[/tex]

For example,

If we have to change the base of log₃(81) to base 5,

It will be written as

log₃(81) = log₅(81) / log₅(3)

The change of base rule is able to covert a logarithm in a given base to a logarithm in a new base. The result will be a quotient, which is a fraction, with the new logarithm as both the numerator as well as a denominator.

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Answer: 72 + 2x = 180

Step-by-step explanation:

The solution to the equation cos(2x + 45°) = 0.8 in the domain of 0° to 180° is x = 15° and X=139° or X=176 °

Because Cos (±37° +360k) = 0.8

0≤2X ≤ 360°

0+45°=2x+45° 360°+45° 45°≤ 2x+45°< 405°

50 2x+45° = 360°-37° or 2x+45° = 360° + 37°

{list the equation} 397° -45°=2X = 323-45°

2X = 323-45°. 2x=397° -45°

2x= 278°.         2x= 352°

X = 139°.          X=176°

So , x = 139° or x = 176°

To discover the solution set of an equation with a particular domain, first insert each domain value into the equation to obtain the associated range values. Make ordered pairs out of these values and put them down as a set. That set is your solution!

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Linear equations in two variables can be relatively easy to understand and work with, as they represent straight lines in the xy-plane. The slope-intercept form of a linear equation, y = mx + b, is a simple way to represent a line with a specific slope and y-intercept.

Graphing linear equations is also straightforward, as you can find the x-intercept and y-intercept and plot the line using these points.

However, solving linear equations in two variables can become more challenging when the equations involve multiple terms or are presented in a different form. Also, understanding the concept of slope, y-intercept, and how to graph the line can be challenging for some students.

Overall, linear equations in two variables can be considered as a fundamental concept in algebra and mathematics and it requires practice to gain mastery over it.

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The range in statistics for a given data set is the difference between the highest and lowest values.

As a result, the range can also be defined as the difference between the highest and lowest observations. The range of observation is the name given to the outcome. In statistics, the range indicates the dispersion of observations.

To find the range in statistics, we need to arrange the given values or set of data or set of observations in ascending order.

For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.

Thus, The range in statistics for a given data set is the difference between the highest and lowest values.

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Answer :

The first one

Step-by-step explanation:

A cube root is a number that, when cubed, is equal to the given number.

It is denoted with an exponent of "1/3".

Example, the cube root of 27 is 27^1/3 = 3.

Now,

[tex]24^{ \frac{1}{3} } \: is \: the \: same \: as \: \sqrt[3]{24} [/tex]

From there, we can simplify

[tex] \sqrt[3]{24} \\ \sqrt[3]{2 \times 2 \times 2 \times 3} \\ \sqrt[3]{ {2}^{3} \times 3} \\ 2 \sqrt[3]{3} [/tex]

To get the sides of the right-angle triangle, we employ the 3 4 5 triangle method.

A right triangle is a particular kind of triangle that only has one right (90°) angle.A mathematical formula for determining the length of the third side of a right triangle given the lengths of the other two sides was developed by the Greek mathematician Pythagoras.

The sides of variables a and b make up the right angle of the triangle. Any side may make use of any variable. The variable c stands for the left side, or the side that leans away from the right angle. The longest side, or side c, is always present and is known as the hypotenuse.

Therefore, to determine the sides of the right-angle triangle, we employ the 3 4 5 triangle method.

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Answer:34xt25

Step-by-step explanation:

The coordinates of the point dividing the segment in the ratio 3:1 will be ( 38 / 4, 6 / 4).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that point A is (2,0) and point B is (2,12) and the line is divided in the ratio of 3:1. the coordinate of the point will be calculated as,

Point = { ( mx₂ + nx₁ ) / ( m + n ) }, { ( my₂ + ny₁ ) / ( m + n ) }

Point = { ( 3 x 12 0 + ( 1 x 2 ) / ( 3 + 1 )], { ( 3 x 2 ) + 0 ) / ( 3 + 1) }

Point = { 38 / 4, 6 / 4 }

Hence, the coordinates of the point dividing the segment by a factor of three will be (38 / 4, 6 / 4).

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The solution of the given expression 9x² + ( 4y / z ) will be 4763.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 9x² + ( 4y / z ) and the values are x=23, y=3, and z=6.

The expression will be solved as below,

E = 9x² + ( 4y / z )

E = 9 x ( 23 ²) + ( 4 x 3 ) / ( 6 )

E = 4761 + 2

E = 4763

Hence, the solution will be 4763.

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The product of (7x - 6)² is  49x² - 84x + 36.

Equation is (7x - 6)²,

⇒ We will solve the given problem using the algebraic identity

(a - b)² = a² + b² - 2ab

Here a = 7x and b = 6

⇒ (7x - 6)² = (7x)² + 6² - 2(7x)(6)

⇒ (7x - 6)² = 49x² + 36 - 84x

⇒ 49x² - 84x + 36

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied.

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Answer:$917.58.

Step-by-step explanation:

The formula for compound interest is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the initial deposit is $500, the annual interest rate is 4%, the number of times compounded per year is 12 (monthly), and the number of years is 12.

So, we can plug in the values into the formula:

A = $500(1 + 0.04/12)^(12*12) = $500(1.003333333)^(144) = $500(1.835170816) = $917.585

The final amount in her account after 12 years is $917.58

To round to the nearest cent, we can use the following method:

If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.

If the digit in the thousandths place is greater than 5, we round up the hundredths digit.

In this case the digit in the thousandths is 5 so, we have to round up the hundredths digit of $917.58.

So, the final amount in her account after 12 years is $917.59.

Answer: $800.516

Step-by-step explanation:

We use the equation

A = P(1 + )^nt

P = principal

r = rate of interest

t = times

Now let's solve

P = $500

r = 4% = 0.04

t = 12 years

A = $500(1 +[tex]\frac{0.04}{12}[/tex] ) ^12 = $800.516

Answer: ratio of 1:   10mins

               ratio of 5:   50mins

Step-by-step explanation:

The ratio of 1:

[tex]\frac{1}{6}[/tex] x 60 (hours should be converted to minutes therefore it is 60 mins and

            the denominator seen here is taken by adding the two values in the

             given ratio and since we're still finding 1 you should divide 1 by the

          added denominator and the same applies when finding the ratio 5)

Answer= 10mins

The ratio of 5:

[tex]\frac{5}{6}[/tex] x 60 (refer to the underlined explanation above)

answer= 50mins

so if you want to verify you add the two values you got to see if you got 60 as 60mins in hours was divided in ratio so when you add it will be 60 which means your answer is correct!

Answer: 12:60

Step-by-step explanation: To find the ratio, we must take 1 h and turn it into minutes. So as we know, it's 60 minutes. So next, we shall change the ratio into fraction form (don't worry it's the same basic format)

[tex]\frac{1}{5} = \frac{?}{60}[/tex]

So with that given information, we know that 60 would be our denominator. So, we need to divide both denominators, and then whatever we get from that, multiply that by the given numerator. So, we would do:

60 / 5

= 12

12 * 1

= 12

Therefore we now know that 1/5 = 12/60 as a ratio. I hope this helped :)

(Attachment included)

Answer:

Dylan's budget is $250, and she is buying pumpkins for $20 each and balloons for $2 each. We can represent the total cost of the pumpkins as 20x and the total cost of the balloons as 2y. The inequality that represents all possible ways she could buy pumpkins and balloons within her budget is:

20x + 2y <= 250

To find the maximum number of balloons she could buy, we can use the equation above and set x = 0, and then solve for y.

20(0) + 2y <= 250

2y <= 250

y <= 125

The maximum number of balloons she could buy is 125.

Answer:

Step-by-step explanation:

Answer: 1/4

Add: 3/4 + 1/6 = 3 · 3 / 4 · 3 + 1 · 2 / 6 · 2 = 9/12 + 2/12 = 9 + 2/12 = 11/12

Subtract:  1 - 2/3 = 11/12 - 2/3 = 11/12 - 2 · 4 / 3 · 4 = 11/12 - 8/12 = 11 - 8/12 = 3/12 = 3 · 1 / 3 · 4 = 1/4

The value of x=3 and y=1 is the solution.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

given equations are,

2x-y=5 and 3x+2y=11

Let  2x-y=5 ----[1]

,  3x+2y=11 ----[2]

Now, solving [1] and [2] by substitution method,

Substitute the value of x from [1] in [2],

x= [tex](\frac{5+y}{2})[/tex]

3x+2y=11

3[tex](\frac{5+y}{2})[/tex] + 2y = 11

[tex](\frac{15+3y}{2})[/tex] + 2y = 11

[tex](\frac{15+3y+4y}{2})[/tex] = 11

15 + 7y = 22

7y = 22 - 15

7y = 7

y = 1

Substitute the value of y=1 in [1],

2x - y = 5

2x - 1 = 5

2x = 6

x = 6 / 2

x = 3

Therefore, The value of x=3 and y=1.

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The First Class Mail (1 oz.) letter rate for postage purchased at the Post Office will increase two cents to $0.60 from $0.58.

Domestic shipping refers to shipping a package via a carrier within a country's borders.

Now, According to the question:

The “Metered Mail” rate for First Class Mail (1 oz.) letters which includes online postage and postage meters, will increase 4 cents to $0.57 from $0.53.

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Most linear systems will have exactly one solution. Nevertheless, it is possible that there are no solutions or infinitely many. (but It is not possible that there are exactly two solutions of a linear system.)

Let's assume a system of two linear equations, then, there are three possibilities of solutions.

The possibilities are:

Two parallel lines

e.g. y = 3x + 1

y = 3x − 2 (with the same slope, different intercepts)

Two (distinct) intersecting lines

As we know two straight lines cannot meet at two points. Two points determine only one line (not two lines).

e.g. y = 3x + 1

y = 5x − 2 (different slopes)

These equations have the same line as their graphs

If two lines do have two points in common, then "the lines coincide" (which really means "there is only one line".) In this case, we say, "the two lines are the same".

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Step-by-step explanation:

density is mass/volume.

usually it is expressed as grams/cm³.

the question does not give us the information about the dimensions for density. so, I am going with my assumption.

the volume of a cylinder is

ground area × height

the ground area is a circle, so this is

pi×r²×height

r is the radius and therefore half of the diameter.

so, we have in our case as volume :

pi×(20/2)²×5 = pi×100×5 = 500pi = 1,570.796326... m³

1 m = 100 cm

1 m³ = 100×100×100 = 1,000,000 cm³

so, the volume of our cylinder is then also

1,570,796,326.7948966192... cm³

1 kg = 1000 g ("kilo" means 1000)

1300 kg = 1,300,000 g

so the standard density is

1,300,000/1,570,796,326.7948966192... g/cm³ =

= 0.000827606... g/cm3

The density of the waste is approximately 0.827 kg/m³.

A physical property is known as density gauges a substance's mass per unit volume. It is referred to as the mass-to-volume ratio.

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height.

Since the diameter of the silo is 20m, the radius is 10m. Therefore, the volume of the silo is:

V = π(10m)²(5m) = 500π m³

Since the silo is full to the top with 1300kg of waste, the density of the waste is:

density = mass/volume

density = 1300kg/(500π m³)

density ≈ 0.827 kg/m³

Therefore, the density of the waste is approximately 0.827 kg/m³.

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Answer:

X

[tex] \frac{y2 - y1}{x2 - x1} - \frac{y - y1}{x - x1} [/tex]

Step-by-step explanation:

in every point given put one as (x1, y1) and the other is (x2, y2)

simplify the formula and you'll get you linear equation

The slope of the equation is 42, and it represents the $42 the artist earns, on is true after analyzing data from recent sales.

Sales in mathematics is the process of exchanging goods or services for money. It is a vital part of the economy and involves the transfer of ownership from the seller to the buyer. In mathematical terms, sales can be expressed as a function where the input is the amount of money paid for goods or services and the output is the goods or services received. Sales can also be expressed as an equation in which the variables are the cost of goods or services, the number of goods or services sold, and the total sale amount.

The slope of the equation is 42, and it represents the $42 the artist earns, on average, for every piece of pottery sold.

The constant -200 represents the cost of renting the booth.

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Step-by-step explanation:

x²-8x+7=0

x²-7x-x+7=0

x(x-7) -1(x-7)=0

(x-7) (x-1)=0

Either, x-7=0 i.e x=7

or, x-1=0 i.e x=1

Answer:

x^2-23

Step-by-step explanation:

Answer:awnsers below

Step-by-step explanation:

a. The probability of selecting 2 red balls is (5/8) * (5/8) = 25/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a red ball on the second draw is also 5/8, since the ball is replaced after each draw.

b. The probability of selecting 1 red ball and then 1 white ball is (5/8) * (3/8) = 15/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a white ball on the second draw is 3/8, since the ball is replaced after each draw.

Answer:

Step-by-step explanation:

a)

P(Red)=5/8

(5/8)^2=25/64

b)

P(Red)=5/8    P(White)=3/8

5/8*3/8=15/64

y = 8/3x + 100 exists the equation of the line in slope-intercept form.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

A line's slope and y intercept are represented in the slope intercept form as y = mx + b.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) contains

m = y₂-y₁/x₂-x₁

At two of the points the line passes through in the accompanying graph.

Let the two points be (0, 100) and (42, 148)

Let the equation be m = y₂-y₁/x₂-x₁

substitute the values in the above equation, we get

Slope = 148-100/42

= 48/42 = 8/3

To find y intercept, we get

100 = 8/3(0) + b

b = 100

So slope intercept form exists y = 8/3x + 100

Therefore, y = 8/3x + 100 exists the equation of the line in slope-intercept form.

The complete question is:

Examine the linear graph. Determine the y-intercept and write the y-intercept in coordinate form. Then write the equation of the line in slope-intercept form.

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Answer: 140 mph

Step-by-step explanation:

3 1/2+40=140 mph

The number of miles traveled in 3(1/2) hours is 140 miles.

We have,

Speed is the ratio of the given distance and time.

It shows how fast an object is moving at a given time.

The formula of speed is used.

Speed = Distance / Time

From the given statement, make an expression.

1 hour = 40 miles

Multiply 3(1/2) on both sides.

3(1/2) hours = 3(1/2) x 40 miles

Simplify the mix fraction.

3(1/2) hours = 7/2 x 40 miles

Simplify the fraction.

3(1/2) hours = 7 x 20 miles

3(1/2) hours = 140 miles

Thus,

The number of miles traveled in 3(1/2) hours is 140 miles.

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Equivalent 7/8 is equals to 56/64 in fractions.

In mathematics, equivalent fractions are those with the same denominator but different numerators. For instance, since they both equal 1, 2/4 and 3/6 are comparable fractions. An element of the whole is a fraction. To represent identical components of the total, equivalent fractions are utilized.

The numerator and denominator of each fraction can be multiplied by the same integer to determine the equivalent fraction. Equivalent fractions are those that, despite visible differences, signify the same value. For instance, if you take a piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.

= 7/8 is equivalent to:

= 7/8 * 8/8

= 56/64

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Correct Question:

What is 7/8 equivalent to in fractions?.

Answer:

the answer 112

Step-by-step explanation:

hope this helps

The designs that meet the condition have leg lengths that are in the ratio of 1: 12.

Two ramps that meet the Americans Disabilities Act are;

The needed measure of the angle of a ramp according to the Americans with Disability Act is θ ≤ 4.8°.

Given, the ratio of the leg lengths is 1: 12, we have;

Expressed as a fraction, we have;

The required ratio of leg lengths = [tex]\frac{1}{12}[/tex]

Probable leg lengths are seen by multiplying the numerator and denominator of the above fraction by a constant as follows;

Possible leg length for the ramp = [tex]\frac{1 * 3}{12 * 3} = \frac{3}{36}[/tex]

A second possible combination of leg length for the ramp = [tex]\frac{1 * 5}{12 * 5} = \frac{5}{60}[/tex]

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The complete question is:

The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4.8 degrees. Remember, a 4.8-degree angle in a right triangle has a 1: 12 ratio for the legs. Design 2 ramps that meet the Americans with Disabilities Act requirements.