In a survey of women in a certain country​ (ages 20 minus​29), the mean height was 66.2 inches with a standard deviation of 2.86 inches. Answer the following questions about the specified normal distribution. ​(a) What height represents the 95th ​percentile? (round to two decimal places as needed)
(b) What height represents the first quartile? (round to two decimal places as needed.)

Answer:

The coefficient of variation for the weight and age are 5.9% and 10.6%.

Step-by-step explanation:

The coefficient of variation (CV) is well defined as the ratio of the standard deviation to the mean. It exhibits the degree of variation in association to the mean of the population.

The formula to compute the coefficient of variation is:

\(CV=\frac{\sigma}{\mu}\times 100\%\)

Here σ = standard deviation and µ = mean.

Compute the mean and standard deviations of the two data set in Excel using the following functions.

Mean=AVERAGE()

Standard deviation=STDEV.S()

Consider the Excel sheet attached.

The mean and standard deviation of weight are:

Mean = 202, Standard deviation = 11.87

And the mean and standard deviation of weight are:

Mean = 25.88, Standard deviation = 2.75

Compute the coefficient of variation for the weight as follows:

\(CV_{weight}=\frac{\sigma}{\mu}\times 100\%\)

              \(=\frac{11.87}{202}\times 100\%\\\\=5.87624\\\\=5.9\%\)

Compute the coefficient of variation for the age as follows:

\(CV_{age}=\frac{\sigma}{\mu}\times 100\%\)

              \(=\frac{2.75}{25.88}\times 100\%\\\\=10.62597\\\\=10.6\%\)

Thus, the coefficient of variation for the weight and age are 5.9% and 10.6%.

Answer:

He will pay $1.20 sales tax.

Step-by-step explanation:

Answer:

  Truck                 Car              Total

Female           5                      35                40

Male              27                     21                48

Total              32                     56                88

P(buying a car given a male )  =  21/88 = .238 ≈ 24%

Step-by-step explanation:

Let B  = Probability of buying a car and being male    21/88

Let M = Probability of being a male  =  48/88

P(B l M)   =  P(B and M) / P(M)   =   (21/88) / (48/88)  = 21/48  = .4375  = 44%

The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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A percentage is a way to describe a part of a whole. The new wage per hour to the nearest cent if it is increased by 9% will be $18.26.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the Medical assistants are to receive a 9% increase in wages per hour. While the current wage of Medical assistance is $16.75 an hour.

Therefore, the new wage per hour to the nearest cent will be,

New wage = Old wage + 9% of old wage

                  = $16.75 + 0.09($16.75)

                  = $18.26

Hence, the new wage per hour to the nearest cent will be $18.26.

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Answer:

2

Step-by-step explanation:

10.5/3.5=2

The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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Answer:

what we have to find or to prove.

Step-by-step explanation:

General line equation: y = mx + c, where m is the slope of the line and c is the y-intercept.

We have y = ax + b.

=> y - b = ax

=> y - b = a(x - 0).

The answer is option A.

Answer:

A

\(general \: equation \: of \: line \\ y = mx + c \\ from \: the \: data \: given \\ m = a \\ c = b \\ y = ax + b \\ y - b = ax \\ y - b = a(x - 0)\)

Answer:

-20

Step-by-step explanation:

(-a/2=10)/-1

=a/2=-10

a=-10*2

a=-20

We know that the sum of the internal angles is equal to 180°, then we write and solve a linear equation to see that the missing angle is 94°.

Remember that for any triangle, we know that the sum of the interior angles is equal to 180°.

In this case we know that two of the angles have a measure of 62° and 24°, and if the third angle is x, then we can write the linear equation:

62° + 24° + x = 180°

To solve this we need to isolate x, we will get:

x = 180° - 24° - 62°

x = 94°

So the measure of the third interior angle is 94 degrees.

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Combinations and Variations of Elements

Let's suppose we have two dogs only, A and B. They can only finish in two possible orders: AB or BA.

If we add a third dog, let's say C, the combinations (better-called variations here) are now ABC, ACB, BAC, BCA, CAB, and CBA, a total of 6 variations.

Note that we added a 3rd element and the variations changed from 2 to 6, that is, the number was multiplied by 3.

If we add a fourth dog, the total number of possible variations is 6*4 = 24

Following this very same pattern, for 9 dogs, there will be a total of

9*8*7*6*5*4*3*2 = 362880 variations.

Out of these possibilities, we are trying to find the probability that the first three places are occupied by three specific dogs, and the other 6 positions can be filled up with a random variation that will give us

6*5*4*3*2 = 720 variations.

Thus the required probability is:

Answer:

2346 dl sheep

Step-by-step explanation:

all well STrxrcgvw'#'zuucrb if ivAr4w3ws4

A.

The domain of a function is the complete set of possible values of the independent variable:

The range of a function is the complete set of possible values of the dependent variable:

A function is a specific type of relation in which each input value has one and only one output value.

Since:

(-5,4) and (-5,4) and (1,2) and (1,-2) belong to the relation. We can conclude that the relation is not a function.

B.

Since:

We can conclude that the relation is a function

The value of Y is 54 degrees

A pentagon is described as any five-sided polygon or 5-gon that has a sum of the internal angles in a simple pentagon is 540°.

we know that every side of a regular pentagon is same.

So we have an isosceles triangle. The  correspond angle of y, must equal to y (degree) too.

we also have that every inner angle of a regular pentagon is 360/5=72.

So we can calculate angle y, by the equation y+y+72=180.

Therefore y=54

In conclusion,  the regular pentagon each interior angle measures 108°, and each exterior angle measures 72°

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Complete question is attached in image;

The circular is around 305 cm in circumeference.

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle.

Substituting d = 97 cm and using the value of π to be 3.14159, we get:

C = πd

C = 3.14159 × 97 cm

C ≈ 304.731 cm

Rounding this to 3 significant figures, we get:

C ≈ 305 cm

Therefore, the circumference of the circle is approximately 305 cm.

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Answer:

The answer is that the simplest fraction form of 34% is 17/50

Step-by-step explanation:

Both the numerator and denominator of the fraction 34/100 can only be divided by 2, to satisfy creating its simplest form.

34% = 17/50

Have an awesome day! :D

Answer:

\(\frac{17}{50}\)

Step-by-step explanation:

To write any fraction as a percent, remember perCENT means per 100. Think of 100 cents in a dollar. So 34 perCENT means 34 of 100, which you write as \(\frac{34}{100}\).

Simplest form means to reduce, so you see if there is any number you can divide out of the top and the bottom.

\(\frac{34}{100}\) = \(\frac{17*2}{50*2}\)= \(\frac{17}{50}\)

At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer:45*15=675 his monthly payment is 675

Step-by-step explanation:It's an easy question to be honest all you have to do is 30,000/2,000=15 and then multiply 45*15=675

Approximately 17.65% of Ana's salary is withheld for taxes.

To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.

Number of hours worked per week (H) = 25 hours

Hourly wage (W) = $10

Net salary (S) = $212.50

Calculate the total earnings before taxes:

Total earnings = Hours worked * Hourly wage

Total earnings = 25 hours * $10/hour

Total earnings = $250

Determine the amount of tax withheld:

Tax withheld = Total earnings - Net salary

Tax withheld = $250 - $212.50

Tax withheld = $37.50

Calculate the percentage of salary withheld for taxes:

Percentage withheld = (Tax withheld / Net salary) * 100

Percentage withheld = ($37.50 / $212.50) * 100

Percentage withheld ≈ 17.65%

Therefore, approximately 17.65% of Ana's salary is withheld for taxes.

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The system of equations has an infinite number of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

3x + 2y = 6 ____(1)

6x + 4y = 12 _____(2)

Applying the substitution method.

3x + 2y = 6

x = (6 - 2y)/3 in (2)

6 (6 - 2y)/3 + 4y = 12

2 (6 - 2y) + 4y = 12

12 - 4y + 4y = 12

12 = 12

This means,

It has an infinite number of solutions.

Thus,

An infinite number of solutions.

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The complete question is:

Graph the system of equations

3x + 2y = 6

6x + 4y = 12

and find the solution to the system.

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

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

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

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

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Answer:

I think that it might be a type-o on the assignment. If I was you I would email your teacher.

The Total length of two sides based on the information will be 7x²+2x+1

The Length of the third side will be 4 x³-10x²-7.

Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Length of the third side = Perimeter - Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

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Answer:

The tank starts with 32300 gallons and is decreasing by -16.15 gallons per minute

After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Answer:

p=2

Step-by-step explanation:

4p+2≤10

    -2   -2

4p≤8

divide by 4

p≤2

Answer:

p ≤ 2

Step-by-step explanation:

Answer:

E

Step-by-step explanation: