the volumes of soda in quart soda bottles can be described by a normal distribution with a mean of 32.3 ounces and a standard deviation of 8.8 ounces. (a) what proportion of bottles will have a volume more than 32 ounces? 0.5136 correct: your answer is correct. (4 decimal places) (b) what is the 85th percentile for this distribution? 23.18 incorrect: your answer is incorrect. (2 decimal places)

The slope and intercept of the line are -2 and 0. The equation of the line is y = -2x

To find the equation of line, we have to find the slope of the equation and its y-intercept.

The slope of a line can be calculated as

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\m = \frac{-4 - (-4)}{6 - 2}\\m = \frac{-8}{4} \\m = -2[/tex]

The slope of the line is equal to -2.

Lets find the intercept of the line;

The line of an equation is given as

[tex]y = mx + c[/tex]

We can pick point A and substitute its values to find c

[tex]y = mx + c\\- 4 = -2(2) + c\\-4 = -4 + c\\c = -4 + 4\\c = 0[/tex]

The equation of the line is y = -2x

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The continuous growth rate per year of the world population is 0.664%.

We've been told to assume that population is growing at an exponential rate. As a result, we can employ the population model shown below.

N(t) = N₀ e∧(kt)

Here, N(t) represents the population after t years, N₀ represents the initial population, and k represents the continuous growth rate.

We've been told that initial population of 6.9 billion will increase to 9 billion in 40 years (2050-2010).

To use this information, we calculate the growth rate using the model described below.

N(40) = 6.9 e∧(40k)

N(40) = 9 (given)

9 =  6.9 e∧(40k)

Taking ㏑ both side

㏑ 9 = ㏑ 6.9 e∧(40k)

40k = ㏑(9/6.9)

k = 0.00664

k = 0.664%

Thus, the continuous growth rate per year of the world population is 0.664%.

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Answer:

2.1875

(in nearest hundredths it would be 2.19(rounded)

The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.

It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.

It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.

Therefore the arrival rate per hour is given by the following relation:

Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes

Given here,

No. of minutes in an hour = 60 minutes

Inter arrival time of the email taken in minutes = 2 minutes

∴ Arrival rate in 1 hr = 60 / 2

                                = 30 emails / hr

Hence the arrival rate is 30 emails per hour.

Now for finding out the service rate we have the following formula:

Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email

Given here,

No. of minutes in an hr = 60 minutes

No. of employes answering = 3

Average time that for writing response email = 2 minutes

∴ Service rate = 60 * 3 / 4

                       = 45 emails / hr

Hence the service rate is 45 emails per hour.

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Solve R:

Multiply both sides of the equation by V:

Divide both sides of the equation by nT:

Then, R is:

Use the given units in the equation above:

The total cost of the skateboard after being discounted by 12% and then sales tax of 6.75% is$74.22.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

As per the given,

Usually, the price of the skateboard = $79.01

The 12% of 79.01 ⇒ (12/100)79.01 = $9.4812

The price after a 12% discount

79.01 - 9.4812 = $69.5288

The 6.75% of 69.5288 ⇒(6.75/100)69.5288 = $4.693194

The total price after applying the 6.75% tax,

$69.5288 + $4.693194 = $74.22

Hence "The total cost of the skateboard after being discounted by 12% and then sales tax of 6.75% is$74.22".

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The measure of center that is a better indication of a "typical” salary at this business is A. The mean is better because it is not affected by the high salaries.

When the majority of the data are gathered on the left of the distribution curve or the histogram, the distribution is said to be positively skewed, or skewed to the right.

If the majority of the data are gathered on the right side of the distribution curve or the histogram, the distribution is said to be negatively skewed, or to the left. It is assumed that many employees at tiny businesses earn extremely low pay while a select few earn very high salaries. In this case, the mean gives between information about the data.

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The domain of the function in this situation as required in the task content is; Choice H; 0 ≤ x ≤ 5.

It follows from the task content that the domain of the function described by the situation is to be determined.

Since the domain is the set of all possible input values, otherwise termed the independent variable, x.

It follows that since one runner runs for at most t hours; the domain is; Choice H ; 0 ≤ x ≤ 5.

Please Note: The set of all possible output values of a function, otherwise termed the dependent variable, y is called the Range.

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Answer:

i'm not sure i looked it up but from it says you you can find the quotient by using the opposite of division which is multiplying again I'm not sure i might be wrong but please let me know if its right

Step-by-step explanation:

Answer: 1/121

Step-by-step explanation:

Any number raised to the power of 0 is 1

11^2 = 121

Answer:

Step-by-step explanation:

Yes

The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

It is known that π radian = 180°.

1° = (π/180) radian.

Multiply both sides by 310

310° = (π/180)310

310° = (31/18)π

Hence "The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π".

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Answer:

⇔[tex]a^{3}[/tex]

Step-by-step explanation:

Law of Indices

Division law:  [tex]\frac{a^{5} }{a^{2} }[/tex] =[tex]a^{5-2} =a^{3}[/tex]

Using simple linear equation we calculate the cost of a sweater as $35 .

A linear polynomial over a field, from which the coefficients are taken, can be equalised to zero to produce a linear equation.

Let the cost of each sweater be x.

Cost of the skirt = $20

Let us form a linear equation to calculate the required cost

4x + 20 = 160

solving we get :

x = 35

Therefore the cost of a skirt is $35.

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Answer:

2/3

Step-by-step explanation:

If 1/3 rd of the fence can be built in 1/2 hr then in 1 hour which is 1/2 x 2 the fraction of the fence that can be built is 1/3 x 2 = 2/3

Answer: Jake spent 62.5% of the money on movie tickets.

Step-by-step explanation: He spent 6 x 4 = $24 on movie tickets.

He spent 7 x 2.25 = 15.75 on drinks

However, it is asking for the amount of money he spent on MOVIE TICKETS. So then it would be 25/40 or 5/8.

All the values with exactly three significant digits are: 0.0807, 1990

Significant digits of a number tell us what the actual meaningful representation of a number is. There are certain rules to figure out which digits in a number are significant such as

Thus the numbers with 3 significant digits are: 0.0807, 1990

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Answer:

Answer down below!

Step-by-step explanation:

Your answer would be 1 11/40

For the steps, refer to the image below!

The solution to the given inequality expression is g <3

Inequality are expressions not separated by an equal sign. They are separated by a less than, greater than, less than or equal to and greater than or equal to.

Given the linear equation below:

g + 3 < 6

We are determine the unknown variable "g"

First, we need to subtract 3 from both sides to have;

g + 3 - 3 <  6-3

g < 6 - 3

g < 3

Hence the solution to the given inequality expression is g < 3

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For a Simple Interest of $160, the amount that he invested is $2000.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Given:

Simple Interest (S.I.) = $160

Rate of Interest (R) = 2%

Time Period (T) = 4 Years

Let the Principal Amount be $P

We know,

[tex]S.I. =\frac{P*R*T}{100}[/tex]

Putting the given values in the formula, we get:

[tex]S.I. =\frac{P*R*T}{100}\\S.I. =\frac{P*2*4}{100} =\frac{P*8}{100}\\ 160 =\frac{P*8}{100} \\P = \frac{160*100}{8} =\frac{16000}{8} = 2000[/tex]

Hence, He Invested $2000

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Answer:

$2,000

Step-by-step explanation:

Simple Interest Formula

[tex]\large\boxed{\sf I = Prt}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for P:

[tex]\implies \sf 160=P \cdot 4 \cdot 0.02[/tex]

[tex]\implies \sf 160=0.08P[/tex]

[tex]\implies \sf P=\dfrac{160}{0.08}[/tex]

[tex]\implies \sf P=2000[/tex]

Therefore, the amount Deshaun invested was $2,000.

Answer:

Step-by-step explanation:

49 = 7/6u

49 * 6/7 = 7/6u * 6/7

42 = u

Answer: 26 inches

Step-by-step explanation:

An isosceles triangle has two congruent legs.

1) Set up the equations

P = b + 2L

b = 2L-6

2) Substitute for variables

46 = (2L - 6) + 2L

3) Solve the equation

46 = 4L - 6

52 = 4L

13 = L

4) Solve the problem

It asks for what is the sum of the two congruent legs

13 + 13 = Ans

26 = Ans

1 1/2 : 1/2 is the rario of wayer to milk

The ratio of water to milk is 3:1.

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other is called ratio.

Water = 1½ cups

         = 3/2 cups

Milk =  1/2 cup

Ratio of Water to milk

= 3/2 : 1/2

= 3/2 ÷ 1/2

= 3/2 x 2/1

= 3/1

so, the ratio of water to milk is 3:1.

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The set of numbers from least to greatest is-

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

For the given numbers;

The given number are-

2/5, 5×10⁻², √3, 6%, 4/9, 2⁻¹.

These number can be written in the decimal form as;

Now arrange the number from least to greatest.

0.058, 0.06, 0.40, 0.44, 0.5, 1.73

Convert the number in given form.

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

Thus, the number represented in the ascending order are-

5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.

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The maximum volume of the box is 54 cm³ .

To obtain the largest volume feasible, multiply each measurement by the largest possible error. To find the least volume that may be created, multiply after subtracting the biggest possible error from each measurement.

Given :

a box is to be constructed from a sheet of cardboard that is 10 cm by 60 cm

cutting out squares of length x by x from each corner and bending up the sides

⇒ (50-2x)(10-2x)(x)

⇒ 500-100x-20x+4x^2) (x)

⇒ 4x^3-120x^2+500x

⇒ dv/dx     12x^2-240x+500=0

⇒ 3x^2-60x+125=0

⇒ Quadratic formula x=[60 ± √2100]/6

⇒ x= 2.36 or 17.64

volume max: 45.28 x 5.28 x 2.36= 564 cm^3

Hence The maximum volume of the box is 54 cm³

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Answer:

B Description is in the picture

Answer:

[tex]2^2*3^2[/tex]

Step-by-step explanation:

By definition of a negative exponent: [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]

In the last step I simply distributed the exponent, but this actually goes both ways! So we can do: [tex]\frac{b^x}{a^x}\implies(\frac{b}{a})^x[/tex]

The next thing you need to know is that: [tex](ab)^x=a^x*b^x[/tex]

and like the previous statement, it works both ways! So this means: [tex]a^x*b^x\implies (ab)^x[/tex]

So the denominator of the expression given can be expressed as:

[tex](2^{-2}*3^{-2})\implies (2*3)^{-2}[/tex]

Lastly you need to understand: [tex]1^x[/tex] just simplifies to one, because [tex]1*1*1*1...\text{ x amount of times}[/tex] will stay equal to one. So we can thing of 1 as being raised to some number, even if not explicitly stated.

This helps because we can write one as: [tex]1^{-2}[/tex]

so now we have the expression:
[tex]\frac{1^{-2}}{(3*2)^{-2}}[/tex]

Well this can because now we can "factor" out this exponent just like how it was demonstrated in the beginning

We get the expression: [tex](\frac{1}{3*2})^{-2}[/tex]

Now we use the definition of a negative exponent, to get the reciprocal giving us the expression

[tex](\frac{3*2}{1})^{2}[/tex]

We can now "distribute" this exponent across the division to get

[tex]\frac{(3*2)^2}{1^2}[/tex]

Well 1 squared just simplifies to 1, so it's redundant to write.

This gives us the expression:
[tex](3*2)^2[/tex]

and as stated before we can distribute this across multiplication, and another way to think of it is:

[tex](3*2)^2\implies (3^2*2^2)\\\\\\text{because } (3*2)^2\implies (3*2)*(3*2)\implies(3*3)*(2*2)[/tex]

we're just grouping the like terms, so we can write them as an exponent.

So this gives us our final expression:
[tex]3^2*2^2[/tex]

or

[tex]2^2*3^2[/tex]

which is the option B, since the order in which we multiply does not matter.

-

nbjhjkghjvhjvhjvhvjvhhklbjklbjblk

The answer to the given notation is 1970

Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 108.

This is already an standard notation : 1.97 × 10³

10 raised to the power three means there are three zeroes.

thus if we were to solve this question it will be

1.97 × 1000

which is equal to 1970.00

= 1970 .

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