At 5:00 p.m., Vera took 400 milligrams
of medicine to help relieve her headache.
The table below shows the amount of
medicine in her system at different
hours. If this pattern continues, find
the approximate amount of medicine in
her system when she wakes up at
7:00 a.m. the next morning. Round to the nearest tenth.
5:00pm - 400mg
6:00pm - 350mg
7:00pm - 306.25mg

The calculated difference volume capacity for cylindrical container and spherical container is 26.2.

The volume capacity refers to maximum amount of space covered by an object in three dimensional space that can be absorbed by an object.

After implementing the principles of volume capacity we break it down to two consecutive cases

First case we find the volume capacity of spherical container using the formula

\(V = \pi r^{2} h\)

\(V=3.14*(5^{2})*(7)\)

\(V = 549.8 ft^{3}\)

Second case we find the volume capacity of cylindrical container using the formula

\(V=\frac{4}{3}\pi r^{3}\)

now staging the values we get

\(V=(\frac{4}{3} )\ *3.14*(5^{3} )\)

\(V = 523.6ft^{3}\)

now, calculating the difference we get

549.8 - 523.6 = 26.2

The calculated difference volume capacity for cylindrical container and spherical container is 26.2.

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Answer:

x=9

y=5

Step-by-step explanation:

u 1 multiple equation 1 by -3

and sum the equation at L.H.S =R.H.S

Answer:

16

Step-by-step explanation:

4 coins 2 out comes each

2 X 2 X 2 X 2 = 16

2^4 = 16

Hope i helped you

Answer:

16

Step-by-step explanation:

Answer: 4.278695 × 10^7

Step-by-step explanation:

Answer: 4.2786950x10^7 or 4.2x10^7

Step-by-step explanation:

To convert a number to scientific notation, move the decimal.

42,786,950

At the and of this number, there is an understood decimal. To find the scientific notation version of it, move the decimal over to the left until you have only one digit to the left of the decimal, as such...

4.2786950

To then find what the exponent you're multiplying by, you count how many places you moved the decimal.

So in the end, you get 4.2786950x10^7

Th different triangles that can you make if three property of the triangle is known and one side must be known, will be one.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

To specify the triangle, atleast one of the sides must be known and any other two property like side-angle, side-side, and angle-angle.

Th different triangles that can you make if three property of the triangle is known and one side must be known, will be one.

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For a 3×3 matrix A, with the real eigenvalue is 2 and two complex conjugate eigenvalues, the complex conjugate eigenvalues of matrix A are equal to 1 ± i.

Eigenvalues are defined as a special set of scalar points that is associated with set of linear equations and matrix equations. We have a matrix A of order 3×3. It has real and complex eigenvalues. As we know number of eigenvalues for 3×3 matrix are 3. The real eigenvalue, λ

= 2

Number of complex eigenvalues= 2

Also, the determinant of matrix A, det(A) = 50

Trace of matrix A, tr(A) = 8

We have to determine the complex eigenvalues.

The characteristic polynomial for 3×3 is written as below, f( λ )= det(A − λI3 )= −λ³ + 4λ² - 6 λ + 4.

For eigenvalues, −λ³ + 4λ² - 6 λ + 4 = 0

Now, one of eigenvalue of matrix is 2, λ = 2. Using the synthesis division, for calculating the remaining, follow the steps present in above figure. In the last step of division we get a quadratic equation, -λ² + 2λ - 2 = 0, solve it by quadratic formula, \(λ = \frac{-2 ± \sqrt{ 2² - 4 (-2)(-1)}}{2(-1)}\)

\(= \frac{-2 ± \sqrt{4 - 8 }}{-2}\)

=> λ = 1 ± i

Hence, required values are 1 ± i.

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Answer:

13.7

Step-by-step explanation:

take 58 degree as reference angle

using tan rule

tan 58 =opposite/adjacent

1.600=22/x

x=22/1.600

x=13.75

x=13.7

Answer:

Equation: 112+x=180

Value of x: x=68

Alejandra paid a total of $97,500 for 15 notebooks at a price of $6,500 each.

To calculate the total amount Alejandra paid for the notebooks, we need to multiply the number of notebooks (15) by the price per notebook ($6,500).

15 notebooks multiplied by $6,500 equals $97,500. Therefore, Alejandra paid a total of $97,500 for the 15 notebooks.

This calculation assumes that all the notebooks were purchased at the same price of $6,500 each and that no additional costs or discounts were involved in the transaction.

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The parameters to the Poisson distribution, to find the probability of exactly 3 arrivals in one thousandth of a​ minute, are given as follows:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute, hence the mean of the distribution is given as follows:

μ = 6000/13719.

The parameter x represents the number of arrivals in each thousandth of a minute, hence it is given as follows:

x = 3.

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Answer:

Flexibility: Stretching

Endurance: Being able to dance for periods of time

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer:

A

Step-by-step explanation:

We have a table listing the number of minutes Trayvon practiced the Backstroke and Butterfly on Monday, Wednesday, and Friday.

We want to find event that Trayvon spent more time practicing.

To do so, we add up all the minutes of one event and compare this to the total minutes of the other event.

Therefore, we can eliminate options C and D. These two options evaluate the time on Wednesday compared to other days, but we want to do is to find which event did Trayvon spend the longest on.

So, let's add up all the minutes spent doing the Backstroke. Trayvon over the course of the three days spent 12.5 mins, 15.67 mins, and 9.32 mins.

Therefore, the total minutes Trayvon spend practicing the Backstroke is:

\(12.5+15.67+9.32=37.49\text{ mins}\)

Now, let's add up all the minutes spent doing the Butterfly. Trayvon spent 14.333 mins, 12.1 mins, and 10.78 mins over the course of three days. So, the total time spent doing the Butterfly is:

\(14.333+12.1+10.78=37.213\text{ mins}\)

Trayvon spent a total of 37.49 minutes doing the Backstroke and 37.213 minutes doing the Butterfly.

37.49 is greater than 37.213. So, Trayvon spent more time practicing the Backstroke.

So, our correct answer is A.

There are some number and calculation errors in B.

And we're done!

Answer:

C

Step-by-step explanation:

On Monday he spent 12.5 min on backstroke and 14.33 min on butterfly.

He spent 26.83 min practicing at the Monday event.

On Wednesday: 15.67 min on backstroke and 12.1 min on butterfly.

He spent 27.77 min on practicing at the Wednesday event.

On Friday: 2.32 min on backstroke and 10.78 min on butterfly.

He spent 13.1 on practicing at the Friday event.

So, he spent more time at the Wednesday event.

Should there be a global effort to sharply reduce the cutting and burning of old-growth forests?

Yes, there should be a global effort to sharply reduce the cutting and burning of old-growth forests. Old-growth forests are vital ecosystems that provide numerous environmental, social, and economic benefits. They are home to diverse species, including endangered ones, and play a crucial role in carbon sequestration, mitigating climate change, and preserving biodiversity.

Cutting and burning old-growth forests contribute to deforestation, habitat loss, and greenhouse gas emissions. It disrupts ecosystems, threatens species survival, and exacerbates climate change. Protecting old-growth forests is essential for maintaining ecological balance and promoting sustainable development.

Numerous references and scientific studies support the importance of preserving old-growth forests. Some relevant sources include:

"The Importance of Old-Growth Forests" by the World Wildlife Fund (WWF): https://www.worldwildlife.org/initiatives/old-growth-forests

"Old-growth forest protection: A key tool in fighting climate change" by The Nature Conservancy: https://www.nature.org/en-us/what-we-do/our-insights/perspectives/old-growth-forest-protection-fighting-climate-change/

"Old-Growth Forests: Function, Fate and Value" by the United Nations Environment Programme (UNEP): https://www.unep-wcmc.org/resources-and-data/old-growth-forests-function-fate-and-value

These resources provide comprehensive information on the importance of old-growth forest conservation and the need for global efforts to reduce cutting and burning practices.

The question provided seems incomplete and unclear. It mentions a relationship between letters of the alphabet and percentages but does not provide any context or options to choose from. Please provide more information or clarify the question, and I'll be glad to assist you further.

The cube roots of 117 441 in rectangular form are: a. 3.00 +4.002, b. –4.96 +0.604, c. -1.96 + 1.964, d. - 124.10 + 11.95, e. 3.00 4.00, f. 4.68 - 1.764, g. 1.96 4.602, and h. 75.00+ 100.00.

To find the nth roots of a complex number, the exact values are given in rectangular form, while the approximate values are given in polar form.

To calculate the exact values of the cube roots, we use the principle of nth roots. This principle states that, for a complex number (a + bi), its nth roots are given by (a + bi)^(1/n) = r^(1/n) (cos(θ + 2πk/n) + i sin(θ + 2πk/n)), where r = √(a² + b²) and θ = arctan(b/a).

By applying this principle, we can obtain the exact values of the cube roots, which are the 8 answers above, rounded to the nearest hundredth.

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Answer: I hope it helps :)

Step-by-step explanation:

1.

\(Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}\)

2.

\(Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23\)

3.

\(Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6\)

4.

\(Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}\)

5.

\(Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y\)

the temperature at 8:00 am is 9°C  This means that every hour from midnight to 8:00 am, the temperature increased by 1.5°C, resulting in a total increase of 12°C over the 8 hour period.

To solve this problem, we need to use the formula for calculating the final temperature based on the initial temperature and the rate of change per hour.

The formula for this is:

Final Temperature = Initial Temperature + (Rate of Change per Hour x Number of Hours)

In this case, the initial temperature is -3°C, the rate of change per hour is 1.5°C, and the number of hours is 8.

Plugging these values into the formula, we get:

Final Temperature = -3 + (1.5 x 8)

Final Temperature = -3 + 12

Final Temperature = 9°C

Therefore, the temperature at 8:00 am is 9°C.

This means that every hour from midnight to 8:00 am, the temperature increased by 1.5°C, resulting in a total increase of 12°C over the 8 hour period.

It's important to note that this problem assumes that the rate of change per hour remains constant throughout the 8 hour period. In reality, the temperature may fluctuate based on various factors, such as wind, cloud cover, and humidity. However, for the purposes of this problem, we can assume that the rate of change per hour remains constant.

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A line graph is used when an independent variable is a continuous quantitative variable. A line graph is a type of chart used to represent data over time with the help of lines connecting various data points.

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Answer:

The height is 12 cm instead of 13 cm

Step-by-step explanation:

use 12 Cm to take out answer

For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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Answer:

82 + -71 = 10

Hope this helps! <3

Answer:4.472136

Step-by-step explanation:

The formula in finding the distance between two points is given below:

Now, you know the distance formula. So, let us try solving the given problem using the distance formula.

Problem: What is the distance between (-2, 3) and (2, 1), using the distance formula?

From inspection on the given problem:

Substitute the given values into the distance formula and solve for d:

Therefore, the distance between two points is 4.47 units.

\(\\\)

Now, wasn't that easy? Try this sample problem:

From the sample problem above, you may solve it on your own to enhance your skill on calculating the distance.

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In this context, the random variable X represents the mean weight in pounds of a sample of 20 heads of lettuce.

The random variable X represents the mean weight in pounds of a sample of 20 heads of lettuce because we are taking a sample of 20 heads of lettuce and calculating the average weight of those 20 heads. Each sample will have a different mean weight, and X represents this mean weight. By considering X as a random variable, we acknowledge that the specific value of the mean weight can vary from sample to sample. The random variable X allows us to analyze the distribution of the sample means and make inferences about the population mean.

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The 99% confidence interval for the difference between mean numbers is given as follows:

(-3.6, -0.8).

The difference between the means for each interval is given as follows:

1.6 - 3.8 = -2.2.

The standard error for each sample is given as follows:

Then the standard error for the distribution of differences is given as follows:

\(s = \sqrt{0.089^2 + 0.538^2}\)

s = 0.545.

The critical value for a 99% confidence interval is given as follows:

z = 2.575.

The lower bound of the interval is given as follows:

-2.2 - 2.575 x 0.545 = -3.6.

The upper bound of the interval is given as follows:

-2.2 + 2.575 x 0.545 = -0.8.

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The type of function that will surpass all the functions when x goes to infinity is given as follows:

Increasing exponential function.

An increasing exponential function is modeled as follows:

y = a(1 + r)^x.

In which:

As the function is increasing, we have that:

1 + r > 1,

Hence, as x goes to infinity, the function will grow in value very quickly as the infinity term is on the exponential, hence an increasing exponential function surpasses all other kinds of functions.

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