Mathematics College

How do you multiply two scientific notation values? Explain the steps you would take to find the product of 6.7 × 106 and 3.2 × 105 written in scientific notation.

Answer is: Calculate the product of the coefficients and powers separately. Apply the product of powers rule to add the exponents. The product is not in scientific notation because the coefficient is greater than 10. Change the coefficient by moving the decimal one place to the left and increasing the exponent by one.

Answers

Answer 1

Yes that is correct

The answer to the above is

2.144 * 10^12

Answer 2

In scientific notation the product is written as [tex](2.144)\times10^{12}[/tex].

Given,

Two scientific notation values are [tex]6.7\times10^6[/tex] and [tex]3.2 \times10^5[/tex].

We have to explain the steps to find the product of these values.

Scientific notation:

Scientific notation is a widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10.

For the product of the above values we multiply coefficients separately like

[tex](6.7\times3.2=21.44)[/tex]

and powers of 10 separately

[tex](10^6\times10^5=10^{11} )[/tex].

So,

[tex]6.7\times10^6 \times 3.2\times10^5=(6.7\times3.2)\times(10^6\times10^5)[/tex].

[tex]6.7\times10^6 \times 3.2\times10^5=(21.44)\times10^{11}[/tex]

Or, in scientific notation form,

[tex]6.7\times10^6 \times 3.2\times10^5=(2.144)\times10^{12}[/tex].

Hence, in scientific notation the product is written as [tex](2.144)\times10^{12}[/tex].

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Related Questions

the system of equations n= 2p+3 and n= 5+p is graphed what is the solution to the system of equations

Answers

It isn't graphed anywhere I can see it. If you can see the graph, read the coordinates of the point of intersection.

.. (p, n) = (2, 7)

The solution is n = 7 and p = 2

Step-by-step explanation:

Graph is not given.

We have

n= 2 p+3

and

n= 5+p

That is

2 p+3 = 5 + p

p = 5 - 3

p = 2

Substituting in n= 5+p

n = 5 + 2 = 7

So the solution is n = 7 and p = 2

find the domain of the following function below. f(x)=3x-5/2

Answers

The domain of the function would be all real numbers. (-infinity, +infinity).
The domain of a linear function is asking what are the x values and because it is a line, it goes in both directions forever.

The domain is:
[tex] - \infty,\infty[/tex]
This is because there are no Real numbers that cause the function to be undefined.

if 0.75 pounds of chicken cost $2.10, how much does the chicken cost per pound?

Answers

$2.80 per pound for chicken.

A central angle measuring 150° intercepts an arc in a circle whose radius is 6. What is the area of the sector of the circle formed by this central angle? 15π 24π 30π 36π

Answers

Answer: 15

Step-by-step explanation: its 15

How many sequences of outcomes are possible if one rolls two identical dice 10 successive times?

Answers

6^(5)/5! = 6•7•8••9•10/2•3•4•5 = 7•4•9 = 252

So 252 is your final answer.
By the way I used • to represent multiplication

caculate the distances tarryn if she drives 7/8 mile each way to and from work, 5 days a week

Answers

[tex]\bf \stackrel{monday}{\cfrac{7}{8}}+\stackrel{tuesday}{\cfrac{7}{8}}+\stackrel{wednesday}{\cfrac{7}{8}}+\stackrel{thursday}{\cfrac{7}{8}}+\stackrel{friday}{\cfrac{7}{8}} \\\\\\ \cfrac{7}{8}\times 5\implies \cfrac{35}{8}\implies 4\frac{3}{8}[/tex]

She will cover 35/8 miles.

What is Unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

total distance in miles = 7/8 miles per day

So, in 5 days in a week.

She will cover

=5*7/8

=35/8 miles.

Hence, She will cover 35/8 miles.

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A massless beam supports two weights as shown. 685 n w l 4 l 4 l 2 l a b find w such that the supporting force at a is zero. answer in units of n.

Answers

Final answer:

To find the weight W such that the support force at A is zero, the principle of static equilibrium is used. By taking moments about point B and setting the sum of moments to zero, W is found to be 342.5 N.

Explanation:

The question requires the application of the principles of static equilibrium to find the unknown weight W that would set the supporting force at point A to zero. In static equilibrium, the sum of all forces and the sum of all torques (moments) about any point must be zero.

We can analyze the forces acting on the beam by taking moments about point B to find the value of W. Because the support at A is required to exert no force, we only consider the gravitational force due to the beam's weight and the weight applied at point B. By setting the sum of moments about B to zero, we can solve for W.

Using the conditions for static equilibrium:

Sum of vertical forces = 0

Sum of moments (torques) = 0

The moment leverage for the 685 N weight is at L/4, and for the unknown weight W, it is at L/2. Assuming the beam is massless the equation for the sum of moments around point B is:

(685 N) * (L/4) - (W) * (L/2) = 0

Solving for W:

W = (685 N) / 2

Thus, W is equal to 342.5 N.

a new truck that sells for $29000 depreciates 12% each year. Write a function that models the value of the truck

Answers

29000×0.88^time(years the trucks been waiting to sell)

The data set below consists of the scores of 15 students on a quiz. for this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? explain your thinking. 90 90 91 91 89 90 89 91 91 90 60 90 89 90 91

Answers

Standard deviation would be the best measurement of variance. Most of the numbers are between 91 and 89 and are thus very close together and most of the data would be within that small range. The outlier of 60 makes the rance variance go from 60 to 91 when all but 6 percent of the class can be represented between 91 and 89.

Final answer:

In the given data set, the standard deviation is the more appropriate measure of variation as it takes all the scores into account and provides a better insight into the data compared to the range.

Explanation:

In the given data set, both range and standard deviation can be used to measure the variation. However, the standard deviation might be a better measure in this instance. The standard deviation provides a numerical measure of the overall amount of variation in the data set. It indicates how far the values are from their average, or mean. In contrast, the range only provides the difference between the highest and lowest values, potentially overlooking the distribution of all the values.

When calculating the standard deviation for your dataset, it becomes evident that most scores are concentrated around the 90s, but there's one score dramatically lower at 60. This single score skews the data set and increases the standard deviation, indicating a larger spread around the mean than what might first be observed. As such, the standard deviation gives us a more detailed understanding of the spread within this set of quiz scores, making it the more useful measure in this case compared to the range.

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An investigation of the ability of a hybrid tomato plant to produce a certain protein found that the amount x of the protein produced in the plant had a mean of 109.9109.9 micrograms per gram of fresh weight with a standard deviation of 8.18.1. consider a random sample of n equals 60n=60 hybrid tomato plants and let x overbarx represent the sample mean amount of the protein produced. would it be expected to observe a value of x overbarx less than 107107 micrograms per gram of fresh weight? explain. consider an event with a probability less than 0.05 unlikely.

Answers

This is a Question of Statistics and an application of standard normal distribution.

Average amount(Mean) of protein produced by the plant = 109.9
Standard Deviation = 8.1

Size of the sample = 60
Average amount of protein for the sample is the same as that of population.So average amount of protein for the sample = 109.9
Standard Deviation of the sample = (Population Standard Deviation) divided by (square root of sample size)
So sample standard deviation = [tex] \frac{8.1}{ \sqrt{60} }=1.046 [/tex]

So, we are to find the probability of amount of protein being produced less than 107 for mean 109.9 and standard deviation 1.046.

First we convert this value to z score.

Z-score = [tex] \frac{107-109.9}{1.046}= -2.77[/tex]

Using z-table, converting this z score to probability we get:

Probability of mean being less than 107 = 0.0028

Since the probability of mean being less than 107 is less than 0.05. This event is highly unlikely.

Mary Ann is buying miniature cars. She wants to buy 20 cars total for a big race she and her friends are having. Black cars $6 dollars each. If she spends $104, how many white cars did she buy?

Answers

The answer will be 624 that's how many white cars she buyed HOPES this helps. :)

A triangular pyramid has a slant height of 13 inches. The triangular base has a perimeter of 23 inches and an area of 15 square inches. Find the surface area
Please show the work so that I understand it. Also please hurry as I need the answer soon.

Answers

A triangular pyramid has a triangle as its base and three triangle faces.
since we are asked to find the surface area of the triangular pyramid, we have to find the area of all three triangle faces and the base.

area of the base is given - 15 square inches
triangular face area - 1/2 x height x length
height of the triangle face is slant height - 13 inches

lets name the triangle faces as a,b and c
lets name the sides of the base triangle as A, B and C respectively
these sides are the lengths of the triangular faces.
area of face a - 1/2 * 13 inches * A
b - 1/2 * 13 * B
c - 1/2 * 13 * C
total area of the faces - (1/2 *13 * A) + (1/2 *13 * B) + ( 1/2 *13 * C)
= 1/2 * 13 (A+B+C)
A+ B+C = total perimeter of the base = 23 inches

therefore total surface area = area of base + total area of triangle faces
= 15 + (1/2 * 13 * 23)
= 15 + 149.5
total area = 164.5 sq.inches

what is 3x5x4x.............. can anyone answer asap pls

Answers

The answer is 60 I hope I helped u

What is the mixed number form for 56.4?

Answers

The answer would be 56 4/10, or 56 2/5 simplified, because .4 into fraction form is 4/10.
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It takes 484848 minutes for 777 people to paint 777 walls. How many minutes does it take 202020 people to paint 202020 walls?

Answers

Answer:

Approximately 391 minutes taken by 20 people to paint 20 walls.

Step-by-step explanation:

Given : It takes 48 minutes for 7 people to paint 7 walls.

To find : How many minutes does it take 20 people to paint 20 walls?

Solution :

7 people to paint 7 walls in 48 minutes.

So, 1 people to paint 7 walls in [tex]\frac{48}{7}[/tex] minutes.

and 1 people to paint 1 walls in [tex]\frac{48}{7\times 7}[/tex] minutes.

Now, We have to find minutes does it take 20 people to paint 20 walls.

20 walls will be painted in [tex]\frac{48\times 20}{7\times 7}[/tex] minutes.

20 people to paint 20 walls in [tex]\frac{48\times 20\times 20}{7\times 7}[/tex] minutes.

i.e. [tex]\frac{48\times 20\times 20}{7\times 7}=\frac{19200}{49}=391.83[/tex]

Therefore, Approximately 391 minutes taken by 20 people to paint 20 walls.

a bin size of __ is most appropriate for the data set shown above??

Answers

Im not sure but I think the answer is most likely...
D) 10.

Hope I helped :-)

ratio as a fraction 8 to 14

Answers

8/14, which can be reduced to 4/7 by dividing 8 by 2 and 14 by 2

So, your answer is 4/7

Hope I helped!

Let me know if you need anything else!

~ Zoe

fractions that name the same number are

Answers

the answer is equilivent

These are called "Equivalent Fractions."

Equivalent fractions may look different from each other, but all equivalent fractions have he same value.

Leia cuts congruent triangular patches with an area of 63 square centimeters from a rectangular piece of fabric that is 27 centimeters long and 21 centimeters wide. How many of the patches can Leia cut from 33 pieces of the fabric?

Answers

Leia can cut a total of 297 triangular patches from 33 pieces of fabric, with each piece yielding 9 patches.

To calculate how many triangular patches can Leia cut from 33 pieces of fabric, we first need to find out how many patches can be cut from a single piece of fabric. The area of each triangular patch is 63 square centimeters. The area of the fabric is length * width, which is 27 cm * 21 cm = 567 square centimeters.

Now, if we divide the area of the fabric by the area of one triangular patch, we get the number of patches per fabric piece: 567 cm2 / 63 cm2 = 9 patches per fabric piece.

Since Leia has 33 pieces of fabric, the total number of patches she can cut is 9 patches * 33 pieces = 297 patches.

Please help me with question 22

Answers

The rule is
(x,y) ---> (-x,y)
The x coordinate changes from negative to positive or vice versa.
The y coordinate stays the same.
This rule reflects the figure over the y axis.

Answer: Choice A

A particular security's default risk premium is 2 percent. for all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.5 percent. the security's liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. the security has no special covenants. calculate the security's equilibrium rate of return.

Answers

To solve this problem and calculate the security's equilibrium rate of return, you should sum the security's default risk premium (2.00%), the inflation risk premium (1.75%), the real risk-free rate (3.50%), the security's liquidity risk premium (0.25%) and the maturity risk premium (0.85%). So, you have:

ij*=2.00%+1.75%+3.50%+0.25%+0.85%
ij*=8.35%

The equilibrium rate of return is 8.3%.

The equilibrium rate of return of a security is the sum of the real risk-free rate, the inflation risk premium, the default risk premium, the liquidity risk premium, and the maturity risk premium.

In this case, the equilibrium rate of return is:

3.5% + 1.75% + 2% + 0.25% + 0.85% = 8.3%

So the answer is 8.3%.

Here is a breakdown of the calculation:

The real risk-free rate is the rate of return that investors would expect to earn on an investment with no risk of default or inflation.

The inflation risk premium is the additional return that investors demand to compensate them for the risk of inflation.

The default risk premium is the additional return that investors demand to compensate them for the risk of default on a security.

The liquidity risk premium is the additional return that investors demand to compensate them for the difficulty of selling a security quickly and easily.

The maturity risk premium is the additional return that investors demand to compensate them for the risk that the value of a security will decline as it approaches maturity.

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A girl throws a 2 kg rock with a net force of 6 N. What is the acceleration of the rock?

12m/s²

0.33m/s²

8m/s²

3m/s²

Answers

Answer:
acceleration = 3 m/s²

Explanation:
From Newton's second law:
Force = mass * acceleration
We are given that:
Force = 6 Newton
mass = 2 kg

Substitute with the givens in the above equation to get the acceleration as follows:
Force = mass * acceleration
6 = 2 * acceleration
acceleration = 6 / 2 = 3 m/s²

Hope this helps :)

Omar owns a sandwich shop, and his best selling sandwich is the BLT. When making BLT sandwiches, it takes of a pound of bacon to make 4 sandwiches. He uses pounds of bacon for every 2 tomatoes used and 5 tomatoes for every full head of lettuce used.
If Omar is making enough BLT sandwiches to use 2 full heads of lettuce, then he is going to use pounds of bacon and will make a total of BLT sandwiches.

Answers

Final answer:

When making enough BLT sandwiches to use 2 full heads of lettuce, Omar will be using 2.5 pounds of bacon and will end up making a total of 40 BLT sandwiches.

Explanation:

The subject of this question is Mathematics, specifically ratios and proportions. Given that Omar uses one full head of lettuce for every 5 tomatoes, for 2 heads of lettuce, he will use 10 tomatoes (2*5). Since he uses 1/2 pound of bacon for every 2 tomatoes, then for 10 tomatoes, he will need 2.5 pounds of bacon (10/2*0.5). Finally, since it takes 1/4 pound of bacon to make 4 sandwiches, with 2.5 pounds of bacon he will make 40 sandwiches (2.5/0.25*4). Therefore, Omar will use 2.5 pounds of bacon and make a total of 40 BLT sandwiches.

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A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent? An image shows the tent, the staked rope, and the measurements as a right triangle. The height of the triangle is unknown. The base of the triangle is 6 feet. The hypotenuse is 8 feet.

Answers

To answer this you can use the Pythagorean Theorem. It states that a squared plus b squares equals c squared. C is the length of the hypotenuse and a and b are the other 2 sides. Please see the attached work to see how to answer this. The approximate height of the tent is 5.3 feet.

The support given to the tent forms a right triangle.

The height of the tent is 5.3 ft

The given parameters are:

[tex]\mathbf{Base = 6}[/tex]

[tex]\mathbf{Hypotenuse= 8}[/tex]

The height is calculated as follows:

[tex]\mathbf{Hypotenuse^2 = Base^2 + Height^2}[/tex]

Substitute known values

[tex]\mathbf{8^2 = 6^2 + Height^2}[/tex]

This gives

[tex]\mathbf{64 = 36 + Height^2}[/tex]

Collect like terms

[tex]\mathbf{Height^2 = 64 - 36 }[/tex]

[tex]\mathbf{Height^2 = 28 }[/tex]

Take square roots

[tex]\mathbf{Height = 5.3 }[/tex]

Hence, the height of the tent is 5.3 ft

Answers

First the function f(x) is multiplied by -3. This involves 2 changes:

a) Multiplication by 3
This implies dilation

b) Multiplication by -1
This implies reflection of function over x-axis

Next x is replaced by x+ 3. This means the function is shifted to left by 3 units.

So this overall transformation results in following 3 changes:
Horizontal Translation, Dilation and Reflection along x-axis

Answer:

Horizontal Translation, Dilation and Reflection along y-axis

Step-by-step explanation:

what is (½)3. ???????

Answers

It is hard to tell your precise intention. Choose the appropriate interpretation.

[tex] \frac{1}{2} \times 3 = \frac{1 \times 3}{2} = \frac{3}{2} = 1\frac{1}{2}[/tex]

[tex] (\frac{1}{2})^{3} = \frac{1^{3}}{2^{3}} = \frac{1}{8}[/tex]

A rectangular prism has a length of 114 centimeters, a width of 4 centimeters, and a height of 314 centimeters.

What is the volume of the prism?

Enter your answer in the box as a simplified mixed number or a decimal.

cm³

Answers

Hello!
----------
The volume of the prism is 143184 cm^3
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WORK: 114*4=456*314=143184
----------
Have a great day!

Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x − 1 , y = 0, x = 9; about the x-axis v = incorrect: your answer is incorrect.4

Answers

Consider this option (there are 2 ways in the attachment).

Write the rate using fraction form. Lisa ran 15 laps in 5 mins

Answers

3/1 is the answer

3laps in 1minute

15 over five i hoped it helped

according to a meteorologist rain gauge 2.785 centimeters of rain fell. which shows a way to represent the 7 in this number

Answers

This is one way.
7 * 10^-1
Hope that's right.
Another way is 7/10

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