What is the quotient of 1.892 x 10^8 and 4.3 x 10^3 expressed in scientific notation?​

Find the midpoint of each pair of points, and then take the average of those midpoints to find the center pc. The radius r is the distance from pc to any of the given points. To find the unit normal vector n, take the cross product of any two vectors between the given points and pc.

To find the center pc, the radius r, and the unit normal vector n of the circle that goes through the three points p1=(5,0,7), p2=(1,3,6), and p3=(7,5,4) in 3D space, follow these steps:

1. Find the midpoint of each pair of points:

Midpoint of p1 and p2 = (3,1.5,6.5)

Midpoint of p2 and p3 = (4,4,5)

Midpoint of p3 and p1 = (6,2.5,5.5)

2. Take the average of the three midpoints to find the center pc:

pc = (4.33, 2.83, 6.17)

3. Calculate the radius r as the distance from pc to any of the given points:

r = √((5-4.33)2+(0-2.83)2+(7-6.17)2)

r = 2.66

4. To find the unit normal vector n, take the cross product of any two vectors between the given points and pc:

v1 = (5-4.33, 0-2.83, 7-6.17)

v2 = (1-4.33, 3-2.83, 6-6.17)

n = v1 x v2

n = (-11.67, 5.67, -7.33)

n = (-0.79, 0.37, -0.48)

Learn more about average here

https://brainly.com/question/2906096

#SPJ4

Thus, Tony runs at a speed of 13 feet per second, Zach runs at a speed of 12.87 feet per second, Ron runs at a speed of 10 feet per second, and Liz runs at a speed of 9.95 feet per second.

Tony runs at a speed of 13 feet per second, which means he covers a distance of 13 feet in one second.

Zach, on the other hand, runs 296 feet in 23 seconds, so we need to calculate his speed. To do that, we divide the distance by the time, which gives us 12.87 feet per second.

Ron runs one mile in 527 seconds, which is equivalent to 5,280 feet. Therefore, his speed is 10 feet per second, which is the same as running at a pace of 6 minutes per mile. Finally, Liz runs 597 feet in one minute, so her speed is 9.95 feet per second.

In summary, Tony runs at a speed of 13 feet per second, Zach runs at a speed of 12.87 feet per second, Ron runs at a speed of 10 feet per second, and Liz runs at a speed of 9.95 feet per second.

It's important to note that the distances and times given in these examples are specific to each person and may vary depending on the circumstances.

However, by calculating their speeds, we can compare their performances and determine who is running faster or slower than the others.

Know more about the speed

https://brainly.com/question/26862717

#SPJ11

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1

As the project progresses, the actual finish times (AFs) of completed activities play a crucial role in determining various aspects of the project schedule.

The AFs are used to calculate the earliest start and earliest finish times for the remaining activities in the network diagram. These calculations are based on the dependencies between activities and the actual durations of completed activities.

By considering the AFs, the project team can determine the earliest possible start and finish times for the remaining activities, taking into account the sequence of activities and any imposed constraints. This information helps in managing the project schedule and identifying any potential delays or critical paths.

Know more about actual finish times here:

https://brainly.com/question/31925763

#SPJ11

A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.

In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.

Based on the information provided above, we can logically deduce the following equation:

22 . a = 242

22 × a = 242

By applying the division property of equality, we have the following:

a = 242/22

a = 11.

Read more on subtraction property of equality here: brainly.com/question/16993368

#SPJ1

Answer:

if we have 3, 2 pound bricks we have 6 pounds

1 pound = 16 ounces

16 × 6 = 96 ounces

96 ÷ 4 = 24

only 24 people got bricks so he needs to give 4 people more

4 ounces each for 4 people is 16 ounces

answer: 16 ounces

Answer:

The function that can be used to describe the number (n) of bacteria after 2 minutes is;

\(P = 4 \cdot e^{\left(\dfrac{ln(32)}{5} \times 2\right)} \approx 4 \cdot e^{\left(0.693\times 2\right)}\)

Step-by-step explanation:

The data in the table are presented as follows;

Number of bacteria; 4, 128, 4,096, 131,072

Number of minutes from initial state; 0, 5, 10, 15

The general equation for population growth is presented as follows;

\(P = P_0 \cdot e^{r\cdot t}\)

Where;

P = The population after 't' minutes

P₀ = The initial population

r = The population growth rate

t = The time taken for the growth in population numbers

At t =  minutes. we have;

\(4 = P_0 \cdot e^{r\times0} = P_0\)

∴ P₀ = 4

At t = 5, we have;

\(128 = 4 \cdot e^{r\times 5}\)

\(\therefore e^{r\times 5} = \dfrac{128}{4} = 32\)

\(ln\left(e^{r\times 5}\right) = ln(32)\)

∴ r × 5 = ㏑(32)

r = ln(32)/5 ≈ 0.693

The number (n) of bacteria after 2 minutes is therefore;

\(P = 4 \cdot e^{\left(\dfrac{ln(32)}{5} \times 2\right)} \approx 4 \cdot e^{\left(0.693\times 2\right)}\)

A confidence interval cannot instantly lead to rejecting the null hypothesis in a hypothesis test. In the given case the null hypothesis is either rejected or rejected based on test statistics.

α = 0.05

μ = 2

If the confidence interval is 1.0 or 2.0, then the null hypothesis value of 2 drops exceeds the interval, this makes the data contradict the null hypothesis and may reject the null hypothesis.

This alone would not be good to decline the null theory - the conclusion to reject or not reject the null hypothesis is determined by the test statistic and the alternate p-value.

To learn more about Hypothesis

https://brainly.com/question/28920252

#SPJ4

False. The statement is not entirely accurate. While significantly different sample variances can impact the assumptions of a t-test, it does not necessarily mean that a t-test cannot be conducted.

In traditional t-tests, there is an assumption of equal variances between the compared groups or populations. This assumption is known as the assumption of homogeneity of variances. If the sample variances are significantly different, it violates this assumption.

However, there are alternative versions of the t-test that can be used when the variances are not equal, such as the Welch's t-test or the modified t-test. These tests do not assume equal variances and can be applied when the variances are significantly different.

Therefore, it is possible to conduct a t-test even when the sample variances are significantly different, using appropriate modifications to the test. However, it is essential to consider the validity and appropriateness of the chosen test based on the specific circumstances and assumptions of the data.

Learn more about t-test here:

https://brainly.com/question/30818311

#SPJ11

Answer:

The equation for the relationship is \(y=\frac{7}{2} \times x\).

Step-by-step explanation:

Given that point \((x,y)=(6,21)\) is part of a direct relationship. That is:

\(y \ \infty \ x\)

\(y=k\times x\) (1)

Where \(k\) is the proportionality constant.

If we know that \(x=6\) and \(y=21\), then the proportionality constant is:

\(k=\dfrac{y}{x}\)

\(k=\dfrac{21}{6}\)

\(k=\dfrac{7}{2}\)

Lastly, the equation for the relationship is \(y=\frac{7}{2} \times x\).

Answer:

Diamond has to pay more

Step-by-step explanation:

I got it correct

Answer:

jamal and then diamond

Step-by-step explanation:

right on edge

The area of figure composing a parallelogram and two semicircles is 399.06 units².

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

The base of the parallelogram is = 18 units

The height of the parallelogram is = 11 units

The area of a parallelogram is given as -

Area = Base × Height

Area = 18 × 11

Area = 198 units²

The diameter of the semicircle is = 16 units

The radius of semicircle is = 8 units

The area of the semicircle is given as -

Area = (1/2)πr²

Area = (1/2)π(8)²

Area = (1/2)π × 64

Area = 32π units²

The total area of the figure is given as -

Total Area = Area of Parallelogram + 2 (Area of semi-circle)

Total Area = 198 + 2(32)π

Total Area = 198 + 64π

Total Area = 198 + 201.06

Total Area = 399.06 units²

Therefore, the area of the figure is 399.06 units².

To learn more about parallelogram from the given link

https://brainly.com/question/3050890

#SPJ1

Answer:

B

Step-by-step explanation:

i took the quiz

Answer:

The answer is B 18ft

Step-by-step explanation: I took the test and i got 100%

Answer:

1.67 gallons

Step-by-step explanation:

Given that:

Original mixture contains 80% detergent and 20% water in a 15 gallon bucket.

New Mixture to contain 60% detergent and 40% water of 5 gallon bucket.

To find:

Volume of Pure water to be added to each 5 gallon bucket to obtain the new mixture.

Solution:

First of all, let us calculate the answer by adding pure water to 15 gallon bucket.

Let the number of gallon of water to be added = \(x\)

New volume = (15+\(x\)) gallons

Now, let us compare the number of gallons of water in the mixture before and after.

\(15\times 20\% + x = (15+x)\times 40\%\\\Rightarrow (3+x)\times 5 = (15+x)\times 2\\\Rightarrow 15+5x=30+2x\\\Rightarrow 3x=15\\\Rightarrow x =5\ gallons\)

Therefore, to a 15 gallon bucket (80% detergent and 20% water)of detergent mixture, if we add 5 gallons of pure water , it will become 60% detergent and 40% water.

To a 5 gallon bucket, the number of gallons of water to be added = \(\frac{5}{3} =\bold{1.67\ gallons}\)

The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

Learn more about Dilation:

https://brainly.com/question/29449871

#SPJ4

The value of 1 cm : 1 km is 6.66666667e-7

The ratio expression is given as:

1 cm : 15 km

Convert km to cm

So, we have

1 cm : 1 km = 1 cm : 1500000 cm

Express as quotient

1 cm : 1 km = 1 cm/1500000 cm

Evaluate the quotient

1 cm : 1 km = 6.66666667e-7

Hence, the value of 1 cm : 1 km is 6.66666667e-7

Read more about ratios at:

https://brainly.com/question/2328454

#SPJ1

a) When 44 is divided by 8, the quotient is the number of times 8 can be subtracted from 44 without going below zero.

44 divided by 8 gives a quotient of 5 with a remainder of 4. Therefore, the quotient is 5 and the remainder is 4.

b) When 777 is divided by 21, we find the quotient and remainder as follows:

777 divided by 21 gives a quotient of 37 with a remainder of 0. Therefore, the quotient is 37 and the remainder is 0.

c) When -123 is divided by 19, we find the quotient and remainder as follows:

-123 divided by 19 gives a quotient of -6 with a remainder of 9. Therefore, the quotient is -6 and the remainder is 9.

To know more about quotient refer here:

https://brainly.com/question/16134410

#SPJ11

x intercept(y=0)

4y-3x=108

4×0-3x=108

-3x=108

x=108/-3

x=-36

y intercept(x=0)

4y-3×0=108

4y=108

y=108/4

y=27

You would first have to turn the fraction into an improper fraction to find the reciprocal of the fraction.

Reciprocal means reverse, so reverse the fraction of 1/7 to get 7/1.

Answer:

D 49

Step-by-step explanation:

just did it

Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

Answer:

The Answer is D

Step-by-step explanation:

Given data:

The given scale is 2 cm= 6 ft.

The given height of the tree is h= 7.8 cm.

The given scale can be written as,

The actual height of the tree is,

Thus, the actual height of the tree is 23.4 ft.

Answer:

A

Step-by-step explanation:

sub each value into x,the value is the minutes,that is, 1,2,3,....and so on to get the answer (gallons of water)

Answer:

We can write 360 distinct passwords using the numbers 1, 2, 3, 4, 5, and 6.

Step-by-step explanation:

We have to find how many passwords with 4 different digits can we write with the numbers 1, 2, 3, 4, 5, and 6.

Firstly, it must be known here that to calculate the above situation we have to use Permutation and not combination because here the order of the numbers in a password matter.

Since we are given six numbers (1, 2, 3, 4, 5, and 6) and have to make 4 different digits passwords.

So, the number of passwords with 4 different digits we can write = \(6 \times 5 \times 4 \times 3\)  = 360 possibilities.

Hence, we can write 360 distinct passwords using the numbers 1, 2, 3, 4, 5, and 6.

If each consumer demands one item of groceries and faces a travel cost of $12 per kilometer. BetaMarket chooses the price of $33.33 in equilibrium.

AlphaMart sells groceries at the west end of Main Street, a street that is one kilometer long. AlphaMart competes with BetaMarket, which is located at the east end of the street. AlphaMart and BetaMarket sell groceries that are identical in every respect, apart from the locations of the two stores. The marginal cost of an item of groceries is $3 for both retailers.

Main Street is home to 200 consumers; the consumers are evenly spaced along the street. Each consumer demands one item of groceries and faces a travel cost of $12 per kilometer. To calculate the equilibrium price of BetaMarket, we first need to find out the quantity demanded at each price point.

The quantity demanded for each price point can be found by subtracting the number of consumers who are closer to AlphaMart than to BetaMarket from the total number of consumers. Let the price charged by BetaMarket be P. If BetaMarket charges P, then the demand for BetaMarket's groceries is given by:

QB = 200/2 - 1/2 (P + 12) = 100 - 1/2 (P + 12)

QB = 100 - 1/2P - 6

We can now write down BetaMarket's profit function as:

πB = QB(P - 3) = (100 - 1/2P - 6)(P - 3)

πB = 100P - 3/2P² - 309

From this, we can find the first-order condition for profit maximization by differentiating the profit function with respect to P and setting it equal to zero:

∂πB/∂P = 100 - 3P = 0P = 100/3

Thus, BetaMarket chooses to set the price at $33.33 in equilibrium.

You can learn more about equilibrium at: brainly.com/question/30694482

#SPJ11

A record's key field is the field whose contents make the record unique among all records in a file.

In computer science and database management, a record's key field, also known as a primary key, is a unique identifier that is used to distinguish one record from another in a database. A key field can be a single field or a combination of fields that uniquely identify a record.

For example, in a database of employee records, the social security number or employee ID number may be used as the key field to identify each employee record. This key field must be unique for each record in the database, and it is typically indexed to allow for faster searching and sorting of records.

The key field plays a crucial role in ensuring data integrity and consistency in a database. It is used to enforce data constraints and relationships between tables, and it is often used as a reference by other tables in a database.

In summary, a record's key field is an important component of a database that uniquely identifies each record and allows for efficient management and organization of data.

To know more about database management, refer here:

https://brainly.com/question/13467952

#SPJ11