The radius of a circular baking tray is 6 cm. Find its area correct to 2 decimal places. Use the π button on your calculator for π in your calculations.

Step-by-step explanation:

r=14/7=28/14=56/28=2    

So it is geometric

By using this equation:  

a(n)=a1*(r)^(n-1)

and we have a(1)=7 , r=2

explicit equation : a(n)=7*(2)^(n-1)

hope this helps

Answer:

El procedimiento para hallar el MCD de 12, 20, 36:Descomponer los números en su factores primos

12 2 6 2 3 3 1

   20 2 10 2 5 5 1

 36 2 18 2 9 3 3 31

Factores primos de 12 = 22 . 3

Factores primos de 20 = 22 . 5

Factores primos de 36 = 22.32

MCD = 21 = 2

Step-by-step explanation:

Answer:

X is 9

X+6x-15=4x+12

3x-15=12

3x=27

x=9

SO x is 9

Answer:

x=9

Step-by-step explanation:

x + 3(2x - 5) = 4x – 12

distrubute left side

3 times 2x; 3 times -5

x+6x-15=4x-12

add like terms

x+6x

7x-15=4x-12

get all variables on the same side

7x-15=4x-12

-4x -4x

3x-15=12

add 15 to both sides

3x-15=12

+15 +15

3x=27

divide by 3 on both sides

3x/3=27/3

x=9

Answer:B. y=0.5x+0.3

Step-by-step explanation:a. p. e. x.

The slope of the points is closer to 0.5 thus y = 0.5x + 1.2 will be the best approximation thus option (B) is correct.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given points,

Let's take two-point (1,1)  and (2,1.5)

The slope associated with the above points will be as,

(1.5 - 1)/(2 - 1) = 0.5

Thus, the line will be y = 0.5x + 0.3

Hence "The slope of the points is closer to 0.5 thus y = 0.5x + 1.2 will be the best approximation".

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Answer:11

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I will assume 16 is tangent.... then this is a right triangle

Pyhtagorean theorem

(8+x)^2 = x^2 + 16^2

x^2 + 16x + 64   = x^2 + 256

16x = 192

x = 12 units

To compute the surface integral of a scalar-valued function f over a cone, we need to parameterize the cone's surface, evaluate f at each point, and integrate the product of f and the surface element.

To compute the surface integral of a scalar-valued function f over a cone using an explicit description of the cone, we need to parameterize the surface of the cone.

We need to define the cone explicitly by specifying its equation in terms of the variables x, y, and z. For example, a cone can be described by the equation z = k√(x² + y²), where k is a constant.

We need to parameterize the surface of the cone using two parameters, typically denoted by u and v. This involves expressing x, y, and z in terms of u and v.

Once we have the parameterization of the cone, we can compute the surface integral by evaluating the function f at each point on the surface and multiplying it by the magnitude of the surface element, which is given by the cross product of the partial derivatives of the parameterization.

We integrate the product of f and the surface element over the range of the parameters u and v to obtain the surface integral.

To compute the surface integral of a scalar-valued function f over a cone, we need to parameterize the cone's surface, evaluate f at each point, and integrate the product of f and the surface element.

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Answer:

$210.25

Step-by-step explanation:

86,000 :)

hope it helped!

Answer:

Find the least common factor.

Step-by-step explanation:

For example, you need to add 4/5 and 4/6.

5 = 1, 5, 10, 15, 20, 25, 30.

6 = 1, 6, 12, 18, 24, 30.

The least common factor is 30.

Now, multiply 5 to get 30, and 6 to get 30. There will be a common denominator.

5 x 6 = 30

6 x 5 = 30

4/5 x 6/6 = 24/30

4/6 x 5/5 = 20/30

Now, just add.

24 + 20 = 44.

The answer is 44/30.

For this case we have the following variables:

x: represents time, in seconds at the start of the test.

y: represents the speed, in miles per hour.

We have then that:

x = 0 ---> y = 0

x = 12 ---> y = 0

Answer:

the electric car is not moving at 0 seconds and 12 seconds

I hope this helps!

the electric car is not moving at 0 seconds and 12 seconds

I hope this helps!

Answer:

no you can only use side side side when all of your triangles are equilateral triangles

Step-by-step explanation:

A Gantt chart is indeed a specialized chart type. Basic chart types include bar charts, line charts, and pie charts, which are commonly used for visualizing data. Specialized chart types, such as Gantt charts, serve more specific purposes.

Yes, there are indeed basic chart types as well as specialized chart types. Basic chart types include things like bar graphs, line graphs, and pie charts, while specialized chart types are designed for more specific purposes, such as organizational charts, flowcharts, and Gantt charts.

In particular, a Gantt chart is a specialized chart type that is commonly used in project management to help visualize the tasks, milestones, and dependencies involved in a project. It is designed to show a timeline of when each task or activity needs to be completed, as well as how long it will take and what resources will be needed.

Overall, while basic chart types are great for general data visualization purposes, specialized chart types like Gantt charts can be incredibly useful for specific tasks or industries, and can help users to more effectively communicate and manage complex information.

A Gantt chart is indeed a specialized chart type. Basic chart types include bar charts, line charts, and pie charts, which are commonly used for visualizing data. Specialized chart types, such as Gantt charts, serve more specific purposes. A Gantt chart is designed for project management and helps visualize a project's timeline, tasks, and progress, making it easier to manage and allocate resources.

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The difference between groups and the sample size makes the results of a study statistically significant.

Statistical significance is a measure of the likelihood that the results of a study are not due to chance. In order for a result to be statistically significant, it must meet two criteria:

The difference between groups must be large enough to be unlikely to occur by chance. This is typically assessed using a statistical test such as a t-test or an ANOVA.

The result of the test is expressed as a p-value, which represents the probability of obtaining the observed results if there were no true difference between groups. A p-value of less than 0.05 (or 5%) is generally considered to be statistically significant.

The sample size must be large enough to reduce the possibility of sampling error. A larger sample size generally increases the power of a study, making it more likely to detect a true effect.

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The point-slope equation of the line is y - 8 = 3(x - 6)

The points are given as:

(x1, y1) = (6, 8)

The slope is given as:

m= 3

The equation is then calculated as:

y - y1 = m(x - x1)

This gives

y - 8 = 3(x - 6)

Hence, the point-slope equation of the line is y - 8 = 3(x - 6)

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Answer:

The answer is B

Step-by-step explanation:

The system of equations has option (iii) infinitely many solutions

The given system of equations is:

2x+ 2y − 2z = 2 (Eq. 1)

2x + 3y + az = 3 (Eq. 2)

x + ay + 3z = 2 (Eq. 3)

We can write this system in matrix form as:

\(\begin{bmatrix} 2 & 2 & -2 \\ 2 & 3 & a \\ 1 & a & 3 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix} =\begin{bmatrix} 2 \\ 3 \\ 2 \end{bmatrix}\)

To determine the values of a for which the system has no solutions, a unique solution, or infinitely many solutions, we can use the method of Gaussian elimination.

Let's apply this method to the given system of equations:

\(\begin{bmatrix} 2 & 2 & -2 & 2\\ 2 & 3 & a & 3 \\ 1 & a & 3 & 2 \end{bmatrix}\)

R2 → R2 - R1:

\(\begin{bmatrix} 2 & 2 & -2 & 2\\ 0 & 1 & a+2 & 1 \\ 1 & a & 3 & 2 \end{bmatrix}\)

R3 → R3 - (1/2)R1:

\(\begin{bmatrix} 2 & 2 & -2 & 2\\ 0 & 1 & a+2 & 1 \\ 0 & a-1 & 4 & 1 \end{bmatrix}\)

R1 → R1 - R2:

\(\begin{bmatrix} 2 & 1 & -4-a & 1\\ 0 & 1 & a+2 & 1 \\ 0 & a-1 & 4 & 1 \end{bmatrix}\)

R1 → (1/2)R1:

\(\begin{bmatrix} 1 & 1/2 & -(4+a)/2 & 1/2\\ 0 & 1 & a+2 & 1 \\ 0 & a-1 & 4 & 1 \end{bmatrix}\)

R1 → R1 - (1/2)R2:

\(\begin{bmatrix} 1 & 0 & -(2a+8)/(2a+2) & (1-a)/(2a+2)\\0 & 1 & a+2 & 1 \\ 0 & a-1 & 4 & 1 \end{bmatrix}\)

R3 → R3 + (a-1)R2:

\(\begin{bmatrix} 1 & 0 & -(2a+8)/(2a+2) & (1-a)/(2a+2)\\ 0 & 1 & a+2 & 1 \\ 0 & 0 & 2a+8 & a+1 \end{bmatrix}\)

Now, we can see that the row echelon form of the augmented matrix has no row of zeros, and the number of non-zero rows (3) is equal to the number of variables (3) if and only if (iff) the coefficient of the z-variable is not zero. In this case, the coefficient of the z-variable is 2a+8, which is zero iff a=-4. Therefore, we have the following three cases:

(i) If a = -4, then the coefficient of the z-variable in the row echelon form is zero, and thus the system has no solutions.

(ii) If a is not equal to -4 and the row echelon form has no row of zeros and the number of non-zero rows is equal to the number of variables, then the system has a unique solution.

(iii) If a is not equal to -4 and the row echelon form has no row of zeros and the number of non-zero rows is less than the number of variables, then the system has infinitely many solutions.

Therefore, the correct option is (iii).

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Answer:

48 in.

Step-by-step explanation:

We know that the dimensions are 144 by 96.

144  = 96(quotient) + remainder,

144 = 96(1) + 48

Solution: side of largest square = 48

Answer:

a. 1.26

b. 0.1038

Step-by-step explanation:

The p-value is 1.0000 (rounded to four decimal places). This means that we fail to reject the null hypothesis, which in this case would be that the population mean is equal to the sample mean of 26.2.

To find the test statistic, we need to use the formula:

test statistic = (sample mean - population mean) / (standard deviation / square root of sample size)

Since the population standard deviation is given as 6, we can plug in the values:

test statistic = (26.2 - population mean) / (6 / √40)

To find the population mean, we can use the fact that the sample mean is an unbiased estimator of the population mean, so:

population mean = sample mean = 26.2

Plugging in the values, we get:

test statistic = (26.2 - 26.2) / (6 / √40) = 0

The test statistic is 0.

To find the p-value, we need to use a t-distribution table or calculator. Since we have a sample size of 40, we can use the t-distribution with 39 degrees of freedom.

Using a calculator or table, we can find that the area to the right of 0 (since the test statistic is 0) is 0.5. Since this is a two-tailed test, we need to double this value to get the p-value:

p-value = 2 * 0.5 = 1.0000
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Answer:

3

Step-by-step explanation:

the bracket just makes it a positive number so if it was 3-6 then it would still be 3 because of brackets

The number of possible sequences with exactly seven heads from 20 coin tosses is 77520.

To find the number of sequences with exactly seven heads, we can use the binomial distribution formula:

C(n,k) = n!/(k!(n-k)!)

Where n is the total number of coin tosses (20), and k is the number of heads (7).

Therefore, the number of sequences with exactly seven heads is:

C(20,7) = 20!/(7!*(20-7)!) = 77520

So there are 77,520 possible sequences of heads and tails that have exactly seven heads when a coin is tossed 20 times.

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Answer:

40

Step-by-step explanation:

Sum of all angles of triangle = 180°

∠W + ∠X + ∠Y = 180

10x + 17 + 2x - 9 + 3x + 7 = 180

10x + 2x  +3x + 17 - 9 + 7 = 180

Combine like terms

15x + 15 = 180

       15x = 180- 15

         15x = 165

            x = 165/15

x = 11

∠Y =  3x +7  = 3*11 + 7 = 33 + 7 = 40

Answer:

X is 11 and after substitution y is 40

Answer:

slope of line is 3/5

Step-by-step explanation:

slope is the ratio of the change in the y-values over the change in the x-values

in this problem, if you go from pt A to pt B, you rise by 3 and go to the right by 5, thus slope of 3/5

if you go from pt B to pt C, you rise by 6 and go to the right by 10

however, 6/10 can be reduced to 3/5

if you start at point (0,2) and rise by 3 and run to the right by 5 you are at point (5,5)

change in y-values is 5-2 or 3

change in x-values is 5-0 or 5

(5-2)/(5-0) = 3/5

answer : 0.0001982 in scientific notation = see picture

The distance between the two planes after 4 hours is approximately 150 km.

to find out how far apart the planes are after 4 hours, we can use the concept of vectors.

Let's start by finding the positions of the two planes after 4 hours.

The first plane flies at a speed of 110 km/h in a direction of 280°. To find its position after 4 hours, we can use the formula: distance = speed × time. So, the distance traveled by the first plane is 110 km/h × 4 hours = 440 km.

To determine the position of the first plane, we need to convert the direction (280°) into components. The x-component is given by: cos(280°) × distance = cos(280°) × 440 km. The y-component is given by: sin(280°) × distance = sin(280°) × 440 km.

Similarly, for the second plane, which flies at a speed of 250 km/h in a direction of 200°, the distance traveled after 4 hours is 250 km/h × 4 hours = 1000 km. To determine its position, we need to convert the direction (200°) into components. The x-component is given by: cos(200°) × distance = cos(200°) × 1000 km. The y-component is given by: sin(200°) × distance = sin(200°) × 1000 km.

Now, let's calculate the x and y components for both planes:

For the first plane:
x-component = cos(280°) × 440 km
y-component = sin(280°) × 440 km

For the second plane:
x-component = cos(200°) × 1000 km
y-component = sin(200°) × 1000 km

the distance between the two planes, we can use the distance formula, which is given by: distance = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the positions of the first and second planes respectively.

Now, substitute the values we calculated into the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)
distance = √((cos(200°) × 1000 km - cos(280°) × 440 km)^2 + (sin(200°) × 1000 km - sin(280°) × 440 km)^2)

After evaluating the above expression, the distance between the two planes after 4 hours is approximately 150 km.

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im pretty sure its 8.94

Answer:

y= 1.8955223

Step-by-step explanation:

Answer:

you spend ethier 3/10 or you spend 5/10

Step-by-step explanation:

try it. because u can only add or subtract with like denominators.

24 minutes are spent working on science homework.

Given,

time spend for homework is

4/5 hours = 4/5×60 = 0.8×60 = 48 minutes

if 1/2 of this time is spent on working science homework

48×1/2= 48×0.5= 24 minutes

Hence, the total minutes spent, working on science homework is 24 minutes.

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The dimensions of the rectangle that minimize the perimeter are 18 feet by 18 feet.

To find the dimensions of a rectangle with an area of 324 square feet and the smallest possible perimeter, we need to minimize the perimeter while maintaining the given area. The area of a rectangle is given by the formula:

Area = length × width

Now, let's find the dimensions that result in the smallest perimeter.


The dimensions of the rectangle that minimize the perimeter are 18 feet by 18 feet.

1. We know the area is 324 square feet, so we can write the equation:

  324 = length × width

2. To minimize the perimeter, the rectangle should be as close to a square as possible because a square has the smallest possible perimeter for a given area.

3. Find the factors of 324 to determine which pair of numbers is closest to being equal. The factors are:

  1×324, 2×162, 3×108, 4×81, 6×54, 9×36, 12×27, and 18×18

4. Among these factor pairs, 18×18 is the closest to being equal, so the dimensions are 18 feet by 18 feet.

5. The smallest possible perimeter is achieved when the rectangle is a square with side lengths of 18 feet. The perimeter can be calculated as:

  Perimeter = 2 × (length + width) = 2 × (18 + 18) = 2 × 36 = 72 feet

So, the dimensions of the rectangle with an area of 324 square feet and the smallest possible perimeter are 18 feet by 18 feet, and the perimeter is 72 feet.

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Answer:

16 it's answer

Step-by-step explanation:

√121 + ³√125

11+5

16