Peter creates balloon animals for different events. He has 644 balloons. He wants to use
the same number of balloons for each of 28 events. How many balloons can Peter use at
each event?

The required answer is  a 5 5 matrix is a diagonalizable.

Explanation,

Yes, the matrix a is diagonalizable. This is because if a 5x5 matrix has two eigenvalues, and one eigenspace is three-dimensional while the other is two-dimensional, then the matrix is guaranteed to be diagonalizable. This is because the sum of the dimensions of the One eigenspace is three-dimensional, and the other eigenspace is two-dimensional. A matrix is diagonalizable if the sum of the dimensions of its eigenspaces is equal to the size of the matrix. In this case, the dimensions of the eigenspaces are 3 and 2, which add up to 5. Since the size of the matrix A is also 5 the sum of the dimensions of the eigenspaces is equal to the size of the matrix. Therefore, matrix A is diagonalizable. must equal the size of the matrix , and because the eigenvectors associated with each eigenvalue form a linearly independent set, it is possible to diagonalize the matrix using those eigenvectors. Therefore, a is diagonalizable because the dimensions of its eigenspaces add up to 5 and its eigenvectors are linearly independent.

The study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices.

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The 95% confidence interval for the average starting salary of all accountants in New York City is:

($47,589 - $7,285) to ($47,589 + $7,285)

or

$40,304 to $54,874

To construct a 95% confidence interval for the average starting salary of all accountants in New York City, we can use the formula:

\(CI = x $ \pm t*(s/\sqrt{n)\)

where x is the sample mean, s is the sample standard deviation, n is the sample size, t is the t-value from the t-distribution with n-1 degrees of freedom and a 95% confidence level, and \($\pm\) represents the margin of error.

In this case, x = $47,589, s = $11,364, and n = 10. The t-value with 9 degrees of freedom and a 95% confidence level is approximately 2.262 (from a t-distribution table or a calculator).

Substituting the values into the formula, we get:

\(CI = $47,589 $\pm 2.262*($11,364/\sqrt{10)\)

Simplifying the expression, we get:

CI = $47,589 \($\pm\) $7,285

Therefore, the 95% confidence interval for the average starting salary of all accountants in New York City is:

($47,589 - $7,285) to ($47,589 + $7,285)

or

$40,304 to $54,874

We can be 95% confident that the true average starting salary of all accountants in New York City falls within this interval.

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Answer:

1/3

Step-by-step explanation:

The probability that a number greater than 2 is rolled is 4/6 {2, 3, 4 and 6} The probability that the coin lands on heads is 1/2

You can multiply 1/2 and 4/6 to find out the total number of possible outcomes: 1/2 × 4/6 = 4/12. This can be simplified to 1/3.

Hope this helps!

The surface area of that part of the plane 10x+7y+z=4 inside the elliptic cylinder x^2/25+y^2/9=1 is equal to πab, where a=5 and b=3. Therefore, the surface area is equal to 45π.

Total area on a three-dimensional shape's surface is known as surface area. The surface area of a cuboid with six rectangular faces can be calculated by adding the areas of each face. Alternatively, you can write down the cuboid's length, width, and height and use the formula surface area (SA)=2lw+2lh+2hw.

The general formula for a cube's surface area is as follows: The area of the base plus the area of the cube's vertical surfaces will add up to the cube's total surface area. The cube's total surface area is calculated using the formula 6a2, where an is the side length.

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Answer:12

Step-by-step explanation:

Area=1/2base xheight

(108×2)÷18

12

Answer:

\(height = 12 \: \: mm\)

Step-by-step explanation:

\(area = \frac{1}{2} \times height \times base \\ 108 = \frac{1}{2} \times h \times 18 \\ 108 = \frac{18h}{2} \\ 108 = 9h \\ \frac{108}{9} = \frac{9h}{9} \\ h = 12\)

hope this helps

brainliest appreciated

good luck! have a nice day!

The blue dot is at -3 on the number line.

In Mathematics, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0):

By critically observing the number line (see attachment), we can logically deduce that each interval represent 3 units. In this context, the blue dot is located 3 units to the left of zero (0);

Blue dot = 0 - 3

Blue dot = -3.

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Answer: Question 1 (x=-3 and y=2)

Step-by-step explanation:

Question 1

Subtract 5x from both sides of the equation

y=-13-5x

6x+6y=-6

then replace all occurrences of y with -13 - 5x in each equation

-24x -78=-6

solve or x in -24x - 78=-6

y=-3

y=-13 - 5x

replace all occurences of x with -3 in each equation

y=2

x=-3

By choosing the inner function g(x) = x and the outer function f(u) = sin(u), we obtain the composite function y = sin(x). Therefore, y = sin(x) is the correct choice for the given composite function y = f(g(x)).

The composite function is given as y = f(g(x)). We need to determine the inner function g(x) and the outer function f(u) such that y = f(g(x)).

In this case, we can choose the inner function as g(x) = x, meaning that there is no transformation or operation applied to x. Then, the outer function can be chosen as f(u) = sin(u).

By substituting g(x) = x into the outer function f(u) = sin(u), we obtain y = sin(g(x)), which simplifies to y = sin(x).

Therefore, the composite function y = sin(x) is derived by letting u = g(x) = x and y = f(u) = sin(u).

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Answer:

0.015252

Step-by-step explanation:

Multiply the two together using a calulator and you will get the same answer as me.

Have a great day!

Step-by-step explanation:

I guess this will help.

when

y=4/3x-1

Answer:

2x-11

Step-by-step explanation:

2 x X = 2x + 11

Answer: $10

Step-by-step explanation:

Angie buys = 1 software package and 1month of gameplay.

Kenny buys = 1 software package and 2 months of game play.

Cost of each software package = $30. Total cost = ​$90​

The total cost is the addition of what Kenny and Angie bought. This will be:

(1 SF + 1 G) + (1 SF + 2 G) = 90

where,

SF = software package = 30

G = game

(1 SF + 1 G) + (1 SF + 2 G) = 90

30 + 1G + 30 + 2G = 90

60 + 3G = 90

3G = 90 - 60

3G = 30

G = 30/3

G = 10

One month of game play cost $10

The given equation is,

On solving we get,

Thus the solution is, x = -4.

Thus, we can say that the system has exactly one real solution.

Option c is the correct answer.

Let (x,y) be an arbitrary point on the circle.

Then d = √[x-3)2 + (y-0)2] = √[x2 - 6x + 9 + y2]

Since x2 + y2 = 1, y2 = 1-x2.

So, d = √[x2 - 6x + 9 + 1 - x2]

     d = √(-6x+10)

Domain:  x is the x-coordinate of a point on the circle centered at (0,0) with radius 1.  So, -1≤x≤1.

             But, for d to be defined, we need -6x+10 ≥ 0.  So, x ≤ 5/3  (True for all x in [-1,1]).

             Domain = [-1,1]

Range:    -1 ≤ x ≤ 1   So, 6 ≥ -6x ≥ -6

                                    16 ≥ -6x+10 ≥ 4

                                     4 ≥ √(-6x+10) ≥ 2   That is, 2 ≤ d ≤4

              Range:  [2,4]

Step-by-step explanation:

Answer: the answer is 2 or C

-8/2 x -3/6

*Always do the recipical*

(-8 x -3) / (2 x 6)

-8 x -3= +24

2 x 6= 12

24/12= 2

The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that the expression is,

-8/2 x -3/6

The expression will be solved as below,

E = (-8 x -3) / (2 x 6)

The numerator will get reciprocal and multiplied to the denominator,

E = 24 / 12

Divide the number 24 by 12 and get the solution,

E = 2

Therefore, the solution of the expression will be 2. The correct option is B.

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Answer:

418.00 cm³

Step-by-step explanation:

The volume of a cylinder is given by πr²h (r being the radius and h being the height)

The radius is half of the diameter: 6.4/2 is 3.2.

The height shown here is 13.

Instead of pi, the question says to use 3.14 instead of pi.

Putting these all together, you get 3.14×(3.2)²×13.

This can be expanded to 3.14×10.24×13.

From there, multiplying it all together gives you 417.9968 cm³.

The problem says to the nearest hundredth, so you want to round it to 2 decimal places. Since the 6 is above 5, it gets rounded up, leaving you with 418.00 cm³.

Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.

Let the radius of the sphere be R.

So, the volume of the sphere is given by,

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

Differentiating the above relation with respect to time 't' we get,

dV/dt = 4\(\pi r^2\). dr/dt

Given that, the change of radius (dr/dt) = 4 mm/s

When the diameter is 80 mm, then the radius = 80/2 = 40 mm

So the volume change when the diameter is 80 mm is given by,

dV/dt \(=4\pi\times40^2\times4\approx 802424.77\) cubic mm/s

Hence the volume increase in 802424.77 cubic mm/s.

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The standard deviation of the heights of these dogs, rounded to the nearest integer, is 63mm.

To find the standard deviation of the heights of these dogs, follow these steps:

1. Calculate the mean (average) height:
(400mm + 370mm + 470mm + 330mm + 500mm) / 5 = 2070mm / 5 = 414mm

2. Calculate the squared differences from the mean:
(400-414)^2 = 196
(370-414)^2 = 1936
(470-414)^2 = 3136
(330-414)^2 = 7056
(500-414)^2 = 7396

3. Calculate the mean of these squared differences:
(196 + 1936 + 3136 + 7056 + 7396) / 5 = 19720 / 5 = 3944

4. Find the square root of this mean:
√3944 ≈ 62.8

The standard deviation of the heights of these dogs, rounded to the nearest integer, is 63mm.

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The standard deviation of the heights of these dogs, rounded to the nearest integer, is 63m

To find the standard deviation of the heights of these dogs, follow these steps:
Calculate the mean (average) height:
(400mm + 370mm + 470mm + 330mm + 500mm) / 5 = 2070mm / 5 = 414mm
Subtract the mean from each height and square the result:
\((400mm - 414mm)^2 = (-14)^2 = 196\)
\((370mm - 414mm)^2 = (-44)^2 = 1936\)
\((470mm - 414mm)^2 = 56^2 = 3136\)
\((330mm - 414mm)^2 = (-84)^2 = 7056\)
\((500mm - 414mm)^2 = 86^2 = 7396\)
Find the mean of these squared differences:
(196 + 1936 + 3136 + 7056 + 7396) / 5 = 19720 / 5

= 3944
Take the square root of the mean of the squared differences to get the standard deviation:
√3944 ≈ 62.8

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Answer:

The width of the tank is approximately 7.9 feet.

Step-by-step explanation:

The pool is a rectangular prism with the following dimensions:

length = 2*x feet

width = x feet

height = 4 feet

With volume equal to 500 cubic feet, therefore:

volume = length*width*height = 500

(2*x)*(x)*(4) = 500

8*x² = 500

x = sqrt(500 / 8)

x = sqrt(62.5)

x = 7.90569 feet

The width of the tank is 7.9 feet.

Answer:

y > 2x+5  and y > 6+ 3z/4

Step-by-step explanation:

solve each inequality and then find the intersection

Answer:

y > - 2x

Step-by-step explanation:

To solve the indefinite integral ∫(e²x + 2)² dx, we can perform a substitution by letting U = e²x + 2. This transforms the integral into ∫U² du, which can be integrated using the power rule of integration.

Let's start by performing the substitution:

Let U = e²x + 2, then du = 2e²x dx.

The integral becomes ∫(e²x + 2)² dx = ∫U² du.

Now we can integrate ∫U² du using the power rule of integration. The power rule states that the integral of xⁿ dx is (xⁿ⁺¹ / (n + 1)) + C, where C is the constant of integration.

Applying the power rule, we have:

∫U² du = (U³ / 3) + C.

Substituting back U = e²x + 2, we get:

∫(e²x + 2)² dx = ((e²x + 2)³ / 3) + C.

Therefore, the indefinite integral of (e²x + 2)² dx is ((e²x + 2)³ / 3) + C, where C is the constant of integration.

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The compound interval for the given interval is (-∞, ∞).

A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".

The given intervals are (-∞, -2] or [-3, ∞).

Now, the compound interval is (-∞, ∞)

Thus, the interval notation is -∞<x<∞

Therefore, the compound interval for the given interval is (-∞, ∞).

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The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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Inferences made from random samples are estimates or approximations and are not exact. When conducting statistical analysis or drawing conclusions about a population based on a random sample, the results are considered to be estimates or inferences.

This is because the sample represents only a subset of the entire population, and it is not feasible or practical to measure or study every individual or element in the population. Random sampling is a method used to select a representative subset of the population, and statistical techniques are applied to analyze the sample data and draw conclusions about the entire population. However, due to the inherent variability and uncertainty in sampling, the results obtained from the sample are estimates rather than precise measurements.

The use of estimates is a fundamental aspect of statistics. Researchers and statisticians make use of sampling techniques, statistical methods, and confidence intervals to provide a range of values within which the true population parameter is likely to fall. These estimates are based on probability theory and statistical principles.

It's important to recognize that estimates derived from random samples are subject to sampling error, which is the discrepancy between the sample estimate and the true population value. The goal of statistical analysis is to minimize sampling error and provide reliable estimates by using appropriate sampling methods, increasing sample size, and employing robust statistical techniques.

In summary, inferences made from random samples are estimates or approximations of population characteristics. They provide valuable insights into the population of interest but are not exact measurements. Statistical techniques and concepts are used to quantify the uncertainty associated with these estimates and to provide a range of values within which the true population parameter is likely to lie.

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Answer:

(2+4)÷12

Step-by-step explanation:

jxkgxljcluckyxlhlusgibibsi do u need an explanation but here

Answer:

20 inches per minute

Step-by-step explanation: You can find the answer by dividing the inches (120) by the minutes (6), 120/6 = 20

Answer:

He moved 2 inches per minute

Step-by-step explanation:

Divide the minutes by the inches.