1. SIMPLIFY EACH EXPRESSION:
8x2 - 7x + 4x3 - 2-3x2 + 9x - 4
5(7 + 3x) - 12
2[z + 3) + 3(5 – 3z)

The determinant of a matrix A is the product of the diagonal entries.

The determinant of a lower triangular matrix (or an top triangular matrix) is the product of the diagonal entries. in particular, the determinant of a diagonal matrix is the made from the diagonal entries.

The determinant of any diagonal n × n matrix is the product of its diagonal entries. yes, the determinant of a diagonal matrix is the made of elements of its diagonal. So, the given condition is real.

A diagonal matrix is sometimes called a scaling matrix, considering matrix multiplication with it consequences in converting scale (length). Its determinant is the fabricated from its diagonal values.

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The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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The domain of the expression is a real number except 1 and the range of the expression is also a real number.

The domain means all the possible values of x and the range means all the possible values of y.

The expression is given below.

(3x² + x - 4) / (x - 1)

The expression can be written as

(3x² + 4x - 3x - 4) / (x - 1)

[(3x + 4)(x - 1)] / (x - 1)

3x + 4

The domain of the expression is a real number except 1 and the range of the expression is also a real number.

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Answer: (a) Let's call the amount of water in the tank after t minutes "W(t)". We know that the rate of change of water in the tank is equal to the rate of brine being pumped in minus the rate of solution being pumped out. Therefore, we can write:

dW(t)/dt = 9 - 5 = 4

This is a first-order linear differential equation, and it can be solved to find W(t). Integrating both sides with respect to t, we get:

W(t) = 4t + C, where C is a constant of integration.

To find the value of C, we can use the initial condition that the tank initially contains 50 litres of water, so:

W(0) = 50

Plugging in t = 0, we get:

50 = 4 * 0 + C

Therefore, C = 50.

So the expression for the amount of water in the tank after t minutes is:

W(t) = 4t + 50

(b) Let's call the amount of salt in the tank after t minutes "x(t)". We know that the rate of change of salt in the tank is equal to the rate of brine being pumped in times the concentration of salt in the brine minus the rate of solution being pumped out times the concentration of salt in the solution. Therefore, we can write:

dx(t)/dt = 11 * 9 - x(t) * 5

This is a first-order linear differential equation, and it describes the amount of salt in the tank after t minutes.

Step-by-step explanation:

In the trash can, there are 648 bricks. when the measurements are 8 by 4 by 2 The right response is so (C).

This same total mass of a three-dimensional shape is referred to as its porous structure. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. The cuboid's length, width, and height can also be labeled, and indeed the surface area (SA) can indeed be calculated using the equation SA=2lw+2lh+2hw.

Based on this equation, surface area is equivalent to two times overall combination of width and length, two times its products of length and height, and two times the ratio of both height and width.

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Answer:

x= 4, y= -2

Step-by-step explanation:

To solve the system by substitution, start by labelling the two equations:

-4x +5y= -26 -----(1)

y= 3x -14 -----(2)

Since the second equation already has y as the subject of formula, we can substitute equation (2) into (1). This means that we can replace all the 'y's in equation (1) with 3x -4, such that equation (1) will only be in terms of x.

Substitute (2) into (1):

-4x +5(3x -14)= -26

Expand:

-4x +15x -70= -26

11x= 70 -26

11x= 44

Divide both sides by 11:

x= 44 ÷11

x= 4

Substitute x= 4 into (2):

y= 3(4) -14

y= 12 -14

y= -2

Answer: all points are a solution except for (4, 2) (and (2, 0) i think)

Step-by-step explanation:

Two ways of writting the linear function are:

A general linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we know that the slope is 2/5, replacing that we will get:

y = (2/5)*x + b

We also know that this line passes through (12, -5), then we can replace these values to get:

-5 = (2/5)*12 + b

-5 = 24/5 + b

-5 - 24/5 = b

-25/5 - 24/5 = b

-49/5 = b

Then the linear equation is:

y = (2/5)*x - 49/5

Other form of writting this is the standard form, multiply both sides by 5.

5y = 2x - 49

5y - 2x = -49

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The volume of the cylinder for the given radius and height is equal to 4973.8 square units

Radius of the cylinder = 12 units

height of the cylinder = 11 units

Value of π = 3. 14

Volume of the cylinder = πr²h

where 'r' is the radius of the cylinder.

And 'h' is the height of the cylinder.

Substitute the value we have in the formula we get,

Volume of the cylinder =  3.14 × ( 12 )² × 11

⇒Volume of the cylinder =  4973.76 square units

⇒Volume of the cylinder =  4973.8 square units (  nearest tenth  )

Therefore, the volume of the cylinder is equal to 4973.8 square units

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Answer:

3x + 1

Step-by-step explanation:

plz mark as the brainliest

Answer:

the answer for question no 8 is. option second...ie 17

The given molecule is a saturated straight-chain alcohol with 6 carbon atoms. This means that the carbon atoms will be arranged in a straight chain, with each carbon atom having one hydrogen atom attached to it and the last carbon atom having an -OH group attached to it.

To draw the corresponding skeletal structure, we need to represent the carbon atoms as points (vertices) and the bonds between the atoms as lines.The molecular formula, C6H13OH, tells us that the molecule has 6 carbon atoms, 13 hydrogen atoms, and one -OH group. Since each carbon atom has four valence electrons and each hydrogen atom has one valence electron, we can determine the total number of valence electrons as follows:Valence electrons in C: 6 x 4 = 24 Valence electrons in H: 13 x 1 = 13

Valence electrons in O: 6 + 1 = 7

Total valence electrons: 24 + 13 + 7 = 44

The -OH group is attached to the last carbon atom in the chain. Therefore, we need to draw a line with a single bond from the last carbon atom to represent the -OH group. The remaining valence electrons are used to form single bonds between the carbon atoms and hydrogen atoms, as shown below:Therefore, the corresponding skeletal structure for the given molecule is shown above.

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The sample size required to achieve a 0.75-hour margin of error at a 99% confidence level is 425 bacteria.

To determine the sample size required to achieve a margin of error of 0.75 hours with a 99% level of confidence, we can use the formula for sample size calculation:

n = (Z * σ / E)²

Where:

n = sample size

Z = Z-score corresponding to the desired level of confidence (in this case, 99% confidence level)

σ = population standard deviation

E = desired margin of error

In this case, we already have a preliminary sample of 30 bacteria, which allows us to estimate the population standard deviation using the sample standard deviation (s). However, since we don't have any specific information about the population distribution, we can conservatively assume a worst-case scenario where the population standard deviation is the same as the sample standard deviation (s = 6 hours).

First, we need to find the Z-score corresponding to the 99% confidence level. This value can be obtained from a standard normal distribution table or using statistical software. For a 99% confidence level, the Z-score is approximately 2.576.

Substituting the values into the sample size formula:

n = (2.576 * 6 / 0.75)²

n = (15.456 / 0.75)²

n = 20.608²

n ≈ 424.07

Rounding up to the nearest whole number, we find that a sample size of 425 bacteria should be gathered to achieve a margin of error of 0.75 hours at a 99% level of confidence.

It's important to note that this calculation assumes a simple random sample and that the preliminary sample is representative of the population of interest. Additionally, other factors such as cost, time, and available resources may also influence the decision on the final sample size.

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In the first few steps for deriving the quadratic formula left side of the equation due to the distributive property for balancing the equation.

A quadratic equation is the equation in which the highest power of the variable is two.

Here, The first few steps in deriving the quadratic formula are shown in the table.

Use the substitution property of equality to solve it further,

-c=-ax² +bx

Now factor out the term a, to solve further as,

    - c = a (x² + b/a x)

for half of the b value and square it to determine the constant of the perfect square trinomial as,

     (b/2a)² = b²/4a²

Now  the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.

  -c + b²/4a² = a(x² + b/a x + b²/4a² )

Thus, the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.

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Answer:

60%

Step-by-step explanation:

To write 9/15 as a percent have to remember that 1 equal 100% and that what you need to do is just to multiply the number by 100 and add at the end symbol % .

The volume of the solid generated for the region bounded by y = 14sinx about x-axis is equal to 98π²cubic units.

Region is revolved about the x-axis.

⇒Solid generate cross-sections perpendicular to the x-axis are disks.

The radius of each disk is the distance from the x-axis to the curve

y = 14 sin x.

⇒|y|/14 = |sin x|

Using the identity sin²x = (1/2)(1 - cos 2x),

⇒|y|/14 = √[sin²x]

⇒|y|/14 = √[(1/2)(1 - cos 2x)]

⇒|y| = 14√[(1/2)(1 - cos 2x)]

⇒|y| = 7√[2(1 - cos 2x)]

Area of each disk is given by π(radius)².

Volume of the solid is equal to

V = \(\int_{0}^{\pi }\)π(7√[2(1 - cos 2x)])² dx

  =49π \(\int_{0}^{\pi }\)2( 1- cos2x ) dx

  = 98π (x - (sin2x/2) ) \(|_{0}^{\pi }\)

  = 98π ( π - 0)

  = 98π²cubic units.

Therefore , the volume of the solid generated about x-axis is equal to 98π²cubic units.

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The above question is incomplete, the complete question is:

Find the volume of the solid generated when the region bounded by y= 14 sin x and y = 0, for 0 ≤x≤π, is revolved about the x-axis. (Recall that sin²x =(1/2)(1- cos 2x).

Step-by-step explanation:

13 cups = ? pints

there are 2 cups per pint so:

13/2 = 6.5

13 cups = 6.5 or \(6\frac{1}{2}\) pints

we estimate that g^-1(4) is approximately 0.8.

To find g^-1(4), we need to find the value of x that satisfies the equation g(x) = 4, where g(x) = 3 + x + e^x.

So, we start by setting g(x) equal to 4 and solving for x:

3 + x + e^x = 4

Subtracting 3 from both sides, we get:

x + e^x = 1

We cannot solve this equation for x algebraically, so we need to use numerical methods to approximate the solution. One common method is to use the graph of the function g(x) and its inverse g^-1(x) to estimate the value of g^-1(4).

First, we graph the function g(x) and look for the point on the curve where the y-coordinate is 4:

Graph of g(x) = 3 + x + e^x

From the graph, we can see that there is a point on the curve where the y-coordinate is close to 4, which is approximately x = 0.5.

Next, we look at the graph of the inverse function g^-1(x), which is simply the reflection of the curve of g(x) across the line y = x:

Graph of g^-1(x)

From the graph, we can see that the point on the curve of g^-1(x) that corresponds to the point (0.5, 4) on the curve of g(x) is approximately g^-1(4) = 0.8.

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Answer:

Step-by-step explanation:

The formula for the y-intecept form is \(y=mx+b\)

Plugin the m and the b we have

\(y=-4x+5\)

Answer:

y=-4x+5

Step-by-step explanation:

Answer:

choice 2, y=1/4x

Step-by-step explanation:

Answer:

The answer is 4

Step-by-step explanation:

3 + x = 7

-3       -3

     x = 4

The coefficient of variation (CV) for the given dataset is approximately 13.79%.

We have a dataset: 9, 9, 11, 12, 8, 7, 10, 8, 9, 12

First, calculate the mean

Mean = (9 + 9 + 11 + 12 + 8 + 7 + 10 + 8 + 9 + 12) / 10 = 95 / 10 = 9.5

Calculate the standard deviation:

Using the formula for sample standard deviation:

Standard deviation = √[(Σ(xi -x_bar )²) / (n - 1)]

where Σ represents the sum, xi represents each value in the dataset, x_bar represents the mean, and n represents the number of values.

Plugging the values:

Standard deviation = √[((9 - 9.5)² + (9 - 9.5)² + (11 - 9.5)² + (12 - 9.5)² + (8 - 9.5)² + (7 - 9.5)² + (10 - 9.5)² + (8 - 9.5)² + (9 - 9.5)² + (12 - 9.5)²) / (10 - 1)]

Standard deviation ≈ √[15.5 / 9] ≈ √1.722 ≈ 1.31

Calculate the coefficient of variation:

Coefficient of Variation (CV) = (Standard deviation / Mean) * 100

CV = (1.31 / 9.5) * 100 ≈ 13.79

Therefore, the coefficient of variation (CV) = 13.79%.

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When your measurement error is between 4.5% and 5%, the number of cases is 450.

The margin of error (MOE) is a measure of the uncertainty or statistical error in a survey's findings. When it comes to determining the survey's accuracy, the MOE is the most important consideration. When determining the sample size required to generate the lowest MOE possible, the survey creator's decision comes into play.

Let us assume that a 95 percent confidence level is used in a survey of a population. The MOE will be larger if a more rigorous confidence level is employed.

Margin of Error = (Critical Value) x (Standard Deviation) / square root of (Sample Size)

If the population size is less than 100,000, the MOE equation is usually used.

The most commonly used equation is n = (Z2 * P * Q) / E2 if the population size is greater than 100,000.

Hence, when the measurement error is between 4.5 and 5%, the number of cases is 450.

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The x-intercepts are the points (-2,0) and (4,0)

A parabola is a symmetrical, curved, U-shaped graph. Parabolas exist in everyday situations, such as the path of an object in the air, headlight shapes and the wire of suspension bridges. The equation of a parabolic graph is y = x² and all quadratic graphs have a line of symmetry which passes vertically through the minimum or maximum point

Find the x-intercepts of the parabola and write them as ordered pairs

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

For x=4 and x=-2 the equation is equal to zero

therefore

The x-intercepts are the points (-2,0) and (4,0)

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Answer:

You find the constant of proportionality by how much u need to add or subtract the same number to get the same answer and in a graph you need to see if the line goes through the origin (0,0).

Step-by-step explanation:

Answer:

the median is 17  the mode is 19

Step-by-step explanation:

17 is in the middle with 6 on each side so it is the median

19 occurs most often so it is the mode

The sole inference whereby the total amount of figures on the cube will be divisible by three.

The cube’s faces are labeled as A, B, C, D, E, and F.

It’s apparent that pairs of opposite sides combine to equal the same value: namely A+F=S, B+E=S, and C+D=S.

Thus, determining the summation of all values entails adding each group of pairs together: (A+F) + (B+E) + (C+D) = 3S.

Unless additional information is provided, the sole inference whereby the total amount of figures on the cube will be divisible by three.

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Answer:

275 dollars every

month

Step-by-step explanation: