Write an equation for the nth term of the sequence 12, 5, -2, -9,...

Answer:

the answer is 7k

Answer:

7k

Step-by-step explanation:

−k−(−8k)

Distribute the minus sign

-k + 8k

Combine like terms

7k

Answer:

1.25

Step-by-step explanation:

Find the average.

-5.1+7.6=2.5

2.5/2

1.25

Answer:

use 1/4 flour to make more than 3 small dinner rolls

The zeros of the polynomial y = 3p³ - 8p² + 4p are calculated to be 0, 2/3, and 2.

The zeros of a function, sometimes referred to as the roots or solutions, are the values of the independent variable (x) for which the function equals zero. In other words, these are the x-coordinates of the points where the graph of the function crosses the x-axis. You can get the zeros of a function by setting its value to zero and then figuring out what value(s) of x the equation needs.

For example, if the function is f(x), you would set f(x) to 0 and then find x:

For example, if the function is f(x), you would set f(x) to 0 and then find x:

f(x) = x² + 2x - 3 = 0

This equation can be written as (x-3)(x+1) = 0.

Inferring from the x-values that x - 3 = 3 or x + 1 = -1, x² + 2x - 3 = -1, 3

As a result, the zeros of the function f(x) = x² + 2x - 3 are -1 and 3.

In the issue at hand, y = 3p³ - 8p² + 4p

y = p(3p - 2)(p - 2) (p - 2)

Taking the zeros,

0 = p(3p - 2)(p - 2)

p = 0,

3p - 2 = 0,

p = 2 / 3,

p - 2 = 0, p = 2

The zeros of the polynomial or roots are (0, 2/3, and 2).

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Step-by-step explanation:

the mean value is the sum of all data points divided by the number of data points.

so, in our case we have after 9 pieces of work

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) / 9 = 46

that means

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) = 46×9 =

= 414

now we need to add a p10, so that

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + p10) =

= 50 × 10 = 500

only then do we get

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + p10)/10 =

= 50

so,

(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) + p10 = 500

414 + p10 = 500

p10 = 500 - 414 = 86%

the student must at least achieve 86% for the 10th piece of work.

Answer:

4.1

Step-by-step explanation:

You would first subtract 55.50 from 71.90 which leaves you with 16.4,

Then you would divide 16.4 by 4 to find how many gigabytes she could use which gives you 4.1

Hope this helped

Answer:

4.1

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

The formulas given work perfectly.

It might help you to think of the tax rate as a percentage. For example, $2.37 per $100 is a rate of 2.37/100 = 0.0237 = 2.37%

Each dollar value is the product of the previous two columns.

  $400,000 × 0.19 = $76,000; $76,000 × 0.0237 = $1801.20 (tax)

  $235,000 × 0.10 = $23,500; $23,500 × 0.0993 = $2333.55 (tax)

  $215,000 × 0.15 = $32,250; $32,250 × 0.1240 = $4000.00 (tax)

__

Where the rates are missing (as on the third line), they can be found by dividing the dollar value on the right of it by the dollar value on the left of it.

  32,250/215,000 = 0.15 = 15%

  4000/32,250 = 0.1240 = $12.40 per $100

_____

Additional comment

To get a tax of exactly $4000 on the last line, the tax rate needs to be specified to 4 decimal places: $12.4031 per $100. Otherwise the value rounds to something less than $4000.

The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

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For the vector, the orthogonal projection of f(x) = 4x² – 4 onto the subspace V spanned by g(x) = x – 1/2 and h(x) = 1 is (-2√(3)/3)(x-1/2) - 8/3.

In this case, we are working with the vector space C° [0,1], which consists of continuous functions on the interval [0,1]. We want to find the orthogonal projection of the function f(x) = 4x² - 4 onto the subspace V spanned by the functions g(x) = x - 1/2 and h(x) = 1.

To find the orthogonal projection of f onto V, we need to first find an orthonormal basis for V. To do this, we will use the Gram-Schmidt process.

First, we normalize g(x) to obtain a unit vector u1:

u1 = g(x) / ||g(x)||, where ||g(x)|| = √(<g,g>) = √(integral from 0 to 1 of (x - 1/2)² dx) = √(1/12).

Thus, u1 = √(12)(x - 1/2).

Next, we find a vector u2 that is orthogonal to u1 and has the same span as h(x) = 1. To do this, we subtract the projection of h(x) onto u1 from h(x):

v2 = h(x) - <h,u1>u1, where <h,u1> = integral from 0 to 1 of (1)(√(12)(x-1/2))dx = 0.

Therefore, v2 = h(x).

We then normalize v2 to obtain a unit vector u2:

u2 = v2 / ||v2||, where ||v2|| = √(<v2,v2>) = √(integral from 0 to 1 of (1)² dx) = √(1) = 1.

Thus, u2 = 1.

Now, we have an orthonormal basis {u1,u2} for V. To find the orthogonal projection of f onto V, we need to compute the inner product of f with each of the basis vectors and multiply it by the corresponding vector. We can then add these two vectors together to obtain the orthogonal projection of f onto V.

proj_V(f) = <f,u1>u1 + <f,u2>u2.

Using the inner product <f,g> = integral from 0 to 1 of f(x)g(x) dx, we can compute the inner products <f,u1> and <f,u2>:

<f,u1> = integral from 0 to 1 of f(x)u1(x) dx = integral from 0 to 1 of 4x²-4(√(12)(x-1/2))dx = -2/3√(3).

<f,u2> = integral from 0 to 1 of f(x)u2(x) dx = integral from 0 to 1 of 4x²-4(1)dx = -8/3.

Therefore, the orthogonal projection of f(x) = 4x² - 4 onto the subspace V spanned by g(x) = x - 1/2 and h(x) = 1 is given by:

proj_V(f) = (-2/3√(3))(√(12)(x-1/2)) + (-8/3)(1).

Thus, the orthogonal projection of f onto V can be written as:

proj_V(f) = (-2√(3)/3)(x-1/2) - 8/3.

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The current is therefore changing at such a rate of -0.6 amp/s. This indicates that current is dropping at a 0.6 amp/s rate.

Resistance is the amount that a substance obstructs or opposes an electric current. Electric current is the term used to describe the motion of electrons. To further comprehend resistance, imagine someone struggling to get from one shop to the next in a crowded market.

V = 12 volts and dR/dt = 0.8 ohms per second at R = 4 ohms are presented to us.

I = V/R calculates the current I via the resistance. With regard to time t, if we take the derivative, we get:

dI/dt = d(V/R)/dt

The quotient rule gives us:

dI/dt = (R dV/dt - V dR/dt) / R²

Inputting the values provided yields:

dI/dt = (4 d(12)/dt - 12 (0.8)) / 4²

Since dV/dt is zero because of voltage is constant, we can write:

dI/dt = (-9.6) / 16

If we simplify, we get:

dI/dt = -0.6 amp/s

Therefore, the current is changing at a rate of -0.6 amp/s. This means that the current is decreasing at a rate of 0.6 amp/s.

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By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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Answer: A

Step-by-step explanation:

Answer:

A≈228.33

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 2 on the left side and the dividend 30 on the right side like this:

2 ⟌ 3 0

Step 2:

The divisor (2) goes into the first digit of the dividend (3), 1 time(s). Therefore, put 1 on top:

1

2 ⟌ 3 0

Step 3:

Multiply the divisor by the result in the previous step (2 x 1 = 2) and write that answer below the dividend.

1

2 ⟌ 3 0

2

Step 4:

Subtract the result in the previous step from the first digit of the dividend (3 - 2 = 1) and write the answer below.

1

2 ⟌ 3 0

- 2

1

Step 5:

Move down the 2nd digit of the dividend (0) like this:

1

2 ⟌ 3 0

- 2

1 0

Step 6:

The divisor (2) goes into the bottom number (10), 5 time(s). Therefore, put 5 on top:

1 5

2 ⟌ 3 0

- 2

1 0

Step 7:

Multiply the divisor by the result in the previous step (2 x 5 = 10) and write that answer at the bottom:

1 5

2 ⟌ 3 0

- 2

1 0

1 0

Step 8:

Subtract the result in the previous step from the number written above it. (10 - 10 = 0) and write the answer at the bottom.

1 5

2 ⟌ 3 0

- 2

1 0

- 1 0

0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 30 divided by 2 calculated using Long Division is:

15

The final volume is 0.1296  \(m^{3}\)

Let the length of the box, l = x

Therefore, according to the question, width, w = length/2 = x/2.

Height, h = 0.5 m (given in the question)

First, we have to calculate the area of the sides.

There are 6 sides in a cuboid (given that base is a rectangle)

Therefore,

Area, A = lw + wh + lh + lw + wh + lh = 2(lw + wh + lh)

Calculating,

A = 2(\(0.5x^{2}\) + 0.25x + 0.5x) = \(x^{2}\) + 1.5x

Given, Area of the 6 sides - Area of the base = 1.08m

 \(x^{2}\) + 1.5x - \(x^{2}\) = 1.08

1.5x = 1.08

x = 0.72

Therefore,

Volume = lwh = 0.5 * 0.72 * 0.72/2 = 0.1296 \(m^{3}\)

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Answer:

(3 x 1) + (3(5) x 1) = a

Step-by-step explanation:

Answer:

79

Step-by-step explanation:

Given the expression

x + 1/x = 9

Square both sides

(x + 1/x)^2 = 9^2

x^2 + 2x(1/x)+ (1/x)^2 = 81

x^2 + 2 + 1/x^2 = 81

x^2+1/x^2+2 = 81

x^2+1/x^2 = 81-2

x^2+1/x^2+ = 79

Hence the value of x^2+1/x^2 is 79

The sum of deviations of the individual observations from their sample mean is zero.

This is because the sample mean is defined as the sum of all the observations divided by the total number of observations. So, when we calculate the deviation of each observation from the sample mean, some deviations will be positive and some will be negative. However, the sum of all these deviations will always equal zero, since the positive and negative deviations will cancel each other out.

This property is known as the "zero sum property of deviations" and is an important concept in statistics, especially when working with measures of variability such as variance and standard deviation.

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We can see that 36 can be arranged in 4 as 6 rows of 6 seeds each, in 6 as 6 rows of 6 seeds each, and in 9 as 4 rows of 9 seeds each.  The smallest number of seeds that can be arranged in 4, 6, and 9 is 36.

To find the smallest number of seeds that can be arranged in 4, 6 and 9, we need to determine the least common multiple (LCM) of these numbers.

LCM of 4, 6, and 9 can be obtained by finding the prime factors of each number. Then the highest powers of all the factors are multiplied.

Therefore,4 = 2²6 = 2 × 39 = 3²LCM of 4, 6 and 9 = 2² × 3² = 36.

Hence, the smallest number of seeds that can be arranged in 4, 6, and 9 is 36.

To verify this, we can see that 36 can be arranged in 4 as 6 rows of 6 seeds each, in 6 as 6 rows of 6 seeds each, and in 9 as 4 rows of 9 seeds each.  The smallest number of seeds that can be arranged in 4, 6, and 9 is 36.

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Answer:the answer is 4.55

Step-by-step explanation:

The mean is the sum of all values divided by the number of values in a set.

The mean (or average) of a set of numbers is the sum of all the numbers divided by the total number of values. For example, if we have the numbers 1, 2, 3, 4 and 5, the mean would be (1 + 2 + 3 + 4 + 5) / 5 = 3. The mean is also known as the arithmetic mean or the average. The formula for calculating the mean is:

Mean = (Σx)/N

Where Σx is the sum of all values and N is the number of values. So, for our example with 1, 2, 3, 4 and 5, we could calculate the mean like this:

Mean = (1 + 2 + 3 + 4 + 5) / 5

 = 15 / 5

 = 3

The mean is the sum of all values divided by the number of values in a set.

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Answer:

-7<x<7

Step-by-step explanation:

Answer:

(4)

Step-by-step explanation:

As the circumference of a circle measures 360 degrees, minor arc AC measures 360-268=92 degrees.

By the inscribed angle theorem, angle ABC measures 46 degrees.

The equation of a line is y = 4x +10

What is an equation of a line?

A line's equation is a unified representation of all of the line's points. Any point on a line will satisfy the equation in its general version, which is of the type ax + by + c = 0. The slope of the line and a point on the line are the two essential elements needed to create the equation of a line.

Here, we have

Given

m = 4

x = -3

y = -2

By applying slope intercept formula, we get

Equation of line is y = 4x + c

There is one unknown term here which is c.

So to find it we will put (-2,-3) in the line.

-2 = (4)(-3) + c

c = 10

Hence the equation of a line is y = 4x +10

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There are now 7 classrooms of 31 and 3 of 30.

A linear equation in mathematics is an equation that can be written as display style a 1x 1+ldots +a nx n+b=0, where x 1, dots, x n are the variables, and display style b, a 1, ldots, a n are the coefficients, which are frequently real integers.

Madison, we first have to add 30 + 31 = 61.

How many times does 61 go into 307

Five,

because 61 x 5 = 305.

This means there are 5 of each classroom.

We still have two students left over, though, so they will have to be added to two of the 30 rooms,

so there are now 7 classrooms of 31 and 3 of 30.

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The transformation T: R^2 → R^2 reflects a point P through the vertical x2-axis and then through the line x2 = x1. The transformed point is given by (-x2, x1).

Lets denote the transformation T: R^2 → R^2. According to the given description, T first reflects points through the vertical x2-axis and then reflects points through the line x2 = x1.

To understand the transformation T, let's consider a point P in the xy-plane with coordinates (x1, x2).

Reflection through the vertical x2-axis:

The reflection through the x2-axis simply changes the sign of the second coordinate, x2. So, the transformed point after this reflection is (x1, -x2).

Reflection through the line x2 = x1:

To reflect a point through the line x2 = x1, we swap the x1 and x2 coordinates. After this reflection, the transformed point becomes (-x2, x1).

Now, we can apply these reflections sequentially to point P:

First reflection (x2-axis): (x1, x2) → (x1, -x2)

Second reflection (x2 = x1 line): (x1, -x2) → (-x2, x1)

Therefore, the final transformed point is (-x2, x1).

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Answer:

it would be 17

Step-by-step explanation:

rounding just means adding 10

The radical expression of a to the four ninths power is (option d) ninth root of a to the fourth power \(\sqrt[9]{a^{4} }\)

Radical expression:

An expression with a square root is referred to as a radical expression. Radicand: A value or phrase included within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.

Given,

The radical expression: a to the four ninths power.

That is,

\(a^{\frac{4}{9} }\)

By using exponential rule :-

\(a^{\frac{m}{n} }\) = \((a^{m})^{\frac{1}{n} }\) = \(\sqrt[n]{a^{m} }\)

Here,

m = 4 and n = 9

So,

\(a^{\frac{4}{9} }\) = \((a^{4} )^{\frac{1}{9} }\) = \(\sqrt[9]{a^{4} }\)

is, the radical expression of a to the four ninths power is (option d) ninth root of a to the fourth power \(\sqrt[9]{a^{4} }\).

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The question is incomplete. Completed question is given below:

Which of the following is the radical expression of a to the four ninths power?

4a9

9a4

fourth root of a to the ninth power

ninth root of a to the fourth power

Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.

The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).

The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.

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well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)