(8h - 4) + (4h to the third power - 8h squared +9h +7)

The square root of - 10 is not a real number but a complex number, an irrational number.

Numbers can be classified in real numbers and complex numbers. Real numbers are classified in natural numbers (i.e. 1, 4, 5), whole numbers (i.e. 0, 1, 4, 5), integers (i.e. - 4, -1, 0, 5, 6) and rational numbers (i.e. 5 / 7, 0, - 13 / 3) and part of the irrational numbers (i.e. √3, π) and the rest of irrational numbers are complex numbers (i.e. i 4, - 4 + i 5).

In consequence, the square root of - 10 is not a real number but a complex number, an irrational number.

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Answer:

h=1-5/k

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

a) It is known that the area of Indian ocean is 25 million square miles.

Lets take the unknown ocean percentage as x, which is bigger than the Indian ocean.

So comparing to the size of that unknown x ocean, Indian ocean is just a small part (39%) of the area.

So,

Now, we have to compare the value of x with the data given in the table. It matches with the Pacific ocean.

Hence Indian ocean is a small part (39%) of Pacific ocean.

b) Given that the area of artic ocean is 5 million square miles. It is just a small percentage (16%) of some bigger ocean given in the table. Let's take the unknown ocean as y.

The estimated total cost of the clothes in your cart is $104.

Estimated costs are approximate projections of future costs associated with producing goods or completing a project. This includes both fixed and variable costs such as labor, materials and capital. Cost forecasting is very important for project-based companies. Upon notice, the parties must comply with the Fixed Price Agreement. Based on the prices you provided, the estimated cost of the items in your cart would be:

$23 (shirt) + $38 (trousers) + $17 (sweatshirt) + $26 (shoes) = $104

Therefore, the estimated total cost of the clothes in the cart is $104. However, please note that this is only an approximation and actual costs may vary due to factors such as sales tax and applicable discounts. 

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Answer:

Step-by-step explanation:

Pedometer

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer:

26.3

Step-by-step explanation:

Perimeter is found by adding up all the sides.

8+6+6+6.3

18.3+8 =26.3

Answer:

26.3

Step-by-step explanation:

First, you find the perimeter of the original image, 6+6+6.3+8 = 26.3

Because the shape is only rotated, they are equal which means all 3 shapes have the same perimeter.

Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

Answer:

13 miles

Step-by-step explanation:

you can go down and to the right or to the left and down but either way it takes 13 miles from her house to Trader Joe's.

The number of the small seats is 30 while the number of the big seats is 94.

We know that from the question, Vicky is an airline attendant. Last week, she worked on flights on 3 small jets and 5 large jets, which could seat a total of 560 passengers. The week before, she was assigned to flights on 5 small jets and 2 large jets, which could seat a total of 338 passengers.

Now;

Let the number of small seats be x and the number of large seats be y

It follows that;

3x + 5y = 560 ----- (1)

5x + 2y = 338 ------(2)

If you multiply (1) by 5 and (2) by 3 we have;

15x + 25y = 2800 ------ (3)

15x + 6y = 1014 -----------(4)

        19 y = 1786

y = 1786/19

= 94

Substitute y = 94 into (1)

3x + 5(94) = 560

x = 560 -  5(94)/3

x = 30

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Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(7-5); B(7,5)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

6 miles

Step-by-step explanation:

To find the miles in an hour, we must found the unit rate. A fraction is a division problem, so we would set this up as a fraction. The numerator is the distance, and the denominator is the time it takes to travel the distance.

10.5/1.75=6

7.5/1.25=

4.5/0.75=

Answer:  6 miles

Step-by-step explanation:

Christy went jogging and covered 4.5 miles in 0.75 hr
and in 1.75 hr she covered 10.5
To find distance she covered in 1 hour = 10.5 - 4.5 (because 1.75 hr - 0.75 hr)

:)

Answer:

Full drum 80 dollars

one lid missing

earn 10 dollars less

Step-by-step explanation:

We need to find the surface area

SA = 2 pi r^2  + 2 pi rh

The diameter is 2 so the radius = 2/2 =1

SA = 2 * pi * 1^2  + 2 * pi * 1 * 3

      = 2 pi + 6pi

      = 8pi

Using pi = 3.14

SA = 8 *3.14 = 25.12 ft^2

We get 3.18 per ft^2

25.12 * 3.18 =79.88

To the nearest dollar

80 dollars

If one of the lids is missing

SA =  pi r^2  + 2 pi rh

        pi + 6pi

        7 pi

Using pi = 3.14

SA = 7 *3.14 = 21.98 ft^2

We get 3.18 per ft^2

21.98 * 3.18 =69.90

To the nearest dollar

70

The difference is 10 dollars

Answer:

\(\Huge \boxed{\mathrm{a) \ \$ \ 80}} \\\\\\\\ \Huge \boxed{\mathrm{b) \ \$ \ 10}}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

Surface area of the cylinder :

2πr² + 2πrh

The diameter is 2 ft, so the radius is 1 ft.

⇒ 2π(1)² + 2π(1)(3)

⇒ 8π ≈ 25.13

$3.18 is getting payed per square foot.

⇒ 25.13 × 3.18

⇒ 79.9221171073 ≈ 80

If the lid was missing:

πr² + 2πrh

π(1)² + 2π(1)(3)

7π ≈ 21.99

$3.18 is getting payed per square foot.

⇒ 21.99 × 3.18

⇒ 69.9318524689 ≈ 70

The difference :

80 - 70 = 10

$10 less if the lid is missing.

\(\rule[225]{225}{2}\)

The value of det(2AB-1) is -97 in the given case.

First, we can use the following property of determinants:

\(det(kA) = k^n * det(A)\)

Determinants are a mathematical concept used in linear algebra to describe certain properties of matrices. The determinant of a square matrix is a scalar value that is calculated using the matrix's elements. It can be used to determine whether a matrix has an inverse, and it also has applications in solving systems of linear equations and finding the area or volume of geometric shapes.

where k is a scalar and A is an n x n matrix.

Using this property, we can simplify det(2AB-1) as follows:

\(det(2AB-1) = 2^3 * det(AB) - det(I)\\= 8 * det(A) * det(B) - det(I)\\= 8 * (3) * (-4) - 1\\= -97\)

Therefore, the value of det(2AB-1) is -97.

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The roots of the given equation is real and equal.

Given , 5\(x^{2} \\\) - 10x+ k=0

The quadratic equation is b² - 4ac = 0

Here, a= 5, b= -10, c= k

substitute in b² - 4ac = 0

(-10)² - 4 * 5* k =0

100 - 20k =0 , let this be equation (1)

100 = 20k

k = \(\frac{100}{20}\)

k = 5.

now, substitute  k= 5 in equation (1)

100 -20k = 0

100 - 20*5 = 0

100 - 100 = 0

Therefore, the given equation is real and equal .

The correct question is 5x² - 10x + k =0

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Answer:

$37.51

Step-by-step explanation:

Just add what Mike paid for pizza to what he has remaining

$31.84 + $5.67 = $37.51

Area of rectangle is increasing at 127 \(cm^{2}\)/second

Length of a rectangle is increasing at a rate = dL/dt = 7 cm/s

Width is increasing at a rate = dw/dt = 6 cm/s

We need rate at which the area is changing (dA/dt) when:

L = 13 cm and w = 7 cm

Equation for area of a rectangle is:

A = Lxw

so, we need product rule when take the derivative.

dA/dt = L (dw/dt) + w (dL/dt)

Now just put in all of the given numbers:

dA/dt = (13)(6) + (7)(7) = 78+49 = 127

Area of rectangle is increasing 127 \(cm^{2}\)/Second.

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Given the data set:

2, 5, 7, 2, 11, 13, 5, 7, 1, 10, 10, 2, 3, 5, 1, 11

Let's find the box plot that correctly displays the data set shown.

If the probability of failure is 0.001, then the probability that

(a) lot is accepted is 0.9277,

(b) lot is rejected on 20th test is 0.000981,

(c) lot is rejected in 10 or fewer trials is 0.01.

Let the random-variable "X" represent number of batteries to test to get the first-battery which fails; in other words, to get first success.

Since, the trials are independent, X has a geometric distribution

Part (a) :

Let X =  the number of trials,

So, the probability that the lot is accepted is :

⇒ P(X=75) = (0.999)⁷⁵×(0.001)⁰ = 0.9277,

Part (b) :

let Y = the numbers of trials before the first failure (geometric distribution and

So, the probability that lot is rejected on 20th-test is :

⇒ P(Y=20) = (0.001)⁰×(0.999)¹⁹ = 0.000981,

Part (c) :

The probability that it is rejected in 10 or fewer trials is :

⇒ 1- P(no Failures)

⇒ 1 – (0.001)⁰(0.999)¹⁰ = 0.01.

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The given expression is a simplified algebraic equation: (1/2) * a^2 - 3b + 2c. It represents a combination of variables a, b, and c with their respective coefficients.

Utilizing symbols and operations, an algebraic equation illustrates the equivalence or inequivalence of two expressions. These generated expressions may hold variables that have varying values.

The premise centered around calculus is to arrive at a solution by acquiring the correct value(s) of these variable(s), ultimately fulfilling the outlined specification in the problem. Algebraic equations can range from uncomplicated linear problems to elaborate polynomials and trigonometric functions.

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The relative extrema of the function   \(g(x) = (1/9)x^9 - x\)  are:

Relative minimum at x = 1 and Relative maximum at x = -1

To find the relative extrema of the function \(g(x) = (1/9)x^9 - x\), we need to first find its derivative and then solve for critical points.

Let's find the derivative of g(x) with respect to x:

\(g'(x) = d/dx [(1/9)x^9 - x]\\= (1/9)(9x^8) - 1\\\\= x^8 - 1\)

To find critical points, we set g'(x) = 0 and solve for x:

\(x^8 - 1 = 0\)

Using the difference of squares, we can factor the equation:

\((x^4 - 1)(x^4 + 1) = 0\)

Now, solve each factor separately:

\(Factor 1: x^4 - 1 = 0\\(x^2 - 1)(x^2 + 1) = 0\\Solving further:\\x^2 - 1 = 0(x - 1)(x + 1) = 0\)

So we have two critical points from this factor: x = 1 and x = -1.

\(Factor 2: x^4 + 1 = 0\)

This factor does not have any real solutions since\(x^4 + 1\) is always positive for real values of x.

Therefore, the critical points are x = 1 and x = -1.

To determine the nature of these critical points, we can analyze the second derivative or observe the behavior of the function around the critical points.

Let's find the second derivative of g(x):

\(g''(x) = d/dx [x^8 - 1]\\= 8x^7\)

Now, substitute the critical points into the second derivative:

\(g''(1) = 8(1)^7 = 8\\g''(-1) = 8(-1)^7 = -8\)

Since g''(1) > 0, the function has a relative minimum at x = 1.

And since g''(-1) < 0, the function has a relative maximum at x = -1.

Therefore, the relative extrema of the function  \(g(x) = (1/9)x^9 - x\)  are:

Relative minimum at x = 1

Relative maximum at x = -1

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Answer:

C

Step-by-step explanation:

Its c im smart trust me

Answer: C

Step-by-step explanation:

2x - y = 1

-2x         -2x

-y = -2x + 1

(-1) -y = -2x + 1 (1)

y = 2x-1

slope is positive 2/1, and the y-intercept is -1

To assess the likelihood of the sample results given the population proportion, we can use statistical inference and conduct a hypothesis test.

In this case, we compare the observed sample proportion to the assumed population proportion.

Define the null hypothesis (H0) and alternative hypothesis (Ha). In this case, the null hypothesis is that the population proportion is equal to 0.49, and the alternative hypothesis is that the population proportion is not equal to 0.49.

Calculate the test statistic using the formula: test statistic = (sample proportion - assumed population proportion) / standard error of the sample proportion.

Compute the standard error of the sample proportion using the formula: standard error = sqrt[(assumed population proportion * (1 - assumed population proportion)) / sample size].

Determine the p-value associated with the test statistic. This represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, assuming the null hypothesis is true.

Compare the p-value to a predetermined significance level (e.g., 0.05) to make a decision. If the p-value is less than the significance level, we reject the null hypothesis and conclude that the observed sample proportion is significantly different from the assumed population proportion.

Based on the result, select the appropriate answer choice that describes the likelihood of a wrong call in the election if exit polling alone is considered.

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Answer:

B

Step-by-step explanation:

hope this helps with the work

Answer:

\(A'(t) = rA(t)\)

Step-by-step explanation:

Given

\(A(t) \to\) Amount

Required

The differential equation

The equation for the amount is:

\(A(t) = A_0 * e^{rt}\)

Where:

\(A_0 \to\) initial amount

\(r \to\) rate

\(t \to\) time

Differentiate\(A(t) = A_0 * e^{rt}\)

\(A'(t) = A_0 * r * e^{rt}\)

So, we have:

\(A'(t) = rA_0 * e^{rt}\)

From the question, we have: \(A(t) = A_0 * e^{rt}\)

So, the equation becomes

\(A'(t) = rA(t)\)

The simplified form of the expression (2⁴)⁻¹ is 1/2⁴ (one over two raised to the power of four).

The integers exponents are the exponents that should be an integer. It can be either a positive integer or a negative integer. In this, the positive integer exponents describe how many times the base number should be multiplied by itself.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

It is given that the expression is (2⁴)⁻¹

Now,

using the integer exponent properties,

=> (2⁴)⁻¹  

=> (2)⁴* ⁻¹

=> (2)⁻⁴

=> 1/2⁴

Therefore, the answer is 1/2⁴ (one over two raised to the power of four) derived using the properties of integer exponents.

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Answer:10°

Step-by-step explanation:

Triangle BDC is an isoceles triangle

180-30=150

150÷2=75

Then triangle ADC

75+30+65=170

180-170=10

Answer:

ΔBDC is isosceles, meaning the two base angles are equal. to find them you need to:

180 - 30 = 150 ÷ 2 = 75. so , each of the base angles is 75°

∠BDC + ∠BCD = ∠ABD

30 + 75 = 105°

so, x = 180 - (105+65) = 10°

you will understand better if you draw the figure and fill in all the angles following my explanation.

x = 10°

The integral over the interval [0, 9] of the function f(x) = \(40.5 + 2.06x - 0.789x^2\) represents the total population in millions of a particular area within the age range from 0 to 90 years.

To find the integral over the interval [0, 9] of the given function f(x), we can use the fundamental theorem of calculus. The integral is calculated as follows:

∫[0,9]\((40.5 + 2.06x - 0.789x^2)\) dx

Integrating term by term, we get:

\((40.5x + 1.03x^2 - (0.789/3)x^3)\) evaluated from 0 to 9

Plugging in the upper and lower limits, we have:  

\((40.5(9) + 1.03(9)^2 - (0.789/3)(9)^3) - (40.5(0) + 1.03(0)^2 - (0.789/3)(0)^3)\)

Simplifying this expression yields the integral value, which represents the total population in millions within the age range from 0 to 90 years.

The integral of the age distribution function over the interval [0, 9] essentially gives us the cumulative sum of the population for each age group from 0 to 90 years. By integrating the function, we are finding the area under the curve, which corresponds to the total population within the specified age range.

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In the context of economics, the term “break-even point” is used to indicate the number necessary to make enough money to keep going, and it is expressed in both units and dollars.

Break-even point is a term used in cost accounting to describe the point at which total cost and total revenue are equal. At this point, there is no profit or loss; it is a neutral zone. At this point, a firm's revenue from the sale of products and services is just sufficient to cover the total costs of producing those products and services.

The break-even point can be expressed in terms of units sold or in terms of total revenue. The point at which the total revenue equals total cost is the break-even point in terms of dollars. The point at which the number of units sold equals the fixed costs divided by the contribution margin per unit is the break-even point in terms of units sold. Therefore, the break-even point is expressed in both units and dollars to show the number necessary to make enough money to keep going.

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