After consulting with his broker, Gregor Mendel purchased 100 shares of a computer company stock at $44. 41 per share. He also purchased 600 shares of a second company's stock at $19. 08 per share. Gregor's online broker charges $0. 04 per share. What is the total cost of the stock including the commission?

based on the principle of mathematical induction, we conclude that \(2^{n}\) > \(n^{2}\) for all n greater than 4.

By using mathematical induction, we can prove that \(2^{n}\) > \(n^{2}\) for all n greater than 4.

Base case (n = 5):

When n = 5, we have \(2^{5}\) = 32 and \(5^{2}\) = 25. Since 32 is indeed greater than 25, the inequality holds for n = 5.

Inductive step:

Assuming the inequality holds for some positive integer k: \(2^{k}\) > \(k^{2}\), we need to show that it also holds for k + 1: \(2^{(k+1) }\) > \((k+1)^{2}\)

Starting with the left-hand side:

\(2^{(k+1) }\) = 2 × \(2^{k}\)

Using the inductive assumption, we can rewrite it as:

\(2^{(k+1) }\) > 2 ×\(k^{2}\)

Now let's consider the right-hand side:

\((k+1)^{2}\) = \(k^{2}\) + 2k + 1

We want to show that 2 × \(k^{2}\) > \(k^{2}\) + 2k + 1.

Simplifying the inequality, we have:

\(k^{2}\) - 2k - 1 > 0

By analyzing the quadratic function f(k) = \(k^{2}\) - 2k - 1, we find that it is positive for all k greater than 4.

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Answer:

The constant of proportionality is \(\frac{9}{2}\)

Step-by-step explanation:

The constant of proportionality is the ratio between two directly proportional quantities

To find the constant of proportionality from the given graph choose a point on the line and substitute x and y in the equation of the proportionality by the coordinates of the point.

∵ Point (4, 18) lies on the line

∴ x = 4, y = 18

∵ The equation is y = kx

→ Substitute x by 4 and y by 18

∴ 18 = k(4)

∴ 18 = 4k

→ Divide both sides by 4 to find k

∴ \(\frac{18}{4}=\frac{4k}{4}\)

∴ \(\frac{18}{4}=k\)

→ Simplify the fraction by dividing up and down by 2

∴ \(\frac{9}{2}=k\)

∴ The constant of proportionality is \(\frac{9}{2}\)

Triangle with sides AB = 8cm , CA = 5cm , BC = 7cm and AB = 7cm , BC = 10cm , CA = 8cm can construct a Triangle.

Condition : For forming the triangle, the sum of two sides must be greater than the third side.

a.  AB = 4cm, CA = 3cm, BC = 10cm

   CA+BC=AB

   3+1=4

   4=4

Therefore, it cannot form a triangle because it is not satisfying the condition.

b.  AB = 8cm , CA = 5cm , BC = 7cm

    AB+CA>BC

    AB+BC>CA

    CA+BC>AB

    Therefore, it can form a triangle because it satisfies the condition.

c.  AB = 7cm, BC = 10cm, CA = 8cm

   AB+BC>CA

   AB+CA>BC

   BC+BC>AB

  Therefore, it can form triangle because it satisfies the condition.

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The probability of more than 1 death in a corps in a year is 0.125 and probability of no deaths in a corps over 6 years is 0.0257.

The variable can only take particular values from a given list of integers, which is most likely infinite, because the Poisson distribution is a discrete probability function. A Poisson distribution calculates the likelihood that an event will happen "x" times in a given amount of time. As a result of the Poisson experiment, we may define it as the probability distribution.

A statistical experiment called a Poisson experiment divides the trial's results into two categories, such as success or failure. A limiting process for the binomial distribution is the poisson distribution.

a. Let X denote the number of soldiers killed by horse kicks in one year. Then, T = 1 X has a Poisson distribution with mean,

EX = λT = 0.61

Therefore, the probability of more than one death in a corps in a year is

P(X>1) = 1 - P(X = 0) - P(X = 1)

= 1 - \(e^-^0^.^6^1\) 0.61⁰/0! - \(e^-^0^.^6^1\) 0.61¹/1!

= 0.125

Therefore, the probability of more than one death in a corps in a year is 0.125.

b) Let X denote the number of soldiers killed by horse kicks in five years. Then, T=5 and X has a Poisson distribution with mean

EX = λT = 0.61 x 6 = 3.66

Therefore, the probability of no death in a corps in a five years

P(X = 0) = \(e^-^3^.^6^6\) 3.66⁰/0!

= 0.0257

Therefore, probability of no death in a corps in a five years is 0.0257.

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Eliminating design confounds from a study can make it easier to determine if the iv influences the dv

Option (c) is correct answer.

Confounding variables are a type of irrelevant variable that are related to a study’s independent and dependent variables. Thus failing to account for confounding variables can cause wrong estimation of the relationship between independent and dependent variables.

Random assignment of study subjects to exposure of any links between exposure and confounders which reduces potential for confounding by generating groups that are fairly comparable with respect to known and unknown confounding variables.

Eliminating designs confounds from a study facilitates estimating the relationship between independent variables and dependent variables and also randomly assigning subjects helps to eliminate confounding variables.

Hence the correct options is (c).

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All these solutions fall within the interval [0, 2π), so the exact solutions to the equation tan(5x) = 0 in the interval [0, 2π) are:

x = 0, π/5, 2π/5, 3π/5, 4π/5

To solve the equation tan(5x) = 0 in the interval [0, 2π), we need to find the values of x that satisfy the equation.

First, let's recall the properties of the tangent function. The tangent function is equal to zero when the angle is an integer multiple of π, or:

tan(x) = 0 if x = nπ, where n is an integer.

Now, let's solve the equation tan(5x) = 0:

5x = nπ

To find the values of x in the interval [0, 2π), we need to consider the values of n that satisfy this equation.

For n = 0:

5x = 0

x = 0

For n = 1:

5x = π

x = π/5

For n = 2:

5x = 2π

x = 2π/5

For n = 3:

5x = 3π

x = 3π/5

For n = 4:

5x = 4π

x = 4π/5

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Thus, the obtained area of sector for the given circle is found as 43.96 in².

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle assessment and radius measurement are both crucial for solving circle-related difficulties.

The curved portion that runs along the circle's perimeter and joins the ends of a two radii that make up a sector is known as the sector arc.

given data:

Formula for the area of sector:

area of sector = Ф /360 * (πr²)

area of sector = 140/360 * (3.14 *6²)

area of sector = 7/18 * 3.14 *36

area of sector = 43.96 in²

Thus, the obtained area of sector for the given circle is found as 43.96 in².

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Answer:

proportional

Step-by-step explanation:

20 : 25 :: 36 : 45

Product of means = 25*36 = 900

Product of extremes = 20 * 45 = 900

Product of means = Product of extremes

So, the number of pages read  is proportional to your time

Answer: $164

Step-by-step explanation:

25*7=175

175+12.5

226.50-187.50

5*25=125+39

Jones family payed $164

Answer:

r = 20 km

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Circumference of a Circle Formula: C = 2πr

Step-by-step explanation:

Step 1: Define

Identify variables

C = 125.6 km

Step 2: Solve for r

Answer:

197.29

Step-by-step explanation:

Multiple the circumfernece by 3.14 and then divide that number by 2.

Answer:

\(f(2)=18\)

Step-by-step explanation:

Assuming the "x" to be an exponent:

\(f(x)=2(3)^x\)

\(f(2)=2(3)^2\)

\(f(2)=2(9)\)

\(f(2)=18\)

Answer: 235 people got a real one

Step-by-step explanation:

The volume of plaster Darla needs for the miniature stairs is 418³.

The volume is the space occupied by a three-dimensional object.

Volume is the product of the multiplication of length, width, and height.

We first calculate the total volume for this situation, assuming that the stairs have not cut portions.

Secondly, calculate the volume of the cut portions and subtract the result from the total volume to get the volume of the stairs, which represents the quantity of plaster required by Darla.

Length of the miniature stairs = 12 cm

Width of the miniature stairs = 11 cm

Height of the miniature stairs = 4 cm

The volume of the stairs with the cut portion = 528 cm³ (12 x 11 x 4)

The length of the cut portion of the stairs = 12 cm

The width of the cut portion of the stairs = 11 cm

The height of the cut portion of the stairs = 2 cm (4 - 2)

The volume of the cut portion of the stairs = 110 cm³ (11 x 5 x 2)

The volume of the stairs without the cut portion = 418 cm³ (528 - 120)

The total volume of plaster can also be computed separately as the volume of the larger object plus the volume of the smaller object.

418 cm³= (7 cm x 4 cm x 11 cm) + (5 cm x 2 cm x 11 cm)

= (308 cm³ + 110 cm³)

Thus, the quantity (volume) of plaster Darla needs is 418 cm³.

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Answer:

Dr. Maette

Step-by-step explanation:

I'm not sure I've never read this :/

Answer:

The answer is D I think :)))

Answer: THE ANSWER IS -1/36

Step by step: Find the LCD then combine

The answer is : -1/36

You forgot the 1 for 18 in the last question lol

Hope this helps, pls mark as brainliest :))))

Altman’s discriminant function is a formula that is used to predict the probability of bankruptcy of a firm.

It takes into account various financial ratios and gives a score known as the Z-score to firms. The formula for Altman’s discriminant function is:

Z=1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

Now we can calculate the z score for the firm by substituting the values of x1, x2, x3, x4 and x5 in the above equation.

Let the values of x1, x2, x3, x4 and x5 be 2.1, 3.5, 4.2, 0.7 and 2.3 respectively.

Then,z = 1.2(2.1) + 1.4(3.5) + 3.3(4.2) + 0.6(0.7) + 1.0(2.3)z = 2.52 + 4.9 + 13.86 + 0.42 + 2.3z = 23.0

Therefore, the z score for the firm is 23.0.

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Answer:

82.6 pounds per cubic meter

Step-by-step explanation:

a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.

b) Nyoko cannot find a value of b so that the equation has no solutions.

The equation 1 is given as follows:

6x - 5 + 2x = 4(2x - 1) - 1.

Combining the like terms and applying the distributive property, the simplified equations are given as follows:

8x - 5 = 8x - 4 - 1

8x - 5 = 8x - 5.

As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.

The equation 2 is given as follows:

3x + 7 = bx + 7.

A system of linear equations will have zero solutions when:

As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.

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Answer:

  yes

Step-by-step explanation:

You want a graph of P = 125 +50W.

The given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.

Usually, the independent variable is graphed on the horizontal axis, which you have done.

The dependent variable is graphed on the vertical axis, which you have done.

The axes are correctly labeled and graduated.

The "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.

The slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.

Yes, you properly graphed the equation.

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The zeros of the polynomial are: x1 = [3√3 + √147]/4 and x2 = [3√3 - √147]/4

In mathematics, a polynomial is an expression consisting of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, but not division by variables. The variables usually represent numbers, but can also represent other mathematical objects such as matrices, functions, or geometrical shapes. The coefficients are usually real or complex numbers, but can also be integers, rational numbers, or elements of other algebraic structures.

To find the zeros of the given polynomial, we need to solve the quadratic equation:

2x² - 3√3x - 15 = 0

We can solve this by using the quadratic formula:

x = [-b ± √(b² - 4ac)]/2a

Here, a = 2, b = -3√3, and c = -15. Substituting these values, we get:

x = [-(-3√3) ± √((-3√3)² - 4(2)(-15))]/(2(2))

x = [3√3 ± √(27 + 120)]/4

x = [3√3 ± √147]/4

Therefore, the zeros of the polynomial are:

x1 = [3√3 + √147]/4

x2 = [3√3 - √147]/4

To verify the relationship between the zeros and coefficients of the polynomial, we can use Vieta's formulas:

The sum of the zeros of a quadratic equation is equal to -b/a.

The product of the zeros of a quadratic equation is equal to c/a.

Here, the sum of the zeros is:

x1 + x2 = [3√3 + √147]/4 + [3√3 - √147]/4

= (6/4)√3/2

= (3/2)√3

The product of the zeros is:

x1x2 = ([3√3 + √147]/4) ([3√3 - √147]/4)

= [27 - 147]/16

= -3

Now, we can compare these values with the coefficients of the given polynomial:

2x² - 3√3x - 15 = 0

Here, a = 2, b = -3√3, and c = -15. We can see that:

-b/a = 3√3/2, which is equal to the sum of the zeros.

c/a = -15/2, which is equal to the negative of the product of the zeros.

Therefore, we have verified the relationship between the zeros and coefficients of the polynomial.

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The gradient of a function represents the vector of its partial derivatives. To compute the gradient of the function f(x, y) = -3x^2 + 5y, we differentiate it with respect to x and y.

The partial derivative with respect to x is found by taking the derivative of -3x^2, which is -6x. The partial derivative with respect to y is found by taking the derivative of 5y, which is 5. Therefore, the gradient of f(x, y) is ∇f(x, y) = (-6x, 5).

To find the gradient at the point (8, -9), we substitute x = 8 and y = -9 into the gradient expression. Thus, ∇f(8, -9) = (-6(8), 5) = (-48, 5). Therefore, the gradient of the function at the given point is -48i + 5j. Hence, the correct option is d. -48i + 5j.

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Part A

The slope of line \(a\) is \(\frac{1}{2}\). Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is \(\boxed{-2}\).

Part B

Using point-slope form, the equation of line \(b\) is \(y-2=-2(x+6)\).

The \(y\)-intercept is where \(x=0\).

\(y-2=-2(0+6) \implies y-2=-12 \implies y=\boxed{-10}\)

Answer: The null hypothesis should be accepted and The results were not statistically significant

Step-by-step explanation:

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The relation O is not reflexive, symmetric, and not transitive is one of the following statements that is true about the relation O.  which is option (C).


Given, \(\forall m, n \in Z, m O n \longleftrightarrow \exists k \in Z \mid(m-n)=2 k+1\)
Let's verify for the following relations :
Reflexive relation:
\(\forall a\in Z, a O a \longrightarrow \exists k\in Z \mid (a-a)= 2k+1\)
\(0\neq 2k+1\) for all k \(\in\) Z
Since 2k+1 can never be zero for any k \(\in\) Z, hence we conclude that the relation O is not reflexive.
Symmetric relation:
Suppose a, b \(\in\) Zsuch that a O b i.e. (a-b)=2k+1, where k\(\in\) Z.
Now, we need to check whether b O a is true or not i.e. (b-a)=2j+1 for some j\(\in\) Z
We have,
\((a-b) = 2k+1 \longrightarrow (b-a) = -2k-1 = 2(-k) - 1\)
Let j=-k-1, then we have j\(\in\) Z and 2j+1 = -2k-1
Hence, (b-a) = 2j+1, and we conclude that the relation O is symmetric.
Transitive relation:
Suppose a, b, c\(\in\) Z such that a O b and b O c.
Now, we need to check whether a O c is true or not.
We have,
(a-b)=2k_1+1 and (b-c)=2k_2+1 for some k_1,k_2\(\in\) Z
(a-b)+(b-c) = 2k_1+1 + 2k_2+1
a-c = 2k_1+2k_2+2
Let j=k_1+k_2+1, then we have j\(\in\) Z and a-c=2j
Hence, (a-c) is even and we conclude that the relation O is not transitive.
Therefore, the relation O is not reflexive, symmetric, and not transitive. Hence, option (C) is the correct answer.

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You should only use a closed dot for the symbols ≤ and ≥.

There are two types of dots used when graphing inequalities, closed and open.

So, for exampe in:

x > 3.

We would put an open dot at 3, because the value x = 3 is not a solution, but all the values at the right of the 3 are solutions.

In the other hand, for:

x ≥ 3

Now 3 is in fact a solution, so here we should use a closed dot.

Then, answering the question.

"When you graph an inequality, you used a closed dot when you use which symbols?"

The ≤ and ≥ symbols.

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Answer:

256pie unit³

Step-by-step explanation:

The volume of a cylinder

=pie x r² x h

= pie x 8² x 4

256pie unit³

Step-by-step explanation:

-3p+6p is 3p

-3 + 6 = 3

So when you simplify the equation you get 3p