If the bath term is n^2-5 what are the first 3 terms and the tenth

The statement "if a > √n and b > √n, then n ≠ ab" is saying that if two positive integers, a and b, are both greater than the square root of another positive integer n, then the product of a and b is not equal to n. This statement can be proven by contradiction.

Suppose the opposite is true, and that n = ab, where a and b are positive integers such that a > √n and b > √n. Then, because n = ab, we have n/a = b and n/b = a. But because both a and b are greater than the square root of n, we have √n < a and √n < b. This leads to a contradiction, because it means that n/a = b > √n, but √n is the largest possible value of b such that b < n/a.

Thus, we have proven that if a > √n and b > √n, then n cannot equal ab, and our original statement is true.

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15

Step-by-step explanation:

20/8 =2.5

6x2.5=15

therefore, 15

The approximate speed of a vehicle that left a skid mark measuring 100 feet is 47.63 miles per hour

Given the formula:

0.75d = s² / 30.25

Where,

d = length of the vehicle’s skid marks in feet = 100 feet

s = speed in miles per hour

Substitute d = 100 feet into the equation

0.75d = s² / 30.25

0.75(100) = s² / 30.25

75 = s² / 30.25

cross product

75 × 30.25 = s²

2,268.75 = s²

find the square root of both sides

s = √2,268.75

s = 47.63 miles per hour

Ultimately, 47.63 miles per hour is the approximate speed of the vehicle.

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The temperature is a function of time, as there is a single temperature for each instant of time.

A relation represents a function when each input value is mapped to a single output value.

For the set in this problem, we have that:

As there are no repeated inputs, the temperature is in fact a function of time.

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Answer:

(4x+1) (x+6)

(y-1)(5y+3)

(k-2)(7k+5)

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

3 is a factor of 81 because on dividing 81 by 3, we get no remainder and 27, that is, the quotient in this division, which is also a factor of 81.

The nucleus of a 125Xe atom (an isotope of the element xenon with mass 125 u) is 6.0 fm in diameter. It has 54 protons and charge q=+54e (1 fm = 1 femtometer = 10-15 meters).

An atom has a charge when it has an unequal number of protons and electrons. Protons have a positive charge, while electrons have a negative charge. When there is an excess of protons, the atom has a positive charge, and when there is an excess of electrons, the atom has a negative charge. These atoms are called ions. The total charge of an atom is calculated by subtracting the number of protons from the number of electrons. The result is the atom's net charge.

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JaCorren's height at the end of the year will be approximately 67.61 inches.

The concept used in this problem is exponential growth. The equation y = 60 * (1 + 0.01)^x models the growth of JaCorren's height over time, where the height (y) increases by 1% each month (x). The exponent (1 + 0.01)^x represents the cumulative effect of the 1% monthly growth over the number of months.

In this equation, 60 is the starting height, 0.01 is the growth rate, and x is the number of months. By increasing the exponent x, we can see how the height (y) changes over time, which represents the exponential growth of JaCorren's height during his growth spurt.

Here's the mathematical equation to model JaCorren's growth spurt over the next year:

y = 60 * (1 + 0.01)^x

Where:

y is the height of JaCorren in inches

x is the number of months

60 is the starting height

0.01 is the growth rate (1% per month)

To find JaCorren's height at the end of the year (x = 12 months), we can substitute x = 12 into the equation:

y = 60 * (1 + 0.01)^12

y = 60 * 1.01^12

y ≈ 67.61 inches

So, JaCorren's height at the end of the year will be approximately 67.61 inches.

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The function that models JaCorren's growth spurt over the next year can be expressed.

y = 60 * (1 + 0.01x)^x

Where x is the number of months, and y is the height of JaCorren in inches. The initial height of JaCorren is 60 inches, and the growth increase is 1% each month, which is represented by 0.01. The function calculates the height of JaCorren after x months by taking into account the monthly growth increase, represented by (1 + 0.01x)^x.

Here is a function in Python that models JaCorren's growth spurt over the next year:

def height_over_time(x):

   y = 60 * (1 + 0.01 * x) ** 12

   return y

This function takes in the number of months x and returns the height y of JaCorren in inches after x months. The formula used is y = 60 * (1 + 0.01 * x) ** 12, which calculates the growth of JaCorren by 1% per month over the next year (12 months).

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Answer:

2 1/2

Step-by-step explanation:

(a)  The function f: r -> r is not one-to-one (injective) since there are two separate inputs (2 and -2) that have the same result. It is defined as f (x) = x2 - 4x + 9. (9).

(b)  The element (-1) that occurs in the codomain of the function f: r -> r, which is defined by f (x) = x2 - 4x + 9, prevents the function from being onto (surjective).

As a result, neither one-to-one nor onto are applicable to the function

f: r -> r defined by f (x) = x2 - 4x + 9.

According to the Question

We must demonstrate that if a function f(x1) = f(x2), then x1 = x2 in order to establish whether the function is one-to-one (injective). To put it another way, no two unique inputs produce the same outcome.

We must demonstrate that there exists an x in the domain of f such that f(x) = y for every element y in the codomain of f in order to establish if a function f is onto (surjective). Alternatively expressed, each output in the codomain has an associated input in the domain.

For the function f: r → r defined by f (x) = x^2 - 4x + 9, we can easily see that it is not one-to-one since f(2) = f(-2) = 9.

It is also not onto, as the codomain of f is all real numbers and there is no real number x such that f(x) = -1.

So, we can conclude that the function f: r → r defined by f (x) = x^2 - 4x + 9 is neither one-to-one nor onto.

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Answer:

6a + 12b + 18c

Step-by-step explanation:

Distribute 6 to all numbers in the parenthesis.

(6(a) + 6(2b) + 6(3c))

[6a + 12b + 18c]

False

If it doesn't have an equal sign ( = ), it's not an equation. It would be considered an expression.

Answer: False

Step-by-step explanation:

The function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

7) The given functions are f(x)=2x+3 and g(x)=x²-3x-6.

Here, f·g(x) =f(x)×g(x)

f·g(x) = (2x+3)×(x²-3x-6)

f·g(x) = 2x(x²-3x-6)+3(x²-3x-6)

f·g(x) = 2x³-6x²-12x+3x²-9x-18

f·g(x) = 2x³-3x²-21x-18

8) The given functions are f(x)=4x-5 and g(x)=2x+8

f·g(x) =f(x)×g(x)

f·g(x) = (4x-5)×(2x+8)

f·g(x) = 4x(2x+8)-5(2x+8)

f·g(x) = 8x²+32x-10x-40

f·g(x) = 8x²+22x-40

Therefore, the function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.

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The total number of pieces of cake will be 2664

A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept.

The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

Ax+By=C is the typical form for linear equations in two variables.

2x+3y=5, for example, is a simple linear equation.

It is rather simple to get both intercepts when an equation is stated in this way (x and y).

Let c be the total number of pieces of cake.

We know that Mindy ate 333 pieces and Troy ate 1/4 of the total,

So, we can write it as:

333 + (1/4)c = 999

Expanding the second term:

333 + c/4 = 999

Solving for c:

c/4 + 333 = 999

Subtracting 333 from both sides:

c/4 = 666

Multiplying both sides by 4:

c = 2664

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The line segment is divided into the x-axis in the ratio 4:3.

The line segment joining the points (2, 4) and (-3, -2) is divided by the x-axis at the point where the y-coordinate is 0.

To find this point, we can set y=0 in the equation of the line that connects the two points.

The equation of the line is given by:

y = mx + c

The slope m can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the two points. Substituting the values, we get:

m = (-2 - 4) / (-3 - 2) = -6/ -5 = 6/5

The y-intercept c can be found using one of the points and the slope:

c = y - mx

Substituting the values, we get:

c = 4 - 6/5 * 2 = 4 - 6/5 * 2 = 4 - 3.2 = 0.8

So, the equation of the line is:

y = 6/5 x + 0.8

Setting y = 0, we get:

0 = 6/5 x + 0.8

-0.8 = 6/5 x

x = -0.8 * 5/6 = -4/3

Therefore, The line segment is divided into the x-axis in the ratio 4:3.

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The function g(x) is given by:

g(x) = (68/π) (1/x²) sin(π/4x²).

We have,

To find the integral of the function g(x) = ∫[0, x] (-34t cos(π/4t²)) dt, we can evaluate the integral using the fundamental theorem of calculus.

The antiderivative of -34t cos(π/4t²) with respect to t can be found by applying the chain rule in reverse.

We set u = π/4t² and find du/dt = -π/2t³.

Rearranging, we have dt = -(2/π) x (1/t³) du.

Substituting back into the integral:

g(x) = ∫[0, x] (-34tcos(π/4t²)) dt

= ∫[0, x] (-34tcos(u)) x -(2/π) x (1/t³) x du

= (68/π) x ∫[0, x] (cos(u)/t²) du.

Now, we can evaluate this integral.

The integral of (cos(u)/t²) with respect to u can be found using basic integration rules:

∫ (cos(u)/t²) du = (1/t²) x ∫ cos(u) du

= (1/t²) x sin(u) + C,

where C is the constant of integration.

Substituting back into the expression for g(x):

g(x) = (68/π)  [(1/t²) sin(u)] evaluated from 0 to x

= (68/π)  [(1/x²)  sin(π/4x²) - (1/0²)  sin(π/4 x 0²)]

= (68/π)  [(1/x²)  sin(π/4x²) - 0]

= (68/π) (1/x²) sin(π/4x²).

Therefore,

The function g(x) is given by:

g(x) = (68/π) (1/x²) sin(π/4x²).

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Answer:

See below

Step-by-step explanation:

Solve the equation using the quadratic formula

[tex]\displaystyle x^2-2x+2=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(2)}}{2(1)}\\ \\x=\frac{2\pm\sqrt{4-8}}{2}\\ \\x=\frac{2\pm\sqrt{-4}}{2}\\ \\x=\frac{2\pm2i}{2}\\ \\x=1\pm i[/tex]

Discriminant and Solution Analysis

As we determined in the quadratic formula, our discriminant is -4 because [tex]b^2-4ac=(-2)^2-4(1)(2)=-4[/tex], under the radical. Because it is negative, our solutions must be imaginary since the square root of a negative number is not real.

An integer is a whole number that can be positive, negative, or zero and is pronounced as "IN-tuh-jer."

Integers include things like -5, 1, 5, 8, 97, and 3,043.

5.643.1, -1.43, 1 3/4, 3.14,.09, and other non-integer numbers are a few examples.

Formally, the following describes the set of numbers designated Z:

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

The four most frequent ones are p, q, r, and s.

An infinite set is the set Z. In spite of the possibility of an unlimited number of items in a set, denumerability refers to the property that each element in the set can be represented by a list that implies its identity. The fact that 356,804,251 and -67,332 are integers whereas 356,804,251.5, -67,332.89, -4/3, and 0.232323... are not can be inferred from the list "..., -3, -2, -1, 0, 1, 2, 3,...."

There are no elements missing from either set when pairing the components of Z with N, the set of natural numbers. Let N = {1, 2, 3, ...}. Following that, the pairing may go like this:

The key criterion for assessing cardinality, or size, in infinite sets is the presence of a one-to-one relationship. Z shares the same cardinality with the sets of natural and rational numbers. Real, fictitious, and complex number sets, however, have cardinality that is more than Z.

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The mean/standard error of the sampling distribution of the proportion is 0.0111.

The root-mean square deviation, commonly known as the standard deviation and represented by the symbol, is the square root of the mean of the squares of all the values of a series calculated from the arithmetic mean.

How dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed value from the mean.

Any distribution will have roughly 95% of its values within two standard deviations of the mean. The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

When the standard deviation is low, the data cluster around the mean; when it is high, the data are more spread.

The formula to calculate the standard error of the sampling distribution of the sample proportion is:

[tex]$ SE(p) =\sqrt{\frac{p(1-p)}{n} }[/tex]

It is given that a bank believes that 8% of the people who receive loans will not make payments on time. That is,

Population proportion, p =0.08

Sample size, n= 800

Using the formula defined :

[tex]$ SE(p) =\sqrt{\frac{0.08(1-0.08)}{600} }[/tex]

[tex]$ SE(p) =\sqrt{0.000123}[/tex]

SE(p) = 0.0111

Thus,  the mean/standard error of the sampling distribution of the proportion is 0.0111.

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Answer:

Step-by-step explanation:you such a nerd and I will never help u

All people come very close to being able to float in water. therefore, 0.007 is the volume (in cubic meters) of a 50-kg woman.

Correct answer will be a. 0.007

The volume of a person in water is determined by their body density and the amount of air in their lungs. The volume can be estimated using the principle of buoyancy, which states that a body floating in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

In this case, we are given the weight of a 50-kg woman and asked to determine her volume in cubic meters. To do this, we can use the formula for buoyancy: Fb = ρf * V * g, where Fb is the buoyant force, ρf is the density of the fluid (water), V is the volume of the woman, and g is the acceleration due to gravity.

Since the woman is floating, the buoyant force is equal to her weight, so we can set these two equal to each other: ρf * V * g = 50 kg * 9.8 m/s^2. Solving for V, we find that V = 50 kg / (ρf * g) = 50 kg / (1000 kg/m^3 * 9.8 m/s^2) = 0.005 m^3.

Comparing this answer to the options given, we can see that the closest option is 0.007 m^3 (choice a), which is our final answer.

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If there is a correlation between two variables a and b, it may be because a causes b, or because b causes a, but it cannot be both is a False .

Any statistical association between two random variables or bivariate data, whether causal or not, is referred to in statistics as correlation or dependency. Although "correlation" can mean any kind of association in the broadest sense, in statistics it typically refers to the strength of a pair of variables' linear relationships.

In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are examined under the assumption or requirement that they are dependent on the values of other variables due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not perceived as dependant on any other factors.

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On [0, 2], A(x) can be represented by the linear equation A(x) = (1/2)x.

This means that for every x in the interval [0, 2], the value of A(x) is equal to one-half times x. For example, when x = 1, A(x) = (1/2)x = (1/2) * 1 = 1/2.

On [0, 2], A(x) can be represented by the linear equation A(x) = (1/2)x.

On (2,4], A(x) can be represented by the linear equation A(x) = ((-1/2)x + 2). This means that for every x in the interval (2,4], the value of A(x) is equal to one-half times x minus 2. For example, when x = 3, A(x) = ((-1/2)x + 2) = (-1/2) * 3 + 2 = 2 - 1.5 = 0.5.

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1. The slope of the secant line in terms of x and h is m(sec) =18x - 6 + 9h.

2. The m(sec) for h= 0.5, 0.1, and 0.01 at x = 1 is 16.5, 12.9 and 12.09 respectively.

3. The equation for the secant line at x = 1 with h = 0.01 is y = 12.09x - 0.09.

The function is g(x) = 9x^2 - 6x + 9

m(sec) = [tex]\frac{g(x+h)-g(h)}{h}[/tex]

m(sec) = [tex]\frac{(9(x+h)^2 - 6(x+h)+9)-(9x^2 - 6x+9))}{h}[/tex]

Simplifying

m(sec) = [tex]\frac{((9x^2+18xh+9h^2) - (6x+6h)+9)-9x^2 + 6x-9)}{h}[/tex]

m(sec) = [tex]\frac{(9x^2+18xh+9h^2 - 6x+6h+9-9x^2 + 6x-9)}{h}[/tex]

m(sec) = [tex]\frac{(18xh+9h^2 +6h)}{h}[/tex]

Taking h common

m(sec) =18x - 6 + 9h

At x = 1

m(sec) =18 - 6 + 9h

m(sec) = 12 + 9h

At h = 0.5

m(0.5) = 12 + 4.5 = 16.5

At h = 0.1

m(0.1) = 12 + .9 = 12.9

At h = 0.01

m(0.01) = 12 + .09 = 12.09

as h = 0 , m(sec) = 12

point-slope form

y - 12 = 12.09(x - 1)

y - 12 = 12.09x - 12.09

Add 12 on both side, we get

y = 12.09x - 0.09

The graph of the part c is given below.

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The difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.

When you hear the phrase "difference quotient formula," what comes to mind? Difference and quotient resemble the slope formula in appearance. Yes, the difference quotient formula does really provide the slope of a secant line drawn to a curve. What is a secant line? A line that joins any two points on a curve is known as the secant line.

Given that the function is f(x) = x³

The value of f(8 + h) = (x+ h)³ = x³ + 3x²h + 3xh³ + h³

The value of f(8) = (8)³ = 512

Substituting the value of f(8 + h) and f(8) we have:

f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h

Hence, the difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.

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Answer:

a person who fortells an event is called

The new price for each pillow case is Php 27.50.

The concept used in this problem is markup pricing, where a certain percentage is added to the cost price of a product to arrive at the selling price.

Markup is the difference between a product's selling price and cost as a percentage of the cost. For example, if a product sells for $125 and costs $100, the additional price increase is ($125 – $100) / $100) x 100 = 25%.

As given, Mr. Mosquera plans to add 10% to the original price which is Php 25. 00 each,

Php 25 * 10/100

= Php 2.50 for each pillow case.

So, the new price for each pillow case is

Php 25 + Php 2.50

= Php 27.50.

Therefore, the new price for each pillow case is Php 27.50.

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Mr. Mosquera ' price for each pillow is 27.50 php. His price for each pillow is 27.50 php.

Here, these values are given,

Total no. of pillows = 50

Original price of each pillow = 25.00 php

Original price of 50 pillows= 125000 php

After, planning to add 10% to the original price'

New price of pillow will increase after adding 10% to the previous price.

New price of each pillow became 25+ 25 of 10%

= 25+ 25 × 10/100

= 25+ 5/2

= 55/2

=27.50 php

New price of each pillow became 27.50 php.

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The value of c at which the function is continuous is 5/6.

For a function to be continuous at a point, the left and right limit of the function must exist and be equal at that point. In this case, the point is x = -5.

The function f(x) = c for x = -5, f(x) = 4 for x = 1, and f(x) = (x^2 - 25) / (x + 5)(x - 7) for x ≠ -5 and x ≠ 7.

To determine the value of c, we need to find the limit of f(x) as x approaches -5 from the left and from the right.

From the left, we have:

lim x→−5− f(x) = lim x→−5− (x^2 - 25) / (x + 5)(x - 7) = 5/6

From the right, we have:

lim x→−5+ f(x) = 5/6

For the function to be continuous at x = -5, we must have:

lim x→−5− f(x) = lim x→−5+ f(x) = c

c = 5/6

--The question is not readable, answering to the question below--

"For what value of c is the function continuous at x = -5?

f (x) = c for x=-5; f(x)=4 for x=1; f(x) = x^2-25 / (x+5)(x-7) otherwise"

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Answer:

Step-by-step explanation:

ill explain How to solve.

A:    

     x+4>15

     15-4=11

      x<11

C:

     6b=>54

     54/6=9

      b=>9

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Answer:

Step-by-step explanation: