Solve the compound inequality:
6< x -2<14

Answer:

.

Step-by-step explanation:

2: 5, 10, 261.8, 785.4, 0.33

3: 7, 20, 1,026.3, 3,078.8, 0.33

4: 8, 6, 402.1, 1,206.4, 0.33

5: 12, 11, 1,658.8, 4,976.3, 0.33

Answer:

Hello,

Step-by-step explanation:

0=x²+17x+72=x²+8x+9x+72=x(x+8)+9(x+8)=(x+8)(x+9)

x=[-9,-8]

Answer:

\(x = - 8 \: - 9\)

Step-by-step explanation:

\(1. \: {x}^{2} + 72 + 17x = 0 \\ 2. \: (x + 8)(x + 9) = 0 \\ 3. \: x = - 8 \: - 9\)

The given equation is: 1 × 3 + 3 × 5 + ... + (2n - 1)(2n + 1) = 2n + 1 / n

To prove that the given equation is correct, we need to verify if it satisfies the Basis Step, Induction Hypothesis and Induction

Step.1. Basis Step:

When n = 1, the left-hand side of the equation is 1 × 3 = 3. Putting n = 1 in the right-hand side of the equation we get:(2 x 1) + 1 / 1 = 3

Hence the Basis Step is verified.

2. Induction Hypothesis:

We assume that the equation holds true for some n = k. That is,1 × 3 + 3 × 5 + ... + (2k - 1)(2k + 1) = 2k + 1 / k3.

Induction Step: We need to prove that the equation holds true for n = k + 1. That is,1 × 3 + 3 × 5 + ... + (2k + 1)(2k + 3) = 2k + 3 / (k + 1)

Now adding (2k + 1)(2k + 3) on both sides of the equation in the Induction Hypothesis, we get:1 × 3 + 3 × 5 + ... + (2k - 1)(2k + 1) + (2k + 1)(2k + 3) = 2k + 1 / k + (2k + 1)(2k + 3) = 2k + 1 + (2k + 1)(2k + 3) / (k + 1)

Factorizing, we get:2k + 1 + (2k + 1)(2k + 3) / (k + 1) = (2k + 3)(k + 1) / (k + 1) = 2k + 3

Thus the Induction Step is verified. Hence proved that the equation1 × 3 + 3 × 5 + ... + (2n - 1)(2n + 1) = 2n + 1 / n is true. Therefore, this is a valid formula for the given equation.

The given formula satisfies the Basis Step, Induction Hypothesis, and Induction Step.

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Answer:

-5/2

Step-by-step explanation:

Slope intercept form = y=mx+b

M=Slope

B=y-intercept

Answer:

-5/2 is the slope

Step-by-step explanation:

the form that it is currently in is slope intercept form

( y= mx+b ) m is the is the slope and x is a variable. -5 is the y intercept.

Jody has created a systematic sampling error by forgetting to include a segment of the population that is relevant to the study.

Systematic sampling is a sampling method where every nth member of a population is selected to be part of the sample. In Jody's case, she forgot to include a specific segment of the population, which means that the sampling process was not systematic. This error can introduce bias and affect the representativeness of the sample.

No calculations are required for this type of error.

Jody's mistake in not including a relevant segment of the population has resulted in a systematic sampling error. To ensure the accuracy and validity of the study, it is important to rectify this error by including the missing segment or adjusting the sampling method accordingly.

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If f and f ◦g are one-to-one, then g is one-to-one.

A function f is one-to-one if it has one and only one preimage in the domain. one-to-one functions are also called injective functions.

i.e., distinct points in the domain will have distinct images.

Mathematically, if f(x) = f(y), then x = y

So here f and f o g are one-to-one.

i.e., f(x) = f(y) ⇒ x = y

and (f o g)(x) = (f o g)(y) ⇒ x = y

So consider g(x) = g(y)

⇒ f(g(x) = f(g(y))

⇒ (f o g)(x) = (f o g)(y)

⇒ x = y [Since f o g is one-to-one]

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As x approaches zero from the left, the expression 4 + x/3 + f(1/x) simplifies to 6. Therefore, the limit lim x → 0- [4 + x/3 + f(1/x)] exists, and its value is 6.

To determine the existence and value of the limit, we need to consider the behavior of the function f(x) as x approaches zero from the left (x → 0-).

Given that lim x → -∞ f(x) = 2, we know that as x approaches negative infinity, f(x) approaches 2. Similarly, from lim x → ∞ f(x) = 4, we can conclude that as x approaches positive infinity, f(x) approaches 4.

Now, let's consider the expression 4 + x/3 + f(1/x). As x approaches zero from the left (x → 0-), the term 4 + x/3 remains constant, and the term f(1/x) becomes f(1/0-) (since 1/x approaches negative infinity).

Since f(x) approaches 2 as x → -∞, we can substitute f(1/x) with 2 in the expression. Thus, the expression becomes 4 + x/3 + 2.

Now, as x approaches zero from the left (x → 0-), the term x/3 approaches 0, while the constant terms 4 and 2 remain unchanged. Therefore, the expression 4 + x/3 + 2 becomes 6.

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Answer:

504 = 12 x 42

Step-by-step explanation:

The highest common factor of 12 and 42 is 6.

So, the numbers are 12 and 42.

You're welcome! :)

Answer:

04x=24

Step-by-step explanation:

04x=24

divide both sides by 4 to let x stand alone

04x÷4=24÷4

x=6

The equation 3+7+2=+2 is actually not true, but false.

The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.

In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.

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The chi-squared statistic can be used to determine whether there is a significant association between the two variables.

What is chi-squared statistic?

When the sample sizes are large, a chi-squared test is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine whether two category factors have independent effects on the test statistic.

To test whether people who kiss more than ten times a day wear brighter colors to work than those who do not, the appropriate test statistic to use would be the chi-squared statistic.

The chi-squared statistic is a measure of the difference between observed and expected frequencies in a contingency table.

Once we have the contingency table, we can calculate the chi-squared statistic using the following formula:

     \(chi-squared = ((observed - expected)^2 / expected)\)

In this case, the null hypothesis is that there is no association between kissing more than ten times a day and wearing bright colors to work. To calculate the expected frequency of each cell, we need to use the formula:

    expected = (row total * column total) / sample size)

Plugging in the values from our contingency table, we can calculate the chi-squared statistic as follows:

     \(chi-squared = (10 - 15)^2 / 15 + (20 - 15)^2 / 15\\\\= 25 / 15 + 25 / 15\\\\= 2\)

The chi-squared statistic can be used to determine whether there is a significant association between the two variables.

Refer following diagram.

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Explanation:

Subtract the second equation from the first one

\(\ \ \ \ 3x+3y-5z = 4 \ \ ... \text{ eq 1}\\-(4x-4y+z = -1) \ \ ... \text{ eq 2}\\---------\\\ \ -x+7y-6z = 5\)

Let's call that result equation 4.

Now focus on equation 3 and equation 4

equation 3 is   -x+7y-6z = 2

equation 4 is   -x+7y-6z = 5

Note how the left hand sides are identical, but the right hand sides are different. This means that we have an inconsistent system with no solutions. No matter what numbers we pick for x,y,z, there is no way to make all three given original equations to be true.

Answer:

B

Step-by-step explanation:

each time the step changes, the amount of vertices(points) increases by 1. the last number of points was 4, so if you increase 4 by 1 you will get 5. figure B has 5 points!

Answer:

Option B

Step-by-step explanation:

With the circle series, there is a figure with an increasing number of points that are on the circle.

Circle one has two dots, circle two has three dots, circle three has four dots, etc.

It would make the most sense if the circle in the next series have five dots.

Option B should be the correct answer.  

If all six bounds (limits of integration) are constant (numerical values, no variables) in cylindrical coordinates, then we must have a rectangular box-like region.

This is because in cylindrical coordinates, we have three variables: radius, angle, and height. When all six bounds are constants, we are essentially fixing the range of each variable, resulting in a rectangular box-like region.

In spherical coordinates, if all six bounds are constant, then we must have a rectangular pyramid-like region. This is because in spherical coordinates, we have three variables: radius, polar angle, and azimuthal angle. When all six bounds are constants, we are essentially fixing the range of each variable, resulting in a rectangular pyramid-like region.

It is not possible to have the exact same region represented with only constants in both cylindrical and spherical coordinates simultaneously. This is because the two coordinate systems have different geometric shapes and different ways of representing the variables. However, it is possible for the regions to have similar shapes and for the bounds to have similar numerical values in both systems.

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To solve this problem, you can use the following formula for simple interest:

where P is the initial amount, r is the rate of interest in decimal form, and t is the time in years.

Substituting A=1920, r=0.08, t=6, and solving for P, you get:

Simplifying, you get:

The required measures are :

the length of the rectangle is equal to 5 + x = 5 + 5 = 10 inches

the breadth of the rectangle = x = 5 inches

Given that perimeter of the rectangle is equal to 30 inch

Let the width be x

thus the length will become 5 + breadth = 5 + x

As we know that the perimeter of rectangle can be calculated by the formula

perimeter = 2 ( length + breadth )

perimeter = 2 ( 5 + x + x )

30 = 10 + 2x + 2x

Bringing the like terms together and we will get

30 - 10 = 4x

this implies

20 = 4x

On dividing 4 on both sides and we will get

5 = x

Thus the length of the rectangle is equal to 5 + x = 5 + 5 = 10 inches

And the breadth of the rectangle = x = 5 inches

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Answer:

6b +8

Step-by-step explanation:

2b + 4b = 6b

5 +3 = 8

I hope this helps

Answer:

x = - 10, x = 10

Step-by-step explanation:

Given

x² - 100 = 0 ( add 100 to both sides )

x² = 100 ( take the square root of both sides )

x = ± \(\sqrt{100}\) = ± 10

solutions are x = - 10, x = 10

Answer:

991041.2

Step-by-step explanation:

You just have to use a calculator and the order of operations

The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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Step 1: problem

Step 2: Concept

Step 3: Method

Final answer

Answer:

D

Step-by-step explanation:

the hypotenuse is 10 cm one leg is 8 cm and the other leg is 6 cm

The temperature was 48° at least once throughout the day as the temperature rises from 43° to 56° and 43° < 48° < 56° .  

The temperature was 43° at 3 PM and it rises to 56°  at 7.30 PM.

So we know that the rise of temperature in linear , hence the temperature will follow the rule of real numbers. Hence the temperature will increase through all the possible numbers between 43 and 56

Again 43° < 48° < 56°  , so at least once the temperature will be 48 ° .

You can think about integers as either independent objects or as a tool for problem-solving. The study of analytical objects (such as the Riemann zeta function) that somehow encode features of integers, primes, or any other number-theoretic objects is often the best method for understanding number theory issues (analytic number theory).

Most people refer to number theory as arithmetic. By the turn of the 20th century, "numerical theory" had taken its place.  (The term "arithmetic" is usually used to refer to "elementary computations," but it has come to signify more concepts in mathematical logic and computer technology, such as floating-point arithmetic.)

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Required correct order is d, c, b, e, a.

What is the correct order?

1) Add or subtract to move the constant to the right-hand side of the equation.

2) Then we need split the middle term of the left hand side into two parts such that the product of these two parts is equal to the coefficient of the x-term.

3) Factor the first three terms of the left-hand side of the equation by grouping.

4) Then Rewrite the left-hand side of the equation as a perfect square trinomial by adding the square of half the coefficient of the x-term

5) The last step will be solve the equation by taking the square root of both sides of the equation.

Therefore, Required correct order is d, c, b, e, a.

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Answer:

Step-by-step explanation:

66 mile per hour .

Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

Distance = 13 units

Point A: (8, -7)

Point B: (-4, -2)

\(\sqrt{(8 + 4)^{2} + (-7 + 2)^{2} }\)

\(\sqrt{(12)^{2} + (-5)^{2} }\)

\(\sqrt{144 + 25 }\)

\(\sqrt{169}\)

\(13\)

Answer:

\(\boxed {d = 13}\)

Step-by-step explanation:

Use the Distance Formula to help you find the distance between the two following points:

\(d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\)

(where \((x_{1}, y_{1})\) represents the first point and \((x_{2}, y_{2})\) represents the second point)

-Apply the two following onto the formula:

\((x_{1}, y_{1}) = (8, -7)\)

\((x_{2}, y_{2}) = (-4, -2)\)

\(d = \sqrt{(-4 - 8)^{2} + (-2 + 7)^{2}}\)

-Solve for the distance:

\(d = \sqrt{(-4 - 8)^{2} + (-2 + 7)^{2}}\)

\(d = \sqrt{(-12)^{2} + 5^{2}}\)

\(d = \sqrt{144 + 25}\)

\(d = \sqrt{169}\)

\(\boxed {d = 13}\)

Therefore, the distance is \(13\).

Answer:

34

Step-by-step explanation:

Answer:

its c trust

Step-by-step explanation:

im trust worthy

Answer:

B. a group of data points around a value

Step-by-step explanation:

A cluster in math is when data is clustered or assembled around one particular value.