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Simplify the following:
Holiday Bonus Problem
(5 Points)
X
{²+ + + ²x - 3X ICE +
R-X
{[(X + A)(X-A)M+A²M]E}
7
ruc
4AS
4AS
+
3X[(E+Y)²-(E-Y)²] * 3E[(Y + X)² – (Y-X)²] 3Y[(X + E)²-(X-E)²]
- BA}Y
4AS

The common difference in the sequence 7, 12, 17, 22, 27,… is that the difference between two numbers increases by five in the ascending order.

A sequence can be referred to or considered as the set of observations, which usually consists of numbers arranged in such a way that they described a common characteristic between them. A sequence can be exhaustive or inclusive, depending upon the numbers being used in the continuity of the sequence. It can also be said that a sequence is a logical arrangement.

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Complete question

what is the common difference in the sequence 7, 12, 17, 22, 27, ...?

one of two or more numbers that multiply together to form a specific product; a number that divides into another number with no remainder is a factor.

A component is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, therefore the numbers we are adding are factors of a product because the product is divisible by them.

Which of these four main types of factoring are they? The Grouping technique, the Differences in Two Squares, the Total or Difference in Cubes, as well as the Greatest Common Factors (GCF) are the four primary methods of factoring.

A factor is a value that completely divides another number. Consequently, the values we are multiplication are factors if multiplying two whole numbers results in a product.

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False. An objective function is necessary for both maximization and minimization problems.

An objective function is an equation that represents the goal of an optimization problem. It is used to evaluate the performance of a certain set of decisions. Regardless of whether the goal is to maximize or minimize an outcome, the objective function is a necessary component of an optimization problem. In a maximization problem, the objective function is used to determine the highest possible output that can be achieved. In a minimization problem, the objective function is used to determine the lowest possible output that can be achieved. Therefore, an objective function is necessary for both maximization and minimization problems.

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Answer:

y = 2x + 6

Step-by-step explanation:

The equation c = 2h + 6 represents the cost of renting tools for a given number of hours. The slope of this line is the rate at which the cost of renting the tools increases as the number of hours increases. Since the cost increases by $2.00 for each hour that the tools are rented, the slope of the line is 2.

A graph of this line would be a straight line with a slope of 2 and a y-intercept of 6. This means that the graph would pass through the point (0, 6), which represents the cost of renting the tools for 0 hours. The correct solution is therefore the graph of the equation y = 2x + 6.

What we should do is plot each part of the graph individually.

Step 1: Plot f(x) = 2x + 6 part

We know it starts at x = -5 (noninclusive) and ends at x = -2 (inclusive). Therefore, we can draw a line between the two points (-5, -4) and (-2, 2), with an open point at x = -5 and a closed point at x = -2

Step 2: Plot f(x) = 1 part

We know it starts at x = -2 (noninclusive) and ends at x = 2 (inclusive). Therefore, we can draw a line between the two points (-2, 1) and (2, 1), with an open point at x = -2 and a closed point at x = 2

Step 3: Plot f(x) = -3x + 10 part

We know it starts at x = 2 (noninclusive) and ends at x = 5 (inclusive). Therefore, we can draw a line between the two points (2, 4) and (5, -5), with an open point at x = 2 and a closed point at x = 5

You should end up with a graph that looks like the attached image!

The given function f(x) has been plotted in the graph piecewise with proper endpoints.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

As per the given piecewise function,

f(x) = [tex]\left \{ {{2x+6 \ \ \ \ -5 < x\leq -2}} \right.[/tex]

f(x) = [tex]\left \{ {{1 \ \ \ \ -2 < x\leq 2}} \right.[/tex]

f(x) = [tex]\left \{ {{-3x+10 \ \ \ \ 2 < x\leq 5}} \right.[/tex]

The function f(x) = 2x + 6 is a linear line with slope 2 and y-intercept 6 shown in red line -5 is excluded while - 2 is included.

The function f(x) = 1 is a constant horizontal line shown in the blue line that -2 excludes while  2 is included.

The function f(x) = -3x + 10 is a linear line with slope -3 and y-intercept 10 shown in the green line 2 is excluded while - 5 is included.

Hence "With the appropriate endpoints, the supplied function f(x) has been piecewise displayed in the graph".

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The curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1) is 0.178

In this question we need to find the curvature of r(t) = <3t, t^2, t^3> at the point (3, 1, 1).

The derivative of r(t) with respect to t is:

r'(t) = <3, 2t, 3t^2>

The point (3, 1, 1) corresponds to t = 1,

and r′(1) = <3, 2(1), 3(1)^2>

r'(1) = <3, 2, 3>

|r'(1)| = √(3^2 + 2^2 + 3^2)

|r'(1)| = √(9 + 4 + 9)

|r'(1)| = √(22)

|r'(1)| = 4.69

Now, r''(t) = <0, 2, 6t>

and r′'(1) = <0, 2, 6(1)>

r''(1) = <0, 2, 6>

r′(1) × r′′(1) = <0, 4, 18>

|r′(1) × r′′(1) |

= √(0^2 + 4^2 + 18^2)

= √(16 + 324)

= √340

= 18.44

So, the curvature of r(t) would be,

κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3

k(1) = 18.44 / 4.69³

k(1) = 0.178

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At [tex]$5 \%$[/tex] level, the data is not strong enough to establish the claim of toothpaste advertisement.

It is recommended to switch to new toothpaste.

(a)

The null and alternative hypotheses are,

[tex]$$\begin{aligned}& H_0: \mu=3 \\& H_1: \mu < 3\end{aligned}$$[/tex]

Here, [tex]$\mu$[/tex] is the hypothesized mean.

Let the sample size be [tex]$n=2500$[/tex].

Let the sample mean be [tex]$\bar{x}=2.95$[/tex].

Let the population standard deviation be [tex]$\sigma=1$[/tex].

Since, the population standard deviation is known, one sample z-test is used to test the claim.

The test statistic is,

[tex]$$\begin{aligned}z & =\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \\= & \frac{2.95-3}{\frac{1}{\sqrt{2500}}} \\& =-2.5\end{aligned}$$[/tex]

So, the test statistic is, [tex]$z=-2.5$[/tex].

Let the level of significance be [tex]$\alpha=0.05$[/tex].

Find the critical value.

Using the standard normal distribution area tables, the left tail critical value is,

[tex]$$z_{0.05}=-1.645$$[/tex]

z score table attached at the end of solution.

The test statistic value is falls in the rejection region. Reject the null hypothesis. Therefore, it can be concluded that this does not support the null hypothesis at 5 percent level. So, at [tex]$5 \%$[/tex] level, the data is not strong enough to establish the claim of toothpaste advertisement.

(b)

The value of test statistic is also less than [tex]$-Z_{0.1}=-2.33$[/tex].

So, the claim cannot be established even at 1 percent level. It is recommended to switch to new toothpaste.

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Answer:

1/ We use the SSS method to prove that triangle CBD = triangle ABD

2/ We use the AA method to prove that <CBD equal < ABD

Step-by-step explanation:

1/ SSS, or side side side method, is the method we use to see if triangles are the same or not, and we know that the sides of both triangles are equal; this proves that both triangles are equal!

2/ AA, or Angle Angle method, is the method we use to see if the angles of triangles are the same or not, and we know that there are marks at <C and <A, these marks prove that both angles are equal! So, <CBD equal <ABD

Solution is 225/42 or 5.35

According to question

5 6/7 + (-2 1/3) + 1 5/6

As it is a mixed fraction we will first solve it

To solve it denominator will get multiplied with the whole number and the solution will be get added to the numerator and the new numerator will get formed.

∴ 41/7 +(-7/3) + 11/6

⇒246-98+77/42.                              (LCM of 7,3,6 is 42)

⇒225/42

∴5.35

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Answer:

x = 13/5 or 2.6

Step-by-step explanation:

First, multiply both sides of the equation by 3.

This leaves us with 5x + 2 = 15.

Next, subtract 2 from both sides to get 5x = 13.

Finally, divide 13 by 5 to get x = 13/5. This cannot be simplified.

Answer: 5x + 10y = or > 75

Step-by-step explanation:

make the number of cookies sold  = x, and the number of cupcakes sold = y, since we don't know the number.

each cookie is $5 so it is 5 times x, and each cupcake is $10 so it is 10 times y.

add those together, and the sum must equal 75. If you have already learned this, it would be an equal to or greater than sign. if not then just use an equal sign.

Answer:

g = 109 degree

h = 71 degree

m = 71 degree

k = 84 degree

Step-by-step explanation:

g= 109 degrees because it is a vertical angle to the 109-degree angle, that is why it is 109 degree

h= 71 degrees because they are supplementary angles which means they add up to 180 degrees. We see that one is 109 degrees, so the other must be 71 degrees.

k = 84 degrees because it is a vertical angle to the 84-degree angle, which is why it is 84 degrees.

m= 71 degrees because m and g must add up to 180 degrees, and we know that g is 109 degrees, so m is 71 degrees!

There may be differences between correlations based on a subset of all potential scores and correlations based on the entire range. Range restriction is the name given to this idea.

When observed sample data are not available across the complete range of interest, it is said to have a restricted range. The most typical situation is when there is a bivariate correlation between two normally distributed variables, one of which has a smaller range than is typically seen in the population as a whole. If data from the complete possible range were studied, the observed connection would be attenuated (lower) than it is in these situations.

Although the variables themselves are not under the researchers' control, correlations are used by researchers to determine whether a relationship between two or more variables exists. A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical strategy for describing simple relationships without making a declaration about cause and effect.

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The value of x for the expression 5log(3x) = 15 is 6.7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 5log(3x) = 15. The value of x for the expression will be calculated as,

5log(3x) = 15

log(3x) = 15 / 5

log(3x) = 3

3x = e³

x = 20 / 3

x = 6.7

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The angle θ is maximized when c = 2 (halfway between two points).

The maximum angle at which a conveyor may be inclined and still deliver a predetermined quantity of bulk material within a given time. As the maximum angle is approached, the rate of handling of bulk material is usually decreased.

Given that, in the figure, find the value of c in the interval [0, 4] on the x-axis that maximizes angle θ.

Express θ as a function of c, Let α be the angle to the left of θ and let β be the angle to the right, then,

tanα = 2/c

and tanβ = 2/(4-c)

At this point, we suppose that it might be easier to use cotangent in order to keep c inn numerator,

cotα = c/2

cotβ = (4-c)/2

We have, α+β+θ = π, so,

θ = π-α-β

= π-cot⁻¹c/2-cot⁻¹(4-c)/2

Differentiate, set equal to 0 and solve

dθ/dc = 1/1+(c/2)².1/2+1/1+(4-c/2)²(1/2)

Put dθ/dc = 0

1/1+(c/2)².1/2+1/1+(4-c/2)²(1/2) = 0

1/1+(c/2)²-1/1+(4-c/2)² = 0

1/1+(c/2)² = 1/1+(4-c/2)²

(4-c/2)² = (c/2)²

(c/2) = (4-c/2)

4-c = c

2c = 4

c = 2

Hence, The angle θ is maximized when c = 2 (halfway between two points).

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Answer: (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.

The point estimate for the population proportion is 514 / 1012 = 0.507.

(b) Verify that the requirements for constructing a confidence interval about p are satisfied.

The sample is stated to be a simple random sample.

The value of n * p = 1012 * 0.507 = 514.7796 is greater than or equal to 10.

The value of n * (1 - p) = 1012 * (1 - 0.507) = 497.2204 is greater than or equal to 10.

The population proportion is less than or equal to 5% of the population size.

Therefore, the requirements for constructing a confidence interval are satisfied.

(c) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without.

The 95% confidence interval for the population proportion is 0.507 +/- 1.96 * sqrt((0.507 * (1 - 0.507)) / 1012) = 0.507 +/- 0.0245 = (0.4825, 0.5315).

We are 95% confident that the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.4825 and 0.5315.

(d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?

It is possible that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval contains 60%. However, it is not likely because the confidence interval is relatively narrow and the point estimate is far from 60%.

(e) Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.

The 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is 1 - 0.5315 = 0.4685 to 1 - 0.4825 = 0.5175. Therefore, the 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is (0.4685, 0.5175).

Step-by-step explanation:

The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = [tex](-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2[/tex]

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

        -----------------------------------------

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when ([tex]x^4-x^3-3x^2+4x+2[/tex]) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, [tex]x^4-x^3-3x^2+4x+2[/tex] ÷ (x+2)

To find the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly, we need to calculate the compound interest on the investment.

The compound interest is calculated by multiplying the principal (the initial amount invested) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 1.9%/12 = 0.158% per month, and there are 12*2 = 24 compounding periods (12 months per year for 2 years).

The compound interest is therefore calculated as follows:

Compound interest = $20,000 * e^(0.158%*24) - $20,000

= $20,000 * e^0.3832 - $20,000

= $20,000 * 1.454 - $20,000

= $4,080 - $20,000

= -$15,920

So the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly is -$15,920. Therefore, the correct answer is [A] $800.

Amount of each monthly statement is 1400.

According to question ,

Cash price of refrigerator =34500

Deposit money=6500

Outstanding money=28000

Rate of interest=10%

Time period=24 months or 2 years

∴Simple interest =(principal ×rate of interest×time)÷100

⇒(28000×10×2)÷100

⇒5600

∴The total amount to be paid in 2 years is 28000+5600 =33600

∴Amount to be paid in one month =33600÷24=1400

∴Amount of each monthly statement is 1400.

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Answer:

----------------------------------------------------

Simplify the expression:

Answer:

[tex]-11-6\sqrt{2}\:i[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(-9-\sqrt{-32}\right)-\left(2+\sqrt{-8}\right)[/tex]

Remove the parentheses:

[tex]\implies -9-\sqrt{-32}-2-\sqrt{-8}[/tex]

Rewrite -32 as 16 · 2 · -1  and rewrite -8 as 4 · 2 · -1 :

[tex]\implies -9-\sqrt{16 \cdot 2\cdot -1}-2-\sqrt{4 \cdot 2\cdot -1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies -9-\sqrt{16} \sqrt{2} \sqrt{-1}-2-\sqrt{4}\sqrt{2}\sqrt{-1}[/tex]

Simplify and apply the imaginary number rule √(-1) = i

[tex]\implies -9-4\sqrt{2}\:i -2-2\sqrt{2}\:i[/tex]

Group like terms:

[tex]\implies -9-2-4\sqrt{2}\:i -2\sqrt{2}\:i[/tex]

Combine like terms:

[tex]\implies -11-6\sqrt{2}\:i[/tex]

The weight of the piknits can be used to predict the number of goggles as there is a Linear equation in variables that may be defined as a linear courting among x and y, that is, variables.

In this case,  let x is the impartial variable, and y relies upon it, so y is called as the established variable.

linear courting (or linear association) is a statistical period used to explain a straight-line courting among variables. Linear relationships may be expressed both in a graphical layout or as a mathematical equation of the shape y = MX + b.

"There is no linear relationship between the weight and the number of glasses"

"There is a linear relationship.

A. Yes, because the scatterplot shows a linear pattern.

C. Yes, because a random sample was taken from Piknits for the scatterplots of the 4th and 5th residuals.

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The table shows that the cost of going to the movies with a group of people is equal to twice the number of people in the group. For example, if the number of people in the group is 2, the cost is 2 * 2 = $16. Similarly, if the number of people in the group is 4, the cost is 2 * 4 = $32, and if the number of people in the group is 8, the cost is 2 * 8 = $64. Therefore, if Tom wants to go to the movies with a group of n people, the cost will be 2 * n dollars.

Answer:

  3.85 minutes

Step-by-step explanation:

You want to know the time it takes for taxis traveling 33 mph and 45 mph toward each other to meet if they start 5 miles apart.

The speed at which the taxis approach each other is (33 mph +45 mph) = 78 mph. The time it takes to close the 5-mile gap is ...

  time = distance/speed

  time = (5 mi)/(78 mi/h) = 5/78 h ≈ 0.0641 h

In minutes, the time is ...

  (5/78 h)(60 min/h) = 300/78 min ≈ 3.85 minutes

__

Additional comment

That's about 3 minutes 50.8 seconds.

Answer:

m∠D = 49°
m∠E = 41°
m∠F = 90°

Step-by-step explanation:

        We know a triangle's angles add up to 180, so we can create an equation and solve for x. We also know the little box represents 90 degrees.

Given:

        90° + 5x° + 14° + 3x° + 20° = 180°

Combine like terms:

        8x° + 124° = 180°

Subtract 124 from both sides of the equation:

        8x° = 56°

Divide both sides of the equation by 8:

        x = 7

        Now, we will plug this value of x back into the angles to solve. Again, the little box represents that Angle F is equal to 90 degrees.

m∠D = 5x° + 14° = 5(7)° + 14° = 49°
m∠E = 3x° + 20° = 3(7)° + 20° = 41°
m∠F = 90°

An equation of the line that passes through the point (-3, -7) and is parallel to the line 2x-3y=24 can be found by taking the slope of the line 2x-3y=24 and using it to write the equation of the line in point-slope form. The slope of the line 2x-3y=24 is 3/2, so an equation of the line that passes through (-3, -7) and is parallel to the line 2x-3y=24 can be written in the form y-y₁ = m(x-x₁), where m is the slope of the line, which is 3/2 in this case. Plugging in the coordinates of the point (-3, -7) and the slope 3/2, we get the equation y-(-7) = (3/2)(x-(-3)), which simplifies to y+7 = 3/2(x+3). Multiplying both sides of the equation by 2/3 to get rid of the fraction on the right-hand side, we get the final equation: 2/3y + 14/3 = x + 3. This is the equation of the line that passes through the point (-3, -7) and is parallel to the line 2x-3y=24.

Answer:

39 children, 201 adults

Step-by-step explanation:

Let c = number of children

a = number of adults

c + a = 240

1.50c + 2.25a = 510.75

--------------------------------

1.50c + 1.50a = 360

1.50c + 2.25a = 510.75

-------------------------------

.75a = 150.75

a = 201, c = 39

To find the function, we need to find the values of x and y.

In the aforementioned example, x and y are the independent and dependent variables, respectively. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).

As we know,

fx = 3x to the power 3

f(x) =

[tex]3x {}^{3 } \: dx \: + c \\ \\ fx = 3x { }^{4} \div 4 + c \\ \\ \\ \\ 3x {}^{3} = - 81 \\ \\ x \: = 243 \\ [/tex]

Hence x is 242

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When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is.

Rotate shape A [tex]$180^{\circ}$[/tex] about point (1,0) is (-1,0)

How do you rotate a shape about a certain point?

Move each point on a shape the specified number of degrees in a circle centered on the point of rotation to rotate it. Make sure that every new point is located the same amount of time away from the point of rotation as its corresponding original point.

There are 360 degrees in a circle's complete revolution. We discovered that a rotation of 270 degrees is virtually a full circle. We learned that a whole rotation of a circle is divided in half by 180 degrees. 90 degrees, or half of 180, are simple to identify as angles.

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Reflection is a type of rigid transformation in which an object is flipped about a reference point or line to produce the required image. The three statements that apply are:Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point

Rigid transformation is a process in which the size, orientation or position of a given object can be changed by applying some principles. Types of rigid transformation are: reflection, translation, dilation, and rotation.

In the given question, the required statements that apply are:

Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point

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No, the statistical notion of an outlier as an infrequently observed value is not meaningful for this data.

Since the points are uniformly distributed on the interval [0,1], they should all be observed with the same frequency. Therefore, there are no outlier values.The statistical notion of an outlier is an infrequently observed value, meaning that it is an observation that is far away from the rest of the data. For a set of points that are uniformly distributed on the interval [0,1], however, all the points should be observed with the same frequency since they are evenly spaced. Therefore, there is no outlier value and the statistical notion of an outlier is not meaningful for this data.

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