John has 3 fewer dimes than quarters. He has twice as many nickels as quarters. Altogether he
has $6.45, how many of each coin does he have?

The transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = x²

The translation 6 units left and 4 units up means that

g(x) = f(x + 6) + 4

So, we have

g(x) = (x + 6)² + 4

This means that the transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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Answer:

The total value of the discount was $10.80.

Step-by-step explanation:

Since we are finding the value of the discount, we just need to find 18% of 60.

We can convert 18% into a decimal.

18%=0.18

Multiply.

0.18*60=10.8

The total value of the discount was $10.80.

The mean of Xt is 0. The autocovariance of Xt is 0, and the autocorrelation is 0 for all lags. Mean: 0. Autocovariance: 2cos(2). Autocorrelation: 2cos²(2).

The mean of Xt is the expected value of the series, which is 0, since the uniform distribution has a mean of 0.5, and when it is multiplied by 2π, it becomes 0. The autocovariance of Xt is the expected value of the product of two variables at different lags, which is 0 because the two variables are uncorrelated. The autocorrelation of Xt is the expected value of the product of two variables at different lags, divided by the product of their variances, which is also 0 since the variables are uncorrelated. The autocovariance and autocorrelation functions are both 2cos²(2πt), which is the expected value of Xt at different lags.

The complete question: Suppose = 2 cos[2( 12 + )], ∈ ℤ, where ~Uniform[0,1]. Find the mean, autocovariance and autocorrelation functions of the time series { , ∈ ℤ}.

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Answer:

10

Step-by-step explanation:

8 ÷ 4/5 = 10

I hope this helps!!

5.25 or 5 1/4

I worked it out I hope this helps :)

The attributes shared by both trapezoids and parallelograms are:

A) 4 sides

C) All sides are straight lines

D) 2 sets of parallel sides

So the correct options are A), C), and D).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The correct form of the particular solution for fn = -6fn-1 + 7fn-2 + 6n is d. n(an+b). To determine the particular solution, we need to first find the characteristic equation, which is r^2 + 6r - 7 = 0. The roots of this equation are r = -7 and r = 1. Therefore, the homogeneous solution is of the form fn = A(-7)^n + B(1)^n.

To find the particular solution, we look at the non-homogeneous term, which is 6n. Since this is a linear function, we can assume that the particular solution is of the form Pn = an + b. We substitute this into the original equation and solve for a and b.

f n = -6fn-1 + 7fn-2 + 6n
(a n +b) = -6(an-1+b) + 7(an-2+b) + 6n
an + b = -6an-1 + 7an-2 + 6n + 6b
an + b = 6(an-2 - an-1 + b) + 6n

Comparing coefficients, we get:
a = 6a - 6a + 0 = 0
b = 6b + 6n

Solving for b, we get b = n. Therefore, the particular solution is Pn = an + n.

Combining the homogeneous and particular solutions, we get:
fn = A(-7)^n + B(1)^n + an + n

Note that we can further simplify this by setting A and B based on initial conditions, if given.

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If the value of this expression is finite, then the series converges. If it is infinite, then the series diverges.

To determine the convergence or divergence of the series ∫f(sin³(20√cos(20)) de,

we need more information about the limits of integration and the function f(e).

Without that information, it is not possible to perform the convergence test.

However, I noticed another series mentioned: ∫ftan(2x)sec²(2x) dx.

To determine the convergence or divergence of this series, we can use the Integral test.

The Integral test states that if f(x) is a positive, continuous, and decreasing function on the interval [a, ∞), and the series ∫f(x) dx converges or diverges, then the series ∑f(n) also converges or diverges.

Let's examine the series ∫ftan(2x)sec²(2x) dx using the Integral test:

Step 1: Check if f(x) is positive and decreasing:

The function f(x) = tan(2x)sec²(2x) is positive for all values of x and is decreasing on the interval [a, ∞).

Step 2: Evaluate the integral:

∫ftan(2x)sec²(2x) dx can be challenging to integrate directly. However, we can use a u-substitution to simplify it.

Let u = 2x

Then, du = 2dx

dx = du/2

Replacing the variables and simplifying, the integral becomes:

∫ftan(u)sec²(u) * (du/2) = (1/2) ∫tan(u)sec²(u) du

The integral of tan(u)sec²(u) du is ln|sec(u)| + C

Thus, the integral becomes:

(1/2) [ln|sec(u)|] + C

Step 3: Determine the convergence or divergence of the integral:

To determine the convergence or divergence of the integral, we need to evaluate it at the limits of integration.

Let's assume the limits of integration are a and b:

∫(a to b) ftan(2x)sec²(2x) dx = (1/2) [ln|sec(2b)| - ln|sec(2a)|]

If the value of this expression is finite, then the series converges. If it is infinite, then the series diverges.

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Using the properties of a triangle, The answer is Yes, The measure of an exterior angle of triangle is sum of the opposite interior angles of the triangle.

An angle is a measure of the amount of rotation between two lines or planes. It is typically measured in degrees or radians. An angle can be defined as the amount of rotation needed to bring one line or plane into coincidence with another. Angles are often represented graphically as a central point, called the vertex, and two rays that extend from the vertex in different directions. The angle is the amount of rotation needed to rotate one ray so that it coincides with the other ray.

A triangle is a three-sided polygon that has three angles and three sides. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on their side lengths and angles, such as right triangles, acute triangles, and obtuse triangles. A right triangle has one angle that measures exactly 90 degrees, while an acute triangle has all angles that measure less than 90 degrees, and an obtuse triangle has one angle that measures greater than 90 degrees. Triangles can also be classified by the length of their sides as equilateral, isosceles and scalene triangle. An equilateral triangle has all sides of equal length, an isosceles triangle has two sides of equal length, and a scalene triangle has no sides of equal length.

z = exterior angle

x, y = opposite interior angles to z.

z= x + y

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Answer:

64

Step-by-step explanation: because he can at least steal 64 packs before   the                 cops get him

Answer:

4

or

4.92753623188  **However you cannot just buy a portion of one pack so you round back down to 4 packs.

Step-by-step explanation:

First we have $25, since he spent $8, we can now claim he has $17, Divide 17 into 3.45, He can buy 4 packs.

In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.

The correct answer is Option D.

The key concept here is that a plane is defined by having at least three non-collinear points.

When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.

Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.

Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.

The correct answer is Option D.

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A turning point associated with the events, ideas, or historical developments related to both the statute law and Article 1 competence of the international tribunal of Rwanda was the assassination of President Juvenal Habyarimana.

The assassination of Rwandan President Juvenal Habyarimana was a turning point in the Rwandan strife because it triggered the ethnic cleansing of the Tutsis.

The statute law of the international tribunal was made to address the prosecution of persons who participated in acts of genocide and violation of human rights. This event was an element of justice that punished wrongdoers for their part in the incident.

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For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer: yes it is proportional

Step-by-step explanation:

I did it on khan

By the incenter property, this angle is half of the measure of ∠AEC Hence, the measure of ∠DEP is half of the measure of ∠AEC.

Since ΔDEP is congruent to ΔDCP by the SAS (Side-Angle-Side) postulate, the corresponding angles of these triangles are equal.

Therefore, the measure of ∠DEP is equal to the measure of ∠DCP.

Since P is the incenter of ΔAEC, ∠DCP is the angle formed by the bisector of ∠AEC.

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Answer:

not possible

........................................

The fact that k≥4≥1 is used in the base case of the inductive proof, not in the inductive step.

In the base case, we need to show that the statement holds for k=4. Since 4≥1, this satisfies the condition. The inductive step assumes that the statement holds for some arbitrary k≥4 and then shows that it holds for k+1. The inductive step of an inductive proof aims to show that if a statement holds true for a certain value, it also holds true for the next value. In the given problem, we need to demonstrate that for k≥4, if 2k≥3k, then 2(k+1)≥3(k+1). The fact that k≥4≥1 is utilized in the base case step of the proof. The base case ensures that the initial condition (k=4) satisfies the given inequality. By showing that the inequality holds true for k=4, we establish a starting point for the inductive step. This allows us to apply the inductive step and generalize the result to all values of k greater than or equal to 4.

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The time when the two companies would cost the same amount is after 3 hours.

Based on the information provided above, beach bikes company charges $10 bike fee and $8 per hour. Therefore, the total cost, y, can be represented by this equation:

y = 8x + 10    .......equation 1.

where:

x represents the number of hours.

For the second option, bikes unlimited charges $5 per hour and a $19 bike fee. Therefore, the total cost, y, can be represented by this equation:

y = 5x + 19    ....equation 1.

By equating equation 1 and equation 2, we have the following:

8x + 10 = 5x + 19

8x - 5x = 19 - 10

3x = 9

x = 9/3

x = 3 hours.

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To write each vector in trigonometric form, we need to express them in terms of magnitude and angle.

18. \(\( \mathbf{b} = (\sqrt{19}, -4) \)\)

The magnitude of vector \(\( \mathbf{b} \) is \( \sqrt{(\sqrt{19})^2 + (-4)^2} = \sqrt{19 + 16} = \sqrt{35} \).\)

The angle of vector \(\( \mathbf{b} \)\) with respect to the positive x-axis can be found using the arctan function:

\(\( \mathbf{b} \) is \( \sqrt{35} \, \text{cis}(\arctan\left(\frac{-4}{\sqrt{19}}\right)) \).\)

So, the trigonometric form of vector \(\( \mathbf{b} \) is \( \sqrt{35} \, \text{cis}(\arctan\left(\frac{-4}{\sqrt{19}}\right)) \).\)

19. \(\( \mathbf{r} = 16i + 4j \)\)

The magnitude of vector \(\( \mathbf{r} \) is \( \sqrt{(16)^2 + (4)^2} = \sqrt{256 + 16} = \sqrt{272} = 16\sqrt{17} \).\)

The angle of vector \(\( \mathbf{r} \)\) with respect to the positive x-axis is 0 degrees since the vector lies along the x-axis.

So, the trigonometric form of vector \(\( \mathbf{r} \) is \( 16\sqrt{17} \, \text{cis}(0^\circ) \).\)

20.  \(\( \mathbf{k} = 4\sqrt{2}i - 2j \)\)

The magnitude of vector \(\( \mathbf{k} \) is \( \sqrt{(4\sqrt{2})^2 + (-2)^2} = \sqrt{32 + 4} = \sqrt{36} = 6 \).\)

The angle of vector \(\( \mathbf{k} \)\) with respect to the positive x-axis can be found using the arctan function:

\(\( \theta = \arctan\left(\frac{-2}{4\sqrt{2}}\right) \)\)

So, the trigonometric form of vector \(\( \mathbf{k} \) is \( 6 \, \text{cis}(\arctan\left(\frac{-2}{4\sqrt{2}}\right)) \).\)

21. \(\( \overrightarrow{CD} \) with C(2, 10) and D(-3, 8)\)

To find the vector \(\( \overrightarrow{CD} \)\), we subtract the coordinates of point C from the coordinates of point D:

\(\( \overrightarrow{CD} = \langle -3 - 2, 8 - 10 \rangle = \langle -5, -2 \rangle \)\)

The magnitude of vector \\(( \overrightarrow{CD} \) is \( \sqrt{(-5)^2 + (-2)^2} = \sqrt{29} \).\)

The angle of vector \(\( \overrightarrow{CD} \)\) with respect to the positive x-axis can be found using the arctan function:

\(\( \theta = \arctan\left(\frac{-2}{-5}\right) = \arctan\left(\frac{2}{5}\right) \)\)

So, the trigonometric form of vector \(\( \overrightarrow{CD} \) is \( \sqrt{29} \, \text{cis}(\arctan\left(\frac{2}{5}\right)) \).\)

22. overnighter \({TU} \) with T(-3, -4) and U(3, 8)\)

To find the vector we subtract the coordinates of point T from the coordinates of point U:

\(\( \overrightarrow{TU} = \langle 3 - (-3), 8 - (-4) \rangle = \langle 6, 12 \rangle \)\)

The magnitude of vector \(\( \overrightarrow{TU} \) is \( \sqrt{(6)^2 + (12)^2} = \sqrt{36 + 144} = \sqrt{180} = 6\sqrt{5} \).\)

The angle of vector \(\( \overrightarrow{TU} \)\) with respect to the positive x-axis can be found using the arctan function:

\(\( \theta = \arctan\left(\frac{12}{6}\right) = \arctan(2) \)\)\(\( \overrightarrow{TU} \),\)

So, the trigonometric form of vector \(\( \overrightarrow{TU} \) is \( 6\sqrt{5} \, \text{cis}(\arctan(2)) \).\)

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Given:

Arc(AB) = 78 degrees

Measure of angle CMD = 106 degrees

To find:

The measure of arc CD.

Solution:

Secant intersection theorem: If two secant of a circle intersect each other inside the circle, then the intersection angle is the average of intercepted arcs.

Using secant intersection theorem, we get

\(m\angle CMD=\dfrac{1}{2}(Arc(AB)+Arc(CD))\)

\(106^\circ=\dfrac{1}{2}(78^\circ+Arc(CD))\)

Multiply both sides by 2.

\(212^\circ=78^\circ+Arc(CD)\)

\(212^\circ-78^\circ=Arc(CD)\)

\(134^\circ=Arc(CD)\)

Therefore, the measure of arc CD is 134 degrees and the correct option is C.

Measures of central tendency, measures of variation, and crosstabulation are all types of descriptive statistics.

Descriptive statistics summarize and describe the main features of a data set, including the typical or central values (measures of central tendency) and the spread or variability of the data (measures of variation). Crosstabulation, also known as contingency tables, is a way to summarize the relationship between two variables by displaying their frequency distributions in a table format.
Measures of central tendency, measures of variation, and crosstabulation are types of descriptive statistics. Descriptive statistics are used to summarize and describe the main features of a dataset in a simple and meaningful way.

Central tendency refers to the measures that help identify the center or typical value of a dataset, such as mean, median, and mode. Variation measures describe the spread or dispersion of data, including range, variance, and standard deviation. Crosstabulation is a method of organizing data into a table format to show the relationship between two categorical variables.

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Answer:

73

Step-by-step explanation: It is 73 because for each problem you add 6

Answer 73

Step-by-step explanation:

IN:67  OUT:73     IN 73     OUT:85   IN:85     OUT:91    

your adding 6 every time.

The amount of Protein intake is 900 kilocalorie.

We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.

Wе have to find out the amount of protein intake.

Percentage of students affected are -  \(\frac{x}{n} \times 100\)

In the question given -

Let the amount of Protein intake be y.

Then -

45 = y % of 2000

45 = \(\frac{y}{2000} \times100\)

y = \(\frac{45\times2000}{100}\)

y = 900 Kilocalorie

Hence, the amount of Protein intake is 900 kilocalorie.

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Answer:

BC ≈ 19.4 cm

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos71° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AB}{BC}\) = \(\frac{6.3}{BC}\) ( multiply both sides by BC )

BC × cos71° = 6.3 ( divide both sides by cos71° )

BC = \(\frac{6.3}{cos71}\) ≈ 19.4 cm ( to 3 significant figures )

There are four levels of measurements in statistics, namely nominal, ordinal, interval, ratio. These levels are important when it comes to analyzing data, since it helps us determine the technique that we can use to support or refute our study.

In the nominal level, we can categorize data but they cannot be ranked. An example would be hair color. In an ordinal data, the data can be both categorize and ranked, but doing mathematical calculation may not make sense. Also, the intervals between rankings doesn't necessarily dictate how close or far apart the data are.

A good example is level of education. In an interval level, the data can be categorized, ranked, and measured but they do not have a true zero. An example could be a range of values that does not include zero. Lastly, in the Ratio level the data can be categorized, rank, and measured, and it has a true zero.

So ratio level is most appropriate for ages of children. Note that ages can be categorized, rank, and measured .Moreover, an age equal to zero means that there is no age or the absence of age.  

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After 6 weeks, John and Thomas will have the same amount of money, using the system of equations.

An equation is a mathematical statement that equates two variables using the equation sign (=).

Using equations, two values are stated to possess equivalent values.

                              John      Thomas

Initial savings         $80          $20

Weekly savings     $20          $30

Let x = weekly savings

John's savings = 80 + 20x

Thomas's savings = 20 + 30x

To determine the week the two savings will equate:

80 + 20x = 20 + 30x

80 - 20 = 10x, subtract 20 from both sides

60 = 10x, divide both sides by 10

6 = x

Check:

80 + 20x

= 80 + 120

= 200

20 + 30x

= 20 + 180

= 200

Thus, after 6 weeks, John and Thomas's money will be equal.

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(a) The shorted distance between point A and point B is 29.1.

(b) The x-coordinate of the point where the ladybug intersected the x-axis is (-1, 12).

The shorted distance between point A and point B is straight line, which is calculated as follows;

\(d = \sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2} \\\\d = \sqrt{(12--1)^2+ (10--16)^2} \\\\d = 29.1 \ unit\)

The x-coordinate of the point where the ladybug intersected the x-axis is determined as;

(Ax, Ay), (Bx, By)

= (Ax, Bx)

= (-1, 12)

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Answer:

its called a googol

Step-by-step explanation:

You dont need one