Juan counts up by 3's and Alex counts up by 5's.What is the smallest number that they both say?

The summation notation is ∑ \((4^{n} -1)\\\)/2.

The common ratio multiplied here to each term to get the next term is a non-zero number.

Given:  1/2+2+8+32+128

Using,

\(a_n= a_1r^{n-1}\)

We have,

a1 =1/2 and r= 4

notation is : An= ∑ \((4^{n} -1)\\\)/2

Hence, the notation is  An= ∑ \((4^{n} -1)\\\)/2.

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Answer:

x = 6

Step-by-step explanation:

use alternate angles

An equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

The given denominator are (x+3), (x−4) and (x+4).

A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.

Here, an equivalent rational expressions is

\(\frac{1}{x+3}+\frac{1}{x-4} +\frac{1}{x+4}\)

The LCM of denominators is (x+3)(x-4)(x+4)

= (x+3)(x²-16)

= x(x²-16)+3(x²-16)

= x³-16x+3x²-48

= x³+3x²-16x-48

Now, \(\frac{(x-4((x+4)+(x+3)(x+4)+(x+3)(x-4)}{x^3+3x^2-16x-48}\)

= (x²-16+x²+7x+12+x²-x-12)/(x³+3x²-16x-48)

= (3x²+6x-16)/(x³+3x²-16x-48)

Hence, an equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

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Answer:

x = -2

y = -4

Step-by-step explanation:

The way systems of equations  work is that you have to substitute to solve for a variable *(only one of the 2 ways to figure this out)*

so, we will use addition property of equality in a form to add the two equations together, since +5y and -5y added together will cancel out.

that would leave

5x = -10

divide both sides by 5

x = -2

Now that we know x = -2, we can plug in -2 into one of the equations to find y.

2 ( -2)  + 5y = -24

-4 + 5y = -24

-4 + 4 + 5y = -24 + 4

5y = -20

y = -4

x = -2

y = -4

The sequence whose nth term is (2n+1)/(3n-1) converges to the number 2/3.

To use L'Hopital's rule, we need to take the limit of the ratio of the nth term and (n-1)th term as n approaches infinity.

Let a_n be the nth term of the sequence. lim (n->∞) a_n / a_(n-1) = lim (n->∞) (2n+1)/(3n-1) / (2n-1)/(3n-4) = lim (n->∞) [(2n+1)/(3n-1)] * [(3n-4)/(2n-1)] = lim (n->∞) [6n^2 - 5n - 4]/[6n^2 - 7n + 4]

By applying L'Hopital's rule, we can find that the limit of this ratio as n approaches infinity is 1. Thus, the sequence converges to the same limit as the ratio of consecutive terms, which is 2/3.

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Eris is a dwarf planet in our solar system that's slightly larger than Pluto. It has a highly elongated orbit that takes about 560 Earth years to complete, and it's known to have a small moon named Dysnomia.

First of all, for those who may not be familiar, Eris is a dwarf planet in our solar system that was discovered in 2005.

It's located in the Kuiper Belt, a region of the solar system beyond Neptune that's home to many other small icy objects.
As you mentioned, Eris is slightly larger than Pluto - in fact, it's currently considered to be the largest known dwarf planet in the solar system.

Its diameter is about 2,326 kilometers, compared to Pluto's diameter of 2,377 kilometers.

One interesting thing about Eris is that its orbit around the Sun is highly elongated.

At its closest point to the Sun (known as perihelion), it's about 5.7 billion kilometers away, while at its farthest point (aphelion), it's more than twice as far away - about 14.6 billion kilometers.

This means that Eris has a very long orbital period - the time it takes to complete one full orbit around the Sun.

In fact, as you mentioned, it takes Eris about 560 Earth years to complete one orbit.

To put that in perspective, Pluto - which also has an elongated orbit - takes about 248 Earth years to complete one orbit. S

o Eris's orbital period is more than twice as long as Pluto's!

Another interesting fact about Eris is that it's known to have a small moon, which is officially named Dysnomia.

Dysnomia is much smaller than Eris - its diameter is only about 350 kilometers - but it orbits Eris at a distance of about 37,000 kilometers.

So in summary, Eris is a dwarf planet in our solar system that's slightly larger than Pluto. It has a highly elongated orbit that takes about 560 Earth years to complete, and it's known to have a small moon named Dysnomia.

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The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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The Sample space includes all possible combinations of the three types of sour candies, taking into account that there can be multiple candies of the same type in the bag.

The correct sample space for the sour candies in the bag is:

Sample space = {lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape}

Each element in the sample space represents a different possible outcome of selecting a sour candy from the bag. The sample space includes all possible combinations of the three types of sour candies, taking into account that there can be multiple candies of the same type in the bag.

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The correct sample space for the sour candies in the bag is (c)  Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

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

3 lemon-lime, 6 watermelon, and 5 grape sour candies

The correct sample space for the sour candies in the bag is the list of items in the bag

So, we have

Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

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Answer:

B

Step-by-step explanation:

Answer:

Initially 18,500 students

Every 1 year

increase by a factor 1.03

Step-by-step explanation:

The missing information is selected from the given options from the drop down menu. The correct answers are : Initially 18,500 students enroll at the university. Every 1 years the number of students who enroll at the university increases by a factor 1.03.

F(t) = 18,500 * (1.03)^t

(a-1) The value of the population mean is unknown.

(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.

(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).

(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.

(e-2) It would be reasonable to conclude that the population mean is 18 eggs.

(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.

(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.

(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.

Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.

In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.

(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.

(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.

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Answer:

B and C are the answers according to the expression

Ellipses that are represented by equations, whose eccentricities are less than 0.5 are:

To identify the ellipses:

For the standard-form equation of an ellipse: Ax^2+Bx+Cy^2+Dy+E=0

We can define:

Then the eccentricity can be shown to be:

For Eccentricity<0.5, we want:

Checking the values of p/q for the given equations, we have p/q= equations (A), (B), and (F) are of ellipses with eccentricity < 0.5.

Therefore, ellipses that are represented by equations, whose eccentricities are less than 0.5 are:

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The complete question is given below:

Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.

(A) 49x2 -98x + 64yz +256y -2,831=0            

(B) 81x2 -648x +100yz +200y -6,704 =0                                      

(C) 6x2 -12x +54y2 +108y -426 =0                  

(D) 49x2 + 196x +36y2 +216y -1,244 =0                                        

(E) 4x +32x +25y2 - 250y +589 =0                

(F) 64x2 +512x +81y2 -324y -3,836 =0

The correct statements regarding the function are:

2. The period of the function is \(2\pi\).

4. The amplitude of the function is 2.5.

5. The midline of the function is y = 1.5.

The amplitude of a function is half the difference between the largest and the smallest value.

In this problem, these values are of 4 and -1, hence the amplitude is:

A = (4 - (-1))/2 = 2.5.

Thus the midline is:

y = -1 + 2.5 = 4 - 1.5 = 2.5.

The period of a function is the distance between it's repetitions. Hence, for this graph, the period is of \(2\pi\).

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Answer:

Step-by-step explanation:

To find the inverse, interchange the variables and solve for

y.

f^-1(x)=√2x,−√2x

There is a 30.85% chance that someone will have to wait longer than 6 minutes.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

z = (raw score - mean) / standard deviation

So,

We can write,

Mean of 6 minutes and variance = 1 minutes, hence:

Standard deviation = √variance = √1 = 1 minutes

For > 6 minutes:

z = (6 - 5)/2 = 1/2=0.5

P(z > 0.5) = 1 - P(z < 0.5)

P(z > 0.5) = 1 - 0.6915

P(z > 0.5) = 0.3085

Therefore,

There is a 30.85% chance that someone will have to wait longer than 6 minutes.

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Option C, A associated samples t-test is the best method for determining the importance of the mean difference.

The weight of an individual before and after a two-day fast is the two variables in this situation.

To use the t-test on paired data, the given observations must be related. Using the variations between the two sets of data, we calculate the test statistic. The degree of freedom for this test is n 1, where n is the overall number of observations.

If the standard deviation is provided and the sample size is large, the statistical hypothesis known as the Z-test is employed to assess if the two samples' computed means are different. The T-test, in contrast, evaluates how averages from distinct data sets differ when the variance or standard deviation is unknown.

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Answer:

24.6 cm^2

Step-by-step explanation:

3.28m = 328 cm

75mm = 0.075 cm

Area of rectangle: L x W

328 times 0.075 = 24.6 cm^2

Answer:

please see the steps in the picture

By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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Answer:

10 inches

Step-by-step explanation:

Given

Shape: Isosceles Triangle

\(Perimeter=24\ in\)

\(Side = 4\ in\)

Required

Find the length of the other two sides

Represent the other sides with x.

Since it is an isosceles triangle, 2 sides are equal.

So, we have:

\(x + x + 4 = 24\)

\(2x + 4 = 24\)

Collect Like Terms

\(2x = 24-4\)

\(2x = 20\)

Divide both sides by 2

\(\frac{2x}{2} = \frac{20}{2}\)

\(x = \frac{20}{2}\)

\(x = 10\)

The other sides are 10in each

Determine how the ABC contingency can be altered to promote more positive behavior. (Option (a) is correct one )

The method that intervention development will be influenced by the ABC data that are gathered on the function of the target behavior is through the determination of how the ABC contingency can be changed to encourage more positive behavior.

By identifying the functional reinforcers that sustain problem behavior, practitioners can create therapies that are more effective (i.e., from a smaller pool of potential interventions to choose from) and efficient.

Linking therapies to the outcomes of functional assessments has become accepted clinical practice and is now covered by both federal and state laws. This represents a significant and advantageous change in the method of behavioral intervention.

Therefore,

Determine how the ABC contingency can be altered to promote more positive behavior. (Option (a) is correct one )

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The food truck sold 122 hamburgers that day.

Let's assume that x is the number of hamburgers that were sold that day..

A food truck sells hamburgers for 5.5 dollars each and drinks for 2 dollars each.

The food truck's revenue from selling a total of 203 hamburgers and drinks in one day was 834 dollars.

Now, as per the given conditions, x + y = 203 where y is the number of drinks sold that day.

The cost of a single hamburger is $5.5The cost of a single drink is $2

The revenue from the sale of 203 hamburgers and drinks is $834.

Thus, we can form another equation as 5.5x + 2y = 834So, we have to solve these two equations to find the value of x. Here, we will use the elimination method to solve the equations.

To eliminate y, we will multiply the first equation by 2, and we get:2x + 2y = 4065.5x + 2y = 834

Now, subtract the two equations:3.5x = 428x = 122

Hence, 122 hamburgers were sold that day.

Therefore, Total revenue = $834.

Number of hamburgers sold = x,

number of drinks sold = y.

We have the following system of equations:

                                x + y = 203 (1)

                                5.5x + 2y = 834 (2)

To solve the system, we will use the elimination method.

Multiplying equation (1) by 2, we get:2x + 2y = 4065.5x + 2y = 834

Now, subtracting equation (1) from equation (2), we get:3.5x = 428x = 122

Hence, the food truck sold 122 hamburgers that day.

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The surface area of the composite figure is 748 cm^2.

To find the surface area of a composite figure, we need to calculate the surface areas of each individual component and then add them together.

Let's break down the composite figure into its components:

There is a rectangular prism with dimensions 5 cm, 6 cm, and 4 cm. The surface area of a rectangular prism can be calculated using the formula: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height respectively. So, the surface area of this rectangular prism is: 2(5)(6) + 2(5)(4) + 2(6)(4) = 60 + 40 + 48 = 148 cm^2.

There is a triangular prism with dimensions 20 cm (base), 12 cm (height), and 6 cm (slant height). The surface area of a triangular prism can be calculated by finding the areas of the two triangular bases and the three rectangular faces. The area of each triangular base is (1/2)(20)(12) = 120 cm^2, and the area of each rectangular face is (20)(6) = 120 cm^2. Therefore, the total surface area of the triangular prism is: 2(120) + 3(120) = 240 + 360 = 600 cm^2.

To find the surface area of the composite figure, we add the surface areas of the rectangular prism and the triangular prism: 148 cm^2 + 600 cm^2 = 748 cm^2.

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Answer:

Step-by-step explanation:

x+9<15

x<6

5>2+y

y<3

z-2.3<4.7

z<7

Answer:

compare them

Step-by-step explanation:

first make the denominators the same, then compare the numerators

Twenty students participated in a psychology experiment which measured their heart rates in two different situations.[75,100] situation shows greater variability.

f(75)=1

f(80)=4

f(90)=5

f(95)=4

f(100)=1

The measure of center should be median as the data is a bit scattered whereas the measure of variability should be the range of it.

Mean should be the measure of center as the data is concentrated in the middle the most whereas the standard deviation should be the measure of variability.

How far apart points are from one another and from the center of a distribution or a data collection is shown by variability. Spread, scatter, and dispersion are other terms for variation.

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The two numbers are x = 3.43 and y = 22.57.

What is a linear equation in two variables?

An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Let the first number be x and the second number be y. Then we can write the given information as a system of equations:

x + y = 26

(2/5)x + (3/8)y = 10

To solve this system, we can eliminate one of the variables by multiplying the first equation by 8 and the second equation by 5, then subtracting the resulting equations:

8x + 8y = 208

10x + 15y = 50

Subtracting these equations gives us:

-2x - 7y = -158

Dividing both sides by -7, we get:

x + y = 22.57

Substituting this back into the first equation, we get:

x + 22.57 = 26

Solving for x, we get:

x = 26 - 22.57

= 3.43

Substituting this back into the original equation x + y = 26, we get:

3.43 + y = 26

Solving for y, we get:

y = 26 - 3.43

= 22.57

Hence, the two numbers are x = 3.43 and y = 22.57.

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The probability values are calculated and listed below

They are both black

Here, we have

Black = 3

Yellow = 5

Sice the balls are not replaced, we have

P(Both black) = 3/8 * 2/7

P(Both black) = 3/28

They are both yellow

Sice the balls are not replaced, we have

P(Both Yellow) = 5/8 * 4/7

P(Both Yellow) = 5/14

The first is yellow and the second is black

Sice the balls are not replaced, we have

P(Yellow and black) = 5/8 * 2/7

P(Both Yellow) = 5/28

One is yellow the other is black

Sice the balls are not replaced, we have

P(One Yellow and One black) = 5/8 * 2/7 * 2

P(One Yellow and One black) = 5/14

They are of the same colour​

Here, we have

P(Same) = 3/28 + 5/14

P(Same) = 13/28

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