Kelly's last quiz scores were 79, 89, 86, and 93. What must her next score be to obtain an average that is more than 88

The given geometric series as shown in the question is seen to; Be converging with its' sum as 81

We are given the geometric series;

27 + 18 + 12 + 8 + ...

Now, we see that;

First term; a₀ = 27

Second Term; a₁ = 2(27/3)

Third term; a₂ = 2²(27/3²)

Fourth term; a₃ = 2³(27/3³)

Thus, the formula is;

2ⁿ(27/3ⁿ)

Applying limits at infinity gives;

2^(∞) * (27/3^(∞)) = 0

Since the  terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

S_n = a/(1 - r)

S_n = 27/(1 - (2/3)

S_n = 81

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To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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Answer:

x = 34

Step-by-step explanation:

Just add 14 on both sides of the equal sign to get x = 34.

Hope this helps :)

Answer:

x = 34

Step-by-step explanation:

hope it helps a lot

that's the final answer

The solution set of the inequality is:

-6 < x ≤ -2

And the graph is on the image at the end.

Here we have the following inequality:

-7 < 2x + 5 ≤ 1

To solve this we need to isolate x.

-7 < 2x + 5 ≤ 1

-7 - 5 < 2x ≤ 1 - 5

-12 < 2x ≤ -4

-12/2 < x ≤ -4/2

-6 < x ≤ -2

To graph this, we need to start with an open circle at x = -6, then a line that goes to the right, and ends with a closed circle at x = -2

We will get the graph you can see at the end.

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Answer:

The answer to your question is 60745736000000

Step-by-step explanation:

I hope this helps and have a wonderful day!

Answer:

Note that I slightly misread the question and in the steps below found the answer to the nearest thousandth.  To the nearest hundredth though, the rectangle has a length of 6.69cm, and a width of 1.35 cm.

Step-by-step explanation:

We are told that the rectangle has an area of nine square centimetres, and that it's length is 4 centimetres more than twice its width. We can express those as:

\(a = 9cm^2\)

and

\(l = 2w + 4\)

We also know that the area of a rectangle is its length times its width:

\(a = l \times w\)

We can take that last expression, and plug in the other two, to solve for w

\(a = l \times w\\9 = (2w + 4) \times w\\9 = w(2w + 4) \\9 = 2w^2 + 4w\\4.5 = w^2 + 2w\\5.5 = w^2 + 2w + 1\\5.5 = (w + 1)^2\\w + 1 = \sqrt{5.5}\\w = \sqrt{5.5} - 1\\w \approx 2.345 - 1\\w \approx 1.345\)

We can then plug that into expression "l = 2w + 4" to find the length:

\(l = 2w + 4\\l = 2(\sqrt{5.5} - 1) + 4\\l = 2 * \sqrt{5.5} - 2 + 4\\l = \sqrt{4} * \sqrt{5.5} + 2\\l = \sqrt{22} + 2\\l \approx 4.690 + 2\\l \approx 6.690\)

Now let's see if we have that right, we can multiply these and see if we get an area of 9:

\(1.345 \times 6.690 \approx 8.998\\\)

Which after accounting for rounding errors is matches the 9 square centimetres.

The value of the t test is 13.36, we have to conclude that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

H0: u = 24000

H1: u > 24000

we have n = 84 homes

bar x = 27500

s = 2400

Next we have to find the test statistic

The formula for this is given as

\(t = \frac{x-u}{s/\sqrt{n} }\)

When we out in the values we would have

\(t = \frac{27500-24000}{2400/\sqrt{84} }\)

This would give us the answeer of the t test as

t test = 13. 3658

We have alpha = 0.02

the degree of freedom = 84 - 1 = 83

we have to find tα/2, df

=  ±2.0865

Given that the value of the test statistic is greater than critical value we would have to then reject the null hypothesis.

Hence the conclusion that we can make is that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

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For the given data, x1 = (8 + 12)/2 = 10;

Mean = Sum of frequencies*components/Sum of frequencies = 590 / 30 = 19.6667

A histogram roughly depicts the distribution of numerical data. Karl Pearson is credited with coining the phrase. To create a histogram, you must first "bin" (or "bucket") the data range, divide it into a series of intervals, and then count how many values fall into each interval. The bins are often defined as discrete intervals that don't overlap. The bins (intervals) must be next to each other and are frequently (but not necessarily) of the same size.

When the bins are the same size, a rectangle is constructed across each bin, with the height being proportional to the frequency—that is, the number of cases in each bin.

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Answer:

Step-by-step explanation:

4m³ + 12xm² - 8m² - 24xm = (4m³ - 8m²) + (12xm² - 24xm)   {Group terms}

                                            =4m²(m - 2) + 12xm(m - 2)    {Factor terms}

                                            = (m - 2)(4m²  + 12xm)

                                            =(m -2) 4m(m + 3x).

Answer:

4m(m+3x)(m-2)

Step-by-step explanation:

4m^3 + 12xm^2 - 8m^2 - 24xm

= 4m(m^2 + 3xm - 2m - 6x)

= 4m(m(m+3x) - 2(m+3x))

= 4m(m+3x)(m-2)

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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Answer:

Step-by-step explanation:

\(4z^2 - 3z - 4​\\z =2\)

Substitute 2 for z in the given equation

\(4(2)^2 - 3(2) -4\\\)

Follow the PEMDAS order of operations

\(\mathrm{Calculate\:exponents}\:\left(2\right)^2\::\quad 4\\=4\cdot \:4-3\left(2\right)-4\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:4\times\:4\::\quad 16\\=16-3\left(2\right)-4\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:3\left(2\right)\::\quad 6\\=16-6-4\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:16-6-4\::\quad 6\)

Answer:

Step-by-step explanation:

Plug in z = 2 in the expression

4z² - 3z - 4 = 4*2² - 3*2 -4

                 = 4*4 - 6 - 4

                 = 16 - 6 - 4

                 = 10 - 4

                 = 6

The inequality that represents the number of streamers x and balloons y the student council can buy is given as follows:

3.50x + 0.75y ≤ 100.

Each streamer costs $3.50, hence the total cost of purchasing x streamers is given as follows:

3.5x.

Each balloon costs $0.75, hence the total cost of purchasing y balloons is given as follows:

0.75y.

Then the total cost of purchasing x streamers and y balloons is given as follows:

3.50x + 0.75y.

The amount spent can be of at most $100, hence the inequality is given as follows:

3.50x + 0.75y ≤ 100.

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Answer:

25 degrees

Step-by-step explanation:

The angle WRS for the given triangle will be ∠WRS = 25°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

Given that the triangle has an angle as shown in the image

The angle TRW → 25x + 30 = 180 -5x

→ x = 5°

Now the angle WRS → 180 - ( 25x + 30)

∠WRS = 25° hence, the correct answer will be this.

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Answer:

220x+5

Step-by-step explanation:

Do I simplify? if yes, here's an explanation

4x^4 that means, 4x*4x*4x*4x, do 4*4*4*4=256,so the first part is 256x.

6x^2 that means, 6*6=36, 36x

Then do , 256x-36x+5=220x+5

That's your answer!

Hope this helps!

Answer:

80

Step-by-step explanation:

edge 2023

SLOPE

=================================================================

There's a little formula we can use to find the slope :

\(k=\cfrac{y_2-y_1}{x_2-x_1}\)

Plugin what you know :

\(k=\cfrac{\stackrel{y_2}{2}-\stackrel{y_1}{2}}{\stackrel{x_2}{14}-\stackrel{x_1}{2}}\)

Simplify :

\(k=\cfrac{0}{12}\)

\(\begin{tabular}{c|1} k=0 & \\\cline{1-4} \end{tabular}\) > (Final answer)

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===============================================================

Answer: the slope is zero

Step-by-step explanation:

The slope of a line through (a, b) and (c, d) is the difference in the second coordinates divided by the difference in the first coordinates.

This is calculated by subtracting the first point coordinates from the second point coordinates. For instance, suppose we had points (1, 3) and (6, 7), the slope would be (7 - 3)/(6 - 1) = 4/5.

For the given problem, we have slope = (2 - 2)/(14  -2) = 0/12 = 0

Notice that since we take the difference of the y-coordinates in the numerator of the slope fraction, that gives us the difference in height from one point to another. So this represents the up or down (vertical) movement as we go from one point to the next.

Since we take the difference of the x-coordinates in the denominator of the slope fraction, that gives us the difference in left-or-right from one point to another. So this represents the side-to-side (horizontal) movement as we go from one point to the next.

Thus, slope is sometimes called "rise over run" as it measures the rise or fall divided by the run towards left or right.

A slope of zero (like we got here) results when the numerator is zero - no rise or fall as we go from one point to the next. Thus, a line through the points would be perfectly horizontal.

A denominator of zero results when there is no side-to-side movement from one point to the next, so a line through the points would be perfectly vertical.

If we get a zero down in the denominator, we are dividing by zero and have an undefined expression. However, this undefined expression still tells us something useful, as it tells us that a line through the points would be perfectly vertical.

Thus, zero slope means a horizontal line and undefined slope means a vertical line.

Some of this is more than you asked for, but I hope that's okay.

I hope it helps.

The insertion sort algorithm will make a total of 10 comparisons to sort the list [4, 5, 1, 2, 3] by comparing each element with the elements on its left side to find its correct position.

To sort the list [4, 5, 1, 2, 3] using insertion sort, we count the number of comparisons made during the sorting process.

In insertion sort, each element is compared with the elements on its left side to find its correct position in the sorted portion of the list.

1. Initially, the first element 4 is considered sorted.

2. The second element 5 is compared with 4. (1 comparison)

3. The third element 1 is compared with 5 and then with 4. (2 comparisons)

4. The fourth element 2 is compared with 5, 4, and 1. (3 comparisons)

5. The fifth element 3 is compared with 5, 4, 2, and 1. (4 comparisons)

Therefore, the insertion sort will make a total of 1 + 2 + 3 + 4 = 10 comparisons to sort the given list [4, 5, 1, 2, 3].

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The given functions are:

To solve for f(g(6)), first we need to find g(6):

So, f(g(6))=f(148), now find f(148):

The answer is f(g(6))=737

b. Find f(f(2)).

Start finding f(2):

Now, f(f(2))=f(7), solve for f(7):

The answer is f(f(2))=32

The general term of the Arithmetic sequence is \(T_{n} = -6n +4\)

The given arithmetic sequence is -2, -8, -14, -20

The first term = a = -2,

The common difference = d = -8 -(-2) = -8 +2 = -6

The general term of the arithmetic sequence is given by

\(T_{n} = a + (n-1)d\)

Now, putting the values of the first term and common difference in the general term.

\(T_{n} = -2 +(n-1) (-6)\\\\T_{n} = -2 -6n +6\\ \\T_{n} = -6n +4\)

Hence, the general term of the Arithmetic sequence is \(T_{n} = -6n +4\)

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Answer:

B

Step-by-step explanation:

Using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\(a^{0}\) = 1

Given

\(9^{c}\) × \(9^{-c}\)

= \(9^{(c-c)}\)

= \(9^{0}\)

= 1 → B

Based on the given question the we can say that Always statement will be - The sum of all angles of a quadrilaterals is always equals to 360°.

The general statement for the n sided polygon is (n-2)*180.

For the above statement, we can say that the value of n should at least be greater than 2 (n>2).

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

A quadrilateral, often known as a square, rectangle, or rhombus, is a polygon with four sides. You are currently staring at a computer screen that is most likely shaped like a quadrilateral. You'll study the quadrilateral in geometry classes.

The answer is clearly always.

Similarly we can create more problems and we should also know that sum of angles of general n sided polygon = (n-2)*180

if we put n = 4 in above equation we get 360 degree as answer.

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Answer:

x=128

Step-by-step explanation:

Answer:128

Step-by-step explanation:

The angles in a trapezoid add up to 360, so if you add all the ones already given then subtract them from 360 you get 128.

The required, there are 8998912 possible license plates that can be generated using this format.

Here, we have,

There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used.

Therefore, there are 8 choices for each of the three digits,

giving us 8 x 8 x 8 = 512 possible combinations for the digits.

Similarly, there are 26 letters that can be used for each of the three letters on the license plate.

Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.

Total number of license plates = number of choices for the digits x number of choices for the letters

= 512 x 17576

= 8998912

Therefore, there are 8998912 possible license plates that can be generated using this format.

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(B) 4X1 + 3X2 ≤ 150 constraints reflects the relationship between X1, X2 and resource 1.

This constraint reflects the fact that each unit of X1 requires 4 pounds of resource 1 and each unit of X2 requires 3 pounds of resource 1.

Since there are only 150 pounds of resource 1 available, the total amount of resource 1 used to produce X1 and X2 cannot exceed 150 pounds.

Therefore, we can write the constraint as 4X1 + 3X2 ≤ 150.

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\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-5)}}}\implies \cfrac{-6}{5+5}\implies \cfrac{-6}{10}\implies -\cfrac{3}{5}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-\cfrac{3}{5}}(x-\stackrel{x_1}{(-5)}) \implies y-1=-\cfrac{3}{5}(x+5) \\\\\\ y-1=-\cfrac{3}{5}x-3\implies y=-\cfrac{3}{5}x-2\)

The given differential equation is:y = (1/2)sin(2x) + C_2, Here, C_2 = 1/2ln|sec(2y) + tan(2y)| + C_1, where C_1 is the constant of integration.

The given differential equation is y′=(cos2x)(cos24y). In order to solve the given differential equation, we need to integrate both the sides of the equation as follows:dy=(cos2x)(cos24y)dx

Integrating the left-hand side of the equation with respect to y and the right-hand side of the equation with respect to x, we get:

y = ∫(cos2x)dx = (1/2)sin(2x) + C …(1)

We need to solve the equation (1) to get the final solution of the given differential equation.

Therefore, we differentiate equation (1) with respect to x as follows:

dy/dx = cos(2x)………(2)

Now, we need to substitute equation (2) in the given differential equation to check whether the value of y obtained from equation (1) is the correct solution or not.

y′=(cos2x)(cos24y)cos(2x) = (cos2x)(cos24y)cos24y = 1/2ln|sec(2y) + tan(2y)| + C_1 …(3)

Therefore, the solution of the given differential equation is:y = (1/2)sin(2x) + C_2Here, C_2 = 1/2ln|sec(2y) + tan(2y)| + C_1, where C_1 is the constant of integration.

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Answer:

I only know some, I'll answer the ones I know:

Question 1 of 5:

1. Obtuse

2. Acute

3. Obtuse

4. Right

Question 4 of 5:

1. Figure A

2. None

3. Figure C

Step-by-step explanation:

Have a good day :)

Answer:

problem 1:

angle a is obtuse, angle b is acute, angle c is obtuse, angle d is right

problem 3:

triangle a is scalene, triangle b is equilateral, triangle c is isosceles, triangle d is isosceles.

problem 5:

a) triangle

b) circle

c) rectangle

problem 2:

triangle a is obtuse, triangle b is obtuse, triangle c is acute, triangle d is right.

problem 4(answers in orders):

figure a, none, figure c

Hope this helped!