What number falls between 7 and 8 on the number line.

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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The constant that needs to be added to complete the square is 121/4.

To complete the square for the quadratic equation x² - 11x - 14 = 0, we need to add the square of half of the coefficient of x, which is (-11/2)² = 121/4. So we add 121/4 to both sides of the equation, which gives us:

x² - 11x - 14 + 121/4 = 121/4

We can simplify the left side by combining like terms:

(x - 11/2)² = 121/4 + 14

(x - 11/2)² = 169/4

Taking the square root of both sides, we get:

x - 11/2 = ±13/2

Solving for x, we get:

x = 11/2 ± 13/2

x = 12 or x = -1

Therefore, the constant that needs to be added to complete the square is 121/4.

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Answer:

8/11 as a decimal is 0.72727272727273

Step-by-step explanation:

GOOD LUCK :)

0.72 or 0.73

It would've been 0.72727272727273 if not cut short.

Answer:

The answer is

\(x^2 = 6y\)

Step-by-step explanation:

On solving the provided question using Pythagoras theorem, we can say that  length of the diagonal of the deck C = 25.08 ft

The basic Euclidean geometry relationship between a right triangle's three sides is known as the Pythagorean Theorem, or simply the Pythagorean Theorem.

This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. The Pythagorean Theorem says that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the total of the squares that span the sides of a right triangle. It is sometimes written as the generic algebraic notation \(a^{2} + b^{2} = c^{2}.\)

The Pythagorean theorem can be used to determine the length of the deck's diagonal since a right triangle will be formed when the diagonal of a rectangle's sides is measured. The Pythagoras Theorem asserts

\(C^{2} = B^{2} + A^{2}\)

where C is the hypotenuse or the diagonal of the rectangles

B and A are the sides of the rectangle

\(C^2 = 10^2 + 23^3\\C^{2} = 629\\C = 25.08 ft\)

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Answer: 10000

Step-by-step explanation:

((1234568)(198765432)+(98765432)(98765432))^1/4

=(245389441853376+(98765432)(98765432))^1/4

=(245389441853376+9754610558146624)^1/4

=10000000000000000^1/4

=10000

Hope this helps!!! :)

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=12\\ \theta =75 \end{cases}\implies 12=\cfrac{(75)\pi r^2}{360}\implies 12=\cfrac{5\pi r^2}{24} \\\\\\ 288=5\pi r^2\implies \cfrac{288}{5\pi }=r^2\implies \sqrt{\cfrac{288}{5\pi }}=r\implies 4.3\approx r\)

The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.

To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.

In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.

Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.

Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.

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When you add -1/4 to itself four times, you get: -1
When you multiply -1/4 by 4, you also get: -1.
Yes, both the results are same which is: -1.

To answer your question, let's break it down into two parts:

1. What do you get if you add -1/4 to itself four times?
To find the answer, you simply add -1/4 four times:
(-1/4) + (-1/4) + (-1/4) + (-1/4) = -1

2. What is -1/4 × 4?
To multiply -1/4 by 4, you perform the multiplication:
(-1/4) × 4 = -1

In conclusion, when you add -1/4 to itself four times, you get -1, and when you multiply -1/4 by 4, you also get -1.

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The Integral test, which is also known as Cauchy's criterion, is a method that determines the convergence of an infinite series by comparing it with a related definite integral.

In a series, the terms can either be decreasing or increasing. When the terms are decreasing, the Integral test is used to determine convergence, whereas when the terms are increasing, the Integral test can be used to determine divergence. For example, consider the series\[S = \sum\limits_{n = 1}^\infty {\frac{{\ln (n + 1)}}{{\sqrt n }}} \]. Now, we'll apply the Integral test to determine the convergence of the above series. We first represent the series in the integral form, which is given as\[f(x) = \frac{{\ln (x + 1)}}{{\sqrt x }},\] and it's integral from 1 to infinity is given as \[I = \int\limits_1^\infty {\frac{{\ln (x + 1)}}{{\sqrt x }}} dx\]. Next, we'll find the integral of f(x), which is given as \[I = \int\limits_1^\infty {\frac{{\ln (x + 1)}}{{\sqrt x }}} dx\]\[u = \ln (x + 1),\] so, the equation can be rewritten as \[I = \int\limits_0^\infty {u^2 e^{ - 2u} du}\]\[I = \frac{1}{{\sqrt 2 }}\int\limits_0^\infty {{y^2}e^{ - y} dy}\]\[I = \frac{1}{{\sqrt 2 }}\Gamma (3)\]. The given series [infinity] 3 cos(n) n n = 1 is a converging series because the Integral test is applied to determine its convergence.

The Integral test helps to determine the convergence of a series by comparing it with a related definite integral. The Integral test is only applicable when the terms of the series are decreasing. If the series fails the Integral test, then it's necessary to use other tests to determine the convergence or divergence of the series. The Integral test is a simple method for determining the convergence of an infinite series. Therefore, the series [infinity] 3 cos(n) n n = 1 is a converging series. The Integral test is applied to determine the convergence of the series and it is only applicable when the terms of the series are decreasing.

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Answer:

B) 20.5

Step-by-step explanation:

The triangle is an illustration of a right-angled triangle

The length of BC is 14.5 inches

From the figure (see attachment), the length of BC can be calculated using the following sine rule

\(\sin(65) = \frac{BC}{16}\)

Multiply both sides of the equation by 16

\(BC = 16 * \sin(65)\)

Evaluate the product

BC = 14.5

Hence, the length of BC is 14.5 inches

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Answer:

D.  -5v+4

Step-by-step explanation:

combine like terms  

Answer:

Line A

Step-by-step explanation:

AAnswer:

Step-by-step explanation:

Answer:

i believe number 1 is 18 and number 2 is 9.

Step-by-step explanation:

if one full circle represents 6 CDs then on wednesday 18 Cds were sold because 6+6+6=18 and on thursday they sold 9 more Cds than on wednesday because they sold 6+6+6+6+3 which equals 9.

Answer:The total number of tennis ball did store sell in all is 948 

Step-by-step explanation:

Answer: 4.75c+1b ≤50

Step-by-step explanation: One cupcake costs $4.75, so “c” cupcakes cost $4.75. One brownie cost $1, so “b” brownies cost 1b. The total 4.75c+1b must be less or equal to $50.

Answer:

3004 square feet

Step-by-step explanation:

  2

(2    )   +3000

2x2+3000

4+3000

3004

Answer:

all of the above

Step-by-step explanation:

The point of portrait orientation is to make it so the picture focuses on the person. In order to do this you need to minimize the background, place attention on the foreground, and show more context

Answer:

all of the above

Step-by-step explanation:

Answer:

use ma th wa y (its all together)

Step-by-step explanation:

Answer:

10. The number of cupcakes Sheldon would have to buy to recieve the same number of cupcakes in a package would be 30 cupcakes in a package.

Step-by-step explanation: Find the least common denominator (LCD) of six and ten which is, 30.

11.  The greatest number of necklaces Samuel would have to make is four.

Step-by-step explanation: Divide 148 necklaces by 36 strings and the answer will be four necklaces.

12. The greatest length, in feet, of each piece of ribbon Karen, would have to cut is six feet.

Step-by-step explanation: Find the greatest common denominator (GCD) of 18 and 12 which is, six.

13. Find the least common denominator of five and three which is, 15 minutes.

Step-by-step explanation:

Jacob will finish his laps in these following minutes, supposing he starts at zero.

3 minutes, 6 minutes, 9 minutes, 12 minutes, 15 minutes...

That is, all instants of time which are multiples of three.

Betty

5 minutes, 10 minutes, 15 minutes, 20 minutes, 25 minutes, ...

That is, all instants of time which are multiples of five.

The MCVST or MCVSD admission test is an entrance exam for students who live in New Jersey and are seeking admission to the Morris County Vocational School District. This test is designed to assess the academic abilities and potential of students.

The MCVST admission test typically includes sections in math, reading comprehension, and language skills. The math section assesses the student's understanding of mathematical concepts and problem-solving skills. The reading comprehension section evaluates the student's ability to understand and analyze written passages. The language skills section tests the student's knowledge of grammar, vocabulary, and sentence structure.

To prepare for the MCVST admission test, there are several practice tests available online. Some websites offer free practice tests specifically designed for this exam. You can search for these practice tests by using keywords like "free MCVST admission test practice" or "MCVSD practice tests."

Remember to utilize these practice tests to familiarize yourself with the types of questions and format of the MCVST admission test. This will help you feel more confident and prepared on test day.

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The boat travels at  18 miles per hour.

What is speed?

Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed.

The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.

Given:  A boat travels 30 miles up the river in the same amount of time it takes to travel 42 miles down the same river. The current is 3 miles per hour.

From the above information we can write,

Let, u is the boat speed in still water, then

\(\frac{30}{u-3} = \frac{42}{u+3}\)

Taking cross multiplication,

30(u + 3) = 42(u - 3)

Solving,

30u + 90 = 42u - 126

42u - 30u -126 -90 = 0

12u = 216

u = 18

Therefore, the speed of boat in still water is, 18 miles per hour.

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Answer:

85%

Step-by-step explanation:

First, let's add up the ratios and use it to divide 120. That way we can find out how many people each ratio is.

17 +3 = 20

120/20 = 6

Each individual ratio is equal to 6.

17 * 6 = 102

3 * 6 = 18

102/120 = percentage of who passed

= 0.85

85 percent of learners passed.

Answer:

14

Step-by-step explanation:

Our goal is to round it so we only have an integer part using the following rules:

If the first digit in the fractional part of 13.62 is less than 5 then we simply remove the fractional part to get the answer.

If the first digit in the fractional part of 13.62 is 5 or above, then we add 1 to the integer part and remove the fractional part to get the answer.

The first digit in the fractional part is 6 and 6 is 5 or above. Therefore, we add 1 to the integer part and remove the fractional part to get 13.62 rounded to the nearest whole number as:

14

89 vegetarian dishes

The unitary technique, in its most basic form, is used to calculate the value of a single unit from a specified multiple. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.

Using unitary method,

152 passengers are served with = 27 dishes

1 passengers are served with = 27/152

500 passengers are served with = 27 x 500 / 152

                                                         = 88. 81

                                                         ≈ 89 vegetarian dishes

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Answer:

\((x+2)(2x-1)(2x+3)\)

Start by multiplying the first two terms:

\((2x^2+3x-2)(2x+3)\)

Now multiply these two terms to prove:

\((4x^3+6x^2+6x^2+9x-4x-6)\)

Simplify:

\((4x^3+12x^2+5x-6)\)

The simplest and most straightforward measure of variability is the range. The range is calculated by subtracting the smallest value in a dataset from the largest value.

It provides a basic understanding of how spread out the data points are. However, the range has limitations as it only considers the extreme values and does not take into account the distribution of the remaining data points.

Therefore, while the range is a simple measure of variability, it is often supplemented or replaced by more robust measures such as the variance and standard deviation, which provide a more comprehensive understanding of the dispersion of data.

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A linear function that relates y to x include the following: B. y = 1/2(x)

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using the various data points from table D as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 1/2

Therefore, the required linear function is given by;

y = kx

y = 1/2(x)

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The area of the tin box without the top is 39100 square cm.

The cost of making this tin box is  Rs. 19550.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, A tin box of 1 m in length, 85cm in width, and 60cm in depth is to be made.

We know the total surface area of a cuboid is 2(lw + wh + wl).

Therefore, The surface area of the cuboid without the top would be,

= 2(lw + wh + wl) - (l×w).

= 2(100×85 + 85×60 + 85×100) - (85×60).

= 2(22100) - 5100.

= 44200 - 5100.

= 39100 square cm.

The cost of making this tin box is Rs.(39100×0.50).

= Rs. 19550.

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Answer:

well for me

Step-by-step explanation:

7 mins

7×60

=420

plus the 30sec

450 sec

450/3600×100

45000/3600

450/36

12.5

that's how I can help

The required percentage is 12.5% of 1 hour which equals 7 minutes 30 seconds.

The percentage is defined as a ratio expressed as a fraction of 100.

To express 7 minutes 30 seconds as a percentage of 1 hour, you first need to convert the time to a common unit, such as seconds.

One hour is equal to 60 minutes, so 7 minutes 30 seconds is equal to 7 × 60 + 30 = 450 seconds.

Next, you need to express the time in terms of the total number of seconds in an hour.

One hour is equal to 60 minutes, and one minute is equal to 60 seconds, so one hour is equal to 60 × 60 = 3600 seconds.

To find the percentage of 1 hour that 7 minutes 30 seconds represents, you would divide the number of seconds by the total number of seconds in an hour, and then multiply the result by 100% to convert it to a percentage.

Using the values above, the calculation would be as follows:

450 seconds / 3600 seconds × 100% = 12.5%

Therefore, 7 minutes 30 seconds is equal to 12.5% of 1 hour.

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