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The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).

In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.

Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).

Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).

Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).

To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:

Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)

Simplifying this expression, we get:

Total number of strings = (n-1) x (n-2)

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The number of miles Ling Jog than Trent can be written as the expression 2.8x - 8

Trent's expression:

2.2x + 8

Ling's expression:

5x

Where,

Number of hours= x

Number of hours Ling Jog than Trent =Ling's expression - Trent's expression

= 5x - (2.2x + 8)

= 5x - 2.2x - 8

= 2.8x - 8

Therefore, Ling jog 2.8x - 8 miles than Trent.

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The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.

Inequality is defined as an equation that does not contain an equal sign.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of minutes and 'y' be the total battery percentage. Then the equation is given as,

y = 3x + 40

The inequality that represents the more minutes are needed to reach 80 of battery is given as,

3x + 40 ≤ 80

Simplify the inequality, then we have

3x + 40 ≤ 80

3x ≤ 40

x ≤ 13.33 minutes

The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.

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We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.

When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.

An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.

Using this property, we can expand the expression as follows:

(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)

Now we can simplify each term separately:

2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110

and

−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165

Therefore, putting the results together, we have:

(2 − 3)(7 2 − + 8) = 110 − 165 = -55

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The requried solutions are as follows,
(1) the original price is $450.   (2)  the original price is $172.40.

Sale price is defined as the price of a product marked including of various price cut such as discounts.

Here,
If the percent of discount is 80% and the sale price is $90, we can use the following formula to find the original price x (let)

Sale price = Original price - Discount

$90 = x - 0.8x

Simplifying the right-hand side:

$90 = 0.2x

x = $450

Therefore, the original price is $450.

If the percent of discount is 15% and the sale price is $146.54, we can use the same formula:

Sale price = Original price - Discount

$146.54 = x - 0.15x

Simplifying the right-hand side:

$146.54 = 0.85x

x = $172.40

Therefore, the original price is $172.40.

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The area of the right triangle with side lengths of 15cm and 12cm is 90 cm².

The area of triangle can be determined using the equation;

Area = 1/2 × base × height.

The angle described forms a right-triangle.

Area = 1/2 × base × height

Area = 1/2 × 12cm × 15cm

Area = 6cm × 15cm

Area = 90 cm²

Therefore, the area of the triangle is 90 cm².

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The equations that are true of the values x, y, and z are :

The line that x degrees and 65 degrees is on, is a straight line which means that they will both add up to 180 degrees :

x degrees + 65 degrees = 180 degrees

x and z are congruent angles which means they are both the same angle measure.

y would be equal to 65 degrees because, just like x and z, y and 65 degrees are congruent.

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Options include:

The area of the shape for the quilt block is 166.5 in²

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape

Given that, a quilt has blocks of design on it, we need to find the area of the block,

To find the area of the block = sum of the areas of the right triangle and the rectangle,

Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²

Hence, the area of the shape for the quilt block is 166.5 in²

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The figure is unavailable is the question is solved for the figure attached

Answer: the number is 6

Step-by-step explanation: First, set up an equation. Two more means +2, 3 times a number means 3x. So your equation would be 3x+2=20. Then solve the equation for x.

Answer:

x = 6

Step-by-step explanation:

Let the number be 'x'

Then, the equation becomes,

2 + 3x = 20
3x = 20 - 2
3x = 18
x = 18/3
x = 6

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Sipho earned R33.15 in simple interest.

The balance of the account at the end of the first 30 days was R2 133.15.

a. To calculate the simple interest earned by Sipho, we need to calculate the total amount deposited and the interest earned on that amount.

Total amount deposited = R600 + R1 000 + R500 = R2 100

Interest earned = R2 100 x 4.5% x 30/365 = R33.15 (rounded to the nearest cent)

Therefore, Sipho earned R33.15 in simple interest.

b. The balance of the account at the end of the first 30 days can be calculated by adding the total amount deposited and the interest earned to the initial deposit:

Balance = R600 + R1 000 + R500 + R33.15 = R2 133.15

Therefore, the balance of the account at the end of the first 30 days was R2 133.15.

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If Kirk had worked for 7 hours he would have made 42 kg of dough.

A unit rate means a rate for one of something.

Given that, Kirk prepared 24 kilograms of dough after working 4 hours, we need to find the amount of dough if he worked for 7 hours.

Calculating the unit rates,

Since, he worked for 4 and made 24 kg,

So, in 1 hour = 24/4 = 6 kg

Therefore, in 1 hour he will make 6 kg

Therefore, in 7 hours he will make = 7x6 = 42 kg

Hence, If Kirk had worked for 7 hours he would have made 42 kg of dough.

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Answer: x is anything from the set {2, 3, 5, 7, 11}

This is the list of primes between 1 and 11. The value 1 is not prime.

Answer:5/8

Step-by-step explanation: you put the numbers in a fraction the smallest goes on top and the more enormous number at the bottom you simply by finding the most significant standard number between the 2 numbers which is in this case 6 divide it by that and that is how you get your answer

The equation that can be used to find the number of gardens that Kalisa welds is given as follows:

200 + 5.5w = 260.50.

Kalisa's earnings are divided as follows:

Hence the equation for the total earnings is constructed follows:

T(w) = 200 + 5.5w.

Her total earnings are of $260.50, hence the number of gardens that Kalisa welds is given as follows:

200 + 5.5w = 260.50.

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The length of the rectangle given the area and width is 21 inches

Area of the rectangle = 357 square inches

Width of the rectangle = 17 inches

Length of the rectangle= l

Area of a rectangle = Length × width

357 = l × 17

357 = 17l

divide both sides by 17

l = 357 / 17

l = 21 inches

In conclusion, 21 inches is the length of the rectangle.

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Answer:

here you go

Step-by-step explanation:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Emily places a 10-foot tall pole to support the guy wire. After placing the pole, Emily measures the distance from the stake to the pole to be 11 ft: She then measures the distance from the pole to the tower to be 23 ft: Find the length of the guy wire, to the nearest foot.

The Distance between A, B based on the information will be 28.705 feet

From the information, the policewoman has positioned herself 500 ft from the intersection of two roads and she has carefully measured the angles of the lines of sight to the points.

Distance between A, B will be:

= 500 tan(15.4) - 500 tan(12.3)

= 500 (tan 15.4 - tan 12.3)

= 500(0.0574)

= 28.705 feet

The speed will be:

= 28.705 / 1.75

= 16.403 ft/s

= 12.3 mph

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Answer:

The value of the investment in 5 years.

Step-by-step explanation:

The description of the function states that it tells us the value of an investment at some point in the future (t), measured in years.  In other words, f(t).  When the time is 5 years, it would be written as f(5), and the t term in the function will be set to 5 for the calculation, which will yield the value of the investment at that time.

Answer:

Step-by-step explanation:

4 = d

5=1/5

3 the first one is 4x1/12 and 2x3/12

Answer: Region Z

Step-by-step explanation: Region X is smaller than Region Y, while Region Y is smaller than Region Z.

The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex

For the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).

Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.

In conclusion, the correct option is C.

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According to the information, we plan to have cruising speed on for a minimum of 3 hours and a maximum of 4.1 hours.

To calculate how many hours we are going to have the cruising speed on we must carry out the following process:

To calculate the minimum we must subtract 35 from 215 and then divide by the speed:

So the minimum hours would be 3 hours.

On the other hand, to calculate the maximum we must add 35 to 215 and divide it by the speed:

So the maximum time would be 4.1 hours.

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Using the definition of congruent triangles, the missing values are:

x = 35

y = 30°

Given that the two triangles in the image above are congruent, it implies that all its corresponding angles and corresponding side lengths have equal measure.

Therefore, we have:

2x - 10 = x + 25

Solve for x:

2x - x = 10 + 25

x = 35

Plug in the value of x to find the missing angles:

y + 90 + (2x - 10) = 180 [triangle sum theorem]

y + 90 + (2(35) - 10) = 180

y + 90 + 60 = 180

y = 30°

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The value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "."

The two triangles are similar thus the measure of its angle are also equal.

Using the similar triangle we have:

Angle D = Angle A = 82 degrees.

Angle F = 67 degrees

Using the sum of interior angles of triangle we have:

∠D + ∠F + ∠E = 180

82 + 67 + ∠E = 180

∠E = 31

From the figure we observe that,

∠E + ∠G = 180 (straight line)

31 + ∠G = 180

∠G = 149

Hence, the value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.

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The estimate for the mean book thickness is 3.2 mm.

What is mean?

In arithmetic, mean is the sum of all the added values of all the data in a set divided by the number of data in the set.

To find the mean book thickness, we can use the formula for the mean (also known as the average):

mean = (sum of all data points) / (number of data points)

Since we don't have the exact thickness of each book, but rather intervals of thickness and the number of books in each interval, we can use a weighted mean to estimate the mean thickness.

Here is the calculation:

First, we'll find the midpoint of each interval:

Interval 1: [0, 2]  -> midpoint: x1 = 1

Interval 2: [2, 4]  -> midpoint: x2 = 3

Interval 3: [4, 6]  -> midpoint: x3 = 5

Next, we'll find the weight of each interval by multiplying the midpoint by the frequency:

Interval 1: x1 * f1 = 1 * 5 = 5

Interval 2: x2 * f2 = 3 * 8 = 24

Interval 3: x3 * f3 = 5 * 7 = 35

Finally, we'll sum up the weights and divide by the total frequency to find the weighted mean:

Weighted mean = (5 + 24 + 35) / (5 + 8 + 7) = 64 / 20 = 3.2

So, the estimate for the mean book thickness is 3.2 mm.

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The volume of storage space that the nursery needs for the wood if 60 crates are delivered in an order is; D: 3360 cubic feet

The formula for volume of a cuboid is;

Volume = Length * width * height

We are given;

Length = 4 feet

Width = 3.5 ft

Height = 4 ft

Thus;

Volume of one crate = 4 * 3.5 * 4

= 56 cubic ft

We need a total of 60 crates. Thus;

Total Volume = 60 * 56

Total volume = 3,360 cubic feet

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