(a) How many vectors (x1, x2, x3, . . . , xn) are there for which each xi is either 0 or 1 andx1 + x2 + · · · + xn = k.(b) Do the same problem as before but under the condition thatx1 + x2 + · · · + xn ≥ k.

The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.

This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.

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the 6th term of the geometric sequence will be 3888.

What is geometric sequence?

A geometric progression or geometric sequence is the order in which each word is different from the next by a common ratio. The next term in the series is produced by adding a constant (that is not zero) to the term that came before it. A, ar, ar2, ar3, ar4, etc. are used as substitutes.

Mathematicians use the term "Geometric Progression" (GP) to describe a type of sequence in which each word is formed by multiplying the previous term by a predetermined number, or "common ratio". An integer geometric series gets that follows a pattern is another name for this development.

The terms are given, 16,48,144

a = 16

r = 48/16 =3

The 6th term will be= a(r)[tex])^{5}[/tex]

= 16(3)[tex])^{5}[/tex]

= 16* 243

=3888

Hence, the 6th term of the geometric sequence will be 3888.

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Answer:

20 miles in 1/2.  That would be 40 miles per hour

Step-by-step explanation:

6 ÷ 1/8 is the same at 6 x 8 = 48

11 ÷1/4 is the same as 11 x 4 = 44

16 x 3/8 is the same as 16 x 8/3 = 42 2/3

20 ÷ 1/2 is the same as 20 x 3 = 40

In poetry, the two main types of feet are iambic and trochaic.

Iambic foot: An iambic foot consists of two syllables, with the first syllable being unstressed and the second syllable being stressed. This creates a rhythmic pattern of "da-DUM" that gives iambic meter its characteristic "rising" sound. Iambic meter is one of the most common types of meter in English poetry, and is often associated with a natural, conversational rhythm.

Trochaic foot: A trochaic foot consists of two syllables, with the first syllable being stressed and the second syllable being unstressed. This creates a rhythmic pattern of "DA-dum" that gives trochaic meter its characteristic "falling" sound. Trochaic meter is less common than iambic meter in English poetry, but is still used in a variety of forms and styles. It can create a sense of tension or urgency, and is often used in poetry that is meant to be dramatic or suspenseful.

It's important to note that these two types of feet are just two of many possible metrical patterns that can be found in poetry. However, they are two of the most basic and widely recognized, and a good starting point for understanding the rhythms and structures of poetic meter.

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If a translation maps H onto J, the option from the following statements which is true is:  ∠I ≅ ∠K (Option 1)

A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. The four fundamental translations or transformations in geometry are:

With regard to the above answer, note that, because both triangles have the same vertex, angle HGI is equivalent to angle JGK. Angle H is parallel to angle J.

As a result, by converting angle I to angle K, their measurements will be equivalent. As a result, the angle I is congruent with angle K.

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Full Question:

If a translation maps H onto J, which of the following statements is true?

1. ∠I ≅ ∠K

2. GH = 2GJ

3. ∠G ≅ ∠K

4. HI = 2JK

The amount of total distance walked (in miles) has walked by Eric in a man made circular lake is 62.8 miles.

A circle's circumference is the length of its perimeter. The circumference of a circle can be calculated using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line.

Let's now discover the components of circumference. The three most crucial components of a circle are those three.

Circumference = D*π

Total distance walked two times = 2.C

=2* D* π

=2x10x3.14

=62.8 miles

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(E) Other

To make 144 slices of cake, Emma will need 18 large eggs.

To solve this problem, we need to know how much 2 dozen is.

So, for every 24 slices of cake, 3 eggs are needed.

To figure out how many slices of cake 1 egg can make, we can divide 24 by 3.

Now, for every 8 slices of cake, 1 egg is needed.

Now, taking 144, we can divide that by 8 to get the number of eggs needed.

Therefore, 18 eggs will be needed to make 144 slices of cake.

Answer:

67%

Step-by-step explanation:

Percent change is the change divided by the original value.  The change for the flower is (70" - 42") = 28"

The original value was 42".

Percent change is (28"/42")*(100%) = 67%

Answer: option c.

Step-by-step explanation:

When h=-17  is b in the plane spanned by a1 and a2.

For the plane spanned by a1 and a2, y is a linear combination of a1 and a2 if it is in the plane,

y = a a1 + b a2

where a and b are constants,

[4,1,h] = a[1,4,-2] + b[-2,-3,7]

[4,1,h] = [a - 2b,4a -3b,-2a+ 7b]

by the rules of vector addition and multiplication.

Vectors are equal if their components are equal:

4 = a - 2b

1 = 4a - 3b

h = -2a + 7b

solve for a and b from the first two equations so that we can find h,

b = -3

h = -17

We see that -2[1,4,-2] - 3[-2,-3,7] = [4,1,-17].

so ,the value of  h=-17  is b in the plane spanned by a1 and a2.

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Step-by-step explanation:

1/4096

0.000244140625

2^-12

1/(2^12)

All of the above expressions are equivalent to (12⁻₂)₈, which is a decimal representation of a number that is obtained by dividing 1 by 2 raised to the power of 12. The first and second expressions are decimal representation of the number, the third one is the representation of the number by using the base 2 logarithm, and the fourth one is the mathematical representation of the number by dividing 1 by 2 raised to the power of 12.

Answer:

2. a)

As per the Angle sum property

∠P +  ∠Q +  ∠R = 180°

22° +  ∠Q + 54° = 180°

∠Q = 180° - 76°

∠Q = 104°

b)

Now as per the question,

ΔABC ≅ ΔPQR

Which implies that

AB = PQ

So,

PQ = 8 cm

Step-by-step explanation:

$10.66 is dollars was the discount .

How does discount work?

Discount is a term that describes a sum or a percentage subtracted from a product's usual selling price. Make sure you need all of the items you plan to buy before waiting until after the holiday when you can frequently find them at a significant discount.

                           Discount is a term that refers to a reduction in the cost of a commodity or service.

Discount:

(13 x 18)/100 = $2.34

13 - 2.34 = $10.66

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Answer:

1/5

Step-by-step explanation:

1/7 * x = 1/35    multiply both sides by 7

x = 7/35 = 1/5

The population of foxes in the preserve after 42 years will be:

1620 foxes.

The function "y = 60 • 3^t" models the population growth of foxes in a wildlife preserve.

"y" represents the population size, "60" is the initial population size, "3" is the factor by which the population triples, and "t" is the number of 14-year periods that have passed.

In this case, we are told that 42 years have passed, so we can calculate the number of 14-year periods as "t = 42/14 = 3".

Substituting this value of "t" into the function, we get: So, t = 42/14 = 3

Substituting that into the function:

So, after 42 years, the population of foxes in the preserve will have grown to 1620 foxes.

Complete Question:

"A population of 60 foxes in a wildlife preserve triples in size every 14 years. The function y = 60 • 3^x models the population growth, where x is the number of 14-year periods. How many foxes will there be after 42 years?"

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Answer:

m = -1

Step-by-step explanation:

Slope = rise/run = (y2 - y1) / (x2 - x1)

Points (-3, 4) (2, -1)

We see the y decrease by 5 and x increase by 5, so the slope is

m = -5/5 = -1

Answer: 5^3

Step-by-step explanation: since we know that 5^2=5x5 (which equals to 5x5x5), our answer is 5^3

The third interior angle of the triangle is 119.9 degrees

Triangle is a closed polygon consist of three sides, three angle or three segment.

Triangle has three angle which if we sum all of those three angle it will be 180 degrees.

Triangle can be divided into several type :

1.  Equilateral triangle which all of the angle is equal ( 180 degrees / 3 = 60 degrees each )

2. Isosceles triangle which have two equal angle, and the third angle is different

3. Scalene triangle which all of the angle is different

From the question, we have data :

1. First Angle is 45.5 degrees

2. Second Angle is 14.6 degrees

For the Third angle, we just simply subtract 180 degrees with the first and second angle. So it will be :

Third Angle = 180 degrees - ( 45.5 degrees + 14.6 degrees )

                    = 180 degrees - 60.1 degrees

                    = 119.9 degrees

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The distances from the midpoint M to the vertices are all the same and equivalent to 5·√2, therefore, the diagonals of the quadrilateral bisect each other.

A diagonal is a line that joins the opposite corners of the quadrilateral.

The question is without the possible options for the response.

The vertices of the quadrilateral are;

P(1, -1), Q(3, -7), R(-9, -11), and S(-11, -5)

The midpoint of the side PR = ((-9 + 1)/2, (-11 + (-1))/2) = (-4, -6)

Midpoint of the diagonal SQ = ((3 + (-11))/2, (-7 - 5)/2) = (-4, -6)

Let M represent the point of intersection of the diagonals, we get;

PM = √((1 - (-4))² + (-1 - (-6))² = 5·√2

MR = √((-9 - (-4))² + (-11 - (-6))² = 5·√2

The length of PM = The length of MR, therefore, the diagonal SQ bisects PM

Similarly, we get;

SM = √((-9 - (-4))² + (-11 - (-6))²) = 5·√2

MQ = √((3 - (-4))² + (-7 - (-6))²) = 5·√2

The length PM = MR and the lengths SM = MQ, therefore, the diagonals bisect each other.

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Answer: the product of the slopes of the diagonals PR and QS is equal to 1. Hence, the diagonals of parallelogram PQRS bisect each other.

Step-by-step explanation:

Answer:

9058 Bagels

Step-by-step explanation:

14x657 I hope this helped!

The unique property of Pythagorean triplets is the square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base.

In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.

Here,
Pythagorean triplet's unique property is that,
The square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base for a right-angled triangle.
hypotenuse² = perpendicular² + base²

Thus, the unique property of Pythagorean triplets is the square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base.

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The solution to the differential equation is ln |y| = 4t - 4.

The given differential equation can be written as ∆y/∆t = y2(4t). This is a first-order separable differential equation, which can be solved using the separation of variables method. To do this, we first isolate the dy/dt term on one side of the equation. We can then separate the two variables (t and y) by moving all terms with t to one side and all terms with y to the other side. This gives us ∆y/y2 = 4∆t. We can then integrate both sides to find the solution.

Integrating both sides with respect to y gives us the following:

ln |y| = 4t + C,

where C is an integration constant. We can use the boundary condition to solve for C. The boundary condition states that y=8 when t=1, so substituting this into the equation above gives us ln |8| = 4 + C. Solving for C gives us C=-4.

Therefore, the solution to the differential equation is ln |y| = 4t - 4. Rearranging this equation gives us y = e4t-4, which is the solution to the differential equation.

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For (a), x must be the 98th percentile of T22. For (b), x must be the 85th percentile value  of T13. For (c), x must be the 26th percentile of T26. For (d), x must be the 97.5th percentile of T2.

For (a), the value of x must be the 98th percentile of T22, which is the value of x such that 98% of the data points of T22 are less than or equal to x. For (b), the value of x must be the 85th percentile of T13, which is the value of x such that 85% of the data points of T13 are less than or equal to x. For (c), the value of x must be the 26th percentile of T26, which is the value of x such that 26% of the data points of T26 are less than or equal to x. For (d), the value of x must be the 97.5th percentile of T2, which is the value of x such that 97.5% of the data points of T2 are less than or equal to x. In order to find these values of x, one must first calculate the percentiles of the given variables. This can be done by sorting the data points in ascending order and then calculating the percentile of each data point. After the corresponding percentile of each data point has been calculated, the desired values of x can be determined by finding the data point whose percentile matches the desired value.

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The original amount of water is  15 cups.

The change in David's water intake is  3 cups.

The percent change is 20 %. This is a percent  decrease.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Given that, David is tracking the amount of water he drinks each day.

On Thursday, he drinks 15 cups of water.

On Friday, he drinks 12 cups of water.

The percent change in his water intake = (12 - 15) / 15 × 100 = -20%

Where minus sign is showing a decrease in the water intake,

The original amount of water is 15 cups.

The change in David's water intake is (15-12) = 13 cups.

Hence, the answers are;

The original amount of water is  15 cups.

The change in David's water intake is  3 cups.

The percent change is 20 %. This is a percent  decrease.

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I need the answer...

Answer:

what is this? ahdhdjxkdjjshsysusiiaiajsjjdyxc

The parabola f(x) = -x² - 6x - 13 is open downward.

Write the equation in vertex form f(x) = a(x-h)² + k

So, f(x) = -x² - 6x - 13

           = -(x² + 6x + 13)

           = -(x² + 6x + 9 + 4)

           = -((x + 3)² + 4)

           = -(x + 3)² - 4

Here, a = -1, h = -3 and k = -4

If a > 0, the parabola is open upward and if a < 0, the parabola is open downward.

In f(x) = -(x + 3)² - 4, a= -1 < 0. Therefore, the parabola is open downward.

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