Ten less than the product of eight and a number is greater than thirty-eight

6 + 2 2 = 2 ( 3 + 11 )

60 + 25 = 5 ( 12 + 5 )

The value of the missing number and the 6th term is 3750

The formula for determining the nth term of a geometric sequence with a common ratio greater than one is expressed as;

Tn = ar^n-1

From the information given, the first term(a) is 6 and we are to find the 5th term, thus, n is 5

Let's substitute into the formula

T5 = 6 × 5^5-1

T5= 6× 5^4

Find the value

T5 = 6 × 625

T5 = 3750

Thus, the value of the missing number and the 6th term is 3750

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The task requires devising a recursive definition for the set S, which contains all strings from A* in which there is no b before an a.

To create a recursive definition for S, we need to consider two cases: a string that starts with an "a" and a string that starts with a "b." For the first case, we can define the set S recursively as follows:

λ ∈ S (the empty string is in S)

If w ∈ S, then aw ∈ S (concatenating an "a" at the end of a string in S results in a string that is also in S)

If w ∈ S and x ∈ A*, then \(wx\) ∈ S (concatenating any string in A* to a string in S results in a string that is also in S)

For the second case, we only need to consider the empty string because any string starting with a "b" cannot be in S. Thus, we can define S recursively as follows:

λ ∈ S

If w ∈ S and x ∈ A*, then xw ∈ S

These two cases cover all possible strings in S, as they either start with an "a" or are the empty string. By using recursive rules to concatenate characters at the beginning or end of strings in S, we can generate all valid strings in the set without generating any invalid strings that contain a "b" before an "a."

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Answer:

12÷4+13>2+22÷2

Step-by-step explanation:

12÷4=3+13=16

2+22=24÷2=12

The two triangles ΔRST and ΔUVW are similar to each other by the SAS property.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

Given that there are two triangles ΔRST and ΔUVW. ΔRST has the angle ∠T = 59° and the sides RT = 15 units and ST = 13 units. The other triangle ΔWVU has the angle ∠W = 59° and the sides WV= 52 units and WU= 60 units.

Firstly the two angles are the same,

∠T= ∠W = 59°

The two sides are dilated by a scale factor of 4,

WV /  ST = 52 / 13 = 4

WU /  RT = 60 / 15 = 4

So these sides are similar.

Hence, from the SAS property, the two triangles are similar.

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Answer:

40 pill bottles

Step-by-step explanation:

pill bottle : ounce of vitamin

1 : 0.033

x : 1.32

\(\frac{1.32}{0.033} *1\) = 40

When comparing variables x and y that are in the list '(AB), the comparison function we use is EQ.

Here's an explanation:

In Lisp, the EQ operator compares whether the two arguments are the same memory location.

EQV, on the other hand, checks whether the two values being compared are equivalent to each other.

For example, EQV will return true for two identical strings, while EQ will not.

The comparison function that should be used to compare variables x and y, which are both in the list '(AB), is EQ.

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Thomas finished 2.4 seconds faster than Mikah which has higher speed than Mikah.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Main body:

200-meter race finished by Thomas =  25.7 sec

200-meter race finished by Mikah = 28.1 sec

The difference between their time shows How much faster did Thomas run the race than Mikah.

=28.1 - 25.7

=2.4 seconds

Hence, Thomas finished 2.4 seconds faster than Mikah which has higher speed than Mikah.

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To find a subset of vectors that forms a basis for the subspace of R4 spanned by S, we need to determine which vectors in S are linearly independent.

Let's write the vectors in S as columns of a matrix:

S = [2, 3, 3, -8; V2, V3, -5, 25; -1, 26, 2, -8; -6, 0, 0, 0]

To find the linearly independent vectors, we can perform row reduction on the matrix to obtain its row-echelon form.

After performing row reduction, we get:

[1, 0, 0, -2; 0, 1, 0, 5; 0, 0, 1, 1; 0, 0, 0, 0]

The row-echelon form shows that the first three rows are linearly independent, while the last row is a zero row. Therefore, the corresponding vectors in S form a basis for the subspace of R4 spanned by S.

The subset that forms a basis for the subspace is: { [2, 3, 3, -8], [V2, V3, -5, 25], [-1, 26, 2, -8] }

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1) Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. 2) The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. 3) trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

1. Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. Therefore, the ratios of the sine, cosine, and tangent of the corresponding angles in similar triangles will also be equal.

2. The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. This means that the sine of an angle is equal to its complement's cosine, and vice versa.

3. Using the appropriate formula based on the given information, trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

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The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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Answer:

The answer is A, k2 + 3g – 6

Step-by-step explanation:

did the assignment on edge2020

A:

Simplify this expression:  One-half k squared + g minus 3 + one-half k squared minus 3 + 2 g

Answer: x=43, y=180

Step-by-step explanation: x is 43 because the 43 next to it has the same value. y is 180 because the angle is a straight line.

To find a recurrence relation for the number of bit strings of length n not containing two consecutive 1s, we simply add the possibilities from cases when the last bit is a 0 and the last bit is a 1.

We are required to find a recurrence relation for the number of bit strings of length n that do not contain two consecutive 1s. To do this, we will consider two cases:

1. The last bit is a 0

2. The last bit is a 1

Case 1: If the last bit is a 0, the bit string of length n can end in any bit string of length n-1 (since adding a 0 at the end does not create consecutive 1s). Let's call the number of such bit strings with no consecutive 1s A_n. So, in this case, there are A_(n-1) possibilities.

Case 2: If the last bit is a 1, the bit string of length n must end in a bit string of length n-2 (since adding a 1 after a 0 does not create consecutive 1s). In this case, there are A_(n-2) possibilities.

To find the total number of bit strings of length n with no consecutive 1s, we simply add the possibilities from both cases. Therefore, the recurrence relation can be defined as:

A_n = A_(n-1) + A_(n-2)

This is the recurrence relation you need to determine the number of bit strings of length n that do not contain two consecutive 1s.

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9:10

That's nine to ten

-Northstar

Therefore , the volume of the  decagonal prism is 246.21468296 cm^3.

The quantity of space that matter takes up is measured by its volume. A physical substance that takes up space and has mass is referred to as matter. Cubic meters are the accepted unit of volume in physical sciences like chemistry (m3). From this, other units like the litre (L) and milliliter (mL) are generated (mL).

Here,

The base of the perpendicular prism is a square-shaped regular decagon with a side length of 8 cm.

The 10 isosceles triangles that make up the regular decagon with side a = 8 cm in length each have an angle at their bases of 90-36/2 = 72 o and an apex of 360/10 = 36 o. (2/2)tan 72 divided by 3.077683537 is the height of the isosceles triangles.

The surface area of each isosceles triangle is equal to 3.077683537*8/2, or 12.310734148cm2.

The decagon's surface measures 123.10734148 cm2 or 12.310734148 * 10 cm2.

123.10734148*2 = 246.21468296 cm3 is the decagonal prism's volume.

The decagonal prism's volume is 246.21468296 cm3, according to this.

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Answer:

443.1 cm²

Step-by-step explanation:

The prism has two bases that are regular decagons and 10 faces that are congruent rectangles.

perimeter = 40 cm

there are 10 sides

perimeter = 10s

10s = 40 cm

s = 4 cm

Each rectangular face measures 4 cm by 8 cm.

LA = 10 × lw = 10 × (4 cm)(8 cm) = 320 cm²

The lateral area is 320 cm².

Each base is a decagon.

The sum of the measures of the interior angles of a decagon is:

(n - 2)180° = (10 - 2)180° = 1440°

Each interior angle measures 1440°/10 = 144°

The base can be divided into 10 congruent isosceles triangles with bases angles measuring 72°.

Half of the base of each triangle measures 2 cm.

tan 72° = h/(2 cm)

h = 2 tan 72° cm

h = 6.155367 cm

The height of each triangle is 6.155 cm, and the base is 4 cm.

The area of the base is

BA = 10 × bh/2 = 10 × 4 cm × 6.155367 cm / 2 = 123.1073 cm²

The total surface are is:

SA = LA + BA = 320 cm² + 123.1073 cm²

SA = 443.1 cm²

The value Newton's interpolating polynomial P 2(x) of f(x) of f[x0, x1] is -4.

In Newton's interpolating polynomial, the coefficients of the linear terms (x) correspond to divided differences. The divided difference f[x0, x1] represents the difference between the function values f(x0) and f(x1) divided by the difference between x0 and x1.

Since we are given P2(x) = \(x^2 + x + 2\), we can substitute the given x-values into P2(x) to find the corresponding function values.

For x0 = -3, substituting into P2(x) gives f(-3) = \((-3)^2 + (-3) + 2 = 12\).

For x1 = 1, substituting into P2(x) gives f(1) = \((1)^2 + (1) + 2 = 4\).

To calculate f[x0, x1], we need to find the divided difference between these two function values: f[x0, x1] = (f(x1) - f(x0)) / (x1 - x0) = (4 - 12) / (1 - (-3)) = -8 / 4 = -2.

Therefore, f[x0, x1] = -2, and the correct answer choice is b. -4.

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The cost of one hamburger will be equal to $2.5.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at the fast food restaurant, one hamburger and five small fries cost $11.25 and two hamburgers and three small fries cost $10.25.

The equations can be written as,

h + 5F = 11.25

2h + 3F = 10.25

Solve the above equation by elimination method,

2h +10F = 22.5

-2h - 3F = -10.25

______________

      7F = 12.25

        F = $1.75

h + 5 x 1.75 = 11.25

h = $2.5

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Answer:

80

Step-by-step explanation:

3.4 divided by 8 equals 0.425

34 divided by 0.425 equals 80

Answer:

10

Step-by-step explanation:

34÷3.4= 10

Answer:

13 units

Step-by-step explanation:

Distance formula:

d = \(\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

In this problem,

d = \(\sqrt{(7 - 2)^2 + (4 - -8)^2}\)

d = \(\sqrt{(5)^2 + (12)^2}\)

d = \(\sqrt{25 + 144}\)

d =      \(\sqrt{169}\)

d = 13

Answer:

z= -3.1111111111

Step-by-step explanation:

-7*3=-21

-7*51= -357

-7*-39= 273

-21z+(-357)+273

simplify

-21z-84

-21z/-21 (canceled)

84/-21= 3.1111111111

Hope this helps.

The statement (b) the sum is a binomial with a degree of 3 is correct.

Expressions are defined as the combination of constants and variables with mathematical operators.

We have expressions:

6s²t – 2st²

4s²t – 3st²

Adding the above two expressions, we get;

= (6s²t – 2st²) + (4s²t – 3st²)

Combining like terms:

= 10s²t - 5st²

The above expression has degree 3(2+1)

Thus, statement (b) the sum is a binomial with a degree of 3 is correct.

Complete question:

What is true about the sum of the two polynomials?

6s2t – 2st2

4s2t – 3st2

a.) The sum is a binomial with a degree of 2.

b.) The sum is a binomial with a degree of 3.

c.) The sum is a trinomial with a degree of 2.

d.) The sum is a trinomial with a degree of 3.

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Answer:

Greater probability of gray than black = 3/25

Step-by-step explanation:

Given:

Total block = 5 x 5 = 25

Number of black blocks = 6

Number of gray blocks = 9

Find:

Greater probability of gray than black

Computation:

Greater probability of gray than black = Probability of gray - Probability of black

Greater probability of gray than black = 9/25 - 6/25

Greater probability of gray than black = 3/25

we can represent this as a trinomial with a perfect square:(y-10)²-100

PRECISE SQUARE TERMINAL: WHAT IS IT?

A quadratic expression that can be factored into a binomial squared is a perfect square trinomial. When it is factored, it follows a pattern where the first and last terms are monomial perfect squares and the middle term is the product of the first two. A given trinomial is not a perfect square trinomial if the pattern does not fit for it1.

For instance, the trinomial x2+6x+9 is a perfect square trinomial since it factors into (x+3)². The square of x is represented by the first term, x², and the square of 3 by the last term, 9. Its result 2(x)(3) is twice as long as the middle term 6x.

Y has a coefficient of -20. A fraction of -20 is -10.

-10 is squared to give 100.

As a result, we can add and take 100 to finish the square.

It is necessary to add and subtract the square of the y-half coefficient's in order to finish the square for y²–20y.

y²-20y+100-100

=(y-10)²-100

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The shipping arrangement which minimizes costs will be 1.5x + 1.2y + 0.8z + 1.1(240 - x - y - z) subject to

x + z + s1 = 160

y + (240 - x - z) + s2 = 90

x - 100 + s3 = 0

y - 140 + s4 = 0

The minimum cost is $372.00.

There will be product left in either warehouse after fulfilling the orders.

Let x be the number of sheets delivered from the north-side warehouse to Customer A,

Let y be the number of sheets delivered from the north-side warehouse to Customer B and z be the number of sheets delivered from the south-side warehouse to Customer A.

Then the objective function to be minimized is:

1.5x + 1.2y + 0.8z + 1.1(240 - x - y - z).

There will be 60 sheets of drywall board left in the north-side warehouse and 70 sheets left in the south-side warehouse after fulfilling the orders.

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Answer:

4.79

Step-by-step explanation:

4.79 is reasonable for the problem

The price of one paint set before the sale is $4.79

We are expected to determine the price of one paint set before the sale.

From the information given:

∴

The amount at which Yuri bought 1 paint set is:

\(\mathbf{= \dfrac{\$6.88}{2.0}}\)

= $3.44

Recall that during the sale, the store reduce the price of each paint set by $1.35

Therefore, the price of one paint set before the sale is = $3.44 + $1.35 = $4.79

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The 100th even natural number is 200

Given the sequence 2, 4, 6, 8, 10....

The nth term of the sequence is expressed as:

Tn  = a + (n - 1)d

a is the first term = 2

d is the common difference = 4 - 2 = 6 - 4 = 2

n is the number of terms

Substitute the given parameters into the formula

Tn = 2(n-1)2

Tn = 2+(2n - 2)

Tn = 2n

Get the 100th term

T10=  2(100) = 200

Hence the 100th even natural number is 200

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Answer:

1)

200

2)  

10100

3)

less than

Step-by-step explanation:

on god

The estimated total number of heartbeats in an average lifetime of 68.4 years is 2.9 billion heartbeats. The maximum number of 91 kg people that can safely occupy an elevator is 10 people.  The diameter of human hair is 0.000056 meters.

(a) To estimate the total number of heartbeats in a lifetime, we multiply the heart rate (69.2 beats/minute) by the number of minutes in a year (60 minutes/hour * 24 hours/day * 365.25 days/year) and then multiply by the number of years in a lifetime (68.4 years). The calculation is: 69.2 beats/minute * 60 minutes/hour * 24 hours/day * 365.25 days/year * 68.4 years ≈ 2,886,699,648 beats. Therefore, the estimated total number of heartbeats in an average lifetime is approximately 2.9 billion heartbeats.

(b) To determine the maximum number of 91 kg people that can occupy the elevator, we divide the maximum mass the elevator can hold (1 metric ton or 1000 kg) by the mass of each person (91 kg). The calculation is: 1000 kg / 91 kg ≈ 10.98. Since we can only have whole numbers of people, the maximum number of people that can safely occupy the elevator is 10.

(c) To express the diameter of a human hair in meters, we convert the given diameter of 56 μm to meters by dividing by 1 million (since 1 μm = 1/1,000,000 meters). Therefore, the diameter of human hair is approximately 0.000056 meters.

(d) To convert 74 miles per hour to meters per second, we multiply the given value by the conversion factor 1609 meters/mile and divide by 3600 seconds/hour. The calculation is 74 miles/hour * 1609 meters/mile / 3600 seconds/hour ≈ 33.12 meters/second. Therefore, 74 miles per hour is approximately equal to 33.12 meters per second.

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