trey paid 42 dollars for 2/3 ton of concrete. he wants to know the price of 3 tons of concrete.

[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ n=10\\ a_1=4\\ r=\frac{1}{4} \end{cases}[/tex]

[tex]{\displaystyle\sum_{n=1}^{10}}~4\left( \frac{1}{4} \right)^{n-1}\implies 4\left( \cfrac{1-\left( \frac{1}{4} \right)^{10}}{1-\frac{1}{4}} \right)\implies 4\left( \cfrac{\frac{1048575}{1048576}}{\frac{3}{4}} \right) \\\\\\ 4\left( \cfrac{349525}{262144} \right) \implies \cfrac{349525}{65536} ~~ \approx ~~ 5.33[/tex]

Answer:

Step-by-step explanation:

Take the meatballs and then add the sauce

after finishing the meat and sauce cook the pasta then

viola perfection  

Answer:

Letting x be the missing length, we have

[tex]7 < x < 23[/tex]

Step-by-step explanation:

According to the Triangle Inequality Theorem:

8 + x > 15 -------> x > 7

8 + 15 > x -------> x < 23

x + 15 > 8 -------> x > -7

So we have 7 < x < 23.

The second x - intercept on the graph of a car that has been travelling for 8 hours, represents the end of the car's journey.

To show a car's journey on a graph with two x-intercepts, determine the scale for your x-axis and y-axis based on the range of values for your car's journey.

The x-intercepts represent the points where the car starts and ends its journey. These points should be plotted on the x-axis at the appropriate values based on your scale. Once you have plotted the x-intercepts and any intermediate points, connect them with a line to show the car's journey.

In conclusion, the second x - intercept shows the end of the car's journey.

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Answer:

(12, 15)

Step-by-step explanation:

Proofs attached to answer

The trigonometry equations when evaluated are ∅ = 82π/125 and ∅ = 28π/23

Equation 1

Given that

cos ∅ = -8/17, π/2 < ∅ < π

Take the arc cos of both sides of the equation

So, we have the following

∅ = 82π/125

Equation 2

The trigonometry equation from the question is given as

tan ∅ = 2/5

The domain of the function is given as

π < ∅ < 3π/2

This means that the definition of the function is

tan ∅ = 2/5, π < ∅ < 3π/2

Take the arc tan of both sides of the equation

So, we have the following

∅ = tan⁻¹(2/5), π < ∅ < 3π/2

Express fraction as decimal

This gives

∅ = tan⁻¹(0.4), π < ∅ < 3π/2

Evaluate the arc tan

∅ = 28π/25

Hence, the measure of the angle is approximately 28π/23

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Considering the expression of a line, an equation for the line best fit to the points (0, 60) and (4, 90) is y=7.5x +60.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂), the slope m can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points, the value of the ordinate to the origin b can be obtained.

In this case, being (x₁, y₁)= (0, 60) and (x₂, y₂)= (4, 90), the slope can be calculated as:

m= (90 - 60)÷ (4-0)

m= 30÷ 4

m= 7.5

Considering point 1 and the slope m, you obtain:

60= 7.5×0 + b

60= 0 +b

60= b

Finally, the equation of the line is y=7.5x +60.

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[tex]\textit{Pythagorean Identities} \\\\ 1+\tan^2(\theta)=\sec^2(\theta)\implies \tan^2(\theta)=\sec^2(\theta)-1 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\stackrel{ \textit{difference of squares} }{[sec(x)+1][sec(x)-1]}}{sin^2(x)}\implies \cfrac{sec(x)^2-1^2}{sin^2(x)}\implies \cfrac{sec(x)^2-1}{sin^2(x)} \\\\\\ \cfrac{tan^2(x)}{sin^2(x)}\implies \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{1}{cos^2(x)}\implies sec^2(x)[/tex]

Answer:

two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle

Let's call the measures of the two angles x and y, where x is the larger angle. We know that the two angles are supplementary, which means they add up to 180 degrees:

x + y = 180

We also know that one of the angles (let's say y) is 12 degrees less than one-third the measure of the other angle (x):

y = (1/3)x - 12

Now we can substitute the second equation into the first equation to solve for x:

x + (1/3)x - 12 = 180

Multiplying both sides by 3 to get rid of the fraction, we have:

3x + x - 36 = 540

Combining like terms, we get:

4x - 36 = 540

Adding 36 to both sides, we get:

4x = 576

Dividing both sides by 4, we get:

x = 144

Now we can use the first equation to solve for y:

144 + y = 180

Subtracting 144 from both sides, we get:

y = 36

Therefore, the measures of the two angles are 144 degrees and 36 degrees.

The sum of the sides of a regular polygon is 96ft, find the measure of it side.

Let's say that the regular polygon has n sides, and each side has length s. The formula for the sum of the sides of a regular polygon is:

sum of sides = n * s

We know that the sum of the sides is 96ft, so we can write:

96 = n * s

We want to find the length of each side, so we need to isolate s on one side of the equation. We can do this by dividing both sides by n:

s = 96/n

Now we can substitute this expression for s into the formula for the perimeter of a regular polygon:

Perimeter = n * s

Perimeter = n * (96/n)

Simplifying this expression, we get:

Perimeter = 96

We know that the perimeter of a regular polygon is the sum of the lengths of all its sides, so we can divide the perimeter by the number of sides to find the length of each side:

s = Perimeter / n = 96 / n

Therefore, the length of each side of the regular polygon is 96/n feet. We cannot determine the value of n from the given information in the problem.

Answer:

These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.

Step-by-step explanation:

We must first locate the three pairs of islands in order to establish which pair is nearest before determining the safest route for the ship.

Give the three islands the letters A, B, and C. The three island groups are designated as AB, AC, and BC. Finding the closest pair is necessary.

We can leverage the separation between the islands to do this. Assuming that the islands are separated by the following distances:

A and B are separated by 10 nautical miles.

A and C are separated by 15 nautical miles.

B and C are separated by 12 nautical miles.

These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.

To find zx and zy, we need to take partial derivatives of z with respect to x and y. Taking z with respect to x, we get zx = 3x2 + 12xy and zy = 6x + 16y. Taking z with respect to y, we get zy = 6x + 16y and g(x, y) = 3xy - 7x. Therefore, gx = 3y - 7 and gy = 3x.

A derivative is a measure of how much a function changes as its input changes. More specifically, the derivative of a function at a particular point is the slope of the function at that point, which describes how quickly the function is changing at that point.

Geometrically, the derivative of a function at a given point can be thought of as the slope of the tangent line to the function at that point.

To find zx and zy, we need to take partial derivatives of z with respect to x and y, respectively.

Given z = [tex]x^3 + 6x^2y + 8y^2[/tex],

Taking partial derivative of z with respect to x, we get:

zx = [tex]3x^2 + 12xy[/tex]

Taking partial derivative of z with respect to y, we get:

zy = 6x + 16y

Therefore, zx = 3x^2 + 12xy and zy = 6x + 16y.

Given g(x, y) = 3xy - 7x,

Taking partial derivative of g with respect to x, we get:

gx = 3y - 7

Taking partial derivative of g with respect to y, we get:

gy = 3x

Therefore, gx = 3y - 7 and gy = 3x.

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Answer:

[tex](-6)^{7}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

[tex](-6)^{5}[/tex] × (- 6)²

= [tex](-6)^{(5+2)}[/tex]

= [tex](-6)^{7}[/tex]

Therefore , the solution of the given problem of equation comes out to be n = 3.

The same variable word is frequently used in mathematical formulas to attempt to ensure consistency between two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Instead of dividing 12 into two portions in this instance, the normalise function adds b + 6 to use the illustration of

y + 6.

Here,

Part 1: We will add 1 to both sides of the equation because we want to separate n in this situation:

=> n - 1 + 1 = 2 + 1

Simplifying:

=> n = 3

Consequently, n = 3 is the answer to the problem n - 1 = 2 when n is taken into account.

To put it up:

=> n - 1 = 2

To both ends, add one:

=> n - 1 + 1 = 2 + 1

Simplify:

=>n = 3

Part 2:

In order to isolate the variable (n) on one side of the equation, we can use inverse operations to answer for n in the equation n - 1 = 2.

Addition is the opposite of reduction. In order to isolate n in this example, we therefore add 1 to both sides of the equation using the inverse process of subtraction.

The steps required are as follows:

=>  n - 1 = 2 (original calculation) (original equation)

To both ends, add one:

=>  n - 1 + 1 = 2 + 1

Simplify:

=> n = 3

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The simplified fοrm οf the expressiοn is 1 - cοs2x.

Trigοnοmetry is the branch οf mathematics that studies the relatiοnship between the sides and angles οf a triangle, particularly a right-angled triangle. The relatiοnship is shοwn by the ratiο οf the sides, which are trigοnοmetric ratiοs. There are six ratiοs in trigοnοmetry: sine, cοsine, tangent, cοtangent, secant, and cοsecant.

We can simplify the expressiοn cοs2x−2cοs2x+1 as fοllοws:

cοs2x − 2cοs2x + 1

= (cοs2x - cοs2x) - 2cοs2x + 1 (using the identity cοs2x = cοs2x - cοs2x + 1)

= -cοs2x + 1

= 1 - cοs2x

Therefοre, the simplified fοrm οf the expressiοn is 1 - cοs2x.

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Answer:

Lowest possible score is 59.865 and you can still maintain an 80 by the end.

Step-by-step explanation:

The pattern fοr the given rule is 5, 6, 7, 8, 9 and sο οn.

What is a pattern?

A pattern is a regular arrangement οf symbοls, such as numbers, geοmetric fοrms, οr cοlοurs. Sοmetimes the term "series" is used tο describe patterns.

We are given a rule as a + 4, where a = 1, 2, 3, 4, 5, ...On substituting the value οf a in the rule, we get

When a = 1, then a + 4 = 5

When a = 2, then a + 4 = 6

When a = 3, then a + 4 = 7

When a = 4, then a + 4 = 8

When a = 5, then a + 4 = 9

and the pattern cοntinues.

Hence, the pattern fοr the given rule is 5, 6, 7, 8, 9 and sο οn.

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Complete question:

This is the only question:

Create a pattern for the rule a + 4.

Answer:

15 is the median by using the formula

hope this helps you a lot

Answer:

the average velocity of the ball on the interval [1, 3/2] is -808 ft/s.

Step-by-step explanation:

The height of the ball at time t is given by the formula:

s(t) = -16t^2 + 50t + 1200

We need to find the average velocity of the ball on the interval [1, 3/2]. The average velocity is defined as the change in position divided by the change in time, or:

average velocity = (s(3/2) - s(1)) / (3/2 - 1)

Substituting the formula for s(t), we get:

average velocity = ((-16(3/2)^2 + 50(3/2) + 1200) - (-16(1)^2 + 50(1) + 1200)) / (3/2 - 1)

Simplifying and solving for the average velocity, we get:

average velocity = (430 - 1234) / (1/2) = -808 ft/s

Therefore, the average velocity of the ball on the interval [1, 3/2] is -808 ft/s.

Answer: 46.39 grams of radium

Step-by-step explanation:

We can use the half-life formula to solve this problem:

A = A₀(1/2)^(t/t₁/₂)

where:

A₀ = initial amount (present)

A = final amount (in 710 years)

t = time elapsed (710 years)

t₁/₂ = half-life (1690 years)

First, we need to calculate the number of half-lives that will occur in 710 years:

n = t / t₁/₂

n = 710 / 1690

n ≈ 0.42

This means that in 710 years, the amount of radium will be reduced to half its current amount (1/2). And then reduced to half again (1/2 * 1/2) in another 1690 years.

Now we can calculate the final amount of radium after 710 years:

A = A₀(1/2)^n

A = 70(1/2)^0.42

A ≈ 46.39 grams

Therefore, after 710 years, approximately 46.39 grams of radium will be left.

SOLUTION

Total no of ties = 45

Number of ties that he feels goes well with jacket = 34

Number of ties that he feels does not go well with jacket = 45 - 34 = 11

a) Probability that tie goes well with jacket =

[tex]\dfrac{\text{Number of ties that goes well with jacket}}{\text{Total number of ties}}[/tex]

                                [tex]=\dfrac{34}{45}[/tex]

b) Probability that a tie does not go well with jacket

[tex]\dfrac{\text{Number of ties that doe not goes well with jacket}}{\text{Total ties}}[/tex]

                                [tex]=\dfrac{11}{45}[/tex]

By derivative rules we find the following conclusions from functions:

In this question we find two cases where the second derivative of a function must be found, this can be done by applying derivative rules twice. The first case consists in determining the second derivative of the following function:

y = 3 / x - 7 · ㏑ x

First derivative

y' = - 3 / x² - 7 / x

Second derivative

y'' = 6 / x³ + 7 / x²

The second case requires the determination and evaluation of the second derivative of the following function:

s = 2 / t - 2 / t², t = 2

First derivative

s' = - 2 / t² + 4 / t³

Second derivative

s'' = 4 / t³ - 12 / t⁴

Evaluation

s'' = 4 / 2³ - 12 / 2⁴

s'' = 1 / 2 - 3 / 4

s'' = - 1 / 4 ft / sec²

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Answer:

X= 135°

Step-by-step explanation:

Let y be equal to x

45° + y = 180°

Y = 180 - 45

Y = 135°

Therefore y = X

When $720 is shared among A, B, and C in the ratio of 1:2:3, each individual will get:

The sharing ratio describes the ratio, proportion, or relative size of profit or an amount that a sharing partner receives.

Ratios are expressed in percentages, decimals, fractions, or in standard ratio form (:).

Sharing ratios are based on some agreed factors or criteria.

The total sum to be shared = $720

The sharing ratio = 1:2:3

The sum of ratios = 6

A's share of $720 = $120 ($720 x 1/6)

B's share of $720 = $240 ($720 x 2/6)

C's share of $720 = $360 ($720 x 3/6)

Thus, based on their sharing ratios, A will receive $120, B $240,and C $360 from the total of $720.

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Share $720 among A, B, and C in the ratio of 1:2:3.

Therefore , the solution of the given problem of function comes out to be  (g - f)(-1) = 29.

The math lesson covers an extensive variety of subjects, including geometry, integers, one's divisions, construction, and both real and imagined geographic places. A work covers the connections between various variable that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinct results for each input.

Here,

We must first evaluate g(-1) and f(-1) before subtracting the results to obtain (g - f)(-1).

We possess

=> g(x) = 5x + 18

=>  g(-1) = 5(-1) + 18 = 13

=>  f(x) = x² - 17

=>  f(-1) = (-1)² - 17 = -16

Therefore:

=>  (g - f)(-1) = g(-1) - f(-1) = 13 - (-16) = 29

So, (g - f)(-1) = 29.

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The length would initially decrease to AB - BC before increasing to a maximum of AB + BC.

We can see from the diagram that two triangles are generated when AB = 3 cm and BC = 1.5 cm.

This would occur if, at point AC, C were to be rotating counterclockwise around A.

As AC moves closer to A, AC will initially decline to AB - BC. It would then grow. The length would be AB + BC at its greatest.

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Answer:

Solve:

y = 2x+5

x+y=8

x-x+y=8-x

y = -x + 8

Now:

y = 2x+5

y = -x+8

SUBSTITUTE

-x+8=2x+5 add x on both sides 8 -5 =3x+5 -5

3 = 3x
x= 1
Now for y :

Substitute:

y=2(1)+5

y=7

SOLUTION: )1,7)

The length and width οf the rectangle are 11 inches and 4 inches, respectively.

Area οf rectangle can be defined as prοduct οf length , breadth οf a rectangle.

Let's denοte the width οf the rectangle as w. Then accοrding tο the prοblem, the length οf the rectangle is 7 inches mοre than the width, sο we can express the length as w + 7.

The area οf the rectangle is given by:

[tex]A = length * width = (w + 7) * w = w^2 + 7w[/tex]

The perimeter οf the rectangle is given by:

[tex]P = 2 * (length + width) = 2 * (w + 7 + w) = 4w + 14[/tex]

According tο the problem, the area of the rectangle is equal to 2 inches mοre than 2 times the perimeter, so we can set up the following equation:

[tex]w^2 + 7w = 2(4w + 14) + 2[/tex]

Simplifying this equatiοn, we get:

[tex]w^2 + 7w = 8w + 28[/tex]

Subtracting 8w + 28 frοm both sides, we get:

[tex]w^2 - w - 28 = 0[/tex]

We can factοr this quadratic equation as:

[tex](w - 4)(w + 7) = 0[/tex]

Therefοre, we have twο sοlutiοns fοr w: w = 4 and w = -7. Hοwever, since the width οf the rectangle cannοt be negative, we reject the sοlutiοn w = -7 and chοοse w = 4 as the width οf the rectangle.

Then, the length οf the rectangle is w + 7 = 4 + 7 = 11 inches.

Therefοre, the length and width οf the rectangle are 11 inches and 4 inches, respectively.

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Therefore , the solution of the given problem of equation comes out to be  the coefficients of the variables x and y and putting them in a matrix.

To guarantee consistency here between two opposing claims, variable terms are frequently used in complicated algorithms. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this instance, the normalise process gives as rather than just an variable that separates 12 in and out of two parts for use with a data from y + 6.

Here,

In order to visualise the formulae

=> 6x + 11y = -4

=> 5x - 9y = 1

We can set up a vector of constants on the right side and use the values of the variables x and y as entries in a matrix to represent the data in matrix form.

The system's matrix shape is:

| 6  11 |   | x |   | -4 |

| 5  -9 | * | y | = |  1 |

Consequently, the following is the system's matrix representation:

| 6  11 |

| 5  -9 |

Notably, we acquire the system's coefficient matrix by taking the coefficients of the variables x and y and putting them in a matrix.

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The solution of the given problem of arithmetic mean comes out to be  given series is therefore a geometric sequence.

A list's values are added up to get the average values, also known as the company's means, which is then multiplied by the maximum population of list elements. Similar development patterns can be seen in math. The median of the actual numbers 5, 8, and 9 is 3, while for mean of the real figures 5, 7, as well as 9 is 4, and the number 21 increased by three (there are currently several three numbers) = seven. This is demonstrated by the following equation.

Here,

It is a geometric sequence that is provided.

A mathematical sequence known as a geometric sequence is one in which each term following the first is obtained by multiplying the preceding term by a fixed ratio known as the common ratio. A geometric sequence's overall formula is

=>  a = a1 + [tex]r^{(n-1)[/tex] (n-1)

where r is the common ratio, n is the amount of terms, and an is the nth term. A1 is the first term.

The first word in the listed order is:

=> a1 = 1/2(4)⁰ = 1/2

Any term can be divided by the preceding term to find the common ratio:

=>  a2/a1 = (1/2(4)¹)/(1/2(4)⁰) = 4/2 = 2

=>  a3/a2 = (1/2(4)²)/(1/2(4)¹) = 4/2 = 2

so forth.

This series is a geometric sequence because the common ratio is constant.

The given series is therefore a geometric sequence.

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Complete question:

Identify the following as arithmetic or geometric,

aⁿ = ½(4)n-1