can someone help me with 26 and 27?

Answer:

the right answer is the third one

Answer:

its the second one

Step-by-step explanation:

took the test

Answer:

I believe so!

Step-by-step explanation: makes since to me!!

The first four terms of the geometric sequence ((\(9^n\)) + 2) / 3 with a common ratio of 3 are 1, 11/3, 83/3, and 731/3.

To find the first four terms of the geometric sequence given by the formula ((\(9^n\)) + 2) / 3, where the common ratio is 3, we can substitute different values of n into the formula. Let's calculate each term step by step:

Step 1: Finding a₁ (the first term)

To find the first term (a₁), we substitute n = 0 into the formula:

a₁ = ((\(9^0\)) + 2) / 3

= (1 + 2) / 3

= 3 / 3

= 1

So, a₁ = 1.

Step 2: Finding a₂ (the second term)

To find the second term (a₂), we substitute n = 1 into the formula:

a₂ = ((\(9^1\)) + 2) / 3

= (9 + 2) / 3

= 11 / 3

So, a₂ = 11/3.

Step 3: Finding a₃ (the third term)

To find the third term (a₃), we substitute n = 2 into the formula:

a₃ = ((9²) + 2) / 3

= (81 + 2) / 3

= 83 / 3

So, a₃ = 83/3.

Step 4: Finding a₄ (the fourth term)

To find the fourth term (a₄), we substitute n = 3 into the formula:

a₄ = ((9³) + 2) / 3

= (729 + 2) / 3

= 731 / 3

So, a₄ = 731/3.

Therefore, the first four terms of the geometric sequence ((\(9^n\)) + 2) / 3 with a common ratio of 3 are as follows:

a₁ = 1,

a₂ = 11/3,

a₃ = 83/3,

a₄ = 731/3.

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The question is -

Find the common ratio and write out the first four terms of the geometric sequence {((9^n)+2)/(3)} . The common ratio is 3 .................... a1=? a2= ? a3=? a4=?

Refractive index of the given unknown liquid = 0.500.

What is angle?

Angle is a geometric figure formed by two rays, called the sides of the angle, that have a common endpoint, called the vertex. An angle is measured in degrees, with a full circle representing 360°.

The refractive index of a material is a measure of how much light is bent when it enters the material from a medium with a different refractive index. When light enters a material with a higher refractive index, it bends towards the normal. The angle of refraction can be used to calculate the refractive index of a material. In this case, the unknown liquid’s refractive index is determined by measuring the angle of refraction.

The angle of refraction of the unknown liquid was 30 degrees, which was used to calculate the refractive index. Using the equation n1 = 1.0003 x sin (angle 2), the refractive index of the liquid was determined to be 0.50015, which was rounded to 3 decimal places to give a result of 0.500.

The refractive index of a material is an important measure of how light behaves when it interacts with a material. Knowing the refractive index of a material is important for applications such as computing the path of light through optical lenses or calculating the velocity of light in various materials, as well as for analyzing the behavior of materials such as metals, plastics and liquids.

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By evaluating both side of divergence theorem for cube define by -0.1< x,y,z < 0.1 if D = 6x\(e^{2y}(\bar a_x+x\bar a_y)\) will get \(\int\limits^._ v\triangle .D dv=0.0481\).

Given that,

We have to evaluate both side of divergence theorem for cube define by -0.1< x,y,z < 0.1 if D = 6x\(e^{2y}(\bar a_x+x\bar a_y)\)

We know that,

Before solving divergence theorem,

First we need to calculate Δ.D

Where,

Δ.D = del operator

Δ = \((\bar a_x \frac{d}{dx}+ \bar a_y \frac{d}{dy}+ \bar a_z \frac{d}{dz})\)

Then, Δ.D = \((\bar a_x \frac{d}{dx}+ \bar a_y \frac{d}{dy}+ \bar a_z \frac{d}{dz})\)6x\(e^{2y}(\bar a_x+x\bar a_y)\)

We know that dot product of two vector field is valid for same unit vector multiplication.

Δ.D = \(\frac{d}{dx}6xe^{2y}(\bar a_x. \bar a_x)+\frac{d}{dy}6x^2e^{2y}(\bar a_y. \bar a_y)+\frac{d}{dz}(0)\)

Δ.D = 6\(e^{2y}+12x^2e^{2y}\)

Now, using divergence theorem,

\(\int\limits^._ v\triangle .D dv=\int\limits^{0.1}_{x=-0.1}\int\limits^{0.1}_{y=-0.1}\int\limits^{0.1}_{z=-0.1}{\triangle.D} \, dx dydz\)

\(\int\limits^._ v\triangle .D dv=\int\limits^{0.1}_{x=-0.1}\int\limits^{0.1}_{y=-0.1}\int\limits^{0.1}_{z=-0.1}{(6e^{2y}+12x^2e^{2y})} \, dx dydz\)

\(\int\limits^._ v\triangle .D dv=\int\limits^{0.1}_{x=-0.1}\int\limits^{0.1}_{y=-0.1}{(6e^{2y}+12x^2e^{2y})} [z]^{0.1}_{z=-0.1}\, dx dy\)

\(\int\limits^._ v\triangle .D dv=(0.2)\int\limits^{0.1}_{x=-0.1}\int\limits^{0.1}_{y=-0.1}{(6e^{2y}+12x^2e^{2y})}\, dx dy\)

\(\int\limits^._ v\triangle .D dv=(0.2)\int\limits^{0.1}_{x=-0.1}{(\frac{6e^{2y}}{2}+\frac{12x^2e^{2y}}{2})^{0.1}_{y=-0.1}}\, dx\)

\(\int\limits^._ v\triangle .D dv=(0.2)\int\limits^{0.1}_{x=-0.1}{[3e^{2(0.1)}+6x^2e^{2(0.1)}-3e^{2(0.1)}-6x^2e^{2(0.1)}]\, dx\)

\(\int\limits^._ v\triangle .D dv=(0.2)\int\limits^{0.1}_{x=-0.1}{[3+6x^2]e^{(0.2)}- [3+6x^2]e^{(-0.2)}\, dx\)

\(\int\limits^._ v\triangle .D dv=(0.2){[(3x+\frac{6x^3}{3})e^{(0.2)}- (3x+\frac{6x^3}{3})e^{(-0.2)}]^{0.1}_{x=-0.1}\, dx\)

\(\int\limits^._ v\triangle .D dv=(0.2){[(3(0.1)+\frac{6(0.1)^3}{3})e^{(0.2)}]- [(3(0.1)\frac{6(0.1)^3}{3})e^{(-0.2)}]\) \(-[(3(-0.1)+\frac{6(-0.1)^3}{3})e^{(0.2)}]+ [(3(-0.1)\frac{6(-0.1)^3}{3})e^{(-0.2)}]\)

\(\int\limits^._ v\triangle .D dv=(0.2){[(0.3+0.002)\times 2\times e^{0.2}-(0.3+0.002)\times 2\times e^{-0.2}]\)

\(\int\limits^._ v\triangle .D dv=(0.2)[0.735-0.4945]\)

\(\int\limits^._ v\triangle .D dv=(0.2)(0.2405)\)

\(\int\limits^._ v\triangle .D dv=0.0481\)

Therefore, By evaluating both side of divergence theorem for cube define by -0.1< x,y,z < 0.1 if D = 6x\(e^{2y}(\bar a_x+x\bar a_y)\) will get \(\int\limits^._ v\triangle .D dv=0.0481\).

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The question is incomplete the complete question is -

Evaluate both side of divergence theorem for cube define by -0.1< x,y,z < 0.1 if D = 6x\(e^{2y}(\bar a_x+x\bar a_y)\)

The maximum rate of return that can be earned for a given rate of interest occurs when interest is compounded continuously.

In theory, continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.

Continuous compounding calculates interest under the assumption that interest will be compounding over an infinite number of periods.

The formula in order to calculate continuous compounding is given by:

\(A=pe^{rt\)

Thus, the maximum rate of return that can be earned for a given rate of interest occurs when interest is compounded continuously.

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Answer:

a four-sided plane rectilinear figure with opposite sides parallel.

Step-by-step explanation:

The value of the Riemann sum for the function f(x) = x² - 1 using the partition P = {1, 2, 5, 7} is V = 105.

To find the value of the Riemann sum, we need to evaluate the function f(x) = x² - 1 at specific points cₖ within each subinterval defined by the partition P = {1, 2, 5, 7} and multiply it by the corresponding width of each subinterval, Δxₖ.

The subintervals in this partition are:

[1, 2]

[2, 5]

[5, 7]

Let's calculate the Riemann sum by evaluating f(x) at the midpoints of each subinterval and multiplying by the width of each subinterval:

For the first subinterval [1, 2]:

\(Midpoint: c_1 = \frac{1+2}{2} = 1.5 \\ Width: \Delta x_1 = 2 - 1 = 1 \\ Evaluate f(x) \: at \: c_1 : f(c_1) = f(1.5) = (1.5)^2 - 1 = 2.25 - 1 = 1.25\)

Contribution to the Riemann sum:

\(f(c_1) \cdot \Delta x_1 = 1.25 \cdot 1 = 1.25\)

For the second subinterval [2, 5]:

\(Midpoint: c_2 = \frac{2+5}{2} = 3.5 \\ Width: \Delta x_2 = 5 - 2 = 3 \\ Evaluate f(x) \: at \: c_2 : f(c_2) = f(3.5) = (3.5)^2 - 1 = 12.25 - 1 = 11.25\)

Contribution to the Riemann sum:

\( f(c_2) \cdot \Delta x_2 = 11.25 \cdot 3 = 33.75

\)

For the third subinterval [5, 7]:

\(Midpoint: c_3 = \frac{5+7}{2} = 6 \\ Width: \Delta x_3 = 7 - 5 = 2 \\ Evaluate f(x) \: at \: c_3 : f(c_3) = f(6) = (6)^2 - 1 = 36 - 1 = 35 \)

Contribution to the Riemann sum:

\( f(c_3) \cdot \Delta x_3 = 35 \cdot 2 = 70\)

Finally, add up the contributions from each subinterval to find the value of the Riemann sum:

V = 1.25 + 33.75 + 70 = 105

Therefore, the value of the Riemann sum for the function f(x) = x² - 1 using the partition P = {1, 2, 5, 7} is V = 105.

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Answer:

x = 18√3

Step-by-step explanation:

From the picture attached,

In a right triangle,

Measure of one angle = 30°

Measure of adjacent side of the angle = 9 units

We have to find the measure of Hypotenuse from the given properties.

By cosine rule,

cos(30°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

\(\frac{\sqrt{3}}{2} =\frac{9}{x}\)

\(x=18\sqrt{3}\)

Therefore, measure of Hypotenuse is 18√3 units.

Answer:

Answer is below

Step-by-step explanation:

Answer:

3

Step by Step:

Subtract the tip ($6) from the total ($39)

11x=33

Then divide 33 by 11, leaving you with the value of x.

x=3

The lesson was 3 hours long.

Answer:

He would receive 25 dollars. Because 500 divided by 4 equals 125 multiply that by 3 get 375 he paid 400 which means he would get back 25 dollars.

Step-by-step explanation:

Answer:

 \(0.2 + 0.9x\)

Step-by-step explanation:

Using BODMAS:

1) \(0.2(x + 1) + 0.7x\)  

2) \(0.2x + 0.2 +0.7x\)

3) \(0.2 + 0.7x +0.2x\)

4) \(0.2 + 0.9x\)

Answer:

length = 20 inches

width = 10 inches

Step-by-step explanation:

Perimeter = twice the length plus twice the width

60 = 2(2x) + 2(x)

60 = 4x + 2x

60 = 6x

x = 10

2x = 20

Answer:

length = 20 inches

width = 10 inches

Step-by-step explanation:

Perimeter = twice the length plus twice the width

60 = 2(2x) + 2(x)

60 = 4x + 2x

60 = 6x

x = 10

2x = 20

Answer:

m < 1200

Step-by-step explanation:

0.10m + 130 < 250

-130                -130

0.10m < 120

/0.10      /0.10

m < 1200

Answer:

The range is {18, 22, 26}

Step-by-step explanation:

The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer:

Options B, D, E

Step-by-step explanation:

If triangle ABC and triangle PQR are congruent,

∠A ≅ ∠P

∠B ≅ ∠Q

∠C ≅ ∠R

AB ≅ PQ

BC ≅ QR

AC ≅ PR

Therefore, Options B, D, E are the correct options.

Answer:

x = amount of paper

10x + 100 = 450

10x = 350

x = 35

Brainiest plz :)

Recall that to determine if a table represents a probability distribution, the sum of the probabilities must add up to 1, and all the probabilities have to be positive numbers less or equal to 1.

Now, notice that:

From the table, we notice that all the given probabilities are positive numbers between 0 and 1. Therefore, we can conclude that the given table represents a probability distribution.

Yes, it is a probability distribution.

Answer:6.16

Step-by-step explanation:

A parametric description of the solution set of a linear system is the same as solving the system is the false statement.

If a linear system has at least one solution, only then can the solution set be stated using a parametric description. The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set. You'll discover what a solution set is in this tutorial and witness an example. By combining two equations with two variables into one equation with one variable, we can solve a system of equations. Since there are two variables in each equation in the system, replacing a variable with an expression can help minimize the number of variables in an equation.

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The speed of the plane in still air is 87 kilometers, and the speed of the wind is 87 kilometers.

A plane traveled 1160 kilometers to Havana and back.

The trip there was with the wind. It took 10 hours.

The trip back was into the wind. The trip back took 20 hours.

What is speed, distance, and time?

The formula speed distance time is used to explain the relationship between speed, distance, and time. That is speed = time/distance. To put it another way, distance divided by speed equals time. You can figure out the third input if you know the first two.

Consider,

s = plane speed in still air

w = speed of the wind

then

(s+w) = ground speed with the wind

and

(s-w) = ground speed against the wind:

A dist equation for each way (dist = speed * time)

10(s+w) = 1160

20(s-w) = 1160

Simplify divide the 1st equation by 13, and the 2nd equation by 26, and you have:

s + w = 116

s - w = 58

Using adding s & eliminates w,

2s = 174

s = 174/2

s = 87 km plane speed in still air

The wind speed

87 + w = 96

w = 9 km is the wind speed

Hence, the speed of the plane in still air is 87 kilometers, and the speed of the wind is 87 kilometers.

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Answer:

f(x)=(x-1)^2+3

Step-by-step explanation:

Both equations vertexes equal (1, 3) while the rest do not match.

f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.

We can use the technique of completing the square to rewrite the given function f(x) in vertex form.

f(x) = 4 + x² - 2x

f(x) = (x² - 2x) + 4

Adding and subtracting (1) inside the parentheses

f(x) = (x² - 2x + 1) + 4 - 1

f(x) = (x - 1)² + 3

So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.

Therefore, the correct option is f(x) = (x - 1)² + 3.

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By using empirical rule, approximately 34% of the students have grade point averages that are greater than 2.11.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

We want to find the percentage of students with a GPA greater than 2.11. To do so, we need to calculate the number of standard deviations that separate 2.11 from the mean of 2.56:z = (2.11 - 2.56) / 0.45 = -1

Here, z represents the number of standard deviations away from the mean. A negative z-value indicates that the value of interest is below the mean.

Now that we have calculated the z-value, we can use the empirical rule to determine the percentage of students with a GPA greater than 2.11. Since the value of interest is below the mean, we need to calculate the percentage of students who fall within one standard deviation below the mean:

68% - 34% = 34%

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To calculate the present value of Ahmed's payments, we can use the formula for the present value of an annuity:

PV = PMT  [(1 - \((1 + r)^{(-n)\)) / r]

Where:

PV = Present Value

PMT = Payment amount per period (BD 5700)

r = Interest rate per period (8% or 0.08)

n = Number of periods (12 years)

Substituting the values into the formula, we get:

PV = 5700 * [(1 - \((1 + 0.08)^{(-12)}\))) / 0.08]

Calculating the expression within the brackets first:

(1 - \((1 + 0.08)^{(-12)\)) / 0.08 = 0.652592574

Now, multiply this value by the payment amount:

PV = 5700 * 0.652592574

PV ≈ BD 3708.349811

Rounding to two decimal places, the present value of Ahmed's payments is approximately BD 3708.35. Therefore, none of the given options (OBD 46392.10, OBD 42955.64, OBD 116823.19, BD 108169.62) are correct.

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Answer:

The dimensions of the field is 185 yards by 48 yards

Step-by-step explanation:

Here, we are interested in calculating the dimensions of the field.

Let the width of the field be x yards

From the question, we are made to know that the length of the field is 7 yards less than quadruple ( 4 times) the width

So mathematically, the length of the field will be ;

(4x -7) yards

The perimeter of the field mathematically is:

2(l + b)

Thus;

2(x + 4x- 7) = 466

2(5x -7) = 466

divide both side by 2

5x - 7 = 466/2

5x - 7 = 233

5x = 233 + 7

5x = 240

x = 240/5

x = 48 yards

Length of field is; 4x -7 = 4(48) -7 = 192 - 7 = 185 yards