The first three terms of a geometric sequence are as follows.
810, 270, 90
Find the next two terms of this sequence.

a. The temperature is about 3.35 degrees Celsius at 340 m/s, the speed of sound.

b. The temperature is about 2.35 degrees Celsius at 320 m/s, or the speed of sound.

Speed is a scalar physical quantity that quantifies the rate of motion of an object. It is described as the distance that an object covers in a specific period of time. Meters per second (m/s) is the SI unit for measuring speed.

The speed formula is as follows:

Speed = distance / time

Depending on the purpose, speed can also be stated in different units, such as kilometres per hour (km/h), miles per hour (mph), or feet per second (ft/s).

The concept of speed, which is used to describe how objects move, is important to physics. It plays a significant role in a variety of fields of science, engineering, and technology, including sports, aircraft, and transportation. For the purpose of analysing and forecasting the behaviour of physical systems, it is essential to comprehend the idea of speed.

a. We can change v = 340 into the equation and solve for t to determine the temperature when the speed of sound is 340 m/s:

v = 20Vt + 273

340 = 20Vt + 273

67 = 20Vt

t = 67/20

Therefore, the temperature is about 3.35 degrees Celsius when the sound travels at 340 m/s.

b. We may once more enter v = 320 into the equation and solve for t to determine the temperature when the speed of sound is 320 m/s:

v = 20Vt + 273

320 = 20Vt + 273

47 = 20Vt

t = 47/20

As a result, the temperature is roughly 2.35 degrees Celsius at 320 m/s, the speed of sound.

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The equaltion for the line of best fit would be,

y = 0.67x + 4.05

The points on the scatter plot are: (1, 3.8), (2, 5.8), (3, 6.2) , (4, 7.5) , (5, 7.2), (6, 8.3), (7, 9.3), and (8, 8.5 )

First we find the mean of the x-values and mean of the y-values.

The mean of the x-values would be,

[tex]\bar{X}[/tex] = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8

[tex]\bar{X}[/tex] = 4.5

and the mean of the y-values would be,

[tex]\bar{Y}[/tex] = (3.8 + 5.8 + 6.2 + 7.5 + 7.2 + 8.3 + 9.3 + 8.5) / 8

[tex]\bar{Y}[/tex] = 7.075

The sum of squares (SSX) = 42

And the sum of products (SP) = 28.2

Regression Equation would be,

y = mx + c

m = SP/SSX

   = 28.2/42

   = 0.67143

And the y-intercept would be,

c =  4.05357

So, the equation for the line of best fit would be,

y = 0.67143x + 4.05357

Number of Households = 0.67143 (time) + 4.05357

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Find the complete question below.

The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.

Scatter plot with x axis labeled Time in Years and y axis labeled Number of Households with points at 1 comma 3 and 8 tenths, 2 comma 5 and 8 tenths, 3 comma 6 and 2 tenths, 4 comma 7 and 5 tenths, 5 comma 7 and 2 tenths, 6 comma 8 and 3 tenths, 7 comma 9 and 3 tenths, and 8 comma 8 and 5 tenths.

Answer:

Step-by-step explanation:

This is a word problem involving percentages. To solve it, we need to follow these steps:

Identify the given information and the unknown quantity. In this problem, we are given that Natalie has $330 to spend at the amusement park, 5% is spent on games, 5/11 is for food and drinks, and she spends $13 on parking. The unknown quantity is the price of one ticket.

Write an equation that relates the given information and the unknown quantity. We can use the fact that the sum of all parts of the whole is 100%1. Let x be the price of one ticket. Then we have:

games+food and drinks+parking+tickets0.05×330+115​×330+13+2x​=total amount=330​

Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:

16.5+150+13+2x2x2xxx​=330=330−16.5−150−13=150.5=2150.5​=75.25​

Therefore, the price of one ticket is $75.25.

Sum

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case (3.2+3.5)/2.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

Answer:

Step-by-step explanation:

Mean is the average of the data vales : 38.7 (sum of all values) divided by 10 (the number of values).  Mean = 38.7/10 = 3.87

Median is the "middle" number" = put the date in order and find the middle value:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4, since there is no middle data value, find the average of the 2 in the middle.

3.2 + 3.5/2 = 6.7 ÷ 2 = 3.35 - median

All values appear once so there is no mode.

First quartile is the middle of the lower set of data = 2.8

Third quartile is the middle of the upper set = 3.8

The outlier is 9.4.

How to calculate the outlier:

First you need the IQR which is the diffence of Q3 - Q1,

so the IQR is 3.8- 2.8 = 1

Outliers are the quartile + or - (1.5)(IQR)

Q1 -(1.5)(1) = 2.8 - 1.5 = 1.3

Q3 - (1.5)(1)= 3.8 + 1.5 =4.5

So anything below 1.3 or above 4.5 is an outlier.

There is one 9.4

a) The transition matrix is  [tex]\left[\begin{array}{ccc} 0.3&0.7 \\ 0.6&0.4\end{array}\right][/tex]

b) After two years, brand A is expected to have 40.4% of the market share.

c) Brand A is expected to have 37.5% of the market share.

a) The transition matrix can be constructed using the probabilities provided in the problem. Let P be the matrix where the (i, j)-th entry represents the probability of transitioning from state i to state j. In this case, there are two states: using brand A (state 1) and not using brand A (state 2).

Using the information given in the problem, we can fill in the entries of the matrix as follows:

P = [tex]\left[\begin{array}{ccc} 0.3&0.7 \\ 0.6&0.4\end{array}\right][/tex]

b) To find the percentage of the market share that brand A gets after two years, we need to multiply the initial market share vector (40% for brand A and 60% for other brands) by the transition matrix twice:

| 0.4 0.6 | × P × P = | 0.404 0.596 |

Therefore, after two years, brand A is expected to have 40.4% of the market share.

c) To find the long-run market share for brand A, we need to find the steady-state vector of the transition matrix P. This is the vector π such that:

πP = π

and

π ₁+ π₂ = 1

where π₁ is the long-run probability of being in state 1 (using brand A) and π₂ is the long-run probability of being in state 2 (not using brand A).

Solving the equations above, we get:

π = | 0.375 0.625 |

This means that in the long run, brand A is expected to have 37.5% of the market share.

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Answer:

Experiencing anxiety on the day of the examination is a common problem for many students, especially those in grade 12 who may feel a lot of pressure to perform well. However, there are several strategies that they can use to minimize the impact of anxiety and enhance their performance in the examination. Some of these strategies include:

1. Get enough sleep: Getting enough sleep is essential for students to perform well on the day of the examination. Students should aim to get at least 7-8 hours of sleep before the exam day. A well-rested brain will be able to function better, and students will be less likely to feel anxious or stressed.

2. Eat a balanced breakfast: Eating a balanced breakfast on the day of the examination can help students feel more alert and focused. A healthy breakfast can also provide the necessary energy needed to get through the examination.

3. Plan your day: Plan your day well ahead of the examination. This will help you feel more in control and reduce feelings of anxiety. Set aside time to review notes, relax and mentally prepare for the exam.

4. Practice relaxation techniques: Practice relaxation techniques such as deep breathing or progressive muscle relaxation to help calm your nerves. These techniques can help students reduce stress levels and anxiety, which in turn can enhance their performance.

5. Avoid last-minute cramming: Cramming at the last minute can increase feelings of anxiety and negatively impact performance. Instead, spend time reviewing notes and practicing past papers in the days leading up to the examination.

6. Stay positive: It is essential to stay positive and avoid negative thoughts or self-doubt. Remind yourself of your hard work and preparation for the exam. Believe in your abilities, and focus on what you can do rather than what you cannot.

By implementing these strategies, grade 12 students can minimize the impact of anxiety on the day of the examination, and enhance their overall performance. Remember that exam performance is not just about what you know, but also about how you manage your anxiety and stress levels.

The time taken for the second car to travel the same distance as the first car is 6 hours.

The time taken for the second car to travel the same distance as the first car is calculated as follows;

let the time taken for the second car to travel the same distance = t

distance traveled by second car = 60t

the time taken for the first car = t + 2

distance traveled by the first car = 45(t + 2)

Since both distance are equal, we will have the following equations;

60t = 45 (t + 2)

60t = 45t + 90

15t = 90

t = 90/15

t = 6

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Step-by-step explanation:

Please it would be very helpful and useful if you try to use a calculator. Good luck.

The probability that a red shirt and black slacks are on the floor is 1/10.

Probability is the odds that a random event would happen. The odds that the event would happen has a probability value that lies between 0 and 1.

Probability that a red shirt and black slacks are on the floor = (number of red shirts / total number of shirts) x (number of black slacks / total number of slacks)

Total number of shirts = 2 + 2 + 1 = 5

Total number of slacks = 1 + 1 = 2

(1/5) x (1/2) = 1 /1 0

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The quadratic equation is solved and discriminant is 5, so it has two real solutions

Given data ,

The given equation is a quadratic equation in the standard form ax² + bx + c = 0, where a = 1, b = -1, and c = -1

The discriminant of a quadratic equation is given by b² - 4ac. So, the discriminant of the given equation is

(-1)² - 4(1)(-1) = 1 + 4 = 5

Since the discriminant is positive (not zero or negative), the equation has two real solutions.

Hence , its discriminant is 5, so it has two real solutions

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Answer:

$10,359.73.

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the amount of money after the specified time

P = the principal amount (the initial amount of money)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $4,000.00

r = 15% = 0.15

n = 1 (compounded annually)

t = 6 years

Substituting into the formula, we get:

A = 4000(1 + 0.15/1)^(1*6)

A = 4000(1.15)^6

A ≈ $10,359.73

Therefore, the amount in the account after 6 years, rounded to the nearest cent, is $10,359.73.

The logarithm expression In(9/x) can be expanded as In(9) - In(x)

From the question, we have the following parameters that can be used in our computation:

In(9/x)

Using the logarithmic identity log a/b = log a - log b, we can expand ln(9/x) as follows:

ln(9/x) = ln(9) - ln(x)

Therefore, ln(9/x) can be expressed as the difference of two natural logarithms: ln(9) and ln(x).

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The graphed line of the equation is attached 2x + 3y = -6

A linear equation is an expression that consists of a single power of the variable(s) in which it contains. This formulation can be impeccably illustrated in the following way:

ax + b = 0

The given equation 2x + 3y = -6 can be rearranged to get

y = -2/3x - 2

The x variables is plugged in to solve for y and used for the table of values for the graph

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Therefore, the width of the bridge is approximately 5.9 feet. Therefore, the height of the bridge is approximately 8.4 feet. Therefore, the length of CH is approximately 36.9 feet. Therefore, the measure of angle BHC is approximately 189 degrees. Therefore, the answer to part (e) is no.

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry, and is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and there are several types of triangles including equilateral, isosceles, and scalene.

Here,

To solve this problem, we will use the fact that AAGC is congruent to AEGC. This means that angle ACG is equal to angle AEC, and angle AGC is equal to angle AEG.

(a) To determine the width AE of the bridge, we can use the tangent function. We have:

tan(27°) = AE/12

Solving for AE, we get:

AE = 12 tan(27°) ≈ 5.9 ft

(b) To determine the height CG of the bridge, we can use the same approach. We have:

tan(36°) = CG/12

Solving for CG, we get:

CG = 12 tan(36°) ≈ 8.4 ft

(c) To determine the length of CH, we can use the Pythagorean theorem. We have:

CH² = CG² + GH²

Substituting the values we found earlier, we get:

CH² = (8.4 ft)² + (40 ft - 5.9 ft)²

CH² = 70.56 ft² + 1288.41 ft²

CH² = 1358.97 ft²

Taking the square root, we get:

CH ≈ 36.9 ft

(d) To determine the measure of angle BHC, we can use the fact that angles AGC and AEG are congruent. We have:

angle BHC = 180° - angle AHC - angle CHB

angle AHC = angle ACG - angle HCG = 27° - 36° = -9° (note that this is a negative angle because it is measured clockwise)

angle CHB = angle CGB - angle HCG = 36° - 36° = 0°

Substituting these values, we get:

angle BHC = 180° - (-9°) - 0°

angle BHC = 189°

(e) To determine whether CH bisects angle ZACG, we need to show that angle CAH is congruent to angle CAG. We have:

angle CAH = 180° - angle HCG - angle ACG

= 180° - 36° - 27°

= 117°

angle CAG = 180° - angle ACG - angle AGC

= 180° - 27° - 27°

= 126°

Since angle CAH is not congruent to angle CAG, we can conclude that CH does not bisect angle ZACG.

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The equation 5ʷ ⁺ ³ = 17 when solved for w is approximately w = 0.41 and the solution to the inequality is b ≤ 1.87

From the question, we have the following parameters that can be used in our computation:

5ʷ ⁺ ³ = 17

Take the logarithm of both sides

So, we have

w + 3 = ln(17)/ln(3)

Evaluate the quotient

This gives

w + 3 = 2.59

So, we have

-3 + w + 3 = 2.59 - 3

Evaluate

w = 0.41

For the second expression, we have

2ᵇ ⁺ ¹ ≤ 7.31

Take the logarithm of both sides

So, we have

b ≤ ln(7.31)/ln(2) - 1

So, we have

b ≤ 1.87

Hence, the equation when solved for w is approximately w = 0.41

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The cost of each admission tickets is 37.5 dollars.

Ms Boi spent a total of 175 dollars for 4 admission ticket and for parking at a baseball game. The cost of each admission ticket was the same amount, including tax. The cost of the parking was 25 dollars.

Therefore, the equation that can be use to determine the cost, i of each admission ticket can be represented as follows:

Therefore,

175 = 4i + 25

subtract 25 from both sides of the equation

175 = 4i + 25

175 - 25 = 4i + 25 - 25

150 = 4i

divide both sides by 4

i  = 150 / 4

i = 37.5 dollars

Therefore,

cost of each admission ticket = 37.5 dollars

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We can see that the percentage is 20%, then 20 percent of the students got a 10.

To find this, we need to use the formula:

Percentage = 100%(number of students with a 10)/(total number of students)

Here we know the that the revelant numbers are:

Number of students with a 10 = 12

total number of students in the class = 60

Replacing that in the formula we will get the percentage:

P  = 100%*(12/60)

P = 20%

So 20% of the total number of students got a 10.

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The value of the function f/g is (x - 1) / (x + 8)

Let's start by writing out the functions we are given:

f(x) = 4 / (x + 8)

g(x) = x / (x - 1)

To find f/g, we need to divide f(x) by g(x). We can do this by multiplying f(x) by the reciprocal of g(x), which is (x - 1) / x. Multiplying f(x) by this reciprocal gives us:

f(x) * (x - 1) / x = 4 / (x + 8) * (x - 1) / x

To simplify this expression, we can first find a common denominator for the two fractions on the right-hand side:

4 / (x + 8) * (x - 1) / x = 4(x - 1) / x(x + 8)

Now we can simplify this expression by canceling out any common factors in the numerator and denominator. In this case, we can cancel out a factor of 4 and a factor of (x - 1):

4(x - 1) / x(x + 8) = (x - 1) / (x + 8)

Therefore, the quotient of f(x) and g(x), or f/g, is:

f/g = (x - 1) / (x + 8)

We can interpret this expression as a new function, h(x), where h(x) = f(x) / g(x) = (x - 1) / (x + 8). This new function takes a value of x and returns the ratio of f(x) to g(x) at that value.

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The solution of the trigonometric problem is  y = -3

Starting with the equation

3/2 cos^-1(y/6) = pi

First, we can simplify by dividing both sides by 3/2 ....

cos^-1(y/6) = pi / (3/2)

cos^- 1(y/6) = 2pi / 3

Next, we can take the cosine of both sides to get...

cos (cos^-1(y/6 ) )

= cos( 2pi/3)

y/6 = -1/2

y = -3

Therefore, the exact solution to the equation 3/2 cos^-1(y/6) = pi is y = -3.

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Answer:

Step-by-step explanation:

Its simple, you need to find x

4 days the same amount of time (x) gives 48 min
4x = 48

x = 48/4

x = 12

then to get the amount of minutes in 9 days it would be:

9x=days

9(12)=108

the answer would be 108 min

Answer:

108 mins

Step-by-step explanation:

48 mins/4 days = x mins/9 days

4x= 432

x=108 mins

An expression for the exact area of each shaded region in the figure include the following:

Shaded area = area of the regular hexagon - area of the regular pentagon  + area of the square - area of the equilateral triangle.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using the following formula:

Area of a regular polygon = (n × s × a)/2

Where:

Based on the diagram (see attachment), the area of the first shaded region is given by;

Area of first shaded region = Area regular hexagon - Area regular pentagon

For the area of the second shaded region, we have;

Area of second shaded region = Area of a square - Area of the equilateral triangle

Therefore, the total area of all of the shaded regions is given by;

Total shaded area = {area of the regular hexagon - area of the regular pentagon} + area of the square - {area of the equilateral triangle}.

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Answer:

n(A U B) = n(A) + n(B) – n(A ∩ B)

putting values we get

50 = 2a + a - 20

solving eqn.

70 = 3a

a = 70 / 3

now n(a) = 2a

= 2 x 70/3

= 140/3

hence, n(a) = 140/3

The estimate of the cost for a 20-ft cord is given as follows:

$74.66.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points in the context of the problem are given as follows:

(3, 12.75), (5, 16), (6, 25.99), (50, 185).

Inserting these points into a calculator, the regression equation is given as follows:

y = 3.6794x + 1.06462.

Hence the estimate of the cost for a 20-ft cord is given as follows:

y = 3.6794(20) + 1.06462

y = $74.66.

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1) (f - g) (x) = f(x) - g(x) = x ≤ 1/4  

Domain of the function is : [1/4, infinity)

2) → [tex]\frac{f}{g}(x) =\frac{f(x)}{g(x)} = \frac{-x+4}{\sqrt{4x-1} }[/tex]        

Domain of the function : (1/4, infinity)

We have the function are as follows:

f(x) = -x + 4

g(x) = [tex]\sqrt{4x+1}[/tex]

To find the f - g and f/g and also their domains using interval  notation.

Now, (f - g) (x) = f(x) - g(x)

                       = [tex]-x+4-\sqrt{4x+1}[/tex]

                       = 4x + 1 ≤ 0

                       = x ≤ 1/4            

Domain of the function is : [1/4, infinity)

→ [tex]\frac{f}{g}(x) =\frac{f(x)}{g(x)} = \frac{-x+4}{\sqrt{4x-1} }[/tex]

=> 4x - 1 > 0

=> x > 1/4

Domain of the function : (1/4, infinity)

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Answer:132.7495cm^2

Step-by-step explanation:
The formula for the area of a circle is πr^2.
We then substitute into this formula using 3.142 as π.
This leaves us with 3.142x6.5(radius is half of diameter)^2
When you type it into your calculator it should give you
132.7495cm^2

The appropriate measure of variability for the data shown and its value is A. The range is the best measure of variability and equals 600.

The range is one of  the three measures of variability.

The range shows the difference between the highest value and the lowest value in a data set.

The other measures of variability are the IQR (Interquartile Range) and the the Standard Deviation.

Highest value = 800 m

Lowest value = 200 m

The range = 600 m (800 - 200)

IQR = 400 (600 - 200)

Mean = 567 (3,400 ÷ 6)

Median = 625 [(650 + 600) ÷ 2]

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The sum of any matrix with the identity matrix of the same size, with respect to addition, will give the matrix itself. Therefore, the sum of matrix A and B, where B is the identity matrix, will give the matrix A.

Applying the Intersecting Secants and Tangents Theorem, the measures are: CD = 19.5 units;     UZ = 12.8 units

a. Apply the intersecting secant-tangent theorem to create the equation below:

EG² = EC * ED

Plug in the values:

13² = 6.5 * (6.5 + CD)

169 = 42.25 + 6.5CD

169 - 42.25 = 6.5CD

126.75/6.5 = CD

CD = 19.5 units

b. Apply the intersecting secants theorem to create the equation below:

UX * UY = UZ * UW

Plug in the values:

8 * 64 = UZ * 40

512/40 = UZ

UZ = 12.8

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The value of the expression 5w–4w–w+6w is 6w

When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

For example, 2( 3a+5) can be simplified by using 2 to multiply both 3a and 5. This will give 6a+10. This means that the simplification of 2(3a+5) = 6a+10.

Similar , 5w-4w-w+6w can be simplified into:

5w+6w-4w-w

= 11w-5w

= 6w.

Therefore,the value of the expression 5w–4w–w+6w is 6w

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