Find the 9th term of the geometric sequence9,−18,36,

Answer:

To find the value of k and the equation of the line, we can use the slope-intercept form of a line: y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope of the line (m) is given as -⅔. To find the y-intercept (b), we can substitute one of the given points and the value of m into the equation.

Let's use the point (3,k) :

y = mx + b

k = -⅔ * 3 + b

k = -2 + b

b = k + 2

Now we have the equation of the line in the slope-intercept form: y = -⅔x + (k + 2)

To find the value of k we can use the other point (-3, 2k) and substitute into the equation:

2k = -⅔(-3) + (k + 2)

2k = 2 + k + 2

k = -2

So the value of k is -2 and the equation of the line is y = -⅔x + (k + 2) = -⅔x - 2

This line is a straight line with the slope of -⅔ which passes through the points (3, k) and (-3, 2k) and its equation is y = -⅔x - 2

A mathematical operation which is the same as dividing a number by 1,000 include the following: C. move the decimal 3 places to the left.

In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.

This ultimately implies that, a quotient in terms of numerical data simply refers to a division of a number (numerator) by another number (denominator).

In terms of determining the decimal place after a division of a number by 1000, we have the following:

Number = 1/1000

Number = 0.001 (3 places to the left.)

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Answer:

Step-by-step explanation:

from the first ... 3y = 3x + 12 or

y = x + 4

This is the same as the second, so D

The height of the triangle which is also called the altitude is; 6.63 cm

The triangle is an Isosceles Triangle that has two congruent sides and we have the parameters as;

Length of congruent sides = 12 cm.

Base length = 10 cm

Half of the base will be 5 cm and as such, we can use the Pythagorean Theorem to find the altitude as;

Altitude² = Hypotenuse² - Base length²

Thus;

A² = 12² - 10²

A = √44

A ≈ 6.63 cm

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The logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x is-

  [tex]g(x)[/tex] = ㏑[tex](x) / 0.4[/tex]

The equation can be written as-

[tex]y = f(x) = e x^{0.4x}[/tex]

The natural logarithm is now applied to both sides of the equality after we have isolated y.

[tex]0.4y = ln x[/tex][tex]y = ln x / 0.4[/tex]

This is how the  exponential model as a logarithmic model that calculates the number of years, g(x) can be explained as.

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The inequality involving absolute value is 2 < x < 4 and the graph is attached below.

The term called inequality in math is defined as when two real numbers or two algebraic expressions are represented with symbols like <, > or ≤, ≥.

Here we need to find the inequality involving absolute value for the graph. And here we also need to find the point that is the same distance from 2 as it is from 4.

Here we have consider that x be the number that the inequality is formed than it can be written as

=> 2 < x < 4

And the graph of the inequality is plotted and attached below.

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Answer: x=2

Step-by-step explanation:

There will be 9 columns which each has 9 blocks and the 10th column will be 5 blocks. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 68 ÷ 7

Simplify the expression, then we have

⇒ 68 ÷ 7

⇒ (63 + 5) / 7

⇒ 63 / 7 + 5 / 7

⇒ 9 + 5/7

There will be 9 columns which each has 9 blocks and the 10th column will be 5 blocks. Then the correct option is D.

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The last D option is missing. The option D is given as,

D. 9 columns which each has 9 blocks and the 10th column will be 5 blocks.

Answer:

Step-by-step explanation:

Oohh yeah

Answer:

36 cm²

Step-by-step explanation:

Area=Length*Width

so... 9*4 = 36

36 cm²

Answer: A = shade the square above and below the third square (3 to the right). B = Make a straight line of 4 and put a square below the first square of the line, and above the second square. (Let me know if you need help.)

Step-by-step explanation:

The total number of ounces needed to serve all guests (6 oz/guest * 80 guests) and then divide that number by the size of the bottle (25.4 oz) to get the total number of bottles needed.

In order to calculate the number of champagne bottles needed to serve all 80 guests, we need to use the formula for calculating the total number of ounces needed. The formula is: Number of bottles * size of bottle + total ounces of glasses * number of guests. In this case, the number of bottles needed is: (6 oz/guest * 80 guests)/25.4 oz bottle = 18.9 bottles. Therefore, 19 champagne bottles will be needed to serve all 80 guests. This is because each bottle holds 25.4 ounces and each guest needs 6 ounces of champagne, so we need to calculate the total number of ounces needed to serve all guests (6 oz/guest * 80 guests) and then divide that number by the size of the bottle (25.4 oz) to get the total number of bottles needed.

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The solution for the expression when x= 3 is 75

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

x² + 22x

Also from the question, we have

x = 3

This means that the value of x is 3, and we calculate the value of the expression

Substitute the known values in the above equation, so, we have the following representation

x² + 22x = 3² + 22 * 3

Evaluate

x² + 22x = 75

Hence, the solution is 75

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Possible question

Given x² + 22x, calculate the value when x = 3

The name of the number property matched below with each step from the previous step.

The commutative property of addition:

Let a and b are numbers.

a + b = b + a

The change in the position of two numbers in an addition operation does not change the sum.

Given:

We have an expression,

[-5 + (1/2 + 5)] × 2

Applying commutative property of addition,

= [-5 + (5 + 1/2)] × 2

= [ (-5 + 5) + 1/2] × 2

Applying inverse property of addition,

= [0 + 1/2] × 2

Applying identity property of addition,

= 1/2 x 2

Applying inverse property of multiplication,

= 1

Therefore, the solution is 1.

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Answer:

see below

Step-by-step explanation:

h = 6

r = 8 ==> area = πr² = 3.14*8² = 3.14 *64 =201.0

top & bottom = 2*200.96 = 401.9

r=8 ==> perimeter = 2πr = 2*3.14 *8 = 16* 3.14 =50.2

lateral area = h*perimeter = 6*50.24 = 301.44

so it's about 100 sq inch less

Jessica's speed is 4 mph and Janine's speed is 8 mph

Let us assume that x represents Jessica's speed.

Janine bikes 4 mph faster than her sister, Jessica.

So, Janine's speed would be (x + 4) mph

We know that the formula for the speed is: speed = distance/time

Here, Janine can ride 24 mi in 3 hr less time than Jessica can ride the same distance.

24/(x+4) = (24/x) - 3

24/(x+4) = (24 - 3x)/x

24x = (24 - 3x)(x + 4)

24x = 24x + 96 - 3x² - 12x

3x² + 12x - 96= 0

After solving above quadratic equation we get.

(x - 4) (x + 8) = 0

x = -8 speed is not possible.

So, x = 4 mph

And x + 4 = 8 mph

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The first 8 terms of the sequence are 12, 16, 22, 30, 40, 52, 66, 82 respectively.

(a) The first 8 terms of the sequence are as follows:

a1 = 1 + (1^2) + (2^3) + 2 = 12

a2 = 1 + (2^2) + (2^3) + 3 = 16

a3 = 1 + (3^2) + (2^3) + 4 = 22

a4 = 1 + (4^2) + (2^3) + 5 = 30

a5 = 1 + (5^2) + (2^3) + 6 = 40

a6 = 1 + (6^2) + (2^3) + 7 = 52

a7 = 1 + (7^2) + (2^3) + 8 = 66

a8 = 1 + (8^2) + (2^3) + 9 = 82

(b) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 4n for all n ≥ 3. Hence, a = 3.

(c) We will prove the statement "an > 4n for all integers n ≥ a" using strong induction.

Base case (n=3): a3 = 28 and 28 > 4 * 3 = 12, which is true.

Inductive step: Suppose an > 4n for all integers n = k (k ≥ 3). We need to show that a(k+1) > 4(k+1).

a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 4k + 3 = 4(k+1)

(d) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 45 for all n ≥ 7. Hence, b = 7.

(e) We will prove the statement "an > 5n for all integers n ≥ b" using strong induction.

Base case (n=7): a7 = 120 and 120 > 7 * 5 = 35, which is true.

Inductive step: Suppose an > 5n for all integers n = k (k ≥ 7). We need to show that a(k+1) > 5(k+1).

a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 5k + 3 = 5(k+1)

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There are 32 home sites on the 8-acre plot.

An acre, a standard unit of measurement used by land sellers, is roughly the same size as a typical football field. An acre is a product of any rectangular land plot with a total area of 4,046 square Metre, or 43,560 square feet. Six plots of 6 x 120 feet each make up an acre.

To find out how many 1/4 acre home sites are on the 8-acre plot, you can divide the total number of acres by the number of acres per home site.

8 acres / 0.25 acres/home site = 32 home sites.

So, there are 32 home sites on the 8-acre plot.

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Answer:

14

Step-by-step explanation:

f(3) = 3(3) - 5 + 10

f(3) = 9 - 5 + 10

f(3) = 4 + 10

f(3) = 14

Answer:

14

Step-by-step explanation:

Start by finding f(3), which would include plugging in a 3 everywhere you see an x

f(3) = 3(3)-5

f(3) = 9-5

f(3) = 4

Now we can use f(3)+10 because we know what f(3) is, it's 4. So replacing it

f(3) + 10 is now 4+10, which equals 14

Answer:

Step-by-step explanation:

The equation x + (60 + 70)° = 180° is used to solve for the measure of the vertical angle x = 50°

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

The angle y and x form vertical angles, so x = y

Angle y form a straight line with 60° and 70° so we have the equation to solve for x as:

x + 60° + 70° = 180° {sum of angles on a straight line}

x + 130° = 180°

x = 180° - 130° {subtract 139° from both sides}

x = 50°

Therefore, the measure of the vertical angle x is equal to 50° derived with the equation x + (60° + 70°) = 180°.

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The recommendations in parts (a) and (b) are not consistent. This is the best example of Simpson’s Paradox.

(a) Allison Feeley's junior year batting average: 15/40 = 0.375 Emily Janson's junior year batting average: 71/201 = 0.353 Allison Feeley's senior year batting average: 76/251 = 0.302 Emily Janson's senior year batting average: 35/120 = 0.292

Using this analysis, Allison Feeley should be awarded the scholarship, as she has the higher batting average in both her junior and senior years.

(b) Outcome: Player | Hit | No Hit | Total At-Bats Fealey | 91 | 200 | 291 Janson | 106 | 215 | 321

Allison Fealey's combined two years batting average: 91/291 = 0.313 Emily Janson's combined two years batting average: 106/321 = 0.331

Using this analysis, Emily Janson should be awarded the scholarship, as she has the higher batting average over the combined junior and senior years.

(c) The recommendations in parts (a) and (b) are not consistent. This is an example of Simpson's Paradox, it shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be different when the crosstabulations are grouped or aggregated.

Therefore, [a] and [b] are not consistent according to Simpson’s Paradox.

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The recommendations in parts (a) and (b) are not consistent. This is the best example of Simpson’s Paradox.

a) Allison Feeley's junior year batting average: 15/40 = 0.375 Emily Janson's junior year batting average: 71/201 = 0.353 Allison Feeley's senior year batting average: 76/251 = 0.302 Emily Janson's senior year batting average: 35/120 = 0.292

Using this analysis, Allison Feeley should be awarded the scholarship, as she has the higher batting average in both her junior and senior years.

(b) Outcome: Player | Hit | No Hit | Total At-Bats Fealey | 91 | 200 | 291 Janson | 106 | 215 | 321

Allison Fealey's combined two years batting average: 91/291 = 0.313 Emily Janson's combined two years batting average: 106/321 = 0.331

Using this analysis, Emily Janson should be awarded the scholarship, as she has the higher batting average over the combined junior and senior years.

(c) The recommendations in parts (a) and (b) are not consistent. This is an example of Simpson's Paradox, it shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be different when the crosstabulations are grouped or aggregated.

Therefore, [a] and [b] are not consistent according to Simpson’s Paradox.

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Answer:

a)12:4

Step-by-step explanation:

We know

The ratio is 3:1; we time 4 and get a ratio is 12:4

So, the answer is A

answer:

1.the total area is quadrupled.

2.(I'm not sure, so sorry!!!!!)

Step-by-step explanation:

somsome else can do number 2 because questions on brainly have a max of 2 answers.... again, so sorry.

Step-by-step explanation:

If one dimension of a figure is quadrupled, its area would increase by a factor of 16 (2 to the power of 4). If one dimension is multiplied by 5, the area would increase by a factor of 25 (5 to the power of 2).

Answer:

m < -1 5/8

Step-by-step explanation:

attached pic

The slope of the Function represents the change in height per day.

A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is

[tex]m=\frac{dy}{dx}[/tex] = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be shown as

tan θ = Δy/Δx

So, the slope of a line is tanΘ.

So as slope represents a change in y per change in x, in the given question as y is height and x is days, slope changes in height per day.

The slope of the Function represents the change in height per day.

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No, these given system specifications are not consistent.

They present a logical contradiction, also known as a paradox. The first claim claims that "Users cannot access the file system if the system software is changed," while the second claim claims that "Users can store new files if they can access the file system."

The third assertion, which reads, "If users cannot save new files, then the system software is not being upgraded," is in direct opposition to the first. All three of the aforementioned assertions cannot be true at the same time.

Hence, these given system specifications are not consistent.

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The probability of an event happening in half an hour cannot be determined simply by multiplying or dividing the probability of the event happening in an hour by a factor of 2.

Probabilities are not linear in that way. The probability of an event happening in half an hour would depend on the specific details of the event and the underlying probability distribution.

The probability of an event happening in half an hour, given an 84% chance of it happening in an hour, cannot be determined without additional information. The probability of an event occurring in half an hour would depend on the specific circumstances of the event and how the 84% probability was determined.

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if there is an 84% chance of an event happening in an hour, then the probability that it happens in half an hour will be 84% = 0.84.

One cannot easily calculate the likelihood of an event occurring in half an hour by multiplying or dividing the chance of the event occurring in an hour by a factor of 2.

In that sense, probabilities are not linear. The likelihood of an event occurring in half an hour is determined by the event's specifics and the underlying probability distribution.

Without further information, the likelihood of an event occurring in half an hour given an 84% chance of occurring in an hour cannot be computed. The likelihood of an event occurring in half an hour is influenced on the event's unique circumstances and how the 84% probability was calculated.

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Answer:

5x + 4

Step-by-step explanation:

Base on the given:

[tex]\mathrm{\frac{9}{3}x+4+2x}[/tex]    → Divide 9 by 3. 9 ÷ 3 = 3

[tex]\mathrm{3x+4+2x}[/tex]    → Combine similar term {2x + 3x = 5x}

No farther can be simplify. Hence, 5x + 4 is the answer.

RevyBreeze

The distance travelled by rick on 2.5 gallons of gasoline is calculated to be 45 mi.

The given function can be written as d = 18 g , where, d is the distance and g is gasoline.

It is also said that, gasoline g = 2.5 gallons

So, to calculate the distance travelled by rick, we should place the value of g in the equation above.

d = 18 g = 18(2.5) = 45 mi

From the graph, the maximum possible gasoline is 10. So, when we place in the above equation, we have,

d = 18 g = 18(10) = 180 gallons

As, the both quantities on the x-axis and y-axis are positive, the graph is possible in first quadrant only.

The given question is incomplete. The complete question is 'How far can rick drive on 2.5 gallons of gasoline?' The picture of graph is attached in the attachment below.

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