Answer:
Its value is approximately:
G = 6.6743 x 10^-11 m^3 kg^-1 s^-2
Step-by-step explanation:
The value of G is the gravitational constant, which is a physical constant that appears in the law of universal gravitation. Its value is approximately:
G = 6.6743 x 10^-11 m^3 kg^-1 s^-2
This value is used to calculate the force of gravitational attraction between two objects, given their masses and the distance between them. The gravitational constant is a fundamental constant of nature and is important in many areas of physics, including astrophysics, cosmology, and mechanics.
A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (-6, 6). What is the vertex of the function defined as g(x) = f(= - 2)?
y=f(x) has vertex (-4,6)
g(x)=-f(x-2) shifts the graph 2 units to the right, not to the left, and the graph is reflected over the x-axis
therefore the vertex is (-2,6) and the reflection over the x-axis has no affect on the vertex
Is this dilation a reduction or an enlargement
As, the scale factor is less than 1 . So, the dilation is the reduction for the image of triangle ABC.
Explain about the dilation:How very much larger (as well as smaller) any item becomes following the transformation is indicated by the dilation factor.
The object doubles in size, for instance, if the dilation factor is 2. In other words, every one of its side lengths are doubled.The converted object is half its original size if the dilation factor is equal to 1. In particular, all of its side lengths would be cut in half.Given data:
A'B'C' is the dilation of triangle ABC.
Scale factor = 1/2 = 0.5
As, the scale factor is less than 1 . So, the dilation is the reduction for the image of triangle ABC
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Help me answer this plss
Answer:
155.5 square feet
Step-by-step explanation:
A = (1/2)(10)(8.6 + 6.3 + 8.6 + 7.6)
= 5(31.1)
= 155.5 square feet
Which is the missing reason in the proof below?
Statements Reasons
∠BAC ≅ ∠DAC Given
AB ≅ AD Give
AC ≅ AC
ΔABC ≅ ΔCDA SAS
Use ≈ 3.14 and round your answer to the nearest hundredth. 10 m 14 m square meters
The area of a rectangle is 140.00 square meters.
What is a rectangle?
A rectangle is a 2-dimensional geometric shape with four sides, where each interior angle is a right angle (90 degrees). It is a special case of a parallelogram, where opposite sides are equal in length and parallel to each other.
I assume you are looking for the area of a rectangle with sides 10 m and 14 m, rounded to the nearest hundredth using the approximation π ≈ 3.14.
The area of a rectangle is given by the formula A = lw, where l and w are the length and width of the rectangle, respectively. In this case, l = 14 m and w = 10 m, so:
A = lw = (14 m)(10 m) = 140 m²
Rounding 140 to the nearest hundredth gives 140.00, so the final answer is:
140.00 square meters.
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Full question:
What is the area of a rectangle with sides of length 10 meters and 14 meters, rounded to the nearest hundredth using the approximation π ≈ 3.14?
Please help! I need to find the perimeter, Predicted perimeter , Predicted area and Area.
The perimeter of the rectangle is 38 feet, the predicted perimeter is 26 feet, the area of the rectangle is 30 square feet, and the predicted area is also 30 square feet.
What is the formula of perimeter and area of Rectangle ?
The formulas for the perimeter and area of a rectangle are:
Perimeter = 2(length + width)
Area = length x width
In these formulas, "length" refers to the longer side of the rectangle, and "width" refers to the shorter side of the rectangle. The perimeter is the total length of the sides of the rectangle, and the area is the amount of space inside the rectangle.
To find the perimeter of the rectangle, we simply add up the lengths of all four sides:
Perimeter = 10 feet + 3 feet + 6 feet + 6 feet + 4 feet + 9 feet
Perimeter = 38 feet
To predict the perimeter, we could use the formula for the perimeter of a rectangle, which is:
Predicted Perimeter = 2(length + width)
We can find the length and width of the rectangle by finding the longest and shortest sides:
Length = 10 feet
Width = 3 feet
Therefore, the predicted perimeter would be:
Predicted Perimeter = 2(10 feet + 3 feet)
Predicted Perimeter = 26 feet
To find the area of the rectangle, we multiply the length by the width:
Area = 10 feet × 3 feet
Area = 30 square feet
To predict the area, we could use the formula for the area of a rectangle, which is:
Predicted Area = length × width
Using the same values for length and width as before, the predicted area would be:
Predicted Area = 10 feet × 3 feet
Predicted Area = 30 square feet
Therefore, the perimeter of the rectangle is 38 feet, the predicted perimeter is 26 feet, the area of the rectangle is 30 square feet, and the predicted area is also 30 square feet.
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A charity is hosting a benefit dinner. They are asking 100 per table plus 40 per person. Nathaniel is purchasing tickets for his friends and does not wnat to spend more than 250
10t + 4p ≤ 25 inequality shows the maximum number of tables and people Nathaniel can invite while staying within his budget.
What is inequality?
In mathematics, an inequality is a statement that two values or expressions are not equal, but rather that one is greater than or less than the other. An inequality is denoted by the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
Let the number of tables Nathaniel buys be represented by t, and the number of people he invites be represented by p.
Then, the total cost can be expressed as:
Cost = 100t + 40p
Since Nathaniel does not want to spend more than 250, we can set up the inequality:
100t + 40p ≤ 250
We can simplify this inequality by dividing both sides by 10:
10t + 4p ≤ 25
This inequality shows the maximum number of tables and people Nathaniel can invite while staying within his budget.
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I am equivalent to 3/8 and the product of my numerator and denominator is 216.What am I
The fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.
To find the fraction equivalent to 3/8 with a numerator and denominator product of 216, follow these steps:
Set up an equation for the product of the numerator and denominator:
x × y = 216.
Since the fraction is equivalent to 3/8, you can write another equation: x / y = 3/8.
Solve for x in terms of y in the second equation:
x = (3/8) × y.
Substitute this expression for x in the first equation:
(3/8) × y × y = 216.
Solve for y: [tex]y^2 = (8/3) × 216.[/tex]
Simplify the equation: y^2 = 576.
Find the square root of both sides: y = 24.
Now, find x using the equation x = (3/8) × y:
x = (3/8) × 24.
Simplify the expression:
x = 9.
So, the fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.
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i need help please Belle is hanging streamers for her brother's surprise birthday party. She secures two streamers of different lengths at the peak of the ceiling. The center of the floor is directly underneath the ceiling peak. The distance along the floor from the center of the room to where the first streamer is attached is 6 feet. The second streamer is attached to the floor further from the center of the floor than the first streamer.
we don't have enough information to determine the exact lengths of the streamers or the distance from the center of the floor to where the second streamer is attached.
Sure, I'd be happy to help! Based on the information you provided, we know that Belle is hanging two streamers of different lengths at the peak of the ceiling for her brother's surprise birthday party. The center of the floor is directly underneath the ceiling peak.
We also know that the distance along the floor from the center of the room to where the first streamer is attached is 6 feet.
Since the second streamer is attached to the floor further from the center of the floor than the first streamer, we can infer that the second streamer is longer than the first streamer.
I hope this helps! Let me know if you have any other questions.
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determine the equation of the circle with center (5,5) containing the point (0,-2)
The equation of the circle with center (5,5) containing the point (0,-2) is [tex](x - 5)^2 + (y - 5)^2 = 74[/tex]
What is the equation of the circle?The standard equation of a circle is given by: (x-h)2 + (y-k)2 = r2 Where (h,k) is the coordinates of center of the circle and r is the radius.
To determine the equation of the circle, we need to find the radius first. Since the center of the circle is (5,5), we can use the distance formula to find the distance between the center and the given point (0,-2):
[tex]distance = \sqrt{[(x2 - x1)^2 + (y2 - y1)^2]}\\distance = \sqrt{[(0 - 5)^2 + (-2 - 5)^2]}\\distance = \sqrt{[(-5)^2 + (-7)^2]}\\distance = \sqrt{[25 + 49]}\\distance = \sqrt{[74]}[/tex]
Therefore, the radius of the circle is sqrt[74].
Now, we can use the standard form of the equation of a circle to find the equation of the circle:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h,k) is the center of the circle, and r is the radius.
Plugging in the values we have:
[tex](x - 5)^2 + (y - 5)^2 = (\sqrt{[74]})^2[/tex]
Simplifying the equation:
[tex](x - 5)^2 + (y - 5)^2 = 74[/tex]
Therefore, the equation of the circle with center (5,5) containing the point (0,-2) is [tex](x - 5)^2 + (y - 5)^2 = 74.[/tex]
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Find the perimeter of the figure (use 3.14 as pi if u can)
The perimeter of a shape is the measurement around its edge and it is 101.36 in.
How is boundary determined?We must sum up the lengths of the quadrilateral four sides to determine its perimeter. Since there are two of each side measurement, it is easy to accomplish this by simply adding the length and width and multiplying the result by two.
Perimeter of given shape = 18 + 27 +27 + perimeter of the arc
the perimeter of the arc = Perimeter of the semicircle = [tex]\pi r[/tex]
Therefore the perimeter of the shape = 72 + 3.14 * 9 = 101.36 in.
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Factor the polynomial Complete the table (8a - 8l)
9a) Factorization from 8d. 9b) Factorization from 8h 9c) Factorization from 8l
PLEASE HELP 30 POINTS
The factorization for 8i is 3x(5x+1)(x-2), which can also be checked by multiplying the factors and verifying that the result is equal to the original polynomial.
Polynomial GCF Factored with GCF Factored TrinomiaL Final
9x^4 + 3x^3 -1222 1 NA NA
2x^2 + 3x - 9 1 NA (2x-3)(x+3) (2x-3)(x+3)
15x^3 - 27x^2 - 6x 3x 3x(5x^2 - 9x - 2) not factorable 3x(5x+1)(x-2)
9a) Factorization from 8d: not factorable
9b) Factorization from 8h: (2x-3)(x+3)
9c) Factorization from 8i: 3x(5x+1)(x-2)
Note: The table shows the factoring process for each polynomial. In question 9, we just need to check the final factorization for each of the polynomials in question 8. The factorization for 8d is not factorable, so there is nothing to check. The factorization for 8h is (2x-3)(x+3), which can be checked by multiplying the factors and verifying that the result is equal to the original polynomial.
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which statement is true about effect size? group of answer choices when the effect size is small, detecting it is easier and can be done with a smaller sample the effect size is the extent to which the null or statistical hypothesis is false there is one type of effect size measure used in research studies
The true statement about effect size is: The effect size is the extent to which the null or statistical hypothesis is false. Effect size is a measure used in research studies to quantify the magnitude of the difference between groups or the strength of an association between variables.
It helps determine the practical significance of the research findings, as opposed to the statistical significance.
When the effect size is small, detecting it is not necessarily easier, and a larger sample size may be required to achieve adequate statistical power. A larger effect size, on the other hand, might be easier to detect and might require a smaller sample size.
There is not just one type of effect size measure used in research studies. There are various measures of effect size, such as Cohen's d, Pearson's correlation coefficient (r), and odds ratio (OR), among others. Each type of effect size is suitable for different research designs and data types.
Choosing the appropriate effect size measure depends on the research question, the design of the study, and the type of data being analyzed.
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working together, it takes two computers 15 minutes to send out a company's email. if it takes the slower computer 35 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? do not do any rounding.
It would take the faster computer 525/20 minutes to do the job on its own.
Let the rate of the faster computer be F and the rate of the slower computer be S. Since they can complete the job together in 15 minutes, we have:
F + S = 1/15
We also know that the slower computer takes 35 minutes to do the job on its own, so:
S = 1/35
Now, we can substitute the value of S into the first equation to solve for F:
F + 1/35 = 1/15
F = 1/15 - 1/35
F = (35 - 15) / (15 * 35)
F = 20 / 525
Therefore, the rate of the faster computer is 20/525. To find how long it takes the faster computer to do the job on its own, we take the reciprocal of this rate:
Time = 1/F = 525/20
So, it would take the faster computer 525/20 minutes to do the job on its own.
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(Best Answer gets BrainLiest)
Find the missing value in the table.
The missing value is [??]
Answer:
20
Step-by-step explanation:
You can find this answer multiple ways.
One way is that each y value increases by 5 so following the pattern of 5, 10, 15 the next one would be 20.
Another way is that the the x value is 3 times the y value so we would just have to divide 60 by 3 to get 20.
Answer: 20
Step-by-step explanation:
y is a result of dividing x by 3
15/3 = 5
30/3 = 10
...
60/3 = 20
CAN SOMEONE PLEASE HELP!!!!
A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 10 feet. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water will it take to fill up the pool completely? Use π = 3.14 and round to the nearest gallon.
63 gallons
471 gallons
1,409 gallons
3,523 gallons
3,523 gallons
adam, benin, chiang, deshawn, esther, and fiona have internet accounts. some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. each of them has the same number of internet friends. in how many different ways can this happen? (2012amc10a problem 23 or 2012amc12a problem 19)
Option A, For the aptitude puzzle, the number of ways each of people has the same number of internet friends is 60.
We want to count the number of ways that the 6 people can be internet friends with each other given that each person has the same number of internet friends and no one has an internet friend outside of the group.
Let k be the number of internet friends each person has. Since each person knows 5 other people in the group, we have 6k = 5 * 6, which means that k=5.
Thus, each person has 5 internet friends. We can choose these 5 friends in 5 to choose 5 times 4 choose 5 times 3 choose 5 times 2 choose 5 times 1 choose 5 = 1 × 0 × 0 × 0 × 0 = 0 ways since we can't choose 5 friends from fewer than 5 people.
Therefore, the answer is (A) 60.
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The question is -
Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen?
a. 60
b. 170
c. 290
d. 320
e. 660
when examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?
A horizontal compression is identified by a factor inside the function, affecting the input variable, while a vertical compression is identified by a factor outside the function, affecting the output variable.
When examining the formula of a function that is the result of multiple transformations, a horizontal compression can be identified by a factor that appears inside the function, affecting the input variable (typically x). For example, if the original function is f(x) and the horizontal compression is by a factor of 2, the function would be written as f(x/2), indicating that the input values are being compressed horizontally.
On the other hand, vertical compression can be identified by a factor that appears outside the function, affecting the output variable (typically y). For example, if the original function is f(x) and the vertical compression is by a factor of 1/2, the function would be written as (1/2)f(x), indicating that the output values are being compressed vertically.
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a three digit number is not an odd number, does not contain 6, and one of the digits appear more than once. how many possible three digit numbers are there?
The total number of possible three-digit numbers is not odd, does not contain 6, and has at least one repeated digit is 13,221,888.
To find the number of possible three-digit numbers we need to use the systematic approach method
Step 1:
we have to find the number of three-digit numbers that are not odd. Number of possible choices for the units digit (0, 2, 4, or 8)= 4
Number of possible choices for tens and hundreds of digits (0-9 excluding 6 = 9
the total number of three-digit numbers that are not odd is,
= 4 x 9 x 9
= 324.
Step 2:
Count the number of three-digit numbers that do not contain 6.
Number of possible choices for each digit (0-5, 7, 8, or 9) = 8
the total number of three-digit numbers that do not contain 6 is,
= 8 x 8 x 8
= 512.
Step 3:
Count the number of three-digit numbers that do not have distinct digits. The number of possible choices for the repeated digit and 9 choices for the other digit = 9
the total number of three-digit numbers that have a repeated digit is
= 9 x 9 = 81.
Step 4:
Find the intersection of the sets of numbers counted in Steps 1-3.
To do this, we multiply the number of choices in each set:
= 324 x 512 x 81
= 13,221,888.
Therefore, 13,221,888 possible three-digit numbers are not odd, do not contain 6, and have at least one repeated digit.
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what is the quadratic equation of y=(x+4)²+3
Answer:
y = x^2 + 8x + 19
Step-by-step explanation:
y=(x+4)²+3
First expand the parentheses:
y = x^2 + 4x + 4x + 16 + 3
y = x^2 + 8x + 19
Is it a function yes or no
Answer:
Step-by-step explanation:
im assuming your saying number 3 which is yes
Draw the image of triangle△ABC under a dilation whose center is C and scale factor is 2
The original triangle ABC is down below.
PLEASE HELP
To draw the image of triangle △ABC under a dilation with center C and scale factor 2, we need to draw the original triangle, draw lines from C to each vertex,
To draw the image of triangle △ABC under a dilation with center C and a scale factor of 2, we need to follow a few steps. Firstly, we need to draw the original triangle △ABC. Then, we need to draw a straight line from the center of dilation C to each vertex of the triangle. These lines will act as our guides for where the new vertices will be located.
Next, we need to use the scale factor of 2 to determine the distance between the original vertices and the new vertices. This means that we need to multiply the distance between each vertex and the center of dilation by 2. We can then plot the new vertices along the lines we drew in the previous step.
Finally, we can connect the new vertices to form the image of the triangle under the dilation. This image will be twice as large as the original triangle and will be located in the same direction as the lines we drew from the center of dilation to each vertex.
use the scale factor to determine the new vertex locations, and finally connect the new vertices to form the image.
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If a cyclist completes a ride in four hours and 15 minutes with an average
speed of 23 km/h, what distance did he cover? just the answer please
Answer:
covered distance = 97.75 kilometers
Step-by-step explanation:
It's known that:
[tex]speed = \frac{distance}{time}[/tex]
Hence,
[tex]distance = speed\times time[/tex] (*)
Given That:
time = 4.25 hours
speed = 23 km/h
then, by substituting in (*):
[tex]distance = 23 \times 4.25 = 97.75 kilometers[/tex]
hope you find this easy to understand....
Have any questions? Write in the comments.
give me brainliest if you found this answer useful
I NEED HELP ASAPPPPPP
Answer:
0.0399148483 is the answer
Answer:
Your answer is 0.0399
Step-by-step explanation:
Use the graph to answer the question. Graph of polygon ABCD with vertices at negative 1 comma negative 1, 1 comma negative 5, 5 comma negative 5, 3 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at 4 comma negative 1, 6 comma negative 5, 10 comma negative 5, 8 comma negative 1. Determine the translation used to create the image. 5 units to the right 1 unit to the right 5 units to the left 1 unit to the left
The polygon is translated five units to the right.
Define translation?A translation does not alter the appearance of a shape; it merely shifts it up, down, or from side to side. A metamorphosis serves as an example of translation. A transformation is a method for changing a shape's size or placement. At each location, the shape is translated in the same direction by the same amount.
The polygon ABCD's vertices are provided to us as A (-1, -1); B (1, -5); C (5, -5) and D (3, -1)
Also, the vertices of second polygon A'B'C'D' are given as A' (4, -1); B' (6, -5); C' (10, -5) and D' (8, -1).
It is evident that neither polygon's y coordinates have changed.
A 5 increment is made to the x-coordinates.
The translation rule in use is therefore (x, y) → (x + 5, y)
As a result, the polygon is translated 5 units to the right.
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The complete question is:
Graph of polygon ABCD with vertices at negative 1 comma negative 1, 1 comma negative 5, 5 comma negative 5, 3 comma negative 1.
A second polygon A' B' C' D' with vertices at 4 comma negative 1, 6 comma negative 5, 10 comma negative 5, 8 comma negative 1.
Determine the translation used to create the image.
1. 5 units to the right
2. 1 unit to the right
3. 5 units to the left
4. 1 unit to the left
will give brainilest
Answer:
[tex]3 \: {cm}^{2} [/tex]
Step-by-step explanation:
Given:
h (height) = 1,5 cm
b (base) = 4 cm
Find: A (area) - ?
[tex]a = \frac{1}{2} \times b \times h[/tex]
[tex]a = \frac{1}{2} \times 4 \times 1.5 = 3 \: {cm}^{2} [/tex]
Question 4(Multiple Choice Worth 2 points)
(Experimental Probability MC)
Louis rolled a fair six-sided die and recorded the number that was facing up on the die. He continued this for a total of 100 rolls. The table shows the frequency of each number rolled.
Outcome 1 2 3 4 5 6
Frequency 17 20 14 18 16 15
Based on the table, what is the experimental probability that the number rolled was even?
53 over 100
47 over 100
5 over 12
1 over 2
The experimental probability that the number rolled was even is 53 over 100.
In a die 2, 4 and 6 are even numbers so sum of there frequency are possible outcome.
Frequency of 2 4 and 6 are 20,18 and 15 respectively.
Possible outcome = 20+18+15 = 53
Total outcome is sum of all frequency, total outcome = 17+20+14+18+16+15 = 100
P(even) = 53/100
Therefore the experimental probability that the number rolled was even is 53 over 100.
The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.
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would it be appropriate to construct a 95% confidence interval with the information in 1(b) through 1(d)? explain why in one sentence.
If a simple random of size n is drawn from a population, then the 95% confidence-interval about "μ", if the sample size "n" is 23 is (101.68 , 110.32).
The population from which a simple random of size "n" is drawn is normally distributed,
We have to construct "95% confidence-interval" when n = 23,
So, c = 0.95, n = 23,
⇒ degree of freedom(df) = 23 - 1 = 22,
from t-distribution table, the critical-value corresponding to c = 0.95 and df = 22 is t = 2.074,
the lower bound is = x' - (t×s)/√n = 106 - (2.074×10)/√23 = 101.68,
the upper bound is = x' + (t×s)/√n = 106 + (2.074×10)/√23 = 110.32,
Therefore, the required 95% confidence interval is (101.68 , 110.32).
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The given question is incomplete, the complete question is
A simple random of size n is drawn from a population that is normally distributed, the sample mean (x') is found to be 106, and the sample standard deviation is 10. Construct a 95% confidence interval about "μ", if the sample size "n" is 23.
which are the first five trems of a geometric in which the second tem is 6 and the forufh trem is 54?
The first five terms are 2, 6, 18, 54, 162.
What are numbers?A number is a fundamental building block of mathematics.
Numbers are used for indexing, counting, measuring, and a variety of other tasks.
According to their characteristics, there are various sorts of numbers, including natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc.
The resultant number can be calculated by using the fundamental arithmetic operations for integers.
Tally marks were formerly used before numbers.
Numbers are a crucial aspect of our daily lives, from the number of rounds we run around the race track to the number of hours we sleep at night, and much more.
According to our question-
a series where each subsequent term is obtained by multiplying the preceding one by a shared ratio.
The order is provided by:
a, ar, ar2, aar3, aar4, aar5,...
What is the nth term provided by-
a_n = ar^(n-1)
Second term = 6
a_2 = ar^(2-1)
6 = ar^1
6 = ar
Hence, The first five terms are 2, 6, 18, 54, 162.
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the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]
What is geometric sequence?Assume that "a" is the first letter of the geometric sequence and "r" is the common ratio.
According to the problem statement, the second term is 6. Therefore, we have:
[tex]ar = 6 .....(1)[/tex]
Similarly, the fourth term is 54, which gives us:
[tex]ar^3 = 54 .....(2)[/tex]
We must first determine the values of "a" and "r" in the geometric sequence. The two equations mentioned above can be solved simultaneously to achieve this.
The result of dividing equation [tex](2)[/tex] by equation [tex](1)[/tex] is
[tex]r^2 = 9[/tex]
When we square the two sides, we obtain:
r = ±3
Now, using equation (1), we can find the value of "a" as follows:
[tex]ar = 6[/tex]
Substituting r = 3, we get:
[tex]3a = 6[/tex]
[tex]a = 2[/tex]
Substituting [tex]r = -3[/tex], we get:
[tex]-3a = 6[/tex]
[tex]a = -2[/tex]
Therefore, the first term of the geometric sequence is either [tex]2[/tex] or [tex]-2[/tex] , and the common ratio is 3 or -3.
If the first term is 2 and the common ratio is 3, then the first five terms of the geometric sequence are: [tex]2, 6, 18, 54, 162[/tex]
The first five terms of the geometric sequence are as follows, if the common ratio is three and the first term is two:
[tex]-2, 6, -18, 54, -162[/tex]
So, the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]
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Which of these actions will cause the expression's value to increase?
1/3A-B^2
Keeping AAAA constant and increasing BBBB
(Choice B) Keeping AAAA constant and decreasing BBBB
B
Keeping AAAA constant and decreasing BBBB
(Choice C) Increasing AAAA and keeping BBBB constant
C
Increasing A and keeping B constant
(Choice D) Decreasing A and keeping B constant
To increase the value of the expression 1/3A-B^2, increasing A and keeping B constant will cause the expression's value to increase.
This is because the expression has a linear term of A and a quadratic term of B^2. Increasing A will result in a larger linear term, which will increase the value of the expression. None of the other options will necessarily increase the value of the expression. Keeping AAAA constant and decreasing BBBB or decreasing A and keeping B constant will both cause the value of the expression to decrease while keeping AAAA constant and increasing BBBB will only increase the quadratic term of the expression and may or may not result in an overall increase depending on the values of A and B.
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