For the given matrix A, a 3x2 matrix B such that AB=I, where I is the 2x2 matrix B = [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex] when AB=I
Given matrix A = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₂ₓ₃
B = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₃ₓ₂
In such a way we know that, that AB = I ₂ₓ₂
therefore = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
we can say that [tex]\left[\begin{array}{ccc}a+2c+e&b+2d+f\\a+c+e&b+d+f\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
then, a+2c+e=1
then, when elaborated we get, a+2(-a-e)+e=1
a-2a-2e+e=1
-a-e=1
a+e = -1
2c-c = 1, c = 1 hence we get the value for c
similarly we can do the same steps for the other values
b+2d+f=0
1-d+2d=0
1+d = 0
d = -1
we get the value of d as well now for the value of a and e we can proceed as shown below:
a+c+e=0
c= -a-e
a+e= -c
a+e= -1
a= -2, e=1
similarly we can proceed as shownfor the values of b and f
b+d+f=1
b+f=1-d
b+f=2
b=1, f=1
when we put these values in the correct order and place we get the value for matrix b such as shown below,
therefore, matrix B = [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex]
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Please anyone help me
The expression that represents all the possible widths of the rectangle is given as follows:
0 < x < 5.
How to obtain the area of the rectangle?The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:
A = lw.
For this problem, the length is 5 meters more than five times the width, hence:
l = 5 + 5w.
Hence the area is given as follows:
A = w(5 + 5w)
A = 5w² + 5w.
The area is less than 100m², hence the inequality is given as follows:
5w² + 5w < 100
5w² + 5w - 100 < 0.
w² + w - 20 < 0.
(w + 5)(w - 4) < 0.
Hence the solutions are:
w + 5 < 0 -> w < 5.w - 4 < 0 -> w > -4.The width cannot be negative, hence the interval is:
0 < x < 5.
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Find the perimeter and area of the rectangle
The perimeter of the rectangle is 2ab² ( 5ab² + 3)
The area of the rectangle is 15a³b^6
What is rectangle?
A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Let l=5a²b^4 , w= 3ab²
Perimeter = 2(l+w)
= 2(5a²b^4 + 3ab² )
=2 [ ab² ( 5ab² + 3)]
= 2ab² ( 5ab² + 3)
Area = l*w
= 5a²b^4 *3ab²
= 15a³b^6
The perimeter of the rectangle is 2ab² ( 5ab² + 3)
The area of the rectangle is 15a³b^6
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The height of a supply curve at a quantity of 100 represents the minimum price required to induce a producer to supply the hundredth unit. True/False?
The statement is True ' The height of a supply curve at a quantity of 100 represents the minimum price required to induce a producer to supply the hundredth unit"
A supply curve: what is it?
The relationship between the quantity of a good that a producer is willing to sell and the price of the good is graphically represented by the supply curve in economics.
The maximum price a producer will accept to sell a given quantity of the good is represented by the height of the supply curve at that quantity.
As a result, the minimum price necessary to persuade a producer to supply the 100th unit of the good is represented by the height of the supply curve at a quantity of 100.
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Nine more than twice a number is less than negative eleven. Find all numbers that make the statement true
All the numbers less than -10 and upto negative infinity will make the mentioned statement true.
Let us assume the number to be x. So, twice the number will be 2x. Then, nine more will be represented as: 2x + 9. Now, the total is less than -11, so representing the information in expression along with sign.
2x + 9 < - 11
Rewriting the expression according to 2x
2x < - 11 - 9
Performing subtraction on Right Hand Side of the equation
2x < - 20
x < - 20/2
Performing division on Right Hand Side of the equation
x < - 10
So, the numbers below -10 will make the statement true.
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the letter grades (a, b, c, d, f) of business analysis students are recorded by a professor. this variable's classification . a. is time series data b. is categorical data c. is quantitative data d. cannot be determined
The letter grades (A, B, C, D, F) for business analysis students are categories that represent different levels of achievement, so the variable's classification is (b) Categorical Data.
The Categorical data are defined as the variables that represent characteristics or attributes, and they are often expressed as labels or categories.
The Quantitative data, on the other hand, are the numerical values which represent measurements or quantities.
Since the letter grades are not numerical values and do not represent a measurement or quantity, they cannot be classified as quantitative data.
Therefore , the letter grades represents a Categorical Variables .
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The given question is incomplete , the complete question is
The letter grades (A, B, C, D, F) of business analysis students are recorded by a professor. this variable's classification .
(a) is time series data
(b) is categorical data
(c) is quantitative data
(d) cannot be determined
question 4
pls help me as soon as possible
i'm being timed i only have a hour
Answer:
∠ B = 121°
Step-by-step explanation:
ABCD is a cyclic quadrilateral
• opposite angles sum to 180°
∠ B and ∠ D are opposite angles , then
∠ B + 59° = 180° ( subtract 59° from both sides )
∠ B = 121°
Suppose that a motorboat is moving at 83 ft/s when its motor suddenly quits, and that 1 s later the boat has slowed to 23 ft/s. Assume that the resistance it encounters while coasting is proportional to the square of its velocity so that dv/dt =-kv^2 where k > 0. How far will the boat coast in the first 2 minutes after its motor quits?
The boat will coast approximately 16752.9 feet (or about 3.17 miles) in the first 2 minutes after its motor quits.
From the problem statement, we know that the velocity of the boat, v, changes from 83 ft/s to 23 ft/s over a period of 1 second. Therefore, we can write:
[tex]dv/dt = -k v^2[/tex]
Separating variables and integrating from v = 83 at t = 0 to v = 23 at t = 1, we get:
[tex]∫83^23 dv / v^2 = ∫0^1 -k dt[/tex]
=> [1/83 - 1/23] = k
So the equation for the velocity of the boat as it coasts is:
[tex]dv/dt = -[(1/83 - 1/23)] v^2[/tex]
The differential equation is separable:
[tex]dv/v^2 = -[(1/83 - 1/23)] dt[/tex]
Integrating both sides, we get:
-1/v = [(1/83 - 1/23)] t + C
where C is an integration constant. Using the initial condition v(0) = 83, we get:
C = -1/83
Substituting this back, we have:
-1/v = [(1/83 - 1/23)] t - 1/83
Solving for v, we have:
v(t) = 83 / [1 + (83/23 - 1) t]
To find the distance traveled, we integrate v(t) from t = 0 to t = 120:
s =[tex]∫0^120 v(t) dt[/tex]
Substituting v(t) and simplifying, we have:
s = 23 ln(1 + 3.6087t) + 60.391t + C
where C is another integration constant. Using the initial condition s(0) = 0, we get:
C = 0
Therefore, the distance traveled by the boat in the first 2 minutes after its motor quits is:
s = 23 ln(1 + 3.6087t) + 60.391t
Evaluating this expression at t = 120 seconds, we get:
s = 23 ln(433.044) + 7246.92 ≈ 16752.9 ft
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Indicate the method you would use to prove the two 's . If no method applies, enter none.
HA
None
LA
LL
HL
Option A is correct. Use HL to prove two triangles are congruent.
Given:
In triangle ABC and triangle DEF as shown in figure below.
AB≅DE [leg] [Given]
AC≅DF [Hypotenuse side] [Given]
∠B = ∠D = 90°
HL(Hypotenuse -Leg) postulates states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Then, by HL postulates;
ΔABC ≅ ΔDEF.
Therefore, the method you use to prove the two triangle congruent is, HL.
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Diego’s history teacher writes a test for the class with 30 problems. The test is worth 50 points and has two types of problems: multiple choice worth 1 point each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning. Diego’s history teacher writes a test for the class with 30 question. The test is worth 50 points and has two types of questions: multiple choice worth 1 points each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning
there are 10 short answer questions on the test, we get this answer after solving.
Let's assume that the number of multiple choice questions on the test is "m", and the number of short answer questions is "s".
From the given information, we can set up a system of equations:
m + s = 30 (The total number of questions on the test is 30)
1m + 3s = 50 (The total number of points on the test is 50)
To solve for "s", we can use the first equation to find "m" in terms of "s":
m = 30 - s
Then we can substitute this expression for "m" into the second equation:
1(30 - s) + 3s = 50
Simplifying and solving for "s", we get:
30 - s + 3s = 50
2s = 20
s = 10
Therefore, there are 10 short answer questions on the test.
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Complete Question
Diego’s history teacher writes a test for the class with 30 question. The test is worth 50 points and has two types of questions: multiple choice worth 1 points each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning.
many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. a particular station says that the probability that an incoming call is for medical assistance is 0.67. this can be expressed as
The probability that an incoming call is for firefighting equipment (or any other reason besides medical assistance) is 0.33 or 33%.
The statement "the probability that an incoming call is for medical assistance is 0.67" can be expressed as:
P(Medical Assistance) = 0.67
This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.67 or 67%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:
P(Not Medical Assistance) = 1 - P(Medical Assistance) = 1 - 0.67 = 0.33
In science, 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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g even rolls suppose you roll a fair six-sided die until you get a 6. what is the expected number of rolls given that all the numbers you see are even?
The expected number of rolls is 12.The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2.
The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2. Therefore, the expected number of rolls can be calculated by multiplying the probability of rolling an even number (1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 12.
The expected number of rolls to get a specific result on a fair die can be calculated by multiplying the probability of achieving that result by the number of sides on the die. For example, if you wanted to know the expected number of rolls to get an odd number on a fair, 6-sided die, you would multiply the probability of rolling an odd number (3/6, or 1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 3. The same calculation could be applied to determine the expected number of rolls to get a specific number (e.g. a 4) on a fair, 6-sided die. The probability of rolling a 4 would be 1/6, and the expected number of rolls to get a 4 would be 1/6 x 6 = 6.
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someone pls answer this I'm giving 30 points
Beth's rate of travel is 2.2 meters per second and Amy's line is steeper
The graphFrom the question, we have the following parameters that can be used in our computation:
The table of values
See attachment for the graph
Beth's rate of travelFrom the graph, we have
Beth's rate of travel = 2.2 meters per second
This is so because from the graph:
As x increases by 1. y increases by 2/2
The steeper lineHere, we have
Amy's rate of travel = 75/30 meters per second
Evaluate
Amy's rate of travel = 2.5 meters per second
The higher the rate, the steeper the line
This means that Amy's line is steeper
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if a restaurateur wants to know how many dollars the restaurant makes per day, which process metric is needed?
To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.
Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.
Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.
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In a density curve, proportion of data is represented by O area above the curve. O area under the curve. O the shape of the curve. o intervals of values on the vertical axis. o intervals of values on the horizontal axis. O the length of the curve. Question 3 1 pts Which ONE of the following is a correct classification of shapes of density curves? O All → Symmetric → Uniform → Normal O All → Nonsymmetric → Bell → Normal O All → Nonsymmetric → Symmetric → Normal O All → Bell → Symmetric → Normal O All → Symmetric → Bell → Normal O All Uniform → Bell → Normal
In a density curve, the proportion of data is represented by the option B) area under the curve and correct classification of shapes of density curves is option E)
What is Density curve?A density curve is a curve on a graph that represents the distribution of values in a dataset.
A density curve, also called a density function, is a graphical representation of the relative frequency distribution of a continuous random variable. The type of distribution most commonly represented by a density curve is the normal distribution, but any distribution of a continuous variable may be represented by a density curve.
Normal distribution curve is a bell shaped curve obtained for the distribution having maximum frequency near the central value of distribution and the frequency gradually tapering off symmetrically on both side.so, All → Symmetric → Bell → Normal
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The difference of a number and
its reciprocal is 15/13. What is the
number.
Solving the equation: x - 1/x = 15/13
We will see that the value of x is 28/13
How to find the number?For a number x, we define the reciprocal number as 1/x.
We know that the difference between theses two is 15/13, then we can write:
x - 1/x = 15/13
(x² - x)/x = 15/13
(x² - x) = (15/13)*x
x² - x - (15/13)*x = 0
x² - (1 + 15/13)*x = 0
x² - (28/13)*x = 0
x*(x - 28/13) = 0
x = 0 is not a solution, because 1/x exists, then the solution is x = 28/13.
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i need this fast Question 7(Multiple Choice Worth 1 points) (05.02 MC) At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000 for 500 tickets, how many students attended the play? 100 200 300 400
The number of students attended the play are 400 in number.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000
5x+10y=3000
The total number of tickets are 500
x+y=500
y=500-x
Now plug this in above equation
5x+10(500-x)=3000
5x+5000-10x=3000
5000-5x=3000
Add 5x on both sides
5000-3000=5x
2000=5x
Divide both sides by 5
400=x
Hence, the number of students attended the play are 400 in number.
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Una compañía de teléfonos ofrece dos planes mensuales. El plan a cuesta $15 más $0. 12 adicionales por cada minuto de llamadas. El plan b cuesta $8 más 0. 17 adicionales por cada minuto de llamadas
¿para cuantos minutos de llamadas los dos planes cuestan lo mismo?
¿cual es el costo al que dos planes cuestan lo mismo?
The two plans cost the same for 60 minutes of calls. And the two plans cost the same for 60 minutes of calls.
We can set the cost of the two plans equal to each other and solve for the number of minutes:
Plan A: $15 + $0.12x (where x is the number of minutes)
Plan B: $8 + $0.17x
$15 + $0.12x = $8 + $0.17x
Subtracting $8 from both sides:
$7 + $0.12x = $0.17x
Subtracting $0.12x from both sides:
$7 = -0.05x + $0.17x
Adding 0.05x to both sides:
$7 + 0.05x = $0.17x
Dividing both sides by 0.12:
x = (7 / 0.12) / (1 - 0.17/0.12) = 60 minutes
So the two plans cost the same for 60 minutes of calls. To find the cost, we can plug x = 60 into either equation:
Plan A: $15 + $0.12 x 60 = $15 + $7.20 = $22.20
Plan B: $8 + $0.17 x 60 = $8 + $10.20 = $18.20
So the two plans cost the same when there are 60 minutes of calls, and they both cost $18.20
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Complete Question
A telephone company offers two monthly plans. The a plan costs $15 plus $0. 12 additional for each minute of calls. Plan b costs $8 plus an additional 0.17 for each minute of calls For how many minutes of calls do the two plans cost the same? What is the cost at which two plans cost the same?
Kendra surveyed 100 people who own a dog or a cat, or both. Of those surveyed, 15 own both a dog and a cat, and the number of people who own a dog is four times the number of people who own a cat. How many people surveyed own a cat?
Answer:
17 people surveyed own a cat.
Step-by-step explanation:
Let d stand for dog, c stand for cat, and b stand for both. In total, d + c + b = 100 people. The number of people who own a dog is four times the number of people who own a cat, so d = 4c. In the problem, it's given that 15 people own both a dog and a cat. So, b can be replaced with 15. Now, d + c + 15 = 100. This system of equations can be solved by substitution.
d = 4c
d + c + 15 = 100
4c + c + 15 = 100
5c + 15 = 100
5c = 85
c = 17
Check:
The number of dog owners is 4 * 17, or 68.
68 + 17 + 15 = 100
Rewrite the expression in terms of ln 5 and ln 6.
ln(27000)
We can rewrite ln(27000) in terms of ln(5) and ln(6) as ln(27000) = 3ln(5) + 3ln(6) by using logarithmic property.
Why are logarithm qualities significant?Due of their connection to exponential functions, logarithmic functions are crucial. Logarithms can be used to examine exponential equations and the properties of exponential functions.
We can use the logarithmic property that says:
log_a(xⁿ) = n×log_a(x)
to break down 27000 into factors that involve 5 and 6.
First, we can write:
27000 = 5³× 6³
When we take the natural logarithm of both sides, we obtain:
ln(27000) = ln(5³ × 6³)
Using the property above, we can simplify this expression as:
ln(27000) = ln(5³) + ln(6³)
Using another logarithmic property that says:
log_a(bⁿ) = c×log_a(b)
we can further simplify the expression:
ln(27000) = 3ln(5) + 3ln(6)
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Using a ruler and a pair of compasses, construct a right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm.
How to construct the right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm.
Constructing the TriangleGiven:
Base = EF = 6 cmHypotenuse = ED=11 cmThe angle between EF and ED= 90֯To find:
Construct a right-angle triangle DEF
1. Draw the line segment2. Then mark the center of the line segment.3. In the compass set its width to 6 cm.4. Keep the pointer of the compass on the midpoint C and marc arcs on both sides of C5. Mark points E and F where the arc crosses the line.6. Again set the width of the compass to the length of the hypotenuse, which is 11 cm.7. Keep the pointer of the compass in E and draw an arc above midpoint C.8. Repeat the above step keeping the pointer on F.9. Label the point as D where the arcs cross.10. Join the points DE and DF with the scale.11. Thus, we get the right-angled triangle DEF of necessary measurements
The constructed right-angle triangle DEF is given below:
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Which statements are correct about the average rate of change for the function given in the table? Select all correct answers. Select 2 correct answer(s) Question 3 options: The rate of change is 3 over the interval 1 ≤ x ≤ 2. The rate of change is 3 over the interval 1 ≤ x ≤ 3. The rate of change is 6 over the interval 1 ≤ x ≤ 4. The rate of change is 6 over the interval 2 ≤ x ≤ 4. The rate of change is 5 over the interval 2 ≤ x ≤ 3.
The two correct statements are a. The rate of change is 3 over the interval 1 ≤ x ≤ 2 & The rate of change is 3 over the interval 1 ≤ x ≤ 3. And as well as The rate of change is 5 over the interval 2 ≤ x ≤ 3 is also correct statement.
How is the average rate determined?Divide the change in y-values by its change in x-values to determine the average rate of change. Identifying changes in measurable parameters as average speed or mean velocity calls for the knowledge of the average rate of change.
What exactly do average and instantaneous rates mean?The average rate is the concentration change over a selected time period. It matters when you take the measurements. The solution is to find the slopes of the line to the concentrations time versus curve at that location.
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One endpoint of MP is M(7, 3), and the midpoint is R(12, 3).
What are the coordinates of the other endpoint?
The coordinates of the other endpoint are (17, 3).
How to determine the coordinates of the other endpoint?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):
Midpoint R = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Next, we would determine the coordinate of MP with midpoint M at (7, 3) as follows;
12 = (7 + x₂)/2
24 = 7 + x₂
x₂ = 24 - 7
x₂ = 17.
For the other co-ordinate of P on line segment MP, we have:
3 = (3 + y₂)/2
6 = 3 + y₂
y₂ = 6 - 3
y₂= 3.
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A. Write the word " SOLUTION" below the point/s that will satisfy the linear inequality y ≥ x + 4.show you solution
pati din B ah
The solution that will satisfy the linear inequality y ≥ x + 4 include the following:
2. (-1, 4).
4. (0, 4).
How to determine the solution?In order to determine which ordered pairs are valid and true solutions based on the given linear inequality, we would have to test the given ordered pairs by substituting their values into the linear inequality as follows;
For ordered pair (0, 0), we have:
y ≥ x + 4
0 ≥ 0 + 4
0 ≥ 4 (False).
For ordered pair (-1, 4), we have:
y ≥ x + 4
4 ≥ -1 + 4
4 ≥ 3 (True).
For ordered pair (2, 3), we have:
y ≥ x + 4
3 ≥ 2 + 4
3 ≥ 6 (False).
For ordered pair (0, 4), we have:
y ≥ x + 4
4 ≥ 0 + 4
4 ≥ 4 (True).
For ordered pair (-1, 4), we have:
y ≥ x + 4
0 ≥ -1 + 4
0 ≥ 3 (False).
In this exercise, we would use an online graphing calculator to plot the given system of inequalities 2x + y < 1 and 4x - 3y ≥ 12 as shown on the number line attached below.
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3. (a) T= 3db Find the value of T' when a 4 and b = 5.
The value of the variable T is 60
What are algebraic expressions?These are described as expressions that are composed of coefficients, factors, constants, variables and terms.
These algebraic expressions are also identified by mathematical or arithmetic operations, such as;
AdditionSubtractionMultiplicationDivisionBracketParenthesesWe have;
T= 3db
Substitute the values
T = 3(4)(5)
expand
T = 60
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the state narcotics bureau must form a 5-member investigative team. if it has agents from which to choose, how many different possible teams can be formed?
the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).
Assuming that the state narcotics bureau has more than 5 agents from which to choose, the number of different possible teams that can be formed is equal to the number of combinations of 5 agents out of the total number of agents the bureau has. This can be calculated using the formula nCr (n choose r), where n is the total number of agents and r is the number of agents in each team, which in this case is 5.
Therefore, the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).
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I need Help i Have a C in my class
Answer:B
Step-by-step explanation:
R^2=Q^2-P^2
R^2=2025
R=45
Answer:
b) 45cm
Step-by-step explanation:
by pythagoras theorem:
R² = P² - Q²
R² = 53² - 28² = 2809 - 784
R² = 2025
R = √2025
R = 45cm
Hope this helps!
Sam is making a model of a stadium using a scale in which 2 centimeters equals 15 feet. If the model is 46.5 centimeters wide, what is the actual width of the stadium, in feet? your answer can be exact or rounded to two decimal places.
Answer:
348.75
Step-by-step explanation:
Find the probability of drawing a face card and then drawing the king of diamonds
without replacement.
Answer:
Step-by-step explanation:
the probability of drawing a face card=12/52
drawing the king of diamonds=1/52
Answer:
Probability of face is 12/52
WILL MARK BRANLIEST!!!
The sum of the 10th terms of the geometric progression is 1023
What is sum of the terms of GPThe sum of the terms of a geometric progression (GP) is a formula used to find the total of a series of numbers that are increasing or decreasing by a common ratio. A geometric progression is a sequence of numbers such that the ratio of any two consecutive terms is constant.
The formula for the sum of the n terms of a geometric progression with first term a and common ratio r is given by:
Sₙ = a(rⁿ - 1) / r - 1
where:
a is the first term of the progression
r is the common ratio
n is the number of terms in the progression
In the problem given;
a = 1, n = 10, r = 2
Using the formula above;
Sₙ = a(rⁿ - 1) / r - 1
Substituting the values into the formula
S₁₀ = 1(2¹⁰ - 1) / 2 - 1
S₁₀ = 1023
Learn more on sum of a geometric progression here;
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Keith and his friends are heading to the Thunder Beach water park. They plan to purchase the group package, which costs $78 for 6 people. That's $3 less per person than the normal cost for an individual. What is the normal cost for an individual?
