Find the first three terms of the geometric sequence using the explicit formula: 5(2)^(n - 1)6, 18, 545, 10, 204, 8, 1610, 20, 40
Answers
Given:
The explicit formula is,
\(5\cdot2^{\lparen n-1)}\)To find:
First three terms
Explanation:
Substituting n = 1 in the explicit formula, we get
\(\begin{gathered} 5\cdot2^{1-1}=5\cdot2^0 \\ =5 \end{gathered}\)Substituting n = 2 in the explicit formula, we get
\(\begin{gathered} 5\cdot2^{2-1}=5\cdot2^1 \\ =10 \end{gathered}\)Substituting n = 3 in the explicit formula, we get
\(\begin{gathered} 5\cdot2^{3-1}=5\cdot2^2 \\ =20 \end{gathered}\)Hence the first three terms of the geometric sequence are 5, 10, and 20.
Final answer:
The first three terms of the geometric sequence are 5, 10, and 20.
Related Questions
Three-fourths of the yard is covered with grass and one-fourth is used as a garden. The sprinkler could only water 1/5 of the yard, so the rest died. Use the model to find out how much of the grass died.
Answers
3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
Let's start by breaking down the information given:
- Three-fourths of the yard is covered with grass.
- One-fourth of the yard is used as a garden.
- The sprinkler could only water 1/5 of the yard.
To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.
Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.
The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.
To find the portion of the grass that died, we subtract the watered portion from the total grass area:
Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.
Simplifying, we get:
Portion of grass that died = 3/5.
Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
for more such question on grass visit
https://brainly.com/question/6204338
#SPJ8
The number line is a graph of the
Rational number
Real numbers
Integers
Answers
The number line is a graph of the Real numbers.
Rational Number And Real Numbers Integers ?Rational and irrational numbers are the two basic categories for real numbers. All fractions and integers are considered rational numbers. The set of integers consists of all whole numbers and negative integers. All natural numbers and zero are considered whole numbers. The only positive and negative whole numbers and natural numbers that fall under the category of integers are real numbers. Due to rational and irrational numbers, real numbers can incorporate fractions; however, integers cannot. Since integers are a collection of all positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity, they are all rational numbers. Decimals and fractions are not included in the set.
To learn more about Rational Number And Real Numbers refer :
https://brainly.com/question/22221295
#SPJ9
Carleigh, Inc., is a pork processor. Its plants, located in the Midwest, produce several products from a common process: sirloin roasts, chops, spare ribs, and the residual. The roasts, chops, and spare ribs are packaged, branded, and sold to supermarkets. The residual consists of organ meats and leftover pieces that are sold to sausage and hot dog processors. The joint costs for a typical week are as follows: Direct materials $84,500 Direct labor 29,000 Overhead 20,000 The revenues from each product are as follows: sirloin roasts, $68,000; chops, $71,000; spare ribs, $33,000; and residual, $9,800. Carleigh’s management has learned that certain organ meats are a prized delicacy in Asia. They are considering separating those from the residual and selling them abroad for $52,000. This would bring the value of the residual down to $2,650. In addition, the organ meats would need to be packaged and then air freighted to Asia. Further processing cost per week is estimated to be $27,500 (the cost of renting additional packaging equipment, purchasing materials, and hiring additional direct labor). Transportation cost would be $12,100 per week. Finally, resource spending would need to be expanded for other activities as well (purchasing, receiving, and internal shipping). The increase in resource spending for these activities is estimated to be $3,120 per week.
Answers
Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.
To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.
The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).
Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.
However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).
Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.
To learn more about incremental revenue, here
https://brainly.com/question/28167612
#SPJ1
Mrs. Collins is buying pumpkin doughnuts for the 7th grade teachers. One pack is $2.99 for 24 doughnuts. Another pack is $5.00 for 40 doughnuts. Which is the better deal?
Answers
Answer:
$5 for 40 donuts is the better deal
Step-by-step explanation:
24 / 2.99 = 8.03 $ / donut
40 / 5 = $8/ donut
8 < 8.03 so it is the better deal
HELLLP FAST
Mathamatics
Answers
Answer:
512 ft and 1,232 ft
Step-by-step explanation:
area is length x width
the pool's area can be calculated doing 32ft x 16ft
the area of the pool is 512 ft
the deck's area can be calculated doing 28ft x 44ft
the area of the deck is 1,232 ft
you're welcome<3
please answer this as well
Answers
Answer:
85 km
Step-by-step explanation:
to find this answer you must use the pythagorean theorem
this formula is basically a^2 + b^2 = c^2
so square the two sides that you have and thats the answer of the hypotenuse squared
68^2 + 51^2 = c^2
4624 + 2601 = 7225
then you must take 7225 to the square root
that is 85
Hello! Please help asap.
Answers
The line graph of the inequality is represented by an open circle at x = - 9 going towards negative infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The given inequality is x + 3 < - 6.
x < - 6 - 3.
x < - 9.
The line graph of the inequality will be represented as an open circle at
x = - 9 extending towards negative infinity because x is strictly smaller
than 9.
learn more about inequalities here :
https://brainly.com/question/28823603
#SPJ1
If cosΦ = 5/13
what is, sin Φ/sin Φ + cos Φ
Answers
Answer:
sin Φ/(sin Φ + cos Φ) = 12/17
Step-by-step explanation:
sin Φ = 12/13
then sin Φ + cos Φ = 12/13 + 5/13
= 17/13
So , sin Φ/(sin Φ + cos Φ) = 12/13 ÷ 17/13
= 12/13 × 13/17
= 12/17
graph h(x)=(x-1)^2-9
Answers
The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.
The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.
The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.
The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).
Based on this information, we can draw the following conclusions:
The graph will be a U-shaped curve with the vertex at (1, -9).
The vertex represents the minimum point of the parabola since it opens upward.
The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.
The graph will extend indefinitely in both directions.
To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.
Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.
for such more question on parabola
https://brainly.com/question/9201543
#SPJ8
We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
Answers
Answer: The answer to your question is C. Brainliest?
Step-by-step explanation:
For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:
2/12 = (2 x 5) / (12 x 5) = 10/60
For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:
2/15 = (2 x 4) / (15 x 4) = 8/60
Now, we can add the two fractions:
10/60 + 8/60 = 18/60
Simplifying this fraction by dividing both numerator and denominator by 6, we get:
18/60 = 3/10
Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.
The answer is C. 0.3.
paul is going to a college where tuition for one year is $14,200. He has a scholarship worth $1,500 and a grant worth $200. He earns $125 a week at this job how many weeks does paul need to work to pay 50% of the remaining tuition.
Answers
Answer:
50
Step-by-step explanation:
if you want an explanation just ask.
Solve the equation by finding the common denominator.
five and four sixths plus two and two eighths equals blank
three and forty four forty eighths
seven and six fourteenths
seven and eight forty eighths
seven and forty four forty eighths
Answers
Answer:
7 11/12 seven and 11 twelths
Step-by-step explanation:
5+2=7
find comon denomnimator
16/24 + 6/24 = 22/24
22/24 reduced to 11/12
put the 7 back in for 7 11/12
A rectangular room is 2 times as long as it is wide, and its perimeter is 48 meters. Find the dimension of the room.
Answers
Answer:
=16cm
Step-by-step explanation:
Let's read the problem carefully:
it says that one side of the rectangular room (let's call it b) is twice as long as the other (let's call it a), which in mathematical terms would be b = 2*a
It also says that the perimeter of the room is 48 meters, which means that (a + b)*2 = 48 => a + 2*a = 48/2 =>
3*a = 24 => a = 8, b = 16
Figure 1Figure 2Figure 3If this pattern continues, how many squares will be in the 10th figure?
Answers
Given:
Number of squares in figure 1 = 5
Number of squares in figure 2 = 8
Number of squares in figure 3 = 11
Let's find the number of squares in figure 10 if the pattern continues.
To solve this, let's apply the arithmetic progression formula:
a(n) = a1 + (n - 1)d
Where:
a1 = first term(squares in figure 1) = 5
n = number of terms = 10
d is the common difference.
To find the common difference, we have:
d = a2 - a1 = 8 - 5 = 3
Thus, the common difference is 3.
To find the number of squares in figure 10 (a10), we have:
a(n) = a1 + (n - 1)d
a(10) = 5 + (10 - 1)3
a(10) = 5 + (9)3
a(10) = 5 + 27
a(10) = 32
Therefore, the number of squares in figure 10 will be 32 squares .
ANSWER:
E. 32
The ratio of girls to boys on the school field trip is 6 to 7. There are 24 girls on the field trip. What is the total number of students on the field trip? NO LINKS!!!
A.28
B.52
C.4
D.13
Answers
Answer:
B.52 is the answer i think for the total number of kids
Please Help Based on the diagram, what is tan A? Enter your answer in the boxes.
Answers
tan A= a/b
the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone
Answers
Answer:
Step-by-step explanation:
V = 3.9V
I = 0.12A
Ohm's Law, V = IR
Rearranging Ohm's Law, R = V/I
R = 3.9/0.12 = 32.5Ω
I NEED HELP PLEASE, THANKS! :)
Answers
Answer: It would be the second one.
Step-by-step explanation:
Inverse means opposite.
Answer:
Option D
Step-by-step explanation:
This is an example of a two by two matrix. To determine if the inverse of R even exists, take the determinant of the matrix, as such -
( 0 * 3 ) - ( 0 * 4 ) = 0 * 0 = 0
As you can see, the determinant is 0, and if so, the inverse of R doesn't exist. Thus, \(R^-\) doesn't exist, as it is present as the inverse of R,
Solution = Option D
State the domain and range of the following function. {(6,-8), (9,3), (-3,5), (1,-6), (5,7)}
Answers
Answer:
Domain { -3,1,5,6,9}
Range { -8,-6,3,5,7}
Step-by-step explanation:
The domain is the inputs
Domain { 6,9,-3,1,5}
We normally put them in order from smallest to largest
Domain { -3,1,5,6,9}
The range is the outputs
Range { -8,-6,3,5,7}
The domain is the set of all x-coordinates.
So here, the domain is {6, 9, -3, 1, 5} which we
can write in ascending order as {-3, 1, 5, 6, 9}.
Note that the domain is usually written in ascending order.
In other words, from least to greatest.
Next, the range is the set of all y-coordinates.
So here, the range is {-8, 3, 5, -6, 7} which we
can write in ascending order as {-8, -6, 3, 5, 7}.
Like the domain, the range is usually written in ascending order.
20÷4×1-5² use pemdas to solve
Answers
Answer:
-20
Explanation:
Given the expression 20÷4×1-5²
We are going to use PEMDAS precedence to solve the expression
P is the parenthesis
E is the exponenent
= 20÷4×1-(5²)
= 20÷4×1-25
Folowed by Multiplication
= 20÷(4×1)-25
= 20÷4-25
Followed by Division
= (20÷4)-25
= 5 - 25
Then finally Subtraction
= -20
Hence the result of the expression is -20
What is the value of n?
2n – 1 = 5
Answers
Answer: n=3
Step-by-step explanation:
Think about it 2*3-1. 2x3=6 then minus 1 equals 5.
Answer:
n=3 thats the answer your welcome
what is the quotient of 60,976 divided by 74
Answers
Answer:
824
Step-by-step explanation:
60976÷74
The quotient is 824
In some countries, the electricity running to a home oscillates between –240 volts to 240 volts, with a frequency of 90 cycles per second.
Answers
Answer:
D
Step-by-step explanation:
Edg2020
HElPP
what is 232 if it's scaled down by a factor of 1/10
Answers
Answer:
23.2
Step-by-step explanation:
Scaling down by a factor of 1/10 is equal to dividing the number by 10.
So 232 getting scaled down by a factor of 1/10 is equivalent to 232/10 i.e. 23.2.
-67.2-61.5−67.2−61.5
Answers
Answer:
-257.4
Step-by-step explanation:
-257.4 trust meh
Answer:
-257.4
mark as brainliest
An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24 inches
The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.
Answers
The area of this blue glass is equal to 144π square inches.
How to calculate the area of this blue glass?In order to calculate the area of this blue glass, we would have to first determine its radius by using the formula for the circumference of a circle. Mathematically, the circumference of a circle can be calculated by using this formula:
C = 2πr
Where:
C represents the circumference of a circle.r represents the radius of a circle.Next, we would determine the radius of this blue glass as follows:
Radius, r = C/2π
Substituting the given parameters into the formula, we have;
Radius, r = 24π/2π
Radius, r = 12 meters.
Mathematically, the area of a circle can be calculated by using this formula:
Area of a circle = πr²
Area of a circle = π × 12²
Area of a circle = π × 144
Area of a circle = 144π square inches.
Read more on area of a circle here: https://brainly.com/question/6615211
#SPJ1
Complete Question:
An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24pi inches. The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.
a package of marbles contains 20 blue marbles, 38 red marbles, 48 green marbles, and 16 yellow marbles. which color of marbles can be divided evenly between 6 people?
Answers
the answer would be 48 green marbles
Step-by-step explanation:
48/6=8
So, each person would get 8 marbles each
Jacinta's softball warm up consists of 12 minutes of stretching, 18 minutes of fielding and 15 minutes of batting. What is the ratio of the time spent batting to the time spent fielding?
Answers
Hi!
With the given information, he spent 15 minutes batting and 18 minutes fielding.
A ratio can be represented as x : y where 'x' and 'y' are numbers. It says to make a ratio with the time spent batting to the time spent fielding, therefore the time spent batting would be 'x' and the time spent fielding would be 'y'.
Therefore:
\(15 : 18\)
Wait! We can simplify this. They are both divisible by 3.
15/3 = 5
18/3 = 6
Therefore:
\(5:6\)
Answer:
5:6
Step-by-step explanation:
Hello!
We know that Jacinta spends 15 minutes batting and 18 minutes fielding.
The ratio is written in order as a : b, given that the first value is the time spent batting, and the second value is the time spent fielding.
So the ratio is :
a : b15 : 183 * 5 : 3 * 6 (take out the greatest common factor)5 : 6Select the correct answer. Which is the correct solution to the expression 3 + 5^2? You can use a calculator to find the answer. A. 10 B. 13 C. 28 D. 64
Answers
The correct solution to the expression 3 + 5^2 is C. 28.
What is an expression?Mathematically, an expression is a combination of variables with numbers, values, or constants.
Mathematical or algebraic expressions use the mathematical operands like addition (+), subtraction (-), division (÷), multiplication (×), exponents (^), etc.
An algebraic expression does not go with the equal symbol (=), unlike an equation.
3 + 5^2
= 3 + 5 x 5
= 3 + 25
= 28
Thus, an evaluation of the algebraic expression 3 + 5^2 gives the solution as Option C.
Learn more about algebraic expressions at https://brainly.com/question/2164351.
#SPJ1
please answer need help
