Answer:
1536
Step-by-step explanation:
Given : A geometric sequence 0.75, 1.5, 3, 6, . . .
To Find:Find the 12th term
Solution:
0.75, 1.5, 3, 6, . . .
First term =a = 0.75
Common difference = [tex]r = \frac{a_3}{a_2} =\frac{a_2}{a_1}=\frac{1.5}{0.75}=\frac{3}{1.5}=2[/tex]
nth term of G.P. = [tex]a_n=a r^{n-1}[/tex]
Where a = First term = 0.75
r = common difference = 2
Substitute n = 12
[tex]a_{12}= 0.75 (2)^{12-1}[/tex]
[tex]a_{12}= 0.75 (2)^{11}[/tex]
[tex]a_{12}= 1536[/tex]
Hence the 12th term in the geometric sequence. 0.75, 1.5, 3, 6, . . . is 1536.
What is the sum of this geometric series?5 + 25 + 125 + 625 + 3,125 + 15,625?
The sum of the given geometric series (5 + 25 + 125 + 625 + 3,125 + 15,625) is -78120.
Explanation:The question is asking for the sum of a geometric series. In a geometric series, each term is multiplied by a common ratio to get the next term. In this case, the first term (a) is 5 and the common ratio (r) is 5 (since we get each term by multiplying the previous one by 5).
The sum (S) of the first n terms of a geometric series can be calculated using the formula S = a * (1 - r^n) / (1 - r). In this case, there are n=6 terms in the series, so we will plug these values into the formula.
Therefore, S = 5 * (1 - 5^6) / (1 - 5). So, the sum of this geometric series is -78120.
Learn more about Geometric Series here:https://brainly.com/question/30264021
#SPJ3
Use the x-intercept method to find all real solutions of the equation. x^3-10x^2+29x+-20=0
Answer:
C. is the answer 1,4 or 5
Step-by-step explanation:
the fish aquarium holds 150 liters of water. How many milliliters dose the aquarium holds?
The scale drawing of a baby blanket has the dimensions of 6 inches by 10 inches. the dimensions of the actual baby blanket are 30 inches by 50 inches. what is the scale factor that is used to make the drawing?
Max recorded the math scores of five of his classmates in the table. What is the range of their test scores? 16 24 88 89
Math Scores98761008882
Answer:
B. 24
Step-by-step explanation:
We have been given a data set that represents the math scores of five of Max's classmates. We are asked to find the range of the given data set.
Math score: 98, 76, 100, 88, 82.
Since we know range is the difference between the largest and smallest values of the data set.
[tex]\text{Range}=\text{The largest value of data set - The smallest value of data set}[/tex]
We can see that largest score is 100 and smallest score is 76.
[tex]\text{Range}=100-76[/tex]
[tex]\text{Range}=24[/tex]
Therefore, the range of the given test scores is 24 and option B is the correct choice.
Help me..... please.....
4/10= heeeeeeellllllppppppppppppp
On a island, the population of flamingos is currently 400, and this population doubles every 3 years. Which of the following functions will correctly model this situation? Assume t is measured in years.
F f(t)= 2 x 400^3t
G f(t)= 400 x 3^t/2
H f(t)= 400 x 2^t/3
J f(t)= 400 x 2^3t
Find three consecutive odd integers such that six times the second decreased by twice the first is equal to twenty more than the sum of the second and third
Two runners ran as a team in a 5,000-m relay race. the first runner ran 500 m farther than the second runner. how many meters did each run?
The height reached by amal's rocket was 1/4 of the height reached by min's rocket. Amal's rocket REAched a height of 15 meters. Which equation could be used to find the height reached by min's rocket
The height reached by Min's rocket could be found by using the equation (1/4)*h = 15, where 'h' denotes the height of Min's rocket. Amal's rocket height is 1/4 of the height of Min's rocket.
Explanation:In the question, it is stated that the height of Amal's rocket is 1/4 of the height reached by Min's rocket. Since the height attained by Amal's rocket is given as 15 meters, we can establish an equation to find the height reached by Min's rocket. Let's denote the height of Min's rocket as h. We know that 1/4 of Min's rocket height equals Amal's rocket height. So it can be represented as:
(1/4)*h = 15
By solving this equation, we can find the height attained by Min's rocket.
Learn more about Height of Rockets here:https://brainly.com/question/29070000
#SPJ12
The price of an iteam has been reduced by 75%. The original price was $45. What is the price of the item now?
The new price of the item after 75% reduction is $11.25.
To find the price of the item after a 75% reduction:
Calculate the amount of the reduction: 75% of $45 is $33.75.
Subtract the reduction from the original price: $45 - $33.75 = $11.25.
During a dig, an archaeological team starts at an elevation of −512 feet. At a rate of 234 feet per hour, the team digs deeper into the surface for 312 hours. For the next 412 hours, the team digs at a rate of 1512 feet per hour. Then the team quits for the day.How many feet did the archaeological team dig after 312 hours? feetWhat was the team's elevation at the end of the day?
The world's biggest rubber band ball has a surface area of 27648. Using 3 as pi for both surface area and volume, estimate the volume of the ball.
Question 5 options:
358966
788428
442368
257854
Which mesurments are greater than 130 fluid ounces 5 quarts, 16 cups, , 9 pints, 2 gallons, or 1 gallon i am not good with math ty?
Answer:
5 quarts , 9 pints, 2 gallons
Step-by-step explanation:
Si un ángulo de un rombo mide 39 grados , ¿ cuánto miden los demás ?
Please help with easy math problem.
What is the value of d to the nearest tenth?
A. 11.2
B. 13.8
C. 16.7
D. 17.5
Answer:
Option B is correct
d = 13.8
Step-by-step explanation:
Definition:
If two secant segments are drawn to a circle from the same external point(P),
the product of the length of one secant segment and its external part is equal to product of the length of the other secant segment and its external part.
As per the statement:
Labelled the diagram:
then;
PA = 14 units , AB = 20 units, PC = 16 units and CD = d units
Find PB and PD:
PB = 14+20 = 34 units
PD = 16+d units
then by above definition we have;
[tex]PA \cdot PB = PC \cdot PD[/tex]
⇒[tex]14 \cdot 34 = 16 \cdot (16+d)[/tex]
⇒[tex]476=16 \cdot (16+d)[/tex]
Divide both sides by 16 we have;
[tex]29.75 = 16+d[/tex]
Subtract 16 from both sides we have;
13.75 = d
or
d = 13.75 units
Therefore, the value of d to the nearest tenth is, 13.8
given that A=43 degrees , B=82 degrees and c=28, solve triangle ABC. Round to the nearest hundredth. A) C= 93 degrees , b= 33.8 , a= 23.3 B) C= 55 degrees , b= 33.8 , a= 23.3 C) C= 55 degrees , b= 23.3 , a= 33.8 D) C= 93 degrees , b= 23.3 , a= 33.8
Toss a coin three times. what is the probability of getting a head on the first toss
How many ways are there to choose a committee of 7 people from a group of 10 people?
720
120
840
5040
Which statement provides a counterexample to the following faulty definition? A square is a figure with four congruent sides. Question 8 options: A six-sided figure can have four sides congruent. A rectangle has four sides. Some triangles have all sides congruent. A square has four congruent angles.
Answer:
1. The six-sided figure can have 4 sides congruent but is not a square.
Step-by-step explanation:
We are given the statement,
'A square is a figure with four congruent sides'.
It is required to find the statement which is the counter-example for the above statement.
For the counter-example, the statement should hold:
1. The figure has 4 congruent sides
2. The figure is not a square.
According to the options, we see that,
The six-sided figure can have 4 sides congruent but is not a square.
Thus, option 1 is true.
A counterexample to the faulty definition will be that A six-sided figure can have four sides congruent.
It should be noted that a rectangle has four sides while there are some triangles that have all their sides congruent and a square has four congruent angles as well.The statement that a six-sided figure can have four sides congruent is the correct option.In conclusion, the correct option is A.
Read related link on:
https://brainly.com/question/3452116
a photographer's camera sits on a tripod that is 1.8 m above the ground. The base of the tripod is 44 m from the base of a tree. The photographer's spot woodpecker in a tree at a 39 degree angle of elevation. To the nearest tenth of a meter, how high above the ground is the woodpecker? A.37.4m B.36.0m C.35.6m D.34.2m
a total of 45mg of medication is dissolved in a solution containing 300ml. if 20ml of the solution are administered to a patient, how many milligrams of medication does the patient receive
A and B have coordinates –2 and 10 on a number line. If it is marked off into 10 congruent segments, which one of the following coordinates is NOT one of the marked points? a. –0.8 c. 1.6 b. –0.6 d. 2.8
Answer:
b. - 0.6
Step-by-step explanation:
Since, the total coordinates from -2 to 10 = 10 - (-2) = 10 + 2 = 12,
Also, if it is divided into 10 congruent segments,
Then, the length of each segment = [tex]\frac{12}{10}[/tex] = 1.2,
That is, the difference between the marked point is 1.2,
So, the marked points from -2 to 10 are,
-2, -0.8, 0.4, 1.6, 2.8, 4.0, 5.2, 6.4, 7.6, 8.8, 10,
Hence, except -0.6 all points are the marked points,
Option b is correct.
Find the arc length of a central angle of 7pi/3 in a circle whose radius is 3 inches
To calculate the arc length, multiply the angle in radians (7pi/3) by the radius (3 inches). After simplifying, the arc length for this circle is 21 inches.
To find the arc length for a central angle of 7pi/3 radians in a circle with a radius of 3 inches, we use the formula for arc length, which is the product of the central angle in radians and the radius of the circle.
The formula for the arc length (As) is given by:
As = r times theta
Where:
r is the radius of the circle.
theta is the central angle in radians.
Substituting the given values, we get:
As = 3 inches times 7pi/3 radians
The 7pi/3 terms cancel out the pi/3 from the angle and /3 from the radius, giving us:
As = 3 times 7 inches
The arc length is therefore 21 inches.
To babysit one child, Fernando charges $10 to drive to the appointment plus $4 per hour. He saves 30% of the total amount he earns. Brenna charges $6 per hour and saves 25% of the total amount she earns. Which equation can be used to determine the number of hours, h, after which Fernando and Brenna will have saved the same amount of money?
Answer:
(C) 0.3(10 + 4h) = 0.25(6h)
Plz press the THANKS button.
Find an explicit rule for the nth term of the sequence.
2, -8, 32, -128, ...
Find the number of sides when:
a. The measure of each interior angle of a regular polygon is 156 degrees.
b. The measure of each exterior angle of a polygon is 36 degrees.
Final answer:
To find the number of sides of a polygon, one can use the relations between interior or exterior angles and the number of sides. For an interior angle of 156 degrees, the polygon has 15 sides. For an exterior angle of 36 degrees, the polygon has 10 sides.
Explanation:
The question is about finding the number of sides of a polygon based on the interior and exterior angles. For part (a), where the measure of each interior angle of a regular polygon is 156 degrees, and for part (b), where the measure of each exterior angle is 36 degrees, we can use specific formulas to find the number of sides.
Part A: Interior Angle 156 Degrees
For a regular polygon, the formula connecting the number of sides (n) to an interior angle (A) is A = [(n-2) * 180] / n. Solving for n when A = 156 degrees gives us:
156 = [(n-2) * 180] / n
Solving this equation yields n = 15, meaning the polygon has 15 sides.
Part B: Exterior Angle 36 Degrees
The measure of each exterior angle of a polygon (E) is related to the number of sides (n) by the formula E = 360 / n. When E = 36 degrees:
36 = 360 / n
Solving for n gives us n = 10. Therefore, the polygon has 10 sides.
Can you please solve this equation?
A rectangular prism measures 6.7 in. by 4.2 in. by 2.5 in. Round each measure to the nearest whole number to estimate the volume.