6th terms of given geometric progression whose common ratio is 3/2 and first term is 4 is 243/8 using the farmula ar^(n-1).
What is a geometric sequence?
A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.
Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).
a = First term where
The common Ratio is r.
nth term = ar^(n-1)
6th terms ar^(6-1) = ar^5.
given is that r =3/2. a = 4.
6th term = 4 * (3/2)^5
= 4 * 3^5/2^5
=4*243/4*8
=243/8.
To know more about geometric progression here:
https://brainly.com/question/4853032
#SPJ4
What does r equal?
Answer: r = ________
For questions 8 and 9, determine if S could lie on the perpendicular bisector of QR with the
given coordinates.
8. Q(-5, -1), R(3, 7), S(4,-2)
9. Q(-5, 4), R(8. -3), S(-2. -5)
Yes S lies as the perpendicular bisector as asked in the question .
The distance is calculated with the use of distance formula,
d = √( x2 - x1 )² + ( y2 - y1 )²
Now , we are suppose to calculate the distance between the points S and R, given their values are ,
S=(4,-2) and
R=(3,7)
Using distance formula ,
d = √( 3 - 4 )² + ( 7 - (-2))²
d = √ 1 + 81
= √82
Now, the distance between Q and S can be found as ,
Q=(-5,-1)
S=(4,-2)
d = d = √(4 + 5)² + ( -2 + 1)²
d = √ 81 + 1
= √82
As the distance between the two ends of the segment and the point S is the same, the point S must lie on the perpendicular bisector of QR, according to the perpendicular bisector theorem.
For question number 9 the distance between Q and S are,
Q=(-5,4)
S=(-2,-5)
d = √( -2 -5)² + ( 5 - 4)²
d = √ 9 + 1
= √10
To learn more about distance
brainly.com/question/15172156
#SPJ4
isabella is setting up a cheese board for a neighborhood Super Bowl viewing party. the top of the cheese board is shaped like a triangle. the base of the triangle is 24 inches long, and its heigh is 20 inches. what is the area of the top of the cheese board
To find the area of a triangle, you can use the formula:
area = (base * height) / 2
In this case, the base of the triangle is 24 inches and the height is 20 inches, so plugging these values into the formula gives:
area = (24 * 20) / 2
area = 240 / 2
area = 120 square inches
So the area of the top of the cheese board is 120 square inches.
Consider the following 8 numbers, where one labelled x is unknown. 28, 39, 21, x , 33, 38, 2, 45 Given that the range of the numbers is 57, work out 2 values of x
The needed two values of x are: 59 and -12.
The difference between a sequence's maximum value and minimum value is referred to as the sequence's range.
A sequence's range is just a set that identifies the sequence. The set x1, x2, x3, and so forth is typically used to describe the range; it is also written as xn; n = 1, 2, 3,...
Given sequence of 8 numbers as: 28, 39, 21, x , 33, 38, 2, 45
Given range of above sequence: 57
Since the value x can assume any value, it have option to be minimum value in the sequence or maximum value in the sequence such that the range remains at 57.
Case 1: x as minimum value of given sequence:
If so, then the maximum value is 45. Then-
range = maximum value - minimum value
57 = 45 - x
x = -12
Case 2: x as maximum value of the given sequence:
If so, then the minimum value of the sequence is 2. Then-
range = maximum value - minimum value
57 = x - 2
x = 59
Thus, the needed two values of x are: 59 and -12.
To learn more about sequence range visit : brainly.com/question/24315217
#SPJ4
The table shows information about the masses of some dogs.
Work out the minimum number of dogs that could have a mass of
more than 27 kg.
Work out the maximum number of dogs that could have a mass of
more than 27 kg.
a) The minimum number of dogs that could have a mass of more than 27 kg is 4.
b) The maximum number of dogs that could have a mass of more than 27 kg is 17.
What is interval?
In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number one may imagine is a real number.
The given table shows information about the masses of some dogs.
a) As, the minimum number of dogs is needed to be found, then -
Assume all dogs present in the interval 20 to 40 have a mass of more than 27 kg so the minimum value out of 13 and 4 is 4.
b) As, the maximum number of dogs is needed to be found, then -
Assume all dogs present in the interval 20 to 40 have a mass of more than 27 kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17.
To learn more about interval from the given link
https://brainly.com/question/17097944
#SPJ1
In 2003 how many African American students attended a school with over 90% of its population being a minority?
According to ProPublica, from 1993 to 2011, there were almost 2.9 million black pupils enrolled in schools where at least 90% of the student body is made up of minorities.
Explain about the minority?The absence of a majority on the territory of a State is indicated by a minority. That essentially indicates that less than 50% of a nation's population belongs to one or more ethnic, religious, or linguistic groups.
According to Section 2(c) of the National Commission for Minorities Act of 1992, the following groups have been designated as minority communities: Muslims, Sikhs, Christians, Buddhists, Jain, and Zorastrians. According to the Census of 2011, minorities make up around 19.3% of the overall population of the nation.
The term "minority" in the 1990s typically refers to four significant racial and ethnic groups: African Americans, American Indians and Alaska Natives, Asians and Pacific Islanders, and Hispanics.
To learn more about population refer to:
https://brainly.com/question/25630111
#SPJ4
What is the Pythagorean triplet of 16?
The Pythagorean triplet of 16 is (8, 15, 17).
This can be calculated using the Pythagorean theorem, which states that in any right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Therefore, given a number, we can find a Pythagorean triplet by calculating the squares of the two legs and then finding the hypotenuse.
Formula:
a² + b² = c²
Find the square of the number.
16² = 256
Subtract the square from the number to get one leg of the triangle.
16 - 256 = -240
Take the square root of the result.
√(-240) = 8
Add the square to the number to get the other leg of the triangle.
256 + 16 = 272
Take the square root of the result.
√(272) = 15
Add the two legs together to get the hypotenuse.
8 + 15 = 23
Take the square of the result.
23² = 529
Subtract the sum of the two legs from the hypotenuse.
529 - 23 = 506
Take the square root of the result.
√(506) = 17
Therefore, the Pythagorean triplet of 16 is (8, 15, 17).
Learn more about Pythagorean triplet here:
https://brainly.com/question/24924762
#SPJ4
The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards, how much fencing does the city need to surround the park?
The length of the fencing that the city needs to surround the park will be 380.50 yards.
What is the area and perimeter of the rectangle?Assume L is the length and W is the width. Then the area is given as,
A = L × W
And the perimeter is given as,
P = 2(L + W)
The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards. Then the length of the rectangular park is calculated as,
8925 = L × 84
L = 106.25 years
Then the length of the fencing that the city needs to surround the park will be given as,
P = 2(106.25 + 84)
P = 2 × 190.25
P = 380.5 yards
The length of the fencing that the city needs to surround the park will be 380.50 yards.
More about the area and perimeter of the rectangle link is given below.
https://brainly.com/question/16572231
#SPJ1
Ana and Darryl answered 80 calls. Ana answered 4 times as many as Darryl. How many calls did ana answer
There were 64 calls that Anna answered in this algebra question,
What is Answered calls?
Total engaged calls, another name for answered calls, is a measurement of all incoming calls that were handled by an agent during regular business hours.
Solution:
If Ana answers more calls than Darryl does, then let D be the number of calls Darryl Answered.
A + D = 80
A = 4D
4D + D = 80
5D = 80
D = 80 / 5
= 16
To know more about algebra visit:-
brainly.com/question/24875240
#SPJ4
According to the algebra, Ana answered 16 calls,
What is algebra, exactly?The area of mathematics known as algebra is used to represent situations or problems using mathematical expressions. In algebra, we use numbers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine numbers with variables like x, y, and z.
Solution:
Let D be the number of calls Darryl answered if Ana answers more calls than he does.
A + D = 80
A = 4D
4D + D = 80
5D = 80
D = 80 / 5
= 16
To know more about algebra visit:-
brainly.com/question/24875240
#SPJ4
Two sectors of a circle of radius $12$ overlap as shown, with $P$ and $R$ as the centers of the respective circles. Determine the area of the shaded region.
The area of the shaded region is 26.088 sq units.
A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced out from the center.
The radius of a circle is measured from the center to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.
Area of a 60-degree sector of a circle with radius 12 = 60/360 pi 12^2 Since, there are two of these minus the area of equilateral triangle = sqrt3 /4 12^2 = 60/360 pi 12^2 * 2 - sqrt3 /4 12^2 *2 = 26.088 sq units
Thus, the area of the shaded region is 26.088 sq units.
To know more about circles visit: brainly.com/question/11833983
#SPJ4
Julie wants to check out a book from her local library, but it is not available. Julie decides to visit the library in Lanberry, 15 kilometers away, to see if that location has a copy of the book. On a map, the two libraries are 25 centimeters apart. What is the scale of the map?
The easiest way to find this is to use the library's catalog. Depending on the integrated library system (or ILS) the library subscribes to, the process might be slightly different. Generally, you can use a catalog system on a computer to search by title, author, subject, and more.
SOME ONE HELP PLSSSS
which number line represents all of the values of x for the equation x2=100?
(picture below)
Are 6x - x + 5 and 6+5 equivalent?
Answer:
no
Step-by-step explanation:
the one equation has variables and numbers go in for the variable and the other equation just equals 11
explanation with steps
Answer:
x = 40° , y = 140° z = 10°
Step-by-step explanation:
the sum of the 3 angles in a triangle is 180° , then
x + 60° + 80° = 180°
x + 140° = 180° ( subtract 140° from both sides )
x = 40°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
y is an exterior angle of the triangle , then
y = 60° + 80° = 140°
x is also an exterior angle , then
30° + z = x
30° + z = 40° ( subtract 30° from both sides )
z = 10°
What is the length of the missing leg? If necessary, round to the nearest tenth.
The length of the other leg is 65 cm
How to find the length of the other legFrom the question, we have the following parameters that can be used in our computation:
Leg 1 = a
Leg 2 = 72 cm
Hypotenuse = 97 cm
The length of the hypotenuse of the right triangle can then be calculated using
Hypotenuse² = Leg 1² + Leg 2²
Substitute the known values in the above equation, so, we have the following representation
97² = a² + 72²
So, we have
a² = 97² - 72²
Evaluate
a² = 4225
Take the square roots
a = 65
Hence, the other leg is 65 cm
Read more about right triangle at
brainly.com/question/1248322
#SPJ1
Please help me!! Find the area of the circle:)
Answer:
2.46
Step-by-step explanation:
Answer:
[tex]A=283.528736986[/tex]
Step-by-step explanation:
The formula for the area of a circle is:
[tex]A=\pi \times r^2[/tex]
Remember that the radius is half the diameter, we are given the diameter which is 19, which means we need to find the radius:
[tex]d=19[/tex]
[tex]19\times\frac{1}{2} =9.5[/tex]
[tex]r=9.5[/tex]
Substitute and solve:
[tex]A=\pi \times9.5^2[/tex]
[tex]9.5^2=9.5\times9.5=90.25[/tex]
[tex]\pi \times90.25=283.528736986[/tex]
[tex]A=283.528736986[/tex]
Since the question doesn't say to round the area is "283.528736986."
Hope this helps.
If m= 2, n=3, and p= -1, then find the value of : 2mn4 – 15m2n + p
In Full Details!! As Soon As Possible
Answer:
-131
Step-by-step explanation:
2×2×3×4-15×2×2×3+-1
48-179
=-131
Marcy made a lane change when. A car was in her side mirror blind spot. She missed the car but immediately crashed into the car ahead of her, causing damage. After Marcy filed the insurance claim, she was notified that her premium for full insurance would increase by 35% what is Marcy new yearly premium if her premium before the accident was $2,140
Peter insurance company is raising his rates after he files a claim . He pays $75 per month and his insurance is set to increase by 30% . What will Peters new monthly premium be ?
Kevin purchases a truck for $35,000 with a down payment of $4,300 . The monthly payment factor is 0.01933. What is the monthly payment for the truck ?
On solving the provided question, we can say that By percentage, the amount that will be covered in the insurance = $749
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a the fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
By percentage.,
35% 0f 2140 =
35/100 X 2140 = 0.35*2140 = $749
the amount that will be covered in the insurance = $749
To know more about percentage visit:
https://brainly.com/question/28269290
#SPJ1
solve the inequality and explain how
Answer:
B. (see attached)
Step-by-step explanation:
You want the solution and graph of the inequality |x+3| > 2.
SolutionThe inequality resolves to two inequalities with different domain definitions:
|x +3| > 2
When the argument is negative, (x+3) < 0, this is ...
-(x +3) > 2
-x -3 > 2 . . . . . . eliminate parentheses
x +3 < -2 . . . . . . multiply by -1
x < -5 . . . . . . . . . subtract 3; consistent with the domain definition
When the argument is positive, (x+3) > 0, this is ...
x +3 > 2
x > -1 . . . . . . . . subtract 3
-1 < x . . . . . . . . same thing using the < symbol
These differing solution sets do not overlap, but elements of either set are solutions to the inequality. The appropriate conjunction is "OR":
solution: x < -5 or -1 < x
The graph is attached.
__
Additional comment
We like to use the < or ≤ symbols when expressing the solution to an inequality. That way, the relation of the variable to the boundary value is the same as its relation on a number line. Solution values are left of -5 or right of -1:
x < -5 or -1 < x
It helps provide a check that the graph is properly drawn.
The inequality can be rewritten as ...
|x -(-3)| > 2
which can be interpreted as saying the positive distance from x to -3 is more than 2. This tells you the graph will have two disjoint branches, and the appropriate conjunction is OR.
If the problem were different, and the inequality were ...
|x -(-3)| < 2
it would be telling you the solution values have a distance less than 2 from -3. They will be in one continuous band from -5 to -1, so the appropriate conjunction is AND. The solution in this case is usually written as a compound inequality with no conjunction: -5 < x < -1. (Note the use of < symbols puts the variable value in the middle, between the boundary values, as in graph D.)
pls solve the question (i will mark u the brainliest)
Step-by-step explanation:
May be (p³)³ would be the answer!!!
BRAINLY ME PLEASE IF HELPFUL!!!
Which equation with exponential expression are true?
Answer: B,D
Step-by-step explanation:
Aaliyah and her friends had a movie marathon. They started watching movies at 1:29 P.M. The movie marathon ended at 9:04 P.M. How long did the movie marathon last?
Answer:
7 hours 35 minutes
Step-by-step explanation:
You want to know the length of the time period between 1:29 pm and 9:04 pm.
HoursRemembering that an hour is 60 minutes, we can rewrite the ending time before we subtract the beginning time.
9:04 -1:29
= 8:64 -1:29 = (8-1):(64-29) = 7:35
The movie marathon lasted 7 hours 35 minutes.
How do the faces of
a three-dimensional figure determine che
two-dimensional shapes created by slicing
the figure?
The process of the faces of a three-dimensional figure determine two-dimensional shapes created by slicing the figure is explained below.
The term three dimensional figure is defined as solid shapes or figures that have three dimensions.
Basically these kind of shapes has length, width and height are the dimensions of 3D shapes and the common names of these shapes are cube, cuboid, cone, cylinder and sphere.
Where as the two dimensional figure is defined as horizontal and vertical axes that is x-axis and y-axis) and it is also known as 2d shapes are flat figures that have only length and width. And thus shapes do not have thickness or height.
To know more about dimensions here.
https://brainly.com/question/15225905
#SPJ4
Solve the following problems using completing the Square
Martha and Miguel volunteered in a Tree Planting Program offered by the school. They also donated packs of seeds for the program. The number of Martha's seeds is represented as 2x-3 packs while Miguel's seeds is twice the number of Martha's seeds. If the product of Martha and Miguel's Pack of seed is 50, how many packs of seeds Martha and Miguel donated?
[Write it on paper please ]
Using factorization method to solve the quadratic equation, the number of seed Martha and Miguel donated are 5 and 10 respectively
What is Quadratic EquationA quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants, and x is an unknown variable. The solution to such an equation is a value of x that will make the equation true.
To determine the number of seeds they donated, we have to write two equations and solve.
data;
Martha = 2x - 3Miguel = 2[2x - 3] = 4x - 6The product of the seeds is (2x - 3)(4x - 6) = 8x² - 24x + 18
This can be written as
8x² - 24x + 18 = 50
Solving the quadratic equation;
8x² - 24x + 18 - 50 = 0
8x² - 24x - 32 = 0
Using factorization method;
8(x - 4)(x + 1) = 0
x - 4 = 0, x = 4
x + 1 = 0, x = -1
x = 4, x = -1
The number of packs Martha donated is
Martha = 2x - 3 = 2(4) - 3 = 5
The number of packs Miguel donated is
Miguel = 2 * 5 = 10
Learn more on quadratic equation here;
https://brainly.com/question/1214333
#SPJ1
what is the leading coefficient of this polynomial? y=5x² + 3x^6 -10x-8,
Explanation:
The equation y = 5x^2+3x^6-10x-8 is not in standard form.
Why not? Because the term with the largest exponent (6) isn't listed first.
The standard form would be y = 3x^6+5x^2-10x-8; note the exponents decrease (6, 2, 1, then 0).
After the polynomial is in standard form, we can read off the leading coefficient to be 3. This is the coefficient of the first term 3x^6.
Side note: The degree is 6 as it's the largest exponent.
URGENT! HOMEWORK DUE TOMORROW MORNING!
Miguel has three times as many dimes as he has quarters. He has as many nickels as he has dimes and quarters combined. The total amount of money he has is $3.00. How many of each coin does Miguel have?
After solving the algebraic equation, Miguel has 4 quarters, 12 dimes and 16 nickels.
What is algebra?
One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.
The number of quarters is taken to be x, then the number of dimes will be 3x, and the number of nickels will be 3x + x = 4x
$3.00 when converted to cents is 300 cents.
The value of nickels is 5 x 4x=20x.
The value of dimes is 10 x 3x=30x.
The value of quarters is 25x.
As the total value of money Miguel has is 300 cents, then the algebraic equation will be -
20x + 30x + 25x = 300
Solve to get the value of x -
75x = 300
x = 4
Therefore, the amount of quarters is x = 4 quarters.
The amount of dimes is x = 3x = 3 x 4 = 12 dimes.
The amount of nickels is 4x = 4 x 4 = 16 nickels.
To learn more about algebra from the given link
https://brainly.com/question/22399890
#SPJ1
Volleyball practice is h hours long. Debbie had 3 volleyball practices last week. Choose the expression that shows the number of hours of practice.
The number of hours of practice is 3 x h or 3h.
What is the number of hours of practice?In mathematics, an expression is a sentence that contains at least one number or variable. Additionally, an expression consists of at least one mathematical operation. There is no equal to sign in an expression.
Given:
Volleyball practice is h hours long. Debbie had 3 volleyball practices last week.
Multiply the number of hours for each practice by the total number of practice to get the expression for the number of practice hours.
The mathematical operation known as multiplication is used to calculate the sum of two or more numbers.
Number of hours of practice
= hours of practice x number of practice
= 3 x h
learn more about Expression here:
https://brainly.com/question/14083225
#SPJ1
A store that specializes in shipping packages reports that the distribution of packages shipped during the winter holidays is normally distributed with a mean of 4. 5 pounds with a standard deviation of 1. 8 pounds
What is the probability that two randomly selected packages are both more than 4. 5 pounds? (assume the packages are independent of each other)
a. ) 0. 5
b. ) 1
c. ) 0
d. ) 0. 25
The correct option is option (d).
To solve this problem, we need to find the probability that two randomly selected packages are both more than 4.5 pounds. Since the distribution is normal, we can use the standard normal distribution table to find the probability.
The first step is to standardize the weight of the packages by subtracting the mean from the weight and dividing it by the standard deviation. The weight of 4.5 pounds is the mean, so the standardized weight is (4.5 - 4.5) / 1.8 = 0.
The probability that a package weighs more than 4.5 pounds is the same as the probability that a standardized package weighs more than 0. This probability is equal to 1 - P(Z < 0) , where Z is the standardized weight.
Using a standard normal distribution table, we find that P(Z < 0) = 0.5. Therefore, the probability that a package weighs more than 4.5 pounds is 1 - 0.5 = 0.5.
Since the two packages are independent, we can find the probability that both packages are more than 4.5 pounds by multiplying the probability of one package being more than 4.5 pounds by itself. So, the probability that two randomly selected packages are both more than 4.5 pounds is 0.5 * 0.5 = 0.25.
In conclusion, the probability that two randomly selected packages are both more than 4.5 pounds is 0.25
Read more about Probability:
https://brainly.com/question/11034287
#SPJ4
A square dining room table has a perimeter of (12x "-40)" feet.Which expression represents the side length of the table (in feet)
The equation that represents the length of the square dining room in feet is (1/4)x - 5/6.
What are the dimensions of a square?The area of a square is a product of it's any two sides or a product of diagonals divided by two. If a side has a length 'a' then the diagonal is a√2.
The perimeter of a square is the sum of the lengths of all the sides.
We know the perimeter of a square is 4×side.
We also know that 1 foot is equal 12 inches.
Given, A square dining room table has a perimeter of (12x - 40)".
Now if we factor out a 4 we'll have the side inside the bracket which is,
4(3x - 10)'', This is in inches to convert it to feet we have to divide what is inside the bracket by 12 which is,
= (3/12)x - 10/12 feet.
= (1/4)x - 5/6 feet.
learn more about squares here :
https://brainly.com/question/28776767
#SPJ1
The temperature of a city at sunset was -2°F. Overnight, the temperature decreased by 12°F. What was the lowest temperature overnight in that city?
Answer:-14°F
Step-by-step explanation:
-2°F -12°F is basically the same as 12°F+2°F which is 14°F and then you inverse it