for a given geometric sequence the seventh term is equal to 19/81 and the 12th term is equal to "-57" find the value of the 15th term
Answers
For the given geometric sequence the seventh term is equal to 19/81 and the 12th term is equal to "-57" the value of the 15th term is 1539.
What is a geometric sequence?
One particular sort of sequence is a geometric sequence. It is a sequence in which each term, with the exception of the first, is multiplied by a fixed integer to obtain the following term. The common ratio must be multiplied by the current term in the geometric sequence to obtain the next term, and the common ratio must be divided by the current term to obtain the previous term.
Solution Explained:
We know, a7 = 19/81, a12 = -57
So, ar^7 = 19/81 and ar^12 = -57 (r= common ratio)
Since r< a15 < 0 [the sign alternate]
Ignoring the signs,
r^12 = r^7 X r^5
57 = 19/81 X r^5
(57 X 81)/19 = r^5
243 = r^5
r = the fifth ratio of 243 = 3
therefore, r = -3
So, a15 = a12 X r^3
= -57 X (-3)^3
= 1539
Hence, the value of the 15th term is 1539.
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Related Questions
using 0-9 as digits,
which 2 digit number has order rotational of 2
which 3 digit number also has order rotational of 2
Answers
The value of 2 digit number has order rotational of 2 is, 16
And, The value of 3 digit number has order rotational of 2 is, 931
Now, For a two-digit number with an order rotational of 2, it means that if you flip the digits, you get a different but still valid number.
Hence, There are a few such numbers, but one example is 16 which becomes 61 when you flip the digits.
And, For a three-digit number with an order rotational of 2, it means that if you rotate the digits, you get a different but still valid number.
And, There are also a few such numbers, but one example is 319 which becomes 931 when you rotate the digits.
Thus, The value of 2 digit number has order rotational of 2 is, 16
And, The value of 3 digit number has order rotational of 2 is, 931
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what is a equation of a line that passes through (7,10) and it's perpendicular to y = 1/2x - 9
Answers
Explanation:
A perpendicular line has a reciprocal and opposite slope. The slope of the given line is 1/2, its reciprocal is 2 and its opposite -2.
We'll have an equation like this:
\(y=-2x+b\)To find the y-intercept b we have to use the point. Replace x = 7, y = 10 and solve for b:
\(\begin{gathered} 10=-2\cdot7+b \\ 10=-14+b \\ b=10+14 \\ b=24 \end{gathered}\)Answer:
The equation is: y = -2x + 24
Housing prices in a small town are normally distributed with a mean of
131,000 and a standard deviation of 8,000
. Use the empirical rule to complete the following statement.
Answers
About 95% of the housing Prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)
Given that housing prices in a small town are normally distributed with a mean of µ. We are to use the empirical rule to complete the following statement.
The empirical rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean,
and approximately 99.7% of the data falls within three standard deviations of the mean.Since we do not have information about the standard deviation of the housing prices,
we cannot provide exact values for the empirical rule. However, we can make some general statements:
About 68% of the housing prices are between (µ - σ) and (µ + σ).
About 95% of the housing prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)
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Translate the sentence into an inequality:
“The sum of 9 and c is greater than -21.”
(will mark brainliest)
Answers
Answer:
9 + c > -21
Step-by-step explanation:
Sum means addition and it is greater than -21 so we get: 9 + c > -21
sum means 9 and c are added, but since c is a variable and not a number, it is 9+c. Then, it say that 9+c is greater than (>) -21.
I need help finding f(-2)
Answers
Answer:
f(-2) = -1
Step-by-step explanation:
f(-2) means find the output value when the input value is -2
The output value is -1 when the input is -2
Which runs faster: a cheetah that can run 60 feet in 6 seconds or a gazelle that can run 100 feet in 10 seconds?
They run at the same speed.
A gazelle runs faster.
A cheetah runs faster.
Answers
Answer:
They run at the same speed
Step-by-step explanation:
First, you have to find a way seeing how fast both animals run in the same amount of time. You can find out how fast they both run in one second.
60 feet in 6 seconds is how many feet in one second? Well, you can do 60/6 (60 divided by 6) and you will see that in one second, the cheetah can run 10 feet
100 feet in 10 seconds is how many feet in one second? Same thing, you can do 100/10 (100 divided by 10) and you will see that the gazelle can run 10 feet in one second.
Finally, you compare the two answers from the two animals. For the cheetah, we learned that it can run 10 feet in one second, and for the gazelle, we learned that it can run 10 feet in one second. So, we know that they run at the same speed.
Thank you! Please let me know if this was helpful!
Answer:
Cheeta's speed = 10 feet per second
Gazelle's speed = 10 feet per second
Hence, They run at the same speed.
Step-by-step explanation:
Determining the Cheeta's speed:
Covered distance = 60 feet
Time taken = 6 seconds
Speed = Covered distance / Time taken
= 60 / 6
= 10 feet per second
Therefore, Cheeta's speed is 10 feet per second.
Determining the Gazelle's speed:
Covered distance = 100 feet
Time taken = 10 seconds
Speed = Covered distance / Time taken
= 100 / 10
= 10 feet per second
Therefore, Gazelle's speed is 10 feet per second.
Conclusion:
Cheeta's speed = 10 feet per second
Gazelle's speed = 10 feet per second
Hence, They run at the same speed.
Which line segments have a positive slope PLS FAST!! THANKS!!
Answers
a-b
it’s the ones where it’s pointing up to the right!
The sixth-grade class was asked the question, “What do you spend the most time on each weeknight?” The results are shown in the table. What percent of the sixth-grade class said that they spend the most time communicating with friends?
A.30%
B.43%
C.70%
D.81%
Answers
30 percent of the sixth-grade class said that they spend the most time communicating with friends. Option A is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
The total number of students,
56+32+81+39+62=270
The number of students involved in communicating with friends is 81.
The percentage of the student involved in communicating with their friend,
=(81/270)×100
=30%
Thus, 30 percent of the sixth-grade class said that they spend the most time communicating with friends. Option A is correct.
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Truck Transport
A truck driver is beginning her haul across the country. The warehouse is 15 miles
from the highway. Once she gets on the highway she maintains a constant rate for
several hours. Complete the table of values for the sequence below that relates hours on
the highway and distance from the warehouse in miles.
Answers
Refer to the attachment for the required table:
What is the unit rate?
A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
From the table,
For 0 hours, distance = 15 miles
For 1 hour, distance = 80 miles
Difference between distances= 80-15=65 miles
Since it is given that, it is at a constant rate, for every hour there is an increase of 65 miles in distance.
The completed table is shown in the attachment.
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List the terms of the polynomial. Give the coefficient of the second term. -4y5 + 6x4 +9w³ - 4w - 1 Separate terms using commas. Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c . Make sure your variables match those in the question. Terms Coefficient
Answers
The coefficient of the second term, 6x⁴, is 6.
The terms of the polynomial are:
-4y⁵, 6x⁴, 9w³, -4w, -1
The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.
The coefficient is 6.
Therefore, the list of terms is:
-4y⁵, 6x⁴, 9w³, -4w, -1
Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.
The coefficients indicate the scalar value by which each term is multiplied.
The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.
Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.
There is a 6 coefficient.
As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.
Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.
The scalar value by which each phrase is multiplied is shown by the coefficients.
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Without multiplying, how can you tell which product will be greater, 3 x 4 or 6 x 2?
Answers
Answer:
we can compare 4 x 3 and 2 x 6, equal to 12. So, we can see that both products are similar and neither is greater.
Step-by-step explanation:
We can use the commutative property of multiplication to see that 3 x 4 is the same as 4 x 3 and 6 x 2 is the same as 2 x 6. When multiplying two numbers, the order of the numbers does not affect the product. Therefore, we can compare 4 x 3 and 2 x 6, equal to 12. So, we can see that both products are similar and neither is greater.
NEED MORE EXPLANATION?
The commutative property of multiplication states that when multiplying two numbers, the order of the numbers does not affect the product. This means that 3 x 4 is the same as 4 x 3, and 6 x 2 is the same as 2 x 6. We can use this property to compare 4 x 3 and 2 x 6, equal to 12. Therefore, we can see that both products are identical and neither is greater.
20% of what numbner is 100
Answers
Answer:
The number is 500.
Step-by-step explanation:
Let n be the number
Convert percent to decimal
20% = 0.20
0.20n = 100
Divide both sides of the equation by 0.20
0.20n/0.20 = 100/0.20
n = 500
A 22 km walk is completed in 5 hours and 30 min.
What is the average speed?
Answers
Answer:
121 km\hr
Step-by-step explanation:
displacement=speed÷time
then. speed = displacement×time
= 22 × 5.5
= 121 km\hr
3. Explain why the polynomial 34 + 5x3 - 7x2 + 3x has a degree 3 and not 4.
Answers
Answer:
See explanation below
Step-by-step explanation:
The degree of a polynomial is the LARGEST power at which the variable/s appear in their expression.
Notice that in the given polynomial, the highest power for the variable x is 3, from the term 5 x^3.
There is no other term with higher power for x.
The variable appear in the expression \(3^{4} + 5x^{3} + 7x^{2} + 3x\) x which has highest power 3 not 4 .
We have to explain, why the polynomial \(3^{4} + 5x^{3} + 7x^{2} + 3x\) has a degree 3 and not 4.
According to the question,
A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
The degree of a polynomial is the largest power at which the variable appear in their expression.
\(Polynomial = 3^{4} + 5x^{3} + 7x^{2} + 3x\)
The given polynomial, the highest power for the variable x is 3, from 5 .
Hence, The variable appear in the expression \(3^{4} + 5x^{3} + 7x^{2} + 3x\) x which has highest power 3 not 4 .
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The Cross Bayou Bridge in Shreveport, Louisiana has trusses that form triangles. The exterior angle of one triangle has a measure of (5 - 3)°. If the two nonadiacent interior angles of the triangle are 43° and (3x)°, what is the value of the exterior angle, in degrees?
Answers
The exterior angle of the triangle is 62°.
What is triangle?
A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.
Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.
Let us take the triangle as ABC.
Here \(m\angle C\)= 180-(5x-3)° [Because straight line angle is 180°].
We know that sum of all angles in triangle is add upto 180° Then,
=> \(m\angle A+m\angle B+m\angle C\)=180
=> 43°+3x°+180-5x+3=180°
=> -2x=180-180-43-3
=> -2x=-46
=> x=13°
Now exterior angle ,
=> 5x-3
=> 5*13-3
=> 65-3
=> 62°
Hence the exterior angle of the triangle is 62°.
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Select the two answers that describe the unit rate at which he walks.
1.5 seconds per meter
90 meters per second
30 meters every second
1.5 meters per second
1 meters every second
30 seconds per meter
Answers
The unit rate at which Darrell walks is 1.5 meters per second.
What is the unit rate?
A ratio that compares two amounts of DIFFERENT types of UNITS is called a rate. When a rate is expressed as a fraction, the denominator is 1 unit. Divide the numerator and denominator of the rate by the denominator to represent a rate as a unit rate.
Here, we have
Given
Darrell is walking for a distance of 90 meters in time 60 seconds.
We have to find the unit rate at which he walks.
To find out the unit rate we must divide the distance traveled by Darrell by the time taken to travel that distance.
The unit rate is given by :
Unit rate = Distance traveled in meters / Time taken in seconds
Unit rate = 90 meters / 60 seconds
Unit rate = 1.5 meters per second.
Hence, the unit rate at which Darrell walks is 1.5 meters per second.
In 60 seconds, Darrell walks 90 meters. Select the two answers that describe the unit rate at which he walks.
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A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal.
The rectangular pen will have three wooden sides, which cost 15 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 55 dollars per foot to construct.
The animal requires an area of 65 square feet in order to be comfortable.
Diagram of State Fair animal pen
Figure 1. Schematic drawing of animal enclosure
If the pen is to be built as cheaply as possible, what are the dimensions of the pen that should be built?
Length of glass front of pen :
5.70
Incorrect: Your answer is incorrect.
feet
Depth of pen :
11.40
Incorrect: Your answer is incorrect.
feet
How much will the pen cost to build?
Cost of pen :
741.11
Incorrect: Your answer is incorrect.
dollars
Give all your answers correct to two decimal places.
Answers
The pen should be 5.70 feet wide and 11.40 feet deep, with the front made of reinforced glass. This will cost $741.11 to construct, as the wood costs $15 per foot and the glass costs $55 per foot.
The pen needs to be 65 square feet in order to provide enough space for the animal, so the dimensions can be calculated by dividing 65 by the width of the pen. The width of the pen will be the glass front, so the width of the pen should be 5.70 feet. The depth of the pen can then be found by dividing 65 by 5.70, which is 11.40 feet. The cost of the pen can then be calculated by multiplying the length of the glass (5.70 feet) by the cost of the glass (55 dollars per foot) to get $313.50. This should then be added to the cost of the wood, which is 15 dollars per foot multiplied by the total length of the pen (17.30 feet), to get $259.50. The total cost of the pen is then $313.50 + $259.50 = $741.11.
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At the conclusion of training, all factory workers are timed as they complete a task. The completion times for the task are normally distributed.
Suppose a worker's completion time is 1.1 standard deviations above the mean. What is the worker's percentile score? Round your result to one decimal place.
The annual salaries for people in a particular profession are known to be normally distributed with a mean of $54,800 and a standard deviation of $2,600.
What percentage of people in this profession earn annual salaries between $54,000 and $57,000? Round your result to one decimal place.
Answers
Using the normal distribution, it is found that:
The worker's score is at the 86.4th percentile.42.2% of people in this profession earn annual salaries between $54,000 and $57,000.In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.Question 1:
1.1 standard deviations above the mean, hence, a z-score of Z = 1.1.
Looking at the z-table, z = 1.1 has a p-value of 0.864, hence, the worker's score is at the 86.4th percentile.Question 2:
Mean of 54800, hence \(\mu = 54800\)Standard deviation of 2600, hence \(\sigma = 2600\).The proportion is the p-value of Z when X = 57000 subtracted by the p-value of Z when X = 54000, then:
X = 57000:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{57000 - 54800}{2600}\)
\(Z = 0.846\)
\(Z = 0.846\) has a p-value of 0.801.
X = 54000:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{54000 - 54800}{2600}\)
\(Z = -0.307\)
\(Z = -0.307\) has a p-value of 0.379.
0.801 - 0.379 = 0.422
0.422 x 100% = 42.2%
42.2% of people in this profession earn annual salaries between $54,000 and $57,000.
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4x+5/x+7
Answers
Answer:
x = 2.4
Step-by-step explanation:
4x + 5 / x + 7
combine like terms
X + 4x = 5x
5 + 7= 12
12/ 5x
Divide
12 /5= 2.4
X= 2.4
d) Suppose you begin making a monthly payment of $75.00. Fill in the table.
Month Current balance
1
2
3
4
5
6
7
8
9
10
11
12
WYPIE
$2750.00
Interest
$45.38
Payment
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
Amount applied to principal
$29.62
Answers
Answer:
Step-by-step explanation:
Answer:
For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.
For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.
Point of view:
Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!
:)
Come One Come All!!!!!
Answers
Answer: 1. is A, 2. is C, i dont know 3. 4. is B i think. then 5. is probably option 2
Step-by-step explanation:
PLEASE SOMEONE HELP ME
Answers
Answer: 50°
Step-by-step explanation:
Remember a straight line must equal 180°
So all angles on the line must add up to 180°
So let's take our given angles of 65° and add them together
65°+65°=130°
Now let's take 180°-130°=50°
Need help don’t know what to do I’m confused
Answers
9514 1404 393
Answer:
no solution
Step-by-step explanation:
You attempt to solve this the same way you would an equation.
4(x +1) ≤ 4x +3 . . . . . . given
4x +4 ≤ 4x +3 . . . . . . . eliminate parentheses
4 ≤ 3 . . . . . . . . . . . . . . subtract 4x from both sides
This is a false statement. There are no values of x that will make it true. So, there is NO SOLUTION.
__
Whenever you run across a false statement in the solution process, you know there is No Solution.
3x + 10 3x + 2 solve for x
Answers
Step-by-step explanation:
find the x-intercept, substitute in
0
for
y
and solve for
x
To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
−
1
53
,
0
)
y-intercept(s):
(
0
,
2
)
jake has 78 toy cars 49 are red and the rest are green how many cars are green
Answers
Answer:
29
Step-by-step explanation:
Subtract 78 by 49, you would get 29.
Answer:
29 are green
Step-by-step explanation:
78 - 49 is 29
find by a digit to make the number divisible by 3 1234?
Answers
A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.
To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.
Let's calculate the sum of the digits in 1234:
1 + 2 + 3 + 4 = 10
The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.
To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.
The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.
1234 + 2 = 1236
we obtain the number 1236, which is divisible by 3.
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2. How do you know if a number is
divisible by 9 without dividing?
Answers
Answer:
Add all the digits of the number, then check if that sum is divisible by 9. If yes, we know the number is divisible by 9.
3.4x=8.5
on a text plz answer
Answers
Answer:
x=.4
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
While riding her bike, Susan burns 450 calories every ½ hour. Based on this rate, how many calories will Susan burn if she rides the bike for 1¾? *
Answers
A dairy needs 258 gallons of milk containing 7% butterfat how many gallons each of milk containing 8% butterfat and milk containing 2% butterfat must be used to obtain the desired 258 gallons
Answers
Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.
The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.
To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.
For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).
For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).
Since we want the final mixture to contain 7% butterfat, we can set up the following equation:
0.08x + 0.02y = 0.07(258)
Simplifying the equation, we have:
0.08x + 0.02y = 18.06
To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.
Substituting this value into the equation above, we get:
0.08x + 0.02(258 - x) = 18.06
Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.
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