The next term for the given series will be equal to a(5) = -4.
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series.
This is a geometric sequence with a common ratio of -1/3 and an initial term of -324. Any geometric sequence can be expressed as:
a(n) = [tex]ar^{n-1}[/tex], in this case a=-324 and r=-1/3 so
a(n) = -324(-1/3)[tex].^{n-1}[/tex] so the 5th term will be
a(5) = -324(-1/3)⁴
a(5) = -324/81
a(5) = -4
Therefore the next term for the given series will be equal to a(5) = -4.
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Ron is half as old as Sam, who is three times as old as Ted. The sum of their ages is 55. How old is Ron?
To find Ron's age, we set up equations based on their age relations and the total sum of their ages. After solving the system of equations, we determine that Ron is 15 years old.
The question deals with a basic age-related algebra problem. To solve for how old Ron is, we can set up a system of equations based on the information provided:
Let R represent Ron's age.
Let S represent Sam's age.
Let T represent Ted's age.
From the information:
Ron is half as old as Sam, so R = 1/2 * S
Sam is three times as old as Ted, so S = 3 * T
The sum of their ages is 55, so R + S + T = 55
Substituting the expressions for R and S in terms of T into the third equation gives:
1/2 * (3 * T) + 3 * T + T = 55
Simplifying and solving for T, we find that:
1.5T + 3T + T = 55
5.5T = 55
T = 10
Now we can find Sam's age:
S = 3 * 10 = 30
And Ron's age:
R = 1/2 * 30 = 15
Therefore, Ron is 15 years old.
Find the area.
Square
A = s^2
s - side.
area = S^2
side = 12 miles
12^2 = 144
area = 144 miles
Which expression is equivalent to radical of 10 over ^4 and the radical of 8.
How do I solve this problem: -2(7-y)+4=-4?
Richard had a balance of −$322.25 in his account, and Scott had a balance of −$241.75 in his account. Which statement explains why Richard owes the bank more than Scott?
Answer: The answer is B if you don't know what B is here:
|–322.25| > |–241.75| is the correct answer.
Hope this helps!
Step-by-step explanation:
Mrs.Lin is planning her daughters birthday party. At parties r us the fee is $80 plus $10 per child. At birthday palace, the fee is $150 plus $5 per child. Write and solve an equation to determine how many children must be invited for the costs to be equal?
Which of these is the algebraic expression for "eight less than some number?"
8 − b
b − 8
Fraction 8 over b
Fraction b over 8
best answer gets brainl;iest
Macy wants to buy a skateboard for $42. She has $95 in her account. She spent $12.99 to buy stationary. She also wants to buy some ice cream bars for $3.07 each. What is the maximum number of ice cream bars, n, that Macy can buy so that she has enough money left to buy the skateboard
Answer:
She can buy 13 ice cream bars
Step-by-step explanation:
Find the volume of a cylinder with a diameter of 10 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest tenth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank)
The volume of the cylinder is 1177.5 cubic inches.
Given that the diameter of the cylinder is 10 inches, the radius r is half of that, so [tex]\( r = \frac{10}{2} = 5 \)[/tex] inches.
The height h is three times the radius, so [tex]\( h = 3r = 3 \times 5 = 15 \)[/tex] inches.
Now, we can substitute these values into the formula for the volume of a cylinder:
[tex]\( V = \pi r^2 h \)\\ \( V = 3.14 \times (5)^2 \times 15 \)\\ \( V = 3.14 \times 25 \times 15 \)\\ \( V = 3.14 \times 375 \)\\ \( V = 1177.5 \) cubic inches.[/tex]
Rounded to the nearest tenth.
Find the balance in the account. $4,100 principal earning 4%, compounded monthly, after 10 years
$4100*(1+0.04/12)^(12*10)
4100*1.490832682=
$6112.41
Jean has 1/3 cup of walnuts for each serving of salad she makes. She has 2 cups of walnuts. How many serving can she make?
An item is regularly priced at $75. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?
what would be the value of 150 after eight years if you earn 12 percent interest per year
Answer:
$371.3944
Step-by-step explanation:
Principal = 150
Time = 8 years
Rate of interest = 12% = 0.12
No. of compounds per year = n = 1
Formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A is the amount
P is the principal
r is the rate of interest in decimals
t = time in years
n = no. of compounds per year
Substitute the values in the formula :
[tex]A=150(1+\frac{0.12}{1})^{8}[/tex]
[tex]A=371.3944[/tex]
Hence the value of 150 after eight years if you earn 12 percent interest per year is $371.3944
Can you please help me
The game stop is having a sale and all games are reduced by 55%. If a game is now $29.99, what was the original price? Round your answer to the nearest cent
A savings account earns 6% (APR) interest calculated monthly, paid into the account at the end of 6 months. Travis deposits $100 into the account at the beginning of the first month. At the end of each month, he deposits an additional $100 into the account. How much interest will Travis have earned after 6 months?
You are selling items from a catalog for a school fundraiser.Write and solve two inequalities to find the range of sales that will earn you between $40 and $50. Earn $5 for every $50 in sales!
To find the range of sales that will earn you between $40 and $50, you can set up two inequalities and solve them to find the minimum and maximum sales required.
Explanation:To find the range of sales that will earn you between $40 and $50, we can set up two inequalities.
First, let's find the minimum sales required to earn $40. We can use the inequality 5x >= 40, where x represents the sales. This inequality represents the condition that earning $5 for every $50 in sales should be greater than or equal to $40.
Next, let's find the maximum sales required to earn $50. We can use the inequality 5x <= 50, where x represents the sales. This inequality represents the condition that earning $5 for every $50 in sales should be less than or equal to $50.
To solve these inequalities:
For the first inequality, divide both sides by 5, giving us x >= 8. This means the minimum sales required to earn $40 is $8.
For the second inequality, divide both sides by 5, giving us x <= 10. This means the maximum sales required to earn $50 is $10.
Therefore, the range of sales that will earn you between $40 and $50 is $8 to $10.
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A graph is shown below:
A graph is shown. The values on the x axis are 0, 3, 6, 9, 12, and 15. The values on the y axis are 0, 9, 18, 27, 36, and 45. Points are shown on ordered pairs 0, 36 and 3, 27 and 6, 18 and 9, 9 and 12, 0. These points are connected by a line
What is the equation of the line in slope-intercept form?
y = 36x − 3
y = −3x + 36
y = −3x + 12
y = −12x + 3
suppose the university bursar said that 600 student entered for business mathematics 300 entered for statistics while 173 students entered for both business mathematics and statistics how many student enrolled in the two courses altogether
what is the ratio of x to y (simplest form)
x= 2 y=6
x=5 y=15
x=8 y=24
Gideon made two errors in the proof. Identify and correct the errors
Answer:
Identify: Step 6 and step 7
Correction:
I think step 6 is just not necessary and should be removed.
And step 7 should be the transitive property of equality not the Substitution Property of Equality
Bart takes a random sample of 50 students in his seventh grade class and finds that 40% of the sample prefers chocolate ice cream over vanilla ice cream. There are 200 students in the seventh grade. Based on the sample proportion , How many students in the seventh grade would be expected to prefer chocolate ice cream over vanilla ice cream??????
Which answer is correct 40,80,50,200
The number of students in the seventh grade would prefer chocolate ice cream over vanilla ice cream is 80
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
If 40% of the sample of 50 students prefer chocolate ice cream, we can use that percentage to estimate the number of students who prefer chocolate ice cream out of the entire seventh-grade class of 200 students.
40% of 50 = (40/100) x 50 = 20 students in the sample prefer chocolate ice cream.
On simplifying the proportion , we get
To estimate the number of students in the entire seventh-grade class who prefer chocolate ice cream, we use the same percentage:
40% of 200 = (40/100) x 200 = 80 students in the seventh grade are expected to prefer chocolate ice cream over vanilla ice cream.
Hence , based on the sample proportion, we can estimate that 80 students in the seventh grade would prefer chocolate ice cream over vanilla ice cream.
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Jackson's football team lost 6 yards from their starring position and then lost another 5 yards. What number represents a loss of 6 yards? A loss of 5 yards?
On the next play, the team gains 12 yards. Will the team ne at their original starting position? Explain
A loss of 6 yards is represented by -6, and a loss of 5 yards by -5. After losses of 6 and 5 yards, and a gain of 12 yards, the team will be 1 yard past their original starting position, not exactly back to the original position.
Explanation:A loss of 6 yards can be represented by the number -6, and a loss of 5 yards can be represented by the number -5.
When the football team on the next play gains 12 yards, we add this value to their previous position, which results from adding -6 and -5. To determine if the team returns to their original starting position, we calculate -6 + -5 + 12. The sum of -6 and -5 is -11, then adding 12 gives 1, which means the team advances 1 yard past the original starting position, not just back to it.
Therefore, the team will not be at their original starting position after gaining 12 yards, they will be 1 yard ahead.
The total charge on 6 particles is -48 units. All the particles have the same charge.
What is the charge on each particle?
Let set A = {1, 3, 5, 7} and set B = {1, 2, 3, 4, 5, 6, 7, 8}
Which notation shows the relationship between set A and set B?
Answer:
A ⊆ B
Step-by-step explanation:
228% of what number is 33.06
Find the value of a and z: (x^8)^3=ax^z
HELP PLEASE!!1!
Part A
First, take a look at Preston’s sequence. How does a 180-degree rotation about the origin change the coordinates of a shape?
How does a translation 7 units up change the coordinates of a shape?
Now look at Chanel’s sequence. How does a reflection across the x-axis change the coordinates of a shape?
please, help me
180° rotation about the origin change the coordinates from (x,y) to (-x,-y). In this exercise:
A = (-4, 5) -> (4, -5)
B = (-3, 1) -> (3, -1)
C = (-5, 2) -> (5, -2)
Translation 7 units up change the coordinates from (x, y) to (x, y+7). Continuing with the exercise:
(4, -5) -> (4, 2)
(3, -1) -> (3, 6)
(5, -2) -> (5, 5)
Which are not the coordinates of triangle DEF.
Reflection across the x-axis change the coordinates from (x, y) to (x, -y). In this exercise:
A = (-4, 5) -> (-4, -5)
B = (-3, 1) -> (-3, -1)
C = (-5, 2) -> (-5, -2)
In 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across x-axis (x, y) becomes (x, -y).
180° rotation about the origin change the coordinates from (x,y) to (-x,-y). It means if an object having coordinates (3,4) then it will be (-3,-4).
Translation 7 units up change the coordinates from (x, y) to (x, y+7). It means if an object having coordinates (3,4) then it will be (3,4+7).
Reflection across the x-axis change the coordinates from (x, y) to (x, -y). It means if an object having coordinates (3,4) then it will be (3,-4).
Hence we can summarize the above phenomenon as in 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across x-axis (x, y) becomes (x, -y).
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The diagonals of rhombus FGHJ intersect at point K. If side GH is equal to x + 9 and side JH is equal to 5x – 2, find x.
Answer:
x = 2.75
Step-by-step explanation:
5x - 2 = x + 9
5x = x + 11
4x = 11