The common ratio of the geometric sequence is: 2/3.
Common Ratio of a Geometric Sequence
Common ratio, r = a term divided by the consecutive term in the series.
Given the geometric sequence, 54,36,24,16...
common ratio (r) = 16/24 = 2/3.
24/36 = 2/3.
36/54 = 2/3.
Therefore, the common ratio of the geometric sequence is: 2/3.
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LaToya had a large collection of basketball cards. She decided to give half of them to her friends, Aaron, and a fourth of them to her brother. She still has 75 cards left. How many cards did she start out with?
LaToya originally had 300 basketball cards. She gave away 3/4 of her collection, keeping 1/4 which is 75 cards. By solving the equation 1/4 x = 75, we find that x equals 300.
Explanation:LaToya originally had a certain number of basketball cards. She gave half of them to Aaron and a fourth of them to her brother, leaving her with 75 cards. To find out how many cards she started with, let's define the total number of cards as x. Given that half and a fourth were given away, this means that 3/4 of x has been given to others, leaving her with 1/4 of her original number of cards.
Now, we can set up the equation: 1/4 x = 75. To solve for x, multiply both sides of the equation by 4, giving us x = 75 * 4, which equals 300. Therefore, LaToya originally had 300 basketball cards.
To find the number of cards LaToya started with, we can set up an equation based on the information given and solve for the unknown value.
Explanation:To find the number of cards LaToya started with, we need to work backwards from the information given. We know that she has 75 cards left after giving half to her friends and a fourth to her brother. Let's assume that the number of cards she started with is 'x'.
If she gave half to her friends, that means she gave x/2 cards to her friends. Then, if she gave a fourth to her brother, she gave x/4 cards to her brother. So the total number of cards given away is x/2 + x/4 = 3x/4.
Since she has 75 cards left, we can set up the equation: x - 3x/4 = 75. Solving this equation will give us the value of x, which represents the number of cards LaToya started with.
A 5000 seat theater has tickets at $27 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $158,400
This math problem can be solved by setting up a system of linear equations. Designate the number of $27 tickets as x and the number of $40 tickets as y. You then form two equations, one for the total number of tickets (x + y = 5000) and one for the total revenue (27x + 40y = 158400). Solve these equations to determine how many of each ticket should be sold.
Explanation:The subject of this question is a problem in algebra, specifically a system of linear equations. Let's denote the number of $27 tickets as x and the number of $40 tickets as y. The total number of tickets sold will be 5000. So, we have our first equation: x + y = 5000. The total revenue is $158,400. The revenue from $27 tickets will be $27x and the revenue from $40 tickets will be $40y. So, we have our second equation: 27x + 40y = 158400. Now, we have a system of linear equations which can be solved to find the number of each ticket type that should be sold. Solve these equations to get the desired quantity of ticket type for generating the required total revenue.
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Which is a better investment 8.3% compounded annually or 8% compounded quarterly.
Using compound interest, the better investment is of 8.3% compounded annually.
What is compound interest?The amount of money earned, in compound interest, after t years of the investment, is given by the following formula:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which the parameters are given as follows:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.For the first option, of 8.3% compounded annually, the multiplier after each year is given as follows:
[tex](1 + \frac{0.083}{1}\right)^{1} = 1.083[/tex]
As the parameters are r = 0.083, n = 1.
For the second option, the parameters are given as follows:
r = 0.08, n = 4.
Hence the multiplier after each year of the investment is given by:
[tex](1 + \frac{0.08}{12}\right)^{12} = 1.0829[/tex]
Due to the higher multiplier, the first option is better, that is, 8.3% compounded annually.
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The 8% compounded quarterly has a higher effective annual rate than 8.3% compounded annually, thereby making it the better investment choice.
To determine which investment is better, we need to compare the effective annual rates (EAR) of the two options: 8.3% compounded annually vs. 8% compounded quarterly. The formula for EAR is (1 + i/n)n - 1, where i represents the interest rate and n is the number of compounding periods per year.
For the 8.3% compounded annually, the EAR is straightforward: (1 + 0.083/1)1 - 1 = 0.083 or 8.3%.
For the 8% compounded quarterly, we calculate the EAR as follows: (1 + 0.08/4)4 - 1 = (1 + 0.02)4 - 1 = (1.02)4 - 1 = 1.082432 - 1 = 0.082432 or 8.2432%.
Comparing the two EARs, the 8% compounded quarterly has a higher effective annual rate than the 8.3% compounded annually, making it the better investment.
Evaluate 5x^3 + 2 for x = -1.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5x^3 + 2}\\\mathsf{= 5(-1)^3+2}\\\\\mathsf{(-1)^3}\\\mathsf{= -1\times-1\times-1}\\\mathsf{=1\times-1}\\\mathsf{= \bf -1}\\\\\mathsf{= 5(-1) + 2}\\\\\mathsf{5(-1)}\\\mathsf{= \bf -5}\\\\\mathsf{= -5 + 2}\\\mathsf{=\bf -3}\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \bf -3}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\frak{Amphitrite1040:)}[/tex]
(3.6)^x=45 solve the exponential equation?
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)?
a; y + 3 = −4(x + 4)
b; y + 3 = –1/4(x + 4)
c; y + 3 = 1/4(x + 4)
d; y + 3 = 4(x + 4)
A sample size of 500 is sufficiently large enough to conclude that the sampling distribution of the sample proportions is a normal distribution, when the estimate of the population proportion is .995.
In a statistical test, the null hypothesis to be made is that the sample proportions do not have any significant differences, which means an equal distribution. This is only rejected when the estimate is equal or less than 0.95. But since in this case it is >0.95, so therefore the null hypothesis is not rejected. Therefore:
False
Each car on the Steel Force train has 3 rows with 2 seats in each row. How many seats are on the train?
To pass a math test, students must correctly answer at least 0.6 of the questions. Donald’s score is 5/8, Karen score is 0.88, Ginosscore is 3/5 and Sierra score is 4/5. How many of the students passed the test
Answer: All students passed except Gino
Step-by-step explanation:
solve the exponential equation. express the solution set in terms of natural logarithms 5^×+7=2
The perimeter of a rectangular garden is 322 feet. If the width of the garden is 72 feet, what is its length?
divide 322 by 2 and then subtract the width
322 /2 = 161
161-72 = 89
length is 89 feet
Ellen drove 220 miles in 3.5hours. To the nearest tenth, find Ellen's average speed in miles per hours
divide total miles by time:
220 / 3.5 = 62.857
rounded to nearest tenth = 62.9 miles per hour
What is an estimate of the solution. If the equation 6n + 3 = 2? Use a table.
What temperature is ten degrees higher than -7°C ?
One number is 2 more than another. The difference between their squares is 32. What are the numbers
The two numbers are 7 and 9, which are determined by setting up an algebraic equation based on the information that one number is 2 more than the other and the difference between their squares is 32.
Explanation:The question involves finding two numbers where one number is 2 more than another and the difference between their squares is 32. To solve this problem, we denote the first number as ‘x’. Therefore, the second number will be '‘x+2’, as it is given to be 2 more than the first number. Next, we set up an equation based on the provided information that the difference between their squares is 32: ‘(x+2)² - x² = 32’.
Expanding the squared terms, we get ‘x² + 4x + 4 - x² = 32’. After simplifying the equation by canceling out ‘x²’ from both sides and subtracting 4 from both sides, we get ‘4x = 28’. Dividing both sides by 4 gives us ‘x = 7’. Thus, the first number is 7, and the second number is 7 + 2, which is 9.
The two numbers in question are 7 and 9, and they meet the criteria given in the problem statement.
y varies jointly as x and z. y equals 80y=80 when x equals 5x=5 and z equals 4z=4. Find y when x equals 4x=4 and z equals 6z=6.
Rosa and Albert receive the same amount of allowance each week. The table shows what part of their allowance they each spent on video games and pizza.
C. Who spent the greater part of their total allowance? How do you know?
Raj is writing 3/2000 as a percent. find his mistake and correct it
What is the interquartile range of this data set 1,5, 12, 14, 29,45,48,61,72,84,96
The interquartile range of the data set is 60
What is the interquartile range of the data set?The interquartile range of the data set is the difference between the lower quartile (Q1) and the upper quartile (Q3)
From the given information:
Data set = 1, 5, 12, 14, 29, 45, 48, 61, 72, 84, 96We need to first identify the middle number(median) = 45
Thus:
Q1 = (1+ 5+ 12+ 14+ 29)/5Q1 = 12.2Q3 = (48+ 61+ 72+ 84+ 96)/5Q3 = 72.2IQR = 72.2 - 12.2
IQR = 60
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The science fair judges will be teachers and volunteers. Each judge will view 5 projects. There are 133 science teachers. What is the fewest number of volunteers needed to have enough judges
If there are 2115 projects in total, then 665 projects will be covered by 133 science teachers. Therefore, an additional 290 volunteers are needed to judge the remaining projects, making the correct answer option A.
Step 1: Calculate projects judged by science teachers
The number of projects each teacher can judge is 5, so:
133 teachers * 5 projects per teacher = 665 projects
Step 2: Calculate additional projects
The total number of projects should be known to determine the additional requirement. Let's denote the total number of projects as P.
If P projects must be judged and 665 projects are already covered, then:
Remaining projects = P - 665
Each volunteer can also judge 5 projects. Let V be the number of volunteers needed:
Step 3: Solve for the fewest number of volunteers
We need enough volunteers to cover the remaining projects:
5 * V ≥ P - 665
To solve this, we need the total number of projects mentioned in options:
If P = 2115, then:
Remaining projects = 2115 - 665 = 1450
1450 / 5 = 290 volunteers
The correct answer is A (290).
The complete question is
The science fair judges will be science teachers and volunteers. Each judge will only have time to view 5 science fair projects. There are 133 science teachers. What is the fewest number of volunteers needed to have enough judges for all of the projects?
A 290
B 396
C 422
D 423
A box of packaged snacks contains 6 individual bags and costs $5.40. Each individual bag contains 18 crackers. What is the cost per cracker?
The cost per cracker from a box of 6 individual bags costing $5.40, with each bag containing 18 crackers, is $0.05.
Explanation:In the process of calculating the cost per cracker, the initial step involves determining the cost per bag. This is accomplished by dividing the total cost of the box, which amounts to $5.40, by the number of bags contained within, totaling 6 bags. Consequently, the cost per bag is determined to be $0.90. Subsequently, to ascertain the cost per individual cracker, the cost per bag is further divided by the number of crackers present in each bag, which is 18. Following this calculation, it is established that each cracker costs $0.05. In essence, the cost analysis method involves dividing the total box cost by the number of bags to derive the cost per bag, and then dividing this value by the number of crackers per bag to determine the precise cost per cracker, amounting to 5 cents per cracker.
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Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly and each person arrives at a different time In how many ways can they arrive?
A car is traveling at a speed of 48 miles per hour. What is the car's speed in miles per minute? How many miles will the car travel in 2 minutes? Do not round your answers.
The car speed in miles per minute is 0.8 miles per minute and the car will travel 1.6 miles in 2 minutes.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
The speed of the car = 48 miles per hour
Speed in miles per minute = 48/60 = 0.8 miles per minute
Time = 2 minutes
Speed = 0.8 miles per minute
Distance = 0.8×2 = 1.6 miles
Thus, the car speed in miles per minute is 0.8 miles per minute and the car will travel 1.6 miles in 2 minutes.
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On Thursday, a local hamburger shop sold a combined total of 258 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the numbers of hamburgers sold. How many hamburgers were sold on Thursday?
The local drugstore is offering 15% off the normal price for a 16-pack of AAA batteries. If a 16-pack of AAA batteries is normally $9.99, what would be the sale price for the batteries after the discount?
Answer:
D: $8.95
Step-by-step explanation:
step 1
Calculate what 15% of the normal price is.
15% as a decimal is 0.15. Multiply this by $9.99.
0.15⋅$9.99 = $1.4985
step 2
Subtract $9.99 by $1.4985 and round the difference to the nearest cent.
$9.99 − $1.4985 = $8.4915 ≈ $8.49
step 3
Match your solution to the correct answer choice.
Answer choice D is the only answer choice that matches your solution. Select answer choice D and move on to the next question.
Find the GCF of 30 * 3 and 12 * 4
Answer:
3
Step-by-step explanation:
Suppose the constant rate of change of y with respect to x is 8.5, and the value of y is 5 when the value of x is 11. what is the value of y when the value of x is 19? what is the value of y when the value of x is –1? what is the value of x when the value of y is 7?
Answer:
(x, y) = (19, 73)(x, y) = (-1, -97)(x, y) = (11 4/17, 7)Step-by-step explanation:
You are given a point and a slope, so you can write the linear equation relating x and y using the point-slope form of the equation for a line. That form for slope m and point (h, k) is ...
y = m(x -h) +k
For your given values, m = 8.5, and (h, k) = (11, 5), the equation relating x and y can be written ...
y = 8.5(x -11) +5
___
Evaluating this for several different x-values can be done with a spreadsheet or calculator. I like to write the function into a graphing calculator and let it do the tedious arithmetic. (See the attachment.)
However, to show you what is involved in doing this by hand, we can ...
let x = 19, then ...
y = 8.5(19 -11) +5 = 8.5·8 +5 = 73
__
let x = -1, then ...
y = 8.5(-1-11) +5 = 8.5·(-12) +5 = -97
____
To find the value of x for y=7, we can realize that to make y go up by 2 (from the given point of 5), we need to have x go up by 2/8.5 (from the given point of 11). That is ...
for y = 7 ...
x = 11 + 2/8.5 = 11 + 4/17 = 11 4/17
To determine values for y based on x in a linear function, use the equation derived. For x = 19, y equals 73; for x = -1, y equals -97. Solving for x when y is 7 gives approximately 11.24.
To solve the given problem, we use the concept of a linear function which states that the change in y with respect to x is constant. Here, the constant rate of change (slope) is given as 8.5.
We can express the linear relationship in the form of the equation:
y = 8.5x + b
We are also given a point on the line: (11, 5). Plugging these values into the equation to find b:
5 = 8.5(11) + b
5 = 93.5 + b
Subtract 93.5 from both sides:
b = 5 - 93.5 = -88.5
So, the equation becomes:
y = 8.5x - 88.5
Now, let's find the values of y for the given x values:
When x = 19: y = 8.5(19) - 88.5 = 161.5 - 88.5 = 73When x = -1: y = 8.5(-1) - 88.5 = -8.5 - 88.5 = -97To find the value of x when y = 7, we can rearrange the equation:
7 = 8.5x - 88.5
Add 88.5 to both sides:
95.5 = 8.5x
Divide by 8.5:
x = 95.5 / 8.5 = 11.2353 (approximately)
A florist has 54 red roses and 36 white roses. If the florist creates the greatest number of identical bouquets possible with a combination of red and white roses without any roses leftover, how many red roses are in each bouquet?
PLEASE ANSWER THIS ASAP!!!!!!!!!!
54-36 =18
they can make 18 bouquets
54/18 =3
36/18 =2
18 bouquets with 3 red and 2 white roses each
Answer:
3
GCF of 54 and 36 = 18
so, 18 bouquets
then,
54 red roses ÷ 18 = 3 red roses in each bouquet
Find the limit. lim θ→0 cos(4θ) − 1 / sin(7θ)
Can't figure this out. Any help is appreciated!
The limit of the given expression is undefined.
Explanation:To find the limit of lim θ→0 cos(4θ) - 1 / sin(7θ), we can simplify the expression first. Using the identity cos(2θ) = 2cos²θ - 1, we can rewrite the numerator as 2(cos²(2θ) - 1). The denominator, sin(7θ), can be rewritten as sin(2θ + 5θ). By applying the sum-to-product identities, we get sin(2θ)cos(5θ) + cos(2θ)sin(5θ), or cos(5θ)sin(2θ) + cos(2θ)sin(5θ).
Now, if we multiply both numerator and denominator by 1/sin(2θ)cos(5θ), we can simplify the expression further:
lim θ→0 (2cos²(2θ) - 1) / (cos(5θ)sin(2θ) + cos(2θ)sin(5θ)) = lim θ→0 (2cos(2θ) - 1/sin(2θ)) / (cos(5θ) + cos(2θ)tan(5θ)).
Now, we can substitute θ = 0 into the expression. Since cos(0) = 1 and sin(0) = 0, the denominator becomes cos(5(0)) + cos(2(0))tan(5(0)) = cos(0) + cos(0)tan(0) = 1 + 1(0) = 1. Thus, the limit is:
lim θ→0 (2cos(2θ) - 1/sin(2θ)) / (cos(5θ) + cos(2θ)tan(5θ)) = (2cos(2(0)) - 1/sin(2(0))) / 1 = (2cos(0) - 1/0) / 1 = (2(1) - 1/0) / 1 = (2 - 1/0) / 1 = 1/0 = undefined.Learn more about Limits here:https://brainly.com/question/8533149
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Let [n] = 1 if n is odd and 0 if n is even, for all positive integer n. if [n] * [n+8] = 0, then what is one possible value of n?