The 4th term of the geometric sequence whose first term is 3 and the common ratio is 2 is 24.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is a
and the term by which we multiply the previous term to get the next term is r then the sequence would look like
a, ar, ar², ar³,...., arⁿ
Thus, the nth term of such sequence would be aₙ = a₁ × r⁽ⁿ⁻¹⁾ (you can easily predict this formula, as for the nth term, the multiple r would've multiplied with initial terms n-1 times).
Given the first term of the sequence is 3, while the common ratio is 2, therefore, the fourth term of the geometric sequence can be written as,
aₙ = a₁ × r⁽ⁿ⁻¹⁾
a₄ = 3 × 2⁽⁴⁻¹⁾
a₄ = 3 × 2³
a₄ = 24
Hence, the 4th term of the geometric sequence whose first term is 3 and the common ratio is 2 is 24.
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A group of pupils take a test. The group consists of 28 boys and 24 girls.
The mean mark for the boys is 28. The mean mark for the girls is 14.
Calculate the mean mark for the whole group.
Give your answer correct to 1 decimal place.
Answer:
21.5 to 1 decimal place.
Step-by-step explanation:
The total number of marks for all the boys = 28*28 = 784 marks.
The total number of marks for all the girls = 24*14 = 336 marks.
So the mean mark for the whole group
= (784+336) / (28+24)
= 1120 / 52
= 21.538
A group of friends are dining at a
pizza parlor. They have 1 1/2 pizzas. If
each friend eats 1/4 of a pizza, how
many friends can have an equal
share?
Answer:
6 friends
Step-by-step explanation:
because 1/4 goes 4 times into a whole 1 and then 2 times into a half, equalling six
2. Find the cosine function that is represented in the graph.
Answer:
[tex]f(x) = cos(x - \frac{\pi }{4} ) -1[/tex]
Step-by-step explanation:
In this graph, we have the coordinate point ([tex]\frac{\pi }{4} , 0[/tex]). Without translations, cos(0) = 0, which means that the graph is shifted to the right by [tex]\frac{\pi }{4}[/tex]. We also know that the graph is shifted down by 1 because we have the point
([tex]\frac{5\pi }{4} , -2[/tex]), but accounting for the right shift, this point should really by ([tex]\pi , -2[/tex]). cos([tex]\pi[/tex]) = -1, but on the graph it is -2, meaning that it is shifted down by 1.
Therefore, accounting for the right shift by [tex]\frac{\pi }{4}[/tex] and the shift down by 1, our equation is [tex]f(x) = cos(x - \frac{pi}{4} ) - 1[/tex].
3. x² +(y + 2)2 = 64
Center:
Radius:
Answer:
Center: (0, -2)
radius: 8
Explanation:
Given equation: x² + (y + 2)² = 64
The Circle Formula:
(x - h)² + (y - k)² = r²
where (h, k) are points of center. r denotes radius
So rewrite the equation in circle formula:
x² +(y + 2)² = 64
(x- 0)² +(y + 2)² = 8²
Identify followings:
h = 0, k = -2, radius = 8
Someone pls help fast!
Answer:
decreasing and linear
Step-by-step explanation:
it just is
Answer:
Decreasing, linear
Step-by-step explanation:
you are going -4 every time
Bruno says that the product n x 4/5 is greater than 4/5 because multiplication always increases a number. Which of the following values for show that Bruno is incorrect? 8/8 6/5 5/4 3/4 2
Answer:
The fourth option shows how Bruno is incorrect
Step-by-step explanation:
Multiplication does not always result in a number greater than the initial value. If n can be any value, then Bruno's claim is false. For instance, multiplying a value greater than one by a decimal will perform the inverse operation (division):
3 × 0.87 = 2.61
When multiplying fractions of 1, this occurs when the multiplied number is greater than the multiplier:
0.55 × 0.21 = 0.1155
If decimals are not allowed, multiplying positive and negative values will give the positive result but with the inverse sign, which is less than the initial one since the result is less than 0:
12 × -2 = -24
Now back to the example. If we let n = 0.75 (3/4);
0.8 × 0.75 = 0.6
Hope that clears things up.
Shreya has 40 pairs of shoes stacked inboxes.
If a pair is 2 shoes, how many shoes does Shreya have?
Answer:
it's either 20 or 80..
Answer:
80 shoes
Step-by-step explanation:
40×2
A castle built for the man who founded the town of Redstone, CO, can now be yours, for $19.75 million. (Sherman, T.)
A coal magnate, John Cleveland Osgood, built the castle for his wife near the town of Redstone, which was founded as a company town for people working in the coal mining industry. Construction began in 1897 and was completed in 1902. (Sherman, T.)
In the early 1900s, John Cleveland Osgood was known as the King of Coal in the West. He was sixth richest of the Robber Barons, a group of elite industrialists. As a social and industrial experiment, Osgood decided he wanted to build a town in the Colorado mountains that would provide better living conditions for the miners working nearby. Instead of the tents and tiny cabins common in mining towns, Osgood built Swiss-style cottages – with electricity and running water - along the river. He also built a clubhouse with a theater, school, library, lodge, community garden and stables. (Kesting, A.).
Known as Redstone Castle and as the "Ruby of the Rockies," the 42-room castle has almost 30,000 square feet of interior space. It also has over 150 acres of land, surrounded by beautiful scenery along the Crystal River. (Sherman, T.)
It's not the first time the castle has been up for sale in recent years. Steve and April Carver purchased it at an auction for $2.2 million in 2016. (Oravetz, J.)
The Carvers worked to renovate and restore the castle and have operated it as a hotel since 2018. (Oravetz, J.)
1. Calculate the annual compound growth rate of the Redstone Castle price since the house was purchased by Steve and April Carver (in 2016) until it was listed for sale in 2020. (The growth rate should be calculated to two decimals in percentage form. Round the number of years to the whole number). Please show your work.
2. Assume that the average compound growth rate prevailed since John Cleveland Osgood built the Castle in 1902 until 2016 was 5.52% per year compounded annually. Calculate the price of the house in 1902. (Round the number of years to the whole number). (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work.
3. You were using the time value of money concept to answer question #2. Think about the timeline for that problem. What year is considered as the time point 0 in that problem? Please explain your answer
4. Assume that the average compound growth rate you were using in the question #2 now is compounded daily. Calculate the price of the house in 1902. Compare with your answer to the question #2. (Round the number of years to the whole number). (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work.
5. Assume that the house was purchased for the price listed in 2020. A commercial bank loaned the buyer the whole price (zero down payment) for 30 years. The loan must be repaid in equal monthly payments at the end of the month. The annual interest rate on the loan is 3.45% of the unpaid balance. What is the amount of the monthly payments? Please show your work.
The annual compound growth rate of the Redstone Castle price is 73.10%.
How to calculate the compound growth rate?From the information given, the formula to calculate the annual compound growth rate will be:
g = (F/P)^(1/n) - 1
where g = growth rate
f = final value = 19750000
p = initial value = 2200000
n = period = 2020 - 2016 = 4
g = (F/P)^(1/n) - 1
g = (19750000/2200000)^(1/4) - 1
g = 73.10%
Therefore, the growth rate is 73.10%
The price of the house in 1902 will be calculated thus:
PV = F/(1 + g)^n
= 19750000/(1 + 73.10%)^4
= $4811
The year that is considered as the time point 0 in that problem is 1902.
When the average compound growth rate in the question #2 now is compounded daily, the price of the house in 1902 will be $4071. The difference in values will be:
= $4811 - $4071
= $740
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Convert 23/9 to decimal. round your answer to the nearest thousandths.
Answer: 2.556
Step-by-step explanation:
23/9 = 2.5555555555 (endless 5)
round to nearest thousandths... three places from the decimal point.
2.5555... round up since 5 is the number next to the thousandth place.
2.556
write 615000 in scientific notation
Answer:
6.15 × 10⁵
Step-by-step explanation:
When converting a number of scientific notation, we need to move the decimal point until the number is greater than 1 and less than 10, then multiply this by 10 to the power of the number of places we moved the decimal point (negative when moving it forwards, positive when moving it backwards).
Therefore, 615000 = 6.15 × 10⁵
What does this add to 3/11 x 3 1/4
Answer:
0.
Step-by-step explanation:
The value of a television t years
after its purchase is modeled by the
exponential function ƒ(t) =
1500(0.83)t. Which best describes
the domain and range of this
exponential function?
Step-by-step explanation:
hope you anderstand
if that's the answer can you brainliest me please thank you
What is the sum of all prime numbers less than 78?
Answer:
712
Step-by-step explanation:
2 + 3 = 5 + 5 = 10 + 7 = 17 + 11 = 28 + 13 = 41 + 17 = 58 + 19 = 77 + 23 = 100 + 29 = 129 + 31 = 160 + 37 = 197 + 41 = 238 + 43 = 281 + 47 = 328 + 53 = 381 + 59 = 450 + 61 = 511 + 67 = 578 + 71 = 649 + 73 = 712
Need help trying to find the answer
Answer:
3/20
Step-by-step explanation:
1. Multiply the numerators
2. Multiply the denominators
3. Your answer, in this case, will be 6/40
4. Simplify fraction to its simplest form* which gives you 3/20
*I halved both numbers as they are both even
Hope this helped :)
help asap please and thank you !!!!!
Answer:
Hope this helps
Step-by-step explanation:
Y = 3x - 10
So, 4x + 5y = 7
= 4x + 5(3x - 10) = 7
= 4x + 15x - 50 = 7
= 19x - 50 = 7
= 19x = 7 +50
= 19x = 57
= X = 57/19
X = 3
Please help me I’m confused
cant delete this answer. my bad
the heat generated by stove element varies directly as a square of the voltage and inversely as a resistance. If the voltage quadruples, what needs to be done to quadruple the amount of heat generated?
Answer:
resistance must quadruple
Step-by-step explanation:
You want to know the change in resistance required to quadruple the amount of heat if heat is proportional to the square of voltage, inversely proportional to resistance, and the voltage is quadrupled.
ResistanceLet H represent the heat generated for voltage V and resistance R. We want to find R, the new resistance required, when V is replaced by 4V, and H is replaced by 4H.
H = V²/R
4H = (4V)²/R'
4(V²/R) = 16V²/R'
R' = (16/4)R . . . . . . . multiply by RR'/(4V²)
R' = 4R
The resistance must quadruple if the amount of heat is to be quadrupled.
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A spinner has three sections. This table shows the results of spinning the arrow on the spinner 80 times.
Section 1=18 Section 2=30 Section 3=32
What is the experimental probability of the arrow stopping on Section 2?
9/40
1/3
3/8
2/5
The experimental probability of the arrow stopping on Section 2 will be [tex]\rm \frac{3}{8}[/tex]. is the ratio of the favorable event to the total number of events.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.
No of arrows given in the different section ;
Section 1=18
Section 2=30
Section 3=32
The probability that the arrow stopping on Section 2 is found as;
[tex]\rm P = \frac{Favourable \ outcomes }{Total \ outcomes } \\\\\ P= \frac{30}{18+30+32} \\\\ P=\frac{30}{80}\\\\ P= \frac{3}{8}[/tex]
Hence, the experimental probability of the arrow stopping on Section 2 will be [tex]\rm \frac{3}{8}[/tex].
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How do you solve for x? X is not 34°, just to let you know.
Answer:
x = 90
Step-by-step explanation:
X is equal to 90 degrees:
As you can see it forms paralell line we know paralell line is equal to 180 degrees just divide it by 2, so 90
Evaluate the following indefinite integral
Step-by-step explanation:
try this solution, the answer is underlined with orange colour.
2/ 2 2/3 = 3/N solve for N
when i put this in my calculator it says unable to solve
Answer:
n = 9 / 2 or 4.5
Step-by-step explanation:
2/3 = 3/N
cross multiply
2 x n = 2n
3 x 3 = 9
2n = 9
divided both sides by 2
2n / 2 = 9 / 2
n = 9 / 2
Help -x/3 > 5
A. X<15
B. X > -15
C. X < -15
D. X > 15
Answer:
Steps
-x/3 >5
Multiply both sides by 3
3(-x/3)>5.3
Simplify
-X> 15
Multiply both sides by - 1 (reverse the inequality)
(-x)(-1)<15(-1)
Simplify
X< -15
so C is the answer
3. Manny's weekly wage as a welder are $520.75. He is single and claims 3 allowances. What amount is
deducted for federal taxes?
If he is single and claims 3 allowances. The amount deducted for federal taxes is $39.8
Federal taxesFederal tax withheld:
Federal tax withheld =6.2% social security + 1.45% Medicare
Federal tax withheld = 7.65%
Deduction:
Deduction= 0.0765 × $520.75
Deduction=$39.8
Therefore the amount deducted for federal taxes is $39.8
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Help please need asap!! Thank you
Answer:
your welcome
Step-by-step explanation:
....bbc
Calculate the following 87124 + 14997=
Answer:
87124 + 14997 = 102121
Hope it helpz~ uh..
Carry on learning :)
Answer:
102121
Step-by-step explanation:
Which one is the correct answer and why?
The null hypothesis is that the observed difference is due to chance alone in a research.
How to illustrate the hypothesis?Your information is incomplete. Therefore, an overview of a hypothesis will be given. A null hypothesis is a hypothesis that states that there is no relationship between two population parameters.
It should be noted that researchers reject or disprove the null hypothesis to set the stage for further experimentation or research that explains the position of interest.
The null hypothesis: H0 is the complement of the alternative hypothesis. Type I error is when we reject the null hypothesis when it is correct.
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What is the measure of Angle A in the triangle
shown?
Answer:
44degrees
Step-by-step explanation:
I've just replaced letter A with x so that I can make it easier for me to get the value of x and after adding 54 + 82 I got 136 and when I transferred it to the other side I subtracted it from 180 because it had a positive sign before it and if it is carried out the other side it becomes a negative which means I should subtract hope you got me.
in short once a positive number is carried to the other side I mean past the equals sign then it changes to negative hope it helps
Please answer if you can 30 points.
What is the y-intercept of the linear function given the following table?
Answer:
The y-intercept is 4
Step-by-step explanation:
You find the y-intercept by finding where x is zero. In the table, when x=0 the y=4. The y-intercept is 4. The graph of the function crosses the x-axis at the point (0,4).
Answer:
4
Step-by-step explanation:
the y-intercept is the y-coordinate where the line intersects the facis.So if we want to figure out the intercept,we're going to set x=0 and sdue for Y.
What is true about the angles of a right triangle?
Answer:
A right triangle has one angle of 90
Step-by-step explanation:
Step-by-step explanation:
It has only one angle of 90°
If a x b = 2a - 3b + ab, then 3 x 5 + 5 x 3 is equal to?
do answer.