The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
What is the sum of terms of a geometric sequence?Let's suppose its initial term is a , multiplication factor is r and let it has total n terms,
then, its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
Given geometric sequence;
85 +85(.9) +85(.9)² + ...
a = 85
r = 0.9
its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
[tex]S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08[/tex]
Thus,
The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
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A person invests 1000 dollars in a bank. The bank pays 6.75% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 2500 dollars?
Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The time for which the person must leave the money in the bank until it reaches $2500 is 1.2.
What is compound interest?Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where A is the final amount
P is the principal amount
r is the rate of interest
n is the number of times interest is charged in a year
t is the number of years
The principal amount is 1000 dollars, while the rate of interest is 6.75% which is compounded monthly. Therefore, the time it will need for the account to reach $2500 is,
2500 = 1000[1+(0.0675/12)¹²ˣⁿ
2.5 = (1.0675)¹²ⁿ
log(2.5)\ log(1.0675) = 12n
14.0278 = 12n
n = 1.1689 ≈ 1.2
Hence, the time for which the person must leave the money in the bank until it reaches $2500 is 1.2.
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Answer: 13.6 years
Step-by-step explanation: Dealta Math Answer
Mary throws a plastic disc to her friend. Her friend
catches the disc six seconds after Mary throws it. The
table shows the height of the disc at one-second
intervals.
Time (seconds)
Height (feet)
0
3
1
A
2
6
3
7
6
4
B
4
5
6
Mark this and return
Assuming that the throw represents projectile motion,
what are the missing values in the table?
O A = 5, B = 3
O A=4, B=0
O A=4, B = 3
O A = 5, B = 0
Submit
Next
By assuming that the motion of the plastic disc thrown by Mary is a projectile motion, the missing values are 4 and 3 respectively.
How to determine the missing height?Since we're assuming that the motion of the plastic disc thrown by Mary is a projectile motion, it simply means that the motion can be represented by a quadratic function (parabolic).
For a projectile motion, the height of the disc at the time when it's at the top would be the same (equal). Thus, we can logically deduce that:
Height at time (t = 1 seconds) = Height at time (t = 5 seconds)
4 = A.
Similarly, Height at time (t = 0 seconds) = Height at time (t = 6 seconds)
3 = B.
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If a 6-foot-tall baby giraffe casts a 4- foot-long shadow, then how tall is an adult giraffe that casts a 10-foot shadow?
Answer:
8- foot shadow? i am not sure
Answer:
i believe its 12 feet!
Step-by-step explanation:
assuming that the difference from the 6 foot giraffe with a four foot shadow is two feet, the 10 foot shadow would be two feet less then the giraffes height.
Use the commutative property of addition to write an expression equivalent to the following.
5a + b
The answer is
Explanation:
The commutative property of addition is where we can add two numbers in any order.
The general equation is x+y = y+x
A more concrete example would be something like 2+3 = 3+2 since both sides simplify to 5.
For 5a+b, it is the same as b+5a. We swap the two terms.
where do banks get the money to lend to consumers
Answer:
Depositors
Step-by-step explanation:
Answer:
Banks get the money from the people that deposit their money at the bank for a low interest rate and lend to the customers with a high interest rate.
EASY POINTS
Which of the following exponential functions represents the graph below?
Answer: It's B.
Step-by-step explanation: It can't be A or D. The y-intercept is 2, not 4 so it is B.
Which of the following numbers is shown plotted on the number line ?
In which triangle is the value of x equal to cos−1(StartFraction 4.3 Over 6.7 EndFraction)?
(Images may not be drawn to scale.)
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle opposite to side with length 4.3 is x.
A right triangle is shown. The length of the hypotenuse is 4.3 and the length of another side is 6.7. The angle between 2 sides is x.
A right triangle is shown. The length of the 2 sides are 6.7 and 4.3. The angle opposite to side with length 4.3 is x.
The correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
The complete figure is attached with the answer below.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
In the given figure of option A, we can see that the hypotenuse is 6.7 and the base is 4.3 and the angle between both the sides is x. Now we will calculate the angle of cosine x.
Cos(x)= Base / Hypotenuse
Cos(x) = ( 4.3 / 6.7 )
(x) = Cos⁻¹ ( 4.3 / 6.7)
Therefore the correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
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Answer:
The answer is A
Step-by-step explanation:
Just took the test
Write the prime factorization of 10
Answer:
2|10
5|5
1
Prime factors of 10 are 2*5
After sales tax, a $600 antique clock costs $642. What is the sales tax percentage?
well, clearly the tax is the added 42 bucks, so hmmm if we take 600 to be the 100%, how much is 42 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 600 & 100\\ 42& x \end{array} \implies \cfrac{600}{42}=\cfrac{100}{x}\implies \cfrac{100}{7}=\cfrac{100}{x} \\\\\\ 100x=700\implies x=\cfrac{700}{100}\implies x=7[/tex]
Answer:
Answer is 7% sales Tax
Step-by-step explanation:
I first like to take one percent of the original value, in this case 1% of 600 is 6 dollars. I then multiply 6 by the number needed to get to 642, which is 107- you will always then subtract 100 from this number and you get 7%. This should work for other problems as well. This is probably not the best explanation btw
3t-2/4 - 2t-3/3 = 2/3 - t
The value of the variable t will be 13 / 12.
What is Algebra?The analysis of mathematical representation is algebra, and the handling of those symbols is logic.
The equation is given below.
3t - 2/4 - 2t - 3/3 = 2/3 - t
Then the value of t will be
t - 3/2 = 2/3 - t
2t = 2/3 + 3/2
2t = 13 / 6
t = 13/12
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Question 2 On the line that passes through point C, mark a point D that is distinct from point C. Use the slope formula along with coordinates of points to find the slopes of and . Show your work.
The slope formula along with coordinates of points ( p,q) and (x,y) [tex]m = \dfrac{y-q}{x-p}[/tex].
What is the slope of a straight line?A slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When the slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to the amount we walk or run on the horizontal axis, the more the slope is.
The slope of a line that passes through points ( p,q) and (x,y)
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
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help pleseeeeeeeeeeeeeeeeeeeeeeee
Complete the information as requested:
1.- Indicated dose: 300 mg of Ceftriaxone ampoules IV every 6 hours for 10 days.
Available: 1.2 g of Ceftriaxone vial. Reconstitute with 5ml of Sterile Water
a) Dose volume … Calculations
b) Number of doses per day to comply with the indication.
c) Number of ampoules needed for the entire treatment
2.- The patient has indicated:
Indicated quantity: 250 mg Tobramycin ampoule every 12 hours
Available Tobramycin 100 mg /ml vial
a) Dose volume for administration according to indication.
b) Number of ampoules needed for one day of treatment.
c) Amount of Tobramycin received per day - mg
3.- A doctor indicates 0.5 g PO c6h x 5 days
The drug available is 125 mg / 5 mL
a) What is the amount of drug administered per dose? in ml
b) how many total doses for the 5 days are required
c) how many 100 ml bottles do I need to deliver
Find the value of x of the given right triangle.
Answer:
In the right triangle, the side a=[tex]4[/tex] and the hypotenuse c=[tex]7[/tex].
To find: the value of x
We have,
[tex]a=6[/tex] and [tex]c=7[/tex]
Now,by the pythagorean theorem,
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Substitute the values,
[tex] {6}^{2} + {x}^{2} = {7}^{2} [/tex]
[tex]36 + {x}^{2} = 49[/tex]
Subtract 36 from each sides,
[tex] {x}^{2} = 13[/tex]
Take square root from each sides,
[tex]x = \sqrt{13} [/tex]
Hence, the value of x is [tex]\sqrt{13}[/tex].
what is two significant digit for 59.3506494?
Answer:
59
Step-by-step explanation:
Round 59.3506494 to the first 2 sig figs which is 59 since the number next to the decimal isnt over or 5, so it stays as 59 instead of 60.
If 0 lies in the quadrant IV. What can be the value of cos 0 ?
Answer:
the value of cos 0 is 7
Step-by-step explanation:
because you have to times it twice
Answer:
Between 0 and 1
Step-by-step explanation:
Cos Θ is the x coordinate of the unit circle. The points of that circle in quadrant IV have an x coordinate of 0≤x≤1.
Solve the inequality |a + 3| > 14
Answer:
a∈(-∝;-17)∩(11;+∝).
Step-by-step explanation:
|a+3|>14; ⇔ 14<a+3<-14; ⇔ 11<a<-17;
Let f(x)=20/5+6e^−0.1x What is (5)? Round your answer to 4 decimal places.
We can conclude that the function evaluated in x = 5 is equal to 2.3150
How to evaluate the function?Here we have the function:
[tex]f(x) = \frac{20}{5 + 6e^{-0.1x}}[/tex]
And we want to evaluate in x = 5, this just means to replace the x by a 5 in the given function:
We can evaluate this with a calculator (as doing it by hand is kinda hard), we will get:
[tex]f(5) = \frac{20}{5 + 6e^{-0.1*5}} = 2.3150[/tex]
So we can conclude that the function evaluated in x = 5 is equal to 2.3150.
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the spec sheet for the actual 1968 corvette shows the front frame dimension to be 32.875 inches. what would this measurement be, in both fractional and decimal form, on the hot wheels 1:64 model? which form of the measurement would be easier to work with?
Answer:
0.513671875 = 263/512 inches
easier to use: depends on the measurement tool
Step-by-step explanation:
The model dimension is found by multiplying the actual dimension by the scale factor.
__
model dimensionmodel frame dimension = actual frame dimension × 1/64
= (32.875 inches)/64 = 0.513671875 inches
In fractional form, this is ...
(32 7/8) / 64 = (263/8) / 64 = 263/512 . . . inches
__
ease of useIt is unlikely that a casual hobbyist will have access to tools that measure with a resolution finer than 0.0001 inches. More common would be a measurement resolution of 0.001 inches. Using such tools, the rounded decimal value 0.5137 or 0.514 inches would be more useful than the fractional measurement.
It is possible that an optical measuring device could be available that would present its result as a fraction of an inch. If such a tool were used, the fractional measurement value would provide an appropriate point of comparison.
In short, the measurement easiest to work with depends on the tool being used to make the measurement.
Una camioneta transportaba 3/4 de tonelada de arena para entregar a diferentes clientes. Si al primer cliente le dejo 1/3 de la carga que fracción de toneladas quedo en la camioneta
The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale. He decides to use a random number table to survey a simple random sample of 50 of the 250 employees. Which of the following correctly labels the population of employees?
000-250
001-250
0-250
1-250
Answer:
1-250 i think
Answer: B
Step-by-step explanation:
trust me bro
Which one of these functions is a quadratic function?
OA Rx) = x-3x+1
OB. f(x)=3*
OC. f(x)=x²³
OD. f(x) = log(x+7)
Answer:
x^2 -3x+1
it is your answer
The function x² - 3x + 1 represents a quadratic function.
A quadratic function is a function of the form f(x) = ax² + bx + c, where a, b, and c are constants.
In option A, we have f(x) = x² - 3x + 1, which fits the form of a quadratic function with coefficients a = 1, b = -3, and c = 1.
In option B, the function is Exponential.
In option C, the function is Exponential.
In option D, the function is logarithm.
Therefore, x² - 3x + 1 represents a quadratic function.
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if x+7y=16 and 3x-7y=4 what is the value of x
Answer:
[tex]x=5\\[/tex]
Step-by-step explanation:
First, put your equations into a system.
[tex]\left \{ {{x+7y=16} \atop {3x-7y=4}} \right.[/tex]
Next, use the method of elimination to solve the system. Elimination is when either x or y has an opposite coefficient (so in this case y has a coefficient of 7 or -7 depending on the equation). You can then add the equations, and y is eliminated as a variable. Now you can solve for x.
[tex]4x=20[/tex]
Lastly, divide by 4 on both sides to get x by itself.
[tex]x=5\\[/tex]
Test Scores Find the percentile rank for each test score in the data set. Round to the nearest whole percentile.
10, 15, 19, 23, 30
Part 1 of 6
The percentile rank for the value 10 is
The percentile rank for 10 will be 10th.
What is percentile rank?The percentile rank of a particular score in statistics refers to the percentage of scores in the frequency distribution that are smaller than that score.
Percentile rank = [(Number of values below x) + 0.5]/ total number of values * 100
For 10,
Percentile rank = {[0 + 0.5]/5} x 100 = 10th
For 15,
Percentile rank = ([1 + 0.5]/5) x 100 = 30st
For 19,
Percentile rank = [2 + 0.5]/5 x 100 = 50th
For 23,
Percentile rank = [3 + 0.5]/5 x 100 = 70th
For 30,
Percentile rank = [4 + 0.5]/ 5 x 100 = 90th
The percentile rank for 10 will be 10th.
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You can buy a car for $5995.67 cash or pay $759.00 as a down payment and $129.95 a month for 4 years.
How much more does the installment plan cost than paying cash?
A. $1000.93
B. $241.93
C. $507.43
D. $2475.27
E. $99.27
well, if you had the cash right now, you can put it down cold for 5995.67 bucks
OR
put as a downpayment now 759 and then over 48 months pay 129.95 each month, well, 129.95 48 times is 129.95 * 48 = 6237.6, now let's add the 759 down and that's 6237.6 + 759 = 6996.6.
well, heck if you had the cash it'd be 5995.67, if you don't is 6996.6, their difference is 6996.6 - 5995.67 = 1000.93.
A candle on Pauline’s dresser is 4 inches tall and burns at a rate of 0.6 inches per hour. How many hours will it take for the candle to burn down to a height of 1.3 inches?
The time taken for the candle to burn down to a height of 1.3 inches is 4.5 hours
What is a Linear Function ?A linear function is what can be written in the form of
y =mx+c
The rate at which the candle is burning is 0.6 inches/ hour
The initial height is 4 inches at t=0
The straight line equation can be written for this as
y =mx +c
as m = -0.6
at x = 0 , y = 4 therefore c =4
y = -0.6x +4
The time at which y = 1.3 inches is
1.3 = -0.6x +4
-2.7 = -0.6 x
x =4.5
4.5 hours is the time taken for the candle to burn down to a height of 1.3 inches.
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To best show a possible linear trend in a scatter plot, draw a _________________.
A. regressive line
B. line of best fit
C. vertical line
D. horizontal line\
Answer:
b. line of best fit
A freight elevator has a weight limit of 2 tons. Each crate that is loaded weighs 80 pounds. What is the greatest number of crates that can be loaded onto the elevator
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be ______ that when the population is not highly skewed a. different from b. the same as c. larger than d. smaller than
Answer:
2
Step-by-step explanation:
the same as...
(2) is the answer
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.
What is the central limit theorem?The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.
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IK
rying the Distributive Property
Try it
Which statement is an example of the distributive property?
O3+ (2)(15)= 3(2) + 3(15)
O3(2+15) = 3 + 2(3) + 15
O3(2+15)= 3(2) + 3(15)
O 3(2+15)= 3(2) + 15
The statement that is an example of the distributive property is (c) 3(2+15)= 3(2) + 3(15)
How to determine the example?The distributive property states that:
a(b + c) = a(b) + a(c)
Using the above property, we have:
3(2+15)= 3(2) + 3(15)
Hence, the statement that is an example of the distributive property is (c) 3(2+15)= 3(2) + 3(15)
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