Answers
The sum is 294903.
_____
This is the sum of 15 terms of a geometric sequence with first term 9 and common ratio 2. That sum is given by the formula
[tex]S_{n}=a\dfrac{r^{n}-1}{r-1}[/tex]
[tex]S_{15}=9\dfrac{2^{15}-1}{2-1}=9\cdot(32768-1)=294903[/tex]
Related Questions
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What is the average rate of change of the function over the interval x = 0 to x = 6? f(x)=2x−1
____
3x+5
Answers
[tex]\bf \cfrac{\left[ \frac{2(6)-1}{3(6)+5} \right]~~-~~\left[ \frac{2(0)-1}{3(0)+5} \right]}{6}\implies \cfrac{\left[ \frac{11}{23}\right]~~-~~\left[-\frac{1}{5} \right]}{6} \\\\\\ \cfrac{\frac{11}{23}+\frac{1}{5}}{6}\implies \cfrac{\quad \frac{78}{115}\quad }{\frac{6}{1}}\implies \cfrac{78}{115}\cdot \cfrac{1}{6}\implies \cfrac{13}{115}[/tex]
The function f(x)=35+15x represents the amount of money, in dollars, mr. lewis earns for working x hours. how much money does mr. lewis earn for working 25 hours?
Answers
You can get this by plugging in the 25 for x in the above equation.
By substituting x with 25 in the equation f(x)=35+15x, we find out that Mr. Lewis would earn $410 for working 25 hours.
Explanation:The function provided is f(x)=35+15x, which represents the amount of money Mr. Lewis earns for working x hours. In the case of Mr. Lewis working for 25 hours, we substitute the value of x with 25 in the equation to calculate his earnings. Therefore, f(25)=35+15(25)=35+375=$410. Hence, Mr. Lewis would earn $410 for working 25 hours.
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Which number would it be if rounded to the nearest foot
7191.51
A. 7191 FT
OR
B. 7192 FT
Answers
If you shift the linear parent function, f(x)=x, down 7 units what is the equation of the new function
Answers
1- You have that following parent function (the most basic function of the linear functions) given in the problem above:
f(x)=x
2- When you graph this parent function, you obtain the graph shown in the figure attached.
3- If you shift the linear parent function 7 units down, you have the following new function:
f(x)=x-7
4- The graph of the new function is shown in the second figure attached.
The answer is: f(x)=x-7
f(x)=x-7 is indeed the correct answer.just got it right
Rewrite 0.85 as a fraction in lowest terms.
Answers
well, 0.85 has two decimals, so we use two zeros,00, at the bottom of the fraction and lose the dot, let's do so,
[tex]\bf 0.\underline{85}\implies \cfrac{085}{1\underline{00}}\implies \cfrac{85}{100}\implies \stackrel{simplified}{\cfrac{17}{20}}[/tex]
The center of a circle is at (2, -5) and it's radius is 12. What is the equation of the circle?
A.) (x+2)^2 + (y-5)^2 =24
B.) (x-2)^2 + (y+5)^2 = 24
C.) (x+2)^2 + (y-2)^2 = 144
D.) (x-2)^2 + (y+5)^2 = 144
Answers
You just have to plug in your coordinates h is the x and k is the y.
The r is radius squared.
so, (x-2)^2+(y-(-5)^2=144
You have to be careful of those tricky negative values. When you distribute the y-(-5) it turns into y+5.
So your answer is D.
Answer:
The answer is D
Step-by-step explanation:
It is D
sabendo que x2 + y2=74 e que xy=35, calcule valor de (x - y2)2
Answers
1. You have the following information given in the problem above:
- x²+y²=74
xy=35
2. Therefore, you have that (x-y)² is:
=(x-y)²
=x²-2xy+y²
=(x²+y²)-2xy
3. When you substitute the values given in the problem, you obtain:
=74-2(35)
=74-70
=4
4. Therefore, as you can see, the correct answer is: 4
A bus covered the 400-km distance between points a and b at a certain speed. on the way back the bus traveled at the same speed for 2 hours and then increased the speed by 10 km/hour until it reached a, thus spending 20 fewer minutes on the return trip. how long did the return trip take?
Answers
xt=400,
On the way back, the 2x+(x+10)(t-7/3), where it was total time minus 2 hours already driven minus 1/3 of hour, the 20 minutes.
2x+xt-(7/3)x+10t-70/3=400
2x+400-(7/3)x+10t-70/3=400
thus
-(1/3)x+4000/x=70/3
multiplying through by x we get:
-(1/3)x^2-(70/3)x+4000=0
x^2+70x-12000=0
x=(1/2)(-70+/-sqrt52900)
x=80 kmp
thus:
it took 5 hours to make the first trip
on way back 2 hours at 80 kph which means he traveled for 160 km at this speed
2 h 40 min at 90 k/h=90*8/3=240 km
The speed going to B is x, the time t and the distance, 400 km.
xt=400, x kph and t in hours
on the way back, the 2x+(x+10)(t-7/3), where it was total time minus 2 hours already driven minus 1/3 of an hour, the 20 minutes.
2x+xt-(7/3)x+10t-70/3=400
2x+400-(7/3)x+10t-70/3=400, 400 cancels, t=400/x
-(1/3)x+4000/x=70/3
multiply by x
-(1/3)x^2-(70/3)x+4000=0
x^2+70x-12000=0
x=(1/2)(-70+/- sqrt 52900); sqrt term=230
x=80 kph
took 5 hours to go there
on way back 2 hours at 80 kph=160 km
2h40m at 90kph=90*8/3=240 km
They add to 400 km.
The return trip took 4h40m
geometry question!! 50 POINTS
Answers
Area ratio is
250 yd^3
radii? First solid has vol 250 yd^3 = (4/3)*pi*r^3; find r^3 = --------------
(4/3)*pi
Then r^3 = 187.5 yd^3, and r = 5.724 yd
Second solid has vol 686 yd^3 .... Please find the radius R using precisely the same method.
Then calculate the ratio of the surface areas of the 2 solids:
Solid 1 surface area 4*pi* R^2
----------------------------- = --------------- where R is the radius of the larger
Solid 2 surface area 4*pi*r^2 solid and r is the radius of the smaller
R^2
This ratio comes out to ----------
r^2
Scale factor? Obviously one solid is larger than the other. We have to figure out by how much, by comparing volumes. Actually, we've already done that (see above). We could also determine how much larger R is than r. That, too, would give us the scale factor.
Answer:
2.74
Step-by-step explanation:
24 inches is 250% of what length
Answers
________________________________________________________
Explanation:
________________________________________________________
24 = 250/100 * x ;
24 = 2.5 x ;
↔ 2.5 x = 24 ;
2.5 x / 2.5 = 24/ 2.5 ;
x = 9.6 ;
The answer is: " 9.6 inches " .
_________________________________________________________
triston is baking specity bread for the school bake sale. she has 10 1/2 cups of flour. the recipe for 1 loaf of bread calls for 2 1/3 cups of flour. How many whole loaves of bread can she make.
Answers
Triston can make 4 whole loaves of bread using her 10 1/2 cups of flour. This was determined by dividing the total flour available by the flour required per loaf. Fractional or partial loaves are not counted.
To determine how many whole loaves of bread Triston can make, we need to perform a simple division of the total amount of flour by the amount required for one loaf.
First, let's convert the mixed numbers to improper fractions:
10 1/2 cups of flour = 21/2 cups of flour2 1/3 cups of flour = 7/3 cups of flourNext, we will divide the total flour by the flour needed per loaf:
(21/2) ÷ (7/3) = (21/2) × (3/7) = (21 × 3) / (2 × 7) = 63/14 = 4.5 loaves
Since we can only make whole loaves, Triston can make 4 whole loaves of bread.
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Ratios
Ms. Grande brought 24 apples and 18 oranges for a party after a class play. Find the ratio of the number of apples to the total number of fruits Ms. Grande bought.
There are 44 chicken and fish filets altogether in a freezer. There are 12 chicken filets. Which is the ratio of the number of chicken filets to the number of fish filets in the freezer?
There were 12 boys and 18 girls in a class. Then, 3 more boys joined the class and 2 girls left. What is the ratio of the number of boys to the number of girls in the class now?
Monica had $42 and Naomi had $18 at first. Monica then gave $6 to Naomi. What is the ratio of the amount of money Monica has to the amount of money Naomi has in the end?
Answers
2) 11:3
3) 15:16
4) 3:2
To find the ratio of the number of apples to the total number of fruits, divide the number of apples by the total number of fruits. Simplify the ratio by dividing both numbers by their greatest common factor. For the ratio of chicken filets to fish filets, divide the number of chicken filets by the total number of filets. Simplify the ratio if possible. To find the ratio of boys to girls, determine the new number of boys and girls after some changes. For the ratio of money, calculate the amounts each person has and simplify the ratio.
Explanation:To find the ratio of the number of apples to the total number of fruits, we divide the number of apples (24) by the total number of fruits (24 apples + 18 oranges = 42). This gives us a ratio of 24:42. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. So the simplified ratio is 4:7.
For the second question, we need to find the ratio of the number of chicken filets to the number of fish filets. There are 12 chicken filets and a total of 44 filets in the freezer. So the ratio is 12:44. This can also be simplified by dividing both numbers by 4, giving us a simplified ratio of 3:11.
In the third question, we start with 12 boys and 18 girls. Then, 3 more boys join and 2 girls leave. So the new number of boys is 12 + 3 = 15, and the new number of girls is 18 - 2 = 16. The ratio of boys to girls is therefore 15:16.
In the fourth question, Monica has $42 and Naomi has $18. When Monica gives $6 to Naomi, Monica will have $42 - $6 = $36 left, and Naomi will have $18 + $6 = $24. The ratio of the amount of money Monica has to the amount of money Naomi has is 36:24, which can be simplified to 3:2.
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What is 6.8 rounded to the nearest ones place?
Answers
6.8 is nearer to 7 than to 6. so, 6.8 ≈ 7
↓
|------|------|------|------|------|------|-----|------|------|------|
6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7
Answer: 7
students have 40 minuets to complete 50 questions on the aspire ___ test
A) math
B) reading
C) english
D) writing
Answers
Answer:
english C)
Step-by-step explanation:
Find the first six terms of the sequence. a1 = -3, an = 2 ● an-1
Answers
According to the formula each next term will be obtained by multiplying the previous term by 2.
So, next terms will be:
Second term = 2 x First Term = 2 x (-3) = - 6
Third term = 2 x (-6) = -12
Fourth term = -24
Fifth term = -48
Sixth term = -96
So, the sequence will be:
-3, -6, -12, -24, -48, -96 ...
What is the surface area of the prism? Include steps.
Answers
Area of a rectangle: Area = Length x Height
- Rectangular Prism Dimensions:
Length: 3m
Width: 4m
Height: 2m
To calculate the surface area of a rectangular prism we first need to realize that he has 3 pairs of equal rectangles.
- The first pair (Photo 1):
Two rectangles with the same measure, so we can say that the area of this pair is: (L x H) x (L x H) or 2 x (L x H).
-> Area (Pair 1) = 2 x (3 x 2) = 2 x 6 = 12m^2
But if we will do the same thing to 3 different pairs, we can describe that:
- Total Surface Area (At):
At = 2 x (L x H) + 2 x (L x H) + 2 x (L x H)
-> At = 2 x ((L x H) + (L x H) + (L x H))
So now, just put the values inside de formula,
- Pair 1: Length = 3m ; Height = 2m
- Pair 2: Length = 4m ; Height = 2m
- Pair 3: Length = 4m ; Height = 3m
*I know that this pair doesn't have a "real Height" but this doesn't change anything when solving, you can consider the 4m as height and the 3m as length or vice versa, the order of the factors doesn't change the product.
-> At = 2 x ((3 x 2) + (4 x 2) + (4 x 3))
-> At = 2 x (6 + 8 + 12)
-> At = 2 x (26)
-> At = 52 m^2
In the circle below, radius mn = 1.4 m and mlmn = 52°. determine the length of arc ln. round your answer to the nearest tenth and use π = 3.14.
Answers
Arc length=θ/360×π×d
θ=52
d=2×1.4=2.8 m
thus
Arc length will be:
52/360×3.14×2.8
=1.27 m
Answer:
1.27 is the answer
Step-by-step explanation:
On average, Scott drinks ½ of a 6-ounce glass of water in ⅔ hour. How much water does he drink in an hour?
a) 0.75 ounces b) 2 ounces c) 4.5 ounces d) 9 ounces
Answers
3/2 = 1.5. He drinks 1.5 ounces in one third of an hour. 1.5 * 3 = 4.5
C. 4.5 ounces in one hour
For what value of a does (1/9)^a+1 = 81^a+1 x 27^2-a?
Answers
Solution:
(1/9)^(a+1)=81^(a+1) x 27^(2-a), then the answer would be a=-3.
Answer:
-4
Step-by-step explanation:
Next time use the internet :)
Is the mean value theorem for integrals the same as the mean value thoerem for derivatives?
Answers
Answer:
a^2 + b^2 =C^2
Step-by-step explanation:
Cam rode her bike 5 times as far as Dante did. Dante rode 187 meters farther than Michael did. Cam rode 15.25 Kilometers. How many meters did Michael ride? Explain how you know you got your answer
Answers
Given that Cam rode 15.25 km
then
5x=15.25
x=3.05 km
thus Dante rod 3.05 km
but
1 km=1000m
thus
3.05 km=3050 m
But Dante rod 187 m more than Michael, the distance Michael will ride then will be:
3050-187
=2863 m
It was found that Michael rode 2863 meters.
To find out how many meters Michael rode, we first need to establish the relationship between the distances Cam, Dante, and Michael rode. According to the problem, Cam rode 5 times as far as Dante did. If Cam rode 15.25 kilometers, we first convert this to meters by multiplying by 1000 (since there are 1000 meters in a kilometer):
15.25 km × 1000 = 15250 meters.
Now that we know Cam rode 15250 meters and that this is 5 times the distance Dante rode, we can find Dante’s distance:
15250 meters / 5 = 3050 meters.
Dante rode 3050 meters, which is 187 meters farther than Michael did. To find the distance Michael rode, we subtract 187 meters from Dante’s distance:
3050 meters - 187 meters = 2863 meters.
Therefore, Michael rode 2863 meters.
Stephanie rdes her bike 2 miles to the post office, and then another 50 yards to the train station. How many yards long was her trip?
Answers
Multiply 1,760 by 2 = 3,520
Add 50 to 3,520 = 3,570
Stephanie's trip was 3,570 yards long.
Write an equation and solve: Twice a number, increased by 3 is 7.
Answers
2x +3=7
-3 -3
2x=4
divide both sides by 2
x=2
the answer is 2
Which transformation is a rotation?
Answers
Answer:
the answer is c.
Step-by-step explanation:
Stan's cookie recipe makes 242424 cookies and calls for exactly 384384384 sprinkles. He is wondering how many sprinkles (p)(p)left parenthesis, p, right parenthesis he will need to make 606060 cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make 606060 cookies?
Answers
For every 242,424 cookies he needs 384,384,384 sprinkles. So how many sprinkles does he need for 606,060 cookies?
242,424/384,384,384 = 606,060/x
384,384,384 * 606,060 = 242,424 * x
232,959,999,767,040 = 242,424 * x
960,960,960 = x
To find the number of sprinkles needed for 60 cookies, determine the number of sprinkles per cookie by dividing 384 by 24, which is 16. Then multiply 16 by 60 to get 960 sprinkles.
The question asks us to calculate the number of sprinkles (p) needed for 60 cookies when a recipe for 24 cookies calls for 384 sprinkles.
To solve this, we start by finding the number of sprinkles per cookie:
Divide the total number of sprinkles (384) by the number of cookies in the recipe (24).Multiply the result by the number of cookies we want to make (60).Therefore:
384 sprinkles ÷ 24 cookies = 16 sprinkles per cookie 16 sprinkles per cookie × 60 cookies = 960 sprinkles for 60 cookiesStan would need 960 sprinkles to make 60 cookies.
Factor each polynomial. Check your answer by distributing. 2x^2+5x+2
Answers
(X+2)(2x+1)
Simplify i to the power 41
Answers
Answer:
It should be just "i"
In circle H, HJ¯¯¯¯¯ is a radius and JK¯¯¯¯¯ is a tangent segment. Which statement must be true?
A) HJ=JK
B) ∠HJK is an obtuse angle.
C) HJ=HK
D) ∠HJK is a right angle.
Answers
D) ∠HJK is a right angle.
Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
Answers
Use the table to determine the following probabilities.
The probability that a randomly chosen person from this group has type B is 3/25
The probability that a randomly chosen person from this group has type AB is 1/25
The probability that a randomly chosen person from this group has type B or type AB blood is 4/25
The probability that a randomly chosen person is:
first person: 3/25
second person: 1/25
third person: 4/25
ProbabilityUse the table to determine the following probabilities.
The probability that a randomly chosen person from this group has type B is 3/25.
The probability that a randomly chosen person from this group has type AB is 1/25.
The probability that a randomly chosen person from this group has type B or type AB blood is 4/25.
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The height of a tree in feet over x years is modeled by the function f(x). f(x)=301+29e−0.5x which statements are true about the growth of the tree? select each correct answer. the tree's maximum height is limited to 30 ft. the tree is initially 2 ft tall. between the 5th and 7th years, the tree grows approximately 7 ft. after growing 15 ft, the tree's rate of growth decreases.
Answers
Final answer:
The tree's maximum height is not limited to 30 ft but approaches 301 ft. Initially, the tree is 30 ft tall, not 2 ft. To verify the growth between the 5th and 7th years, one must calculate f(5) and f(7). The rate of growth indeed decreases over time.
Explanation:
When analyzing the function f(x) = 301 + 29e^{-0.5x} to understand the growth pattern of a tree, it is apparent that some statements about the tree's growth can be identified as true or false.
The tree's maximum height is not limited to 30 ft; instead, the model suggests that the height approaches 301 ft as x increases indefinitely, because the exponential term decreases towards zero.The tree is initially 30 ft tall, not 2 ft tall, since f(0) = 301 + 29 × 1 = 330 ft.Between the 5th and 7th years, the growth can be calculated using f(5) and f(7) to determine if it grows approximately 7 ft during that period.After growing 15 ft, the rate of growth would decrease since the exponential function's growth rate decreases as x increases.