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Rina8888 [55]
3 years ago
15

Driving 65 mph, it takes Alicia 3 hours to reach the airport to go on a vacation. It then takes her 4 hours to get to her destin

ation with the jet traveling at a speed of 400 mph. How many miles does Alicia travel to get to her destination?
Mathematics
1 answer:
Oksanka [162]3 years ago
8 0

Answer:

1,795 mi. traveled in total

Step-by-step explanation:

3 × 65 = 195 mi. driven by car

4 × 400 = 1,600 mi. flown by jet

1,600 + 195 = 1,795 mi. traveled in total.

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Find S^20 if the series 1 + 1.1 ..... is a (a) arithmetic (b) geometric
quester [9]
I'm guessing S^20 is actually referring to the 20th partial sum S_{20}, with

S_{20}=1+(1+1\times0.1)+(1+2\times0.1)+\cdots+(1+18\times0.1)+(1+19\times0.1)

in the arithmetic case, and

S_{20}=1+1.1+1.1^2+\cdots+1.1^{18}+1.1^{19}

in the geometric case.

(a) Combining like terms, we have

S_{20}=20+0.1(1+2+\cdots+18+19)

and invoking the formula

1+2+\cdots+(n-1)+n=\dfrac{n(n+1)}2

we end up with

S_{20}=20+0.1\dfrac{19\times20}2=39

(b) Multiply S_{20} by 1.1, then subtract this from S_{20}:

1.1S_{20}=1.1+1.1^2+1.1^3+\cdots+1.1^{19}+1.1^{20}

S_{20}-1.1S_{20}=-0.1S_{20}=1-1.1^{20}
\implies S_{20}=\dfrac{1.1^{20}-1}{0.1}\approx57.275
7 0
3 years ago
Write an equation for the nth term of<br> the arithmetic sequence: <br> 15,28,41 ....
11111nata11111 [884]

Answer:

The equation for the nth term of  the given arithmetic sequence is: \mathbf{a_n=13n+22}

Step-by-step explanation:

We need to write an equation for the nth term of  the arithmetic sequence:

15,28,41 ....

The equation for arithmetic sequence is: a_n=a_1+(n-1)d

Where a_n is the nth term, a_1 is first term and d is common difference

In the given sequence we have:

a₁ = 15

a₂ = 28

We can find common difference using the formula:

a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13

So, the common difference d is 13

Now, equation for nth term will be:

a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2

So, the equation for the nth term of  the given arithmetic sequence is: \mathbf{a_n=13n+22}

where n=1,2,3..

4 0
3 years ago
Who is good with math like trig.??
Mnenie [13.5K]
I am good with all math from alg-calc
4 0
3 years ago
A 16.5 ft tall giraffe casts a 12 ft shadow. At the same time, a zookeeper casts a 4 ft shadow. ​How tall is the zookeeper?
Stels [109]

12 ft shadow / 4 ft shadow = 3

16.5 ft / 3 = 5.5 ft

The zookeeper is 5.5 feet tall

7 0
3 years ago
Read 2 more answers
One number is nine more than the other. Their sum is 33. Find the numbers. (Enter your answers as a comma-separated list.)
Bas_tet [7]

Answer:

The numbers are 12, 21.

Step-by-step explanation:

x+(x+9)=33

x+x+9=33

2x+9=33

2x=33-9

2x=24

x=24/2

x=12

--------

x+9=12+9=21

Please mark me as Brainliest if you're satisfied with the answer.

5 0
3 years ago
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