We'll use the exponent rule that a^(b+c) = a^b*a^c
to break up 17^16 into 17^(14+2) = 17^14*17^2
That allows us to factor like so
17^16+17^14
17^14*17^2+17^14*1
17^14(17^2 + 1)
Computing 17^14 is a lot more difficult compared to computing 17^2 + 1, assuming you only could use paper and pencil.
Note that 17^2 = 17*17 = 289, so 17^2 + 1 = 289+1 = 290
Because 290 ends in a 0, this means that 5 is a factor
290 = 5*58
This makes 5 to be a factor of the original expression.
----------------
So overall,
17^16+17^14 = 17^14(17^2 + 1) = 17^14*290 = 17^14*5*58 = 5*17^14*58
The stuff "17^14*58" doesn't matter. All we care about is that factor of 5.
Since 5 is a factor, this means that 17^16+17^14 is a multiple of 5, or 17^16+17^14 is divisible by 5.
Phrased another way, 17^16+17^14 all divided over 5 leads to some integer. In this case, the integer would be the result of 17^14*58.
The time for one complete swing of a pendulum can be modeled by the formula P=2π√L/32 where L represents the length of the pendulum in feet and P represents the period of the pendulum in seconds. If the pendulum's period is 2.4 seconds, which of the following best represents the length of the pendulum?
A. 1.7 ft
B. 5.4 ft
C. 4.7 ft
D. 4.4 ft
Answer:
two ways to get this
1 by unit analysis
l / g → m / (m/s^2) → s^2
so you'd need
root of l/g to get s (time units)
2
from the formula
T = 2 pi sqrt(L/g)
Step-by-step explanation:
two ways to get this
1 by unit analysis
l / g → m / (m/s^2) → s^2
so you'd need
root of l/g to get s (time units)
2
from the formula
T = 2 pi sqrt(L/g)
It costs James an initial $7 fee to ride a taxi. Plus 6$ a minute. He ends up paying
$139. How many minutes did he ride the taxi for?
Answer:
$78
Step-by-step explanation:
Can i be brain list
PLEASE HELP ME
Mr. Frankel bought 5 tickets to a puppet show and spent $29. He bought a
combination of child tickets for $5 each and adult tickets for $7 each. Which system
of equations below will determine the number of adult tickets, a, and the number of
child tickets, c, he bought?
A. a = c-7
7a + 5c = 29
B.
a+c= 145
a +c= 5
C. 5a + 5c = 34
a+c=5
D.
7a + 5c = 29
a+c= 5
Help please!!! I’ve tried everything
Answer:
4.5%
Step-by-step explanation:
We know she made 21/22. That means she miss 1 so subtract 21 from 22. We get 1. then divide 22 by 1. So the equation is
[tex] \frac{1}{22} [/tex]
which is about 0.454. Then multiply by 100 to get the percent which is 4.54. Round to nearest tenth and we get 4.5%
PLEASE HELP !!!!!
describe the process of solving a proportion.
The process of solving a proportion is given below.
We are given that;
To show the process of solving a proportion
Now,
A proportion is an equation that states that two ratios are equal. For example, if we have 2 4 = 3 6[tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {3} {6}}}[/tex] , then we have a proportion.
To solve a proportion, we need to find the value of a missing term that makes the equation true. There are different methods to solve a proportion, but one common method is cross-multiplication. Here are the steps to solve a proportion by cross-multiplication:
Multiply the numerator of one ratio by the denominator of the other ratio.
For example, if we have 2 4 = x 6
[tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}[/tex] , then we multiply 2 by 6 and get 12.
Multiply the denominator of the first ratio by the numerator of the second ratio.
For example, if we have 2 4 = x 6
[tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}[/tex] , then we multiply 4 by x and get 4x.
Set the two products equal to each other. For example,
if we have [tex]2 4 = x 6 {\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}[/tex], then we set 12 = 4x.
Solve for the missing term. For example, if we have 12 = 4x, then we divide both sides by 4 and get x = 3.
Check your answer by plugging it back into the original proportion.
For example, if we have x = 3, then we plug it back into 2 4 = x 6 [tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {x} {6}}}[/tex] and get 2 4 = 3 6
[tex]{\\displaystyle {\\frac {2} {4}}= {\\frac {3} {6}}}[/tex] , which is true.
Therefore, by proportion answer will be given below.
More can be learned about proportions at;
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The point is (8,9) is a solution to this system
Answer:
False
Step-by-step explanation:
I got that they intercepted at (10.857,0.4286)
y=1/2x-5
y=-3x+33
please help me asap.
The length of a rectangular garden
is (y + 5). The width is (y). Write a
simplified expression to represent
the perimeter of the garden.
Show your Work.
PLS HURRY!!!!
Answer:
4y + 10
Step-by-step explanation:
Since the perimeter of a rectangle is 2(l + w), where l is the length and w is the width, the perimeter of this rectangle would be
2((y + 5) + y)
To simplify this, just add similar terms inside the parentheses and multiply them both by 2.
2(2y + 5)
4y + 10
Which of these four sets of side lengths will form a right triangle?
Set 1
10 cm, 26 cm, 24 cm
Set 2
4 in., 2 in., 6 in.
Set 3
14 mm, 13 mm, 15 mm
Set 4
10 ft, 30 ft, 20 ft
Set 1
Set 2
Set 3
Set 4
Answer:
Set 1 Yes
Set 2 No
Set 3 and Set 4 ???
Step-by-step explanation:
Use the converse of the Pythagorean theorem. Square the lengths and see if 2 results add up to the third result.
So, Set 1
[tex]10^{2} = 100 \\26^{2} = 676\\24^{2} = 576[/tex] 100 + 576 = 676 Therefore we have a right triangle
Set 2
[tex]4^{2} = 16\\2^{2} = 4\\6^{2} = 36[/tex]
16 + 4 ≠ 36 Therefore we do NOT have a right triangle
I will let you do Set 3 and Set 4. OK?
set 1 is the answer ............................................................
hey do you mind helping me out?
Answer:
20
Step-by-step explanation:
60%-> 12
100%->20
Answer:
20
Step-by-step explanation:
If you combine all the baking soda from the recipes that use exactly 1 1/4
teaspoons, how much baking soda will you have in all?
Write your answer as a fraction, mixed number, or whole number.
Answer:
Note that per 1/4 tsp of baking soda you need ample amount of acidity which is about 1 cup of buttermilk, 1 cup of brown sugar, 1 teaspoon of lemon juice, or 1 teaspoon of vinegar. Baking Without Baking Soda OR Baking Powder
Step-by-step explanation:
2. For the competition, each band member needs $12 for food. To get to the competition, the school rents 3 buses that cost $580 each. Write and evaluate an expression for these costs.
Answer:
(75 × 12) + (3 × 580) = 2640
Step-by-step explanation:
There is a TV that is $189.00. There is a coupon offering 15% off any television purchase. If the sales tax on the TV is 8%, how much will the TV cost total?
Answer:
175.77 dollars
Step-by-step explanation:
15% off 189.00 is 160.65 then you take that answer and add on the sales tax from the original price. Doing 189.00 x 8 percent gets you 15.12 dollars.
Add 160.65 + 15.12 to get 175.77 dollars.
Which inequality is the solution to 20+2 <
Ž -8?
Answer:
the 20 +2
Step-by-step explanation:
What is the measure of N
Answer:
C) 27 degrees
Step-by-step explanation:
N+63=90
-63. -63
N=27
PLEASE HELP IM DYING RN.
WHAT IS X? 6(x+2)=2(x-3)
Answer:
-9/2
Step-by-step explanation:
6(x+2)=2(x-3)
6x+12=2x-6
6x-2x+12=-6
4x+12=-6
4x=-6-12
4x=-18
x=-18/4
simplify
x=-9/2
120 times 1/2
Do not divide, whole number times fraction.
Answer:
60
Step-by-step explanation:
write 120 like this: 120/2
Then just multiply the numerators.
Which gets you 120/2.
Then change it it to a mixed fraction which is 60.
PLEASE HELP SIMPLE NTH TERM
So, i need to find out the nth term of the sequence
25 20 15 10 5
Please help quickly i will give brainliest
Answer:
-5n + 20
Step-by-step explanation:
n stands for the term number so if you want to find the 50th term all you have to do is substitute n with 50
first of all find the difference between each number in the sequence
the difference between 25 and 20 is -5
the difference between 20 and 15 is -5
the difference between 15 and 10 is -5
the difference between 10 and 5 is minis -5
because
25-5=20
20-5=15
15-5=10
10-5=5
now that you know the the difference you place the number in front of n like this
-5n
to find the rest all you need to do is use the difference between each number which is -5 and do it on the first number
so 25 - 5
this gives 20
so our nth term is -5n + 20
if you still don't get i can re-explain it to you
What is the area of this face?
help quickly!!!!!!!!
find the value of each variable in the parallelogram
Answer:
Step-by-step explanation:
for the width
16-h=7
16-7=h
h=9
(g+4)=65
g=65-4
g=61degrees
The value of each variable in the parallelogram:
h = 9 and g = 61°.
What is parallelogram?A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
Given:
The shape is a parallelogram.
That means, the opposite sides are parallel and equal.
16 - h = 7
h = 16 - 7
h = 9
And opposite angles of a parallelogram are also equal.
g+4 = 65
g = 65 - 4
g = 61°
Therefore, the values are g = 61° and h = 7.
To learn more about the parallelogram;
https://brainly.com/question/29133107
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Question 17 The probability that a customer's order is not shipped on time is 0.02. A particular customer places three orders, and the orders are placed far enough apart in time that they can be considered to be independent events. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that all are shipped on time
Answer:
0.941192 = 94.1192% probability that all are shipped on time
Step-by-step explanation:
For each order, there are only two possible outcomes. Either they are shipped on time, or they are not. The probability of an order being shipped on time is independent of other orders. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that a customer's order is not shipped on time is 0.02.
So 1 - 0.02 = 0.98 probability of being shipped on time, which means that [tex]p = 0.02[/tex]
A particular customer places three orders
This means that [tex]n = 3[/tex]
(a) What is the probability that all are shipped on time
This is [tex]P(X = 3)[/tex].
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.98)^{3}.(0.02)^{0} = 0.941192[/tex]
0.941192 = 94.1192% probability that all are shipped on time
Which fraction is the least?
A. 1/2
B. 1/5
C. 1/7
D. 1/10
Helppp pleasee need asapp!!!
Two friends decide to rent an apartment and split the cost evenly. They each paid $752 towards the total move in cost which included first and last month’s rent and a security deposit of $499. What will be the cost of rent per month for each of them?
Answer:
They will both pay $63.50 a month
Step-by-step explanation:
Since they paid $752 total and $499 as a security deposit, you subtract the two, getting you $253 in rent for both months. Divide that answer by 2 to get $126.5 to get how much they payed each month together, then divide by 2 again to get how much they each payed which is $63.50
A system may become infected by some spyware through the internet or e-mail. Seventy percent of the time the spyware arrives via the internet, thirty percent of the time via e-mail. If it enters via the internet, the system detects it immediately with probability 0.6. If via e-mail, it is detected with probability 0.8. What percentage of times is this spyware detected
Answer:
This spyware is detected 66% of times.
Step-by-step explanation:
We have these following percentages:
Seventy percent of the time the spyware arrives via the internet, and in this case is detected 60% of the time.
Thirty percent of the time the spyware arrives via e-mail, and in this case is detected 80% of the time.
What percentage of times is this spyware detected
0.7*0.6 + 0.3*0.8 = 0.66
This spyware is detected 66% of times.
Please help me on this
Answer:
61
Step-by-step explanation:
90 divided by 36 is 2.5 add 10 to the 90 then multiply 10 by 2.5 you get 25 then add 25 to 36 witch gives u 61. 90/36=2.5x10=25+36=61
/ is for division. Hope it helps.
Help!
I fallen and can’t get up.
boo hoo let me play you a sad song on the world's smallest violin
2 digit multiplication using standard algorithm
54x23
Answer:
answer = 1242
Step-by-step explanation:
please follow me
Bobby’s farm is always subject to the weather. A bad storm or drought can devastate his crop. What type of risk does Bobby’s business face?
A.
internal
B.
external
C.
avoidable
D.
controllable
The population of a certain species of insect is given by a differentiable function P , where P(t) is the number of insects in the population, in millions, at time t , where t is measured in days. When the environmental conditions are right, the population increases with respect to time at a rate that is directly proportional to the population. Starting August 15, the conditions were favorable and the population began increasing. On August 20, five days later, there were an estimated 10 million insects and the population was increasing at a rate of 2 million insects per day. Which of the following is a differential equation that models this situation?
a. P=2(tâ5)+10
b. dP/dt=2/5t
c. dP/dt=1/5P
d. dP/dt=5P
Answer:
Option C, dP/dt=1/5P
Step-by-step explanation:
The change is population of insects is directly proportional to the rate of change of population
Hence,
[tex]\frac{dP}{dt} \alpha P[/tex]
Or [tex]\frac{dP}{dt} = kP[/tex]
where K is the proportional constant
We will find the value of k
Keeping the given values of rate of change of population and population in above equation, we get -
[tex]\frac{2}{10} = k\\k = \frac{1}{5}[/tex]
Hence,
[tex]\frac{dP}{dt} = \frac{1}{5} P[/tex]
I need help pleaseeeees