The simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3
How to evaluate the expression?The expression is given as:
3^2018 + 3^2015 / 3^2017 + 3^2016
Factor out 3^2015 in the expression
So, we have
3^2015(3^3 + 1)/3^2015(3^2 + 3)
Cancel out the common factor
(3^3 + 1)/(3^2 + 3)
Evaluate the exponents
(27 + 1)/(9 + 3)
This gives
28/12
Simplify
7/3
Hence, the simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3
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Exit Ticket
A plumber charges a one-time surcharge fee of $50 for
emergency calls plus a rate of $65 per hour. Write a function
using function notation to determine the total amount charged
for an emergency service call. Then find f(4.5), and explain the
real-world interpretation of f(4.5).
Answer:
f(x) = $65x + $50
f(4.5) = $342.5
The real-world interpretation of f(4.5) would be an emergency service call where they have to work for 4.5 hours.
Step-by-step explanation:
We will write a function where x is the hours. Since you pay $65 for every hour, we will multiply $65 by x. Next, there is a fee of $50 so we will add that onto the end.
f(x) = $65x + $50
Now, we will plug 4.5 into the function for x and solve.
f(x) = $65x + $50
f(4.5) = $65(4.5) + $50
f(4.5) = $292.5 + $50
f(4.5) = $342.5
The real-world interpretation of f(4.5) would be an emergency service call where they have to work for 4.5 hours.
The left and right page numbers of an open book are two consecutive integers whose sum is 387. Find these page numbers.
The two page numbers are
(Use a comma to separate answers as needed.)
Answer:
193 and 194
Step-by-step explanation:
Left page = X
Right page = X + 1
You know the total sum.
X + (X + 1) = 387
2X + 1 = 387
2X = 387 - 1
2X = 386
X = 193
When you plug X in you get the following;
Left page = 193
Right page = 193 + 1 = 194
AP Calculus ab question: what is the derivative function, f'(x), using the definition of derivative for : f(x) = 3X^2 + 1. Please show your work with the method shown below:
f'(x)= lim (h->0) [f(x+h) - f(x)] /h
Answer: f'(x)=6x
Step-by-step explanation:
f'(x)= lim (h->0) [f(x+h) - f(x)] /h
f'(x)= lim (h->0) [3(x+h)^2 + 1 - (3x^2 + 1)] /h
f'(x)= lim (h->0) [3(x^2+2hx+h^2) + 1 - 3x^2 - 1] /h
f'(x)= lim (h->0) [3x^2+6hx+3h^2 - 3x^2] /h
f'(x)= lim (h->0) [6hx+3h^2] /h
f'(x)= lim (h->0) [6x+3h]
f'(x)= [6x+3(0)]
f'(x)=6x
The US government spent
$2500 billion. If 21% was
spent for Social Security, how
much was that
Answer:
If your number was 250,000,000,000
The amount of social security would be 52,000,000,000
Step-by-step explanation:
Which number is a rational number?
13
16
9
|୯
2
V34
√49
Answer:
49
Step-by-step explanation:
(b) If you put $7750 in the ATM each day, what percent of the days in a month should you expect to run out of cash?
The percent of the days in month that the cash will run out is given as: 23.33%. See the computation below.
What is the explanation that justified the above answer?Money put in ATM per day=$7750
We have to find the percent of days in a month you should expect to run out of cash.
From the given information
There are 7 days in which you run out cash more than $7750
Assuming that the total number of days in a month = 30
Hence, we can arrive at the above value by saying:
(Corresponding days/Total number of Days) * 100
From we above we state:
(7/30) * 100
= 23.33%
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A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $1.90 and then an additional 6 cents per minute of use. In
Plan B, there is no monthly fee, but the customer pays 7 cents per minute of use.
For what amounts of monthly phone use will Plan A Cost than Plan B?
Use m for the numbers of minutes of phone use in a month, and solve your inequality for m.
Step-by-step explanation:
sadly you skipped the key word in the question.
should we check under what circumstances plan A costs more than plan B ? or costs less than plan B ?
so, I don't know which inequality to solve.
but I can tell you the facts, and you need to pick the right direction for your answer.
cost of plan A for used minutes m :
cA(m) = 1.9 + 0.06m
plan B
cB(m) = 0 + 0.07m = 0.07m
to find the intersecting point, where both plans cost the same :
1.9 + 0.06m = 0.07m
1.9 = 0.01m
m = 1.9 / 0.01 = 190 minutes
up until 190 minutes plan B is cheaper.
if there are more than 190 minutes, than plan A is cheaper.
so,
m < 190 B is cheaper
m > 190 A is cheaper
m = 190 A and B cost the same
If the perimeter of the irregular figure is 35 2/3 cm, then what is the missing side length?
The two numbers on top are 4 3/4 and 3 1/2
the ones inside left to right is 1 1/3 1 1/3 again and 3 1/2
Then the one in the outside bottom is 9.25 cm
The one at the right outside is 6.6 cm
Left outside is the missing one
srry for bad photo quality
The missing side of the figure if the perimeter is 35 2/3 cm, is calculated as: 10.9 cm.
How to Find the Perimeter of a Figure?The perimeter of a figure is the total length surrounding the figure.
We are given that the figure shown below has a perimeter of 35 2/3 cm, which means all the total length of all its sides equals 35 2/3 cm.
To find the missing length, sum all the given lengths and subtract it from the perimeter of the figure.
Sum of all the given lengths = 4 3/4 + 3 1/2 + 1 1/3 + 1 1/3 + 3 1/2 + 9.25 + 6.6 = 4.75 + 2.3 + 1.3 + 1.3 + 2.3 + 9.25 + 6.6
Sum of all the given lengths = 27.8 cm
The missing side = 38 2/3 - 27.8 = 38.7 - 27.8
The missing side = 10.9 cm.
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The ticket sales at a movie theater were $4,740. Adult tickets are $15, and senior tickets are $10. The
number of senior tickets sold was 37 less than twice the number of adult tickets. Determine the
number of adult tickets and number of senior tickets sold.
How many adult tickets were sold?
How many senior tickets were sold?
Answer: 291 with a remainder of 375
Step-by-step explanation: What you need to do first is multiply the senior tickets by 37 which is 370. Now subtract 4,740 by 370 which equals 4370. Then divide 4370 by 15. 4370 divided by 15 equals 291. Multiply 291 by 15 (just to find the remainder) which equals 4,365. 4,740 subtracted by 4,365 equals 375. So the answer is 375
A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 12 feet less than 3 times the height. Find the width and the height if the carpenter
expects to use 22 feet of lumber to make it.
Width:
feet
Height:
feet
Answer:
The width is 3 feet and the height is 6 feet.
Step-by-step explanation:
37+1/2-(x+1/4)=9(4x-7)+5
Can you please help me
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 80 and 120? (b) What percentage of people has an IQ score less than 60 or greater than 140? (c) What percentage of people has an IQ score greater than 160?
Using the Empirical Rule, the percentages are given as follows:
a) 68%.
b) 5%.
c) 0.15%.
What does the Empirical Rule state?It states that, for a normally distributed random variable, approximately:
68% of the values in the distribution are within 1 standard deviation of the mean.95% of the values in the distribution are within 2 standard deviations of the mean.99.7% of the values in the distribution are within 3 standard deviations of the mean.For item a, 80 and 120 are within one standard deviation of the mean, hence:
68% of people has an IQ score between 80 and 120.
For item b, the bounds are within two standard deviations of the mean, hence 5% of the observations are outside this interval, that is:
5% of people has an IQ score less than 60 or greater than 140.
For item c, 160 is three standard deviations above the mean. Considering the symmetry of the normal distribution, 0.3/2 = 0.15% of people has an IQ score greater than 160?.
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How to write an expression for number of tokens needed for v video games if each game takes 4 tokens
Answer: 4v
Step-by-step explanation:
If 4 tokens are needed for each video game, then you multiply 4 by the number of video games v.
For example, 3 video games, each requiring 4 tokens, would require a total of 12 tokens. This can be also defined as:
v = 3
4*(3) = 12
commencement of business with cash 10000 and goods 5000
The answer to given question is given below in detailed manner.
Business Commencement Date means the first date on which the Company or any Affiliate, licensee or sublicensee of the Company makes a commercial sale of any Product within the Field of Activity in the Territory that would generate a payment to the Partnership or the Class A Limited Partners.
Hence here commencement date is not applicable;
for starting capital required=10000+5000
Now adding commencement of business with cash 10000 and goods 5000 as date commencement is not applied here so we get =15000
The capital account is a liability for business this amount is needed to return to investor one day.
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Answer: The answer to given question is given below:
Step-by-step explanation:
Business Commencement Date means the first date on which the Company or any Affiliate, licensee or sublicensee of the Company makes a commercial sale of any Product within the Field of Activity in the Territory that would generate a payment to the Partnership or the Class A Limited Partners.
hence here
commencement date is not applicable;
for starting capital required=10000+5000
=15000
The capital account is a liability for business
this amount is needed to return to investor one day.
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Fill in the blanks. (5 x 3) x __) a b 4x( x 9) = 72 C 7x (2x __) = 42 d (_____________× 5) x 5 = 75 x __) = 27 e (3 x 3) x = 60
The solution to each division problem is;
1) 4
2) 2
3) 3
4) 3
5) 3
1) We are given the expression;
(5 * 3) * ___ = 60
To get the blank answer, we will divide both sides by (5 * 3) to get;
60/(5 * 3) = 4
2) We are given the expression;
4 *( ___ * 9) = 72
To get the blank answer, we will divide both sides by (4 * 9) to get;
72/(4 * 9) = 2
3) We are given the expression;
7 * (2 * ___) = 42
To get the blank answer, we will divide both sides by (7 * 2) to get;
42/(7 * 2) = 3
4) We are given the expression;
(___ * 5) * 5 = 75
To get the blank answer, we will divide both sides by (5 * 5) to get;
75/(5 * 5) = 3
5) We are given the expression;
(3 * 3) * ___ = 27
To get the blank answer, we will divide both sides by (3 * 3) to get;
27/(3 * 3) = 3
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during last year my car depreciated by 30%. If the value of my car is $25,000 today, then what was the value of my car one year ago?
The value of my car one year ago was $35,714.3
INTEREST FORMULA: The interest formula includes two types of interests - simple interest and compound interest. Interest is the cost a borrower pays a lender for a loan. This additional sum, or the interest, must be paid in addition to the loan itself. The compound interest formula and the simple interest formula are both discussed in the interest formula.
Present value of the car = A = $25,000
Depreciation rate = r = 30% per annum
Time = t = 1 year
Let the initial value be p
We know the formula, A = P(1 – r/100)^t
$25,000 = P [1 – 30/100] ^1
$25,000 = P (7/10)
P = (25,000 * 10) / 7
P = $35,714.3
Therefore, One year ago, my car's value was worth $35,714.3.
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Given: 2 ( x + 3)-8=10
Prove: x = 6
Answer:
x=6
Step-by-step explanation:
2(x+3)-8=10
use 2 to multiply the one in the bracket
(2x+6)-8=10
group like terms
2x-2=10
send all constant terms to one side of the equation
2x=10+2
2x=12
divide both side by the coefficient of x
2x/2=12/2
x=6
Does anyone know the answer to 0.038 ounces to mg? Please
Answer:
1,077.281879 mg is the answer
2) Let a =i+2j-7k and b=5i-2j+4K Find
a) a.b
b) axb
C) The direction cosine of axb
D) The Unit Vector Perpendicular to both a&b
a) Dot product: recall that
i • i = j • j = k • k = 1
i • j = i • k = j • k = 0
Then
a • b = (i + 2j - 7k) • (5i - 2j + 4k)
a • b = 5 (i • i) - 4 (j • j) - 28 (k • k)
a • b = 5 - 4 - 28
a • b = -27
b) Cross product: recall that
i × i = j × j = k × k = 0
i × j = -(j × i) = k
j × k = -(k × j) = i
k × i = -(i × k) = j
Then
a × b = (i + 2j - 7k) × (5i - 2j + 4k)
a × b = -2 (i × j) + 4 (i × k) + 10 (j × i) + 8 (j × k) - 35 (k × i) + 14 (k × j)
a × b = -12 (i × j) - 6 (j × k) - 39 (k × i)
a × b = -6i - 39j - 12k
c) Recall the dot product identity
x • y = ||x|| ||y|| cos(θ)
We have
||a × b|| = √((-6)² + (-39)² + (-12)²) = 9√21
Then the direction cosines α, β, γ of a × b are
(a × b) • i = ||a × b|| ||i|| cos(α)
⇒ cos(α) = -6/(9√21) = -2/(3√21)
(a × b) • j = ||a × b|| ||j|| cos(β)
⇒ cos(β) = -39/(9√21)
(a × b) • k = ||a × b|| ||k|| cos(γ)
⇒ cos(γ) = -12/(9√21) = -4/(3√21)
d) a × b is perpendicular to both a and b, so we can get a unit vector by scaling this down by its magnitude. This is the same as the vector of direction cosines:
(a × b)/||a × b|| = (-6i - 39j - 12k)/(9√21)
(a × b)/||a × b|| = -2/(3√21) i - 39/(9√21) k - 4/(3√21) k
The population of deer in a national forest has consistently increased by 5% each year. This year, the population of deer is 5,000. If the population increases at the same rate, what number of deer is expected to be in the national forest next year?
Select the correct answer below:
4,750
5,025
5,250
5,263
5,512
Answer:
5250.
Step-by-step explanation:
Consistent = Population of deer increases 5% each year.
This year = 5000
105% of 5000 = 5250
The graph of a normal curve is given. Use the graph to identify the value of and . μ sigma
From the given graph the value of μ is 530 and the value of σ is 15.
In the Normal Curve the value at which the shape of the graph is highest is called it's mean(μ) and the value on the left of mean is μ-σ and the value on the right of the mean is μ + σ .
In the Given question
the shape of the graph is highest at 530,
hence the value of mean(μ) = 530. ....(i)
we know that the value on the left of mean is μ-σ .....(ii)
From the graph the value to the left of mean(μ) is 515. ...(iii)
Equating equation (ii) and (iii) we get ,
μ-σ = 515
Substituting the value of μ from equation (i) we get ,
530 - σ = 515
σ = 530 - 515
σ = 15
Therefore , From the graph the value of μ is 530 and the value of σ is 15.
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1/4 of a pizza is 150 calories how much is a whole pizza?
What would the Median of 112 113 116 118 119 124 be?
5. Explain how to determine which operation to complete first when simplifying the expression (15 ÷ 5+4²) − [4³ − |(13² + 2) ÷ (4 − 1)]. Be specific.
Answer: Parentheses
Step-by-step explanation: Parentheses always go first because if you look at the work PEMDAS, P= parentheses, E= exponents, M= Multiplication, D= division, A= addition, and S= subtraction.
Find the perimeter of the rectangle.
X+1
2.5x - 4
Answer: 7x-6
Step-by-step explanation:
P=perimeter. L=length. W=width
P=2L+2W
P=2(x+1)+2(2.5x-4)
P=2x+2+5x-8
P=2x+5x+2-8
P=7x-6
Tucker ran five 3/8 miles on Monday and three 3/4 miles on Tuesday how far did you run on both days
Answer:
9/8 mile or 1 and 1/8 mile
Step-by-step explanation:
Add 3/8 + 3/4
LCD is 8 so it would be 3/8 + 6/8 which is 9/8 (which can be converted to the mixed number 1 and 1/8)
Alonso's family rented a car when they flew to
Orlando for a 4-day vacation. They paid $39
per day and $0.09 for each mile driven. How
much did it cost to rent the car for 4 days and
drive 350 miles, not including tax?
Answer:
$187.5
Step-by-step explanation:
39 (4) + 0.09 (350)
156 + 31.5
$187.5
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Answer:
$187.5
Step-by-step explanation:
You need to multiply the daily cost by the days. In this case, 39*4 = 156. Then, we can get the cost for the miles driven, being 0.09*350 = 31.5.
We can now add the two numbers together:
156 + 31.5 = $187.5
100 more than 365 is equal to 65more then
Answer:
x = 400Step-by-step explanation:
100 more than 365 is equal to 65more then
we can solve with an equation
100 + 365 = 65 + x
100 + 365 - 65 = x
465 - 65 = x
400 = x
------------
check
100 + 365 = 65 + 400
465 = 465
the answer is good
f(x) = 7_4z
20
What is the value of f (6).?
0-0
10
10
5
O
O
15
Answer:
f(6) = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
substitute x = 6 into f(x)
f(6) = [tex]\frac{6^2-4(6)}{20}[/tex] = [tex]\frac{36-24}{20}[/tex] = [tex]\frac{12}{20}[/tex] = [tex]\frac{3}{5}[/tex]