Assume the cost in dollars of a call, y, is a linear function of the time in minutes, the linear equation that gives the cost of a Sunday call is y = 0.05x + 0.34
How to model a linear functionThe linear equation is represented as follows:
y = mx + b
where
m = slope
b = y -intercept
Therefore,
(44, 2.54)(10, 0.84)
m = [tex]\frac{0.84-2.54}{10-44}[/tex]
m = [tex]\frac{-1.7}{-34}[/tex]
m = $0.05
Therefore,
y = cost in dollars
x = time in minutes
0.84 = 0.05(10) + b
0.84 - 0.5 = b
b = 0.34
Therefore,
y = 0.05x + 0.34
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Let f(x)=[tex]\footnotesize \rm \lim_{n \to \infty } \left \lgroup \frac{ {n}^n(x + n) \bigg( x + \dfrac{n}{ 2} \bigg) \dots \bigg(x + \dfrac{n}{n} \bigg)}{n!( {x}^{2} + {n}^{2}) \bigg( {x}^{2} + \dfrac{ {n}^2 }{4} \bigg) \dots \bigg( {x}^{2} + \dfrac{ {n}^{2} }{ {n}^{2} } \bigg) } \right \rgroup^{ \dfrac{x}{n} } \\ [/tex] , for all x > 0. Then
[tex]\rm(A) \: f \bigg( \dfrac{1}{2} \bigg ) \geq f(1)[/tex]
[tex]\rm(B) \: f \bigg ( \dfrac{1}{3} \bigg) \leq f \bigg ( \dfrac{2}{3} \bigg)[/tex]
[tex]\rm(C) \: f'(2) \leq0[/tex]
[tex] \rm(D) \: \frac{f'(3)}{f(3)} \geq \frac{f'(2)}{f(2)} \\ [/tex]
Use the old exp-log trick and properties of the logarithm to rewrite the limit as
[tex]\displaystyle \lim_{n\to\infty} \left(\frac{n^n \left(x+\frac n1\right) \left(x+\frac n2\right) \cdots \left(x+\frac nn\right)}{n! \left(x^2+\left(\frac n1\right)^2\right) \left(x^2+\left(\frac n2\right)^2\right) \cdots \left(x^2+\left(\frac nn\right)^2\right)}\right)^{\frac xn}[/tex]
[tex]\displaystyle = \exp\left[\lim_{n\to\infty} \frac xn \ln \left(\frac{n^n \left(x+\frac n1\right) \left(x+\frac n2\right) \cdots \left(x+\frac nn\right)}{n! \left(x^2+\left(\frac n1\right)^2\right) \left(x^2+\left(\frac n2\right)^2\right) \cdots \left(x^2+\left(\frac nn\right)^2\right)}\right)\right][/tex]
[tex]\displaystyle = \exp\left[x \lim_{n\to\infty}\frac1n\ln\left(\frac{n^n}{n!}\right) + \frac1n \sum_{k=1}^n \ln\left(x+\frac nk\right) - \frac1n \sum_{k=1}^n \ln\left(x^2+\left(\frac nk\right)^2\right)\right][/tex]
[tex]\displaystyle = \exp\left[x \lim_{n\to\infty}\frac1n\ln\left(\frac{n^n}{n!}\right) + \frac1n \sum_{k=1}^n \ln\left(x+\frac1{k/n}\right) - \frac1n \sum_{k=1}^n \ln\left(x^2+\frac1{\left(k/n\right)^2}\right)\right][/tex]
The first limit converges to 0, since n! asymptotically behaves like nⁿ, so ln(nⁿ/n!) → ln(1) = 0.
The two remaining sums converge to definite integrals:
[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{k=1}^n \ln\left(x + \frac1{\frac kn}\right) = \int_0^1 \ln\left(x + \frac1y\right) \, dy = \frac{(x+1) \ln(x+1)}x[/tex]
[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{k=1}^n \ln\left(x^2 + \left(\frac1{\frac kn}\right)^2\right) = \int_0^1 \ln\left(x^2 + \frac1{y^2}\right) \, dy = \frac{2\tan^{-1}(\sqrt x)}{\sqrt x} + \ln(1+x)[/tex]
It follows that
[tex]f(x) = \exp\left[x\left(0 + \dfrac{(x+1)\ln(x+1)}x - \dfrac{2\tan^{-1}(\sqrt x)}{\sqrt x} - \ln(x+1)\right)\right][/tex]
[tex]f(x) = \exp\left[\ln(x+1) - 2\sqrt x \tan^{-1}(\sqrt x)\right][/tex]
[tex]f(x) = (x+1) e^{-2\sqrt x \tan^{-1}(\sqrt x)}[/tex]
By computing f'(x) and f''(x), it's easy to show that f'(x) ≤ 0 and f''(x) ≥ 0 for all x > 0. So f(x) is decreasing and f'(x) is increasing, and
• (A) f(1/2) ≥ f(1) is true
• (B) f(1/3) ≤ f(2/3) is false
• (C) f'(2) ≤ 0 is true
• (D) f'(3)/f(3) ≥ f'(2)/f(2) ⟺ f'(3)/f'(2) ≥ f(3)/f(2) ⟺ (something larger than 1) ≥ (something smaller than 1) is true
50 POINTS PLUS BRANLEST ANSWER!!!!!!!!!!
Complete the table by writing the two missing forms of the number. Make sure your fractions are reduced to lowest terms.
Answer: Look at picture
Answer:
a.) 0,51
b.) 51%
c.) 1/100
d.) 1%
e.) 3/20
f.) 0,15
Step-by-step explanation:
[tex]a.) \: \frac{51}{100} = 51 \div 100 = 0.51[/tex]
[tex]b.) \: \frac{51}{100} = 51\%[/tex]
[tex]c.) \: 0.01 = \frac{1}{100} [/tex]
[tex]d. )\: 0.01 = \frac{1}{100} = 1\%[/tex]
[tex]e.) \: 15\% = \frac{15}{100} = \frac{3}{20} [/tex]
[tex]f.) \: 15\% = \frac{15}{100} = 0.15[/tex]
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Which of the binomials below is a factor of this trinomial?
x^2 - 13x + 30
A. x + 5
B. x - 10
C. x^2 + 5
D. x + 6
Answer:
B. x - 10
Step-by-step explanation:
x² - 13x + 30 = (x - 3)(x - 10)
x² + (a + b)x + ab = (x + a)(x + b)
find the solution set of x² - 7x = -12?
a. {-2, 4}
b. {-4, 1}
c. {4, -4}
d. {3,4}
Answer:
The answer is d.
Step-by-step explanation:
[tex]x^{2} -7x+12=0\\(x-3)(x-4)=0\\x-3=0; x=3\\x-4=0; x=4\\(3,4)[/tex]
93x + 7 = 95x - 3
Solve the equation
Answer:
x=5
Step-by-step explanation:
Sergio found 4 pennies on the ground his sister said that she found 2times as many pennies Sergio figured out that his sister found 6 pennies .what did Sergio do wrong
Answer:
Sergio found 4 pennies on the ground and her sister said that she found twice as many as him
When his sister said that she found twice as many, sergio added 2 to his number of pennies instead of multiplying by 2
That's where Sergio made a mistake and got the answer wrong
help. I cant seem to figure this out.I'll give brainliiest.
This trapezoid represents the base of a right prism that has a surface area of 1280 square feet. The sum of the lengths of the legs of the trapezoid is 52 feet. What is the height of the prism? Enter your answer in the box.
PLEASE HELP I WILL GIV BRAINLY. 50 POINTS.
Answer:
6
Step-by-step explanation:
i took the test
The height of the prism is 49.2 feet
How to determine the height?The given parameters are:
Area = 1280 square feetThe sum of the length legs = 52 feetThe area of the trapezoid is:
Area = 0.5 * (Sum of opposite sides) * Height
So, we have:
1280 = 0.5 * 52 * Height
This gives
1280 = 26 * Height
Divide both sides by 26
Height = 49.2
Hence, the height of the prism is 49.2 feet
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In Martina's bucket there are 6 brown worms and 7 red worms.
Martina is going to choose 9 worms at random from the bucket to use for fishing.
What is the probability that she will choose 4 brown worms and 5 red worms? Round your answer to three decimal places.
Ethan is packing bags with treats for a party. He wants every bag to have exactly the same treats in it. Ethan had 96 granola bars and 64 lollipops. If he wants to make the most number of bags possible, how many bags can he make?
Answer:
32 Bags.
Step-by-step explanation:
PLEASE HELPPP!:( i’ll mark brainlest!
Question 1 Solve 18>12+x. Graph the solution. The solution is .
Answer:
6 greater than x
Step-by-step explanation:
I did the math on paper
Which scale of measurement most reasonably applies to Confidence in Education?
Answer:
I guess how many times out of x they will do something.
for example how many times out of 10 will bob ask out his crush vs Joe
Step-by-step explanation:
There isn't really an easy way to measure this.
The scale of measurement most reasonably applies to Confidence in Education would be the Ordinal scale.
What is the scale of measurement?The scale of measurement deals with how the variables are defined and categorized.
There are 4 types of scales of measurement;
1. Nominal scale
2. Ordinal scale
3. Interval scale
4. Ratio scale
We know that the Ordinale scale is used for variables in ranked order but the difference between them could not be determined.
Hence, The scale of measurement most reasonably applies to Confidence in Education would be the Ordinal scale.
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How far from the door must a ramp begin in order to rise 5 ft with an 11-degree angle of elevation? Round off your answer to the nearest hundredth.
PS. Please put a drawing/illustration. Thank you!
The door of the ramp must begin at a distance of 25.72ft in order to raise the ramp by 5ft.
Data;
height (opposite) = 5ftangle = 11°distance (adjacent) =xTrigonometric RatioTo solve this problem, this is a right angle triangle and we can use trigonometric ratio SOHCAHTOA here.
Since we have the value of angle and opposite and solving only for adjacent, we can use tangent of the angle.
[tex]tan \theta = \frac{opposite}{adjacent} \\[/tex]
Let's substitute the values into the formula above and solve
[tex]tan 11 = \frac{5}{x} \\x = \frac{5}{tan 11} \\x = 25.72ft[/tex]
The door of the ramp must begin at a distance of 25.72ft in order to raise the ramp by 5ft.
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Tom is reading an article about the population of a city. The city's exact population is 175,901 people. Tom says that the city's population rounded to the nearest thousand is 175,000. Is Tom correct?
Answer:
nope, it’s actually 176,000. the 901 is very high if u compare it to 499 which is the lowest number to round down to.
Step-by-step explanation:
The total yearly cost to rent a trumpet is $114. The monthly cost is constant with no initial fee.
A person rents a trumpet for 3 years and 5 months.
Show your work or explain how you would find the total cost, in dollars, for the person to rent the trumpet?
Write an equation that represents the relationship between m, the number of months a trumpet is rented, and t, the total cost to rent the trumpet.
Explain your equation.
Enter your answer and your work or explanation in the space provided.
Step-by-step explanation:
There are 12 months in a year so,
114/12= 9.5$/month
t=9.5m
Since T represents the total cost, we want to express it in terms of months by multiplying m which refers to the number of months by the monthly fee which i have already calculated.
Using this equation we can find out the answer to your previous question.
t=9.5m
but m=3×12+5=41 months (3 years 12 months each)
t=9.5(41)
t=389.5 $
Which words have vertical symmetry for all of the letters in the word? Check all that apply.
MOM
DIZZY
НІТ
SEAT
WAXY
Answer:
MOM
HIT
WAXY
I just did this on edge
Answer:
1 3 6
Step-by-step explanation:
thanks again everyone
Answer:
4x^3
Step-by-step explanation:
GCF is the Greatest Common Factor
12x^6 + 4x^4 + 28x^3
= 4x^3(3x^3 + x + 7)
GCF is 4x^3
Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.
Answer:divide both sides of the equation by 10.4
Step-by-step explanation:
Answer:
its d
Step-by-step explanation:
Which angles are adjacent to each other?
Answer:
Angles 7 and 8
Step-by-step explanation:
They are next to each other, and share a common side.
if m x and l m = 6 and l = 2 find the value of l when m = 15
Answer:
5
Step-by-step explanation:
6 / 2 = 15 / l
3 = 15 / l
l = 15 / 3
l = 5
what are the partial products when finding 1,643×4.
Answer:
4,000
600
160
12
Step-by-step explanation:
When using partial products, you basically break up the number into ones, tens, hundreds, thousands, etc.
So the partial products of 1,643 x 4 will be,
1,000 x 4
600 x 4
40 x 4
3 x 4
The partial products of the multiplication problems are,
4000
600
160
12
The answer will be 4,772.
The partial products of the multiplication problems are,
4000, 2400, 160 and 12
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
When using partial products, you basically break the number into ones, tens, hundreds, thousands, etc.
So the partial products of 1,643 x 4 will be,
1,643 can be written as 1000+600×40+3.
Now multiply with 4.
(1000+600×40+3)×4
1,000 x 4+600 x 4+40 x 4+3 x 4
4000+2400+160+12
Hence the partial products of the multiplication problems are,
4000, 2400, 160 and 12 and The answer will be 4,772.
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HELP! Should be easy for people who have taken the class.
Answer:
See below
Step-by-step explanation:
Definitions are:
1. Straight line2. Transitive 3. Subtraction 4. ∠1 ≅ ∠3Write the ratio in the simplest form 25 to 45
Answer: 5/9 is the simplified fraction for 25/45 by using the GCD or HCF method. Thus, 5/9 is the simplified fraction for 25/45 by using the prime factorization method.
Help me pleasse i need help asap whoever answers it first get brainliest
if f(a)=b and g(b)=c are functions then domain and range of fog and gof equals to
Answer:
fog =gofthen it will be equal
Slove for x
Show all work
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
[tex]x^2=8(8+42)[/tex]
[tex]x^2=8*50[/tex]
[tex]x=20[/tex]
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What is the sum of all positive 1 digit integers that 4221462 is divisible by?
9514 1404 393
Answer:
19
Step-by-step explanation:
The prime factorization of 4221462 is ...
4221462 = 2·3·7·100511
so, the 1-digit divisors are ...
1, 2, 3, 6, 7
The total of these numbers is 19.
What is the gradient of the graph shown?
Gradient = Slope.
Use two points on the line to find the slope.
Slope = change in y over change in x
Points: (-4,0) and (0,-4)
Slope = (-4 - 0) / (0 - -4)
Slope = -4/4 = -1
Slope = -1
P = 0.5e - 5 to determine P
Answer:
Let's solve your equation step-by-step.
p=(0.5)(2.718282)−5
Step 1: Simplify both sides of the equation.
p=(0.5)(2.718282)−5
p=1.359141+−5
p=(1.359141+−5)(Combine Like Terms)
p=−3.640859
p=−3.640859
Answer:
p=−3.640859
Step-by-step explanation: