Answer:
y-incercepts:
sinh(x):0, cosh(x)=1
Limits:
positive infinity: sinh(x): infinity, cosh(x): infinity
negative infinity: sinh(x): - infinity, cosh(x): infinity
Step-by-step explanation:
We are given that
[tex]\sinh(x)=\frac{e^{x}-e^{-x}}{2}[/tex]
[tex]\cosh(x)=\frac{e^{x}+e^{-x}}{2}[/tex]
To find out the y-incerpt of a function, we just need to replace x by 0. Recall that [tex]e^{0}=1[/tex]. Then,
[tex]\sinh(0) = \frac{1-1}{2}=0[/tex]
[tex]\cosh(0) = \frac{1+1}{2}=1 [/tex]
For the end behavior, recall the following:
[tex]\lim_{x\to \infty}e^{x} = \infty, \lim_{x\to \infty}e^{-x} = 0[/tex]
[tex]\lim_{x\to -\infty}e^{x} = 0, \lim_{x\to -\infty}e^{-x} = \infty[/tex]
Using the properties of limits, we have that
[tex]\lim_{x\to \infty} \sinh(x) =\frac{1}{2}(\lim_{x\to \infty}e^{x}-\lim_{x\to \infty}e^{-x})=(\infty -0) = \infty[/tex]
[tex]\lim_{x\to \infty} \cosh(x) =\frac{1}{2}(\lim_{x\to \infty}e^{x}+\lim_{x\to \infty}e^{-x}) =(\infty -0)= \infty[/tex]
[tex]\lim_{x\to -\infty} \sinh(x) =\frac{1}{2}(\lim_{x\to -\infty}e^{x}-\lim_{x\to -\infty}e^{-x}) = (0-\infty)=-\infty[/tex]
[tex]\lim_{x\to -\infty} \cosh(x) =\frac{1}{2}(\lim_{x\to -\infty}e^{x}+\lim_{x\to -\infty}e^{-x}) =(0+\infty)= \infty[/tex]
is (1,3) a solution to this system of equations?
4x + 5y = 19
x + 5y = 16
Answer:
Yes
Step-by-step explanation:
I graphed both of the equations on the graph below to show you that they intersect at the point (1,3), making it the solution to the system.
If this answer is correct, please make me Brainliest!
Answer: Yes
Step-by-step explanation:
Seemas little sister is now 5 years old.if Her age is 2 years more than 1/4 of seemas age, how old is seems
Answer:
12
Step-by-step explanation:
Seema’s little sister is 2 years more than ¼ of Seema’s age, so you should subtract 2 from 5 to find ¼ of Seema’s age. If 3 is ¼ of Seema’s age, all you do is multiply it by 4 to get the original number. 3x4 is 12, so the final answer is that Seema is 12.
If 15+3x=3(2−2x), then x= [blank]
Answer:
x = -1
Step-by-step explanation:
15+3x=3(2−2x)
Distribute
15+3x = 6 -6x
Add 6x to each side
15+3x+6x = 6-6x+6x
15+9x = 6
Subtract 15 from each side
15-15+9x = 6-15
9x = -9
Divide by 9
9x/9 = -9/9
x = -1
Robin is 11 years old. Her mother, Gwen, is 2 years more than 3 times Robin’s age. How old is Gwen?
Answer:
35 years old.
Step-by-step explanation:
To find the age of Gwen, multiply Robin's age, which is 11, by 3, which gives you 33. Then add two to 33 to get Gwen's age, which is 35 years.
Answer:
Gwen is 35 years old
Step-by-step explanation:
In order to understand the word problem better, I turned it into and equation.
Since Gwen is 2 years older than 3 times Robins age, the equation would be:
Gwens age = (3 • Robins age) + 2
G = (3 • 11) + 2
G = (33) + 2
G = 35
So Gwen is 35 years old.
In circle G, r = 3 units. Maria draws a circle with double the area of circle G.
What is the area of Maria’s circle?
Answer:
The answer 28.27 *2 = 56.54
Step-by-step explanation:
A= πr^2
The area of Maria's circle, which is double the area of circle G is: 56.52 sq. cm.
What is the Area of a Circle?Area of a circle = πr²r = radius of the circleGiven:
Radius (r) of circle G = 3 units
Area of circle G = π(3²) = 28.26 sq. units.
Area of Maria's circle = 2(area of circle G)
Therefore:
Area of Maria's circle = 2(28.26)
Area of Maria's circle = 56.52 sq. cm.
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1. Michael rented a car for one day at a daily rate of $42. He also had to pay
$0.55 per mile driven, but there were no other fees. If Michael returned the.
car at the end of the day and paid $114.60, how many miles did he drive? *
Answer:
132 Miles
Step-by-step explanation:
First you must subtract $42 from $114.60.
[tex]114.60 - 42 = 72.6[/tex]
Then, you need to divide $0.55 by $72.6.
[tex]72.6 \div 114.60 = 132[/tex]
Hope this helped! :)
Which is true of the number 55,555?
A.Each digit has a value less than the value of the digit to its right and greater than the value of the digit to its left.
B.Each digit has a value 10 times the value of the digit to its right and 10 times the value of the digit to its left.
C.Each digit has a value 110 of the value of the digit to its right and 10 times the value of the digit to its left.
D.Each digit has a value 10 times the value of the digit to its right and 110 of the value of the digit to its left.
Answer:
D. Each digit has a value 10 times the value of the digit to its right and 1/10 of the value of the digit to its left
Step-by-step explanation:
Digits increase in value by a factor of 10 for each place you move to the left. Hence a digit to the right has 1/10 the value.
_____
Comment on place value
The multiplier for a base-10 (decimal) number system is 10 as you move one place to the left. In some other base, the multiplier is that base. In a binary (base-2) number system, each "bit" increases in value by a factor of 2 as you move to the left.
Therefore, the "Choice D" is the only correct answer.
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Mary walks the 3 day breast cancer walk. They break the 62 miles evenly for each day. How
4
many miles does she walk in one day?
Answer:
she would walk at least those 62 miles
Step-by-step explanation:
We are told that in the 3 days of the walk to fight cancer, Mary breaks the 62 mile barrier every day, that is to say that every day she travels 62 miles or more.
You ask us how much she walks in a single day, considering what the statement that goes at least 62 miles each day says, she would walk at least those 62 miles on a normal day.
Kelly contracts with Raphael for Raphael to bring a pony to her daughter's birthday party in exchange for $100. Kelly later learns her daughter is frightened of ponies. She contacts Raphael and Raphael agrees to bring a donkey to the party for $50 instead. What is true of the original agreement involving the pony and the $100?
Answer:
It was discharged by substituted contract
Step-by-step explanation:
In this situation, instead of simply canceling their original contract and terminating their interaction, Raphael and Kelly reached another agreement and stablished a substituted contract in place of the original one.
Therefore, the original agreement involving the pony and the $100 was discharged by substituted contract .
Complete parts ​(a) through ​(c) below. ​(a) Determine the critical​ value(s) for a​ right-tailed test of a population mean at the alphaequals0.05 level of significance with 15 degrees of freedom. ​(b) Determine the critical​ value(s) for a​ left-tailed test of a population mean at the alphaequals0.10 level of significance based on a sample size of nequals10. ​(c) Determine the critical​ value(s) for a​ two-tailed test of a population mean at the alphaequals0.05 level of significance based on a sample size of nequals13.
Answer:
a) [tex] t_{\alpha}= 1.753[/tex]
b) [tex] t_{\alpha}= -1.383[/tex]
c) [tex] t_{\alpha/2}= \pm 2.179[/tex]
Step-by-step explanation:
Part a
For this case we know that the degrees of freedom are:
[tex] df = 15[/tex]
And we want a right tailed test so then we need to find in the t distribution with degrees of freedom =15 a critical value who accumulate 0.05 of the area in the right and we got:
[tex] t_{\alpha}= 1.753[/tex]
Part b
For this case the significance is [tex]\alpha=0.1[/tex] the degrees of freedom are:
[tex] df = n-1= 10-1=9[/tex]
And since is a left tailed test the critical value for this case would be:
[tex] t_{\alpha}= -1.383[/tex]
Part c
For this case the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2=0.025[/tex] the degrees of freedom are:
[tex] df = n-1= 13-1=12[/tex]
And since is a two tailed test the critical values for this case would be:
[tex] t_{\alpha/2}= \pm 2.179[/tex]
Which choice is equivalent to the expression below?
28.24
O A. 28 + 22/10 + 24/100
O B. 28+ 2/10 + 4/10
O C. 28. 22/10. 24/100
O D. 28. 224/10
Answer:
C
Step-by-step explanation:
Rearrange the equation so u is the independent variable.
-12u + 13 = 8w - 3
w = __
Answer: w = -3u/2 + 2
Step-by-step explanation:
-12u + 13 = 8w - 3
-12u + 13 + 3 = 8w -3 + 3
-12u + 16 = 8w
w = -3u/2 + 2
A rectangular room is 12 1/2 feet long and 10 1/3 feet wide. What is the area of the room?
Answer:120 1/6 feet sq.
Step-by-step explanation: Area of a rect. = length×breadth(width)
Area=12 1/2× 10 1/3
Area= 120 1/6
Please rate 5 stars and vote as brainliest:)
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Pip and Sara win some money and share it in the ratio 7:5. Pip gets £30 more than Sara. How much did Sara get?
Answer:
75 sweets.
Step-by-step explanation:
Pip gets 7/(7+5) = 7/12 .
Let Sara get x sweets so Pip gets 7/5 x sweets.
7/5 x = x + 30
2/5 x = 30
x = 5/2 * 30 = 75.
Sara gets 75 sweets.
Answer:
Sara has £75
Step-by-step explanation:
Pip : Sara
7 : 5
If Pip gets £30 more than Sara, then
5x+30=7x
Where x is £?
Subtract 5x from both sides
30=2x
Divide both sides by 2
x=£15
£15
Pip : Sara
105: 75
How many cubes with side lengths of 1/2 does it take to fill the prism? The prism has dimensions of 1, 2, and 2 1/2 cm
Answer:
The volume of the cube is 1/2 x 1/2 x 1/2 = 1/8
length x width x height = volume
1x2x2.5=5
2 1/2 = 2.5 because 1/2=0.5
to divide fractions multiply the reciprocal. The reciprocal is the fraction flipped over
5 / 1/8 = 5 x 8/1
5x8/1=40
40 cubes
Step-by-step explanation:
There are seven black socks, eight blue socks, 10 white socks, and five patterned socks in the drawer. What is the probability of pulling a blue sock, replacing it, and then drawing a patterned sock out of the drawer?
Answer:
2/45
Step-by-step explanation:
Total socks:
7 + 8 + 10 + 5 = 30
P(blue) × P(patterned)
8/30 × 5/30
4/15 × 1/6
2/45
Answer:
2/45
Step-by-step explanation:
The total number of socks is 7+8+10 +5
30
P(blue) = number of blue socks / total
= 8/30 = 4/15
Then we replace it so we have the same number of socks
P(patterned) = number of patterned socks / total
= 5/30 = 1/6
P(blue, replace/patterned) = 4/15*1/6
=2/45
A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of the suspects. After further investigation, it is determined that the guilty party has a blood type found in only 10% of the population at large. Suspect A does have this blood type; the blood type of Suspect B is unknown.
Define the following 3 events A, M and C.
A: "A is guilty" (Thus ° denotes "B is guilty')
M: "A’s blood type matches that of the guilty party"
C: "B's blood type matches that of the guilty party"
A. The police reported that suspect A is not a relative of suspect B. Is it reasonable to set P( MA)=P(C|A)=10%? Why?
B. Assume that P(MAC)=P(C|A)=10%. Given the information from the further investigation of the crime scene, what is the probability that A is the guilty party?
C. Assume that P( MA)=P(C/A)=10%. Given the information from the further investigation of the crime scene, what is the probability that B’s blood type matches that of the guilty party?
Answer:
a) MA conditional with C can be interpreted as A which is known and C which is unknown match
b) 10/11
c) 2/11
Step-by-step explanation:
A={A is the guilty party}
[tex]M_A[/tex] = {A blood type matches that of the guilty party}
C = {B is the guilty party}
[tex]M_C[/tex] = {B blood type matches that of the guilty party}
a) The chance is 10% because MA conditional with C can be interpreted as A which is known and C which is unknown match
b) the probability that A is the guilty party is given by [tex]P(A/M_A)[/tex]. Using bayes theorem:
[tex]P(A/M_A)=\frac{P(M_A/A)P(A)}{P(M_A/A)P(A)+P(M_C/C)P(C)} =\frac{1*1/2}{(1*1/2)+(1/10*1/2)} =\frac{10}{11}[/tex]
c) the probability that B’s blood type matches that of the guilty party is given as [tex]P(M_C/M_A)[/tex]. Using LOTS Therefore:
[tex]P(M_C/M_A)=P(M_C/M_A,A)P(A/M_A)+P(M_C/M_A,A)P(C/M_A)=\frac{1}{10}*\frac{10}{11} +1*\frac{1}{11} =\frac{2}{11}[/tex]
Using the image of ⊙O to find the value of x, y and z.
Answer:
x = 30°
y = 60°
z = 96°
Step-by-step explanation:
Well the angle from the center that intercepts 120° is equal to 120° since it is a central angle.
y = 60° because oof supplementary angles.
The measure of z is 48 * 2 because the 48° is an inscribed angle.
z = 96°
And, the arc that angle y intercepts is also the arc the x intercepts.
That arc is 60° because 180° - 120° = 60°
x is an inscribed angle, so x = 1/2 * 60°
x = 30°
Hope this helps.
Andrea got 3 times as much candy than Stacy.If Stacy and Andrea got 28 pieces,how many pieces did Andrea get?
Answer:
Step-by-step explanation:
28x3=84
Answer:
The answer is 84
Because 28x3=84
Find the balance earned on an account that has $60,000 deposited for 6 years at 1.125% interest compounded continuously? Please help
Answer:
The balance of the account is $64,190.
Step-by-step explanation:
The amount of money after t years of continous compounding is given by the following equation:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial deposit and r is the interest rate, as a decimal.
$60,000 deposited for 6 years at 1.125% interest compounded continuously.
This means that [tex]P = 60000, r = 0.01125, t = 6[/tex]
So
[tex]P(6) = 60000e^{0.01125*6} = 64190[/tex]
The balance of the account is $64,190.
What is the length of the diagonal in a rectangular prism that measures 8mm by 14mm by 6m? Round your answer to the nearest tenth
Answer:
17.2
Step-by-step explanation:
It's kinda like the pythagorean theorem where you square the sides, add them, and then square root the answer. I hope this is correct
Get 14 points, Plz help me with this question, and give the right answer cause it's important
All angles are of triangle and thus give sum of 180⁰
x + 5 + 7x - 5 + x = 180⁰
9x = 180⁰
x = 20⁰
Answer:
it's 20
Step-by-step explanation:
(X+5)° + (7x-5)° + x°= 180° { sum of the three angles of the triangle is 180°}
X+5+7x-5+X = 180
X+7x+X+5-5= 180
9x+0 = 180
9x = 180
therefore X= 180/9
= 20
Please do it on a piece of paper if possible <3
a is 100% more than b.
Which of these shows the ratio a:b?
2:1
100:1 1:100
1:2
A
B
C
D
Answer:
2-1=1 so A. is 100% more than B because A is 2 times bigger than B.
A. is the answer 2:1
Hope this helps
Step-by-step explanation:
The option that shows the ration A: B is Option C - 1:2. See the rationale below.
How to compute the aboveIf A is 100% more than B, it means that A is equal to B plus 100% of B. In other words, A is twice the value of B.
Therefore, the ratio of A to B is 1:2, indicating that A is twice as much as B.
Recall that a ratio is a quantitative relationship between two or more quantities, indicating how many times one quantity is contained or repeated in relation to another quantity.
It is expressed as a fraction or with a colon (:), representing the relative comparison of the quantities.
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In a restaurant there are 8 starter 15 main dishes 9 dessert Jane is going to choose one of the following how many different ways are there for her to choose
Answer:
1335
Step-by-step explanation:
Starter + Main = 8 x 15 = 120
Main + Dessert = 15 x 9 = 135
Starter + Main + Dessert = 8 x 15 x 9 = 1080
120 + 135 + 1080 = 1335 possibilities
Answer:
Step-by-step explanation:
STARTER + MAIN:
8 x 15 = 120
MAIN + DESSERT:
15 x 9 = 135
STARTER + MAIN + DESSERT:
8 x 15 x 9 = 1080
120 + 135 + 1080 = 1335 possibilites
In a new experimental teaching method, when students have questions in class, they send them to the instructor via a laptop computer. From time to time, the instructor pauses to read the questions and to provide the answers, without revealing the identities of the students who are asking the questions. This new method is supposed to eliminate the reluctance of students to ask questions for fear of revealing their lack of understanding in public. In a study of this new method, 69 male students and 73 female students participated. Treat these as if they were simple random samples. Of the male students, 38 said that they liked the new method better than the traditional one in which students raise their hands to ask questions. Of the female students, only 20 said they liked the new method better
(a) Construct a 95% confidence interval for the difference between the proportions of male and female students who like the new method better. Let p1, denote the proportion of male students who like the new method better and let p2 denote the proportion of female students who like the new method better.
(b) A 95% confidence interval for the difference between the proportions of male and female students who like the new method better is __________.
Answer:
a) (0.124, 0.435)
b) I am 95% confident that the proportion difference is between 0.124 and 0.435
Step-by-step explanation:
Given that:
For male students: number of male students ([tex]n_m[/tex]) = 69, number who liked the new method (x) = 38
For female students: number of female students ([tex]n_f[/tex]) = 73, number who liked the new method (x) = 20
a) The probability that a male student like the new method ([tex]P_1[/tex]) is given as:
[tex]P_1=\frac{38}{69} =0.55[/tex]
The probability that a female student like the new method ([tex]P_2[/tex]) is given as:
[tex]P_2=\frac{20}{73} =0.27[/tex]
c = 95%, α = 1 -c = 0.05
[tex]z_{\frac{\alpha }{2} }=1.96[/tex]
the difference between the proportions of male and female students who like the new method better = [tex]P_1-P_2[/tex] ± [tex]z_{\frac{\alpha }{2} }\sqrt{\frac{P_1(1-P_1)}{n_m} +\frac{P_2(1-P_2)}{n_f}}[/tex] = [tex]0.55-0.27[/tex] ± [tex]1.96\sqrt{\frac{0.55(1-0.55)}{69} +\frac{0.27(1-0.27)}{73}}[/tex] = (0.124, 0.435)
b) I am 95% confident that the proportion difference is between 0.124 and 0.435
A vertical pole stands in the sea. A mark, X, on the pole is 1.6m above sea level at low tide, the sea level is 3.9m higher than at
low tide.
(a) Find the distance of x below sea level at high tide.
(b) What is the position of x from sea level at the time when the sea level is exacly half way between high tide and low tide?
Answer:
ummm I would say a angle of 7.65
Step-by-step explanation:
Answer:
7.65
Step-by-step explanation:
The product of 2 and 8 divided by 8 is equal to?
Answer:
2
Step-by-step explanation:
product of 2 and 8= multiply
2x8=16
Divide by 8
16/8=2
How much wood will Moritz need to create his ramp?
Moritz is creating a wooden ramp with the given
dimensions. The ramp will not need a bottom face.
ft2
5 ft
3 ft
4 ft
6 ft
5 ft
6 ft
3 ft
4 ft
Answer:
60 ft
Step-by-step explanation:
got it right
Answer:
60
Step-by-step explanation:
PLEASE HELP ITS FOR MATH
The answer is b. none. This is because the lines are parallel and therefore do not intersect at a point, meaning that there are no solutions.