Answer:
[tex]2 = ln(4) [/tex]
Step-by-step explanation:
[tex] {x}^{2} = 4[/tex]
Since the power is 2 and our answer is 4 our natural log equation look like
[tex]2 = ln(4) [/tex]
Each of three friends flips a coin 36 times.Angel records ”tails” 20 times,Santi records “tails” 17 times.Kataleya records “tails” 23 times. Find the relative frequency with which each friend records “tails” Which friend has a relative frequency that is closest to the theoretical probability of flipping “tails” 36 times?Explain.
Answer:
The one with 17
Step-by-step explanation:
Heads/tails=1/2 or 50%
20/36=56%
17/36=47%
20/36=64%
47% is closer to 50%
When driving in England, Brian drove through several speed cameras. On one drive, Brian left his hotel and after 7 minutes he was 2.5 km away and at that moment was measured going 0.5 kpm (kilometers per minute). Later, 18 minutes after he started driving, he was 14.8 km from the hotel and at that moment was measured going 0.8 kpm.
A. Find the linearization at 7 minutes.
B. Find the linearization at 18 minutes.
C. Compute two approximations for Brian's distance from his hotel at 14 minutes, using the linearizations from parts a and b.
D. Which approximation do you think is better? Why?
Solution :
The formula for the linearization of a function [tex]$f(x)$[/tex] at a point [tex]$x$[/tex] = a is given as
[tex]$L(x)=f(a)+(x-a)f'(a)$[/tex]
Assuming the time is t and the distance travelled is [tex]$f(t)$[/tex], that makes the speed as [tex]$f'(t)$[/tex].
So substituting them in the linearization formula,
A. At t = 7 minutes
f(7) = 2.5 km
f'(7) = 0.5 kpm
∴ [tex]$L_7(t)=f(7)+(t-7)f'(7)$[/tex]
[tex]$=2.5+(t-7)0.5$[/tex]
[tex]$=2.5+0.5t-3.5$[/tex]
[tex]$=0.5t-1$[/tex]
B. At t = 18 minutes
f(18) = 14.8 km
f'(18) = 0.8 kpm
∴ [tex]$L_{18}(t)=f(18)+(t-18)f'(18)$[/tex]
[tex]$=14.8+(t-18)0.8$[/tex]
[tex]$=14.8+0.8t-14.4$[/tex]
[tex]$=0.8t-0.4$[/tex]
C. Substituting the value of t as 14 in both the linearization to determine the position at 14 minutes, we get
[tex]$L_7(14)=0.5(14)-1.0$[/tex]
= 7 - 1
= 6 km
[tex]$L_{18}(14)=0.8(14)+0.4$[/tex]
= 11.2 + 0.4
= 11.6 km
D. According to the linearization at 7, the distance travelled between the 7 minutes and 14 minutes is = 6 km - 2.5 km
= 3.5 km
And between the 14 minutes and 18 minutes is = 14.8 km - 6 km
= 8.8 km
This is an average speed of 0.5 kpm in the first interval and an average speed of 2.2 kpm.
Now, according to the linearization of 18, the distance travelled between the 7 minutes and the 14 minutes is = 11.6 km - 2.5 km
= 9.1 km
And between 14 minutes and 18 minutes is = 14.8 km - 11.6 km
= 3.2 km
This gives an average speed of 1.3 kpm in the first interval and 0.8 kpm in the second interval.
Therefore, the second approximation is the better one since the average speed are closer to the actual readings in the second linearization.
Help will give brainly of aw ser is right
Answer:
40 is your answer:)
Step-by-step explanation:
4x3= 12
12/2=6
6x4=24
4x4=16
24+16= 40
***** Help asap! *****
The central limit theorem
A. states conditions under which a variable involving the sum of Y1,..., Yn i.i.d. variables becomes the Student t distribution.
B. postulates that the sample mean is a consistent estimator of the population mean.
C. only holds in the presence of the law of large numbers.
D. states conditions under which a variable involving the sum of Y1,..., Yn i.i.d. variables becomes the standard normal distribution.
Answer:
Option D (States.......distribution) is the appropriate choice.
Step-by-step explanation:
The superposition principle says that perhaps the sample distribution better reflects the regular distribution.
Because this sample size or group grows, all observations appear identical although irrespective of that same population demographics or distributions.It shows everybody precisely how the measures are to be distributed if we take a friendly reminder from some kind of population group.The latter choices should not affect the situation involved. The reaction, then, is the right one.
X^2/3 •5x =5x^5/3
Can someone explain how the exponent is 5/3?
Solve for y: 3d = 7y + 5
Answer:
d = [tex]\frac{7y+5}{3}[/tex]
Step by step explanation:
3d = 7y+5
Divide both sides by 3
[tex]\frac{3d}{3}[/tex]= [tex]\frac{7y}{3}[/tex]+ [tex]\frac{5}{3}[/tex]
Simplify
[tex]\frac{7y+5}{3}[/tex]
A savings account starts with $181.25. After 7 years of continuous compounding at an interest rate, r, the account has $1450.
What is the interest rate percentage?
Round the answer to the nearest hundredth.
Answer:
29.71
Step-by-step explanation:
Continuous Compounding Formula = P x e^(r x t)
= 181.25 x e^(0.29710000000000003 x 7) = 1450.37
Can someone help me with this? I am a little confused
How do I find the range of this rational function, how do I do the steps in order to find it, please help!!!
Answer:
Range= (0,∞) and (-∞,0)
Step-by-step explanation:
Theres no real process to finding this out you just look at what type of function you have, your graph and your asymptote. We can see that the parts above the asymptote go up and towards ∞ and the part below goes down to -∞ but they can not cross 0
Answer:
(-infinity, -32/81] U (0, positive infintiy).
( use the sideways 8 symbol for infinity).
Step-by-step explanation:
The range is all possible y values in a function.
We can find the inverse of the function to find the range.
[tex]y = \frac{8}{ {x}^{2} - 7x - 8 } [/tex]
Replace x with y
[tex]x = \frac{8}{ {y}^{2} - 7y - 8 } [/tex]
Write the LCD as two binomial,
[tex]x = \frac{8}{(y + 1)(y - 8)} [/tex]
Multiply both sides by both binomial
[tex]x(y + 1)(y - 8) = 8[/tex]
[tex](xy + x)(y - 8) = 8[/tex]
[tex]x {y}^{2} - 8yx + xy - 8x = 8[/tex]
[tex]xy {}^{2} - 8yx + xy = 8 + 8x[/tex]
[tex]y( {x}^{2} - 8x + x) = 8 + 8x[/tex]
[tex] \frac{8 + 8x}{ {x}^{2} - 7x } [/tex]
[tex] {x}^{2} - 7x = 0[/tex]
[tex] {x}^{2} - 7x + 12.25 = 12.25[/tex]
[tex](x - 3.5) {}^{2} = 12.25[/tex]
[tex](x - 3.5) = 3.5[/tex]
[tex]x = 3.5[/tex]
Plug that in to the function to find it range.
We get approximately
[tex] - \frac{35}{81} [/tex]
So this means a point on our function must include -35/81.
The vertical asymptote is 0 so our y cannot be zero but it goes infinitely up so our range is
(-infinity, -32/81]U (0, positive infintiy).
( use the sideways 8 symbol for infinity).
what is the expression for one-sixth of the sum of 7 and s plus the product of 2 and q
Answer:
= [tex]\frac{1}{6}[/tex] (7 + s) + ( 2 × q )
I'm pretty much sure that this is correct.
Can somebody help please
PLEASE ANSWER WITHIN THE NEXT 5 MINUTES!!!!!!! Kara and Steven are biking around a 105 kilometer path. They start biking from the same place, at the same time. Kara bikes at a speed of 15 km/h and Steven bikes at a speed of 30 km/h. How long will it take Steven to be at the same place at the same time with kara.
Step-by-step explanation:
105/30=3.5 hours for steven
105/15=7 hours for Kara.
they would be b at the same place in 7 hours when Kara catches up at 105km lol
Answer:
7 hrs
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
the graph (shown in red) below shows the solution set of which inequality?
Answer:
I think that is a
Step-by-step explanation:
If x=7-4 √3 then find the value of (x+1/x)^2
Answer:
29.03703703
Step-by-step explanation:
7-4 √3 = 5.196152423
(5.196152423 + 0.19245009)^2
Angles c and d are complementary. If angle c is 2x and angle d is 66, what is the value of x?
Answer:
x=12
Step-by-step explanation:
Complementary angles add up to 90 degrees. 90-66=24. 24 divided by 2 is 12.
A child weighing 59 lb has a bad infection and is to be given Cefaclor.
The dosage is 15 mg per kg.
The drug will be delivered in an oral suspension with concentration 250 mg/5 mL.
How many mL will she receive?
Round to the nearest whole number.
You will need to convert her weight to kg, using 1 kg = 2.2 lb.
Answer:
Step-by-step explanation:
59:2,2=26,81
15*26,81:250=1,6086
Does anyone know the answer?
Step-by-step explanation:
Yes sure.
a. New value of painting=60/100×$550=$330
b. New value of vase=70/100×$395=$276.5
c. New value of clock=180/100×$1175=$2115
d. New value of chair=95/100×$745=$707.75
Pls help me with this
HELP NEEDED PLSS
Given the following diagram, find the trigonometric ratios.
Leave answers as reduced fractions (improper fractions are fine).
B
sinA=
COSA =
Answer:
Sin A = 3/5
Cos A = 4/5
Step-by-step explanation:
To find trigonometric ratio, recall SOHCAHTOA.
Thus:
Reference angle = <A
Opposite side to <A = 6
Adjacent side = 8
Hypotenuse = AB = √(8² + 6²) = 10 (pythagorean theorem)
Therefore,
✔️Sin A = Opp/Hyp
Sin A = 6/10 = 3/5
✔️Cos A = Adj/Hyp
Cos A = 8/10 = 4/5
Two college instructors are interested in whether or not there is any variation in the way they grade math exams. They each grade the same set of 10 exams. The first instructor's grades have a variance of 58.9. The second instructor's grades have a variance of 84.8. Test the claim that the first instructor's variance is smaller. (In most colleges, it is desirable for the variances of exam grades to be nearly the same among instructors.) The level of significance is 10%. (Recall: that the larger of the 2 variances needs to be in the numerator as the test is 1-tailed to the right)
Answer:
Since the calculated value of F = 1.4397 is less than the critical value of
F (9,9)= 2.4403 we conclude that the first instructor's variance is smaller and reject H0.
Step-by-step explanation:
1)Formulate the hypothesis that first variance is equal or greater than the second variance
H0: σ₁²≥σ₂² against the claim that the first instructor's variance is smaller
Ha: σ₁²< σ₂²
2) Test Statistic F= s₂²/s₁²
F= 84.8/ 58.9= 1.4397
3)Degrees of Freedom = n1-1= 10-1= 9 and n2 = 10-1= 9
4)Critical value at 10 % significance level= F(9,9)= 2.4403
5)Since the calculated value of F = 1.4397 is less than the critical value of
F (9,9)= 2.4403 we conclude that the first instructor's variance is smaller and reject H0.
order the numbers 0.3, 2/5, -0.85, 0.09, 3/4, 3/20 least to greatest
Answer:
-0.85, 0.09, 3/20, 0.3, 2/5, 3/4
Step-by-step explanation:
Turn all the fractions into decimals
2/5 -> .4
3/4 -> .75
3/20 -> .15
Then order them
-.85, 0.09, 0.15, 0.3, 0.4, 0.75
Find the slope of the line.
help me please :(*****
Answer:
54
dcutvihvihvtuutcigciyvihvihvo
Answer:
Step-by-step explanation:
Select the point that is a solution to the system of inequalities.
A- (2,6)
B- (0,8)
C-(-2,-4)
D-(4,2)
HELP PLEASE!!!!!
Answer:
its A
Step-by-step explanation:
How much is 24% of 78,000
Answer: 18,720
Step-by-step explanation:
Let's take this equation
78,000(n)
n will equal 0.24, since we are trying to find 24% of 78,000
78,000(0.24)
18,720
Answer:
18720
Step-by-step explanation:
24/100 × 78,000
=18720
if you actually know plz give an explanation to the answer so i know you aren't just answering for points, please help this is due before 12:00
Answer:
B
Step-by-step explanation:
There is a 1/4 probability of getting an A out of a bag with letter MATH
For B) There are two A's our of 8 letters is ADMIRALS.
2/8 is the same as 1/4
The answer is B
A) is wrong because that 1/6
C) is wrong because that's 1/8
D) is wrong because that's 2/9
Answer:
B
Step-by-step explanation:
Probability of finding A in a word = number of A / number of letters in that word
Probability of finding A in MATH = 1/4
A. Probability of finding A in BECAME = 1/6
B. Probability of finding A in ADMIRALS = 2/8 = 1/4
C. Probability of finding A in USERNAME = 1/8
D. Probability of finding A in AFTERMATH = 2/9
So we have a match with option B
Let x2
+ 10x = 6.
What values make an equivalent number sentence after completing the square?
Answer:
3/5 OR 0.6
Step-by-step explanation:
find the length of the unknown side
Answer:
20
Step-by-step explanation:
15^2 + b^2 = 25^2
Which of the following statements is an opinion?