Answer:
280 miles
Step-by-step explanation:
We want to determine what speed Camden is going first so we can find the distance. To do so, you can divide the total miles (320) by the number of hours (8) to find he is driving 40 miles per hour. Then, you can take that and multiple it by the number of hours he will drive (7) to get 280 miles. I hope this helps! :)
integral of x+2/
[tex] \sqrt{x { + 2x + 3}^{2} } [/tex]
Looks like the integral should be
[tex]\displaystyle\int\frac{x+2}{\sqrt{x+(2x+3)^2}}\,\mathrm dx[/tex]
Expand the denominator:
[tex]\displaystyle\int\frac{x+2}{\sqrt{4x^2+13x+9}}\,\mathrm dx[/tex]
Notice that
[tex]u=4x^2+13x+9\implies \mathrm du=(8x+13)\,\mathrm dx[/tex]
In order to use this substitution, expand the integral as
[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx+\frac38\int\frac{\mathrm dx}{\sqrt{4x^2+13x+9}}[/tex]
In the first integral, use the previously mentioned substitution:
[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx=\frac18\int\frac{\mathrm du}{\sqrt u}=\frac14\sqrt u[/tex]
[tex]=\dfrac14\sqrt{4x^2+13x+9}[/tex]
In the second integral, complete the square in the denominator:
[tex]4x^2+13x+9=4\left(x+\dfrac{13}8\right)^2-\dfrac{25}{16}[/tex]
Now substitute
[tex]x=\dfrac58\sec t-\dfrac{13}8\implies\mathrm dx=\dfrac58\sec t\tan t\,\mathrm dt[/tex]
so that
[tex]\sec t=\dfrac{8x+13}5[/tex]
Then
[tex]4x^2+13x+9=\dfrac{25}{16}(\sec^2t-1)=\dfrac{25}{16}\tan^2t[/tex]
and the integral becomes
[tex]\displaystyle\frac{\frac{15}{64}}{\frac54}\int\frac{\sec t\tan t}{\sqrt{\tan^2t}}\,\mathrm dt=\frac3{16}\int\sec t\,\mathrm dt[/tex]
[tex]=\dfrac3{16}\ln|\sec t+\tan t|[/tex]
[tex]=\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|[/tex]
So, the integral is
[tex]\dfrac14\sqrt{4x^2+13x+9}+\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|+C[/tex]
What is 9.1% of 80? Round to the nearest hundredth (if necessary).
Answer:
7.28
Step-by-step explanation:
Answer: 7.28
Step-by-step explanation:
Assume that the standard deviation of daily returns for Marcus, Inc. stock in a recent period is 1.5 percent. Furthermore, a 95 percent confidence interval is desired for the maximum loss. Daily returns are normally distributed, and the expected daily return is 0.05 percent. What is the lower boundary of the maximum expected loss
Answer:
= - 2.43%
Step-by-step explanation:
From the information given:
Since the variable (daily returns) is normally distributed, Then, using empirical rule at 95% confidence interval level, we have:
[tex]( \mu - 1.96 \sigma \ , \ \mu + 1.96 \sigma)[/tex]
where;
The expected mean daily return [tex]\mu = 0.05 \%[/tex]
The standard deviation [tex]\sigma = 1.5\%[/tex]
Given that the 95% confidence interval is expected to be a maximum loss, then the probability is left-tailed which is 1.65[tex]\sigma[/tex] away from the average.
Thus the distribution of the lower boundary can be computed as:
= [tex](0.05 - 1.65 \times 1.5)\%[/tex]
= [tex](0.05 - 2.475)\%[/tex]
= [tex]( - 2.425)\%[/tex]
= - 2.43%
The senior class had a car wash to raise money for the senior trip. It cost them $35 for supplies. They washed 75 cars and charged $6 for each car.
Which of the following expressions represents the money they raised for their trip?
Answer: $415
Step-by-step explanation: 75 x $6 = 450. 450 - 35 = 415
In the 2019 NBA Eastern Conference semi‐finals, Philadelphia 76ers (PHI) played the (eventual 2019 NBA Champion) Toronto Raptors (TOR) in a best‐of‐7 series where the first team to win 4 games wins the series. Assume that the outcome of each game is independent. (a) Assuming that either team has a win probability of 0.5, what is the probability that after the first 4 games, the teams would be tied 2‐2? Clearly show all your steps.
Answer: 0.375
Step-by-step explanation:
Given the following :
Both teams have an equal probability of winning = 0.5
Find the probability that both teams are tied after 4 games, that is 2-2 ( this means each team has exactly 2 successes and 2 losses).
This problem can be modeled using a binomial probability :
P(x) = nCx * p^x * (1-p)^(n-x)
x = number of successes = 2
P = probability of success = 0.5
(1-p) = probability of failure = 0.5
n = number of trials = 4
P(x = 2 ) = 4C2 * 0.5² * 0.5^(4-2)
P(x = 2) = 6 * 0.5² * 0.5²
P(x = 2) = 6 * 0.25 * 0.25
P(x = 2) = 0.375
the inequality 13q<7q-29 and write the solution in fraction formats and interval notations
Answer:(-infinity,-29/6)
Step-by-step explanation:
Interval notation of this problem.
A salt mixture has 8 parts water and 2 parts salt. Suppose one part of each is added. What is the new ratio of salt to water?
2 to 9
3 to 8
3 to 9
9 to 3
Answer:
c. 3 to 9
Step-by-step explanation:
It was right on edg 2020
Hi I am totally confuse with this math can you please help
thank yo I will give you the brainlest I aapreciate any help
Answer:
#5 is b) -250, -200, 0, 300
Step-by-step explanation:
Point L is on line segment km. Given km =5x+10, LM=4x, and KL=3x, determine the numerical length of kL
Answer:
KM= KL+LM
5x+10=3x+4x
5x+10=7x
2x=10
x=5
now
kl=3x=3*5=15
A rectangular rug measures 8 feet long and 12 feet wide
what is 4 fourths of a dollar
Answer: The answer is 25%
Step-by-step explanation:
A marble is selected at random from a jar containing 5 red marbles, 2 yellow marbles & 3 green marbles. What is the probability that a)the marble is red
b)the marble is not yellow
c)the marble is either red or green
d)the marble is neither red nor green
Answer:
5/11
explanation
Probability here is the chance of selection out of a total. So, we need to first find the total number of marbles.
total
=
5
+
3
+
2
+
1
=
11
So there are
11
marbles total. The probability that we pick one of the
3
green marbles out of the
11
is simply that ratio:
P
green
=
3
11
Same idea for yellow:
P
yellow
=
2
11
The probability of picking either of these colors is simply the sum of their probabilities.
P
green or yellow
=
P
green
+
P
yellow
=
3
11
+
2
11
=
5
11
simplify (4x+1)(3+9x)
Answer:
36 x 2 + 21 x + 3
Step-by-step explanation:
Simplify the expression.
Add and subtract the second term to the expression and factor by grouping. You get 3 ( 4 x + 1 ) ( 3 x + 1 )
A scuba diver returning to the surface swims to move up quickly, then waits a few meters below the surface to avoid pressure issues. They complete the ascent more slowly. The function f represents the diver's distance from sea level over time, in seconds. Which of the following is true for f? f(x)= { 3x+1, if −9 < x ≤ −2 f(x)= {−5, if. −2 < x ≤ 1 f(x)= { x−6, if 1 < x < 7 Group of answer choices The domain is the depth interval (−26, 1). The domain is the depth interval (−9, 1]. The domain is the set of times −9 < x < −2, −2 < x < 1, and 1 < x < 7. The domain is the time interval (−9, 7). Group of answer choices domain: (–3, 3] negative: (–3, –2), (2, 5] range: (–3, 4] decreasing: (–1, 4) increasing: (–3, –1) positive: (–2, 2)
Answer:
See below
Step-by-step explanation:
Given:
f(x)= { 3x+1, if −9 < x ≤ −2 f(x)= {−5, if. −2 < x ≤ 1 f(x)= { x−6, if 1 < x < 7Combination of domain for the function is the following union:
(-9, 2]∪ (-2, 1]∪(1, 7) = (-9, 7)Group of answer choices:
The domain is the depth interval (−26, 1).
incorrect as (-26, -9) interval is not covered in given functionThe domain is the depth interval (−9, 1].
incomplete rangeThe domain is the set of times −9 < x < −2, −2 < x < 1, and 1 < x < 7.
incorrect as doesn't include x = -2 and x = 1The domain is the time interval (−9, 7).
This is correct as it is same with the domain set we got above.10 gallons equals how many liters
37.8541
roll another one
i will give u brainlyist plz When 1/3 is written as a repeating decimal, which digits are repeating? A. 27 B. 37 C. 73 D. 28
Answer:
1/3 in decimal format is .333333333333... so none of these are correct
Answer the question marks, and tell me what sequence number 8 is.
Answer:
f[1] = 60; f[n+1] = f[n] -30f[n] = 60 -30(n-1)Step-by-step explanation:
You observe that each term is 30 less than the previous one. This is the recursive rule. It also means the sequence is arithmetic with a common difference of -30.
Recursive equation
f[1] = 60; f[n+1] = f[n] -30
__
Explicit equation
The general form of the explicit equation is ...
f(n) = f(1) +d(n -1)
Here, we have f(1) = 60 and d = -30, so your equation is ...
f(n) = 60 -30(n -1)
40 fewer than a number t
0 40-t
Ot+40
O -400
O t-40
Answer:
The answer is the last one - t-40
Graph the image of the given triangle under a dilation with a scale factor of –4 and center of dilation (0,0).
Step-by-step explanation:
Hey there!
The coordinates of a triangle are;
A (1,2)B (1,-2)C (-2,-2)Scale factor = -4 and centre at (0,0)Now, We have;
P(x,y)----------- P'(kx, ky)
Keep formula;
A(1,2)---------- A'(-4×1 ,-4×2)
= A'(-4, -8)
B(1,-2)------------- B'(-4,8)
C(-2,-2)-------------C'(8,8)
[ The A' should be kept in (-4,-8). There was no place in this graph so, i kept it just below -7. Please while plotting remember to keep it on "-8".]
Hope it helps..
is 2.4444 rational or irrational
Answer:
Rational.
Step-by-step explanation:
Irrational are these.
[tex]\sqrt{2} , \sqrt{5}[/tex] ,π
Yes, the given number is a rational number.
What are rational numbers?Rational numbers are numbers that can be written in the form p/q, where p and q are integers and q≠0.
Given that, a number 2.4444...
Repeating decimals are considered rational numbers because they can be represented as a ratio of two integers.
Hence, 2.4444 is a rational number.
For more references on rational numbers, click;
https://brainly.com/question/24398433
#SPJ2
Melissa used her credit card to buy a $745 refrigerator. She kept the refrigerator for exactly nine years, during which time it consumed an average of $0.19 of electricity every day. Melissa’s credit card has an APR of 16.84%, compounded monthly. Melissa paid off her refrigerator by making identical monthly payments for four years. If she made no other purchases with her card, what percentage of the lifetime cost of the refrigerator did the electricity make up? (Assume that two of the years were leap years, and round all dollar values to the nearest cent.) a. 59.17% b. 18.48% c. 66.99% d. 37.77%
Answer:
37.77
Step-by-step explanation:
P= PV x i / 1- (1+i)^-n
PV = 745
I = .1684 / 12 = .01403
N = 4 x 12 = 48
.19 x (365 x 9) = 624.53
21.4338469 x 48= 1028.12
624.53 / (624.53+1028.12) = 37.77
The percentage of the lifetime cost of the refrigerator did the electricity make up is : d. 37.77%.
Percentage of the lifetime costUsing this formula
P= Pv x i / 1- (1+i)^-n
Where:
Present value = 745
Interest= .1684 / 12 = .01403
Number of months = 4 x 12 = 48
Hence:
Percentage=.19 x (365 x 9)/(.19 x (365 x 9)+(21.4338469 x 48)
Percentage=624.53 / (624.53+1028.12)
Percentage= 37.77%
Inconclusion the percentage of the lifetime cost of the refrigerator did the electricity make up is : d. 37.77%.
Learn more about percentage here:https://brainly.com/question/24304697
on the day of the test, Rebeccas instructor says that the test will be to attempt 25 vases
Favorite type of music, choose the correct level of measurement
Answer:
The answer is "Nominal"
Step-by-step explanation:
Some of the data is missing which is defined in the attached file. please find it.
The standard measuring degree is nominal for the favorite type of music because the type of music it can be listening for depends on a variety of factors, like age, social or local environment, etc, and the wrong choice can be defined as follows:
It is wrong because the Ordinal does have a nominal or measuring element, however, the name system allows a ranked or a specific series of variables for all the variables to also be organized. The ratio has the structure infections rate property, as well as the quantities ranges of the variable, provide value, that's why it is incorrect. It is wrong because the internal has the property of ordinal level rate as well as the vector values have significance.Calculate 19.25 tons equal how many pounds
Answer:
38,500 pounds
Step-by-step explanation:
1 ton = 2000 pounds
plz help me with these two questions ( show work plz)
Step-by-step explanation:
3. 7 = -2y + 4
2y = 4 - 7
2y = -3
y = -1.5
5. -3x - 2 = -17
17 - 2 = 3x
15 = 3x
3x = 15
x = 15/3
x = 5
a.
b.
Select the following statement that is true
about shape a and shape b.
What is another nonterminating decimal number that can not be written as a fraction?
Answer:
0.6066066606666066666...(increasing numbers of 6)
Step-by-step explanation:
One way to make a decimal non-repeating is to extend a pattern by one digit each time you write the pattern. That is the structure of the number Sophia and Nora are looking at. It is also the structure of the number in your question ...
https://brainly.com/question/17546271
__
Any irrational number will have a non-repeating decimal: √2, for example.
104 percent of 102 is what
Answer:
106.08
Step-by-step explanation:
Answer:
106.08 percent
please help me with this question! WILL MARK BRAINLIEST
Answer:
as reference angle is a
h=5
b=3
p=4
sinA= p/h= 4/5
cosA= b/h= 3/5
tanA= p/b=4/5
Step-by-step explanation:
Step-by-step explanation:
[tex]sine \: A = \frac{4}{5}\\\\
cosine \: A = \frac{3}{5}\\\\
tangent \: A = \frac{4}{3}\\\\[/tex]
Describe how each model can help you round a decimal.
You