Answer:
(x-2)(x-2) or (x+2)(x+2)
Step-by-step explanation:
since you are squaring it, technically the terms are negative, but the product will be positive. when you multiply two negative factors, you get a positive answer. so either both can be negative or both can be positive.
A taxi company charges $2.25 for the first 5 miles and $0.75 for each mile. If a passenger spent $6 on a trip, how many miles did he travel? Write an equation to solve.
Find the limit, if it exists. lim (x^3 -3x^2 +3)
Answer:
-1
Step-by-step explanation:
Assuming problem is: x->2 (x^3 -3x^2 +3)
Since the expression is continuous at x=2,
then the limit can be found just by evaluating the expression at x=2.
2^3-3(2)^2+3
8-3(4)+3
8-12+3
-4+3
-1
Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin which the concentration of the blood increases mostrapidly. Based on certain tests in seawater, theconcentration of blood(in parts per million) at point P(x,y) on thesurface is approximated by:
C(x,y)= e^- (x^2+2y^2).10^4
where x and y are measured in meters in a rectangularcoordinate system with the blood source at the origin.
a. Identify the level curves of the concentration function andsketch several members of this family together with a path that ashark will follow to the source.
b. Suppose a shark is at the point (xo, yo) when it first detects the presenceof blood in the water. Find an equation of the shark's path bysetting up and solving a differential equation.
Solution :
a). The level curves of the function :
[tex]$C(x,y) = e^{-(x^2+2y^2)/10^4}$[/tex]
are actually the curves
[tex]$e^{-(x^2+2y^2)/10^4}=k$[/tex]
where k is a positive constant.
The equation is equivalent to
[tex]$x^2+2y^2=K$[/tex]
[tex]$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$[/tex]
which is a family of ellipses.
We sketch the level curves for K =1,2,3 and 4.
If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.
Then we know the shark's path is perpendicular to the level curves it intersects.
b). We have :
[tex]$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$[/tex]
[tex]$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$[/tex] and
[tex]$\triangledown C$[/tex] points in the direction of most rapid increase in concentration, which means [tex]$\triangledown C$[/tex] is tangent to the most rapid increase curve.
[tex]$r(t)=x(t)i+y(t)j$[/tex] is a parametrization of the most [tex]$\text{rapid increase curve}$[/tex] , then
[tex]$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$[/tex] is a tangent to the curve.
So then we have that [tex]$\frac{dr}{dt}=\lambda \triangledown C$[/tex]
[tex]$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4} $[/tex]
∴ [tex]$\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$[/tex]
Using separation of variables,
[tex]$\frac{dy}{y}=2\frac{dx}{x}$[/tex]
[tex]$\int\frac{dy}{y}=2\int \frac{dx}{x}$[/tex]
[tex]$\ln y=2 \ln x$[/tex]
⇒ y = kx^2 for some constant k
but we know that [tex]$y(x_0)=y_0$[/tex]
[tex]$\Rightarrow kx_0^2=y_0$[/tex]
[tex]$\Rightarrow k =\frac{y_0}{x_0^2}$[/tex]
∴ The path of the shark will follow is along the parabola
[tex]$y=\frac{y_0}{x_0^2}x^2$[/tex]
[tex]$y=y_0\left(\frac{x}{x_0}\right)^2$[/tex]
Which previewing strategy would work best for a topic you have heard of before?
a.
using prior knowledge
c.
skim the introduction and conclusion
b.
identify text structure
d.
none of the above
Answer:
A- using prior knowledge
Step-by-step explanation:
3. To make sure the sweater she is knitting will be the right size, Gale knits a sample that is 2 inches long. She knits a second sample that is 14 times as long as the first sample. How many inches long is the second sample?
please help, will mark u brainliest plz plz plz
Hello and good day.
For this question you will use multiplication.
We know that the first same is 2 inches long and the second sample is 14 times long as the first sample.
When some thing says times, it uses multiplication, especially when mentioned in word problems.
So 14 times 2 = 28.
The answer is: The second sample is 28 inches.
28
14x2=28 bro get this right >:P
The difference of seven and two tenths and a number is more than twenty nine.
56 times a number minus 13 is equal to 6 less than the number.
Step 1 of 2: Write out the equation.
Answer:
The equation is 56x - 13 = x - 6
Step-by-step explanation:
Let's say our 'number' is x. If it says it's 56 times our number, it's 56x. Minus 13, which is 56x - 13. If it is equal than 6 less than the number, then it is x - 6.
So the equation is 56x - 13 = x - 6
The Antique Auto News charges $10 for a 10-word classified ad. Each additional word costs $0.40. For an extra $40, a seller can include a photo in the ad. How much would a 20-word ad with a photo cost?
Answer: $60
Step-by-step explanation:
Here is why:
For 20 -word ad it will be $20 because of twice the amount of the 10 word amount. and another $40 for the photo!
And you get $60!
Any Questions
It will cost $54 for an 20 word ad and a photo.
We have Antique Auto News agency which charges $10 for a 10-word classified ad. Each additional word costs $0.40 and for an extra $40, a seller can include a photo in the ad.
We have to determine much would it cost for a 20-word ad with a photo.
Starting from x, if the bacteria count rises by 5 every second, then determine the formula to calculate the bacteria count after 30 seconds.Initial count = x
Count increasing per second = 5
Assume that the bacteria count after t seconds is y. Then -
y = x + 5t
for t = 30 ↔ y = 150 + x
According to the question, we have -
Cost of 10-word classified ad → $10
Additional word cost → $0.40
Additional Photo cost → $40
Therefore -
Assume that for a 20-word ad with a photo costs $x.
Therefore -
x = 10 + 0.40 x 10 + 40
x = 10 + 4 + 40
x = 54
Hence, it will cost $54 for an 20 word ad and a photo.
To solve more questions on Amount estimation , visit the link below-
https://brainly.com/question/8158280
#SPJ2
10h + hx=d-5 solve for h
Answer:
Hey!!
Step-by-step explanation:
h = d − 5 /10 + x
Hope this helps!
Have a nice day<3
Help me somebody pleaseeee
What is m ZPQR?
R
(x + 3)
(3x + 5)
S.
Р
Answer:
3 x 2 − 2 x -5
Step-by-step explanation:
The following box plot shows the number of years during which 40 schools have participated in an interschool swimming meet:
A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years.
At least how many schools have participated for more than 1 year and less than 6 years?
4 schools
8 schools
10 schools
20 schools
Answer:
20 schools is your answer
Have a good day
Answer:
20 is ur answer!
Step-by-step explanation:
I took the test and got it right, also credit goes to the other guy! Have a good day/night! <3
HELP PLEASE
NO RANDOM ANSWERS OR PHOTO ANSWER ANY OF THAT WILL BR REPORTED
Answer: The answer for the second one is solid figure
Step-by-step explanation: In geometry, three-dimensional shapes are solid figures.
A large national bank determines if each of its branches is profitable or not profitable. Additionally, the location of each branch is classified as urban, suburban, or rural. A summary of the profitability and location type of a random sample of 175 of the bank’s branches is shown in the table.
Profitable Not Profitable
Urban 64 17
Suburban 39 22
Rural 18 15
(a) From the sample of 175 branches summarized above:
(i) What proportion of branches are profitable?
(ii) What proportion of branches from an urban location are profitable?
(iii) What proportion of branches from a rural location are profitable?
(b) Assuming the conditions for inference are met, does the data provide convincing statistical evidence that profitability and location type are independent for the bank at a 5 percent level of significance? Complete the appropriate inference procedure to support your answer.
Answer:
Step-by-step explanation:
i) (64+39+18)/(175)=0.691
ii) 64/(64+17)=0.79
iii) 18/(18+15)=0.55
(1) The proportion of branches that are profitable 121/175.
2) Proportion of branches from an urban location that is profitable 64/175.
3) The proportion of branches from a rural location is profitable 33/175.
It is given that:
From the sample of 175 branches,
Profitable Not Profitable
Urban 64 17
Suburban 39 22
Rural 18 15
Total number of samples = 175
What is a proportion?Proportion is a part, share, or number considered in comparative relation to a whole.
(1) The proportion of branches that are profitable:
= (64+39+18)/175
=121/175
2) Proportion of branches from an urban location that is profitable:
=64/175
3) The proportion of branches from a rural location is profitable:
=(18+15)/175 = 33/175
Therefore, (1) The proportion of branches that are profitable 121/175.
2) Proportion of branches from an urban location that is profitable 64/175.
3) The proportion of branches from a rural location is profitable 33/175.
To get more about proportions visit:
https://brainly.com/question/18437927
3(y+2/5)=−1/5
Solve for y
Answer:
y = -7/3 or -2.333
Step-by-step explanation:
3(y+2 / 5) = -1/5 ------- First you need to do what is outside of the paranthesis which is 3, so divide both sides by 3.
(y + 2 / 5) = -1/15 ------- Next, you multiply both sides by 5 given the denominator is 5 on the left side.
y + 2 = -1/3 -------- Now you just subtract 2 from both sides.
y = - 7 /3 ---------- Answer
Santino fires a paintball 3 meters from the ground such that the initial trajectory is perfectly horizontal. Assume the paintball does not hit anything and the ground is level. When will the paintball hit the ground?
When rounded to the ten thousands place, which of the numbers below round to 230,000
Answer:
Here are some correct options:
225,891
234,567
232,987
Step-by-step explanation:
Find the domain of the expression:
-((18a^2b^2)/(5cd))/-((9ab^3)/(5c^2d^4))
I can't seem to get it right, I've already tried a, b, c, and d not equal to 0 and it is still not right.
Answer:
2acd^3b^-1
Step-by-step explanation:
About the domain, I don't understand that but i tried to help you.
9514 1404 393
Answer:
a≠0 and b≠0 and c≠0 and d≠0
Step-by-step explanation:
No denominator is allowed to be zero. 'c' and 'd' are in the denominator of the numerator and denominator terms. 'a' and 'b' are in the numerator of the denominator term, so will make that term zero if they are zero. In short, none of a, b, c, or d may be zero.
__
The fact that the expression simplifies to ...
2acd^3/b
does not mean that the only restriction is b≠0.
Given the function g(x)=−x^2+3x, which of the following is the correct limit definition of g′(2)?
Answer:
solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
0
,
0
)
,
(
−
3
,
0
)
y-intercept(s):
(
0
,
0
)
Step-by-step explanation:
hope it helps make brainlliest ty the
The table shows the ages of Mark's family members.
Name
Age (years)
381
Phil
Tammy
32
4
Liam
?
Chris
91
4
Andi
4
2
The combined age of all five family members is 95 years. What is Liam's age?
A. 10
years
B.
12 years
o c. 141
years
OD. 15 years
Answer:
b
Step-by-step explanation:
it's b if I am wrong I am sorry
Write down the reciprocal of 8
Answer: 1/8
Step-by-step explanation:
Concept
Reciprocal is any number that is reverse to the given value. This means the original number times the reciprocal will equal 1. For a more graphical explanation, please refer to the attachment below.
Solve
8×(x)=1
x=1/8
Hope this helps!! :)
Please let me know if you have any questions
First USA, a major credit card company, is planning a new offer for their current cardholders. The offer will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for the offer. To test the effectiveness of the campaign, First USA recently sent out offers to a random sample of 50,000 cardholders. Of those, 1184 registered. Give a 95% confidence interval for the true proportion of those cardholders who will register for the offer.
Answer:
The answer is "[tex]0.02235 \ and \ 0.02501[/tex]".
Step-by-step explanation:
Given:
[tex]x= 1184\\\\n = 50000\\\\c = 95\% = 0.95[/tex]
The sample proportion is computed by subtracting that sample size by both the successes:
[tex]\hat{p}=\frac{x}{n} =\frac{1184}{50000}= 0.02368[/tex]
Determine [tex]z_{\frac{\alpha}{2}} = Z_{0.025}[/tex] using table Z in Table Z for trust level [tex]1 -\alpha = 0.95[/tex]
add using appendix F ((0.025) inside the table, therefore the z-score is the found z-score with negative sign):
So, the boundaries of the confidence interval:
[tex]\to \hat{p}-z_{\frac{\alpha}{2}} \cdot \sqrt{\frac{\hat{p} (1-\hat{p})}{n}} = 0.02368 - 1.96 \cdot \sqrt{\frac{0.02368(1-0.02368)}{50000}}\approx 0.02235 \\\\\to \hat{p}-z_{\frac{\alpha}{2}} \cdot \sqrt{\frac{\hat{p} (1-\hat{p})}{n}} = 0.02368 + 1.96 \cdot \sqrt{\frac{0.02368(1-0.02368)}{50000}}\approx 0.02501\\\\[/tex]
What is the magnitude of -10 + 24i?
Answer:
The magnitude of the complex number is 26.
Step-by-step explanation:
Magnitude of a complex number:
The magnitude of a complex number in the format of a + bi is:
[tex]\sqrt{a^2 + b^2}[/tex]
What is the magnitude of -10 + 24i?
a = -10, b = 24. So
[tex]\sqrt{(-10)^2 +(24)^2} = \sqrt{100+576} = \sqrt{676} = 26[/tex]
The magnitude of the complex number is 26.
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
50%
Step-by-step explanation:
The distance between each dot is 25%
From 68 to 70 is 25% and 70 to 74is 25%
Above 68 is 25+25 or 50 %
A gift box has dimensions of: 8 12 inches, 5 12 inches, and 2 12 inches, respectively. How many cubes with side lengths of 12 inches would be needed to fill the gift box?
116.875 cubes
163.5 cubes
935 cubes
1870 cubes
Answer:
163.5 cubes
Step-by-step explanation:
Answer:
A gift box has dimensions of: 8 12 inches, 5 12 inches, and 2 12 inches, respectively. How many cubes with side lengths of 12 inches would be needed to fill the gift box?
116.875 cubes
163.5 cubes
935 cubes
1870 cubes
163.5 cubes
Step-by-step explanation:
A gift box has dimensions of: 8 12 inches, 5 12 inches, and 2 12 inches, respectively. How many cubes with side lengths of 12 inches would be needed to fill the gift box?
116.875 cubes
163.5 cubes
935 cubes
1870 cubes
163.5 cubes
It takes 24 hours to drive from town A to town B. At an average speed of 31 mph, how far is it?
Answer:
744 miles
Step-by-step explanation:
each hour is 31 miles
the drive is 24 hours
31*24=744
Answer:
744 miles
Step-by-step explanation:
One card is pulled from a full 52 deck of cards. What is the probability of pulling a queen and an ace?
0
8/52
2/13
1
Answer: 8/52
Step-by-step explanation:
In a deck of cards, we have a total number of 52 cards. Out of the 52 cards, there are 4 aces and also 4 queens.
Therefore, the probability of picking a queen or an ace will be:
= P(queen) + P(ace)
= 4/52 + 4/52
= 8/52
simplify this question
Answer:
8192
Step-by-step explanation:
The answer is 8192 but in your multiple-choice problem it's [tex]2^{13}[/tex]
answer please! i will give brainliest !!!!
Answer:
B. WATER CAN DISSOLVE SO MANY SUBSTANCES
Step-by-step explanation:
help me its due in 15 min
Answer:
x = 3, 8
Step-by-step explanation:
[tex]x^{2} +11x +24\\(x + 8)(x + 3)[/tex]
Answer:
x= -8, -3
Step-by-step explanation:
(x+8)(x+3)
x= -8, -3