Answer:
The slope is -4.
Step-by-step explanation:
Slope(m)=(y2-y1)/(x2-x1)
y2=-7, y1=-19, x2=-2, x1=1
(-7+19)/(-2-1)
=12/-3
=-4
Answer: -4
Step-by-step explanation:
The slope formula is: [tex]y_{2} -y_{1}/x_{2}-x_{1} \\[/tex]
So it is: (-7+19)/(-2-1) = 12/-3 = -4
I hope this helped!
2.5 cm in the ratio of 1:500000
Answer:
1250000cm
Step-by-step explanation:
1:500000
1x2.5 : 500000x2.5
2.5:1250000
Find the slope of the graphed line
Answer:
4
Step-by-step explanation:
Pick two points on the line
(0,-5) and (1,-1)
We can find the slope using
m = (y2-y1)/(x2-x1)
= ( -1 - -5)/(1 - 0)
(-1+5)/(1-0)
4/1
= 4
A two-digit number is of the number
7
formed by reversing its digits. When the
number is increased by 2 times the sum of
its digits, it becomes 54. Find the number.
Answer:
C
Step-by-step explanation:
A car is advertised with a price of $16336. The payment plan to own a car is $474 per month for 8 years. What is the
amount of interest paid?
Find two power series solutions of the given differential equation about the ordinary point x = 0. Compare the series solutions with the solutions of the differential equation obtained using the method of Section 4.3. Try to explain any differences between the two forms of the solution. y'' − y' = 0 y1 = 1 − x2 2! + x4 4! − x6 6! + and y2 = x − x3 3! + x5 5! − x7 7! + y1 = x and y2 = 1 + x + x2 2! + x3 3! + y1 = 1 + x2 2! + x4 4! + x6 6! + and y2 = x + x3 3! + x5 5! + x7 7! + y1 = 1 + x and y2 = x2 2! + x3 3! + x4 4! + x5 5! + y1 = 1 and y2 = x + x2 2! + x3 3! + x4 4! +
You're looking for a solution in the form
[tex]y(x) = \displaystyle \sum_{n=0}^\infty a_nx^n[/tex]
Differentiating, we get
[tex]y'(x) = \displaystyle \sum_{n=0}^\infty na_nx^{n-1} = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]
[tex]y''(x) = \displaystyle \sum_{n=0}^\infty (n+1)na_{n+1}x^{n-1} = \sum_{n=1}^\infty (n+1)na_{n+1}x^{n-1} = \sum_{n=0}^\infty (n+2)(n+1)a_{n+2}x^n[/tex]
Substitute these for y' and y'' in the differential equation:
[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1)a_{n+2}x^n - \sum_{n=0}^\infty (n+1)a_{n+1}x^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1)a_{n+2}-(n+1)a_{n+1}\bigg)x^n = 0[/tex]
Then the coefficients of y are given by the recurrence
[tex]\begin{cases}a_0=y(0)\\a_1=y'(0)\\a_{n+2}=\frac{a_{n+1}}{n+2}&\text{for }n\ge0\end{cases}[/tex]
or
[tex]a_n = \dfrac{a_{n-1}}n[/tex]
But we cannot assume that [tex]a_0[/tex] and [tex]a_1[/tex] depend on each other; we can only guarantee that the recurrence holds for n ≥ 1, so that
[tex]a_2=\dfrac{a_1}2 \\\\ a_3=\dfrac{a_2}3=\dfrac{a_1}{3\times2} \\\\ a_4=\dfrac{a_3}4=\dfrac{a_1}{4\times3\times2} \\\\ \vdots \\\\ a_n=\dfrac{a_1}{n!}[/tex]
So in the power series solution, we split off the constant term and we're left with
[tex]y(x) = a_0 + a_1 \displaystyle \sum_{n=1}^\infty \frac{x^n}{n!}[/tex]
so that the fundamental solutions are
[tex]y_1=1[/tex]
and
[tex]y_2=x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!}+\cdots[/tex]
If p is a given sample proposition n is the sample size, and a is the number of standard deviations at a confidence level, what is the standard error of the proportion?
Answer:
The standard error of a proportion p in a sample of size n is given by: [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
The standard error of a proportion p in a sample of size n is given by: [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Find the length of AC
Answer:
377.19 (rounded off to 2dp)
Step-by-step explanation:
since its a right angled triangle, we can use tangent
tan(x) =opp/adj
tan(5) =33/AC
AC =33/tan(5)
If a over 2 equals b over 3 then b over a equals what?
Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The students collect a random sample of 48 students. The mean of the sample is 12.4 units. The sample has a standard deviation of 1.7 units.
Required:
What is the 95% confidence interval for the average number of units that students in their college are enrolled in?
Answer:
[11.906 ; 12.894]
Step-by-step explanation:
Given :
Sample mean, xbar = 12.4
Sample standard deviation, s = 1.7
Sample size, n = 48
We use the T distribution since we are using the sample standard deviation;
α - level = 95% ; df = n - 1 = 48 - 1 = 47
Tcritical = T(1 - α/2), 47 = 2.012
Using the confidence interval for one sample mean
Xbar ± Tcritical * s/√n
12.4 ± (2.012 * 1.7/√48)
12.4 ± 0.4936922
C. I = [11.906 ; 12.894]
About 6% of the population of a large country is math phobic. If two people are randomly selected, what is the probability both are math phobic?
Answer:
0.0036
Step-by-step explanation:
Given that :
Proportion of population that are math phobic = 6% = 6/100 = 0.06
P(math phobic) = 0.06
If two selections are made ; probability that both are math phobic ;
P1 = selection 1 = 0.06
P2 = selection 2 = 0.06
Probability that both are math phobic :
P1 * P2 = (0.06 * 0.06) = 0.0036
Simplify Square root (150n^2)
Answer:
12
Step-by-step explanation:
Answer please answer!!
I need the answer asap
Answer:
35 cm
Step-by-step explanation:
is the correct answer
A car rental firm has 410 cars. Sixty-five of these cars have defective turn signals and 35 have defective tires. (Enter your probabilities as fractions.)
(a) What is the probability that one of these cars selected at random does not have defective turn signals?
(b) What is the probability that one of these cars selected at random has no defects if no car has 2 defects?
Answer:
(a)
Number of cars with defective turn signals = 65
Number of cars with no defective turn signals = 410 - 65 = 345
Required probability:
P = 345/410*100% ≈ 84.15%(b)
Number of cars with defects = 65 + 35 = 100
Number of cars with no defects = 410 - 100 = 310
Required probability:
P = 310/410*100% ≈ 75.61%Find the area of the quadrilateral and round to the nearest tenth
Answer:
24
Step-by-step explanation:
(4+8)×4/2
= 12×4/2
= 24
Answered by GAUTHMATH
if x¹=xcosA+ysinA and y¹=xsinA-ycosA, show that (x¹)²+(y¹)²=x²+y²
Expanding each square on the left side, you have
(x cos(A) + y sin(A))² = x² cos²(A) + 2xy cos(A) sin(A) + y² sin²(A)
(x sin(A) - y cos(A))² = x² sin²(A) - 2xy sin(A) cos(A) + y² cos²(A)
so that adding them together eliminates the identical middle terms and reduces to the sum to
x² cos²(A) + y² sin²(A) + x² sin²(A) + y² cos²(A)
Collecting terms to factorize gives us
(y² + x²) sin²(A) + (x² + y²) cos²(A)
(x² + y²) (sin²(A) + cos²(A))
and sin²(A) + cos²(A) = 1 for any A, so we end up with
x² + y²
as required.
lim ₓ→∞ (x+4/x-1)∧x+4
It looks like the limit you want to find is
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4}[/tex]
One way to compute this limit relies only on the definition of the constant e and some basic properties of limits. In particular,
[tex]e = \displaystyle\lim_{x\to\infty}\left(1+\frac1x\right)^x[/tex]
The idea is to recast the given limit to make it resemble this definition. The definition contains a fraction with x as its denominator. If we expand the fraction in the given limand, we have a denominator of x - 1. So we rewrite everything in terms of x - 1 :
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\dfrac{x-1+5}{x-1}\right)^{x-1+5} \\\\ = \left(1+\dfrac5{x-1}\right)^{x-1+5} \\\\ =\left(1+\dfrac5{x-1}\right)^{x-1} \times \left(1+\dfrac5{x-1}\right)^5[/tex]
Now in the first term of this product, we substitute y = (x - 1)/5 :
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(1+\dfrac1y\right)^{5y} \times \left(1+\dfrac5{x-1}\right)^5[/tex]
Then use a property of exponentiation to write this as
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\left(1+\dfrac1y\right)^y\right)^5 \times \left(1+\dfrac5{x-1}\right)^5[/tex]
In terms of end behavior, (x - 1)/5 and x behave the same way because they both approach ∞ at a proportional rate, so we can essentially y with x. Then by applying some limit properties, we have
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty} \left(\left(1+\dfrac1x\right)^x\right)^5 \times \left(1+\dfrac5{x-1}\right)^5 \\\\ = \lim_{x\to\infty}\left(\left(1+\dfrac1x\right)^x\right)^5 \times \lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)^5 \\\\ =\left(\lim_{x\to\infty}\left(1+\dfrac1x\right)^x\right)^5 \times \left(\lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)\right)^5[/tex]
By definition, the first limit is e and the second limit is 1, so that
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = e^5\times1^5 = \boxed{e^5}[/tex]
You can also use L'Hopital's rule to compute it. Evaluating the limit "directly" at infinity results in the indeterminate form [tex]1^\infty[/tex].
Rewrite
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \exp\left((x+4)\ln\dfrac{x+4}{x-1}\right)[/tex]
so that
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty}\exp\left((x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ = \exp\left(\lim_{x\to\infty}(x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ =\exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right)[/tex]
and now evaluating "directly" at infinity gives the indeterminate form 0/0, making the limit ready for L'Hopital's rule.
We have
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\ln\dfrac{x+4}{x-1}\right] = -\dfrac5{(x-1)^2}\times\dfrac{1}{\frac{x+4}{x-1}} = -\dfrac5{(x-1)(x+4)}[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{x+4}\right]=-\dfrac1{(x+4)^2}[/tex]
and so
[tex]\displaystyle \exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right) = \exp\left(\lim_{x\to\infty}\frac{-\dfrac5{(x-1)(x+4)}}{-\dfrac1{(x+4)^2}}\right) \\\\ = \exp\left(5\lim_{x\to\infty}\frac{x+4}{x-1}\right) \\\\ = \exp(5) = \boxed{e^5}[/tex]
The population p(t) of a culture of the bacterium Pseudomonas aeruginosa is given by ,p(t)= -1683t^2+75,000t+ 10,000 where is the time in hours since the culture was started. Determine the time the population was at its maximum. Round to the nearest hour.
Answer:
22hrs
Step-by-step explanation:
hope it is well understood?
1. Carlos wants to deposit $900 into savings accounts at three different
banks: Bank of Chance, Merchant Bank, and Utopian Financing. He will
deposit two times as much into Merchant Bank as Bank of Chance
because they offer a higher interest rate. He also expects the Utopian
Financing deposit to be only 20% of the total of the other two deposits.
How much will Carlos deposit into the Utopian Financing savings account
(4 points)
O $180
$250
$500
$150
Answer:
$150
Step-by-step explanation:
0.2 X 750 = 150
hope this helps
A noted psychic was tested for extrasensory perception. The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star, a cross, a circle, a square, or three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime. How large a sample n would you need to estimate p with a margin of error of 0.01 with 95% confidence? Use the hypothesized value p = 0.20 as the value for p*.
Answer:
r3jehejn wbbwbwbbwmwkwkwjwjwhhejehehehhe
find the missing length indicated
============================================================
Explanation:
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
--------------------------------
Now shift your attention solely on the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
240.
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
Now shift your attention solely to the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the Pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
What is Pythagorean Theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Learn more about the Pythagorean theorem at
https://brainly.com/question/343682
#SPJ2
find the value of trigonometric ratio
Instruction: Find the average rate of change for the scenario below.
A rocket is 1 mile above the earth in 30 seconds and 5 miles
above the earth in 150 seconds. What is the rockets rate of
change in miles per second?
Rate of Change
miles/second
Answer:
Step-by-step explanation:
Use the coordinates (30, 1) and (150, 5) to solve this. Time is always an x thing, while things like distance and weight and value are y things. Put them into the slope formula:
[tex]m(\frac{miles}{sec})=\frac{5-1}{150-30}=\frac{4}{120}=\frac{1}{30}[/tex] This translates to:
The rocket is ascending at a constant rate of 1 mile every 30 seconds; or, conversely, for every 30 seconds the rocket is flying, it is traveling 1 mile.
Will give brainliest answer
Answer:
14 hours
Step-by-step explanation:
Take any two consecutive high tides and to find their x coordinatey and sub them..
The probability of a customer arrival at a grocery service counter in any one second is equal to 0.4. Assume that customers arrive in a random stream, so an arrival in any one second is independent of all others. (Round your answers to four decimal places.) (a) Find the probability that the first arrival will occur during the seventh one-second interval. 0.0187 Correct: Your answer is correct. (b) Find the probability that the first arrival will not occur until at least the seventh one-second interval.
Answer:
a. approximately 0.0187
b. 0.047
Step-by-step explanation:
q = 1-p
= 1-0.4
q = 0.6
a. the probability that the first arrival will occur during seventh one-second interval
probability(7) = 0.6⁷⁻¹ x 0.4
= 0.6⁶ x 0.4
= 0.046656 x 0.4
= 0.0186624
approximately 0.0187
b. probability that the first arrival will not occur until at least the seventh one second interval
p(y≥7) = 1-p(x<7)
= 1-[(0.4)(0.6)⁰ + (0.4)(0.6)¹ +(0.4)(0.6)²+(0.4)(0.6)³+(0.4)(0.6)⁴+(0.4)(0.6)⁵]
= 1-(0.4+0.24+0.144+0.0864+0.05184+0.031104
= 1-0.95334
= 0.04667
= 0.047
Fo quality control purposes, we collect a sample of 300 items and find 36 defective items in it. Construct a 90% confidence interval [a, b] for the proportion of defective items in the whole shipment.
Answer:
(0.089 ; 0.151)
Step-by-step explanation:
Given :
Sample size, n = 300
Number of defective items, x = 36
The confidence interval required here is that for a one sample proportion :
The confidence interval is defined thus :
Phat ± Zcritical * √[Phat(1 - phat) / n]
Zcritical at 90% = 1.645
Phat = x / n = 36 / 300 = 0.12
Hence,
C.I = 0.12 ± 1.645 * √[0.12(1 - 0.12) / 300]
C.I = 0.12 ± (1.645 * 0.0187616)
C.I = 0.12 ± 0.0308629
C.I = (0.089 ; 0.151)
Find m<1.
33°
47°
42°
28°
Answer:
<1 = 33
Step-by-step explanation:
The sum of the angle of a triangle is 180
31+116+x = 180
x+147=180
x = 180-147
x = 33
Which statement best applies to the slope of the line below?
A.
the slope is negative
B.
the slope is zero
C.
the slope is positive
D.
the line has no slope
Answer:
D
Step-by-step explanation:
fro the diagram below there line has no slope
Answer: B) The slope is zero
============================================================
Explanation:
Any horizontal line will always have a slope of 0. This is because there is no change in y (aka the rise is 0).
So we could say something like
slope = rise/run = 0/1 = 0
The run can be anything we want, and we'd still get 0 every time.
------------
Another way to see this is to pick two points from this line. Whichever points are selected, they are plugged into the slope formula
m = (y2-y1)/(x2-x1)
You'll find that the y2-y1 expression turns into 0. Why? Because y1 and y2 are the same, so they subtract to 0. It doesn't matter what x2-x1 turns into.
Solve the following equation for n. Be sure to take into account whether a letter is capitalized or not.
t=n-r
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]n = t + r[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'n'...}}\\\\t = n - r\\----------\\\rightarrow t + r = n -r + r\\\\\rightarrow t+r = n\\\\\rightarrow \boxed{n=t+r}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Building A is 170 feet shorter than building B. The total height of the two buildings is 1520 feet. what is the height of each building?
Answer:
Step-by-step explanation:
If A is 170 less than B, than the equation for that is:
A = B - 170 (1) where the word "is" means equals and less than is subtraction.
If the total of A + B is 1520, then
A + B = 1520 (2). Sub equation (1) into equation (2):
(B - 170) + B = 1520 and
2B - 170 = 1520 and
2B = 1690 so
B = 845. Building B is 845 feet tall and Building A is
A = 845 - 170 (this is equation (1) with the height of B subbed in) so
A = 675 feet
675 + 845 should equal 1520 according to our equation. And of course it does.
Answer: 675 + 845 should equal 1520 according to our equation. And of course it does.
What is a corresponding pair for f(-7)=5
Answer:
An ordered pair for a function f(x) looks like (x, f(x)). So the ordered pair here would be (5, f(5)) or (5, 7). Either one would work, as they are the same.
