Answer:
B. y = e^(-2/x).
Step-by-step explanation:
dy/dx = 2y / x^2
Separate the variables:
x^2 dy = 2y dx
1/2 * dy/y = dx/x^2
1/2 ln y = = -1/x + C
ln y = -2/x + C
y = Ae^(-2/x) is the general solution ( where A is a constant).
Plug in the given conditions:
e = A e^(-2/-2)
e = A * e
A = 1
So the specific solution is y = e^(-2/x).
Final answer:
The separable differential equation [tex]dy/dx = 2y/x^2[/tex] can be solved by separating variables, integrating both sides, and then applying the given initial condition y(-2) = e to find the specific solution, which is [tex]y = e^{-2/x},[/tex] corresponding to answer option B.
Explanation:
To solve the given separable differential equation [tex]dy/dx = 2y/x^2[/tex], we first separate the variables:
[tex]\( \frac{dy}{y} = \frac{2}{x^2}dx \)[/tex]
Next, we integrate both sides:
[tex]\( \int \frac{1}{y}dy = \int 2x^{-2}dx \)[/tex]
Which gives:
[tex]ln|y| = -2/x + C[/tex]
Now, we apply the initial condition y(-2) = e to find C:
ln(e) = [tex]-2/(-2) + C \Rightarrow 1 = 1 + C \Rightarrow C = 0[/tex]
Thus, the specific solution is:
[tex]y = e^{-2/x}[/tex]
So, the correct answer is option B, y equals e raised to the negative 2 over x power.
Marissa bought 2 1/2 of a gallon of orange juice to make punch how many qaurts of orange juice did marissa buy?
Answer:
10 quarts
Step-by-step explanation:
There are 4 quarts to a gallon, and she bought 2 1/2 gallons, or 2.5 gallons, so she bought 4(2.5) = 10 quarts
A poll reported that 66% of adults were satisfied with the job the major airlines were doing. suppose 15 adults are selected at random and the number who are satisfied is recorded. complete parts (a) through (e) below.
The statistical technique applicable here is simple random sampling and binomial distribution. The formula for a binomial distribution is used to estimate the probabilities of a specific number of satisfactions among the randomly selected 15 adults. The average number and variability can also be calculated for this binomial distribution.
Explanation:This question is about statistics, particularly a technique called simple random sampling. In the given scenario, it's reported that 66% of adults are satisfied with the major airlines' job. We're asked to conjecture about a scenario where 15 adults are chosen at random and the number who are satisfied is observed.
First, this scenario is modeled with a binomial distribution. A binomial distribution is appropriate here because you're considering a certain number of 'trials' (15 adults), and for each trial, there are two possible outcomes - the adult is either satisfied or not satisfied with the airlines. The 'success' probability (satisfaction) remains constant (66%).
A. If we want to know the probability of exactly x adults satisfied, the formula for a binomial distribution is used: P(X = k) = C(n, k) * (p^k) * ((1 - p)^(n - k)), where C(n, k) is combinations of n things taken k at a time, n is number of trials (15), p is the probability of success (66% or 0.66), and k is the number of successes we want exact probability for.
B. If we want to know the expected value or the average number of adults satisfied, it's simply n*p, in this case 15*0.66 = 9.9, meaning, on average, about 10 adults out of 15 should be satisfied according to the poll report.
C. If we want to compute the variability, we can calculate the standard deviation. For a binomial distribution, the standard deviation, sigma, is square root of [ n*p*q ], where q = 1-p is the probability of 'failure', or an adult not satisfied.
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It was 8 degrees at nightfall. The temperature dropped 10 degrees by midnight. what was the temperature at midnight?
Answer: The temperature would be -2 degrees at midnight.
Step-by-step explanation:
If you take 8 and minus 10 then you get -2!
Answer:
-2
Step-by-step explanation:
hope it will help youu!!!
Grades on a standardized test are known to have a mean of 1000 for students in the US. The test is administered to 453 randomly selected students from Queens College, and they obtained an average grade of 1013 and a standard deviation of 108. a. Construct a 95 % confidence interval for the true average test score for Queens College students. b. With 5% significance level, Is there a statistical evidence that Queens College students perform differently than other students in the US? The same 453 students selected earlier are now given a two-hour tutoring session and then asked to take the test a second time. The average change in their test scores is 9 points, and the standard deviation of the change is 60 points. Assume the changes are from a Normal distribution. c. You are asked by the school administration to study whether students have performed better in their second attempt. State in terms of , the relevant null and alternative hypothesis in conducting this study. d. Compute the t statistic for testing against ; obtain the p- value for the test. e. Do you reject at the 5% level? At the 1% level? f. Provide a short summary of your conclusions from this study. Comment on the practical versus statistical significance of this estimate.
Answer:
a: 1003 < µ < 1023
b: See attached photo for answers
c: see below
d and e: See second attached photo
f: See below
Step-by-step explanation:
a. to find a confidence interval, first find the error with the formula,
E = Z(σ/√n) where Z is the value of the z-score that relates to the confidence level, σ is the standard deviation of the population (or of the sample if the population standard deviation isn't given), and n is the sample size
For this problem, E = 1.96(108/√453) = 9.95 = 10
Now add and subtract that value form the sample average...
x - E < µ < x + E becomes 1013 - 10 < µ 1013 + 10
simplifies to 1003 < µ < 1023
b. See attached photo for hypothesis test results...
c. H0: µ = 1013
Ha: µ > 1013 (claim)
They want to test if it's greater than their first attempt, so this claim becomes the alternate hypothesis. We're testing against their first attempt, that's why µ = 1013, not 1000
d and e. See second attached photo for hypothesis test results...
f. There is enough evidence to support the claim that the students second attempt was an improvement from their first attempt. They happened to take a 2 hour tutoring course between tests. This doesn't prove that the tutoring was effective thought. It very well might have been effective, but also, the students taking the test again means they've already seen the test and know what to expect, which could have also boosted their scores.
Evaluate the log.
[tex]log\frac{1}{27} 81[/tex]
Answer:
−115.940465
Step-by-step explanation:
Simplified = −115.940465
Answer:
-4/3.
Step-by-step explanation:
Using the change of base formula convert to log 3:
logb x = loga x / loga b
log(1/27) 81 = log3 81 / log3 1/27
log3 81 = 4 ( because 3^4 = 81) and log3 1/27 = -3 (because 3^-3 = 1/27)
So log(1/27) 81 = 4/-3 = -4/3.
Find the value of x and the value of y.
This would be D cause these are 30,60, 90 angles. 30 (X) 60(X square root of 3 and 90 2x).
Answer:
C
Step-by-step explanation:
Using the sine ratio on the right triangle on the right side
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{8}[/tex]
Multiply both sides by 8 × sin30° = y
⇒ y = 8 × [tex]\frac{1}{2}[/tex] = 4 → C
Explain how to solve 4x 2- 5x = 16 by completing the square. What are the solutions?
How would you solve mathematical problem?
Answer:
[tex]r=\dfrac{I}{Pt}[/tex]
Step-by-step explanation:
Solve this the way you do any "solve for" problem. Locate the variable of interest and identify what has been done to it. Undo that.
Here, the variable of interest is "r". It has been multiplied by Pt. We undo that multiplication by dividing by that product:
[tex]I=Prt\\\\\dfrac{I}{Pt}=\dfrac{Prt}{Pt}\\\\\dfrac{I}{Pt}=r \quad\text{simplify}[/tex]
The service time distribution describes the probability P that the service time of the customer will be no more than T hours. If m is the mean number of customers serviced in an hour, then P=1-e^mt
Answer: option d.
Step-by-step explanation:
You have the following formul given in the problem:
[tex]p=1-e^{-mt}[/tex]
You know that:
The number of customers serviced in an hour by the technical support representative is 6 costumbers, therefore:
[tex]m=6[/tex]
As the problem asked for the probability that a costumber will be on hold less than 30 minutes, we know that:
[tex]t=0.5[/tex]
Substitute the values above into the formula.
Then, you obtain:
[tex]p=1-e^{-(6)(0.5)}=0.95[/tex] or 95%
Courney buys 2bags of apples.Each bag has 20 apples.How many apples does she buy?
Is there a way to calculate sin, cos, and tan without a calculator?
If so, could you please do it with this problem...
Tan(90°) = DE/4
Also, could you please explain it step by step.
Thanks!
Answer:
yes, and no
Step-by-step explanation:
There are a few trig functions that are "simple" and can be memorized. Usually, these are the ones for angles of 0°, 30°, 45°, 60°, 90°. See below for a table.
To solve an equation like this for DE, you multiply both sides of the equation by 4 (cancelling the denominator).
4·tan(90°) = DE
The tangent of 90° is "infinity." So, the length of DE will be infinite for an angle of 90°.
_____
Trig functions of multiple angles and half angles can be derived from those in the table using the appropriate formulas. The math can get messy fast.
Of course, SOH CAH TOA reminds you of the relationships between trig function values and right triangle side measures. You may not know the angle measure (and it may be irrelevant), but you can find the trig function value.
Answer:
See below.
Step-by-step explanation:
You can find them by constructing a right angled triangle with the given angle and measuring the sides giving sin = opposite / hypotenuse , cos = adjacent / hypotenuse and tan = opposite / adjacent ( SOH-CAH-TOA).
For tan 90 degrees you think of an 'imaginary' triangle where opposite side = hypotenuse and the adjacent side = 0 ( in fact a vertical line!) .Now tan x = opposite / adjacent = opposite / 0 which is indeterminate. There is no value for the tan of 90 degrees and so there is no solution to your problem.
For questions 4-5, how many solutions does the system have?
4. -4y+4=x
2x+8y=8
A. One Solution
B. Two Solutions
C. Infinitely Many Solutions
D. No Solution
5. 6x+2=y
3y-18x=12
A. One Solution
B. Two Solutions
C. Infinitely Many Solutions
D. No Solution
Answer:
[tex]\large\boxed{Q4.\ C.\ \text{Infinitely Many Solutions}}\\\boxed{Q5.\ D.\ \text{No Solution}}[/tex]
Step-by-step explanation:
[tex]Q4.\\\\\left\{\begin{array}{ccc}-4y+4=x&(1)\\2x+8y=8&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(-4y+4)+8y=8\qquad\text{divide both sides by 2}\\-4y+4+4y=4\qquad\text{combine like terms}\\4=4\qquad\bold{TRUE}\\\\\text{Infinitely Many Solutions}[/tex]
[tex]Q5.\\\\\left\{\begin{array}{ccc}6x+2=y&(1)\\3y-18x=12&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3(6x+2)-18x=12\qquad\text{divide both sides by 3}\\6x+2-6x=4\qquad\text{combine like terms}\\2=4\qquad\bold{FALSE}\\\\\text{No Solution}[/tex]
On a winter morning, the temperature before sunrise was 11 degrees. The temperature then rose by 1/2 degree each hour for 7 hours before dropping by 2 1/4 each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours/
Answer:
7.75 F
Step-by-step explanation:
you will do 7/2 *
convert 2.25 to imporper fraction
multiply the denomintor
Answer:
7.75
Step-by-step explanation:
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. If you randomly choose your character and tool, what is the probability that you'll be a magic elf?
Answer:
1/15
Step-by-step explanation:
You have a 1/3 chance of being an elf.
You have a 1/5 change of having the magic tool.
1/3 × 1/5 = 1×1/3×5 = 1/15
Answer:
it is 1/15
Step-by-step explanation:
If 50 is increased by 40%, what is the new amount?
Answer:
70
Step-by-step explanation:
50+20 = 70
ANSWER
70
EXPLANATION
We want to increase 50 by 40%
Method 1
New amount =50+40% of 50
[tex] = 50 + \frac{40}{100} \times 50[/tex]
[tex] = 50 + \frac{40}{2} [/tex]
[tex] = 50 + 20[/tex]
[tex] = 70[/tex]
Method 2.
50 corresponds to 100%.
New amount corresponds to (100+40=140)%
This implies that, New amount
[tex] = 140\% \times 50[/tex]
[tex] = \frac{140}{100} \times 50[/tex]
[tex] = \frac{140}{2} [/tex]
[tex] = 70[/tex]
Write the recursive formula and the explicit formula for the sequence {-15,-7,1,9, 17,...}.
ANSWER
Explicit formula:
[tex]a_n= 8n - 23[/tex]
Recursive
[tex]a_{n}= a_{n - 1} + 8,a_1=-15[/tex]
EXPLANATION
The first term of the sequence is
[tex]a_1=-15[/tex]
The common difference is
[tex]d = - 7 - - 15[/tex]
[tex]d = 8[/tex]
The nth term is given by the formula,
[tex]a_n=a_1 + d(n - 1)[/tex]
[tex]a_n= - 15+ 8(n - 1)[/tex]
[tex]a_n= - 15+ 8n -8[/tex]
The explicit formula is;
[tex]a_n= 8n - 23[/tex]
The recursive definition is
[tex]a_{n}= a_{n - 1} + 8,a_1=-15[/tex]
Later 7 students joined group 2 (41 students)and one student left to join group 1. (44 students) Now 20 students play trombone and 7 more students play trumpet as play saxophone. How many students play each instrument?
48 students in group 2
43 students in group 1
So in total there are 91 students
7 students play the trump
And 20 play the trombone
Therefore it is known that 27 students play those two instruments in total
Because of this, Subtract 27 from 91 to get the num of students who doesn't play those instruments.
My sister is 14 years old my brother says that his age minus 12 is equal to my sisters age how old is my brother
Answer:
26
Step-by-step explanation:
Let his age = x
Equation
x - 12 = 14
Solution
Add 12 to both sides.
x - 12 +12 = 14 + 12
x = 26
He is currently 26 years old.
What is the discriminant of the polynomial below? 2x^2+3x-7
Answer:
Option C. [tex]65[/tex]
Step-by-step explanation:
we know that
The discriminant of a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]D=b^{2}-4ac[/tex]
in this problem we have
[tex]2x^{2} +3x-7[/tex]
so
[tex]a=2\\b=3\\c=-7[/tex]
substitute
[tex]D=3^{2}-4(2)*(-7)[/tex]
[tex]D=9+56[/tex]
[tex]D=65[/tex]
The discriminant of the giving polynomial is 65. The correct option is C. 65
The discriminant of a quadratic functionFrom the question, we are to determine the discriminant of the given polynomial
The given polynomial is
2x²+3x-7
This is a quadratic function
The discriminant of a quadratic function is simply the value in the square root of the quadratic formula
That is,
Discriminant, D = b² - 4ac
In the given quadratic function, 2x²+3x-7
a = 2, b = 3 and c = -7
∴ D = 3² -4(2)(-7)
D = 9 +56
D = 65
Hence, the discriminant of the giving polynomial is 65. The correct option is C. 65
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What is the value of x in the equation 3(2x + 4) = ?6? (4 points) ?3 1 12 19
Answer:
2
Step-by-step explanation:
3(2x + 4)=?
6x + 12
6x/6=x
12/6=2
x=2
Third-grade students at washington School read 530 books in march.They read 469 books in April.How many books did they read in the two months?
Answer:
999
530
+469
----------
999
Every year 39 million cars cross the Golden Gate Bridge in San Francisco. Which kind of function best models the relationship between time and the cumulative number of cars that have crossed the Golden Gate Bridge, exponential or linear?
Answer:
Linear
Step-by-step explanation:
Hello
Is linear
Best regards
Answer:
Linear
Step-by-step explanation:
Linear function : if the value increases with the constant value per period,
It can written as y = a + bx
Where, a = initial value, b = constant value per period,
Exponential function : if the value increases with the constant rate per period,
It can be written as,
[tex]y=ab^x[/tex]
Where, a = initial value, b = growth factor per period.
∵ Every year 39 million cars cross the Golden Gate Bridge in San Francisco.
Then after x years, the number of cars ( in million )
f(x) = 39x
⇒ f(x) = 0 + 39x
By the above explanation,
Hence, the function that represents the number of cars that have crossed the Golden Gate Bridge is linear.
For which equation would x = 5 be a solution?
4x - 7 = 27
3x + 6 = 21
12 - 2x = 13
7 + 6x = 27
Answer:
The second option.
3x + 6 = 21.
Step-by-step explanation:
3x + 6 = 21.
If x = 5, plug it in.
3 · 5 + 6 = 21
15 + 6 = 21
Hope this helps,
Davinia.
Answer:
Second Option
Step-by-step explanation:
When solving equation which is the best first step to begin to simplify the equation -2(x+3)=-10
Final answer:
The best first step to simplify the equation -2(x+3)=-10 is to distribute the -2 to the terms inside the parentheses and simplify. Then, solve for x by isolating the variable.
Explanation:
The best first step to simplify the equation -2(x+3)=-10 is to distribute the -2 to the terms inside the parentheses. This can be done by multiplying -2 with each term inside the parentheses.
So, -2(x+3) becomes -2x-6. The equation now becomes -2x - 6 = -10.
Now, we can proceed with solving the equation by isolating the variable x.
We can begin by adding 6 to both sides of the equation to get -2x = -4.
Finally, we divide both sides of the equation by -2 to solve for x.
So, x = 2.
The correct answer is option c. [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]
When solving the equation -2(x+3)=-10, the best first step is to divide both sides by 2. This simplifies the equation by making it easier to solve.
Here are the steps:
Divide both sides by 2: [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]Equation simplifies to: -(x+3) = -5Open parantheses: -x-3 = -5Rearrange: x = 5-3 = 2By dividing first, you simplify the algebraic manipulation and make solving the equation straightforward.
The complete question is:
When solving equation which is the best first step to begin to simplify the equation -2(x+3)=-10
a. [tex](-2)(-2)(x+3) = -10(-2)[/tex]
b. [tex]\frac{-1}{\ 2}(-2)(x+3) = (-10)\frac{-1}{\ 2}[/tex]
c. [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]
d. [tex]\frac{-2}{-10}(x+3) = \frac{-10}{-10}[/tex]
Mark and Henry win some money and share it in the ratio 1:3. Mark gets ?9. How much did Henry get?
What is the value of the square root of 15 to the nearest tenth? Show or explain how you got your answer.
Answer:
3.9
Step-by-step explanation:
A calculator is useful for this.
If two angles form a linear pair and the m<1 =2x + 20 and m< 2 = 48x, find the measure of each angle
Answer:
[tex]m<1=26.4\°[/tex]
[tex]m<2=153.6\°[/tex]
Step-by-step explanation:
we know that
If m<1 and m<2 form a linear pair
then
[tex]m<1+m<2=180\°[/tex] -----> by supplementary angles
substitute the values and solve for x
[tex](2x+20)+48x=180\°[/tex]
[tex]50x=180\°-20\°[/tex]
[tex]50x=160\°[/tex]
[tex]x=3.2\°[/tex]
Find the measure of each angle
[tex]m<1=(2x+20)=2(3.2\°)+20\°=26.4\°[/tex]
[tex]m<2=48x=48(3.2\°)=153.6\°[/tex]
A factory makes boxes with length to width ratio of 6 inches to 1 inch. What should be the width of a box with a length of 30 inches
Length:width
6 inches: 1 inch
30 inches: 5 inches
Since the ratio for length is multiplied by 5, you would do the same for width.
Can anyone please help me!? Help!
Subject: Expanding and Simplifying Expressions
7th-grade Mathematics!
-------------------------------------------------------------------------------------
Question #1: Write an expression that is equivalent to 2/3 (4x + 9).
A) 8/3x + 6
B) 8/3x + 9
C) 2/3x + 6
D) 2/3x + 9
-------------------------------------------------------------------------------------
Question #2: Which expression is equivalent to 1/3p + 15?
A) 1/3(p + 45)
B) 1/3(p + 5)
C) 3(p + 45)
D) 3(p + 5)
Answer:
[tex]\large\boxed{Q\#1.\ A)\ \dfrac{8}{3}x+6}\\\boxed{Q\#2.\ A)\ \dfrac{1}{3}(p+45)}[/tex]
Step-by-step explanation:
[tex]Q\#1:\\\\\dfrac{2}{3}(4x+9)\qquad\text{use the distributive property}\\\\=\left(\dfrac{2}{3}\right)(4x)+\left(\dfrac{2}{3}\right)(9)=\dfrac{8}{3}x+(2)(3)=\dfrac{8}{3}x+6\\\\Q\#2:\\\\\dfrac{1}{3}p+15=\dfrac{1}{3}p+\dfrac{1}{3}\cdot(3)(15)=\dfrac{1}{3}p+\dfrac{1}{3}\cdot45=\dfrac{1}{3}(p+45)[/tex]
Jill measured the length of her eraser. She wrote 5 on her paper without the unit which metric unit of measure should Jill include?
Answer:
Centimeter
Step-by-step explanation:
Erasers are pretty small so I would say it was about 5 cm.