Answer:
13
Step-by-step explanation:
1. Collect like-terms
-23=-a-10
2.Isolate variable
-13=-a
a=13
Answer:
A=13
Step-by-step explanation:
-23=-2a-10+a
add 10 to -23 which is now
-13=-2a+a
now add -2a and a together to get -1a
-13=-1a
divide -1 into both sides to get
13=a
Consider the following autonomous first order differential equation.
dy/dx=(−(y−4)2)(y+9)
The critical points are y=4 and y=−9. Classify these critical points (in the given order) as asymptotically stable, unstable, or semi-stable.
(A) semi-stable and unstable
(B) asymptotically stable and asymptotically stable
(C) asymptotically stable and unstable
(D) asymptotically stable and semi-stable
(E) unstable and asymptotically stable
(F) unstable and semi-stable
(G) semi-stable and semi-stable
(H) semi-stable and asymptotically stable
(I) unstable and unstable
Answer: (D) asymptotically stable and semi-stable
Step-by-step explanation:
Given that:
dy/dx=(−(y−4)2)(y+9)
The critical points are y=4 and y=−9
We have to check the sign of dy/dx in the intervals (-inf,-9), (-9,4), (4, infinity)
In (-inf, -9), dy/dx , let's take y = -10, so we have
(-(-10-4)^2(-10+9) > 0
In (-9,4), let's take y = 0
dy/dx = (-(0-4)^2)(0+9) < 0
In (4, inf), let's take y = 10
So we have (-(10-4^)2(10+9) < 0
So at y = -9, sign change for dy/dx from positive to negative. SO it is asymptotically stable
And at y = 4, sign is negative on both sides. So 4 is semi stable
I need help please I can only find 2 of these solutions
Step 1: Isolate the Sin Operator
\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)
Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable
Note that since trig functions have 2 general solutions, this will give us one of our general solutions.
\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)
x₁= 0.48
Solving for x₂
Use the period identity for Sin Functions
\(sin(x)=sin(\pi -x)\)
X in this case is arcsin(0.25)
\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)
So our two general solutions are 0.48 and 5.52
Step 3: Period
Trig Functions have periodic behavior and this function period is
\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)
So our general solutions are
0.48±12k, where k is an integer
5.52±12k, where k is an integer
Let k=1, and we get our next set of solutions:
12.48 and 17.52
So our answer is 0.48,5.52,12.48,17.52
which expression is equivalent to 4(6x+11) A.68 B.68x C.24x+11 D.24x+44
\(\huge\text{Hey there!}\)
\(\large\text{4(6x + 11)}\)
\(\large\text{Distribute}\)
\(\large\text{4(6x) + 4(11)}\)
\(\large\text{4(6x) = 24x}\)
\(\large\text{4(11) = 44}\)
\(\large\text{= 24x + 44}\)
\(\boxed{\boxed{\large\text{Answer: \bf{24x + 44}}}}\huge\checkmark\) ☑️
\(\text{Good luck on your assignment and enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
What is the area of this polygon? Enter your answer in the box. units² K Q Search
Answer:
45 units²
Step-by-step explanation:
You want the area of the figure comprised of a triangle atop a rectangle.
Composite areaThe area of the whole will be the sum of the areas of the parts. Here, we can decompose the figure into a rectangle of width 5 -(-4) = 9 units and height -2 -(-4) = 2 units.
The triangle above the rectangle has the same base width, and height 4 -(-2) = 6 units.
The total area is ...
\(A = bh_r +\dfrac{1}{2}bh_t\qquad\text{$h_r$=rectangle height; $h_t_$=triangle height}\\\\A=b(h_r+\dfrac{1}{2}h_t)= 9(2+\dfrac{6}{2})=9\cdot5=45\)
The area of the polygon is 45 units².
__
Additional comment
When finding the area of composite figures, we often find it useful to treat the area of a triangle as equal to the area of a rectangle of the same width and half the height, or the same height and half the width.
You can figure the area other ways, too. You can subtract the triangle corner areas from the 9 wide by 8 high enclosing rectangle. You can draw a vertical line through N and divide the figure into two trapezoids with bases 2 and 8. Or, you can simply add the areas of rectangle and triangle after computing them separately.
how to rewrite equation 5x+7y-35=0 in slope intercept form?
What is the circumference of this circle
Answer: 12.56 km
Step-by-step explanation:
C=2(3.14)r
C=2(3.14)2
C=12.56
Which of these figures has a line of symmetry drawn correctly?
Shape A and Shape B
Shape B and Shape D
Shape A
Shape C
A figure is shown, where lines CE and FD intersect at point B.
.
A figure is shown, where lines CE and FD intersect at point B.
.
Angle ABC is complementary to angle DBC.
What is the measure, in degrees of ?
Answer:
Step-by-step explanation:
Its 4.51
Three of 25 students in an art class are left-handed. in another words, 12% of the students in the class are left handed what does number 3 represent
Answer:
The number of students that are left handed
Step-by-step explanation:
Answer:
it represent 3 students
20 points Which of the following is NOT an advantage of using wind turbines to generate wind power? Wind turbines are not suitable for all geographical locations. O Wind turbines are affordable. Wind turbines do not emit carbon dioxide and do not require sunshine. O Wind turbines cause little disruption of ecosystems.
the first one is the answer
Help me learn how to solve this please
The percentage that can be filled with $3 in 1990 is: 29.41%
How to solve percentage increase problems?To calculate percentage growth rate:
Beginning:
Calculate the difference (increase) between the two numbers you are comparing. after that:
Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.
We are told that it cost $3 to fill a gas tank as at 1970.
Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:
Cost of a gallon in 1970 = $0.36
Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank
Now, in 1990, the cost is $1.23 and as such:
Quantity that can be bought = 3/1.23 = 2.45 gallons
Percentage of tank filled = 2.45/8.33 * 100% = 29.41%
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find the value of ...B
Answer:
b=–2
Step-by-step explanation:
we've got:
(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243
and we've also got the coefficient of x³ as –720
90b³=–720===> b³=–8===> b=–2
what is (7g-6)-(-3n-4) help me wit this asap
Answer:
Step-by-step explanation:
7g-6+3n+4= 7g+3n-2
the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes
The standard deviation of the response time is 1.53 minutes.
What is the standard deviation of the response time?To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.
Z-score = z = (x - μ) / σ
For the lower bound of 10 minutes:
z = (10 - 13) / σ
For the upper bound of 16 minutes:
z = (16 - 13) / σ
As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.
Using z-scores, we set up equations:
(10 - 13) / σ = -1.96
(16 - 13) / σ = 1.96
Solving the first equation:
-3 / σ = -1.96
σ = -3 / -1.96
Solving the second equation:
3 / σ = 1.96
σ = 3 / 1.96
Dividing both sides by 1.96:
-3 / 1.96 = σ
1.53 = σ
Full question:
The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.
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Find the identical expression for the following plz show work
-27.8÷1/7=
what is the answer
Answer:
The answer should be -194.6
Step-by-step explanation:
Have a great day :)
A rare manuscript increased in value 800% over the past 5 years. This was an increase of $2,000. What was the value of the manuscript 5 years ago? What is the value of the manuscript now?
Value of the manuscript is as follows
A. The value of the manuscript 5 years ago is $250.
B. The value of the manuscript now is $10,000.
Appreciation is an increase in the value of an asset over time. This is unlike depreciation, which lowers an asset's value over its useful life. The appreciation rate is the rate at which an asset grows in value.
% increase=(new price - original price) / original price
8.0= 2000/original price
8*original price = 2000
original price = $250
So the value of the manuscript 5 years ago is $250.
Increase is 2000 , 5 times that.
new price is $10,000
The value of the manuscript now is $10,000.
Hence , the manuscript has the following value:
A. The manuscript was worth $250 five years ago.
B. The manuscript is currently worth $10,000.
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Which of the following sets are continuous? Check all that apply.
A. {2, 4, 6, 8, ...)
B. (-0, +00)
C. (30, 45]
D. [60, 100)
E. {3,7)
Answer: The correct answer option is B.
Step-by-step explanation:
We are to determine whether which of the given data sets in the answer options are continuous.
For this, we need to know what a continuous data set is.
A data set that has no definite end to its value but keeps on continuing.
Here, the data sets are given in A, C, D, and E have definite starting and ending points.
While B is a continuous set as its values are continuing to infinity.
Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230. Find the probability that next year there will be no snowfall in that town on January 1.
1. 0.770
2. 4.348
3. 0.299
4. 1.230
The probability that next year there will be no snowfall in that town on January 1 is,
P (no snowfall) = 0.770
The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230.
Now, WE get;
the probability that next year there will be no snowfall in that town on January 1 is,
P (no snowfall) = 1 - P (snowfall)
P (no snowfall) = 1 - 0.230
P (no snowfall) = 0.770
Thus, The probability that next year there will be no snowfall in that town on January 1 is,
P (no snowfall) = 0.770
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How do you solve this problem
Answer:
4.5 in
Step-by-step explanation:
IT si 4.5 inches because the scale factor is 1 inch to 4 feet, and 18/4 = 4.5 inches.
A rectangular garden measures 27 ft by 38 ft. Surrounding (and bordering) the garden is a path 3 ft wide. Find the area of this path. Be sure to include the correct unit in your answer.
The area of this rectangular walk is 390\(ft^{2}\)
What is a rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
The width of the walk is constant and is 2ft, length of the walk is determined by the part of the rectangular yard.
Area of walk = 3 x 27 +3x27 + 3 x 38 + 3 x 38 which is 390\(ft^{2}\)
In conclusion the area of the walk is 390\(ft^{2}\)
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Simplify this expression.
6x + 3 – 4x + 2y + 7
Answer:
2x + 10 + 2y
Step-by-step explanation:
6x + 3 – 4x + 2y + 7
(6x - 4x) = 2x
2x + 3 +2y + 7
(3 + 7) = 10
Answer: 2x + 10 + 2y
15% of 9 is what number and how to solve using proportions
Answer:
Step-by-step explanation
Okay so lets solve step by step/
15% can be written as a fraction: 15/100
The of in the equation means multiplying.
15/100= 3/20
3/20*9= 270/20
27/2 is answer
Write 2.71 repeating as a simplified fraction.
271/100 is wrong
Answer:
269/99
Step-by-step explanation:
Write a linear function that passes through the points (0, 3) and (1,6)What is the domain and range of the function?
ok
P1 = (0, 3)
P2 = (1,6)
1.- Find the slope
m = (y2 - y1) / (x2 - x1)
m = (6 - 3) / (1 - 0)
m = 3/1
m = 3
2.- Find the equation of the function
y - y1 = m(x - x1)
y - 3 = 3(x - 0)
y - 3 = 3x
y = 3x + 3 This is the equation of the function
3.- This is a linear function. The domain of a linear function is all real numbers and the range of a linear function are also all real numbers.
is the ordered pair a solution to the equation. y=-7; (-5,6)
Answer: No
To check if (-5,6) is a solution to the equation y=-7, we need to substitute -5 for x and 6 for y in the equation.
If the equation is true, then the ordered pair is a solution to the equation.
If we put (-5,6) into y=-7, we get 6=-7, which is not true.
So, (-5,6) is not a solution to the equation y=-7.
A research company wants to determine whether there is a difference in effectiveness of a brand-name ibuprofen and generic ibuprofen. What are the appropriate hypotheses for this testing scenario? Let equal the mean of the effectiveness of brand-name ibuprofen and equal the mean of the effectiveness of generic ibuprofen
The alternative hypothesis is a two-tailed hypothesis because it examines whether there is a difference in effectiveness, which can be positive or negative.
What is null hypothesis?A null hypothesis is a type of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Sample data is used to assess the viability of theories. H0 represents what is referred to as "zero" on occasion. The researchers make the assumption that there may be a relationship between the factors. The null hypothesis, on the other hand, claims that no such relationship exists. Although it may not appear to be significant, the null hypothesis is an important part of research.
The following hypotheses would be appropriate for testing the difference in effectiveness between brand-name and generic ibuprofen:
The null hypothesis (H0) states that there is no difference in the mean effectiveness of brand-name and generic ibuprofen.
Alternative hypothesis (Ha): The mean effectiveness of brand-name ibuprofen and generic ibuprofen differs.
These hypotheses can be expressed symbolically as follows:
H0: _generic = _brand-name\\
Ha: _trademark _generic
Where _brand-name denotes the population mean efficacy of brand-name ibuprofen and _generic denotes the population mean efficacy of generic ibuprofen. The alternative hypothesis is a two-tailed hypothesis because it examines whether there is a difference in effectiveness, which can be positive or negative.
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Answer:
H0: μ1 – μ2 = 0
Ha: μ1 – μ2 ≠ 0
Step-by-step explanation:
took the quiz :)
Which of the following functions best describes this graph?
A. y = x^2 + x - 12
B. y = x^2 - 9x + 18
C. y = x^2 + 9x + 18
D. y = x^2 - 5x + 6
Find the difference -9.6-7.3
Answer:
-9.6-7.3 = -16.9
Step-by-step explanation:
Which equation is correct?
O a
52 x 7 = 50+ 2 × 7
Ob
b
52 x 7 = 50 x 7+2
Oc
52 x 7 = 50 x 7+2x7
Od
52 x 7 = 500 ×7+2×7
Answer:
52 x 7= 50 x 7 + 2 x 7
Step-by-step explanation: