The solution to the differential equation satisfying the initial condition p(1) = 2 is p(t) = 2e^(2t-2).
To find the solution, we first need to solve the differential equation. Integrating both sides, we have ∫dp = ∫2p dt. This gives us ln|p| = 2t + C, where C is the constant of integration. Taking the exponential of both sides, we get |p| = e^(2t+C). Since p(1) = 2, we can substitute t = 1 and p = 2 into the equation to find C.
Thus, 2 = e^(2(1)+C) = e^(2+C), which implies C = ln(2). Substituting this value back into the equation, we have |p| = e^(2t+ln(2)) = 2e^(2t). Finally, we can drop the absolute value sign to obtain the solution p(t) = 2e^(2t-2).
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What are the signs of the first and second coordinates of a point in quadrant II?
The signs of the first and second coordinates of a point in quadrant II are negative.
To determine the signs of the coordinates of a point in quadrant II, we can use the following formula:
Sign of coordinate 1: (-1) * (x-axis)
Sign of coordinate 2: (-1) * (y-axis)
For example, if we need to determine the signs of the coordinates of the point (4, -5) in quadrant II, we can use the formula above. The sign of the first coordinate is (-1) * (+4), which is -4. The sign of the second coordinate is (-1) * (-5), which is +5. Therefore, the signs of both coordinates of the point (4, -5) in quadrant II are negative.
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Kayden has a collection of 120 coins. How many coins represent 5% of his collection?
Since , solution of percentage problem is Kayden has a collection of 120 coins, the number of coins that represent the 5% of his collection is 6.
What is a percentage?A percentage is a way to express a number as a fraction of 100.To calculate percentage increase, subtract the original value from the new value and divide by the original value. To calculate percentage decrease, subtract the new value from the original value and divide by the original value.
Here,
As given by the question , the total number ko coins Kayden has in his collection is , 120 coins.
To know how many of his coins represent 5%, we can calculate ,
5% of 120 coins
= 5/100 * 12
= 6 coins
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what is the slope of a line that goes through the points (-5,-4) and (-2,-5).
Answer:
-1/3
The Slope
Slope is a measure of steepness of a line. In Algebra 1, It is how much the y-value changes when the x-value increases by 1.
Slope Formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in your points accordingly to find the slope.
Q)What is the slope of a line that goes through the points (-5,4) and (-2-5)
1) To solve, first find your y-values and x-values. y-values are the second value in the coordinate form and a measure of height on a 2D coordinate plane. x-values are the first value in coordinate form and a measure of horizontal distance on a 2D coordinate plane.
(x,y)
y-values: -4, -5
x-values: -5, -2
2) Plug into the formula listed above.
[tex]\frac{-5-(-4)}{-2-(-5)}[/tex]
Simplify.
[tex]-\frac{1}3}[/tex]
Your slope is -1/3.
Answer:
-1/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-(-4))/(-2-(-5))
m=(-5+4)/(-2+5)
m=-1/3
find the sum of these polynomials. (4x^2+3x-1) + (x^2-5x-6)=
The sum of the polynomials (4x^2+3x-1) + (x^2-5x-6) is 5x^2-2x-7
we will add the coefficients of the same degree terms.
(4x^2+3x-1) + (x^2-5x-6) = (4x^2+x^2) + (3x-5x) + (-1-6) = 5x^2-2x-7
Therefore, the sum of the polynomials (4x^2+3x-1) + (x^2-5x-6) is 5x^2-2x-7
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please this is due tonight and its for a test I did this all day
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
An unfair comparison between two numbers or other mathematical expressions is referred to as an inequality. It is most frequently used when comparing the sizes of two numbers on a number line. The attachment contains the graph for each inequality or equation.
What is graph?A graph is a graphical representation of statistical data or the functional relationship of variables. Graphs can highlight broad trends in the quantitative behaviour of data, which is useful for forecasting. They can, however, be inaccurate and occasionally deceptive as mere approximations.
Most graphs have two axes: one for independent variables and one for dependent variables. A broken-line graph is the most common type of graph, with time serving as the independent variable.
16. 2y – 4x < 8
= 2y < 4x + 8
= y < 2x + 4
17. -4y > -x + 12
= y > x/4 + -3
18. | x + 3 |= y
y = | x + 3 |
19. |2x – 6| + 2 = y
y = |2x – 6| + 2
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How do you find out if a number is a multiple of 8?
If the last three digits of a number are divisible by 8, then the number is completely divisible by 8. So we can check the last three digits of a number to know whether they are a multiple of 8.
A multiple of 8 is a number that can be evenly divided by 8 without a remainder. To determine if a number is a multiple of 8, you can divide it by 8 and check if the quotient is an integer (a whole number with no remainder).
For example, to check if the number 96 is a multiple of 8, you can divide 96 by 8 and the quotient is 12, which is an integer, so 96 is a multiple of 8.
Another way to check if a number is a multiple of 8 is to check if the last three digits of the number are 000 or divisible by 8. This is because 8 is a power of 2 (2^3=8), and any number that is a multiple of 8 will be divisible by 2^3, which means it must have 3 trailing zeroes.
A more general method to check if a number is a multiple of any number is by using the modulo operator, which returns the remainder of a division. If x is a multiple of y, then x mod y = 0. Therefore, you can use x % 8 == 0 to check if x is a multiple of 8.
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Do the sides 7 cm 24 cm and 25cm form a right-angled triangle give reasons?
The sides 7 cm, 24 cm and 25 cm can form a right-angled triangle. The Pythagorean theorem can be used to verify this.
From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angles triangle.
Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. Then the equation, can be written as,
CA² = AB² + BC²
Now, let us check this rule for the above given sides of the triangle.
Longest side² = Sum of squares of other two sides
25² = 24² + 7²
625 = 625
Thus, the sides 7 cm, 24 cm and 25 cm can form a right-angled triangle.
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The graph and table show the total cost of memberships compared to the number of months you are a member at two different gyms, EZ Fitness and Buff Up Gym. Use the information to answer Parts A-B.
Alegbra I (Freshman-highschool)
EZ Fitness shows a monthly cost of $20 dollars per month. Buff Up Gym membership shows a monthly membership cost of $25 dollars per month.
How to find the slope of linear equation?
The slope between 2 coordinates can be found using the formula;
Slope = (y₂ - y₁)/(x₂ - x₁)
For the Buff Up Gym, we will pick the coordinates;
(2, 50) and (4, 100)
Thus;
Slope = (100 - 50)/(4 - 2)
Slope = $25 per month
For the function table for EZ Fitness, we pick two coordinates; (1, 20) and (2, 40). The slope is;
Slope = (40 - 20)/(2 - 1)
Slope = $20 per month
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What is an example of no solution?
As an example, consider 3x + 5 = 3x - 5. This equation has no solution. There is no value that will ever satisfy this type of equation.
What is infinite solution?
Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".
What is an infinite number?
There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.
The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.
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Ellen Andrzejewski purchased the car in the ad for $7775. She made a down payment of $775.00. She financed the remainder at $331.16 per month for 24 months. What is the APR?
474 is the Annual percentage rate (APR).
What is APR in plain English?
If you have a balance on your credit card, you will pay an annual percentage rate (APR) of interest. The cost of borrowing money is what you pay in interest on a credit card. The interest rates on credit cards are often expressed as an annual rate. The yearly percentage rate is used to describe this (APR).
Certain credit cards feature variable APRs, which means that your rate may increase or decrease over time.
$331.16 * 24 + 775 - 7775 = 947.84
She over paid $ 947.84
24 months equals two years.
947.84/2 = 473.92 ≈ 474
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Halima is on her way home in her car. She has driven 9 kilometers so far, which is one-third of the way home. What is the total length of her drive?
Answer:
27
Step-by-step explanation:
If 9 kilometers is 1/3, the total length of her drive would be 9: 1/3=9•3/1=27
Answer:
27
Step-by-step explanation:
if 9 kilometers is 1/3 of her journey then you should take 9 times 3 to find the total distance she needs to travel which is 27 kilometers
Determine the value of y, if x is 5.
y = x² - 6
Answer:
19
Step-by-step explanation:
if x=5
y=x^2 - 6
y= 5^2 - 6
y= 25- 6
y=19
Algebra 2, I remember doing this but i’m confused bc I remember like (f)g)(x) something like that so do I multiply or what?
The (g·g)(t) of the function is (g·g)(t) = 16t - 15
How to find (g·g)(t) of the function?A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable
Since g(t) = -4t + 5
What (g·g)(t) means is that you should replace t with the value of g(t) (i.e. -4t + 5) in the same equation. That is:
(g·g)(t) = g(g(t))
(g·g)(t) = -4(-4t + 5) + 5
(g·g)(t) = 16t - 20 + 5
(g·g)(t) = 16t - 15
Thus, the value of g·g)(t) is 16t - 15
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Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly. How much would Katherine need to invest, to the nearest ten dollars, for the value of the account to reach $960 in 16 years?
Katherine need to invest $432.4 for the value of the account to reach $960 in 16 years.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly.
We know that;
⇒ [tex]A = P e^r^t\\[/tex]
Let the invest amount = x
Here, The amount = $960
And, The time = 16 years
And, Rate = 5.8% = 0.058
So, We can formulate;
⇒ [tex]A = P e^r^t\\[/tex]
⇒ [tex]960 = P * e^{0.058 * 16} \\[/tex]
⇒ 960 = P × 2.22
⇒ P = 960 / 2.22
⇒ P = $432.43
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Derek has $82 in his bank account. There is a service fee of $5.50 charged every month. For 6 months, Derek deposits $11.25 in the account. If he doesn’t make any other deposits or withdrawals, how much is in the account after 11 months?
After 11 months, Derek would have $89 in his account
How to calculate the amount of money that Derek would have in his account after 11 months?Derek has $82 in his account
The bank charges a service fee of $5.50 each month
For 6 months Derek deposits $11.25 in his account
Therefore the amount of money in his account after 11 months can be calculated as follows
82 + 11.25(6)
82 + 67.5
= 149.5
The service charge for the entire 11 months is
= 5.50(11)
= 60.5
The money in the account is
149.5-60.5
= 89
Hence Derek has $89 in his account after 11 months
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Which description best matches the graph below? Please explain why you chose the answer. I will mark you brainliest.
Gill walks for a minute away from home for several minutes, and then turns toward home and walks for a few minutes. He stops when he knows and they talk for a few minutes. Then he starts walking away from home.
Hence option C is correct.
What is a graph?
In discrete mathematics, and more specifically in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way. The items correspond to mathematical abstractions known as vertices, and each pair of connected vertices is known as an edge.
Given graph represents the y-axis is the distance from home and the x-axis is the number of minutes.
There are 4 straight lines in the graph
The first line is increasingly and represents Gill walking away from home.
The second line is decreasing and represents Gill walking toward home.
The third line is parallel to x-axis. It means he stands a point for a few minutes.
The fourth line is increasingly and represents Gill walking away from home.
Hence option C is the correct option.
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A certain blogger has 460 followers on his social media accounts, but is losing followers at a rate of 6 people per day based on his comments. Another blogger has 128 followers on her social media accounts and gains an average of 10 new followers per day.
Which equation can be used to find d, the number of days it will take before both bloggers have the same number of followers?
21 days it will take before both bloggers have the same number of followers
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given a blogger has 460 followers on his social media accounts, but is losing followers at a rate of 6 people per day based on his comments.
y=460-6d
Where d represents the number of days
Another blogger has 128 followers on her social media accounts and gains an average of 10 new followers per day.
y=128+10d
We need to find equation to find the number of days it will take before both bloggers have the same number of followers
460-6d=128+10d
Add 6d on both sides
460=128+16d
Subtract 128 on both sides
460-128=16d
332=16d
d=20.75=21
Hence, 21 days it will take before both bloggers have the same number of followers
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4.
What is the solution of the system of equations?
y = –4x + 10
y = –2x – 6
What is the formula of mirror image?
A mirror equation is an equation relating object distance and image distance with focal length. It is also known as the mirror formula.
1/f= 1/u + 1/v.
u is the Object distance
v is the Image distance
f is the Focal Length given by f=R/2.
R is the radius of curvature of the spherical mirror
The above formula is valid under all situations for all types of concave and convex and for all object positions.
Linear magnification is defined as the ratio of the image size to the object size;
Magnification= Image size/ Object size.
it can be expressed as the ratio of the distance of the image to the distance v of object u from the mirror. Magnification has no unit.
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Your family decides to go to the Fox Theater to watch a
musical. There is valet parking (where someone parks your
car for you) available across the street. Your dad decides to
leave a tip of 15% to the valet person. The cost of parking
is $35. How much tip will he leave?
The cost of tip will he leave for the valet person is, $5.25.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Your dad decides to leave a tip of 15% to the valet person.
And, The cost of parking is $35.
Here, The cost of parking is $35.
Hence, The cost of tip for the valet person = 15% of $35
= 15/100 × $35
= $5.25
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Graph work
Y=Mx+C
NEED ASAP
WILL GIVE BRAINILY TO FIRST CORRECT ANSWER
Answer: y = 6x + 20, or E = 6t + 20
Step-by-step explanation:
Taking two points on the graph, (10, 80) and (30, 200), you can find the slope ("E") with the equation (y2-y1)/(x2-x1), which when plugged into the formula would be (200-80)/(30-10) = 120/20 = 6. To get your "t", you would plug this back into the formula y=mx+b along with any point on the graph, which would be:
80 = 6(10) + b
80 = 60 + b
b = 20
So the final equation should be y = 6x + 20
hellppppp meeee pleasseee
Answer: -1/4
Step-by-step explanation:
Answer: the answer to your question I believe is d= -1/4 = -0.25
Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. He finds the mean is 14. His steps for finding the standard deviation are below.
The mistake that Yuri has made is that : he divided the equation by n instaed of dividing the equation by n-1
What is the mistake that is made in the solution?While finding the standard deviation of a group of scores, the formula has the denominator as n - 1
where n is the total number of values in the data set.
the data set is 12, 14, 9 and 21. Hence n = 4
N - 1 = 3
Going ahead to work with n = 4 would give a wrong result.
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the correct question is
Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. he finds the mean is 14. his steps for finding the standard deviation are below. what is the first error he made in computing the standard deviation
The image is attached as well to the question
How do you find the quotient of a division fraction?
Take the reciprocal of the second fraction, and Multiply it by the first fraction. later reduce the resultant fraction to its lowest terms.
The quotient of a fraction is the whole number that is obtained when we simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction.
The quotient can also be the solution to a division problem involving two fractions. That division is a method of sharing equally and putting into equal groups. We divide a whole number by the divisor to get the quotient.
The reciprocal of a fraction is a simple way of interchanging the fraction's numerator and denominator.
Consider an example:
2 3/7=3 *2/7 =3 + 2/7
3 is the quotient
2 is the remainder
7 is the divisor
23 is the dividend
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Write an equation in slope-intercept form to represent the linear relationship shown in the table.
The equation in y = 2x + 8 for the given coordinates.
What is the slope-intercept form of a line?Finding the equation of a straight line in the coordinate plane is done using the slope-intercept form. A straight-line's equation will be that relationship that:
any place on the line's coordinates must meet.
Any point that is not on the line will not have coordinates that satisfy.
Given coordinates
x -2 -1 0 1
y 4 6 8 10
equation is given by y = mx + c
m is the slope and c is y-intercept
let x₁ = -2, x₂ = -1
y₁ = 4, y₂ = 6
m = (y₂ - y₁)/(x₂ - x₁)
m = (6 - 4)/(-1 - (-2))
m = 2
so y = mx + c
substitute value of m
y = 2x + c
at x = 0 and y = 8
8 = 2(0) + c
c = 8
equation of line y = mx + c
y = 2x + 8
Hence the equation is y = 2x + 8.
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the complete question is in image.
Which phrase represents this expression? (30 - 10) × 5
A. 5 times the difference of 30 and 10
B. 5 times the difference of 10 and 30
C.the difference of 30 and the product of 5 times 10
D.the difference of the product of 5 times 10 and 30
Answer:
Step-by-step explanation:
A - Since there are parenthesis on 30 and 10, you would want to find the difference between 30 and 10 first, and then multiply it by 5, hence getting you 5 times the difference of 30 and 10.
NEED HELP ASAP!!!!!!!
Select all the ordered pairs that are solutions to 3x - y = 1.
A. (-2,-7)
B. (-1,-4)
C. (0, 1)
D. (3,8)
E. (4,2)
Answer:
A, B, and D
Step-by-step explanation:
Substitute all the coordinates into the equation. (x, y)
3(-2) - (-7) = 1
-6 - (-7) = 1
1 = 1
3(-1) - (-4) =1
-3 - (-4) = 1
1 = 1
3(0) - (1) = 1
0 - (1) = 1
-1 does not equal 1
3(3) - (8) = 1
9 - (8) = 1
1 = 1
Points (-4,-8) and (-2,-5) fall on a line. Calculate the y-intercept of the line. What is the y-intercept?
Answer:
y-intercept: -2
Step-by-step explanation:
The Y-intercept is when x = 0. So, to find the y-intercept we just need to put in 0 for x and get the answer of -2. So, the y-intercept is located at (0, -2)
Marge said that she subtracted 20 from both sides of an equation to solve it. Colin thinks that the equation she was solving could have been 6 + t = 20. Does Colin's reasoning make sense? Explain.
Answer:
Colin's reasoning makes sense. If Marge subtracted 20 from both sides of an equation, the equation she was solving could have been 6 + t = 20. On the left side of the equation, 6 + t would be simplified to t. On the right side of the equation, 20 would be subtracted from 20, resulting in a value of 0. So, the equation t = 0 would be the result of Marge's actions.
Answer: Colin's reasoning makes sense. If Marge subtracted 20 from both sides of an equation, the equation she was solving could have been 6 + t = 20. On the left side of the equation, 6 + t would be simplified to t. On the right side of the equation, 20 would be subtracted from 20, resulting in a value of 0. So, the equation t = 0 would be the result of Marge's actions.
Step-by-step explanation:
Rename 1 foot with an equivalent factor in inches.
Answer:
12 inches
Step-by-step explanation:
1 foot = 12 inches
(12 inches)/(1 foot) = 1
1 foot × (12 inches)/(1 foot) = 12 inches