Let c be a positive number. A differential equation of the form dy dt = ky1 + c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky1 + c is larger than the exponent 1 for natural growth. (a) Determine the solution that satisfies the initial condition y(0) = y0.
Answers
Answer:
\(y(t)=(\frac{1}{-ckt+y^{-c}_0})^{\frac{1}{c}}\)
Step-by-step explanation:
We are given that differential equation
\(\frac{dy}{dt}=ky^{1+c}\)
Where k=Positive constant
c=Positive number
\(\int \frac{dy}{y^{1+c}}=\int kdt\)
\(-\frac{1}{c}y^{-c}=kt+C\)
Initial condition
\(y(0)=y_0\)
\(-\frac{1}{cy^c}=kt+c\)
Substitute the value of initial condition
\(-\frac{1}{c(y_0)^{c}}=C\)
\(-\frac{1}{c(y)^{c}}=kt-\frac{1}{c(y_0)^{c}}\)
\(\frac{1}{y^c}=-ckt+(y_0)^{-c}\)
\(y^c=\frac{1}{-ckt+y^{-c}_0}\)
\(y(t)=(\frac{1}{-ckt+y^{-c}_0})^{\frac{1}{c}}\)
Differential equation is used to relate equations and their derivatives.
The solution that satisfies the initial condition is: \(\mathbf{y(t) = ((y0)^{-c} -c kt)^{-c}}\)
The differential equation is given as:
\(\mathbf{\frac{dy}{dt} = ky^{1 + c}}\)
Multiply both sides by dt
\(\mathbf{dy = ky^{1 + c} dt}\)
Divide both sides by \(\mathbf{y^{1 + c}}\)
\(\mathbf{\frac{dy}{y^{1 + c}} = k dt}\)
Integrate both sides
\(\mathbf{ \int\limits\frac{dy}{y^{1 + c}} = \int\limits k dt}\)
Remove constants
\(\mathbf{ \int\limits\frac{dy}{y^{1 + c}} = k \int\limits dt}\)
Rewrite as:
\(\mathbf{ \int\limits dy\ y^{-1 - c} = k \int\limits dt}\)
Now, integrate both sides
\(\mathbf{ \frac{y^{1-1 - c}}{1-1 - c} = kt + c}\)
\(\mathbf{ \frac{y^{- c}}{- c} = kt + c}\)
This gives
\(\mathbf{ -\frac{1}{cy^c} = kt + c}\)
At the initial condition, \(\mathbf{y(0) = y0}\)
So, we have:
\(\mathbf{ C = -\frac{1}{c(y0)^c} }\)
Substitute \(\mathbf{ C = -\frac{1}{c(y0)^c} }\) in \(\mathbf{ -\frac{1}{cy^c} = kt + c}\)
\(\mathbf{-\frac{1}{cy^c} = kt - \frac{1}{c(y0)^c}}\)
Multiply through by c
\(\mathbf{-\frac{1}{y^c} = ckt - \frac{1}{(y0)^c}}\)
Rewrite as:
\(\mathbf{-\frac{1}{y^c} = ckt - (y0)^{-c}}\)
Take inverse of both sides
\(\mathbf{-y^c = \frac{1}{ckt - (y0)^{-c}}}\)
Multiply both sides by -1
\(\mathbf{y^c = \frac{1}{(y0)^{-c} -c kt}}\)
Take c-th root of both sides
\(\mathbf{y = \frac{1}{((y0)^{-c} -c kt)^c}}\)
Express as exponents
\(\mathbf{y = ((y0)^{-c} -c kt)^{-c}}\)
Express y as a function of t
\(\mathbf{y(t) = ((y0)^{-c} -c kt)^{-c}}\)
Hence, the solution that satisfies the initial condition is: \(\mathbf{y(t) = ((y0)^{-c} -c kt)^{-c}}\)
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Related Questions
My checking account balance was $443 on February 1st and $872 on February 7th. Show the rate of change
Answers
Answer:
$61.29 per day.
Step-by-step explanation:
Checking account balance on February 1st: $443
Checking account balance on February 7th: $872
Difference in balances: $872 - $443 = $429
Number of days between February 1st and February 7th: 7 days
Rate of change = Difference in balances / Number of days
Rate of change = $429 / 7 days
To find the rate of change per day, divide the difference in balances by the number of days:
Rate of change = $429 / 7 days ≈ $61.29 per day
Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.
Can anyone help me solve this or atleast give me the answers
Answers
The measure of the angles formed between parallel lines and their transversals indicates;
(c)(e)(a)(d)(b)(f)(e)(a)m∠MNP = 56°m∠WXZ = 130°9. m∠3 = 97°, m∠5 = 97°, m∠10 = 97°, m∠7 = 83°
What are parallel lines?Parallel lines are lines that maintain the are equidistant from each other and have the same slope on the coordinate plane.
The angles formed between the parallel lines and their transversal are;
1. Alternate exterior angles; (c) ∠9 and ∠16
2. Supplementary angles (e); ∠15 & ∠11
3. Alternate interior angles (a); ∠10 & ∠15
4. Vertical angles (d); ∠12 & ∠15
5. Corresponding angles (b); ∠9 & ∠11
6. None (f); ∠9 & ∠15
7. Supplementary angles (e); ∠13 & ∠14
8. Alternate interior angles; ∠14 & ∠11
9. The alternate interior angles theorem indicates that we get;
(a + 28) = 2·a
Therefore; 2·a - a = 28
2·a - a = a, therefore;
a = 28
∠MNP = (a + 28)° = (28 + 28)° = 56°
10. The alternate interior angles theorem indicates that we get;
5·y° = (2·y + 78)°
Therefore;
5·y - 2·y = 78
3·y = 78
y = 78/3 = 26
The measure of the angle WXZ, m∠WXZ = 5·y°
Therefore; m∠WXZ = 5 × 26 = 130
m∠WXZ = 130°
9. ∠2 ≅ ∠3 (Vertical angles theorem)
m∠2 = m∠3
Therefore; m∠3 = m∠2 = 97°
m∠5 + m∠6 = 180° (Linear pair angles theorem)
m∠5 + 83° = 180°
m∠5 = 180° - 83° = 97°
∠10 and ∠2 are corresponding angles, therefore;
m∠10 = m∠2 = 97°
∠7 and ∠6 are vertical angles, therefore;
m∠7 = m∠6 = 83°
∠9 and ∠3 are same side interior angles, therefore;
m∠9 + m∠3 = 180°
m∠9 = 180° - m∠3
m∠9 = 180° - 97° = 83°
∠8 and ∠6 are linear pair angles, therefore; m∠8 = 180° - 83° = 97°
∠16 and ∠6 are same side exterior angles, therefore;
m∠16 + m∠6 = 180°
m∠16 = 180° - 83° = 97°
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A friend recently planned a camping trip. He had two flashlights, one that required a single 6-V battery and another that used two size-D batteries. He had previously packed two 6-V and four size-D batteries in his camper. Suppose the probability that any particular battery works is p and that batteries work or fail independently of one another. Our friend wants to take just one flashlight. For what values of p should he take the 6-V flashlight
Answers
Answer:
The values of p = 0 < p ≤ 2/3
Step-by-step explanation:
First we write the probability of 6V flashlight working representing it as a binomial mass function of a binomial random variable
P ( 6v flashlight working ) = P ( at least one 6V battery works )
= P ( 1 6v battery work ) + P ( 2 6v battery work )
= b( 2; 2, p ) + b( 1; 2, p )
write out a formula of b( 2; 2, p ) + b( 1; 2, p )
P ( 6v flashlight working ) = p^2 + 2p( 1 - p )
Next we write the probability of D flashlight working representing it as a binomial mass function of a binomial random variable
P ( D flashlight works ) = p ( at least two D batteries works )
= b( 4; 4, p ) + b(3;4, p ) + b(2; 4, p )
write out a formula of b( 4; 4, p ) + b(3;4, p ) + b(2; 4, p )
P ( D flashlight works ) = \(P^4 + 4p^3 ( 1- p ) + 6p^2 ( 1- p)^2\)
attached below is the remaining solution
Find the value of each variable.
7
(4x + 8)
x=
Answers
Answer:
x=-1/4 or -.25
Step-by-step explanation:
I took the test and double checked it
Calc II Question
Find the volume of the solid obtained by rotating the region bonded bt the given curves about the specified line.
Y = e^-x
Y = 1
X = 2
About the Y = 2
Answers
Answer:
\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Step-by-step explanation:
This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution. I'll show how to do it with both:
Shell Method (Horizontal Axis)
\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)
Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)
Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))
Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)
Plugging in our integral, we get:
\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Washer Method (Parallel to x-axis)
\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)
Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))
Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))
Bounds: \([a,b]=[0,2]\)
Plugging in our integral, we get:
\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)
\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!
5/8 entre 6 personas
Answers
Based on the information we can infer that 5/8 between 6 people is equal to 15/24.
How to divide 5/8 between 6 people?To calculate the part that corresponds to each person, divide the fraction 5/8 by the number of people, which in this case is 6. To simplify the fraction, you can reduce the numerator and denominator by dividing both by their maximum common factor, which is 3.
5 ÷ 3 = 1 and 2 remainder8 ÷ 3 = 2 and 2 remainder
So the fraction can be simplified to 1 2/8, which can also be expressed as 1 1/4 or 5/4 in its most simplified form. This means that each person would receive 5/4 of the original share, and since there are 6 people in total, you can multiply 5/4 by 6 to get the total share that corresponds to all 6 people:
(5/4) x 6 = 30/4 = 15/2 = 15/24
So each person would receive 15/24 of the original amount.
Note: Here is the question in English:
5/8 divided in 6 people
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-x^3-3x^2=6x+4 find all the zeros of the equation
Answers
This is consistent with the solutions for the equation \(x^{2}\) - 6x + 5 = 0 being x = 1 and x = 5.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.
The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation \(x^{2}\) - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.
The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation \(x^{2}\) - 6x + 5 = 0 being x = 1 and x = 5.
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Full explanation and answers on these 2 questions please. Also only answer if u know what ur doing.
Answers
Step-by-step explanation:
Q3
25 - (x-8)²/4 = [100 - (x-8)²]/4
[100 - (x²- 16x + 64)]/4
(100 - x² + 16x - 64)/4 = (-x² + 16x + 36)/4
(36 + 16x - x²)/4 = (36 - 2x + 18x - x²)/4
[2(18 - x) + x(18 - x)]/4 = [(2 + x)(18 - x)]/4
....proved
Q4
3(ax + 7) - 2(x + b) = 4x + 29
expanding,
3ax + 21 - 2x - 2b = 4x + 29
3ax - 2x + 21 - 2b = 4x + 29
Comparing terms; x terms,
3ax - 2x = 4x
3a - 2 = 4
3a = 6
a = 6/3
a = 2
constant terms,
21 - 2b = 29
21 - 29 = 2b
2b = -8
b = -8/2
b = -4
.... proved
what is 1/10+ 3/100 in fraction from
Answers
Answer:
0.13
Step-by-step explanation:
1/10 + 3/100 =
10/100 + 3/100 =
13/100
Hope that this helps you and have a great day:)
Example 1: Every Number Has an Opposite
Locate the number 8 and its opposite on the number line. Explain how they are related to zero.
-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Exercises 2-3
2. Locate and label the opposites of the numbers on the number line.
9
-2
4
a.
b.
C.
8
Answers
Answer:
To locate the number 8 and its opposite on the number line, we can use the given number line:
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Number 8 is located to the right of zero. Its opposite can be found by moving an equal distance to the left of zero. Since the number line is symmetric about zero, the opposite of 8 would be -8.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
↑ ↑
So, the opposite of 8 is -8. They are related to zero as equal distances on opposite sides of zero on the number line.
Now, let's address exercises 2-3:
a. To locate the opposite of 9, we need to move an equal distance to the left of zero. The opposite of 9 is -9.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
↑
b. To locate the opposite of -2, we need to move an equal distance to the right of zero. The opposite of -2 is 2.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
↑
c. To locate the opposite of 4, we need to move an equal distance to the left of zero. The opposite of 4 is -4.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
↑
So, the opposites of the given numbers are:
9 → -9
-2 → 2
4 → -4
They are related to zero as equal distances on opposite sides of zero on the number line.
Step-by-step explanation:
If the p-value for a hypothesis test is 0.027 and the chosen level of significance is a=0.05, then the correct conclusion is to
Answers
Answer:
\( p_v = 0.027\)
And for this case we have a significance level \( \alpha=0.05\) and then:
\( p_v <\alpha\)
So then we have enough evidence to reject the null hypothesis. And we can conclude in favor the alternative hypothesis.
Step-by-step explanation:
For this case we have the following hypothesis:
\(Null hypothesis: p =p_o\)
\(Alternative hypothesis: p \neq p_o\)
And for this case we got the following hypothesis:
\( p_v = 0.027\)
And for this case we have a significance level \( \alpha=0.05\) and then:
\( p_v <\alpha\)
So then we have enough evidence to reject the null hypothesis. And we can conclude in favor the alternative hypothesis.
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
What makes things concurrent?
Answers
Answer:
When the are intercepted by other lines (math)
Existing, happening at the same time (definition)
Write a real-life word problem that corresponds to the equation below.
x2 = 144
Scoring Rubric
Scoring Rubric
Sample Responses:
Shane has a square garden. The area of the garden is 144 square feet. What is the side length of the garden?
Zane has a square frame that has an area of 144 square inches. What is the side length of the frame?
The area of Kelly’s square dog kennel is 144 square meters. What is the side length of the dog kennel?
Kylee’s bedroom is in the shape of a square and has an area of 144 square feet. What is the length of one wall?
2 Points
The response indicates proficiency in representing quadratic equations by writing a real-life word problem that matches a given equation. The student correctly completes the task.
1 Point
The response indicates partial proficiency in representing quadratic equations by writing a real-life word problem that matches a given equation. The student correctly completes the task but makes a minor error. Answers that give a word problem but do not involve a real-life situation receive 1 point.
0 Points
The response indicates no proficiency in representing quadratic equations by writing a real-life word problem that matches a given equation. The student shows no understanding of the concept or task. Answers that solve the quadratic equation but do not give a word problem receive 0 points.
Answers
The real life problem that corresponds to the equation will be "The area of a farmer's square garden is 144 square feet. What is the length of the garden?"
How to solve the equationA real-life word problem that corresponds to the equation x² = 144 will be that the area of a farmer's square garden is 144 square feet. What is the length of the garden?
In this case, the length of the garden will be the square root of 144. This will be calculated thus:
x² = 144
x = ✓144
x = 12
Therefore, the length of the garden is 12 feet.
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If joes shoes cost 44 dollars and 20 cents and joe has 10
dollars and 68 cents. How much money does joe need?
Answers
Answer: 44.20-10.68=33.52
He need 33.52$
Step-by-step explanation:
I NEED HELP ASAP!! like now
Answers
Answer:
1) exponent
2) base
3) power
4) order of operations
5) algebraic expression
6) evaluating
7) like terms
8) variable
Gate posts are parallel and m<4 =47, what is m<1
Answers
The value of angle 1 given the value of angle 4 as 47° will be 133°
How to explain parallel linesParallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.
Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.
The value will be:
= 180° - 47°
= 133°
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Please answer today or tomorrow. The outside temperature was 5 degrees Fahrenheit. How many degrees below the freezing point of water was the temperature?
Answers
Answer:
water freezes in 32 degrees
so 32-5=27
so it was 27 degrees bellow the freezjng point of water
write the equation of a circle given the center (-4, 4) and radius r = 5
Answers
Given : the center of the circle = (-4 , 4)
And the radius of the circle = r = 5
The general equation of the circle is :
\((x-h)^2+(y-k)^2=r^2\)Where (h,k) is the center of the circle and r is the radius of the circle
So, ( h , k ) = ( -4 , 4 ) and r = 5
so, the equation of the circle will be :
\(\begin{gathered} (x-(-4))^2+(y-4)^2=5^2 \\ \\ (x+4)^2+(y-4)^2=25 \end{gathered}\)help asap please help
Answers
Answer:
Answer:
The Prime Factorization is:
2 x 5 x 11
Step-by-step explanation:
what is differnciation
Answers
Answer:
Differentiation is concerned with things like speeds and accelerations, slopes and curves ect. These are Rates of Change, they are things that are defined locally. The Fundamental Theorem of Calculus is that Integration and Differentiation are the inverse of each other.
Endeye needs to split 1/5 of the dinner left over from last week to feed her 3 siblings. What fraction of the original dinner will each sibling have to eat tonight?
Answers
Answer:
They each had 1/20 of the original meal
Step-by-step explanation:
To begin, there are 4 people. Her siblings, and herself. She is splitting the 1/5 leftover to feed them. To do this, we simply take 1/5 and put it into a fraction to get 0.2. Next, we can put 0.2 / 4 into a calculator to get how much each person can get.
0.2 / 4 = 0.05.
Now, we need to turn it into a fraction to find out how much they had in fraction form of the original.
0.05 = 1/20
They each had 1/20 of the original meal
Find the probability.
A bag contains 10 blue marbles, 5 red marbles, and 5 green marbles. You pick three
marbles from the bag, replacing the marble you chose each time. What is the probability
of choosing 3 green marbles?
O1/57
O 1/114
O 1/64
O 1/32
Answers
Answer:
Probability that the first marble drawn is blue is 10/27, since there are 10 blue marbles and 27 altogether
Probability that the second marble drawn is green is 5/26, since there are 5 green marbles and 26 altogether (a blue one is gone, remember?)
Probability that the third marble drawn is yellow is 12/25, since there are 12 yellow marbles and 25 altogether (both a blue and a green one are now gone)
Probability that all happen is product of all individual odds = 10/27*5/26*12/25 = 3.42%
Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each.
Then on the way to the register, Lisa notices a cool pair of shoes that cost $39. If she wants those shoes and the jeans, how many t-shirts will she be able to purchase? Create an inequality to represent the number of t-shirts that Lisa can purchase?
Answers
Answer:
To determine the number of shirts that Lisa can buy, knowing that each one is worth $ 14, that she can spend a maximum of $ 150 and that she will also buy a pair of jeans for $ 58 and a pair of shoes for $ 39, the following calculation must be performed:
(150 - 58 - 39) / 14 = X
53/14 = X
3.78 = X
53 - (14 x 3) = X
11 = X
Therefore, Lisa can buy 3 T-shirts, and she will have 11 dollars left over.
Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.
Answers
No, what they said is not fact.
The statement "producing great engineers who benefit science and technology in India is the most important function of IITs" and "IITs are greatly improving the image of India in the West" are both important functions of IITs, and the priority of these functions may depend on individual perspectives and goals.
Some people might argue that producing engineers is more crucial for the development of India's technology and economy, while others might argue that improving the image of India in the West is equally important for increasing its global recognition and competitiveness. Both functions play important roles and it is a matter of perspective which one is considered more important.
Correct Question :
Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west
Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.
What they said is fact or not? Explain.
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a set of data is summarized by the stem and leaf plot below. stem123leaf002444788889225578344555666799 provide your answer below: there are values in the data set which are greater than or equal to 10 and less than or equal to 19. there are values in the data set which are greater than or equal to 30 and less than or equal to 39. there are values in the data set which are greater than or equal to 20 and less than or equal to 29.
Answers
Yes, there are values in the data set that are greater than or equal to 10 and less than or equal to 19. This is evident from the presence of "2" in the leaf plot, which indicates that there are values in the data set that are between 20 and 29.
No, there are no values in the data set that are greater than or equal to 30 and less than or equal to 39. This is evident from the absence of any leaves with a value of "3".
Yes, there are values in the data set that are greater than or equal to 20 and less than or equal to 29. This is evident from the presence of "2" in the leaf plot, which indicates that there are values in the data set that are between 20 and 29.
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ALGEBRA please put a very small explanation to the awnser
Answers
Certainly! The problem can be solved using the Pythagorean theorem,
which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.
The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.
By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.
Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.
We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.
Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.
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in mr carrs math class, 9 of the 14 said they like math , and 7 of the 16 boys said they like math . if miss carr randomly a selects , what is the probability that she chooses a girl or someone who likes math
Answers
For the 1st fraction, since 14 × 1 = 14,
9
14
=
9 × 1
14 × 1
=
9
14
Likewise, for the 2nd fraction, since 7 × 2 = 14,
6
7
=
6 × 2
7 × 2
=
12
14
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
9
14
<
12
14
or
9
14
<
6
7
help help exponents help
Answers
Answer:
3
Step-by-step explanation:
The base is the number below the exponent.
Gwen spent $12.50 to purchase 5 bracelets. Each 4.
bracelet costs the same amount. What is the unit rate
for each bracelet?
Answers
Answer:
simply divide 12.50 by 5. Therefore each bracelet costs $2.05 : 2$ and 5 cents.
Step-by-step explanation:
The cost of each bracelet will be $2.5.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The cost of 5 bracelets = $12.50
Now,
Since, The cost of 5 bracelets = $12.50
So, The cost of 1 bracelets = $12.50 ÷ 5
= $2.5
Thus, The cost of each bracelet will be $2.5.
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