Find the general solution of the differential equation 254" + 80y' + 64y = 0. = NOTE: Use C1, C2 for the constants of integration. Use t for the independent variable. y(t) =
Answers
The general solution of the differential equation is\(y(t) = C1e^((-8/5)t) + C2te^((-8/5)t)\)
To find the general solution of the differential equation 254" + 80y' + 64y = 0, we can use the method of solving linear homogeneous second-order differential equations.
First, we assume a solution of the form \(y(t) = e^(rt)\), where r is a constant to be determined.
Taking the first and second derivatives of y(t), we have:
\(y'(t) = re^(rt)\)
\(y''(t) = r^2e^(rt)\)
Substituting these derivatives into the differential equation, we get:
\(25(r^2e^(rt)) + 80(re^(rt)) + 64(e^(rt)) = 0\)
Dividing through by \(e^(rt),\)we have:
\(25r^2 + 80r + 64 = 0\)
This is a quadratic equation in terms of r. We can solve it by factoring or using the quadratic formula.
Using the quadratic formula, we have:
r = (-80 ± √(\(80^2\) - 42564)) / (2*25)
r = (-80 ± √(6400 - 6400)) / 50
r = (-80 ± √0) / 50
r = -80/50
r = -8/5
Since the discriminant is zero, we have a repeated root, r = -8/5.
Therefore, the general solution of the differential equation is:
\(y(t) = C1e^((-8/5)t) + C2te^((-8/5)t)\)
Here, C1 and C2 are constants of integration that can be determined by applying initial conditions or boundary conditions, if provided.
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Related Questions
8
Which does NOT describe the quadrilateral below?
O A. trapezoid
B. square
C. parallelogram
О
D. rectangle
Answers
Compute the partial derivative of ℎ(,)=e^3zx- 4x^2z^3.
Answers
The partial derivative of \(h(x, z) = ex^{3zx} - 4x^2z^3\) with respect to x can be computed using the chain rule of differentiation. The derivative is given by ∂h/∂x = \(3z e^{3zx} - 8xz^3\)
To explain the answer, we apply the chain rule of differentiation. The function h(x, z) consists of two terms: \(e^{3zx}\) and \(-4x^2z^3\). When computing the partial derivative with respect to x, we treat z as a constant. For the first term, the derivative of \(e^{3zx}\) with respect to x is found by applying the chain rule: the derivative of the outer function \(e^{3zx}\) multiplied by the derivative of the inner function (3zx) with respect to x. The derivative of \(e^{3zx}\) is \(e^{3zx}\), and the derivative of 3zx with respect to x is 3z. Therefore, the derivative of the first term is 3z \(e^{3zx}\). For the second term, \(-4x^2z^3\), the derivative of \(x^2\) with respect to x is 2x, while the derivative of z³ with respect to x is 0 since z is treated as a constant. Thus, the derivative of the second term is -8xz³. Adding the derivatives of the two terms, we obtain the partial derivative of h(x, z) with respect to x as 3z \(e^{3zx}\) - 8xz³.
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HELP ME giving brainlest
Answers
Answer:
The answer is false.
Step-by-step explanation:
THE reason why it is false is because if so that wouldnt make any sense.
What is 6 3/4 + 19 6/7 in fraction form
Answers
6 3
4
+
19 6
7
= (6 + 19) + (
3
4
+
6
7
)
= 25 +
3 × 7
4 × 7
+
6 × 4
7 × 4
= 25 +
21
28
+
24
28
= 25 +
21 + 24
28
= 25 +
45
28
= 25 +
1 17
28
=
26 17
28
Answer: In fraction form, the answer is \(26\frac{17}{45}\).
Step-by-step explanation: We are given \(6\frac{3}{4} +19\frac{6}{7}\) and have to find what the sum of the two numbers are. Before we can starting however, the first step is to make the denominators the same to do this, find the least common multiple of 7 and 4, and make that the denominator. Multiply the numerator as well to make the fraction the same. The least common multiple of 4 and 7 is 28. That gives us the problem \(6\frac{21}{28}+19\frac{24}{28}\). (Sorry I don't think I explained that well.)
The next step is to add the numerators of the fractions together. 21 +24 = 45, and the denominator stays the same. Also add the whole numbers together to make one mixed number. This gives us \(25\frac{45}{28}\).
The finals step is to get rid of the improper fraction next to 25. To do this, subtract 28 from 42, and get 17. Add 1 to the 25, and you get \(26\frac{17}{28}\).
Show work:\(6\frac{3}{4} +19\frac{6}{7}\)
\(6\frac{3(7)}{4(7)}+19\frac{6(4)}{7(4)}\)
\(6\frac{21}{28} +19\frac{24}{28}\)
\((6+19)+(\frac{21}{28} +\frac{24}{28})\)
\(25+\frac{45}{28}\)
\(25(+1)\frac{45(-28)}{28}\)
\(26\frac{17}{28}\)
Hope this helps! Have a great day!
Solve analytically Laplace's equation Au=0 in the square [0, 1]²2 with boundary conditions u(x,0) = 0 = u(0, y), u(x, 1) = u(1, y) = 1.
Answers
The Laplace equation is defined as Au=0. The aim is to solve analytically Laplace's equation in the square [0, 1]²2 with boundary conditions u(x,0) = 0 = u(0, y), u(x, 1) = u(1, y) = 1.
Let's consider the Laplace equation as followsAu = ∂²u/∂x² + ∂²u/∂y²= 0Given boundary conditions areu(x, 0) = 0u(0, y) = 0u(x, 1) = u(1, y) = 1The solution of the Laplace equation is as followsu(x,y) = X(x).Y(y)Let's find the boundary conditionsu(x, 0) = 0
Let's substitute the value of Y(0) in the solution to get X(x).Y(0) = 0, which implies Y(0) = 0Similarly, u(0, y) = 0 => X(0).Y(y) = 0 => X(0) = 0Now, let's find the remaining boundary conditionsu(x, 1) = 1X(x).Y(1) = 1 => Y(1) = 1/X(x)u(1, y) = 1 => X(1).Y(y) = 1 => X(1) = 1/Y(y)Now, let's put the values of X(0) and X(1) in the below equationX(0) = 0, X(1) = 1/Y(y)X(x) = x
Now, let's put the values of Y(0) and Y(1) in the below equationY(0) = 0, Y(1) = 1/X(x)Y(y) = sin(n.π.y) /sinh(n.π)Therefore, the solution of Laplace's equation u(x, y) is as follows;u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π)Answer:Therefore, the solution of Laplace's equation u(x, y) is u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π).
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the gram-schmidt process produces from a linearly independent set {x1, x2, . . . , xp} an orthogonal set {v1, v2, . . . , vp} with the property that span{v1, . . . , vk}
Answers
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.
Given that,
From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.
Whether the claim is true or false must be determined.
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.
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Write a real world problem that can be represented by 10x-40=100
Answers
Answer:
10x - 40 = 100, x = 14
Step-by-step explanation:
At a flower shop, there are 10 bouquets with the same amount of flowers in each of them. In total, 40 flowers were purchased. Now, there are 100 flowers left in the shop. How many flowers are in a bouquet?
This situation can be represented by
10x
(the number represents the bouquets, while the variable x represents the amount of flowers in a bouquet)- 40
(this represents the flowers that were purchased)= 100
(this represents the flowers remaining)the ph measurements of water specimens from various locations along a given river basin are normally distributed with mean 8 and standard deviation 0.3. what is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2? 0.7475 0.2525 0.7525 0.2475
Answers
0.7475 is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2
P( A ≥ 8.2) = P( (Z ≥ 8.2 − 8)/0.3)
= P(Z ≥0.66)
= 0.7475
normsdist(0.666666) =0.7475
The standard normal cumulative distribution function is returned. The mean of the distribution is 0 (zero), while the standard deviation is one. Instead of a table of standard normal curve areas, use this function.The concentration of hydronium (H3O+) ions in an aqueous solution is measured by pH. It is measured from 0 to 14 on a negative logarithmic scale.
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What is the acceleration of the moon toward earth due to their mutual attraction the massive earth is 5. 98×10 to the 24th power kilograms the distance between them is 3. 8×10 to the eighth power meters and G equals 6. 673×10 to the -11th power newton meter squared per kilograms squared?
Answers
Answer:
2.76×10^-3 m/s²
Step-by-step explanation:
You want to know the acceleration of the moon toward the Earth, given its distance is 3.8×10^8 meters, Earth's mass is 5.98×10^24 kg, and the gravitational constant is 6.673×10^-11 N·m²/kg².
AccelerationThe acceleration of one body by another is ...
a = GM/r²
where G is the gravitational constant, M is the body creating the gravitational field, and r is the distance between the masses.
Applicationa = (6.673×10^-11)(5.98×10^24)/(3.8×10^8)² N/kg
a = (6.673·5.98/3.8²)×10^(-11+24-16) m/s² ≈ 2.76×10^-3 m/s²
Es el valor de la incógnita en la siguiente igualdad: x/Sen30°= 8/Sen45°
Answers
Respuesta:
x = 5.656854249
Explicación paso a paso:
[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]
x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]
x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]
x = 5.656854249
If it costs 0. 15 per square inch for the wood then what is the cost for design A and Design B
Answers
To calculate the cost for Design A and Design B, we need to know the size of each design in square inches. Once we have that information, we can multiply the size of each design by the cost per square inch of wood to determine the total cost.
Let's say Design A is 10 inches by 10 inches, which is a total of 100 square inches. To calculate the cost for Design A, we would multiply 100 by 0.15, which gives us a total cost of $15.
Similarly, let's say Design B is 8 inches by 12 inches, which is a total of 96 square inches. To calculate the cost for Design B, we would multiply 96 by 0.15, which gives us a total cost of $14.40.
Therefore, the cost for Design A is $15 and the cost for Design B is $14.40.
In summary, the cost of a wooden design can be calculated by multiplying the size of the design in square inches by the cost per square inch of wood. In this case, we used a cost of 0.15 per square inch and calculated the cost for Design A and Design B. It is important to know the size of the design before calculating the cost.
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(3x4 – x3 + 5x - 1) Evaluate x = 3
help
Answers
Answer:230
Step-by-step explanation:
3(34)−33+(5)(3)−13(34)−33+(5)(3)−1=230
If I Helped, Please Mark Me As Brainliest, Have A Great Day :D
Answer:
17 or 41
Step-by-step explanation:
if the bolded 'x' (3x4 - x3 + 5x - 1) is a multipication symbol then it is 17, if the bolded 'x' is an 'x', then the answer is 41.
The heat capacity of 1.00 kg of water is 4186 J/K. What is the temperature change of the water if (a) 505 J of heat is added to the system, or (b) 1010 J of heat is removed
Answers
(a) The temperature change of the water when 505 J of heat is added to the system is :0.121K
(b) The temperature change of the water when 1010 J of heat is removed is: -0.241K
Heat capacity:
We use the formula for heat capacity is:
The heat Q to a given object, and its temperature increases by the amount ∆T. The heat capacity, C in this object is defined as follow:
C = Q/ ∆T
The heat capacity C has SI unit: J/K = J/C°.
Note that,
Q is positive if ∆T, is positive; that is, it means heat is added to a system.
Q is negative if ∆T, is negative; that is, if heat is removed from a system.
We have the information from the question is:
The heat capacity of 1.00 kg of water is 4186 J/K.
To find the temperature change of the water.
(a) We calculate the ∆T for Q = 505 J.
∆T = Q/C = 505 J/ 4186 J/K = 0.121K
(b) Since heat is removed from the system, and Q = −1010 J, the change in temperature ∆T:
∆T = Q/C = -1010 J / 4186J/K = -0.241K.
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Let P be some predicate. Check the box next to each scenario in which ∀n ∈ N, P(n) must be true.
a) For every natural number k > 0 , if P(i) holds for every natural number i < k, then P(k) holds.
b) P(0) holds and for every natural number k > 0, if P(i) does not hold, then there is some natural number i < k such that P(i) does not hold.
c) For every natural number k, if P(i) holds for every natural number i < k, then P(k) holds.
d) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold.
Answers
Answer:
A
Step-by-step explanation:
a) ✔️
This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.
b) ❌
There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.
c) ❌
This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.
d) ❌
This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.
a pair of football cleats cost $42 Samantha makes $1.75 every time she washes the dishes right and solve an equation that will find how many times man will have to wash dishes to buy the football cleats
Answers
We have from the question the following information:
1. The football cleats cost $42.
2. Samantha makes $1.75 every time she washes the dishes.
We can write the next equation that represents this situation:
\(1.75x=42\)That is, Samantha, each time she washes the dishes right, she earns $1.75. We need to know how many times does she need to wash the dishes right? The answer is to solve the previous equation by 1.75 to both sides of it:
\(\frac{1.75x}{1.75}=\frac{42}{1.75}\Rightarrow x=24\)Therefore, Samantha needs to wash the dishes 24 times (right) to have the exact amount of money to buy the football cleats.
Help....me...............
Answers
Answer:
z=3
Step-by-step explanation:
6z-30=-12
6z=18
z=3
Answer:
z = 3
Step-by-step explanation:
When solving for z, we have to isolate the variable (z). We do this by adding, subtracting, multiplying, and dividing. When we do one of them, we must do it for both sides to "keep it even".
We can start by seeing that the 3 on the left is not in the parentheses meaning multiplication. So, to get z alone, the first step is dividing both sides by 3.
3(2z-10) = -12
/3 /3
2z-10 = -4
The next step to getting z alone is adding 10 to both sides.
2z-10 = -4
+10 +10
2z = 6
For the final step in getting z alone, we can see that on the left sides, it says 2z, meaning 2 times z. To undo this and get it alone, we can divide both sides by 2
2z = 6
/2 /2
z = 3
Therefore, the answer is z = 3
can someone please someone please help me solve the following?
Answers
We need to solve the following equation:
\(\frac{5x}{x-1}+5=\frac{15}{x-1}\)Notice that x ≠ 1, since x = 1 makes zero the denominators. Then, multiplying all the terms by x-1, we obtain:
\(\begin{gathered} \frac{5x}{x-1}\cdot(x-1)+5(x-1)=\frac{15}{x-1}\cdot(x-1) \\ \\ 5x\cdot\frac{x-1}{x-1}+5x-5=15\cdot\frac{x-1}{x-1} \\ \\ 5x+5x-5=15 \\ \\ 10x-5=15 \\ \\ 10x-5+5=15+5 \\ \\ 10x=20 \\ \\ \frac{10x}{10}=\frac{20}{10} \\ \\ x=2 \end{gathered}\)HELP ME THIS PLEASE THIS IS MY HOMEWORK
Answers
Answer:
2xy -yz -5
Step-by-step explanation:
3xy+yz-xy-2yz-5
=(3xy-xy) +(yz-2yz) +(-5)
=2xy -yz -5
hope this work
Answer:
2xy - yz - 5
Step-by-step explanation:
assuming you require to simplify the expression
3xy + yz - xy - 2yz - 5 ← collect like terms
= (3xy - xy) + (yz - 2yz) - 5
= 2xy + (- yz) - 5
= 2xy - yz - 5
There is a probablity of ____ that any individual at a random from
a population will fall (plus or minus) one standard deviation of
the mean.
Answers
Step-by-step explanation:
I hope this answer is helpful ):
On the last day of April 2009, the price of a share of stock in a major entertainment corporation was $5.36. Over the next 4 years, the annual growth rate was 4.15%. The growth in the price of this stock can be modeled by the function where P represents the price, in dollars, and t represents the number of years since the last day in April 2009. Which function can be used to represent the price of a share of stock in this entertainment corporation on the last day in June 2011?
Answers
The function that can be used to represent the price of a share of stock is given below. Then the correct option is C.
\(\rm P = 5.36 \left [ \left (1.0415 \right )^{\frac{1}{12}} \right ]^{26}\)
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
On the last day of April 2009, the price of a share of stock in a major entertainment corporation was $5.36.
Over the next 4 years, the annual growth rate was 4.15%.
The growth in the price of this stock can be modeled by the function
\(\rm P = 5.36 \times (1.0415)^t\)
Where P represents the price, in dollars, and t represents the number of years since the last day in April 2009.
Then the function can be used to represent the price of a share of stock in this entertainment corporation on the last day of June 2011 will be
The number of the years will be
t = 26 / 12
Then the function will be
\(\rm P = 5.36 \left [ \left (1.0415 \right )^{\frac{1}{12}} \right ]^{26}\)
Then the correct option is C.
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0.431431 is rational or not
Answers
Answer: rational
Step-by-step explanation:
It's rational because it has a pattern. and probably repeats
If X is correlated with Y, what must be true about X and Y? Explain your reasoning. a. A corelation exists between two variables when both variables increase together b. Increasing values of X go with either increasing or decreasing values of Y. A comelation exists between two variables when both variables increase or decrease together c. Increasing values of X go with either increasing or deoreasing values of Y. A correlation exiss between X and Y when higher values of X consistently go with higher values of Y or when higher values of X consistently go with lower values of Y d. X causes Y. If Y decreases as X increases, then X must cause Y to change. e. Increasing values of X go with increasing values of Y. A correlation exists between two variables when both viariables decrease togetherf. X causes Y. If Y increases as X increases, then X must cause Y to change-
Answers
Answer:
it is a statistical measure of the relationship between two variables that indicates the extent to which the variables change together in the same or opposite direction. Correlation does not imply causation, meaning that a correlation between two variables does not necessarily mean that one variable causes the other.
Based on this definition, the correct answer is b. Increasing values of X go with either increasing or decreasing values of Y. A correlation exists between two variables when both variables increase or decrease together. This statement captures the idea that correlation can be positive or negative, and that it reflects a linear relationship between two variables.
Step-by-step explanation:
a is wrong because it only describes positive correlation, not negative correlation.
c is wrong because it confuses correlation with consistency. Correlation does not require that higher values of X always go with higher or lower values of Y, only that they tend to do so on average.
d and f are wrong because they assume causation from correlation, which is a logical fallacy.
e is wrong because it contradicts itself. It says that increasing values of X go with increasing values of Y, which is positive correlation, but then it says that a correlation exists when both variables decrease together, which is negative correlation.
If X is correlated with Y, it implies a predictive statistical relationship between X and Y. This correlation can be positive or negative implying respective increase or decrease in values of both variables. But, this correlation doesn't prove causation.
Explanation:If X is correlated with Y, it indicates a statistical relationship between the two variables, X and Y. This relationship can be positive or negative. If it is a positive correlation, as X increases, Y will also increase and similarly, as X decreases, Y will also decrease. Contrarily, in a negative correlation, as X increases, Y decreases and vice versa. However, it is important to understand that correlation does not imply causation. That is, if X and Y are correlated, it does not necessarily mean that changes in X cause changes in Y or vice versa. It only means that they move in a predictable manner relative to each other.
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Which value of AB would make line EB parallel to line DC?
Answers
The value of AB in triangle ADC and AEB such that it make line EB parallel to line DC is given by to option d. 36.
To make line EB parallel to line DC,
Ensure that triangle AED and triangle ABC are similar triangles.
This can be achieved by having the corresponding sides of the triangles in proportional lengths.
Let us find the value of AB that would make line EB parallel to line DC.
In triangle AED, we have AE = 51 and ED = 17.
In triangle ABC, we have BC = 12.
If the triangles are similar, then the ratio of corresponding sides should be equal.
This implies,
AB/BC = AE/ED
Plugging in the values we get,
⇒ AB/12 = 51/17
Cross-multiplying and get the value ,
⇒ AB × 17 = 12 × 51
⇒ AB = (12 × 51) / 17
⇒ AB = 36
Therefore, the value of AB that would make line EB parallel to line DC is equal to option d. 36.
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The above question is incomplete, the complete question is:
Which value of AB would make line EB parallel to line DC?
Attached diagram.
a spinner with 6 equal sections is shown. 1,. 2,. 3,. 4,. 5,. 6,. what is the probability of spinning a number greater than 4? a 1 over 6 b 2 over 3 c 1 over 2 d 1 over 3
Answers
The probability of spinning a number greater than 4 on a spinner with 6 equal sections is 1 over 3. (option d)
A spinner with 6 equal sections has an equal probability of landing on any of the 6 sections. To find the probability of spinning a number greater than 4, we need to find the fraction of sections that meet this criterion. In this case, there are 2 sections that satisfy this condition (5 and 6).
Therefore, the probability of spinning a number greater than 4 is 2/6, or 1/3.
It's important to remember that when working with probability, the values can only be between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of any event must be a number between 0 and 1, inclusive.
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The manager wants to control the maximum probability of Type I error at 1% (i.e. the manager wants the significance level to be 1%). Calculate the critical value the manager should use to conduct the hypothesis test of interest. The null hypothesis is that mean daily output is no greater than 200, and the alternative hypothesis that it is greater than 200. Continue to assume that daily output levels are approximately normally distributed, with standard deviation 18 units. A random sample of 81 days of output will be collected to conduct the test.
Continued. Using the critical value you calculated in the previous question, what is the probability of Type II error if the population mean is 205?
Continued. If the sample mean turns out to be 205, what is the conclusion of the test?
Answers
The manager wants to control the maximum probability of Type I error at 1% (i.e. the manager wants the significance level to be 1%). To calculate the critical value, we need to find the Z-score associated with a 1% significance level.
To find the critical value, we can use a Z-table or a Z-score calculator. Since the significance level is 1% (0.01), we need to find the Z-score corresponding to the area of 0.99 (1 - 0.01) in the upper tail of the standard normal distribution.
By looking up the Z-table or using a Z-score calculator, we find that the Z-score corresponding to a 0.99 cumulative probability is approximately 2.33. The critical value the manager should use to conduct the hypothesis test is 2.33.
To calculate the probability of Type II error, we need to specify an alternative hypothesis and determine the corresponding population mean value. In this case, the alternative hypothesis is that the mean daily output is greater than 200, and the specified population mean value is 205.
To calculate the probability of Type II error, we need to find the area under the null hypothesis distribution that falls to the right of the critical value. In other words, we need to find the probability that the test statistic, assuming the null hypothesis is true, falls in the rejection region. Since we are assuming the population mean is 205, we can calculate the Z-score using the formula:
Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
Substituting the values, we get:
Z = (205 - 200) / (18 / sqrt(81)) = 5 / (18 / 9) = 5 / 2 = 2.5
Now, we can calculate the probability of Type II error by finding the area under the null hypothesis distribution to the right of the critical value, which is 2.33. Using the Z-table or a Z-score calculator, we find that the probability of Type II error is approximately 0.0062, or 0.62%.
If the sample mean turns out to be 205, we compare it to the critical value. If the sample mean is greater than the critical value (2.33), we reject the null hypothesis. In this case, since the sample mean is 205, which is greater than the critical value of 2.33, we would reject the null hypothesis. The conclusion of the test would be that there is sufficient evidence to suggest that the mean daily output is greater than 200.
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Explain why you cannot factor the trinomial x2 – 15x + 3
A. There are no factors of 3 that add up to -15
B. It can be factored
C. There are no factors of -15 that add up to 3.
Answers
Answer:
there are no factors of -15 that add up to 3
Answer:
It is A trust me
Step-by-step explanation:
Which 3 expressions are equivalent to the
expression : 3x-12-2(x+12)
Answers
Answer:
second option , third option and last option
Step-by-step explanation:
3x - 12 - 2(x + 12)
=3x - 12 -2x - 24
=x - 36
24. generalize what are the attributes of fractions
that are equivalent to 100%
Answers
Answer:
when a fraction equals 100% it means it has the same numbers for its numerator and denominator such as 4/4 or 18/18
Step-by-step explanation:
When it has the same numbers for its numerator and denominator it will be 100%
1 If one leg of a right triangle is 3 meters, and the hypotenuse is 5 meters, what is the length of the
missing leg?
Answers
i'm gonna assume that "leg" refers to length of the triangle, so comment if you think it is wrong.
Now when it comes to a right-angled triangle, the pythagoras theorem formula can be used.
Using algebra,
let the missing length be X.
By pythagoras theorem,
5² = 3² + X²
5² - 3² = X²
X² = 5² - 3²
X = sq root ( 5² - 3² )
= 4 m
Therefore, the length of the missing leg is 4m .
2 years ago, father's age was nine times the son's age but 3 years letter it will be 5 times only. Find the present ages of the father and the son
Answers
The required present ages of the father and the son are 47 years and 7 years respectively.
Let the present age of the father and the son be x years and y years, respectively.
According to the question,
Condition I,
2 years ago, the father's age was nine times the son's age.
or,(x−2)=9(y−2)
or,x−2=9y−18
or,x=9y−18+2
or,x=9y−16 - (i)
Condition II,
3 years later, the father's age will be five times the son's age.
or,(x+3)=5(y+3)
or,x+3=5y+15 - (ii)
Put the value of x from equation (i) in equation (ii), and we get,
or,(9y−16)+3=5y+15
or,9y−16=5y+15−3
or,9y−5y=12+16
or,4y=28
or,y=284
∴y=7
Put the value of y in equation (i), and we get,
or,x=9×7−16
or,x=63−16
∴x=47
So, (x,y) = (47,7)
Therefore, the required present ages of the father and the son are 47 years and 7 years respectively.
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