81x^2=25 solve by factoring

Jiri's age is 20

Let Pamela's ae be P and Jiri's age be J

From the equation;

P = J + 5 ...............(i)

This is as Pamela is 5 years older

Adding their ages, we have 45

P + J = 45 ........................(ii)

Substitute i into ii

J + 5 + J = 45

2J + 5 = 45

2J = 45-5

2J = 40

J = 40/2

J = 20

The equivalent statement for ~q → ~p is p → q.

Two or more expressions with an Equal sign is called as Equation.

To determine the equivalent statement for ~q → ~p, we can use the rule of logical equivalence, which states that:

~(p → q) ≡ p ∧ ~q

Using this rule, we can rewrite ~q → ~p as ~(~p) ∨ (~q), which is equivalent to p ∨ (~q).

Therefore, the equivalent statement for ~q → ~p is p ∨ (~q).

Now, let's translate the original statements p and q into logical statements:

p: n is a multiple of two this can be written as n = 2k, where k is some integer.

q: n is an even number. This can also be written as n = 2m, where m is some integer.

Using the definition of these statements, we can see that p and q are logically equivalent, as they both mean that n can be written as 2 times some integer.

Therefore, we can rewrite p as q, and the equivalent statement for ~q → ~p is p → q.

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Answer:

f(-3) = -18

Step-by-step explanation:

f(x)=2x^3+4x^2, find f(-3); let's rewrite

f(x) = 2\(x^{3}\) + 4\(x^{2}\); substitute -3 for x

f(-3) = 2\((-3)^{3}\) + 4\((-3)^{2}\); do the exponents

f(-3) = 2(-27) + 4(9); multiply and add

f(-3) = -54 + 36 = -18

The value of the function  f(x) = 2x³ + 4x² at f(-3) is - 18.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = 2x³ + 4x².

Now, The value of the function f(-3) can be obtained by replacing

x with - 3.

Therefore, f(-3) = 2(-3)³ + 4(-3)².

f(-3) = 2×-27 + 4×9.

f(-3) = - 54 + 36.

f(-3) = - 18.

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Answer: ??

Step-by-step explanation:

Answer:

Step-by-step explanation:

huh

We can use the result from Problem 1 to find the Fourier series for g(x), which will give us the Fourier series for f(x).

To find the Fourier series for the function defined by f(x) = 0, -1 < x < 0 and f(x) = 1, 0 < x < π, we can use the result obtained from Problem 1.

In Problem 1, we found the Fourier series for a periodic function f(x) defined on the interval (-π, π).

The function defined in Problem 2 is periodic with period 2π, so we can extend it to be defined on the interval (-π, π) by repeating the pattern. Therefore, we have:

f(x) = 0, -π < x < -1

f(x) = 1, -1 < x < 0

f(x) = 1, 0 < x < π

To obtain the Fourier series for this function, we can subtract the average value of f(x) from f(x) to make it a periodic function with zero average. Let I denote the average value of f(x). Then we have:

I = ∫[0,π] f(x) dx = ∫[0,π] 1 dx = π

Next, we subtract I from f(x) to obtain:

g(x) = f(x) - I

For the given function, g(x) will be:

g(x) = 0 - π, -π < x < -1

g(x) = 1 - π, -1 < x < 0

g(x) = 1 - π, 0 < x < π

Now we can use the result from Problem 1 to find the Fourier series for g(x), which will give us the Fourier series for f(x).

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The constraint can then be written as: S ≤ 0.07 × T. This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.

The constraint can then be written as: S ≤ 0.07 × T, This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.

We are given that the amount of sulfur relative to the total output produced of chemical X may not exceed 7%. To express this constraint in a linear programming model, we can use the following equation:

Sulfur Content ≤ 0.07 × Total Output

Here, the "Sulfur Content" represents the total amount of sulfur present in the chemical blend, while "Total Output" refers to the total amount of chemical X produced. By setting the constraint to be less than or equal to 7% (0.07) of the total output, we are ensuring that the sulfur content does not exceed the given limit.

In a linear programming model, we usually use variables to represent quantities. Let S represent the Sulfur Content and T represent the Total Output. The constraint can then be written as:

S ≤ 0.07 × T

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Answer: $50,750

Step-by-step explanation: To get the percentage of a number, you need to turn the percent into a decimal, then multiply it with the number you need the percentage of. 35% translates into 0.35. Then you would multiply 145,000 by 0.35, getting 50,750 as your answer!

Answer:

Given the mean = 205 cm and standard deviation as 7.8cm

a. To calculate the probability that an individual distance is greater than 218.4 cm, we subtract the probability of the distance given (i.e 218.4 cm) from the mean (i.e 205 cm) divided by the standard deviation (i.e 7.8cm) from 1. Therefore, we have 1- P(Z\(\leq 1.72\)). Using the Z distribution table we have 1-0.9573. Therefore P(X >218.4)= 0.0427.

b. To calculate the probability that mean of 15 (i.e n=15) randomly selected distances is greater than 202.8, we subtract the probability of the distance given (i.e 202.8cm) from the mean (i.e 205 cm) divided by the standard deviation (i.e 7.8cm) divided by the square root of mean (i.e n= 15)  from 1. Therefore, we have 1- P(Z\(\leq -1.09\)). Using the Z distribution table we have 1-0.1378. Therefore P(X >202.8)= 0.8622.

c. This will also apply to a normally distributed data even if it is not up to the sample size of 30 since the sample distribution is not a skewed one.

Step-by-step explanation:

Given the mean = 205 cm and standard deviation as 7.8cm

a. To calculate the probability that an individual distance is greater than 218.4 cm, we subtract the probability of the distance given (i.e 218.4 cm) from the mean (i.e 205 cm) divided by the standard deviation (i.e 7.8cm) from 1. Therefore, we have 1- P(Z\(\leq 1.72\)). Using the Z distribution table we have 1-0.9573. Therefore P(X >218.4)= 0.0427.

b. To calculate the probability that mean of 15 (i.e n=15) randomly selected distances is greater than 202.8, we subtract the probability of the distance given (i.e 202.8cm) from the mean (i.e 205 cm) divided by the standard deviation (i.e 7.8cm) divided by the square root of mean (i.e n= 15)  from 1. Therefore, we have 1- P(Z\(\leq -1.09\)). Using the Z distribution table we have 1-0.1378. Therefore P(X >202.8)= 0.8622.

c. This will also apply to a normally distributed data even if it is not up to the sample size of 30 since the sample distribution is not a skewed one.

Answer:

D because non of them work lol

Step-by-step explanation:

Hope this Helped

Answer:

36

Step-by-step explanation:

Answer:

-12-15 is -27

Step-by-step explanation:

when subtracting negatives imagine there being a plus sign in the middle and pair that subtraction sign with the 15

Answer:

Construct an angel bisector

In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the error term come from a normal distribution.

In a simple linear regression model, the normal quantile plot of the residuals is a graphical tool used to assess the normality assumption of the error term (also known as the residual). The error term represents the difference between the actual value of the dependent variable and the predicted value by the model.

Assuming that the error term follows a normal distribution is important for various reasons. Firstly, the normal distribution is a very common assumption in statistics, and many statistical methods rely on it. Secondly, a normal distribution of the error term is essential for making reliable predictions and for computing valid confidence intervals.

The normal quantile plot of the residuals compares the distribution of the residuals against a theoretical normal distribution. The plot consists of a straight line if the residuals are normally distributed. However, if the plot shows deviations from the straight line, it indicates non-normality in the residuals.

If the normality assumption is not satisfied, we need to explore the reasons for the non-normality and consider alternative methods to analyze the data, such as non-parametric methods.

Therefore, the normal quantile plot of residuals is an essential diagnostic tool in simple linear regression, as it allows us to evaluate the assumption of normality and make appropriate adjustments to the model.

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The data we get from the question is a random experiment can result in one of the outcomes {a,b,c,d} with probabilities from that information, P(A U B U C) = 0.8.
         

The given probabilities of events and outcomes are:

       P({a}) = 0.4,P({b}) = 0.1,P({c}) = 0.3,P({d}) 0.2

 So the given events are:

        A = {a,b},B = {b,c,d},C = {d}

   We have to find P(A U B U C) Using the formula of the probability of the union of two events,

    we get:

          P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Now we will find the values of all probabilities:

                  P(A) = P({a}) + P({b})

                         = 0.4 + 0.1

                         = 0.5

                   P(B) = P({b}) + P({c}) + P({d})

                          = 0.1 + 0.3 + 0.2

                           = 0.6

                   P(C) = P({d})

                            = 0.2

                      P(A ∩ B) = P({b})

                                     = 0.1

                      P(A ∩ C) = P({d})

                                     = 0.2

                      P(B ∩ C) = P({d})

                                     = 0.2

               P(A ∩ B ∩ C) = 0

 (No common event) Put all the above values in the formula:

           P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) +

                                     P(A ∩ B ∩ C)

                                 = 0.5 + 0.6 + 0.2 - 0.1 - 0.2 - 0.2 + 0

                                 = 0.8

         Therefore, P(A U B U C) = 0.8 is the required probability.

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Answer:

\(\frac{965777}{55555}\)

Step-by-step explanation:

The answer is quite simple, just divide both sides and rewrite the equation to get it. Maybe focus more on the question rather than yourself next time :)

∂z/∂s = 3cos(t)/y, ∂z/∂t = 3s*cos(t)/y - sin(s)/x (using the chain rule to differentiate each term and substituting the given expressions for x and y)

To find ∂z/∂s and ∂z/∂t using the chain rule, we start by finding the partial derivatives of z with respect to x and y, and then apply the chain rule.

First, let's find ∂z/∂x and ∂z/∂y.

∂z/∂x = ∂/∂x [ln(5x^3y)]

= (1/5x^3y)  ∂/∂x [5x^3y]

= (1/5x^3y) 15x^2y

= 3/y

∂z/∂y = ∂/∂y [ln(5x^3y)]

= (1/5x^3y) ∂/∂y [5x^3y]

= (1/5x^3y)  5x^3

= 1/x

Now, using the chain rule, we can find ∂z/∂s and ∂z/∂t.

∂z/∂s = (∂z/∂x)  (∂x/∂s) + (∂z/∂y)  (∂y/∂s)

= (3/y)  (cos(t)) + (1/x)  (0)

= 3cos(t)/y

∂z/∂t = (∂z/∂x)  (∂x/∂t) + (∂z/∂y)  (∂y/∂t)

= (3/y) * (scos(t)) + (1/x)  (-sin(s))

= 3scos(t)/y - sin(s)/x

Therefore, ∂z/∂s = 3cos(t)/y and ∂z/∂t = 3s*cos(t)/y - sin(s)/x.

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Answer:

x = -9
y = 9

Step-by-step explanation:

If we know that x  =  -5y + 36
The second line says that
5x + 5y = 0
We can substiute the value of x from the first line into the second line.

So it becomes
5 ( -5y+36) + 5y = 0
Distribute the 5 over the parentheses
-25y + 180 +5y = 0
Then we can add things that are alike; so that means we can add the y values
-20y + 180 = 0
Then add 20y to both sides of the equation
180 = 20y
Then you divide by 20.
You get 9 = y!
Now that you have the value of y, you can put it back into the intial question.
5x+5y = 0
5x + 5(9) = 0
5x + 45 = 0
5x = -45
x = -9

Answer:

x=-9 y=9

Step-by-step explanation:

Substitute x:

5(-5y+36)+5y=0

Use Distributive property

-25y+180+5y=0

Add Like terms

-20y+180=0

Subtract 180 from both sides

-20y=-180

divide -20 from both sides

y=9

Solve for x by substituting the value of y into the equation x= -5y + 36

to get x=-9

Answer:

hi

Step-by-step explanation:

Answer:

sure why not .

Hi!:D

Step-by-step explanation:

can I have brainiest

Answer:

y=7*3^x

Step-by-step explanation:

y=ab^x

(0,7) ⇒ 7=ab^0 ⇒ 7=a

(5, 1701) ⇒ 1701= 7b^5 ⇒ b^5=243 ⇒ b^5= 3^5 ⇒ b=3

y=7*3^x

The probability is approximately 0.2190, indicating that there is a chance the elevator may be overloaded. Therefore, the elevator does not appear to be entirely safe based on this probability.

The elevator's maximum capacity is stated as 1352 lb-8 passengers, which means that the weight of 8 passengers should not exceed this limit. To determine if the elevator is overloaded, we need to calculate the probability that the mean weight of these 8 adult male passengers exceeds 169 lb.

We are given that the weights of males are normally distributed with a mean of 177 lb and a standard deviation of 29 lb. Since we are interested in the mean weight of 8 passengers, we need to use the distribution of the sample mean.

The distribution of the sample mean follows a normal distribution with the same mean as the population (177 lb) and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 8.

Therefore, the standard deviation of the sample mean can be calculated as:

Standard deviation of sample mean = 29 lb / √8 ≈ 10.27 lb.

To find the probability that the mean weight of 8 passengers exceeds 169 lb, we can calculate the z-score corresponding to this value:

z = (169 lb - 177 lb) / 10.27 lb ≈ -0.78.

Using a standard normal distribution table or a calculator, we can find the probability corresponding to this z-score. The probability of the mean weight exceeding 169 lb is approximately 0.2190.

So, there is a probability of approximately 0.2190 that the elevator is overloaded based on the mean weight of 8 adult male passengers exceeding 169 lb.

Considering this probability, it appears that the elevator may not be entirely safe as there is a non-negligible chance of it being overloaded. It would be advisable to either reduce the maximum capacity or limit the number of passengers to ensure safety.

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Answer:i think its 115 degres

Step-by-step explanation:

To convert the polar equation r = 2 into a Cartesian equation, we can use the following conversions:
x = r * cos(theta) y = r * sin(theta)

correct conversion is option D: x^2 + y^2 = 4.

Let's substitute these equations into each option:
A. y^2 = 4

Substituting y = r * sin(theta), we have:
(r * sin(theta))^2 = 4 r^2 * sin^2(theta) = 4
B. x = 2

Substituting x = r * cos(theta), we have:
r * cos(theta) = 2
C. y = 2

Substituting y = r * sin(theta), we have:
r * sin(theta) = 2
D. x^2 + y^2 = 4

Substituting x = r * cos(theta) and y = r * sin(theta), we have:

(r * cos(theta))^2 + (r * sin(theta))^2 = 4 r^2 * cos^2(theta) + r^2 * sin^2(theta) = 4

Since r^2 * cos^2(theta) + r^2 * sin^2(theta) simplifies to r^2 (cos^2(theta) + sin^2(theta)), option D can be rewritten as:

r^2 = 4

Therefore, the correct conversion of the polar equation r = 2 to a Cartesian equation is option D: x^2 + y^2 = 4.

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Answer:

c < 3

Step-by-step explanation:

2c + 4 < 10 ( subtract 4 from both sides )

2c < 6 ( divide both sides by 2 )

c < 3

Answer:

2c + 4 < 10

2c < 10 - 4

2c < 6

c < 6/2

c < 3

brainliest plz

Answer:

its d..................

The sum of the expressions (-10x³ + 4x + 5) + (5x² - 2x) is -10x³ + 5x² + 2x + 5.

Thus, option (D) is correct.

In mathematics, an expression is a combination of numbers, variables, and operators (such as addition, subtraction, multiplication, division, and exponentiation) that represents a mathematical statement.

To find the sum of the given expressions (-10x³ + 4x + 5) and (5x² - 2x).

Simply combine like terms:

(-10x³ + 4x + 5) + (5x² - 2x)

Combining the like terms, we have:

-10x³ + 5x² + (4x - 2x) + 5

Simplifying further, we get:

-10x³ + 5x² + 2x + 5

Therefore, the sum is: \(-10x^3 + 5x^2 + 2x + 5\).

Thus, option (D) is correct.

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Answer:

whar state ment

Step-by-step explanation:

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

you have to provide the recipie

Step-by-step explanation:

Answer:

whats the question?

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(x=\frac{- b+ \sqrt{b^{2}-4ac} }{2a}\)   \(x=\frac{- b- \sqrt{b^{2}-4ac} }{2a}\)        

x=-5, 4.7

Answer:

B, C, E

Step-by-step explanation:

right on edge