find the percentage rate of chnage of f(x) at the inidcated value of x.
f(x)=126 + 32x; x=9
the percentage rate of change of f(x) at x=7 is ___%

Answer:

a) The total weight of fruits is \(8\,\frac{1}{4}\) kilograms, b) The weight of the fruits left is \(4\,\frac{1}{2}\) kilograms.

Step-by-step explanation:

a) The total weight of fruits (\(m_{T}\)) is calculated by the following formula:

\(m_{T} = m_{a} + m_{m}+m_{o}\)

Where:

\(m_{a}\) - Total weight of apples, measured in kilograms.

\(m_{m}\) - Total weight of mangoes, measured in kilograms.

\(m_{o}\) - Total weight of oranges, measured in kilograms.

If \(m_{a} = 1\,\frac{1}{2} \,kg\), \(m_{m} = 5\,\frac{1}{4}\,kg\) and \(m_{o} = 1\,\frac{1}{2}\,kg\), then:

\(m_{T} = 1\,\frac{1}{2}\,kg + 5\,\frac{1}{4}\,kg + 1\,\frac{1}{2}\,kg\)

\(m_{T} = \frac{6}{4}\,kg + \frac{21}{4}\,kg + \frac{6}{4}\,kg\)

\(m_{T} = \frac{33}{4}\,kg\)

\(m_{T} = 8\,\frac{1}{4}\,kg\)

The total weight of fruits is \(8\,\frac{1}{4}\) kilograms.

b) The weight eaten by her family is determined by the following expression:

\(m_{E} = m_{a,e} + m_{m,e} + m_{o,e}\)

Where:

\(m_{a,e}\) - Eaten weight of apples, measured in kilograms.

\(m_{m,e}\) - Eaten weight of mangoes, measured in kilograms.

\(m_{o,e}\) - Eaten weight of oranges, measured in kilograms.

Given that \(m_{a,e} = \frac{3}{4}\,kg\), \(m_{m,e} = 2\,\frac{1}{2}\,kg\) and \(m_{o,e} = \frac{1}{2}\,kg\), the weight eaten by her family is:

\(m_{E} = \frac{3}{4}\,kg + 2\,\frac{1}{2}\,kg + \frac{1}{2}\,kg\)

\(m_{E} = \frac{3}{4}\,kg + \frac{10}{4}\,kg + \frac{2}{4}\,kg\)

\(m_{E} = \frac{15}{4}\,kg\)

\(m_{E} = 3\,\frac{3}{4}\,kg\)

The weight of the fruits left is found by subtraction:

\(m_{R} = m_{T}-m_{E}\)

\(m_{R} = 8\,\frac{1}{4} \,kg -3\,\frac{3}{4}\,kg\)

\(m_{R} = \frac{33}{4}\,kg-\frac{15}{4}\,kg\)

\(m_{R} = \frac{18}{4}\,kg\)

\(m_{R} = 4 \,\frac{1}{2}\,kg\)

The weight of the fruits left is \(4\,\frac{1}{2}\) kilograms.

Answer: 22800

Step-by-step explanation: Round each digit i don't really know how to explain it sorry

Answer:

22800

Step-by-step explanation:

Answer:

Hi your question lacks the required options attached are the options

a) there is no correlation between number of inhabitants and amount of trash produced

b) there is a correlation between the number of inhabitants and the amount of trash produced however there is no causation, this is because there is probably an increase in the amount of trash produced with an increase in the number of inhabitants

c) there is correlation between the number of inhabitants and the amount of trash produced, there may or may not be causation , further studies would have to be done to determine this

Answer : there is correlation between the number of inhabitants and the amount of trash produced, there may or may not be causation , further studies would have to be done to determine this

Step-by-step explanation:

What can be determined from a study that shows that houses with more inhabitants same number of trash as houses with fewer inhabitants is that:  there is correlation between the number of inhabitants and the amount of trash produced, there may or may not be causation , further studies would have to be done to determine this.

This is due to the fact that an increase in population is suppose to have an equivalent increase in trash been produced but in this study the increase in population had no effect in the increase or decrease in trash therefore further studies would have to be conducted to determine the causation of such .

The significance level is set at 5%, and the probability of the result is 0%, which is less than the significance level. The result is statistically significant.

We are given that;

The probability of the result=(7.7/9.2/4.6/5/7.8)%

Now,

To determine the probability of the treatment group’s mean being lower than the control group’s mean by 15 points or more, we need to find the difference between the two sample means and compare it to the standard error of the difference. The standard error of the difference can be estimated using the formula:

SE = √(s1^2 / n1) + (s2^2 / n2)

where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes.

Assuming that the treatment group is group 1 and the control group is group 2, we can plug in the values given in the question:

SE = √(9.2^2 / 30) + (7.7^2 / 30)

SE = √3.02

SE = 1.74

The difference between the two sample means is:

x1 - x2 = 85 - 100

x1 - x2 = -15

To find the probability of this difference or lower, we need to find the z-score and use a normal distribution table or calculator3:

z = (x1 - x2) / SE

z = (-15) / 1.74

z = -8.62

Using a normal distribution table or calculator, we can find that P(z ≤ -8.62) ≈ 0, which means that the probability of the treatment group’s mean being lower than the control group’s mean by 15 points or more is very close to zero.

Therefore, by probability the answer will be statistically significant.

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The statement "correlation is measured on a scale from 0 to 1, where 0 indicates no linear relationship between two variables, and 1 indicates a perfect linear relationship" is true.

The correlation coefficient, typically denoted as r, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 represents a perfect negative linear relationship, 1 represents a perfect positive linear relationship, and 0 indicates no linear relationship or correlation between the variables.

A correlation coefficient of 0 means that there is no linear association between the variables being analyzed. As the correlation coefficient moves closer to 1 or -1, it indicates a stronger linear relationship between the variables. Therefore, the scale from 0 to 1 is commonly used to represent the extent of correlation, where 0 signifies no linear relationship and 1 signifies a perfect linear relationship.

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Answer:

1.335

Step-by-step explanation:

you have to do this equation .445 x 3 =1.335

Diversity encompasses multiple dimensions such as life experiences, educational background, geographic origin, and age that is option E.

Diversity encompasses a range of factors including life experiences, educational background, geographic origin, and age. It goes beyond a single dimension and encompasses various aspects that contribute to differences among individuals. By embracing diversity in all its forms, organizations and communities can benefit from a wider range of perspectives, ideas, and talents.

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Fifty observations were generated to compare the approximate asymptotic distribution of the estimates with results from a bootstrap experiment for a Gaussian AR(1) model with Ø = 0.99 and ow = 1.

A Gaussian AR(1) model with parameters Ø = 0.99 and ow = 1 is a time series model in which each observation depends on the previous observation with a lag of 1 and the error follows a Gaussian distribution. Various techniques such as maximum likelihood estimation and method of moments can be used to estimate the parameters. Once an estimate is obtained, its approximate asymptotic distribution can be derived based on the statistical properties of the estimation method used.

A bootstrap experiment can be performed to assess the accuracy and variability of the estimation. In this experiment, resampling from the original data with replacement produces B=200 bootstrap samples. The estimates are recomputed for each bootstrap sample to obtain the distribution of the bootstrap estimates. This distribution can be used to estimate standard errors, construct confidence intervals, or perform hypothesis tests. 

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The exponential distribution may be used to predict the failure rate of certain items over time. An LED light bulb has an expected lifetime of 25000 hours. Assuming that the lifetime of the LED light bulb follows the exponential distribution, the probability that it will last more than 3 years is closest to (C) 53%. Correct answer is option C

This is because the lifetime of an LED light bulb can be estimated using the following equation : P(x > 3 years) = 1 - P(x ≤ 3 years)where x is the lifetime of the LED light bulb.If we convert 3 years to hours, we get 3 * 365 * 24 = 26280 hours. As a result, P(x ≤ 3 years) = P(x ≤ 26280 hours)

Using the formula for exponential distribution, the probability of the LED light bulb failing after 26280 hours is : Probability = 1 - e^{-λx} Where λ is the failure rate per hour and x is the length of time in hours.We can now calculate the value of λ by dividing the expected lifetime of the bulb by the total number of hours.

 λ = 1/25000 hours  This implies that the probability of the LED light bulb failing after 26280 hours is : P (x ≤ 26280 hours)

Therefore, the probability that the LED light bulb will last more than 3 years is approximately 53 percent. The Correct answer is option C

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9514 1404 393

Answer:

  $18.48

Step-by-step explanation:

If we assume the account earned simple interest, the amount is given by the formula ...

  I = Prt . . . . interest on principal P at annual rate r for t years

  1.155 = P·0.0125·5

  P = 1.155/0.0625 = 18.48

Jake initially deposited $18.48 as his principal.

_____

Additional comment

The amount $1.155 is an unusual specification for an amount of money. If you mean $1,155.00, then the principal amount is likewise multiplied by 1000: $18,480.

The approximate value of the function at (−4.9,0.9) using the tangent plane at (-5,1) is f(-5,1) + 2.001.

To use the tangent plane at (-5,1) to approximate the value of the function at (−4.9,0.9), we first need to find the equation of the tangent plane.

Let f(x,y) be the function in question. The equation of the tangent plane at (-5,1) is given by:

z = f(-5,1) + f_x(-5,1)(x+5) + f_y(1,1)(y-1)

where f_x and f_y represent the partial derivatives of f with respect to x and y, evaluated at (-5,1).

To find these partial derivatives, we can use the definition:

f_x(x,y) = lim(h->0) [f(x+h,y) - f(x,y)]/h

f_y(x,y) = lim(h->0) [f(x,y+h) - f(x,y)]/h

Evaluating these at (-5,1), we get:

f_x(-5,1) = lim(h->0) [f(-5+h,1) - f(-5,1)]/h

f_x(-5,1) = lim(h->0) [(-5+h)^2 + (1)^2 - 10] - [(-5)^2 + (1)^2 - 10)]/h

f_x(-5,1) = lim(h->0) [-10h + h^2]/h

f_x(-5,1) = -10 + h

Similarly,

f_y(-5,1) = lim(h->0) [f(-5,1+h) - f(-5,1)]/h

f_y(-5,1) = lim(h->0) [(-5)^2 + (1+h)^2 - 10] - [(-5)^2 + (1)^2 - 10)]/h

f_y(-5,1) = lim(h->0) [-10h + 2h^2]/h

f_y(-5,1) = -10 + 2h

Plugging these values into the equation of the tangent plane, we get:

z = f(-5,1) + (-10+h)(x+5) + (-10+2h)(y-1)

Now, to approximate the value of the function at (−4.9,0.9), we simply plug in these values for x and y:

z = f(-5,1) + (-10+h)(-4.9+5) + (-10+2h)(0.9-1)

z = f(-5,1) - 0.1(-10+h) - 0.2(10-2h)

Since we are only interested in the approximation of the value of the function, we can take h to be very small, say h=0.01. Then:

z ≈ f(-5,1) - 0.1(-9.99) - 0.2(10.01)

z ≈ f(-5,1) + 2.001

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Answer:

3.2z + 5y  - 70

Step-by-step explanation:

Answer:

\(\frac{12}{22}\) and \(\frac{6}{11}\)

Step-by-step explanation:

Both \(\frac{12}{22}\) and \(\frac{6}{11}\) are equal to 0.54 as a repeating decimal

Answer:

374.85

Step-by-step explanation:

The nonlinear system of equations graphed below have two solutions.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. AS 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

To find the solutions, the nonlinear system of equations graphed below have.

We have given Graph of parabola and straight line parallel to x axis   .

According to the graphical method, the graph of the system of equations. The intersection points of the two graph will give us the solution.

we can conclude that there are one intersection points then there would be 1 solutions .

Therefore, Two solution .

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Answer:

3lny - ln7

Step-by-step explanation:

We need to look at two properties that can determine our answer, first off is the obvious rule of subtraction between two logs, when subtracted, the numbers on the right of the log must be divided together.

The other one is the y^3, which means that we need to look for a logarithm that has 3 in the front of it because when a number in front of a logarithm exists, it must turn into an exponent of the number of the right of the logarithm.

With this, we can cross out the ones without the 3 in front, which would be D. lny - ln7 + 3

Now, we see that y is the one with the exponent, meaning that the equation with the 3 in front of the logarithm of y is correct, cross out the ones without, which is A. 3ln7 - ln7

Now when subtracting, the first logarithm will be the numerator while the second logarithm will be the denominator. Leaving us with our final answer being C. 3lny - ln7

(y^3 [3lny] / 7 [ln7])

Answer:

3 ln 4 + 3 ln a

Step-by-step explanation:

Answer:

Option D :

The figure defined by the intersection of a cone and a plane.

Multiply the original by the first 50% discount:

40,000 x 0.5 = 20,000

Now multiply that by the second 50 % discount:

20,000 x 0.5 = 10,000

The price would be 10,000 rupees

Answer:

Step-by-step explanation:

\(\frac{50}{100}\) × 40 000 = 20 000

Answer:

550 to 5.5

Step-by-step explanation:

Answer:

19, 39

Step-by-step explanation:

10 colums w/ 2 rows = 20 with 1 non blue = 19 blue blocks

20 columns w/ 2 rows = 40 with 1 non blue = 39 blue blocks

Answer:

A

Step-by-step explanation:

A.

at 1.5 seconds

h=-16(1.5)²+30(1.5)+6

=-16×2.25+45+6

=-36+45+6

=15 ft

which is correct.

B.

h=-16(t²-30/16 t)+6

=-16(t²-30/16t+(15/16)²-(15/16)²)+6

=-16(t-15/16)²-16(-225/256)+6

=-16(t-15/16)²+225/16 +6

=-16(t-15/16)²+(225+96)/16

=-16(t-15/16)²+321/16

it is at maximum height when t=15/16 seconds

so B is not true.

C.

when t=15/16 seconds

h=321/16 ft=20 1/16 ft

height of fence=20 ft

so it will clear the fence.

C is not true.

D.

when h=0

-16t²+30t+6=0

8t²-15t-3=0

\(t=\frac{15\pm\sqrt{225-4 \times 8 \times (-3)} }{2 \times 8} \\=\frac{15 \pm \sqrt{225+96} }{16} \\=\frac{15\pm \sqrt{321} }{16} \\rejecting~negative~sign\\t=\frac{15+\sqrt{321}}{16} \approx. 2.057 seconds\)

it hits the ground in 2.057 seconds

so D is not true.

Answer:

2 times 11 times 3511

Step-by-step explanation:

i kinda dont know what your asking but i tried

The common prime factor of the numbers  77 and 242? will be 11.

A number can be expressed as the product of its prime factors through the process of prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, let's use the number 30. Even though we are aware that 30 = 5 6 is not a prime number,

Given that the numbers are 77 and 242. The prime factor of the numbers is calculated as,

77 / 11 = 7

242 / 11 = 22

Hence, the number 11 is completely dividing both the numbers 77 and 242 so the prime factor of the numbers is 11.

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The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Given

In line with the posed question.

Triangle ABC's vertices are A(-2, 3), B(0, 0), and C. (1, 2).

As we are aware,

The x-coordinates of each point must be negative while keeping the y-value constant in order to reflect a triangle over the y axis.

As a result, when triangle ABC is mirrored across the y-axis, its vertices are

A'(2,3)

B'(0, 0)

C'(-1, 2)

The vertices of the triangle will also change when it is dialated by a scale factor of 2.

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

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Answer:

answer is 8 hours landing

Answer:

Step-by-step explanation:

1. (2m - 8n + 6) + (4n - 3) =  2m - 4n +3

2. (4y2 - 3xy + x2) + (y2 + 3xy + 3x2) =  4 -  6xy + 4x2

3. (8x + 7) + (2x - 6) = 10x + 1

4. (n + 5) + (2n + 7) =  3n + 12 which can also be written as common factor;  3(n +4).

5. (2a + 8) + (a + 2) =  3a + 10

6. (4m + 3n - p) + (2p - 3n + 2m) =  6m + p

7. (5x2 - 3x + 6) + (x2 + 5x - 15) =  6x^2 + 2x - 9

8. (3d - 4e + 6) + (2d +5e + 1) =  d - e + 6

9. (5x - 3y) + (10y - 4z) + (2x - 3z) = 7x + 7y - 7z

10. (2a + 3) + (a - 9) = 3a - 6,  common factor 3 (a-2)



Answer:

4.16

Step-by-step explanation:

4.16

because thousanth is 5

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )