Evaluate the function rule for the given value.
y = 8.3x for x = 4

Since the roots are complex, the general solution of the differential equation can be written as: y(t) = e^(50t/20)(c1cos(√(300)t/20) + c2sin(√(300)t/20))

To solve the initial value problem for the given differential equation 10y'' - 50y' + 65y = 0, we need to find the general solution of the equation and then apply the initial conditions to determine the specific solution.

The characteristic equation for the given differential equation is:

10r^2 - 50r + 65 = 0

Solving this quadratic equation, we find that the roots are complex:

r = (50 ± √(50^2 - 41065))/(2*10)

= (50 ± √(-300))/(20)

= (50 ± √(300)i)/(20)

Since the roots are complex, the general solution of the differential equation can be written as:

y(t) = e^(50t/20)(c1cos(√(300)t/20) + c2sin(√(300)t/20))

Now, let's apply the initial conditions to find the specific solution. Since the problem does not provide the initial conditions, we cannot proceed further without knowing the specific values for y(0) and y'(0).

Please provide the initial conditions, and I'll be able to find the specific solution and check if it satisfies the differential equation and initial conditions.

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Answer:

\(-10x + 4 y + 27\)

Step-by-step explanation:

Answer: -10x+4y+27

Step-by-step explanation: first, combine the like terms

20 + 7= 27

-9x-x=-10x

4y stays the same so, if simplified this equals

-10x+2y+27

Answer:

r = 8

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

16 pi = 2 * pi r

Divide each side by 2 pi

16 pi /2 pi  = 2 pi r / 2 pi

8 = r

Answer:

\(radius = 8\)

Step-by-step explanation:

\(r = \frac{c}{2\pi} \\ r = \frac{16\pi}{2\pi} \\ r = 8\)

hope this helps

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The following are the values:

a) $(fg)'(5) = -16$.

(b) $\left(\frac{f}{g}\right)'(5) = -\frac{1}{16}$.

(c) $\left(\frac{g}{f}\right)'(5) = \frac{19}{8}$.

(d)  $u'(1) = -13$.

(e) $v'(5) = -\frac{1}{16}$.

a) We have $(fg)'(5) = f'(5)g(5) + f(5)g'(5) = (3)(-8) + (4)(2) = -16.$ Therefore, $(fg)'(5) = -16$.

(b) We have $\left(\frac{f}{g}\right)'(5) = \frac{f'(5)g(5) - f(5)g'(5)}{g^2(5)} = \frac{(3)(-8) - (4)(2)}{(-8)^2} = -\frac{1}{16}.$ Therefore,  fraction $\left(\frac{f}{g}\right)'(5) = -\frac{1}{16}$.

(c) We have $\left(\frac{g}{f}\right)'(5) = \frac{g'(5)f(5) - g(5)f'(5)}{f^2(5)} = \frac{(2)(4) - (-8)(3)}{4^2} = \frac{19}{8}.$ Therefore, $\left(\frac{g}{f}\right)'(5) = \frac{19}{8}$.

(d) We have $u'(1) = f'(1)g(1) + f(1)g'(1) = (2)(-2) + (3)(-3) = -13$. Therefore, $u'(1) = -13$.

(e) We have $v'(5) = \frac{f'(5)g(5) - f(5)g'(5)}{g^2(5)} = \frac{(3)(-8) - (4)(2)}{(-8)^2} = -\frac{1}{16}.$ Therefore, fraction $v'(5) = -\frac{1}{16}$.

Overall, The values are : a) $(fg)'(5) = -16$, (b) $\left(\frac{f}{g}\right)'(5) = -\frac{1}{16}$, (c) $\left(\frac{g}{f}\right)'(5) = \frac{19}{8}$,(d)  $u'(1) = -13$,(e) $v'(5) = -\frac{1}{16}$.

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No, randomly selecting 852 of the 1,330 children to be in the book group is not the same as randomly assigning the children to the two experimental groups.

Random selection only involves choosing a group of participants out of a larger population, while random assignment involves assigning each participant to either the experimental group or the control group.

Random selection involves choosing a group of participants out of a larger population, while random assignment involves assigning each participant to either the experimental group or the control group. Random selection could be used to select the participants for the two groups, but it is not the same as random assignment. Random assignment requires that each participant is randomly assigned to either the experimental group or the control group. This ensures that both groups are similar and that any differences in outcomes can be attributed to the intervention. Therefore, randomly selecting 852 of the 1,330 children to be in the book group is not the same as randomly assigning the children to the two experimental groups.

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The histogram Illustrated shows that the data is negatively skewed.

Negatively skewed distribution means that the distribution type where more values plot on the graph's right side, the tail of the distribution is longer on the left side.

When a distribution is negatively skewed in statistics, more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.

From the histogram we can easily say that most of the population of US are lying on the left of histogram therefore the given data is negatively skewed

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The absolute maximum and minimum values of the function `f(x) = x⁴ − 2x² + 6` on the interval `[-2, 2]` are `18` and `3`, respectively. And the x-values at which they occur are `-2` and `1`, respectively.

Given the function `f(x) = x⁴ − 2x² + 6` on the interval `[-2, 2]`,

we need to find the absolute maximum and minimum values of the function and indicate the x-values at which they occur.

To find the maximum and minimum values of `f(x)` on the given interval, we use the First Derivative Test and the Second Derivative Test.

Let's start with the first derivative of the function:

`f(x) = x⁴ − 2x² + 6

`

Differentiating `f(x)` w.r.t `x`, we get:

`f'(x) = 4x³ − 4x`

Setting `f'(x) = 0` to find critical numbers:

`f'(x) = 4x³ − 4x = 4x(x² - 1) = 0`

⇒ `x = -1, 0, 1`

Therefore, `-2, 2` and endpoints `x = -2, 2` are critical points of `f(x)`.

Now, we can use the Second Derivative Test to determine the nature of the critical points.

Let's take `x = -1` as an example. We have:

`f''(x) = 12x² - 4`

⇒ `f''(-1) = 12(1) - 4

= 8`

Since `f''(-1) > 0`, `f(x)` has a local minimum at `x = -1`.

Similarly, we can check that `f(x)` has a local maximum at `x = 1`.

Now, we need to check the endpoints `x = -2, 2` to find the absolute maximum and minimum values.

We have:

`f(-2) = 18`

`f(2) = 14`

Therefore, the absolute maximum value of `f(x)` is `f(-2) = 18`, which occurs at `x = -2`.

The absolute minimum value of `f(x)` is `f(1) = 3`, which occurs at `x = 1`.

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Answer:

i know right? It's so difficult till I'm brainless when I try to solving it

Answer:

same tbh

Step-by-step explanation:

Answer:the photo is for part A.

B) the weight would be Invnorm(.25,77,6)=72.95

C)the weight would be 81.04 but this is the work invnorm(.75,77,6)=81.04

D)IQR=Q3-Q1

81.04-72.95=8.09

E)9.12 is the answer the work normalcdf(85,1000,77,6)=.0912

F).6892 or 68.92% are the answers the work normalcdf(60,80,77,6)=.6892

G).0227 or 2.27% is the answer and the work normalcdf(0,65,77,6)=.0227

Step-by-step explanation:

Using the normal distribution, we have that:

----------------------

Problems of normal distribution can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

----------------------

----------------------

Item b:

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.675 = \frac{X - 77}{6}\)

\(X - 77 = -0.675(6)\)

\(X = 72.95\)

A weight of 72.95 pounds would represent the 25th percentile.

----------------------

Item c:

\(Z = \frac{X - \mu}{\sigma}\)

\(0.675 = \frac{X - 77}{6}\)

\(X - 77 = 0.675(6)\)

\(X = 81.05\)

A weight of 81.05 pounds would represent the 75th percentile.

----------------------

Item d:

The interquartile range is the difference between the 75th and the 25 percentile, thus:

\(81.05 - 72.95 = 8.1\)

The interquartile range is of 8.1 pounds.

----------------------

Item e:

The proportion is 1 subtracted by the p-value of Z when X = 85, thus:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{85 - 77}{6}\)

\(Z = 1.33\)

\(Z = 1.33\) has a p-value of 0.9082.

1 - 0.9082 = 0.0918.

0.0918 = 9.18% of male adult Labrador retrievers weigh above 85 pounds.

----------------------

Item f:

The proportion is the p-value of Z when X = 80 subtracted by the p-value of Z when X = 60, thus:

X = 80:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{80 - 77}{6}\)

\(Z = 0.5\)

\(Z = 0.5\) has a p-value of 0.6915.

X = 60:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{60 - 77}{6}\)

\(Z = -2.83\)

\(Z = -2.83\) has a p-value of 0.0023.

0.6915 - 0.0023 = 0.6892.

0.6892 = 68.92% of male adult Labrador retrievers weigh between 60 and 80 pounds.

----------------------

Item g:

This proportion is the p-value of Z when X = 65, thus:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{65 - 77}{6}\)

\(Z = -2\)

\(Z = -2\) has a p-value of 0.0228.

0.0228 = 2.28% of male adult Labrador retrievers weigh less than 65 pounds.

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Given half-cup of milk. if we find how many  milliliters are there in this cup we get it approximately equal to 120 milliliters.

In cooking and baking, cup measurements are commonly used. However, it's important to note that cup measurements can vary slightly depending on the country or region. In the United States, a standard cup measurement is equal to 240 milliliters.

A half-cup is exactly half of this measurement, which means it would be approximately equal to 240/2 = 120 milliliters. Therefore, option C, 120, is the closest approximation to the number of milliliters contained in a half-cup of milk. It's worth noting that for more precise measurements, it's always advisable to use a kitchen scale or measuring cup with milliliter markings.

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Answer:

can u add more info plz

Step-by-step explanation:

Answer:

The absolute value of a number is how far that number is from 0.

|-9| = 9

This is true because the absolute value of 9 is 9 spaces away from 0.

The option that summarizes a t-test that was significant and associated with a large effect size is: d. t(12) = 2.95, p < .05, d = .82

In this option, the t-value is 2.95, indicating a significant result. The p-value is less than .05, indicating that the result is statistically significant at the chosen significance level. Furthermore, the effect size is large, with a Cohen's d value of .82. A large effect size suggests a substantial difference between the groups being compared.

The summary presented in option d is as follows:

t(12) = 2.95, p < .05, d = .82

- t(12) represents the t-value and the degrees of freedom (df) associated with the t-test. In this case, the t-value is 2.95, indicating the magnitude of the difference between the groups being compared. The degrees of freedom is 12, which is determined by the sample size and the design of the study.

- p < .05 indicates the p-value, which is a measure of the probability of obtaining the observed results by chance alone. In this case, the p-value is less than .05, indicating that the difference observed is statistically significant at the .05 significance level.

- d = .82 represents the effect size, specifically Cohen's d. Effect size measures the magnitude of the difference between groups or the strength of the relationship between variables.

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Step-by-step explanation:

for straight Line AE:

110° + AČB = 180° ( angles on straight line )

A Č B = 70°

for triangle "A C B"

65° + 70° + x = 180° (sum of angles on triangle)

x = 45°

DO THE SAME THING FOR THE UPPER PART ( straight line A E and triangle A D C) PLEASE GIVE ME BRAINLIEST ANSWER

Answer:

Step-by-step explanation:

use formula

(x,y)=(kx,ky)   (k means scale factor)

A(1,1)=A'(1*2,1*2+

A'=(2,2)

B(3,1)=B'(3*2,1*2)

B'=(6,2)

C(3,-3)=C'(3*2,-3*2)

C'=(6,-6)

The given statements are,

1. BC and B'C' are the same line, is true.

And, 2. AB and A'B' are both parallel to x - axis, is true.

Here,

Triangle A'B'C' is the result of dilating ABC about point P by a scale factor of 2.

What is dilation?

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

Now,

For finding the points of A', B', C' we used formula,

(x, y) = (kx, ky)

Where k is scalar factor.

Here, A = ( 1, 1 ) ⇒A' = ( 2X1, 2X1) = ( 2, 2 )

And, B = ( 3, 1 ) ⇒ B' = ( 2X3, 2X1 ) = ( 6, 2 )

And, C = ( 3, -3 ) ⇒C' = ( 2X3, 2X-3 ) = ( 6 , -6 )

Hence, clearly by all points,

BC and B'C' are on the same line.

And, AB and A'B' are both parallel to x - axis.

Both are true.

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If the class collected $660 from ticket sales, the drama class sold a total of 90 student tickets. Let's assume that the number of adult tickets sold is x.

Since the drama class sold 25 more student tickets than adult tickets, the number of student tickets sold can be expressed as (x + 25).

The total revenue from ticket sales is given as $660. Adult tickets cost $6 each and student tickets cost $3 each. Therefore, the total revenue can be expressed as 6x + 3(x + 25).

Setting up the equation: 6x + 3(x + 25) = 660.

Simplifying the equation: 6x + 3x + 75 = 660.

Combining like terms: 9x + 75 = 660.

Subtracting 75 from both sides: 9x = 585.

Dividing both sides by 9: x = 65.

Therefore, the drama class sold 65 adult tickets.

To find the number of student tickets sold, we substitute the value of x into the expression (x + 25): (65 + 25) = 90.

Thus, the drama class sold 90 student tickets.

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Answer:

-89c+56.7=145.7is correct answer

Answer:A conductor is mapping a trip and records the distance the train travels over certain time intervals. time (hours) Distance (miles) 0.5 22.5 1 45 1.5 67.545 The train travels at a constant speed. What is its speed in miles per hour?

Step-by-step explanation:

do not uses this site i got all my answers wrong going here

The equation of the transformed function, after being compressed horizontally by a factor of 3 and translated up 2 units, is g(x) = sqrt(x/3) + 2.

If f(x) is a function, and we want to compress it horizontally by a factor of 3 and translate it up 2 units, we can apply the following transformations:

Horizontal compression by a factor of 3 means that we need to replace x with x/3 in the function.

Translation up 2 units means that we need to add 2 to the function.

The equation of the transformed function is g(x) = sqrt(x/3) + 2, which represents a function that has been compressed horizontally by a factor of 3 and translated up 2 units from the original function f(x) = sqrt(x).

Therefore, the equation of the transformed function is:

g(x) = sqrt(x/3) + 2

Note that g(x) represents the transformed function, and we have used the square root symbol to indicate that the function is the square root of x/3.

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The answer is very simple

The total deductions would be

total deductions = 3000*0.062 + 3000*0.0145 + 3000*0.125 + 300

total deductions = 904.5

Answer: The square will fit.

Step-by-step explanation:

the diameter of the circle is large enough that since the square is 7cm across, (each side is the same length, therefore the diameter is the same,) The square will fit on the inside of the circle.  

Answer:

x = 54

Step-by-step explanation:

In this line, I am going to assume lines l and m are parallel.

Each flat surface is half of a circle, therefore it has 180 degrees. We are given one side and told to find the other.

180 - 116 = 64.

The other angle's total value must be 64.

Now, to solve for x, subtract 10 from 64 [inverse operations].

64-10=54

The value of x in this equation is 54 degrees.

Answer:

  9 cm²

Step-by-step explanation:

Sometimes these inscribed polygon problems respond nicely to a little geometrical thinking. The figure is symmetrical about the vertical line through the center of the square(s).

__

That line of symmetry divides the figure into halves that are twice as tall as wide. That same ratio applies to both the outer square and the inner (blue shaded) square.

In other words, a line from the center of the top segment through either bottom corner of the figure will pass through the corners of both squares. That line will have a slope of ±2, making it easy to find the coordinates of one of the lower corners of the shaded square.

__

Analytically, we can write the equation of the right circle shown in the attachment as ...

  x² +y² = 5²

and the equation of the line as ...

  y = 2x +5

__

Then the x-value of the lower left corner will be found where these intersect.

  x² +(2x +5)² = 25 . . . . . . substitute for y

  x² +4x² +20x +25 25 . . . . eliminate parentheses

  5x² +20x = 0 . . . . . . . . . . . . subtract 25

  5x(x +4) = 0 . . . . . . factor

  x = -4 or 0 . . . . . the x-coordinates of the points of intersection

The y-coordinate of the lower left point is ...

  y = 2(-4) +5 = -3

__

Since the top edge of the blue square has a y-coordinate of 0, this means the square is 3 cm on a side. Its area is ...

  A = s² = (3 cm)² = 9 cm² . . . . area of the blue shaded square

Answer:

$25.5

Step-by-step explanation:

Answer:

v = b/0.75 - 0.95s/0.75

Or

v = (b - 0.95s) / 0.75

Step-by-step explanation:

Solve 0.75v + 0.95s = b for v

This means making v the subject of the formula

0.75v + 0.95s = b

Subtract 0.95s from both sides

0.75v + 0.95s - 0.95s = b - 0.95s

0.75v = b - 0.95s

Divide both sides by 0.75

v = (b - 0.95s) / 0.75

v = b/0.75 - 0.95s/0.75

The equation will be useful in determining the number of vegetarian

The parametric equations for the line passing through points A(-3, 2) and B(5, 0) ar; x(t) = -3 + 8t, and y(t) = 2 - 2t.

option C

The parametric equations for the line passing through point A(-3, 2), and point B(5, 0) is calculated as follows;

The x-coordinate (x(t)) of a point on the line is calculated as follows;

\(x(t) = x_A + (x_B - x_A)t\)

Where;

x(t) = -3 + (5 - (-3))t

x(t)  = -3 + 8t

x(t)  = -3 + 8t

The y-coordinate (y(t)) of a point on the line is calculated as;

\(y(t) = y_A + (y_B - y_A)t\)

Where;

y(t) = 2 + (0 - 2)t

y(t)  = 2 - 2t

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Simplifying this expression would involve expanding and combining like terms, but the above expression represents the derivative of the function F(x).

To find the derivative of the function F(x) = (4x + 5)^3 (x^2 − 9x + 5)^4, we can use the product rule and the chain rule.

Let's denote the first factor as u(x) = (4x + 5)^3 and the second factor as v(x) = (x^2 − 9x + 5)^4.

Using the product rule, the derivative of F(x) is given by:

F'(x) = u'(x)v(x) + u(x)v'(x)

To find u'(x), we apply the chain rule. The derivative of (4x + 5)^3 with respect to x is:

u'(x) = 3(4x + 5)^2 * (4) = 12(4x + 5)^2

To find v'(x), we also apply the chain rule. The derivative of (x^2 − 9x + 5)^4 with respect to x is:

v'(x) = 4(x^2 − 9x + 5)^3 * (2x − 9)

Now, substituting these values into the derivative expression, we have:

F'(x) = 12(4x + 5)^2 * (x^2 − 9x + 5)^4 + (4x + 5)^3 * 4(x^2 − 9x + 5)^3 * (2x − 9)

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Answer:

11/20

Step-by-step explanation:

55% = 55/100

by simplifying this fraction (divide top and bottom by 5), you get 11/20

Answer:

$51.2

Step-by-step explanation:

If you subtract 64 to 20% then you end up with $51.2

Answer:

Complementary angles

Step-by-step explanation:

When two angles get added to form 90° those two angles are called Complementary angles.

Here, <1 + <2 = 90°

Hence, both are Complementary Angles (Ans)