The approximation of I = * cos(x3 - - dx using composite Simpson's rule with n=3 is:

The cups of smoothie mixture should be fruit is 2.4

To find how many cups of the smoothie mixture should be fruit when 4 cups of smoothie are to be made, we can use proportions.

Let's call the number of cups of fruit needed x.

So, we have

x = percentage of fruit * number of cups

Substitute the known values in the above equation, so, we have the following representation

x = 60% * 4

Evaluate

x = 2.4

Hence, 2.4 cups of the smoothie mixture should be fruit to make 4 cups of smoothie with a 60% fruit and 40% water ratio.

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Answer:

  8

Step-by-step explanation:

Give a prime factorization consisting of two primes, with one of them cubed, you want to know the number of positive integer divisors.

The number of divisors is the product of the exponents of the prime factorization, each increased by 1.

Your number is ...

  n = (a^3)(b^1)

so the number of positive divisors is ...

  (3+1)(1+1) = 4·2 = 8

The number n has 8 different positive divisors.

__

Additional comment

The divisors are ...

  1, a, b, a², ab, a³, a²b, a³b

Example: 24 = 2³·3 has divisors ...

  1, 2, 3, 4, 6, 8, 12, 24

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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9514 1404 393

Answer:

  (x, y) = (-1, 5/2)

Step-by-step explanation:

The only variable with a coefficient that has a magnitude of 1 is x in the first equation. Using that equation, we can write an expression for x:

  x = 2y -6

This can be substituted for x in the second equation.

  (7/2)(2y -6) +7y = 14

  7y -21 +7y = 14 . . . . . . eliminate parentheses

  14y = 35 . . . . . . . . . . . add 21

  y = 35/14 = 5/2 . . . . . divide by the coefficient of y

  x = 2(5/2) -6 = -1

The solution is (x, y) = (-1, 5/2).

For the given angle of 69°, its complement is calculated as 90° - 69° = 21°.

An angle's complement is the angle that, when combined with the given angle, adds up to 90°. In this case, the given angle is 69°, so its complement is 90° - 69° = 21°.

To answer this question, we need to understand the definition of an angle's complement. An angle's complement is the angle that, when added to the given angle, forms a right angle. A right angle is an angle that measures 90°.

Using this definition, we can answer the question. The given angle is 69°, so its complement is 90° - 69° = 21°.

We can visualize this by thinking of a triangle and labeling the angles. Let's say we label the given angle as angle A, and its complement as angle B.

Since angle A + angle B = 90°, and angle A is 69°, angle B must be 21°. Therefore, the measure of the given angle's complement is 21°.

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The range is 250 calories and the standard deviation is 57.5 calories.

In a neighbourhood donut shop, one type of donut has 440 calories, five types of donuts have 350 calories, seven types of donuts have 530 calories, five types of donuts have 330 calories, and five types of donuts have 580 calories

The formula for the range is given by;`

range = maximum value - minimum value`

The minimum value in this case is 330 and the maximum value is 580Therefore, `range = 580 - 330 = 250`

The formula for standard deviation is given by;`s = sqrt [Σ(x - µ)² / N]`

where Σ is a symbol of summation, x is the value, µ is the mean, N is the number of data and s is the standard deviation.

Calculate the mean (µ)`µ = Σ fx / N = 11960 / 23 ≈ 520.87`Substitute the values in the formula above and calculate;

Calories (x)fx(x - µ)² 3301750(-190.87)² 3501750(-170.87)² 440440(-80.87)² 5303710(9.13)² 5802900(59.13)²Total = 352191.55`s = sqrt (352191.55 / 23)≈ 57.5 calories

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Answer:

80% of a serving

Step-by-step explanation:

First, convert  2/3 into 6ths

2/3 = 4/6

She drank 4 of 5 6ths

This is 80% of a serving

los lados faltantes del triángulo rectángulo son de 5.1 y 11.83.

Para resolver este problema, necesitamos recordar las propiedades de un triángulo rectángulo. Primero, sabemos que uno de los ángulos es de 90 grados. Además, el lado opuesto al ángulo recto se llama hipotenusa y los otros dos lados se llaman catetos.

En este caso, sabemos que uno de los ángulos es de 25 grados, por lo que el otro ángulo es de 90 - 25 = 65 grados. Ahora podemos usar la ley de senos para encontrar la longitud del otro cateto.

La ley de senos establece que la longitud de un lado dividida por el seno del ángulo opuesto es igual a la longitud de otro lado dividido por el seno del ángulo opuesto. Entonces, podemos escribir:

12 / sen(90) = x / sen(25)
x = 12 * sen(25) / sen(90) = 5.1

Por lo tanto, el lado faltante tiene una longitud de 5.1. Para encontrar la longitud del otro cateto, podemos usar el teorema de Pitágoras, que establece que la suma de los cuadrados de los catetos es igual al cuadrado de la hipotenusa. Entonces, podemos escribir:

a^2 + b^2 = 12^2 - 5.1^2 = 130.19
a^2 + b^2 = 130.19
b = sqrt(130.19 - a^2)

Donde "a" es la longitud del cateto que conocemos y "b" es la longitud del cateto que queremos encontrar. Podemos usar la ecuación anterior para encontrar la longitud de "b" para diferentes valores de "a". Por ejemplo, si "a" fuera de 4, tendríamos:

b = sqrt(130.19 - 4^2) = 11.83

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Answer:

20/27

Step-by-step explanation:

Answer:

Frankie's weight change since last week was the opposite of Victor's.

Step-by-step explanation:

Because the graph always has a consistent slope of +2, the table x|y-2| 4|0| 6|2| is an illustration of a linear function table.

In order for a table to represent a linear function, there must be a constant rate of change (slope) between any two points on the graph. In other words, the relationship between the x-values and y-values should follow a consistent pattern.

The correct table that represents a linear function is: x|y-2| 4|0| 6|2|This is because there is a constant rate of change of +2 between any two points on the graph. For example, when x goes from 2 to 4, y increases from -2 to 0. When x goes from 4 to 6, y increases from 0 to 2.

This constant rate of change indicates that the relationship between x and y is linear.

In summary, a table represents a linear function when there is a constant rate of change between any two points on the graph. The table x|y-2| 4|0| 6|2| is an example of a linear function table because there is a consistent slope of +2 between any two points on the graph.

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The equation for the line in point-(1, 1) is y = -0.5x + 0.5.

Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.

Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.

To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.

Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5

Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.

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Answer:

The numbers i and V3 are elements of the set.

Step-by-step explanation:

The rational numbers are those which can be written as fractions. These are the numbers which can be repeating elements and terminating decimals. All integers can be set of rational numbers. The statements which is not true is statement  which states that numbers i and V3 are elements of the set.

Answer:

25km/h

Step-by-step explanation:

Answer:

5km

Step-by-step explanation:

in the end you rode 15km, 15km divided by the 3 hours of riding equals 5 km, so it should be 5 km an hour.

Answer:

= 1619.15

Step-by-step explanation:

Hope this is correct :)

Answer:

Thanks same to you :)

Step-by-step explanation:

Answer:

More than likely it looks like a right angle or 90 degrees so the answer is mostly 51.

Step-by-step explanation:

90 - 39 = 51

a. ANOVA table:

Source SS df MS F

A 1568.5 1 1568.5 7.31

B 6420.0 2 3210.0 14.96

AxB 1012.5 2 506.25 2.36

Error 8967.0 54 166.0

Total 17968.0 59  

b. The p-value for Factor A is 0.009. The p-value is less than the significance level of 0.05, so we reject the null hypothesis and conclude that there is a significant difference in waiting times due to the method of loading and unloading.

c. The p-value for Factor B is less than 0.001. The p-value is less than the significance level of 0.05, so we reject the null hypothesis and conclude that there is a significant difference in waiting times due to the type of ride.

d. The p-value for the interaction of factors A and B is 0.1. The p-value is greater than the significance level of 0.05, so we fail to reject the null hypothesis and conclude that there is no significant interaction between the method of loading and unloading and the type of ride.

e. Based on the ANOVA results, the amusement park should focus on improving the method of loading and unloading to reduce waiting times. However, it is also important to consider the type of ride, as different types of rides have different waiting time characteristics. The park could potentially use the results to allocate resources to improve the loading and unloading process for the rides that have the longest waiting times.

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We can write the measurements as -

a = 7.8

b = 9.24

(B) = 50°

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that two triangles in the map below are similar.

We can write -

{ 1 } -

sin (A) = a/c

a = c sin(A)

a = 12 sin(40°)

a = 12 x 0.65

a = 7.8

{ 2 } -

cos (A) = b/c

b = c cos(A)

b = c cos(40°)

b = 12 x 0.77

b = 9.24

{ 3 } -

tan (B) = b/a

tan (B) = 9.24/7.8

tan (B) = 1.19

(B) = 50°

Therefore, we can write the measurements as -

a = 7.8

b = 9.24

(B) = 50°

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Step-by-step explanation:

f(x) = x³ - ax² - 13x + b.

f(1) = 1³ - a(1)² - 13(1) + b = 0

=> 1 - a - 13 + b = 0, b - a - 12 = 0.

f(-3) = (-3)³ - a(-3)² - 13(-3) + b = 0

=> - 27 - 9a + 39 + b = 0, 12 - 9a + b = 0.

Therefore, b - a - 12 = 12 - 9a + b. 8a = 24, a = 3.

=> b - (3) - 12 = 0, b = 15.

Answer:

you have it correct sir

Step-by-step explanation:

Answer:

1422cm²

Step-by-step explanation:

Triangle:

First; 24 x 14 = 336

second: since there is 2 triangle u x 2

so its 672

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

Rectangle:

third; 25 x 10 = 250

forth; since there is 3 rectangle u x3

so its 750

last u add all ur answer for triangle and rectangle and u get

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

672 + 750 =

1422cm²

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Answer:

_____

Step-by-step explanation:

its saying that the height of the tree is half of 160

(i think)

Answer: C. Mount Everest is about 23 times as tall as the Empire State Building

Step-by-step explanation:

The options are:

A.There is no way to compare these heights

B.Mount Everest is about 40 times as tall as the Empire State Building

C.Mount Everest is about 23 times as tall as the Empire State Building

D.The Empire State Building is about 23 times as tall as Mount Everest

Mount Everest = 8.8×10^3 meters = 8800 meters

Empire State Building = 3.8×10^2 = 380 meters

Mount Everest is (8800 / 23) = 33 times as tall as the Empire State Building. Therefore, the correct option is C.

Answer:

Mount Everest is about 23 times as tall as the Empire State Building. Hope that helps!

In regression analysis , the error term ε is a random variable with expected value of 0.

What is regression analysis?

A set of statistical procedures known as regression analysis is used to estimate the relationships between a dependent variable and one or more independent variables.

Main Body:

In regression analysis, the model in the form is called regression model.

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as regression equation.

So the answer  to error term is 0.

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(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:

1 1/2 hours i think

Step-by-step explanation:

Answer:

1.92x5=9.6 pounds everyday.

Step-by-step explanation:

Answer:

I think that it is 1) E, F, G, H, J