6x +1.5x = 2
What is x=


Answer:

C

Step-by-step explanation:

C

The maximum possible error is 2/3.

The Maclaurin series for cosine function is given by:

\(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using the first three nonzero terms, we get:

\(cos(x) ≈ 1 - x^2/2! + x^4/4!\)

To estimate the error, we can use the Taylor remainder formula:

\(Rn(x) = f(n+1)(c) * (x-a)^(n+1) / (n+1)!\)

where f(n+1)(c) is the (n+1)th derivative of f evaluated at some value c between a and x.

In this case, we have:

f(x) = cos(x)

a = 0

n = 2

x = 2

To find an upper bound for the error, we need to find the maximum value of the absolute value of the third derivative of cosine function over the interval [0,2]. Since the third derivative of cosine is -cos(x), the maximum value of its absolute value is 1.

Therefore, we have:

\(|R2(2)| ≤ 1 * (2-0)^(2+1) / (2+1)!\)

≤ 4/3!

≤ 2/3

So the maximum possible error is 2/3.

To know more about Maclaurin series refer to-

https://brainly.com/question/31745715

#SPJ11

Since the test statistic (-2.24) falls outside the range of the critical values (-1.96 to 1.96), we reject the null hypothesis.

What is sign test?

The sign test is a non-parametric statistical test used to determine whether the median of a distribution is equal to a specified value. It is a simple and robust method that is applicable when the data do not meet the assumptions of parametric tests, such as when the data

The given problem can be solved using the one-sample sign test to test the null hypothesis that the mean of the population is 19.4 minutes against the alternative hypothesis that it is not 19.4 minutes.

(a) Using Table I:

Step 1: Set up the hypotheses:

Null hypothesis (H0): The mean of the population is 19.4 minutes.

Alternative hypothesis (H1): The mean of the population is not 19.4 minutes.

Step 2: Determine the test statistic:

We will use the sign test statistic, which is the number of positive or negative signs in the sample.

Step 3: Set the significance level:

The significance level is given as 0.05.

Step 4: Perform the sign test:

Count the number of observations in the sample that are greater than 19.4 and the number of observations that are less than 19.4. Let's denote the count of observations greater than 19.4 as "+" and the count of observations less than 19.4 as "-".

In the given sample, there are 5 observations greater than 19.4 (18.1, 20.3, 19.3, 19.5, and 20.0), and 15 observations less than 19.4 (18.3, 15.6, 16.8, 17.6, 16.9, 17.0, 16.5, 18.6, 18.8, 19.1, 17.5, 18.5, and 18.0).

Step 5: Calculate the test statistic:

The test statistic is the smaller of the counts "+" or "-". In this case, the test statistic is 5.

Step 6: Determine the critical value:

Using Table I, for a significance level of 0.05 and a two-tailed test, the critical value is 3.

Step 7: Make a decision:

Since the test statistic (5) is greater than the critical value (3), we reject the null hypothesis.

(b) Using the normal approximation to the binomial distribution:

Alternatively, we can use the normal approximation to the binomial distribution when the sample size is large. Since the sample size is 20 in this case, we can apply this approximation.

Step 1: Set up the hypotheses (same as in (a)).

Step 2: Determine the test statistic:

We will use the z-test statistic, which is calculated as (x - μ) / (σ / √n), where x is the observed number of successes, μ is the hypothesized value (19.4), σ is the standard deviation of the binomial distribution (calculated as √(n/4), where n is the sample size), and √n is the standard error.

Step 3: Set the significance level (same as in (a)).

Step 4: Calculate the test statistic:

Using the formula for the z-test statistic, we get z = (5 - 10) / (√(20/4)) ≈ -2.24.

Step 5: Determine the critical value:

For a significance level of 0.05 and a two-tailed test, the critical value is approximately ±1.96.

Step 6: Make a decision:

Since the test statistic (-2.24) falls outside the range of the critical values (-1.96 to 1.96), we reject the null hypothesis.

Rework Exercise 16.16 using the signed-rank test based on Table X:

To provide a more accurate solution, I would need additional information about Exercise 16.16 and Table X.

To know more about sign test visit:

https://brainly.com/question/31486709

#SPJ4

Answer:big brrrrrrd

Step-by-step explanation:

yes

Answer:

11/16 pounds

Step-by-step explanation:

The difference between their weights can be found by subtracting 6 1/4 pounds from 5 9/16 pounds to find the difference. To do this we must transfer it from 1/4 to sixteenths which is 4 sixteenths. Then we subtract.

 6 4/16

- 5 9/16

    11/16

brainliest please . . . uwu

Answer:

B

Step-by-step explanation:

Answer:

the answer B

Step-by-step explanation:

Answer:

See attached image

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

hypotenuse =13cm

base=10cm

perpendicular =?

Step-by-step explanation:

by using Pythagoras law

hypotenuse=perpendicular²+base²

13²=perpendicular²+10²

perpendicular =√(13²-10²)=√69=8.3cm

the measure of the other leg is 8.3cm

The measure of the other leg is 8.3 cm .

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Formula of Pythagoras theorem :

(Hypotenuse)² = (Base)² + (Perpendicular)²

According to the question

Hypotenuse of a right triangle = 13 cm

Perpendicular of a right triangle = 10 cm

Now,

Base of a right triangle  

By using formula of Pythagoras theorem :

(Hypotenuse)² = (Base)² + (Perpendicular)²  

Substituting the values

(13)² = (Base)² + (10)²  

169 = (Base)² + 100

69 = (Base)²

Base = \(\sqrt{69}\)

Base = 8.3 cm

Hence,  the measure of the other leg is 8.3 cm .

To know more about Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ3

The E field produced by the sheets at the coordinate (x, y, z) = (1, 1, 0.5) is zero.

The E field produced by the sheets at the coordinate (x, y, z) = (1, -1, 1.5) is also zero.

To calculate the electric field (E) produced by the charged sheets at the given coordinates, we need to consider the contributions from each sheet separately and then add them together.

For the coordinate (x, y, z) = (1, 1, 0.5):

The distance between the point and the sheet in the z=1 plane is 0.5 units, and the distance to the sheet in the z=-1 plane is 1.5 units. Since the sheets have equal charge densities and are parallel, their contributions to the electric field cancel each other out. Therefore, the net electric field at this coordinate is zero.

For the coordinate (x, y, z) = (1, -1, 1.5):

The distance to the sheet in the z=1 plane is 0.5 units, and the distance to the sheet in the z=-1 plane is 0.5 units. Again, due to the equal charge densities and parallel orientation, the contributions from both sheets cancel each other out, resulting in a net electric field of zero.

The electric field produced by the charged sheets at the coordinates (x, y, z) = (1, 1, 0.5) and (x, y, z) = (1, -1, 1.5) is zero. The cancellation of electric field contributions occurs because the sheets have equal charge densities and are parallel to each other.

To know more about E field visit:

https://brainly.com/question/19878202

#SPJ11

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Answer:

80 degrees

Step-by-step explanation:

What we see in this drawing is a triangle formed by three lines. In order to solve this problem, we need to know that when two lines intersect, the two angles formed are supplementary (meaning they add up to 180 degrees). For example, the 150-degree angle, and the angle right next to it (the angle on the left side of the triangle) add up to 180 degrees. This means that the left-most angle of the triangle is 180-150, which is 30 degrees

We can figure out the topmost angle of the triangle using the same method. We know that the angle outside the triangle is 130 degrees, so the angle right next to it (in this case, right below it), is 180-130, or 50 degrees.

Next, we use the fact that triangles are 180 degrees on the inside to figure out the third angle (the one on the right, right next to angle 1). We know that the other two angles are 30 and 50 degrees, and if you add that up, you get 80 degrees. The last angle, then, is 180-80, or 100 degrees.

Lastly, we know that the rightmost angle of the triangle and angle 1 add up to 180 degrees. In other words, 100+Angle1=180. Therefore, Angle 1 is 180-100 or 80 degrees.

Answer:

\(2x^3-3x^2-10x+15\\\)

Step-by-step explanation:

To find (fg)(x), we have to look at f(x) and g(x) and multiply the two quantities together. We are already given the two quantities individually so all that is left is the multiplication:

\((fg)(x)=(-2x+3)(5-x^2)=-10x+2x^3+15-3x^2\\\)

If we reorder the terms to go from highest degree to lowest, we get our final answer to be the following:

\(2x^3-3x^2-10x+15\)

Answer:

-14

Step-by-step explanation:

3r2-5s+6t

3.2.2-5(-4)+6.(-1)

12-20-6

12-26

-14

Answer:

(3r2 -5s +6t if r=2 s= -4 t= -1 ) =-2

In essence, a function is a rule that assigns to each value of the input set (also known as the domain), a unique value of the output set (also known as the range).

A function is a fundamental mathematical concept that is used to describe the relationship between two sets of values.

To understand the idea of a function, imagine a machine that takes in an input and produces an output. The input values are the domain of the function, and the output values are the range. A function can be represented as an equation, a graph, or a table. For example, the equation f(x) = x + 3 represents a function that takes in an input value x and produces an output value that is 3 greater than the input value.

One of the key features of a function is that each input value must have a unique output value. This means that if you input the same value into the function twice, you should get the same output value both times. In mathematical terms, we say that a function is well-defined if it has a unique output value for each input value.

Functions are used in a wide range of mathematical applications, from algebra and calculus to statistics and data analysis. They provide a powerful tool for describing and analyzing relationships between different sets of values.

To know more about function here

https://brainly.com/question/28193995

#SPJ4

Answer:

4

Step-by-step explanation:

4 is the intersecting point which states p intersect q giving both tennis and basketball players

Answer:

x = \(\frac{3}{2}\), x = \(\frac{13}{2}\)

Step-by-step explanation:

Given

4x² - 16x = 16x - 39 ( subtract 16x - 39 from both sides )

4x² - 32x + 39 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term, that is

product = 4 × 39 = 156 and sum = - 32

The factors are - 26 and - 6

Use these factors to split the x- term

4x² - 26x - 6x + 39 = 0 ( factor the first/second and third/fourth terms )

2x(2x - 13) - 3(2x - 13) = 0 ← factor out (2x - 13) from each term

(2x - 13)(2x - 3) = 0

Equate each factor to zero and solve for x

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \(\frac{3}{2}\)

2x - 13 = 0 ⇒ 2x = 13 ⇒ x = \(\frac{13}{2}\)

⇒ x² - 6x = -8

\(\sf add \ 9 \ on \ both \ sides\)

⇒ x² - 6x + 9 = -8 + 9

\(\sf simplify \ and \ complete \ square\)

⇒ x² - 3x - 3x + 9 = 1

\(\sf factor \ common \ term\)

⇒ x(x - 3) - 3(x - 3) = 1

\(\sf collect \ into \ groups\)

⇒ (x - 3)² = 1

\(\sf square \ root \ both \ sides\)

⇒ x - 3 = ±√1

\(\sf simplify\)

⇒ x - 3 = ±1

\(\sf change \ side\)

⇒ x = 1 + 3, -1 + 3

\(\sf simplify\)

⇒ x = 4, 2

\(\rightarrow \sf 4x^2 + 12x + 11 = 0\)

\(\rightarrow \sf 4\left(x^2+3x+\dfrac{11}{4}\right) = 0\)

\(\rightarrow \sf 4\left(x^2+3x+\dfrac{11}{4}+\left(\dfrac{3}{2}\right)^2-\left(\dfrac{3}{2}\right)^2\right) = 0\)

\(\rightarrow \sf 4\left(x+\dfrac{3}{2}\right)^2+2 = 0\)

\(\rightarrow \sf \left(x+\dfrac{3}{2}\right)^2 = -\dfrac{2}{4}\)

\(\rightarrow \sf \left(x+\dfrac{3}{2}\right)^2 = -\dfrac{1}{2}\)

\(\rightarrow \sf x+\dfrac{3}{2} = \pm \sqrt{-\dfrac{1}{2} }\)

\(\rightarrow \sf x+\dfrac{3}{2} = \pm i\sqrt{\dfrac{1}{2} }\)

\(\rightarrow \sf x= \pm i\sqrt{\dfrac{1}{2} }-\dfrac{3}{2}\)

P = 3.2qThis is the equation that relates p and q when p varies directly with q.

When two variables are directly proportional to each other, they are said to be varying directly. This suggests that when one variable is multiplied by a fixed value, the other variable will also be multiplied by the same fixed value to obtain the product.

Let's say p is directly proportional to q. Then, we can write:  p = kq, where k is a constant of variation. We can obtain the equation that relates p and q by substituting the given values p = 9.6 and q = 3.  p = kq ⇒ 9.6 = k(3)

Solving for k:k = 9.6/3k = 3.2Now that we know k, we can substitute it back into the equation p = kq:p = 3.2q

This is the equation that relates p and q when p varies directly with q.

To confirm, let's check that it works for other values of p and q. If q = 2,p = 3.2(2) = 6.4If q = 5,p = 3.2(5) = 16

Know more about equation here,

https://brainly.com/question/29538993

#SPJ11

Answer:

\(23\)

Step-by-step explanation:

\(g+\frac{h}{7}\)

First, divide 36 by 7:

Add 14 and 9:

________________________

Answer:

14 cm

Step-by-step explanation:

The solution to the equation cos(2x + 45°) = 0.8 in the domain of 0° to 180° is x = 15° and X=139° or X=176 °

Because Cos (±37° +360k) = 0.8

0≤2X ≤ 360°

0+45°=2x+45° 360°+45° 45°≤ 2x+45°< 405°

50 2x+45° = 360°-37° or 2x+45° = 360° + 37°

{list the equation} 397° -45°=2X = 323-45°

2X = 323-45°. 2x=397° -45°

2x= 278°.         2x= 352°

X = 139°.          X=176°

So , x = 139° or x = 176°

To discover the solution set of an equation with a particular domain, first insert each domain value into the equation to obtain the associated range values. Make ordered pairs out of these values and put them down as a set. That set is your solution!

To learn more about Cos to refer

brainly.com/question/16498526

#SPJ1

Suppose we have a random sample X₁, X₂,..., Xn from a probability density function (PDF) f₀(x) defined as 1/x² if 0 < x < 1, and zero otherwise. In this case, we discuss its implications for the random sample.

The given PDF, f₀(x), is a continuous function defined over the interval (0, 1). It takes the value 1/x² for 0 < x < 1 and is zero elsewhere. This means that the PDF is unbounded as x approaches zero, and it approaches zero as x approaches infinity.

When we have a random sample X₁, X₂,..., Xn from this PDF, it means that each observation in the sample is independently and identically distributed according to f₀(x). The sample can consist of any positive values between 0 and 1, but cannot include values outside this range due to the zero density outside the interval.

To analyze this sample further, we can explore properties such as the sample mean, sample variance, or other statistical measures. However, it's important to note that the properties of this sample will depend on the specific values observed within the interval (0, 1) and the sample size, n. The behavior of the sample statistics will be influenced by the underlying distribution defined by the PDF f₀(x).

In summary, the given random sample X₁, X₂,..., Xn is generated from a probability density function that assigns a density of 1/x² for values within the interval (0, 1). Analyzing the properties and behavior of this sample will require examining specific observed values within the interval and considering the effects of the underlying PDF on the sample statistics.

Learn more about PDF here:

https://brainly.com/question/31039386

#SPJ11

Answer:

35 mm

Step-by-step explanation:

Formula:multiply the length value by 10

Answer:

0.35

Step-by-step explanation:

3.5÷10=0.35