To solve the system of linear equations 8 x + 5 y = 18 and 6 x + y = negative 2. By using the linear combination method, Amos decided that he should first multiply the second equation by –5 and then add the two equations together to eliminate the y-terms. His calculations are as shown. 8 x + 5 y = 18. + 6 x minus 5 y = 10. 14 x = 28. StartFraction 14 x Over 14 EndFraction = StartFraction 28 Over 14 EndFraction. X = 2. 6 x + y = negative 2. 6 (2) + y = negative 2. 12 + y = negative 2. 12 + y minus 12 = negative 2 minus 12. Y = negative 14. Amos's solution is (2, –14). What did he do wrong?

To find the skewness of x, we need to first determine its probability density function (PDF) and its moments. Since x is a continuous uniform random variable with a minimum value of 1 and a maximum value of 1, its PDF is simply a constant function over the interval [1, 1]:

f(x) = 1/(1-1) = 1, for 1 ≤ x ≤ 1
     = 0, otherwise

The first moment of x is: μ₁ = E[X] = ∫₁¹ x*f(x) dx = ∫₁¹ x dx = 1/2

The second moment of x is: μ₂ = E[X²] = ∫₁¹ x²*f(x) dx = ∫₁¹ x² dx = 1/3

The third moment of x is: μ₃ = E[X³] = ∫₁¹ x³*f(x) dx = ∫₁¹ x³ dx = 1/4

Using these moments, we can calculate the skewness of x: γ₁ = (μ₃ - 3μ₁μ₂ + 2μ₁³) / σ³

where σ² = μ₂ - μ₁² is the variance of x. Plugging in the values we found earlier, we get: σ² = 1/3 - (1/2)² = 1/12
γ₁ = (1/4 - 3(1/2)(1/3) + 2(1/2)³) / (1/12)^(3/2) = 0

Therefore, the skewness of x is zero, which means that its distribution is perfectly symmetrical around its mean.

To know more about skewness visit:

https://brainly.com/question/32067372

#SPJ11

Answer:

Step-by-step explanation:

4x - 25 = 75° (opposite angles)

4x= 75+25

4x= 100

x= 100/4= 25°

Answer:

It’s 3 because 24 divide by 8 is 3

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

for such more question on system of equations

https://brainly.com/question/4262258

#SPJ8

The equation that relates dA/dt to dr/dt for a circle with radius R and area a = πr^2 is: dA/dt = 2πR * (dR/dt).

To derive this equation, we start with the formula for the area of a circle:

a = πr^2

Taking the derivative of both sides with respect to time, we get:

dA/dt = 2πr * (dr/dt)

But we want to express dA/dt in terms of R and dR/dt, so we need to substitute r = R into this equation. Using the fact that a = πR^2, we can solve for r in terms of R:

r = sqrt(a/π) = sqrt(R^2) = R

Substituting r = R and simplifying, we arrive at the equation:

dA/dt = 2πR * (dR/dt)

This equation allows us to relate the rate of change of the area of a circle to the rate of change of its radius, which can be useful in various applications such as physics, engineering, and geometry.

Learn more about area of circle here:

https://brainly.com/question/11952845

#SPJ11

Answer:

11x11 is 121

11 x 11 can also be rewritten as 11^2.

Answer:

121

Step-by-step explanation:

There are two ways to doing this.

1.  multiplying double digits using the traditional algorithm

A small p-value provides strong evidence against the null hypothesis. The null hypothesis is the hypothesis that there is no significant difference or relationship between two variables.

The p-value is the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.
If the p-value is small, typically less than 0.05, it means that the observed result is unlikely to have occurred by chance alone if the null hypothesis is true. This suggests that there is strong evidence against the null hypothesis and that we should reject it in favor of the alternative hypothesis. .
For example, if we conduct a hypothesis test to determine whether a new drug is more effective than a placebo, a small p-value would indicate that the drug is indeed more effective. This is because the observed results are highly unlikely to occur if the drug is not effective.
In summary, a small p-value provides strong evidence against the null hypothesis and supports the alternative hypothesis. It suggests that the observed results are not due to chance and that there is a significant difference or relationship between the variables being studied.

To know more about Value visit:

https://brainly.com/question/19881297

#SPJ11

Answer:

Step-by-step explanation:

25x3x15

The inverse of the secant function is the arcsecant function, also known as the inverse secant or the arccosecant.

The secant function is defined as the reciprocal of the cosine function, while the arcsecant function is defined as the inverse of the secant function.

The arcsecant function takes a value as its argument and returns an angle whose secant is equal to the input value. In other words, it answers the question "What angle has a secant equal to x?"

The domain of the arcsecant function is limited to values greater than or equal to 1 and less than or equal to -1. The range of the function is typically limited to values between 0 and pi or between -pi/2 and pi/2, depending on the convention used.

The notation for the arcsecant function is usually "arcsec(x)" or "asec(x)". It is an important mathematical function in trigonometry, and is used in many applications, including physics, engineering, and computer graphics.

To learn more about click trigonometry on,

https://brainly.com/question/1447063

#SPJ4

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

here click on my files.com/3_& and it should give you the answer

Answer:28

Step-by-step explanation:

Break it up! 6x3 is 18. Then 18 + 10 is 28 :P

Hope this helps :D

Answer:

f. 85

Step-by-step explanation:

All triangles add up to 180 degrees

BCE=25

then you need to find DBC, you can do that since ABD is isocilies that means all sides are equal in length and angle so 180 divided by 3 (number of side) is 60

isoceles triangle have 2 sides that are equiangular, cince we know BCA is 25 we also know BAC is 25, leaving angle ABC to be 130 (180-50=130)

we subtract angle ABD from angle ABC to get angle DBC, leaving angle DBC to equal 70 degrees

since 70 (angle DBC) + 25 (Angel BCA)= 95

we just subtrract 95 from 180 to get the answer 85 (:

Answer:

85 degrees

Step-by-step explanation:

if Δ ABD is equilateral  then the 3 sides and three angles are equal

sum of angles of Δ=180

180/3=60 degrees (∠A,∠B,∠D)

ΔBCA is isosceles then the two angles A and C are equal = 25

∠B=180-50=130

∠B in Δ BEC=130-60=70

∠E+∠B+∠C in Δ BEC=180

∠E= 180-70-25=85 degrees

Answer:

Step-by-step explanation:

Looking at the tables, we observe that:

Answer:

The answer is D.

Step-by-step explanation:

If the sample size were n=48, the margin of error would be larger.  Part 1 of 2: Margin of error is used to measure the accuracy level of the population parameter based on the given sample statistic.

It is the range of values above and below the point estimate, which is the sample mean and represents the interval within which the true population mean is likely to lie at a certain level of confidence.

The formula to calculate margin of error is:

Margin of error (ME) = z*(σ/√n)

Where, z is the z-score representing the level of confidenceσ is the standard deviation of the population n is the sample size From the given information, Sample size,

n = 61

Standard deviation, σ = 6

Confidence level, 99%

The z-score for 99% confidence level can be found by using the formula as shown below:

z = inv Norm(1-(α/2))

=  inv Norm(1-(0.01/2))

= inv Norm(0.995)

≈ 2.576Substituting the values into the formula of the margin of error,

Margin of error (ME) = z*(σ/√n) = 2.576*(6/√61) = 1.967 ≈ 1.967

So, the margin of error for a 99% confidence interval for μ is 1.967.

Part 2 of 2: If the sample size were n = 48, the margin of error will be larger because of a lower sample size. As the sample size decreases, the accuracy level decreases, resulting in the wider range of possible values to represent the population parameter with the same level of confidence. This leads to a larger margin of error. The formula for margin of error shows that the sample size is in the denominator. So, as the sample size decreases, the denominator gets smaller and hence the value of margin of error increases.  

To know more about statistic  visit:-

https://brainly.com/question/32201536

#SPJ11

Answer: Pretty sure it is perpendicular.

Step-by-step explanation:

If B is perpendicular to A and B and C are parallel, that means C is also perpendicular to A. Since D is perpendicular to C, it is parallel to A. E is perpendicular to D, so it goes back to perpendicular to A.

Answer:y ≥ 15 − 5x

Step-by-step explanation:

Answer:

$7.20

Step-by-step explanation:

The linear equation is y= 0.07x + 5.1.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

For 15 minutes, costs= $4.05

For 40 minutes, costs= $5.80

slope of the linear equation

slope= \((y_2- y_1)/ (x_2- x_1)\)

slope= (5.80- 4.05)/(40-15)

slope= 1.75/25

slope= 175/ 25 x 100

slope= 7/100

slope= 0.07

and, the linear equation

y- 4.05= 0.07(x- 15)

y- 4.05= 0.07x - 1.05

y= 0.07x + 5.1

Hence, the linear equation is y= 0.07x + 5.1.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ2

The value of the given expression will be 3√5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression c² = 45 will be solved as below:-

c² = 45

Take the square root of the number 45.

c = √45

c = √ 9 x √5

c = 3√5

Therefore, the value of the given expression will be 3√5.

To know more about an expression follow

https://brainly.com/question/738531

#SPJ1

Answer:

The domain is;

{-4,-9,-4,8}

The range is

{2,-5,12,-8}

Step-by-step explanation:

The domain refers to the values of the function on the x-axis while the range refers to the values of the function on the y-axis

The domain is thus;

{-4,-9,-4,8}

The range is;

{2,-5,12,-8}

Answer:

9

Step-by-step explanation:

9 squared + 12 squared= 15 squared

Answer:

hi

Step-by-step explanation:

we can do this with Pthyagorean teorem

\( {12}^{2} + {x}^{2} = {15}^{2} \\ 144 + {x}^{2} = 225 \\ {x}^{2} = 225 - 144 \\ {x}^{2} = 81 \\ x = \sqrt{81} \\ x = 9 \: cm\)

BC is 9

hope it helps

have a nice day

Answer:

24 miles

Step-by-step explanation:

Let the number of miles = x.

U-Haul:

1.89x + 20.95

Public Storage:

1.19x + 37.95

Set the costs equal and solve for the mileage, x.

1.89x + 20.95 = 1.19x + 37.95

0.7x = 17

x = 24.29

Answer: 24 miles

The correct option is A. The volume is 6.77 cubic units

The function and interval given are f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6].

We want to find the volume of the solid of revolution when the region is rotated about the x-axis.

Let's consider the graph of the function: graph{(x-1)^(-1/4) [-10, 10, -5, 5]}

To set up the integral to find the volume of the solid of revolution, we can use the disk method.

We need to integrate the area of each disk perpendicular to the x-axis from x = 1 to x = 6.

The area of a disk is given by the formula: A = πr²

where r is the radius of the disk and is equal to f(x) in this case.

Therefore, the area of a disk is: A = πf(x)²

Let's substitute f(x) into this formula and integrate from x = 1 to x = 6 to get the volume of the solid.

We have The integral that should be used to find the volume of the solid is given as:

V = ∫₁⁶ πf(x)² dx

We substitute f(x) = (x - 1)^(-1/4) into this expression and integrate to get the volume.

We have: V = ∫₁⁶ π(x - 1)^(-1/2) dx

Let u = x - 1, so that du/dx = 1 and dx = du.

When x = 1, u = 0, and when x = 6, u = 5.

Therefore, we have: V = ∫₀⁵ πu^(-1/2) du= 2π[u^(1/2)]₀⁵= 2π(√5 - 1) ≈ 6.77 cubic units.

The volume of the solid of revolution when the region is rotated about the x-axis is approximately 6.77 cubic units.

Thus, the correct option is A. The volume is 6.77 cubic units.

To know more about disk method visit:

https://brainly.com/question/28184352

#SPJ11

Answer:

30%

Step-by-step explanation:

smart highschooler brain

There are two possible answers

There are two answers because there are 2 points given. Both equations convert to the slope intercept form equation y = (3/8)x + 29/8

=================================================

Work Shown:

First we need the slope

m = (y2 - y1)/(x2 - x1)

m = (1-4)/(-7-1)

m = -3/(-8)

m = 3/8

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

Using this slope along with the point (x1,y1) = (1,4) gets us the following equation

y - y1 = m(x - x1)

y - 4 = (3/8)(x - 1)

which is one way to express the equation in point-slope form

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

Or we could easily use the other point as (x1,y1). The order of the points does not matter.

y - y1 = m(x - x1)

y - 1 = (3/8)(x - (-7))

y - 1 = (3/8)(x + 7)

is another valid answer.

Math is considered to have a sequential learning pattern because concepts and skills are introduced in a specific order, building upon previously learned material.

In math, concepts and skills are typically organized in a sequential manner, where each new topic builds upon what has been previously learned. This sequential learning pattern allows students to develop a solid foundation and gradually progress to more advanced topics.

For example, in elementary school, students first learn basic arithmetic operations like addition and subtraction before moving on to multiplication and division. These foundational skills are essential for understanding more complex mathematical concepts later on, such as algebra, geometry, and calculus. By following a sequential learning pattern, students can gradually develop their mathematical understanding and problem-solving abilities. They are able to connect new concepts to what they have already learned, reinforcing their knowledge and enabling them to apply it in different contexts. This sequential approach also ensures that students have the necessary prerequisite knowledge and skills to comprehend more advanced mathematical concepts. It helps create a logical progression in mathematical education, allowing students to build upon their previous knowledge and continually expand their mathematical abilities.

learn more about calculus here:
https://brainly.com/question/22810844

#SPJ11

Answer:

a. sin 300 = -∛3/2, cos 300 = 1/2

b. sin -225 = √2/2, cos -225 = √2/2

c. sin 5π/6 = 1/2, cos 5π/6 = -3√2

d. sin -4π/3 = √3/2, cos -4π/3 = -1/2

Step-by-step explanation:

See unit circle

Answer:

0.05, 0.2, 0.48, 0.6

Hope it helps

Answer:

A

Step-by-step explanation:

0.05 < 0.2 < 0.48 < 0.6

Answer:

there were 200 children and 500 adults at the show

Step-by-step explanation:

7x+10y=6400

x+y=700

x=700-y

7(700-y)+10y=6400

4900-7y+10y=6400

-7y+10y=1500

3y=1500

y=500

x=700-y

x=700-500

x=200

the Answer:

200 Children & 500 Adults

Step-by-step explanation:

(A) Set up two equations from the given info:

1) 7C + 10A = 6,400 (amount of money brought in)

2) C + A = 700 (the total amount of people in attendence)

(B) set up a substitution:

A = 640 - 0.7C (can also solve for C, but in this case would be more difficult)

(C) use substitution in the second equation:

C+(640-0.7C)= 700

(D) do the algebra and solve for C:

C= 200

(E) insert the actual value of C back into the equations and solve for A:

200+A = 700 so A=500 (again, you could use either equation, this one is just simpler)

HOPE THIS HELPS!

Answer:

x<-1

Step-by-step explanation:

-5(x-1)>10, distribute the -5

-5x+5>10, subtract 5 from both sides

-5x>5, divide by -5

x<-1

(When you divide an inequality by a negative, the sign flips)