ABC
ABCD ]````````````````````` .```````````````````[

Answer:

a) [tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]

[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]

Now we just take square root on both sides of the interval and we got:

[tex] 19.08 \leq \sigma \leq 66.56[/tex]

b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Step-by-step explanation:

423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0

Part a

The confidence interval for the population variance is given by the following formula:

[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]

On this case we need to find the sample standard deviation with the following formula:

[tex]s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}

And in order to find the sample mean we just need to use this formula:

[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}[/tex]

The sample deviation for this case is s=30.23

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

[tex]df=n-1=9-1=8[/tex]

The Confidence interval is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and the critical values are:

[tex]\chi^2_{\alpha/2}=20.09[/tex]

[tex]\chi^2_{1- \alpha/2}=1.65[/tex]

And replacing into the formula for the interval we got:

[tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]

[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]

Now we just take square root on both sides of the interval and we got:

[tex] 19.08 \leq \sigma \leq 66.56[/tex]

Part b

For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Answer:

  (x, y, z) = (1, -3, 1)

Step-by-step explanation:

Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:

  (x, y, z) = (1, -3, 1)

__

Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.

Using the first equation to write an expression for z, we have ...

  z = 4x +3y +6

Substituting that into the second and third equations gives ...

  6x -y +3(4x +3y +6) = 12   ⇒   18x +8y = -6

  8x +2y +4(4x +3y +6) = 6   ⇒  24x +14y = -18

Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:

  3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)

  10y = -30

  y = -3

Substituting into the first equation (of the equations in x and y), we have ...

  18x +8(-3) = -6

  18x = 18

  x = 1

Finally, substituting into the equation for z gives ...

  z = 4(1) +3(-3) +6 = 1

The solution is (x, y, z) = (1, -3, 1).

___

The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.

Answer: [tex]x = \frac{35}{2}[/tex] or [tex]x = 17.5[/tex]



Step-by-step explanation:

[tex]\frac{4}{7} = \frac{10}{x}[/tex]

[tex]\frac{4x}{4} = \frac{70}{4}[/tex]

[tex]x = \frac{35}{2}[/tex]

or [tex]x = 17.5[/tex]

Answer:

The temperature difference in 5 minutes will be 12.38ºC

Step-by-step explanation:

The difference in temperature after t minutes is given by the following equation:

[tex]T(t) = T(0)(1-r)^{t}[/tex]

In which T(0) is the initial temperature and r is the decrease rate, as a decimal.

Decreases by 5% every minute.

This means that [tex]r = 0.05[/tex]

What will the temperature difference be in 5 minutes if it is currently 16°C

This is T(5) when [tex]T(0) = 16[/tex]

So

[tex]T(t) = T(0)(1-r)^{t}[/tex]

[tex]T(t) = 16(1-0.05)^{t}[/tex]

[tex]T(t) = 16*(0.95)^{t}[/tex]

[tex]T(5) = 16*(0.95)^{5} = 12.38[/tex]

The temperature difference in 5 minutes will be 12.38ºC

Answer:

XY = 5268

Step-by-step explanation:

XY = XZ (originating from the same point)

85b+83=91b-283

85b-91b=-283-83

-6b=-366

Dividing both sides by -6

b = 61

Now

XY = 85b+83

= 85(61)+83

= 5268

this one is kinda Hard ill do sum research and help

Answer:

1 hour

Step-by-step explanation:

From Distance = speed × time

time = Distance/ speed

=66/66 = 1 hour

Answer:

8

Step-by-step explanation:

[tex] a = 1 - \sqrt{2} [/tex]

[tex] (a - \dfrac{1}{a})^3 = [/tex]

[tex] = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 [/tex]

[tex] = (\dfrac{a^2 - 1}{a})^3 [/tex]

[tex] = (\dfrac{(a + 1)(a - 1)}{a})^3 [/tex]

[tex] = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 [/tex]

[tex]= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3[/tex]

[tex] = 2^3 [/tex]

[tex] = 8 [/tex]

Answer:

by finding something to factor it by

Answer:

1) first eliminate constant (number without variable) you eliminate constant by doing the inverse operation (if constant is being added, then subtract) (if constant is being subtracted, then add it)

ex: if  x+9=32

subtract 9 from both sides to get rid of it

x=23

2) if there is another constant but this constant is being multiplied/divided then do the opposite operation to remove it

you could multiply by 3 on both sides:

x+9=69

x=60

Answer:

24?

Step-by-step explanation:

Answer:

It's B I think.

Step-by-step explanation: If they the lines intersected then it'd mean they crashed.

The graph below shows a recent 10-meter race between two remote-control automobiles. The racial assertions in A, B, and C are true.

A graph that shows the relationship between two or more variables, each of which is measured along one of two axes that are at right angles to one another.

At 6 meters into the race, the blue car overtook the red car because, at that moment, the blue car had a bigger distance than the red car.

Due to the greater slope of the blue vehicle's path compared to the red car's line, the blue car is faster.

Because the blue car's x-intercept is at (3, 0), where x stands for time and y for distance from the starting line, it began 3 seconds later than the other cars.

Hence Statements B, C, and D about race are true.

Q.The graph below represents a recent 10-meter race between two remote control cars.

A graph titled Remote Control Car Race has seconds after the race starts on the x-axis and distance from the start line (meters) on the y-axis. A line labeled red car goes through (3, 2) and (6, 4). A line labeled blue car goes through (3, 0) and (5, 2).

Which statements about race are true? Check all that apply.

The red car won the race because it started above the blue car.

The cars crashed 9 seconds into the race because that is the point of intersection, and neither car continued on after that point in time.

The blue car passed the red car at 6 m into the race because that is the point of intersection, and the blue car has a greater distance than the red car after that time.

The blue car is faster because the slope of its line is steeper than the slope of the line representing the red car.

The blue car started 3 seconds late because it has an x-intercept of (3, 0) and x represents the time and y represents the distance from the starting line.

learn more about graphs here :

https://brainly.com/question/10712002

#SPJ6

Answer:

(A)129 Pounds

Step-by-step explanation:

Let x be the number of 23% zink alloy

Therefore:

Since the total result is 516 pounds

The number of pounds of 42% zink alloy =516-x pounds

We then have the resulting equation:

0.23x+0.42(516-x)=0.3725*516

0.23x+216.72-0.42x=192.21

Colect like terms

0.23x-0.42x=192.21-216.72

-0.19x=-24.51

Divide both sides by 129

x=129 pounds

Therefore, the number of pounds of 23% zink alloy that must be mixed is 129 pounds.

Answer:

  D.  129°

Step-by-step explanation:

Angles XZY and XZV form a linear pair, so are supplementary.

 angle XZV = 180° -51° = 129°

Answer: Infintely many

Step-by-step explanation:

5(x + 10) - 25 = 5x + 25

5x +50 - 25 = 5x + 25

5x +25 = 5x + 25

Same equation

Two shaped are merged so

One is square and the other is trapezoid so,

AREA OF SQUARE=4*4

=16

AREA OF TRAPEZOID=(2+4)x4/2

So,rhe answer will be

12+16=28

HOPE IT IS HELPFUL

Answer: 28 units^2

Step-by-step explanation:

You basically have a square and a trapezoid merged together

4*4=16 for the square

(2+4)*4/2=12 for the trapezoid

so

12+16=28 is your answer

Answer:

22 is the answer but which country are you from

Answer:

22

Step-by-step explanation:

Answer:

Domain: [-3, 5]

Range: [-5, 4]

Step-by-step explanation:

The first thing is to define what is the domain and the range. The domain of a function f (x) is the set of all the values for which the function is defined, and the range of the function is the set of all the values that f takes.

In other words, the domain is the value on the "x" axis and the range is the value on the "y" axis.

In this case, both are an interval, the domain would be from -3 to 5 and in the case of the range it would be from -5 to 4.

Domain: [-3, 5]

Range: [-5, 4]

Answer:

5 times

Step-by-step explanation:

There is a 1/2 (50%) chance each time it is flipped that it will land on heads. Therefore, if flipped 10 times, 1/2 of 10 is 5

Answer:

2.08 x 10^11

Step-by-step explanation:

To put a number into scientific notation you move the decimal to the spot right after the first digit. To figure out what the power is you count how many digits you moved it past in order to get to the spot you want it (right after the first digit; in this case the 2)

So in this case you would move the decimal from the end of the number backwards past 9 zeros, the 8, and another zero, which is a total of 11 digits.

From there you take the number with the new decimal place and multiply by 10 to the power of the number you counted earlier, which for this example is 11

So the final answer is 2.08 x 10^11

Answer:

-6ab^3sqrtac^2 option b

Step-by-step explanation:

i just did it

Answer:

Step-by-step explanation:

Answer:

[/tex]y2=e^(-x)[/tex]

Step-by-step explanation:

CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION

Answer:

7

Step-by-step explanation:

∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹)

This is the sum of the first 3 terms of the sequence.

The first 3 terms are:

4 × (½)¹⁻¹ = 4

4 × (½)²⁻¹ = 2

4 × (½)³⁻¹ = 1

So the sum is:

∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹) = 4 + 2 + 1 = 7

Answer:

y = x/6 - 17/6

Step-by-step explanation:

     x - 6y = 17

<=>6y = x - 17  

<=> y  =x/6 - 17/6

Hope this helps!

Answer: The system of equations is:

x + 2y + 2 = 4

y - 3z = 9

z = - 2

The solution is: x = -22; y = 15; z = -2;

Step-by-step explanation: ONe way of solving a system of equations is using the Gauss-Jordan Elimination.

The method consists in transforming the system into an augmented matrix, which is writing the system in form of a matrix and then into a Row Echelon Form, which satisfies the following conditions:

For this question, the matrix is a Row Echelon Form and is written as:

[tex]\left[\begin{array}{ccc}1&2&2\\0&1&3\\0&0&1\end{array}\right][/tex][tex]\left[\begin{array}{ccc}4\\9\\-2\end{array}\right][/tex]

or in system form:

x + 2y + 2z = 4

       y + 3z = 9

               z = -2

Now, to determine the variables:

z = -2

y + 3(-2) = 9

y = 15

x + 30 - 4 = 4

x = - 22

The solution is (-22,15,-2).

Answer:

a) margin of error ME = 5.77

b) Margin of error becomes smaller

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-ME

Where margin of error ME = zr/√n

a)

Given that;

Mean = x

Standard deviation r = 25

Number of samples n = 72

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

ME = 1.96(25/√72)

ME = 1.96(2.946278254943)

ME = 5.774705379690

ME = 5.77

b)

For n = 89

ME = 1.96(25/√89)

ME = 1.96(2.649994700015)

ME = 5.193989612031

ME = 5.19

5.19 is smaller than 5.77 in a) above. So,

Margin of error becomes smaller

Answer:

C: x = 10

Step-by-step explanation:

PO = QR (so having equal central angles)

Now

4x-11 = 2x+9

4x-2x = 9+11

2x = 20

Dividing both sides by 2

x = 10

Answer:

x=10

Step-by-step explanation:

2x+9=4x-11

-2x      -2x

9=2x-11

+11  +11

20=2x

:2     :2

x=10

Answer:

  5.972 cm

Step-by-step explanation:

Using implicit differentiation, we have ...

  0 = (2πr +π(√(r^2+h^2) +r^2/√(r^2+h^2))·dr/dh +πrh/√(r^2+h^2)

For the given values of r and h, this is ...

  0 = (12π +π(10 +36/10))dr/dh +48π/10

  dr/dh = -4.8/(12+13.6) = -0.1875

Then the tangent line is ...

  r = -0.1875(h -8) +6

__

For a height of 8 +15/100 = 8.15, the estimated value of r is ...

  r = -0.1875(8.15 -8) +6 = -0.1875(0.15) +6 = 5.971875

The estimated value of r is 5.972 cm.

Answer:

1/8

Step-by-step explanation:

Answer:

When you simplify it, you get the answer of 1.

Step-by-step explanation:

Order of operation rules are required that you multiply and divide before you carrying out addition and/or subtraction.

So, simplify 2/3 / (-4) first, obtaining -1/6.

Now, you have -1/6 - 1/6 + 8/6, which combines to 1 or 6/6.

Answer:

Step-by-step explanation:If you choose any 3 of the 7 vertices, you can connect them with lines to create a unique triangle.

So, the question becomes "In how many different ways can we select 3 vertices from 7 vertices?"

Since the order in which we select the 3 vertices does not matter, we can use COMBINATIONS.

We can select 3 vertices from 7 vertices in 7C3 ways.

Answer:

my butt

Step-by-step explanation:

my poop

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