What is the area of polygon XYZ?

Answer:

Step-by-step explanation:

Given that:

A simple random sample n = 28

sample standard deviation S = 12.65

standard deviation [tex]\sigma[/tex] = 11.53

Level of significance ∝ = 0.05

The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.

The null hypothesis and the alternative hypothesis can be computed as follows:

Null hypothesis:

[tex]H_0: \sigma^2 = \sigma_0^2[/tex]

Alternative hypothesis:

[tex]H_1: \sigma^2 \neq \sigma_0^2[/tex]

The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.

[tex]X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}[/tex]

[tex]X_0^2 = \dfrac{(28-1)(12.65)^2}{(11.53)^2}[/tex]

[tex]X_0^2 = \dfrac{(27)(160.0225)}{132.9409}[/tex]

[tex]X_0^2 = \dfrac{4320.6075}{132.9409}[/tex]

[tex]X_0^2 = 32.5002125[/tex]

[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}[/tex]

[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}[/tex]

From the chi-square probabilities table at 0.975 and degree of freedom 27;

[tex]X^2_{0.975 , 27}[/tex] = 14.573

[tex]X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}[/tex]

[tex]X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}[/tex]

From the chi-square probabilities table at 0.975 and degree of freedom 27;

[tex]X^2_{0.025 , 27}=[/tex] 43.195

Decision Rule: To reject the null hypothesis if [tex]X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}[/tex] ; otherwise , do not reject the null hypothesis:

The rejection region is [tex]X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573[/tex]

Conclusion:

We fail to reject the null hypothesis since  test statistic value 32.5002125  lies  between 14.573 and 43.195.

Step-by-step explanation:

here's the answer to your question

Answer:

259200

Step-by-step explanation:

so there are 86400 in one day. multiply by 3.

Answer:

259200

Step-by-step explanation:

60x24x3x60=

Answer:

1.56x+10.15

Step-by-step explanation:

Answer:

1.56x + 10.15

Step-by-step explanation:

(5.23x + 3.76) – (3.67x – 6.39)

(a + b) – (c – d) = a + b – c + d

Remove the parentheses and change the signs as needed:

5.23x + 3.76 – 3.67x + 6.39.

Group the like terms and simplify:

5.23x – 3.67x + 3.76 + 6.39

1.56x +10.15.

The simplified form of (5.23x + 3.76) – (3.67x – 6.39) is 1.56x + 10.15.

Answer:

Median: 14.6, Q1: 6.1, Q3: 27.1, IR: 21, outliers:  none

Step-by-step explanation:

Step 1: order the data from the least to the largest.

2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, 14.6, 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5

Step 2: find the median.

The median is the middle value, which is the 8th value in the data set.

2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, [14.6,] 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5

Median = 14.6

Step 2: Find Q1,

Q1 is the middle value of the lower part of the data set that is divided by the median to your left.

2.8, 3.9, 5.3, (6.1), 6.5, 7.1, 12.5, [14.6], 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5

Q1 = 6.1

Step 3: find Q3.

Q3 is the middle value of the upper part of the given data set.

2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, [14.6], 16.4, 16.4, 20.8, (27.1), 28.1, 30.9, 53.5

Q3 = 27.1

Step 4: find interquartile range (IR)

IR = Q3 - Q1 = [tex] 27.1 - 6.1 = 21 [/tex]

Step 5: check if there is any outlier.

Formula for checking for outlier = [tex] Q1 - 1.5*IR [/tex]

Then compare the result you get with the given values in the data set. Any value in the data set that is less than the result we get is considered an outlier.

Thus,

[tex] Q1 - 1.5*IR [/tex]

[tex]6.1 - 1.5*21 = -25.4[/tex]

There are no value in the given data set that is less than -25.4. Therefore, there is no outlier.

9514 1404 393

Answer:

  x = A/y

Step-by-step explanation:

Divide both sides of the equation by y

  A = xy

  A/y = (xy)/y . . . . . . divide by y

  A/y = x . . . . . . . . . .simplify

  x = A/y . . . . . . . . . write with x on the left

9514 1404 393

Answer:

  none

Step-by-step explanation:

Multiplying the second equation by -3 gives ...

  6x -3y = -24

Values of x and y that satisfy this equation cannot also satisfy the first equation ...

  6x -3y = 5

There are no solutions to this system of equations.

__

The equations describe parallel lines. There is no point of intersection.

Answer:

[tex]\frac{8}{5}[/tex]

Step-by-step explanation:

Given

7.2 : 4.5 ← multiply both parts by 10

= 72 : 45 ← divide both parts by 9

= 8 : 5

= [tex]\frac{8}{5}[/tex]

Answer:

z = 83/( -c+6-t)

Step-by-step explanation:

-cz + 6z = tz + 83

Subtract tz from each side

-cz + 6z -tz= tz-tz + 83

-cz + 6z - tz = 83

Factor out z

z( -c+6-t) = 83

Divide each side by ( -c+6-t)

z( -c+6-t)/( -c+6-t)  = 83/( -c+6-t)

z = 83/( -c+6-t)

Answer:

Could you ask your question in English?

Step-by-step explanation:

Answer:

Slope : 2

slope-intercept: y = 2x + 6

Point-slope (as asked): y - 4 = 2 (times) (x + 1)

standered: 2x - y = -6

Step-by-step explanation:

Answer:

insert values of x and y

r - ( -4(-4) - ( -3-3))

r - ( 16 +6 )

r - 22

Doneeeeeeeeeeeeeeeeee3

As your first step to this problem, change the minus sign to plus a negative.

So we have 8y + -9y.

8y + -9y simplifies to -1y which is our final answer.

Note that if you wrote -y instead, it means the same thing.

However, use the 1 to help avoid confusion if you need it.

Answer:

2/3

Step-by-step explanation:

We can find the slope using the slope formula

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

   = (1- -7)/(9 - -3)

   = ( 1+7)/( 9+3)

   = 8/12

Simplifying

   = 2/3

Answer:

C. 2/3

Step-by-step explanation:

You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.

y2 is equal to the y coordinate of the second point: 1

y1 is equal to the y coordinate of the first point: -7

x2 is equal to the x coordinate of the second point: 9

x1 is equal to the x coordinate of the first point: -3

So if you plug these values into the equation, you will get:

1 - (-7)/ 9- (-3)

= 1 + 7/ 9 + 3

= 8/12

= 2/3

Answer:

a?

Step-by-step explanation:

Answer:

  [tex]\dfrac{2x-11}{x-2}[/tex]

Step-by-step explanation:

Simplify the fractions, then add.

  [tex]-\dfrac{7}{x-2}+\dfrac{2x}{x}=\dfrac{-7}{x-2}+2=\dfrac{-7}{x-2}+\dfrac{2(x-2)}{x-2}\\\\=\dfrac{2x-4-7}{x-2}=\boxed{\dfrac{2x-11}{x-2}}[/tex]

_____

Note that this comes with the restriction that x ≠ 0.

Answer: it is a

Step-by-step explanation:

Answer:

Mr. Shim would record the number +10 or 10 for Ben because of the word "more".

For Gail, Mr. Shin would record the number -8 because of the word, "less''.

Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.

I hope this helps better

Answer:

P(1 |F) = 10/17

Step-by-step explanation:

Let events

1 = restaurant 1

2 = restaurant 2

F = full-time worker chosen

P = part-time worken chosen

P(1 and F) = 1/2 * 10/16 = 5/16

P(2 and F) = 1/2 * 7/16 = 7/32

P( (1 or 2) and F ) = P(F) = 5/16+7/32 = 17/32

P(1 | F)          Probability of choosing restaurant 1 given a full-time was chosen

= P(1 and F) / P(F)

= 5/16  / (17/32)

= 5/16 * 32/17

= 10 / 17

Answer:

14.13 cubic feet of lake water can fill the given balloon.

Step-by-step explanation:

concept used:

volume of sphere = 4/3 [tex]\pi r^3[/tex]

where r is the radius of sphere

we take [tex]\pi[/tex] = 3.14

_____________________________________

shape of balloon can be taken as spherical.

Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.

Given radius of balloon = 1.5 feet

Thus, volume of balloon = 4/3 [tex]\pi[/tex] 1.5^3 = 4/3*3.14*1.5^3

volume of balloon = 42.39/3 = 14.13 cubic feet

Thus, 14.13 cubic feet of lake water can fill the given balloon.

Answer:

t >± 1.895

t= 0.1705

Step-by-step explanation:

The null and alternative hypotheses are

H0: μd=0 Ha: μd>0

Significance level is set at ∝= 0.05

The critical region for  t  df=7       t >± 1.895

The test statistic under H0 is

t = d/ sd/ √n

Which has t distribution with n-1 degrees of freedom

Employee        After  Before         d = after - before        d²

1                          6         5               1                                  1

2                         6          2               4                               16

3                         7          1                6                               36

4                         7           3              4                               16

5                         4          3              1                                 1

6                         3          6              -3                               9

7                         5          3              2                               4

8                          6        7               -1                                1      

∑                                                    14                              84    

d`= ∑d/n= 14/8= 1.75

sd²= 1/8( 84- 14²/8) = 1/8 ( 84 - 24.5) = 59.5

sd= 7.7136

t= 3/ 7.7136/ √8

t= 0.1705

Since the calculated value of t= 0.1705 < ± 1.895  therefore reject the null hypothesis at 5 % significance level . On the basis of this we cannot conclude that the number of absences has declined.

9514 1404 393

Answer:

  (18 1/48)π ≈ 56.61 units

Step-by-step explanation:

Arc length is the product of radius and intercepted arc in radians:

  s = rθ

  s = (21 5/8)(5π/6) = (18 1/48)π ≈ 56.61 . . . units

Answer:

true

Step-by-step explanation:

what else would it be. that is exactly the reason why we have constants.

9514 1404 393

Answer:

  C. EGD

Step-by-step explanation:

A major arc is typically named using the end points and a point on the arc. Here, the end points are E and D, and points on the major arc include C, G, and F. The major arc ED could be named any of

Of course, the reverse of any of these names could also be used: DCE, DGE, DFE.

Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.

Step-by-step explanation:

Let's construct g(x) in baby steps.

Ok, we start with f(x) = x^2

The first thing we have is a horizontal translation of A units (where A is not known)

A vertical translation of N units to the right, is written as:

g(x) = f(x - N)

Then we have:

g(x) = (x - A)^2 = x^2 - 2*A*x + A^2

Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.

Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)

Then if we apply also a reflection over the x-axis, we have:

g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44

Then:

2*A = 16

A*A = 44.

The first equation says that A = 16/2 = 8

But 8^2 is not equal to 44.

Then we need another constant coefficient, which is related to a vertical translation.

If we have a relation y = f(x), a vertical translation of N units up, will be

y = f(x) + N.

Then:

g(x) = -f(x - A) + B

-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44

Now we have:

2*A = 16

-A^2 + B = - 44

From the first equation we have A = 8, now we replace it in the second equation and get:

-8^2 + B = -44

B = -44 + 64 = 20

Then we have:

The transformation is:

First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.

Answer:

hello attached is the missing part of your question and the answer of the question asked

answer : 0.2951

Step-by-step explanation:

Given data:

number of persons allowed in the elevator = 15

weight limit of elevator = 2500 pounds

average weight of individuals = 152 pounds

standard deviation = 26 pounds

probability that an individual selected weighs more than 166 pounds

std = 26 ,  number of persons(x) = 15, average weight of individuals(u) = 152 pounds

p( x > 166 ) = p( x-u / std,  166 - u/ std )

                  = p (  z > [tex]\frac{166-152}{26}[/tex] )

                  = 1 - p( z < 0.5385 )

p( x > 166 ) = 1 - 0.70488 = 0.2951

Answer:

-84 + 10i

Step-by-step explanation:

Standard Complex Form: a + bi

Step 1: Evaluate

√-100 = √-1 x √100 = i x 10 = 10i

-84 = -84

Step 2: Combine

10i - 84

Step 3: Rearrange

-84 + 10i

Answer:

Last Option

Step-by-step explanation:

√-100 - 84

(√(100×-1)) - 84

(√100)(√-1)-84

√-1 = i

10i - 84 or -84 + 10i

Answer:

meter

10 meters

Or

a dekameter

Answer:

15

Step-by-step explanation:

15 is the greatest number that divides 45 60 75 without leaving remainder

Answer:

15

Step-by-step explanation:

Let write the factors of each number:

45: (1,3,5,9,15,45)

60:(1,2,3,4,5,6,10,12,15,20,30,60)

75:(1,3,5,15,15,75).

The greatest common factor is 15. So the answer is 15.