Y = 9(x – 8)2 + 17 Standard form

Simplify the expression: 4(2 + 8v) =

yawa3891 [41]

Answer:

8 + 32v

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test th

lubasha [3.4K]

Answer:

33.293 ± 0.01= 33.303 and 33.383,

Step-by-step explanation:

We first need to fit a normal distribution , but neither the mean nor the standard deviation is given . We therefore estimate the sample mean and sample standard deviation s. Using the data we find ∑fx=378 and

∑fx²=1344 so that mean x` = 2.885 or 2.9 and standard deviation s =1.360

x f fx x² fx²

1 27 27 1 27

2 30 60 4 120

3 29 87 9 261

4 21 84 16 336

5 24 120 25 600

∑f=131 ∑fx=378 ∑fx²=1344

Mean = x`= ∑fx/ ∑f= 2.9

Standard Deviation = s= √∑fx²/∑f-(∑fx/∑f)²

s= √1344/131 - (378/131)²

s= √10.26-(2.9)²

s= √10.26- 8.41

s= √1.85= 1.360

Next we need to compute the expected frequencies for all classes and the value of chi square. The necessary calculations for expected frequencies , ei`s ( ei= npi`) where pi` is the estimate of pi together with the value of chi square are shown below.

Categories zi` P(Z<z) pi` Expected Observed

frequency ei Frequency Oi

1 -1.39 0.0823 0.0823 10.78 27

2 -0.66 0.2546 0.1723 22.57 30

3 0.07 0.5279 0.2733 35.80 29

4 0.808 0.7881 0.2602 34.08 21

5 1.54 0.937 0.1489 19.51 24

Next we need to compute the expected frequencies for all classes and the value of chi square. The necessary calculations for expected frequencies , ei`s ( ei= npi`) where pi` is the estimate of pi together with the value of chi square are shown below.

Categories Expected Observed (oi-ei)²/ei

frequency ei Frequency Oi OBSERVED VALUE

1 10.78 27 24.41

2 22.57 30 1.54

3 35.80 29 1.29

4 34.08 21 5.02

5 19.51 24 1.033

Total 131 33.293

There are five categories , we have used the sample mean and sample standard deviation , so the number of degrees of freedom is 5-1-2= 2

The critical region is chi square ≥ chi square (0.001)(2) =9.21

CONCLUSION:

Since the calculated value of chi square =9.21 does not fall in the critical region we are unable to reject our null hypothesis and conclude normal distribution provides a good fit for the given frequency distribution.

7 0

4 years ago

2x − 3y + 4z = 23 x + 2y − 4z = −10 3x − y + 2z = 19 2 -3 4 1 2 -4 3 -1 2 Correct: Your answer is correct. x y z = 23 −10 19 Fin

Annette [7]

Answer:

(x, y, z) = (4, -1, 3)

Step-by-step explanation:

To solve the system of equations:

2x − 3y + 4z = 23 .........................(1)

x + 2y − 4z = −10 ..........................(2)

3x − y + 2z = 19..............................(3)

Simultaneously, we do that by first eliminating one variable from any two equations to have an equation in two variables. The process is repeated with one of the used equations and the third unused equation to have a second equation in two variables. The two equations in two variables obtained can then be easily solved simultaneously.

Let us eliminate z from (1) and (2)

Add (1) and (2)

(1) + (2):

3x - y = 13 ........................................(4)

Multiply (3) by 2

(3) × 2

6x - 2y + 4z = 38 ............................(5)

Add (5) and (2)

(5) + (2):

7x + 0 + 0 = 28

x = 28/7 = 4

Putting this in (4)

3(4) - y = 13

y = 12 - 13 = -1

Putting this in (3)

3(4) - 4(-1) + z = 19

z = 19 - 16 = 3

Therefore,

(x, y, z) = (4. -1, 3)

7 0

3 years ago

In which step did Rena make the first error? Step 1 Step 2 Step 3 Step 4

Komok [63]

The only step that arena make wrong is step number 2

4 0

3 years ago

You flip a coin 100 times in the air and find that it lands on heads 65 times. Determine the theoretical and experimental probab

scoundrel [369]

Answer:

The experimental probability --> $\frac{13}{20}$

The theoretical probability --> $\frac{1}{2}$

Step-by-step explanation:

Key skills needed: Experimental vs theoretical probability, Fractions

1) The first thing you need to understand is experimental probability vs theoretical probability. (Do not include this in your work!!)

- Theoretical probability is based on simple reasoning

- Experimental probability is based on the results a person gets (so the experiment you did by flipping the coin)

2) Now with this, let's start solving:

Experimental probability ---> $\frac{heads}{total}$ --> You flipped the coin a total of 100 times, so the denominator would be 100. 65 of those would be heads so 65 is our numerator.
So our experimental probability is --> $\frac{65}{100}$ --> Both have the factor of 5, so take the factor of 5 out of the numerator and denominator and you will get --> $\frac{13}{20}$
Now onto theoretical probability --> $\frac{heads}{total}$ --> There are 2 faces of a coin, 1 side is heads, and 1 side is tails --> The total number of faces is 2, so 2 is our denominator. There is only 1 side that is heads, so 1 is the numerator. This means --> Our theoretical probability is $\frac{1}{2}$

Hope you understood and have a nice day!! :D

5 0

3 years ago

Read 2 more answers