Tiffany ate 1/4 of a pizza. If there were 16 slices of pizza to begin with, how many slices did Tiffany eat?

With a perfectly balanced roulette wheel, in the long run, red numbers should turn up 18 times in 38. To test its wheel, one cas

topjm [15]

Answer:

a) more than 18/38

b) The null says that the percentage of reds in the box is 2842.105. The alternative says that the percentage of reds in the box is -0.933521

c) z= -0.933521 , p≤ z= 17.105%

d) p-value is 17%

Step-by-step explanation:

1. We are counting the number of reds, so we have a box with "1" s for reds and "0"s for others. The question is what proportion of 1's and 0' are in the box.

a) The null hypothesis is that the wheel is balanced, so the box contains 18 "1"s and 20 "0"s. Or you might state this in terms of the proportion of 1's (18/38) and 0's (20/38). The alternative hypothesis if that the wheel favors reds, so the proportion of 1's is more than 18/38.

b) Under the null hyp., we expect 6000*(18/38)= 2842.105 Reds. The SE is sqrt(6000)* SD(Box)= Sqrt(6000)*(1-0)*sqrt((18/38)*(20/38))= 38.67615. We observed2806, which is fewer than we expected. The question is , is it much fewer that we suspect foul play, or it is the usual sort of variation we expect due to chance? The test statistic is z=(obs-expected)/SE =(2806-2842.105)/38.67615= -0.933521.

c) The p-value is the probability of gettinga test statistic as extreme or morer extreme than this, which in this case means seeing a test statistic less than or equal to - 0.933521. The closest value gives a probability of (100-65.79)/2 = 17.105%

d) If we reject H0 and claim the roullette wheel is unfair, then there's a 17.105% chance we are wrong. This is a large probability of making a serious mistake, and it would be reasonable to not reject and conclude that there is insufficient evidence to suspect the wheel is unfair. (we would reject H10 if the p-value were less than 5%. Since it is 17%, we won't reject)

6 0

2 years ago

Compute i^1+i^2+i^3....i^99+i^100

fgiga [73]

Good morning ☕️

Answer:

Step-by-step explanation:

Consider the sum S = i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰

S = i¹ + i² + i³ + . . . + i⁹⁹ + i¹⁰⁰

S = a₁ + a₂ + a₃ +. . . + a₉₉ + a₁₀₀

then, S is the sum of 100 consecutive terms of a geometric sequence (an)

where the first term a1 = i¹ = i and the common ratio = i

FORMULA:______________________

$S=(term1)*\frac{1-(common.ratio)^{number.of.terms}}{1-(common.ratio)}$

_______________________________

then

$S=i*\frac{1-i^{100} }{1-i}$

or i¹⁰⁰ = (i⁴)²⁵ = 1²⁵ = 1 (we know that i⁴ = 1)

Hence

S = 0

7 0

2 years ago

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which

Dmitrij [34]

Answer: All the real values except x ≠ 7 and the x for which f(x)≠-3

Step-by-step explanation:

Since, For function f , the domain is R - {7}

That is, If x is any element of the domain of the function f,

Then, x ≠ 7

(gof)(x) = g(f(x))

Since, For the function g, the domain is R - {-3}

Thus, If f(x) is any element of the domain of the function g,

Then f(x)≠ -3

Hence, Fourth Option is correct.

8 0

2 years ago

There are 8 soccer matches per day at Greenville's annual soccer tournament, which lasts 17 days. Estimate the number of soccer

Gnesinka [82]

Answer:

140

Step-by-step explanation:

8 per day

17 days

8*17 = 136 soccer matches in the tournament

136 rounded to the nearest 10 = 140

7 0

2 years ago

Tia Veronica Pam and Lily are sisters. Tia is eight years old and she’s two years older than Pam. Pam is five years younger than

Nastasia [14]

Answer:

Pam (6 years), Tia(8 years), Veronica(11 years) , Lily (15 years)

Step-by-step explanation:

Age of Tia = 8 years

______________________________________________

Given Tia is 2 years older than Pam

mathematically

age of Pam + 2 years = age of Tia

age of Pam + 2 years = 8 years

age of Pam = 8 years- 2 years = 6 years

______________________________________________

Given Pam is five years younger than Veronica

we can infer that age of veronica is age of Pam + 5 more years

mathematically

age of Pam + 5 years = age of Veronica

6 years + 5 years = age of Veronica

age of Veronica = 11 years

______________________________________________

Given Veronica is four years younger than Lily

we can infer that age of Veronica is (age of Lily - 4 years)

mathematically

age of Veronica = age of lily - 4 years

11 years = age of lily - 4 years

age of lily = 11 years + 4 years = 15 years

age of lily = 15 years

______________________________________________

Arranging the list from youngest to oldest we have

age of Pam = 6 years

Age of Tia = 8 years

age of Veronica = 11 years

age of lily = 15 years

Arranging sisters in order of youngest to oldest

Pam, Tia, Veronica , Lily

3 0

2 years ago

Tiffany ate 1/4 of a pizza. If there were 16 slices of pizza to begin with, how many slices did Tiffany eat?​

Tiffany ate 1/4 of a pizza. If there were 16 slices of pizza to begin with, how many slices did Tiffany eat?