Is the function even, odd, or neither?

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 380 babies were born, a

Alex Ar [27]

Answer:

The 99% confidence interval estimate of the percentage of girls born is (86.04%, 93.96%). Considering the actual percentage of girls born is close to 50%, the percentage increased considerably with this method, which means that it appears effective.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

In the study 380 babies were born, and 342 of them were girls.

This means that $n = 380, \pi = \frac{342}{380} = 0.9$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{380}} = 0.8604$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{380}} = 0.9396$

As percentages:

0.8604*100% = 86.04%.

0.9396*100% = 93.96%.

The 99% confidence interval estimate of the percentage of girls born is (86.04%, 93.96%). Considering the actual percentage of girls born is close to 50%, the percentage increased considerably with this method, which means that it appears effective.

4 0

3 years ago

Sarah is carrying out a series of experiments which involve using mcreasing amounts of a chemical. In the

Marianna [84]

Sarah is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment she uses 6g of the chemical and in the second experiment she uses 7.8 g of the chemical

(i)Given that the amounts of the chemical used form an arithmetic progression find the total amount of chemical used in the first 30 experiments

(ii)Instead it is given that the amounts of the chemical used for a geometric progression. Sarah has a total of 1800 g of the chemical available. Show that the greatest number of experiments possible satisfies the inequality: $1.3^N \leq 91$ and use logarithms to calculate the value of N.

Answer:

(a)963 grams

(b)N=17

Step-by-step explanation:

(a)

In the first experiment, Sarah uses 6g of the chemical

In the second experiment, Sarah uses 7.8g of the chemical

If this forms an arithmetic progression:

First term, a =6g

Common difference. d= 7.8 -6 =1.8 g

Therefore:

Total Amount of chemical used in the first 30 experiments

$S_n=\dfrac{n}{2}[2a+(n-1)d] \\S_{30}=\dfrac{30}{2}[2*6+(30-1)1.8] \\=15[12+29*1.8]\\=15[12+52.2]\\=15*64.2\\=963$ grams$

Sarah uses 963 grams in the first 30 experiments.

(b) If the increase is geometric

First Term, a=6g

Common ratio, r =7.8/6 =1.3

Sarah has a total of 1800 g

Therefore:

Sum of a geometric sequence

$S_n=\dfrac{a(r^N-1)}{r-1} \\1800=\dfrac{6(1.3^N-1)}{1.3-1} \\1800=\dfrac{6(1.3^N-1)}{0.3}\\$Cross multiply\\1800*0.3=6(1.3^N-1)\\6(1.3^N-1)=540\\1.3^N-1=540\div 6\\1.3^N-1=90\\1.3^N=90+1\\1.3^N=91$

Therefore, the greatest possible number of experiments satisfies the inequality

$1.3^N \leq 91$

Next, we solve for N

Changing $1.3^N \leq 91$ to logarithm form, we obtain:

$N \leq log_{1.3}91\\N \leq \dfrac{log 91}{log 1.3}\\ N \leq 17.19$

Therefore, the number of possible experiments, N=17

3 0

3 years ago

Which of the sets of ordered pairs represents a function?

iogann1982 [59]

(x,y)
if x repeats with a differnt y then it is not a function

A. none of them repeat, it's a function
B. none of them repeat, it's a function

both of them are functions

5 0

3 years ago

Solve the equation 9x = 7(x + 2). <br> A) -7 <br> B) -1 <br> C) 1 <br> D) 7

HACTEHA [7]

Answer:

The solution of the equation 9x=7(x+2) is:

Option D) 7

Step-by-step explanation:

9x=7(x+2)

Eliminating the parentheses applying distributive property:

9x=7(x)+7(2)

Multiplying:

9x=7x+14

Grouping the x's on the left side of the equation: Subtracting 7x both sides of the equation:

9x-7x=7x+14-7x

Subtracting:

2x=14

Solving for x: Dividing both sides of the equation by 2:

2x/2=14/2

Dividing:

x=7

Solution: x=7 (option D)

7 0

4 years ago

Read 2 more answers

Jeff brought cookies to school for his

kupik [55]

24 classmates each got 3 cookies.

24 * 3 = 72

24 classmates got a total of 72 cookies.

Jeff brought 72 cookies to school.

5 0

4 years ago

Read 2 more answers