Evaluate 8 ÷ -2

Find the length of the darkened arc. Leave your answer in terms of pi.

jonny [76]

Answer:

$\frac{15 }{4} \pi \:$

Step-by-step explanation:

Radius of circle (r) = 18/2 = 9 ft

Central angle = 180° - 30° = 150°

$length \: of \: arc \\ = \frac{150 \degree}{360 \degree} \times 2\pi \: r \\ \\ = \frac{150 \degree}{360 \degree} \times 2 \times \pi \: \times 9\\ \\ = \frac{5 }{12 } \times 18 \times \pi \: \\ \\ = \frac{5 }{4} \times 3\times \pi \:\\ \\ = \frac{15 }{4} \pi \:$

6 0

3 years ago

What numbers between 49 and 95 that are multiples of 2,3,and9

Alex777 [14]

There are 45 numbers between 49 and 95

Numbers in the fifties: 50,51,52,53,54,55,56,57,58,59

Numbers in the sixties: 60,61,62,63,64,65,66,67,68,69

Numbers in their seventies: 70,71,72,73,74,75,76,77,78,79

Numbers in their eighties: 80,81,82,83,84,85,86,87,88,89

Numbers in their nineties: 90,91,92,93,94

Multiples of 2:

50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94

Multiples of 3:

51,54,57,60,63,66,69,72,75,78,81,84,87,90

Multiples of 9:

54,63,72,81,90

Notice that all multiples of nine are also multiples of three? That is because three is a factor of nine

4 0

3 years ago

"Suppose that allele D produces long toes and allele d produces normal toes. A heterozygous male with the Dd genotype mates with

VARVARA [1.3K]

Answer:

30%

Step-by-step explanation:

The crossing of a male with genotype Dd with a female with genotype dd, yields the following possible outcomes:

Dd, dD, dd, dd.

Therefore, there is a 2 in 4, (50%) chance that their offspring will have the dominant allele. Since its penetrance is 60%, the dominant trait will only manifest itself in 60% of heterozygous individuals. Therefore, the probability that their offspring will have long toes is:

$P = 0.50*0.60\\P=30\%$

The probability is 30%.

7 0

3 years ago

Directions for questions 4 & 5: We selected a random sample of 100 StatCrunchU students, 67 females and 33 males, and analyz

GaryK [48]

Answer:

The 95% confidence interval for the difference between means is (-2164.21, -299.13).

The lower limit on the confidence interval is -$2164.21.

The upper limit on the confidence interval is -$299.13.

Step-by-step explanation:

The sample data is:

Gender Mean Std. dev. n

Female 2577.75 1916.29 67

Male 3809.42 2379.47 33

We have to calculate a 95% confidence interval for the difference between means, with a T-model.

The sample 1, of size n1=67 has a mean of 2577.75 and a standard deviation of 1916.29.

The sample 2, of size n2=33 has a mean of 3809.42 and a standard deviation of 2379.47.

The difference between sample means is Md=-1231.67.

$M_d=M_1-M_2=2577.75-3809.42=-1231.67$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1916.29^2}{67}+\dfrac{2379.47^2}{33}}\\\\\\s_{M_d}=\sqrt{54808.468+171572.045}=\sqrt{226380.513}=475.795$