Two children are sharing 1/2 of a sandwich. how much will each child get

Factor the polynomial expression 15x^2 - 2x - 8

AVprozaik [17]

Answer:

(3 x + 2) (5 x - 4)

Step-by-step explanation:

Factor the following:

15 x^2 - 2 x - 8

Factor the quadratic 15 x^2 - 2 x - 8. The coefficient of x^2 is 15 and the constant term is -8. The product of 15 and -8 is -120. The factors of -120 which sum to -2 are 10 and -12. So 15 x^2 - 2 x - 8 = 15 x^2 - 12 x + 10 x - 8 = 5 x (3 x + 2) - 4 (3 x + 2):

5 x (3 x + 2) - 4 (3 x + 2)

Factor 3 x + 2 from 5 x (3 x + 2) - 4 (3 x + 2):

Answer: (3 x + 2) (5 x - 4)

4 0

2 years ago

HJ is twice JK. J is between H and K. If HJ= 4x and HK=78, find Jk.

ss7ja [257]

You'll find it easier to understand if you illustrate the problem as what is shown in the attached picture. From the illustration and the problem description, two equations can be formulated:

HJ = 2JK
HJ + JK = HK

2JK + JK = 78
3JK = 78
JK = 78/3
JK = 26

6 0

2 years ago

A construction company is considering submitting bids for two contracts. It will cost the company \$10{,}000$10,000dollar sign,

baherus [9]

Answer:

0 dollars

=E(M)

=μ

M

=−$10,000(0.81)+$40,000(0.18)+$90,000(0.01)

=−8,100+7,200+900

=0

8 0

2 years ago

Read 2 more answers

A team of dermatological researchers were studying skin cancer among 60-70 year old American men. Suppose you were a part of the

Lostsunrise [7]

Answer:

The correct answer is Option A.) The standard deviation of the distribution of sample means is less than the population standard deviation of the number of cancer spots.

Step-by-step explanation:

The standard deviation of the distribution of sample means is less than the population standard deviation of the number of cancer spots.

3 0

1 year ago

A pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome). In the first sta

Akimi4 [234]

Answer:

95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

Step-by-step explanation:

We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).

In the first stages of a clinical trial, it was successful for 7 out of the 14 women.

Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of women who find success with this new treatment = $\frac{7}{14}$ = 0.50

n = sample of women = 14

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the true proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.50-1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ , $0.50+1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ ]

= [0.238 , 0.762]

Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

4 0

2 years ago