Matt can buy an 8-ounce jar of salsa for $2.79 or a 15-ounce jar of salsa for $5.54. Which jar has the best unit rate?

Solve. 3(x + 1) - 2x = -6 * x = 1 x = 5 x = -7 x = -9

Vadim26 [7]

The answer is x=9 because if you do 3x+-2 that gives you 1 and 1 divided by 9 is 9 and you get that by getting rid of your 6 first and adding it to the 3 from 3(x+1)

7 0

3 years ago

Can the quadratic polynomial x2+kx+k have equal zeroes for some odd integer k>1

PilotLPTM [1.2K]

No.
The only value that can be put in K that would have the same zeros would be 4 but 4 is not an odd integer. If there was an odd integer that the sum and product would be the same then it would lie on the x-axis. but only 4 fits the criteria.

7 0

3 years ago

A box of Georgia peaches has 3 bad and 12 good peaches. (a) If you make a peach cobbler of 12 peaches randomly selected from the

Eddi Din [679]

Answer:

a) 0.21% probability that there are no bad peaches in the peach cobbler.

b) 99.79% probability of having at least 1 bad peach in the peach cobbler

c) 7.91% probability of having exactly 2 bad peaches in the peach cobbler.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the peaches are chosen is not important. So the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

(a) If you make a peach cobbler of 12 peaches randomly selected from the box, what is the probability that there are no bad peaches in the peach cobbler?

Desired outcomes:

12 good peaches, from a set of 12. So

$D = C_{12,12} = \frac{12!}{12!(12 - 12)!} = 1$

Total outcomes:

12 peaches, from a set of 15. So

$T = C_{15,12} = \frac{15!}{12!(15 - 12)!} = 455$

Probability:

$p = \frac{D}{T} = \frac{1}{455} = 0.0021$

0.21% probability that there are no bad peaches in the peach cobbler.

(b) What is the probability of having at least 1 bad peach in the peach cobbler?

Either there are no bad peaches, or these is at least 1. The sum of the probabilities of these events is 100%. So

p + 0.21 = 100

p = 99.79

99.79% probability of having at least 1 bad peach in the peach cobbler

(c) What is the probability of having exactly 2 bad peaches in the peach cob- bler?

Desired outcomes:

2 bad peaches, from a set of 3.

One good peach, from a set of 12.

$D = C_{3,2}*C_{12,1} = \frac{3!}{2!(3-2)!}*\frac{12!}{1!(12 - 1)!} = 36$

Total outcomes:

12 peaches, from a set of 15. So

$T = C_{15,12} = \frac{15!}{12!(15 - 12)!} = 455$

Probability:

$p = \frac{D}{T} = \frac{36}{455} = 0.0791$

7.91% probability of having exactly 2 bad peaches in the peach cobbler.

3 0

2 years ago

Light bulbs manufactured at a certain factory have a 3% probability of being defective. what is the probability that 5 out of a

lbvjy [14]

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that 5 out of a shipment of 30 will be defective is 0.001617.

<h3>What is Binomial distribution?</h3>

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

The probability of the bulb being defective is 3%(0.03) and the probability of the bulb not being defective is 97%(0.97).

Now, it is needed to be found that the probability that 5 out of a shipment of 30 will be defective can be written as,

P(x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

P(x=5) = ³⁰C₅ (0.03)⁵ (0.97)²⁵

P(x=5) = 0.001617

Hence, the probability that 5 out of a shipment of 30 will be defective is 0.001617.

Learn more about Binomial Distribution:

brainly.com/question/14565246

#SPJ2

3 0

1 year ago

9. Determine whether or not the number 257 is prime.

Sladkaya [172]

Answer:

257 is prime.

Step-by-step explanation:

To evaluate if a number is prime, we just need to evaluate it for the prime numbers that are equal or lesser than the said number's square root.

In this case, √257 = 16.03 so we just need to see if 257 is divisible by 2, 3, 5, 7, 11 and 13 (the prime numbers that come before 16)

257 is odd, so it is not divisible by 2.

The sum of its digits is 14, therefore, it is not divisible by 3.

257 ends in 7, therefore it's not divisible by 5.

257/ 7 = 36.71 so it's not divisible by 7.

257/ 11 = 23.36 so it's not divisible by 11

Finally 257 / 13= 19.76 so it's not divisible by 13.

Therefore, 257 is prime.

7 0

2 years ago