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2 years ago

The solution to -2x/3+7<15 is the set

Mathematics

1 answer:

svlad2 [7]2 years ago

5 0

Answer:

1) x > -12

Step-by-step explanation:

first, subtract 7 from each side of the inequality to get:

-2/3x < 8

multiply each side by the reciprocal of -2/3 which is -3/2 to get:

x > -24/2

notice the symbol has been reversed because that is the rule whenever you multiply or divide an equality be a negative value

simplified, answer is x > -12

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Jack and Diane were saving money to go to a rock n roll concert. They need at least $750 in order to go if you count their gas,

nataly862011 [7]

Answer:

$\left\{\begin{array}{l}y\le 4x\\ \\x\ge 10\\ \\50x+25y\ge 750\end{array}\right.$

Step-by-step explanation:

Let x represents the number of nights Jack worked and y represents the number of nights Diane worked.

1. The number of nights Diane is scheduled to work is no more than four times the number of nights Jack is scheduled to play. Then

$y\le 4x$

2. Diane will work at least 10 times before the concert. Then

$x\ge 10$

3. Jack earns $50 per night that he plays, then he earned $50x in x nights. Diane earns $25 each night she works, then she earns $25y in y nigths. They need at least $750, so

$50x+25y\ge 750$

4. We get the following set of constraints to model the problem:

$\left\{\begin{array}{l}y\le 4x\\ \\x\ge 10\\ \\50x+25y\ge 750\end{array}\right.$

4 0

3 years ago

Jamal worked from 3:20 until 9:55. How many minutes did he work?

AnnyKZ [126]

Answer:

395 minutes

Step-by-step explanation:

See above for the answer

6 0

3 years ago

Read 2 more answers

In how many different ways can someone arrange 6 books on a shelf

enot [183]

Number of ways = 6!
Number of ways = 6 x 5 x 4 x 3 x 2 x 1
Number of ways = 720

------------------------------
Answer: 720 ways
------------------------------

6 0

3 years ago

Read 2 more answers

Roberto is cutting 3 loaves of homemade bread into halves to give to his neighbors. How many neighbors can he give ½ loaf of bre

statuscvo [17]

Answer:

6 neighbors

Step-by-step explanation:

1 bread can be given to 2 neighbors when cut in half(1/2). This case, you have 3 bread so 3x2=6

6 0

3 years ago

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A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye

Katena32 [7]

Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we select appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.

Then, the mean of the distribution of the sum of values of X is given by,

$\mu_{x}=n\mu$

And the standard deviation of the distribution of the sum of values of X is given by,

$\sigma_{x}=\sqrt{n}\sigma$

The information provided is:

μ = $970

σ = $129

n = 102

Since the sample size is quite large, i.e. n = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

$\sum X\sim N(\mu_{x}=98940,\ \sigma_{x}=1302.84)$

Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:

$P (\sum X \leq 100,000) =P(\frac{\sum X-\mu_{x}}{\sigma_{x}}$

$=P(Z$

*Use a z-table for the probability.

Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

6 0

2 years ago