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valkas [14]
3 years ago
7

Solve the inequality 2x - 5 \le -x +12. Give your answer as an interval.

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
6 0

Answer: \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \frac{17}{3}\:\\ \:\mathrm{Decimal:}&\:x\le \:5.66666\dots \\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:\frac{17}{3}]\end{bmatrix}

Step-by-step explanation:

2x-5\le \:-x+12

2x\le \:-x+17\\

2x+x\le \:-x+17+x

3x\le \:17

\frac{3x}{3}\le \frac{17}{3}

x\le \frac{17}{3}

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What is the sum of the first 47 terms of the sequence? -215, -201, -187, -173, ...​
Andru [333]

Answer:

5029

Step-by-step explanation:

There is a common difference between consecutive terms, that is

d = - 201 - (- 215) = - 187 - (- 201) = - 173 - (- 187) = 14

This indicates the sequence is arithmetic with sum to n term

=  [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 215 and d = 14 , then

=  [ (2 × - 215) + (46 × 14) ]

    = 23.5 (- 430 + 644)

   = 23.5 × 214

   = 5029

6 0
3 years ago
On a certain hot​ summer's day, 769 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for
pickupchik [31]
579 adults and 190 children I’m pretty sure this is right
6 0
3 years ago
It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work i
Salsk061 [2.6K]

Answer:

(-\infty, 0.2661)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

n=60 represent the sample size  

X=12 represent the number of masks that had lenses pop out at 250°

\hat p =\frac{12}{60}=0.2 represent the estimated proportion of masks that  had lenses pop out at 250°

p represent the population proportion of masks that  had lenses pop out at 250°

Confidence =0.9 or 90%

\alpha=0.1 represent the significance level

Confidence interval

On this case we want a interval on this form : (-\infty,\hat p +z_{\alpha}\sqrt{\frac{\hat p (1-\hat p)}{n}})

So the critical value would be on this case z_{\alpha}=1.28 and we can use the following excel code to find it: "=NORM.INV(1-0.1,0,1)"

We found the lower limit like this:

0.2 +1.28\sqrt{\frac{0.2 (1-0.2)}{60}}=0.2661

And the interval would be: (-\infyt, 0.2661)

3 0
4 years ago
1000 coins are tossed find the probability of getting exactly 500 heads.
ipn [44]

Answer:

probability of getting exactly 500 heads= 1

Step-by-step explanation:

If a coin is tossed, the probability of obtaining a head = 0.5

If a coin is tossed, the probability of obtaining a tail= 1- probability of obtaining a head

If a coin is tossed, the probability of obtaining a tail=1-0.5

If a coin is tossed, the probability of obtaining a tail=0.5

So if 1000 coin are tossed, the probability of getting exay 500 heads which is already the half of 1000 is 1

5 0
3 years ago
Consider the expression
mixer [17]

Answer:

 -12 b + 6 c + 18

Step-by-step explanation:

-4 b + 8 c + 12 - 8 b - 2 c + 6

5 0
3 years ago
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