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3 years ago

Which number line represents the solution set for the inequality 3(8-4x)<6(x-5)?

Mathematics

2 answers:

KATRIN_1 [288]3 years ago

4 0

3(8-4x)<6(x-5)
24 - 12x < 6x - 30
18x > 54
x > 3
answer is B. x > 3

djverab [1.8K]3 years ago

3 0

we have

$3(8-4x) 54\\ x > (54/18)\\x > 3$

the solution is the interval -------> (3,∞)

therefore

the answer in the attached figure

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X² - 5x + 6 = 0 (R: 2, 3)

Firlakuza [10]

I'm sending you two screenshots of the explanation I hope this helps.

4 0

3 years ago

riangle XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding point

tester [92]

Answer:

5 units

Step-by-step explanation:

According to the given statement Δ XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z' which means that each point in ΔXYZ is moved 4 units up and moved 3 units left.

To find the distance of each corresponding point we will use the Pythagorean theorem which states that the square of the length of the Pythagorean of a right triangle is equal to the sum of the squares of the length of other legs

The square of the required distance = 4^2+3^2 = 16+9 =25

By taking root of 25 we get:

√25 = 5

Thus, we can conclude that the the distance between any two corresponding points on ΔXYZ and ΔX′Y′Z′ is 5 units. ..

7 0

3 years ago

Find the slope of a line perpendicular to 4x-y=6

ratelena [41]

Answer:

The slope is -1/4

Step-by-step explanation:

perpendicular line is $y=-\frac{1}{4}x-6$

8 0

3 years ago

An article presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new meth

Anna35 [415]

Answer:

With 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.

Step-by-step explanation:

We are given that the effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 655.6 vehicles per hour, with a standard deviation of 311.7 vehicles per hour.

A traffic engineer states that the mean improvement is between 583.1 and 728.1 vehicles per hour.

Let $\bar X$ = sample mean improvement

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = mean improvement = 655.6 vehicles per hour

$\sigma$ = standard deviation = 311.7 vehicles per hour

n = sample of simulations = 50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the mean improvement is between 583.1 and 728.1 vehicles per hour is given by = P(583.1 < $\bar X$ < 728.1) = P( $\bar X$ < 728.1) - P( $\bar X$ $\leq$ 583.1)

P( $\bar X$ < 728.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{728.1-655.6}{\frac{311.7}{\sqrt{50} } }$ ) = P(Z < 1.64) = 0.9495

P( $\bar X$ $\leq$ 583.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{583.1-655.6}{\frac{311.7}{\sqrt{50} } }$ ) = P(Z $\leq$ -1.64) = 1 - P(Z < 1.64)

= 1 - 0.9495 = 0.0505

So, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.64 in the z table which has an area of 0.9495.

Therefore, P(583.1 < $\bar X$ < 728.1) = 0.9495 - 0.0505 = 0.899 or 89.9%

Hence, with 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.

6 0

3 years ago

Rick, Maya, and Tom work in a call center. On a particular day, Rick worked 5 and ½ hours, Maya worked 6.1 hours, and Tom worked

storchak [24]

5h 30m + 6h 6m + 6h 30m = 17 hours and 66 minutes or 18 hours and 6 minutes.

1,110 minutes total.

Hope I helped! :)

5 0

4 years ago