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4 years ago

In the expression -16t2 − 8t + 24, what does the constant term represent?

Mathematics

2 answers:

-Dominant- [34]4 years ago

7 0

It represents the value of the expression when the variable (t) is zero.

_____

If this is supposed to be an expression for ballistic motion, the constant could represent the initial height of the object in feet. There is nothing in your problem statement indication what this expression is suppose to represent. It could be pennies of profit for selling t trinkets, for all we know—where the constant term represents some initial balance you have before you sell any.

hammer [34]4 years ago

6 0

It can represent many things depending on what context the expression is used in. Most commonly, the constant term represents the y-intercept of the expression when it is graphed e.g. the graph of y = -16t² - 8t + 24 has a y-intercept of 24.

It can also represent the initial value if the expression is used in a word problem context

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5) Two machines M1, M2 are used to manufacture resistors with a design

Basile [38]

Answer:

Since M1 has the higher probability of being in the desired range, we choose M1.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two machines M1, M2 are used to manufacture resistors with a design specification of 1000 ohm with 10% tolerance.

So we need the machines to be within 1000 - 0.1*1000 = 900 ohms and 1000 + 0.1*1000 = 1100 ohms.

For each machine, we need to find the probabilty of the machine being in this range. We choose the one with the higher probability.

M1:

Resistors of M1 are found to follow normal distribution with mean 1050 ohm and standard deviation of 100 ohm. This means that $\mu = 1050, \sigma = 100$

The probability is the pvalue of Z when X = 1100 subtracted by the pvalue of Z when X = 900. So

X = 1100

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1100 - 1050}{100}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915.

X = 900

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{900 - 1050}{100}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.6915 - 0.0668 = 0.6247.

M1 has a 62.47% probability of being in the desired range.

M2:

M2 are found to follow normal distribution with mean 1000 ohm and standard deviation of 120 ohm. This means that $\mu = 1000, \sigma = 120$

X = 1100

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1100 - 1000}{120}$

$Z = 0.83$

$Z = 0.83$ has a pvalue of 0.7967.

X = 900

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{900 - 1000}{120}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033

0.7967 - 0.2033 = 0.5934

M2 has a 59.34% probability of being in the desired range.

Since M1 has the higher probability of being in the desired range, we choose M1.

8 0

3 years ago

Solve. Write the solution in interval notation. -2x>-8 and -5x<20.

Novosadov [1.4K]

Answer:

The interval notation of the solution is (-4 , 4)

Step-by-step explanation:

* Let us explain a very important point in solving inequality

- When you multiply or divide an inequality by negative number we

must reverse the symbol of the inequality

- Ex:

∵ 2 < 3

- If we multiply the both sides of the inequality by -1, then the

inequality will be -2 < -3 and this is completely wrong, so we must

reverse the symbol of the inequality

∴ -2 > -3

* Now let us solve the problem

∵ -2x > -8

- Divide both sides by -2 and remember to reverse the symbol of the

inequality

∴ x < 4

∵ -5x < 20

- Divide both sides by -5 and remember to reverse the symbol of the

inequality

∴ x > -4

- From both solutions

∴ -4 < x < 4

∴ The solution is {x : -4 < x < 4}

- Interval notation is a way of writing the solutions of inequalities

( , ) if x does not equal the end numbers

[ , ] if x equals the end numbers

[ , ) , ( , ] if x equals one of the two end numbers

* The interval notation of the solution is (-4 , 4)

4 0

3 years ago

What that called for math?This symbol #

AVprozaik [17]

Answer: Pound key

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

In the figure below, lines 1 and 2 are parallel. Lines 3 and 4 are also parallel.

attashe74 [19]

I don’t see a diagram, but I assume that you must use these things.

Opposite interior angles. (Which are equal)
Same side interior angles (which are supplementary or they add up to 180)
Corresponding angles (which are equal)
Vertical angles (which are equal)

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3 years ago

| 5t-1 |=6 <br><br> Show all work

kipiarov [429]

Answer:

t = 1.4

Step-by-step explanation:

If you multiply 5 and 1.4 together, you get 7. Then, you do 7 - 1, and you get 6.

The inverse operation symbol things don't matter if the answer you get inside the two vertical bars is positive.

5 0

3 years ago

Read 2 more answers