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3 years ago

If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to (t*s)(x) ?

Mathematics

2 answers:

Inessa05 [86]3 years ago

8 0

Hello,

(t*s)(x)=t(x)*s(x)=(4x²-x+3)*(x-7)

Answer D

Gemiola [76]3 years ago

4 0

The expression (t*s)(x) may also be written as t(x)*s(x) which means that the functions are just multiply to each other. From the given,
t(x)*s(x) = (4x² - x + 3)(x - 7)
Thus, the answer for this item is letter D.

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You’re given three angle measurements of 30°, 70°, and 80°. How many triangles can you construct using these measurements?

Katyanochek1 [597]

Only one cause it takes 180 degrees to make a triangle so all you do is add it up

6 0

3 years ago

To decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger a

Komok [63]

Answer:

The probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

Step-by-step explanation:

Let the random variable X be defined as the height of chimneys in factories.

The mean height is, μ = 100 meters.

The standard deviation of heights is, σ = 12 meters.

It is provided that a random sample of n = 40 chimney heights is obtained.

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample means is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample means is given by,

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

Since the sample selected is quite large, i.e. n = 40 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean heights of chimneys.

$\bar X\sim N(\mu_{\bar x},\ \sigma^{2}_{\bar x})$

Compute the probability hat the sample mean height for the 40 chimneys is greater than 102 meters as follows:

$P(\bar X>102)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}})>\frac{102-100}{12/\sqrt{40}})$

$=P(Z>1.05)\\=1-P(Z$

*Use a z-table fr the probability.

Thus, the probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

8 0

3 years ago

H(n)=-2n(2)+4; Find h(4)

anygoal [31]

Answer:

h(4) = –12

Step-by-step explanation:

⇒ What the question is asking is that when the function h(n) = –2n(2) + 4 is h(4), what will the function repond to when solving for h(4)? So, solve for the function h(4):

h(4) = –2n(2) + 4

⇒ Since n was replaced with 4 in the function h(4), substitute any n for 4 into the function:

h(4) = –2(4)(2) + 4

⇒ Simplify:

h(4) = –16 + 4

⇒ Solve:

h(4) = –12

Answer: h(4) = –12

I hope you understand and that this helps with your question! :)

8 0

2 years ago

1. Contaminated water is subjected to a cleaning process. The concentration of the

Leokris [45]

Answer:

The concentration of pollutants in the water can be defined as the quotient between the mass of pollutants and the total mass of water.

Assuming that 1L of water weighs 1000 grams, we know that:

Mass of pollutants = 5mg = 0.005g.

Initial concentration = 0.005g/1000g = 0.000005

If we multiply this by 100%, we get the percentage:

0.000005*100% = 0.0005%

Now, the mass of pollutants decreases by 10% each hour.

So if initially, we have 5mg

After one hour, we will have: 5mg - 0.1*5mg = 5mg*(0.9).

After another hour, we will have: 5mg*(0.9) - 0.1*5mg*0.9 = 5mg*(0.9)^2.

And so on, then after n hours, the mass of pollutants will be:

M(n) = 5mg*(0.9)^n

Or we can write this in grams as:

M(n) = 0.005g*(0.9)^n

Then the concentration as a function of time in hours will be:

C(n) = M(n)/1000g = (0.005g/1000g)*(0.9)^n

Notice that the thing between the parentheses is the initial concentration, then if we write this in percentage form:

c(n) = 100%*(0.005g/1000g)*(0.9)^n = 0.0005%*(0.9)

The function that represents the concentration of polution in the water as a function of hours is:

c(n) = 0.0005%*(0.9)

6 0

3 years ago

Sound travels through sea

azamat

For this you need to multiply 1,500 by 60 (because there are 60 seconds in a minute) and then multiply that by 2 (because there are 2 minutes), wich makes the answer 180,000 meters.
Does this help?

5 0

3 years ago