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3 years ago

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It costs Guido $0.20 to send a text message from his cell phone. He has already spent $4 in text messages this month. If he has

a total of $10 that he can spend this month on text messages, write and solve an inequality that will give the greatest number of text messages that he can send. Interpret the solution.

2 answers:

denis-greek [22]3 years ago

7 0

Answer: $x \leq 30$ is the required inequality.

Step-by-step explanation:

Let x be the greatest number of text message that he can do,

And, According to the question,

The cost of one text message = $0.20

And, Initially the amounts he has = $10

But, after spending $4 the remaining amount he has = 10 - 4 = $ 6

Now, total cost of the x messages = 0.20 x dollar

Again according to the question,

$0.20x \leq 6$

⇒ $x \leq \frac{6}{0.2}$

⇒ $x \leq 30$

Which is the required inequality.

By this we can say that he can do maximum 30 messages with the money he has.

Anon25 [30]3 years ago

4 0

Answer:

$0.20x\leq 6$

$x\leq 30$

Step-by-step explanation:

Given : cost of one text message = $0.20

the amounts he has = $10

he already spent $4

Solution:

the remaining amount he has after spending =10 - 4 = $ 6

So, Let the greatest number of text message that he can do be x

so,total cost of the x messages = 0.20 x dollar

as given in the question he cannot spend more than 10 dollar and at present he is left only with 6 dollar so right now he can spend only less than or equal to 6 dollar.

so inequality will be $0.20x\leq 6$ ---(A)

$x\leq \frac{6}{0.20}$

$x\leq 30$

Hence (A) is the required inequality.

So, he can do maximum 30 messages with $6.

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3 years ago

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Read 2 more answers

Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π

lorasvet [3.4K]

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The <em>instantaneous</em> rate of change at a given value of $x$ can be found by concept of derivative, which is described below:

$g(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Where $h$ is the <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> rate of change of $g$ if $f(x) = \sin x$ and evaluate the resulting expression for $x = \frac{\pi}{3}$ . Then, we have the following procedure below:

$g(x) = \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}$

$g(x) = \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}$

$g(x) = \lim_{h \to 0} \frac{\sin h}{h}\cdot \lim_{h \to 0} \cos x$

$g(x) = \cos x$

Now we evaluate $g(x)$ for $x = \frac{\pi}{3}$ :

$g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}$

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. $\blacksquare$

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

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2 years ago

A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. (a) What must be true

valentina_108 [34]

Answer:

(a) The distribution of the sample mean ( $\bar x$ ) is <em>N</em> (68, 4.74²).

(b) The value of $P(\bar X$ is 0.7642.

(c) The value of $P(\bar X\geq 69.1)$ is 0.3670.

Step-by-step explanation:

A random sample of size <em>n</em> = 10 is selected from a population.

Let the population be made up of the random variable <em>X</em>.

The mean and standard deviation of <em>X</em> are:

$\mu=68\\\sigma=15$

(a)

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. <em>n</em> = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

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

$\mu_{\bar x}=\mu=68$

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

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{10}}=4.74$

Thus, the distribution of the sample mean ( $\bar x$ ) is <em>N</em> (68, 4.74²).

(b)

Compute the value of $P(\bar X$ as follows:

$P(\bar X$

$=P(Z$

*Use a <em>z</em>-table for the probability.

Thus, the value of $P(\bar X$ is 0.7642.

(c)

Compute the value of $P(\bar X\geq 69.1)$ as follows:

Apply continuity correction as follows:

$P(\bar X\geq 69.1)=P(\bar X> 69.1+0.5)$

$=P(\bar X>69.6)$

$=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{69.6-68}{4.74})$

$=P(Z>0.34)\\=1-P(Z$

Thus, the value of $P(\bar X\geq 69.1)$ is 0.3670.

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3 years ago