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3 years ago

Question 5

Mathematics

1 answer:

aev [14]3 years ago

4 0

Answer:

C. $12$

Step-by-step explanation:

The function t, where $t(x) = 9.50 x$ represents the amount of money Fernando earns given the number of hours, x, he works.

The domain of the function $t(x)$ are all possible values for x.

It is known that Fernando works between 12 and 25 hours each week, so the number of hours, x, he works satisfies the inequality

$12$

You might be interested in

Translate the sentence into an equation. Twice the difference of a number and 7 is equal to 2. Use the variable y for the unknow

PolarNik [594]

Answer:

pls brainliest

Step-by-step explanation:

The difference btw the number and 7= y-7

so twice:2(y-7)=2

2y-14=2

7 0

3 years ago

Dy/dxif y = 4x3 + 3x2 + 2

DIA [1.3K]

The function is

$\displaystyle{ y=4x^3+3x^2+2$ .

We recall that the derivative of each monomial $ax^b$ is $a\cdot b\cdot x^{b-1}$ , and the derivative of a constant (function) is 0.

According to this:

$\frac{d}{dx}(4x^3+3x^2+2)=4\cdot 3\cdot x^2 + 3\cdot 2\cdot x+0 =12x^2+6x$ .

Answer: $12x^2+6x$

7 0

3 years ago

A particle is moving with the given acceleration function and initial conditions. Find the velocity function and the position fu

Lerok [7]

Answer:

The velocity function is the particle is $v(t)=-2\cos (t)-4\sin (t)-1$ .

Step-by-step explanation:

The acceleration function of a moving particle is

$a(t)=2\sin (t)-4\cos (t)$

The initial conditions are v(0) = −3, s(0) = 5.

Integrate the acceleration function with respect to time to find the velocity function.

$\int a(t)=\int (2\sin (t)-4\cos (t))dt$

$v(t)=-2\cos (t)-4\sin (t)+C_1$

Use the initial condition v(0) = −3 to find the value of C₁.

$-3=-2\cos (0)-4\sin (0)+C_1$

$-3=-2(1)-4(0)+C_1$

$-3=-2+C_1$

$-3+2=C_1$

$-1=C_1$

So the velocity function is the particle is

$v(t)=-2\cos (t)-4\sin (t)-1$

Integrate the acceleration function with respect to time to find the position function.

$\int v(t)=\int (-2\cos (t)-4\sin (t)-1)dt$

$s(t)=-2\sin (t)+4\cos (t)-t+C_2$

Use the initial condition s(0) = 5 to find the value of C₂.

$5=-2\sin (0)+4\cos (0)-(0)+C_2$

$5=-2(0)+4(1)+C_2$

$5=4+C_2$

$1=C_2$

So, the position function is the particle is $s(t)=-2\sin (t)+4\cos (t)-t+1$ .

5 0

3 years ago

In a recent poll, 370 people were asked if they liked dogs, and 7% said they did. Find the margin of error of this poll, at the

Dennis_Churaev [7]

Answer:

$ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218$

Step-by-step explanation:

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".

$p$ represent the real population proportion of interest

$\hat p=0.07$ represent the estimated proportion for the sample

n=370 is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And replacing into formula (a) the values provided we got:

$ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218$

The margin of error on this case would be ME=0.0218

5 0

4 years ago

a coffee mug collection includes four red mugs, eight yellow mugs and two white mugs. What is the probability of selecting two w

Kruka [31]

Assuming that the selection process was done without replacement, the probability of selecting two white mugs without replacement is 1/28

<h2>Given data</h2>

Sample Space

Red mugs = 4

yellow mugs = 8

white mugs = 2

Sample Size = 4+8+2 = 14

We are going to assume the selection was done with out replacement

Hence the probability of selecting the first white mug is

<em>The probability of selecting the second white mug is </em>

<em />

Hence the probability of selecting two white mugs one after another

= 1/4*1/7

=1/28

Learn more about probability at:

brainly.com/question/25839839

6 0

2 years ago