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2 years ago

Juanita is 13 years older than her cousin. The sum of their ages is no less than 103 years.

1 answer:

4 0

Juanita = x+13
Cousin = x

No less than is the same as greater than or equal to . If I am wrong on this the answer is 46 instead of 45.

(x+13) + x >= 103
2x + 13 >= 103
2x >= 90
x >= 45
Juanita's cousin must be at least 45 years old.
Juanita is at least 58 years old.

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Consider coordinate system a, with the x axis along the plane. which forces lie along the axes?

Butoxors [25]

It seem like there are information missing on the question posted. Let me answer this question with all I know. So here is what I believe the answer is, the horizontal force.

Hope my answer would be a great help for you. If you have more questions feel free to ask here at Brainly.

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2 years ago

If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

kiruha [24]

Answer:

$[1,\infty)$

Step-by-step explanation:

$b(x)=\sqrt{x-4}$

$a(x)=3x+1$

Since we want to know the domain of $(b \circ a)(x)$ , let's first consider the domain of the inside function, that is, that of $a(x)=3x+1$ . Every polynomial function has domain all real numbers.

So we can plug anything for function $a$ and get a number back.

Now the other function is going to be worrisome because it has a square root. You cannot take square root of negative numbers if you are only considering real numbers which that is the case with most texts.

Let's find $(b \circ a)(x)$ and simplify now.

$(b \circ a)(x)$

$b(a(x))$

$b(3x+1)$

$\sqrt{(3x+1)-4}$

$\sqrt{3x+1-4}$

$\sqrt{3x-3}$

Now again we can only square root positive or zero numbers so we want $3x-3 \ge 0$ .

Let's solve this to find the domain of $(b \circ a)(x)$ .

$3x-3 \ge 0$

Add 3 on both sides:

$3x \ge 3$

Divide both sides by 3:

$x \ge 1$

So we want $x$ to be a number greater than or equal to 1.

The option that says this is $[1,\infty)$

-------------------------------

Give an example why option A fails:

A number in the given set is -2.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(-2)=3(-2)+1=-6+1=-5$ and $b(-5)=\sqrt{-5-4}=\sqrt{-9} \text{ which is not real}$ .

Give an example why option B fails:

A number in the given set is 0.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(0)=3(0)+1=0+1=1$ and $b(1)=\sqrt{1-4}=\sqrt{-3} \text{ which is not real}$ .

Give an example why option D fails:

While all the numbers in set D work, there are more numbers outside that range of numbers that also work.

A number not in the given set that works is 3.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(3)=3(3)+1=9+1=10$ and $b(1)=\sqrt{10-4}=\sqrt{6} \text{ which is real}$ .

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2 years ago

Read 2 more answers

In 2012, Gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that

nirvana33 [79]

Answer:

There is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.

Step-by-step explanation:

We have to answer the population proportion for Vermont.

We can only do it by a confidence interval, as we only have information from a sample.

This sample, of size n=100, has a proportion p=0.653.

The degrees of freedom are:

$df=n-1=100-1=99$

We will calculate a 95% confidence interval, which for df=99 has a critical value of t of t=1.984.

The margin of error can be calculated as:

$E=t*\sigma_p=t\sqrt{\dfrac{p(1-p)}{n}}=1.984\sqrt{\dfrac{0.653*0.347}{100}}\\\\\\E=1.984*\sqrt{0.00226}=1.984*0.0476=0.094$

Then, the upper and lower bounds of the confidence interval are:

$LL=p-E=0.653-0.094=0.559\\\\UL=p+E=0.653+0.094=0.747$

Then, we can say that there is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.

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2 years ago

The Substitution Property of Equality allows you to say that if 7j + 14k = 28, and j = 2, then _____.

Naddik [55]

The answer is 7*2+14k=28
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2 years ago

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A ship captain is attempting to contact a deep sea diver

DaniilM [7]

Yes, the boat can communicate with the diver.

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