I just need a little help figuring this out<br><br>find the value of X<br>

The functions g and h are given by g(x) = x + 1 and h(x) = x²

Delvig [45]

Answer:

x = - $\frac{3}{2}$ , x = 2

Step-by-step explanation:

To find h(g(x)) substitute x = g(x) into h(x) , that is

h(g(x))

= h(x + 1)

= (x + 1)²

= x² + 2x + 1

For h(g(x)) = 3x² + x - 5 , then

3x² + x - 5 = x² + 2x + 1 ← subtract x² + 2x + 1 from both sides

2x² - x - 6 = 0 ← in standard form

(2x + 3)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - $\frac{3}{2}$

x - 2 = 0 ⇒ x = 2

5 0

3 years ago

A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was fo

borishaifa [10]

Answer:

a) $P(5$

And we can find this probability with this difference:

$P(-1.90$

And using the norma standard distribution or excel we got:

$P(-1.90$

b) $P(X>6) =P(Z> \frac{6-7.37}{1.25}) = P(Z>-1.096)$

And using the complement rule we got:

$P(Z>-1.096) =1-P(Z$

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(7.37,1.25)$

Where $\mu=7.37$ and $\sigma=1.25$

We are interested on this probability

$P(5$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(5$

And we can find this probability with this difference:

$P(-1.90$

And using the norma standard distribution or excel we got:

$P(-1.90$

Part b

For this case we want this probability:

$P(X>6)$

And we can use the z score and we got:

$P(X>6) =P(Z> \frac{6-7.37}{1.25}) = P(Z>-1.096)$

And using the complement rule we got:

$P(Z>-1.096) =1-P(Z$

8 0

3 years ago

Raffle tickets were sold for a school fundraiser to parents, teachers, and students. 563 tickets were sold to teachers. 888 more

Llana [10]

Given :

Raffle tickets were sold for a school fundraiser to parents, teachers, and students. 563 tickets were sold to teachers. 888 more tickets were sold to students than to teachers. 904 tickets were sold to parents.

To Find :

How many tickets were sold to students.

Solution :

Ticket sold to teachers, T = 563 .

Ticket sold to parents, P = 904 .

Let, ticket sold to students are S.

Now, it is given that :

S = T + 904

S = 563 + 904

S = 1467 students

Therefore, tickets sold to students are 1467 .

Hence, this is the required solution.

6 0

3 years ago

I can't seem to figure this out

lesya [120]

To answer this question, you would need a protractor, which is a device that measures angle. Because this is a picture, I cannot help you. I'm sorry....

What I can tell you is that the angle is less than 90 degrees.

5 0

3 years ago

1,868 to the nearest hundred

Citrus2011 [14]

Answer: 1,900

Step-by-step explanation:

You would round up to 1,900 because in the tens place is a 6 and when you have a number greater than or equal to 5 you round up. Hope this helps!

7 0

3 years ago

I just need a little help figuring this outfind the value of X​

I just need a little help figuring this outfind the value of X