If ƒ(x ) = x 2 + 1, find ƒ(a + 1).

In a data set with a normal distribution, the mean is 59 and the standard deviation is 3.

lakkis [162]

Answer:

a) $P(53$

$P(-2$

b) $a=59 +1.96*3=64.88$

And for the other limit we have:

$a=59 -1.96*3=53.12$

And we will have 95% of the values between (53.12, 64.88)

Step-by-step explanation:

Part a

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

$X \sim N(59,3)$

Where $\mu=59$ and $\sigma=3$

We are interested on this probability :

$P(53$

And we can solve this using the z score:

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

Using the last formula we got:

$P(53$

And we can find this probability with this difference:

$P(-2$

And uing the normal standard distribution or excel we got:

$P(-2$

Part b

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.025$ (a)

$P(X$ (b)

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.96.

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.96$

And if we solve for a we got

$a=59 +1.96*3=64.88$

And for the other limit we have:

$a=59 -1.96*3=53.12$

And we will have 95% of the values between (53.12, 64.88)

5 0

3 years ago

Find the dicontinuities of the function. f(x) = x2 + 12x + 27 x2 + 4x + 3 . There is a removable discontinuity at (, ).

ValentinkaMS [17]

Solution-

$f(x)=\frac{x^{2}+12x+27 }{x^{2} +4x+3} =\frac{x^{2}+9x+3x+27 }{x^{2} +3x+x+3}=\frac{(x+3)(x+9)}{(x+3)(x+1)}$

Equating the denominator to 0,

⇒ (x+3)(x+1) = 0

⇒ x= -3, -1

∴ Discontinuities of the function f(x) is at -3, -1

As (x+3) is also a factor of the numerator, you will have what's called a removable discontinuity. That will show up as a hole in the graph.

∴ At x = -3, you will have removable discontinuity.

4 0

3 years ago

Read 2 more answers

Which best explains how the division equation relates to the diagram? (11 7/8) ÷ (2 3/8) =5

xxMikexx [17]

Answer:

When you split the fraction $2\frac{3}{8}$ into 5 parts it will equal to $11\frac{7}{8}$ .

Step-by-step explanation: I hope this helps. UwU

4 0

3 years ago

Evaluate 4(2a – b) when a = –1 and b = 5.

grin007 [14]

Hey There!

<h2>Question:-</h2>

$\sf \longmapsto \: 4(2a - b)$

This is a algebraic expression. The values of a and b are given. The values are as follows :-

a = -1

And,

b = +5 .

<h2>Solution:-</h2>

$\sf \longmapsto4(2a - b)$

Note that a is multiplied with 2 that is :-

$\sf \longmapsto4(2 \times a \: - b)$

Now, Insert the values that is a = -1 and b = 5 :-

$\sf \longmapsto4(2 \times - 1 - 5)$

Here,we need to follow BODMAS Rule.

B = Brackets

O = Orders

D = Division

M = Multiplication

A = Addition

S = Subtraction

We need to solve the bracket's calculations first as it is the rule.

So, Firstly Multiply (2 × -1) :-

$\sf \longmapsto4( - 2 - 5)$

Note that, (-) × (-) equals to (+).

So, it will be 5+2,But as 5 is bigger number than 2, 5 contains a minus sign.So the result will be -7.

$\sf \longmapsto4( 5+ 2)$

On Simplification:-

$\sf \longmapsto4( - 7)$

$\sf \longmapsto4 \times (- 7)$

$\sf \longmapsto \: - 28$

______________________________________

Henceforth the solution of the algebraic expression is :-

$\bf \:- 28$

Option B is correct!

______________________________________

I hope this helps!

Please let me know if you have any questions.

~MisterBrian

3 0

2 years ago

Read 2 more answers

Jeanette purchased a concert ticket on a website. The original price of the ticket was $75. She use a coupon code to receive a 2

devlian [24]

The remaining cost is $66 after 20% discount and 10% service fee

4 0

3 years ago