Need help with number 4

Mathematics

1 answer:

Reil [10]3 years ago

6 0

$\bf \begin{cases}
g(x)=2x\\
h(x)=x^2+4
\end{cases}\qquad 
\begin{array}{llll}
(h\circ g)(x)\implies h[~~g(x)~~]\\\\
(h\circ g)(-5)\implies h[~~g(-5)~~]
\end{array}\\\\
-------------------------------\\\\
g(-5)=2(-5)\implies g(-5)=-10
\\\\\\
h[~~g(-5)~~]\implies h[~~-10~~]\implies h(-10)=(-10)^2+4
\\\\\\
h(-10)=100+4\implies h(-10)=104$

You might be interested in

A playground is shaped like a quaderaleteral with all sides 27 feet long, with two angles measures of 65 degrees and two angles

Ksivusya [100]

Answer:

Rhombus

Step-by-step explanation:

Shape of a playground is a quadrilateral

It is given that all sides of a quadrilateral are= 27 feet

Since all the sides of a quadrilateral are equal that it can be either a rhombus or it can be a square

Two angle are 65° each

And other two angers are 115° each

65°+ 115°= 180°

It forms a co-interior angle

Hence the quadrilateral is a parallelogram

Since all the four sides of parallelogram are equal, than the given figure must be rhombus

Hence, geomatric shape best describes the shape of the playground is Rhombus.

7 0

3 years ago

A high-tech company wants to estimate the mean number of years of college education its employees have completed. A sample of 15

valentinak56 [21]

Answer:

$4 - 2.14 \frac{0.7}{\sqrt{15}}=3.61$

$4 + 2.14 \frac{0.7}{\sqrt{15}}=4.39$

The 95% confidence interval is given by (3.61;4.39)

Step-by-step explanation:

Notation and definitions

n=15 represent the sample size

$\bar X=4$ represent the sample mean

$s=0.7$ represent the sample standard deviation

m represent the margin of error

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".

Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . The degrees of freedom are given by: