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2 years ago

Part A

Mathematics

1 answer:

Nat2105 [25]2 years ago

4 0

Answer:

A. $f(n) =0.2n+4.8$

B. The y intercept is 4.8

Step-by-step explanation:

Given

$a_n= 5 + 0.2(n-1)$

Solving (a): Write as a function.

To do this, we simply substitute f(n) for $a_n$

$a_n= 5 + 0.2(n-1)$ becomes

$f(n)= 5 + 0.2(n-1)$

Open Bracket

$f(n) = 5 + 0.2n-0.2$

Collect Like Terms

$f(n) =0.2n-0.2 + 5$

$f(n) =0.2n+4.8$

B. The y intercept.

To get the y intercept, we set n to 0

i.e

$f(0) =0.2 * 0+4.8$

$f(0) =0+4.8$

$f(0) =4.8$

Hence, the y intercept is 4.8

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The terms, coefficients, and constants in the expression 3x+10

xz_007 [3.2K]

Answer:

Terms = x

Coefficients = 3

Constants = 10

Hope this helped! :)

4 0

3 years ago

Vertex = (2,5), Point (0, 1)

Rama09 [41]

Answer:

therefore y= - (x-2)^2 + 5

Step-by-step explanation:

u do this by using this format here ..,

y=a(x-h)^2+k

sub in the vertex points as h=2 and k = 5 , since the 2 is positive its sign will be -2 in the brackets because when solving for x-2=0 it is x=2

y=a(x-2)^2+5

then with your (0,1) points plug that in as y and x

1=a(0-2)^2+5

1=a(-2)^2+5

1=4a+5

1-5=4a

-4=4a

a=-1

therefore y= - (x-2)^2 + 5

8 0

2 years ago

A circular patio has a diameter of 12 feet. Holly is stringing lights around the edge of the patio. Approximately how many feet

Bogdan [553]

Answer:

2.15

Step-by-step explanation:

I worked out the problem use calculator yo double check

5 0

2 years ago

Consider the following random sample from a normal population: 14, 10, 13, 16, 12, 18, 15, and 11. What is the 95% confidence in

seraphim [82]

Answer:

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

Step-by-step explanation:

Previous concepts

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".

Data: 14, 10, 13, 16, 12, 18, 15, 11

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=13.625$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.669 represent the sample standard deviation

n=8 represent the sample size

Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=8-1=7$

Since the confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.365$

Now we have everything in order to replace into formula (1):

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

3 0

3 years ago

What is 5×5×345÷7654a=234548689<br> Find a and round to the whole number.

Oxana [17]

4.80 , i hope this can help!

8 0

3 years ago