Someone please help this is due in an hour

if tom spins the spinner 80 times work out an estimate for the number of times the spinner will land on 3 please help me

NNADVOKAT [17]

Answer:

The estimated number of times the spinner will land on 3 is 20.

Step-by-step explanation:

The complete question is:

A four-sided spinner is provided. If Tom spins the spinner 80 times then work out an estimate for the number of times the spinner will land on 3.

Solution:

Assume that the four-sided spinner is unbiased.

That is all the four outcomes are equally likely to be selected.

The probability that the spinner lands on any of the four numbers is:

P(1) = P (2) = P (3) = P (4) = 0.25

It is provided that Tom spins the spinner n = 80 times.

The spinner can land on any of the four numbers independently.

The random variable X, defined as the number of times the spinner lands on 3, follows a Binomial distribution with parameters n = 80 and p = 0.25.

The expected value of X is:

$E(X)=np$

$=80\times 0.25\\=20$

Thus, the estimated number of times the spinner will land on 3 is 20.

7 0

2 years ago

Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125

Savatey [412]

we have that

$300 + 150 + 75 +...$

Let

$a1=300\\ a2=150\\ a3=75$

we know that

$\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50$

$\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50$

so

$a(n+1)=an*0.50$

Is a geometric sequence

Find the value of $a4$

$a(4)=a3*0.50$

$a(4)=75*0.50$

$a(4)=37.5$

Find the value of $a5$

$a(5)=a4*0.50$

$a(5)=37.5*0.50$

$a(5)=18.75$

Find $S5$

$S5=a1+a2+a3+a4+a5\\ S5=300+150+75+37.5+18.75\\ S5=581.25$

therefore

the answer is

$581.25$

Alternative Method

Applying the formula

$S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25$