1/2 plus 1/6 find each sum.

Approximately how many feet is John away from the base of the building

pav-90 [236]

120 ft... a flat vertical line is 180 degrees, and since this is a 30,60,90 triangle, your equation is... 180-60=distance John is to the base

5 0

2 years ago

Read 2 more answers

What is the solution set of x2 + 5x + 1 = 0?

DerKrebs [107]

Answer:

$\huge\boxed{\left\{-\dfrac{5+\sqrt{21}}{2};\ \dfrac{-5+\sqrt{21}}{2}\right\}}$

Step-by-step explanation:

$x^2+5x+1=0\\\\\text{Use the quadratic formula:}\\\\\text{For}\ ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\\text{if}\ \Delta < 0,\ \text{then the equation has no real solution}\\\text{if}\ \Delta=0,\ \text{then the equation has one real solution}\ x=\dfrac{-b}{2a}\\\text{if}\ \Delta>0,\ \text{then the equation has two real solution}\ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}$

$\text{We have}\\\\a=1,\ b=5,\ c=1\\\\\Delta=5^2-4(1)(1)=25-4=21>0\\\\x=\dfrac{-5\pm\sqrt{21}}{2(1)}=\dfrac{-5\pm\sqrt{21}}{2}$

3 0

3 years ago

Jane is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a number

sleet_krkn [62]

Answer:

The expected value of playing the game is $0.75.

Step-by-step explanation:

The expected value of a random variable is the weighted average of the random variable.

The formula to compute the expected value of a random variable X is:

$E(X)=\sum x\cdot P(X=x)$

The random variable X in this case can be defined as the amount won in playing the game.

The probability distribution of X is as follows:

Number on spinner: 1 2 3 4 5 6

Amount earned (X): $1 $4 $7 $10 -$8.75 -$8.75

Probability: 1/6 1/6 1/6 1/6 1/6 1/6

Compute the expected value of X as follows:

$E(X)=\sum x\cdot P(X=x)$

$=(1\times \frac{1}{6})+(4\times \frac{1}{6})+(7\times \frac{1}{6})+(10\times \frac{1}{6})+(-8.75\times \frac{1}{6})+(-8.75\times \frac{1}{6})$

$=\frac{1}{6}+\frac{4}{6}+\frac{7}{6}+\frac{10}{6}-\frac{8.75}{6}-\frac{8.75}{6}$

$=\frac{1+4+7+10-8.75-8.75}{6}$

$=0.75$

Thus, the expected value of playing the game is $0.75.

5 0

3 years ago

Ms.Wooldridge walks laps around her pool for exercise each day. She walks at a constant rate of 30 seconds per lap. It takes her

nasty-shy [4]

Answer: it will take her 58 minutes to walk one mile.

Step-by-step explanation:

She walks at a constant rate of 30 seconds per lap and it takes her 46 steps to walk one full lap. It means that she walks 46 steps in 30 seconds.

If each step is approximately 1 foot, it means that the number of feet that she walks in 30 seconds is 46 feet.

1 foot = 0.000189 miles

Therefore, 46 feet would be

46 × 0.00189 = 0.008694 miles

Therefore, if she she walks 0.008694 miles in 30 seconds,

The time it will take her to walk 1 mile would be

30/0.008694 = 3450.66 seconds

Converting to minutes, it becomes

3450.66/60 = 58 minutes

7 0

2 years ago

What is the sum of the first five terms of a geometric series with a = 10 andr = 1/5?

Zinaida [17]

Answer:

12.496

Step-by-step explanation:

Here, to calculate the sum of the first five terms of the series, we use the formula for the sum of terms in a geometric series.

Mathematically, that would be;

Sn = a(1-r^n)/1-r

where Sn = ?

a = 10

r = 1/5 = 0.2

n = 5

Substituting these values into the equation above, we have;

Sn = 10(1-(0.2)^5)/1-0.2

Sn = 10(0.99968)/0.8

Sn = 12.496

3 0

2 years ago