10x+2 = 3x + 30 Find x (please)

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. A medical center o

viktelen [127]

Answer:

1) 0.1504

2) 0.432

Step-by-step explanation:

1) The given information are;

The proportion of the morning appointments that are with elderly patients = 60%

The number of patients in the appointments = 10 patients

The proportion of the morning appointments that are with non-elderly patients = 100 - 60 = 40%

The binomial probability distribution is given as follows;

$P(X = r) = \dbinom{n}{r}p^{r}\left (1-p \right )^{n-r}$

$P(X = 0) = \dbinom{10}{0}0.6^{0}\left (1-0.6 \right )^{10}$ = 0.000105

$P(X = 1) = \dbinom{10}{1}0.6^{1}\left (1-0.6 \right )^{9}$ = 0.0016

$P(X = 2) = \dbinom{10}{2}0.6^{2}\left (1-0.6 \right )^{8}$ = 0.01062

$P(X = 3) = \dbinom{10}{3}0.6^{3}\left (1-0.6 \right )^{7}$ = 0.0425

The probability that the first four patients are elderly is 0.000105 + 0.0016 + 0.1062 + 0.0425 = 0.1504

2) The probability that exactly 2 out of 3 morning patients are elderly patient is given as follows

$P(X = 2) = \dbinom{3}{2}0.6^{2}\left (1-0.6 \right )^{1}$ = 0.432

8 0

4 years ago

If i u have 110 dogs and the ratio of puppies is 2:3. How many puppies

navik [9.2K]

Question: You have 110 dogs (which is the total amount of dogs/pups) and the ratio of the puppies is 2:3. How many puppies are there?

Add 2 and 3 which adds to 5 (You need to combine all the "pie pieces")

Now, divide 110 by 5

$110$ ÷ $5=22$

Now multiply 2 and 22

$2*22=44$

Now multiply 3 and 22

$3*22=66$

The ratio is 44:66

Answer: There are 44 puppies

4 0

3 years ago

Let t = cosA + sinA<br> find values of t if <br> 2 - sin2A = 2(cosA + sinA)

Zinaida [17]

$2 - \sin(2A) = 2(\cos A + \sin A)\\\\2-2\sin A\cos A=2\cos A+2\sin A\\\\2\sin A\cos A+2\cos A+2\sin A-2=0\\\\1+2\sin A\cos A+2\cos A+2\sin A-3=0\\\\\sin^2 A+\cos^2 A+2\sin A\cos A+2\cos A+2\sin A-3=0\\\\(\sin A+\cos A)^2+2\cos A+2\sin A-3=0\\\\(\sin A+\cos A)^2+2(\cos A+\sin A)-3=0\\\\\\t^2+2t-3=0\\\\t^2+2t+1-4=0\\\\(t+1)^2=4\\\\t+1=2\qquad\vee \qquad t+1=-2\\\\\\\boxed{t=1\qquad\vee\qquad t=-3}$

When $A\in\mathbb{R}$

$t=\cos A+\sin A\in[-\sqrt{2};\sqrt{2}]\approx[-1.4142;1.4142]$

and there is only one answer t = 1.

For $A\in\mathbb{C}$ both values are correct.

4 0

4 years ago

Ms. Spencer is packing orders for her bath supply business. One customer ordered 8 bath fizzies and 4 jars of sugar scrub. Each

sergey [27]

8 bath fizzes * 5 (ounces) = 40 ounces. 4 jars of sugar scrub * 1.5 (pounds) = 6 pounds. So 6 pound and 40 ounces. (40 ounces = 2.5 pounds. So 8.5 pounds in total.) ( If you want to convert the answer to ounces, 8.5 pounds is 136 ounces.)

8 0

3 years ago

Solve this system of equations by

dimulka [17.4K]

Answer:

(5,-5)

x=5

y=-5

Step-by-step explanation:

How to solve using elimination method.

First, add the two equations.

2x - 3y = 25

+ <u>5x + 3y = 10</u>

7x=35

The y values got eliminated.

Next, divide 7 from both sides.

7x/7=35/7

x=5

Next, plug-in x=5 into one of the equations.

2(5) - 3y = 25

10-3y=25

Subtract 10 from both sides.

-3y=15

Divide -3 from both sides.

y=-5

Remember a positive divided by a negative is a negative.

Hope this helps!

If not, I am sorry.

7 0

2 years ago