Question 1 (1 point)

Melanie is 2 years older than twice her brother Bill’s age. If Bill is 5 years old,how old is Melanie

arlik [135]

she would be 12 because

10 * 2 = 10

10 + 2 = 12

hope this helps :)

8 0

3 years ago

Read 2 more answers

I need help with this probability problem. I’m helping my brother with his homework and I don’t know how to solve this question.

Aleksandr-060686 [28]

Hello from MrBillDoesMath!

Answer:

Number marbles >= 5

Discussion:

The only certain thing we can say is the jar contains at least 5 (green) marbles. The table shows probabilities, not certainties, and is no guarantee that any other marbles even exist in the jar,

Thank you,

MrB

5 0

3 years ago

A math teacher gets a starting salary of $30,000. IF she gets a 1.5% increase in salary each year, what will her total income be

kolezko [41]

No it is not base e. It is 1.015.

An increase of 1.5 % = 1.015

Year     1,   2,   3,.........................., 30.
   30000, 3000(1.015), 30000(1.015)²,........... 30000(1.015)²⁹

Her Total Income is sum over the thirty 30 year period:

Sn = a(r^n - 1) / (r - 1); a = 30000, r = 1.015, n = 30

Sn = 30000 ( 1.015^30 - 1) / (1.015 - 1)

      = 30000 (1.56308022 - 1) / (0.015) = 1126160.44

Total = $ 1 126 160.44

5 0

2 years ago

A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While

Murljashka [212]

Answer:

The expected number of appearance defects in a new car = 0.64

standard deviation = 0.93(approximately)

Step-by-step explanation:

Given -

7% had exactly three, 11% exactly two, and 21% only one defect in cars.

Let X be no of defects in a car

P(X=3) = .07 , P(X=2) = .11 , P(X=3) = .21

P(X=0 ) = 1 - .07 - .11 - .21 = 0.61

The expected number of appearance defects in a new car =

E(X) = $\nu$ = $= \sum X P(X) =3\times 0.07 + 2\times0.11 + 3\times0.21 + 0\times0.61$ = 0.64

$\sigma^{2}$ = variation of E(X) = $\sum (X - \nu) ^{2}P(X)$ = $(3 - 0.64) ^{2}\times0.07 + (2 - 0.64) ^{2}\times0.11 + (1 - 0.64) ^{2}\times0.21 + (0 - 0.64) ^{2}\times0.61$

= $(2.36) ^{2}\times0.07 + (1.36) ^{2}\times0.11 + (.36) ^{2}\times0.21 + ( 0.64) ^{2}\times0.61$ = 0.8704

standard deviation = $\sqrt{\sigma^{2}}$ = $\sqrt{0.8704^{2}}$ = 0.93(approximately)

4 0

3 years ago

Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and

Anastaziya [24]

The problem is modelled in the first picture shown below

To work out the resultant vector, we modelled the vectors 150N and 75N as triangle AOB is shown in the second picture with AB as the resultant vector.

We use the cosine rule to work out the length AB
$AB^{2}= 75^{2}+ 150^{2}-(2*75*150*cos(60))$
$AB^{2} =28125-11250$
$AB^{2}=16875$
$AB= \sqrt{16875} =130$ (nearest whole number)

The third picture shows the full diagram of the vectors

To work out the direction of the resultant vector, we use the sin rule to find the size of angle A and angle B

Angle A
$\frac{130}{sin(60)}= \frac{75}{sin(A)}$
$130sin(A)=75sin(60)$
$sin(A)= \frac{75sin(60)}{130}$
$sin(A)=0.4996300406$
$A= sin^{-1}(0.4996300406)$
$A=30$ (rounded to nearest whole number)

Angle B
$B=180-60-30=90$

Direction is 60° toward negative x-axis

Answer: Magnitude 130N and direction 60° toward negative x-axis

3 0

3 years ago