Find how much should be invested to have $12,000 in 11 months at 6.1% simple interest.

There are 30 singers in a show. The ratio of singers to dancers is 5:6. How many dancers are there?

Tamiku [17]

Answer: 32 dancers

Step-by-step explanation:

I drew a chart and on the side with the singers you count by 5's until u get to 30. On the dancers side of the chart you count by 6's until it lines up with 30 on the singers side.

5 0

3 years ago

Read 2 more answers

Graph the line. y=-4x+6 what the graph

Aloiza [94]

So the -4x is the M and then 6 is the B. So m is the slope and B is the y-intercept. The 6 goes on the y axis and the -4 will be how the line looks. It’ll be rise (-4) over run (1).

4 0

2 years ago

Show that every positive integer is of the form 2q and that every odd integer is of the

irinina [24]

IF n is a positive integer THEN n mod 2=0
IF n is an odd integer THEN n mod 2=1
SO you can draw that conclusion.
You are welcome.

6 0

3 years ago

The computers of nine engineers at a certain company are to be replaced. Four of the engineers have selected laptops and the oth

Gala2k [10]

Answer:

(a) There are 70 different ways set up 4 computers out of 8.

(b) The probability that exactly three of the selected computers are desktops is 0.305.

(c) The probability that at least three of the selected computers are desktops is 0.401.

Step-by-step explanation:

Of the 9 new computers 4 are laptops and 5 are desktop.

Let X = a laptop is selected and Y = a desktop is selected.

The probability of selecting a laptop is = $P(Laptop) = p_{X} = \frac{4}{9}$

The probability of selecting a desktop is = $P(Desktop) = p_{Y} = \frac{5}{9}$

Then both X and Y follows Binomial distribution.

$X\sim Bin(9, \frac{4}{9})\\ Y\sim Bin(9, \frac{5}{9})$

The probability function of a binomial distribution is:

$P(U=k)={n\choose k}\times(p)^{k}\times (1-p)^{n-k}$

(a)

Combination is used to determine the number of ways to select <em>k</em> objects from <em>n</em> distinct objects without replacement.

It is denotes as: ${n\choose k}=\frac{n!}{k!(n-k)!}$

In this case 4 computers are to selected of 8 to be set up. Since there cannot be replacement, i.e. we cannot set up one computer twice or thrice, use combinations to determine the number of ways to set up 4 computers of 8.

The number of ways to set up 4 computers of 8 is:

${8\choose 4}=\frac{8!}{4!(8-4)!}\\=\frac{8!}{4!\times 4!} \\=70$

Thus, there are 70 different ways set up 4 computers out of 8.

(b)

It is provided that 4 computers are randomly selected.

Compute the probability that exactly 3 of the 4 computers selected are desktops as follows:

$P(Y=3)={4\choose 3}\times(\frac{5}{9})^{3}\times (1-\frac{5}{9})^{4-3}\\=4\times\frac{125}{729}\times\frac{4}{9}\\ =0.304832\\\approx0.305$

Thus, the probability that exactly three of the selected computers are desktops is 0.305.

(c)

Compute the probability that of the 4 computers selected at least 3 are desktops as follows:

$P(Y\geq 3)=1-P(Y$

Thus, the probability that at least three of the selected computers are desktops is 0.401.

6 0

3 years ago

Vector V is in standard position and makes an angle of 50° with the positive x-axis. Its magnitude is 18. Write V in component f

Umnica [9.8K]

Answer:

11.57 units east, 13.79 units upwards

11.57i + 13.79j

Step-by-step explanation:

V = 18 units at an angle of 50° to the positive x-axis

In component Form, this is how each component is calculated

a = 18cos50° = 11.57 units east

b = 18sin50° = 13.79 units upwards

check if your answer is correct

$\sqrt{11.57^{2} +13.79^{2} } = 18.0$

In vector component form ai + bj = 11.57i + 13.79j

7 0

3 years ago