What is the interest earned on $400 invested at the rate of 6% for one year?

4p = 14.4 What is the value of p? A. 3.6 B 3.8 C.10.4 D.57.6

4vir4ik [10]

The answer to your question is A.

answer: 3.6

6 0

3 years ago

Explain why segments connecting any pair of corresponding vertices of congruent pentagons are congruent. make a sketch to suppor

Veronika [31]

Answer:

Congruence between pentagons

Step-by-step explanation:

The relationship occurs because having two congruent Pentagons and generating a segment within them (or outside), congruence is extrapolated to the triangles generated within them. Thus, if there is congruence among the pentagons, it will exist between the formed triangles. In other words since the two pentagons are congruent, the corresponding angle pair is congruent. also the two corresponding side pairs are also congruent.

In the attached image for example, the ABCDE and KLMNO pentagons are congruent, so all of their internal division lines are also congruent (AC and KM)

8 0

3 years ago

A certain kind of sheet metal has, on average, 3 defects per 18 square feet. Assuming a Poisson distribution, find the probabili

Fofino [41]

Answer:

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

In this problem, we have that:

3 defects per 18 square feet.

So for 31 square feet, we have to solve a rule of three

3 defects - 18 square feet

x defects - 31 square feet

$18x = 3*31$

$x = \frac{31*3}{18}$

$x = 5.17$

So $\mu = 5.17$

Assuming a Poisson distribution, find the probability that a 31 square foot metal sheet has at least 4 defects.

Either it has three or less defects, or it has at least 4 defects. The sum of the probabilities of these events is decimal 1.

So

$P(X \leq 3) + P(X \geq 4) = 1$

We want $P(X \geq 4)$

So

$P(X \geq 4) = 1 - P(X \leq 3)$

In which

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-5.17}*(5.17)^{0}}{(0)!} = 0.0057$

$P(X = 1) = \frac{e^{-5.17}*(5.17)^{1}}{(1)!} = 0.0294$

$P(X = 2) = \frac{e^{-5.17}*(5.17)^{2}}{(2)!} = 0.0760$

$P(X = 3) = \frac{e^{-5.17}*(5.17)^{3}}{(3)!} = 0.1309$

So

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0057 + 0.0294 + 0.0760 + 0.1309 = 0.242$

Finally

$P(X \geq 4) = 1 - P(X \leq 3) = 1 - 0.242 = 0.758$

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

8 0

4 years ago

Evaluate x+x-x for x=4

Dafna1 [17]

The answer is x=4 because 4+4 is 8 and 8 minus 4 is 4

3 0

3 years ago

Solve the system by substitution. 1. y = -6x – 7 y = -7x 2. -y=x 3x+5y=20

Drupady [299]

Answer:

For no. 1:

One of the equations say that y=-7x

So plug in -7x to the other equation as y so you equation would be

-7x= -6x-7

And then, just solve for the variable:

*add -6x to both sides*:

-x= -7

*multiply both by negative one to get a positive variable*

FOR NUMBER 1, THE ANSWER IS:

x=7

Y=-7

For no. 2:

-y=x and your other equation is 3x+5y=20

Plug in x as -y:

-3y+5y=20

*simplify*

2y=20

*divide by 2 on each side to get 1 variable alone*

Y=10

FOR NUMBER 2, THE ANSWER IS:

x=-y

Y=10

8 0

3 years ago