Help me solve using either elimination or comparison.

. A high school currently has a 30% dropout rate. They’ve been tasked to decrease that rate by 20%. Find the equivalent percenta

Crazy boy [7]

Answer:

The equivalent percentage point drop = 10%

Step-by-step explanation:

The percentage point change is the difference between the final and initial values.

The percentage change is the difference between the final and initial values

divided by the initial value

It is required to decrease the dropout rate from 30% to 20%

The point change = 20 - 30 = -10 (-ve change ⇒ decrease)

The percentage change = $\frac{10}{30}*100 = 33.33_%$ %

So, the equivalent percentage point drop = <u>10%</u>

And the percentage change = <u>33.33%</u>

3 0

3 years ago

In order to finish the order on time the factory was supposed to produce 70 items daily. After hiring three more people they wer

maria [59]

Answer:

40 days

Step-by-step explanation:

Let x represent the original production time. Then 70x is the order quantity involved.

When the same order quantity is produced at a rate of 80 items per day for x-5 days, we have the equation ...

70x = 80(x -5)

70x = 80x -400

0 = 10x -400 . . . . . subtract 70x

0 = x -40 . . . . . . . . divide by 10

40 = x . . . . . . . . . . add 40

The original schedule was for production to take 40 days.

8 0

3 years ago

A foreman for an injection-molding firm admits that on 55% of his shifts, he forgets to shut off the injection machine on his li

motikmotik

Answer:

0.8594

Step-by-step explanation:

Let a denote the event of forgetting to shut off machine and b be the event of being defective.

-A foreman forgets to shut off machine 55% of the time.

-If he forgets, 15% of molds are defective.

-If he does not, 3% of molds are defective.

#The probability that he forgot to shut off the machine is calculated as:

$P(a \ and \ b)=0.55\times 0.15\\\\=0.0825\\\\$

P(a and ~b)=0.55(1-0.15)=0.4675

P(~a and b) = (1-0.55)*0.03=0.0135

P(~a and ~b) = (1-0.55)*(1-0.03)=0.4365

#Conditional probability is defined as:

$P(a|b)=\frac{P(a \ and\ b)}{P(a)}\\\\=\frac{P(a \ and \ b)}{[(P(a \ and \ b)+P(\~a \ and \ b)}\\\\\\=\frac{0.0825}{0.0825+0.0135}\\\\\\=0.8594$

Hence, the probability that the foreman forgot to shut off the machine the previous night is 0.8594

5 0

3 years ago

2x+10=6(x-1) What does x equal

Gennadij [26K]

Answer:

x=4

Step-by-step explanation:

2x+10=6(x-1)

2x+10=6x-6

10=6x-2x-6

10=4x-6

16=4x

4=x

4 0

3 years ago

Which equation represents a circle that contains the point (-5, 3) and has a center at (-2, 1)? Distance formula: vaa -02 (x - 1

natali 33 [55]

Given:

The center of the circle = (-2,1).

Circle passes through the point (-5,3).

To find:

The equation of the circle.

Solution:

Radius is the distance between the center of the circle and any point on the circle. So, radius of the circle is the distance between the points (-2,1) and (-5,3).

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(-5-(-2))^2+(3-1)^2}$

$r=\sqrt{(-5+2)^2+(2)^2}$

$r=\sqrt{(-3)^2+(2)^2}$

On further simplification, we get

$r=\sqrt{9+4}$

$r=\sqrt{13}$

The standard form of a circle is:

$(x-h)^2+(y-k)^2=r^2$

Where, (h,k) is the center of the circle and r is the radius of the circle.

Substitute h=-2, k=1 and $r=\sqrt{13}$ .

$(x-(-2))^2+(y-1)^2=(\sqrt{13})^2$

$(x+2)^2+(y-1)^2=13$

Therefore, the equation of the circle is $(x+2)^2+(y-1)^2=13$ .

8 0

3 years ago