A function is graphed on the coordinate plane.

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

stiks02 [169]

Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

$A=b^{2}$

where b is the length side of the square

we have

$A=49\ units^2$

substitute

$49=b^{2}$

$b=7\ units$

therefore

$AB=BE=ED=AD=7\ units$

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

$A=(AC)(AG)$

substitute the given values

$A=(9)(10)=90\ units^2$

step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

$A=(DE)(DG)$

we have

$DE=7\ units$

$DG=AG-AD=9-7=2\ units$

substitute

$A=(7)(2)=14\ units^2$

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

$A=(EF)(CF)$

we have

$EF=AC-AB=10-7=3\ units$

$CF=BE=7\ units$

substitute

$A=(3)(7)=21\ units^2$

step 5

sum the shaded areas

$14+21=35\ units^2$

step 6

Divide the area of of the shaded region by the area of ACIG

$\frac{35}{90}$

Simplify

Divide by 5 both numerator and denominator

$\frac{7}{18}$

therefore

The fraction of the area of ACIG represented by the shaped region is 7/18

5 0

3 years ago

A quantity with an initial value of 9100 grows continuously at a rate of 0.85% per hour. What is the value of the quantity after

ycow [4]

Answer:

$10,962,54$

Step-by-step explanation:

we know that

The equation of a exponential growth is equal to

$y=a(1+r)^x$

where

a is the initial value

r is the rate of growth

x is the time in hours

y is the value of the quantity

we have

$a=9,100\\r=0.85\%=0.85/100=0.0085$

substitute

$y=9,100(1+0.0085)^x$

$y=9,100(1..0085)^x$

For x=22 hours

substitute

$y=9,100(1..0085)^{22} =10,962,54$

4 0

4 years ago

Solve for angel GLN<br><br> please help asap, need help

likoan [24]

Answer:

119

Step-by-step explanation:

$\mathrm{Supplementary\:angles\:add\:up\:to}\:180^{\circ }$

$\angle \:GKO \mathrm{\:is\:supplementary\:angle\:of\:} \angle \:KNL$

$\mathrm{So\:}\angle \:GKO+\angle \:KNL=180$

$\angle \:GKO+61=180$

$\angle \:GKO=119$

6 0

3 years ago

An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you th

aliya0001 [1]

Answer:

0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .