How do you find the inverse of a function on a graph

This figure is the pre-image of a prism that has undergone a dilation with a scale factor of 3/4.

belka [17]

The surface area of the image after the dilation is 219 3/8 m²

Area is the amount of space occupied by a two dimensional shape or object.

The surface area of the prism = 2(0.5 * 5 * 12) + (5 * 11) + (11 * 12) + (13 * 11) = 390 m²

The surface area of the image after the dilation = scale factor² * 390 m² = (3/4)² * 390 m² = 219 3/8 m²

The surface area of the image after the dilation is 219 3/8 m²

Find out more on area at: brainly.com/question/25292087

5 0

2 years ago

Determine the average speed of the current in a river if a boat moves at 20 miles/hour in still water and takes 3 hours to trave

Taya2010 [7]

The speed of the current in a river is 6 miles per hour

Solution:

Given that,

Speed of boat in still water = 20 miles per hour

Time taken = 3 hours

Distance downstream = 78 miles

To find: Speed of current

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:

Speed downstream = (u + v) km/hr

Speed upstream = (u - v) km/hr

Therefore, speed downstream is given as:

$\text{ speed downstream } = \frac{distance}{time} = \frac{78}{3}\\\\\text{ speed downstream } = 26 \text{ miles per hour }$

We know that,

Speed downstream = (u + v)

26 = 20 + v

v = 26 - 20

v = 6 miles per hour

Thus speed of the current in a river is 6 miles per hour

3 0

3 years ago

The area of a rectangle is 30 square root 3750 square inches, and the length is 3 square root 250 inches what is the width of th

Ann [662]

Answer:

$width=10\sqrt{15}\ in$

Step-by-step explanation:

-A rectangle's area is given by:

$A=lw\\\\l=length\\w=width$

Given A= $30\sqrt{3750}$ and $l=3\sqrt{250}$ , we substitute in the formula to solve for the width as follows:

$A=lw\\\\30\sqrt{3750}=3\sqrt{250}\times w\\\\w=\frac{30\sqrt{3750}}{3\sqrt{250}}\\\\w=10\frac{\sqrt{3750}}{\sqrt{250}}\\\\=10\times \sqrt{\frac{3750}{250}}\\\\=10\sqrt{15}\ in$

Hence , the rectangle's width is $10\sqrt{15}\ in$

6 0

3 years ago

Suppose you invested $10,000 part at 6% annual interest and the rest at 9% annual interest. If you received $684 in interest aft

victus00 [196]

Assuming simple interest (i.e. no compounding within first year), then
At 6%, interest = 10000*0.06=$600
At 9% interest = 10000*0.09 = $900

Two ways to find the ratio
method A. let x=proportion at 6%
then
600x+900(1-x)=684
Expand and solve
300x=900-684=216
x=216/300=0.72 or 72%
So 10000*0.72=7200 were invested at 6%
10000-7200=2800 were invested at 9%

method B: by proportions
Ratio of investments at 6% and 9%
= 900-684 : 684-600
=216 : 84
= 18 : 7
Amount invested at 6% = 18/(18+7) * 10000 = 0.72*10000 = 7200
Amount invested at 8% = 7/(18+7)*10000=0.28*10000=2800

5 0

3 years ago

The lengths of nails produced in a factory are normally distributed with a mean of 4.84 centimeters and a standard deviation of

Helga [31]

Answer:

Top 3%: 4.934 cm

Bottom 3%: 4.746 cm

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 4.84, \sigma = 0.05$