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stepan [7]
3 years ago
11

The region R enclosed between the graph of the function y=x^2−4x+5 and the x-axis for 0≤x≤4 is partitioned into four subinterval

s. Determine the areas of the four rectangles using MRAM and then approximate the area of R. Round areas to the nearest hundredth. Show and explain your work.
The answer I got for this problem is 9 square units.

Mathematics
2 answers:
Paul [167]3 years ago
8 0

Answer:

9 units²

Step-by-step explanation:

f(x) = x² - 4x + 5

Four intervals, their midpoints and f(MP) for heights:

0≤x<1 --> 0.5 --> 3.25

1<x≤2 --> 1.5 --> 1.25

2<x≤3 --> 2.5 --> 1.25

3<x≤4 --> 3.5 --> 3.25

All four intervals have a width of 1 unit

Sum of areas = total area

= 1×3.25 + 1×1.25 + 1×1.25 + 1×3.25

= 9

Marina CMI [18]3 years ago
7 0

Answer:

9.00 square units

Step-by-step explanation:

The width of the interval is 4 − 0 = 4.  Divided by 4 equal subintervals, the width of each subinterval is 4/4 = 1.

The subintervals are:

0 ≤ x ≤ 1

1 ≤ x ≤ 2

2 ≤ x ≤ 3

3 ≤ x ≤ 4

MRAM is midpoint rectangular approximation method.  So we use the midpoints of each interval to find the height of the rectangle:

f(0.5) = (0.5)² − 4(0.5) + 5 = 3.25

f(1.5) = (1.5)² − 4(1.5) + 5 = 1.25

f(2.5) = (2.5)² − 4(2.5) + 5 = 1.25

f(3.5) = (3.5)² − 4(3.5) + 5 = 3.25

So the total approximate area is:

A = 3.25 + 1.25 + 1.25 + 3.25

A = 9.00

Graph: desmos.com/calculator/x8dcibqszo

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2. The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of
IgorC [24]

Answer:

a) 37.31 b) 42.70 c) 0.57 d) 0.09

Step-by-step explaanation:

We are regarding a normal distribution with a mean of 35 and a standard deviation of 6, i.e., \mu = 35 and \sigma = 6. We know that the probability density function for a normal distribution with a mean of \mu and a standard deviation of \sigma is given by

f(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp[-\frac{(x-\mu)^{2}}{2\sigma^{2}}]

in this case we have

f(x) = \frac{1}{\sqrt{2\pi}6}\exp[-\frac{(x-35)^{2}}{2(6^{2})}]

Let X be the random variable that represents a row score, we find the values we are seeking in the following way

a)  we are looking for a number x_{0} such that

P(X\leq x_{0}) = \int\limits^{x_{0}}_{-\infty} {f(x)} \, dx = 0.65, this number is x_{0}=37.31

you can find this answer using the R statistical programming languange and the instruction qnorm(0.65, mean = 35, sd = 6)

b) we are looking for a number  x_{1} such that

P(X\leq x_{1}) = \int\limits^{x_{1}}_{-\infty} {f(x)} \, dx = 0.9, this number is x_{1}=42.70

you can find this answer using the R statistical programming languange and the instruction qnorm(0.9, mean = 35, sd = 6)

c) we find this probability as

P(28\leq X\leq 38)=\int\limits^{38}_{28} {f(x)} \, dx = 0.57

you can find this answer using the R statistical programming languange and the instruction pnorm(38, mean = 35, sd = 6) -pnorm(28, mean = 35, sd = 6)

d) we find this probability as

P(41\leq X\leq 44)=\int\limits^{44}_{41} {f(x)} \, dx = 0.09

you can find this answer using the R statistical programming languange and the instruction pnorm(44, mean = 35, sd = 6) -pnorm(41, mean = 35, sd = 6)

6 0
3 years ago
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Aleks04 [339]
Balance in account cannot be less than
7 0
3 years ago
You are knitting a blanket. You want the area of the blanket to be 24 ft². You want the length of the blanket to be 2 feet longe
Finger [1]
With the facts you got here, you can make the following equation:

x*(x+2)=24

x^2+2x=24
x^2+2x-24=0

Then you can use the following formula (which you might have seen before):
x = (-b +/- sqrt(b^2-4ac))/2a

where
ax^2+bx+c=0

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3 0
3 years ago
Read below i need some help please
Anton [14]

Answer:

<u><em>8/20</em></u>

Step-by-step explanation

<em>boys left handed=3 </em>

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<em>girls left handed=2 </em>

<em>girls right handed=6 </em>

<em>what is the probability that a student chosen from random is a girl? give answer as a fraction please and include step by step process</em>

<em>girls left handed: 2</em>

girls right handed: 6

6+2=8

total all students 20

<em>8/20</em>

4 0
3 years ago
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Paladinen [302]

Answer: B 5+5=10+4+4+4=12+3 10+12+3 25 lol

Step-by-step explanation:

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