1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anuta_ua [19.1K]
2 years ago
14

Can someone help me out with this Area question​

Mathematics
1 answer:
Elena L [17]2 years ago
3 0

Answer:

  • b = 10.1459
  • h = 16.8541

Step-by-step explanation:

The area of a rectangle is the product of its length and width:

  A = 171 = bh

The perimeter of a rectangle is the sum of the lengths of its sides:

  P = 54 = b + h + b + h = 2(b +h)

We can use the latter equation to write an expression for h that can be substituted into the first equation.

  27 = b + h . . . . divide by 2

  h = 27 -b . . . . . subtract b

Now, the area is ....

  171 = b(27-b) = -b^2 +27b

Multiplying by -1 we get ...

  b^2 -27b = -171

adding the square of half of 27, we can "complete the square":

  b^2 -27b +13.5^2 = -171 +13.5^2 = 11.25

  (b -13.5)^2 = 11.25 . . . . write as a square

  b -13.5 = -√11.25 . . .  . . find the negative square root

  b = 13.5 -√11.25 ≈ 10.1459

  h = 27 -b ≈ 16.8541

The missing measurements are approximately ...

  b = 10.1459

  h = 16.8541

_____

<em>Comment on the problem</em>

We suspect a typo in the problem. If the perimeter were 56, then the dimensions would be 9 and 19, integer factors of 171.

You might be interested in
-4/9 repeating decimal
Liula [17]

Yes that is a repeating decimal the answer would be -0.4444444.. and so on.

4 0
3 years ago
Which expressions are equivalent to (5g+3g+4)x2
FrozenT [24]
It’s A, cuz the 4*2 equals 8
4 0
3 years ago
Help me with this helpppppppppppppp worth 20 points
MariettaO [177]
I think its 2/12 but not 100% sure
5 0
3 years ago
Read 2 more answers
A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sur
Finger [1]

Answer:

The area of the triangle should be: [(1 + 5 + 4) × 11]/2= 55 (ft²)

The area of the rectangle should be: 5 × 2 = 10 (ft²)

The area of the shaded region is: 55 - 10 = 45 (ft²)

7 0
3 years ago
The web logs of a certain website show that the average number of hits in an hour is 75 with a standard deviation equal to 8.6.
Wittaler [7]

Answer:

a) There is a 10.75% probability of observing less than 60 hits in an hour.

b) The 99th percentile of the distribution of the number of hits is 95.21 hits.

c) There is a 24% probability of observing between 80 and 90 hits an hour

Step-by-step explanation:

Problems of normally distributed samples can be 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}

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. The sum of the probabilities is decimal 1. So 1-pvalue is the probability that the value of the measure is larger than X.

In this problem, we have that

The web logs of a certain website show that the average number of hits in an hour is 75 with a standard deviation equal to 8.6, so \mu = 75, \sigma = 8.6.

a) What’s the probability of observing less than 60 hits in an hour? Use the normal approximation

This is the pvalue of Z when X = 60. So

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

Z = \frac{60 - 75}{8.6}

Z = -1.74

Z = -1.74 has a pvalue of 0.1075. This means that there is a 10.75% probability of observing less than 60 hits in an hour.

b) What’s the 99th percentile of the distribution of the number of hits?

What is the value of X when Z has a pvalue of 0.99.

Z = 2.35 has a pvalue of 0.99

So

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

2.35 = \frac{X - 75}{8.6}

X - 75 = 20.21

X = 95.21

The 99th percentile of the distribution of the number of hits is 95.21 hits.

c) What’s the probability of observing between 80 and 90 hits an hour?

This is the pvalue of the zscore of X = 90 subtracted by the pvalue of the zscore of X = 80.

For X = 90

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

Z = \frac{90 - 75}{8.6}

Z = 1.74

Z = 1.74 has a pvalue of 0.95907

For X = 80

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

Z = \frac{80 - 75}{8.6}

Z = 0.58

Z = 0.58 has a pvalue of 0.71904

So

There is a 0.95907 - 0.71904 = 0.24003 = 24% probability of observing between 80 and 90 hits an hour

6 0
3 years ago
Other questions:
  • Write 10 5/12 as an equivalent improper fraction.
    10·1 answer
  • How do you integrate arctan(x dx? i think that if you simplify the integral you get:?
    15·1 answer
  • kate spent 3/5 of her money on a manicure and had $45 left. how much money did she have at first?(PLEASE SHOW STEPS!)
    8·2 answers
  • The measure ∠BQS of is 80°. What is the m∠NQS? 42° 48° 128° 32°
    9·2 answers
  • The square root of 110 is between which two integers
    6·1 answer
  • 3) What is the greatest common factor of 5x7, 30x4, and 10x3?
    13·2 answers
  • Please help!
    11·1 answer
  • Given points B(−12,2), T(−8,10), A(−7,12), F(−6,10), and G(−2,2), which of the following proves that △BAG~△TAF?
    5·1 answer
  • What the Algebraic Rule? How many tiles?
    11·1 answer
  • ASAP kinda need help atm if anyone can solve this?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!