All categories

3 years ago

The area of a rectangle is 60 in² and the length of the rectangle is 7 in. longer than the width.

Mathematics

1 answer:

8090 [49]3 years ago

7 0

Answer:

w(w+7)=60

Step-by-step explanation:

Ideally,Area of a triangle is given by A=L×W ,where A= area, L=length and W= width

and from the expression the length is seven more than the width means :7+W

Also t from the expression

The area of a rectangle is found by multiplying the length times the width
makes the equation become

A= W(W+7)As the formula.

You might be interested in

Which expresions are equivalent to x+2y+x+2? yall please help....

Iteru [2.4K]

Answer:

2x + 2y + 2

Step-by-step explanation:

x+ 2y + x +2 (combine like terms)

x + x + 2y + 2

2x + 2y + 2

8 0

2 years ago

Using 5 letters followed by 2 digits, how many passwords are possible?

Deffense [45]

Since there is no condition whatsoever for this arrangement, I can consider the 2 digits and the 5 letters as 7 different objects.

Total permutation (with no repetition):
7 chosen among 7 , that is 7 ! = 5040 arrangements

Total permutation (WITH REPERTITION):

7⁷ = 823 543

6 0

2 years ago

According to a survey, 65% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed

monitta

Answer:

a) $P(X=41)=(50C41)(0.65)^{41} (1-0.65)^{50-41}=0.00421$

b) $P(X=36)=(50C36)(0.65)^{36} (1-0.65)^{50-36}=0.0714$

$P(X=37)=(50C37)(0.65)^{37} (1-0.65)^{50-37}=0.0502$

$P(X=38)=(50C38)(0.65)^{38} (1-0.65)^{50-38}=0.0319$

And adding these values we got:

$P(36 \leq X \leq 38)= 0.1535$

c) We can find the expected value given by:

$E(X) = np =50*0.65 = 32.5$

And the standard deviation would be:

$\sigma = \sqrt{np(1-p)} \sqrt{50*0.65*(1-0.65)}= 3.373$

We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:

$\mu -2\sigma = 32.5- 2*3.373 = 25.75$

And then we can consider a value of 18 as unusual lower for this case.

Step-by-step explanation:

Let X the random variable of interest "number cleared by arrest or exceptional", on this case we can model this variable with this distribution:

$X \sim Binom(n=50, p=0.65)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

We want this probability:

$P(X=41)=(50C41)(0.65)^{41} (1-0.65)^{50-41}=0.00421$

Part b

We want this probability:

$P(36 \leq X \leq 38)$

We can find the individual probabilities:

$P(X=36)=(50C36)(0.65)^{36} (1-0.65)^{50-36}=0.0714$

$P(X=37)=(50C37)(0.65)^{37} (1-0.65)^{50-37}=0.0502$

$P(X=38)=(50C38)(0.65)^{38} (1-0.65)^{50-38}=0.0319$

And adding these values we got:

$P(36 \leq X \leq 38)= 0.1535$

Part c

We can find the expected value given by:

$E(X) = np =50*0.65 = 32.5$

And the standard deviation would be:

$\sigma = \sqrt{np(1-p)} \sqrt{50*0.65*(1-0.65)}= 3.373$

We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:

$\mu -2\sigma = 32.5- 2*3.373 = 25.75$

And then we can consider a value of 18 as unusual lower for this case.

6 0

3 years ago

a delivery man weighs 200 pounds. he is delivering cartons that each weigh 48 pounds. he wants to know how many cartons he can s

Anastasy [175]

The inequality is:

48 c + 200 ≤ (the maximum load allowed on the elevator) .

8 0

3 years ago

The area of a parallelogram is 96 cm2. The height of the parallelogram is 4 cm less than the length of the base. What is the len

Valentin [98]

96/4=24 so the length of a standerd paralleegram is 24