All categories

3 years ago

The area of the rectangle to the right is 68 square feet

Mathematics

1 answer:

den301095 [7]3 years ago

6 0

Step-by-step explanation:

We know that

Area of the rectangle=Length×Breadth

➝(x+4)(x-9)=68

➝x(x-9)+4(x-9)=68

➝x^2-9x+4x+-32=68

➝x^2-5x-32=68

➝x^2-5x=68+32

➝x^2-5x=100

➝x^2-5x-100=0

The equation has no real roots hence this situation can't be possible

You might be interested in

According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated e

slamgirl [31]

Answer:

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that $p = 0.09$

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{12,0}.(0.09)^{0}.(0.91)^{12} = 0.3225$

$P(X = 1) = C_{12,1}.(0.09)^{1}.(0.91)^{11} = 0.3827$

$P(X = 2) = C_{12,2}.(0.09)^{2}.(0.91)^{10} = 0.2082$

$P(X = 3) = C_{12,3}.(0.09)^{3}.(0.91)^{9} = 0.0686$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3225 + 0.3827 + 0.2082 + 0.0686 = 0.982$

Finally

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.982 = 0.0180$

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

6 0

3 years ago

Please help asap ty !!

Advocard [28]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

An air conditioning technician charged Robert $77.25 to repair his air conditioning system after 3 hours of work. The technician

agasfer [191]

Answer:B

Step-by-step explanation:

He charged the man $25.75 for each hour and he worked for 3 hours so multiply $25.75 x 3 = $77.25

5 0

3 years ago

How much 20% solution needs to be added to a 60% solution to make 400 ml of a 40% solution

Scorpion4ik [409]

Let $x$ be the volume of 20% solution, $y$ the volume of the 60% solution. We want a total volume of 400 mL in the final mixture, so

$x+y=400$

Each mL of either solution will contribute a corresponding concentration, and in the final mixture we want the 400 mL to have a 40% concentration, which means we should also have

$0.2x+0.6y=0.4\times400=160$