3(2/3) of 4 ÷ 2(1/4) + 2/6

The area of a rectangular fountain is x2 + 9x + 20 square feet. A 3-foot walkway is built around the fountain. Find the dimensio

Leto [7]

Answer:

(x+11) by (x+10)

Step-by-step explanation:

We know that Area = Length x width

Given: Area = x²+9x+20

Lets sort this out first

Area = x²+5x + 4x + 20

Area = x(x+5) + 4(x+5)

Area = (x+5) (x+4)

Therefore, it is concluded that:

Length 'l' = (x+5) feet

Width 'w' = (x+4) feet

if a 3-foot walkway is built around the fountain, we'll add 3 feet on both sides

Therefore,

Outer Length = (x+5+3+3) = (x+11) feet

Outer Width = (x+4+3+3) = (x+10) feet

Answer:

The fountain is (x+5) by (x+4).

dimensions of the outside border of the walkway are (x+11) by (x+10)

8 0

3 years ago

20x^2-30=4x solve for x

ankoles [38]

Answer:

x=1.3288 or -1.1288

Step-by-step explanation:

Given $20x^{2}-30=4x$

Subtract 4x from both sides

$20x^{2}-4x-30=0$

Since we can factor out 2 from whole equation, let's factor out 2.

$2(10x^{2}-2x-15)=0$

Divide with 2 on both sides

$10x^{2}-2x-15=0$

We got the quadratic equation, we can solve for x using quadratic formula.

$x=\frac{-b\pm\sqrt{b^{2}-4ac} } {2a}$

$x=\frac{2\pm\sqrt{2^{2}-4X10X(-15)} } {2X10}$

$x=\frac{2\pm\sqrt{604} }{20}$

$x=\frac{2\pm2\sqrt{151}}{20}$

$x=1.3288or-1.1288$

8 0

3 years ago

Read 2 more answers

A manufacturer of televisions subjects the equipment to a comprehensive testing process for all essential functions before the t

Scorpion4ik [409]

Answer:

The probability is $P(X \le 9) =0.9138$

Step-by-step explanation:

From the question we are told that

The probability of the television passing the test is p = 0.95

The sample size is n = 10

Generally the comprehensive testing process for all essential functions follows a binomial distribution

i.e

$X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial distribution is

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

Here C stands for combination hence we are going to be making use of the combination function in our calculators

Generally the probability that at least 9 pass the test is mathematically represented as

$P(X \le 9) = P(X = 9) + P(X = 10 )$

=> $P(X \le 9) = [^{10}C_9 * (0.95)^9 * (1- 0.95)^{10-9}]+ [^{10}C_{10} * {0.95}^{10} * (1- 0.95)^{10-10}]$

=> $P(X \le 9) = [10 * 0.6302 * 0.05 ]+ [1 *0.5987 * 1 ]$

=> $P(X \le 9) =0.9138$

8 0

3 years ago

What is the slope of the line?

Simora [160]

Answer:

The slope is 0.5 or (1/2)

Step-by-step explanation:

Find the rise over run.

from -3 to -1 and 2 to 3 rises 1 runs 2 so then you divide 1/2 and get 0.5.

8 0

3 years ago

The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.03t3 + 0.5t2 + 9t + 4. Find S'(t).

o-na [289]

Answer:

S'(t) = 0.09t^2 + t + 9

S(2) = 24.24

S'(2) = 11.36

S(11) = 203.43 means that the sales of the company 11 months from now is $203,430,000.

S'(11) = 30.89 means that, 11 months from now, the rate at which sales change is $30,890,000 per month

Step-by-step explanation:

The derivate of the sales function S'(t) , which is the rate at which sales vary with time in months, is:

$\frac{dS(t)}{dt} =S'(t) = 0.09t^2 + t + 9$

S(2) is found by applying t=2 to S(t):

$S(2) = 0.03*(2^3) + 0.5*(2^2) + 9*2 + 4\\S(2)= 24.24$

S'(2) is found by applying t=2 to S'(t):

$S'(2) = 0.09*(2^2) + 2 + 9\\S'(2) = 11.36$

Since the sales function gives the amount of sales in millions of dollars,

S(11) = 203.43 means that the sales of the company 11 months from now is $203,430,000.

S'(t) represents the rate of change in sales in millions of dollars per month.

S'(11) = 30.89 means that, 11 months from now, the rate at which sales change is $30,890,000 per month

8 0

3 years ago

3(2/3) of 4 ÷ 2(1/4) + 2/6 - 1/2​

3(2/3) of 4 ÷ 2(1/4) + 2/6 - 1/2