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faltersainse [42]
3 years ago
11

It takes Hank 40 minutes (2/3 hours) to mow a lawn. Penny can mow the same size lawn in 30 minutes (1/2 hour). Hank and Penny fo

rm a small lawn care company and have contracts for 7 lawns of the same size previously mentioned. How long should it take both of them working together to mow the 7 lawns? (Hint: find a combined hourly rate of ""lawns per hour"" for Hank and Penny.)
Mathematics
1 answer:
ivolga24 [154]3 years ago
8 0

Answer: it will take them 2 hours to now 7 lawns

Step-by-step explanation:

It takes Hank 40 minutes (2/3 hours) to mow a lawn. This means that his unit rate of working is 1/40

Penny can mow the same size lawn in 30 minutes (1/2 hour). This means that his unit rate of working is 1/30

If they form a small lawn care company, they will be working together and simultaneously at a faster combined rate. Since their rates are additive.

If they finish one lawn in t hours, working together, then their combined working rate for one lawn is 1/t. Therefore

1/40 + 1/30 = 1/t

1/t = 7/120

t = 120/7 = 17.14

They will now one lawn in 17.14 minutes

For 7 lawns, it will take them 17.14 × 7 = 119.98 minutes. It is approximately 120 minutes.

We will convert from minutes to hour.

60 minutes = 1 hour

120 minutes = 120/60 = 2 hours

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Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an lg sm
GuDViN [60]
Answer: 0.951%

Explanation:

Note that in the problem, the scenario is either the adult is using or not using smartphones. So, we have a yes or no scenario involved with the random variable, which is the number of adults using smartphones. Thus, the number of adults using smartphones follows the binomial distribution.

Let x be the number of adults using smartphones and n be the number of randomly selected adults. In Binomial distribution, the probability that there are k adults using smartphones is given by

P(x = k) = \frac{n!}{k!(n-k)!}p^k (1-p)^{n-k}

Where p = probability that an adult is using smartphones = 54% (since 54% of adults are using smartphones). 

Since n = 12 and k = 3, the probability that fewer than 3 are using smartphones is given by

P(x \ \textless \  3) = P(x = 0) + P(x = 1) + P(x = 2)
\\ \indent = \frac{12!}{0!(12-0)!}(0.54)^0 (1-0.54)^{12-0} + \frac{12!}{1!(12-1)!}(0.54)^1 (1-0.54)^{12-1} + \\ \indent \frac{12!}{2!(12-2)!}(0.54)^2 (1-0.54)^{12-2}
\\
\\ \indent = \frac{12!}{(1)(12!)}(0.46)^{12} + \frac{12(11!)}{(1)(11!)}(0.54)(0.46)^{11}+ \frac{12(11)(10!)}{(2)(10!)}(0.54)^2(0.46)^{10}
\\
\\ \indent = (1)(0.46)^{12} + (12)(0.54)(0.46)^{11}+ (66)(0.54)^2(0.46)^{10}
\\ \indent \boxed{P(x \ \textless \  3) \approx 0.00951836732 }


Therefore, the probability that there are fewer than 3 adults are using smartphone is 0.00951 or 0.951%.


5 0
3 years ago
Halle solved 664/48 below. She got a quotient of 13 with a remainder of 40. How could she solve 659/48 without redoing the work?
Lerok [7]
She should multiply the quotient by 48.
3 0
3 years ago
Someone help plz!! I will give Brainlist!
ElenaW [278]

Answer: -3

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3 years ago
For f(x)=x/4-3 and g(x)=4x^2+2x-4 find (f+g)(x)
blondinia [14]

f(x)=\dfrac{x}{4}-3=\dfrac{1}{4}x-3\\\\g(x)=4x^2+2x-4\\\\(f+g)(x)=f(x)+g(x)=\dfrac{1}{4}x-3+4x^2+2x-4\\\\=4x^2+\left(\dfrac{1}{4}x+2x\right)+(-3-4)=4x^2+2\dfrac{1}{4}x-7

3 0
2 years ago
The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled
GarryVolchara [31]

Answer:

7 centimeters of rain will produce the maximum number of mosquitoes (49 millions of mosquitoes)

Step-by-step explanation:

we have the function

m(x)=-x^2+14x

where

m(x) is the number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes)

x is the rainfall (in centimeters)

This is a vertical parabola open downward

The vertex represent a maximum

The x-coordinate of the vertex represent the centimeters of rain that will produce the maximum number of mosquitoes

so

Convert the quadratic equation into vertex form

m(x)=-x^2+14x

Factor -1

m(x)=-(x^2-14x)

Complete the square

m(x)=-(x^2-14x+7^2)+7^2

m(x)=-(x^2-14x+49)+49

Rewrite as perfect squares

m(x)=-(x-7)^2+49

The vertex is the point (7,49)

therefore

7 centimeters of rain will produce the maximum number of mosquitoes (49 millions of mosquitoes)

4 0
3 years ago
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