Angles 4 and 5 form what type of angles?

Find the dimensions of a rectangle with perimeter 112 m whose area is as large as possible. step 1 if a rectangle has dimensions

Veronika [31]

Please use the solution below:
Let P = perimeter, A = area
As provided above, a = xy and
We know that the formula to solve for the perimeter of a rectangle is P = 2x + 2y. Using the given 112m, we can solve the perimeter using the formula:
112 = 2x + 2y
56 = x + y

x = 56-y or y = 56-x
Let's solve the perimeter in terms of y using the formula below:
A = (56-y)(y)
Find the derivative of A = 56-y^2 to get the value of y.
dA/dy = 56-2y = 0
y = 56/2
y = 28
To find X, substitute the value of y in the equation x = 56 - y.
x = 56 - 28
Therefore, x = 28.
We can conclude that the figure is not a rectangle but a square.

7 0

3 years ago

A person participates in a state lottery by selecting six numbers from 1 through 51. If the six numbers match the six drawn by t

Licemer1 [7]

There are

$\dbinom{51}6=\dfrac{51!}{6!(51-6)!}=18,009,460$

total ways to draw any 6 numbers from the range 1 to 51, regardless of order.

Given 6 selected numbers that match those drawn by the lottery, there are

$6!=720$

ways of rearranging them. So the probability of winning 1st prize is

$\dfrac{720}{18,009,460}=\dfrac{36}{900,473}\approx0.0000399790$

Next, given 6 selected numbers of which 5 match those drawn by the lottery, there are

$5!=120$

ways of rearranging those 5 matching numbers. There are 46 remaining numbers that didn't get drawn, so the probability of winning 2nd prize is

$\dfrac{46\cdot120}{18,009,460}=\dfrac{12}{39,151}\approx0.0003065$

7 0

3 years ago

What is the sum of 13+52 as the product of their GCF and another sum

vova2212 [387]

GCF(13; 52) = 13

13 = 13 · 1
52 = 13 · 4

13 + 52 = 13 · 1 + 13 ·4 = 13·(1 + 4)

Used distributive property: a(b + c) = ab + ac

4 0

2 years ago

Suppose you need to get the dent in your car fixed. You see the ads in the newspaper above (mikes repair shop $100 service charg

Norma-Jean [14]

Answer:

Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295, so I will take the car to Amy's shop

Point of intersection: (x,y) = (4,360)

Explanation:

Part 1 )

Let x = number of hours worked

Let y = total cost to you

Determining where to take the car:

Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295

Mike's repair shop:

Service fee: $100

Per hour rate: $65

Let x is the number of hours worked on. Total cost will be equal to the service fee plus hourly charges. Charges per an hour are $65, so for x hours the charges will be 65x.

Therefore, total cost for Amy's repair shop can be written as:

y = 100 + 65x ------(1)

For 3 hours work: y = 100 + 65(3)

Cost at Mike's, y = $100 + $195 = $295

Amy's repair shop: 

Service fee: $40

Per hour rate: $80

Charges per an hour are $40, so for x hours the charges will be 80x.

Therefore, total cost for Amy's repair shop can be written as:

y = 40 + 80x ------(2)

For 3 hours work: x = 3

y = 40 + 80(3)

Cost at Amy's, y = $40 + $240 = $280

Part 2)

Find the point of intersection

Using elimination method:

y = 100 + 65 x ------1

y = 40 + 80x ------2

As the y coefficients are equal we will subtract eq1 from eq2

y - y = 40 + 80x - 100 - 65x

0 = -60 + 15x

60 = 15x

x = $\frac{60}{4}$

x = 4

put x = 4 in eq 1

we get y = 100 + 65 (4) = 100 + 260 = 360

x = 4, y = 360

Point of intersection: (x,y) = (4,360)

8 0

3 years ago

A poll shows that 41% of voters in a city favor of a $0.0.1 tax increase. If 25 voters are selected at random, what is that exac

juin [17]

Answer:

The probability is 0.026 to 3 d.p

Step-by-step explanation:

To calculate this , we shall be using the Bernoulli approximation.

let P = percentage of voters supporting the increase = 41% = 41/100 = 0.41

q = percentage of voters not supporting = 100-41% = 59% = 59/100 = 0.59

Now we want to calculate that exactly 15 out of 25 will vote in favor

Mathematically that would be ;

25C15 p^15 q^10

= 25C15 0.41^15 0.59^10

= 0.025981307443 or simply 0.026 to 3 decimal places

5 0

3 years ago