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2 years ago

a homeowner wants to carpet two rooms that each measure 12 ft by 15 ft. how many square yards of carpet should be ordered

Mathematics

1 answer:

Lelu [443]2 years ago

7 0

3 feet = 1 yard

12/3 =4

15/3 = 5

4*5 = 20 square yards per room

20*2 = 40 square yards total

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Sylvester and Lin go to the amusement park. Sylvester plays 5 rounds of mini golf and takes 4 turns in the batting cages for $60

leva [86]

Answer:

Step-by-step explanation

let's use g for golf and b for batting cages

So let's start with Sylvester

he plays 5 rounds of mini golf so 5g

and he takes 4 turns in the batting cages so 4b

and he pays 60 dollars for this

SO his equation is 5g+4b=60

Now onto Lin

3g for 3 rounds of golf

6b for 6 turns in the batting cages

He pays 45 dollars

SO his equation is 3g+6b=45

Both equations:

5g+4b=60

3g+6b=45

Now you need to cancel out one variable so you can multiply the first equation by 3 and the second one by -5

15g+12b=120

-15g-30b=-225

Now the g will cancel out when you add both equations

-18b=-105

b=105/18 which is about 5.83 dollars

Now plug in 105/18 into any of the original equations and solve for g

4 0

2 years ago

An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be

ludmilkaskok [199]

Answer:

a. f(n+1) = f(n) + 20

Step-by-step explanation:

The second hour, f(2) = 130 is the wage of the first hour f(1) = 110, plus 20.

_____

You have to look at the answers and understand what they mean. (This can be difficult when they are nonsense, as here.)

b — means each successive hour of pay is 110 more than the previous one. Clearly that is not the case for the sequence given

c — equates 0 to 20, total nonsense

d — equates 0 to 110, also total nonsense

4 0

2 years ago

Read 2 more answers

Suppose you take the small prism and stack it on top of the larger prism. What will be the volume of the composite figure?

Degger [83]

Find the volume of the first figure, then find the volume of the second figure, then add them together.
V=lwh
V(1)=(15)(12)(6)
= 1,080in^3
V(2)=(12)(6)(6)
= 432in^3
--------------------------------------------
1,080+432= 1,512 in^3
--------------------------------------------
Your answer should be 1,512

3 0

2 years ago

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.a. exactly norm

maxonik [38]

Answer:

Approximately normal for large sample sizes

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

The distribution is unknown, so the sampling distribution will only be approximately normal when n is at least 30.

So the correct answer should be:

Approximately normal for large sample sizes

7 0

2 years ago

Evaluate the line integral by the two following methods. xy dx + x2y3 dy C is counterclockwise around the triangle with vertices

nadezda [96]

Answer:

$\frac{2}{3}$

Step-by-step explanation:

a) The first part requires that we use line integral to evaluate directly.

The line integral is

$\int_C xydx + {x}^{2} {y}^{3} dy$

where C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 2)

The boundary of integration is shown in the attachment.

Our first line integral is

$L_1 = \int_ {(0,0)}^{(1,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is y=0, x varies from 0 to 1.

When we substitute y=0 every becomes zero.

$\therefore \: L_1 =0$

Our second line integral is

$L_2 = \int_ {(1,0)}^{(1,2)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is:

$x = 0 \implies \: dx = 0$

y varies from 1 to 2.

We substitute the boundary and the values to get:

$L_2 = \int_ {1}^{2}1 \cdot y(0) + {1}^{2} \cdot \: {y}^{3} dy$

$L_2 = \int_ {1}^2 {y}^{3} dy = \frac{8}{3}$

The 3rd line integral is:

$L_3 = \int_ {(1,2)}^{(0,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is

$y = 2x \implies \: dy = 2dx$

x varies from 0 to 1.

We substitute to get:

$L_3 = \int_ {1}^{0} x \cdot \: 2xdx + {x}^{2} {(2x)}^{3}(2 dx)$

$L_3 = \int_ {1}^{0} 8 {x}^{5} + 2 {x}^{2} dx = - 2$

The value of the line integral is

$L = L_1 + L_2 + L_3$

$L = 0 + \frac{8}{3} + - 2 = \frac{2}{3}$

b) The second part requires the use of Green's Theorem to evaluate:

$\int_C xydx + {x}^{2} {y}^{3} dy$

Since C is a closed curve with counterclockwise orientation, we can apply the Green's Theorem.

This is given by:

$\int_C \: Pdx +Q \: dy = \int \int_ R \: Q_y - P_x \: dA$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int \int_ R \: 3 {x}^{2} {y}^{2} - y \: dA$

We choose our region of integration parallel to the y-axis.

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \int_ 0^{2x} \: 3 {x}^{2} {y}^{2} - y \: dydx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: {x}^{2} {y}^{3} - \frac{1}{2} {y}^{2} |_ 0^{2x} dx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: 8{x}^{5} - 2 {x}^{2} dx = \frac{2}{3}$

8 0

2 years ago