MATHEMATICS HIGH SCHOOL

Collin is buying dirt to fill a garden bed that is a 9ft by 16ft rectangle. If he wants to fill it to a depth of 4 inches, how many cubic yards of dirt does he need? If dirt costs $25 per yard cubed, how much will the project cost?

Answers

Answer 1

Answer:

Answer:

Cubic yards of dirt needed for project = $1(7)/(9)$ cubic yards

Cost of Project = About $44.44

Step-by-step explanation:

To find number of cubic yards of dirt needed, we need to find the volume.

Rectangular Prism Volume = length * width * depth

Note: Length is 9ft, width is 16ft, depth is 4 inches. We need to change depth to ft. So 4 inches = $(1)/(3)$ feet.

Now finding the volume (in cubic ft) = $9*16*(1)/(3)=48$

We know 3 feet is 1 yard. To convert cubic feet to cubic yards, we have to divide it by (3)^3 = 27. Hence:

$(48)/(27)=(16)/(9)$ cubic yards

* Since dirt is $25 per cubic yard, to find cost, we multiply 25 by 16/9. Hence

Cost of Project = 25 * 16/9 = 400/9 = $44.44

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A rectangle's length is three times its width. Let w denote the rectangle's width. What polynomial represents the rectangle's area?

Answers

Hello,

w=width
3w=the length
Area=3*w*w=3w²

A card is drawn from a standard 52-card deck. What is the probability that the card is a red jack, given that the card is a face card (a jack, queen, or king)?

Answers

Answer:

The answer is B

Step-by-step explanation:

only 20 chars.....

Round 75.4614 to the nearest thousandth

Answers

$75.4614\approx75.461$

3x+4y=5 2x-5y=8
Is this consistent and independent, consistent and dependent, or inconsistent

Answers

3x + 4y = 5
2x - 5y = 8

To answer this question, we need to put both of these equations into Slope-Intercept form, or in other words, solve for y.

3x + 4y = 5 Subtract 3x from both sides
4y = -3x + 5 Divide both sides by 4
y = $-(3)/(4)$ + $(5)/(4)$

2x - 5y = 8 Subtract 2x from both sides
-5y = -2x + 8 Divide both sides by -5
y = $(2)/(5)$ - $(8)/(5)$

When you look at the two equations, you can see that their slopes are completely different, so they aren't parallel, or inconsistent. Since $(2)/(5)$ is not the same as $-(3)/(4)$ , they aren't the same line, or dependent. So, the only option left is that they are consistent and independent.

Which of the following accurately shows the range of the function defined below?

Answers

Answer: The answer is (b) (2, ∞)

Step-by-step explanation: We are given a function f(x) in the figure and we are to select out of the given options that accurately shows the range of the function defined.

$\textup{For }x < 0, \textup{we have}~f(x)=3.$

$\textup{For }0\leq x<2,\textup{ we have }f(x)=x^2+2\geq 2.$

$\textup{For }x\geq 2,\textup{ we have }f(x)=(1)/(2)x+5\geq 5.$

Therefore, the range of the function f(x) will be greater then or equal to 2. So, the range will be [2, ∞).

Thus, the correct option is (b) (2, ∞).

Answer:
it's b

Step-by-step explanation:

Jim, Carla and Tomy are members of the same family. Carla is 5 years older than Jim. Tomy is 6 years older than Carla. The sum of their 3 ages is 31 years. How old is each one of them?

Answers

let the age of jim be x
carla's age= x+5
tomy's age= 6+5+x
sum of their ages=31
x+x+5+x+5+6=3x+16=31
3x=31-16
=15
x=15 divided by 3
= 5
jim's age=5
carla's age=10
tomy's age = 16

x - Jim
y - Carla
z - Tomy

$y=x+5\n z=y+6\n x+y+z=31\n\n x=y-5\n z=y+6\n x+y+z=31\n\n y-5+y+y+6=31\n 3y=30\n y=10\n\n x=10-5\n x=5\n\n z=10+6\n z=16$

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