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3 years ago

Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the

Mathematics

1 answer:

Annette [7]3 years ago

8 0

Answer:

(a) 3 inches

(b) Her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches because the dimensions are not proportional to the scale.

Explanation:

(a) What is the length of the garden in her model? Show your work, including your proportion

<u>1. Scale</u>:

model length / real length = 1 inch / 2 feet

<u>2. Proportion</u>:

Naming x the model length:

1 inch / 2 feet = x / 6 feet

Cross multiply:

1 inch × 6 feet = 2 feet × x

Divide both sides by x:

x = 1 inch × 6 feet / 2 feet = 3 inch.

Answer: 3 inches

(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?

Both the width and the length must use the same scale, thus the corresponding sides of the scale model and the drawing must be proportional.

In the model the ratio of the length to the width is 3 inch / 5 inch

In the paper the ratio of the length to the width is 8.5 inch / 7 inch

Hence, you can see that in the model the length (mumerator of the fraction) is less than the width (denominator) while in the paper it is the opposite. Bieng the two ratios different, they are not proportional, and you conclude that her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches.

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The diagram above shows a rectangle inscribed in a circle AB=10 and AC =12 caculate the total surface area of the shaded part

erastova [34]

Answer:

$71.63 \: \: \mathrm{cm^2 }$

Step-by-step explanation:

Once we know the diameter of the circle, we can figure out the problem.

The diameter of the circle = The diagonal of the rectangle inscribed in the circle

To find the diagonal of the rectangle, we can use a formula.

$d=\sqrt{w^2 + l^2}$

The width is 10 cm and the length is 12 cm.

$d=\sqrt{10^2 + 12^2}$

$d \approx 15.62$

The diagonal of the rectangle inscribed in the circle is 15.62 cm.

The diameter of the circle is 15.62 cm.

Find the area of the whole circle.

$A=\pi r^2$

The $r$ is the radius of the circle, to find radius from diameter we can divide the value by 2.

$r = \frac{d}{2}$

$r=\frac{15.62}{2}$

$r=7.81$

Let’s find the area now.

$A=\pi (7.81)^2$

$A \approx 191.625$

Find the area of rectangle.

$A=lw$

Length × Width.

$A = 12 \times 10$

$A=120$

Subtract the area of the whole circle with the area of rectangle to find area of shaded part.

$191.625-120$

$71.625 \approx 71.63$

5 0

3 years ago

Evan's rectangular lawn measures 8 yards by 10 yards. He planted a hedge

bezimeni [28]

Answer:

Length of rectangular lawn =72 meters

Breadth of rectangular lawn =18 meters

Perimeter of rectangle =2(Length+Breadth)

So, Perimeter of rectangle =2(72+18)=2(90)=180 meters

If three shrubs can be planted in a meter of hedge.

Then, Number of shrubs planted in whole perimeter will be=3×180=540

Step-by-step explanation:

8 0

2 years ago

A basketball-player scores a free-throw with probability 0.9. What is the probability that her first miss occurs on the 6th shot

-BARSIC- [3]

Answer:

$Pr = 0.059049$

Step-by-step explanation:

Given

$p = 0.9$ --- probability of scoring

Required

Probability that his first miss is his 6th shot

Let q represent the event that he did not score.

Using complement rule:

$q = 1 - p = 1 - 0.9 = 0.1$

The event that his first miss is his 6th is represented as:

p p p p p q ---- That he scoress the first 5 attempts

So, the probability is:

$Pr = p^5 * q$

$Pr = 0.9^5 * 0.1$

$Pr = 0.059049$

7 0

3 years ago

Barbara is making candy bags with her birthday party she has 24 lollipops, 12 candy bars, and 42 pieces of gum she wants each ba

Arisa [49]

She can make about 5 bags and there will be 4 lollipops, 2 candy bars, and 7 pieces of gum in each bag.

So this is how to solve it:
Basically what you’re doing here is called finding the gcf, or greatest common factor. What you have to do is find what number can divide by 24, 12, and 42; so I chose 2.
After dividing all these numbers by two you get 12, 6, and 21.
3 can divide by all these numbers
After dividing by three you get 4(lollipops), 2(candy bars) and 7(pieces of gum)
Since you can not divide by one number for all of these numbers, 4, 2 and 7 are your final answers.

To find how many’s bags you can make, the answer is 5 since you divided by 2 and 3 and you add them together.

I hope I explained this well! Good luck :D

3 0

3 years ago

Hey guys I need your help on this!!

kogti [31]

Answer:

Domain: (-∞, ∞) or All Real Numbers

Range: (0, ∞)

Asymptote: y = 0

As x ⇒ -∞, f(x) ⇒ 0

As x ⇒ ∞, f(x) ⇒ ∞

Step-by-step explanation:

The domain is talking about the x values, so where is x defined on this graph? That would be from -∞ to ∞, since the graph goes infinitely in both directions.

The range is from 0 to ∞. This where all values of y are defined.

An asymptote is where the graph cannot cross a certain point/invisible line. A y = 0, this is the case because it is infinitely approaching zero, without actually crossing. At first, I thought that x = 2 would also be an asymptote, but it is not, since it is at more of an angle, and if you graphed it further, you could see that it passes through 2.

The last two questions are somewhat easy. It is basically combining the domain and range. However, I like to label the graph the picture attached to help even more.

As x ⇒ -∞, f(x) ⇒ 0

As x ⇒ ∞, f(x) ⇒ ∞

7 0

3 years ago