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3 years ago

5

Monica made a drawing of her patio using the scale 1 inch equals 4 feet. The length of the patio in her drawing was 11 inches. W

hat was the length of the actual patio?

1 answer:

kow [346]3 years ago

6 0

1 inch = 4 feet

11 inches = 44 feet (multiply both sides by 11)

<h3>Answer: 44 feet</h3>

You might be interested in

(3.2 x 10^14) (5.1 x 10^2) in scientific notation

tresset_1 [31]

Those expressions are already in scientific notation.

6 0

3 years ago

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measure SL 42,000 ft

horsena [70]

Answer:

a= 200

b = 210

Step-by-step explanation:

My assumption is, we have to find the length of sides of rectangle

Given

perimeter = 2a + 2b = 820 ft (i) (here a is smaller side and b is larger side)

area = a*b = 42,000 ft^2 (ii)

from eq (1)

2a + 2b = 820

=> 2(a+b) = 820

=> a+b = 820/2

=> a + b = 410

=> a = 410-b (iii)

putting the value of a in eq(ii), we get

(410-b) *b = 42,000

410b - b^2 = 42,000

0 = b^2 - 410b + 42000

b^2 - 410b + 42000 = 0

b^2- 200b- 210b + 42000 = 0

b(b-200)-210(b-200) = 0

(b-200)(b-210) = 0

or

b= 210 and b = 200

if b is larger side than b =210

By putting value of b in eq(iii),

a = 410 -210 = 200

6 0

3 years ago

Thomas decides on a destination for his vacation. If he takes the train there, it will take 5 1/8 hours to get there. If he take

Allisa [31]

Answer: 2 11/24

Step-by-step explanation:

How many hours does the plane save?

Time taken for the train = 5 1/8

Time taken for the plane = 2 2/3

The number of hours saved will then be:

= 5 1/8 - 2 2/3

Let the lowest common multiple be 24

= 5 3/24 - 2 16/24

= 2 11/24

The number of hours saved by the plane will be 2 11/24

8 0

3 years ago

2. When a large truckload of mangoes arrives at a packing plant, a random sample of 150 is selected and examined for

kirza4 [7]

a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).

b) The margin of error is: 2.45%.

c) The 90% confidence is the level of confidence that the true population percentage is in the interval.

d) The needed sample size is: 271.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions has the bounds given by the rule presented as follows:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

The variables are listed as follows:

$\pi$ is the sample proportion, which is also the estimate of the parameter.

z is the critical value.

n is the sample size.

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of $\frac{1+0.90}{2} = 0.95$ , so the critical value is z = 1.645.

The sample size and the estimate are given as follows:

$n = 150, \pi = \frac{15}{150} = 0.1$

The margin of error is of:

$M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%$

The interval is given by the estimate plus/minus the margin of error, hence:

The lower bound is: 10 - 2.45 = 7.55%.

The upper bound is: 10 + 2.45 = 12.45%.

For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}$

$\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}$

$(\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2$

n = 271 (rounded up).

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

3 0

1 year ago

sergejj [24]

Answer:

A

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = \left\{ \begin{array}{ll} 2\cos(\pi x) \text{ for } x \leq -1 \\ \\ \displaystyle \frac{2}{\cos(\pi x)}\text{ for } x > -1 \end{array} \right.$

And we want to find:

$\displaystyle \lim_{x\to -1}f(x)$

So, we need to determine whether or not the limit exists. In other words, we will find the two one-sided limits.

Left-Hand Limit:

$\displaystyle \lim_{x\to-1^-}f(x)$

Since we are approaching from the left, we will use the first equation:

$\displaystyle =\lim_{x\to -1^-}2\cos(\pi x)$

By direct substitution:

$=2\cos(\pi (-1))=2\cos(-\pi)=2(-1)=-2$

Right-Hand Limit:

$\displaystyle \lim_{x\to -1^+}f(x)$

Since we are approaching from the right, we will use the second equation:

$=\displaystyle \lim_{x\to -1^+}\frac{2}{\cos(\pi x)}$

Direct substitution:

$\displaystyle =\frac{2}{\cos(\pi (-1))}=\frac{2}{\cos(-\pi)}=\frac{2}{(-1)}=-2$

So, we can see that:

$\displaystyle \displaystyle \lim_{x\to-1^-}f(x)=\displaystyle \lim_{x\to -1^+}f(x) =-2$

Since both the left- and right-hand limits exist and equal the same thing, we can conclude that:

$\displaystyle \lim_{x \to -1}f(x)=-2$

Our answer is A.

8 0

3 years ago