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lozanna [386]
3 years ago
7

The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measure

s 120 ft by 80 ft, and the expansion will increase its area by 4,400 ft2. By how many feet should the length of the parking lot be increased?
Mathematics
1 answer:
nasty-shy [4]3 years ago
4 0

Present area = 120 * 80 = 9600 ft^2 so the new area will be 9600 + 4400 = 14000

So if increase in length = x we have

(x + 120)(x + 80) = 14,000

x^2 + 200x + 9600 - 14000 = 0

x^2 + 200x - 4400 = 0

x = 20 feet answer

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Mrs. Lay's Instagram followers went from<br> 40 to 72. What was the percent increase?
anastassius [24]

<u>Answer:  </u>

The percentage increase when Mrs.Lay’s instagram followers went from 40 to 72 is 80%

<u>Solution:</u>

The percentage increase can be found out by dividing change in value by initial value. This is given as,

\bold{\text { percentage increase } = \frac{( \text {final count-initial count} }{\text {initial count}} \times 100}

From question, we get

Initial count of Mrs.Lay = 40

Final value of Mrs.Lay = 72

So percentage increase when Mrs Lay’s Instagram followers went from 40 to 72 is

\text { percentage increase }=\frac{72-40}{40} \times 100= \frac{32}{40} \times 100

=\frac{4}{5} \times 100

= 80  

Hence percentage increase when Mrs Lay’s Instagram followers went from 40 to 72 is 80%.

4 0
3 years ago
A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mea
uysha [10]

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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.

For sums of size n, the mean is \mu*n and the standard deviation is s = \sqrt{n}*\sigma

In this question:

n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250

The 90th percentile for the distribution of the total contributions

This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

1.28 = \frac{X - 6328125}{11250}

X - 6328125 = 1.28*11250

X = 6342525

The 90th percentile for the distribution of the total contributions is $6,342,525.

3 0
3 years ago
Please help marking brainliest if correct!!
BlackZzzverrR [31]

Answer:

Step-by-step explanation:

2x=5x+60.

0=3x+60 ( subtract 2x from both sides)

-60=3x(subtract 60 on both sides)

x=-20

Hope this helps plz mark brainliest if correct :D

6 0
3 years ago
Read 2 more answers
Find the circumference of the circle 8.5cm
Vanyuwa [196]

Answer: The circumference of the circle is 53.38 cm.

Step-by-step explanation:

Circumference of the circle is the distance around the circle.

Formula used:

C = 2\pi r

Where,

C is circumference of circle

r is radius of circle

Given:

Radius of circle = 8.5 cm

Now putting all the given values in the above formula, we get:

C = 2\pi r\\C=2\times 3.14\times 8.5cm\\C=53.38cm

Therefore, the circumference of the circle is 53.38 cm.

8 0
3 years ago
The sum of twice a number and 4 is equal to the sum of the number and 8
zalisa [80]

Answer:

4

Step-by-step explanation:

Variable: X = Unknown Number

2x + 4 = x + 8

2x - x = 8 - 4

x = 4

Check:

2(4) + 4 = 4 + 8

8 + 4 = 12

12 = 12

3 0
3 years ago
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