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20 days ago

Hikers came across a part of a redwood stump. If the length of the chord is 8 feet, what was the diameter of the tree?

1 answer:

7 0

In this scenario, the chord length corresponds to the circumference of the tree. To find the diameter, we utilize the circumference formula for a circle:

C = 2π * Radius

First, we must determine the tree's radius using this formula:

Radius = C /2π = 8/6.2832 = 1.2732 ft
Diameter = 2*radius = 2 * 1.2732 = 2.5464 feet

In conclusion, the tree's diameter measures 2.546 feet.

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Helena has taken out a $9,300 unsubsidized Stafford loan to pay for her college education. She plans to graduate in four years.

Leona [12618]

The effective annual interest rate calculations yield:
i = (1 + 0.064/12)^12 - 1 = 0.066
For year 1: the interest amounts to $613.80 (calculating $9300 multiplied by 0.066)
For year 2: the interest totals $654.31 (adding year 1’s interest to $9300 and multiplying by 0.066)
For year 3: the interest is $656.98 (following the same process as year 2)
For year 4: the interest is $657.16

The cumulative interest totals: $2582.25
The present value of this sum is:
P = 2582.23 / (1 + 0.066)^4 = $1999.72

Thus, the final answer is $1999.72.

8 0

1 month ago

Read 2 more answers

Lee has a bag with 500 quarters. Some are the older eagle quarters, and others are the newer state quarters. She pulls out 10 qu

tester [12383]

I couldn't write it out in detail, so the solution is 200. The work is visible in the image below if you need clarification. I hope this is useful to you!

7 0

1 month ago

Jeffery has grades of 93 and 81 on the first two testes of the quarter. Progress reports are sent home after the third test. He

PIT_PIT [12445]

96 or 97

5 0

1 month ago

Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has writt

Svet_ta [12734]

Answer:

The inequality used to calculate the number of articles written by Mustafa for his school paper is $x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$ .

Mustafa has authored over 8 articles.

Step-by-step explanation:

Details given:

Total combined number of articles = 22

Let 'x' represent the articles written by Mustafa.

Now stated:

Heloise has authored $\frac{1}{4}$ as many articles as Mustafa.

Heloise's articles number = $\frac{1}{4}x$

Gia has penned $\frac{3}{2}$ as many articles as Mustafa.

Gia's article count = $\frac{3}{2}x$

It follows that;

The total of articles from Mustafa, Heloise, and Gia must be more than or equal to the total combined articles.

Expressing it in an equation gives us;

$x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$

Thus the inequality for finding the number of articles penned by Mustafa for his school project is $x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$ .

Now simplifying the inequality:

By taking the LCM to standardize the denominator, we get:

$\frac{x\times 4}{4}+\frac{1\times1}{4\times1}x+ \frac{3\times2}{2\times2}x\geq 22\\\\\frac{4x}{4}+ \frac{x}{4}+\frac{6x}{4}\geq 22\\\\\frac{4x+x+6x}{4} \geq 22\\\\11x\geq 22\times4\\\\11x\geq 88\\\\x\geq \frac{88}{11} \\\\x\geq 8$

Thus, Mustafa has written in excess of 8 articles.

5 0

1 month ago

Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% a

tester [12383]

Answer:

a) P=0.24

b) P=0.31

c) Not independent.

Step-by-step explanation:

The question is incomplete.

a) What’s the probability that a randomly chosen order will be wrapped and sent to a different person?

$P(W\&SOP)=P(SOP)*P(W|SOP)=0.30*0.60=0.24$

W: wrapped

SOP: sent to different individuals

b) What’s the probability that a randomly selected order will be gift wrapped?

$P(W)=P(SOP)*P(W|SOP)+P(SR)*P(W|SR)\\\\P(W)=0.3*0.6+0.7*0.1=0.24+0.07=0.31$

SR: sent to the correct recipient

c) Is gift wrapping independent of the order’s destination? Please provide a statistical justification.

To establish their independence, both conditions must be satisfied:

P(x|y) = P(x), for all values of X and Y.

P(x ∩ y) = P(x) * P(y), for all values of X and Y.

Starting with the second condition.

$P(W\cap SR)=0.1\\\\P(W)*P(SR)=0.31*0.7=0.217\\\\\\P(W\cap SR)\neq P(W)*P(SR)$

This condition is unmet, indicating that these variables are not independent.

4 0

17 days ago