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at the same time a 15 foot pole casts a 7.5 foot shadow a nearby tree casts an 11 foot shadow how tall is the tree

Answers

Answer 1

Answer:

answer: 22

15/7.5 = x/11

cross multiply

7.5x = 165

divide by 7.5 on both sides to get the x alone

7.5x/7.5 = 165/7.5

x = 22

the tree is 22 feet

sorry if it’s wrong

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Factor the following expression: 7x + 28x2 + 21x

Answers

Answer:2

Step-by-step explanation:

Answer:

84x

Step-by-step explanation:

If you have any questions feel free to ask in the comments.

Write an equivalent unit rate to eating chips in 1/4 mins

Answers

Answer:

Here we have the case where:

"one chip is eaten in 1/4 mins."

(that means unit rate, the amount of a given variable that we need to do a unit of another variable)

Then the unit rate would be:

4 chips per minute.

Or, in a more mathematical way to write this:

4 chips/min.

Now we could write this in other units, for example.

We know that 1 min = 60s.

Then we have that (1/4) min = 60s/4 = 15s.

Then we have the unit rate:

1 chip every 15 seconds, or:

(1/15) chips/second.

Now, the variable in this case is time, t = time, let's multiply bot our unit rates by the same amount of time, and see if we have the same outcome.

Let's use t = 2 min.

1) (4chips/min)*2min = 8 chips.

2) ((1/15) chips/second)*2min

First, 2 min = 120 seconds.

((1/15) chips/second)*2min = ((1/15) chips/second)*120seconds = 8 chips.

So both unit rates are equivalent.

An algebraic relationship of that quantity is greater than or less then another quantity ?

Answers

Answer:

Inequality

Step-by-step explanation:

calculate the variance and standard deviation for the following samples set of data. 83.6,92.3,56.5,43.8,77.1,66.7. (Do not round intermediate calculation. Round your final answers and the nearest tenth.)

Answers

Answer:

Variance: 322.4479999999996

Standard Deviation: 17.956837137981722

Final answer:

To calculate the variance and standard deviation for the given sample set of data, find the sample mean, calculate the squared differences, and then find the sample variance and standard deviation.

Explanation:

To calculate the variance and standard deviation for the given sample set of data (83.6, 92.3, 56.5, 43.8, 77.1, 66.7), follow these steps:

Calculate the sample mean by adding all the values together and dividing by the total number of values: (83.6 + 92.3 + 56.5 + 43.8 + 77.1 + 66.7) / 6 = 69.8.
Calculate the squared differences between each value and the sample mean: (83.6 - 69.8)^2, (92.3 - 69.8)^2, (56.5 - 69.8)^2, (43.8 - 69.8)^2, (77.1 - 69.8)^2, (66.7 - 69.8)^2.
Calculate the sample variance by summing up the squared differences and dividing by (n-1), where n is the total number of values: (83.6 - 69.8)^2 + (92.3 - 69.8)^2 + (56.5 - 69.8)^2 + (43.8 - 69.8)^2 + (77.1 - 69.8)^2 + (66.7 - 69.8)^2 = 300.46. Sample variance = 300.46 / 5 = 60.1.
Calculate the sample standard deviation by taking the square root of the sample variance: √60.1 = 7.79. Rounded to the nearest tenth, the sample standard deviation = 7.8.

Learn more about Calculating Variance and Standard Deviation here:

brainly.com/question/35392129

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Trisha Long wants to buy a boat in five years. She estimates the boat will cost $15,000 at that time. What must Trisha deposit today in an account earning 5% annually to have enough to buy the boat in five years?

Answers

We use the formula for compound growth to figure this problem out. Formula is:

$P=P_(0)(1+(r)/(n))^(nt)$

Where,

P is the future value
$P_(0)$ is the initial deposite
r is the rate of interest annually
n is the number of times compounding occurs (n=1 for annual compounding, n=2 for semiannual compounding etc.)
t is time

Given P=15,000, r=5%=0.05 (in decimal), n=1 (since annual compounding), and t=5 years, we can solve:

$15000=P_(0)(1+(0.05)/(1) )^((1)(5))\n15000=P_(0)(1+0.05)^(5)\nP_(0)=(15000)/((1+0.05)^(5))\nP_(0)=(15000)/(1.05^(5))\nP_(0)=11,752.89$

So, Trisha Long needs to deposit $11,752.89 today in the account.

ANSWER: $11,752.89

$\bf \qquad \textit{Compound Interest Earned Amount}\n\nA=P\left(1+(r)/(n)\right)^(nt)\qquad \begin{cases}A=\textit{compounded amount}\to &15000\nP=\textit{original amount deposited}\nr=rate\to 5\%\to (5)/(100)\to &0.05\nn=\begin{array}{llll}\textit{times it compounds per year}\n\textit{annually means, once}\end{array}\to &1\nt=years\to &5\end{cases}$

solve for "P", to see how much Principal she should deposit today

I need help on this please.Ivanna is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 51 feet and its width is 32 feet. Suppose each can of wood stain covers 102 square feet. How many cans will she need to cover the court?