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12345 [234]
3 years ago
15

A square pyramid has a base with a side length of 7.5 feet and lateral faces with heights of 16 feet. Write an expression that c

an be used to find the surface area, in square feet, of the square pyramid.
Please provide an expression, not just the surface area please :)
Mathematics
1 answer:
dybincka [34]3 years ago
3 0

Check the picture below.

so the surface area of the pyramid will be the sum of the areas of the base and the four triangular faces.

\stackrel{\textit{\Large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(7.5)(16) \right]}~~ + ~~\stackrel{\textit{rectangular base}}{(7.5)(7.5)}}\implies 240~~ + ~~56.25\implies 296.25~ft^2

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According to records kept by Mariposa County, the average (mean) amount of time that it takes for employees to be reimbursed for
Aloiza [94]

Answer:

The probability of receiving reimbursement within 42 days of filing is 0.8849 = 88.49%

Step-by-step explanation:

Let P(a \leq x \leq b) the probability of being reimbursed in an interval of a to b days, we want P(0 \leq x \leq 42)

First, standardize x by doing the change

z=\frac{x-\mu}{\sigma}

where \mu is the mean of our original distribution and \sigma the standard deviation. So

z=\frac{x-36}{5}

This change transforms the original distribution in a normal distribution N(0,1) with mean 0 and standard deviation 1.

This is done in order to easily compute the area under the normal curve.

Since,  

0 \leq x \leq 42\Rightarrow -36 \leq x -36 \leq 6\Rightarrow \frac{-36}{5} \leq \frac{x -36}{5} \leq \frac{6}{5}

we then have

-7.2 \leq z \leq 1.2

And we want the area under the normal curve between -7.2 and 1.2. This can be done either by using a table or a computer, and we find this area is 0.8849,  

Hence, the probability of receiving reimbursement within 42 days of filing is 0.8849 = 88.49%

4 0
4 years ago
The derivative of the function f is given by f′(x)=−3x+4 for all x, and f(−1)=6. Which of the following is an equation of the li
Viefleur [7K]

Answer:

The equation of the line tangent to the graph of f at x = -1 is y = 7\cdot x +13.

Step-by-step explanation:

From Analytical Geometry we know that the tangent line is a first order polynomial, whose form is defined by:

y = m\cdot x + b (1)

Where:

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

m - Slope, dimensionless.

b - Intercept, dimensionless.

The slope of the tangent line at x = -1 is:

f'(x) = -3\cdot x +4 (2)

f'(-1) = -3\cdot (-1) +4

f'(-1) = 7

If we know that m = 7, x = -1 and y = 6, then the intercept of the equation of the line is:

b = y-m\cdot x

b = 6-(7)\cdot (-1)

b = 13

The equation of the line tangent to the graph of f at x = -1 is y = 7\cdot x +13.

3 0
3 years ago
What is 2.085 * 10^6 in standard form
qaws [65]
<span>What is 2.085 * 10^6 in standard form??

= 2,085,000</span>
8 0
3 years ago
Read 2 more answers
CALLING ALL EXPERTS, PLEASE HELP ME WITH MY HOMEWORK!! WORTH A LOT OF POINTS AND WILL GIVE BRAINLIEST!!
laiz [17]

Answer:

1= 1 7/8 or 1.875

2= 235.75

3= 10 1/2 or 10.5

4=191.53

5=1 5/12 or 1.4166667

6=239.13

hope this helps

3 0
3 years ago
Read 2 more answers
Guengle works in urban landscape design a truck arrived pouring a cone shaped pile of gravel six feet high with a diameter at th
Dennis_Churaev [7]

Answer:

105.56\ ft^3 of gravel was used.

Step-by-step explanation:

Given that,

The height of a cone, h = 6 feet

The diameter of the base of cone, d = 8.2 feet

Radius, r = 4.1 feet

We need to find the amount of gravel was delivered. The volume of a cone is given by :

V=\dfrac{1}{3}\pi r^2 h\\\\=\dfrac{1}{3}\times 3.14\times 4.1^2\times 6\\\\V=105.56\ ft^3

So, 105.56\ ft^3 of gravel was used.

8 0
3 years ago
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