Write the number in 2 equivalent forms as a fraction, decimal, or percent.

A square pyramid and a cube have the same surface area don’t of each side of the base of the Square pyramid is 10 feet the width

o-na [289]

Answer:

The lateral height of the square pyramid is $5.8\ ft$

Step-by-step explanation:

step 1

Find the surface area of the cube

The surface area of the cube is equal to

$SA=6b^{2}$

where

b is the length side of the cube

w have

$b=6\ ft$

substitute

$SA=6(6^{2})=216\ ft^{2}$

step 2

Find the lateral height of the square pyramid

we know that

the surface area of the square pyramid is equal to

$SA=B+4(\frac{1}{2}bh)$

where

B is the area of the base

b is the base of the lateral triangle (base of the square)

h is the lateral height of the square pyramid

$B=(10^{2})=100\ ft^{2}$

$SA=216\ ft^{2}$ -----> is the same surface that the cube

$b=10\ ft$

substitute the values and solve for h

$216=100+4(\frac{1}{2}*(10)*h)$

$216-100=20h$

$h=116/20=5.8\ ft$

6 0

3 years ago

Find the midrange for the group of data items.<br> 2, 2, 5, 5, 8, 8, 10

elena55 [62]

Answer:

5

Step-by-step explanation:

Answer:5

Start striking off the numbers one from the left and then from the right continuously until you're left with a number in the middle

3 0

3 years ago

Assume that there are an equal number of births in each month so that the probability is that a person chosen at random was born

NikAS [45]

Answer:

0.2773 = 27.73% probability that at the May celebration, exactly two members of the group have May birthdays

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have a birthday in May, or they do not. The probability of a person having a birthday in May is independent of any other person. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Probability of a person being in May:

May has 31 days in a year of 365. So

$p = \frac{31}{365} = 0.0849$

Group of 20 friends:

This means that $n = 20$

What is the probability that at the May celebration, exactly two members of the group have May birthdays?

This is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{20,2}.(0.0849)^{2}.(0.9151)^{18} = 0.2773$

0.2773 = 27.73% probability that at the May celebration, exactly two members of the group have May birthdays

3 0

3 years ago

What is the first term in a geometric sequence if the common ratio is − 2 and the sum of the first six terms is −105?

Serggg [28]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-2\\
n=6\\
S_6=-105
\end{cases}$

$\bf -105=a_1\left( \cfrac{1-(-2)^6}{1-(-2)} \right)\implies -105=a_1\left( \cfrac{1-(64)}{1+2} \right)
\\\\\\
-105=a_1\left( \cfrac{-63}{3} \right)\implies -105=a_1(-21)
\\\\\\
\cfrac{-105}{-21}=a_1\implies 5=a_1$

7 0

3 years ago

What will be the total cost of Devon's first year?

ELEN [110]

Answer: Q1: $8,050

Q2: $5,400

Q3: $2,650

Step-by-step explanation:

4 0

3 years ago

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Write the number in 2 equivalent forms as a​ fraction, decimal, or percent.

Write the number in 2 equivalent forms as a fraction, decimal, or percent.