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3 years ago

Solve the equation using square roots. x2 + 5 = 41

Mathematics

2 answers:

Stells [14]3 years ago

3 0

X*2 +5 =41
Subtract 5 from both sides
X*2=36

Square root of 36 is 6

X=6

Solve

6*2+5 =41
This’s correct!

Kipish [7]3 years ago

3 0

Answer: The required solution is x = 6, -6.

Step-by-step explanation: We are given to solve the following quadratic equation using square roots :

$x^2+5=41~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To solve a quadratic equation by square root method, we need to take x² term on one side and the constant term on the other. After that, the square root on both the sides are taken.

From equation (i), we have

$x^2+5=41\\\\\Rightarrow x^2=41-5\\\\ \Rightarrow x^2=36\\\\\Rightarrow x=\pm\sqrt{36}~~~~~~~~~~~~\textup{[taking square root on both the sides]}\\\\\Rightarrow x=\pm 6.$

Thus, the required solution is x = 6, -6.

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3 years ago

23% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and as

zlopas [31]

Answer:

a) There is a 29.42% probability that the number of college students who say they use credit cards because of the rewards program is exactly two.

b) There is a 41.37% probability that the number of college students who say they use credit cards because of the rewards program is more than two.

c) There is a 69.49% probability that the number of college students who say they use credit cards because of the rewards program is between two and five, inclusive.

Step-by-step explanation:

There are only two possible outcomes. Either the student use credit cards because of the rewards program, or they use for other reason. So, we can solve this exercise using the binomial probability distribution.

Binomial probability distribution

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

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

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

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

And $\pi$ is the probability of X happening.

In this problem, we have that:

10 students are randomly selected, so $n = 10$ .

23% of college students say they use credit cards because of the rewards program. This means that $\pi = 0.23$

(a) exactly two

This is P(X = 2).

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

$P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942$

There is a 29.42% probability that the number of college students who say they use credit cards because of the rewards program is exactly two.

(b) more than two

This is $P(X > 2)$ .

Either a value is larger than two, or it is smaller of equal. The sum of the decimal probabilities of these events must be 1. So:

$P(X \leq 2) + P(X > 2) = 1$

$P(X > 2) = 1 - P(X \leq 2)$

In which

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{10,0}.(0.23)^{0}.(0.77)^{10} = 0.0733$

$P(X = 1) = C_{10,1}.(0.23)^{1}.(0.77)^{9} = 0.2188$

$P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0733 + 0.2188 + 0.2942 = 0.5863$

$P(X > 2) = 1 - P(X \leq 2) = 1 - 0.5863 = 0.4137$

There is a 41.37% probability that the number of college students who say they use credit cards because of the rewards program is more than two.

(c) between two and five inclusive.

This is

$P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

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

$P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942$

$P(X = 3) = C_{10,3}.(0.23)^{3}.(0.77)^{7} = 0.2343$

$P(X = 4) = C_{10,4}.(0.23)^{4}.(0.77)^{6} = 0.1225$

$P(X = 5) = C_{10,3}.(0.23)^{5}.(0.77)^{5} = 0.0439$

$P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.2942 + 0.2343 + 0.1225 + 0.0439 = 0.6949$

There is a 69.49% probability that the number of college students who say they use credit cards because of the rewards program is between two and five, inclusive.

8 0

3 years ago

I JUST NEED HELP ASAP HELP ME FAST PLZ ILL GIVE YOU BRAINLIST AND 5 STARS

artcher [175]

A:
add up all the money he deposited
3.98+51.02+38.52+12.70=$106.22
and all the money withdrew:
-5.23-5.22-3.50-4.39=-18.34

b-
3.50, 3.98, 4.39, 5.22, 5.23, 12.7 38.52 51.02
just look at the digits from left to right the bigger they are the bigger the number is.if they were equal look at the next digit:
example:
3.50 and 12.7
there is a 1 in 12.7 tenth place but 3.50 doesn't even have a tenth place(or rather, it has a zero on it's tenth place) so 12.7 is bigger than 3.50

c-add all deposits and subtract all withdrawals:
106.22+98-18.34=185.88

6 0

3 years ago