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larisa86 [58]
3 years ago
9

The Odd and even numbered hotel rooms are on different sides of the hall room 23q is between which two rooms

Mathematics
1 answer:
diamong [38]3 years ago
6 0
It is between room 21 and 25
You might be interested in
The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep
Alchen [17]
Ooh, fun

geometric sequences can be represented as
a_n=a(r)^{n-1}
so the first 3 terms are
a_1=a
a_2=a(r)
a_2=a(r)^2

the sum is -7/10
\frac{-7}{10}=a+ar+ar^2
and their product is -1/125
\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3

from the 2nd equation we can take the cube root of both sides to get
\frac{-1}{5}=ar
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r
subsituting -1/5 for ar
\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r
which simplifies to
\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for ax^2+bx+c=0
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}
so
for 2r²-5r+2=0
a=2
b=-5
c=2

r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}
r=\frac{5 \pm \sqrt{25-16}}{4}
r=\frac{5 \pm \sqrt{9}}{4}
r=\frac{5 \pm 3}{4}
so
r=\frac{5+3}{4}=\frac{8}{4}=2 or r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}

use them to solve for the value of a
\frac{-1}{5}=ar
\frac{-1}{5r}=a
try for r=2 and 1/2
a=\frac{-1}{10} or a=\frac{-2}{5}


test each
for a=-1/10 and r=2
a+ar+ar²=\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}
it works

for a=-2/5 and r=1/2
a+ar+ar²=\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}
it works


both have the same terms but one is simplified

the 3 numbers are \frac{-2}{5}, \frac{-1}{5}, and \frac{-1}{10}
6 0
3 years ago
Answers for the homies that don’t wanna do the work edge 202
trapecia [35]
Wait what’s edge 202:|
7 0
3 years ago
Which expression is equivalent to 20+8y_9y_21​
viktelen [127]

Answer: 4(5+2y)-3(3y+7)

Step-by-step explanation:

Use the distributive property for this ^^^

3 0
2 years ago
Evaluate the expression when m=9 and n=7.<br> 5m +n
lozanna [386]

Answer:

52

Step-by-step explanation:

5m +n

Let m =9 and n=7

5*9 +7

Multiply first

45+7

Add

52

7 0
3 years ago
Read 2 more answers
A consumer products company found that 42​% of successful products also received favorable results from test market​ research, w
blagie [28]

Answer:

(1) The probability of a successful product given the product is favorable is 0.7778.

(2) The probability of a successful product given the product is unfavorable is 0.2391.

(3) The probability of a unsuccessful product given the product is favorable is 0.2222.

(4) The probability of a unsuccessful product given the product is favorable is 0.7609.

Step-by-step explanation:

Denote the events as follows:

<em>S</em> = a product is successful.

<em>F</em> = a product is favorable.

The information provided is:

P(S\cap F)=0.42\\P(S\cap F^{c})=0.11\\P(S^{c}\cap F)=0.12\\P(S^{c}\cap F^{c})=0.35\\

The law of total probability states that:

P(A)=P(A\cap B)+P(A\cap B^{c})

Use the law of total probability to compute the probability of a favorable product as follows:

P(F)=P(S\cap F)+P(S^{c}\cap F)\\=0.42+0.12\\=0.54

The probability of a favorable product is 0.54.

The conditional probability of an event <em>A</em> given that another event <em>B</em> has already occurred is:

P(A|B)=\frac{P(A\cap B)}{P(B)}

(1)

Compute the value of P (S|F) as follows:

P(S|F)=\frac{P(S\cap F)}{P(F)}=\frac{0.42}{0.54}=0.7778

Thus, the probability of a successful product given the product is favorable is 0.7778.

(2)

Compute the value of P(S|F^{c}) as follows:

P(S|F^{c})=\frac{P(S\cap F^{c})}{P(F^{c})}=\frac{0.11}{(1-0.54)}=0.2391

Thus, the probability of a successful product given the product is unfavorable is 0.2391.

(3)

Compute the value of P (S^{c}|F) as follows:

P (S^{c}|F)=\frac{P(S^{c}\cap F)}{P(F)}=\frac{0.12}{0.54}=0.2222

Thus, the probability of a unsuccessful product given the product is favorable is 0.2222.

(4)

Compute the value of P (S^{c}|F^{c}) as follows:

P (S^{c}|F)=\frac{P(S^{c}\cap F^{c})}{P(F^{c})}=\frac{0.35}{(1-0.54)}=0.7609

Thus, the probability of a unsuccessful product given the product is favorable is 0.7609.

8 0
3 years ago
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