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Kamila [148]
3 years ago
6

The rational number lies between −67/7 and−78/8

Mathematics
1 answer:
zheka24 [161]3 years ago
7 0

9514 1404 393

Answer:

   -135/14

Step-by-step explanation:

There are an infinite number of rational numbers between any pair of numbers you name. These two number have the decimal values ...

  -67/7 = -9 4/7 = -9.571428... (repeating)

  -78/8 = -9 3/4 = -9.75

So, numbers like -9.6 = -48/5, or -9.7 = -97/10 are rational numbers that lie in the range you specified.

If you like, you can convert these numbers to ones with a common denominator (56).

 -67/7 = -536/56

 -78/8 = -546/56

These limits suggest several possible rational numbers with 56 as a denominator: -540/56 = -135/14, for example.

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Find which term in the geometric sequence 1,3,9,27,... is the first to exceed 7,000.
Zielflug [23.3K]

The common ratio between terms is 3, so the sequence has general n-th term

a_n=3^{n-1}

for n\ge1. The term exceeds 7000 when

3^{n-1}>7000\implies n-1>\log_37000\implies n>1+\log_37000\approx9.06

which means the first time a_n exceeds 7000 occurs when n=10. Indeed,

a_{10}=3^{10-1}=19,683

while the previous term would have been

a_9=3^{9-1}=6561

8 0
4 years ago
benito read 14 books in 3 months, which was 35% of the number of books he had signed up to read during the school year .how many
lianna [129]
14 books in 3 months is 35%
all of books is 100%

14- 35%
x- 100%
we calculate from proportions, crosswise:
x=\frac{14*100}{35}=\frac{1400}{35}=40

Answer: Benito sign up to read 40 books.

Greetings,
n00nst00p :)
7 0
3 years ago
The solutions to (x + 3)^2- 4=0 are x = -1 and x = -5<br><br> True or false
Neko [114]

Answer:

THE ANSWER WOULD BE TRUE MY FRIEND

6 0
3 years ago
Forty percent of households say they would feel secure if they had $50,000 in savings. you randomly select 8 households and ask
Kay [80]

Answer:

Let X be the event of feeling secure after saving $50,000,

Given,

The probability of feeling secure after saving $50,000, p = 40 % = 0.4,

So, the probability of not  feeling secure after saving $50,000, q = 1 - p = 0.6,

Since, the binomial distribution formula,

P(x=r)=^nC_r p^r q^{n-r}

Where, ^nC_r=\frac{n!}{r!(n-r)!}

If 8 households choose randomly,

That is, n = 8

(a) the probability of the number that say they would feel secure is exactly 5

P(X=5)=^8C_5 (0.4)^5 (0.6)^{8-5}

=56(0.4)^5 (0.6)^3

=0.12386304

(b) the probability of the number that say they would feel secure is more than five

P(X>5) = P(X=6)+ P(X=7) + P(X=8)

=^8C_6 (0.4)^6 (0.6)^{8-6}+^8C_7 (0.4)^7 (0.6)^{8-7}+^8C_8 (0.4)^8 (0.6)^{8-8}

=28(0.4)^6 (0.6)^2 +8(0.4)^7(0.6)+(0.4)^8

=0.04980736

(c) the probability of the number that say they would feel secure is at most five

P(X\leq 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

=^8C_0 (0.4)^0(0.6)^{8-0}+^8C_1(0.4)^1(0.6)^{8-1}+^8C_2 (0.4)^2 (0.6)^{8-2}+8C_3 (0.4)^3 (0.6)^{8-3}+8C_4 (0.4)^4 (0.6)^{8-4}+8C_5(0.4)^5 (0.6)^{8-5}

=0.6^8+8(0.4)(0.6)^7+28(0.4)^2(0.6)^6+56(0.4)^3(0.6)^5+70(0.4)^4(0.6)^4+56(0.4)^5(0.6)^3

=0.95019264

8 0
3 years ago
Give a number that is not in the domain of <br><br> f(x) = √3x-6
Harman [31]
Any number that is less than 2 will work. It is impossible to find the square root of a negative number (you can only get imaginary number) since anything square is a positive number.
PS. If you are confused by the answer, just ask me.
5 0
3 years ago
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