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3 years ago

Which conjunction or disjunction is equivalent to the open sentence |a – 7| ≤ 5?

Mathematics

1 answer:

Dimas [21]3 years ago

7 0

Answer:

This is the same as a-7≤5 and 7-a≤5.

So a≤12 and a≥2, which is written 2≤a≤12, so a lies between 2 and 12 or a has the interval [2,12].

Step-by-step explanation:

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Which statement best describes a ratio

user100 [1]

Answer: Where are the options?

Step-by-step explanation:

4 0

3 years ago

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the o

Korvikt [17]

Answer:

a) $k = 0.000124$

b) According to these data, the Shroud of Turin has around 760 years.

Step-by-step explanation:

The amount of carbon-14 is modeled by the following equation:

$C(t) = C_{0}e^{-kt}$

In which $C_{0}$ is the initial amount and k is the rate of decrease.

(a) Find the value of the constant k in the differential equation.

Half-life of 5595 years.

So $C(5595) = 0.5C_{0}$

$C(t) = C_{0}e^{-kt}$

$0.5C_{0} = C_{0}e^{-5595k}$

$e^{-5595k} = 0.5$

Applying ln to both sides

$-5595k = -0.69$

$k = 0.000124$

b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material. How old is the Shroud of Turin, according to these data?

This is t when $C(t) = 0.91C_{0}$

$C(t) = C_{0}e^{-kt}$

$0.91C_{0} = C_{0}e^{-0.000124t}$

$e^{-0.000124t} = 0.91$

Applying ln to both sides

$-0.000124t = -0.094$

$t = 760.57$

According to these data, the Shroud of Turin has around 760 years.

8 0

4 years ago

A 222-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.

viktelen [127]

Answer:

The shorter piece is <u>37</u> inches long.

Step-by-step explanation:

Let the length of the shorter piece be x and the longer piece be 5x.

Short piece + Long piece = 222 inches

x + 5x = 222

6x = 222

x = 222 ÷ 6

x = 37

5 0

3 years ago

Out of her 5 gigabyte data plan, Debbie has used 37%. How much data does she have left?

givi [52]

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4 0

3 years ago

Read 2 more answers

An automobile manufacturer has discovered that 20% of all the transmissions it installed in a particular style of truck are defe

Hatshy [7]

Answer:

0.148 = 14.8% probability that they will need to order at least one more new transmission

Step-by-step explanation:

For each transmission, there are only two possible outcomes. Either it is defective after a year of use, or it is not. The probability of a transmission being defective is independent of any other transmission. 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.

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