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3 years ago

Cadence is substituting t=4 and t=6 to determine if the two expressions are equivalent.

Mathematics

2 answers:

liberstina [14]3 years ago

3 0

Answer:

Both expressions are equivalent to 78 when t = 6 ⇒ answer A

Step-by-step explanation:

* To solve this problem substitute the value of t and then check

the answer

∵ The first expression is 2(7t - 3) ⇒ simplify it

# 2(7t) = 14t

# 2(3) = 6

∴ 2(7t - 3) = 14t - 6

- Substitute t by 4

∴ 14t - 6 = 14(4) - 6 = 56 - 6 = 50

- Substitute t by 6

∴ 14t - 6 = 14(6) - 6 = 84 - 6 = 78

∵ The second expression is 15t - 12

- Substitute t by 4

∴ 15t - 12 = 15(4) - 12 = 60 - 12 = 48

- Substitute t by 6

∴ 15t - 12 = 15(6) - 12 = 90 - 12 = 78

- The first expression has two values

# 50 when t = 4

# 78 when t = 6

- The second expression has two values

# 48 when t = 4

# 78 when t = 6

- From these information

# The two expressions have the same value 78 when t = 6

∴ Both expressions are equivalent to 78 when t = 6

trapecia [35]3 years ago

3 0

Answer: A

Step-by-step explanation: Both expressions are equivalent to 78 when t= 6.

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An example problem in a Statistics textbook asked to find the probability of dying when making a skydiving jump.

MArishka [77]

Answer:

(a) 0.999664

(b) 15052

Step-by-step explanation:

From the given data of recent years, there were about 3,000,000 skydiving jumps and 21 of them resulted in deaths.

So, the probability of death is $\frac{21}{3000000}==0.000007$ .

Assuming, this probability holds true for each skydiving and does not change in the present time.

So, as every skydiving is an independent event having a fixed probability of dying and there are only two possibilities, the diver will either die or survive, so, all skydiving can be regarded as is Bernoulli's trial.

Denoting the probability of dying in a single jump by $q$ .

$q=7\times 10^{-6}=0.000007$ .

So, the probability of survive, $p=1-q$

$\Rightarrow p=1-7\times 10^{-6}=0.999993.$

(a) The total number of jump he made, n=48

Using Bernoulli's equation, the probability of surviving in exactly 48 jumps (r=48) out of 48 jumps (n=48) is

$=\binom(n,r)p^rq^{n-r}$

$=\binom(48,48)(0.999993)^{48}(0.000007)^{48-48}$

$=(0.999993)^{48}=0.999664$ (approx)

So, the probability of survive in 48 skydiving is 0.999664,

(b) The given probability of surviving =90%=0.9

Let, total $n$ skydiving jumps required to meet the surviving probability of 0.9.

So, By using Bernoulli's equation,

$0.9=\binom {n }{r} p^rq^{n-r}$

Here, r=n.

$\Rightarrow 0.9=\binom{n}{n}p^nq^{n-n}$

$\Rightarrow 0.9=p^n$

$\Rightarrow 0.9=(0.999993)^n$

$\Rightarrow \ln(0.9)=n\ln(0.999993)$ [ taking $\log_e$ both sides]

$\Rightarrow n=\frac {\ln(0.9)}{\ln(0.999993)}$

$\Rightarrow n=15051.45$

The number of diving cant be a fractional value, so bound it to the upper integral value.

Hence, the total number of skydiving required to meet the 90% probability of surviving is 15052.

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3 years ago

Alvin had some marbles in a box. He kept 1/3 of them and gave the remainder to Joyce and Sean. Joyce got 5/8 of the remainder. W

Zigmanuir [339]

First, Alvin gave Joyce and Sean 2/3 of the remainder, to solve first find the common denominator, which in this case is 24. Then, 1/3=?/24, 24/3=8 so it is 8/24 for the total given by Alvin. Joyce got 5/8, 5/8=?/24, 24/8=3,3 x 5=15, 15/24.
15/24 - 8/24= 7/24 is the answer

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Arte-miy333 [17]

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3 years ago

The school soccer coach records the number of goals some players have scored so far this season. The dot plot of the number of g

yuradex [85]

Answer:

the means absolute deviation is 1.8

the striking deviation is 7

(it is because the data point on the far right of the graph)

Step-by-step explanation:

calculate the absolute deviation:

1. calculate the mean (add all numbers and divide by 10) = 2.6

2. find the absolute value of each

2.6 - 0 = 2.6

2.6 - 1 = 1.6 (you have 1's 4 times so each one will be 1.6)

2.6 - 3 = 0.4

2.6 - 4 = 1.4 (you have 4's 3 times)

2.6 - 7 = 4.4

3. Then add all of those values together

2.6 + 1.6 + 1.6 + 1.6 + 1.6 + 0.4 + 1.4 + 1.4 + 1.4 + 7.4 = 18

4. find the mean of the difference

18/10 = 1.8

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Ne4ueva [31]

You would have half a billion

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