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3 years ago

(Need Answer!)

Mathematics

1 answer:

zalisa [80]3 years ago

8 0

Answer:

k = 7

Step-by-step explanation:

Applying,

S = (y₂-y₁)/(x₂-x₁)................ Equation 1

Where S = slope of the line.

From the question,

Given: y₂ = 10, y₁ = 4, x₂ = k, x₁ = 1, S = 1

Substitute these values into equation 1

1 = (10-4)/(k-1)

crossmultiplying,

(k-1) = (10-4)

k-1 = 6

k = 6+1

k = 7

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Thepotemich [5.8K]

Use the compound amount formula:

A = P*(1+r/n)^(nt)

Here,

A = $3500*(1+0.0375/12)^(12*12) = $5485.24

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3 years ago

The box plot below represents some data set. What is the interquartile range (IQR) of

vesna_86 [32]

Answer:

I think the IQR is 100

Step-by-step explanation:

You would have to find the first and third quartiles first. After that you would subtract the third quartile by the first to get the IQR

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3 years ago

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dolphi86 [110]

Answer:

$\lim_{x \to 2^-} x^3=2^3=\boxed8\\ \lim_{x \to 2^+} 3x-4=3\cdot 2-4=6-4=\boxed2$

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Step-by-step explanation:

Inserting 2 to both formulas, you get different results. In that cases, a limit does not exist

6 0

3 years ago

Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally dis

nikitadnepr [17]

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = the interval of time between the eruptions

So, X ~ N( $\mu=72, \sigma^{2} =23^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 minutes is given by = P(X > 82 min)

P(X > 82 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{82-72}{23}$ ) = P(Z > 0.43) = 1 - P(Z $\leq$ 0.43)

= 1 - 0.6664 = 0.3336

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let $\bar X$ = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes is given by = P( $\bar X$ > 82 min)

P( $\bar X$ > 82 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{82-72}{\frac{23}{\sqrt{13} } }$ ) = P(Z > 1.57) = 1 - P(Z $\leq$ 1.57)

= 1 - 0.9418 = 0.0582

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let $\bar X$ = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is given by = P( $\bar X$ > 82 min)

P( $\bar X$ > 82 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{82-72}{\frac{23}{\sqrt{34} } }$ ) = P(Z > 2.54) = 1 - P(Z $\leq$ 2.54)

= 1 - 0.9945 = 0.0055

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 minutes, then we conclude that the population mean must be more than 72, since the probability is so low.

6 0

3 years ago

If p and q are non-zero rational numbers, and s and t are irrational numbers, select all of the statements that are always false

Svetllana [295]

Answer:

The false choices are A, C, and E

Step-by-step explanation:

Let's make an example:

p=1

q=2

s=sqrt(3)

t=sqrt(6)

Since pq=1*2=2, the answer is rational and A is false.

Since pt=1*sqrt(6)=sqrt(6), the answer is irrational and B is true.

Since p/q=1/2=0.5, the answer is rational and C is false.

Since st=sqrt(3)*sqrt(6)=sqrt(18), the answer is irrational and D is true.

Since s/t=sqrt(3)/sqrt(6)=sqrt(1/2), the answer is irrational and E is false.

4 0

3 years ago