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3 years ago

The first term of an arithmetic sequence is-3 and the 15 term is 53. What is the common difference of the sequence?

1 answer:

6 0

$a_2=a_1+d$
$a_3=a_2+d=a_1+2d$
$a_4=a_3+d=a_1+3d$
...
$a_{15}=a_1+14d$

Since $a_1=-3$ and $a_{15}=53$ , the common difference $d$ is

$53=-3+14d\implies d=4$

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From 5 a.m. to noon, the temperature rose 15 °F to a high of 10 °F.

kodGreya [7K]

Answer:

The temperature was 5 °F

7 0

3 years ago

Suppose a sample of 100 families of four vacationing at Niagara Falls resulted in sample mean of $282.45 spent per day and a sam

Juli2301 [7.4K]

Given Information:

Mean = μ = $282.45

Standard deviation = σ = $64.50

Sample size = n = 100

Confidence level = 95%

Required Information:

95% Confidence interval = ?

Answer:

95% Confidence interval = ($269.81, $295.09)

Step-by-step explanation:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

What is Confidence Interval?

The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.

The confidence interval is given by

$CI = \bar{x} \pm MoE\\$

Where $\bar{x}$ is the mean and MoE is the margin of error given by

$MoE = z_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\$

Where σ is the standard deviation, n is the sample size and $z_{\alpha/2}$ is the z-score corresponding to 95% confidence level.

$z_{\alpha/2} = 1 - 0.95 = 0.05/2 = 0.025\\\\z_{0.025} = 1.96$

$MoE = 1.96\cdot \frac{64.50}{\sqrt{100} } \\\\MoE = 1.96\cdot 6.45\\\\MoE = 12.64\\$

Finally, the confidence interval is

$CI = \bar{x} \pm MoE\\\\CI = 282.45 \pm 12.64\\\\CI = 282.45 - 12.64 \: and \: 282.45 + 12.64\\\\CI = \$269.81 \: and \:\:\$295.09\\$

Therefore, we are 95% sure that the true population mean amount spent per day by a family of four visiting Niagara Falls is within the interval of ($269.81, $295.09)

3 0

3 years ago

Linda left home and drove for 2 hours. She stopped for lunch then drove for another 3 hours at a rate that is 10 mph higher than

Verdich [7]

Answer:

44 mph

Step-by-step explanation:

Given that:

Before lunch :

Time taken = 2hrs ; at speed = x mph

After lunch :

Time taken = 3hrs ; at speed = x + 10 mph

Total distance covered = 250 miles :

Distance = speed * time

(2 * x) + (3 * (x + 10)) = 250

2x + 3x + 30 = 250

5x + 30 = 250

5x = 250 - 30

5x = 220

x = 220/ 5

x = 44 mph

Rate before lunch is 44mph

6 0

3 years ago

QUESTION 3

eduard

Athe answer is -2 because it is behind the 0 and will be negative and it is two lines away from the 0 so the answer is -2

3 0

3 years ago

You start at (-3,-2). you move down 1 and left 1 unit. where do you end?

Roman55 [17]

You will end at (-4, -3)

7 0

3 years ago