Answers

Answer 1
Answer:

Answer: x=8

Step-by-step explanation:


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A meteorologist is studying the speed at which thunderstorms travel. A sample of 10 storms are observed. The mean of the sample was 12.2 MPH and the standard deviation of the sample was 2.4. What is the 95% confidence interval for the true mean speed of thunderstorms?

Answers

Answer:

The 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].

Step-by-step explanation:

Given information:

Sample size = 10

Sample mean = 12.2 mph

Standard deviation = 2.4

Confidence interval = 95%

At confidence interval 95% then z-score is 1.96.

The 95% confidence interval for the true mean speed of thunderstorms is

CI=\overline{x}\pm z*(s)/(√(n))

Where, \overline{x} is sample mean, z* is z score at 95% confidence interval, s is standard deviation of sample and n is sample size.

CI=12.2\pm 1.96(2.4)/(√(10))

CI=12.2\pm 1.487535

CI=12.2\pm 1.488

CI=[12.2-1.488, 12.2+1.488]

CI=[10.712, 13.688]

Therefore the 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].

Norma and Jane go to the store to buy stocking stuffers. Norma spends $8 more than Jane. Total, Norma and Jane spend $52. How much did each girl spend?

Answers

Answer:

Norma spent $30

Jane spent $22

Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither. f(x) = x + 4 if x < 0 ex if 0 ≤ x ≤ 1 8 − x if x > 1 x = (smaller value) continuous from the right continuous from the left neither

Answers

Using continuity concepts, it is found that the function is left-continuous at x = 1.

-------------------------------

A function f(x) is said to be continuous at x = a if:

\lim_(x \rightarrow a^(-)) f(x) = \lim_(x \rightarrow a^(+)) f(x) = f(a)

  • If only \lim_(x \rightarrow a^(-)) f(x) = f(a), the function is left-continuous.
  • If only \lim_(x \rightarrow a^(+)) f(x) = f(a), the function is right-continuous.

-------------------------------

The piece-wise definition of the function f(x) is:

x + 4, x < 0

x, 0 \leq x \leq 1

8 - x, x > 1

We have to check the continuity at the points in which the definitions change, that is, x = 0 and x = 1.

-------------------------------

At x = 0:

  • The definition at 0 is f(0) = 0
  • Approaching x = 0 from the left, we have values less than 0, thus:

\lim_(x \rightarrow 0^(-)) f(x) = \lim_(x \rightarrow 0) x + 4 = 0 + 4 = 0

  • Approaching x = 0 from the right, we have values greater than 0, thus:

\lim_(x \rightarrow 0^(+)) f(x) = \lim_(x \rightarrow 0) x = 0

Since the limits are equal, and also equal to the definition at the point, the function is continuous at x = 0.

-------------------------------

At x = 1:

  • The definition at 1 is f(1) = 1
  • Approaching x = 1 from the left, we have values less than 1, thus:

\lim_(x \rightarrow 1^(-)) f(x) = \lim_(x \rightarrow 1) x = 1

  • Approaching x = 1 from the right, we have values greater than 1, thus:

\lim_(x \rightarrow 1^(+)) f(x) = \lim_(x \rightarrow 1) 8 - x = 8 - 1 = 7

To the right, the limit is different, thus, the function is only left continuous at x = 1.

A similar problem is given at brainly.com/question/21447009

Answer:

the function is continuous from the left at x=1 and continuous from the right at x=0

Step-by-step explanation:

a function is continuous from the right , when

when x→a⁺ lim f(x)=f(a)

and from the left when

when x→a⁻ lim f(x)=f(a)

then since the functions presented are continuous , we have to look for discontinuities only when the functions change

for x=0

when x→0⁺ lim f(x)=lim  e^x = e^0 = 1

when x→0⁻ lim f(x)=lim  (x+4) = (0+4) = 4

then since f(0) = e^0=1 , the function is continuous from the right at x=0

for x=1

when x→1⁺ lim f(x)=lim  (8-x) = (8-0) = 8

when x→1⁻ lim f(x)=lim e^x = e^1 = e

then since f(1) = e^1=e , the function is continuous from the left at x=1

A bookstore keeps track of books sold in one day? Approximately how many books sold were hardcover nonfiction?

Answers

Answer:

27%

Step-by-step explanation:

The total books sold were 182 and the amount of books sold that were nonfiction hardcover were 49 as represented in the frequency table.

To find the percentage we must divide the nonfiction hardcover by the total books.

49/182≈0.269 or 0.27

Multiply the decimal by a 100 to change it into a percentage, so our answer is 27%.

Answer:a 27%

Step-by-step explanation:

Create and solve
an equation with
2 variables(x).

Answers

Answer:

5x-2=3x+4

x=3

Step-by-step explanation:

Hope I helped!

The amount of chlorine needed to treat a swimming pool is directly proportional to the volume of the poolWhat is the constant of proportionality for this relationship

Answers

The amount of chlorine needed to treat a swimming pool is directly proportional to the volume of the poolWhat is the constant of proportionality for this relationship

The answer to this question is 0.002