Can the binomial distribution be approximated by a normal distribution? n = 31, p = 0.9 Explain why or why not.​

Answer:

Step-by-step explanation:

25.

[tex]cos 45=\frac{x}{18\sqrt{2} } \\\frac{1}{\sqrt{2}} =\frac{x}{18\sqrt{2} } \\x=\frac{18\sqrt{2}}{\sqrt{2}} \\x=18[/tex]

  26.

sin30=30/x

[tex]\frac{1}{2} =\frac{30}{x} \\x=30 \times 2=60[/tex]

Step-by-step explanation:

h(-2) = 25

h(-1) = 5

h(0) = 1

h(1) = 1/5

h(2) = 1/25

Answer:

A≈1.83m²

Step-by-step explanation:

Using the formulas

A=πr2C=2πr

Solving forAA=C24π=4.824·π≈1.83346m²

Answer:

1.83 (approximate)

Step-by-step explanation:

First, we need to find the radius of the circle.

Using the formula:

[tex]C=2 \pi r[/tex]

We have to reorganize terms:

[tex]r=\frac{C}{2\pi}[/tex]

[tex]\frac{4.8}{2 \times \pi}[/tex]

r ≈ 0.76

Now we have the radius and the circumference in order to find the area.

Use the formulas:

[tex]A= \pi r^2[/tex]

[tex]C=2 \pi r[/tex]

A = C^2/4[tex]\pi[/tex]  = 4.8^2 / 4 * pi = 1.83

Answer:

57

Step-by-step explanation:

Okay, So we have this person That has 81% average before the quiz. For a course That score includes everything, but the final, which counts for 25% of the course grade, was the best course grade you your friend can earn. Okay, The best course grade given to me makes me. Mhm. 100. So we have .81 times. Actually we'll keep this as 81, times .75 right Plus 100 times. Excuse ME, Time 0.25. This is equivalent to 81 times 0.75. Mhm. This is equivalent to 81 times .75 plus 100 times 0.25, Which equals 85.75%. Now that's for part one. Report to we have what is the minimum score? Turn to 75%. So we have 75 equal to 81 times 0.75 Plus X. Times zero 25. So 81 times 0.75 equals 60.75 75- is value mhm. Is equal to 14.25. So we have 0.25 x. And if we divide 14.25 over 0.25, we isolate X. So the minimum score to get a 75 is a 57

James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.

Prοbability is a measure οf the likelihοοd οf an event οccurring. It is a numerical value between 0 and 1, where 0 means the event is impοssible and 1 means the event is certain tο οccur. Fοr example, the prοbability οf flipping a fair cοin and getting heads is 1/2 οr 0.5.

Tο calculate the tοtal cοst in Singapοre dοllars, we need tο cοnvert the US dοllars tο Singapοre dοllars using the given exchange rate, and then add the twο cοsts tοgether.

The cοst οf the item in Singapοre dοllars is:

75 USD * 1.65 SGD/USD = 123.75 SGD

The shipping and handling cοst in Singapοre dοllars is:

39 USD * 1.65 SGD/USD = 64.35 SGD

The tοtal cοst in Singapοre dοllars is the sum οf these twο cοsts:

Tοtal cοst = 123.75 SGD + 64.35 SGD = 188.10 SGD

Therefοre, James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.

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The largest printed area of the poster would be when the width and height of the poster are equal. To find the width of the poster, we need to subtract the total area of the margins from the total area of the poster.

The total area of the margins is 6 cm x 4 cm + 4 cm x 6 cm = 88 cm2.

Therefore, 245 cm2 - 88 cm2 = 157 cm2.

We can then use the formula A = W x H, where A is the area and W and H are the width and height of the poster, respectively.

Therefore, 157 cm2 = W x W.

We can solve for W by taking the square root of both sides.

Therefore, W = √157 = 12.5 cm.

Therefore, the width of the poster should be 12.5 cm in order to have the largest printed area.

Answer:

x = 4

Step-by-step explanation:

If we use A*B = C*D we get 2*6 = 3*x which is 12 = 3x. Dividing both sides by 3 you get 4 = x

The probability that a vehicle will weigh between 1,946 and 4,455 pounds is 0.8076.

To solve this problem, we need to find the probability that a randomly chosen car weighs between 1,946 and 4,455 pounds. Since weight is uniformly distributed, we know that the probability density function is constant over the entire range of possible values.

First, we need to find the total range of possible values:

Range = maximum weight - minimum weight

Range = 4,665 - 1,557

Range = 3,108

Next, we need to find the range of values that fall between 1,946 and 4,455:

Target range = 4,455 - 1,946

Target range = 2,509

Finally, we can calculate the probability of a randomly chosen car falling within this target range:

Probability = Target range / Range

Probability = 2,509 / 3,108

Probability = 0.8076 (rounded to 4 decimal places)

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The best chart to represents changes in the stock portfolio over the last 12 months by financial advisor is shown by option 1. a line chart.

The best type of chart to use to show how a stock portfolio has changed over time is a line chart.

A line chart can show the trend in the portfolio's value over the 12-month period.

Which is useful for identifying patterns and changes in performance.

A histogram is used to show the distribution of a single variable.

While a pie chart is used to show the proportion of a whole made up by different parts.

A bar chart is useful for comparing different categories or groups.

However, for tracking changes in a single variable over time, a line chart is the most appropriate choice.

Therefore, the best chart for financial advisor to show changes in stock portfolio over the last 12 months is given by option 1. a line chart.

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Answer:

r = -2

Step-by-step explanation:

5r + 20/10 = 3r -6/3

5r + 2 = 3r - 2

2r + 2 = -2

2r = -4

r = -2

Answer: r = -2

Step-by-step explanati

Answer:

The square root of 20 is approximately between 4 and 5.

To find this, you can estimate the square root of 20 by finding the square root of the closest perfect squares, which are 16 (4^2) and 25 (5^2):

√16 = 4

√25 = 5

Since 20 is closer to 25 than 16, we know that the square root of 20 must be closer to 5 than to 4. Therefore, the square root of 20 lies between 4 and 5.

The set of ordered pairs does not represent a function is the one in the third option.

{(-1,9), (-8, 5), (-1, 3), (-9, 1)}

A relation maps elements from one set, the domain, into elements of other set, the range.

Such that these mappings are of the form (x,y).

A function is a relation where each input is mapped into a single one output, then if you see a relation that has two points with the same value of x and different values of y, then that relation is not a function.

Particularly, if you look at the third option:

{(-1,9), (-8, 5), (-1, 3), (-9, 1)}

You can see that the first and second points have the same input and different outputs, then this is not a function, and that is the correct answer.

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Part A :  the probability that a randomly chosen recipient served in the army, navy, or marines is 0.993. Part : the probability that a randomly chosen recipient served in the Air Force is 0.0038.

Probability is a branch of mathematics that deals with the study of chance or randomness. It involves the measurement of the likelihood or chance of an event occurring. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a coin and it landing on heads is 0.5 or 50%, assuming a fair coin.

The total number of recipients in the pie chart is the sum of all the values: 2393 + 743 + 296 + 13 + 8 + 1 = 3454.

Part A: The number of recipients who served in the army, navy, or marines is 2393 + 743 + 296 = 3432. Therefore, the probability that a randomly chosen recipient served in the army, navy, or marines is:

P(Army or Navy or Marines) = (2393 + 743 + 296) / 3454 ≈ 0.993

Part B: The number of recipients who were civilians is 8. Therefore, the probability that a randomly chosen recipient was a civilian is:

P(Civilian) = 8 / 3454 ≈ 0.0023

Therefore, the probability that a randomly chosen recipient served in the Air Force is:

P(Air Force) = 13 / 3454 ≈ 0.0038.

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The value of 3302 mod 385 is 51179.

To use Fermat's little theorem to compute the expression, we need to first identify two relatively prime numbers that we can use as the base and the modulus. Let's choose 2 and 384, respectively.

Then, we have:

2³⁸⁴ ≡ 1 (mod 385)

Multiplying both sides by 3302, we get:

2³⁸⁴ × 3302 ≡ 3302 (mod 385)

Now, we can use the Chinese remainder theorem to find the value of 2³⁸⁴ × 3302 mod 385.

From the part (a) of this question, we know that:

2³⁸⁴ ≡ 1 (mod 7)

2³⁸⁴ ≡ 1 (mod 5)

2³⁸⁴ ≡ 16 (mod 11)

Using the Chinese remainder theorem, we can combine these congruences to get:

2³⁸⁴ ≡ 166 (mod 385)

Substituting this into the expression we derived earlier, we have:

2³⁸⁴ × 3302 ≡ 166 × 3302 (mod 385)

Multiplying out, we get:

2³⁸⁴ × 3302 ≡ 51179 (mod 385)

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Answer:

X=18

Step-by-step explanation:

Answer:

x = 3.5 units (nearest tenth)

Step-by-step explanation:

The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.  

Therefore, the formula for the ratio of the sides is x : x : x√2 where:

As the hypotenuse of the given right triangle is 5 units:

[tex]\implies x\sqrt{2} = 5[/tex]

To find the measure of x, solve for x:

[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x =3.5355339...[/tex]

[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]

Therefore, the length of side x to the nearest tenth is 3.5 units.

The best interpretation of the confidence interval is We are 95% confident that the difference in proportions for smokers and nonsmokers with CVD in the population is between −0.01 and 0.04 that is option B.

Confidence interval is estimate of Parameter were parameter is difference in proportion of smokers and non smokers in population.

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.

Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.

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Answer:

P(5,6) = 63

Step-by-step explanation:

Test each point to see which ordered pair maximizes the objective function:

(0,0): p = 3(0) + 8(0) = 0

(2,7): p = 3(2) + 8(7) = 6 + 56 = 62

(5,6): p = 3(5) + 8(6) = 15 + 48 = 63

(8,1): p = 3(8) + 8(1) = 24 + 8 = 32

Hence, (5,6) is the ordered pair that maximizes the objective function.

The answer of the given question based on the  transformation from its parent function the explanation part is given below and The equation of the function is y = -2(x+3)².

In mathematics,  function is  relation between  set of inputs and  set of possible outputs with  property that each input is related to exactly one output. It is  rule that assigns to each input value exactly one output value. Functions can be represented in various ways, like algebraic expressions, graphs, tables, and words. They are used to model relationships between variables, to describe how one quantity depends on another, and to make predictions about future values. Functions are  important concept in many fields of mathematics, as well as in science, engineering, economics, and other areas where quantitative analysis is used.

a. The graph appears to be a reflection of the parent function f(x) = x² over the x-axis followed by a vertical stretch by a factor of 2 and a horizontal shift to the left by 3 units.

b. The equation of the function is y = -2(x+3)².

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The probability that a data value is between 46 and 47 in a normal distribution with mean 48 and standard deviation 2 is approximately A. 15.0%.

To solve this problem, we need to first standardize the given values using the standard normal distribution formula:

z = (x - μ) / σ

where z is the standardized value, x is the data value, μ is the mean, and σ is the standard deviation.

For x = 46:

z = (46 - 48) / 2 = -1

For x = 47:

z = (47 - 48) / 2 = -0.5

Next, we can use a standard normal distribution table or calculator to find the area under the standard normal curve between these two standardized values.

Using a calculator or table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = -0.5 is 0.3085.

Therefore, the area between z = -1 and z = -0.5 is:

0.3085 - 0.1587 = 0.1498

Finally, we can convert this area back to a probability by rounding to the nearest tenth of a percent:

0.1498 ≈ 15.0%

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The surface area of the surface generated by rotating the curve y = x² about the y-axis, and we found that the surface area is approximately 54.33 square units.

In this case, the curve we want to rotate is y = x², and we want to rotate it about the y-axis. To use the formula above, we need to express the equation of the curve in terms of x. Therefore, we need to rewrite y = x² as x = √y.

Next, we need to find the derivative of x = √y with respect to y, which is:

dx/dy = 1/2√y

Substituting this into the formula for the surface area, we get:

Surface Area = 2π ∫[0,4] √y √(1+(1/2√y)²) dy

Simplifying the expression inside the square root, we get:

Surface Area = 2π ∫[0,4] √(y+(1/4)) dy

We can evaluate this integral using the power rule of integration, which gives:

Surface Area = 2π [2/3(y+(1/4))^(3/2)]₀⁴

Simplifying further, we get:

Surface Area = 2π [2/3(17/4)^(3/2)]

Surface Area ≈ 54.33 square units

Therefore, the surface area of the surface generated by rotating the curve y = x² about the y-axis is approximately 54.33 square units.

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Complete Question:

How do you find the area of the surface generated by rotating the curve about the y-axis y = x^2 , 0 ≤ x ≤ 2 ?

319 is the correct answer.

Answer:

15.

The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.

So, the answer to the question "what is 5 divided by 1/3?" is
15!

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The frequency table is completed as follows

Number of books           frequency

0 - 9                                      1

10 - 19                                    10

20 - 29                                  9

A frequency table is a way of organizing data in a table that shows the number of times each value or category appears in a dataset.

The table lists the unique values or categories in one column, and the frequency (or count) of occurrences of each value or category in the dataset in another column.

In the table attached, the solution is achieved by examining the tally column

Each item in the tally column is counted to get the numbers in place of l

A B C and D

Examining the table, we can say that

A = 1

B = 5 + 5 = 10

C = 5 + 4 = 9

D = 3

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Answer:

Step-by-step explanation:

To find the zeros of the function, we set y to zero and solve for x:

y = (x+1)(x-2)(x-6) = 0

Setting each factor equal to zero and solving for x gives us the zeros:

x+1 = 0 or x-2 = 0 or x-6 = 0

x = -1, x = 2, x = 6

So the zeros of the function are -1, 2, and 6.

To graph the function, we can use the zeros and the leading coefficient to sketch a rough graph. The leading coefficient is positive, so the graph will open upward. The zeros are -1, 2, and 6, so the graph will intersect the x-axis at those points. We can also find the y-intercept by plugging in x = 0:

y = (0+1)(0-2)(0-6) = 12

So the y-intercept is (0, 12).

Using this information, we can sketch the graph:

The correct answer to the given question is:

Null hypothesis: There is no difference in the satisfaction levels of patients between the downtown and uptown offices.

Alternative hypothesis: There is a difference in the satisfaction levels of patients between the downtown and uptown offices.

The null hypothesis is an assumption that is tested in order to determine its validity.

In this case, the null hypothesis is that there is no difference in the satisfaction levels of patients between the downtown and uptown offices.

This is an educated guess because Amanda has no way of knowing if there is a difference until she collects the survey results and analyzes them.

The alternative hypothesis is the opposite of the null hypothesis. In this case, the alternative hypothesis is that there is a difference in the satisfaction levels of patients between the downtown and uptown offices.

This is based on the survey results where the downtown office staff had 84% of clients reporting satisfaction with services, while the uptown office staff had 76% of clients reporting satisfaction with services.

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Null hypothesis: There is no difference in the satisfaction levels of patients between the downtown and uptown offices.

Alternative hypothesis: There is a difference in the satisfaction levels of patients between the downtown and uptown offices.

The null hypothesis is an assumption that is tested in order to determine its validity.

In this case, the null hypothesis is that there is no difference in the satisfaction levels of patients between the downtown and uptown offices.

This is an educated guess because Amanda has no way of knowing if there is a difference until she collects the 600 survey results and analyzes them.

The alternative hypothesis is the opposite of the null hypothesis.

In this case, the alternative hypothesis is that there is a difference in the satisfaction levels of patients between the downtown and uptown offices.

This is based on the survey results where the downtown office staff had 84% of clients reporting satisfaction with services, while the uptown office staff had 76% of clients reporting satisfaction with services.

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The answers are a)the sample mean, which is $1,235. b) margin of error = $58.50. c)95% .d)the average monthly rent is at least $1,300.e)The z-score for a 92% confidence interval is 1.75.

a) The sample mean is the point estimate of the true mean monthly rent for one-bedroom apartments available for rent near BCIT, which is $1,235.

(b) At a 95% confidence level, the margin of error on the true mean monthly rent estimate is calculated as follows:

Margin of error = Z * (standard deviation / square root of sample size), where Z is the desired confidence level's z-score, which is 1.96 for a 95% confidence level.

Thus, the margin of error is equal to 1.96 * (150 / sqrt(36)) = $58.50.

(c) The 95% confidence interval for the true mean monthly rent is calculated as follows:

Lower value = point estimate minus margin of error = $1,235 minus $58.50 equals $1,176.50

Upper estimate + margin of error = $1,235 + $58.50 = $1,293.50.

(d) To see if the confidence interval supports the friend's claim that the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300, we need to see if the lower limit of the confidence interval is greater than or equal to $1,300.

Given that the confidence interval is $1,176.50 $1,300, we can conclude that the confidence interval does not support the friend's claim that the

average monthly rent is at least $1,300. As a result, the answer is "No."

(e) A standard normal distribution table or calculator can be used to calculate the z-score corresponding to a 92% confidence interval.

A 92% confidence interval has a z-score of 1.75. (to two decimal places).

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Step-by-step explanation:

Lisa started with $25 on her prepaid debit card. After her first purchase, she had $22.90 left. Therefore, she spent:

$25 - $22.90 = $2.10

We know that the price of the ribbon was 14 cents per yard. To find out how many yards Lisa bought, we can set up an equation:

$2.10 ÷ $0.14/yd = 15 yards

Therefore, Lisa bought 15 yards of ribbon with her prepaid debit card.

Answer:

y = 5x - 35

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

m = 5

The y-intercept is located at (0, -35)

So, the equation is y = 5x - 35

Answer: y=5x-35

Step-by-step explanation:

The formula I believe you are looking for would be y=mx+b. M is your slop and B is your y-intercept. Since the slope is already given, you would fill in the rest of the formula with that and the (x,y) you were provided, and it should look like this:

5=5(8)+b.

Then you solve that for b as follows:

5=5(8)+b

5=40+b

-35=b

Therefore the equation would be y=5x-35