in estimating a population mean with a confidence interval based on a random sample x1,...,xn from a normal distribution with an unknown mean and a known variance, compare the length of the 95% and 90% confidence intervals for the unknown mean based on x1,...,xn.

The Area of the given sector is 14.1 yd²

Define Sector of a Circle

A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.

Given,

radius = 6 yd

Angle θ = 45°

The formula for,  Sector Area = (θ / 360°) * πr²

Now, plug in the values

Sector Area = (45 / 360) * 3.14 * 6²

                    = 14.1 yd²

Hence, the Area of the given sector is 14.1 yd²

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Answer: 4.5

Step-by-step explanation:

sector area = 4.5 on 14.143 yd ^2

The given confidence interval is correct and it is between 22% to 38%.

The formula for calculating the confidence interval of population proportion is

[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]

Here the sample proportion is represented by [tex]\bar{p}[/tex].

It is given that,

The 95% confidence interval has a sample size of n = 120 and the number of successes = 36.

So, the sample proportion [tex]\bar{p}[/tex] = 36/120 = 0.3

For the 95% confidence interval, α = 1 - 0.95 = 0.05

And α/2 = 0.05/2 = 0.025

Then, the z-score for α/2 = 0.025 is [tex]z{\alpha/2|=1.96[/tex].

And the standard deviation, [tex]\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }=\sqrt{\frac{0.3(1-0.3)}{120} }[/tex] = 0.0418

So, the interval is in between

C.I = 0.3 ± 1.96 × 0.0418

Upper limit = 0.3 + 1.96 × 0.0418 = 0.38 = 38%

Lower limit = 0.3 - 1.96 × 0.0418 = 0.218 = 0.22 = 22%

Therefore, the given confidence interval is correct.

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Therefore the value of function f(g(x)) comes out to be x[tex]e^{2}[/tex] +[tex]e^{2}[/tex]-3

An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. If anything is entered for x, there is just one output for y. Since x is the input value, we can state that y is a function of x.

Here,

Given: f(x)=x[tex]e^{2}[/tex]-3  and g(x)=x+1

To find the value of f(g(x))

we put g(x) in f(x)

So,

=> f(g(x))= g(x)[tex]e^{2}[/tex]-3

=>f(g(x))= (x+1)[tex]e^{2}[/tex]-3

=> f(g(x))= x[tex]e^{2}[/tex] +[tex]e^{2}[/tex]-3

Therefore the value of function f(g(x)) comes out to be x[tex]e^{2}[/tex] +[tex]e^{2}[/tex]-3

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On solving the question - Use the z distribution if the population variances are known; if not, use the -tdf distribution.

A measure of the distribution of a set of data points is called population variance. It measures the mean squared departure from the mean, specifically. As a result, the variance will be minimal if all of the data points are very near to the mean. The variation will be high if the data points are dispersed throughout a wide range.

The difference between the mean and the mean squared is known as the variance, and the standard deviation is the square root of that difference. Although in different units, both measurements capture the distribution's variability. The same units are used to express standard deviation and the original value.

Use the z distribution if the population variances are known; if not, use the -tdf distribution.

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Answer:

30/4+5•3-9

= 7.5+15-9

= 22.5-9

= 13.5

Step-by-step explanation:

the inequality of the number line will be -6<x<2.

What is number line?

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

In this number line the max point its marked is 2

and the minimum point is -6

So the value of unknown x should lie in between

-6<x<2

So, the inequality of the number line will be -6<x<2.

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(a) The total score of Jesse's card is 1

(b) The value of each of the two cards can either be 0 or cards with different signs

In the question,

(a) Jesse's card are 3 , -5 , 9 and -6

We have to find the total

You should know that,

Adding a positive integer is like addition but adding a negative integer is like subtraction

So, Total score = 3 + (-5) + 9 + (-6)

=> 3 - 5 + 9 - 6

=> 1

Jesse's total score is 1

(b) Jesse has picked two cards which are not affecting her total score

So, either he got two zeroes or two cards with opposite signs with same magnitudes

Like 1 and -1 etc.

The two doesn't affect his score because their effect got cancelled out

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The chi-square test is 5.02 higher than critical value 3.841 so the two states does not differ with regards of shopping habits, and p value is 0.025.

O = observed value

E = expected value

n = size of sample = 2

df = degree of freedom = n - 1 = 2 - 1

α = significance level = 5% = 0.05

Chi-square is a one of many test statistic, chi-square is a test to see the different from observed value and expected value.

Chi-square formula is,

[tex]\chi^2[/tex] = [tex]\sum\frac{(O_i - E_i)^2}{E_i}[/tex]

Since, in question only give us the observed value, we need to calculate the expected value first.

Expected value conscientious state A can be calculate by this formula

E(ca) = total of state A value × total of conscientious value ÷ grand total

Repeat this process to all observed value.

We use excel to simplified and for precise calculation. Then, we put the obtained value from excel formula to Chi-square formula,

[tex]\chi^2[/tex] = 0.69 + 1.69 + 0.76 + 1.88

= 5.02

a) Critical value for df = 1 and α = 0.05 from chi-square table is 3.841

Since, the result is 5.02 higher than 3.841, it can be concluded that the two states does not differ with regards of shopping habits.

Assumptions for we use is the study group is independent and the each expected value is higher than 5.

b) We use chi-square p-value calculator with P([tex]\chi^2[/tex] > 5.02) and df = 1, α = 0.05. So, we get 0.025.

Thus, two states doesn't differ with regards of shopping habits since chi-square result is higher than critical value, and p value is 0.025.

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Answer:

d = h(cot1 - cot2)

d = 100(cot30 - cot45))

d = 100* (1.732 - 1)

d = 100*0.732

d = 73.2 m

Answer:

Yes

Step-by-step explanation:

y-8= -8(x-2)  ==> solve for y

y = -8(x - 2) + 8  ==> add 8 on both sides to isolate y

y = (-8 * x - 2(-8)) + 8  ==> distribute -8 to x and -2 using the distribution

                                         property

y = (-8x - (-16)) + 8 ==> simplify

y = (-8x + 16) + 8  ==> subtracting by a negative number is equivalent to

                               adding by a positive number.

y = -8x + 16 + 8

y = -8x + 24  ==> Degree of x in the equation is 1, so the function is linear

The chocolate bar costs 9 cents. The little girl is missing 10 cents and the little boy is missing 1 cent, so together they are missing 11 cents.

Cost is a monetary measure of the amount of resources, such as time or money, that must be expended to produce a product or service. It is a fundamental factor of economic production, as it is necessary to make products and services available to consumers. Cost can be determined in a variety of ways and can be linked to economic theory through the concept of opportunity cost. In business, cost is a major factor in decisions related to production, pricing, and marketing. Cost is also a factor in accounting and budgeting, as it is necessary to track and report the costs of organizational operations.

The chocolate bar costs 9 cents. The little girl is missing 10 cents and the little boy is missing 1 cent, so together they are missing 11 cents. If the chocolate bar cost 9 cents, that would leave 1 cent for them to split.

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The amount of the investment at a rate of 7% for 6 months will be $2200.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Harriett Weiss procured $77 in straightforward premium in a half year at a yearly loan fee of 7%.

Then the amount of the investment is given as,

$77 = [P x 7 x (6/12)]/100

$7700 = P x 7 x 1/2

7P = $15400

P = $2200

The amount of the investment at a rate of 7% for 6 months will be $2200.

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Answer:

  b.  40

Step-by-step explanation:

You want the missing leg length in a right triangle with one side of length 9 and the hypotenuse of length 41.

The missing side of any triangle will be between the sum and difference of the other two side lengths.

  c-a < b < c+a

  32 < b < 50

In a right triangle, every side length is less than the length of the hypotenuse:

  b < c

  32 < b < 41

There is only one answer choice in this range: b = 40.

__

Additional comment

You can make use of your knowledge of Pythagorean triples. One of them is {9, 40, 41}, which tells you that b=40.

Or, you can use the Pythagorean theorem to compute b:

  a² +b² = c²

  9² +b² = 41²

  b² = 1681 -81 = 1600

  b = √1600 = 40

For any odd integer, there is a Pythagorean triple with sides 1 unit apart such that those longer side lengths are about half of the square of that odd integer:

  9² = 81 = 40+41

so {9, 40, 41} is a Pythagorean triple.

The simplest of these is ...

  3² = 9 = 4+5   ⇒   {3, 4, 5} is a Pythagorean triple.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

Hence, in this problem, the function g(x) is exponential, as when the input x is increased by one, the output g(x) is multiplied by two.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

Hence, in this problem, the function f(x) is linear, as when the input x is increased by one, the output f(x) is increased by a constant of six.

The problem is given by the image shown at the end of the answer.

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Answer:

Step-by-step explanation:

1. Inequality will switch

2. Inequality will stay the same

3. Inequality will stay the same

4. Inequality will switch

Answer:

here this should help you

The trade this country will import is given by the option (C) 300 pair of shoes.

The number of shoes exported will be calculated by the formula -

Import = quantity demanded - quantity supplied. The formula is based on the concept that the import of shoes will be carried out once the manufacturing is more than the demand.

The graph indicates the quantity demanded is 1000 and the quantity supplied is 1300. Keep the values in formula to find imports.

Imports = 1300 - 1000

Performing subtraction on Right Hand Side of the equation

Imports = 300

Hence, the import is 300.

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The complete question is attached in figure.

72 mph = 105.6 ft/second

In order to convert any value from mph the following formula can be referred to:

speed in miles per hour x  5,280 = speed in foot per second

Therefore when 72 miles per hour is converted to foot per second would equal to the following value:

105.6 feet per second

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Answer: 792 Combinations

B.A quadrilateral with two pairs of parallel sides

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

Few examples of a parallelogram are rhombus, rectangle, and square.

A quadrilateral with both pairs of opposite sides parallel is known as a parallelogram.

Additionally, a parallelogram has the following qualities:

Congruent opposite angles;

The opposing factions are in agreement;

Additional angles can be found nearby;

The diagonals cut each other in half.

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Answer: the best estimate could be 20 liters

Step-by-step explanation: it is 20 liters because 1 liter is = 264 gallons so we round up the number and then use regular estimate methods.

Answer:

15 liters

Step-by-step explanation:

4 gal  /  .264 gal / liter   = 15.15 liters  = ~ 15 liters

a) The approximate mean shipping time: X{bar} = 1.64

b) The approximate variance and standard deviation:

S² = 27.03, σ = 5.2

In this question, we have been given the frequency distribution of shipping times (number of hours between the time an order is placed and the time the order is shipped) for a random sample of 40 orders.

We need to find the approximate mean shipping time, variance and standard deviation.

Number of Hours        fi                midpoint

      4 < 10                  8                    7

     10 < 16                15                  13

     16 < 22                10                  19

     22 < 28                  7                   25

       SUM:                  40

a) the approximate mean shipping time:

X{bar} = (7.8 + 13.15 + 19.10 + 25.7)/40

X{bar} = 65.75/40

X{bar} = 1.64

b) the approximate variance:

S² = [(7.8 - 1.64)² + (13.15 - 1.64)²+(19.10 - 1.64)²+(25.7 - 1.64)²] / 39

S² = 1054.16/39

S² = 27.03

And the standard deviation:

σ = √S²

σ = √27.03

σ = 5.2

Therefore, for given frequency distribution,

a) mean = 1.64

b) variance = 27.03 and standard deviation = 5.2

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A segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole .

Given :

given a segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole .

You are asked to construct P such that :

PB / AP = AP / AB

This ratio is the reciprocal of the Golden Ratio.

( AP )^2 = PB * AB

( AP )^2 = PB * ( AP + BP )

( AP )^2 = PB ( AP ) + ( BP )^2

Divide by PB^2 on both sides

ф^2 = ф + 1

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The system that has linear inequalities has the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.

We know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

In option B, we have

y > -3 ----> inequality A

y ≥ 2/3x - 4 ----> inequality B

In both inequality, change the values of x and y at the point (3, -2) and then compare the outcomes.

Inequality A

y > -3 ----> is true

Inequality B

y ≥ 2/3x - 4 ----> is true

Therefore

The ordered pair is a solution of the system B

As a result, the point (3, -2) in the solution set of the system with linear inequalities is y > -3; y 2/3x - 4.

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If the owner's beliefs are correct,  Event A and Event B are not mutually exclusive and are independent and must be true for event A and event B.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative. In the sections that follow, let's go into greater detail on the fundamentals of probability.

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Answer:

2.1 cm

Step-by-step explanation:

All the sides of a cube are equal.

let x = side of a cube

Volume of a cube = x³

Therefore x = [tex]\sqrt[3]{9.261}[/tex] = 2.1 cm

Answer:

6

Step-by-step explanation:

3 is 3/5 of 5 therefore 6 would be 3/5 of 10 and the triangles are similar so

This is one way of writing a quadratic function:

[tex]f(x)= a(x-h)^2+k[/tex]

We're given:

[tex]f(x) = -6x^2 - 60x - 151[/tex]

To write a quadratic function in vertex form, we must complete the square.

⇒ Put parentheses around the first two terms containing x and x²:

[tex]f(x) = (-6x^2 - 60x) - 151[/tex]

⇒ Factor out -6 (keeping the x's in the parentheses):

[tex]f(x) = -6(x^2+10x) - 151[/tex]

⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.

[tex]f(x) = -6(x^2+10x+25) - 151[/tex]

⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:

[tex]f(x) = -6(x^2+10x+25) - 151-(-6*25)\\f(x) = -6(x^2+10x+25) - 151-(-150)\\f(x) = -6(x^2+10x+25) - 151+150\\f(x) = -6(x^2+10x+25) - 1[/tex]

⇒ Finally, complete the square.

[tex]f(x) = -6(x+5)^2 - 1[/tex]

[tex]f(x) = -6(x+5)^2 - 1[/tex]