Here are summary statistics for the weights of Pepsi in randomly selected cans: n=36, x=0.82412 lb, s=0.00573 lb.
Use a confidence level of 90% to complete parts (a) through (d) below.
a. Identify the critical value ta/2 used for finding the margin of error.
¹a/2=
(Round to two decimal places as needed.)

Answer:

Step-by-step explanation:

1). Since, XM is the radius of the circle,

   Therefore, area of the circle = \(\pi r^{2}\)

                                                   = \(\pi (XM)^2\)

                                                   = \(\pi (12)^2\)

                                                   = 452.39 units²

2). Circumference of a circle = 2πr

                                                = 2π(XM)

                                                = 2π(12)

                                                = 24π

                                                = 75.40 units

3). By applying Pythagoras theorem in ΔYXM,

    YM² = XY² + XM²

    (43)²= (XY)² + (12)²

     1849 - 144 = (XY)²

     XY = 41.29 units

4). tan(∠M) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

                  = \(\frac{XY}{XM}\)

    m∠M = \(tan^{-1}(\frac{41.29}{12} )\)

              = 73.79°

5). Area of ΔXYM = \(\frac{1}{2}(\text{Base)}(\text{Height})\)

                             = \(\frac{1}{2}(41.29)(12)\)

                             = 247.74 square units

6). Area of the minor sector created by ΔXYM = \(\frac{\theta}{360}(\pi r^2)\)

                                                                             = \(\frac{73.79}{360}(452.39)\)

                                                                             = 92.73 units²

Answer:

Its 69.1 cm

Step-by-step explanation:

To find circumstance of any circle main formula is 2*pie*r .

Here pie is equal to 3.14 approx and r =11 cm

so

2*3.14*11 = 69.08 cm

This little difference is just because of pie's approximately value used

The first option is correct. When the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified the result is -x² + 3x - 8.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

We shall simply the polynomial -3x² + 2x - 4 - (-2x² - x + 4) as follows:

open bracket;

-3x² + 2x - 4 + 2x² + x - 4

group like terms;

-3x² + 2x² + 2x + x - 4 - 4

- x² + 3x - 8.

Therefore, the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified to give the result is -x² + 3x - 8.

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Answer:

A length of a ray cannot be measured therefore it's refferd to as infinite. same

The perimeter and area of the square are; 24√2 units and 12 units² respectively

Given the coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)

But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.

SQ = √(x₂ - x₁)² + (y₂ - y₁)²

SQ = √(2 - (-4)² + (5 - 11)²

SQ = 6√2

Let's find QU

QU = √(-4 - 2)² + (-1 - 5)²

QU = 6√2

Let's find UA ;

UA = √(-10 - (-4))² - (5 - (-1)²

UA = 6√2

And the distance AS = 6√2

The perimeter of the square = 4 (6√2)

Perimeter = 24√2 units

The area of the square = l²

Area of the square = (6√2)²

Area of square = 12 units²

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To find the measure of Angle A, we'll need to use a trigonometric function.

Remember: SOH-CAH-TOA

Looking from Angle A, we know the opposite side and the hypotenuse. Therefore, we should use the sine function.

sin(A) = 9 / 18

---To solve for A, you'll need to use the inverse sin function on your calculator. It should look like so: sin^-1()

The inverse sin of 1/2 = 30

Answer: first option, 30 degrees

Hope this helps!

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

60 ft.

Step-by-step explanation:

The missing side length would be 6 ft.

14-8=6

Add up all the sides: 14+16+6+9+8+7=60

Hence, the perimeter is 60 ft.

Hope this helps!

To find the answer we have to compare all of the options to 1.32 until we find a decimal number that is greater than 1.32

Option a. 1.02

In the following number line, 1.02 is shown in green and 1.32 is shown in red:

As we can see, 1.02 is NOT

From the given diagram, the following statements are true:

AB = BC

3y = 5y - 22

3y - 5y = -22

-2y = -22

y = 11

Similarly, m<DBE = 50 degrees

m<BED = 90 - m<DBE

m<BED = 90 - 50

m<BED = 40 degrees

Since BE = BC = 3y

BE = BC = 3(11) = 33

Also, 7x  - 2 = 40

7x = 40 + 2

7x = 42

x = 6

Get the measure of m<BEA

m<BEA = 7x - 2

m<BEA = 7(6) - 2

m<BEA = 40 degrees

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The best class width for dividing the data into 6 classes is 0.7.

To find the minimum and maximum data values from the given table, we can sort the data in ascending order:

2.1, 2.4, 2.5, 2.9, 3.4, 3.5, 4.1, 4.2, 4.5, 4.9, 5.1, 5.7, 6.2

The minimum data value is 2.1, which is the smallest value in the table.

The maximum data value is 6.2, which is the largest value in the table.

To determine the best class width when dividing the data into 6 classes, we need to calculate the range of the data and divide it by the number of classes.

Range = Maximum value - Minimum value = 6.2 - 2.1 = 4.1

To find the class width, we divide the range by the number of classes:

Class Width = Range / Number of Classes = 4.1 / 6 ≈ 0.6833 (rounded to four decimal places)

The best class width would be 0.7. Rounding to the larger tenths place ensures that the class width is not too small, allowing for more meaningful intervals and easier interpretation of the data.

Therefore, the best class width for dividing the data into 6 classes is 0.7.

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The rate of change of the function h(x) = 2x on the interval 2 ≤ x ≤ 4 is 6.

a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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Answer:

4:42 a.m.

Step-by-step explanation:

The earliest low tide occurs by 2:00 a.m. and the earliest high tide occurs by 8:00 a.m.

Between these hours, 6 hours elapsed.

The lowest point is 1.1 m and increases steadily to 5.3 m.

Let us take 2:00 a.m. as the zeroth hour, and 8:00 a.m. as the 6th hour, we can safely interpolate as below,

0 = 1.1 m

x = 3 m

6 = 5.3 m

we solve as \(\frac{x - 0}{6 - 0}\) = \(\frac{3 - 1.1}{5.3 - 1.1}\)

\(\frac{x}{6}\) = \(\frac{1.9}{4.2}\)

4.2x = 11.4

x = 2.71 hours from 2:00 a.m.

= 2 hrs + (0.71 x 60)min = 2 hrs 42.6 min

the time will approximately be by 4:42 a.m.

9514 1404 393

Answer:

  0.927184

Step-by-step explanation:

Assuming you want cos(338°), it is equal to cos(22°). This value is an irrational root of a 26th-degree polynomial. (Neither the polynomial, nor the root are easy to find by hand.)

The values of trig functions for 30° and 45° are well-known, as are half-angle and angle sum/difference formulas. The nearest angle for which cosine is relatively easy to find is 22.5°. A 2nd-order Maclaurin series expansion of the cosine function about that angle gives the approximation ...

  cos(x) ≈ cos(π/8)(1 -π²/128) +π/8·sin(π/8) +(π/8·cos(π/8) -sin(π/8))x -1/2·cos(π/8)x²

For your angle of 22°, the value of x needed in this expression is 11π/90. The values of cos(π/8) and sin(π/8) are the irrational numbers ...

  cos(π/8) = √(2 +√2)/2 ≈ 0.92387953

  sin(π/8) = √(2 -√2)/2 ≈ 0.38268343

If you use the approximation pi ≈ 355/113, both for the above formula and for the angle of interest, this reduces to the sum ...

  cos(22°) ≈ 71√(2-√2)/16272 +132383951√(2+√2)/264777984

This would be tedious to calculate by hand, but is not impossible. The value this sum produces will be correct when rounded to 7 decimal digits.

__

Before calculators, trig function values were found in published tables. These days, tables are available on-line. Previously, they were published in books, usually along with information that helped with interpolation between table values, when necessary. The attachment shows a portion of an online cosine table suitable for answering your question.

_____

Additional comment

Before calculators, mathematicians spent lifetimes calculating accurate trig tables. For all but a very few angles, the cosine function of rational degree values will be an irrational number, as it is for cos(22°).

Answer:

Step-by-step explanation:

the graph is known to be the infinite set of points on the line

The graph of the modulus function is plotted

Given data ,

Let the modulus function be represented as A

Now , the value of A is

| x | + 1 < 3

On simplifying the inequality , we get

Subtracting 1 on both sides , we get

| x | < 2

When x is positive or zero: In this case, the absolute value of x is equal to x itself. Therefore, we have x < 2

When x is negative: In this case, the absolute value of x is equal to -x. Therefore, we have -x < 2

Hence , the graph of function is plotted

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Answer:

1+tan2x=sec2x.

Explanation: Change to sines and cosines then simplify.

Answer:

9599

Step-by-step explanation:

use technology.

Answer:

9595

Step-by-step explanation:

x = 331 x 29

= 9595

331

x 29

----------

9595

Answer:

obese people eating millions a day.

Step-by-step explanation:

Answer:

Its answer A !!!! Whoever said C was wrong.

Step-by-step explanation:

An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal.

Answer: 81.64 feet

Step-by-step explanation:

Circumference of a circle = pi * diameter

Circumference of a circle = 3.14 * 26 feet

Circumference of a circle = 81.64 feet

Step-by-step explanation:

Volume of a cylinder = pi r^2 h      diameter =1.5 ft so r = .75 ft

                                  pi * .75^2 * 25 = 44.18 ft^3

Find price (based on $ 12.09 /ft^3)

44.18 ft^3  *  $  12.09 /ft^3  = $ 534.12

Answer:

$39.13

Step-by-step explanation:

559 x 7 is 3913 divided by 100 since its a percent is 39.13

The required amount paid for tax is obtained as $39.13.

In order to calculate the percent value take the ratio of the tax amount to the amount of the goods and then multiply it by 100.

The tax value is often written in terms of percent.

The price of laptop is given as $559.

And, the percent value of sales tax is 7%.

The amount of tax can be calculated as follows,

7% × Price of laptop

= 7% × 559

= 7/100 × 559

= $39.13

Hence, the amount paid by Dwade for the sales tax is $39.13.

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Answer:

they gave 18 donuts to the school.

Answer:

2 dozen= 24 + 6 = 30 donut.

Answer:

x<_2

Step-by-step explanation:

first off solve this like a regular equation the >_ dosent matter till later

so basically first multiply - by 13 and -x so you get -13 and x (multiplying two negatives = a positive)

so its 5x-13+x>_9x-7

add 5x and x to get 6x-13 on one side

then you get 6x-13>_9x-7 then subtract -9x from both sides

so its now -3x-13>_-7 add 13 so you get -3x>_6

then divide both sides by -3 (when you divide an equation with a >< or <_ >_ by a negative number that sign switches) so it will now be x<_2

that your final answer hope this helps :)

Equation: \(\boxed{\pi}(8^2)\)

Area: \(64\pi \approx 201.06\)

Answer:

60% decrease

Step-by-step explanation:

Subtract to find how much money it went down by

95 - 38= 57

then use proportions

x/100 = 57/95

then cross multiply

5700 = 95x

60 = x

In increasing order according to their capacity:

The capacity of a container, such as a cup, bottle, or tank, is the amount of fluid or material it can hold. It is usually stated in volume quantities such as liters, milliliters, gallons, or ounces.

Capacity is a necessary concept in engineering, manufacturing, and transportation, where it is used to design and run systems involving the storage, movement, and processing of fluids or materials.

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