ABCD is a rectangle. Find the missing information

====================================================

Explanation:

s = 32 = sample standard deviation

n = 40 = sample size

Despite not knowing the population standard deviation (sigma), we can still use the Z distribution because n > 30. When n is this large, the student T distribution is approximately the same (more or less) compared to the standard Z distribution. The Z distribution is nicer to work with.

At 90% confidence, the z critical value is roughly z = 1.645. This can be found using either a Z table or a calculator.

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

We have these values:

Plug these values into the margin of error formula.

\(E = z*\frac{s}{\sqrt{n}}\\\\E \approx 1.645*\frac{32}{\sqrt{40}}\\\\E \approx 8.32311480156318\\\\E \approx 8.323\\\\\)

The margin of error is roughly 8.323

I rounded to 3 decimal places because z = 1.645 is rounded to 3 decimal places. If your teacher wants some other level of precision, then be sure to follow those instructions.

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

9:20 am

Step-by-step explanation:

So, lets go over two things.

Minutes and hours.

Minutes changes the second number.

You know how when a number goes from 9 to 10 how the ones place is set to 0, and the tens place goes up? Its the same with time, only when the number goes from 59 to 60, the hour goes up.

Hours changes the hours place, and when it hits 12, it resets to 1, and the words am go to pm, or pm goes to am.

In this case. we are moving the minutes place up by 5:

15+5=20

So the minutes place is 20, and does not change the hours place since it is below 60.

Next we have a increase in hours by 2:

8+1=9

So the hours place is 9, and does not reset or change the pm/am since its below 12.

Answer:

9:20am

Hope thias helps!

Answer:

9:20 am

Step-by-step explanation:

Add 1 hour

8:15 to 9:15

Add 5 minutes

9:15 to 9:20

Answer:  600,000 + 70,000 + 5,000 + 400 + 30 + 2

Explanation:

Each digit forms a different number depending on its place value.

The 6 is in the hundred thousands place value, so the 6 in 675,432 corresponds to 600,000. Similar ideas apply for the other digits as well

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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Answer:

Range: 10.4

Step-by-step explanation:

Range = maximum(xi) - minimum(xi), where xi represents the set of values

= 11.6 -  1.2

= 10.4

Answer:

Range-

{

11.6

,

11.5

,

11.4

}

Step-by-step explanation:

The given equation y = 3x + 45 in form ax+by=c is 3x - y = - 45.

So,  y=3x+45 into ax+by=c form:

Therefore, the given equation in form ax+by=c is 3x - y = - 45.

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Answer:

is every whole number a natural number

Answer:

Length = 16 or -5 feet.

Width = 5 or -16 feet.

Step-by-step explanation:

Let the length of the concrete pad = l

Let the width of the concrete pad = w

Given the following data;

Area of concrete pad, a = 80ft²

Translating the word problem into an algebraic equation, we have;

\( l = 11 + w\)

We know that, the area of rectangle, A = length * width

\( A = l*w\)

Substituting the values into the equation, we have;

\( 80 = (11 + w)w\)

Expanding the bracket, we have;

\( 80 = 11w + w^{2}\)

\( w^{2} + 11w - 80 = 0\)

*Solving the quadratic equation by using factorization method*

\( w^{2} + 16w - 5w - 80 = 0\)

\( w(w + 16) - 5(w + 16) = 0\)

\( (w - 5)(w + 16) = 0 \)

Width, w = 5 feet or w = -16 feet.

Therefore, the width of the concrete pad is 5 feet or -16 feet.

To find its length, l;

\( l = 11 + w\)

When w = 5 feet

\( l = 11 + 5\)

Length, l = 16 feet

When w = - 16 feet

\( l = 11 + (-16)\)

\( l = 11 - 16\)

Length, l = -5 feet.

Hence, the dimensions of the concrete pad is 16 by 5 feet or -5 by -16 feet.

First, we need to find the cross-sectional area of each figure:

Since the cross-sectional areas are equal at every level, we can set up the following equation:

5x = 9π

Solving for x, we get:

x = 9π/5

Now, we can find the volume of the rectangular prism:

V = 5x * 8 = 72π cubic meters

And the volume of the cylinder:

V = π(3^2) * 8 = 72π cubic meters

Since the volumes are equal, we can set up the following equation:

72π = 72π

Simplifying, we get:

9πx = 40π

Solving for x, we get:

x = 40/9

Rounding to the nearest tenth, we get:

x ≈ 4.4 meters

Therefore, the width of the rectangular prism is approximately 4.4 meters.

The surface area of given triangular prism = 24 ft².

For the given triangular prism

Base = 2 ft

height = 3 ft

side = 3ft

We know that,

Surface area of triangular prism

= side x base + 3x base x height

=  3 x 2  + 3x2x3

= 6 + 18

= 24 ft²

Thus,

Surface area = 24 ft²

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The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

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Answer:

3

Step-by-step explanation:

djifididusueieieiwuwu

The first cell phone bill of Ms. Trowbridge after 40% discount is $51.

Given information:

The discount on first cell phone bill = 40%

The flat charges on bill = $25

The charge per minute = $0.20

Since $0.20 is charged per minutes, the amount charged for 300 minutes will be :

300 x 0.20 = $60

Her monthly cell phone plan charges a flat monthly fee of $25.00.

the total amount charged will be;

$60 + $25 = $85

There is a 40% discount , then we have 40% of $85

= $34

So, the amount of her first cell phone bill ,

= $85 - $34

= $51.00

Hence, the first cell phone bill of Ms. Trowbridge after 40% discount is $51.

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Answer:

x= 24

I hope it's helps you

Answer:

-2

Step-by-step explanation:

absolute value is the distance from zero. it will never be negative. so -6 is 6 away from zero, -8 is 8 away from zero. you can just take off the negative sign and use the number by itself.

|-6| - |-8|

6 - 8

-2

Answer:

\( - 2\)

Step-by-step explanation:

\(|−6|−|−8|\)

Simplify each term.

The absolute value is the distance between a number and zero. The distance between −6 and 0 is 6.

\(6−|−8|\)

The absolute value is the distance between a number and zero. The distance between −8 and 0 is 8.

\(6−1 \times 8\)

Multiply −1 by 8.

\(6−8\)

Subtract 8 from 6.

\( - 2\)

We can make 30 non congruent rectangles.

There are several approaches to this issue, but one is to count the number of rectangles of various sizes.
A 4x4 geoboard can contain the following:

1 rectangle is of size = 4x4

4 rectangles are of size = 3x3

9 rectangles are of size = 2x2

16 rectangles are of size = 1x1

Use the following formula to determine the number of rectangles can be created within given these dimensions:

(Number of rows + 1 - Height of rectangle) (Number of columns + 1 - width of the rectangle)

For instance, we have (4 + 1 - 2) while counting the number of 2x2 rectangles. × (4 + 1 - 2) = 3 × 3 = 9

The total number of rectangles can be calculated as follows:

1 + 4 + 9 + 16 = 30.

So, on a 4x4 geoboard, there are 30 rectangles that can be created, none of which can be congruent.

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Answer:

Opal saves more

Step-by-step explanation:

Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

Answer:

7

Step-by-step explanation:

Answer:

5.34* 100000000=534000000

Step-by-step explanation:

8 hope this helps good luck

Option • 12 is the answer .The number of treatments in the experiment is 12.

The understudy is directing a trial to comprehend the connection between microwave power and time on the quantity of unpopped bits in a pack of popcorn. There are three degrees of microwave power: low, medium, and high. Each sack of popcorn can be popped for either 3 minutes or 4 minutes, which provides us with a sum of double cross variables. To cover every one of the potential mixes of time and power, the understudy runs 12 distinct medicines (3 degrees of force x 2 degrees of time). Every treatment addresses one sack of popcorn that is popped for a particular time frame and with a particular power setting. The quantity of unpopped parts is recorded for every treatment, and the outcomes are utilized to make determinations about the impacts of microwave power and time on the quantity of unpopped pieces.

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A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.

Here, we have

Given:

Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C

After 14 days, the percentage οf the mοοn is zerο

A = (max-min)/2 = 50/2 = 25

The periοd = 28 days

P = Acοs(BT = t) + c

B = 2π/periοd = 2π/28 = π/14

c = min + A = 0 + 25 = 25

We get,

P = 25cοs(π/14t) + 25,

Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.

Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

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A. The following are sets A and B:

A = {2, 3, 5, 7, 11}

B = {1, 2, 3, 4, 6, 12}

C. Elements not in A or A' = ∅

B. The Venn diagram is attached

A universal set is a set which consists of all elements related to the given sets. It is denoted by U.

A. Set A:

A = {2, 3, 5, 7, 11}

Set B:

B = {1, 2, 3, 4, 6, 12}

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A' = {1, 4, 6, 8, 9, 10, 12}

C. Elements not in A or A' = ∅

Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.

Hence, the Venn diagram of sets A, B and U has been attached.

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Answer: y = 5x-2

Step-by-step explanation:

Answer:

8- 26 cm

7- 85 cm^2

1-23 cm

Answer: 10 because if they have the same shape then it must be 10.

I'm not sure if they want the same area or the same length. But if you want the volume then it would be 2. Because 2 x 75 = 150 and 15 x 10 = 150. Wait for more responses if needed.

Complete Question

Assisted-Living Facility Rent.Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486 (the Wall Street Journal, October 27, 2012). Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is s = $650. a. Develop a 90% confidence interval estimate of the population mean monthly rent.

Answer:

\(CI: 3388.39<X<3583.61\)

Step-by-step explanation:

Sample Size n=120

Mean \=x =3486

Standard Deviation \sigma=650

Confidence interval CI=0.9

Therefore

Level of sig \(\alpha=0.1\)

Therfore

The Critical Value from table is

Z_c=1.645

Generally the equation for Standard error is mathematically given by

\(S.E=\frac{\sigma}{\sqrt{n}}\)

\(S.E=\frac{650}{\sqrt{120}}\)

\(S.E=59.3366\)

Generally the equation for Margin error is mathematically given by

\(M.E= = Z_c * SE\)

\(M.E=1.65 * 59.34\)

\(M.E= 97.61\)

Therefore

\(CI= \=x \pm M.E\)

\(CI= 3486 \pm 97.61\)

Lower limit

\(LL= \=x-M.E=3486-97.6087\)

\(LL= 3388.39\)

Upper limit:

\(UL= \=x+E=3486+97.6087\)

\(UL= 3583.61\)

Therefore The  90% confidence interval estimate of the population mean monthly rent.

\(CI: 3388.39<X<3583.61\)