A rectangle deck has a length of 12 feet and a perimeter of 36 feet. What is the width and area

Answer:

mean 16.75

median 15.5

mode 13

range 16

Answer:

25.5 is the median, 22 is the mode, 24.7 is the mean and 34 is the range

Step-by-step explanation:

mean is the average, you get this by adding up all the numbers and then dividing the total by the amount of numbers there are.

the median is the number with the middle value, in this case there were 2 medians because the was an even number of numbers so you average the medians

mode is the number the occurs the most out of the whole set. For example in this case all the numbers occurred twice except 22 which occured 3 times

Last is the range which takes the highest number and subtracts it by the lowest number. It's just that simple!

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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This question is incomplete, the complete question is;

According to a study of political​ prisoners, the mean duration of imprisonment for 33 prisoners with chronic​ post-traumatic stress disorder​ (PTSD) was 34.2 months. Assuming that σ = 40 ​months.

determine a 95​% confidence interval for the mean duration of​ imprisonment, ​μ , of all political prisoners with chronic PTSD. Interpret your answer in words.

Answer:

⇒ ( 20.6, 47.8 )

Therefore, 95% confidence interval for the mean duration of imprisonment μ of all political prisoners with PTSD is between 20.6 months and 47.8 months.

Step-by-step explanation:

Given the data in the question;

sample size; n = 33

standard deviation σ = 40 months

x' = 34.2 months

Now, at 95% confidence interval;

we know that z-value of 95% confidence interval is 1.96

so we substitute into the formula below;

⇒ x' ± Z( σ/√n )

⇒ 34.2 ± 1.96( 40/√33 )

⇒ 34.2 ± 13.647

so

we have

( 34.2 - 13.647 ), ( 34.2 + 13.647 )

⇒ ( 20.6, 47.8 )

Therefore, 95% confidence interval for the mean duration of imprisonment μ of all political prisoners with PTSD is between 20.6 months and 47.8 months.

The general solution u(t,x) of the boundary value problem for the heat equation with homogeneous Neumann boundary conditions would be   \(u(t,x) = \sum Cn * sin(n * \pi * x / L) * e^(-n^2 * \pi ^2 * k * t / L^2)\)

What is homogeneous Neumann boundary conditions?

For example, d2ydx2+4y=0 if your differential equation is homogeneous (it equals zero and not any function). y(x=0)=0 and y(x=2)=0 were given as the boundary conditions, and you were requested to answer the equation. Then the aforementioned boundary conditions are homogenous boundary conditions.

To find the general solution of the boundary value problem for the heat equation with homogeneous Neumann boundary conditions, we can start by considering the form of the general solution for the heat equation with homogeneous boundary conditions.

The general solution of the heat equation with homogeneous boundary conditions is given by:

\(u(t,x) = \sum Cn * f(n,x) * g(n,t)\)

Cn are constants, f(n,x) and g(n,t).

In the case of homogeneous Neumann boundary conditions, we have \(d_u(t,0)\) = 0 and \(d_u(t,L) = 0\), which means that the normal derivative of the solution at the boundaries is zero. This suggests that we can use the functions\(f(n,x) = sin(n * \pi * x / L)\)and \(g(n,t) = e^(-n^2 * \pi ^2 * k * t / L^2)\) in the general solution, where k is the thermal conductivity of the material and L is the length of the domain.

Therefore, the general solution of the boundary value problem for the heat equation with homogeneous Neumann boundary conditions is given by:

\(u(t,x) = \sum Cn * sin(n * \pi * x / L) * e^(-n^2 * \pi ^2 * k * t / L^2)\)

where the constants Cn can be determined from the initial conditions of the problem.

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Answer:

x = 15

Step-by-step explanation:

since the sides are bisected, the inner line is parallel to the largest side.

8x+9 + 5x-24 = 180

The change should Juan received = $4.18

Given that,

Juan's buy2 pencils

Sales tax = $0

Juan's school supplies would cost a total

= $5.82 ($0.24 x 2 for pencils + $1.37 for notebook + $2.97 for ruler), based on the pricing provided in the table.

Juan still owes $5.82 in total

Because there is no sales tax to be paid.

In order to give Juan change if he pays with a $10 bill,

The cashier would deduct $5.82 from the total.

Hence,

Juan should be given $4.18 in change.

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Answer: 2 Cups

Step-by-step explanation:

1/3 * 3 = 1

2/3 * 2 = 2

Answer:

you will need 2 cups of sugar for 1 batch of brownies

Step-by-step explanation:

2/3 cup ×3 = 6/3 cups or 2 cups

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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The Option C is correct.

Given equations are,

             \(y = 2x - 6\\\\y= -4x + 3\)

When we draw the graph of both equation of line.

Then these lines intersect at a point \((1.5,-3)\).

So that option C is correct.

The correct graph is attached below.

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The statement that best describes the solution to the inequality in this problem is given as follows:

all real numbers except x = 1.

The inequality in the context of this problem is defined as follows:

2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7

The solution to the first inequality is given as follows:

2(x + 7) – 1 > 15

2x + 14 > 16

2x > 2

x > 1.

The solution to the second inequality is given as follows:

3(x + 2) < 2x + 7

3x + 6 < 2x + 7

x < 1.

The or operation includes the elements that belong to the solution set of at least one of the inequalities, hence the solution is given as follows:

all real numbers except x = 1.

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Answer:

(7)(7)(1)=49 mm^3

Step-by-step explanation:

Answer:

49mm³

Step-by-step explanation:

\(v = 7mm \times 7mm \times 1mm = 49m {m}^{3} \)

Answer

Step by step explantion:

bsf= 26

Eliana:98

SS teacher=203

David=55

Step-by-step explanation:

m= music

bsf: m

eliana:4m-6

David:2m+3

SS teacher: 2(4m-6)+7

m+4m-6+2m+3+8m-12+7

382=15m-7

7+ +7

389=15m

/15m /15m

m=26

multiply 26 to each one of them

Based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.

The reading specialist is trying to estimate the population mean word length of an elementary school history textbook, but it is not practical or possible to measure the word length of every single word in the book. So, instead, the specialist takes repeated random samples of 100 words from the book and calculates the mean word length of each sample. Based on these repeated samples, the specialist estimates that the mean word length of the book is 4.9 letters. This means that, on average, the words in the book are about 4.9 letters long. The specialist also calculated the standard deviation of the sampling distribution, which is a measure of the variability of the sample means. In this case, the standard deviation of the sampling distribution is estimated to be 0.15 letters. This means that the mean word length of each random sample is expected to vary by about 0.15 letters from the population mean. It is important to note that these estimates are based on a specific set of samples and are subject to sampling variability. If the specialist were to take different random samples, the estimates may be slightly different. However, based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.

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Using the z-distribution and the information given, it is found that the 89% confidence interval for the difference in the proportions that get sick with Selttiks vs the placebo is (-0.07, -0.002).

The proportions, and it's respective standard errors, are given by:

\(p_s = 0.13, s_s = \sqrt{\frac{0.13(0.87)}{560}} = 0.0142\)

\(p_p = 0.166, s_p = \sqrt{\frac{0.166(0.834)}{560}} = 0.0157\)

The distribution of the difference has mean and standard error given by:

\(\pi = p_s - p_p = 0.13 - 0.166 = -0.036\)

\(s = \sqrt{s_s^2 + s_p^2} = \sqrt{0.0142^2 + 0.0157^2} = 0.021\)

The interval is:

\(\pi \pm zs\)

The critical value using the z-distribution, for a 89% confidence interval, is z = 1.598, hence:

\(\pi - zs = -0.036 - 1.598(0.021) = -0.07\)

\(\pi + zs = -0.036 + 1.598(0.021) = -0.002\)

The 89% confidence interval for the difference in the proportions that get sick with Selttiks vs the placebo is (-0.07, -0.002).

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Answer:

D 21

Step-by-step explanation:

Good Luck!

Answer:

Here's a table showing the possible numbers of positive real, negative real, and complex zeros of the given polynomial function:

Number of Positive Real Zeros Number of Negative Real Zeros Number of Complex Zeros

0 3 2

In this case, the polynomial function f(x) = -7x^4 - 12x^3 + 9x^2 - 17x + 3 has no positive real zeros, three negative real zeros, and two complex zeros.

Step-by-step explanation:

GIVE ME BRAINLIEST PLS

Answer:  0 is the answer

if my answer is correct mark as brainliest

Rewrite the fractions as improper fractions:

2 1/4 = 9/4

1 4/5 = 9/5

Rewrite the fractions to have a common denominator:

9/4 = 45/20

9/5 = 36/20

The sum is adding the two together:

45/20 + 36/20 = 81/20

Rewrite as a mixed number:

81/20 = 4 1/20

Product is multiplication:

For multiplying you can use different denominators so you can use the first improper fractions:

9/4 x 9/5 = (9x9)/(4x5) 81/20

Rewrite as a mixed number: 4 1/20

Now subtract to find the difference: 4 1/20 - 4 1/20 = 0

The difference = 0

a) The number of ways to deal the cards without getting one of the designated cards are equals to the 2250829575120.

b) The number of ways to deal each player 7 cards, regardless of whether the designated cards come out are equals to the 21945588357420.

c) The probability of a successful hand that will go all the way till everyone gets 7 cards is 0.1026.

Six friends group is playing poker one night. They have a standard 52-card deck. So, here, total number of possible outcomes of game = 52

Now, the designated cards are , Queen of Clubs, 10 of Hearts. So,

a) Number of cards are in the deck that are not one of the designated cards

= 52 - 2 = 50

Number of cards that need to be dealt in order for each player to have 7 cards

= 5× 7 = 35

Thus total possible number of ways

= ⁵⁰C₃₅ = 2250829575120, which are ways to deal the cards without getting one of the designated cards.

b) Number of cards are in the deck = 52

Number of cards that need to be dealt in order for each player to have 7 cards = 5× 7 = 35

Thus total possible number of ways

= ⁵²C₃₅ = 21945588357420

Which are ways to deal each player 7 cards, regardless of whether the designated cards come out.

c) The probability of a successful hand that will go all the way till everyone gets 7 cards is = Number of ways to deal the cards without getting one of the designated cards/Total number of ays to deal the cards

= 2250829575120/21945588357420

= 0.10256410256

Hence, required probability is 0.1026.

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Answer:

well that depends on how many pieces of gum are in one pack, once you have that info multiply it by 4.

Step-by-step explanation:

Answer:

\(x + y = \frac{1000}{9}\)

Step-by-step explanation:

Step 1: Identify the approach:

With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value \((x + y)\) is on the left side and all of other components which do not contain \(x\) or \(y\) are on the right side.

Step 2: Analyze:

\(9x + 2y^{2} - 3z^{2} = 132\\9y - 2y^{2} + 3z^{2} = 867\)

Realize that in both equations, the \(2y^{2}\) and \(3z^{2}\) are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.

Step 3: Perform manipulation:

\(9x + 2y^{2} - 3z^{2} + 9y - 2y^{2} - 3z^{2} = 132 + 867\)

Rearrange:

\((9x + 9y) + (2y^{2} - 2y^{2}) +(3z^{2} - 3z^{2}) = 132 + 867\)

Simplify:

\(9(x + y) + 0 + 0 = 1000\)

Simplify:

\(x + y = \frac{1000}{9}\)

Hope this helps!

:)

The greatest value ABAB can have is 7272.

The given parameters:

The counting number can be expanded as follows;

ABAB = 100 x AB  + AB

          = AB00 + AB

          = AB(100 + 1)

          = AB(101)

101 is a prime factor of AB and has only two factors.

The prime factor of 101 = 1 x 2

Since 101 is prime, the counting number AB must 2-digits multiples of 36.

The greatest value ABAB can have is calculated as follows;

ABAB = (36 x 2)(36 x 2)

ABAB = 7272

Thus, the greatest value ABAB can have is 7272.

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Answer

Explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

m = slope = 3

Point = (x₁, y₁) = (-1, -3)

x₁ = -1

y₁ = -3

y - y₁ = m (x - x₁)

y - (-3) = 3 (x - (-1))

y + 3 = 3 (x + 1)

y + 3 = 3x + 3

y = 3x + 3 - 3

y = 3x

So, we can easily find points on this line by inserting values for x and solving for y

if x = 1

y = 3x

y = 3 (1)

y = 3

First point = (1, 3)

I

Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side

The reflection of the point (–4, 6) across both axes is (b) (4, -6)

From the question, we have the following parameters that can be used in our computation:

Point = (-4, 6)

The rule of reflections across both axes is

(x, y) = (-x, -y)

Using the above as a guide, we have the following:

Image = (4, -6)

Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)

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Answer:

\(a^2(ab^{3}-b^{2}-c^{2})\)

Step-by-step explanation:

Given

\(a^{3}b^{3}-a^{2}b^{2}-a^{2}c^{2}\)

Required

Factor

\(a^{3}b^{3}-a^{2}b^{2}-a^{2}c^{2}\)

Factor out \(a^2\)

\(a^2(ab^{3}-b^{2}-c^{2})\)

The expression cannot be further factored

Answer:

A) y=9x

B) y=45 when x=5

Step-by-step explanation:

Part A

\(y=kx\\-27=k(-3)\\-27=-3k\\9=k\\y=9x\)

Part B

\(y=9(5)\\y=45\)

The range of values of  (f + g)(x) is for all values of x  -infinity to + infinity

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We are Given f(x) = |x| + 9 and g(x) = –6,

Required the range of (f + g)(x)

First, calculate

(f + g)(x) = f(x) +  g(x)

Substitute values for f(x) and g(x)

(f + g)(x) = |x| + 9 - 6

(f + g)(x) = |x| + 3

The above expression shows that (f + g)(x) ≥3

Range = (f + g)(x) ≥3 for all values of x

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The value of g(h(10)) is 2√2. the correct option is A.

Given that the functions are g(x)=√x-4 and h(x)=2x-8.

A function is defined as the relationship between a set of inputs where each input has an output.

Firstly, we will find the value of h(10) by substituting x=10 in the function h(x)=2x-8.

h(10)=2(10)-8

h(10)=20-8

h(10)=12

Now, we will find g(h(10)) where h(10)=12.

By substituting h(10)=12 in g(h(10)), we get

g(h(10))=g(12).

Further, we will find g(12) by substituting x=12 in the function g(x)=√x-4, we get

g(12)=√(12-4)

g(12)=√8

g(12)=2√2

Hence, the value of function g(h(10)) when g(x)=√x-4 and h(x)=2x-8 is 2√2.

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The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is