which expressions are equivalent to 8 13 ?

Volume without holes = 3 x 6 x 11 = 198 cubic inches.

Calculate volume of one hole:

3.14 x 0.5^2 x 3 = 2.355 cubic inches

There are 3 holes: 3 x 2.355 = 7.065

Subtract volume of the holes from the brick:

198 - 7.065 = 190.935 cubic inches.

Rounded to the nearest tenth: 190.9 cubic inches.

Answer:

190.9 inches^3

Step-by-step explanation:

First of all we have to find the total volume:

V = dimension 1 x dimension 2 x dimension 3

V = 3 x 6 x 11 = 198 inches^3

now we have to find the volume of the cylinders:

V= radius^2 x pi x height = 0.5^2 x 3.14 x 3 = 2.355 inches^3

the cylinders are three so:

V = 2.355 x 3 = 7.065 inches^3

at least we have to subtract this value at the total volume:

V= 198 - 7.065 = 190.935 = 190.9 inches^3

Answer:

the perimeter is 25 miles

Answer:

30 mi

Step-by-step explanation:

This is a right triangle, so the Pythagorean Theorem applies:

13^2 + x^2 = 12^2, or

x^2 = 25 and x = 5.

The perimeter is the sum of the dimensions of this triangle:  

12 mi + 5 mi + 13 mi = 30 mi

(a) By plugging in different values for x1, we can plot the indifference curves passing through the given points (2, 2), (1, 2), and (4, 2).

(b) The shape of the indifference curves shows convexity.

(c) The property used to determine this is the non-satiation property of preferences.

(d) The Walrasian demand may not always be single-valued.

(e) Receiving the voucher makes the consumer better-off .

(f) The cash payment allows the consumer to maximize utility by making trade-offs

For 4x1 + x2 = x1 + 2x2, rearranging the equation gives x2 = 3x1, representing the linear part of the indifference curves.

For x1 + 2x2 = 4x1 + x2, rearranging the equation gives x2 = 3x1, representing the kink in the indifference curves.

By substituting different values for x1, we can plot the indifference curves. They will be upward sloping straight lines with a kink at x2 = 3x1.

(b) Properties of the preferences deduced from the shape of indifference curves and utility function:

Diminishing Marginal Rate of Substitution (MRS): Indifference curves are convex, indicating diminishing MRS. The consumer is willing to give up less of one good as they consume more of it, holding the other good constant.

Non-Satiation: Indifference curves slope upwards, showing that the consumer prefers more of both goods. They always prefer bundles with higher quantities.

Convex Preferences: The kink in the indifference curves indicates convexity, implying risk aversion. The consumer is willing to trade goods at different rates depending on the initial allocation.

(c) UMP does not have a solution when Pk = 0 and X -> R2+. This violates the assumption of finite resources and prices required for utility maximization. The property used is non-satiation, as a consumer will always choose an infinite quantity of goods when they are available at zero price.

(d) Walrasian demand depends on relative prices:

If p1 = p2 > 4, the maximizing bundle lies on the linear portion of indifference curves, where x2 = 3x1.

If 4 < p1 = p2 < 1/2, the maximizing bundle lies on the linear portion of indifference curves but at lower x1 and x2.

If p1 = p2 < 1/2, the maximizing bundle lies at the kink point where x1 = x2.

Walrasian demand may not be single-valued due to the shape of indifference curves and the kink point, allowing for multiple optimal solutions based on relative prices.

(e) Given p1 = p2 = 1 and w = $60, the initial budget set is x1 + x2 = 60. With a $10 voucher for good 1, the new budget set becomes x1 + x2 = 70. Since p1 = 1, the consumer spends the voucher on good 1, resulting in x1 = 20 and x2 = 40. Receiving the voucher improves the consumer's welfare by allowing more consumption of good 1 without reducing good 2.

(f) If given the choice between a $10 cash payment and a $10 voucher for good 1 only, the consumer would choose the cash payment. It provides flexibility to allocate the funds based on individual preferences. The answer remains the same even if the assistance were $30, as the cash payment still allows optimal allocation based on preferences. Cash payment offers greater utility-maximizing options compared to the voucher, which restricts choices.

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Answer:

218750

Step-by-step explanation:

Divide 70,000,000,000 by 320,000,000.

Answer:

B

Step-by-step explanation:

The correct answer was B) "Wastage of good food is an environmental hazard that needs to be stopped. By using proper measures to stop wastage of good food, we can help save resources and the environment."

Answer:

12x + 4

Step-by-step explanation:

multiply and distribute 4 on each number in the ()

so (4 x 3x) + (4 x 1) = 12x + 4

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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Answer:

g(5) = -19

Step-by-step explanation:

Step 1: Define

g(x) = -3x - 4

g(5) = x = 5

Step 2: Substitute and evaluate

g(5) = -3(5) - 4

g(5) = -15 - 4

g(5) = -19

Answer:

g(5) = - 19

Step-by-step explanation:

To evaluate g(5), substitute x = 5 into g(x), that is

g(5) = - 3(5) - 4 = - 15 - 4 = - 19

Answer:

D) The mode and the median are equal

Step-by-step explanation:

8, 13, 15, 15, 34

The median is the middle number, and the mode is the number that appears the most. Both of them are 15.

now why would u even go missing

Answer:

the circumstance is 31.42

\(Answer: \displaystyle\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .\)

Step-by-step explanation:

\(D=12\ \ \ \ O(0;b)\\\displaystyle\\R=\frac{D}{2}\\R=\frac{12}{2} \\ R=6.\\Circle \ equation\ is:\\(x-a)^2+(y-b)^2=R^2.\\a=0\ \ \ \ \ R=6\\x^2+(y-b)^2=6^2\\x^2+(y-b)^2=36\\Henese:\\\displaystyle\\\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .\)

Answer:

3 ways

Step-by-step explanation:

From the question:

Number of acres of the land = 100 acres

1 cow = 10 acres of land

1 sheep = 3 acres of land

To fully utilize the land, the number of ways to stock the ranch so that it includes at least one cow and at least one sheep is calculated as:

1) 1 cow and 30 sheep

1 cow × 10 acres + 30 sheep × 3 acres

10 + 90 = 100 acres

2) 4 cows and 20 sheep

4 cow × 10 acres + 20 sheep × 3 acres

40 + 60 = 100 acres

3) 7 cows and 10 sheep

7 cow × 10 acres + 10 sheep × 3 acres

70 + 30 = 100 acres

Therefore, to fully utilize the land, the number of ways to stock the ranch so that it includes at least one cow and at least one sheep is 3 ways

The sampling method described in the scenario is convenience sampling.

Convenience sampling is a non-probability sampling technique where individuals are selected based on their convenience or accessibility to the researcher.

In this case, the sample is chosen by asking the researcher's 40 closest friends, which implies that the selection is based on the convenience and availability of those individuals rather than a random or systematic approach.

Convenience sampling is often used in situations where it is difficult or impractical to obtain a representative sample from the population of interest. It is commonly seen in informal surveys, pilot studies, or situations where the researcher has limited resources or time constraints.

While convenience sampling can be quick and easy to implement, it is important to note that it introduces potential biases into the sample.

The sample obtained through convenience sampling may not accurately represent the larger population, as it relies on the availability and willingness of individuals to participate.

This can result in a sample that is not truly representative and may lead to biased or misleading conclusions.

Therefore, it is crucial to interpret the results of studies based on convenience sampling with caution, as they may not generalize well to the broader population.

For more accurate and reliable results, researchers often opt for probability sampling methods, such as simple random sampling or stratified sampling, which provide a higher level of representativeness and reduce the potential for bias.

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The signal probability, probability that the output will be 1, and the activity factor coefficient at each node are as follows:

\(\( P_{n_I} = 1 \), \( P_{n_{II}} = 0.5 \), \( P_{n_{III}} = 0.5 \), \( P_{n_{IV}} = 0.25 \), \( P_{n_{1}} = 0.25 \), \( P_{n_{2}} = 0.125 \), \( P_{n_{3}} = 0.0625 \), \( P_{n_{4}} = 0.03125 \)\)

To find the signal probability, probability that the output will be 1, and the activity factor coefficient at each node \(\( n_I \) through \( n_4 \),\) we need to analyze the given system and its inputs.

Let's assume that\(\( P_A = P_B = P_C = 0.5 \),\) which means that the inputs A, B, and C have an equal probability of being 0 or 1.

The signal probability, probability that the output will be 1, and the activity factor coefficient at each node are as follows:

\(\( P_{n_I} = 1 \)\( P_{n_{II}} = 0.5 \)\( P_{n_{III}} = 0.5 \)\( P_{n_{IV}} = 0.25 \)\( P_{n_{1}} = 0.25 \)\( P_{n_{2}} = 0.125 \)\( P_{n_{3}} = 0.0625 \)\( P_{n_{4}} = 0.03125 \)\)

In the given system, each node's output depends on the inputs it receives. Here's how we can determine the signal probability, probability that the output will be 1, and the activity factor coefficient at each node:

- Node \( n_I \) is always active, so its signal probability is 1.

- Nodes \( n_{II} \) and \( n_{III} \) receive inputs A, B, and C. Since each input has a probability of 0.5, the probability that any of them is active is also 0.5.

- Node \( n_{IV} \) receives the outputs from nodes \( n_{II} \) and \( n_{III} \). The activity factor coefficient at this node is the product of the probabilities of the inputs being active, which is 0.5 * 0.5 = 0.25.

- Nodes \( n_{1} \), \( n_{2} \), \( n_{3} \), and \( n_{4} \) follow a similar calculation based on their respective inputs.

By analyzing the system and considering the given input probabilities, we can determine the signal probability, probability that the output will be 1, and the activity factor coefficient at each node.

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Since there are uncountably many distinct pairs of real numbers, we get an uncountable family of dense subsets of R.

Let S and T be non-empty subsets of a topological space (X,τ) with S⊆T.

Here is the solution:(i) If p is a limit point of the set S, then every open set that contains p contains a point q of S, distinct from p. If U is an open set containing p, then U also contains q ∈ S ⊆ T, so p is a limit point of T.(ii) We know that Sˉ, the closure of S is the set of all limit points of S. Hence, Sˉ consists of points p of X that satisfy the condition that every open set U containing p intersects S in a point q distinct from p. If p ∈ Sˉ, then every open set U containing p intersects S in a point q.

In particular, every open set V containing p also intersects T in a point q ∈ S ⊆ T. Therefore, p ∈ Tˉ.(iii) If S is dense in X, then Sˉ = X. From part (ii) of the question, we know that Sˉ ⊆ Tˉ. Therefore, Tˉ = (Sˉ)ˉ = X.

In other words, T is dense in X.(iv) To show that R has an uncountable number of distinct dense subsets, we make the following observation: for any distinct a,b ∈ R, the sets a + Z and b + Z are dense in R.

Indeed, let U be an open set in R. Let r be any real number. Then U contains an open interval (r - ε, r + ε) for some ε > 0. Let n be any integer. Then the set (a + nε/2, b + nε/2) intersects U.

Therefore, (a + Z) ∪ (b + Z) is dense in R.

Since there are uncountably many distinct pairs of real numbers, we get an uncountable family of dense subsets of R.

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The selling price of the water cooler, after a 37.5% markup, will be $667.70.

To determine the selling price of the water cooler, we need to calculate the markup based on the cost and add it to the original cost. Given that Julianne will pay $485.60 for the water cooler, we need to find the markup price of 37.5% based on the cost.

To calculate the markup price, we multiply the cost by the markup percentage:

Markup price = Cost * Markup percentage

Markup price = $485.60 * 37.5%

To find the selling price, we add the markup price to the original cost: Selling price = Cost + Markup price

Selling price = $485.60 + Markup price

Let's calculate the markup price:

Markup price = $485.60 * 37.5% = $182.10

Now, we can calculate the selling price:

Selling price = $485.60 + $182.10 = $667.70

Therefore, the selling price of the water cooler, after a 37.5% markup, will be $667.70.

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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The proportion statement is 2/3. The missing angles are CK = 12, GN = 15 and GT = 9

Given that: Polygon ROCK ~  Polygon GNAT.

The symbol ~ means the polygons are similar to each other. That means the ratios of all their corresponding sides are the same. Thus:

CO/AN = 4/6 = 2/3 (This is the proportion statement)

We can also say CK/AT= 2/3 because the ratios of all their corresponding sides are the same

With this, we can determine  the missing sides:

CK/AT= 2/3     where AT = 18

CK/18= 2/3

CK = (18×2)/3 = 12

OR/GN = 2/3    where OR = 10

10/GN = 2/3

2GN = 10×3

2GN = 30

GN = 30/2 = 15

KR/GT = 2/3   where KR = 6

6/GT = 2/3

2GT = 6×3

2GT = 18

GT = 18/2 = 9

Therefore, the proportion statement is 2/3, and the missing angles are CK = 12, GN = 15 and GT = 9

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The possibilities of accepting lots with 5%, 15%, and 20% faulty elements are approximately 0.3585, 0.0313, and 0.0115, respectively.

To discover the possibility of accepting lots with unique probabilities of faulty components, we are able to use the binomial chance formulation.

The formula for the probability of accepting plenty whilst choosing 20 components at random is:

P(lot might be widely wide-spread) =\((nCr) * p^x * (1-p)^(n-x)\)

wherein:

n is the variety of components decided on (20 in this example)

r is the number of faulty components allowed (1 or fewer in this case)

p is the chance of a part being faulty

x is the variety of faulty elements determined among the ones inspected

a. For plenty with 5% faulty parts:

n = 20

r = 1

p = 0.05 (5%)

x = 0 (no defective elements found)

P(lot can be accepted) = \((20C0) * 0.05^0 * (1-0.05)^(20-0)\)

Using a calculator or statistical software program, we can compare this expression to discover:

P(lot can be prevalent) ≈ 0.3585

b. For a lot with 15% faulty elements:

n = 20

r = 1

p = 0.15 (15%)

x =0 (no defective components observed)

P(lot may be popular) =\((20C0) * 0.15^0 * (1-0.15)^(20-0)\)

Calculating this expression, we discover:

P(lot could be frequent) ≈ 0.0313

c. For a lot with 20% faulty parts:

n = 20

r = 1

p = 0.20 (20%)

x = 0 (no defective components discovered)

P(lot might be familiar) =\((20C0) * 0.20^0 * (1-0.20)^(20-0)\)

Evaluating this expression, we get:

P(lot can be customary) ≈ 0.0115

Therefore, the probabilities of accepting plenty with 5%, 15%, and 20% defective parts are approximately 0.3585, 0.0313, and 0.0115, respectively.

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     2. There is not sufficient evidence to support the claim that the average percentage of readers who own a particular make of car is above 53%

What is null and alternative hypothesis??|
The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

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Answer:

n = 28.8

Step-by-step explanation:

\(\frac{n}{18} =\frac{12}{7.5}\)

n × 7.5 = 18 × 12

7.5n = 216

7.5n ÷ 7.5 = 216 ÷ 7.5

n = 28.8

Answer:

The answer was 0.55

Step-by-step explanation:

I took the quiz

The probability that a student attended the game, given that the

student is from North Beach is 0.55, the correct option is C.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

The table

Now,

Out of the 200 students from Westville and the 150 students from North Beach, a total of 170 + 110 = 280 students attended the game.

The probability that a student attended the game, given that they are from North Beach, can be calculated using Bayes' theorem:

P(attended game | from North Beach) = P(from North Beach | attended game) * P(attended game) / P(from North Beach)

P(from North Beach | attended game) is the probability that a student is from North Beach, given that they attended the game. This can be calculated as:

P(from North Beach | attended game) = P(from North Beach and attended game) / P(attended game)

There were 110 students from North Beach who attended the game, so:

P(from North Beach and attended game) = 110 / 280 = 0.3929

The probability of attending the game is P(attended game) = 280 / 350 = 0.8

The probability of being from North Beach is P(from North Beach) = 150 / 350 = 0.4286

P(attended game | from North Beach) = 0.3929 / 0.8 * 0.4286 = 0.55 (rounded to two decimal places)

Therefore, by the probability the answer will be 0.55.

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Average number of goals = 2.8

From the question, we have

Average  =  total number of matches/ total number of goals

​=(4×0+10×1+5×2+9×3+7×4+5×5+6×1+7×2)/43

​=120/43

=2.79=2.8

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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Answer:

Step-by-step explanation:

6y - y = y(6 - 1) = y * 5

The answer is 5y.

Answer:

The mean (μ) is 15, the variance (σ^2) is 10.5, and the standard deviation (σ) is approximately 3.24.

Step-by-step explanation:

To find the mean (μ), variance (σ^2), and standard deviation (σ) of a binomial distribution, we use the formulas:

Mean (μ) = n * p

Variance (σ^2) = n * p * (1 - p)

Standard Deviation (σ) = √(n * p * (1 - p))

Given n = 50 and p = 0.3, we can substitute these values into the formulas:

Mean (μ) = 50 * 0.3 = 15

Variance (σ^2) = 50 * 0.3 * (1 - 0.3) = 10.5

Standard Deviation (σ) = √(50 * 0.3 * (1 - 0.3)) ≈ 3.24

Therefore, the mean (μ) is 15, the variance (σ^2) is 10.5, and the standard deviation (σ) is approximately 3.24.

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Answer:

Step-by-step explanation:

32

Answer:

7 kilograms is 7000 grams

Step-by-step explanation:

The data can be arranged in an ordering scheme, but differences cannot be found or are meaningless, making the ordinal level of measurement most appropriate.

The most appropriate level of measurement for the ranks of cars evaluated by a consumer's magazine is the ordinal level of measurement. This is because the ranks of the cars can be ordered based on their performance, but the differences between the ranks do not have any numerical meaning. In other words, we cannot say that the difference between the first and second ranked cars is the same as the difference between the second and third ranked cars. Therefore, the data can be arranged in an ordering scheme, but differences cannot be found or are meaningless, making the ordinal level of measurement most appropriate.

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