Base perimeter of a square prism is 32cm and its height is 15cm. what is its
lateral surface area?

The sampling technique used in each study is as follows: (a) convenience sampling, (b) systematic sampling, and (c) stratified random sampling.

(a) In the first study, where a journalist goes to a campground to ask people about their feelings regarding air pollution, the sampling technique used is convenience sampling. This is evident because the journalist approaches individuals who are readily available and easily accessible at the campground. However, convenience sampling may introduce bias as it does not ensure a representative sample of the population.

(b) In the second study, where every tenth machine part is selected from an assembly line for measurement, the sampling technique used is systematic sampling. Systematic sampling involves selecting every nth element from a population after establishing a sampling interval. In this case, every tenth machine part is selected to ensure a systematic and unbiased approach to quality assurance.

(c) In the third study, where attitudes about smoking are studied at a college and students are divided by class and then randomly sampled from each class for interviews, the sampling technique used is stratified random sampling. Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each subgroup. By dividing the students into different class strata and randomly selecting samples from each class, this study aims to ensure representation from each class in the final sample.

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Answer:

Option D

Step-by-step explanation:

Area of triangle = \(\frac{1}{2}\) × (Base of triangle) × (Perpendicular height of triangle)

                          = \(\frac{1}{2}\) × [(20 - 10) inches] × [(15 - 5) inches]
                          = \(\frac{1}{2}\) × (10 inches) × (10 inches)

                         = 50 square inches

∴Area of each triangular piece = 50 square inches

∴Option D

The probability of being dealt a 3, 4, 5, 6, 7, all in the same suit is approximately 0.0000031.

To calculate the probability of being dealt a 3, 4, 5, 6, 7, all in the same suit, we can use the following formula:

P = (number of favorable outcomes) / (total number of possible outcomes)

the order in which the cards are chosen does not matter, so we need to divide by the number of ways we can arrange 5 cards, which is 5! (5 factorial).

Therefore, the total number of possible outcomes is (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1), which simplifies to 2,598,960.

Finally, we can calculate the probability of being dealt a 3, 4, 5, 6, 7, all in the same suit:

P = 8 / 2,598,960

P = 0.00000308 (rounded to seven decimal places)

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the value of the side a will be 20feet.

What is Pythagoras theorem?

The Pythagoras theorem says that if a triangle has a straight angle (90 degrees), the square of the hypotenuse is equal to the sum of the squares of the other two sides. To illustrate this, the triangle ABC has the formula BC2 = AB2 + AC2. This equation includes the bases AB, height AC, and hypotenuse BC. It is important to note that the hypotenuse is the right-angled triangle's longest side.

h²=b²p²

b²=25²-15²

b²=675-215

b=√400

b=20 feet

Hence, the value of the side a will be 20feet.

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Step-by-step explanation:

in 24 hours they will drink 32.7 cups

in 18 hours they will drink 24.3

32.7+24.3=56.7

Answer:

8

Step-by-step explanation:

-12 x -2 = 24. 24-16=8

Referring to Table 3.1, if the government imposes a price of $3, a shortage will result.

To determine the outcome when the government imposes a price of $3, we need to compare the quantity demanded and quantity supplied at this price level.
According to Table 3.1, at a price of $3, the quantity demanded is 30 units, while the quantity supplied is 40 units. The quantity demanded (30 units) is less than the quantity supplied (40 units), resulting in a situation known as a shortage.
A shortage occurs when the quantity demanded exceeds the quantity supplied at a given price. In this case, a shortage of 10 units occurs because consumers are willing to buy more than what producers are offering at the price of $3.
To summarize, if the government imposes a price of $3 based on Table 3.1, a shortage will result. This means that the quantity demanded exceeds the quantity supplied at the given price, indicating that consumers are unable to purchase all the units they desire.

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 the complete question is:

Table 3.1
Quantity Demanded.
Price per Unit
Quantity supplied
10
$5
50
20
30
$4
$3
40
30
40
50
$2
$1
20
10
Refer to Table 3.1. If the government imposes a price of $3.
a shortage will result.
Market is in equilibrium.
the price will fall to $1 because producers will be forced to incur losses.
a surplus will result.

The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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Any element x satisfying either condition belongs to both sets, we can conclude that (A\B) = A ∩ (A ∪ B).

To prove that (A\B) = A ∩ (A ∪ B), we need to show that the sets have the same elements.

Let's consider an element x:

1. Suppose x ∈ (A\B), which means x is in A but not in B.

  - This implies that x ∈ A (since x is in A) and x ∉ B (since x is not in B).

  - Since x ∈ A, it is also in the union A ∪ B.

  - Since x ∉ B, it is not in the intersection A ∩ B.

  - Therefore, x ∈ A ∩ (A ∪ B) since it is in A and not in the intersection A ∩ B.

2. Suppose x ∈ A ∩ (A ∪ B), which means x is in both A and (A ∪ B).

  - This implies that x ∈ A and x ∈ (A ∪ B).

  - Since x ∈ (A ∪ B), it is either in A or in B (or both).

  - Since x ∈ A, it is not in the complement of A, which means it is not in B.

  - Therefore, x ∈ (A\B) since it is in A and not in B.

Since we have shown that any element x satisfying either condition belongs to both sets, we can conclude that (A\B) = A ∩ (A ∪ B).

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Answer:

3 : 4, D

Step-by-step explanation:

Since the ratio is 9 : 12, simply put it in fraction form and simplify.

A complete list of the numbers in the pattern: 3, 6, 10, 14, 18, etc.

The number pattern you described is as follows:

3,

(2*5)-4 = 6,

(2*7)-4 = 10,

(2*9)-4 = 14,

(2*11)-4 = 18,

The first number is 3, and then each subsequent number is found by multiplying the previous odd number by 2 and then subtracting 4.

For example, the second number is found by multiplying the first number by 2 and then subtracting 4, which gives us 6. The third number is found by multiplying the second number by 2 and then subtracting 4, which gives us 10.

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The slope of the line tangent to the curve y³-xy²+x³=5 at the point (1,2) is option (B) 1/8.

To find the slope of the line tangent to the curve at the point (1,2), we first need to find the derivative of the curve with respect to x, and then evaluate it at x=1, y=2.

Taking the derivative of both sides of the equation y³-xy²+x³=5 with respect to x using the product rule, we get

3y²(dy/dx) - y² - 2xy(dy/dx) + 3x² = 0

Simplifying this expression and solving for dy/dx, we get:

dy/dx = (y² - 3x²)/(3y² - 2xy)

Substituting x=1 and y=2, we get:

dy/dx = (2² - 3(1)²)/(3(2)² - 2(1)(2))

dy/dx = (4 - 3)/(12 - 4)

dy/dx = 1/8

Therefore, the correct option is (B) 1/8

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Answer:

None of the answers are right

Step-by-step explanation:

Since a hexagon has 6 sides, and perimeter is the length of all the sides summed up, we can multiply 6 by 2x+y to find the perimeter.

6(2x+y)

Distribute the 6 to each term in the parentheses:

6(2x)+6(y)

12x+6y is the perimeter. None of the answers are right.

Answer:

\(\frac{1}{4}\)

Step-by-step explanation:

Using the rule of exponents / radicals

\(a^{\frac{m}{n} }\) = \((\sqrt[n]{a})^m\)

\(a^{-m}\) = \(\frac{1}{a^{m} }\) , then

\(-8^{-\frac{2}{3} }\)

= \(\frac{1}{-8^{\frac{2}{3} } }\)

= \(\frac{1}{(\sqrt[3]{-8})^2 }\)

= \(\frac{1}{-2)^{2} }\)

= \(\frac{1}{4}\)

In linear programming, the feasible region is the set of all feasible solutions that satisfy the constraints of the problem. The feasible corner points are the extreme points of the feasible region, which represent the optimal solutions to the problem. In this case, we have four feasible corner points: (48,84), (0,120), (0,0), and (90,0).

To find the maximum possible value for the objective function, we need to evaluate the objective function at each of the feasible corner points and select the one that gives the highest value. The objective function is a linear combination of the decision variables and represents the quantity that we are trying to maximize or minimize.

Assuming that the objective function is in the form of z = ax + by, where x and y are the decision variables and a and b are constants, we can evaluate the objective function at each of the feasible corner points:

At (48,84): z = a(48) + b(84)

At (0,120): z = a(0) + b(120)

At (0,0): z = a(0) + b(0)

At (90,0): z = a(90) + b(0)

Since we don't have the values of a and b, we cannot calculate the maximum possible value of the objective function. However, we can compare the values of the objective function at each of the feasible corner points and select the one that gives the highest value.

Therefore, we can conclude that the maximum possible value for the objective function will be obtained at one of the feasible corner points: (48,84), (0,120), (0,0), or (90,0).

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Writing linear equations given two points can be a useful skill when graphing linear equations.

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Answer:

67

Step-by-step explanation:

Answer:

The volume of the gas under these circumstances is 30 cm³.

Step-by-step explanation:

To determine the variation equation for this situation, we start with the formula V = Tk/P

where k is the constant of variation.

To solve for k, we use the initial values of V, T, and P

V = 42 cm³, T = 84 °C, P = 50 mmHg

Substituting these values into the formula, we get

42 = 84k/50

Solving for k, we have

k = (42 x 50)/84 = 25

Therefore, the variation equation for this situation is

V = 25T/P

To find the volume of gas when T = 48 °C and P = 40 mmHg, we substitute these values into the variation equation

V = 25 x 48/40 = 30 cm³

Therefore, the volume of the gas under these circumstances is 30 cm³.

The language A, defined as the set of all strings that are repeated twice (e.g., "00", "0101", "1111"), is not regular.

To show that A is not a regular language, we can use the pumping lemma for regular languages. The pumping lemma states that for any regular language, there exists a pumping length such that any string longer than that length can be divided into parts that can be repeated any number of times. Let's assume that A is a regular language. According to the pumping lemma, there exists a pumping length, denoted as p, such that any string in A with a length greater than p can be divided into three parts: xyz, where y is non-empty and the concatenation of xy^iz is also in A for any non-negative integer i. Now, let's consider the string s = 0^p1^p0^p. This string clearly belongs to A because it consists of the repetition of "0^p1^p" twice. According to the pumping lemma, we can divide s into three parts: xyz, where |xy| ≤ p and |y| > 0. Since y is non-empty, it must contain only 0s. Therefore, pumping up y by repeating it, the resulting string would have a different number of 0s in the first and second halves, violating the condition that the string must be repeated twice. Thus, we have a contradiction, and A cannot be a regular language.

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Answer:

f(2) = 0

Step-by-step explanation:

Evaluate: f(2) if f(x) = 4 - 2x; plug in 2 for x

f(2) = 4 - 2(2) = 4 - 4 = 0

Answer:

f(2) = 0

Step-by-step explanation:

Put 2 in the place of x,

f(2) = 4 - 2(2)

f(2) = 4 - 4

f(2) = 0

Answer:

a -25/6 is the least and then -2/3 then 1 1/6 and 1 15/6

Answer:

I'm not reallu sure.. but 5

Step-by-step explanation:

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Answer:

The second answer, 7y - 4x =12 would make the system have no solution.

The required number of children and adults for sitting in the theater are 300 and 50 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.

Let be consider number of children be x and that of adults is y.

We have,

x + y = 350-------(1)

y = 350 - x

And 5x + 10y = 2000------------------(2)

Put value of y in equation (2)

5x + 10( 350 - x) = 2000

5x + 3500 - 10x = 2000

-5x = -1500

x = 300

Then

y = 350 - x = 350 - 300 = 50

Thus, There will be 300 children and 50 adults in the  theater .

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Answer: A is the answrr. Percentage

Step-by-step explanation:

Answer:

the correct awnser is B we look for the rate

Answer:

Inverse relationship

Step-by-step explanation:

The equation we are looking at is;

y = 87.2/x

which implies xy = 87.2

If it was a direct relationship

y = constant * x

if it was inverse, it would have been

y * x = constant

since 87.2 is a constant, the question looks exactly like the second scenario.

This means that what we have is an inverse relationship