in the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. in addition, there is a weight limit of 2,700 pounds. assume that the average weight of students, faculty, and staff on campus is 165 pounds, that the standard deviation is 33 pounds, and that the distribution of weights of individuals on campus is approximately normal. suppose a random sample of 16 persons from the campus will be selected. (a) what is the mean of the sampling distribution of x? (b) what is the standard deviation of the sampling distribution of x? (c) what mean weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,700 pounds? (d) what is the probability that a random sample of 16 people will exceed the weight limit?

Answer:

\(a=3\frac{1}{3}\)

Step-by-step explanation:

\(a+5\frac{2}{3} =9\)

\(a+5\frac{2}{3}-5\frac{2}{3}=9-5\frac{2}{3}\)

\(a=3\frac{1}{3}\)

We have one possible triangle, ABC, with angles A = 33 degrees, B ≈ 82.2 degrees, and C ≈ 64.8 degrees, and sides a = 15 in., b ≈ 16.7 in., and c ≈ 12.6 in.

We can use the sine formula to find the length of side b:

sin(A) = opposite/hypotenuse

sin(33) = 9/b

b = 9/sin(33) ≈ 16.7 in.

Now, we can use the law of cosines to find the length of side c:

c^2 = a^2 + b^2 - 2abcos(C)

cos(C) = (a^2 + b^2 - c^2)/(2ab)

cos(C) = (15^2 + 16.7^2 - c^2)/(215*16.7)

cos(C) ≈ 0.417

C ≈ 64.8 degrees

So we have one possible triangle, ABC, with angles A = 33 degrees, B ≈ 82.2 degrees, and C ≈ 64.8 degrees, and sides a = 15 in., b ≈ 16.7 in., and c ≈ 12.6 in.

However, we could also have another triangle, DEF, with angles D = 147 degrees, E ≈ 82.2 degrees, and F ≈ 10.8 degrees, and sides d = 9 in., e ≈ 16.7 in., and f ≈ 15 in. This is because the given measurements only determine the ratios of the sides of a triangle, and it is possible to construct a triangle with the given ratios but with different angles.

Therefore, there are two distinct triangles that can be made with the given measurements.

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Answer:

is it a negative 1/2 if so the answer is 4

Step-by-step explanation:

you multiply -1/2 times a negative 3 u would get a positive 3/2=4

Answer:

<2= 65°

<3= 65°

<4= 115°

<5= 115°

<6= 65°

<7=65°

<8=115°

Unit price = total price / quantity

Unit price = 45.50 / 10

Unit price = $4.55

Answer:

$4.55 because I look it up

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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Answer:

8 + 7.

Step-by-step explanation: It is absolute value.

The AU per mole of carbon is 345.349 kJ/mol.

To calculate ΔU per mole of carbon (AU), we need to use the equation:

ΔU = q - w

where q is the heat transferred to the system and w is the work done by the system.

In this case, we can assume that the work done is negligible because the reaction is taking place in a constant-volume calorimeter, so w = 0.

To calculate q, we can use the equation:

q = mcΔT

where m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

First, let's calculate the heat transferred to the water (q_water):

q_water = mcΔT

Given:
m = 754 g (mass of water)
c = 4.184 J/g-K (specific heat capacity of water)
ΔT = 27.28 °C - 24.85 °C = 2.43 °C

q_water = (754 g)(4.184 J/g-K)(2.43 K)
q_water = 7720.86 J

Since the heat capacity of the bomb is given as 897 J/K, we can assume that the heat transferred to the bomb is:

q_bomb = 897 J

Now, let's calculate the total heat transferred to the system (q_total):

q_total = q_water + q_bomb
q_total = 7720.86 J + 897 J
q_total = 8617.86 J

Finally, we can calculate ΔU per mole of carbon (AU):

AU = ΔU/moles of carbon

To find the moles of carbon, we need to use the molar mass of carbon (C), which is 12.01 g/mol.

Given:
Mass of carbon burned = 0.300 g

moles of carbon = (0.300 g)/(12.01 g/mol)
moles of carbon = 0.02496 mol

AU = ΔU/moles of carbon
AU = (8617.86 J)/(0.02496 mol)
AU = 345349.27 J/mol

However, the question asks for the answer in kJ/mol. To convert J to kJ, we divide by 1000:

AU = 345.349 kJ/mol

Therefore, the AU per mole of carbon is 345.349 kJ/mol.

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AU ≈ 91.496 kJ/mol

i.e. the change in internal energy per mole of carbon is approximately 91.496 kJ/mol.

To calculate ΔU per mole of carbon (AU) for the given reaction, we need to use the equation:

ΔU = q - w

where ΔU is the change in internal energy, q is the heat transferred, and w is the work done.

In this case, the reaction took place in a constant-volume calorimeter, which means that no work was done (w = 0) because the volume of the system remained constant. Therefore, the equation simplifies to:

ΔU = q

Now, let's calculate the heat transferred (q) using the equation:

q = mcΔT

where q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

Given that the mass of water is 754 g and the specific heat capacity of water is 4.184 J/g-K, we can calculate the heat transferred from the water.

q_water = (mass_water) * (specific heat capacity_water) * (ΔT_water)

q_water = (754 g) * (4.184 J/g-K) * (27.28 °C - 24.85 °C)

q_water = 101.46 J

Now, to find the heat transferred for the combustion of carbon, we need to use the heat capacity of the bomb (Cp_bomb) and the change in temperature (ΔT_bomb) of the calorimeter.

q_bomb = (Cp_bomb) * (ΔT_bomb)

Given that the heat capacity of the bomb is 897 J/K and the change in temperature of the calorimeter is 27.28 °C - 24.85 °C, we can calculate the heat transferred from the bomb.

q_bomb = (897 J/K) * (27.28 °C - 24.85 °C)

q_bomb = 2183.91 J

Now, we can calculate the total heat transferred:

q_total = q_water + q_bomb

q_total = 101.46 J + 2183.91 J

q_total = 2285.37 J

Since ΔU = q_total, we have:

ΔU = 2285.37 J

To convert ΔU to kilojoules per mole of carbon (AU), we need to convert the mass of carbon burned to moles. The molar mass of carbon (C) is 12.01 g/mol.

moles of carbon (C) = mass of carbon (C) / molar mass of carbon (C)

moles of carbon (C) = 0.300 g / 12.01 g/mol

moles of carbon (C) ≈ 0.02498 mol

Finally, we can calculate AU:

AU = ΔU / moles of carbon (C)

AU = 2285.37 J / 0.02498 mol

AU ≈ 91495.76 J/mol

To convert AU to kilojoules per mole, we divide by 1000:

AU ≈ 91.496 kJ/mol

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Answer:

y = -6/5x - 8

Step-by-step explanation:

Use the slope-intercept form y = mx + b and substitute slope(m) = -6/5 and the point (-5, -2). After that solve for b

y = mx + b

-2 = -6/5(-5) + b

-2 = 6 + b

-8 = b

For the equation  substitute into y = mx + b ;  y = -6/5x - 8

Answer:

x = 50

Step-by-step explanation:

101 + (x + 29) = 180

130 + x = 180

x = 180 - 130

x = 50

Answer:

50°

Step-by-step explanation:

in order ro find x you would need to solve for 101° ( x + 29) = 180° if you replace x with 50 then you equation would be true!

Answer:

pupil question:

3 6 1

3 have brothers

6 have both

1 has sisters

Step-by-step explanation:

3+6+1+2=12

Answer:

15.1 mm²

Step-by-step explanation:

Lateral surface area of a cylinder = 2πrh

(where r is the radius and h is the height)

Given:

Substitute given values into the formula:

⇒ Lateral surface area = 2π(1.2)(2)

                                      = 4.8π

                                      = 15.1 mm²  (nearest tenth)

Answer:

What is the probability that a randomly selected person is on the swim team?

28 out of 67 people are on the swim team

so that's 28/67

41.7910448% round to the nearest tenth

41.8% is the answer.

Step-by-step explanation:

Answer:

Locate the y-intercept on the graph and plot the point.

From this point, use the slope to find a second point and plot it.

Draw the line that connects the two points

Step-by-step explanation:

y-intercept: The value of y at the point where a curve crosses the y-axis.

slope: The steepness of a line expressed as a ratio, using any two points on the line.

linear equation: An equation whose solution is a straight line.

I also gave examples! :)  

Remember that brainliest!

Have a great day!

Answer:

look it up

Step-by-step explanation:

Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test

Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test. Content validity refers to the extent to which a test accurately measures the specific content or domain it is intended to assess. By involving subject matter experts, who are knowledgeable and experienced in the domain being tested, in the evaluation of each test item, we can gather expert opinions on the relevance, representativeness, and alignment of the items with the intended content. Their input can help ensure that the items are appropriate and adequately cover the content area being assessed, thus enhancing the content validity of the test.

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Answer: 7 cm

Step-by-step explanation:

We know that, Triangle's area= 0.5 × Base × Height

So,

28 = 0.5 × 8 × Height

⇒Height= {28/(0.5 ×8)} = 7 cm

The tripling time for the population of deer can be determined by finding the value of t when the population P(t) becomes three times its initial value.

The given population growth function is P(t) = \(299^3,\) where t represents the number of years since the time of introduction. To find the tripling time, we need to solve the equation P(t) = 3P(0), where P(0) is the initial population.

Substituting the given function into the equation, we have:

\(299^3 = 3P(0)\)

To solve for P(0), we divide both sides of the equation by 3:

\(P(0) = (299^3) / 3\)

Now, to find the value of t, we set P(t) equal to 3P(0) and solve for t:

\(299^3 = 3P(0)\)

\(299^3 = 3 * [(299^3) / 3]\)

\(299^3 = 299^3\)

Since the equation \(299^3 = 299^3\)is true for any value of t, it means that the tripling time for this population of deer is undefined. In other words, the population will never triple from its initial value according to the given growth function.

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Answer:

6x+6

Step-by-step explanation:

10x+7−4x−1

=10x+7+−4x+−1

Combine Like Terms:

=10x+7+−4x+−1

=(10x+−4x)+(7+−1)

=6x+6

The expression that will calculate its area is Option D. 4x² - 6x + 9.

The region is the amount that expresses the extent of vicinity on the aircraft or on a curved surface. The region of a plane vicinity or plane location refers to the area of a shape or planar lamina, whilst floor vicinity refers back to the region of an open surface or the boundary of a 3-dimensional item.

Calculation:-

side of square is given by = 2x-3

area of square = side²

= ( 2x-3)²

= 4x² + 3² - 2× 2x×3

= 4x² + 9 - 12x

The area is the quantity of area occupied by means of a two-dimensional figure. In other phrases, it's far the amount that measures the range of unit squares that cowl the surface of a closed determine. the same old unit of the vicinity is square devices that's usually represented as rectangular inches, square feet, etc.

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Answer:

i cant see a parrellogram!

please post a picture

The value of the conversion is;

16, 666. 67 minutes

277.78 hours

Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.

From the information given, we have;

10⁶ seconds

But, we have to take note of;

60 seconds = 1 min

Then 10⁶ seconds = x min

cross multiply

x = 16, 666. 67 minutes

Also,

60 minutes = 1 hour

Then 16, 666. 67 minutes = x

cross multiply

x = 277.78 hours

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The required probabilities are:-

a) P(8 of the players numbers are drawn) = 1.3×10⁻⁸

b) P(7 of the players number are drawn) = 3.33×10⁻⁶

c) P(at least 6 of the players number were drawn) = 1.84×10⁻⁴

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then performs an experiment that selects 8 of these 40 numbers.

Players has 8 combinations of numbers from 1-40. The outcome S contains all the combinations of 8 out of 40

a) P(8 of the players numbers are drawn) = 1/40/8 = 1.3×10⁻⁸

b) Number of ways of drawing 78 selected numbers from 1-40 = 8×(40-7)8×32

P(7 of the players number are drawn) = 8×32/40 =3.33×10⁻⁶

c) P(at least 6 players numbers are drawn)= 32/2×(8/6) ways to draw.

P(at least 6 players numbers are drawn) = P(all 8 chosen are drawn) + P(7 players numbers drawn) + P(6 chosen are drawn) = 1+8 x32/40/8 +[8\6 ×32/2]

P(at least 6 players numbers are drawn) = 1.84×10⁻⁴

Hence, the required probabilities are:-

a) P(8 of the players numbers are drawn) = 1.3×10⁻⁸

b) P(7 of the players number are drawn) = 3.33×10⁻⁶

c) P(at least 6 of the players number were drawn) = 1.84×10⁻⁴

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The value of given operation for all integers x and y is given as -6 therefore option (C) is correct.

An integer is a mathematical concept that represents a whole number without any fractional or decimal part. In other words, it is a number that can be expressed without any remainder or fractional component. Integers include positive numbers (such as 1, 2, 3), negative numbers (such as -1, -2, -3), and zero (0). Integers are used in various mathematical operations, such as addition, subtraction, multiplication, and division.

In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation.

The given operation is defined as follows:

x ⊕ y = x × y - 3 ·x

We can substitute the values provided in the question to evaluate the expression (3 ⊕ 5) ⊕ 2:

(3 ⊕ 5) ⊕ 2

= (3 * 5 - 3 * 3) ⊕ 2 [Using the definition of the given operation]

= (15 - 9) ⊕ 2

= 6 ⊕ 2

= 6 * 2 - 3 * 6 [Using the definition of the given operation]

= 12 - 18

= -6

Therefore, the value of (3 ⊕ 5) ⊕ 2 is -6, which corresponds to option (C) in the provided choices.

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The value of given operation for all integers x and y is given as -6 therefore option (C) is correct.

An integer is a mathematical concept that represents a whole number without any fractional or decimal part. In other words, it is a number that can be expressed without any remainder or fractional component. Integers include positive numbers (such as 1, 2, 3), negative numbers (such as -1, -2, -3), and zero (0). Integers are used in various mathematical operations, such as addition, subtraction, multiplication, and division.

In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation.

The given operation is defined as follows:

x ⊕ y = x × y - 3 ·x

We can substitute the values provided in the question to evaluate the expression (3 ⊕ 5) ⊕ 2:

(3 ⊕ 5) ⊕ 2

= (3 * 5 - 3 * 3) ⊕ 2 [Using the definition of the given operation]

= (15 - 9) ⊕ 2

= 6 ⊕ 2

= 6 * 2 - 3 * 6 [Using the definition of the given operation]

= 12 - 18

= -6

Therefore, the value of (3 ⊕ 5) ⊕ 2 is -6, which corresponds to option (C) in the provided choices.

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The number in which the value of 3 is 3-1/100 is 345. The correct option is a.

The given number is 43,781.

The value of the 3 in 43,781 is 3,000.

The value of 3-1/100 is 2.99.

We are supposed to find out in which number 2.99 is the value of the 3 in 43,781.

Given options are:

a. 345

b. 237,895

c. 5,732

We'll calculate the values of 3-1/100 in each option.

a. The value of 3-1/100 in 345 is 2.99.

So, the correct option is a.

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Answer: 0.02777777777

Step-by-step explanation:

Step-by-step explanation:

A square prism is a cube. The equation that represents the volume of a cube is:

length*width*height

or, in your case, b*b*h

If you are talking about a square-based pyramid, then you use 1/3 * length * width * height or 1/3 * b * b * h. You can use the exponents where needed.

Answer:

7

Step-by-step explanation:

28 divided by 4 is 7

Answer:

1: $5

2: 7

3: 18

4: 17

5: 2

6: 1,029

Step-by-step explanation:

To rewrite the integral ∫(2x)\(e^{4x^{2} }\)dx using integration by parts, we'll consider the function f(x) = (2x) and g'(x) = \(e^{4x^{2} }\).

Integration by parts states that ∫u dv = uv - ∫v du, where u and v are functions of x.

Let's assign:

u = (2x) => du = 2 dx

dv = \(e^{4x^{2} }\) dx => v = ∫\(e^{4x^{2} }\) dx

To evaluate the integral of v, we need to use a technique called the error function (erf). The integral cannot be expressed in terms of elementary functions. Hence, we'll express the integral as follows:

∫\(e^{4x^{2} }\) dx = √(π/4) × erf(2x)

Now, we can rewrite the integral using integration by parts:

∫(2x)\(e^{4x^{2} }\) dx = uv - ∫v du

= (2x) × (√(π/4) × erf(2x)) - ∫√(π/4) × erf(2x) × 2 dx

= (2x) × (√(π/4) × erf(2x)) - 2√(π/4) × ∫erf(2x) dx

The integral ∫erf(2x) dx can be further simplified using substitution. Let's assign z = 2x, which implies dz = 2 dx. Substituting these values, we get:

∫erf(2x) dx = ∫erf(z) (dz/2) = (1/2) ∫erf(z) dz

Therefore, the final expression becomes:

∫(2x)\(e^{4x^{2} }\) dx = (2x) × (√(π/4) × erf(2x)) - √(π/2) × ∫erf(z) dz

Please note that the integral involving the error function cannot be expressed in terms of elementary functions and requires numerical or tabulated methods for evaluation.

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