vadim weighs himself on his bathroom scale. the smallest divisions on the scale are 1-pound marks, so the least count of the instrument is 1 pound. vadim reads his weight as closest to the 142-pound mark. he knows his weight must be larger than 141.5 pounds (or else it would be closer to the 141-pound mark), but smaller than 142.5 pounds (or else it would be closer to the 143-pound mark). so vadim's weight must be

Answer:

A) 234 feet

B) Area of new parking lot = 28080 square feet

C) The new parking lot will be able to fit 20 more cars than the original parking lot.

Step-by-step explanation:

We are given the following information:

Length of parking lot = 180 feet

Width of parking lot = 120 feet

Number of cars that can be parked = 75

A) Increase in length  = 30%

New length =

B) New area =

C) Space required by 1 car = 288 square feet

Number of cars we want to fit = 75 + 20 = 95

Area required =

Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.

Answer:

To dilate by a scale factor of 2, multiply the length of each side of the shape by 2. If the shape is on a coordinate plane, multiply the coordinates of each vertex of the shape by 2.

Hope it helps

Answer:

Step-by-step explanation:

The circumference of the wheel of cheese is approximately 56.52 inches.

To calculate the circumference of a wheel of cheese, you need to know its radius.

The radius is the distance from the center of the wheel to its outer edge. In this case, the radius of the wheel is given as 9 inches.

The formula for the circumference of a circle is:

Circumference = 2π x radius

In the formula, "π" represents the mathematical constant pi, which is approximately equal to 3.14.

Let's substitute the given values into the formula:

Circumference = 2 x 3.14 x 9

Calculating this expression, we get:

Circumference = 56.52 inches

Therefore, the circumference of the wheel of cheese is approximately 56.52 inches.

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The gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

To find the gradient of the function \(\( f(x, y) = e^{3x} \sin(4y) \)\) at the point \(\((-1, -3)\)\), we need to compute the partial derivatives with respect to \(\(x\) and \(y\)\) and evaluate them at that point.

The gradient of a function is given by:

\(\[\nabla f(x, y) = \left(\frac{{\partial f}}{{\partial x}}, \frac{{\partial f}}{{\partial y}}\right)\]\)

Let's calculate the partial derivatives:

\(\[\frac{{\partial f}}{{\partial x}} = \frac{{\partial}}{{\partial x}}\left(e^{3x} \sin(4y)\right) = 3e^{3x} \sin(4y)\]\)

\(\[\frac{{\partial f}}{{\partial y}} = \frac{{\partial}}{{\partial y}}\left(e^{3x} \sin(4y)\right) = 4e^{3x} \cos(4y)\]\)

Now, we can evaluate these derivatives at the point \(\((-1, -3)\):\)

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{3(-1)} \sin(4(-3)) = 3e^{-3} \sin(-12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{3(-1)} \cos(4(-3)) = 4e^{-3} \cos(-12)\]\)

Simplifying further:

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{-3} \sin(-12) = -3e^{-3} \sin(12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{-3} \cos(-12) = 4e^{-3} \cos(12)\]\)

Therefore, the gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

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a)Favourite sport Frequency Fraction of people

Baseball 5 5/8

Swimming 3 3/8

b)[Image of a pie chart with 8 slices. The first slice is labeled "Baseball" and has a size of 5/8. The second slice is labeled "Swimming" and has a size of 3/8.]

Title: Favourite Sport of 8 People

Examining the figure, the missing angles are

angle AOC = 148 degrees

angle OCD =  21 degrees

Line AB and CB are tangents to the circle and hence will make angle 90 degrees at the point of tangent.

OA bisects angle AOC and angles ABC

In triangle AOB

90 + 32/2 + angle AOB = 180 degrees

angle AOB = 180 - 90 - 32 / 2

angle AOB =  74 degrees

angle AOC = 74 x 2 = 148 degrees

Using inscribed angle theorem

angle D = 1/2 x angle AOC

angle D = 74 degrees

In quadrilateral ABCD

143 + 32 + 74 + angle C = 360

angle C = 360 - 143 - 32 - 74

angle C = 111 degrees

angle OCD = 111 - 90

angle OCD = 21 degrees

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The efficiency of the Zumba class system is approximately 69.2%, and its utilization is approximately 54.5%.

To calculate the efficiency of the system, we can divide the actual output (number of employees trained) by the designed capacity (maximum number of employees that can be trained per month) and multiply by 100 to get a percentage.

Efficiency = (Actual Output / Designed Capacity) * 100

Efficiency = (600 / 850) * 100 = 70.6%

Therefore, the efficiency of the system is approximately 70.6%.

To calculate the utilization of the system, we can divide the actual output (number of employees trained) by the capacity (maximum number of students per month) and multiply by 100.

Utilization = (Actual Output / Capacity) * 100

Utilization = (600 / 1100) * 100 = 54.5%

Therefore, the utilization of the system is approximately 54.5%.

The Zumba class system at the local gym has an efficiency of approximately 69.2% and a utilization rate of approximately 54.5%. The efficiency indicates how well the system is performing relative to its designed capacity, and in this case, it suggests that the system is operating at a reasonably high level. The utilization rate, on the other hand, indicates how much of the available capacity is being utilized, and in this case, it suggests that the system is operating at around half of its maximum capacity. This information can be used by the gym to evaluate the performance of their Zumba class program and make informed decisions regarding resource allocation and potential improvements.

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The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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Answer:

(8,3)

Step-by-step explanation:

f(8) = 3

The input is 8 and the output is 3

(8,3)

The transformation of the function \(f(x)=x^2\) \(g( x)=(x+4)^2\)−1 involves a horizontal translation 4 units to the left.

Therefore, the answer is B. a horizontal translation 4 units to the left.

We can see this by comparing the two functions. The function g(x) is the same as f(x) except that the argument of the squared term has been replaced by (x+4). This means that the graph of g(x) is the same as the graph of f(x), but shifted horizontally 4 units to the left.

A function is a mathematical relationship between two variables, typically denoted as f(x). A function takes an input value x and produces an output value y, according to a specific rule or equation.

The input value x is called the independent variable, while the output value y is called the dependent variable. The rule or equation that determines how the input value is transformed into the output value is called the function's formula or expression

Therefore, the answer is B. a horizontal translation 4 units to the left.

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Answer:

Area:238 ft²

Perimeter: 62 ft

Step-by-step explanation:

You weren't clear on what you asked, so I can only assume that the question is asking for the area or perimeter.

To find the area, just multiply \(lw\).

14·17

=238

To find the perimeter, add 14 and 17 then multiply by 2:

\(2(14+17)\\=62\)

Hope this helps! :)

Answer:

k is 23876

Step-by-step explanation:

you have to multiply 254 and 94 by eachothe then that's your answer!

Step-by-step explanation:

\( \frac{ \frac{8}{9} }{ \frac{2}{3} } \\ = \frac{8 \times 3}{9 \times 2} \\ = \frac{24}{18} \\ = \frac{4}{3}\)

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

It’s B

Step-by-step explanation:

Answer:

i think the answer is c because it has to do with the congruence of porportional relationships

Step-by-step explanation:

The probability that the sample mean is 36 or more pieces of candy is approximately 18.67%.

To calculate the probability that the sample mean is 36 or more pieces of candy, we need to use the properties of the normal distribution. Given that the population mean is 35 pieces of candy and the standard deviation is 5 pieces, we can use the Central Limit Theorem.
The Central Limit Theorem states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the population distribution. Since the sample size is 40, we can assume a normal distribution.
To calculate the probability, we need to standardize the sample mean using the formula z = (x - μ) / (σ / √n),

where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.
In this case, x = 36, μ = 35,

σ = 5, and n = 40.

Plugging these values into the formula, we get z = (36 - 35) / (5 / √40)

≈ 0.8944.
To find the probability that the sample mean is 36 or more, we need to calculate the area under the normal curve to the right of z = 0.8944. Using a standard normal table or a calculator, we find that the probability is approximately 0.1867, or 18.67%.
Therefore, the probability that the sample mean is 36 or more pieces of candy is approximately 18.67%.

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The top right graph could show the arrow's height above the ground over time.

The initial and the final height are both at eye level, which is the reference height, that is, a height of zero.

This means that the beginning and at the end of the graph, it is touching the x-axis, hence either the top right or bottom left graphs are correct.

The trajectory of the arrow is in the format of a concave down parabola, hitting it's maximum height and then coming back down to eye leve.

Hence the top right graph could show the arrow's height above the ground over time.

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Answer:

x^2-4

Step-by-step explanation:

Use FOIL

F:x^2

O:-2x

I:2x

L:-4, now add them all together

x^2-4 is the area of the photograph

Answer:

they skided 242 feet

Step-by-step explanation:

Answer:

20x20)(20)20000)$yes

answer:

A, D, E

step-by-step explanation:

A — 13 - 1 = 12

B — 15 - 7 = 8

C — 12 - 12 = 0

D — 28 - 16 = 12

E — 36 - 24 = 12

F — 29 - 25 = 4

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of 5 line pairs per millimeter (B).

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of B. 5 line pairs per millimeter.
Here's a step-by-step explanation:

1. The sampling frequency is given as 10 pixels per millimeter.
2. According to the Nyquist-Shannon sampling theorem, the maximum spatial frequency (in line pairs per millimeter) that can be accurately represented is half of the sampling frequency.
3. Divide the sampling frequency (10 pixels per millimeter) by 2: 10/2 = 5 line pairs per millimeter.

So, the answer is B. 5 line pairs per millimeter.

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Answer:

24.5%

Step-by-step explanation:

Answer:

62

Step-by-step explanation:

This is a two digit number, 6 is 3 times the number 2 and the ssum of 6 and 2 is 8.

Hope this helps.

The exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).

The following equation can be used to calculate an exponential function again for number of women graduating from four-year colleges in t years after 1930:

A(t) = A₀e∧(rt)

In which A₀ is the starting point and r is the exponential growth rate expressed as a decimal.

In 1930, 48780 women received a bachelor's degree.

This implies that;

A₀ = 48780

In 2004, approximately 756000  people

The year 2003 is 73 years after 1930, that also means

Using the equation as an example:

A(t) = A₀e∧(rt)

Put the values;

756000 = 48780 e∧(73r)

e∧(73r) = 756000/ 48780

e∧(73r) = 15.49

Taking log both side;

73r = ㏑ 15.49

r = 2.7/7

r = 0.037

The function becomes;

A(t) = A₀e∧(0.037t)

Thus, the exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).

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Employees in the transportation and shipping industry today are required to know advanced math for several reasons. Here are some of the most important ones:

1. Efficiency: In the transportation and shipping industry, time is money. To maximize efficiency, workers need to be able to calculate distances, speeds, and travel times accurately.

This requires a solid understanding of advanced math concepts such as algebra, calculus, and trigonometry.

2. Safety: Transporting goods and people comes with risks. To ensure safety, employees need to understand the physics of motion, forces, and momentum.

This requires knowledge of advanced math concepts such as vectors, kinematics, and dynamics.

3. Technology: The transportation and shipping industry is becoming increasingly automated and technology-driven. Employees need to be able to understand and use complex algorithms, statistical models, and data analysis tools.

This requires advanced math skills such as statistics, probability theory, and linear algebra.

4. Regulations: The transportation and shipping industry is subject to a wide range of regulations, including safety standards, environmental laws, and trade policies.

Compliance with these regulations often requires complex calculations and data analysis. Advanced math skills are essential for navigating this regulatory landscape.

In summary, advanced math skills are essential for employees in the transportation and shipping industry to ensure efficiency, safety, technology adoption, and compliance with regulations.

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In this scenario, Marcos is planning to travel from Phoenix to Flagstaff, and we are using variables to represent different aspects of his journey.

The variable t represents the number of hours since Marcos left Phoenix, which serves as a measure of time elapsed since the start of the journey. It allows us to track the progress of Marcos over time and analyze various time-related aspects such as the duration of the journey or the rate at which he is traveling. On the other hand, the variable d represents the number of miles Marcos has traveled from Phoenix. It serves as a measure of distance covered, indicating how far Marcos has progressed on his route. By monitoring the value of d, we can determine the distance remaining to reach Flagstaff or calculate other distance-related parameters such as average speed or total distance traveled.

By using these variables, we can establish a relationship between time and distance traveled by Marcos. This relationship can be represented by a function or equation that describes Marcos' progress over time, such as a velocity equation or a distance-time equation. These variables and their relationship allow us to analyze and make predictions about Marcos' journey. We can determine when he is expected to reach certain milestones, calculate his average speed or rate of travel, and estimate the time required to complete the journey. Additionally, these variables provide a framework for solving various problems or making decisions related to Marcos' travel, such as optimizing his route or estimating fuel consumption based on distance traveled.

In summary, by using the variables t and d to represent time and distance traveled, respectively, we can effectively describe and analyze Marcos' journey from Phoenix to Flagstaff, enabling us to make informed decisions and predictions about his travel experience.

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The corresponding angle of X is angle Q

Corresponding sides are the sides that are in the same position in any different 2-dimensional shapes. For any two polygons to be congruent, they must have exactly the same shape and size. This means that all their interior angles and their corresponding sides must be the same measure.

For two congruent shapes, the corresponding are equal.

if polygons WXYZ and PQRS are congruent, then, line XY= line QS

Therefore angle X= angle Q

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After pouring some water from container A into container B, the new height of the water in both containers will be equal.

When container A is filled with water to the brim, it reaches its maximum capacity. Let's assume the initial height of the water in container A is h.

When some water is poured from container A into container B, the water level in both containers will gradually equalize until they reach the same height. Let's denote this new height as H.

The reason the water levels equalize is due to the principle of fluid equilibrium. When the containers are connected and the water is allowed to flow, the water seeks a common level. This occurs because the pressure at the same height in a fluid is equal.

Therefore, after pouring water from container A to container B, the final height of the water in both containers will be H, which indicates that the water has reached an equilibrium point where the pressure is equal in both containers.

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