to increase strength and/or muscle mass, weight trainers will try different approaches. one approach is to apply an electrical impulse through a
muscle as the person is lifting a weight. a researcher wants to determine if adding this electrical impulse increases the amount of weight a person
can lift. to conduct his research, he selects one hundred people, and randomly divides them into two groups. one group wears a device that
sends an electrical impulse through the muscle used to repeatedly lift a 5 pound weight. the other group lifts the same weight without the electrical
impulse. the researcher counts the number of repetitions until the subjects can no longer lift the weight. is this an example of an observational
study or an experiment?

On solving the provided question we can say that from statistical data she obtains data from 167 currently enrolled students. in this context, the variable of interest would be age

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.

she obtains data from 167 currently enrolled students. in this context, the variable of interest would be age

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Answer:

1/6

Step-by-step explanation:

Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!

0 and 2

f(x) = g(x) will be the input or x value at which f and g have the same output or y value. Look in the table where two numbers repeat right next to each other.

−1 −7/2 −9/2

0 −3 −3

1 −2 −3/2

2 0 0

3 4 3/2

4 12 3

5 28 9/2

There are two solutions to f(x) = g(x) which are x=0 and x=2.

There are two solutions to f(x) = g(x) which are x=0 and x=2.

f(x) = g(x) will be the input or x value at which f and g have the same output or y value.

A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.

Look in the table where two numbers repeat right next to each other.

−1 −7/2 −9/2

0 −3 −3

1 −2 −3/2

2 0 0

3 4 3/2

4 12 3

5 28 9/2

There are two solutions to f(x) = g(x) which are x=0 and x=2.

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We can evaluate the integral on the right side to find the particular solution for the given initial condition y(0) = 5.

(i) To determine if the given differential equation is linear, we need to check if the dependent variable y and its derivatives appear linearly (raised to the power of 1) and without any products or compositions. In the given differential equation dy/dx = e^(-x^2) (2x+1)sin(x) - 2xy, we can see that y and its derivative dy/dx appear linearly. Therefore, the given differential equation is linear.

(ii) In a linear first-order differential equation in the form dy/dx + p(x)y = q(x), the coefficient of y is denoted as p(x), and the right-hand side of the equation is denoted as q(x). Comparing this with the given differential equation dy/dx = e^(-x^2) (2x+1)sin(x) - 2xy, we can identify p(x) as -2x and q(x) as e^(-x^2) (2x+1)sin(x).

(iii) To find the particular solution given the initial condition y(0) = 5, we can solve the differential equation. Rearranging the given equation, we have:

dy/dx + 2xy = e^(-x^2) (2x+1)sin(x)

This is a linear first-order ordinary differential equation. We can solve it using an integrating factor. The integrating factor is given by the exponential of the integral of p(x) dx:

I(x) = e^(∫2x dx) = e^(x^2)

Multiplying the entire differential equation by the integrating factor, we get:

e^(x^2) dy/dx + 2xye^(x^2) = e^(-x^2) (2x+1)sin(x) e^(x^2)

Simplifying the left side using the product rule, we have:

d/dx (e^(x^2) y) = e^(-x^2) (2x+1)sin(x) e^(x^2)

Integrating both sides with respect to x, we obtain:

e^(x^2) y = ∫(e^(-x^2) (2x+1)sin(x) e^(x^2)) dx

The integral on the right side can be simplified as it cancels out the exponential terms:

e^(x^2) y = ∫(2x+1)sin(x) dx

Integrating the right side using integration techniques, we can find the antiderivative. Once we have the antiderivative, we divide both sides by e^(x^2) to isolate y:

y = (1/e^(x^2)) ∫(2x+1)sin(x) dx

Using numerical or numerical approximation methods, we can evaluate the integral on the right side to find the particular solution for the given initial condition y(0) = 5.

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Answer:

1

Step-by-step explanation:

One adult at the front ~ ten students in a line ~ Second adult

Answer:

(4) * (63)

252

(*￣3￣)╭

Answer:

Rational

Step-by-step explanation:

You can write it as a ratio of a/b

Answer:

Irrational

Step-by-step explanation:

Irrational- anything that can be written as a decimal.

Rational- anything that can be written as a fraction.

Hope this helps. Plz give brainliest.

Answer:

1234567890

Step-by-step explanation:

Answer:

401 people

Step-by-step explanation:

First, find the percentage of students that went to the Youth Wing on Saturday, this is 463/463+474+335

464/1272

=36.4779874%

Multiply it now by the Sunday visitors, 0.364779874 x 1100

= 401.2578616

=401 people

Answer: 400

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

3(-4)^2 + 2(-4)

3(16) - 8

48-8

40

Answer:

(1,2)

Step-by-step explanation:

look at the slope

pick two points that connect like Γ

list which one connects to x and which one connects to y

Answer:

. 28%

Step-by-step explanation:

I=Prt I = interest paid, P = principal r=rate t=term

33,829.50- 28500=5329.50 to get I

28500x r x 66=1,881,000r

5329.50=1,881,000r

5329.50/1881000=. 0028333 convert to % is .28%

Answer:

y = 3x + 4

Step-by-step explanation:

y = mx + c where m is the slope and c is the y intercept.

Slope  = \(\frac{rise}{run}\)

Slope (taken from points (0, 4) and (1, 7)) = \(\frac{7-4}{1-0}\)

                                                                   = 3

y-intercept = 4

Equation: y = 3x + 4

Answer:

b jwtvd vgakdbbfqbbbq8jrbw5rl17rgsndbgwy

Answer: H - 4,500 mL

Step-by-step explanation:

Check picture below. Hope it's right

The value of x in the algebraic equation 7 / 2x - 2 / x + 1 = 1 / 4  is 7 and -2

let's find the value of x in the algebraic equation.

7 / 2x - 2 / x + 1 = 1 / 4

Therefore, let's solve the left side.

7 / 2x - 2 / x + 1  = 7(x + 1) - 4x / 2x(x + 1) = 7x + 7 - 4x / 2x² + 2x = 3x + 7 / 2x² + 2x

3x + 7 / 2x² + 2x  = 1 / 4

cross multiply

4(3x + 7) = 2x² + 2x

12x + 28 = 2x² + 2x

2x² + 2x  - 12x - 28 = 0

2x² - 10x  - 28 = 0

x² - 5x - 14 = 0

Therefore,

(x + 2)(x - 7)

hence,

x = -2 or x = 7

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Based on the information provided in the question:

Car b finished in the second position in the first race.

Velocity:

Velocity is the directional velocity of a moving object, observed from a given frame of reference and indicating the rate of change of position measured at a given time reference (eg 60 km/h northward). Velocity is a fundamental concept in kinematics, a branch of classical mechanics that describes the motion of bodies.

Velocity is a physical vector quantity. Both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is called velocity, and its magnitude is a consistent derived unit measured in the SI (metric) system as meters per second (m/s or m⋅s−1). For example, "5 meters/second" is a scalar, but "5 meters/second east" is a vector. An object is said to be accelerating if its velocity, direction, or both change.

According to the question:

Let tₐ = time of finish of car A in sec

Let \(t_b\)= time of finish of car B in sec

Let \(t_c\)  = time of finish of car C in sec

Let \(t_d\) = time of finish of car D in sec

Let \(t_e\) = time of finish of car E in sec

According to the above information:

(1) \(t_a = t_d -1\)

(2) \(t_b= t_e -6\)

(3) \(t_e =t_a +3\)

(4) \(t_a = t_c+5\)

Now,

From (3),

(3) \(t_a = t_e -3\)

and

(2) \(t_e =t_b+6\)

and

(1)\(t_d =t_a +1\)

Therefore, the series would be

Car C, Car B, Car A, Car D, Car E

the above series is the position of race from 1st to last.

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It will take approximately 131 months for the value of the building to reach $416,200.

To find the number of months it will take for the value of the building to reach $416,200, we need to set up an equation using the given information.

The equation for the value of the building, y, after x months of use is given as:

y = 652,000 - 1800x

We can set this equation equal to $416,200 and solve for x:

416,200 = 652,000 - 1800x

To isolate x, we can subtract 652,000 from both sides of the equation:

416,200 - 652,000 = -1800x

-235,800 = -1800x

Now, divide both sides of the equation by -1800:

-235,800 / -1800 = x

x ≈ 131

Therefore, it will take approximately 131 months for the value of the building to reach $416,200.

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Answer: C) 150°

Step-by-step explanation: all the angles are the same

Answer:

c

Step-by-step explanation:

(a) The volume of the paint in the can is approximately 0.003086 cubic meters.

(b) The thickness of the layer of wet paint on the wall is approximately 0.06182 meters.

:(a) To convert the volume of the paint from gallons to cubic meters, we need to use the conversion factor 1 U.S. gallon = 0.00378541 cubic meters. Given that the paint can has 0.816 U.S. gallons of paint left, we can calculate the volume in cubic meters by multiplying 0.816 by the conversion factor. The result is approximately 0.003086 cubic meters.

(b) To find the thickness of the layer of wet paint on the wall, we need to divide the volume of the paint (in cubic meters) by the area of the wall (in square meters). The remaining paint can cover an area of 13.2 square meters, so dividing the volume of the paint (0.003086 cubic meters) by the wall area (13.2 square meters) gives us approximately 0.0002333 meters or 0.06182 meters when rounded.

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Answer:

30 dollars

Step-by-step explanation:

if the mom and son have 30 and 36, the highest value you can get from both would be 30

Answer:

The greatest donation they can make is 30 dollars

Step-by-step explanation:

Money Word Problem

Let us analyze the given problem.

What is asked?

The greatest donation that Anthony and Jennifer can make.

What are the given?

Anthony's money - 30 dollars

Jennifer's money - 36 dollars

Finding the greatest donation that they can make, means finding their greatest common factor. Then, find out how many of their common factor they can get from their money.

How to find the greatest common factor?

There are three steps to find the GCF of two numbers:

1. Find all the factors of each number.

2. Find the common factors.

3. Choose the greatest factor or number.

Solution:

30 = 1, 3, 5, 6, 10, 30

36 = 1, 2, 3, 4, 6, 9, 12, 36

The greatest common factor is 6.

Now we need to know how many sixes we can get from their money.

30 = 6+6+6+6+6

36 = 6+6+6+6+6+6

Therefore, we can get 5 sixes from their money.

5 × 6 = 30

Final Answer:

The greatest donation that they can make is 30 dollars.

"An inaccurate assumption often made in statistics is that variable relationships are linear". The statement is true.

In statistics, it is indeed an inaccurate assumption to assume that variable relationships are always linear. While linear relationships are commonly encountered in statistical analysis, many real-world phenomena exhibit nonlinear relationships. Nonlinear relationships can take various forms, such as quadratic, exponential, logarithmic, or sinusoidal patterns.

By assuming that variable relationships are linear when they are not, we risk making incorrect interpretations or predictions. It is essential to assess the data and explore different types of relationships using techniques like scatter plots, correlation analysis, or regression modeling. These methods allow us to identify and account for nonlinear relationships, providing more accurate insights into the data.

Therefore, recognizing the possibility of nonlinear relationships and employing appropriate statistical techniques is crucial for obtaining valid results and making informed decisions based on the data.

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Answer:

27 in

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

you can perform the calculations for both the surface and triple integrals to verify the Divergence Theorem for the given vector fields and regions.

To verify the Divergence Theorem for the given vector fields and regions, we need to evaluate both the surface integral and the triple integral over the region E and confirm that they are equal.

(a) For the vector field F(x, y, z) = y^2z^3i + 2yzj + 4z^2k and the solid E enclosed by the paraboloid z = x^2 + y^2 and the plane z = 9:

According to the Divergence Theorem, the surface integral of F over the closed surface S bounding E is equal to the triple integral of the divergence of F over the region E.

Surface Integral:

∫∫S F · dS

Triple Integral:

∫∫∫E ∇ · F dV

To calculate the divergence of F, ∇ · F, we need to find the partial derivatives of each component and then take their sum:

∇ · F = ∂(y^2z^3)/∂x + ∂(2yz)/∂y + ∂(4z^2)/∂z

= 0 + 2z + 8z

= 10z

Now, we can proceed with the calculations of the surface and triple integrals.

(b) For the vector field F(x, y, z) = <x^2, -y, z> and the solid cylinder E where y^2 + z^2 ≤ 9 and 0 ≤ x ≤ 2:

Similarly, we need to evaluate the surface integral and the triple integral to verify the Divergence Theorem.

Surface Integral:

∫∫S F · dS

Triple Integral:

∫∫∫E ∇ · F dV

To find the divergence of F, ∇ · F, we take the sum of the partial derivatives of each component:

∇ · F = ∂(x^2)/∂x + ∂(-y)/∂y + ∂z/∂z

= 2x - 1 + 1

= 2x

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the complete question is;

Verify that the Divergence Theorem is true for the vector field F on the region E.

(a). F(x,y,z)=y2z3i+2yzj+4z2k, E is the solid enclosed by the paraboloid z=x2+y2 and the plane z=9.

(b). F(x,y,z)=<x2,-y,z>, E is the solid cylinder y2+z2\leq9, 0\leqx\leq2

The required volume and total surface area of the pentagonal pyramid are 15√3

Using the Pythagorean theorem, we can find s:

s² = (3√2)² + (s/2)²

s²2 = 18 + (s²/4)

3s²/4 = 18

s² = 24

s = 2√6

Now, we can find the area of each triangle:

Area of triangle = (1/2) * apothem * side

Area of triangle = (1/2) * 3√2 * 2√6

Area of triangle = 3√3

The total area of the base pentagon is 5 times the area of each triangle:

Area of base = 5 * 3√3

Area of base = 15√3

Now, we can find the volume of the pentagonal pyramid:

V = (1/3) * Base Area * Height

V = (1/3) * 15√3 * 3

V = 15√3

To find the surface area of the pentagonal pyramid,
Area of triangular face = (1/2) * side * slant height
The slant height is the distance from the midpoint of one of the sides of the pentagon to the apex of the pyramid.
slant height² = height² + (s/2²
slant height² = 9 + 6
slant height = √15

Now, we can find the area of each triangular face:
Area of triangular face = (1/2) * 2√6 * √15
Area of triangular face = 3√10

There are five triangular faces, so the total area of the triangular faces is:

Total area of triangular faces = 5 * 3√10
The total area of triangular faces = 15√10

Adding the area of the pentagonal base, we get the total surface area:

Total surface area = 15√3 + 15√10

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Answer:

Minus 12 from 48, divide the answer by 2 and the answer you get will be the number of men. Then add 12 to the answer and you will get the number of women

Step-by-step explanation:

Use unitary method

18 men

30 women

=====================================================

Explanation:

m = number of men

m+12 = number of women, which is 12 more than the number of men

Adding the two counts gets us 48 senior citizens total

(men) + (women) = 48 total

(m) + (m+12) = 48

2m+12 = 48

2m = 48-12

2m = 36

m = 36/2

m = 18

There are 18 male senior citizens.

m+12 = 18+12 = 30

And there are 30 female senior citizens.

-----------

Check:

18 men + 30 women = 48 total

30 women - 18 men = difference of 12

The answer is confirmed.

There are two lakes that have crocodiles and alligators in the same proportion.The two lakes are Lake Winnipeg and Lake Champlain.

This is the only lakes where this is the case, making them the only lakes with a proportional relationship between the number of crocodiles and the number of alligators. crocodiles and alligators have been known to live in the same body of water, but they are usually not found in the same proportion. In these two lakes, however, they are found in equal numbers.

Crocodiles and alligators are both reptiles that belong to the same order, which is why they can live in the same environment and in the same proportion.It is most likely because these lakes have a warm climate which is suitable for these reptiles.

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Answer: x= 11√3= 19.0525 = 19.1

Step-by-step explanation:

Let the reference angle be 30

so

cos 30 = b/h

√3/2 = x/22

or, 22√3 = 2x

or. x = (22√3)/2

so, x = 11√3

Answer:

x = 19.1 cm

Step-by-step explanation:

→ Find the name of the side you are not given

Opposite

→ Find a formula without opposite in it

Cos = Adjacent ÷ Hypotenuse

→ Rearrange to make adjacent the subject

Adjacent = Cos × Hypotenuse

→ Substitute in the values

Adjacent = Cos ( 30 ) × 22

→ Simplify

Adjacent = 19.1

The four integers are 11, 11, 43, and 54.

We are given that four integers have a mean of 9. The mean of a set of integers is the sum of all the integers divided by the total number of integers. Therefore, the sum of the four integers is 4 times 9, which is 36.

We are also given that the median of the four integers is 11. The median is the middle value when the integers are arranged in order. Therefore, the two middle integers must be 11.

Furthermore, we are given that the mode of the four integers is 11. The mode is the integer that appears most frequently in the set. Therefore, one of the integers must be 11.

Finally, we are given that the range of the four integers is 12. The range is the difference between the largest and smallest integers in the set. Therefore, the largest integer minus the smallest integer is equal to 12.

From the information we have, we know that two of the integers are 11. Let's assume that one of the other integers is x. Then, we can write an equation based on the information given:

(11 + 11 + x + y)/4 = 9

y - x = 12

where y is the largest integer. Simplifying the first equation, we get:

22 + x + y = 36 x 4

x + y = 98

Now we have two equations with two unknowns. We can solve for x and y by substituting the second equation into the first:

x + (x + 12) = 98

2x = 86

x = 43

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Complete Question:

Four integers have a mean of 9, a median of 11, a mode of 11 and a range of 12.

Find the four integers.

\(x = 15 \sqrt{2} \)

\(y = 15 \sqrt{2} \)

Answer:

x = y = 15\(\sqrt{2}\)

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = \(\frac{\sqrt{2} }{2}\) , then

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{30}\) ( multiply both sides by 30 )

30 × sin45° = x , then

x = 30 × \(\frac{\sqrt{2} }{2}\) = 15\(\sqrt{2}\)

The triangle is a right isosceles triangle thus the legs are congruent, then

x = y = 15\(\sqrt{2}\)