A team of psychologists was curious if omega-3 fatty acid supplements could help treat depression in adolescents. They recruited 50 adolescents with varying levels of depression to participate in an experiment. The researchers randomly assigned each subject to take either an omega-3 supplement or a placebo daily, and they monitored subjects' depression levels throughout the study. What is the main reason for randomly assigning the subjects?
A. To identify confounding variables
B. To control against nonresponse
C. To reduce the impact of sampling variability
D. To ensure both the subjects and researchers are blind to who is in which group
E. To create groups that are as similar as possible so the main difference between the groups is the treatment

Answer:

g=24

Step-by-step explanation:

g/4 -5 = 1

g/4 = 6

g = 24

Answer:

\(g=24\)

Step-by-step explanation:

When given the following equation,

\(\frac{g}{4}-5 = 1\)

Solve for the variable (g) using inverse operations,

\(\frac{g}{4}-5=1\)

Add (5) to both sides

\(\frac{g}{4}=6\)

Multiply both sides by (4)

\(g=24\)

Answer:

y=3/4x-2

Step-by-step explanation:

The first thing you would do is you would get a graph.

Now write down the point (8,4) (remember to label)

Remember (8,4) is where x is 8 and y is 4

A slope of 3/4 is also known as rise/run. This means in this problem you would rise 3 and move to the right 4. If the slope were negative you would do the opposite direction. For example -1/2 would be go down one move right four.

*You should graph points above and below your point

After that you would go from the point (8,4) and rise 3 and move over to the right 4. This gives you the point (12,7).

Write down that point.

Next you would do another point. So that means you could go down 3 and move 4 to the left which gives you the point, (4,1)

*I recommend having more than two points, but only two points are needed to make a line.

Now you can find the y-intercept with your graph and put it on your equation.

if you want to do it without a graph you need to know this formula.

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

Next, put in the equation what you already know so m=3/4.

That give you y=3/4x+b

Next, to find the y intercept plug in the point (8,4). This way you can find the y intercept.

this gives you: 4=3/4(8)+b

Solve for b.

b=-2 so that your y intercept.

So your equation is: y=3/4x-2.

*I recommend checking my work, but this is what I got.

Hope this helped!

Ms. Ann can use 160 pounds of candy that costs $1.80 per pound to maintain an average cost of $2.00 per pound for the candy mix.

Let's assume Ms. Ann wants to use x pounds of candy that costs $1.80 per pound.

The total cost of the candy mix can be calculated as follows:

Total cost = Cost of selected candy + Cost of additional candy

The cost of selected candy is given as 80 pounds at $2.40 per pound:

Cost of selected candy = 80 pounds * $2.40/pound = $192.00

The cost of additional candy is x pounds at $1.80 per pound:

Cost of additional candy = x pounds * $1.80/pound = $1.80x

Since the total cost should be $2.00 per pound for the candy mix, we can write the equation:

Total cost = Cost of selected candy + Cost of additional candy = $2.00 per pound * (80 pounds + x pounds)

Substituting the values:

$192.00 + $1.80x = $2.00 * (80 + x)

Simplifying the equation:

$192.00 + $1.80x = $160.00 + $2.00x

Rearranging the terms:

$0.20x = $32.00

Dividing both sides by $0.20:

x = $32.00 / $0.20

x = 160 pounds

Therefore, Ms. Ann can use 160 pounds of candy that costs $1.80 per pound to maintain an average cost of $2.00 per pound for the candy mix.

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Answer:

  $160 pounds

Step-by-step explanation:

You want to know how much candy that costs $1.80 per pound to add to 80 pounds of candy costing $2.40 per pound to make a mix that costs $2.00 per pound.

The proportion of the components in the mix is the reverse of the proportion of the differences between the component value and the mix value. The attached diagram shows this.

The difference between the high-value component value ($2.40 per pound) and the mix value ($2.00 per pound) is $0.40 per pound. Likewise the difference between the mix value and the low-value component is $2.00 -1.80) = $0.20 per pound. Then the ratio of high-value component to low-value component will be 0.20 : 0.40 = 1 : 2.

If there are 80 pounds of expensive candy, there needs to be 2×80 = 160 pounds of cheap candy in the mix to makes its value $2.00 per pound.

Ms. Ann should use 160 lb of candy costing $1.80 per pound.

__

Additional comment

This sort of X-diagram can be used for mixtures of all sorts. Some checks you can used are ...

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Factor when divides the function the remainder is zero. The factorized form of the function f(x)=125x⁶-8 is (5x²-2)(25x⁴ + 10x²+4).

A factor of a function is a factor which when multiplied by another the result is the function itself.

We know that in order to factorize a function, we need to take the common terms out from the expression,

\(f(x)=125x^6-8\)

The given function can be written as,

\(f(x)=125x^6-8\\\\f(x)=5^3x^6-2^3\\\\f(x)=(5x^2)^3-2^3\)

Now, we will use the algebraic property to solve the function.

\(f(x)=(5x^2)^3-2^3\\\\f(x)=(5x^2-2)(25x^4+10x^2+2^2)\\\\f(x)=(5x^2-2)(25x^4+10x^2+4)\)

Hence, the factorized form of the function f(x)=125x⁶-8 is (5x²-2)(25x⁴ + 10x²+4).

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Answer:

C

Step-by-step explanation:

Answer:

A. Genevieve

B. Sierra

Step-by-step explanation:

Genevieve uses 5 balloons per animal, but Sierra uses 6. We can find this by subtracting 360 from 440 (which gets us 80). To find the unit rate, we divide 20 into 80 (the amount of balloons used when she made 20 animals), and we get 4. So, Sierra uses 4 balloons per animal.

Since Genevieve uses more balloons per animal and started with less balloons than Sierra (she started with 425, versus Sierra, who started with 440), Sierra will have made more animals by the end of the day.

I hope this helps!

Answer:

he is correct

Step-by-step explanation:

tanR as a fraction in simplest terms is tanR=3/4.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, in triangle RST, ST=18 and RT=30.

By using Pythagoras theorem, we get

RT²=ST²+SR²

30²=18²+SR²

900=324+SR²

SR²=576

SR=24 units

Now, tanR=Opposite/Adjacent

tanR=18/24

tanR=3/4

R=36.86°

Therefore, tanR as a fraction in simplest terms is tanR=3/4.

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f(1) is the minimum value of f(x) within the interval [-1, 1].

What is a critical points of a function?

A critical point of a function is a point where the derivative of the function is either zero or undefined. It is a point where the function may have a maximum, minimum, or an inflection point.

To find the minimum value of the function f(x) within the given interval

[-1, 1], we can analyze the critical points and endpoints of the interval.

First, let's find the critical points by setting the derivative f'(x) equal to zero and solving for x:

\(f'(x) = e^{-x} * cosx^2 = 0\)

Since the exponential function \(e^{-x}\) is always positive and non-zero, we can conclude that the critical points occur when \(cosx^2\) = 0.

The cosine function is equal to zero at values of \(x^2\) that are odd multiples of\(\frac{ \pi}{2}\), i.e.,\(x^2 = (2n + 1)\frac{\pi}{2}\), where n is an integer.

Solving for x in each case, we have:

\(x^2 = (2n + 1)\frac{\pi}{2}\)

\(x=\pm}\sqrt{ (2n + 1)\frac{\pi}{2}}\)

However, we are only interested in the interval [-1, 1]. Let's determine the values of x within this interval that satisfy the critical points:

For n = 0:

\(x=\pm}\sqrt{ \frac{\pi}{2}}\)≈ ±1.253

For n = 1:

\(x=\pm}\sqrt{3\frac{\pi}{2}}\) ≈ ±2.201

Since all the critical points fall outside the interval [-1, 1], we can conclude that the minimum value of f(x) within the given interval occurs at one of the endpoints.

Now let's evaluate f(x) at the endpoints:

\(f(-1) = e^{-(-1)}cos(-1)^2= ecos(1)\\ f(1) = e^{-1}cos(1^2) = e^{-1}cos(1)\)

To determine which one is smaller, we can compare the values of ecos(1) and \(e^{-1}cos(1)\). Since the value of e is approximately 2.71828, we can calculate the values:

\(ecos(1)= 2.71828cos(1)= 1.24203\\ e^{-1}cos(1)= 0.36788 cos(1) = 0.36788\)

Comparing these values, we can see that \(f(1) = e^{-1}cos(1) = 0.36788\) is the minimum value of f(x) within the interval [-1, 1].

Therefore, the correct answer is option C: f(1).

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Answer:

n = -8

Step-by-step explanation:

Hopes this helps.

Answer:

n=-8

Step-by-step explanation:

1. Distribute

-3(n+3)=15

-3n-9=15

2. Add 9 to both sides

-3n-9=15

-3n-9+9=15+9

3.SImplify

-3n=24

4.Divide

-3n=24

-3n/-3=24/-3

5.SImplify

n= -8

The values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.

We can use the logarithm properties to find the value of log57 given that log75 is 0.83.

One of the logarithm properties states that:

log(a * b) = log(a) + log(b)

Using this property, we can express log57 in terms of log75:

log57 = log(5 * 3 * 19)

Now, we can use the fact that log75 is 0.83 to find log5, log3, and log19, and then add them together to get the value of log57:

log57 = log(5 * 3 * 19)

log57 = log5 + log3 + log19

However, since the values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.

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The equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.

To find log57 using the given information log75 = 0.83, we can use the change of base formula:  

if log75 = 0.83, then log57 ≈ 0.827. To find log57 using the given information log75 = 0.83, we can use the change of base formula:log_b(a) = log_c(a) / log_c

Here, we want to find log57 (log_7(5)) using the given information log75 (log_5(7)).

We can rewrite the change of base formula as:log_7(5) = log_x(5) / log_x(7)We know that log_5(7) = 0.83,

so we can substitute this value into the equation:log_7(5) = log_x(5) / 0.83

Now we can use any common base, like base 10 or base e, to find the value of log_7(5). Let's use base 10:log_7(5) = log_10(5) / log_10(7)Now

we can calculate the values of log_10(5) and log_10(7) using a calculator:log_10(5) ≈ 0.69897log_10(7) ≈ 0.84510

Now substitute these values back into the equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.

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P = 35/128  is the probability that the number of heads obtained from flipping the two fair coins is the same.

Describe probability using an example?

P( oH )  = ³C₀ (1/2)³ . ⁴C₀ (1/2)⁴  = 1 . 1/128

P( 1H) = ³C₁ (1/2)³ . ⁴C₁( 1/2 )⁴ = 12/128

P( 2H ) = ³C₂ (1/2)³ . ⁴C₂ (1/2)⁴ = 18/128

P( 3H) = ³C₃ ( 1/2)³ . ⁴C₃ ( 1/2)⁴ = 4/128

P = 1/128 + 12/128 + 18/128 + 4/128

P = 35/128

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Answer:

The answer is 15x - 10y = -8

If water is being poured into the trough at a rate of 5 ft^3/min, the rate at which the water level is rising when the depth is 8 inches is 15√3/32 ft/min.

Length (L) = 8 feet

Side = 2 feet

If water is being poured into the trough at a rate of 5 ft^3/min. So

dV/dt = 5 ft^3/min

The depth is 8 inches.

h = 8 inches = 2/3 feet

The formula of volume (V) = √3/4 b^2 · L

Now putting the value

V = √3/4 b^2 · 8

Simplify

V = 2√3b^2

Using the Pythagorean Theorem

b/h = 2/√3

So b = 2/√3 h

Now putting the value of h in the volume V

V = 2√3(2/√3 h)^2

V = 2√3 × 4/3 × h^2

V = 8/√3 × h^2

Differentiating the equation with respect to t

dV/dt = 8/√3 d/dt(h^2)

dV/dt = 8/√3 × 2h dh/dt

dV/dt = 16h/√3 × dh/dt

As dV/dt = 5. So

5 = 16h/√3 × dh/dt

Multiply by √3 on both side, we get

16h dh/dt = 5√3

Divide by 16h on both side, we get

dh/dt = 5√3/16h

As h = 2/3. So

dh/dt = 5√3/(16×2/3)

After solving

dh/dt = 15√3/32 ft/min

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Answer:

-23 .......................

Answer:

240 nickels

Step-by-step explanation:

Answer:

x = \(\frac{3}{2}\)

Step-by-step explanation:

Given

f(x) = 4x² - 12x + 9

To obtain the zero let f(x) = 0 , that is

4x² - 12x + 9 = 0 ← in standard form

(2x - 3)² = 0 ← in factored form , then

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \(\frac{3}{2}\)

The zero of the function f (x) = 4x² - 12x + 9 will be 3/2.

What is Quadratic polynomial?

A polynomial which has highest power 2 is called a quadratic polynomial.

Given that;

The function is;

f (x) = 4x² - 12x + 9

Now, To find zero of the function we equate the function to zero.

We get;

f (x) = 4x² - 12x + 9

4x² - 12x + 9 = 0

Solve the function by quadratic formula we get;

x = - (-12) ± √12² - 4 × 4 × 9 / 2 × 4

x = 12 ± √144 - 144 / 8

x = 12 ± 0 / 8

x = 12/8

x = 3/2

Thus, The zero of the function f (x) = 4x² - 12x + 9 will be 3/2.

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Answer:

(m-6) (m-4).

Step-by-step explanation:

m2-6m-4m+24

m(m-4)-6(m-4).

therefore answer is (m-6) (m-4).

At least 1 percent of all people end up spending all or most of their waking hours online, mostly gaming or on social media.

Social media is sometimes referred to as a social network and it can be defined as a collection of websites and Internet software programs (applications) that are designed and developed to avail its end users an ability to add, share, and discuss different information, as well as facilitate e-commerce, collaboration, social movements, and debates between community members over the world wide web (WWW) or the Internet.

Generally speaking, some examples of social media platforms that are used around the world include the following:

According to research on abnormal psychology, it was gathered that one (1) percent of the world's population (people) spend all or most of their waking hours online to play games or surfing on social media

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The first step to solve for r is (J) He should divide both sides of the equation by π.

The equation is given as:

A= πr^2

Divide both sides of the equation by π.

So, we have:

r^2 = A/π

Hence, the first step to solve for r is (J) He should divide both sides of the equation by π.

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Answer:

a,g,e

Step-by-step explanation:

Answer:

since angles x and y are equal, then sides WX and WY should also be equal

x=8

Step-by-step explanation:

54=6x+6

48=6x

8=x

Answer:

11

Step-by-step explanation:

Let the number be x.

Then by the question,

2x+4 = 3x-7

x=11

Answer:

Let the no. be x

then according to the question,

\((x \times 2) + 4 = 3x - 7\)

\(2x - 3x = - 7 - 4 \\ = > - x = - 11 \\ = > x = 11\)

Answer:

points at (0,-1) and (1,4) will have a slope of 1/4 and a negative y-intercept

Step-by-Step Explanation:

Answer:

D

Step-by-step explanation:

C and D are the location for -1 and 1

....-2  -1  0  1  2 ...

Using Mathematica, we can find the roots of the function y = x^3 Exp[-x] Sin[2x] by substituting x = 3t and evaluating the expression for t in the range [0,1]. The roots correspond to the values of t where the function crosses the x-axis.

To find the roots of the given function, we substitute x = 3t into the expression y = x^3 Exp[-x] Sin[2x]. This gives us y = (3t)^3 Exp[-3t] Sin[2(3t)]. Simplifying further, we have y = 27t^3 Exp[-3t] Sin[6t].

Using Mathematica, we can evaluate this expression for t values ranging from 0 to 1. The roots of the function correspond to the values of t where y equals zero, indicating that the function crosses the x-axis. By plotting the function or using numerical methods such as FindRoot or NSolve in Mathematica, we can determine the values of t where y = 0, thus finding the roots of the function.

In summary, by substituting x = 3t and evaluating the expression y = x^3 Exp[-x] Sin[2x] for t in the range [0,1] using Mathematica, we can find the roots of the function, which represent the values of t where the function crosses the x-axis.

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This is an infinite series that converges for values of x within the radius of convergence of the series.

To find a power series representation for the function f(x) = x^5/9 - x^2, we can express it as a sum of terms involving powers of x.

Let's start by expanding the first term, x^5/9, as a power series. We know that the power series representation for 1/(1-x) is:

1/(1-x) = 1 + x + x^2 + x^3 + ...

By substituting -x^2/9 for x, we can rewrite it as:

1/(1+x^2/9) = 1 - x^2/9 + (x^2/9)^2 - (x^2/9)^3 + ...

Now, let's consider the second term, -x^2. This is a simple power series with only one term:

-x^2 = -x^2

Combining the two terms, we have:

f(x) = (1 - x^2/9 + (x^2/9)^2 - (x^2/9)^3 + ...) - x^2

Simplifying and collecting like terms:

f(x) = 1 - x^2/9 + x^4/81 - x^6/729 + ... - x^2

The resulting power series representation for f(x) is:

f(x) = 1 - x^2/9 + x^4/81 - x^6/729 + ...

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Answer:

the last option 5(p-3)=63

Step-by-step explanation:

since there are 5 posters p will always have to multiplied by 5 and the discount is 3 so we subtract that from each poster and since there are 5 thst also has to be multiplied so this is the only solution

Given that 25% of students solved at least two tasks and there were 32 students who wrote the test, we can prove that there was at least one task that no more than 12 students solved.

There was at least one task that no more than 12 students solved, we can use a proof by contradiction.

Assume that all five tasks were solved by more than 12 students. This means that for each task, there were at least 13 students who solved it. Since there are five tasks in total, this implies that there were at least 5 * 13 = 65 students who solved the tasks.

However, we are given that only 25% of students solved at least two tasks. If we let the number of students who solved at least two tasks be S, then we can write the equation:

S = 0.25 * 32

Simplifying, we find that S = 8.

Now, let's consider the remaining students who did not solve at least two tasks. The maximum number of students who did not solve at least two tasks is 32 - S = 32 - 8 = 24.

If all five tasks were solved by more than 12 students, then the total number of students who solved the tasks would be at least 65. However, the maximum number of students who could have solved the tasks is 8 (those who solved at least two tasks) + 24 (those who did not solve at least two tasks) = 32.

This contradiction shows that our initial assumption is false. Therefore, there must be at least one task that no more than 12 students solved.

Hence, we have proven that there was at least one task that no more than 12 students solved if 32 students wrote the test.

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Answer:

P(p∩Q) = 0.

Step-by-step explanation:

Given the Addition Rule:

P(p∪Q) = P(p) + P(Q) - P(p∩Q)

P(p or Q) = P(p) + P(Q) - P(p and Q)

Events p and Q are disjoint (or mutually exclusive) if they cannot occur at the same time. (That is, disjoint events do not overlap.)

Hence, whenever p and Q are disjoint, P(p and Q) becomes zero in the formal addition rule, so for disjoint events p and Q we have:

P(p or Q) = P(p) + P(Q).

Therefore, the cardinal number of P(p∩Q) = 0.