John bought stock for $350. A year later, he sold it for $385. What is his gain in dollars? What is his return on investment? (Round to the nearest whole percent. ) I need help, please

When the bottom of the 6-foot ladder is 2 feet from the wall, the bottom is moving along the ground at 1 foot per second.

To find the rate at which the bottom of the ladder moves along the ground, we can use the Pythagorean theorem and related rates. Let x be the distance from the bottom of the ladder to the wall, and y be the height of the ladder on the wall. The Pythagorean theorem is x² + y² = 36.

Differentiating both sides with respect to time (t) gives 2x(dx/dt) + 2y(dy/dt) = 0. We are given that dy/dt = -2 ft/s, and we need to find dx/dt when x = 2 feet.

To find y, we can use the Pythagorean theorem: 2² + y² = 36, so y² = 32, and y = 4√2. Plugging these values into the differentiated equation, we get 2(2)(dx/dt) + 2(4√2)(-2) = 0. Solving for dx/dt, we find that dx/dt = 1 ft/s.

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For the two lines to be parallel, the value of n must be 3

When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line. If the slopes are the same then the lines are parallel.

The slope of each line is calculated as (y2-y1)/x2-x1

for line AB, the slope = (6n-n)/10-4 = 5n/6

for line CD, the slope= 8n-(-6)/9-(-3)=( 8n+6)/12

for AB and CD to be parallel,

5n/6 = (8n+6)/12

multiply both sides by 12

10n= 8n+6

collect like terms

10n-8n= 6

2n= 6

n= 6/2= 3

therefore for the value of n= 3 line CD and AB are parallel.

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Answer:

-9=9

Step-by-step explanation:

that the answer I think

18 root

2

Step-by-step explanation:

In this question imagine there is no y

It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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Answer: First we evaluate g(0), then plug the value into f(x).

g(0) = -2(0) + 7 = 7.

Thus, we need to do f(7).

f(7) = 3(7)-4 = 21 - 4 = 17.

Step-by-step explanation: Hope it helped :)

The fraction 1/9 is greater than the fraction 1/11.

Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction.

To compare unlike fractions:

Step 1: Observe the denominators of the given fractions: .

Step 2: Now, let us convert them in such a way that the denominators become the same.

Step 3: Compare the fractions:

Step 4: The fraction with the larger numerator is the larger fraction.

The given fractions are 1/9 and 1/11.

Here, LCM of denominator 9 and 11 is 99

Then, fractions becomes 11/99 and 9/99

11/99>9/99

1/9>1/11

Therefore, the fraction 1/9 is greater than the fraction 1/11.

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Answer:

x^-(3/2) which is (1)

Step-by-step explanation:

squared root of x³ is basically x^(3/2)

And if the question is 1/x^(3/2), then you can simply answer x^-(3/2) which is (1)

The equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.

According to the question,

We have the following information:

Points through which line is passing =  (-2,-6) and (1,2)

Now, we have the following values:

x1 = -2, y1 = -6

x2 = 1 and y2 = 2

We know that the following formula is used to find the slope of the line:

m = (y2-y1)/(x2-x1)

m = (2+6)/(1+2)

m = 8/3

Now, the following formula is used to find the equation of the line:

y-y1 = m(x-x1)

y+6 = 8/3(x+2)

y+6 = 8x/3+16/3

Subtracting 6 from both sides:

y = 8x/3+16/3-6

y = 8x/3-2/3

Hence, the equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.

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Answer:

.50x+40

Step-by-step explanation:

Option a, Yes players with future transfer plans do experience significant points variance if those plans have an impact on their point performance.

There are two probable conclusions: (a) players with a future transfer plan do indeed have a greater point variance, and (b) players with a future transfer plan do indeed have a higher point median.

The presentation of players with and without move expectations ought to be analyzed, jumbling variables ought to be considered, and factual tests ought to be rushed to survey the legitimacy of these speculations.

The outcome of this research would ultimately establish whether or not the possibility of a future transfer plan had an impact on a player's point production.

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The measure of side length x in the right triangle is approximately 13.0.

The figure in the image is a right triangle, having one of interior angle at 90 degrees.

Let;

Angle θ = 30 degree

Adjacent to angle θ  = x

Hypotenuse = 15

To solve for the missing side length x, we use the trigonometric ratio.

Note that: cosine = adjacent / hypotenuse

Hence:

cosθ = adjacent / hypotenuse

Plug in the given values and solve for x.

cos( 30° ) = x / 15

Cross multiplying, we get:

x  = cos( 30° ) × 15

x = 13.0

Therefore, the value of x is 13.0.

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Answer:

m<a is 32º

Step-by-step explanation:

4x-8=2x+12

   +8       +8

4x=2x+20

-2x     -2x

2x=20

÷2

x=10

4x-8

4(10)-8

40-8

32

To solve this problem, we can use the method of mixtures. Let x be the number of pounds of chocolate to be mixed with the trail mix. We can set up the following equation based on the given information:

(21.10x + 3.10(14)) / (x + 14) = 12.41

Simplifying and solving for x, we get:

21.10x + 43.40 = 12.41x + 173.54

8.69x = 130.14

x = 15

Therefore, the store owner should mix 15 pounds of chocolate costing $21.10 per pound with 14 pounds of trail mix costing $3.10 per pound to create a mixture worth $12.41 per pound.

To check this answer, we can verify that the total cost of the mixture equals the total cost of the chocolate and trail mix:

15(21.10) + 14(3.10) = 315 + 43.40 = 358.40

And the total weight of the mixture is:

15 + 14 = 29

So the cost per pound of the mixture is:

358.40 / 29 = 12.41

which matches the desired cost per pound.

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In a nonexperimental method, relationships between variables are studied by making observations or measures of the variables of interest.

Research without either the manipulation of an independent variable, the random assignment of individuals to conditions or orders of conditions, or both, is referred to as non-experimental research.

The non-experimental study is entirely dependent on variables that the researcher has no control over. By whatever means, they cannot manipulate, control, or change the subjects. Thus, all they can do is continue their research while monitoring and interpreting their subjects.

It is safe to assume that a non-experimental research design is used when there is no specific cause-effect study problem and the researcher simply wants to grasp a topic in depth without constraining it with variables. They examine the natural phenomena as they take place.

Therefore, in a nonexperimental method, relationships between variables are studied by observing or measuring the variables of interest.

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Answer:

D

19+5 is the total in her collection

multiply by three to triple

(19+5)x3

Answer:

D(19+5)x3

Step-by-step explanation:

she has 19, then don gave her 5 more

19+5

her father also offered to buy her three times so

(19+5)x3

Answer:

The answer is 3/5

Step-by-step explanation:

The ratio of two numbers, say x and y is:

x:y or x/y.

Hence, the ratio 18kg 30kg will be:

18kg/30kg = 18/30

In simplest form:

18/30 = 3/5

Answer:

1.) 42/55 x = the quotient. 2.) x = -1

Step-by-step explanation:

Answer:

x = - 7/9 and x = - 1

Step-by-step explanation:

Equation 1:

Step 1:

22 + 54x = - 20    Equation

Step 2:

54x = - 42   Subtract 22 on both sides

Step 3:

- 42 ÷ 54   Divide

Answer:

x = - 42/54 or - 7/9

Equation 2:

Step 1:

- 5x - 16 = 8x - 3   Equation

Step 2:

- 16 = 13x - 3   Add 5x on both sides

Step 3:

- 13 = 13x   Add 3 on both sides

Step 4:

- 13 ÷ 13   Divide

Answer:

x = - 1

Hope This Helps :)

Answer:

i. 33

ii. 1488

iii. 65

Step-by-step explanation:

i. 4x² − 3y² + 5z²

Putting the values x=2, y=-1 and z=2

4(2)² − 3(-1)² + 5(2)²

4×4 − 3×(1)² + 5×(4)

(16) -  (3×1) + (20)

16 -  3+ 20

36 - 3

33

ii. 3x³ − 2x(4yz+5x²)

Putting the values x=2, y=-1 and z=2

[3(2)³ − 2×2(4×(-1)×2 + 5×(2)²)]

[3(8)³ − 2×2(-8 + 5×4)]

[3 ×512 -  2×2(-8 +20)]

[1536 - 4(12)]

[1536 - 48]

1488

iii. 1−4x(yz+3xy)

Putting the values x=2, y=-1 and z=2

[1 - 4 × 2((-1)×2 + 3×2×(-1))]

[1- 8(-2 + (-6))]

[1- 8 (-2 -6)]

[1 - 8(-8)]

[1 +64]

65

(A) The matrix Y has no real eigenvalues (B) The quantity trace(X) - det(X) can be calculated by substituting the coefficients of the characteristic polynomial of X into the formula.

A) The characteristic polynomial of Y is λ² - 6λ - 4. To determine if Y has real eigenvalues, we can check the discriminant of the characteristic polynomial. The discriminant is given by Δ = b² - 4ac, where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = -6, and c = -4. Calculating the discriminant, Δ = (-6)² - 4(1)(-4) = 36 + 16 = 52. Since the discriminant is positive, Y has two distinct real eigenvalues.

B) The quantity trace(X) - det(X) can be calculated by substituting the coefficients of the characteristic polynomial of X into the formula. From the characteristic polynomial λ² - 4λ + 17, we can see that the trace of X is the coefficient of λ with the opposite sign, which is -(-4) = 4. The determinant of X is the constant term of the polynomial, which is 17. Therefore, trace(X) - det(X) = 4 - 17 = -13.

C) To calculate the rank of matrix Y, we can perform row operations to obtain its row-echelon form and count the number of nonzero rows. The rank of a matrix is equal to the number of nonzero rows in its row-echelon form.

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Answer:

Thank you so much!

Step-by-step explanation:

<3

The estimator hat mu1 is unbiased and efficient, while hat mu2 is biased and less efficient.

In the first step, let's examine the bias of the estimators. To determine whether an estimator is unbiased, we compare its expected value to the true parameter value. For hat mu1, we have:

E(hat mu1) = E((n - 1)/n * hat Y)

Since the expected value is a linear operator, we can rewrite this as:

E(hat mu1) = (n - 1)/n * E(hat Y)

Now, since each Y_i is drawn from a normal distribution with mean mu, we have E(hat Y) = mu. Substituting this in, we get:

E(hat mu1) = (n - 1)/n * mu

This shows that hat mu1 is an unbiased estimator, as its expected value is equal to the true parameter mu. On the other hand, for hat mu2, we have:

E(hat mu2) = E(hat Y + 2/n)

Again, using linearity of expectation, we can split this into two terms:

E(hat mu2) = E(hat Y) + E(2/n)

Since E(hat Y) = mu, we can simplify further:

E(hat mu2) = mu + 2/n

This indicates that hat mu2 is biased, as its expected value is mu + 2/n, which is different from the true parameter mu.

Moving on to efficiency, we compare the variances of the estimators. The efficiency of an estimator is determined by its variance, with a more efficient estimator having a smaller variance. For hat mu1, the variance is:

Var(hat mu1) = Var((n - 1)/n * hat Y)

Since the observations are independent and identically distributed (iid) from a normal distribution, we can use the properties of variance to simplify this expression:

Var(hat mu1) = \(((n - 1)/n)^2 * Var(hat Y) = ((n - 1)/n)^2 * (sigma^2/n)\)

On the other hand, for hat mu2, the variance is:

Var(hat mu2) = Var(hat Y + 2/n)

Again, using the properties of variance, we get:

Var(hat mu2) = Var(hat Y) + Var(2/n) = Var(hat Y) + 0 = Var(hat Y)

Comparing the two variances, we find that Var(hat mu1) < Var(hat mu2), indicating that hat mu1 is more efficient than hat mu2.

In summary, hat mu1 is an unbiased and efficient estimator, while hat mu2 is biased and less efficient.

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Answer:

they are both correct due to the commutative property

Deangelo's pace for the last 1.5 hrs of his half-marathon practise was p = 7 miles/hr.

By using the basic principles of speed and distance, we answer this question. Let's evaluate this question step-by-step.

After Deangelo starts the practice half-marathon, he jogs for half an hour at a pace of 5.5 miles per hour.

His speed  = 5.5 miles/hr

Time = 1/2 hr

From the Speed formula:

Speed = distance/time

Distance = Speed * Time

              = 5.5 * (1/2)

              = 5.5/2

              = 2.75 miles.

Since he completes his track, we can assume he traveled the rest of the distance in the last 1.5 hrs.

Distance Left = 13.25 - 2.75

                      = 10.5 miles.

Time Taken = 1.5 hrs.

His pace = 'p' miles/hr

Again applying the same formula,

p = 10.5/1.5

p = 7 miles/hr

Thus, we can complete the given statement as follows.

p = 7  = Deangelo's rate for the last 1.5 hrs of his run, in miles per hour.

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Answer:

\(x = 53\)

Step-by-step explanation:

Given

See attachment for triangle

Required

Find x

From the attachment, we have x and 127 on a straight line.

So, we have:

\(x + 127 = 180\) --- angle on a straight line

Subtract 127 from both sides

\(x + 127 - 127 = 180-127\)

\(x = 180-127\)

\(x = 53\)

If Tina's score is in the 50th percentile and the grades were normally distributed, Tina's score on the exam is 78.

A percentile refers to the comparison score between a particular score and the scores of the rest of a group. It represents the percentage of scores that a specific score surpassed. For example, if the score of 75 points on a test is ranked in the 85th percentile, it implies that the score 75 is higher than 85% of the scores. The 50th percentile, which is also the median score implies that 50% of the score is below or above the average score in a normally distributed data. In the given situation, if the grades are normally distributed with a mean of 78, that implies that 50% of the scores are above 78 and 50% of the scores are below 78. The standard deviation in this case is irrelevant. As Tina’s score is at the 50th percentile, her score on the exam would be 78.

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The correct solution to this problem is option e. 1/e. We can find it in the following manner.

The time constant of an RC circuit is the time in which the current decreases to 1/e (approximately 0.368) of its initial value.

This can be derived from the equation for the current in an RC circuit:

\(I=10 * e^({-t/RC} )\)

where I is current at time t, I0 is the initial current, R is the resistance, C is the capacitance, and e is the mathematical constant approximately equal to 2.71828.

To find the time constant, we set the exponent to -1:

\(e^({-t/RC} ) = 1 /e\)

Solving for t/RC, we get:

t/RC = 1

Therefore, the time constant is equal to RC, and the current decreases to 1/e of its initial value in one time constant.

So the answer is e. 1/e.

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