simplify 9^2/3/9^1/5

Answer:

-15

Step-by-step explanation:

if its just asking for what number would represent a loss of 15 it would be negative 15

i dont know if there's more to the problem or not

Answer:

-15

Step-by-step explanation:

This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,

hope this helps!

Answer: Jayden would practice for 630 minutes.

Step-by-step explanation:

You know that he practices for 420 minutes in 2 weeks. Divide them by each other. \(\sqrt[2]{420}=210\)

If one week is 210 minutes, 210x3=630 minutes.

The dependent variable in the given research description is sleep quality.

Given variables :1) participants, 2) sleep quality, 3) organic cotton shirts and organic linen shirts, 4) different clothing materials.

We have to identify the dependent variable among all the variables.

Dependent variable is a variable whose quantity depends on other variables.

Independent variable is a variable whose value does not depend on other variables.

In the given research there are four variables:

1) participants,

2) sleep quality,

3) organic cotton shirts and organic linen shirts,

4) different clothing materials.

Among all these sleep quality is a dependent variable because it depends on the quality of clothes whether they or organic shirts or organic linen shirts.

It may be possible that some people get quality sleep in organic cotton shirts and some may get in organic linen shirts.

Hence the dependent variable is sleep quality.

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The base of the Eiffel Tower in Frank's model is 4 inches.

A ratio indicates the number of times one number contains another.

Given, the height of the Eiffel Tower is 984 feet and the width at its base is 328 feet.

The ratio of height to base of the Eiffel Tower is given by:

984/328

=3

Therefore, the ratio of height to base for Frank's model should also be 3, Which is given by:

12/(base)=3

12/3=base

4 = base

Hence, the base of the Eiffel Tower in Frank's model is 4 inches.

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The term for this kind of sample is cluster sampling

Given

that, At a major ten university, 200 of the 30,000 undergraduate students and 100 of the 5,000 graduate students are chosen to represent a sample of student opinion.

What is cluster sampling ?

Cluster sampling involves breaking up a population into smaller units called clusters. Then, they randomly select a sample from each of these clusters. Cluster sampling is a probability sampling technique that is frequently used to examine large populations, especially those that are widely geographically dispersed.

Researchers frequently refer to pre-existing groups like cities or schools when referring to clusters. With an SRS of 200 students and an SRS score of 100, clusters have been utilized in this instance. Cluster sampling is the name given to this type of sample as a result.

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Answer: Credit cards

Step-by-step explanation:

(you can search it up as well)

Bahama Foods sets the selling price per unit at $39.50, which allows them to cover both their fixed costs and variable costs per unit.

To find the selling price per unit at Bahama Foods, we need to consider the break-even point, fixed costs, and variable costs.

The break-even point represents the level of sales at which total revenue equals total costs, resulting in zero profit or loss. In this case, the break-even point is given as 1,600 units.

Fixed costs are costs that do not vary with the level of production or sales. Here, the fixed costs are stated to be $44,000.

Variable costs, on the other hand, are costs that change in proportion to the level of production or sales. It is mentioned that the variable cost per unit is $12.

To determine the selling price per unit, we can use the formula:

Selling Price per Unit = (Fixed Costs + Variable Costs) / Break-even Point

Substituting the given values:

Selling Price per Unit = ($44,000 + ($12 * 1,600)) / 1,600

= ($44,000 + $19,200) / 1,600

= $63,200 / 1,600

= $39.50

Therefore, the selling price per unit at Bahama Foods is $39.50.

This means that in order to cover both the fixed costs and variable costs, Bahama Foods needs to sell each unit at a price of $39.50.

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Answer:

True

Step-by-step explanation:

Answer:

the answer is true

Step-by-step explanation:

because they do not intersect

Solving a linear equation we conclude that the helicopter will take 4 minutes to reach the ground.

We know that the equation that models the height of the helicopter is:

y = -300*x + 1200

Where y is the height and x is the time in minutes.

The helicopter will reach the ground when y = 0, then we need to solve:

0 = -300*x + 1200

Now we can solve this linear equation for x, it will give:

300*x = 1200

x = 1200/300 = 4

x = 4

Then, we conclude that the helicopter will take 4 minutes to reach the ground.

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Answer:

facundo3141592Ace12.2K answers78.3M people helpedSolving a linear equation we conclude that the helicopter will take 4 minutes to reach the ground.How long does it take to reach the ground?We know that the equation that models the height of the helicopter is:y = -300*x + 1200Where y is the height and x is the time in minutes.The helicopter will reach the ground when y = 0, then we need to solve:0 = -300*x + 1200Now we can solve this linear equation for x, it will give:300*x = 1200x = 1200/300 = 4x = 4Then, we conclude that the helicopter will take 4 minutes to reach the ground.If you want to learn more about linear equations

Step-by-step explanation:

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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To find the size of angles ABC, BCD, and AFE, we need to consider the properties of a hexagon and the given information.

The sum of the interior angles of a hexagon is equal to (6 - 2) * 180° = 720°.

We are given that angles ABC, BCD, and AFE are all equal.

Let's denote the measure of each of these angles as x.

Using the information provided, we can set up the equation:

x + x + x + 128° + 134° + 86° = 720°

Combining like terms, we have:

3x + 348° = 720°

Subtracting 348° from both sides, we get:

3x = 372°

Dividing both sides by 3, we find:

x = 124°

Therefore, the size of angles ABC, BCD, and AFE is 124°.

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6.666666666666666 (6.6 repeating, I just don’t know how to use the sign online)

I multiplied 3 1/3 by 2

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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The median splits the data in the box and whisker plot into two equal halves, with 50% of the data falling below the median and 50% above the median.

In a box and whisker plot, the median is represented by a vertical line or box within the plot. The box represents the interquartile range (IQR), which contains the middle 50% of the data. The lower edge of the box corresponds to the first quartile (Q1), where 25% of the data falls below, and the upper edge of the box corresponds to the third quartile (Q3), where 75% of the data falls below.

The whiskers extend from the box and represent the minimum and maximum values in the dataset, excluding any outliers. The length of the whiskers may vary depending on the range of the data and the presence of outliers.

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Answer:

7.5km/h

Step-by-step explanation:

Given data

Distance= 15km

Time = 2 hours

We know that the expression for the speed is

Speed= distance/time

Substitute

Speed= 15/2

Speed= 7.5 km per hour

Hence the speed is 7.5km/h

For the expression 5.6j - 0.12 = 4 + 1.1j, the value of variable j is 0.92.

The operations of addition, subtraction, multiplication, and division do not change the truth value of any equation is called the property of equality.

The given expression is 5.6j - 0.12 = 4 + 1.1j.

To solve the above expression, we will use the following steps.

Step 1:

By the subtraction property of equality, subtract 1.1j on both sides. We get the expression,

\(5.6j - 0.12 -1.1j = 4 + 1.1 j - 1.1 j\)

\(4.5 j -0.12 = 4\)

Step 2:

By the addition property of equality, add 0.12 on both sides. We get the expression,

\(4.5j -0.12 + 0.12 = 4 + 0.12\)

\(4.5 j = 4.12\)

Step 3:

By the division property of equality, divide the above expression by 4.5. We get the expression,

\(\dfrac {4.5j}{4.5 }= \dfrac {4.12}{4.5}\)

\(j = \dfrac {4.12}{4.5}\)

\(j = 0.92\)

Hence we can conclude that the value of variable j is 0.92.

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Answer:

76124

Step-by-step explanation:

CORRECT 100%

The area of the region enclosed by the curves is (3√3 - 13)/3.

To sketch the region enclosed by the given curves 4x+y^2=12, and x=y, we can begin by graphing the curves.

First, let's graph the curve 4x+y^2=12 by rewriting it in terms of y:

\(y^2 = 12 - 4x\)

This is a parabola that opens to the right and is centered at (3,0), with a width of 2√3.

Next, let's graph the line x=y, which passes through the origin at a 45-degree angle.

The region enclosed by the curves is the shaded region in the figure below:

To find the area of this region, we need to integrate with respect to x or y. Since the curves intersect at x=3, it's convenient to use vertical strips and integrate with respect to x.

The height of each strip is given by the difference between the y-coordinates of the parabola and the line at the corresponding x-value, which is:

y = √(12 - 4x) - x

The width of each strip is dx.

Thus, the area of the region is given by the integral:

S = ∫[0,3] (√(12 - 4x) - x) dx

We can simplify this integral by using the substitution u = 12 - 4x, du/dx = -4:

S = ∫[0,3] (√u - 3 + u/4) (-du/4)

S = ∫[0,12] (√u - 3 + u/4) (-du/4) (by extending the limits of integration)

S = [\(-u^{(3/2)/6} - 3u/4 + u^{2/32\)]_[0,12]

S = (3√3 - 13)/3

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Answer:

here you go! :)

hope it helps!

Step-by-step explanation:

Answer:

a circle

Step-by-step explanation:

yeah-ya... right?

The formula of integration by parts is ∫ u dv = uv - ∫ v du

The integration by parts formula is a technique used to integrate the product of two functions. It is often written in the following form:

∫ u dv = uv - ∫ v du

where u and v are functions of x and dv and du are their differentials.

To use this formula, one selects u and dv such that the integral on the right-hand side is easier to evaluate than the original integral on the left-hand side. The goal is to eventually reduce the integral to a form that can be evaluated using basic integration rules.

To integrate a given function f(x) using the integration by parts formula, one typically follows these steps:

1) Choose u and dv. Typically, u is chosen as a part of the integrand that will simplify when differentiated, and dv is chosen as the remaining part.

2) Compute du and v. Differentiate u to obtain du, and integrate dv to obtain v.

3) Plug u, du, v, and dv into the integration by parts formula.

4) Simplify the resulting expression by combining like terms and evaluating any remaining integrals.

5) If necessary, repeat the process with the remaining integral until a solution is obtained.

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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Section 10.2: Problem 8Given that vector a = (4, 1) is based at P = (2, 4). We know that the endpoint of a vector is represented by the terminal point.

\(Using the formula; terminal point = (initial point) + (vector)i.e terminal point = (2, 4) + (4, 1) = (6, 5)\)

\(Hence, the terminal point of the vector a = (4, 1) based on P = (2, 4) is (6, 5).\)

Section 10.2: Problem 9 We are to find a vector that has the same direction as (-6, 8).

Vectors have the same direction if they are parallel to each other.

Since two vectors that are parallel have the same direction, then if we multiply a scalar by a vector, the resulting vector will be parallel to the given vector.

We are given vector (-6, 8) which we will call vector b.

Since we know that scalar multiplication does not affect the direction of a vector, we can find a vector that has the same direction as vector b by multiplying it by any scalar.

Let's choose a scalar of 3.

\(Hence a vector a that has the same direction as vector (-6, 8) is given by: vector a = 3 * vector b = 3 * (-6, 8) = (-18, 24)\)

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Section 10.2: Problem 8: Terminal point of the vector a = (4,1) based at P = (2, 4)

The formula to calculate the terminal point of a vector that starts at point P and ends at Q isQ = P + a

Where,

P is the initial point, a

is the vector, and

Q is the terminal point of the vector a.

The initial point P = (2, 4) and the vector a = (4,1).

Therefore, the terminal point Q can be calculated as follows;

Q = P + aQ = (2, 4) + (4,1)

Q = (6, 5)

Therefore, the terminal point of the vector a = (4,1) based at P = (2, 4) is (6, 5).

Section 10.2: Problem 9: A vector with the same direction as (-6, 2)

To find a vector a with the same direction as vector b = (-6, 2), we need to determine the magnitude and direction of vector b.

The magnitude of vector b can be calculated as follows; |b| = √(b1² + b2²)

= √((-6)² + 2²)

= √40 = 2√10

To find the direction of vector b, we need to find the angle θ that vector b makes with the positive x-axis.

The tangent of θ is given by; tanθ = (b2 / b1)

= 2 / -6 = -1/3

Therefore,θ = tan⁻¹(-1/3) = -18.4° or 161.6°

The direction of vector b is in the fourth quadrant, i.e., between 90° and 180°.

Therefore, we need to add 180° to the value of θ to find the direction of vector a.θ = -18.4° + 180° = 161.6°

The vector a with the same direction as vector b = (-6, 2) can be found as follows;

a = |b| (cosθ, sinθ)a = 2√10 (cos161.6°, sin161.6°)a = (4.5, -1.4)

Therefore, the vector a with the same direction as (-6, 2) is (4.5, -1.4).

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A VWX has vertices at V(-1,0), W(6,8), and X(4,-3). If the triangle is translated f(,y) —— (x-1,y–5), then the new coordinates will be OV'(0, -5), W'(-7, -13), X'(-5, -2).

Explanation: A coordinate plane is used to determine the position of figures, and it has four quadrants labeled I, II, III, and IV. A geometric figure's coordinates must be given in order to reflect it on a coordinate plane.

A geometric figure's image obtained by moving it is known as a translation. If the triangle's vertices V(-1,0), W(6,8), and X(4,-3) are translated by the vector (-1,-5), the new coordinates will be obtained by subtracting the coordinates of (-1,-5) from each vertex. So, V' (-1,0) + (-1,-5) = (0,-5) or OV' (0,-5), W'(6,8) + (-1,-5) = (-7,-13) or W'(-7,-13), and X'(4,-3) + (-1,-5) = (-5,-8) or X'(-5,-2).

Hence, the correct answer is option (A) OV'(0, -5), W'(-7, -13), X'(-5, -2).

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The equation of straight line in the cartesian plane with slope and y-intercept of -1 is  y+x+1=0

A straight line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.

Given the slope = y-intercept= -1

Therefore m = -1 and c = -1 .

Substituting the values of m and c in the general equation of a straight line we get :

y = -x - 1

or, y + x+ 1 = 0

Therefore the equation of the straight line is y + x+ 1 = 0.

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Answer:

Step-by-step explanation:

                   x

(f/g)(x) = -----------

                x + 1

Notice that x cannot be -1, which would lead to division by zero.  Thus, x = -1 is the vertical asymptote.  Also notice that if x grows increasingly large, the fraction shown tends towards x/x, or 1, so we know that the horizontal asymptote is y = 1.

Draw a set of x-y axes and graph y = 1 and x = -1.  Plot (0, 0).  Again, note that the graph of this function never touches/crosses x = -1.  So, for (-1, 0) the graph is a curve caught between x = -1 and x = 0 that increases as x increases.  For (0, infinity), the graph heads upward at a slow pace and then levels off nearly parallel to y = 1 (the horizontal asymptote).

As x increases from left to right, y starts out slightly greater than y = 1 and then (while still in Quadrant II) curves upward and approaches the vertical asymptote x = -1.

It is observed that the equation satisfies, therefore, \(X(t) = e^{At} Ce^{Bt}\) is the solution to \(\frac{dX(t)}{dt} = AX(t) + X(t)B\).

Given:

A differential equation is given as:

\(\frac{dX(t)}{dt} = AX(t) + X(t)B\)

where \(X(t) = e^{At} Ce^{Bt}\).

Finding the derivative of \(X(t)\):

\(\frac{dX(t)}{dt} = \frac{d}{dt}(e^{At} Ce^{Bt})\)

\(\frac{dX(t)}{dt} = Ce^{Bt} \frac{d}{dt}(e^{At}) + e^{At} \frac{d}{dt}(Ce^{Bt})\)

\(\frac{dX(t)}{dt} = Ce^{Bt} A e^{At} + e^{At} B e^{Bt} C\)

\(\frac{dX(t)}{dt} = e^{At}(CA + B) e^{Bt} C\)

Substituting the value of \(\frac{dX(t)}{dt}\) in the given differential equation, we get:

\(e^{At}(CA + B) e^{Bt} C = Ae^{At} Ce^{Bt} + e^{At} Ce^{Bt} B\)

This can be simplified as:

\(Ae^{At} Ce^{Bt} + e^{At} Ce^{Bt} B = e^{At}(CA + B) e^{Bt} C\)

Therefore, \(X(t) = e^{At} Ce^{Bt}\)

The given differential equation has been verified with the solution.

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As a result, the total distance traveled by Mary in her round trip is 3/2 mile + 3/2 mile = 6/2 mile = 3 mile

We can calculate the total distance traveled by a body with position function s (t) if it moves along a coordinate line without changing direction from t = a to t = b. If the body changes direction during the journey, we must integrate the body's speed |v (t)| to find the total distance traveled.

Therefore,

We know Mary spent only a third of the time coming from school as she did going because she traveled three times as fast coming from school as she did going to school (6 miles per hour versus 2 miles per hour). If x represents the time it took her to get to school, then x/3 represents the time it took her to return.

Knowing that the total trip took 1 hour, we have:

x + x/3 = 1

3x/3 + 1x/3 = 1

4x/3 = 1

x  = 3/4

So we know it took Mary 3/4 of an hour to get to school (and 1/4 of an hour to get home).

Remembering that distance = rate × time, Mary's commute to school was (2 miles per hour) × (3/4 of an hour) = 3/2 mile. Furthermore, because she returned via the same route, she must have traveled 3/2 of a mile.

As a result, the total distance traveled by Mary in her round trip is 3/2 mile + 3/2 mile = 6/2 mile = 3 mile.

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Answer:

The statement "The Taylor series centered at 0 (aka MacLaurin Series) for f(x) = \(x^{11}\) sin x has only even powers of x" is false.

The Taylor series centered at 0 (or MacLaurin series) for the function f(x) = \(x^{11}\) sin(x) includes terms with both even and odd powers of x. The general form of the Taylor series for this function is:

f(x) = f(0) + f'(0)x + f''(0)\(x^{2}\)/2! + f'''(0)\(x^{3}\)/3! + ...

The derivative of f(x) = \(x^{11}\) sin(x) involves both the derivative of \(x^{11}\) (which has only even powers) and the derivative of sin(x) (which has both even and odd powers). Therefore, when the Taylor series is expanded, terms with both even and odd powers of x will be present.

Hence, the statement is false.

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