Rebecca is on the swim team. If you can swing 24 labs in six minutes how long would it take her to swim 36 laps

Answer:

Since there are a total of six friends and they each use a $2 off coupon then what you first want to do is multiply:

2 times 6 = 12

Then you want to add:

42 + 12 = 54

So the total that they would have spent without the discount would be $54.

Step-by-step explanation:

Hope it helps! =D

The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).

It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):

1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).

To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.

2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.

In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.

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Reflexive Property of congruence justifies the statement

∠K ≅ ∠K

The Reflexive Property of congruence states that any geometric figure is congruent to itself. The figures are being the reflection of itself. They have the line segments of same length, an angle has the same angle measure and the figure has same shape and size as itself.

If two triangles have a common side or a common angle, then Reflexive Property of congruence is used to prove that the two triangles are congruent.

Since the given angle is K, therefore by the Reflexive Property of congruence  we could say that the angle K is congruence to angle K.

⇒ ∠K ≅ ∠K

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Look at the picture I put. I hope that helps you!

The Unique Representation Theorem holds, stating that if B = {v₁, ..., vₙ} is a basis for a vector space V, then for each v in V, there is a unique set of scalars c₁, ..., cₙ such that v = c₁v₁ + ... + cₙvₙ.

To prove the Unique Representation Theorem, we will assume that there exist two sets of scalars, c₁, ..., cₙ and d₁, ..., dₙ, such that v = c₁v₁ + ... + cₙvₙ and v = d₁v₁ + ... + dₙvₙ. We will show that these two representations must be the same, implying uniqueness.

Starting with the given representations:

v = c₁v₁ + ... + cₙvₙ

v = d₁v₁ + ... + dₙvₙ

By subtracting the second representation from the first, we have:

0 = (c₁ - d₁)v₁ + ... + (cₙ - dₙ)vₙ

Since B = {v₁, ..., vₙ} is a basis for V, every vector in V can be uniquely expressed as a linear combination of the basis vectors. Therefore, for the above equation to hold, each coefficient in front of the basis vectors must be zero. This leads to the following system of equations:

c₁ - d₁ = 0

...

cₙ - dₙ = 0

From these equations, we can conclude that c₁ = d₁, ..., cₙ = dₙ.

This shows that the two sets of scalars are the same, and hence the representation of v as a linear combination of the basis vectors is unique.

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Answer:

A

Step-by-step explanation:

(-3,13) and (4,-15) have a slope of 11.

Rounding to the nearest whole number, we can estimate that approximately 308 students will score between 48 and 62.

To determine the number of students that are expected to score between 48 and 62, we first need to find the z-scores for these values using the formula:

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation.

For x = 48:

z = (48 - 50) / 10 = -0.2

For x = 62:

z = (62 - 50) / 10 = 1.2

Using a standard normal distribution table, we can find the probability of a z-score between -0.2 and 1.2, which is 0.3849.

Finally, we can calculate the approximate number of students that will score between 48 and 62 by multiplying the probability by the total number of students:

Number of students = 0.3849 x 800 = 307.92

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The median, because the data distribution is skewed to the right.

Given that

The box plot with the following parameters:  

Minimum value at 11,

First Quartile, Q1 at 22.5,

Median at 34.5,

Third Quartile, Q3 at 36,

Maximum value at 37.5.

According to the question

When a distribution has a longer tail to one of its sides, then it is said to be skewed.

Since the tail is longer to the left, it is said to be left-skewed.

The data distribution is skewed to the left because the median (34.5) is closer to the third quartile (36) than to the first quartile  (22.5).

For skewed data, we always prefer the median because it is less affected by the outliers and if the mean is chosen, the value of the mean is biased towards the side that has larger values while the median does not get affected by it. So, we choose the median.

For skewed distributions, the median is the best measure of center.

Hence, the median, because the data distribution is skewed to the right.

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Step-by-step explanation:

25.

\( \frac{t}{5} = b\)

where b is the no. if 5 dollar bills.

26.

\(x +( x + 2) +( x + 4) = x + (x + 2)\)

\(3x + 6 + 9 = 2x + 2\)

\(3x + 15 = 2x + 2\)

\(x + 15 = 2\)

\(x = - 13\)

Since x=-13 the intergers are

\( - 13\)

\( - 11\)

\( - 9\)

27.

Represent the function as

\(x + x + 6 = 44\)

\(2x + 6 = 44\)

\(2x = 38\)

\(x = 19\)

The shorter piece should be 19 inches.

28.

Solve for h.

\(s = 2\pi \times rh + 2\pi {r}^{2} \)

\(s - 2\pi {r}^{2} = 2\pi \times rh\)

\( \frac{s - 2\pi {r}^{2} }{2\pi \times r} = h\)

29.

\( \frac{16 + x}{2} \times 6 = 108\)

\( \frac{16 + x}{2} = 18\)

\(16 + x = 36\)

\(x = 20\)

Step-by-step explanation:

Hope this helps, cheers!!!

a) The actual distance between towns K and L is: 100 km

b) As shown in the attached file

c) The bearing of town L from town K is 117 degrees.

The scale of the map is given as:

1 cm to represent 50 km

Now, when we measure the distance between K and L on the map, we see that it gives us a distance of 2 cm.

Using the scale of 1 cm: 50 km, we can say that:

Actual distance between towns K and L = (2 * 50)/1 = 100 km

b) Using a compass and it’s 3cm aiming down {South} as seen in the attached photo. Then a line was drawn aiming {South} with a ruler. On the end of the line the (x) point was put there to get the mark.

c) Measuring the angle gives the bearing of town L from town K which is 117 degrees.

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Answer: the mean absolute deviation is 1 1/3.

Step-by-step explanation: first find the average of all the numbers by adding them together and then dividing the sum by 6 (since there’s 6 numbers). The average is 5.5. Find the absolute deviation of each number from 5.5. For example, 4 is 1.5 units away from 5.5. Do this with every number, and add the sum of these numbers. Then find the average of the absolute deviations.

To find the maximum profit, we can look for the vertex of the parabolic function representing the profit.

The given profit function is:

\(Z = -3x^2 + 12x + 25\)

We can see that the coefficient of the \(x^2\) term is negative, which means the parabola opens downwards. This indicates that the vertex of the parabola represents the maximum point.

The x-coordinate of the vertex can be found using the formula:

\(x = \frac{-b}{2a}\)

In our case, a = -3 and b = 12. Plugging these values into the formula, we get:

\(x = \frac{-12}{2 \cdot (-3)}\\\\x = \frac{-12}{-6}\\\\x = 2\)

To find the maximum profit, we substitute the x-coordinate of the vertex into the profit function:

\(Z = -3(2)^2 + 12(2) + 25\\\\Z = -12 + 24 + 25\\\\Z = 37\)

Therefore, the maximum profit is 37.

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Answer:

x < 10

Step-by-step explanation:

2x-8 <12

Add 8 to each side

2x-8+8 <12+8

2x< 20

Divide by 2

2x/2 < 20/2

x < 10

Answer:

The third one is the answer.

The maximum height which the rocket attains is 80 m and the time taken by the rocket is 8 sec.

Given,

the following formula yields the height h,

h= -5t² + 40t +45

45m is the height of the launch pad.

We take the first derivative of the function h and then set it to zero to determine the height the rocket reaches.

h' = 0

-10t + 40 =0

-10t = -40

 t = 4

Therefore, height reached by the rocket in time t = 4 is,

h= -5t² + 40t +45

  = -5(4)²  + 40(4) + 45

  =125 m

As a result, the rocket can reach:

125- 45

= 80 m

(To determine the real height the rocket travels, we have subtracted the height of the launch pad.)

The rocket takes twice as long to launch as it does to reach the peak.

t = 2*4 = 8 sec

Therefore,

the rocket goes 80 meters in height

the rocket's flight time is 8 seconds.

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The standard bus takes x + 29 minutes and the airplane takes x / 2 minutes.

The express bus from Dublin to Belfast takes x minutes, and the standard bus takes 29 minutes longer.

To find the time the standard bus takes, we simply add 29 minutes to the time the express bus takes.

The expression for the time the standard bus takes is:
Standard bus time = x + 29
The airplane takes half the time the express bus takes.

To find the time the airplane takes, we divide the time the express bus takes by 2.

The expression for the time the airplane takes is:
Airplane time = x / 2.

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Baseball doughnuts are weights placed on baseball bats during warmup. A high school team uses baseball doughnuts that weigh 5 ⅐ ounces each. The team brings 8 baseball doughnuts to away games. What is the total weight of the baseball doughnuts?

Part A: 5 1/7 x 8

Part B: 36/7 x 8/1 = 288/7

Sry i.d.k C

Step-by-step explanation:

The present value of an initial investment a parent wants to make is given as $\(70,000\) due 19 years from now. This value is determined using the concept of compound interest as $\(25,460.72\).

To determine the initial investment that will grow to $70,000 for a child's education at age 19, we need to calculate the present value of $70,000 due 19 years from now. This means we need to find the initial investment that will grow to $70,000 in a term-length of 19 years of continuous compounding at 5% interest rate.
The formula for continuous compounding is given as,

\(A = P\cdot e^{(rt)}\), where \(A\) is the final amount, \(P\) is the initial investment, \(e\) is the mathematical constant approximately equal to \(2.71828\), \(r\) is the interest rate, and \(t\) is the term-length in years. We can use this formula to solve for the initial investment as follows,
\(70,000 = P\cdot e^{(0.05\times 19)}\)
\(70,000 = P\cdot e^{(0.95)}\)
\(P=\frac{70,000}{e^{0.95}}\)
\(P=25,460.72\)
Therefore, the initial investment needed to grow to $70,000 for a child's education at age 19, with continuous compounding at a 5% interest rate, is approximately $25,460.72.

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The net magnetic field at point P is (6e-5 j + 0.57 k) T in 1, 1, k notation.

We can use the Biot-Savart Law to calculate the magnetic field at point P due to each wire, and then add the two contributions vectorially to obtain the net magnetic field.

The magnetic field due to a current-carrying wire can be calculated using the formula:

d = μ₀/4π * Id × /r³

where d is the magnetic field contribution at a point due to a small element of current Id, is the vector pointing from the element to the point, r is the distance between them, and μ₀ is the permeability of free space.

Let's first consider the wire carrying current I₁ (in the positive X direction). The contribution to the magnetic field at point P from an element d located at position y on the wire is:

d₁ = μ₀/4π * I₁ d × ₁ /r₁³

where ₁ is the vector pointing from the element to P, and r₁ is the distance between them. Since the wire is infinitely long, we can assume that it extends from -∞ to +∞ along the X axis, and integrate over its length to find the total magnetic field at P:

B₁ = ∫d₁ = μ₀/4π * I₁ ∫d × ₁ /r₁³

For the given setup, the integrals simplify as follows:

∫d = I₁ L, where L is the length of the wire per unit length

d × ₁ = L dy (y - 1/2 L) j - x i

r₁ = sqrt(x² + (y - 1/2 L)²)

Substituting these expressions into the integral and evaluating it, we get:

B₁ = μ₀/4π * I₁ L ∫[-∞,+∞] (L dy (y - 1/2 L) j - x i) / (x² + (y - 1/2 L)²)^(3/2)

This integral can be evaluated using the substitution u = y - 1/2 L, which transforms it into a standard form that can be looked up in a table or computed using software. The result is:

B₁ = μ₀ I₁ / 4πd * (j - 2z k)

where d = 5 mm = 5×10^-3 m is the distance between the wires, and z is the coordinate along the Z axis.

Similarly, for the wire carrying current I₂ (in the negative X direction), we have:

B₂ = μ₀ I₂ / 4πd * (-j - 2z k)

Therefore, the net magnetic field at point P is:

B = B₁ + B₂ = μ₀ / 4πd * (I₁ - I₂) j + 2μ₀I₁ / 4πd * z k

Substituting the given values, we obtain:

B = (2×10^-7 Tm/A) / (4π×5×10^-3 m) * (30A - (-30A)) j + 2(2×10^-7 Tm/A) × 30A / (4π×5×10^-3 m) * (15×10^-2 m) k

which simplifies to:

B = (6e-5 j + 0.57 k) T

Therefore, the net magnetic field at point P is (6e-5 j + 0.57 k) T in 1, 1, k notation.

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Answer:

it would be $12

Step-by-step explanation:

I used the equation y = (x / 100)y

To say that two variables are negatively correlatted means that when one variable increases, the other variable decreases.

Negative correlation refers to a relationship between two variables where they tend to move in opposite directions. When one variable increases, the other variable tends to decrease, and vice versa. This negative relationship indicates an inverse association between the two variables.

Option A, "When one variable increases, the other decreases," accurately describes negative correlation. As one variable increases, the other variable decreases, reflecting the negative relationship between them.

Negative correlation does not imply that both variables change at the same rate (Option D). In negative correlation, the relationship is characterized by the opposite direction of change, not necessarily the same magnitude or rate of change.

Option B, "When variable increases, the other also," suggests a positive correlation, where both variables move in the same direction. This is not the case in negative correlation.

Option C, "When one variable decreases, the other also decreases," is a misinterpretation of negative correlation. In negative correlation, when one variable decreases, the other variable tends to increase, not decrease.

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In probabilistic simulation, one or more of the independent variables follows certain probability distributions.

This is also known as Probabilistic Analysis. It is an analysis that tells or gives room for network assessment that is done using probabilistic input data.

Note that it is vital  when there is input parameters known to be random and as such, one or more of its independent variables follows a specific probability distributions.

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Answer:

(2/5)

Step-by-step explanation:

(-2/5) = -(2/5)

|-(2/5)| = (2/5)

The given statement mentions a large population that exhibits a bimodal distribution. Bimodal distribution means that the data has two distinct peaks or modes.

Additionally, it states that samples of size 40 are drawn from this population, resulting in a sampling distribution.

A sampling distribution refers to the distribution of a statistic, such as the mean or proportion, calculated from multiple samples drawn from the same population. In this case, samples of size 40 are drawn, which means that each sample consists of 40 observations from the population.

The statement does not provide specific details about the purpose or objective of analyzing the sampling distribution. However, studying the sampling distribution can provide valuable insights into the behavior and properties of the population. It allows researchers to make inferences about the population parameters based on the statistics calculated from the samples.

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Answer:105

Step-by-step explanation:

From the given diagram, we can identify two right-angled triangles. The triangles are shown below:

Using trigonometric ratios, we can find x as follows

We can equate the expressions for DF as follows:

Solving for x:

Answer:

x = 5

The perimeter of the given rectangle above which is QRST would be = 134.

Given that QT = 10 The Pythagorean formula should be used to calculate TS.

That is :

c² = a² + b²

where;

c = TS = ?

a=QS = 36√2

b = QT = 10

c² = (36√2)²+10²

= 2601+100

c =√2701

= 52

But QR = RS

using the sine rule;

a= QR=?

A= 45°

c= 36√2

C= 90°

a/sin45°=36√2/sin90°

That is;

a/sin45° = 51/1

a/0.707106781 = 51

a = 51×0.707106781

a= QR = RS = 36

The perimeter of the rectangle = 10+52+36+36 = 134

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The equation of the new function g(x) is g(x) = 2 - |x+2|

Transformation is. way of changing the position of an object on an xy-plane.

Given the parent function  f(x) = |x+3|.

If the function is translated 2 units down and 1 unit right, then the resulting function will be |x+3 - 1| - 2 which is equivalent to  |x+2| - 2

The reflection of the resulting function across the x-axis is given as:

g(x) = -(|x+2|-2)

g(x) = 2 - |x+2|

Hence the new function g(x) if the parent function undergo the transformation is g(x) = 2 - |x+2|

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Step-by-step explanation:

The answer is In the picture above