Rosa paid $107.40 for 12 audio books that were all the same price. Which is the best estimate of the cost of each audio book?

Answer:

6%

Step-by-step explanation:

for this is divided the fee by the price of the item.

To prove that AC ≅ BD in square ABCD, we can use the properties of a square:

Given: Square ABCD

To prove: AC ≅ BD

Proof:

Since ABCD is a square, all sides are congruent.

Therefore, AB ≅ BC ≅ CD ≅ AD (by definition of a square).

AC is a diagonal of square ABCD.

BD is also a diagonal of square ABCD.

Diagonals of a square are congruent and bisect each other.

Therefore, AC ≅ BD (by the properties of diagonals in a square).

Thus, we have proved that AC ≅ BD in square ABCD, showing that the diagonals are congruent and bisect each other.

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An equation describing r as a function of A and π is r = √(A/π).

Mathematically, the area of a circle can be calculated by using this formula:

A = πr²

Where:

In this exercise, you are required to make "r" the subject of the formula in the given mathematical expression by using the following steps.

By dividing both sides of the mathematical expression by π, we have the following:

r² = A/π

By taking the square root, we have:

r = √(A/π)

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Complete Question:

Make r the subject: A = πr²

The x-intercepts of the graph are -5 and 3.

There are a few steps involved in sketching the graph and finding the x-intercepts. Here are the steps:
Step 1: Turn on your graphing calculator and enter the equation y = x^2 + 2x - 15. Make sure to use the "^" symbol to indicate exponents.
Step 2: Once you have entered the equation, press the graph button to see the graph on your screen. You should see a parabola (a U-shaped curve) that opens upwards.
Step 3: Take a closer look at the graph and try to estimate the x-intercepts. These are the points where the graph crosses the x-axis, meaning that y = 0 at those points. To estimate the x-intercepts, you can look for the points where the graph touches or crosses the x-axis. You can also use the trace function on your calculator to get more accurate values.
Step 4: To find the x-intercepts more precisely, you can use the quadratic formula. The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, the equation is y = x^2 + 2x - 15, which means that a = 1, b = 2, and c = -15. Plugging these values into the quadratic formula, we get:
x = (-2 ± sqrt(2^2 - 4(1)(-15))) / 2(1)
Simplifying this expression, we get:
x = (-2 ± sqrt(64)) / 2
x = (-2 ± 8) / 2
x = -5 or 3
So the x-intercepts of the graph are -5 and 3.
Step 5: Once you have found the x-intercepts, you can mark them on the graph by drawing vertical lines through those points. This will help you visualize the shape of the parabola and understand how it intersects with the x-axis.

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Answer:

Appropriate weight gain for a pregnant woman with a BMI of 17 is 28-40 pounds. Appropriate weight gain for a pregnant woman with a BMI of 32 is 11-20 pounds.

Step-by-step explanation:

Answer:

Step-by-step explanation:

X=5      2x+y=10

you already have x

just need to find y

2x+ y=10

2 (5)+y=10

10 + y=10

y=10- 10 ( when you change the number place the sign should change too, if it was - it will turn +)

y=10-10

y=0

(5,0)

I really hope it work

The probability The odds for E are: 0.13 The odds against E are: 0.87.

When two events are mutually exclusive, it means that they cannot happen at the same time. Therefore, the probability of their union (E U F) is simply the sum of their individual probabilities:
P(E U F) = P(E) + P(F)
We are given that P(F) = 0.55 and P(E U F) = 0.85, so we can use the above equation to solve for P(E):
0.85 = P(E) + 0.55
P(E) = 0.3
Now, to find the odds for E, we need to use the formula:
odds for E = P(E) / (1 - P(E))
Substituting the value of P(E) that we just found, we get:
odds for E = 0.3 / (1 - 0.3) = 0.43
To find the odds against E, we simply subtract the odds for E from 1:
odds against E = 1 - odds for E = 1 - 0.43 = 0.57
Therefore, the answers to the given problem are:
The odds for E are: 0.43
The odds against E are: 0.57
Using the same method for the second problem, we get:
P(E) = 0.12
odds for E = 0.13
odds against E = 0.87

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A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

a. 5 hours

b. 40 kph

Step-by-step explanation:

300 km ÷ 60 km = 5 hours

200 km ÷ 5 hours = 40 kilometers per hour

The equation for Jayden's paycheck is,

$9.64h+ 82.35= $14.86h+ $17.10

How to construct an algebraic equation?

STEPS TO CONSTRUCT AN ALGEBRAIC EQUATION---

let the number of hours Jayden works be h hours.

so, Jayden has got the total from the jewelry store is,,$9.64h+ 82.35

Jayden has got the total from the sales bonuses is,  $14.86h+ $17.10

so, the total paycheck from the jewelry store is,,$9.64h+ 82.35

and from the sales bonuses is $14.86h+ $17.10.

as they are equal, the equation is, $9.64h+ 82.35= $14.86h+ $17.10

Hence, the equation is,$9.64h+ 82.35= $14.86h+ $17.10

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Answer:

0.5km/h

Step-by-step explanation:

Assume lake has no current.

.

V=distance / time

V=39km / 3h

V=13km/h

In water Assume boat used same power travelling

V=35km / 2h

V= 12.5km/h

Current is the difference 0.5km/h

The maximum value of the function f(x) = 1 + n*sin(x) with an amplitude of 4 = 5.

To find the maximum value of function f(x) = 1 + n*sin(x), we need to consider the amplitude and the function's equation.

The amplitude of a sine function is the distance from the maximum or minimum point to the midline (which is the average value of the function). In this case, the amplitude is given as 4.

Since the function is f(x) = 1 + n*sin(x), the midline is y = 1. To find the maximum value of f, we need to add the amplitude to the midline:

Maximum value of f = midline + amplitude
Maximum value of f = 1 + 4
Maximum value of f = 5

Therefore, we can state that the maximum value of the function f(x) = 1 + n*sin(x) with an amplitude of 4 is 5.

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Answer:

ok so the answer is:

6x + 4y= 4   --->  y = -3/2x + 1

12y = -3x + 4  ---> y = -1/4x + 1/6

happy to help!

Answer:

x-intercept = (38/7,0) y-intercept= (0,-38)

Answer:

f = -6g/5

Step-by-step explanation:

6f + 9g = 3g + f

combine like terms

6f -f = 3g - 9g

5f = -6g

divide both sides of the equation by 5

f = -6g/5

Answer:

f= -6/5.      aka].  answer B

Step-by-step explanation:

Yes, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Here,

The differential equation (1-xy)y' = y^2

And,  y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

To show y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2, we have to find the solution of differential equation.

The differential equation is;

\((1-xy)y'=y^2\\\\\\\\\)

\((1-xy) \frac{dy}{dx} = y^2\)

\(\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }\)

It is form of  \(\frac{dx}{dy} + Px = Qy\),

Where, P is the function of y and Q is the function of x.

Hence, Integrating factor = \(e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y\)

The solution is;

\(x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c\)

\(xy = lny + c\)

Take c = 0, we get;

\(xy = lny\\\\y = e^{xy}\)

Hence, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

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Answer:

quotient: 7084

remainder: 5

Step-by-step explanation:

1.they should divide each person into 3 teams

Answer: 280

Step-by-step explanation: So you have 9 people. One out of those 9 people could go in any of the spots for participants. You could start off with 9*8*7 because you want to work your way down and it doesn't matter which order but just the number of people in each group. 9*8*7 is one group, 6*5*4 is the second group and 3*2*1 is the third group. Now, you want to take each of those equations and divide them by 3!. You do this because there are 3 teams and 9 people are being distributed between them.

9*8*7                        6*5*4                            3*2*1

--------     = 84         -----------     =20 and      -----------  =1

 3!                              3!                                   3!

Now that you have 84, 20 and 1, you multiply them and once again divide the product by 3! or cancel. You will get 14*20*1 =280

Hope it helps!

Answer:

Option (4)

Step-by-step explanation:

Given equation of the linear graph is,

\(y=-\frac{5}{8}x+\frac{2}{3}n\)

By comparing this equation with the slope-intercept form of the linear equation,

y = mx + b

m = \(-\frac{5}{8}\)

And b = \(\frac{2}{3}n\)

Since, y-intercept 'b' = -12 [given]

\(\frac{2}{3}n=-12\)

n = \(-12\times \frac{2}{3}\)

n = -8

Therefore, Option (4) will be the answer.

Answer:

5 he'll pay

Step-by-step explanation:

Answer:

496 + 2 (115) = 496 + 230

Step-by-step explanation:

The standard deviation uses the mean, which is 496 in this example. About 95% of the data falls withinTWO standard deviations from the mean. Double 115 and you get 230.

Answer is 496 + 2 (115) = 496 + 230

The property of circumcircle is that the circumcircle always passes through all three vertices of a triangle.

A circumcircle is a circle that traverses a triangle's three vertices. It is also known as a "circumscribed circle." Every triangle's three vertices fall within the circumcircle.

The object's Center is defined as the point at where all of the triangle's perpendicular bisectors intersect. The circumcenter is the name of this Centre. The triangle's triangle might have its  Centre within or outside the circle. The radius of the circumcircle is also known as the triangle's circumradius. In a right triangle, the Centre is located precisely at the midpoint of the hypotenuse, and the hypotenuse is a diameter of the circumcircle.

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a) |α⟩ is normalized if α = |α|² and α is a positive real number.

b) |α⟩ is an eigenvector of the lowering operator with eigenvalue λ = |α|.

c) |α⟩ is also an eigenvector of the transpose operator t with eigenvalue μ = |α|.

d) The eigenvalue of |α⟩ with respect to t is μ = |α|.

a) To show that |α⟩ is normalized, we need to compute its norm, which is given by ⟨α|α⟩. Let's calculate it:

⟨α|α⟩ = e(-|α|²) ∑n=0 [infinity] (n!/\(\alpha^n\) ∑m=0 [infinity] (m!/\(\alpha^m\)) ⟨n|m⟩

Since the states |n⟩ form an orthonormal basis, ⟨n|m⟩ = δ_n,m (Kronecker delta), which equals 1 when n = m and 0 otherwise. Therefore, the sum simplifies to:

⟨α|α⟩ = e(-|α|²) ∑n=0 [oo] (n!/αⁿ)

Using the identity eˣ = ∑k=0 [infinity] (\(x^k\) / k!), we can rewrite the sum as:

⟨α|α⟩ = e(-|α|²) \(e^\alpha\) = e(α - |α|²)

Now, to show that |α⟩ is normalized, we need to confirm that ⟨α|α⟩ = 1:

e(α - |α|²) = 1

This equation holds true when α - |α|² = 0, which implies that α = |α|². Since α is a complex number, we can write it as α = |α|e(iθ). Substituting this into the equation, we get:

|α|e(iθ) = |α|²

Dividing both sides by |α|, we obtain:

e(iθ) = |α|

This equation is satisfied when θ = 0, which means α is a positive real number. Therefore, |α⟩ is normalized.

b) To show that |α⟩ is an eigenvector of the lowering operator, we need to demonstrate that a|α⟩ = λ|α⟩, where a is the lowering operator. The lowering operator is defined as a = ∑n=0 [oo] √(n+1) |n⟩⟨n+1|.

Let's compute a|α⟩:

a|α⟩ = ∑n=0 [oo] √(n+1) |n⟩⟨n+1| (\(e^{-1/2}\)|α|²/2 ∑m=0 [infinity] (m!/α) |m⟩)

We can interchange the order of the sums and use the property of the Kronecker delta to simplify the expression:

a|α⟩ = ∑n=0 [oo] √(n+1) (e(-1/2)|α|²/2 (n+1)!/αⁿ⁺¹) |n⟩

Next, we can factor out the common terms:

a|α⟩ = (\(e^{-1/2}\)|α|²/2) ∑n=0 [oo] √(n+1) (n+1)!/αⁿ⁺¹ |n⟩

Now, notice that the term in the sum is precisely the coefficient of αⁿ in the series expansion of eᵃ. Therefore, we can rewrite the expression as:

a|α⟩ = (\(e^{-1/2}\)|α|²/2) eᵃ |α⟩

Since |α⟩ is defined as \(e^{-1/2}\)|α|²/2 ∑n=0 [oo] (n!/αⁿ) |n⟩, we can simplify further:

a|α⟩ = |α| |α⟩

Therefore, we have shown that |α⟩ is an eigenvector of the lowering operator with eigenvalue λ = |α|.

c) To show that |α⟩ is an eigenvector of the t operator, we need to demonstrate that t |α⟩ = μ |α⟩, where t is the transpose operator.

The transpose operator acts on the ket vectors by taking the complex conjugate of their components. Therefore, we have:

t |α⟩ = (t \(e^{-1/2}\)|α|²/2) ∑n=0 [oo] (n!/αⁿ) (t |n⟩)

Since the transpose of |n⟩ is its bra vector, we can write:

t |α⟩ = (t \(e^{-1/2}\)|α|²/2) ∑n=0 [oo] (n!/αⁿ) ⟨n|

Now, using the definition of the transpose of a complex number, we have:

t |α⟩ = (\(e^{-1/2}\))|α|²/2) ∑n=0 [oo] (n!/αⁿ) ⟨n|

Finally, notice that the expression inside the sum is the same as the coefficient of αⁿ in the series expansion of eᵃ. Therefore, we can simplify further:

t |α⟩ = (\(e^{-1/2}\)|α|²/2) eᵃ ∑n=0 [oo] (n!/αⁿ) ⟨n|

Since |α⟩ is defined as \(e^{-1/2}\)|α|²/2 ∑n=0 [oo] (n!/αⁿ) |n⟩, we can rewrite the expression as:

t |α⟩ = |α| |α⟩

Therefore, |α⟩ is an eigenvector of the t operator with eigenvalue μ = |α|.

d) The eigenvalue of |α⟩ with respect to the t operator is μ = |α|.

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Answer:

numbers

Step-by-step explanation:

numbers

Answer:

4(x+3)-10+6x

4x+12-10+6x

10x+2

hope this helps

have a good day :)

Step-by-step explanation:

Jordan scored a total of 4.4 points on all five tests combined. Therefore, Jordan needs a score of 1 point on the sixth test to achieve an average of 90% over all six tests.

a. To find the total score Jordan received on all five tests, we can multiply his mean score (88%) by the total number of tests (5). The calculation is as follows:

Total score = Mean score x Number of tests

Total score = 88% x 5

To calculate the total score, we convert 88% to its decimal form by dividing it by 100:

Total score = 0.88 x 5 = 4.4

Therefore, Jordan scored a total of 4.4 points on all five tests combined.

b. To calculate the score Jordan needs on the sixth test to achieve an average of 90%, we need to consider the total number of tests and the desired average.

Let's assume the sixth test is worth 100 points (as the previous tests were). Jordan's goal is to have an average of 90% over the six tests.

To find the score he needs on the sixth test, we can set up the following equation:

(4.4 + x) / 6 = 90%

Here, x represents the score on the sixth test. We multiply the average by the total number of tests to find the sum of all scores. Solving the equation:

4.4 + x = 6 * 0.90

4.4 + x = 5.4

x = 5.4 - 4.4

x = 1

Therefore, Jordan needs a score of 1 point on the sixth test to achieve an average of 90% over all six tests.

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