At Garcia's Bike Rentals, it costs $33 to rent a bike for 6 hours.
How many dollars does it cost per hour of bike use?

Sonny get 240=240 because  the cross products of the proportion are equal.

Proportion : Two ratios are said to be in proportion when the two ratios are equal.

For Example , If Smith walks 5 km in 1 hour then he will walk 25 km in 5 hours. denoted by

\(\frac{5}{1} =\frac{25}{5} \\ \\ 5=5\).

According to the given question the equation can be written as

\(\frac{16}{x} =\frac{48}{15}\)

Sonny substituted 5 for x in the proportion , the equation can be written as

\(\frac{16}{5} =\frac{48}{15} \\ \\ Doing .the .cross.product\\ \\ 16*15=48*5\\ \\ 240=240\)

Therefore , Sonny get 240=240 because  the cross products of the proportion are equal.

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The average is calculated by adding up all the data sets, then dividing that total by the total number of data points. She used 6 gallons of gas on her trip.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The two unit rates of (30 miles per gallon) and can be used to convert three hours to gallons of gas (60 miles per hour).

30 miles = 1 gallon of gas used

For (30 × 2) 60 miles = 2 gallons of gas used

2 gallons of gas she used per hour.

Susan goes 180 miles in 3 hours (60 miles per hour).

Therefore,

For 3 hrs = 3 × 2 = 6 gallons of gas used.

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Answer:

3.37

Step-by-step explanation:

Answer:

2−12x+36

Step-by-step explanation:

Answer:

(x-6)² = (x-6)(x-6) = x² - 12x + 36

Step-by-step explanation:

Answer:

6/12 = 1/2

Step-by-step explanation:

One dice has 3 even and 3 odd numbers. Since there are two dice there will be 6 even and 6 odd. Therefore, the probability of getting an odd number is 1/2

Answer: I believe 90 degrees

Step-by-step explanation: Please give brainliest if correct

The statement "If two lines intersect to form congruent adjacent angles, then the lines are perpendicular" is sometimes true.

Explanation:

When two lines intersect, they form two pairs of adjacent angles. If these adjacent angles are congruent (i.e., have the same measure), it is possible for the lines to be perpendicular. In this case, the statement is true.

However, it is also possible for the lines to intersect and form congruent adjacent angles without being perpendicular. This occurs when the lines are not perpendicular but are instead parallel or at an angle other than 90 degrees. In these cases, the statement is false.

Therefore, the statement is sometimes true, depending on the specific configuration of the intersecting lines.

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Answer:

-2.4x + 7.12x = -14.16

4.72x = -14.16

x = -3

Step-by-step explanation:

hope this helps :)

Answer:

0

Step-by-step explanation:

(-321) * {603 * 0   } = [(-321)*  0 ] * 603 = 0

Property :  Associative property of multiplication

Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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f(x) = (x - 5)² + 7

Translations are transformations that change the position of the graph of a function. The general shape of the graph of a function translates up, down, to the right, or to the left.

Vertical translations:

Let k > 0:

To graph y = f (x) + k, shift the graph up k units.

To graph y = f (x) -k, shift the graph of k units down.

Horizontal translations:

Let w>0

To graph y = f (x-w), shift the graph w units to the right.

To graph y = f (x + w), shift the graph w units to the left.

Let:

f(x) = x²

Shift f(x) 7 units up:

f(x) = x² + 7

And shift f(x) 5 units to the right:

f(x) = (x - 5)² + 7

Answer:

9/3

Step-by-step explanation:

12x43=168

168 divided by 56=3

Answer:

the Volume is 33.51

To find the value of the sculpture in 9 years, we can use the formula for compound interest:

V = P * (1 + r/100)^t

where V is the final value, P is the initial value (37,000), r is the annual interest rate (3.5%), and t is the number of years (9).

Plugging in the values into the formula, we get:

V = 37,000 * (1 + 3.5/100)^9

= 37,000 * 1.0355^9

= 37,000 * 1.978044

= approximately 73,656.78

So, the sculpture will be worth approximately 73,656.78 in 9 years if the owner's estimate is correct and its value increases by 3.5% every year.

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After Sophia finished her portion of the party's pizza, there was still half of it.

The equation 2/5p = 1/2 can be used to find the total number of pizzas left over from the party, where p is the total number of pizzas. We can solve for p as follows:

2/5p = 1/2

Multiplying both sides by 5/2, we get:

p = (5/2) * (1/2) = 5/4

Therefore, there were a total of 5/4 pizzas left over from the celebration. However, we are aware that Sophia carried home 2/5 of the leftover pizza, which equates to half of a full pizza.

So, using the following formula, we can determine the quantity that is left over:

2/5 * (5/4) = 1/2

2/4 = 1/2

So there was 1/2 of a pizza left over from the party after Sophia took her share.

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Answer:

The answer is below

Step-by-step explanation:

A square pyramid is a pyramid with a square base. Therefore it is composed of 4 identical triangles and a square base.

From the image attached:

Area of each of the triangle = (1/2) * 3 m * 4.5 m = 6.75 m²

Area of base = 3 m * 3 m = 9 m²

Since the sides are covered in blue fabric, hence:

Surface area of blue fabric = 4 * area of each triangle = 4 * 6.75 m² = 27 m²

The base is covered with brown fabric, hence Surface area of brown fabric = 4 * area of each triangle = 4 * 9 m² = 36 m²

Answer:

20

Step-by-step explanation:

Answer: -2.4

Step-by-step explanation:

When you do -8/3 you're dividing so it would just come out as -2.6

Answer:

9

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

-14.4

Step-by-step explanation:

-6x(-0.6)x(-4)= -14.4

\( - \frac{6(5 - 2x)}{5x} \)

i hope its help

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Since we are working with an equation written in scientific notation and we are dealing with a negative exponent, we are going to divide 4.7 by 10 three times.

4.7 / 10 = 0.47

0.47 / 10 = 0.047

0.047 / 10 = 0.0047

Best of Luck!

Answer:

7x is the slope,9 is the y-intercept

Step-by-step explanation:

7x is the constant/unit rate,9 is what gets added after which makes the expression non-proportional.

Answer:

Step-by-step explanation:

Can you write it in lines instead of like that, I can answer if you do that.

Answer:

yes is rhe anwers that was that i put