Joanne paid $28,000 for her new car. In addition, she paid $1,400 in taxes. What was the tax rate Joanne paid on her new car

Answer: 3

Step-by-step explanation:

The scale factor is the ratio of corresponding side lengths of the two triangles.

In the given triangles, the length of the corresponding sides of the triangles are:

For the first triangle:

Side A = 15 units

Side B = 15 units

For the second triangle:

Side A = 45/2 units

Side B = 45/2 units

To find the scale factor, we can divide the length of one side of the second triangle by the corresponding length of the first triangle.

For example, we can use Side A:

Scale factor = (length of Side A of the second triangle) / (length of Side A of the first triangle)

Scale factor = (45/2) / 15

Scale factor = (45/2) * (1/15)

Scale factor = 3/2

Since the two triangles are scaled copies of each other, the scale factor should be the same for all corresponding sides.

Thus, the scale factor is 3 (in simplest form).

When 94.7 g of neon gas undergoes isothermal contraction, there will be a decrease in entropy.

To explain why, we can start by recalling that entropy is a measure of the number of ways in which energy can be distributed among the particles of a system. When a gas undergoes isothermal contraction, its volume decreases while its temperature remains constant. This means that the particles in the gas are now more confined and have fewer ways in which they can move around. As a result, the energy of the particles becomes more constrained, which leads to a decrease in entropy.

To calculate the exact change in entropy, we would need to know more about the specifics of the contraction (such as the pressure and volume before and after). However, we can say with confidence that the change in entropy will be negative because the gas is becoming more ordered and its energy is becoming more constrained. Therefore, the change in entropy when 94.7 g of neon gas undergoes isothermal contraction will be negative.

Therefore, When 94.7 g of neon gas undergoes isothermal contraction, there will be a decrease in entropy.

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Step-by-step explanation:

mean value : the sum of the measurements of all 10 plants divided by 10 (the number of measurements).

A)

since the 2 measurement errors are compensating each other in the sum of measurements (-5 cm vs. +5 cm), the sum stays the same, the number of measurements stays the same (10), so the mean value stays the same (72 cm).

B)

the mean absolute deviation was the mean value of the absolute values of the differences of each measurement to the plant measurements.

since the mean value stayed the same, so did the difference of the 8 originally correct measurements to that mean value.

the only change is with the 2 corrected measurements.

the original (but wrong) measurement of 65 had a difference of 7 (to 72).

and now it is only 2 (70 to 72).

and the other one had a difference of 6 (72 to 78).

and now it is only 1 (73 to 72).

so, the sum of all the differences decreased by (7-2) + (6-1) = 5 + 5 = 10.

we had originally a mean absolute deviation of 8.5. the sum of all 10 original differences was therefore 8.5×10 = 85.

now this sum went down to 85-10 = 75.

and the new mean absolute deviation is 75/10 = 7.5.

Answer:

9 is divisable by 3.

A number that has 9 as a factor can be divided by 9 so it can also be divided by 3.

The dimensions of the rectangle are 8cm by 16cm

Remember that for a rectangle of length L and width W, the perimeter is.

P = 2*(L + W)

Here we know that:

L = 2*W

And that the perimeter is 48cm, so:

48cm = 2*(L + W)

So we have a system of equations:

L = 2*W

48cm = 2*(L + W)

Replacing the first equation in the second one, we will get:

48 cm = 2*(2W + W)

48cm = 6W

48cm/6 = W

8cm = W

And the length is:

L = 2W = 2*8cm = 16cm

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To find the surface area of the smaller pyramid, we can use the concept of similarity. The ratio of the base areas of the two pyramids is equal to the square of the ratio of their heights.

Let's call the height of the larger pyramid h1 and the height of the smaller pyramid h2. The ratio of their heights is h1/h2 = √(base area of larger pyramid/base area of smaller pyramid) = \(√(16 cm^2/12.2 cm^2).\)

Given that the surface area of the larger pyramid is 56 cm^2, we can find the surface area of the smaller pyramid by using the formula: surface area of smaller pyramid = (base area of smaller pyramid) * (height of smaller pyramid + (base perimeter of smaller pyramid * (h1/h2)) / 2.

Plugging in the values, we get: surface area of smaller pyramid =\(12.2 cm^2 * (h2 + (4 * h1/h2)) / 2.\)

We can simplify this equation to: surface area of smaller pyramid = \(12.2 cm^2 * (h2 + 2h1/h2).\)

To find the surface area of the smaller pyramid, we need to substitute the value of h1 and the given surface area of the larger pyramid into this equation. Unfortunately, the information given does not include the height of the larger pyramid. Therefore, we cannot determine the surface area of the smaller pyramid.

Regarding the second part of your question, without any information about the dimensions or properties of the other triangular prisms, it is impossible to determine which prism is similar to the described prism.

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The correct answer is the first Option i.e., 40.1 cm². The surface area of the smaller pyramid is approximately 40.1 cm². The surface area of a pyramid is found by adding the area of the base to the sum of the areas of the lateral faces. Since the two pyramids are similar, the ratio of their surface areas will be the square of the ratio of their corresponding side lengths.

Let's find the ratio of the side lengths first. The ratio of the base areas is given as 12.2 cm² : 16 cm². To find the ratio of the side lengths, we take the square root of this ratio.

    \(\sqrt {\frac{12.2}{16} } = \sqrt {0.7625} \approx 0.873\)

Now, we can find the surface area of the smaller pyramid using the ratio of the side lengths. We know the surface area of the larger pyramid is 56 cm², so we can set up the equation:

    (0.873)² × surface area of the smaller pyramid = 56 cm²

Solving for the surface area of the smaller pyramid:

    (0.873)² × surface area of the smaller pyramid = 56 cm²
=> Surface area of the smaller pyramid = 56 cm² / (0.873)²

Calculating this value:

    Surface area of the smaller pyramid ≈ 40.1 cm²

Therefore, the surface area of the smaller pyramid is approximately 40.1 cm².

In conclusion, the surface area of the smaller pyramid is approximately 40.1 cm².

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Answer:

B)

Step-by-step explanation:

This is hope i got it and it may or may not be helpful 10 divide by 430

a) √2 t |1, -1>

b ) t√0 |0, 1>=0

c) 2t² |1, -1> are the eigenstates of S² with the appropriate eigen value.

What is meant by eigen value?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it. The associated eigenvalue, generally indicated by lambda, is the factor by which the eigenvector is scaled.

Eigenvalues and eigenvectors play an important role in the analysis of linear transformations. The prefix eigen- comes from the German word eigen, which means "property," "characteristic," or "own."

a) S- |1,0>= t√(1+0)(1-0+1) |1, 0-1>

=t√2 |1, -1>

=√2 t |1, -1>

∴S±(s, m>=t√(s±m)(s±m+1) |s, m±1>

b) S₊ |0, 0>= t√(0-0)(0+0+1) |0, +1>

=t√0 |0, 1>=0

S₋ |0, 0>=t√(0+0)(0-0+1_) |0. -1>

c) S² |1, 1>= 1(1+1)t² |1, 1>

=2t² |1, -1>

∴ S² |s, m>=s(s+1)t² |s, m>

Hence, |1, -1> and |1, -1> are eigen function of S² with eigen value 2t²s.

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The given radical expression is (√x)^5. To rewrite it in rational exponent form, we need to express the square root (√) as a fractional exponent.

The square root (√) of x can be written as x^(1/2).

To raise x^(1/2) to the power of 5, we can multiply the exponents: (x^(1/2))^5 = x^(5/2).

Therefore, the radical expression (√x)^5 can be rewritten as x^(5/2) in rational exponent form.

In summary, (√x)^5 is equivalent to x^(5/2) in rational exponent form.

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Answer:

Step-by-step explanation:

favorable events ={5,6}

number of favorable events=2

P=2/6=1/3

Answer:

The equation of the line is;

Explanation:

Given that

the slope of a line is -2 and it passes through the point (4,-5).

Applying the slope-intercept form of equation;

Substituting the values of the slope and coordinates;

Therefore, the equation of the line is;

Answer:

2x + y = 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 5 ) into the partial equation

- 5 = - 8 + c ⇒ c = - 5 + 8 = 3

y = - 2x + 3 ← in slope- intercept form

add 2x to both sides

2x + y = 3 ← equation in standard form

Answer:

the answer should be, A. im pretty good at this kind of thing so It should be right but if not, sorry.

Step-by-step explanation:

The polynomial correctly combines the like terms and puts the given polynomial in standard form is \(\rm 8x^6+ 8x^4y^2 - 5x^3y^3 +x^2y^4 -7xy^5.\)

The correct option is D.

Given

Expression; \(\rm -5x3y^3 + 8x4y^2 - xy^5 - 2x2y^4 + 8x^6 + 3x^2y^4 - 6xy^5\)

A polynomial is an expression consisting of coefficients and variables which are also known as indeterminates.

We have to combine the like terms which means the terms with the same degree.

Therefore,

The correctly combines the like terms;

\(\rm =-5x^3y^3 + 8x^4y^2 - xy^5 - 2x^2y^4 + 8x^6 + 3x^2y^4 - 6xy^5\\\\=8x^6 +8x^4y^2--5x^3y^3+ 3x^2y^4- 2x^2y^4 - xy^5 -6xy^5\\\\= 8x^6+ 8x^4y^2 - 5x^3y^3 +x^2y^4 -7xy^5.\)

Hence, the polynomial correctly combines the like terms and puts the given polynomial in standard form is \(\rm 8x^6+ 8x^4y^2 - 5x^3y^3 +x^2y^4 -7xy^5.\)

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

For the values of x , the corresponding values of y are :

The reasonable domain for this function is 0 < x < 50

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Given;

A = 50W - W2

The area of a rectangle cannot be negative;

The practical domain of A is determined when;

50W-W^2>0

Taking common factor W

W(50-W)>0

Since W must be positive W>0

50-W>0

Or equivalently

50>w

W<50

The total interval is

0<W<50

Therefore, the domain of the function will be 0 < x < 50

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Answer:

The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

Step-by-step explanation:

umm....I really hope this helps u

Answer:

\(\large\fbox{\green{\underline{Cylinder P :- \blue{ 794.0275 in ³}}}}\)

\(\large\fbox{\green{\underline{Cylinder Q :- \blue{1,307.81 in³}}}}\)

Step-by-step explanation:

Volume of cylinder = π × ( radius ) ² × h

1.) Here, radius = 4.25 in and height = 14 in.

Volume of cylinder = π × ( radius ) ² × height

substitute the values

Volume of cylinder P = 3.14 × ( 4.25 in ) ²×14 in.

now, simplify

= 3.14 × 18.0625 in²× 14 in.

= 3.14 × 252.875 in³

multiplying the value

= 794.0275 in³

\( \small \: \: \sf \: \fbox{ cirumference \: of \: cylinder \: P \: = {794.0275 in³}}\)

2.) Here, radius = 7 in. and height = 8.5 in.

Volume of cylinder Q = π × ( radius ) ² × height

substitute the values

Volume of cylinder Q = 3.14 × ( 7 in )² × 8.5 in.

Simplify

= 3.14 × 49 in² × 8.5 in.

multiply the values

= 3.14 × 416.5 in³

\( \small \sf \fbox{Volume of cylinder Q = 1,307.81 in ³}\)

Answer:

A formula to express this would be:

60 = 32 + 4h

This simplifies down to 7 for h

The signal will be transmitted approximately 25km before the power drops to 20μW.

To find the distance at which the signal power is attenuated to 20μW, we need to determine how many times the power drops by a factor of 10 until it reaches that level. Given that the power drops by a factor of 10 approximately every 2.5km, we can create a table to track the signal power vs. distance.

Let's calculate the table:

Distance (km) Signal Power (W)

0 0.2

2.5 0.2 * 10^(-2)

5 0.2 * 10^(-4)

7.5 0.2 * 10^(-6)

10 0.2 * 10^(-8)

12.5 0.2 * 10^(-10)

15 0.2 * 10^(-12)

...

We can see that the signal power decreases by a factor of 10 for every 2.5km increment. Since we want to find the distance at which the power is attenuated to 20μW (0.2 * 10^(-5) W), we can observe from the table that this occurs at 25km

If optical fiber were used instead of coaxial cable, we would expect the calculated distance value to increase. This is because optical fiber has lower signal attenuation compared to coaxial cable, meaning the signal can travel a longer distance before the power drops to a certain level. Optical fibers have lower signal loss due to the use of light signals that experience less interference and degradation compared to electrical signals in coaxial cables.

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Answer:linear

Step-by-step explanation:

To find the number of elements in the intersection of two sets, we can use the formula derived from the inclusion-exclusion principle. In this case, we are given the number of elements in sets J and K, as well as the number of elements in their union. Using these values, we can calculate the number of elements in the intersection of sets J and K.

The inclusion-exclusion principle states that to find the number of elements in the intersection of two sets, we need to add the number of elements in each set separately and then subtract the number of elements in their union to avoid double counting.

In this case, we are given that n(J) = 205, n(K) = 180, and n(J ∪ K) = 359. To find n(J ∩ K), we can rearrange the formula as follows:

n(J ∩ K) = n(J) + n(K) - n(J ∪ K)

Substituting the given values, we have:

n(J ∩ K) = 205 + 180 - 359 = 26

Therefore, the number of elements in the intersection of sets J and K is 26.

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2/9 ÷ 1/2 gives you 4/9 , hope this helps you

Answer: The answer to this basic math question about dividing the basic fractions with 2 given basic fractions is \(\frac{4}{9}.\)

Step-by-step explanation: As always to remember, dividing 2 fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction, so here are 2 basic steps in order to divide 2 given basic fractions:

Step 1. First, let's take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication that looks in the equation form like this: \(\frac{2}{9}*\frac{1}{2}=?\)

Step 2. Last but not least is fraction multiplication, for fraction multiplication, let's multiply both numerators and the denominators that looks in the equation form like this: \(\frac{2*2}{9*1}=\frac{4}{9}.\)

Hence, this fraction can't be reduced, so therefore, your answer to this basic math question about dividing the basic fractions with 2 given basic fractions is \(\frac{4}{9}.\)

I hoped that my full given basic answer with my full given basic step-by-step explanation is very helpful to your own math question about dividing the basic fractions with 2 given basic fractions, please mark me as Brainliest, take care, always be safe, and have a great rest of the weekend! :D

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The larger number is 51, and the smaller number is 33.

Let's represent the larger number as 'x' and the smaller number as 'y.' According to the given information, the difference between the two numbers is 18. Mathematically, this can be expressed as x - y = 18.

The sum of the two numbers is given as 84, which can be expressed as x + y = 84. Now we have a system of two equations:

Equation 1: x - y = 18

Equation 2: x + y = 84

To solve this system of equations, we can use a method called elimination. Adding Equation 1 and Equation 2 eliminates the 'y' variable, resulting in 2x = 102. Dividing both sides of the equation by 2 gives us x = 51.

Substituting the value of x back into Equation 2, we can find the value of y. Plugging in x = 51, we have 51 + y = 84. Solving for y, we find y = 33.

Therefore, the larger number is 51, and the smaller number is 33.

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Answer:

width is 3 inches, length is 11 inches.

Step-by-step explanation:

Let l be the length and w be the width.

We have:

\(l = 2w + 5\)

\((2w + 5)(w) = 33\)

\(2 {w}^{2} + 5w = 33\)

\(2 {w}^{2} + 5w - 33 = 0\)

\((w - 3)(2w + 11) = 0\)

\(w = 3\)

\(l = 2(3) + 5 = 11\)

Solution:

Let's make,

mechanic #1's rate = x

mechanic #2's rate = y

Note that their rate is dollars per hour.

Now, mechanic #1 worked for 20 hours. Then, we get the following equation:

20x = money earned by mechanic #1

On the other hand, mechanic #2 worked for 15 hours. Then, we get the following equation:

15y = money earned by mechanic #2

together they charged a total of $2250. So the amount of money earned by both mechanics is:

20x + 15y = 2250 EQUATION 1

On the other hand, the sum of the two rates was:

x + y = 125 EQUATION 2

From the equation, if we solve for x, we get:

x = 125-y EQUATION 3

plug (125-y) in for "x" in equation 1 to get everything in terms of one variable:

20(125-y)+15y = 2250

this is equivalent to

2500-20y +15y = 2250

this is equivalent to

2500 -5y = 2250

this is equivalent to

-5y = 2250 -2500

this is equivalent to:

-5y = -250

or

5y = 250

solving for y, we get:

now, replacing this into equation 3, we get:

x = 125-y = 125 - (50) = 75

so that, we can conclude that the correct answer is:

mechanic #1 charged 75 $/hr

mechanic #2 charged 50 $/hr

Answer:

b

Step-by-step explanation: