what is the solution to the system of equation below Y equals -1/3 X +6 and X equals -6

Answer:

$38.40 × 1.06 = $40.70 before tip

$40.70 × .15 = $6.11 tip

The tip on a restaurant bill that comes to $38.40 before tax and tip, with a 6% tax added and a 15% tip included, is $6.11.

To solve this problem, we need to first calculate the total cost of the meal with tax.

The tax is calculated by multiplying the pre-tax amount ($38.40) by the tax rate (6% expressed as a decimal, which is 0.06):

Tax = $38.40 x 0.06 = $2.30

So the total cost of the meal with tax is:

Total cost = $38.40 + $2.30 = $40.70

Next, we need to calculate the amount of the tip by multiplying the total cost by the tip rate (15% expressed as a decimal, which is 0.15):

Tip = $40.70 x 0.15 = $6.11

Therefore, the tip amount is $6.11.

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Answer:

x = \(\sqrt{13}\) or 3.61 to 3 significant figures

Step-by-step explanation:

First find CD which is \(\sqrt{5^{2}-3^{2} }\) = 4

6 - 4 = 2 which is FC

so do \(\sqrt{2^{2}+3^{2} }\) = \(\sqrt{13}\) or 3.61 to 3 significant figures

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Explanation:

The decrease is 0.4 million since 3.2 - 2.8 = 0.4

Divide this decrease over the initial population

0.4/3.2 = 0.125

This converts to 12.5% when you move the decimal 2 spots to the right.

The population decreased by 12.5%

Answer:

unbiased, I think

Step-by-step explanation:

Answer:

it is unbiasied i think....

The clock will represent 4.5 billion years as 2.67 hours.

Its numerals and the movement of the hour and minute hands on the clock also help us keep track of hours and hours. Example: Calculate the number of hours elapsed from clock A to clock B.

Data provided in the question:

Total time of history of Earth = 4.5 billion years

Representation of total time of history of Earth on clock = 12 hours

Therefore,

4.5 billion years = 12 hours

or

⇒ 1 billion year = 12 hours/4.5

or

⇒ 1 billion year = 2.67 hours

Hence,

the clock will represent 4.5 billion years as 2.67 hours.

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Answer:

  x ∈ {−2.18723​509003, 1.687​23509003}

Step-by-step explanation:

You want the value of x that satisfies the equation (4x +2)(x -1)(3x)(2x +3) = 194.

The fact that 194 is not divisible by 3 means the real solutions will not be integer values, likely irrational. A graphical solution and some iterations tell us the solutions are ...

  x = −2.18723​509003

or

  x = 1.687​23509003

__

Additional comment

The product has units of square meters, so we presume these dimensions come in pairs of factors. It appears that both the positive and negative values of x will give factors pairs that have a positive product.

Any rational solutions would be multiples of 1/24. These solutions are not rational.

Answer:x − x^{2} − 1.

Step-by-step explanation:

.

Answer:

The required range is \(7<C<23\).

Step-by-step explanation:

Consider the provided information.

Let the side A = 15 and the side B = 8

Theorem 1: For a triangle with sides A, B, and C the sum of the lengths of any two sides of a triangle must be greater than the third side:

\(A+B>C\) ....(1)

\(B+C>A\)  ...(2)

\(A+C>B\)  ....(3)

By using equations 1 and 2.

Therefore, \(A-B<C<A+B\)

\(15-8<C<15+8\)

\(7<C<123\)

Hence, the required range is \(7<C<23\).

Answer:

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Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Hypothesis tests can provide evidence against the null hypothesis but cannot conclusively prove it, as they can suggest if a scale might be out of calibration, but cannot demonstrate it with absolute certainty.

What are the limitations of hypothesis tests in determining the true calibration of a scale and why can't they conclusively prove the null hypothesis to be true?

It is not possible to demonstrate conclusively that the scale is in calibration using a hypothesis test. Hypothesis tests, including the one stated with H0 : μ = 9 and H1 : μ ≠ 9, can only provide evidence against the null hypothesis (H0) if the test results are statistically significant. However, hypothesis tests cannot definitively prove the null hypothesis to be true.

How does a hypothesis test help in determining the calibration of a scale?
In this scenario, a hypothesis test can help determine whether there's enough evidence to reject the null hypothesis, which would suggest that the scale may not be in calibration. However, if the test results are not statistically significant, it doesn't prove that the scale is perfectly calibrated; it only indicates that there is not enough evidence to reject the null hypothesis.
To summarize, hypothesis tests can provide evidence against the null hypothesis, but they cannot prove it conclusively. In the case of checking the calibration of a scale, a hypothesis test can suggest whether the scale might be out of calibration, but it cannot demonstrate with absolute certainty that the scale is in calibration.

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Answer:

first one

Step-by-step explanation:

Answer:

Therefore, required equation is N = 100 x \(2^{- \frac{t}{5730 }\)

Step-by-step explanation:

According to the question it is given that

Amount of carbon atom when animal was alive is \(N_0\) =  100g

Half life of C-14 is 5730 years

Let 'N' be the amount of carbon atom present after 't' time

since the differential equation of decay process of radioactive atom is

\(\frac{dN}{dt} = \lambda N\) where, λ is the decay constant

on solving this we get

\(N = N_0 e^{-\lambda t}\)

on further solving and substituting \(\lambda = \frac{ln2}{T_{1/2}}\) we get

\(N = N_0 2^{- \frac{t}{T_{1/2}} }\)

on substituting the value of  \(N_0\) =  100g and \(T_{1/2}\) = 5730 we get

N = 100 x \(2^{- \frac{t}{5730 }\)

The direct and Inverse variation relationship,x = 2 and z = 1, the value of y is 12.

the direct and inverse variation relationship:

y = k * (x^2) / z

where k is the constant of variation.

Given that y = 4 when x = 4 and z = 12, we can substitute these values into the equation:

4 = k * (4^2) / 12

Simplifying, we have:

4 = k * 16 / 12

To solve for k, we can cross-multiply and divide:

4 * 12 = k * 16

48 = 16k

Dividing both sides by 16:

48 / 16 = k

k = 3

Now that we have determined the value of k, we can use it to find y when x = 2 and z = 1.

Substituting these values into the equation, we have:

y = 3 * (2^2) / 1

Simplifying further

y = 3 * 4 / 1

y = 12

Therefore, when x = 2 and z = 1, the value of y is 12.

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P ( A or B ) ≠ P(A) + P(B) Hence, A and B are not mutually exclusive.

therefore the given condition is not true and hence statement is not true for the given events

Two events are called mutually exclusive they are independent to each other.

Also, If A and B are any two events,

Then they are called mutually exclusive,

If P(A ∪ B ) = P(A) + P(B)

Or P ( A or B ) = P(A) + P(B)

Here, P(A) = 0.37, P(B) = 0.38 and P(A or B) = 0.27

Since,

0.27 ≠ 0.37 + 0.38

⇒  P ( A or B ) ≠ P(A) + P(B)

Hence, A and B are not mutually exclusive.

therefore the given condition is not true and hence statement is not true

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The quotient of the expression \((\frac{n+3}{2n-6})/ (\frac{n+3}{3n-9} )\) is given as 3/2

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the expression:

\((\frac{n+3}{2n-6})/ (\frac{n+3}{3n-9} )\\\\Simplifying\ the\ expression:\\\\=(\frac{n+3}{2(n-3)})/ (\frac{3(n-3)}{n+3} )\\\\=\frac{3}{2}\)

The quotient of the expression \((\frac{n+3}{2n-6})/ (\frac{n+3}{3n-9} )\) is given as 3/2

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Answer:

  £8279.27

Step-by-step explanation:

The given relationship is ...

  (original price) × (1 - 18%) = £6789

Dividing by the coefficient of the original price, we find it to be ...

  original price = £6789/0.82 = £8279.27

The original price of the car was £8279.27.

Answer:

20

Step-by-step explanation:

If 50% of machines are washing machines and there are 10, then add 10 again to get 100% of the total machines

$30500                                                                                                                       ..............................................................................................................................

The total surface area of the rectangular pyramid would be -

TSA = l√[h² + (w/2)²] + w√[h² + (l/2)²] + (l x w).

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.

Given is the surface area of the rectangular pyramid.

Slant height of length face of the pyramid = √[h² + (w/2)²]

Slant height of width face of the pyramid = √[h² + (l/2)²]

We know that -

The area of a triangle = ½ × base × height

Area of the triangle that has a length as the base = ½ × l × {√[h² + (l/2)²]}

Area of the triangle that has a width as the base = ½ × w × {√[h² + (w/2)²}

Lateral Surface Area →

½ × l × {√[h² + (w/2)²]} + ½ × w × {√[h² + (l/2)²} + ½ × l × {√[h² + (w/2)²]}

+ ½ × w × {√[h² + (l/2)²}

2 × {½ × l ×√[h² + (w/2)²]} + 2 × {½ × w ×√[h² + (l/2)²]}

Lateral Surface Area → l√[h² + (w/2)²] + w√[h² + (l/2)²]        

Now -

TSA = l√[h² + (w/2)²] + w√[h² + (l/2)²] + (l x w)

Therefore, the total surface area of the rectangular pyramid would be -

TSA = l√[h² + (w/2)²] + w√[h² + (l/2)²] + (l x w).

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Answer:

12e-6f-8 is the answer

Step-by-step explanation:

did work on peice of paper

Answer:

12e - 6f - 8

Step-by-step explanation:

By using the distributive property,, the answer is

(6e x 2) - (3f x 2) - (4 x 2)

12e - 6f - 8

The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).

In this question we have a graph of a quadratic equation translated to another place of a Cartesian plane, whose form coincides with the vertex form of the equation of the parabola, whose form is:

g(x) = C · (x - h)² - k     (1)

Where:

By direct comparison we notice that (h, k) = (5, 1) and C = 1. Now we proceed to check if the points (x, y) = (2, 10) and (x, y) = (8, 10) belong to the parabola.

x = 2

g(2) = (2 - 5)² + 1

g(2) = 10

x = 8

g(8) = (8 - 5)² + 1

g(8) = 10

The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).

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Answer: B

Step-by-step explanation:

looked at the points from the dude above, or below, anyway i hope this helps

Answer:

B

Step-by-step explanation

Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

Step-by-step explanation:

The slope of the line is - 5, the equation will be y=-5x-1.

y+5x=-1

Answer:

The anwser to this is 41

Step-by-step explanation:

91 - 7 = 82, 82/2 = 41

Answer:

y = 1/2 x + 1.

Step-by-step explanation:

A line perpendicular to a line with slope m will have a slope of -1/m.

The line y = -2x - 7 will have a slope of -1/ -2 = 1/2.

Using the point-slope form of a straight line

y - y1 = m(x - x1)

Here m = 1/2 and (x1, y1) = (4, 3).

So, y - 3 = 1/2(x - 4)

y = 1/2x - 2 + 3

y = 1/2 x + 1.

A structural break occurs when we see A. an unexpected shift in time-series data.

It is the change in a time series's data-generating mechanism, it is a phenomenon that occurs when a significant event or structural shift in the economy alters the underlying data-generating mechanism. A structural break can happen for several reasons, including natural catastrophes, changes in economic policy, new inventions, and other reasons that alter the way the data is generated.

In the presence of a structural break, we can't assume that the relationships between variables before and after the break are the same. The primary objective of identifying structural breaks in the time-series is to detect changes in the behavior of the series over time, such as changes in the variance of the series, changes in the mean of the series, and changes in the covariance of the series. So therefore the correct answer is A. an unexpected shift in time-series data, the structural break occurs.

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Let the amount of the 30% solution be x gallons.

Then the amount of the 10% solution is (100 - x) gallons.

The amount of juice in the 30% solution is 0.3x gallons.

The amount of juice in the 10% solution is 0.1(100 - x) gallons.

When the two solutions are mixed, we get 100 gallons of a 12% juice solution, which means:

0.3x + 0.1(100 - x) = 0.12(100)

Simplifying this equation, we get:

0.3x + 10 - 0.1x = 12

0.2x = 2

x = 10

Therefore, 10 gallons of the 30% solution was used.

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