According to government tests, a late model hybrid car gets 45 miles per gallon of gas. If gasoline sells
at $3.20 per gallon, how many miles will the car travel on $20.00 of gas?

Answer:  There is a total of 900 seats in the auditorium.

Step-by-step explanation:

there is a formula for this

t - n = a + ( n - 1) d

It is called a Arithmetic Progression.

We use this to find the number of seats in the last row first.

a = initial value, 12

d = common difference for each successive term

n = is the number of terms in the sequence

t - 25 = 12 + (25 -1) * 2

We ignore the left side for now, just solve the right and we get 60.

Now we use the equation,

n / 2 (2a + n -1 * d)

So,

25/2 ( 24 + 24 * d)

The answer is 900

The property that justifies the following statement, if 7(x-3)=35 then 35=7(x-3) is the symmetric property.

Symmetric property is one of the properties of equality which states that if there is an equality sign (=) between two values or numbers, then the two values will always remain equal even if you change the sides of the values. Therefore if ab = cd, then cd = ab

Hence, according to this property, the left side of the equation can be transferred to the right side and the right side of the equation can be transferred to the left side as the order of the equation can be ignored.

The symmetric property also justifies that if the values on the two sides are not equal, then they will remain unequal even if the sides are changed. That is if ab ≠ cd, then cd ≠ ab.

So, according to the symmetric property, the statement, if 7(x-3)=35 then 35=7(x-3) is valid.

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Answer:

0.06  

Step-by-step explanation:

hope this helps

6 divide by 100= 0.06

Answer:

Step-by-step explanation:0.06

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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To express the quadratic function f(x) = x^2 - 18x + 63 in standard form, we need to complete the square.

First, we can factor out the coefficient of x^2, which is 1: f(x) = 1(x^2 - 18x + 63), Next, we want to find the value that completes the square for the expression inside the parentheses,

which is (-18x + 63). To do this, we take half of the coefficient of x, which is -9, square it, and add it to both sides: f(x) = 1(x^2 - 18x + 81 - 81 + 63).

Notice that we added and subtracted 81 inside the parentheses, which is the value we got from (-9)^2. This allows us to write the expression as a perfect square trinomial, which can be factored as: f(x) = 1[(x - 9)^2 - 18].

Finally, we can simplify this expression by distributing the 1 and adding 63 outside the brackets: f(x) = (x - 9)^2 - 18 + 63, So the quadratic function f(x) in standard form is: f(x) = (x - 9)^2 + 45.

Note that standard form for a quadratic function is usually written as ax^2 + bx + c, where a, b, and c are constants. In this case, we factored out the coefficient of x^2, which is why our standard form expression doesn't have an "a" term.

A quadratic function in standard form is written as f(x) = a(x - h)^2 + k, where a, h, and k are constants. Our goal is to rewrite the given function in this format. So, the standard form of the given quadratic function is: f(x) = (x - 9)^2 - 18

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Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.

Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.

This statement is referring to a specific vector-valued function, which we can write as:

f(t) = (0, t^2, ct)

where c is a constant.

The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.

The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.

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Answer: (1, -1)

Step-by-step explanation:

The linear model for the snow (S) in terms of hours (h) during the snowstorm is S = 2h + 8, where S represents the snow in inches and h represents the number of hours since the start of the snowstorm.

To write a linear model for the snow (S) in terms of hours (h) during the snowstorm at the ski resort, we can use the information given:

The initial amount of snow on the ground when the snowstorm began is 8 inches.

The snow is falling at a rate of 2 inches per hour.

Based on this information, we can establish the following linear relationship:

S = 2h + 8

In this linear model, 'S' represents the amount of snow in inches, and 'h' represents the number of hours since the start of the snowstorm. The coefficient of 'h' is 2, representing the rate of snowfall per hour. The constant term 8 represents the initial amount of snow on the ground before the snowstorm started.

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When a boulder is pushed off a cliff, the potential energy of the boulder will be at its maximum just before it starts to fall and at its minimum just as it hits the ground.The potential energy of the boulder is at its maximum just before it starts to fall because it is at its highest point and has not yet begun to move.

The potential energy of an object is determined by its location relative to other objects and the conditions that surround it. When a boulder is pushed off a cliff, the energy stored in it is converted from potential energy to kinetic energy.

Therefore, when a boulder is pushed off a cliff, the potential energy of the boulder will be at its maximum just before it starts to fall and at its minimum just as it hits the ground.The potential energy of the boulder is at its maximum just before it starts to fall because it is at its highest point and has not yet begun to move.

At this point, the boulder has stored the maximum amount of energy that can be converted into kinetic energy when it starts to fall. At this point, the potential energy is equal to the gravitational potential energy (GPE) of the boulder, which is given by the equation GPE = mgh, where m is the mass of the boulder, g is the acceleration due to gravity, and h is the height of the cliff.The potential energy of the boulder is at its minimum just as it hits the ground because it has no more height to lose.

At this point, all of the potential energy that the boulder had at the top of the cliff has been converted into kinetic energy as it fell, and this kinetic energy has been transferred to other objects as the boulder collided with them. Therefore, the potential energy of the boulder is zero at this point.

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Answer:

24units

Step-by-step explanation:

2(4y + 3) + 2(5y - 1) = 94

18y + 4 = 94

y = 5

WX = 5y - 1 = 5(5) - 1 = 24units

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First we need to find the value of y .

\(Perimeter = 2 \times ( \: (4y + 3) + (5y - 1) \: ) \\ \)

\(Perimeter = 2 \times (9y + 2)\)

\(Perimeter = 18y + 4\)

Question told us that perimeter is 94 ,

Thus :

\(94 = 18y + 4\)

\(18y + 4 = 94\)

Subtract sides 4

\(18y + 4 - 4 = 94 - 4\)

\(18y = 90\)

Divide sides by 18

\( \frac{18y}{18} = \frac{90}{18} \\ \)

\(y = 5\)

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The face sides in the rectangular are same.

Thus :

\(VY = WX\)

So ;

\( WX = 5y - 1\)

\(WX = 5(5) - 1\)

\(WX = 25 - 1\)

\(WX = 24\)

Done...

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To solve for r, we can divide both sides of the equation by Pt: r = (A-P)/Pt

The formula A=P+Prt is used to calculate the total amount of money (A) after a certain period of time when a principal amount (P) is invested at a certain interest rate (r) for a certain amount of time (t). To solve for the specified variable r, we need to rearrange the formula and isolate r on one side of the equation. Here are the steps to do so:

Step 1: Subtract P from both sides of the equation to get:
A - P = P + Prt - P

Step 2: Simplify the right side of the equation to get:
A - P = Prt

Step 3: Divide both sides of the equation by Pt to get:
(A - P) / Pt = r

Step 4: Simplify the left side of the equation to get:
r = (A - P) / Pt

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Answer:

x=130

Step-by-step explanation:

(x - 129) * 129 = 129

Then solve

If x exists decreased by 129 and then that number exists multiplied by 129, the result exist 129 then the value of x exists 130.

In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown."

Any of the algebraic expressions, including addition, subtraction, multiplication, and division, should be used. Bring the variable to the left and the remaining values to the right to estimate the value of x. To estimate the outcome, estimate the values.

If x exists decreased by 129 and then that number exists multiplied by 129, the result exist 129.

(x - 129) × 129 = 129

Divide both sides by 129

((x-129) × 129) / (129) = (129) / (129)

Simplifying the above equation, we get

x - 129 = 1

Add 129 to both sides

x - 129 + 129 = 1 + 129

x = 130

Therefore, the value of x exists 130.

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The approximate price per square inch of the cookie cake is $0.50

The area of a circle is given through the formulation:

A = πr^2

In which r is the radius of the circle.

for the reason that diameter of the cookie cake is 6 inches, the radius is half of of that, or three inches.

Substituting this into the formulation, we've:

A = π(3^2) = 28.26 square inches (approximate)

The value per square inch is the overall value of the cookie cake divided with the aid of its area:

value per square inch = $14.13 / 28.26 sq.in = $0.50 (approximate)

Therefore, the approximate price per square inch of the cookie cake is $0.50

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The length of the rectangle is equal to \(L < 11\;inches\).

Given the following data:

To write an equation and solve for the length of the rectangle:

Mathematically, the area of a rectangle is given by this formula:

\(A=LW\)

Where:

Substituting the given parameters into the formula, we have;

\(5L < 55\\\\L < \frac{55}{5} \\\\L < 11\;inches\)

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To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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26400 is what they travel in feet in a day divide that by 24 and that should be your answer

The given statement " The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate " is false because the allowable range for an objective function coefficient assumes that the original estimates for other coefficients are approximately correct

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are approximately correct, but not necessarily completely accurate. The allowable range takes into account the potential variability or uncertainty in the estimated values of the other coefficients, as well as the impact of any errors or discrepancies in the data used to estimate the model.

Therefore, the allowable range provides a range of values within which the objective function coefficient can vary while still producing a valid and useful model. It does not assume that the other coefficients are completely accurate or that this is the only coefficient whose true value may differ from its original estimate.

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Answer:

\(m = \frac{-y+x}{2}\)

Step-by-step explanation:

\(2m - x + 3y = 2y\)

Take \(-x\) and \(+3y\) on the other side of the equal to sign:

\(2m = 2y +x-3y\)

Now solve for y:

\(2m = -y +x\)

Take 2 one the other side of the equation:

\(m = \frac{-y +x}{2}\)

Hope this helps :)

Answer:

Answer:

Step-by-step explanation:

Which statements about the relationship between the two triangles below are true? Check all that apply.Mark this and return

Answer:

Open this picture I send you

I hope I helped you :3

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\( \huge \mathrm{ Answer : }\)

\( \boxed{ \mathrm{circumference = 2\pi r}}\)

_____________________________

\( \boxed{Area = \pi {r}^{2} }\)

Area of circle = 2464 unit²

_____________________________

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Answer:

12 square feet is your answer.

Step-by-step explanation:

If you find this helpful please mark 5 stars and brainliest!

Answer:

Answer is below. Hope this helped, Have a Wonderful Day!!

Step-by-step explanation:

The sides can be found by taking the square root of the area.

(Area)1/2=s, where s = side.

(48)1/2= 24

So the length of a side is 24 ft.

This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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Answer:

$50.40

Step-by-step explanation:

To find how much Lana will pay in total follow these steps.

First, multiply 40 by 1.05.

40×1.05=42.

This is how much she will pay for the food plus tax.

Now, multiply 42 by 1.2.

42×1.2=50.40

This is how much she will pay for the food, tax, and tip.

Lana will pay a total of $50.40.

Hope this helps!

Answer:

x = 39º; y = 45º

Step-by-step explanation:

97 + 44 + x = 180

141 + x = 180

x = 39º

y + 52 = 97

y = 45º

Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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From the given table, let's complete the stem and leaf plot.

Part (a):

From the given table, we have 27 data.

It consists of just the data for the round-trip commute time for the employees.

Therefore, data were collected for 1 quantitative variable.

Part (b):

The data constitute a sample

Part (c):

To compute the stem and leaf plot, we have:

Stems------------->Leaves

5--------------------> 0, 0, 3, 3, 3, 4, 7, 7, 9

6----------------------> 0, 1, 3, 4, 5, 7, 8, 8

7------------------------> 0, 3, 4, 4, 5

8------------------------>0, 1, 9

9-------------------------> 0, 4

Part d:

The shape of the data can be said to be right skewed .

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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