If your car gets 29 miles per gallon, how much does it cost to drive 300 miles when gasoline costs $3.20 per gallon?

The likelihood of the event is 1/2

Answer:

x = 38°, y = 68°, z = 55°

Step-by-step explanation:

This would be easier to explain if the vertices were labelled , however

Angles at the circumference of the circle subtended on the same arc are congruent.

x and 38 are subtended on the same arc

y and 68 are subtended on the same arc

z and 55 are subtended on the same arc

Thus

x = 38°, y = 68° and z = 55°

1. Simplify \(\frac{1}{3} x\) to \(\frac{x}{3}\)

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

2. Subtract \(\frac{x}{3}\) from both sides

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

3. Divide both sides by 2

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

4. Simplify \(\frac{8-\frac{x}{3} }{2}\) to \(\frac{8}{2}\) - x/3/2

y=8/2-x/3/2

5. Simplify 8/2 to 4

y=4-x/3/2

6. Simplify x/3/2 to x/3x2

y=4-x/3x2

7. Simplify 3x2 to 6

-y=4-x/6

The t-value is often used instead of the z-value in statistical tests because the assumptions of the z-value are violated when the sample size is 30 or less.

The t-value is preferred over the z-value in certain scenarios due to the violation of assumptions associated with the z-value when the sample size is small (30 or less). The z-value assumes that the population standard deviation is known, which is often not the case in practice. In situations where the population standard deviation is unknown, the t-value is used because it relies on the sample standard deviation instead. By using the t-value, we account for the uncertainty associated with estimating the population standard deviation from the sample.

Additionally, the t-value is easier to calculate and interpret compared to the z-value. The t-distribution has a wider range of degrees of freedom, allowing for more flexibility in analyzing data. Moreover, the t-value is more widely known among statisticians and is readily available in statistical software packages, making it a convenient choice for conducting hypothesis tests and confidence intervals.

Overall, the t-value is preferred over the z-value when the assumptions of the z-value are violated or when the population standard deviation is unknown.

Learn more about deviation here:

https://brainly.com/question/23907081

#SPJ11

Answer:

- 1/80

Step-by-step explanation:

I dont know sorry but i bet someone else knows

You didn't include the equations.

Answer:

b.

give me a brainlist

Step-by-step explanation:

The slash indicates a fraction.

=============================================

Proof:

We'll need to consider 4 different cases.

-----------------------

Case (1): j > 0 and k > 0

If j > 0, then 3j > 0 and 3/j > 0

If k > 0, then 3k > 0 and 3/k > 0

The two points (3j, 3k) and (3/j, 3/k) are both in quadrant 1.

-----------------------

Case (2): j > 0 and k < 0

If j > 0, then 3j > 0 and 3/j > 0

If k < 0, then 3k < 0 and 3/k < 0

Points (3j, 3k) and (3/j, 3/k) are both in quadrant 4.

------------------------

Case (3): j < 0 and k > 0

If j < 0, then 3j < 0 and 3/j < 0

If k > 0, then 3k > 0 and 3/k > 0

Points (3j, 3k) and (3/j, 3/k) are in quadrant 3.

------------------------

Case (4): j < 0 and k < 0

If j < 0, then 3j < 0 and 3/j < 0

If k < 0, then 3k < 0 and 3/k < 0

Points (3j, 3k) and (3/j, 3/k) are in quadrant 4.

------------------------

For nonzero integers j and k, we've shown that Points (3j, 3k) and (3/j, 3/k) are in the same quadrant. This concludes the proof.

Answer:

D

Step-by-step explanation:

A vector orthogonal to the plane defined by points P(1,0,0), Q(1,1,1), and R(2,-1,3) is:

(4, 1, -1).

To find a vector orthogonal to the plane defined by points P(1,0,0), Q(1,1,1), and R(2,-1,3), follow these steps:

1. Find two vectors that lie in the plane by subtracting the coordinates of the given points. Let's use PQ and PR:
  PQ = Q - P = (1-1, 1-0, 1-0) = (0, 1, 1)
  PR = R - P = (2-1, -1-0, 3-0) = (1, -1, 3)

2. Calculate the cross product of PQ and PR to obtain a vector orthogonal to the plane:
  PQ x PR = (PQ_y*PR_z - PQ_z*PR_y, PQ_z*PR_x - PQ_x*PR_z, PQ_x*PR_y - PQ_y*PR_x)
           = (1*3 - 1*(-1), 1*1 - 0*3, 0*(-1) - 1*1)
           = (3 + 1, 1 - 0, 0 - 1)
           = (4, 1, -1)

Therefore, we can state that a vector orthogonal to the plane defined by points P(1,0,0), Q(1,1,1), and R(2,-1,3) is (4, 1, -1).

To learn more about vector orthogonal visit : https://brainly.com/question/30905184

#SPJ11

Answer:36

Step-by-step explanation: 3X4 or 3 rectangles plus tow rectanges that = 12

Answer:

=4x2+12x+9

hope it helps you!

Step-by-step explanation:

Answer:

4x2−12x+9

Step-by-step explanation:

expand using the foil method

Simplify and combine like terms

and you get the answer

Answer:

-2, -1, 0, 1

Step-by-step explanation:

-2

-1

0

1

All the possible values of t in the inequality - 3 < t < 2 is,

t = - 2, - 1, 0, 1

Used the concept of inequality that states,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given that;

The inequality is,

- 3 < t < 2

Here the given inequality means all the values of t are lies between - 3 and 2.

That is,

t = - 2, - 1, 0, 1

Therefore, the value of t are t = - 2, - 1, 0, 1

To learn more about inequality visit:

https://brainly.com/question/25944814

#SPJ3

The differential equation that models this situation is dx/dt = kx(M - x) (option c).

To determine the differential equation that models the situation, let's analyze the problem statement.

The rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized and the number of words that have not been memorized.

Let's denote the number of words memorized as "a" and the number of words not yet memorized as "M - a" (where M is the total number of words in the list).

The problem states that the rate of memorization is proportional to the product of "a" and "M - a". We can express this mathematically as:

Rate of memorization ∝ a * (M - a)

To convert this proportionality into an equation, we introduce a positive constant k:

Rate of memorization = k * a * (M - a)

The left side of the equation represents the rate of change of the number of words memorized (da/dt), and the right side represents the product of "a" and "M - a" multiplied by the constant k.

Therefore, the differential equation that models this situation is:

da/dt = k * a * (M - a)

Comparing this with the given options, we can see that the correct choice is option C:

dx/dt = k * x * (M - x)

The complete question is:

At any time t > 0 the rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized and the number of words that have not been memorized. If a denotes the number of words memorized at time t, which differential equation models this situation? Assume k is a positive constant.

A. dx/dt = kx

B. dx/dt = kx(x - M)

C. dx/dt = kx(M - x)

D. dx/dt = kt(M - t)

To know more about differential equation:

https://brainly.com/question/32524608

#SPJ4

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

for such more question on scale factor

https://brainly.com/question/3381225

#SPJ8

With a ratio of 5 : 3, the amount of cocoa powder used to make the icing is 27g.

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other. On the other hand, proportion is the equality of two ratios, such that a : b = c : d.

If the combined weight of the iced cake (batter + icing) is 480 g, of which 15% is cocoa powder, then the total mass of the cocoa powder used is:

total mass of the cocoa powder = 15% of 480g

total mass of the cocoa powder = 0.15(480g)

total mass of the cocoa powder = 72 g

If the amount of cocoa powder used in the batter of a chocolate cake and the amount of cocoa powder used in the icing for the cake is in the ratio 5 : 3, and its total mass is 72g, using proportion, solve for the weight used to make the icing.

a + b = 72   ⇒   a = 72 - b

where a = amount of cocoa powder used in the batter

b = amount of cocoa powder used in the icing

5 : 3 = a : b

5 : 3 = 72 - b : b

5b = 3(72 - b)

5b = 216 - 3b

5b + 3b = 216

8b = 216

b = 27

amount of cocoa powder used in the icing = 27 g

Learn more about ratio and proportion here: brainly.com/question/12024093

#SPJ4

Your Answer:

50+(0.25 x t)

t = text messages

Answer:

please see the analysis

Step-by-step explanation:

Solution:

the Integer between \(-3So \(Z=-2 , -1 ,\)

So \(P=\left\{-2\middle|-1\right\}\) {write all the value of Z}

The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

Learn more about Erosion: https://brainly.com/question/17905503

#SPJ4

1. It's impossible to determine exactly when Lin's battery will die without more information on her phone's battery capacity and usage patterns. However, we can estimate that it will likely die sometime after noon if the rate of battery drain remains constant.

2. Yes, battery life is a function of time. The longer a battery is in use, the more its charge will deplete. However, it is not necessarily a linear function as the rate of battery drain can vary depending on factors such as usage patterns, app activity, and temperature. In this specific case, it appears that the rate of battery drain may be slowing down as the percentage decrease from 90% to noon is less than the decrease from fully charged to 90%.

In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often used. A linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input.

Linear functions are related to linear equations.

To know more about linear function. Click on the link.

https://brainly.com/question/20286983

#SPJ11

Adding and subtracting fractions involves combining or separating two or more fractional values. The process of adding or subtracting fractions requires finding a common denominator, which is the least common multiple of the denominators of the fractions being added or subtracted.

Here's the step-by-step process for adding or subtracting fractions:

Find a common denominator: The denominator of a fraction represents the number of equal parts into which a whole is divided. To add or subtract fractions, the denominators must be the same. If the denominators are different, you must find a common denominator by finding the least common multiple (LCM) of the denominators.

Convert the fractions to equivalent fractions with the common denominator: Once you have found a common denominator, you must convert each fraction to an equivalent fraction with the same denominator. You can do this by multiplying both the numerator and denominator of each fraction by the same number.

Add or subtract the numerators and place the sum over the common denominator: After converting each fraction to an equivalent fraction with the same denominator, you can add or subtract the numerators and place the sum over the common denominator to find the result.

Simplify the answer: Finally, simplify the answer by dividing both the numerator and denominator by their greatest common factor, if possible.

To learn more about adding and subtracting fractions, visit

https://brainly.com/question/10354322

#SPJ11

In this scenario, Marcos is planning to travel from Phoenix to Flagstaff, and we are using variables to represent different aspects of his journey.

The variable t represents the number of hours since Marcos left Phoenix, which serves as a measure of time elapsed since the start of the journey. It allows us to track the progress of Marcos over time and analyze various time-related aspects such as the duration of the journey or the rate at which he is traveling. On the other hand, the variable d represents the number of miles Marcos has traveled from Phoenix. It serves as a measure of distance covered, indicating how far Marcos has progressed on his route. By monitoring the value of d, we can determine the distance remaining to reach Flagstaff or calculate other distance-related parameters such as average speed or total distance traveled.

By using these variables, we can establish a relationship between time and distance traveled by Marcos. This relationship can be represented by a function or equation that describes Marcos' progress over time, such as a velocity equation or a distance-time equation. These variables and their relationship allow us to analyze and make predictions about Marcos' journey. We can determine when he is expected to reach certain milestones, calculate his average speed or rate of travel, and estimate the time required to complete the journey. Additionally, these variables provide a framework for solving various problems or making decisions related to Marcos' travel, such as optimizing his route or estimating fuel consumption based on distance traveled.

In summary, by using the variables t and d to represent time and distance traveled, respectively, we can effectively describe and analyze Marcos' journey from Phoenix to Flagstaff, enabling us to make informed decisions and predictions about his travel experience.

Learn more about variables here: brainly.com/question/32263664

#SPJ11

Answer:

102 inches squared

Step-by-step explanation

A = (b x h) / 2

A = (12 x 17) / 2

= 102

Answer:

i^3=i×i×i

Step-by-step explanation:

i^3(means i is multiplying(×) it self 3 times

Answer:

4Pounds 1ounce

Step-by-step explanation:

First bag is 3pound 5ounces

Second bag 12ounces

Add both

3 Pounds and 17ounces

16ounces make 1Pound so 17ounces becomes 1Pound and 1ounces

Add to the 3Pounds

You have 3 Pounds + 1 Pound 1ounce

Answer:

x = 108°

Step-by-step explanation:

In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

Learn more about linear equation

brainly.com/question/21835898

#SPJ4    

Answer:

no pic available. please show the question

Answer:

pls where is tthpe picture

The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

Learn about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

Learn more about integrating factor here

https://brainly.com/question/32554742

#SPJ4