Question 2: A local dealership collects data on customers. Below are the types of cars that 206 customers are driving. Electric Vehicle Compact Hybrid Total Compact-Fuel powered Male 25 29 50 104 Female 30 27 45 102 Total 55 56 95 206 a) If we randomly select a female, what is the probability that she purchased compact-fuel powered vehicle? (Write your answer as a fraction first and then round to 3 decimal places) b) If we randomly select a customer, what is the probability that they purchased an electric vehicle? (Write your answer as a fraction first and then round to 3 decimal places)

1)

\(f(x) = 2x - 5\\f(4) = 2(4) - 5 = 8 - 5 = 3\)

2)

\(f(x) = 2x - 5\\f(-6) = 2(-6) - 5 = -12 - 5 = -17\)

3)

\(g(x) = x + 3\\g(8) = 8 + 3 = 11\)

4)

\(h(x) = 4x\\h(5) = 4 \cdot 5 = 20\)

5)

\(k(x) = x^2 + 2x - 5\\k(6) = 6^2 + 2 \cdot 6 - 5 = 36 + 12 - 5 = 43\)

6)

\(k(x) = x^2 + 2x - 5\\k(-3) = (-3)^2 + 2(-3) - 5 = 9 - 6 - 5 = -2\)

7)

\(g(x) = x + 3\\g(3x) = 3x + 3 = 3(x + 1)\)

8)

\(f(x) = 2x - 5\\f(4x) = 2(4x) - 5 = 8x - 5\)

9)

\(h(x) = 4x\\h(5t) = 4(5t) = 20t\)

10)

\(k(x) = x^2 + 2x - 5\\k(4t) = (4t)^2 + 2(4t) - 5 = 16t^2 + 8t - 5\)

11)

\(f(x) = 2x - 5\\f(x + 3) = 2(x + 3) - 5 = 2x + 6 - 5 = 2x + 1\)

12)

\(f(x) = 2x - 5\\g(x) = x + 3\\f(g(x)) = 2(x + 3) - 5 = 2x + 6 - 5 = 2x + 1\)

26°F in July would be the percent of increase between the average low and high temperatures.

So, the month's typical daily maximum temperature is 90°F.

When comparing the two temperatures, the result is:

The daily low-temperature increase as a percentage:

Therefore, 26°F in July would be the percent of increase between the average low and high temperatures.

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Answer: y-100= 0.25(x-160)

Step-by-step explanation:

Given: Charge per mile = $0.25

Total amount driver pays = $100

Number of miles he drove = 160 miles

Total cost = Flat fee +  ( Number of miles he drove) (Charge per mile) ...(i)

i.e. 100= Flat fee +  (160)(0.25)

⇒ Flat fee = 100 - (160)(0.25)

If y= total cost , x= number of miles, then

y= ( 100 - (160)(0.25))+ (x)(0.25)  [Substitute value of flat fee in (i)]

⇒ y= 100 - (160)(0.25)+ (x)(0.25)

⇒ y-100= (x)(0.25)- (160)(0.25)

⇒  y-100= 0.25(x-160)

Hence, the required equation:  y-100= 0.25(x-160)

Answer: 7/3

Mixed Number: 2 1/3

Step-by-step explanation:

Favorite sport bar graph with the words "favorite sport," "sport" on the x-axis, and "y-axis" labelled. The correct graph to display the data is: C.

The data gathered from the middle school kids is best represented by a bar graph since it enables us to compare distinct categories (in this case, sports) and their related frequencies (number of pupils).

The information in this case is as follows:

Basketball: 17 students

Baseball: 12 students

Soccer: 27 students

Tennis: 44 students

To identify the subject of the data being depicted, the label "Favorite Sport" is used in the appropriate bar graph.

Basketball, baseball, soccer, and tennis are listed in separate, unique categories along the "Sport" axis. The frequency or count of students who selected each sport as their favourite is shown on the "Number of Students" y-axis.

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Graph attached below,

Statistical guidance should perform well in situations such as clinical trials and market research where rigorous data analysis and inference are necessary. Statistical methods provide a systematic approach to control biases, handle variability, and draw reliable conclusions, ensuring accurate decision-making and predictions based on the data.

Statistical methods are crucial in determining sample sizes, designing the study, and analyzing the data to draw valid conclusions about the effectiveness and safety of the treatment.

In this situation, statistical guidance should do well because it provides a systematic framework to control for biases, random variability, and confounding factors, ensuring robust and reliable results that can be generalized to a larger population.

One example where statistical guidance should perform well is in clinical trials for new drugs or treatments.

Another example is in market research and opinion polling. Statistical techniques can be used to collect and analyze data from a representative sample of the target population, allowing for accurate estimation and prediction of consumer preferences, market trends, or election outcomes.

Statistical guidance should do well in this situation because it provides methods for random sampling, hypothesis testing, and confidence interval estimation, which help minimize sampling errors and increase the reliability of the findings.

Additionally, statistical models can capture complex relationships and make accurate predictions based on the observed data.

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The electric field (E-field) associated with the given potential function V(x, z) = 4bx^2 + 4az^3 - 3cz^3 is E = -8bx i - (12az^2 - 9cz^2)j.

To find the electric field (E-field) associated with the given potential function, we need to calculate the negative gradient of the potential. The E-field is given by the following formula:

E = -∇V

Where ∇ is the gradient operator. In this case, the potential function V(x, z) is defined as:

V(x, z) = 4bx^2 + 4az^3 - 3cz^3

To calculate the E-field, we need to take the partial derivatives of V with respect to x and z and then apply the negative sign. Let's calculate each component separately:

Partial derivative with respect to x (dV/dx):

dV/dx = 8bx

Partial derivative with respect to z (dV/dz):

dV/dz = 12az^2 - 9cz^2

Now, we can write the E-field vector as:

E = -∇V = -(dV/dx)i - (dV/dz)j

Substituting the calculated partial derivatives, we have:

E = -8bx i - (12az^2 - 9cz^2)j

Therefore, the electric field (E-field) associated with the given potential function V(x, z) = 4bx^2 + 4az^3 - 3cz^3 is:

E = -8bx i - (12az^2 - 9cz^2)j

Note that the positive constants b and c are included in the E-field expression.

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The total number of seats in the amphitheater is 2992.

The number of seats in each row of the amphitheater forms an arithmetic sequence. So we can find the total number of seats by applying the formula for the sum of first n terms.

The formula for the sum of first n terms of an arithmetic sequence is as follow:

s(n) = n/2(2a + (n-1)d)

n = total no of terms

a = first term

d = common difference

In this question first term is 22 , common difference is 4 and a total of 34 terms (corresponding to the 34 rows).

So putting the values in the formula we have:

s(n)= 34÷2 ( 2×22 + (34-1)×4 )

s(n) = 17 ( 44 + 132)

s(n) = 17 ×176

s(n) = 2992

Therefore, The total number of seats in the amphitheater is 2992.

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Answer:

She drinks 4.8 ounces of water per hour

Step-by-step explanation:

We know

Yasmin drank 3/4 of an 8-ounce glass of water in 1 1/4 hours

3/4 of 8 ounce = 6 ounces

1 1/4 = 5/4 = 1.25 hours

How much can she drink per hour?

6 divided by 1.25 = 4.8 ounces of water per hour

So, she drinks 4.8 ounces of water per hour.

With the given ratio of red to blue cars, which is 3:4, Evan has 16 blue toy cars.

To find the number of cars, follow these steps  -

1: Identify the ratio - Red cars:Blue cars = 3:4

2: Determine the number of red cars - Evan has 12 red toy cars.

3: Find the ratio equivalent to the number of red cars - 12 red cars / 3 (from the ratio) = 4

4: Multiply the ratio of blue cars by the equivalent found in step 3 - 4 (from the ratio) * 4 = 16

So, Evan has 16 blue toy cars.

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Answer: 3.6hours

Step-by-step explanation:

Since we are given the information that Eleniz is using her phone all day and that her battery life is down to 2/5 and it drains another 1/9 every hour.

The number of hours that the battery last will be:

= 2/5 ÷ 1/9

= 2/5 × 9/1

= 18/5

= 3.6 hours

Therefore, the battery will last for 3.6hours

(a)We have to use a continuous exponential growth model to write a formula relating to t and N(t), where t is the time (in years) since the initial population is introduced, and N(t) is the number of fish at time t. Continuous exponential growth models can be expressed as;
N(t) = N₀ * e^(kt)
where N₀ is the initial population, t is the time elapsed, k is the continuous growth rate, and e is Euler's number.

(b)Given that the initial population is introduced into a lake and it grows according to a continuous exponential growth model. The number of fish in the lake is 300 after 4 years. Using N(t) = N₀ * e^(kt);300 = N₀ * e^(4k)So, the formula relating to t and N(t) is;
N(t) = N₀ * e^(kt)
Putting the values into the formula;
N(t) = 300/ e^(4k)We know the number of fish in the lake after 4 years is 300.
Therefore;300 = N₀ * e^(4k)
Dividing by N₀; 300/N₀ = e^(4k)
We have; N(t) = N₀ * e^(kt)
Putting the values into the formula;
N(t) = N₀ * e^(kt)N₀ = N(t) / e^(kt)
At t = 0; N₀ = N(0) / e^(k*0)N₀ = N(0) / e^0
N₀ = N(0)
Now we can substitute the value of N₀ into the formula;
N(t) = N(0) * e^(kt)
Substituting the values in N(t) = N₀ * e^(kt);
N(t) = 1000 * e^(0.23t)

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The Center of the circle is (4, -8) and radius of the circle is 11 units.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

We have given circle in the plane has the equation;

x² + y² -8x + 16y=41

Now we will convert this equation to the standard form of the circle;

x² + y² -8x + 16y=41

[x² - 2(4)x] + [y² + 2(8)x] =41

[x² - 2(4)x + 4²] + [y² + 2(8)y + 8²] = 4² + 8² +41

(x - 4)² + (y + 8)² =  16 + 64 +41

(x - 4)² + (y + 8)² = 121

(x - 4)² + (y + 8)² = 11²

By comparing this equation with the standard equation of the circle as;

(x - h)² + (y - k)² = r²

The Center of the circle=  (4, -8)

The radius = 11 units.

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Answer:

x = ⅖

Step-by-step explanation:

13x+7=3+23x

4 = 10x

x = 4/10

x = ⅖(simplest form)

Answer:

\(x = \frac{2}{5}\)

Step-by-step explanation:

13x + 7 = 3 + 23x

Subtract 7 from both sides of the equation:

13x + 7 - 7 = 3 + 23x - 7

13x  =  23x - 4

Next, subtract 23x from both sides of the equation:

13x -23x =  23x - 4 - 23x

13x - 23x =  - 4

Combine like terms:

-10x = -4

Divide both sides of the equation by -10 and solve for x:

\(\frac{-10x}{-10} = \frac{-4}{-10} = \frac{2}{5}\)

Therefore, \(x = \frac{2}{5}\)

Answer:

(5,6)

Step-by-step explanation:

10-5=5

the number of days cannot be negative, so this solution is not valid.

Let's denote the number of problems in the packet as P.

According to the given information, Annie solved six problems each day and finished four days after Ben did. This means that Annie worked for (B + 4) days, where B represents the number of days Ben worked. Therefore, the total number of problems Annie solved is 6(B + 4).

Claire solved three more problems each day than Ben did and finished two days before he did. This means that Claire worked for (B - 2) days. Therefore, the total number of problems Claire solved is (B + 3)(B - 2).

To find the total number of problems in the packet, we need to sum up the number of problems solved by each person:

P = 6(B + 4) + (B + 3)(B - 2)

We can simplify this equation:

P = 6B + 24 + B² - 2B + 3B - 6

Combining like terms:

P = B² + 7B + 18

Now, we know that Annie, Ben, and Claire each worked at a constant rate, so the number of problems solved is directly proportional to the number of days worked.

Since the problem states that Annie finished four days after Ben did, we can set up the equation:

6(B + 4) = B

Simplifying this equation:

6B + 24 = B

5B = -24

B = -24/5

However, the number of days cannot be negative, so this solution is not valid. Therefore, there must be an error in the problem statement, as the information given leads to an inconsistent situation.

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The distance from boat A to the port is approximately 5.196 miles.

Let's let point P represent the port.

Here A represent boat A and B represent boat B.

It is also given distance between A and B as 12 miles.

Next, we are finding the angles which boat A and boat B make with the line connecting them.

Let's call this line AB.

We can find these angles by subtracting the given bearings from 180 degrees.

For boat A, the angle it makes with AB is 180° - 60° = 120°

For boat B, the angle it makes with AB is 180° - 35° = 145°

Now we can use trigonometry to find the distance from boat A to the port. Let's call this distance x.

We can use the law of sines, which states

sin A / a = sin B / b = sin C / c

where A, B, and C are angles of a triangle and a, b, and c are the side lengths opposite those angles.

In our case, we can use the angle at boat A (which is 60 degrees) and the angle at the port (which is 120 degrees) along with the side opposite the angle at boat A (which is x) and the side opposite the angle at the port (which is 12-x), sin 60° / x = sin 120° / (12 - x)

We are Simplifying,

√3 / x = √3 / (12 - x)

Multiplying both sides by x(12-x),

12√3 - 3x√3 = x√3

Simplifying further,

12√3 = 4x√3

Dividing both sides by 4√3,

x = 3√3

Therefore, the distance from boat A to the port is approximately 5.196 miles.

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\(\cos 3\pi = \cos \pi =-1\)

Answer:

It's C

Step-by-step explanation:

Answer:

468

Step-by-step explanation:

Employee : instructor = 24 : 2

If there are 39 instructors

Employee = x

Employee : instructor = x : 39

Equate both ratios

24 : 2 = x : 39

24/2 = x/39

Cross product

24 * 39 = 2 * x

936 = 2x

x = 936/2

x = 468

Employees = x = 468

Answer:

The answer is 1,000

It is possible to have a triangle with sides 3,6, and 7 according to the triangle inequality theorem.

What is the triangle inequality theorem?

The triangle inequality theorem states that the sum of any two sides of a given triangle is always greater than the third side of the same triangle.

Now using this theorem, let's check if the given sides can form a triangle.

3+6 > 7, follows the theorem

3+7 > 6, follows the theorem

6+7 > 3, follows the theorem

Therefore it is possible to form a triangle using sides 3,6 and 7.

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Answer: \(3\frac{21}{30} ,3\frac{14}{28},\frac{15}{25},0.5,-0.7\)

Step-by-step explanation:

\(-0.7=-0.7\\\\3\frac{21}{30}=3.7\\\\3\frac{14}{28}=3.5\\\\0.5=0.5\\ \\\frac{15}{25}=0.6\)

Answer:

4ac

Step-by-step explanation:

Assuming you're referring to the equation \(ax^2+bx+c=0\).

Since the discriminant \(D=b^2-4ac\) has to be equal to 0 in order for there to be exactly one real solution, then we have the following:

\(0=b^2-4ac\\b^2=4ac\)

Therefore, b² needs to be the same value as 4ac.

The inverse of the function (1/2)^x/3

Given function,

y = 3\(log_{1/2}\) x

Now,

y = 3\(log_{1/2}\) x

Let y = f(x)

then,

x = \(f^{-1} (y)\)

Now put \(f^{-1} (y)\) in the place of x,

y = 3\(log_{1/2}\) \(f^{-1} (y)\)

Simplifying,

y/3 = \(log_{1/2} f^{-1} (y)\)

\(f^{-1} (y) = 1/2^{y/3}\\\)

Replace y variable with x,

\(f^{-1} (x)\) = \((1/2)^{x/3}\)

Hence the inverse of function is \((1/2)^{x/3}\) .

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Data

• Morning: 156 times

• Lunch: x times

• Afternoon: 201 times

• Whole day: 562 times

Procedure

To know how many times did it ring at lunch, we have to build a relation, in which we know that the addition of the times in the morning, lunch, and afternoon equal the times it rang the whole day:

Then, we have to solve for x considering that it represents the times it rang during the lunch.

Answer: It rang 205 times during the afternoon.

Answer:

F

Step-by-step explanation:

rise/run is 3/2 which is the number before the x and the y intercept (the last number in the equation) is 3