The price of a gallon of gasoline is $3.15. The price when Ryan's mother started driving was of the current price. What was the price of gasoline when Ryan's mother started driving?

Answer:

H (Height) = 3

Step-by-step explanation:

We have the formula A = 1/2(a+b)h

Let's identify all variables

A = 24

a = 9

b = 7

h = ?

Lets plug all that in:

24 = 1/2(9+7)h

9+7 = 16

24 = 1/2(16)h

Half of 16 is 8 so to simplify the rest...

24 = 8h

To get h alone we will divide both sides of the equation by 8

24/8 = h

24/8 = 3

Making H = 3

Answer:

Angle A

Step-by-step explanation:

Remember:

SOH CAH TOA

Opposite = Directly across from.

Adjacent = Next to.

Hypotenuse = Longest side.

Tangent = Opposite Side / Adjacent Side.

✓ Tan A = 6 / 8 = 3 / 4 = 3 / 4

× Tan B = 8 / 6 = 4 / 3 ≠ 3 / 4

× Tan C = 10 / 8 = 5 / 4 ≠ 3 / 4

Answer:

6 years ago

Step-by-step explanation:

\(6(14-x)=54-x\\84-6x=54-x\\30-6x=-x\\30=5x\\6=x\)

So, Pete's grandfather was 6 times as old as Pete 6 years ago. This means that when Pete was 8 years old, his grandfather was 48 years old.

Therefore , the solution of the given problem of probability comes out to be  likelihood that a pupil who received a B is male is therefore 1/5,

or 0.2.

The primary goal of the schemes within a technique known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any figure between 0 and 1, with 0 typically signifying probability and 1 typically signifying a degree of certainty, can represent chance. A probability diagram shows the chance that a specific event will occur.

Here,

The Bayes theorem can be used to determine the likelihood that a pupil is male given that they received a B.

=> P(Male | B) = P(B | Male) * P(Male) / P(B)

where P(Male) is the likelihood that the student is male, P(Male) is the likelihood that the student is male, and P(B) is the chance that the student will receive a B overall.

Using the data in the chart, we can determine these probabilities:

P(B | Male) = 4/25

P(Male) = 25/65

P(B) = (4+16)/65 = 20/65

By entering these numbers, we obtain:

=> P(Male | B) = (4/25) * (25/65) / (20/65)

=>  4/20

=>  1/5

The likelihood that a pupil who received a B is male is therefore 1/5, or 0.2.

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i) The equation in vertex form is f(x) = (x - 2)² - 1.

ii) The vertex is (2,-1) and the axis of symmetry is x = 2.

iii) The x-intercepts are (1, 0) and (3, 0), and the y-intercept is (0, 3).

i) To write the equation in vertex form, we need to complete the square.

f(x) = x² - 4x + 3

f(x) = (x² - 4x + 4) - 1

f(x) = (x - 2)² - 1

ii) From the vertex form, we can see that the vertex of the parabola is at (2,-1). The axis of symmetry is the vertical line passing through the vertex, which is x = 2.

iii) To find the x-intercept, we need to set f(x) = 0 and solve for x

0 = (x - 2)² - 1

1 = (x - 2)²

x - 2 = ±√1

x = 2 ± 1

x = 1, 3

So the x-intercepts are (1, 0) and (3, 0).

To find the y-intercept, we need to set x = 0 and evaluate f(x):

f(0) = (0)² - 4(0) + 3

f(0) = 3

So the y-intercept is (0, 3).

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The given question is incomplete, the complete question is:

Consider the parabola f(x) = x² - 4x + 3 i) Write the equation in vertex form. ii) Find the vertex and axis of symmetry. iii) Find the x-intercept and the y-intercept

Answer:

173 degrees

Step-by-step explanation:

we know AED + AEB + BEC + CED = 360

AEB = 112

to find BEC, we have B + BCE + BEC = 180 because they form a triangle. so BEC = 180 - B - BCE = 180 - 73 - 79 = 28

to find CED, follow the same steps as BEC: 180 - 37 - 96 = 47

now AED = 360 - AEB - BEC - CED = 360 - 112 -  28 - 47 = 173

Answer:

The total are of the three triangles is 36 square units.

The area of the figure is 60 square units.

Answer:

first box 36 second box 60

Step-by-step explanation:

If the fund manager consistently achieves an annual return of 10%, the amount of money in the investment fund will be approximately $46,610,000 in 16 years.

To calculate the future value of the investment fund after 16 years with a consistent annual return of 10%, we can use the compound interest formula:

Future Value = Present Value * (1 + Interest Rate)^Time

In this case, the present value (initial investment) is $8,000,000, the interest rate is 10% (or 0.10), and the time is 16 years. Plugging these values into the formula, we get:

Future Value = $8,000,000 * (1 + 0.10)^16

Simplifying the equation, we have:

Future Value = $8,000,000 * (1.10)^16

Calculating this expression, we find that the future value of the investment fund after 16 years is approximately $46,610,000.

Therefore, if the fund manager consistently achieves his target returns of 10%, there will be around $46,610,000 in the fund in 16 years.

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Out of the four options provided, Rome had the most influence on the structure of the U.S. government.

The Founding Fathers studied the government systems of ancient Greece and Rome and incorporated aspects of their political systems, such as a bicameral legislature and the concept of a republic, into the design of the U.S. government. Additionally, the U.S. system of checks and balances, which ensures no one branch of government has too much power, can be traced back to Roman political ideas. In short, the Roman civilization played a significant role in shaping the structure of the U.S. government. Key aspects of the U.S. system, such as separation of powers and the system of checks and balances, have been inspired by Roman political principles. Additionally, the concept of a representative democracy with elected officials can be traced back to the Roman Republic.

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Step-by-step explanation:

Here, Unitary Method is used. It tells:-

\(\bf{1 \ hour =}\) $ \(\bf{7.75}\)

\(\bf{28.5 \ hours =}\) $ \(\bf{(7.75 \times 28.5)}\)

$ \(\bf{220.875}\) is the answer.

Hope it helps :D

The probability that the mean contents of the bottles in a six-pack is less than 295 ml is approximately 0.1587, or 15.87%.

To solve this, use the standard normal distribution and the cumulative distribution function (CDF) of the normal distribution.

Standardize the value of 295 ml by subtracting the mean of the distribution (298 ml) and dividing by the standard deviation (3 ml):

Z = (295 - 298) / 3 = -1

The CDF of the standard normal distribution gives us the probability that a random variable from a standard normal distribution is less than or equal to a certain value. Using a standard normal table or a calculator with normal distribution functions, we find that the probability that a standard normal random variable is less than or equal to -1 is approximately 0.1587.

Since the contents of the bottles are normally distributed with mean 298 ml and standard deviation 3 ml, we can use the standard normal distribution and the standard score Z to approximate the probability of observing a mean contents of less than 295 ml in a six-pack of bottles. This probability is approximately 0.1587, or 15.87%.

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The output when the given pseudocode is executed with A = 5 and B = 3 will be "25, 16, 9, 4, 1".

The given pseudocode includes a loop that iterates as long as A is greater than or equal to B. In each iteration, the square of A is displayed, and A is decremented by 1. We are asked to determine the output when A is initially 5 and B is 3.

Step 1: Initialization

A is set to 5 and B is set to 3.

Step 2: Iteration 1

Since A (5) is greater than or equal to B (3), the loop executes.

The square of A (5²) is displayed, resulting in the output "25".

A is decremented by 1, so A becomes 4.

Step 3: Iteration 2

A (4) is still greater than or equal to B (3).

The square of A (4²) is displayed, resulting in the output "16".

A is decremented by 1, so A becomes 3.

Step 4: Iteration 3

A (3) is still greater than or equal to B (3).

The square of A (3²) is displayed, resulting in the output "9".

A is decremented by 1, so A becomes 2.

Step 5: Iteration 4

A (2) is still greater than or equal to B (3).

The square of A (2²) is displayed, resulting in the output "4".

A is decremented by 1, so A becomes 1.

Step 6: Iteration 5

A (1) is still greater than or equal to B (3).

The square of A (1²) is displayed, resulting in the output "1".

A is decremented by 1, so A becomes 0.

Step 7: Loop termination

Since A (0) is no longer greater than or equal to B (3), the loop terminates.

Therefore, The output generated by the code execution will be "25, 16, 9, 4, 1" as the squares of A (starting from 5 and decreasing by 1) are displayed in each iteration of the loop.

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Answer:

Step-by-step explanation:

Given is an isosceles triangle.

Sum of interior angles is 180°:

Correct choice is B

Answer:

Trinomial  of degree 2

Step-by-step explanation:

The given expression cannot be reduce any further as far as number of terms (there are no like terms in it), so it is a trinomial.

Also, the largest power for the variable  init (y) is the power 2, therefore it is a trinomial of degree 2.

Two organ systems that help maintain homeostasis after exercise are the respiratory system and the cardiovascular system.

1. Respiratory System:

During exercise, the increased activity of muscles leads to an increased demand for oxygen, and as a result, the cells produce more carbon dioxide (CO2) as a byproduct of cellular respiration. The respiratory system plays a vital role in maintaining homeostasis by regulating the levels of oxygen and carbon dioxide in the body.

After exercise, the respiratory system responds by increasing the rate and depth of breathing. This elevated ventilation allows for a greater intake of oxygen from the inhaled air. The oxygen-rich air enters the lungs, where it diffuses across the thin walls of the alveoli and into the bloodstream. Simultaneously, the increased ventilation facilitates the removal of carbon dioxide from the bloodstream into the alveoli, ready to be exhaled.

By adjusting the rate and depth of breathing, the respiratory system helps restore homeostasis by replenishing oxygen levels and eliminating excess carbon dioxide. This ensures that the body's cells receive the necessary oxygen for energy production while preventing the buildup of carbon dioxide, which can be detrimental if allowed to accumulate.

2. Cardiovascular System:

The cardiovascular system, composed of the heart, blood vessels, and blood, works in conjunction with the respiratory system to maintain homeostasis after exercise. Its primary function is to deliver oxygen and nutrients to the tissues while removing waste products, including carbon dioxide.

During exercise, the cardiovascular system responds to the increased demand for oxygen and the accumulation of carbon dioxide. The heart rate increases, leading to a higher cardiac output. The cardiac output is the amount of blood pumped by the heart per minute, and it increases to meet the heightened oxygen requirements of the active muscles.

As the heart pumps more vigorously, blood flow to the muscles is enhanced. This allows for the delivery of oxygen and nutrients to the working tissues, promoting their optimal function. Simultaneously, the increased blood flow facilitates the removal of carbon dioxide produced during exercise.

The blood vessels also play a role in maintaining homeostasis after exercise. They undergo vasodilation, which means the blood vessels widen to accommodate the increased blood flow to the muscles. This vasodilation helps dissipate heat generated during exercise and allows for efficient oxygen and nutrient delivery to the tissues.

Together, the respiratory system and the cardiovascular system work synergistically to maintain homeostasis after exercise. The respiratory system ensures an adequate supply of oxygen and the elimination of excess carbon dioxide, while the cardiovascular system delivers oxygen and nutrients to the tissues while removing waste products. This coordinated effort helps restore the body's internal balance and supports efficient cellular function.

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The correct table to show the test on the outbreak of strep infection is d. actually had strep infection test positive for strep tests negative for strep total yes 9 1 10 no 18 72 90 total 27 73 100.

Out of a total of one hundred students, ten have strep infection. The test is successful in correctly identifying the disease in ninety percent of those affected; meaning 0.9 x 10 equalling nine individuals tested positive and the lone tenth student tested negative.

Regarding the remaining ninety students without strep infection, the test corresponds to an accurate result with eighty percent accuracy. Thus, the calculation 0.8 x 90 performing the duty of rejection in 72 pupils and making affirmative tests with the remaining eighteen students.

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Answer:

-x

Step-by-step explanation:

I'm not sure if every teacher does this but my teacher does.

The Python script above prompts the user for the values of a, b, c, x, and y, and then tests whether the point (x, y) lies on the parabola described by the equation y=ax^2+bx+c. If the point lies on the parabola, the script prints out a message stating this. Otherwise, the script prints out a message stating that the point does not lie on the parabola.

The function is_on_parabola() takes in the values of a, b, c, x, and y, and then calculates the value of the parabola at the point (x, y). If the calculated value is equal to y, then the point lies on the parabola. Otherwise, the point does not lie on the parabola.

The main function of the script prompts the user for the values of a, b, c, x, and y, and then calls the function is_on_parabola(). If the point lies on the parabola, the script prints out a message stating this. Otherwise, the script prints out a message stating that the point does not lie on the parabola.

To run the script, you can save it as a Python file and then run it from the command line. For example, if you save the script as parabola.py, you can run it by typing the following command into the command line:

python parabola.py

This will prompt you for the values of a, b, c, x, and y, and then print out a message stating whether or not the point lies on the parabola.

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Answer:

D. 1024

Step-by-step explanation:

Each question can be answered 4 ways.

4 * 4 * 4 * 4 * 4 = 1024

D. 1024

The equation of the line is x = 25, in accordance with the given conditions.

Given:

To find: Equation of the line.

Finding:

Let the equation of the line be: (y - y') = m (x - x'),

where, (x',y') = point through which the line passes and m = slope of the line.

The slope of the first line = \(\frac{1}{0}\) , i.e., the y-intercept of this line does not exist and it is a vertical line.

Hence, the equation of the line is 0 = 1 (x - x')

Thus, the equation of the line => 0 = 1 (x - 25)

=> x = 25.

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Answer:

which class

Step-by-step explanation:

.,........

The center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

The equation of the circle is given as x² + y² - 32x+24y +396 = 0.

Comparing the given equation with general equation of circle, x² + y² + 2gx + 2fy + c = 0.

The center of circle is C = (-g, -f)

The radius of circle is r = √g² + f² - c

Therefore, from the given equation,

2g = -32

g = -16

2f = 24

f = 12

C( -16, 12)

And the radius is

r = √(-16)² + (12)² - 396

= √256 + 144 -396

=√4

= 2

Hence, the center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

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Answer:

The correct answer is A

Step-by-step explanation:

20% x 12 = 2.4

2.4 + 12 = 14.4

20% x 8 = 1.6

1.6 + 8 = 9.6

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Answer:

x, y

Step-by-step explanation:

Answer:

Step-by-step explanation:

6c + 18-4c + 16

Solving like terms

2c + 34

Answer: 2c + 2

6(c + 3) - 4(c + 4)

= 6c + 18 - (4c + 16)

= 6c + 18 - 4c - 16

= 2c + 2

Step-by-step explanation:

Answer:

1/27

Step-by-step explanation:

Ok this looks like a huge number but if you break it into smaller numbers its easier to work with

3^5=243 so we can write...

(3^5)^-3/5

Rule of exponents state that you can multiply powers

5*3/5=15/5=-3

Because its negative we would make it over 1

1/3^3

And simplify...

1/3*3*3

1/27

The z-score associated with a 95% confidence level is approximately 1.96.

The z-score associated with a 95% confidence level is the value of the standard normal distribution that corresponds to an area of 0.95 to the left of the z-score.

Using a standard normal distribution table or calculator, we can find that the z-score associated with a 95% confidence level is approximately 1.96.

Therefore, if we want to calculate the z-score for a 95% confidence level, we can use the formula

z = invNorm(1 - α/2)

where α is the significance level (α = 0.05 for a 95% confidence level), and inv Norm is the inverse normal cumulative distribution function. Using this formula, we can calculate the z-score as:

z = inv Norm(1 - 0.05/2)

= inv Norm(0.975) ≈ 1.96

Therefore, the z-score is 1.96

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According to the ratio, it doesn't make sense to have a total of 9 people in the dance competition.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

The ratio of boys to every girls is 3:2 in a dance competition.

Let's find if it will make sense to have a total of 9 people in the competition.

Therefore,

number of boys = 3 / 5 × 9 = 27 / 5 = 5.4

number of girls = 2 / 5 × 9 = 18 / 5 = 3.6

Therefore, it doesn't make sense to have 9 people in the competition because the actual number of boys and girls will be in decimal which is impossible.

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Answer:

c = 3, -19

Step-by-step explanation:

\(-9|c+8|=-99 \\ \\ |c+8|=11 \\ \\ c+8=\pm 11 \\ \\ c=-8 \pm 11 \\ \\ =3, -19\)