Carey's graph will be a straight line with a slope of -1 and a y-intercept of 3.
Carey correctly graphs a linear function with a slope of -1 and a y-intercept of 3. A linear function is represented by the equation y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope is -1, which means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1 unit. The y-intercept is 3, indicating that the graph intersects the y-axis at the point (0, 3).
To plot the graph, Carey starts by marking the point (0, 3) on the graph. Then, for every unit increase in the x-coordinate, Carey moves one unit downward. Similarly, for every unit decrease in the x-coordinate, Carey moves one unit upward. These steps ensure the correct slope of -1.
After connecting the points, Carey will obtain a line that starts at the y-intercept (0, 3) and slants downward, with a slope of -1. The resulting graph will be a straight line extending to both sides of the coordinate plane.
In conclusion, it is represented by the equation y = -x + 3.
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Suppose it is known that 20% of college students work full time.
Part A: If we randomly select 12 college students, what is the probability that exactly 3 of the 12 work full time? Round your answer to 4 decimal places.
Answer:
0.2369
Step-by-step explanation:
To find the probability of exactly 3 out of 12 randomly selected college students working full time, we can use the binomial probability formula.
The formula for the probability of exactly k successes in n trials, where the probability of success is p, is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
In this case, n = 12 (number of trials), k = 3 (number of successes), and p = 0.20 (probability of success, i.e., percentage of college students working full time).
Plugging in the values:
P(X = 3) = (12 choose 3) * 0.20^3 * (1 - 0.20)^(12 - 3)
Calculating the expression:
P(X = 3) = (12! / (3! * (12 - 3)!)) * 0.20^3 * (0.80^9)
= (12! / (3! * 9!)) * 0.008 * 0.134217728
≈ 0.2369 (rounded to 4 decimal places)
Therefore, the probability that exactly 3 out of the 12 randomly selected college students work full time is approximately 0.2369.
Hope this helps!
Hayden bikes 1.8 miles in 6 minutes. His friend Jordan bikes 3.2 miles in 8 minutes. Part A: Who bikes at a faster speed? Explain your answer.
Jordan bikes at a Faster speed than Hayden because he covers a greater distance in the same amount of time.
To determine who bikes at a faster speed, we can compare the rates at which Hayden and Jordan cover distance over a given time period.
Hayden bikes 1.8 miles in 6 minutes, which can be expressed as a rate of 1.8 miles / 6 minutes = 0.3 miles per minute.
Jordan bikes 3.2 miles in 8 minutes, which can be expressed as a rate of 3.2 miles / 8 minutes = 0.4 miles per minute.
Comparing the two rates, we can see that Jordan bikes at a faster speed. Jordan covers a greater distance (3.2 miles) in the same amount of time (8 minutes) compared to Hayden, who only covers 1.8 miles in 6 minutes. Therefore, Jordan's rate of 0.4 miles per minute is greater than Hayden's rate of 0.3 miles per minute, indicating that Jordan bikes at a faster speed.
In summary, Jordan bikes at a faster speed than Hayden because he covers a greater distance in the same amount of time.
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A system of equations is given.
Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7
Explain how to eliminate x in the system of equations.
Step-by-step explanation:
To eliminate x in the system of equations:
1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:
Equation 1: 36x -54y = 90
Equation 2: -36x - 8y = -28
2. Add the two equations together to eliminate x:
(36x - 54y) + (-36x - 8y) = 90 - 28
Simplifying, we get:
-62y = 62
3. Solve for y:
y = -1
4. Substitute y = -1 into one of the original equations, say Equation 1:
4x - 6(-1) = 10
Simplifying, we get:
4x + 6 = 10
5. Solve for x:
4x = 4
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.
Find the value of each variable
The value of x is calculated as 30.
The value of y is calculated as 28.
What is the measure of angle x and y?The measure of x and y is calculated by applying the following circle theorem as follows;
If line XZ is the diameter of the circle, then angle XYZ will be equal to 90 degrees.
The value of x is calculated as;
3x = 90
x = 90 / 3
x = 30
The value of y is calculated as follows;
2y + 34 = 90 (complementary angles sum up to 90 degrees)
2y = 56
y = 56/2
y = 28
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Solve the equation log(base 2)(x) + log(base 4)(x+1) = 3.
We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:
log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))
Using the rule log_a(b^c) = c*log_a(b), we can simplify further:
log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))
Now we can rewrite the equation as:
log_2(x(x+1)^(1/2)) = 3
Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:
x(x+1)^(1/2) = 2^3
Squaring both sides, we get:
x^2 + x - 8 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 1, and c = -8. Plugging in these values, we get:
x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)
x = (-1 ± sqrt(33)) / 2
x ≈ -2.54 or x ≈ 3.54
However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:
log_2(3.54) + log_4(4.54) = 3
0.847 + 0.847 = 3
So x = 3.54 is the valid solution to the equation.
If the diameter of pulley A is 5.74 cm and the diameter of pulley B is 8.61 cm, what is the pulley ratio? please explain the steps.
The pulley ratio is approximately 0.6667, calculated by dividing the Diameter of pulley A (5.74 cm) by the diameter of pulley B (8.61 cm).
The pulley ratio, we need to compare the diameters of the two pulleys. The pulley ratio is the ratio of the diameters of pulley A to pulley B.
Given that the diameter of pulley A is 5.74 cm and the diameter of pulley B is 8.61 cm, we can calculate the pulley ratio using the following steps:
Step 1: Write down the diameters of pulley A and pulley B.
Diameter of pulley A = 5.74 cm
Diameter of pulley B = 8.61 cm
Step 2: Calculate the pulley ratio.
Pulley ratio = Diameter of pulley A / Diameter of pulley B
Substituting the given values, we have:
Pulley ratio = 5.74 cm / 8.61 cm
Step 3: Simplify the ratio if possible.
In this case, the ratio cannot be simplified further since the diameters do not have any common factors other than 1.
Step 4: Calculate the final result.
Pulley ratio = 5.74 cm / 8.61 cm ≈ 0.6667 (rounded to four decimal places)
Therefore, the pulley ratio is approximately 0.6667.
When discussing technical concepts and calculations, it is important to maintain academic integrity and avoid plagiarism. Plagiarism involves using someone else's work or ideas without proper attribution. To ensure originality, it is essential to express the information in your own words and provide accurate calculations based on the given data.
In conclusion, the pulley ratio is approximately 0.6667, calculated by dividing the diameter of pulley A (5.74 cm) by the diameter of pulley B (8.61 cm).
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The measure of angle 1 is 130⁰.
The measure of angle 1 is given as 130 degrees.the measure of angle 1 is 130 degrees provides specific information about the amount of rotation between the two rays or lines
An angle is a geometric figure formed by two rays or lines that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays or lines.
In this case, angle 1 has a measure of 130 degrees. This means that if we were to rotate one of the rays or lines forming the angle by 130 degrees, it would coincide with the other ray or line.
The degree is a unit of measurement for angles, and it is based on dividing a full circle into 360 equal parts. Each part, or degree, corresponds to a specific amount of rotation. In this case, angle 1 is measured to be 130 degrees, which is less than half of a full circle.
When interpreting the measure of angle 1, it's important to consider the context in which it is being used. Angles can be found in various settings, such as geometry, trigonometry, or real-world applications. Depending on the context, the measure of an angle can have different interpretations and implications.
In geometry, angles are used to describe the relationships between lines, shapes, and spatial configurations. They are often classified based on their measures, such as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), or straight (exactly 180 degrees).
In trigonometry, angles are used to define the ratios of sides in right triangles and to study periodic functions such as sine and cosine.
In real-world applications, angles can be used to measure directions, inclinations, or orientations of objects or phenomena.
Therefore, knowing that the measure of angle 1 is 130 degrees provides specific information about the amount of rotation between the two rays or lines
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You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly.
How much should you deposit each month?
Round your answer to the nearest cent. Do not include the dollar sign in the answer box below.
The calculation of this can be done by first determining the future value of the monthly payments of $327.50
The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,
which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.
The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35
This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.
Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.
for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).
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