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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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.
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!
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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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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