10.45% of all marathon runners also enjoy
biking. If many samples of 60 marathon
runners are taken and the proportion of those
who also enjoy biking is calculated for each
sample, what will be the approximate value of
the mean of the sample proportions?
Answer choices:
0.30
0.45
0.60
0.75

Answer:

21

Step-by-step explanation:

The average rate of change of function f(x) from x = a to x = b is

\( \dfrac{f(b) - f(a)}{b - a} \)

Here we have

a = -1

b = 2

f(a) = f(-1) = 1

f(b) = f(2) = 64

\( \dfrac{f(b) - f(a)}{b - a} = \)

\( = \dfrac{f(2) - f(-1)}{2 - (-1)} = \)

\( = \dfrac{64 - 1}{2 + 1} \)

\( = \dfrac{63}{3} \)

\( = 21 \)

The equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.

To test the validity of the equation x = x₀ + v₀t + (1/2)at², we can check if the dimensions on both sides of the equation are consistent.

Breaking down the dimensions of each term:

x: Displacement has dimensions of length (L).

x₀: Initial displacement has dimensions of length (L).

v₀t: Velocity times time has dimensions of (L/T) * T = L.

(1/2)at²: Acceleration times time squared has dimensions of (L/T²) * T² = L.

Since the dimensions on both sides of the equation are consistent (L = L), the equation x = x₀ + v₀t + (1/2)at² is valid.

Now, let's use dimensional analysis to find the relationship of the periodic time T of a simple pendulum using the factors affecting it: mass of the bob (m), length (L) of the pendulum, and acceleration due to gravity (g).

The factors affecting the periodic time T of a simple pendulum are:

Mass (m): Denoted by [M].

Length (L): Denoted by [L].

Acceleration due to gravity (g): Denoted by [LT⁻²].

The periodic time T of a simple pendulum is expected to depend on these factors in some way.

By applying dimensional analysis, we can determine the relationship between these factors. The equation is given as T = 2π √(L/g), where T is the periodic time, π is a constant, L is the length, and g is the acceleration due to gravity.

Breaking down the dimensions of each term:

T: Periodic time has dimensions of time (T).

2π: A constant, so it is dimensionless.

√(L/g): The square root of the ratio of length to acceleration due to gravity has dimensions of √([L]/[LT⁻²]) = √(T²) = T.

Therefore, the equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.

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Answer:

Step-by-step explanation:

4 and 1/6

a. To approximate the given quantity using Taylor polynomials with n=3, we need to use the formula for the Taylor polynomial of degree n:

Pn(x) = f(a) + f'(a)(x-a) + (1/2!)f''(a)(x-a)^2 + (1/3!)f'''(a)(x-a)^3 + ... + (1/n!)f^(n)(a)(x-a)^n
where f(x) = sinh(x), a = 0. The derivatives of sinh(x) are:
f'(x) = cosh(x), f''(x) = sinh(x), f'''(x) = cosh(x), and so on.
Therefore, the Taylor polynomial of degree 3 for sinh(x) centered at a = 0 is:
P3(x) = x + (1/2!)(x)^3
To approximate sinh(0.24), we substitute x = 0.24 into the formula above:
P3(0.24) = 0.24 + (1/2!)(0.24)^3 = 0.240008
b. To compute the absolute error in the approximation assuming the exact value is given by a calculator, we need to subtract the actual value of sinh(0.24) from the approximation we obtained in part a:
Error = |P3(0.24) - sinh(0.24)| = |0.240008 - 0.241663| = 0.001655
Therefore, the absolute error in the approximation is 0.001655.
To approximate sinh(0.17), we use the same formula and substitute x = 0.17:
P3(0.17) = 0.17 + (1/2!)(0.17)^3 = 0.170005
To compute the absolute error in this case, we subtract the actual value of sinh(0.17) from the approximation we obtained:
Error = |P3(0.17) - sinh(0.17)| = |0.170005 - 0.17031| = 0.000305
Therefore, the absolute error in the approximation for sinh(0.17) is 0.000305.

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True, if a ∈ Z and a ≡ 1 (mod 5), then a^2 ≡ 1 (mod 5). a^2 - 2a + 1 = 25k^2 = 0, which implies that a^2 - 2a + 1 is divisible by 5, i.e., a^2 ≡ 1 (mod 5). Hence, the statement is true.

We can prove this by using the definition of modular congruence. Since a ≡ 1 (mod 5), we know that a - 1 is divisible by 5, i.e., a - 1 = 5k for some integer k. Squaring both sides of this equation, we get:

a^2 - 2a + 1 = 25k^2

Adding 4a - 4a to the left-hand side, we get:

a^2 - 2a + 1 + 4a - 4a = 25k^2

Rearranging, we get:

(a^2 - 2a + 1) - 4a = 25k^2 - 4a

Factorizing the left-hand side, we get:

(a - 1)^2 - 4a = 25k^2 - 4a

Since a ≡ 1 (mod 5), we can substitute 1 for a in the above equation to get:

(1 - 1)^2 - 4(1) = 25k^2 - 4(1)

Simplifying, we get:

-4 = 25k^2 - 4

Adding 4 to both sides, we get:

0 = 25k^2

This implies that k = 0, since k is an integer. Therefore, a^2 - 2a + 1 = 25k^2 = 0, which implies that a^2 - 2a + 1 is divisible by 5, i.e., a^2 ≡ 1 (mod 5). Hence, the statement is true.

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Answer:

62.5%

Step-by-step explanation:

1875 diveded by 3000 = 62.5

Based on the amount deposited into the account every month, the amount that Andrew will deposit in the account is $72,548.64. The interest earned will be $17,451.36.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

here, we have,

What amount does Andrew deposit?

This can be found by the formula:

= Amount deposited every month x Number of years x Number of months in a year

= 503.81 x 12 x 12

= $72,548.64

What amount of interest is earned?

This can be found as:

= Future value of amount - Amount deposited

= 90,000 - 72,548.64

= $17,451.36

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Using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.

In mathematics, a quantity or ratio known as A% stands for a percentage of 100.

There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.

To represent percentages, the symbol "%" is typically written after the number.

So, we know that:

The bond is $350.

The return is 125% when Greg turns 30.

Then, the amount after she turns 30 will be as follows:

350/100 * 125

437.5

Bonds value: 437.5 + 350 = $787.5

Therefore, using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.

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Yes, if a figure can be rotated 360° to be mapped onto itself, it is considered to have rotational symmetry.

This is because a 360° rotation means that the figure will return to its original position, making it symmetrical. Rotational symmetry is a type of symmetry where a figure can be rotated about a central point and still look the same. The degree of rotational symmetry depends on the number of times a figure can be rotated to match its original appearance. Therefore, if a figure can be rotated 360° and maintain its original appearance, it is said to have rotational symmetry of degree 1. This is true regardless of the size, orientation, or position of the figure. Yes, a figure that can be rotated 360° to be mapped onto itself is considered to have rotational symmetry. Rotational symmetry occurs when an object can be rotated around a central point and still appear the same as its original position. In the case of a 360° rotation, the figure returns to its initial configuration, confirming its rotational symmetry.

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Answer:

y=-2x

Step-by-step explanation:

y-4=-2(x-(-2))

y-4=-2(x+2)

y-4=-2x-4

y=-2x-4+4

y=-2x

Answer:

2,889,124,530

The size of the segments are  15. 52cm, 34. 94cm and 50. 64cm respectively

From the information given, we have that;

Now, the sum of the segments is equivalent to;

first segment + second segment + third segment

Substitute the values, we get;

4/9y + y + 4/9y + 16 = 82

collect like terms

4/9y + 4/9y + y = 82 - 16

Add or substract like terms

4y + 4y + 9y/9 = 66

Add the numerators

17y = 66(9)

17y = 594

Divide both sides by 17

y = 34. 94

Hence, the segments are  15. 52cm, 34. 94cm and 50. 64cm

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Answer:

5/2

Step-by-step explanation:

10 multiplied by 5/2 gives us 25, so the scale factor is 5/2.

An equation of the line with the given gradient and points is \(y=\frac{2x}{3} -\frac{7}{3}\)

Given the following data:

To find an equation of the line with the given gradient and points:

Mathematically, the equation of a line is given by this formula:

\(y-y_1 =m(x-x_1)\)

Where:

Substituting the given parameters into the formula, we have;

\(y-(-3) =\frac{2}{3} (x-[-1])\\\\y+3=\frac{2}{3} (x+1)\\\\3y+9=2x+2\\\\3y=2x+2-9\\\\3y=2x-7\\\\y=\frac{2x}{3} -\frac{7}{3}\)

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The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.

a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.

Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.

The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35

The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62

The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95


b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.

Expected number of cars = 1/p = 1/0.23 ≈ 4.35

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The area of a triangle is given by:

Where:

b = base

h = height = 8.2

A = Area = 12

Therefore:

Answer:

A) 3 inches

Answer:

21.6%

Step-by-step explanation:

Answer:

pi

Step-by-step explanation:

First solve the integral

\(\int\ {(1+ cos x} )\, dx\)

\(\int\ {1} \, dx +\int\ {cos x} \, dx\)

\(\int\ {1} \, dx = x\) and \(\int\ {cos x} \, dx = sin x\)

x + sin x

Now consider the limit from 0 to π

\(\lim_{0 \to \\pi } (x+sin x)\)

(π +sin π) -(0 +sin 0)

sin π = 0 and sin 0 = 0

π-0

π

Answer:

\(\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx=\pi\)

Step-by-step explanation:

\(\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx\\\\=x+\sin x\biggr|^{\pi}_0\\\\=[\pi+\sin\pi]-[0+\sin0]\\\\=\pi\)

Remember your antiderivatives!

Answer:

C and A

Step-by-step explanation:

Comparison or relational operations, such as <, >, =, allow for comparing numbers. They determine if a number is less than, greater than, equal to, or not equal to another number, enabling decision-making and comparisons within arithmetic and programming operations.

When comparing numbers, you can use various relational operators to determine the relationship between them. Here are the commonly used comparison operators:

Less than (<): This operator compares two numbers and returns true if the first number is smaller than the second number. For example, 5 < 10 is true.

Greater than (>): This operator compares two numbers and returns true if the first number is larger than the second number. For example, 10 > 5 is true.

Less than or equal to (<=): This operator compares two numbers and returns true if the first number is smaller than or equal to the second number. For example, 5 <= 5 is true.

Greater than or equal to (>=): This operator compares two numbers and returns true if the first number is larger than or equal to the second number. For example, 10 >= 10 is true.

Equal to (==): This operator compares two numbers and returns true if they are equal. For example, 5 == 5 is true.

Not equal to (!=): This operator compares two numbers and returns true if they are not equal. For example, 5 != 10 is true.

These comparison operators allow you to compare numbers and make decisions based on their relationships within arithmetic or programming operations.

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Answer:

A = 720 mm²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 40 and h = 18 , then

A = 40 × 18 = 720 mm²

Answer:

x=−4

Step-by-step explanation:

Rearrange terms

20−2=−7

−2+20=−7

Subtract 20 from both sides of the equation

−2+20=−7

−2+20−20=−7−20

Subtract the numbers

−2=−7−20

Add 7 to both sides of the equation

−2=−7−20

−2+7=−7−20+7

Simplify

5=−20

Divide both sides of the equation by the same term

5x=-20

5x/5=-20/5

Simplify

x=-4

Answer:

plane

Step-by-step explanation:

Answer:

B. A plane

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer: Reform

Step-by-step explanation:

Reform means make changes in order to improve it.

There are 7 different orders possible if the series goes four games.

If the series goes exactly four games, then one team must win at least three of those games in order to win the series.

Without loss of generality, let's assume that the American League (AL) team wins the series in four games.

There are several possible ways that this could happen:

Therefore, there are 7 different orders possible if the series goes four games.

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Answer:

144

Step-by-step explanation:

do 5 into 600 and u get 12 have a good day!!!

Answer:

$144

Step-by-step explanation:

first, we need to divide 600 by 50, to get them organized for the best packages. 600/50 = 12.

then, we multiply that (the 12) by the cost ($12/ea) so 12*12 which is $144 if they use the bundling.

The monthly revenue of the business grows by 8%, monthly.

The definition of revenue?

The total income a firm receives from the sale of products or services that are connected to its core business operations is referred to as revenue.

                           Since it appears at the top of the income statement, revenue, also known as gross sales, is frequently referred to as the "top line." An organization's whole earnings or profit is known as income, or net income.

An exponential function is represented as

   y = abˣ

From the  table we have the following ordered pair

(x,y) = {(0,72000) (3,90000)}

So, we have

   90000 = 72000 * b³

     Divide both sides by 72000

      b³  = 1.25

Take the cube roots of both sides

   b = ∛1.25

    b = 1.08

Recall that

b = 1 +r

  1 + r = 1.08

  r = 0.08

  r = 8%

Hence, the monthly revenue of the business grows by 8%, monthly.

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