Circle O is shown with points A, B, C, and D on Circle O.



If x=50, what is the value of y and the angle measurement of ∠AOB?

Answer:

-8 ≤ y ≤ 7

Step-by-step explanation:

The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

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The maximum horsepower of the ice cream truck engine is 827.025.

For quadratic equation y = ax² + bx + c, the maximum value of y is given by:

y(max) =  c- b²/4a

Since the horsepower generated by the ice cream truck engine power curve is approximated by Y = -X²/5000 + 19x/23 -26

In this case, a = -1/5000, b = 19/23 and c = -26

Thus, the maximum horsepower will be:

maximum horsepower =  -26 - (19/23)²/[4*(-1/5000)]

maximum horsepower = 827.025 horsepower

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Answer:

Given:

Total women -  189

Smokers - 74

Non-smokers - 115

The difference in 2 samples mean birth weight = 281.7 grams

95% confident that the mean weight = between 76.5 grams to 486.9  

solution:

The best interpretation would be -

95% confident that the babies of nonsmokers have a mean weight between 76.5 grams to 486.9 grams which is much more than the babies of women smokes by comparing smokers to nonsmokers from given data.

Consider the expression 4(8x + 5)

Complete 2 descriptions of the parts of the expression.

1. The entire expression is the product of 2 factors.

2. On its own, (8x + 5) is a sum with 2 terms.

The total change in yards where the team started is 3x

The given parameters in the question are:

Yards per play = unknown

Number of plays = 3 consecutive plays

Represent the yards per play with x

So, we have

Yards per play = x

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = x * 3

Evaluate

Total change = 3x

Hence, the total change is 36 yards

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Answer:

a. The mean of a sample from a population that is not normally distributed will tend towards a normal distribution if the sample size is large.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

So, according to the above text, the correct answer is given by option a, that is, if the sample is large, the sampling distribution of the sample mean will be approximately normal, that is, trend towards a normal distribution.

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

The Volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.

The volume of each bead, the volume of a sphere using its diameter. The formula for the volume of a sphere is given by:

V = (4/3) * π * r^3

where V is the volume and r is the radius of the sphere.

Given that the diameter of each bead is 1.5 millimeters, we can calculate the radius as half of the diameter:

r = 1.5 mm / 2 = 0.75 mm

Now, we can substitute the value of the radius into the volume formula:

V = (4/3) * π * (0.75 mm)^3

Using the value of π ≈ 3.14 and performing the calculations:

V ≈ (4/3) * 3.14 * (0.75 mm)^3

V ≈ (4/3) * 3.14 * 0.421875 mm^3

V ≈ 1.767 mm^3 (rounded to the nearest tenth)

the volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.

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Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.

In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.

The intersection of two sets contains only the elements that are present in both sets. In this case,

R ∩ S = {x | x > 0 and x < 3}

The integers that are present in this set are 1 and 2.

Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

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which statements about Ancient Greek life are shown by the story of perseus

Answer:

110 base 4

Step-by-step explanation:

The answer is 110 base 4

The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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D

Step-by-step explanation:

the y is -2

and the slope is 2/5

which means it is y=2/5x -2

Answer:

(x − 1)² + (y − 2)² = 25

Step-by-step explanation:

Equation of a circle is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.

Answer:

-5 degrees

Step-by-step explanation:

In this scenario, since the final temperature was the temperature that existed at midnight then that value is subtracted from the initial temperature which was at 6:00 PM. Therefore we do the following calculation...

(-2) - 3 = x

-5 = x

Finally, we can see that there was a change in temperature of -5 degrees between 6:00 P.M. and Midnight. Meaning that the temperature during this time dropped a total of 5 degrees. Since, real numbers include negatives then the answer to this question is -5 degrees

The answer is Option D

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer:

C becausee I'm trying to help

Answer:

let

custard pie be x

Step-by-step explanation:

1/7 x = 185

x=185× 7

x=1395

1/8 of x= 1395/8

1/8 of x=174.3

1/4 of x = 1395/4

=348.75

1/6 of x =1395/6

=232.5

Answer:

Drew burns 300 calories per hour playing basketball and 600 calories per hour canoeing.

Step-by-step explanation:

To solve this problem, we need to use a system of equations. Let's define two variables:

b = number of calories Drew burns per hour playing basketball

c = number of calories Drew burns per hour canoeing

Using these variables, we can set up two equations based on the information given:

Equation 1: 1b + 2c = 1500 (calories burned on Friday)

Equation 2: 2b + 3c = 2400 (calories burned on Saturday)

To solve for b and c, we can use elimination or substitution. Let's use elimination:

Multiply Equation 1 by 2:

2b + 4c = 3000

Subtract Equation 2 from this new equation:

(2b + 4c) - (2b + 3c) = 4c - 3c

c = 600

Now that we know c = 600, we can substitute this value into either Equation 1 or Equation 2 to solve for b. Let's use Equation 1:

1b + 2(600) = 1500

1b + 1200 = 1500

1b = 300

b = 300

Therefore, Drew burns 300 calories per hour playing basketball and 600 calories per hour canoeing.

Answer:

14 plates in one stack

Answer:

12:28

Step-by-step explanation:

yesterday the ratio would be 6:14 so then you double that to get 12:28

We are given two curves on a graph paper and we have to find the y values for the given x.

From the graph we can check for a value of x, what is the value of y from the curve.

x     -3     -2     -1    0      1         2        3

Exp  8      4      2    1      0.5  0.25  0.125

Lin.   7.5   6    4.5   3      1.5     0     -1.5

We find that the two have the same values where the two curves intersect.

From the graph we find that near to -3 and near to 2 both have the same values.

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The missing graph is attached below.

Answer: 3^3 Square root 3

Step-by-step explanation:

Answer:

a) 1.93

b) 97.32% of men are SHORTER than 6 feet 3 inches

c) 2.71

d) 0.34% of women are TALLER than 5 feet 11 inches

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

For man, \(\mu = 69.8, \sigma = 2.69\)

A feet has 12 inches, so this is Z when X = 6*12 + 3 = 75. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{75 - 69.8}{2.69}\)

\(Z = 1.93\)

b. What percentage of men are SHORTER than 6 feet 3 inches?

Z = 1.93 has a pvalue of 0.9732

97.32% of men are SHORTER than 6 feet 3 inches

c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

For woman, \(\mu = 64.1, \sigma = 2.55\)

Here we have X = 5*12 + 11 = 71.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{71 - 64.1}{2.55}\)

\(Z = 2.71\)

d. What percentage of women are TALLER than 5 feet 11 inches?

Z = 2.71 has a pvalue of 0.9966

1 - 0.9966 = 0.0034

0.34% of women are TALLER than 5 feet 11 inches