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10. find the measure of angle 1

11. find the measure of angle 2

12. given that AE=13, find the measure of segment DB

Answer: 3/8, 0.375, 37.5%

Step-by-step explanation:

Count the number of cards with odd numbers that are greater than 4. 5, 7, and 9 are odd numbers greater than 4. There are 3 cards with odd numbers greater than 4. Probability is found by dividing this by the total number of cards, 8. This gets you a fraction of 3/8.

The probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

This problem can be solved using the binomial distribution, since we are interested in the probability of a certain number of successes (adults who exercise regularly) in a fixed number of trials (selecting 11 adults randomly).

Let X be the number of adults who exercise regularly out of 11. Then X has a binomial distribution with parameters n = 11 and p = 0.25, since the probability of success (an adult who exercises regularly) is 0.25.

We want to find the probability that four or less adults exercise regularly, which is equivalent to finding the probability of X ≤ 4. We can use the binomial cumulative distribution function to calculate this probability:

P(X ≤ 4) = Σ P(X = k), for k = 0, 1, 2, 3, 4

Using a calculator, spreadsheet software, or a binomial probability table, we can find the probabilities for each value of k, and then add them up to get the cumulative probability:

P(X = 0) = (11 choose 0) * (0.25)^0 * (0.75)^11 = 0.0563

P(X = 1) = (11 choose 1) * (0.25)^1 * (0.75)^10 = 0.2015

P(X = 2) = (11 choose 2) * (0.25)^2 * (0.75)^9 = 0.3159

P(X = 3) = (11 choose 3) * (0.25)^3 * (0.75)^8 = 0.2747

P(X = 4) = (11 choose 4) * (0.25)^4 * (0.75)^7 = 0.1340

P(X ≤ 4) = 0.0563 + 0.2015 + 0.3159 + 0.2747 + 0.1340 = 0.9824

Therefore, the probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

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The average hours per day spent watching TV among all students at the school. It only mentions a survey conducted on smartphone ownership among 50 students at the school .

To determine the average hours per day spent watching TV among all students, a separate survey or study would need to be conducted.he sample size of 50 is relatively small, so the confidence interval may be wider than if a larger sample was used. The confidence level of 95% means that if 100 independent samples were drawn from the population, 95 of the intervals would contain the true population proportion of smartphone ownership.

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Using 3 different methods, we can find that YZ = 25m

Method 1:

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations -

sin(θ) = (opposite side)/Hypotenuse

cos(θ) = (adjacent side)/Hypotenuse

tan(θ) = (opposite side)/(adjacent side)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent side

YZ = opposite side.

We want to find YZ, so with the known things, we can use the first relation:

sin(30°) = YZ/50m

YZ = sin(30°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 2:

We know that the sum of the measure of all the internal angles of a triangle is always equal to 180°.

In a right-angled triangle, we have an angle equal to 90°.

Then we can write -

Z + 90° + 30° = 180°

Z = 180° - 90° - 30°

Z = 60°

From this angle, the side YZ is the adjacent side, then we can use the second trigonometric relation:

cos (60°) = YZ/50m

YZ = cos(60°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 3:

With the same angle of 60° we could find side XY, the opposite side as follows:

sin(60°) = XY/50m

XY = sin(60°) * 50m

XY = √3/2 *50m

XY = 25m

Now that we know one of the sides, we can use the last trigonometric relation-

tan(60°) = XY/YZ

tan(60°) = 43.3m/YZ

YZ =  43.3m/tan(60°)

YZ = 25m

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The complete question is -

Describe three ways to determine the measure of segment YZ.

Triangle XYZ is shown. Angle XYZ is a right angle and angle ZXY is 30 degrees. The length of hypotenuse XZ is 50 meters.

Answer:

C. y=x

Step-by-step explanation:

If you use a graphing calculator and plot the points (-3,5) & (5,-3) and then graph y=x you can see it is the line of reflection.

Also when reflecting over the line y=x, we switch our x and y.

The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

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Answer:

Step-by-step explanation:

Angles EBC and EDC are the same. and straight lines equal 180

so now to solve for x

\(180=134+10x+6\\180-134=134+10x+6-134\\46=10x+6\\46-6=10x+6-6\\40=10x\\40/10=10x/10\\4=x\)

Step-by-step explanation:

y = 37 + x

the 4th angle (bottom right) is

360 - 90 - 90 - 125 = 55°

because the sum of all angles in any quadrilateral is 360°.

now we can assume a right-angled triangle on the right side of the trapezium.

one leg is 15 cm (like the left side), the other leg is x cm. and the right side of the trapezium is the Hypotenuse.

the bottom right angle is 55°.

the upper angle is 125 - 90 = 35°.

we can use the law of sine to get x.

the law of sine is

a/sin(A) = b/(sin(B) = c/sin(C)

with a, b, c being the sides of the triangle opposite of the corresponding angles A, B, C.

so,

15/sin(55) = x/sin(35)

x = 15×sin(35)/sin(55) = 10.50311307... cm

y = 37 + 10.50311307... = 47.50311307... ≈

≈ 47.5 cm

The number of people attending affects how much food is prepared for a catered event. The number of people attending is the explanatory variable in this scenario.

One kind of independent variable is an explanatory variable. Both words are frequently used interchangeably. This is the variable that changes as we change it or watch it change. In other words, it is a factor that a researcher has changed in an experiment.

In the given situation, the number of people attending is an explanatory variable and the amount of food prepared is a dependent variable. As the number of people attending increases, the amount of food prepared also increases. This means the effect of one variable alters the effect of another variable. The change of one variable is called an independent variable while the change that occurs because of the independent variable is a dependent variable.

Therefore, the required answer is the number of people attending.

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All you have to do is add up all of the numbers and then yo uwill have your answer

Answer: The simplified answer will be: x^5

Step-by-step explanation:

x4x

=x4*x1

=(x*x*x*x)*(x)

=x*x*x*x*x

=x^5

Answer:

x⁵

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

x⁴ · x

Step 2: Simplify

Based on the given parameters, the expected value of x is 1.1

The table of values is given as

x 0 1 2 3

P(X=x) 0.3 a 0.2 0.1

The sum of probabilities is 1

So, we have

0.3 + a + 0.2 + 0.1 = 1

This gives

0.6 + a = 1

Evaluate

a = 0.4

The expected value of x is calculated as

E(x) = Sum of (x * P(x))

So, we have

E(x) = 0 * 0.3 + 1 * a + 2 * 0.2 + 3 * 0.1

This gives

E(x) = 0 * 0.3 + 1 * 0.4 + 2 * 0.2 + 3 * 0.1

Evaluate

E(x) = 1.1

Hence, the expected value of x is 1.1

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Answer:

see explanation

Step-by-step explanation:

To determine if (3, 1 ) is a solution to the system

Substitute x = 3 into both equations and evaluate. If the result is y = 1 for both then the point is a solution.

y = \(\frac{4}{3}\) × 3 - 3 = 4 - 3 = 1

y = - 2(3) + 7 = - 6 + 7 = 1

Since both equations equal 1 then

(3, 1 ) is a solution to the system

The radial acceleration of the Juno satellite in its circular orbit around Jupiter, with a radius of 100×10³ km and a speed of 200×10³ km/h, is approximately 1.272×\(10^(^-^2^)\) km/h².

To calculate the radial acceleration, we can use the formula for centripetal acceleration:

a = v² / r

where "a" is the radial acceleration, "v" is the velocity of the satellite, and "r" is the radius of the orbit.

Given that the velocity of Juno is 200×10³ km/h and the radius of the orbit is 100×10^3 km, we can substitute these values into the formula:

a = (200×10³ km/h)² / (100×10³ km) = 4×\(10^4\) km²/h² / km = 4×10² km/h²

Thus, the radial acceleration of Juno in its circular orbit around Jupiter is 4×10² km/h², or 0.4×10³ km/h², which is approximately 1.272× \(10^(^-^2^)\)km/h² when rounded to three significant figures.

Using the same formula as before:

a = v² / r

We know the new speed, v, is 300×10³ km/h, and the radial acceleration, a, remains the same at approximately 1.272×\(10^(^-^2^)\) km/h². Rearranging the formula, we can solve for the new radius, r:

r = v² / a

Substituting the given values:

r = (300×10³ km/h)² / (1.272×\(10^(^-^2^)\) km/h²) ≈ 7.08×\(10^6\) km

Therefore, the new radius of the circular trajectory, when the speed is increased to 300×10³ km/h while maintaining the same radial acceleration, is approximately 7.08× \(10^6\)km.

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Answer:

320 teenagers

Step-by-step explanation:

10% = 0.1

Take 3200 times 0.1 = 320

So, there are 320 teenagers attended the football game.

The values of y when x=5.7 will be 5. In the graphs, the function is represented as y=⌊x⌋

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

In the graphs the function y=⌊x⌋

The value of the y obtaining will be the whole number of the left axis of the integers.5 is the nearest whole number to the 5.7.

The given value of the function is ;

y = [ 5.7 ] = 5

Hence the value of the y is 5.

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Answer:

Step-by-step explanation:

In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.

Central Limit Theorem:

The sampling distribution of the sample percentage for a proportion p in a sample of size n will be roughly normal with a mean (μ = p) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n} }\).

In a given year, 3% of books checked out from the library are downloaded.

That means p = 0.03

and n = 75

By the Central Limit Theorem

Mean = μ = p = 0.03

Standard deviation =  \(s = \sqrt{\frac{p(1-p)}{n} }\)

                                   \(s = \sqrt{\frac{(0.03)(0.97)}{75} }\)

                                   \(s=0.0197\)

Hence,

         In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

The end behavior of the Polynomial f(x) = -4x⁶ + 6x² - 52 is;

B. f(x) is an even function so both ends of the graph go in the same

direction

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

Now, we are given the polynomial;

f(x) = -4x⁶ + 6x² - 52

Let us first test if the polynomial is even;

f(1) = -4(1)⁶ + 6(1)² - 52

f(1) = -50

Similarly;

f(-1) = -4(-1)⁶ + 6(-1)² - 52

f(-1) = -50

Since f(1) = f(-1), we can say that both ends of the graph go in opposite

directions.

Lastly, the leading coefficient is negative because it is -4 and as such it means that the left end goes down.

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Answer:

Should be 9 in.

The probability solved by binomial distribution that all will survive is 0.8154.

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

Computation of probability of all survived people from heart attack;

A heart attack patient has a 0.04 percent chance of dying from the attack (i.e., 4 of 100 die of the attack).

What is the likelihood that each of the five patients who experience a heart attack will survive?

We'll refer to a victory in this scenario as a heart attack (p = 0.04). In other words, we are interested in the likelihood that none of our n=5 patients will die (0 successes).

Each attack has a chance of being fatal or not, with a probability of 4 percent for all patients, and each patient's result is independent.

Assume for the purposes of this example that the five individuals being examined are unrelated, of the same age, and free of any concomitant disorders.

By binomial distribution,

\(\begin{gathered}P(0 \text { successes })=\frac{5 !}{0 !(5-0) !} 0.04^{0}(1-0.04)^{5-0} \\P(0 \text { successes })=\frac{5 !}{5 !}(1)(0.96)^{5}=(1)(1)(0.8154)=0.8154\end{gathered}\)

Therefore, with a 4 % chance that anyone will die, there is an 81.54% chance that every patient will survive the onslaught. The outcomes in this example could be 0, 1, 2, 3, 4 or 5 successes (fatalities).

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Answer:

a.) 20 kilometers

b.)1.67 hours

Step-by-step explanation:

a.) formula= speed =distance/time

Speed= 10km/hr

Distance=unknown

Time=2hrs

Therefore from formula, distance=speed x time

10 x 2

20 kilometers

b.) If average speed is increased by 2km/hr then

total speed= 2+10=12km/hr

Distance remains constant therefore distance= 20km

Therefore time =distance/speed

20/12

= 1.67 hours

Let's analyze the scenario of flipping a coin with a probability 'p' of coming up heads successively until two of the most recent three flips are heads.

If the first two flips are heads, then 'n' would be equal to 2. This is because we have already achieved the condition of two heads in the most recent three flips.

Now, let's consider the case where the first two flips are not heads. In this situation, we need to continue flipping the coin until we get two heads in the most recent three flips. This means that the previous two flips could be either heads or tails.

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a coin having probability p of coming up heads is successively flipped until two of the most recent three flips are heads. let n denote the number of flips. Then N = ?.

Answer: To find the circumference of a circle, use the formula, 2(3.14)(r) (r is the radius, and if it gives the diameter, divide the diameter by 2 [to get the radius]). To find the actual circumference of the circle, multiply 2 and 3.14, becoming 6.28. Then, multiply 6.28 by whatever the radius is. Hope you find this useful!

Note: I am going based on no given picture and measurements of the circle, the other person that answered is, also, correct, and you could multiply the first two numbers (and then multiply the other number by the answer you received) OR multiply the first number, being 2, by the radius (and multiply that answer by the number of 3.14). For an example, the radius=10 units. You could either do 2x10=20, then 20x3.14=62.8 units^2 or multiply 3.14x2=6.28 units, then multiply 6.28 by 10, which is 62.8 units^2.

To determine the times interest earned ratio for 2012, we need to have information about the company's earnings before interest and taxes (EBIT) and interest expense for that year. Unfortunately, the provided numbers don't include the necessary data for this calculation.

What is times interest earned ratio: The times interest earned (TIE) ratio is a measure of a company's ability to meet its debt obligations based on its current income. The formula for a company's TIE number is earnings before interest and taxes (EBIT) divided by the total interest payable on bonds and other debt.The result is a number that shows how many times a company could cover its interest charges with its pretax earnings.Obviously, no company needs to cover its debts several times over in order to survive. However, the TIE ratio is an indication of a company's relative freedom from the constraints of debt. Generating enough cash flow to continue to invest in the business is better than merely having enough money to stave off bankruptcy.Once you have the EBIT and interest expense for 2012, you can calculate the times interest earned ratio using the following formula:
Times Interest Earned Ratio = EBIT / Interest Expense.

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Answer:

The given geometric series is 2 + 4 + 8 + ...

We can see that the first term is 2 and the common ratio is 4/2 = 2.

The sum of a geometric series with a first term a and common ratio r, summed to n terms, is given by:

S_n = a(1 - r^n) / (1 - r)

Substituting the given values, we get:

a = 2

r = 2

n = 20

S_20 = 2(1 - 2^20) / (1 - 2)

S_20 = 2(1 - 1048576) / (-1)

S_20 = -2097150

Therefore, the sum of the given geometric series is -2097150.

Step-by-step explanation:

The given geometric series is 2 + 4 + 8 + ...

We can see that the first term is 2 and the common ratio is 4/2 = 2.

The sum of a geometric series with a first term a and common ratio r, summed to n terms, is given by:

S_n = a(1 - r^n) / (1 - r)

Substituting the given values, we get:

a = 2

r = 2

n = 20

S_20 = 2(1 - 2^20) / (1 - 2)

S_20 = 2(1 - 1048576) / (-1)

S_20 = -2097150

Therefore, the sum of the given geometric series is -2097150.

The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are:

2.3p – 10.1 = 6.4p – 4

2.3p – 14.1 = 6.4p – 4

To find the equations that have the same solution as the given equation, we need to simplify the equation using properties of equality. By combining like terms, we can rewrite the equation as follows:

2.3p – 10.1 = 6.5p – 4 – 0.01p

2.3p – 10.1 = 6.49p – 4

Now, we can compare the simplified equation with the options provided:

2.3p – 10.1 = 6.4p – 4

Here, the constant terms on both sides of the equation are the same, -10.1 = -4, but the coefficients of p are different.

2.3p – 14.1 = 6.4p – 4

In this equation, the constant terms on both sides are different, -14.1 ≠ -4, but the coefficients of p are the same.

Therefore, the equations that have the same solution as the given equation are 2.3p – 14.1 = 6.4p – 4.

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Answer:

Step-by-step explanation:

-31

Answer:

-31

Step-by-step explanation:

just enter -5 into x and solve