PLEASE PLEASE PLEASE HELP!!!!! And show your work!!!!! *Grade 9 work*

*see attachment below for the diagram being referred to

Answer:

∠RXZ and ∠YXZ

Step-by-step explanation:

Supplementary angles are angles whose sum gives us 180°.

Let's consider each pair of angles given as options and see which of them are supplementary angles considering the given diagram:

Option 1: ∠RXZ and ∠YXZ.

∠RXZ and ∠YXZ are angles on a straight line, and they form a linear. A linear pair = 180°. Therefore, ∠RXZ and ∠YXZ pair is supplementary.

Option 2: ∠PXQ and ∠RXS do not form a linear pair, neither are they angles in a straight line, therefore, the angle pair ∠PXQ and ∠RXS, is not supplementary.

Option 3: ∠YZX and ∠UZT.

∠YZX and ∠UZT are vertical angles. Therefore, the angle pair ∠YZX and ∠UZT is not supplementary.

Option 4: ∠WZX and ∠XYZ.

There's no special relationship between ∠WZX and ∠XYZ, other than being angles of ∆XYZ. Therefore, the angle pair ∠WZX and ∠XYZ, is not supplementary.

Answer:

A. ∠RXZ and ∠YXZ

Step-by-step explanation:

EDU 2020

Answer:

I believe the answer is substitution

Step-by-step explanation:

Hope this Helps :)

i think its called a regular expression.. but i'm not 100% sure. Sorry if im wrong.

The expected value of a turn in this game is 166.5 points. This means that, on average, a player would expect to gain 166.5 points per turn. The statement "the expected value of a turn is 1.51.51, point, 5 points" is not accurate, as our calculation demonstrates that the correct expected value is 166.5 points.

The expected value of a turn in this game is calculated by multiplying the probability of getting heads (0.5) by the point value for heads (111) and adding it to the probability of getting tails (also 0.5) multiplied by the point value for tails (222). This gives us an expected value of 166.5 points per turn.

Therefore, the following statements are true:
- If Anouk and Tessa play this game for many turns, the average number of points they will earn per turn will be close to 166.5.
- On average, a player is more likely to receive 222 points per turn than 111 points per turn.
- The expected value of a turn is greater than both the point values for heads and tails individually.

It is important to note that while the expected value can help us understand the average outcome of a game, it does not guarantee that a player will always receive this exact amount in any given turn. The outcome of each flip is still subject to chance.

In the game Anouk and Tessa are playing, a coin is flipped, awarding 111 points for heads and 222 points for tails. To determine the expected value of a turn, we must calculate the probability-weighted average of the possible outcomes.

There are two possible outcomes when flipping a coin: heads and tails. Since a coin has two sides, the probability of getting heads is 1/2, and the probability of getting tails is also 1/2. We can now use these probabilities to calculate the expected value.

Expected Value (EV) = (Probability of Heads × Points for Heads) + (Probability of Tails × Points for Tails)

EV = (1/2 × 111) + (1/2 × 222)

EV = (55.5) + (111)

EV = 166.5 points

Thus, the expected value of a turn in this game is 166.5 points. This means that, on average, a player would expect to gain 166.5 points per turn. The statement "the expected value of a turn is 1.51.51, point, 5 points" is not accurate, as our calculation demonstrates that the correct expected value is 166.5 points.

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Answer:

7

Step-by-step explanation:

We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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Answer:

Step-by-step explanation:

\((x-3)^{2} =49\\1)x-3=7\\x=10\\2)x-3=-7\\x=-4\)

Answer:

36π mm²

Step-by-step explanation:

Formula: πr²

r=radius

r=6

π6²=36π

4.5 kilos to pounds equal 9.9208. We convert one kilogram (kg) to 2.2 pounds (lb), which is a rough conversion.

Simply multiply the amount in kilograms by the conversion factor, 2.204622622, to convert 4.5 kilograms to pounds.

Therefore, 4.5 kilos in pounds = 9.920801798319491 pounds when multiplied by 2.204622622.

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Step-by-step explanation:

Break down the word expression:

The sum of 5 and b divided by two

the sum (+) of 5 and b (5 + b) divided by 2.

Expression:

\( \frac{(b + 5)}{2} \)

Parentheses represent that we need to add first, in order to divide the sum by 2.

Answer:

y = - 4/1 x - 3

Step-by-step explanation:

The equation of a circle in center-radius form is given by

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

To solve for the center and radius of a given circle, first rearrange the equation to make x and y the subject:

x = ±√(r2 - (y - k)2) + h

y = ±√(r2 - (x - h)2) + k

Then set the equation equal to 0 and solve for r:

r2 = (x - h)2 + (y - k)2

Finally, substitute the x and y coordinates of the center point into the equation and solve for r:

r2 = (h - h)2 + (k - k)2

r = 0

Therefore, the center of the circle is (h, k) and the radius is 0.

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Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

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Answer:

$541.67 per month

Step-by-step explanation:

Tuition and other expenses = $8,250 per semester.

There are two semesters in a year

She has 4 years to spend

Total semester=4years*2semesters

=8 semesters

4 years in college which is a total of 8 semesters.

Total Tuition and other expenses = $8,250 * 8

= $66,000

She needs a total of $66,00 to complete her college

Assistance from parents=$15,000

Financial aid(per semester)=$4750

Total financial aid=$38,000

Total assistance=

Assistance from parents+ financial aid

=$15000+$38,000

=$53,000

Total savings=Total amount needed - Total assistance

=$66,000 - $53,000

=$13,000

She needs to save $13,000 in two years

There are 12 months in one year

2 years=2*12=24 months

Monthly savings=Total savings/24 months

=$13,000/24

=$541.666666

To the nearest cent

=$541.67

Answer: $541.67

Step-by-step explanation: Got it right on TTM.

The oil prospector drills wells with a success probability of 0.15. The probability of finding the first productive well in the third attempt is 0.108375 and the probability that the prospector fails to find productive well in the first 5 attempts is  0.26724 or 26.724%

Let Y be the number of drilling trials on which the prospector will find the first productive well. As Y is a geometric random variable with p=0.15 where p is the probability of being successful on any drilling. Let q = 1- p be the probability of being unsuccessful in drilling a well. q = 1 - 0.15 = 0.85

The probability that the first productive well is found on the third attempt is when outcomes are independent

P(Y=3) = q * q * p = 0.85^2* 0.15 = 0.108375

We want to find the probability that 5 wells are drilled and not a productive one is found. That is we need to find p(Y>5). Y is a binomial random variable with several wells drilled at most as n. Given n=5 and p=0.15, q = 0.85

We know the geometric probability is p(y) = \(q^{y-1}\)p

Then corresponding probabilities are added

p(Y≤ 5 ) = p(0) + p(1) +p(2) + p(3) +p(4) +p(5)= 0.73276

Using the complement rule:

p(Y>5) = 1 - p(Y≤5) = 1- 0.73276 = 0.26724 = 26.724 %

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Lines x + 5 = 0 and y = 4x + 4 intersect on a standard (x, y) coordinate plane.

To find the y-coordinate of the point where the two lines intersect.

given lines  are x +5 =0 and y=4x+4

we need to find point of intersection at point of intersection both line will have same point

Let point of intersection be (a,b)

then

a+5 = 0 and b = 4a+4

from 1st equation we have

a = -5

from the 2nd

b = 4a+4

b = 4(-5)+4

b = -20+4

b = -16

Hence y coordinate of point of intersection is -16

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The gas station serves 16 vehicles per hour, and 72 vehicles arrive in 4 hours. The vehicles will spend 4.50 hours at the gas station.



To find the total time the vehicles will spend at the gas station, we need to calculate the total number of vehicles that arrive and then divide it by the rate at which the gas station serves vehicles.

Given:

Arrival rate: 18 vehicles per hour

Service rate: 16 vehicles per hour

Time: 4 hours

First, let's calculate the total number of vehicles that arrive during the 4-hour period:

Total number of vehicles = Arrival rate * Time

                      = 18 vehicles/hour * 4 hours

                      = 72 vehicles

Since the gas station can serve 16 vehicles per hour, we can determine the time it takes to serve all the vehicles:

Time to serve all vehicles = Total number of vehicles / Service rate

                         = 72 vehicles / 16 vehicles/hour

                         = 4.5 hours

Therefore, the vehicles will spend 4.5 hours at the gas station. Rounded to 2 decimal places, the answer is 4.50 hours.

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Answer:

\(6000(1.065)^{ 365t } \)

Step-by-step explanation:

Since the exponent is in years, we just have to convert it to days:

\(t \: years \times \frac{365 \: days}{1 \: year} = 365t \: \)

Answer:

-3(2x-5)<5(2-x)

Step-by-step explanation:

hope this helps

Answer:

x ≥ -3/4

Step-by-step explanation:

3(2x + 5) ≥ 2(x + 6)

Distribute

6x+15 ≥ 2x + 12

Subtract 2x from each side

6x-2x+15 ≥ 2x-2x + 12

4x+15 ≥ 12

Subtract 15 from each side

4x+15-15 ≥ 12-15

4x ≥ -3

Divide each side by 4

4x/4 ≥ -3/4

x ≥ -3/4

If Abby deposited $3000 and has $3600 at the end of 8 years, then the interest-rate is 2.5%.

The "Simple-Interest" is the interest which is calculated based only on principle amount of a loan or investment, without taking into account any additional interest earned on previous periods.

We can use the simple interest formula to find the annual interest rate:

⇒ Simple Interest = Principle × Rate × Time,

Where: Principle is = initial deposit of $3000,

Rate = annual interest rate (what we need to find)

Time = number of years the money was invested = 8,

The Simple Interest earned over 8 years : $3600 - $3000 = $600,

Substituting the values,

We get,

⇒ $600 = $3000 × Rate × 8,

⇒ Rate = 600/(3000 × 8),

⇒ Rate = 0.025, or 2.5%.

Therefore, the annual interest rate on the account is 2.5%.

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(a) The interval on which f is increasing: (0, ∞)

The interval on which f is decreasing: (0, 1)

(b) Local minimum: At x = 1, f(x) has a local minimum value of -1.

There is no local maximum value.

(c) Inflection point: At x ≈ 0.293, f(x) has an inflection point.

The function f(x) = x^2 - x - ln(x) is a quadratic function combined with a logarithmic function.

To find the interval on which f is increasing, we need to determine where the derivative of f(x) is positive. Taking the derivative of f(x), we get f'(x) = 2x - 1 - 1/x. Setting f'(x) > 0, we solve the inequality 2x - 1 - 1/x > 0. Simplifying it further, we obtain x > 1. Therefore, the interval on which f is increasing is (0, ∞).

To find the interval on which f is decreasing, we need to determine where the derivative of f(x) is negative. Solving the inequality 2x - 1 - 1/x < 0, we get 0 < x < 1. Thus, the interval on which f is decreasing is (0, 1).

The local minimum is found by locating the critical point where f'(x) changes from negative to positive. In this case, it occurs at x = 1. Evaluating f(1), we find that the local minimum value is -1.

There is no local maximum in this function since the derivative does not change from positive to negative.

The inflection point is the point where the concavity of the function changes. To find it, we need to determine where the second derivative of f(x) changes sign. Taking the second derivative, we get f''(x) = 2 + 1/x^2. Setting f''(x) = 0, we find x = 0. Taking the sign of f''(x) for values less than and greater than x = 0, we observe that the concavity changes at x ≈ 0.293. Therefore, this is the inflection point of the function.

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Answer:

1.2

I checked in the RSM system thing

Answer:

9cm and 2cm

Step-by-step explanation:

∴ They're similar triangles.

∴ \(\frac{a}{3}\)= \(\frac{6}{b}\) = \(\frac{3}{1}\)

∴ a = 9cm

∴ b = 2cm

The factored form of 9a² - b² - 4c² + 4bc is

(3a + b - 2c) (3a - b + 2c)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

9a² - b² - 4c² + 4bc

9a² - (b² + 4c² - 4bc)

Now,

(b² + 4c² - 4bc)

This can be written as,

= (b² - 4bc + 4c²)

= (b - 2c)²

Now,

9a² - (b - 2c)²

(3a)² - (b - 2c)²

This is in the form of a² - b².

a² - b² = (a + b) (a - b)

So,

(3a + b - 2c) (3a - b + 2c)

Thus,

(3a + b - 2c) (3a - b + 2c) is the factored form.

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B) FALSE. The symbol ∃ is actually called the existential quantifier, not the universal quantifier.

In logic and mathematics, quantifiers are used to express the scope of a statement over a set of elements. The universal quantifier, denoted by ∀, expresses that a statement holds for all elements in a given set. On the other hand, the existential quantifier, denoted by ∃, expresses that there exists at least one element in the set for which the statement is true.

For example, the statement  means that for every element x in the set S, the property P(x) is true. This is the universal quantifier.

In contrast, the statement "∃x ∈ S, P(x)" means that there exists at least one element x in the set S for which the property P(x) is true. This is the existential quantifier.

So, it is incorrect to say that the symbol ∃ is called the universal quantifier. It is specifically used to denote the existential quantifier.

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The approximate trend line of data is shown in the next picture.

From the picture, the attendance at a movie theater with 8 screens will be approximately 120 people