The figures below are congruent. Name the corresponding angles.

Answer:

19

Step-by-step explanation:

Since these two are vertical angles, their measure must be equal. Therefore:

\(3x-3=6(x-10) \\\\3x-3=6x-60 \\\\3x+57=6x \\\\3x=57 \\\\x=19^{\circ}\)

Hope this helps!

Answer:

19

Step-by-step explanation:

The two angles are vertically opposite angles, so they are equal.

3x - 3 = 6 (x - 10)

3x - 3 = 6x - 60

3x - 6x = - 60 + 3

-3x = -57

x = -57/-3

x = 19

Answer: 9.7

Step-by-step explanation: add up the mixed numbers

Answer:

Step-by-step explanation:

3x+y = 18 x= -2y + 1 Solve by substitution

Answer:

i think its 4.9 or 6.8

Step-by-step explanation:

(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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The variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.


To find the variance of a random variable X, you need to follow these steps:
1. Calculate the mean (average) of X.
2. Calculate the squared difference between each value of X and the mean.
3. Calculate the expected value of the squared differences.
4. The result obtained in step 3 is the variance of X.
Let’s apply these steps to the given values of X: 28, 46, 73, and 73.
Step 1: Calculate the mean (average) of X.
Mean(X) = (28 + 46 + 73 + 73) / 4 = 220 / 4 = 55
Step 2: Calculate the squared difference between each value of X and the mean.
(28 – 55)^2 = 27^2 = 729
(46 – 55)^2 = 9^2 = 81
(73 – 55)^2 = 18^2 = 324
(73 – 55)^2 = 18^2 = 324
Step 3: Calculate the expected value of the squared differences.
Expected value = (729 + 81 + 324 + 324) / 4 = 1458 / 4 = 364.5
Step 4: The result obtained in step 3 is the variance of X.
Variance(X) = 364.5
Therefore, the variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.

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Answer:

Yes. When a function is linear, it means that it will always be a straight line. For this to hold true, the slope must always be constant.

Step-by-step explanation:

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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Answer:

The area of the trapezoid:

A = (base1 + base2) x height/2

  = (6 + 12) x 8/2

  = 18 x 4

  = 72

Hope this helps!

:)

The indifference curve equation given is x2 = 20 - 4x^(1/2)*1, where x1 and x2 represent the quantities of two goods Ambrose is consuming.

The marginal rate of substitution (MRS) measures the rate at which Ambrose is willing to trade one good for the other while remaining on the same indifference curve. It is calculated as the negative ratio of the derivatives of the indifference curve with respect to x1 and x2, i.e., MRS = -dx1/dx2. Given that Ambrose is consuming the bundle (4,16), we can substitute these values into the indifference curve equation to find the corresponding MRS.  Plugging in x1 = 4 and x2 = 16, we have: 16 = 20 - 4(4)^(1/2)*1; 16 = 20 - 8; 8 = 8. This confirms that the bundle (4,16) lies on the indifference curve. Now, we are given that the MRS at this point is 25/4.

Therefore, we can set up the following equation: dx1/dx2 = 25/4. Simplifying, we have: dx1/dx2 = -25/4. This indicates that the rate at which Ambrose is willing to trade good x1 for good x2 at the bundle (4,16) is -25/4. The MRS represents the slope of the indifference curve at a given point and reflects the trade-off between the two goods. In this case, it indicates that Ambrose is willing to give up 25/4 units of good x1 in exchange for one additional unit of good x2 while maintaining the same level of satisfaction.

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Answer:

Everything is in the picture above

Step-by-step explanation:

Hope it helps

Answer:

The answers to your questions are given below.

Step-by-step explanation:

Polynomial 1:

12x² + 23x – 2

Name by degree: Quadratic because the highest power in the equation is 2.

Polynomial 2:

7x + 2

Name by number of terms: Binomial because the equation has two terms

Polynomial 3:

12

Name by degree: Constant because it has no variable

Name by number of terms: Monomial because it has only one term.

Answer:

x = 46

Step-by-step explanation:

These 2 angles would add up to 180 degrees.

So 41 + (3x+1) = 180

Let's solve for x.

41 + 3x + 1 = 180

Combine like terms.

42 + 3x = 180

subtract 42 from both sides

3x = 180-42

3x = 138

divide both sides by 3

x = 46

The samples in the first proposal are independent, while the samples in the second proposal are dependent.

In the first proposal, where the manufacturer randomly samples 10 different dealerships for each set of sales numbers (last year and 15 years ago), the samples are independent. This is because the selection of dealerships for one set of sales numbers does not affect or influence the selection of dealerships for the other set of sales numbers. Each dealership is chosen randomly and independently for each set.

On the other hand, in the second proposal, where the manufacturer randomly samples 10 dealerships for both sets of sales numbers, the samples are dependent. This is because the selection of dealerships for one set of sales numbers is directly tied to the selection of dealerships for the other set of sales numbers. The same 10 dealerships are chosen for both sets, so the samples are not independent.

The choice between independent and dependent samples can have implications for statistical analysis. Independent samples allow for direct comparisons between the two sets of sales numbers, while dependent samples may introduce potential bias or confounding factors due to the shared dealership selection.

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Answer:

Step-by-step explanation:

338.33 ft

Answer:3x+5y=4

Step-by-step explanation:

Answer:

x=(4/3,0)

y=(0,4/5)

Step-by-step explanation:

We say a definite integral is improper if one or both of the limits of integration is infinite, or if the integrand is infinite.

From the question, we have the following parameters that can be used in our computation:

The missing blanks

By the definition of definite integral, we have

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Answer: 25 feet

Step-by-step explanation:

Answer:

25 feet

Step-by-step explanation:

10 times 2 is 20 and half of 10 is 5 so 20 and 5 = 25

Answer:

The momentum for the truck and cargo is 150000 kg·km/h

Step-by-step explanation:

p = mv

p = (2000 kg + 1000 kg)(50 km/h)

p = (3000 kg)(50 km/h)

p = 150000 kg·km/h

The surface area of a cylinder is found using the following formula:

Replace for the given values of radius and height:

It means that the surface area of the cylinder is 622.

The correct answer is D. 622 sq units.

Answer:

86.2 in squared

Step-by-step explanation:

Harons formula

Answer:

93.7

Step-by-step explanation:

The most likely happened in Sandy's experiment is that,

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

Option D is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Tossing a coin:

The probability of getting a head = 1/2

The probability of getting a tail = 1/2

This is the theoretical probability.

Now,

Experiment probability:

Virtual coins too have the same probability of getting a head and a tail as compared to the theoretical probability.

Thus,

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

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Answer:Not Sure but it is not D at all so please don't use that!

Step-by-step explanation:

a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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Answer:

Step-by-step explanation:

At the point of intersection the coordinate can be found with

10 - 2x = 4  (is the required equation).

Solving this we find the first coordinate (x) to be 3.

The interquartile range (IQR) is found as the 20.24. The correct option is (d) 20.24.

Given that X N(300, 15), find the Interquartile Range (IQR).

The given distribution is normal with mean μ = 300 and standard deviation σ = 15.

We need to calculate the interquartile range (IQR).IQR is defined as the difference between the third quartile (Q3) and the first quartile (Q1).

The first quartile (Q1) is the value below which 25% of the data fall and the third quartile (Q3) is the value below which 75% of the data fall.

We can find these values using the standard normal distribution table.

For the first quartile,

z1 = invNorm(0.25)

= -0.67449

Q1 = μ + σ × z1

= 300 + 15 × (-0.67449)

= 289.88

≈ 289.89

For the third quartile,

z3 = invNorm(0.75)

= 0.67449

Q3 = μ + σ × z3

= 300 + 15 × 0.67449

= 310.12

Therefore, the interquartile range (IQR)

= Q3 – Q1

= 310.12 – 289.89

= 20.23

≈ 20.24

Hence, the correct option is (d) 20.24.

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Answer:

5ft to 49in 5ft/49in 5ft:49in

Step-by-step explanation:

The correct answer is stratified random sampling.

A type of sampling method where every person in the population has an equal chance of being chosen for the research is known as random sampling.

This sampling method does not require the researcher to divide the population into categories or strata before selecting a sample.

According to the given question, Verizon Wireless is interested in studying the pricing expectations of its customers.

If the study calls for selecting at random 100 people from each of three age groupings, stratified random sampling is being used.

Stratified random sampling is a sampling method in which the researcher divides the population into strata or categories based on some specific variables that the researcher wants to investigate.

In this type of sampling method, a random sample is chosen from each stratum based on some proportionate allocation.

The researcher might divide the population into categories based on age, gender, income, or any other variable relevant to the research question.

Stratification is an effective technique for reducing sampling bias since it guarantees that each stratum is adequately represented in the sample.

Hence, the correct answer is stratified random sampling.

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The time at which the system fails, denoted by X, is the minimum of the lifetimes of the five components.

In this system, each component has a lifetime that follows an exponential distribution with a parameter λ = 0.01. The exponential distribution is commonly used to model the time until an event occurs in a system with a constant failure rate.

The probability that a component lasts at least t hours is given by P(Ai) = e^(-λt), where Ai is the event that the ith component lasts at least t hours.

Since the components fail independently of one another, the probability that all five components last at least t hours is the product of their individual probabilities: P(A1 ∩ A2 ∩ A3 ∩ A4 ∩ A5) = e^(-λt)^5 = e^(-5λt).

Now, let X be the time at which the system fails, which is the minimum of the lifetimes of the five components. Since X is the minimum, we can write X = min(T1, T2, T3, T4, T5), where Ti represents the lifetime of the ith component.

The probability distribution of X can be obtained by considering the complement event. The complement of X > t is that all five components last at least t hours, which is P(X > t) = P(A1 ∩ A2 ∩ A3 ∩ A4 ∩ A5) = e^(-5λt).

Therefore, the time at which the system fails, X, follows an exponential distribution with a parameter of 5λ = 0.05. This means that the system has a constant failure rate of 0.05 and the probability density function (pdf) of X is given by f(x) = 0.05 * e^(-0.05x).

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