If two lines intersect, prove that vertically opposite angles are equal.

Answer:

a = 2

b = 3

c = 2³ or 8

Step-by-step explanation:

Exponent Rule: \(\frac{b^m}{b^n} =b^{m-n}\)

log₂(4) = 2 or 2² = 4

2⁵/2² = 2³

2³ = 8

Answer:

a=2

b=3

c=8

Step-by-step explanation:

a=2, 2^a must equal 4

b=3, 2^b must equal 8 which is answer to 2⁵/4

c=8, the answer to 2⁵/4, and

\(7z + 5 = 9z - 3 \\ 5 + 3 = 9z - 7z \\ 8 = 2z \\ z = \frac{ \cancel{8}} {\cancel{2}} \frac{4}{1} \\ z = 4\)

Put the value z = 4

\(7z + 5 = 9z - 3 \\ 7(4) + 5 = 9(4) - 3 \\ 28 + 5 = 36 - 3 \\ 33 = 33\)

\(\therefore\) L.H.S = R.H.S

Answer:

\( \sf \: z = 4\)

Step-by-step explanation:

\( \sf7z + 5 = 9z - 3 \)

First, subtract 7z by both sides.

\( \sf5 = 9z - 3 - 7z\)

Combine like terms.

\( \sf5 = 2z - 3\)

Now, add 3 to both sides.

\( \sf5 + 3 = 2z \\ \sf8 = 2z\)

Now, divide both sides by 2.

\( \sf4 = z\)

Answer:

y=1x+200

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Which segment shows what  happens when x>2? What happens when x = 2 and which line shows it best. Which question is easier to answer?

It's not C or D.

Look at A. If x = 2 then -x + 4 =  -2 + 4 = 2. I admit you can't let it be that way, but it gives you an indication of what to do. That is what happens to the short line on the right.

What is the long line doing? -2(2) - 1 = -5.  Who does that? A does

So the Answer is A

The probability of an even number is twice as likely to occur as an odd number is 2/9 and 1/9 respectively.

Probability in math term is defined as  a number that reflects the chance or likelihood that a particular event will occur.

Here we have given that an unfair/biased die is considered as an even number is twice as likely to occur as an odd number.

And here we need to find the probability of the event.

Here let us consider that probability of getting an even number = x and let probability of getting odd number = y

Then it can be written as

=> 3x+3y=1

Here we write it as because probability of getting even number or odd number = 1 since those two are the only possibilities.

Then we have to apply the value of x=2y (given)

Now, we have to solve these two, then we get,

=> x=2/9 and y=1/9

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Step-by-step explanation:

Answer is this hope it helps to you

The first step is to convert angle A = 23°23' to degrees. Recall, the interpretation of angle A is 23 degree 23 minutes. Also,

1 degree = 60 minutes

Let x = 23 minutes. Thus, we have these equations

1 = 60

x = 23

By crossmultiplying,

60x = 23

x = 23/60 = 0.3833

Thus,

angle A = 23 degrees + 0.3833 degrees = 23.3833 degrees

The triangle is shown below

Taking angle A as the reference angle,

hypotenuse = 42.75

opposite side = a

adjacent side = b

To find a, we would apply the sine trigonometric ratio which is expressed as

Sin# = opposite side/hypotenuse

Sin 23.3833 = a/47.25

By crossmultiplying,

a = 47.25Sin 23.3833

a = 18.75

To find b, we would apply the cosine trigonometric ratio which is expressed as

Cos# = adjacent side/hypotenuse

Cos 23.3833 = b/47.25

By crossmultiplying,

b = 47.25Cos 23.3833

b = 43.37

The given triangle is a right triangle. This means that one of its angles is 90 degrees. Thus,

angle C = 90 degrees

The sum of the angles in a traingle is 180 degrees. This means that

angle A + angle B + angle C = 180

23.3833 + angle B + 90 = 180

angle B + 113.3833 = 180

angle B = 180 - 113.3833

angle B = 66.62 degrees

The trigonometric functions sine and cosecant have a positive sign.

In this problem we must determine what trigonometric functions associated with a vector of the form (x, y) have a positive sign. This can be done by computing on each function:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

If we know that x = - 12 and y = 5, then the values of the trigonometric functions are, respectively:

sin θ = 5 / √[(- 12)² + 5²]

sin θ = 5 / 13

cos θ = - 12 / √[(- 12)² + 5²]

cos θ = - 12 / 13

tan θ = - 5 / 12

sec θ = - 13 / 12

csc θ = 13 / 5

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The probability that a person had either apple pie for dessert or pork for dinner at the event is 0.608

To find the probability that a person had apple pie for dessert or pork for dinner, we need to add the number of people who had apple pie for dessert and the number of people who had pork for dinner, and then divide by the total number of people who attended the event.

From the table, we can see that:

85 people had apple pie for dessert

105 people had pork for dinner

35 people had both apple pie for dessert and pork for dinner

To avoid double-counting the people who had both apple pie for dessert and pork for dinner, we need to subtract the number of such people from the sum:

85 + 105 - 35 = 155

Therefore, the probability that a person had apple pie for dessert or pork for dinner is:

155/255 ≈ 0.608

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The given question is incomplete, the complete question is:

The following table shows what entrees and desserts were served at a charity event that 255 people attended. what is the probability that a person had apple pie for dessert or pork for dinner?

The integer would be -250, since it is a decrease.

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

  11.7 years

Step-by-step explanation:

You want the number of years it takes for an annuity of $40 per month earning 7.5% interest compounded daily to achieve a value of $9000.

The formula for the future value of an ordinary annuity is ...

  FV = P((1 +r)^n -1)/(r -1)

where P is the periodic payment, r is the periodic interest rate, and n is the number of periods.

This problem is a bit tricky in that the payment period is 1 month, but the compounding of interest is done daily. That means the effective monthly interest rate (r) is ...

  1 +r = (1 +0.075/365)^(365/12) ≈ 1.00626892594

This is the 12th root of the effective annual rate.

Solving for n, we get ...

  9000 = 40(1.0063^n -1)/0.0063

  0.0063·225 = 1.0063^n -1

  log(0.0063·225 +1)/log(1.0063) = n ≈ 140.7885 . . . . . . months

We want the time in years, so we need to divide by 12:

  years = 140.7885/12 ≈ 11.7324 ≈ 11.7

It will be about 11.7 years until Abby can afford her vacation.

a. The 95% confidence interval for the population mean is (2.925, 9.075).

b. Based on the 95% CI, there is evidence to suggest that the population c. The 98% confidence interval for the population mean is (2.139, 9.861).

A confidence interval is a range of values that provides an estimated range of plausible values for an unknown population parameter. It is often used in statistical inference to estimate the true value of a population parameter, such as the population mean or proportion, based on a sample of data.

a. To construct a two-sided 95% confidence interval (CI) for the population mean, we can use the t-distribution since the sample size is small (n = 9) and the population variance is unknown. The formula for the confidence interval is:

CI = sample mean ± t * (sample standard deviation / √n)

where t represents the critical value from the t-distribution based on the desired confidence level and n is the sample size.

In this case, the sample mean is 6, and the sample standard deviation can be estimated using the known variance of 16:

sample standard deviation = √(known variance) = √16 = 4

Since we want a two-sided 95% CI, we divide the significance level (α) by 2, resulting in α/2 = 0.05/2 = 0.025. Looking up the critical value for a t-distribution with n-1 degrees of freedom (9-1 = 8) and α/2 = 0.025, we find t = 2.306.

Plugging the values into the formula, we have:

CI = 6 ± 2.306 * (4 / √9) = 6 ± 2.306 * (4 / 3) = 6 ± 3.075

Therefore, the 95% confidence interval for the population mean is (2.925, 9.075).

b. To determine whether the claim that the population mean is less than 2 is reasonable, we can check if the lower bound of the 95% CI falls below 2. In this case, the lower bound is 2.925, which is greater than 2. Therefore, based on the 95% CI, there is evidence to suggest that the population mean is not less than 2, and the claim seems unreasonable.

c. To construct a two-sided 98% confidence interval for the population mean, we follow a similar procedure as in part a. The only difference is the critical value. For a two-sided 98% CI, α/2 = 0.02/2 = 0.01. Looking up the critical value for a t-distribution with 8 degrees of freedom and α/2 = 0.01, we find t = 2.896.

Plugging the values into the formula, we have:

CI = 6 ± 2.896 * (4 / √9) = 6 ± 2.896 * (4 / 3) = 6 ± 3.861

Therefore, the 98% confidence interval for the population mean is (2.139, 9.861).

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The bank should not recall its card from a customer who has missed a monthly payment, as the probability of default is less than the threshold of 0.20 set by the bank.

(a) Let D denote the event that a customer defaults and M denote the event that a customer misses a monthly payment. We need to find P(D|M). We can use Bayes' theorem to solve for this:

P(D|M) = P(M|D) * P(D) / P(M)

We know that P(D) = 0.03, P(M|D) = 1, and P(M|not D) = 0.21. To find P(M), we can use the law of total probability:

P(M) = P(M|D) * P(D) + P(M|not D) * P(not D)

= 1 * 0.03 + 0.21 * 0.97

= 0.2391

Therefore, we have:

P(D|M) = 1 * 0.03 / 0.2391

= 0.1258 or approximately 0.13 (rounded to 2 decimal places)

So the probability that a customer will default given that they have missed a monthly payment is about 0.13.

(b) The bank should recall its card from a customer who has missed a monthly payment if the probability that the customer will default is greater than 0.20. From part (a), we know that the probability of default given that a customer has missed a monthly payment is about 0.13, which is less than 0.20. Therefore, the bank should not recall its card from this customer.

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Answer:

Hey!

Step-by-step explanation:

Legit just like make a graph like this:

10 | 1

20 | 2

30 | 3

And so on and so forth

No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.

A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.

When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.

However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.

In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.

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Answer:

d. 2y - x = 0

Step-by-step explanation:

Convert this into slope-intercept form for easiest analyzation.

y = mx + b

1. 2y - x = 0

2.   = 2y = x

3.   = y = 1/2x

4. The slope is 1/2

Step one is given.

In step two, x was added to both sides.

In step 3, both sides were divided by 2.

In step 4, it was analyzed that the slope is 1/2 because if you plug it into y = mx + b, m would be 1/2, and m represents the slope in the equation.

Interposition refers to the belief that a state has the right to intervene between the federal government and its citizens to protect them from unconstitutional laws, while nullification is the belief that a state has the power to declare federal laws null and void within its borders.

Interposition and nullification are two theories of state sovereignty that were debated during the early years of the United States. Interposition refers to the belief that a state has the right to interpose itself between the federal government and its citizens to protect them from unconstitutional laws.

On the other hand, nullification is the belief that a state has the power to declare federal laws null and void within its borders. The main difference between interposition and nullification is the extent of state power they propose.

Interposition allows a state to protect its citizens from unconstitutional federal laws, while nullification allows a state to effectively veto a federal law within its borders. While interposition has been recognized as a legitimate theory of state sovereignty.

Nullification has been largely discredited and is not recognized as a valid legal doctrine under the U.S. Constitution.


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The calculated t-statistic (-2.98) is less than the critical t-value (-2.571), we have sufficient evidence to reject the null hypothesis.

To test the hypothesis that the blood pressure has decreased after the training in the "biofeedback exercise program," we can conduct a one-sample t-test. The t-test allows us to determine whether the mean difference in blood pressure is significantly different from zero.

Given data:

Sample size (n) = 6

Mean difference (xd) = -10.2

Standard deviation of the differences (sd) = 8.4

Null hypothesis (H0): The mean difference in blood pressure is zero (i.e., no change after the training).

Alternative hypothesis (Ha): The mean difference in blood pressure is less than zero (i.e., blood pressure has decreased after the training).

Step 1: Calculate the t-statistic.

The formula for the t-statistic in a one-sample t-test is given by:

t = (xd - μd) / (sd / √n)

Where:

μd = the hypothesized population mean difference (under the null hypothesis), which is zero in this case.

t = (-10.2 - 0) / (8.4 / √6)

t = -10.2 / (8.4 / 2.45)

t = -10.2 / 3.43

t ≈ -2.98

Step 2: Determine the degrees of freedom (df).

The degrees of freedom for a one-sample t-test is (n - 1). In this case, df = 6 - 1 = 5.

Step 3: Determine the critical t-value.

Since we are conducting a one-tailed test (Ha: mean difference < 0), we need to find the critical t-value corresponding to the desired significance level (e.g., α = 0.05) and the degrees of freedom (df = 5). From t-tables or statistical software, the critical t-value for α = 0.05 and df = 5 is approximately -2.571.

Step 4: Compare the t-statistic with the critical t-value.

Since the calculated t-statistic (-2.98) is less than the critical t-value (-2.571), we have sufficient evidence to reject the null hypothesis.

Step 5: Interpret the results.

The test results indicate that there is a statistically significant decrease in blood pressure after the training in the "biofeedback exercise program." The participants' blood pressure has significantly reduced as a result of the training.

Distribution for the test:

The distribution for the test is a t-distribution with 5 degrees of freedom, as it is a one-sample t-test with a sample size of 6. The t-distribution is used because the population standard deviation is unknown, and we are estimating it using the sample standard deviation in the formula for the t-statistic.

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Complete question is below

An experiment is conducted to show that blood pressure can be consciously reduced in people trained in a "biofeedback exercise program." Six (6) subjects were randomly selected and the blood pressure measurements were recorded before and after the training. The difference between blood pressures was calculated (after − before) producing the following results: xd = −10.2, sd = 8.4. Using the data, test the hypothesis that the blood pressure has decreased after the training. What is the distribution for the test?

Answer:

(B). 50°

Step-by-step explanation:

(5x + 55)° = (2x + 100)°

5x + 55 = 2x + 100

5x - 2x = 100 - 55

3x = 45

x = 15

5(15) + 55 = 130°

m∠2 = 180° - 130° = 50°

The method used for the computation of volume created by revolving the region bounded by y = x² and y = √x about the line x = 2, is using the washers method. The summation of the volumes of each cylinder gives the volume created by revolving the region bounded by y = x² and y = √x about the line x = 2.

The volume generated by revolving the region bounded by y = x² and y = √x about the line x = 2 using the washers method is computed using the following steps:Step 1: Sketch the graphThe first step to finding the volume of the region is to sketch the graph of the given equations y = x² and y = √x. The intersection of the two equations is (0, 0) and (1, 1). The resulting graph looks like this:Graph of y = x² and y = √x.Step 2: Determine the limits of integration The limits of integration are the points at which the two functions intersect. From the graph above, the limits of integration are 0 and 1.Step 3: Determine the radius of the washer at a given xThe radius of the washer is the distance between the two curves. At any given x value, the distance between the curves is given by:r = 2 - x² - √xStep 4: Determine the height of the washerThe height of the washer is the infinitesimal change in x, which is given by:dxStep 5: Determine the volume of the washerThe volume of the washer is given by:πr²dxStep 6: Integrate to get the total volumeTo get the total volume, integrate the volume of each washer with respect to x:∫₀¹ π(2 - x² - √x)² dx= π∫₀¹ 4 - 4x² - 4x√x + x³ + 2x²√x - x dx= π(4x - 4/3 x³ - 8/15 x⁵ + 1/4 x⁴ + 2/3 x^(5/2) - 1/2 x²)₀¹= π(4 - 4/3 - 8/15 + 1/4 + 2/3 - 1/2)= π(41/30)Therefore, the volume created by revolving the region bounded by y = x² and y = √x about the line x = 2 is π(41/30).

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Answer:

\(2950 - 125 - 50 \\ = 2950 - (125 + 50) \\ = 2950 - 175 \\ = \boxed{2775}\)

Answer:

g5654

Step-by-step explanation:

The probability of getting one marble of each color will be 0.044.

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A random event's recurrence is the subject of this area of mathematics. The range of the number is 0 to 1. The degree to which something is likely to happen is essentially what probability means. You will discover the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

In this question,

Total number of balls=4+5+6=15

probability of red ball= 4/15

probability of white ball = 5/14  (Since the number of balls are decreasing

probability of blue ball= 6/13

probability of getting one marble of each color= 4/15×5/14×6/13    

                                                                              = 0.044

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Answer:

slope is -1

Step-by-step explanation:

slope is

m= (y2-y1) / (x2-x1) = -5+6 /2-3 = 1/-1 = -1

Answer:

is it to late now??

Step-by-step explanation:

We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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The value of x in the given equation, 2^(3x+1)=1/4, is x = -1

From the question, we are to solve the given given equation.

The given equation is

2^(3x+1) = 1/4

To solve the equation, we will determine the value of x.

Solving for x in the equation

2^(3x+1) = 1/4

Express 1/4 in index form

NOTE: 1/4 = 4^-1 = 2^-2

Thus,

The equation becomes

2^(3x+1) = 2^-2

Now, equate the powers

That is,

(3x + 1) = -2

3x + 1 = -2

Subtract 1 from both sides of the equation

3x + 1 - 1 = -2 - 1

3x = -3

Divide both sides of the equation by 3

3x/3 = -3/3

x = -1

Hence, the solution is x = -1

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Answer:

Step-by-step explanation:

F(x)=5

Answer:f(x) = x^5

Step-by-step explanation: