select all of the following expressions that are equivalent to 9 1/2

Answer:

a 2 = -39

a 2 = a 1 + 12

- 39 = a 1 + 12

a 1 = - 39 - 12

a 1 = - 51 ( first term )

The common difference is : d = 12

The explicit rule for the arithmetic sequence:

a n = a1 + ( n - 1 ) d

a n = -51 + ( n - 1 ) · 12

Step-by-step explanation:

In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.

The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.

Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.

Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.

By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.

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Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

72

Step-by-step explanation:

7(10) + 2

70 + 2

72

Answer:

10°

Step-by-step explanation:

According remote interior angles, 4k + 5 + 6k + 10 = 115.

10k + 15 = 115

10k = 100

k = 10

Hope this helps :)

Have a nice day!

Answer:

k = 10°

Step-by-step explanation:

      According to the exterior angle theorem, the exterior angle will be equal to the two opposite inside angles added together. It will look like the following, and we solve for k from there.

115° = (4k + 5)° + (6k + 10)°

115° = 4k° + 5° + 6k° + 10°

115° = 6k° + 4k° + 10°  + 5°

115° = 10k° + 15°

100° = 10k°

10° = k

k = 10°

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

The Power of a Point Theorem I states that if two chords of a circle intersect at a point inside the circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

The Power of a Point Theorem II states that if a point is located outside a circle and two rays are drawn from that point intersecting the circle, then the product of the lengths of the segments of one ray is equal to the product of the lengths of the segments of the other ray. These theorems provide useful relationships between the lengths of segments formed by chords and rays intersecting a circle.

Power of a Point Theorem I: Consider two chords of a circle, AB and CD, intersecting at a point X inside the circle. According to the theorem, the product of the lengths of AX and BX is equal to the product of the lengths of CX and DX: AX * BX = CX * DX. This relationship holds true for any pair of intersecting chords inside a circle.

Power of a Point Theorem II: Suppose there is a point P located outside a given circle. Draw two rays, PA and PB, from point P intersecting the circle at points A and B, and PC and PD intersecting the circle at points C and D, respectively. The theorem states that the product of the lengths of PA and PB is equal to the product of the lengths of PC and PD: PA * PB = PC * PD. This relationship applies to any pair of rays drawn from a point outside a circle and intersecting the circle.

These theorems provide geometric relationships that can be utilized in various geometric proofs and problem-solving involving circles. They help establish connections between the lengths of segments formed by chords and rays intersecting a circle, enabling the calculation of unknown segment lengths based on known ones.

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Answer:

x = 20

Step-by-step explanation:

By exterior angle theorem, we have:

\((4x + 2) \degree + (2x - 9) \degree = (5x + 13) \degree \\ \\(4x + 2 + 2x - 9) \degree = (5x + 13) \degree\\ \\(6x - 7) \degree = (5x + 13) \degree \\ \\ 6x - 7 = 5x + 13 \\ \\ 6x - 5x = 13 + 7 \\ \\ x = 20\)

Prior probability is the initial probability based on the present level of information. The given statement is true.

Prior probability, also known as prior belief or prior distribution, is the initial probability assigned to an event or hypothesis based on the available information before new data or evidence is observed or collected. It represents the degree of belief or probability of an event before considering any new evidence or information.

The prior probability is updated using Bayes' theorem after considering new evidence or data, resulting in a posterior probability that represents the revised probability of the event or hypothesis.

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To determine if the water is unsafe based on the given data, we can conduct a hypothesis test using the sample mean and the provided information.

Null Hypothesis (H₀): The mean PCB concentration in the water is equal to or less than 5 ppm.

Alternative Hypothesis (H₁): The mean PCB concentration in the water is greater than 5 ppm.

We will use a one-sample t-test to assess the evidence.

Test statistic and p-value calculation:

The test statistic for a one-sample t-test is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

In this case:

Sample mean (x) = 5.2 ppm

Hypothesized mean (μ₀) = 5 ppm

Sample standard deviation (s) = 0.6 ppm

Sample size (n) = 36

t = (5.2 - 5) / (0.6 / sqrt(36))

  = 0.2 / (0.6 / 6)

  = 0.2 / 0.1

  = 2

To find the p-value associated with this test statistic, we need to consult the t-distribution table or use statistical software. Assuming a one-tailed test (since we're testing if the mean is greater than 5 ppm), the p-value is the probability of observing a t-value greater than or equal to 2.

With the calculated test statistic of t = 2 and the associated p-value, we can compare the p-value to a significance level (α) to make a decision. Common significance levels include 0.05 or 0.01.

Suppose we choose a significance level of α = 0.05. If the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis.

Since the p-value was not provided, please consult a t-distribution table or use statistical software to determine the exact p-value for t = 2. Once you have the p-value, compare it to the chosen significance level (e.g., α = 0.05) to draw a conclusion about whether the data substantiates that the water is unsafe.

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Answer:

Zack = x

Tony = x + 6

x + x + 6 = 42

2x + 6 = 42

2x = 36

x = 18

So,

Zack = x = 18

Tony = x + 6 = 18 + 6 = 24

Answer:

13.3

Step-by-step explanation:

The solution set of the equation 3X=-6/1-X for x # 1 is {-2,1)

3x = -6/(1-x)

3x(1-x) = -6

3x – 3x2 = -6

Taking 3 as common from both sides

x –x2 = -2

x2 – x +2 =0

Using factorisation method we will get two factors

Factoring quadratics is a method of expressing the quadratic equation ax2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax2 + bx + c = 0. This method is also is called the method of factorization of quadratic equations. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc.

( x – 2)(x+1)=0

So, x = 2 , -1

Now, when x ≠ 1

The solution of the equation will vary from {-2,1) .

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Answer:

abc is a triangle so ,

a is ( 9,6 )

b is ( 9,3 )

and c is ( 3,3 )

1+4/x                       x + 4

------------   =            -------------  

1-16 x^2           x(-4x + 1) (4x + 1)

hope this helps, it probs won't but-

Answer: \(\frac{x+{4} }{x - 16x^{3} }\)

Steps:

Sorry about the delay. Hope this helps!

An ogive is used to plot cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class when displaying quantitative data. Option B.

An ogive is a graph that represents a cumulative distribution function (CDF) of a frequency distribution. It shows the cumulative relative frequency or cumulative frequency of each class plotted against the upper limit of the corresponding class. In other words, an ogive can be used to represent data through graphs by plotting the upper limit of each class interval on the x-axis and the cumulative frequency or cumulative relative frequency on the y-axis.

An ogive is used to display the distribution of quantitative data, such as weight, height, or time. It is also useful when analyzing data that is not easily represented by a histogram or a frequency polygon, and when we want to determine the percentile or median of a given set of data. Based on the information given above, option B: "Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class" is the correct answer.

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The simplest form is (-2 ±√12)/2.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: x = (-4 ±√48)/4

We have to simplify the given term.

x = (-4 ±√48)/4

x =  (-4 ±√12×4)/4

x =(-4 ±2√12)/4

Now, we take 2 as common and get

x = (-2 ±√12)/2

Hence, the simplest form is (-2 ±√12)/2.

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Answer:

letter D.

Step-by-step explanation:

im not sure but I try it

-----------------------------

a) To find the number of customers who have both checking and money market savings accounts, we need to use the principle of inclusion and exclusion.

Let A be the set of customers with checking accounts, B be the set of customers with money market savings accounts, and C be the set of customers with both checking and money market savings accounts. Then we have:

|A ∪ B| = |A| + |B| - |A ∩ B|

We know that |A| = 168, |B| = 120, and |A ∩ B| = ? (what we need to find)

We can also use the fact that the total number of customers is 250, so:

|A ∪ B| = 250 - |A' ∩ B'|

where A' and B' are the complements of A and B, respectively. Since no customer is allowed to have both regular savings and money market savings accounts, we know that:

|B ∩ C| = 0

So we can use the principle of inclusion and exclusion again to find:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |C ∩ A| + |A ∩ B ∩ C|

We know that |A ∪ B ∪ C| = 250 and |A|, |B|, and |C| are given. We also know that |B ∩ C| = 0 and we can use the fact that:

|A' ∩ B' ∩ C'| = |(A ∪ B)' ∩ (B ∪ C)' ∩ (C ∪ A)'|

= |(A' ∩ B') ∪ (B' ∩ C') ∪ (C' ∩ A')|

= |A' ∩ B'| + |B' ∩ C'| + |C' ∩ A'| - |A' ∩ B' ∩ C'|

We know that |A' ∩ B'| = |(A ∪ B)'| = 250 - |A ∪ B| and |C' ∩ A'| = |(C ∪ A)'| = 250 - |C ∪ A|. Since we already know |A ∪ B| and |C ∪ A| from the previous calculations, we can find |A' ∩ B' ∩ C'|. Then we can use the principle of inclusion and exclusion to find |A ∩ B|:

|A ∩ B| = |A| + |B| + |C| - |A ∪ B ∪ C| + |A' ∩ B' ∩ C'|

Substituting the given values, we get:

|A ∩ B| = 168 + 120 + 0 - 250 + (250 - 168 - 75 - 120 + |A ∩ B|)

Solving for |A ∩ B|, we get:

|A ∩ B| = 26

Therefore, there are 26 customers who have both checking and money market savings accounts.

b) To find the number of customers who have a checking account but no savings account, we can use the same principle of inclusion and exclusion. Let D be the set of customers with no savings account. Then we have:

|A ∩ D| = |A| - |A ∩ B ∪ A ∩ C|

We know that |A| = 168 and we just found |A ∩ B| = 26. To find |A ∩ C

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The word in the problem that indicates that a negative sign should be used is "descend"

We know that he stops for water breaks four times, and between each water break, he descends 15 meters.

The written equation is:

4*(-15)m = -60m

Why the negative sign is used?

The negative sign is used because the hiker is descending, so its height is decreasing. The word in the problem that indicates that a negative sign should be used is "descend"

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If two lines intersect, then the vertical angles formed must be both equal in measure.

The  intersection of a line can be described as when two or more lines cross each other in a plane as a result of this they are been referred to as   intersecting lines.

Therefore, intersecting lines share a common point, hence , If two lines intersect, then the vertical angles formed must be both equal in measure.

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Answer:

$176.30

Step-by-step explanation:

7 1/2% can be simplified to 7.5%

7.5% of 164.00 is 12.30

12.30+164.00=176.30

$176.30

The value of A is 3 and the value of B is 2.

They are the numbers represented by positive real numbers where the fractions and decimal numbers are not included.

The question gives:

Thus, you need to find A and B for these conditions.

When we calculated the  Least Common Multiple ( LCM ) between 3 and 11, we can rewrite the equation as:

                                            \(\frac{A}{11}+\frac{B}{3} =\frac{31}{33}\\ \\ \frac{3A+11B}{33}=\frac{31}{33}\)

Thus, we have:

                                          \(3A+11B=31\\ \\ 3A=31-11B\\ \\ A=\frac{31-11B}{3}\) (1)

From this condition, for that A is a whole number, then 31-11B >0.

Then,

                                                    \(31-11B > 0\\ \\ -11B > -31\\ \\ 11B < 31\\ \\ B < 2.8\)

In this case, for that B should be a whole number, B can be 0,1 and 2.

Now, you should replace probable numbers for B in equation (1). The value of B will be the number from that you will find the whole number for A. See below.

For B=0, you have \(A=\frac{31-11*0}{3}=\frac{31}{3}=10.33\) . In this case, A is not a whole number. Then, B can't be 0 (zero).

For B=1, you have \(A=\frac{31-11*1}{3}=\frac{31-11}{3}=\frac{20}{3}=6.67\) . In this case, A is not a whole number. Then, B can't be 1 (one).

For B=2, you have \(A=\frac{31-11*2}{3}=\frac{31-22}{3}=\frac{9}{3}=3\) . In this case, A is a whole number (3). Then, B can be 2 (two).

Let's replace this information in the given equation in your question.

                                                    \(\frac{A}{11}+\frac{B}{3} =\frac{31}{33}\\ \\ \frac{3}{11}+\frac{2}{3} =\frac{31}{33}\\ \\ \frac{9+22}{33}= \frac{31}{33}\\ \\ \frac{31}{33}=\frac{31}{33}\)  

Hence, A=3 and B=2.

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Answer:

y = - 3x + 24

Step-by-step explanation:

Step 1:

y = mx + b         Slope Intercept Form

Step 2:

- 3x - y = - 24         Equation

Step 3:

- 3x = y - 24       Add y on both sides

Step 4:

- 3x + 24 = y        Add 24 on both sides

Answer:

y = - 3x + 24

Hope This Helps :)        

Answer:

4 hours

Explanation:

Mike can build a wall in 5 hours. His work rate is:

His son can do the job in 20 hours. The son's work rate is:

Let the time it takes both of them = x hours. Then, their joint rate is:

Therefore:

We solve the equation for x:

It takes them 4 hours to build a wall together.

As we know that

So , we need to find side of square first

Using area of square = Side²

➩ 144 = S²

➩ S = √144

➩ Side = 12 cm

Now ,

➨ Diagonal = √2 ( 12 )

➨ Diagonal of square = 12√2

The only reasonable side length is x = 8 is "The solutions are -8 and 8, but only 8 is a reasonable side length."

The equation provided and evaluate the solutions in the context of the problem.

The equation mentioned in the problem is not explicitly provided, so we'll proceed with the given information.

Let's assume the side length of the square prism cake box is x.

The volume of a square prism can be calculated using the formula:

Volume = Length × Width × Height

Since the cake box is a square prism, the length and width are the same, so we can write:

Volume = x × x × 5.5

Given that the volume of each box must be 352 cubic inches, we can set up the equation:

x^2 × 5.5 = 352

Now, let's solve this equation to find the possible solutions for x:

x^2 = 352 / 5.5

x^2 ≈ 64

Taking the square root of both sides, we have:

x ≈ ±8

The solutions to the equation are -8 and 8.

Since we are dealing with a physical length, a negative side length doesn't make sense in this context.

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