The diagram shows a circle with centre O.
Write an expression in terms of x and/or y for
a) angle OAC.
b) angle OBA.

Answer:

To find the value of a5, we need to know the formula for the nth term of the sequence. We know that a1 = 2, so we can start by finding the common difference (d) between consecutive terms. an-1 + 5 = a1 + (n-2)d + 5 Simplifying this equation, we get: an-1 = a1 + (n-2)d Substituting a1 = 2, we get: an-1 = 2 + (n-2)d We also know that a5 is the 5th term of the sequence, so n = 5. Substituting n = 5, we get: a4 = 2 + (5-2)d a4 = 2 + 3d We don't have enough information

If your dependent variable is measured on a ratio scale, you should use statistical procedure of parametric test. The correct answer is D).

Parametric tests are statistical tests that assume a normal distribution of data and require interval or ratio scale measurements. Examples of parametric tests include t-tests, ANOVA, and linear regression. Non-parametric tests, on the other hand, do not assume a normal distribution of data and can be used for nominal, ordinal, interval, or ratio scale measurements.

Examples of non-parametric tests include the chi-square test for goodness of fit and the chi-square test for independence. However, these tests are not appropriate for ratio scale measurements, so you should use a parametric test. So, the correct option is D).

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--The given question is incomplete, the complete question is given

"what type of statistical procedure should you use if your dependent variable is measured on a ratio scale? select one:

A) chi-square test for goodness of fit

B) chi-square test for independence

C) non-parametric test

D) parametric test"--

The discriminant shows that the volume will reach 2750 shares in 24.6 weeks, but will never reach 4000 shares in a week.

What is the volume of a company's stock and will it ever reach certain values using the given equation and discriminant?

To determine if the volume will ever reach a certain value, we need to solve the equation V = 250t - 5t^2 for t and see if there are any real solutions for t that satisfy the condition.

a) For V = 2750, we have:

2750 = 250t - 5t^2

Rearranging and simplifying, we get:

5t^2 - 250t + 2750 = 0

Using the quadratic formula, we can find the solutions for t:

t = (-(-250) ± sqrt((-250)^2 - 4(5)(2750))) / (2(5))

t = (250 ± sqrt(62500 - 55000)) / 10

t = (250 ± sqrt(7500)) / 10

t ≈ 24.6 or t ≈ 5.4

Since one solution is positive and the other is negative, the only solution that makes sense in this context is t ≈ 24.6 weeks. Therefore, the volume will reach 2750 shares in 24.6 weeks.

b) For V = 4000, we have:

4000 = 250t - 5t^2

Rearranging and simplifying, we get:

5t^2 - 250t + 4000 = 0

Using the discriminant, which is b^2 - 4ac in the quadratic formula, we have:

b^2 - 4ac = (-250)^2 - 4(5)(4000) = 2500

Because the discriminant is positive, there are only two possible solutions for t. Therefore, the volume will reach 4000 shares in a week at some point. However, we need to solve the equation to find the exact solutions:

t = (-(-250) ± sqrt((-250)^2 - 4(5)(4000))) / (2(5))

t = (250 ± sqrt(62500 - 80000)) / 10

t = (250 ± sqrt(-17500)) / 10

There are no real solutions for t that satisfy the condition because the square root of a negative number is not a real number. Therefore, the volume will never reach 4000 shares in a week.

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We can solve for the time when the stone will be 698 feet above the planet's surface by setting h = 698 and solving for t in the equation h = 500 + 110t - 5.5t²:

698 = 500 + 110t - 5.5t²

Rearranging, we get:

5.5t² - 110t + 198 = 0

Dividing both sides by 5.5, we get:

t² - 20t + 36 = 0

This is a quadratic equation that we can solve using the quadratic formula:

t = (-(-20) ± sqrt((-20)² - 4(1)(36))) / (2(1))

Simplifying, we get:

t = (20 ± sqrt(64)) / 2

t = 10 ± 4

So the possible values of t are t = 14 or t = 6. We can check which value is correct by plugging each value into the original equation and seeing if it gives a height of 698:

When t = 14:

h = 500 + 110(14) - 5.5(14)²

h = 500 + 1540 - 1078

h = 962

When t = 6:

h = 500 + 110(6) - 5.5(6)²

h = 500 + 660 - 198

h = 962

So both values of t give a height of 698. Therefore, the stone will be 698 feet above the planet's surface at t = 6 seconds or t = 14 seconds.

"Triangle CFE is congruent to triangle PTR" is true.

If Triangle CFE is congruent to triangle PTR, we can make the following statements:
The corresponding sides of the triangles are congruent:

This means that CF = PT, FE = TR, and CE = PR.
The corresponding angles of the triangles are congruent:

This means that angle CFE is congruent to angle PTR, angle FCE is congruent to angle PRT, and angle ECF is congruent to angle TPR.
The triangles are equal in area: Since the triangles are congruent, they have the same shape and size. Therefore, they will have the same area.
The triangles can be superimposed on each other: This means that we can place triangle CFE on top of triangle PTR in such a way that their corresponding sides and angles overlap.
If we know the measurements of the sides and angles of one triangle, we can find the measurements of the sides and angles of the other triangle: Since the triangles are congruent, we know that their corresponding sides and angles are equal.

Therefore, if we know the measurements of the sides and angles of one triangle, we can find the measurements of the sides and angles of the other triangle by using the congruence criteria.
In conclusion, if Triangle CFE is congruent to triangle PTR, we can make several statements about their corresponding sides and angles, their areas, and their ability to be superimposed on each other.

We can also use the congruence criteria to find the measurements of the sides and angles of one triangle if we know the measurements of the sides and angles of the other triangle.

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The correct angle measure in degrees for each exterior angle is 5.5. The other values provided in the question, 6.4, 173.6, and 9720, are not relevant to the problem.

What is Exterior angles ?

In a polygon, an exterior angle is an angle formed by a side and an extension of an adjacent side. The measure of an exterior angle of a regular polygon with n sides is given by 360/n degrees.

To find the measure of each exterior angle of a regular polygon, we use the formula:

Measure of each exterior angle = 360 degrees / number of sides

In this case, the polygon is a regular 66-gon, so the number of sides is 66. Thus,

Measure of each exterior angle = 360 degrees / 66 = 5.454545...

Rounding to the nearest tenth, we get:

Measure of each exterior angle ≈ 5.5 degrees

Therefore, the correct angle measure in degrees for each exterior angle is 5.5. The other values provided in the question, 6.4, 173.6, and 9720, are not relevant to the problem.

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Finally, using the first term a1 = 2500 and the common ratio r = 0.6, we can formulate the explicit rule for the sequence as follows: a = 2500 × 0.6^(n-1) (n-1)

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given :

We can use the fact that each word is produced by multiplying the previous term by the common ratio r to determine the value of r. Thus:

1500/2500 = 0.6 = r

We can keep adding r to the preceding term to find the next two terms:

900 × 0.6 = 540

540 × 0.6 = 324

540 and 324 are the next two terms as a result.

Finally, using the first term a1 = 2500 and the common ratio r = 0.6, we can formulate the explicit rule for the sequence as follows:

a = a1 × r^(n-1) (n-1)

The clear rule is as follows: a = 2500 × 0.6^(n-1) (n-1).

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Answer:

The correct answer is D. Enough to feel rested.

To find the length of the hypotenuse of a right triangle, we need to use the Pythagorean Theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

c^2 = a^2 + b^2

In this case, we have two sides with lengths given by the expressions 5x + 7 and 3x. When x = 14, we can substitute this value into the expressions to find the lengths of the sides:

a = 5x + 7 = 5(14) + 7 = 77

b = 3x = 3(14) = 42

Now we can use the Pythagorean Theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2 = 77^2 + 42^2 = 5929 + 1764 = 7693

Taking the square root of both sides, we get:

c = sqrt(7693) ≈ 87.7

Therefore, when x = 14, the length of the hypotenuse of the triangle is approximately 87.7 units. I

Answer:

Step-by-step explanation:

The geometric sequence for the value of a₁= 3 r= 1/10 n=8 is [tex]a_{8} = \frac{3}{10000000}[/tex] i.e option c is correct.

What does the term "geometric sequence" mean?

A geometric sequence is a set of integers where the ratio between each pair of succeeding terms is fixed. The geometric sequence's general ratio is the name of this constant.

We can use the following algorithm to determine the nth term (an) of a geometric sequence:

[tex]a_{n} = a_{1} * r^{n-1}[/tex]

where a1 is the first term in the series, r represents the common ratio, and n denotes the term's number.

Since a1 = 3, r = 1/10, and n = 8, we get:

[tex]a_{8} = 3 * (\frac{1}{10})^{8-1} = 3 *( \frac{1}{10})^{7}[/tex]

[tex]= 3 * \frac{1}{10^{7} }[/tex]

Now, we can condense this equation to get the solution:

a₈ = [tex]\frac{3}{10000000}[/tex]

The solution is therefore [tex]\frac{3}{10000000}[/tex] that option c.

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Answer: We can start by factoring the given expression for the area of the rectangle:

Area = 144x^2 - 81

Area = (12x)^2 - (9)^2

Area = (12x + 9)(12x - 9)

We can see that the area is expressed as the product of two binomials (12x + 9) and (12x - 9), which represent the length and width of the rectangle, respectively. Therefore:

Length = 12x + 9

Width = 12x - 9

Note that we can check that the product of the length and width indeed equals the area:

Length x Width = (12x + 9)(12x - 9) = 144x^2 - 81 = Area

So, the expressions for the dimensions of the rectangle are:

Length = 12x + 9

Width = 12x - 9

Step-by-step explanation:

The number of students who earned a score of 90 or less in class 2 is 7, and the number of students who earned less than 75 in class 1 is 3. The difference between the two is 4.

The given problem presents two box plots representing the test scores for two different classes. Class 1 has 17 students, while class 2 has 13 students. It is required to find the difference between the number of students who earned a score of 90 or less in class 2 and the number of students who earned less than 75 in class 1.

By analyzing the box plots, we can see that 7 students in class 2 earned a score of 90 or less, while only 3 students in class 1 earned less than 75. Therefore, the difference between the two is 4. It is important to understand box plots and their interpretation to solve such problems.

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The mathematical function model for Bailey's income is: Regular earning +overtime pay=total earnings

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

So, we've said the:

12$ =1hours

initial forty hours a week

Then after a week, 18 dollars per hour.

We must ascertain the function that represents Bailey's income.

Then, the formula for regular earnings:

regular hour × regular rate=regular eaning

40(12)=480$

overtime hours × overtime rate=overtime pay

Regular earning +overtime pay=total earnings

The overtime hours in this case are unknown.

Because of this, we are unable to determine total earnings.

Therefore, the mathematical function model for Bailey's income is: Regular earning +overtime pay=total earnings

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Correct question:
Each week, Bailey earns $12 per hour for the first 40 hours she works, and $18 for each hour of work after 40 hours. Her weekly earnings are a function of the amount of time she works.

Which function models the amount of money that Bailey earns?

Answer:

Step-by-step explanation:

A dilation maintains the shape of a figure but changes its size.

A reduction would mean the new figure will be a smaller version of the original.

An enlargement would mean the new figure will be a bigger version of the original.

This particular question doesn’t include a photo so depending on these definitions, one can easily identify the correct answer.

Answer:

In geometry, a dilation is a transformation that changes the size of a figure while keeping its shape the same. Imagine taking a picture of a shape and then making it bigger or smaller without changing its proportions or angles.

If a dilation makes the figure smaller than the original, we call it a reduction. This means that the new figure is a scaled-down version of the original. Conversely, if a dilation makes the figure larger, we call it an enlargement. In this case, the new figure is a scaled-up version of the original.

So, to summarize, dilations can change the size of a figure while preserving its shape, and we can describe the resulting figure as either a reduction or an enlargement depending on whether it is smaller or larger than the original.

Step-by-step explanation:

Answer:

The probability of the coin landing heads up on any given flip is 1/2, and the probability of it landing tails up is also 1/2. Therefore, we can use the binomial distribution formula to calculate the probability of getting exactly 27 heads out of 90 flips: P(27 heads) = (90 choose 27) * (1/2)^27 * (1/2)^63 = 1.452 x 10^-9 So the probability of getting exactly 27 heads out of 90 flips is approximately 1.452 x 10^-9.

is would be 50 percent! you're welcome

For given dilation of the figure, the distance from the center of dilation to point A' is approximately 1.414 units.

What exactly is dilation in mathematics?

In mathematics, dilation is a transformation that changes the size of a figure but not its shape. It is also known as scaling, enlargement, or reduction.

To perform a dilation, a figure is multiplied or divided by a scale factor, which is a positive number greater than zero. If the scale factor is greater than 1, the figure is enlarged, while if it is less than 1, the figure is reduced. If the scale factor is equal to 1, the figure remains the same size.

Now,

To find the distance from the center of dilation to point A', we need to use the fact that the distance between the center of dilation and any point on the preimage is multiplied by the scale factor to get the corresponding distance on the image.

First, let's find the distance from the center of dilation to point A:

distance from center to A = √((6-2)² + (-2-2)²) = √(4² + (-4)²) = √32 ≈ 5.657 units (rounded to three decimal places)

Next, we can use the fact that the scale factor is 1/4 to find the distance from the center of dilation to point A':

distance from center to A' = (scale factor) x (distance from center to A)

= (1/4) x 5.657

= 1.414 units (rounded to three decimal places)

Therefore, the distance from the center of dilation to point A' is approximately 1.414 units.

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The total value of Mary's investment after two years is $233.

Answer:

81 eggs

Step-by-step explanation:

already had 9 eggs

6 crates x 12 eggs in each crate

= 72 eggs

72+9=81

Therefore, the slope is 1/3 and the y-intercept is 0.

a. The equation is in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 4, and the y-intercept is 1. Therefore, the slope is 4 and the y-intercept is 1.

b. This equation is also in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 1, and the y-intercept is -2. Therefore, the slope is 1 and the y-intercept is -2.

c. This equation is already in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 1/3, and the y-intercept is 0 (since there is no constant term). Therefore, the slope is 1/3 and the y-intercept is 0.

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The price that would generate more revenue for the company will be $5 because p(5) > p(17) based on the revenue generation on the graph.

As we change the price of the product, the quantity sold may also change. This means that the revenue curve will not be a straight line, but rather a curve that increases and then decreases as we move from lower to higher prices. The price point that generates the highest revenue will be the one at which the revenue curve reaches its maximum value.

It is important to note that the price point that maximizes revenue may not necessarily be the same as the price point that maximizes profit, as profit is influenced by both revenue and costs. Therefore, companies must carefully consider both revenue and cost factors when determining the optimal price point for their products.

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Answer: $4.20

Step-by-step explanation:

   To answer this question, we will find 5% of $84.

   First, a percent divided by 100 becomes a decimal.

5% / 100 = 0.05

   Next, we are finding 5% of $84. In mathematics, "of" means multiplication.

0.05 * $84 = $4.20

17-x

Because he sends more than you we subtract your value,x,from his 17,mostly because we are unaware of the number of texts you send.Which means 17 minus x will give you the amount of texts he sends more.

The nurse is responsible for giving Medication G in a quantity of 30 mL, which is approximately equivalent to 1.014 fluid ounces.

First, we need to convert 0.6 g to mg:

0.6 g = 600 mg

Next, we need to calculate how many mL are needed to deliver 600 mg of Medication G. From the label, we know that there are 100 mg of Medication G in 5 mL, so we can set up a proportion:

100 mg / 5 mL = 600 mg / x mL

Cross-multiplying, we get:

100x = 5 * 600

Simplifying, we get:

x = 30 mL

Finally, we can convert 30 mL to fluid ounces. There are 29.5735 mL in one fluid ounce, so:

30 mL / 29.5735 mL/oz ≈ 1.014 fl oz

Therefore, the nurse should administer 30 mL (or approximately 1.014 fluid ounces) of Medication G.

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a. To test whether the population mean daily number of texts for one age group differs from the population mean daily number of texts for another age group, we should use the following alternative hypothesis:
H1: μ1 ≠ μ2

b. To compute the p-value, we need to perform the following steps:
1. State the null hypothesis: H0: μ1 = μ2
2. Calculate the test statistic:
  t = (sample mean - hypothesized mean difference) / (population standard deviation / √n)
  Assuming the hypothesized mean difference is 0, and plugging in the given values:
  t = (sample mean - 0) / (population standard deviation / √30)
3. Find the p-value using a t-distribution table or calculator, and round to four decimal places.
c. If the p-value is less than the level of significance (α), we reject the null hypothesis and conclude that there is a significant difference in the population mean daily texts between the two age groups.

If the p-value is greater than or equal to α, we do not reject the null hypothesis and cannot conclude that there is a significant difference.
d. For the critical value approach, we compare the test statistic (t) with the critical value (±1.96).

If the test statistic falls in the rejection region (outside of ±1.96), we reject the null hypothesis and conclude that the population mean differs.

If the test statistic falls within the acceptance region (inside ±1.96), we do not reject the null hypothesis and cannot conclude that the population mean differs.

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Answer:

  use SSS

Step-by-step explanation:

Given two congruent chords AB and BC in circle O, you want to prove ∆AOB is congruent to ∆COB.

1. circle O, AB≅BC . . . . given

2. OB ≅ OB . . . . reflexive property of congruence

3. OA ≅ OC . . . . definition of a circle

4. ∆AOB ≅ ∆COB . . . . SSS postulate

__

Additional comment

Your erased statement 2 shows you know exactly how to do this.

All the radii of a circle are the same length, so it is easy to show congruence by SSS, given that AB≅BC.

Answer:

To solve this problem, we need to first find the numbers that are multiples of 4 or 6 between 1 and 15, inclusive.

Multiples of 4: 4, 8, 12

Multiples of 6: 6, 12

The number 12 is a multiple of both 4 and 6, so we only count it once.

So, there are a total of 4 possible outcomes that meet the condition of being a multiple of 4 or 6.

Therefore, the probability of getting a multiple of 4 or 6 is:

P(multiple of 4 or 6) = 4/15

Answer: 4/15.

Hope This Helps!

Based on the given information, Mike's grandmother deposited $6,000 into the savings account.

What is simple interest?

Simple interest is a method of calculating interest on a principal amount, where the interest is calculated only on the original amount of the loan or investment, without taking into account any interest that may have been previously earned. The formula for calculating simple interest is I = P * r * t, where I is the interest earned, P is the principal amount, r is the annual interest rate as a decimal, and t is the time period in years.

We are given that the interest rate is 8% and the interest earned after 10 years is $4,800. So we can write:

4,800 = P * 0.08 * 10

Simplifying the equation, we get:

4,800 = 0.8P

Dividing both sides by 0.8, we get:

P = 6,000

Therefore, Mike's grandmother deposited $6,000 into the savings account.

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