REASONING
5. In problem #4, there is a relationship between the measure of the smaller are intercepted by the tangents and
the measure of the exterior angle.
(a) Determine the relationship. If you need to,
generate more examples using the same
diagram. Illustrate the relationship with at
least one pair.
(b) If mAB=x, prove the relationship you
found in (a).

Answer:

<

Step-by-step explanation:

because 42.18 is smaller than 42.7

False.

The number of vectors in the span of a set of vectors depends on the linear independence of the vectors.

The number of vectors in the span of a set of vectors depends on the linear independence of the vectors. If a set of vectors is linearly independent, then only the zero vector is in the span of the set. If a set of vectors is linearly dependent, then the span of the set contains infinitely many vectors.

So, the number of vectors in span {a1, a2, a3} can be 1, 2, or 3, depending on whether the set {a1, a2, a3} is linearly dependent or independent.

For example, if a1 = (1,0,0), a2 = (0,1,0), and a3 = (0,0,1), then {a1, a2, a3} is a linearly independent set, and the span of {a1, a2, a3} is just the set of all linear combinations of these vectors, which is the entire space R3. So, there are infinitely many vectors in the span of {a1, a2, a3}.

On the other hand, if a1 = (1,0,0), a2 = (2,0,0), and a3 = (0,1,0), then {a1, a2, a3} is a linearly dependent set, since a2 is a scalar multiple of a1. In this case, the span of {a1, a2, a3} is just the set of all linear combinations of a1 and a3, which is a plane in R3. So, there are infinitely many vectors in the span of {a1, a2, a3}.

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Answer:

8,911,248

Step-by-step explanation:

8,923,283 - 12,035 = 8,911,248

Answer:

The fact that "b varies directly with a" means that there exists a constant k such that b = ka. Since "a" and "b" are located the same distance from 0 in opposite directions, we know that a and b have the same absolute value but different signs. Therefore, we can write a = -b or b = -a.

Substituting -a for b in the equation b = ka, we get:

-a = ka

Solving for k, we get:

k = -a/a = -1

Substituting k = -1 back into the equation b = ka, we get:

b = -a

Therefore, the equation that represents the direct variation between a and b is:

b = -a

The driving time along this stretch was reduced by 36% for a person who always drives at the speed limit.

To calculate the percent reduction in driving time along the stretch, we need to consider the effects of both the distance decrease and the speed increase.

First, let's assume the original distance of the stretch was D. After the reconstruction, the distance is now 0.8D (since it was decreased by 20%).

Next, let's assume the original speed limit was S. After the reconstruction, the speed limit is now 1.25S (since it was increased by 25%).

To calculate the original driving time along the stretch, we would use the formula: time = distance / speed. So the original driving time would be D/S.

After the reconstruction, the driving time would be (0.8D) / (1.25S) = 0.64D/S.

To calculate the percent reduction in driving time, we can use the formula: (original time - new time) / original time * 100%.

Plugging in the values we calculated, we get:

(original time - new time) / original time * 100% = (D/S - 0.64D/S) / (D/S) * 100% = 36%.

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The volume of the piñata is 3.375 cubic feet.

Now, To find the volume of the piñata, we need to calculate the volume of a cube.

Hence, We can do this by multiplying the length of one edge by itself three times.

In this case, each edge of the piñata is 1.5 feet long,

so we can write;

Volume of piñata = (1.5 feet) x (1.5 feet) x (1.5 feet)

Simplifying this expression, we get:

Volume of piñata = 3.375 cubic feet

Therefore, the volume of the piñata is 3.375 cubic feet.

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If the true population distribution is close to the population distribution assumed in the null hypothesis, the power tends to be lower.

Explanation:
1. True population distribution refers to the actual distribution of the population.
2. Null hypothesis is the assumption that there is no significant difference between the observed and expected data.
3. Power is the probability of correctly rejecting the null hypothesis when it is false.

So if the true population distribution is close to the null hypothesis distribution, it is less likely that significant differences will be found in the sample.

When the true population distribution is close to the null hypothesis, it becomes more difficult to detect a significant difference, leading to a lower power in the statistical test.

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The area of each of the circles are:

Area of Circle A = 64π

Area of Circle B = 121π

Area of circle C = 225π

Area of circle D = 169π

The formula for the area of a circle is:

A = πr²

where:

A is Area

r is radius

Thus:

Area of Circle A = π * 8²

Area of Circle A = 64π

Radius of circle B is 3 mm greater than that of circle A. Thus:

Radius of circle B = 3 + 8 = 11 mm

Area of Circle B = π * 11²

Area of Circle B = 121π

The radius of Circle C is 4 mm greater than the radius of Circle B.

Radius of circle C = 4 + 11 = 15 mm

Area of circle C = π * 15²

Area of circle C = 225π

The radius of Circle D is 2 mm less than the radius of Circle C. Thus:

Radius of circle D = 15 - 2 = 13 mm

Area of circle D = π * 13²

Area of circle D = 169π

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Answer:

The only value of n that makes the inequality true is 5.

Explanation:

To solve the inequality, we need to isolate n on one side of the inequality symbol. First, we can multiply both sides by 7/3 to get:

n > (4/3) × 27/7

Simplifying, we get:

n > 4

So any value of n greater than 4 would make the inequality true. Among the given choices, only 5 is greater than 4, so it is the only value that satisfies the inequality.

To declare variable's length, width, and area that can hold decimal values like 13.5 and 14.6, the following code can be used: var length = 13.5;

var width = 14.6; var area = length * width; The variables length and width hold the decimal values of 13.5 and 14.6 respectively, and the variable area is calculated by multiplying the length and width variables.

These variables can be used to represent the dimensions of a rectangular shape in a program or application. Additionally, if the values of length and width are subject to change, they can be updated to reflect the new values and the area variable can be recalculated accordingly.

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Answer:

y = 3x + 15

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-3,6) (-2,9)

We see the y increase by 3 and the x increase by 1, so the slope is

m = 3

Y-intercept is located at (0,15)

So, the equation is y = 3x + 15

Answer:

3 months

Step-by-step explanation:

To find the amount of months, m, we will have to solve the equation given. If you don't have any experience solving equations, this could be tricky, but hopefully my work below will be helpful.

15m + 35 = 10(m + 5)

15m + 35 = 10m + 50

15m - 10m + 35 = 10m - 10m + 50

5m + 35 = 50

5m + 35 - 35 = 50 - 35

5m = 15

5m/5 = 15/5

m = 3

After 3 months the cost of the gyms will be the same. Let me know if you need more clarification or were confused by my work. :)

Answer:

-13 < x < 13

Step-by-step explanation:

let base, b = 11

side, a = 7

missing side, hypotenuse, c = x

according to the phythagoras theorem,

a² + b² = c²

7² + 11² = c²

49 + 121 = c²

170 = c²

thus, third side = +- 13

This statistics is an example of the "interference theory" in motor learning.

Interference theory suggests that when individuals learn multiple skills or movements in a random order, they perform better in retention and transfer tests compared to those who learn the same skills or movements in a blocked or constant order. The random practice group in this scenario was able to better transfer their knot-tying skills to new situations because they learned the knots in a more varied and unpredictable way, which helped them develop more adaptable and flexible motor patterns.

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Applying SOHCAHTOA, the value of the missing side in the right triangle is calculated as: x ≈ 11.2.

SOHCAHTOA is an acronym for the basic trigonometric ratios that can be used to find the missing side of a right triangle. It means:

SOH implies sin ∅ = opposite / hypotenuse

CAH implies cos ∅ = adjacent / hypotenuse

TOA implies tan ∅ = opposite / adjacent.

To find the missing side, x, we will apply SOH:

sin 36 = x/19

19 * sin 36 = x

x ≈ 11.2

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Answer: The slope-intercept form of the equation of a line is y = mx + b, where "m" is the slope and "b" is the y-intercept.

We know that the slope of the line is 2/7. We can also find the y-intercept by plugging in the coordinates of the given point (7,0) and solving for "b".

0 = (2/7) * 7 + b

0 = 2 + b

b = -2

So the equation of the line in slope-intercept form is:

y = (2/7)x - 2

Step-by-step explanation:

Answer:   [tex]y=\frac{2}{7}x-7[/tex]

Step-by-step explanation:

m=slope=2/7

point(7,0)

put into point-slope formula

[tex](y-y_{1})=m(x-x_{1)}[/tex]    where    [tex](x_{1} ,y_{1)} =(0,7)[/tex]

[tex]y-7=\frac{2}{7}(x-0)[/tex]        now put into slope- intercept(y=mx+b) form by simplifying, 0 goes away, and add 7 to both sides

[tex]y=\frac{2}{7}x-7[/tex]          b is your y-intercept, where it hits y-axis

There are several potential sources of probability in this study that could affect the results.

Selection bias could occur if the 249 individuals chosen for the study were not representative of the larger population of obese individuals. For example, if the study only recruited participants from a certain geographic area or demographic group, the results may not be generalizable to other populations.

Measurement bias could occur if the methods used to measure BMI were inaccurate or inconsistent. If the measurements were taken in a non-standardized way, or if the same person was not consistently measuring BMI throughout the study, the results may not be reliable.

Attrition bias could occur if participants dropped out of the study at different rates depending on whether they received the new drug or a placebo. For example, if participants who experienced negative side effects from the new drug were more likely to drop out, the results may overestimate the drug's effectiveness.

Reporting bias could occur if participants in the study provided inaccurate or incomplete information about their weight or BMI. For example, if participants underreported their weight or failed to record their weight on certain days, the results may not be accurate.

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Answer:

a) For help, plot the points on the graphing calculator.

b) Generate a linear regression equation:

y = -2.2857x + 16.8571

y = (-16/7)x + (118/7)

c) See part b.

d) The data shows a negative association.

e) We expect the number of losses to decrease by about 2.2857 per week. The y-intercept, 16.8571, is meaningless since the gamer received the video game at

x = 0.

Based on the information, we can infer that Lin's graph has an error because each fragment must equal 35 pages and not 55.

To identify and explain Lin's error, we must take into account how many pages the book has. In this case there are 175 pages, if Andre says that he has read 1/5 of the book we must divide the total number of pages by 5 to find out how many pages Andre has read.

So if Andre has read 1/5, he has read 35 pages and Elena will have read 55 pages. Due to the above, the error in Lin's graph is that each of the segments that divide the total pages into 5 has the wrong value because each one should equal 35 and the fragment that Elena read must take a complete segment and part of another

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The possible coordinates of point​ A is: (-7, -4)

The formula for the distance between two coordinates is:

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

We are given:

(x₂, y₂) = (1, 2)

(x₁, y₁) = (-7, y₁)

Thus, if AB = 10, then we have:

√[(2 - y₁)² + (-7 - 1)²] = 10

(2 - y₁)² + 64 = 100

(2 - y₁)² = 100 - 64

(2 - y₁)² = 36

(2 - y₁) = √36

2 - y₁ = 6

2 - 6 = y₁

y₁ = -4

Thus, the coordinate of point A is: (-7, -4)

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This stage of group development is known as forming.

The group development process is a series of stages that a group goes through as they form, develop, and eventually come to an end. The first stage of this process is known as forming. During this stage, group members are getting to know each other and trying to establish common goals and a shared understanding of how the group will operate. They may be polite and reserved, as they are still trying to feel out the dynamics of the group.

Once the group has established its purpose and members have a sense of what is expected of them, they move into the norming stage. During this stage, group members begin to work together more closely and develop norms for behavior and communication. They may start to form stronger relationships with each other and trust begins to build.

The third stage of group development is storming. During this stage, conflicts may arise as group members struggle for power and influence. There may be disagreements about how the group should function or how tasks should be completed. However, if the group is able to work through these conflicts, they will move on to the next stage of development.

The final stage of group development is adjourning. During this stage, the group comes to an end. This may be due to the completion of a task or project, or it may be due to other reasons, such as members leaving the group or the group disbanding. During this stage, members may reflect on their accomplishments and evaluate the group's overall success.

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The number of ways we can pick five students for a student council if we have twelve people running would be 792 ways.

The formula needed to calculate the number of possible ways for a student council consisting of five individuals, from a pool of twelve candidates, is the combination equation.

n choose k = n! / (k! x (n - k)!)

= 12 ! / ( 5 ! ( 12 ! - 5 ) !)

= 12 ! / ( 5 ! x 7 !)

= 792 ways

Thus, it has been determined that there exist 792 feasible options for selecting members for this student council out of the aforementioned dozen contestants.

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Option D (9) is not a probability and is not a possible answer choice for a probability question.

To find the probability of the intersection of events A and B (denoted as P(A ∩ B)), we need to know how many elements are in both A and B. Since there are 2 repeated elements between the events, this means that there are a total of 7 - 2 = 5 distinct elements between them.

Therefore, P(A ∩ B) = 5/7.

Note that none of the answer choices provided match this result exactly. Option A is the closest with a probability of 4/7, but this is the probability of A alone, not the intersection of A and B. Option B (2/7) is the probability of B alone and option C (5/7) is the probability of either A or B occurring, not the intersection.

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It will take approximately 23.3 years for Caleb's account to grow to $12,700 with 3% simple interest, assuming he makes no withdrawals or deposits during that time.

To solve this problem, we need to use the formula for simple interest:

I = P * r * t

where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the time period.

We know that Caleb invests $10,000 and earns 3% simple interest. So,

I = 10,000 * 0.03 * t

Simplifying this expression, we get:

I = 300t

Now, we need to find out how long it will take for the account to grow to $12,700. That means the total amount in the account will be the principal plus the interest:

P + I = 12,700

Substituting the expression for I that we found above, we get:

10,000 + 300t = 12,700

Solving for t, we get:

t = 23.3

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Answer:702

Step-by-step explanation:n*n-1

To set up a partial fraction decomposition for a rational expression, we want to express it as a sum of simpler fractions, with each denominator being a linear factor (i.e. a factor of the form ax + b, where a and b are constants). The general form of a partial fraction decomposition is:

f(x) = A/(ax + b) + B/(cx + d) + ...

where A, B, etc. are constants that we'll need to solve for.

Note that we're not trying to find specific values for A, B, etc. in this question - we're just setting up the decomposition.

So, for each rational expression, we'll need to factor the denominator into linear factors (if it's not already in that form). Then we'll set up the partial fraction decomposition using the formula above. Here are a few examples:

Example 1: (x^2 + 5x + 6)/(x^2 + 4x + 3)

First, let's factor the denominator: x^2 + 4x + 3 = (x + 1)(x + 3). So we can write:

(x^2 + 5x + 6)/(x^2 + 4x + 3) = A/(x + 1) + B/(x + 3)

Note that we have two linear factors in the denominator, so we need two terms in the partial fraction decomposition. We don't know what A and B are yet - we'll need to solve for them.

Example 2: (2x + 5)/(x^2 - 4)

The denominator here is not yet in factored form, so we'll need to factor it first: x^2 - 4 = (x + 2)(x - 2). Then we can write:

(2x + 5)/(x^2 - 4) = A/(x + 2) + B/(x - 2)

Again, we have two linear factors in the denominator, so we need two terms in the partial fraction decomposition.

Example 3: (4x^2 - 2x + 1)/(x^3 + x)

The denominator here is not in factored form, so we'll need to factor it: x^3 + x = x(x^2 + 1). Then we can write:

(4x^2 - 2x + 1)/(x^3 + x) = A/x + B/(x^2 + 1)

In this case, we have one linear factor (x) and one quadratic factor (x^2 + 1), so we need two terms in the partial fraction decomposition.

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The diameter of the sphere with a volume of 2171 m3, to the nearest tenth of a meter, is 16.1 m.

To find the diameter of a sphere with a volume of 2171 m³, we'll use the following formula for the volume of a sphere:

V = (4/3)πr³

Here, V is the volume and r is the radius of the sphere. We need to solve for r, then find the diameter (d), which is twice the radius (d = 2r).

Step 1: Substitute the given volume (2171 m³) into the formula:
r = (3V/4π)^(1/3)

Plugging in the given volume of 2171 m3, we get:

2171 = (4/3)πr³

Step 2: Solve for r³:

r³ = 2171 × (3/4) / π

r³ ≈ 520.44

Step 3: Find the cube root of r³ to get r:

r ≈ 8.05

Step 4: Find the diameter (d) by multiplying r by 2:

d = 2 × 8.05

d ≈ 16.1

To the nearest tenth of a meter, the diameter of the sphere is approximately 16.1 meters.

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