Lin plays a game involving a fair spinner labeled 1 through 4 and a deck of eight cards,
each card numbered 1 through 8. If both the spinner and card have the same number,
Lin receives another turn. Otherwise, play continues to the next player. Lin spins the
spinner once and randomly selects one card from the deck. What is the probability
Lin receives another turn? Explain your thinking.

Answer:

  5/8 apple

Step-by-step explanation:

You want to know each person's share if 5 apples are shared equally among 8 people.

A 1/8 share of the 5 apples is ...

  (1/8) × (5 apples) = 5/8 apple

Each person gets 5/8 apple.

__

Additional comment

This can be nicely accommodated by dividing 4 apples in half, and one apple into 8 equal slices. Then each person gets 1/2 + 1/8 = 5/8 of the total number of apples.

A graph of the piecewise function is shown on the coordinate plane in the image attached below.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is decreasing over the interval x < -1 and increasing over the interval x ≥ −1.

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To solve any amount of whole numbers or variables raised to a positive power, you need to apply the power to each individual term within the parentheses and simplify as needed.

To solve any amount of whole numbers or variables raised to a positive power, you simply need to apply the power to each term within the parentheses. For example, (2x) raised to the 4th power would be solved by taking 2 to the 4th power (which is 16) and x to the 4th power (which is [tex]x^4[/tex]), and then multiplying these terms together: [tex]16x^4[/tex].

Similarly, (4 times x raised to the 2nd power) raised to the 4th power would first require you to solve the term within the parentheses, which is x raised to the 2nd power (or [tex]x^2[/tex]), multiplied by 4 (to get 4x^2). Then, you raise this entire term to the 4th power, which means you multiply it by itself 4 times: [tex](4x^2)^4 = 4^4 * (x^2)^4 = 256x^8[/tex].

So, in summary, to solve any amount of whole numbers or variables raised to a positive power, you need to apply the power to each individual term within the parentheses and simplify as needed.

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There are 12 possible ways Barney can wear his shorts and shirts.

Now, We can draw a tree diagram as;

Shorts

  /      |       \

Pair1 Pair2 Pair3

 / \   / \   / \ / \

S1 S2 S1 S2 S1 S2

 Shirts

 /   |    |   \

S1 S2 S3 S4

So, Barney can choose from 3 different pairs of shorts and 4 different shirts.

Hence,  To find the total number of possible combinations, we just need to multiply the number of options for each category together.

Now, In this case, Barney has 3 options for shorts and 4 options for shirts,

Hence, the total number of possible ways he can wear his outfit is;

3 x 4 = 12

Thus, There are 12 possible ways Barney can wear his shorts and shirts.

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The expected number of patients experiencing flulike symptoms is 17.33.

Based on the information given, researchers selected 825 patients at random who take a certain widely-used prescription drug daily. In a clinical trial, 22 out of the 825 patients complained of flulike symptoms. The researchers' hypothesis is that more than 2.1% of this drug's users experience flulike symptoms as a side effect.

To test this hypothesis, we can use a one-tailed hypothesis test with a significance level of 0.01. The null hypothesis (H0) is that the proportion of patients experiencing flulike symptoms is equal to or less than 2.1%. The alternative hypothesis (Ha) is that the proportion of patients experiencing flulike symptoms is greater than 2.1%.

To calculate the test statistic, we first need to find the expected number of patients experiencing flulike symptoms under the null hypothesis. This is equal to the sample size (825) multiplied by the proportion of patients experiencing flulike symptoms under the null hypothesis (0.021). So, the expected number of patients experiencing flulike symptoms is 17.33.

Next, we can calculate the test statistic using the formula:

z = (x - μ) / σ

where x is the observed number of patients experiencing flulike symptoms (22), μ is the expected number of patients experiencing flulike symptoms under the null hypothesis (17.33), and σ is the standard deviation of the sampling distribution, which can be approximated by:

σ = sqrt[(p * (1 - p)) / n]

where p is the proportion of patients experiencing flulike symptoms under the null hypothesis (0.021) and n is the sample size (825).

Plugging in the values, we get:

z = (22 - 17.33) / sqrt[(0.021 * (1 - 0.021)) / 825] = 2.17

Looking up the critical value for a one-tailed test with a significance level of 0.01, we find that it is 2.33. Since our test statistic (2.17) is less than the critical value (2.33), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that more than 2.1% of this drug's users experience flulike symptoms as a side effect at the 0.01 level of significance.

In the given scenario, researchers selected 825 patients who take a certain prescription drug daily. Out of these, 22 patients experienced flulike symptoms. The hypothesis being tested is whether more than 2.1% of this drug's users experience flulike symptoms as a side effect at the α=0.01 level of significance. Since np₀(1-p₀) = 17.0 > 10, the sample size is less than 5% of the population size, and the patients were selected randomly, all requirements for testing the hypothesis are satisfied.

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If we know the 4 numbers used but do not know the order, there are 24 possible combinations to use to find the password.

When you have 4 distinct numbers and need to find the order, you are looking to determine the number of possible combinations.
A combination is an arrangement of items in a specific order. In your case, you are trying to find the possible arrangements for the 4 numbers you know, which can be used to unlock the password.
To calculate the number of combinations, you can use the formula for permutations, which is n!/(n-r)!, where n is the total number of items (numbers) and r is the number of items you want to arrange.
In this situation, n = 4 (the 4 numbers you know), and r = 4 (since you want to arrange all of the numbers). Applying the formula, you'll have:
4!/(4-4)!
4! (which is 4 x 3 x 2 x 1) divided by 0! (0! is equal to 1)
4! = 24
So, you have 24 different possible combinations for the order of the 4 numbers. To find the correct password, you would need to try each of these 24 combinations.

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AnswerAnswer:1/11

Step-by-step explanation:

The area of the polygon to the nearest tenth is 471.7 units²

A polygon is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. Examples of polygon include triangle, quadrilateral, pentagon e.t.c.

The area of a polygon is expressed as;

A = 1/2( asn)

where a is the apothem and s is the side length and n is the number of side.

To calculate the area, we have to know the side length.

side length = apothem × 2tan(180/n)

= 12 × 2 tan(180/9)

= 12 × 2 × 0.364

= 8.736

Therefore area of the polygon

= 1/2 × 12 × 8.736 × 9

= 943.49/2

= 471.7 units² (nearest tenth)

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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

The 95% confidence interval suggests if the nicotine patch is used for 2 months, there is a high likelihood that the proportion of individuals who will report no smoking incidents.

In the following year will fall between 17.4% and 24.8%. This means that the study results are statistically significant and reliable within this range, and it is likely that the nicotine patch can be effective in reducing smoking incidents for a significant proportion of users.
In the study of the nicotine patch, the appropriate interpretation of the 95% confidence interval (17.4%, 24.8%) is that we can be 95% confident that the true proportion of people who reported no smoking incidents in the following year after using the patch for 2 months lies between 17.4% and 24.8%.

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Therefore, there are 8820 groups of 9 that contain 5 women and 4 men using combination formula.

To solve part (b)(i), we need to use the combination formula. The number of ways to choose 5 women out of 9 is given by the combination C(9,5), which is:

C(9,5) = 9! / (5! * 4!)

= 126

Similarly, the number of ways to choose 4 men out of 8 is given by the combination C(8,4), which is:

C(8,4) = 8! / (4! * 4!)

= 70

To get the total number of groups of 9 that contain 5 women and 4 men, we need to multiply these two numbers:

126 * 70 = 8820

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The rectangular coordinates of each point (4, 60°) are (2, 2 * sqrt(3)). To find the rectangular coordinates of a point given in polar coordinates, we use the following formulas:

[tex]x = r cos(theta)[/tex]
[tex]y = r sin(theta)[/tex]

where r is the distance from the origin (also known as the radial coordinate) and theta is the angle between the positive x-axis and the line connecting the point to the origin (also known as the angular coordinate).

For example, let's say we have a point given in polar coordinates as (4, 60°). To find its rectangular coordinates, we plug in the values into the formulas:

x = 4 cos(60°) = 4 * 0.5 = 2
y = 4 sin(60°) = 4 * sqrt(3)/2 = 2 * sqrt(3)

Therefore, the rectangular coordinates of the point (4, 60°) are (2, 2 * sqrt(3)).

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We need to use a different test, such as the ratio test or the root test, to make a conclusion.

For the first series, we have:

∑[infinity]k=1 (2+k)/(3-k²)

Using the divergence test, we consider the limit of the general term as k approaches infinity:

lim (k→∞) (2+k)/(3-k²)

We can see that the denominator, k², grows much faster than the numerator, k. Therefore, as k approaches infinity, the term approaches zero. However, the denominator approaches infinity, meaning that the terms do not go to zero fast enough for the series to converge. Therefore, we can conclude that the series diverges.

For the second series, we have:

∑[infinity]k=1 (2e^k)/(3+k)

Using the divergence test, we consider the limit of the general term as k approaches infinity:

lim (k→∞) (2e^k)/(3+k)

We can see that the denominator, 3+k, grows much faster than the numerator, e^k. Therefore, as k approaches infinity, the term approaches zero. However, the denominator approaches infinity, meaning that the terms do go to zero fast enough for the series to converge. Therefore, we cannot conclude anything about the convergence or divergence of the series using only the divergence test. We need to use a different test, such as the ratio test or the root test, to make a conclusion.

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Does the representation show a quadratic function f(x) = 2x² + 1: B. yes.

In Mathematics and Geometry, a quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Where:

By comparison, we have the following:

ax² + bx + c = 2x² + 1

a = 2

b = 0

c = 1

In conclusion, we can logically deduce that f(x) = 2x² + 1 represent a quadratic function.

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Answer:

mean is the answer

Step-by-step explanation:

because mean or average is when the numbers of different value is added over the number you added

for example

the average of 5+4+5+6+4 is

5+4+5+6+4/5

24/5=4.8

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We can say with 90% confidence that the true mean concentration of uric acid in the population lies between 4.32 and 6.24 mg/dl.

To find the 90% confidence interval for the population mean concentration of uric acid, we can use the formula:

CI = x' ± z*(σ/√n)

where:

x' = sample mean concentration = 5.28 mg/dl

z = z-score for 90% confidence level = 1.645 (from standard normal distribution table)

σ = population standard deviation = 1.77 mg/dl

n = sample size (number of tests taken) = 13

Substituting the given values into the formula, we get:

CI = 5.28 ± 1.645 x (1.77/√13)

CI = 5.28 ± 0.96

CI = (4.32, 6.24)

Therefore, we can say with 90% confidence that the true mean concentration of uric acid in the population lies between 4.32 and 6.24 mg/dl.

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False.

If A is a 5×4 matrix and B is a 4×3 matrix, then the entry of AB in the 3rd row / 2nd column is obtained by multiplying the 3rd row of A by the 2nd column of B, not the 3rd column of A by the 2nd row of B.

If A is a 5×4 matrix and B is a 4×3 matrix, then the entry of AB in the 3rd row / 2nd column is obtained by multiplying the 3rd row of A by the 2nd column of B, not the 3rd column of A by the 2nd row of B.

To see why, let C = AB be the product of A and B. Then, by definition, the entry in the i-th row and j-th column of C is given by the dot product of the i-th row of A and the j-th column of B. That is, Cij = Ai1B1j + Ai2B2j + ... + Ai4B4j, where Ai1, Ai2, ..., Ai4 are the entries in the i-th row of A and B1j, B2j, ..., B4j are the entries in the j-th column of B.

So, in this case, the entry in the 3rd row / 2nd column of C is given by C32 = A31B12 + A32B22 + A33B32 + A34B42. This involves multiplying the 3rd row of A by the 2nd column of B, not the 3rd column of A by the 2nd row of B.

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The unit circle), and the curve does not oscillate rapidly or change direction abruptly, so we would expect the arc length to be less than 2.

To find the arc length traced out by the parametric curve x = cos(cos(4t)), y = sin(cos(4t)) as t goes through the range 0 to 1, we can use the following formula for arc length:

L = ∫√(dx/dt)^2 + (dy/dt)^2 dt, where the integral is taken over the range of t.

Taking the derivatives of x and y with respect to t, we have:

dx/dt = -sin(4t)sin(cos(4t))

dy/dt = cos(4t)sin(cos(4t))

Substituting these into the formula for arc length, we get:

L = ∫√((-sin(4t)sin(cos(4t)))^2 + (cos(4t)sin(cos(4t)))^2) dt

L = ∫√(sin^2(4t)sin^2(cos(4t)) + cos^2(4t)sin^2(cos(4t))) dt

L = ∫√(sin^2(cos(4t))) dt

L = ∫|sin(cos(4t))| dt

Since we know that the sine function oscillates between -1 and 1, we can see that the absolute value of sin(cos(4t)) is always between 0 and 1. Therefore, the integral of |sin(cos(4t))| over the range 0 to 1 gives us the total distance traced out by the curve, which is the arc length.

Evaluating the integral, we get:L = ∫|sin(cos(4t))| dt = ∫sin(cos(4t)) dt

Let u = cos(4t), then du/dt = -4sin(4t), and dt = -du/(4sin(4t))

Substituting for dt and u, we have:

L = ∫sin(u) * (-du/(4sin(4t))) = (-1/4) ∫sin(u) du = (-1/4)cos(u) + C

Substituting back for u and simplifying, we get:

L = (-1/4)cos(cos(4t)) + C

To find the constant C, we use the fact that L = 0 when t = 0:

0 = (-1/4)cos(cos(0)) + C = (-1/4)cos(1) + C

C = (1/4)cos(1)

Therefore, the arc length traced out by the parametric curve x = cos(cos(4t)), y = sin(cos(4t)) as t goes through the range 0 to 1 is:

L = (-1/4)cos(cos(4t)) + (1/4)cos(1)

L = (-1/4)cos(cos(4)) + (1/4)cos(1)

L ≈ 0.615

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In the year 2003, which is one year after 2002, 500 hamburgers were consumed per person in Michigan.

y = ( 5,000 175,000 x)(1/2)   where y represents the average number of hamburgers consumed by people in Michigan and x is the number of times since 2002.   To find the time when 500 hamburgers were consumed per person, we need to  break for x in the equation  

500 = ( 5,000 175,000 x)(1/2)  

Squaring both sides of the equation,

we get   =  5,000 175,000 x  

Simplifying, we have   x =  245,000

 Dividing both sides by 175,000, we get   x = 1.4  

thus, 500 hamburgers were consumed per person in Michigan1.4 times after 2002. To find the time, we add1.4 to 2002  

20021.4 = 2003.4

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The volume using the dimensions 13m 5m and 9m​ is 585 cubic meters

Volume is calculated using the three dimensions, hence to talk about volume we have a 3 dimensional perspective.

The formula for volume is given as the product of length, width, and depth or thickness.

this is represented mathematically as

length x width x depth

Information from the problem have it that

length = 13 m

width = 5m

depth = 9m

plugging in the values results to

= 13 * 9 * 5

= 585 cubic meters

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The distance between (-5, 3) and (2, -2) on the coordinate plane is approximately 8.6 units.

The formula to find the distance between the two points is usually given by

d=√{(x₂-x₁)² + (y₂-y₁)²}

Here:

x₂ = 2, x₁ = -5, y₂ = -2, and y₁ = 3.

Substitute the provided values,

d = √((2 - (-5))²  + (-2 - 3)²)

= √(7²  + (-5)²)

= √(49 + 25)

= √(74)

Rounding to the nearest tenth, we get:

d ≈ 8.6

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Answer:

-4/-12 or simplified would be 1/3

Step-by-step explanation:

I understand you're asking about the volume percentage removed from a solid box when a cube is removed from each corner. Let's consider the dimensions of the original box as L cm x W cm x H cm. When a cube of side length x cm is removed from each corner, there are a total of 8 corners (since a box has 8 corners).

The volume of each removed cube is x^3 cubic cm. Since there are 8 cubes removed, the total volume removed is 8 * x^3 cubic cm. The volume of the original box is L * W * H cubic cm.

Now, to calculate the percentage of the original volume removed, we use the formula:

[tex]Percentage removed = (Total volume removed / Original volume) * 100[/tex]

In this case, it would be:

Percentage removed = (8 * x^3) / (L * W * H) * 100

Keep in mind that the specific values of L, W, H, and x would be needed to calculate the exact percentage of the original volume removed. However, the general formula above can be used to determine the percentage removed for any solid box with given dimensions and removed cubes.

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The value of x is 3 in a right triangle for the u side angle having equation u = 9x+6.

Angle v = 57

Angle u =9x+6

The right angle triangle follows a rule that the sum of the two acute angles is 90 degrees. That means the angles u + v must be equal to 90 degrees.

v + u = 90

From the given angle equations, we can write

57 + 9x + 6 = 90

9x + 63 = 90

9x = 90-63

9x = 27

x = 27 ÷ 3

x = 3

Therefore we can conclude that the value of x is 3.

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It cannot be determined whether the data supports the conclusion that blocking was effective in reducing experimental error at the 95% confidence level. To assess the effectiveness of blocking, it is necessary to examine the specific data and perform appropriate statistical tests, such as Analysis of Variance (ANOVA).

Blocking is a technique used in experimental design to control for extraneous factors that may affect the results. It involves grouping experimental units with similar characteristics and then applying treatments within those groups. This method helps isolate the effect of the treatment and reduce variability in the data.

To determine if there is sufficient evidence to conclude that blocking is effective in this case, one must examine the experimental data and conduct a statistical test, such as ANOVA. This test allows researchers to compare the means of different groups and determine if there are significant differences. If the p-value obtained from the ANOVA test is less than the significance level (typically 0.05 for a 95% confidence level), it can be concluded that blocking was effective in reducing experimental error.

In summary, without access to the specific data and results from statistical tests, it is not possible to confirm whether the blocking method was effective in reducing experimental error at the 95% confidence level.

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The speed of sound at the coldest place on Earth. Temperatures on the East Antarctic Plateau can reach -100° C is B. 231 m/s

In this equation, v signifies the pace of sound measured in meters per second, while T represents the temperature expressed in Celsius degrees; and 273.15 denotes the standardized temperature in Kelvin.

When substituting T value as -100°C into our function implies that:

v = 331.3 * ✓(-100)/273.15)

v = 231 m/s

Thus, select option indicating 231 m/s.

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Step-by-step explanation:

four million seven hundred thousand can be written by

4,700,000

Answer:

-3,825

Step-by-step explanation:

When two numbers vary directly, they have a proportional relationship. That is to say that there is a constant ratio between them. In this case, we are given the ratio of x to y as:

x : y

1/2 : 150

We can make this a unit ratio by multiplying both sides by 2.

x : y

1 : 300

What this unit ratio tells us is that to find the corresponding y-value for any value of x, we can multiply the x-value by 300:

[tex]-\dfrac{51}{4} \cdot 300 = \boxed{-3,825}[/tex]

The maximum total number of observations with a deviation of at least 5 is 1.

If the sum of deviations of 100 observations from 20 is 5, then the maximum total number of them, such that each of which is at least 5, can be found by considering the minimum deviation for the other observations.

Since we want the maximum total number of observations with a deviation of at least 5, let's assume all other observations have a deviation of 0 (meaning they are equal to 20). Let x be the number of observations with a deviation of at least 5. Then, the sum of deviations can be represented as:

5x + 0(100-x) = 5

Solving for x, we get:

5x = 5
x = 1

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The given triangle with side lengths 3, 4, and 5 is a right triangle which can be proved by applying the Pythagoras theorem.

To prove that the given measures of a triangle are typically the measures of a right triangle, we will use the support from Pythagorean theorem. It states that in a right triangle, the sum of the squares of the base and perpendicular is equal to the square of the hypotenuse of the triangle. Hypotenuse is the side opposite to the perpendicular which is diagonally inclined.

In this case, we will put the values as follows:

3² + 4² = 5²

= 9 + 16 = 25

= 25 = 25

This triangle is a right triangle because the squares of the two shorter sides added together equal the square of the longest side.

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Correct question:

Decide if the triangle is a right triangle. Use pencil and paper. How can you use your results to decide if a triangle with side lengths 3​, 4​, and 5 is a right​ triangle?