Luis paid a total of $72.00 for 3 pairs of shorts. If each pair of shorts costs the same amount, what is the price of one pair of shorts?

a) an = 3(n-2) if n is even and an = 3(n-3) if n is odd

b)  It is proved that an = n².

a)Given recurrence relation is an = 3an-2, Q1 = 1, Q2 = 2.  

We have to find an in terms of n.

Step 1: Finding the pattern

Let us find the values of a1, a2, a3 and a4  a1 = Q1 = 1, a2 = Q2 = 2, a3 = 3, a1 = 3, a4 = 3a2 = 3 x 2 = 6

Let us represent it as a table

Step 2: Writing the general expression

The sequence obtained is an = 1, 2, 6, 18, 54, …We can see that an = 3an-2

If n is even, then an = 3(n-2)

If n is odd, then an = 3(n-3)

Step 3: Writing the final expression

The general expression of an is as follows:

an = 3(n-2) if n is even and an = 3(n-3) if n is odd

b) Given recurrence relation is an = an-1 + 2n – 1, a1 = 1, using induction

Let us prove that an = n² by induction

Step 1: Verification of base case

When n = 1an = a1 = 1

We have to prove that a1 = 12 an = n2 = 1

Therefore, the base case is verified.

Step 2: Let us assume that an = n2 is true for some k such that k > 0i.e., ak = k² (Inductive Hypothesis)

Step 3: Let us verify that an = n2 is true for n = k+1i.e., prove that ak+1 = (k+1)²

Using the recurrence relation given, we haveak+1 = ak + 2k+1 – 1 = k2 + 2k + 1 = (k+1)²

Therefore, the proof is complete. It is proved that an = n².

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The parametric equations for the circle with radius 4 and centered at (-3,4), traced clockwise starting at (-3,0), are x = -3 + 4cos(t) and y = 4 + 4sin(t), where t is the parameter representing the angle of rotation. The domain for these equations is 0 ≤ t ≤ 2π.

To obtain the parametric equations for the circle, we start by considering the general equation of a circle centered at (h,k) with radius r:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

In this case, the circle is centered at (-3,4) and has a radius of 4, so the equation becomes:

[tex](x + 3)^2 + (y - 4)^2 = 16[/tex]

To represent the circle parametrically, we can use the trigonometric functions cosine and sine to describe the x and y coordinates, respectively. We can rewrite the equation as:

(x + 3) = 4cos(t)

(y - 4) = 4sin(t)

Simplifying, we obtain:

x = -3 + 4cos(t)

y = 4 + 4sin(t)

These equations describe the x and y coordinates of points on the circle as a function of the angle t. The parameter t represents the angle of rotation around the circle. To trace the circle clockwise, we need to assign decreasing values to t. The domain for t is 0 ≤ t ≤ 2π, which corresponds to a full revolution around the circle.

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Answer:

9 [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Answer:

the answer is 9

Step-by-step explanation:

Answer:

$1,625

Step-by-step explanation:

Given:

Total cost = 325 + 100d

Where,

325 = fixed cost

100 = cost per day

d = number of days

Find the total cost when d = 13 days

Total cost = 325 + 100d

= 325 + 100d

= 325 + 100(13)

= 325 + 1,300

= 1,625

Total cost = $1,625

Answer:

[tex]y = 3x - 0.5[/tex]

Step-by-step explanation:

Given

Goes through

[tex]C = (1.5,4)[/tex]

Parallel to AB

[tex]A = (2,-1)[/tex]

[tex]B = (4,5)[/tex]

Required

Determine the line equation

First, calculate the slope of AB

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{5--1}{4-2}[/tex]

[tex]m = \frac{6}{2}[/tex]

[tex]m = 3[/tex]

The line is said to be parallel to AB. This implies that their slopes are equal.

The equation of the line is then calculated as:

[tex]y = m(x - x_1) + y_2[/tex]

Where:

[tex](x_1,y_1) = (1.5,4)[/tex]

So:

[tex]y = 3*(x - 1.5) + 4[/tex]

[tex]y = 3x - 4.5 + 4[/tex]

[tex]y = 3x - 0.5[/tex]

Answer:

684 π

Step-by-step explanation:

volume of a sphere = (4/3) x (n) x (r^3)

n = 22/7

r = radius

volume of larger sphere

4/3 x n x 9³ = 972 n

4/3 x n x 6³ =288n

972n - 288n = 684n

Answer:

I dot know good luck

Step-by-step explanation:

Answer: not sure

Step-by-step explanation:

The property which is represented in the equation : "2 + (√6 + √4) = (2 + √6) + √4" is (a) Associative.

The "Associative-Property" is a fundamental property of addition that states that the grouping of numbers being added does not affect the sum. In other words, when adding three or more numbers, the way they are grouped does not change the result.

In the given equation : 2 + (√6 + √4) = (2 + √6) + √4, we see that the numbers (√6 + √4) and (2 + √6) are grouped differently, but the sum remains the same. This is because the associative property , which allows us to rearrange the brackets and change the grouping without affecting the final result.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

State the name of the property illustrated : 2 + (√6 + √4) = (2 + √6) + √4

(a) Associative

(b) Distributive

(c) Commutative

(d) Both associative and commutative.

The given permutation (62848X) can be expressed as the product of disjoint cycles as (1 6 2 8 4) and as the product of transpositions as (1 6)(6 2)(2 8)(8 4).

To express the given permutation (62848X) as a product of disjoint cycles, we start by examining each element and its corresponding image under the permutation.

1 maps to 6.

6 maps to 2.

2 maps to 8.

8 maps to 4.

4 maps to 8 (since X represents a fixed point, meaning it remains unchanged).

Now, let's write these mappings as disjoint cycles:

(1 6 2 8 4)

The cycle notation indicates that 1 maps to 6, 6 maps to 2, 2 maps to 8, 8 maps to 4, and 4 maps back to 1.

Next, we'll express this permutation as a product of transpositions. A transposition swaps two elements.

We can achieve this by breaking down the cycle (1 6 2 8 4) into transpositions:

(1 6)(6 2)(2 8)(8 4)

Each pair of adjacent elements within the cycle forms a transposition. For example, (1 6) represents the transposition that swaps 1 and 6, (6 2) swaps 6 and 2, and so on.

Thus, the given permutation (62848X) can be expressed as the product of disjoint cycles as (1 6 2 8 4) and as the product of transpositions as (1 6)(6 2)(2 8)(8 4).

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Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : [tex]$h(x)=x^2-7x+6$[/tex]

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

[tex]$h(0)=0^2-7(0)+6$[/tex]

       [tex]$=0-0+6$[/tex]

       [tex]$=6$[/tex]

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

   It is the minimum height which represents the depth Kendra dives into the water.

So the [tex]$x$[/tex] coordinate of the vertex is = [tex]$\frac{-b}{2a}$[/tex]

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴  x coordinate = [tex]$\frac{-(-7)}{2 \times 1} $[/tex]

                         [tex]$\frac{7}{2}=3.5$[/tex]

Now substituting to find f(x),

[tex]$h(3.5)=(3.5)^2-7(3.5)+6$[/tex]

         = -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ [tex]$0=x^2-7x+6$[/tex]

Factorizing, we get   [tex]$(x-1)(x-6)=0$[/tex]

∴ [tex]$x=1 \text{ or}\ x=6$[/tex]

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has [tex]$\text{two}$[/tex] x intercepts. These two x intercepts  are the points where the parabola crosses the x-axis, which is the height [tex]$h(x)=0$[/tex]. The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is [tex]$x=6$[/tex] for [tex]$h(x)=0$[/tex].

Thus Kendra dives out of the water surface at 6 feet from the board.

The statement that eta-squared, partial eta-squared, and R-squared are all measures of effect size that refer to the proportion of variance explained within a study. This statement is true.

In order to better understand what eta-squared, partial eta-squared, and R-squared are, we must first understand what the proportion of variance explained is. The proportion of variance explained refers to the amount of variation in one variable that is accounted for by another variable or variables. All three of these measures are measures of effect size, which means they are used to determine the strength of the relationship between two variables. They also all refer to the proportion of variance explained within a study. However, they differ in terms of how much variance they account for. Eta-squared is a measure of effect size that is used in ANOVA to determine the proportion of variance in the dependent variable that is accounted for by the independent variable. Partial eta-squared, on the other hand, is used to determine the proportion of variance that is accounted for by the independent variable when controlling for other variables.

Finally, R-squared is a measure of effect size that is used in regression analysis to determine the proportion of variance in the dependent variable that is accounted for by the independent variable.

In conclusion, all three of these measures of effect size are used to determine the proportion of variance explained within a study.

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The set in problem 8 was not a subspace because one of the subspace axioms requires that the zero vector, which is the additive identity element, is included in the set. In the given problem, the zero vector was not part of the set, so it failed to satisfy this axiom

a. The set F is a subset of the vector space of continuous functions on some interval, which we have studied this semester.

b. To prove whether F is a subspace of the vector space of continuous functions, we need to check if F satisfies the three subspace axioms: closure under addition, closure under scalar multiplication, and the zero vector property.

Let f and g be two functions in F, and let c be a scalar. To show closure under addition, we need to prove that f + g is also in F. Since both f and g have the property that f'(2) = 0 and g'(2) = 0, their sum (f + g) will also have the property that (f + g)'(2) = f'(2) + g'(2) = 0 + 0 = 0. Therefore, f + g is in F.

To show closure under scalar multiplication, we need to prove that cf is also in F. Again, since f has the property that f'(2) = 0, multiplying f by any scalar c will not change the derivative at 2. Therefore, (cf)'(2) = c × f'(2) = c × 0 = 0, and cf is in F.

Finally, the zero vector property states that the zero function, denoted as 0, must be in F. The zero function has the property that its derivative is always zero, including at 2. Therefore, 0'(2) = 0, and the zero function is in F.

Since F satisfies all three subspace axioms, we can conclude that F is a subspace of the vector space of continuous functions.

c. We can get away with not checking the other eight axioms (associativity, commutativity, distributivity, etc.) because F is a subset of a known vector space. By being a subset of a vector space, F inherits those axioms from the larger vector space. The other eight axioms are properties of vector spaces that hold true for all vectors in the larger vector space, including the vectors in F. Therefore, if F satisfies the subspace axioms, it automatically satisfies the other eight axioms by virtue of being a subset of a vector space.

d. It was not okay to only check the two subspace axioms on problem 8 from exam 2 because the set in that problem did not satisfy the zero vector property. One of the subspace axioms requires that the zero vector, which is the additive identity element, is included in the set. In the given problem, the zero vector was not part of the set, so it failed to satisfy this axiom. As a result, the set in problem 8 was not a subspace.

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The magnitude of the average induced electric field, e, in a loop can be expressed in terms of δφ, r, and δt.

When a magnetic field changes within a loop, it induces an electric field according to Faraday's law of electromagnetic induction. The magnitude of the average induced electric field, e, can be determined by the change in magnetic flux δφ, the radius of the loop r, and the change in time δt. The magnetic flux is a measure of the total magnetic field passing through the loop and is given by the product of the magnetic field strength and the area of the loop. As the magnetic field changes, the magnetic flux through the loop changes, leading to an induced electric field. The magnitude of this induced electric field is directly proportional to the rate of change of the magnetic flux, which is δφ/δt. Additionally, the magnitude of the induced electric field is inversely proportional to the radius of the loop, meaning a smaller radius will result in a stronger induced electric field. Therefore, the magnitude of the average induced electric field, e, can be expressed as e = (δφ/δt) / r.

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If The results of the study reveal that n=40, sample mean = $16,000, and sample standard deviation = $5,000 then the probability is about 65.54%.

To calculate the probability that a randomly selected recent graduate has savings of $18,000 or more, we first need to calculate the z-score using the formula z = (x - μ) / σ, where x is the value we're interested in, μ is the mean, and σ is the standard deviation. In this case, x = $18,000, μ = $16,000, and σ = $5,000.

Substituting these values into the formula, we get z = (18,000 - 16,000) / 5,000 = 0.4.

Next, we can use a z-table or calculator to find the corresponding probability.

Looking up the z-score of 0.4 in the z-table, we find that the probability is approximately 0.6554, or about 65.54%.

Therefore, the probability that a randomly selected recent graduate has savings of $18,000 or more is approximately 65.54%.

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The central limit theorem,option (A) is correct

According to the central limit theorem, the following statement is correct:

a. Regardless of the underlying distribution, the distribution of the sum (or average) of a large number of independent variables with identical distributions will be approximately normal.

Regardless of the original distribution's shape, the central limit theorem states that independent and identically distributed variables tend to approximate a normal distribution when added together or averaged. We are able to draw conclusions about the parameters of the population based on the statistics of the sample because this is one of the fundamental principles of statistical inference.

The central limit theorem is unrelated to the other statements (b, c, and d). Statements b, c, and d all refer to common-cause variation rather than the central limit theorem, while statement d does not accurately describe the central limit theorem.

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The null distribution used for a hypothesis test of a single population proportion is the standard normal distribution. The correct answer is b).

When conducting a hypothesis test for a single population proportion, we use the standard normal distribution as the null distribution. This is based on the assumption that the sampling distribution of the sample proportion follows a normal distribution when the sample size is sufficiently large.

The hypothesis test for a single population proportion involves comparing the observed sample proportion to the hypothesized population proportion. We calculate the test statistic, which is the standard error of the sample proportion under the null hypothesis, divided by its standard deviation.

Since the test statistic follows a normal distribution under the null hypothesis, we compare it to critical values from the standard normal distribution to determine the p-value and make a decision regarding the null hypothesis.

Therefore, correct option is B.

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Answer:

utility cost, direct labor costs, cost of raw materials used in production

The mean weight of adult trout is 3.224 pounds is the answer.

Given, A normal model is used to describe the weights of adult trout, with a standard deviation of 1.2 pounds. It is known that only 7% of adult trout weigh more than 5 pounds.

To calculate the mean weight (in pounds) of adult trout, the following steps need to be followed:

Step 1: Find the z-score for the given percentage value.

The z-score formula is given by: z = (x - μ) / σ where x is the value of the variable, μ is the mean, and σ is the standard deviation.

Step 2: Once we have the z-score, we can find the corresponding value of x using the z-score table.

We need to find the z-score corresponding to the 93rd percentile as only 7% of the trout weigh more than 5 pounds.z = (x - μ) / σ

For a one-tailed distribution with α = 0.07, the z-score is 1.48, approximately.

Therefore, we have1.48 = (5 - μ) / 1.2Multiplying both sides by 1.2, we get1.776 = 5 - μ

Subtracting 5 from both sides, we getμ = 5 - 1.776μ = 3.224

Therefore, the mean weight of adult trout is 3.224 pounds.

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Answer:

Given that average mass of an ant grams.

Given that average mass of a giraffe  Kilograms.

Now we have to find about how many times more mass does a giraffe have than an ant. Before carring out any comparision, we must make both units equal.

Like convert kilogram into gram or gram into kilogram.

I'm going to convert kilogram into gram using formula

1 Kg = 1000 g

So the average mass of a giraffe  grams.

Now we just need to divide mass of giraffe by mass of ant to find the answer.

=666666666.667

Hence final answer is  which is approx 666666666.667.

Hope this Helps!

To test the hypothesis of mean differences in artificially sweetened drink consumption among BMI groups, assuming a normal distribution, the researcher might use a one-way ANOVA.

The one-way ANOVA compares the means of three or more independent groups and determines if there are statistically significant differences among them. In this case, the BMI groups (normal weight, overweight, and obese) represent the independent groups, and the number of artificially sweetened drinks consumed is the dependent variable. By conducting a one-way ANOVA, the researcher can assess if there are significant differences in mean consumption among the BMI groups and draw conclusions regarding their hypothesis.

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Answer:

XY = 9

Step-by-step explanation:

Similar polygons have corresponding sides with proportional lengths.

WX/AB = XY/BC

12/8 = XY/6

8XY = 12 * 6

8XY = 72

XY = 9

Answer:

1/3, 1/2, 3/4

Step-by-step explanation:

okay sorry

Step-by-step explanation:

i just wanted point

Answer:

Domain is all real numbers. Range is [36- negative infinity]