A random sample of 50 purchases from a particular pharmacy was taken. The type of item purchased was recorded, and a table of the data was created.


Item Purchased Health & Medicine Beauty Household Grocery
Number of Purchases 10 18 15 7


Which graphical representation would be best to display the data?
Box plot
Line plot
Histogram
Stem-and-leaf plot

The phrase :  the difference between 17m and 3 can be written as 17m - 3.

We have,

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a phrase : the difference between 17m and 3.

We can write the given phrase as -

17m - 3

Therefore, the phrase :  the difference between 17m and 3 can be written as 17m - 3.

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complete question:

What is the algebraic expression for the following word phrase: the difference between 17m and 3?

A. 17m + 3

B. 17m • 3

C. 17m ÷ 3

D. 17m - 3

Hi help me please

The sequence given by an = n^2 - 3n + 1, with n starting from 1, produces the values 0, 0, 2, 6, 12, 20, .... This sequence has a closed formula of a_n = (n-1)n, where n is a positive integer.

To find the first few terms of the sequence, we substitute the values of n starting from 1 into the formula an = n^2 - 3n + 1. This gives us the sequence: 0, 0, 2, 6, 12, 20, ....

To find the closed formula for the sequence, we can observe that each term is the sum of the previous term and n(n-1). In other words, a_n = a_(n-1) + n(n-1), where a_1 = 0. We can then use this recursive definition to find a closed formula. We start by finding the first few terms: a_1 = 0, a_2 = 2, a_3 = 6, a_4 = 12, a_5 = 20, ...

We notice that the difference between consecutive terms is n(n-1), so we can express the nth term in terms of the first term and the sum of n(n-1) from k=1 to n-1:

a_n = a_1 + ∑(k=1 to n-1) k(k-1)

Simplifying the sum using the formula for the sum of the first n integers and the sum of the first n squares, we get:

a_n = (n-1)n

Therefore, the closed formula for the sequence starting with a1 is a_n = (n-1)n, where n is a positive integer.

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The new surface area of the figure is given as follows:

S = 164.61 ft².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The prism in this problem is composed as follows:

Hence the surface area of the original prism is given as follows:

S = 2 x (6.5 x 5.5 + 5.5 x 10.6 + 6.5 x 10.6) + 2 x (4.3 x 10.6 + 4.3 x 8.1 + 10.6 x 8.1)

S = 658.44 ft².

The new surface area is one fourth of the original surface area, hence it is given as follows:

S = 0.25 x 658.44

S = 164.61 ft².

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Answer:

y = 0.0633 x^2

Step-by-step explanation:

Since the vertex of the parabola is at the origin, the equation of the parabola can be written in the form:

y = a x^2

where a is a constant that determines the shape of the parabola.

The focus of the parabola is at the point (0,-7.9). Recall that the focus of a parabola is a point that is equidistant from the vertex and the directrix. Since the vertex is at the origin, the directrix must be a horizontal line that is 7.9 units above the vertex. Therefore, the equation of the directrix is:

y = 7.9

The distance between the vertex and the focus is equal to the distance between the vertex and the directrix. This distance is given by:

d = |-7.9 - 0|/2 = 3.95

Therefore, the constant a can be found by solving the equation:

a = 1/(4d) = 1/(4(3.95)) = 0.0633

So the equation of the parabola is:

y = 0.0633 x^2

Step-by-step explanation:

To find f(t), we need to take the inverse Laplace transform of 1/(s^2 - 4s + 5).

We can start by factoring the denominator of the Laplace transform:

1/(s^2 - 4s + 5) = 1/[(s - 2)^2 + 1^2]

We can recognize this as the Laplace transform of the function f(t) = e^2t * sin(t). Therefore,

ℒ^{-1} {1/(s^2 - 4s + 5)} = e^{2t} sin(t)

Thus, f(t) = e^{2t} sin(t).

The figures that Jamal could be constructing are: Circumcenter and circumscribed circle

- Centroid is the point of intersection of all the three medians.

- Circumcenter is the point where the perpendicular bisectors of the sides of that particular triangle intersect.

- Incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle

- Orthocenter is the point where all three altitudes of the triangle intersect.

- Center of mass is also the centroid of a triangle which is the intersection of the three medians of the triangle.

- For the circumscribed circle, we will need the perpendicular bisectors

Thus, only Circumcenter and circumscribed circle are correct.

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The bearing form D from A, according to the figure is

205 degrees

Bearings are measured form the North and in the clockwise direction

Examining the figure and applying the clockwise direction to measure the angles, we have the bearing as

bearing form D from A = angle N to B + angle B to C + angle C to D

angle C to D is not given and solved using sum of angles in a point

angle C to D = 360 - 155 - 15 - 166

angle C to D = 24 degrees

plugging in the values

bearing form D from A = 15 + 166 + 24

bearing form D from A = 205 degrees

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The  requried rationalized form of 1/(7-3√2) is (7+3√2)/31.

To rationalize the denominator, we need to eliminate the radical in the denominator. To do this, we can multiply the numerator and denominator by the conjugate of the denominator, which is 7+3√2:

1/(7-3√2) * (7+3√2)/(7+3√2) = (7+3√2)/(49-18) = (7+3√2)/31

Therefore, the rationalized form of 1/(7-3√2) is (7+3√2)/31.

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There are no relative maximum or minimum points for the function f (x, y) = x^2y^2 - 18x - 8y - 5.

To find the relative maximum and minimum of the function f (x, y) = x^2y^2 - 18x - 8y - 5, we need to find the critical points and classify them using the second derivative test.

First, we find the partial derivatives of f with respect to x and y:

f x (x, y) = 2xy^2 - 18

f y (x, y) = 2x^2y - 8

To find the critical points, we set the partial derivatives to zero and solve for x and y:

2xy^2 - 18 = 0

2x^2y - 8 = 0

Solving these equations simultaneously, we get:

x = ±√9y^2

y = ±√2

So the critical points are:

(3√2, √2)

(3√2, -√2)

(-3√2, √2)

(-3√2, -√2)

To classify these critical points, we need to find the second partial derivatives:

f x x (x, y) = 2y^2

f y y (x, y) = 2x^2

f x y (x, y) = 4xy

Then, we evaluate the second partial derivatives at each critical point:

f x x (3√2, √2) = 4

f y y (3√2, √2) = 18

f x y (3√2, √2) = 12√2

f x x (3√2, -√2) = 4

f y y (3√2, -√2) = 18

f x y (3√2, -√2) = -12√2

f x x (-3√2, √2) = 4

f y y (-3√2, √2) = 18

f x y (-3√2, √2) = -12√2

f x x (-3√2, -√2) = 4

f y y (-3√2, -√2) = 18

f x y (-3√2, -√2) = 12√2

At each critical point, we have:

D = f x x (x, y) * f y y (x, y) - f x y (x, y)^2 = (4) (18) - (12√2)^2 = -288 < 0

Since the discriminant D is negative at each critical point, we can conclude that f has a saddle point at each critical point.

Therefore, there are no relative maximum or minimum points for the function f (x, y) = x^2y^2 - 18x - 8y - 5.

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Answer:

P(less than 2) = P(1) = 1/6

A is correct.

[tex]E=\{0,1,2,3,4,5\}[/tex]

The remainders from dividing a natural number by a natural number [tex]n[/tex] are [tex]0,1,2,3,\ldots,n-1[/tex].

There will be 10 confidence intervals obtained in a Tukey multiple comparison of 5 populations.

In a Tukey multiple comparison, the confidence intervals are constructed to compare the means of all pairs of groups. To calculate the number of confidence intervals, we use the following formula:

C = n(n-1)/2

Where C is the number of confidence intervals, and n is the number of groups. In this case, there are five populations being compared, so n=5. Plugging this into the formula, we get:

C = 5(5-1)/2 = 10

Each confidence interval will provide information about the difference between the means of two groups, with a certain level of confidence. These confidence intervals can be used to identify which pairs of groups have significantly different means.

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Compute covariance matrix, perform eigen decomposition, determine its numbers, and then find standard deviation.

To answer your question, we need some additional information about the dataset and the desired percentage of variance explained. However, I can provide you with a general explanation of the process involved in reducing dimensionality while retaining a specified level of variance explained.

1. Compute the covariance matrix of the dataset to identify the relationships between different dimensions.

2. Perform eigendecomposition on the covariance matrix to obtain eigenvalues and eigenvectors.

3. Sort the eigenvalues in descending order and select the corresponding eigenvectors. The sorted eigenvalues represent the variances of the principal components (new dimensions), while the eigenvectors indicate the directions of these components.

4. Determine the number of dimensions to reduce to by considering the desired level of variance explained. Calculate the cumulative percentage of the total variance explained by adding the variances of the principal components (eigenvalues) in descending order. Stop when the desired percentage is reached or exceeded.

5. The number of dimensions you have considered up to this point will be the reduced dimensions.

6. To find the standard deviation for the selected dimensions, simply take the square root of the corresponding eigenvalues.

Keep in mind that this explanation assumes you are using Principal Component Analysis (PCA) for dimensionality reduction. Without specific information about your dataset and desired variance explained, it's not possible to provide the exact number of reduced dimensions and their standard deviations.

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Answer: The best prediction possible for the number of times you roll a three is 1/6 of a roll.

Step-by-step explanation:

When you find the statistics of something like rolling a die, you will need to divide how many times you roll the die by how many sides are on the die.

6 - how many times you roll the die

6 - how many sides are on the die

When you divide 6 by 6,  you will get one. Since both of the statistical numbers are the same, you will get an 1/6 chance of rolling a 1, 2, 3, 4, 5, and 6. So 1/6 is the answer! Hope this helps!!!

P.S (I learned this in 5th grade :))

To determine if distance can be an instrumental variable (IV) for attendance in the model of given performance, we need to ensure that it satisfies the following assumptions: Relevance, Exogeneity and Exclusion restriction.

1. Relevance: Distance must be correlated with attendance, meaning that it has a significant effect on attendance. Intuitively, students living closer to the lecture hall may attend classes more frequently.
2. Exogeneity: Distance must not be directly correlated with the error term (u) in the performance equation, meaning that it should not have any direct effect on student performance apart from its impact on attendance. The assumption given already states that distance and u are uncorrelated, which fulfills this requirement.
3. Exclusion restriction: Distance should not have any direct effect on performance except through its influence on attendance. In other words, after controlling for attendance, ACT scores, and GPA, distance should not be a significant predictor of performance.
Additionally, we must assume that there are no other unobserved variables that could be driving the relationship between distance and performance. If these assumptions are met, we can use distance as an instrumental variable to identify the causal effect of attendance on performance.

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The probability of drawing a card that is both odd and divisible by 4 from a deck of 16 cards numbered 1 through 16 is 0.

To see why, note that a number that is both odd and divisible by 4 does not exist in the given set of numbers. Every even number in the set is divisible by 2 but not 4, while every multiple of 4 in the set is even and not odd. Therefore, the intersection of the sets of odd and multiples of 4 is the empty set, and the probability of drawing a card that belongs to this set is 0.

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The limit along the line y = x is different from the limits along the x-axis and y-axis, the limit as (x, y) approaches (0, 0) does not exist for the given expression.

To find the limit as (x, y) approaches (0, 0) of the expression y^2 sin(x^2) / (x^4 y^4), we can analyze the limit along different paths and see if they converge to the same value. If they do not, the limit does not exist.

Let's consider the limit along the x-axis first, where y = 0:

lim(x->0) [0^2 sin(x^2) / (x^4 * 0^4)] = 0.

Next, let's consider the limit along the y-axis, where x = 0:

lim(y->0) [y^2 sin(0^2) / (0^4 * y^4)] = 0.

Now, let's examine the limit along the line y = x:

lim(x->0) [x^2 sin(x^2) / (x^4 * x^4)] = lim(x->0) [sin(x^2) / x^6].

By applying L'Hôpital's rule repeatedly, we can find the limit:

lim(x->0) [sin(x^2) / x^6] = lim(x->0) [2x cos(x^2) / 6x^5] = lim(x->0) [2 cos(x^2) / 6x^4] = lim(x->0) [cos(x^2) / 3x^4] = lim(x->0) [(-2x sin(x^2)) / (12x^3)] = lim(x->0) [(-2 sin(x^2)) / (12x^2)] = lim(x->0) [(-4x cos(x^2)) / (24x)] = lim(x->0) [(-4 cos(x^2)) / 24] = (-4/24) = -1/6.

Since the limit along the line y = x is different from the limits along the x-axis and y-axis, the limit as (x, y) approaches (0, 0) does not exist for the given expression.

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The curve has horizontal tangents at the points (0,0) for all values of t. To find the points at which the curve has a horizontal tangent, we need to find the values of t that make the derivative of y(t) equal to zero.

First, we need to find the derivative of y(t):

y'(t) = 8cos(t)

Next, we set y'(t) equal to zero and solve for t:

8cos(t) = 0

cos(t) = 0

This occurs when t = π/2 or 3π/2.

Now, we can plug these values of t back into the original equations to find the corresponding points:

When t = π/2,

x(π/2) = 4cos(π/2) = 0

y(π/2) = 4sin(2(π/2)) = 0

So the point is (0,0).

When t = 3π/2,

x(3π/2) = 4cos(3π/2) = 0

y(3π/2) = 4sin(2(3π/2)) = 0

So the point is also (0,0).

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The coordinate matrix of x in rn relative to the basis b' is [-3, 2] because x can be expressed as -3 times the first vector in b' plus 2 times the second vector in b'.

To find the coordinate matrix of x in rn relative to the basis b', we need to express x as a linear combination of the basis vectors in b', and then write the coefficients of that linear combination as entries in the coordinate matrix. In this case, we have:

x = (-31, 37)

b' = {(-7, 8), (4, -3)}

We want to find scalars a and b such that:

x = a(-7, 8) + b(4, -3)

Solving this system of equations, we get:

a = -3

b = 2

Therefore, the coordinate matrix of x in rn relative to the basis b' is:

[-3, 2]

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Mike saved his money for 7 years to earn $280 in interest at a simple interest rate of 2%.

The simple interest formula:

I = P × r × t

Where:

I is the interest earned

P is the principal (the initial amount of money saved)

r is the interest rate

t is the time (in years)

We know that Mike saves $2000 at a simple interest rate of 2% and he earns $280 in interest.

So we can plug in these values and solve for "t":

280 = 2000 × 0.02 × t

Dividing both sides by (2000 × 0.02):

280 / (2000 × 0.02) = t

t = 7

I = P r t is the formula for calculating interest.

P stands for principle, which is the original sum of money saved and r stands for interest rate.

The date is (in years).

We are aware that Mike gets $280 in interest on his savings of $2000 at a basic interest rate of 2%.

Thus, we may enter these numbers and find the value of "t":

280 = 2000 × 0.02 × t

by (2000 0.02), divide both sides:

280 / (2000 × 0.02)= 7

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The researchers estimate for the proportion of patients with high BMD in the population is equal to the sample proportion since they used a random sampling method with replacement. Therefore, their estimate for the proportion of patients with high BMD in the population is 0.267 or 26.7%.

In statistics, a population refers to the entire group of individuals, objects, or events that meet certain criteria. A sample, on the other hand, is a smaller subset of the population that is selected to represent the larger group.
In this case, the population is comprised of 622 patients, of whom 147 have high bone mineral density (BMD). The researchers selected a sample of 30 subjects from this population with replacement. This means that after selecting a subject, they put it back in the population before selecting the next subject.
Of the 30 subjects in the sample, 8 have high BMD. To estimate the proportion of patients with high BMD in the population, the researchers use the sample proportion.
The sample proportion is calculated by dividing the number of subjects with high BMD in the sample (8) by the total number of subjects in the sample (30).
Sample proportion = 8/30 = 0.267
It's important to note that the larger the sample size, the more accurate the estimate will be. However, in this case, the sample size is relatively small, so there may be some error in the estimate. Nonetheless, the researchers estimate provides a good indication of the proportion of patients with high BMD in the population.

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Answer:

A = 24.15cm2 ~ 24.2cm2

Step-by-step explanation:

Area is calculated by

[tex]a = l \times w[/tex]

a = area

l = length = 6.9cm

w = width = 3.5cm

A= 3.5cm × 6.9cm

A = 24.15 cm2

so the area is 24.15cm2 ~ 24.2cm2

Answer:

b=35

Step-by-step explanation:

We are given that:

b=4a-5

and are asked to find b when a=10

So, we can first substitute in 10 for a:

b=4(10)-5

simplify

b=40-5

b=35

So, b=35.

Hope this helps! :)

Edit: There is not a c variable?  I'm confused so I left this out.

If there is no variability (all the scores of the variable have the same value), measures of dispersion will equal 0. Option A) 0 is the correct answer.

When there is no variability, it means all the scores of the variable have the same value. Therefore, there is no difference between the scores, and the deviation of each score from the mean is zero. As a result, all measures of dispersion such as the range, variance, and standard deviation will be zero because they are all based on the deviation of scores from the mean.

Therefore, option A) 0 is the correct answer.

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b. Central Limit Theorem. in this scenario, we would use the Central Limit Theorem to determine the probability that the mean life expectancy will be less than 70 years.

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution. In this case, a sample of 50 people is selected, which is reasonably large.

Since the mean and standard deviation of the population are known, we can calculate the z-score for a sample mean of 70 years. The z-score is calculated as:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

= (70 - 72) / (5.3 / sqrt(50))

≈ -1.19

By referring to a standard normal distribution table or using a calculator, we can find the probability of a z-score less than -1.19. This probability corresponds to the probability that the sample mean will be less than 70 years.

Using the Central Limit Theorem, we can approximate the distribution of the sample mean as a normal distribution and calculate the desired probability.

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Answer:

radius is 6 meters

Step-by-step explanation:

perimeter of semicircle = πr + 2r

πr + 2r = 30.84

3.14r + 2r = 30.84

5.14r = 30.84

r = 30.84 ÷ 5.14

r = 6

The exact value of the expression tan(arccos(sqrt(3)/2)) is 1/√3. To solve this expression, we can use the trigonometric identity: tan(arccos(x)) = √(1 - x^2) / x

First, we need to find the value of arccos(sqrt(3)/2). Since the cosine function is positive in the first quadrant, we know that arccos(sqrt(3)/2) is an angle in the first quadrant that has a cosine of sqrt(3)/2. This means that arccos(sqrt(3)/2) = π/6.

Now we can substitute π/6 for x in the trigonometric identity:

tan(arccos(sqrt(3)/2)) = √(1 - (sqrt(3)/2)^2) / (sqrt(3)/2)

Simplifying the expression under the square root gives:

√(1 - (sqrt(3)/2)^2) = √(1 - 3/4) = √(1/4) = 1/2

Substituting this value into the expression gives:

tan(arccos(sqrt(3)/2)) = (1/2) / (sqrt(3)/2) = 1/√3

Therefore, the exact value of the expression tan(arccos(sqrt(3)/2)) is 1/√3.

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A perpendicular bisector originates from the midpoint of the triangle at an inside OR outside of the triangle. A perpendicular bisector intersects a side of its triangle forming a right angle.

A perpendicular bisector divides the side of two congruent segments.  The interior angles of the perpendicular bisector triangle formed are all right angles.

A perpendicular bisector originates from the midpoint of an aspect of a triangle. It can be visualized as a line that begins at the midpoint of an aspect and extends outward, both inner or outside of the doors of the triangle.

The term "originates" shows that the perpendicular bisector begins from a particular point. In the context of the triangle, it originates from the midpoint of a facet.

The word "at a ______ OR ________ of the triangle" implies that the perpendicular bisector can begin either interior or out of doors the triangle. Depending on the area of the midpoint of the side, the perpendicular bisector can make it bigger into the interior of the triangle or beyond its barriers.

A perpendicular bisector intersects an aspect of the triangle, forming a proper angle. The factor of intersection among the perpendicular bisector and the aspect creates a right angle (ninety degrees). This is a belonging of perpendicular traces, where two lines intersect at a proper perspective.

A perpendicular bisector divides the aspect of the triangle into two congruent segments. By connecting the endpoints of the side to the point of intersection with the perpendicular bisector,  segments are created. These segments are equal in period, that's a result of the bisector dividing the side into two congruent components.

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The estimated mouse population after 5 years is 7,680 mice. (a) The mouse population is doubling every year,

which means that the population at any time t will be double the population at time t-1. We can use this information to write the function N(t) that models the number of mice after t years as follows: N(t) = 240 * 2^t

(b) To estimate the mouse population after 5 years, we can simply substitute t=5 into the function we found in part (a): N(5) = 240 * 2^5 = 7,680

Therefore, the estimated mouse population after 5 years is 7,680 mice. However, it is important to note that this is only an estimate based on the assumption that the population is doubling every year.

In reality, there may be factors such as limited resources and predation that could affect the growth rate of the population.

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