The owner of a local chain of grocery stores is always trying to minimize the time it takes her customers to check out. In the past, she has conducted many studies of the checkout times, and they have displayed a normal distribution with a mean time of 11.2 minutes, and a standard deviation of 2.4 minutes. She has implemented a new schedule for cashiers in hopes of reducing the mean checkout time. A random sample of 33 customers visiting her store this week resulted in a mean of 9.8 minutes. Does she have sufficient evidence to claim the mean checkout time this week was less than 11.2 minutes? Use a = 0.02. (a) Find z. (Round your answer to two decimal places.) = (ii) Find the p-value. (Round your answer to four decimal places.) (b) State the appropriate conclusion. O Reject the null hypothesis. There is significant evidence that the mean checkout time is less than 11.2 minutes. O Reject the null hypothesis. There is not significant evidence that the mean checkout time is less than 11.2 minutes. O Fail to reject the null hypothesis. There is significant evidence that the mean checkout time is less than 11.2 minutes. Fail to reject the null hypothesis. There is not significant evidence that the mean checkout time is less than 11.2 minutes.

Answer:

6)C,120

7)B,60°

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True. If p(x) is the Taylor series for f centered at 0, then p(x-1) is not the Taylor series for f centered at 1. Instead, to obtain the Taylor series for f centered at 1, you would need to compute a new series with the center shifted to 1.

True. Shifting the center of a Taylor series by adding or subtracting a constant simply results in a new Taylor series centered at the shifted point. In this case, we are shifting the center from 0 to 1 by replacing x with (x-1) in the Taylor series for f, resulting in p(x-1).
In mathematics, the Taylor series or Taylor expansion of a function is an infinite number of points defined by the function at one point. For most ordinary functions, the partial function and its Taylor series are equal at point. The first n + 1 terms of the Taylor series form an n-order polynomial called the nth-order Taylor polynomial function. Taylor polynomials are generally approximate for functions that get better as n increases. Taylor's theorem provides a quantitative estimate of the resulting error using this approach. If the series of Taylor functions converge, the sum is the limit of an infinite number of Taylor polynomials.

A function can diverge from the equation of the Taylor series even if the Taylor series converges. A function is the definition of a point x if it is equal to the sum of the Taylor series over an open interval (or opening in the complex plane) containing x. This means that transactions are resolved anywhere on the clock (or disk).

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The compound formed between Sr and P is strontium phosphide (Sr₃P₂).

To determine the formula for the compound formed between Sr and P, we need to consider the charges of the ions involved.

Strontium (Sr) is a metal from Group 2 of the periodic table, and it tends to lose two electrons to achieve a stable electron configuration. Therefore, it forms Sr²⁺ ions.

Phosphorus (P) is a nonmetal from Group 15, and it tends to gain three electrons to achieve a stable electron configuration. Therefore, it forms P³⁻ ions.

To form a neutral compound, the total positive charge from the cations should equal the total negative charge from the anions. In this case, the charges need to balance.

Since the charge on the Sr²⁺ ion is 2+ and the charge on the P³⁻ ion is 3-, we need two Sr²⁺ ions to balance the charge of three P³⁻ ions. This gives us the formula Sr₂P₃.

However, we need to simplify the formula to its simplest whole-number ratio. By dividing both subscripts by their greatest common divisor, we obtain the simplest ratio of 1:1.

Therefore, the final formula for the compound formed between Sr and P is Sr₃P₂.

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From the definition of the definite integral, \(lim_{n\to\infty} \dfrac{3}{n}\sum_{k=1}^n(\dfrac{6k}{n}+sin(\dfrac{6k\Pi}{n}))\) is equivalent to \(\int_0^3(2x+sin(2\Pi x))dx\).

The definite integral is an elementary concept in calculus that represents the accumulated area between the graph of a function and the x-axis over a specific interval.

The given expression is  \(lim_{n\to\infty} \dfrac{3}{n}\sum_{k=1}^n(\dfrac{6k}{n}+sin(\dfrac{6k\Pi}{n}))\) ...(1)

It is known that

\(\int_a^bf(x)dx = lim_{n\to \infty} \Delta x \sum_{i=1}^n f(x_i)\) ...(2)

where, \(\Delta x = \dfrac{b-a}{n}\)

Comparing equations (1) and (2),

\(\Delta x = \dfrac{3}{n}\) ...(3)

and

\(f(x_i) = \dfrac{6k}{n}+sin(\dfrac{6k\Pi}{n})\)...(4)

Take equation (3),

\(\Delta x = \dfrac{3}{n}\\\dfrac{b-a}{n} = \dfrac{3-0}{n}\)

a = 0 and b = 3.

Also, it is known that

\(x_i = a+k\Delta x\)

    \(= 0+k\dfrac{3}{n}\\=\dfrac{3k}{n}\)

So, from above and equation (4), it can be concluded that:

\(f(\dfrac{3k}{n}) = \dfrac{6k}{n}+sin(\dfrac{6k\Pi}{n})\\f(\dfrac{3k}{n}) = 2\dfrac{3k}{n}+sin(2\Pi\dfrac{3k}{n})\)

Replace \(\dfrac{3k}{n}\) by x in the above equation:

\(f(x) = 2x+sin\ x\)

a, b, and f(x) have been obtained. Now, the definite integral can also be obtained.

Substitute for a,b, and f(x) in the left-hand side of equation (2) to get the definite integral as follows:

\(\int_0^3 (2x+sin\ x)dx\)

Thus, the given expression is equivalent to the definite integral \(\int_0^3 (2x+sin\ x)dx\).

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There are 120 boats in the marina using algebraic equation.

We shall represent the number of boats in the marina with the letter x so that we derive an algebraic equation to solve for x as follows:

number of white boats = 5x/6

number of blue boats = 2/5 of (x - 5x/6)

number of blue boats = 2/5 × x/6

number of blue boats = x/15

number of red boats = 12

so that;

5x/6 + x/15 + 12 = x

LCM of the denominators is 30

(25x + 2x + 360)/30 = x

27x + 360 = 30x {cross multiplication}

30x - 27x = 360 {collect like terms}

3x = 360

x = 360/3 {divide through by 3}

x = 120

Therefore, there are 120 boats in the marina using algebraic equation.

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Answer:

an inequality that has an absolute value sign with a variable inside.

Step-by-step explanation:

Answer:

2 + 2 = 4

Step-by-step explanation:

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer: the area of the star is 1.94in squared

Step-by-step explanation: One part of the quarter circle has a radius of 1.5 inches because 3 inches is the height of the square.

So the diameter of 4 of the quarters would be 3 inches because 4 quarters of a circle would make a full circle with a diameter of 3. The area of a full circle with the diameter of 3 is 7.06. The area of the square is 9 because 3x3 is 9. 9 minus 7.06 leaves 1.94 in area left in the square. :) 1.94 is rounded also

Step-by-step explanation:

PRIMERO ENCONTRAMOS EL ÁREA DE UNO DE LOS

SEGMENTOS DE C´RCLO SUPONIENDO QUE EL RADIO

ES IGOAL A LA MITAD DEL LADO DEL CUADRO

A = \((1.5 in)^{2}\) - 3.14\(/1.5 in)^{2}\)/4 = \(0.49 in^{2}\)

LUEGO SE MULTIPLICA POR 4

\(1.96 m^{2}\)

SE ENCUENTRA EL ÁREA DEL CUADRADO

A = \(3 in ^{2}\) = \(9 in^{2}\)

FINÁLMENTE SE ENCUENTRA EL ÁREA DE LA ESTRELLA

A = \(9 in^{2}\) - \(1.96 in^{2}\) = \(7.04 in^{2}\)

Answer: domain: x>-3

range: y > -1

Step-by-step explanation:

Answer:

the amount is duplicating every time from 1 to 2 from 8 to 16

Step-by-step explanation:

Answer:

it's being multiplied by 2 every time, so 1×2=2 and it just keeps going on. 2×2=4, 4×2=8 and so fourth

$.01×2=$.02

ANSWER

R1, R2, R3, R4, G1, G2, G3, G4. Option B.

The speed that Jo walked for the first 15 minutes is; 6 km/hr

The distance - time graph is missing and so i have attached it.

Now, the formula for speed is;

Speed = Distance/time

The distance after 15 minutes from the graph is 1.5km.

Now, 15 minutes when converted to hours is 15/60 = ¹/₄ hr

Thus, the speed that Jo walked for the first 15 minutes is;

Speed = 1.5/(¹/₄)

Speed = 6 km/hr

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Answer:

B

Step-by-step explanation:

Option B) The IQR is the best measure of variability and equals 4, is the appropriate answer.

Explanation:

The range (highest value minus lowest value) is a measure of variability, but it can be sensitive to outliers, which are extreme values that are significantly different from the other values. In this case, the highest value (19) is significantly different from the other values, so the range would not be the best measure of variability.

The mean (average) is also a measure of variability, but it can also be sensitive to outliers. In this case, the mean would be approximately 11.0, but again, the value of 19 is significantly different from the other values, so the mean would not be the best measure of variability.

The median (middle value) is a more robust measure of variability, as it is not affected by outliers. In this case, the median is 10, which gives some indication of the typical or central value of the data.

The interquartile range (IQR) is another robust measure of variability, which is defined as the difference between the third quartile (Q3) and the first quartile (Q1). The quartiles divide the data into quarters, so that 25% of the data falls below Q1, 50% falls below the median, and 75% falls below Q3. In this case, Q1 is 7 and Q3 is 11, so the IQR is 11 - 7 = 4. The IQR gives some indication of the spread of the middle 50% of the data, and is not affected by outliers. Therefore, the appropriate measure of variability for this data is the IQR, and its value is 4.

The ratio of flour and raisin in cookie recipe is,

Determine the cups of raisins required for 3 cups of floor.

Thus, cups of raisins required is 1 1/4.

The linear equation that can be used to find the height considering all the information is h2 = h1 + (-0.5)(t2 - t1)

The height of a candle can be modeled by a linear function with a slope of -0.5 cm/hour.

If the height of the candle after t1 hours is h1 centimeters, then the height of the candle after t2 hours is given by h2 = h1 + (-0.5)(t2 - t1).

So, if the height of the candle after t1 hours is h1 centimetres, and after t2 hours is h2 centimeters, we have:

h2 = h1 + (-0.5)(t2 - t1)

We can use the given information to find the value of h1, and then use the equation above to find the value of h2.

However, the information given in the question is not enough to solve for h1 and h2. We need more information such as the height of the candle after a certain number of hours.

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Answer:

a dilation with a scale factor less than 1 and then a translation

Answer:

Yes

Step-by-step explanation:

Plug in the coordinate (5,9) into the equation

9=3(5)-6

9=15-6

9=9

Answer: 77m

Step-by-step explanation:

The equation for the perimeter of a rectangle is: p = 2(length) + 2(width). We are given both perimeter and the length, so we can plug in these values to solve for what is missing.

332m = 2(89) + 2(width)

332m = 178 + 2(width)

154 = 2(width)

width = 77

Just combine like terms and get the variable (width) by itself on one side of the equation to solve. Hope this helps!

Answer:

width = 77 m

Step-by-step explanation:

Perimeter = sum of all sides

As a rectangle has 2 lengths and 2 widths making a total of four sides;

P = 2 ( l + w)

332 = 2 ( 89 + w)

332/2 = 89 + w

166 = 89 + w

166 - 89 = w

77 = w

Therefore, the width of the pool is 77 m

The answer is  ( D ),   y ≤ 6

The range begins from minimum value to maximum value.

However, in the graph. There's no minimum value as it's heading toward negative infinity.

So we use y ≤ 6 instead.

So the clear answer is y ≤ 6 or ( D )

Answer:

Step-by-step explanation:

Given: An electronic product contains 54 integrated circuits. The probability that any integrated circuit is defective is 0.01,and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. Find the probability that the product operates. To find:

The probability that the product operates. Solution: Let E be the event that the product operates. E'= product does not operate = at least one integrated circuit is defective. Total number of integrated circuits = 54The probability that any integrated circuit is defective = 0.01P(E')

= probability that at least one integrated circuit is defective \(P(E') = 1 - P(E)P(E) =\) probability that all 54 integrated circuits are not defective \(P(E) = (0.99)54P(E) ≈ 0.599\)Therefore,

P(E') = 1 - P(E)P(E') = 1 - 0.599P(E') ≈ 0.401Hence, the probability that the product operates is approximately 0.401.Answer: Therefore, the probability that the product operates is approximately 0.401.

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Answer:

true

Step-by-step explanation:

Answer:

True!

Step-by-step explanation:

Brainliest plz!

Answer:

36in

Step-by-step explanation:

P=2×3,14×r

113.04=2×3.14×r

r=18in

d=2×r

=2×18in=36in

To calculate the marginal cost, find the change in total cost when one additional unit is produced.

Variable Fixed Total Average Variable Average Total Marginal Cost

Cost Cost Cost

0 $30 $30 - - -

2 $30 $34 $17 $17 $4

5 $30 $47 $9.4 $9.4 $13

6 $30 $56 $9.3 $9.3 $9

8 $30 $78 $9.75 $9.75 $22

10 $30 $100 $10 $10 $22

12 $30 $132 $11 $11 $32

Note: To calculate the average variable cost, divide the total variable cost by the quantity produced. To calculate the average total cost, add the total variable cost and the total fixed cost and divide by the quantity produced. To calculate the marginal cost, find the change in total cost when one additional unit is produced.

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The probability that a randomly chosen test-taker will score between 470 and 530 is 0.2358 (or 23.58% when expressed as a percentage).

To solve this problem, we need to use the standard normal distribution formula:
Z = (X - μ) / σ
where Z is the standard score (z-score) of a given value X, μ is the mean, and σ is the standard deviation.
First, we need to convert the given values of 470 and 530 to z-scores:
Z1 = (470 - 500) / 100 = -0.3
Z2 = (530 - 500) / 100 = 0.3
Next, we need to find the probability that a randomly chosen test-taker will score between these two z-scores.

We can use a standard normal distribution table or a calculator to find the area under the curve between -0.3 and 0.3.
Using a calculator or an online tool, we find that the area under the curve between -0.3 and 0.3 is approximately 0.2358.

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Answer:

Step-by-step explanation:

is there a height? Is the triangle with a 90 degrees angle? Is there any other conditions that are given?

Answer:

False

Step-by-step explanation:

Like terms have the same variable and are raised to the same exponent, and 6x has a variable of x while 6 has none at all, so they are not like terms.

By using normal distribution of probability, it is obtained that

Percentile rank of a turtle whose length is 21 inches is 22%

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here, Normal Distribution of probability is used

Mean = 25.9 inches

Standard deviation = 6.3 inches

P(X \(\leq\) 21) = P(z \(\leq\) \(\frac{21 -25.9}{6.3}\))

               = P(z \(\leq\) -0.78)

               = 0.22

               = 22%

Percentile rank of a turtle whose length is 21 inches is 22%.

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