A Random Sample Of 16 Pharmacy Customers Showed The Waiting Times Below (in Minutes).20 27 24 23 19 21 (2024)

Answer:

Step-by-step explanation:

its b

The construction that the figure represents is perpendicular bisector

What is perpendicular bisector?

A perpendicular bisector is a line that cuts through the intersection of two other line segments at a right angle.

So, a perpendicular bisector always splits a line segment through its middle, as we can see. By definition, the word "bisect" denotes an even or uniform division.

Perpendicular Bisector Properties for AB in the figure

It cuts AB in half, or into two equal halves.

It is perpendicular to AB or at right angles to it.

The distance between each point along the perpendicular bisector from points A and B is equal.

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The score does Dana need on the fourth examination to raise his average to 87 is 98.

What is the average of numbers?

Average by adding a group of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined. For instance, the sum of 2, 3, 3, 5, 7, and 10 is equal to 30 divided by 6, which equals 5. Median the central number in a set of numbers.

Given: Dana received scores of 85, 92, and 73.

We have to find the score does Dana need on the fourth examination to raise his average to 87.

Suppose the score on the fourth examination is x.

The average of scores is 87.

⇒

[tex]87 = \frac{85 + 92 + 73 + x}{4} \\348 = 250 + x\\x = 348 - 250\\x = 98[/tex]

Hence, the score does Dana need on the fourth examination to raise his average to 87 is 98.

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Answer:228

Step-by-step explanation:

All you have to do is add 108 to 120.

0+8=8, 2+0=2, 1+1=2

120

108

+_____

228

Answer:

In this problem, the temperature of the hot liquid (T) is being modeled as a function of the number of minutes (n) that it has been in the refrigerator. The model is a linear function, which means that the temperature will change at a constant rate as the number of minutes increases.

The parameter -8 represents the rate at which the temperature is changing. Specifically, it represents the amount by which the temperature decreases in degrees Fahrenheit for every one minute that passes. For example, if the hot liquid has been in the refrigerator for 10 minutes, its temperature will have decreased by (-8 * 10) = -80 degrees Fahrenheit.

The parameter 175 represents the initial temperature of the hot liquid when it was first placed in the refrigerator. This is the temperature at n = 0, or when no time has passed.

So in the context of this problem, the parameters -8 and 175 represent the rate at which the temperature changes and the initial temperature of the hot liquid, respectively.

The volume V of the solid is obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2 is 81π/5

Shell method:

The shell method is an integration for calculating the volume of a solid of revolution when integrating along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.

V=2π∫01(2-x). 27x³dx

= 2π.27([tex]x^{4}[/tex]/2 - [tex]x^{5}[/tex]/5)01

=54π(1/2-1/5)

= 81π/5

Therefore The volume V of the solid is obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2 is 81π/5

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Nikki can use modern portfolio theory to assess the risk and return behaviors associated with different combinations of assets X and Y.

Modern portfolio theory involves calculating the expected return and risk of a portfolio of assets by analyzing the correlations between the assets. It also looks at the diversification benefits of combining different assets and the impact of adding riskier assets to a portfolio. By quantifying the risk and return behaviors of different portfolios, Nikki can make informed decisions about which portfolios are most suitable for her.Modern portfolio theory is used to assess the risk and return behaviors of different combinations of assets X and Y. It considers correlations between the assets, the diversification benefits of combining them, and the impact of adding riskier assets. By quantifying the risk and return behaviors, Nikki can make informed decisions about which portfolios are most suitable for her.

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Situation which illustrates best the concept of absolute advantage is: Option A - A German factory can build more sports cars than foreign factories.

Absolute advantage is the potential of an individual, a company, or a country to produce a higher quantity of output than its competitors while using the same inputs. It means an institution with absolute advantage has more efficiency in producing a particular commodity than its rivals. It utilizes lower marginal cost (materials and labor), making its output much cheaper than others.

A factory in German has an absolute advantage because it can produce more sports car than foreign countries. Absolute advantage makes the factory more competitive in the market than its rivals.

Therefore, the correct answer is option A.

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11

According to question

-5xy²+7x²y+3y³-8x³

putting x=2 and y=3

⇒ -5(2)(3)²+7(2)²(3)+3(3)³-8(2)³

⇒-5(18)+7(12)+3(27)-8(8)

⇒-90+84+81-64

∴ 11

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The correct question is find the value of equation if x=2 and y=3 , -5xy² + 7x²y+3y³ - 8x³

Frequency is the number of occurrences of a repeating event.

What do you mean by frequency?

The frequency of an occurrence or a value is the number of times it happens. A frequency table is a list of objects with the frequency of each item shown in the table.

The information that is gathered is called data. The quantity of occurrences of an event or value is referred to as its frequency. A frequency table is a table that lists items and displays how frequently each item happens.

The number of times a specific data value occurs is the frequency of that data. We use f to symbolise the frequency of a data value.

As an illustration, the grade A is said to occur frequently if five students received an A in science.

Here we have the events:

shopping time between occurrences frequency

18 to 22: 20, 18 2

23 to 27: 27, 24, 26, 24, 24 5

28 to 32 29, 31 2

33 to 37 37, 34, 35, 33, 36, 32 6

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Answer:

for g(-2)

we wil take -1/4 x -1

so g(-2) = - 1/2

for g(1)

we will take (x+1)²

so g(1) = (1+1)² = 4

for g(2)

we will take (x+1)²

so g(2)= ,(2+1)² = 9

Treatment remains the same. Do not Reject.

Test Statistics:

[tex]f = \frac{\text{treatment}}{\text{error}} = 5.37[/tex]

Reject Null Hypothesis if [tex]f > f(a, a-1, N-a)[/tex]

Critical Value [tex]f(0.01, 3, 15) = 5.42 \text{ (From F Table)}[/tex]

[tex]\because 5.37 < 5.417[/tex]

We fail to Reject [tex]H0[/tex]

[tex]\therefore[/tex] Do not Reject.

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Answer:

in the picture

Step-by-step explanation:

in the picture

The analysis of variance compares the differences between treatments to determine the variance attributed to treatment effects, not the variance within treatments.

An analysis of variance (ANOVA) is a statistical technique used to compare the means of two or more groups. This technique is used to determine the variance attributed to differences between treatments. The variance between treatments is the variance between the group means of the different treatments, while the variance within treatments is the variability of the data within each treatment group. In an ANOVA, only the variance between treatments is considered to be caused by the treatment effect. This is because the within-treatment variance is assumed to be caused by random sampling error, which is independent of the treatment. Thus, in an ANOVA, only the between treatments variance is attributed to treatment effects, while the within-treatment variance is not. This allows the analyst to better understand and explain the differences between treatments.

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The appropriate test to perform is one sample t test

The rejection reason is t statistic less than -2.012 or t statistic more than -2.012

The p value of the test is 0.0292

Firstly,

As the population standard deviation is unknown and the sample size is more than 30, it is appropriate to use one sample t test for this hypothesis testing

Testing if the mean is changed from 700 levels or not

Null and alternate hypothesis are 700

Degree of freedom,

n-1

= 48-1

= 47

Using alpha level 0.05 and t critical table, we found the following two critical values

t critical values= -2.012 and 2.012

So, the rejection reason is t statistic less than -2.012 or t statistic more than -2.012

Now,

Population means = 700 hours

Sample mean = 675 hours

n = 48

So,

Test statistic= (mean-alternate hypothesis)/(s/√n)

= (675-700)/ (77/√48)

=-25/11.1140

= -2.249

Degree of freedom = n-1

= 48-1

= 47

With t distribution table for -2.249 and 47 degrees of freedom obtain p value of 0.0292

So, pvalue= 0.0292

Reject null hypothesis since the p value is less than alpha level

So, we conclude that the mean has changed from 700 hours

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After evaluating the given integral by changing to polar coordinates we get [tex]7 e^8-31[/tex]

As per the details shared in the above question it is given that,

[tex]$x^2+y^2=64$[/tex]

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

[tex]d A=r d r d \theta.[/tex]

Further solving above we get,

[tex]r^2=64 \\\Rightarrow & r=8 . \\0 \leq r \leq 8 ; & 0 \leq \theta \leq \pi / 2[/tex]

The polar coordinate,

[tex]\iint_{R} y e^x d A=\int_0^{\frac{\pi}{2}} \int_0^8 r^2 \sin \theta e^{r \cos \theta} d r d \theta[/tex]

[tex]& =\int_0^8 \int_0^{\frac{\pi}{2}} r^2 \sin \theta e^{r \cos \theta} d \theta ; \\& =\int_0^8\left[-r e^{r \cos \theta}\right]_0^{\pi / 2} d r[/tex]

[tex]=\int_0^8 r\left[-e^{r \cos \left(\frac{\pi}{2}\right)}+e^\alpha\right] d r .[/tex]

[tex]=\int_0^8 r e^r d r-\left.\frac{r^2}{2}\right|_0 ^8[/tex]

Now substituting the value we get,

[tex]7 e^8-31[/tex]

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Note the correct question should be ,

Evaluate the given integral by changing to polar coordinates.

[tex]\iint_R y e^x d A[/tex] , where R is the region in the first quadrant enclosed by the circle [tex]x^2+y^2=64[/tex].

The upper control limit is 16.4 if our desired confidence interval is 99.73%.

Given 131 population

standard deviation = 5

sample size = 11.

mean = 131/11 = 11.9.

determine the upper control limit if desired

confidence interval is 99.73%

What is Confidence interval?

In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.

Confidence interval = sample mean ± margin of error

Upper limit = sample mean + margin of error.

margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex].

margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].

value of z* for 99.73% confidence interval is 3.00.

so margin of error = 4.5.

Upper limit = 11.9 + 4.5

Upper limit = 16.4

The upper control limit is 16.4 if our desired confidence interval is 99.73%.

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Answer:

20.0°C

Step-by-step explanation:

To find the final temperature of the water after it has transferred thermal energy to the ice cube, we need to use the equation:

Q = cmΔT

where Q is the amount of thermal energy transferred, c is the specific heat capacity of the substance, m is the mass of the substance, and ΔT is the change in temperature.

In this case, we are given that Q = 4,200 J and m = 200 g. The specific heat capacity of water is 4.184 J/g°C.

Substituting these values into the equation gives us:

4,200 J = (4.184 J/g°C)(200 g)(ΔT)

Solving for ΔT gives us:

ΔT = 4,200 J / [(4.184 J/g°C)(200 g)] = 10°C

Since the initial temperature of the water was 10.0°C, the final temperature of the water is 10.0°C + 10°C = 20.0°C.

Therefore, the temperature of the water in the glass is 20.0°C after it has transferred 4,200 J of thermal energy to the ice cube.

The tri-linear inequality with the required 80% confidence interval of 54.1 to 57.7 shows the genuine mean value by which the drug decreases the average patient's systolic blood pressure.

A confidence interval expresses the likelihood that a population parameter will fall between a range of values a predetermined percentage of the time. It is the estimate's mean plus or minus the estimate's range of values.

Given the confidence level is 80%, the significance level α=100-80=20% = 0.20. The sample mean [tex]\overline{x}[/tex] is 55.9, the sample standard deviation s is 7.4, and the sample size n is 29.

We are using t-distribution to population standard deviation first. For that first find the degree of freedom and critical value of t.

Degree of freedom,

df = n - 1

df = 29 - 1

df = 28.

The critical value of t calculated from the t-distribution table is,

[tex]\begin{aligned}t_{\text{critical}}&=t_{\alpha/2,df}\\&=t_{0.10,28}\\&=\pm1.3125 \end{aligned}[/tex]

Then, an 80% confidence interval is,

[tex]\begin{aligned}\mu&=\overline{x}\pm\frac{t\cdot s}{\sqrt{n}}\\&=55.9\pm\frac{1.3125\times7.4}{\sqrt{29}}\\&=55.9\pm1.80\end{aligned}[/tex]

Then, the interval is written as

55.9 - 1.80 < μ < 55.9 + 1.80

54.1 < μ < 57.7

The required interval is 54.1 < μ < 57.7.

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To find Kaitlyn's original body weight, we need to determine how much weight she lost and add that amount back to her current weight.

Kaitlyn lost 8% of her body weight, which is equal to 8/100 * 222 pounds = <<8/100*222=17.76>>17.76 pounds.

Therefore, Kaitlyn's original body weight was 222 pounds + 17.76 pounds = <<222+17.76=239.76>>239.76 pounds.

The cone will fit in 4 times and the volume of the cone is 535.89 in³

Volume of a Cone

A cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the center of the base. It is also called right circular cone.

The formula of volume of a cone is given as;

V = 1/3πr²h

v = volume of the coner = radius of the coneh = height of the cone

However, we have to calculate the volume of the sphere which is given as

V = 4/3 πr³

The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³

The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³

The number of times it will fit into will be 2143.57 / 535.89 = 4

It will fit in 4 times

b)

The volume of the cone is 535.89in³

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The population standard deviation of {5, 8, 8, 5} is 3

The given population is

{5, 8, 8, 5}

The mean of the population = Sum of the terms / Number of Terms

Find the values and substitute the values in the equation

Sum of terms = 5 + 8 + 8 +5

= 26

Number of terms = 4

The mean of the population= 26 / 4

= 6.5

The variance of the population = (5 - 6.5)^2 + (8 - 6.5)^2 + (8 - 6.5)^2 + (5 - 6.5)^2

= (-1.5)^2 + (1.5)^2 + 1.5^2 + (-1.5)^2

= 2.25 + 2.25 + 2.25 + 2.25

= 9

The standard deviation of the population = [tex]\sqrt{9}[/tex]

= 3

Therefore, the standard deviation is 3

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The required simplified solution of the expression is given as,
1. -2√15 2.3c 4. -5
3. √6 5. 2a

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
1.
[tex]=\sqrt{(3 -\sqrt{15} )^2} - \sqrt{(3 +\sqrt{15} )^2} \\=3 -\sqrt{15} - (3 +\sqrt{15})\\=3 -\sqrt{15} -3 -\sqrt{15}\\= -2\sqrt{15}[/tex]

Similarly, the solution of the various expression can be determined.
2.3c
3. √6
4. -5
5. 2a

Thus, the solution of the expression are given above

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Hazel's new balance in the account is $1197

How to determine her new balance?

From the question, we have the following parameters that can be used in our computation:

Previous balance = $876.21.

$2.39 in interest,

$616.46 in deposits,

$298.06 in withdrawals

Her new balance can be calculated using

New balance = Previous balance + interest + deposits - withdrawals

Substitute the known values in the above equation, so, we have the following representation

New balance = 876.21 + 2.39 + 616.46 - 298.06

Evaluate

New balance = 1197

Hence, the new balance is $1197

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Answer:

Step-by-step explanation:

-7-9=-16

The roots of the given polynomial using the rational zero theorem are; 2, -4 and 6.

How to use the rational zero theorem?

We are given the polynomial;

y = x³ - 4x² - 20x + 48

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 48

Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

These are the possible values for p.

The leading coefficient (the coefficient of the term with the highest degree) is 1.

These are the possible rational roots:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0

Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.

Thus, these are the roots of the given polynomial.

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3x2-3(y+1)+9x2+12; reflection in the y-axis, a vertical stretch by a factor of 3, and a translation 1 unit down

The reflection in the y-axis can be achieved by changing the sign of the x-terms while leaving the y-term unchanged. Afterwards, the function needs to be stretched vertically by a factor of 3. This means that all terms will be multiplied by 3. Lastly, the function requires a translation 1 unit down. This can be done by adding a -1 to the y-term. Therefore, the final equation is 3x2-3(y+1)+9x2+12 which includes the reflection in the y-axis, vertical stretch by a factor of 3, and translation 1 unit down.

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The blanks are completed as follows:

s/(s² - 18s + 81) = s/(s - 9)².F(s) = s/(s - 9)².

Then the inverse Laplace transform is given as follows:

f(t) = e^(9t) + 9te^(9t).

How to obtain the inverse Laplace transform?

The function for this problem is given as follows:

F(s) = s/(s² - 18s + 81).

Completing the squares at the denominator, we have that:

F(s) = s/(s - 9)².

Applying partial fraction decomposition, the function can be defined as follows:

s/(s - 9)² = A/(s - 9) + B/(s - 9)²

Expanding the right side, we have that:

s/(s - 9)² = [A(s - 9) + B]/(s - 9)²

Hence:

As - 9A + B = s.

Then the system for the coefficients is given as follows:

A = 1.-9A + B = 10-> B = 9A -> B = 9.

Thus the function in the transform domain is of:

F(s) = 1/(s - 9) + 9/(s - 9)².

Applying the inverse Laplace transform, the function in the time domain is given as follows:

f(t) = e^(9t) + 9te^(9t).

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Answer:

just substitute each value of x into the function

Step-by-step explanation:

1. (x=-2) y= 4(-2)+2

2. (x=0) y= 4(0)+2

3. (x=2) y= 4(2)+2

4. (x=4) y= 4(4)+2

use the same steps but change the value of x. go ahead a use your calculator

Given the function y=4x+2, x is the input and y is the output. So, we can input x values to find y values because y is a function of x.

Substitute the x values into the function:

Row 1:

y=4(-2)+2

y=-8+2

y=-6

Row 2:

y=4(0)+2

y=2

Row 3:

y=4(2)+2

y=8+2

y=10

Row 4:

y=4(4)+2

y=16+2

y=18