If θ is an angle in standard position and its terminal side passes through the point (2,-1), find the exact value of \tan\thetatanθ in simplest radical form.

A The population mean is greater than 10 B The population mean is equal to 10 C The population mean is less than 10 D The population mean is not equal to 10 with probability.

1. The average weight of female athletes is a discrete random variable because it can take on a discrete set of values.

2. A sample point is a single point in a sample space, which is a set of all possible outcomes of an experiment.

3. The standard deviation is a measure of spread of a random variable, which measures how much the values in the set deviate from the mean.

4. The median of the set of numbers is 4, since there are an equal number of numbers below and above the median.

5. The variance of the set of numbers is 36, since it is calculated by taking the sum of the squares of the differences between each number and the mean, and dividing by the number of values.

6. The null hypothesis for a hypothesis test is that the population mean is equal to 10.

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S(x) of Alex's new probability distribution will be 0.599.

What is Probability distribution ?

A mathematical function called a probability distribution explains how likely it is that a variable will take on several possible values. Utilizing graphs or probability tables, probability distributions are frequently represented.

Given, The no. of cups of coffee he drank with the probability.

If he drinks 1.471 cups per day, So the S(X) will be calculated in the following manner:

Step 1 : calculate the deviation of X from N.( here N = 1.471 )

Step 2 : find the square of (X- N).

Step 3 : multiply it with the given P(X).

Step 4 : find the sum of the (X-N)^2* P(X).

Hence, By following the given steps, we get S(X) as 0.599.

(Refer to the table given in Excel file).

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The percentage that she spent on present for her sister is 26.67%

What does % example mean?

Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Given that :

She spent = 360 * 1/5 = $72 on presents for her parents

she spent = 360 - 72 = 288 * 2/3 = $192 on presents for her friends

She spent = 288 - 192 = $96 on presents for her sister

Percentage of the $360 that she spent on presents for her sisters is

96/360 * 100 = 26.67%

Hence the percentage that she spent on present for her sister is 26.67%

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Answer: 1280 Kg

Step-by-step explanation:

The weight of the object given = 128 Kg

Time 1 = 10 hr

Time 2 = 1 hr

Cancel the hours,

128×10 = 1280 Kg

Answer:  x=12,-4

Step-by-step explanation:

The line parallel to the line x + 2y = 8 is y = -(1/2)x - 7 Or (1/2)x + 7 = - 7.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

The given line is x + 2y = 8 ⇒ 2y = - x + 8 ⇒ y = -(1/2)x + 8.

We know line parallel to each other have the same slope and it passing through (-2, - 6).

∴ - 6 = -(1/2)(-2) + b.

- 6 = 1 + b.

b = - 7.

So, The required line is y = -(1/2)x - 7.

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By analizying the zeros on the graph, we conclude that the equation that could represent the graph is:

y = (x  + 5)²*(x - 3)²

On the graph, we have a polynomial.

Remember that the degree of the polynomial is related to the zeros of the polynomial. Here we can see that we have two double zeros, one at x = -5 and other at x = 3

We know that are double zeros because the curvature of the polynomial changes there.

Then the equation will be something like:

y = (x  + 5)²*(x - 3)²

So that is the correct option, top right.

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The solution for x in the pentagon is 90

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

Shape = pentagon

This means that

n = 5

The sum of the internal angles is calculated as

Angles = 180(n - 2)

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

Angles = 180(5 - 2)

So, we have

Angles = 540

This means that

x + 90 + 90 + 135 + 135 = 540

So, we have

x + 450 = 540

Evaluate

x = 90

Hence, the value of x is 90

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We specify the one-way anova model in the model statement of proc glm is model response variable; (the grouping variable is only specified in the class statement.)

So option b. is the correct option of the given statement.

Information that needs to be accessed and changed by a computer program is stored in variables. In order to make our programs more understandable to ourselves and the reader, they also offer a mechanism to label data with a descriptive name.

Values can be stored in variables. In order to use a variable, we must first declare it so the program is aware of it and then assign it so the program is aware of the value we are storing in the variable.

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Answer:

1. using the formula (aX2/h)-22

17

Step-by-step explanation:

Take area multiply by 2

234x2=468

Divide answer by height which is 12 you get 39

39subtract 22 you get your answer as 17

According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

It is given to us that -

Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving

Company now advertises that its new small cars average more than 45 miles per gallon in highway driving

52 automobiles were tested

Sample average is 46.1 miles per gallon

Sample standard deviation is 5.3 miles per gallon

Significance level is 0.01

We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.

Let us assume that -

p = population of average gasoline of new small cars in highway driving

According to the given information,

Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -

[tex]H_{0}[/tex] : [tex]p\leq 45[/tex] miles per gallon

Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -

[tex]H_{A}[/tex] : [tex]p > 45[/tex] miles per gallon

For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.

According to one sample z test, the value of test statistic is given as -

[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }[/tex] ------ (1)

where,

[tex]X_{avg}[/tex] = Sample mean

p = hypothesized population mean

S = Sample standard deviation

n = Sample size

According to the given information, we have

[tex]X_{avg}[/tex] = 46.1 miles per gallon

p = 45 miles per gallon

S = 5.3 miles per gallon

n = 52

Substituting the above values in equation (1), we have

[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }\\= > T = \frac{(46.1 -45)}{\frac{5.3}{\sqrt{52} } }\\= > T = \frac{1.1}{0.735}\\ = > T = 0.634[/tex]

It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.

But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,

0.634 < 2.58

This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.

Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

It is given to us that -

Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving

Company now advertises that its new small cars average more than 45 miles per gallon in highway driving

52 automobiles were tested

Sample average is 46.1 miles per gallon

Sample standard deviation is 5.3 miles per gallon

Significance level is 0.01

We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.

Let us assume that -

p = population of average gasoline of new small cars in highway driving

According to the given information,

Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -

H0 = p<= 45 :  miles per gallon

Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -

HA : p > 45 :  miles per gallon

For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.

According to one sample z test, the value of test statistic is given as -

T = (X - p)/(SD/√n)

where,

X = Sample mean

p = hypothesized population mean

S = Sample standard deviation

n = Sample size

According to the given information, we have

X = 46.1 miles per gallon

p = 45 miles per gallon

S = 5.3 miles per gallon

n = 52

Substituting the above values in equation (1), we have

T = 46.1-45/(5.2/√52)

T = 1.1/0.735

T = 0.634

It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.

But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,

0.634 < 2.58

This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.

Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.

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The Perimeter of the Pathway around the pool is 38.4m

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Length of the Pathway = 12m + 80cm + 80cm = 12m + 1.6m = 13.6m

Breadth of the Pathway = 4m + 80cm + 80 cm = 4m + 1.6m = 5.6m

Perimeter of Rectangle = 2(l+b)

Perimeter = 2(13.6 + 5.6)

Perimeter = 2(19.2)

Perimeter = 38.4m

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Answer:

72 = -4s

72 / (-4) = (-4s) / (-4)

-18 = s

The distance between the two lines from the graph is 1 unit.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given equations are as below,

y = x - 1

And,

y = 2x - 4

They can be drawn on a graph as follows,

From the graph the distance between two lines can be calculated as the difference between their x-intercepts as,

2 - 1 = 1 unit.

Hence, the distance between the two lines is given as 1 unit.

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Answer:

16

Step-by-step explanation:

4 / 2

2 / 2

1

4 = 2²

16/2

8/2

4/2

2/2

1

16 = 2^4

lowest common denominator = 2^4 = 16

The manufacturer of allay pain reliever offered a free sample of the product to visitors who registered at its website. in this case, the communications objective of the website was to increase awareness of Allay Pain Reliever and generate customer leads.

Communication objectives are the aims and principles that guide how a person or company interacts with customers, staff, or other stakeholders. Workplaces can establish and uphold uniform standards for every contact by adopting communication strategies.

In order to achieve marketing goals with an increase in the rate of purchases or information requests, the communication objectives must first develop a good consumer attitude.

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An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data.

In statistics, a truly random sample involves selecting people from a population with an equivalent probability; in other words, picking individuals from a group without bias.

Failing to accomplish this appropriately will result in a sampling bias, which can dramatically increase the sample error in a systematic fashion. For instance, using a sample from just one nation to estimate the average height of all people on Earth could lead to a significant over- or underestimation.

In practice, it might be challenging to select an impartial sample because various criteria (for instance, nation, age, gender, and so on) may substantially bias the estimator. It is important to make sure that none of these aspects are taken into consideration when choosing the sample.

Hence, An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data.

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absolute maximum =  3.033

absolute minimum = -1.846

A point where the function achieves its highest value is known as an absolute maximum point. Similar to this, an absolute minimum point is the location at which the function's maximum value is obtained.

f(x) = x[tex]e^{-x^{2}/50 }[/tex] , [−2, 10]

f'(x) = x[tex]e^{-x^{2}/50 }[/tex] (-2x/50) + [tex]e^{-x^{2}/50 }[/tex] (1)  = 0

-2[tex]x^{2}[/tex]/50 + 1 = 0

2[tex]x^{2}[/tex]/50 = 1

2[tex]x^{2}[/tex] = 50

[tex]x^{2}[/tex] = 25

x = +5 , -5

f(-2) = -2 [tex]e^{-2^{2} /50}[/tex] = -1.846

f(10) = 1.3353

f(5) = 3.033

absolute maximum = 3.033

absolute minimum = -1.846

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Answer:

husband = wife earn + 2450

wife = 9 470

Husband earnings:

9 470 + 2 450 = sh 11 920

husband + wife

11 920 + 9 470 = sh 21 390

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

.046 is lost each year meaning  (1 - .046) remains

A(t) = 300 ( 1 - .046)^t        will show milligrams remaining after 't' years (where t is the years since 2004)

From the various triangle proofs below, we have been able to show that; 3A F = AC

A median of a triangle is defined as a line segment from a vertex of the triangle to the midpoint of the side opposite that vertex.

We are given that;

AD is the median of ΔABC.

E is the midpoint of AD

Through D, we draw DG parallel to BF

In ΔADG, E is the midpoint of AD and EF is parallel to DG

By using the converse of midpoint theorem, we have;

F is midpoint of AG and A F = FG     ------(eq 1)

Likewise, In ΔBCF ;

D is the midpoint of BC and DG is parallel to BF  

G is midpoint of CF and FG is congruent to GC (FG ≅ GC) .........(eq 2)

From equations 1 and 2, we will get;

A F = FG = GC     -------(3)

Thus;

A F + FG + GC = AC

A F + A F + A F = AC (from eq 3)

3A F = AC

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Following the Sampling Theorem of statistics, the answer is True.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.

Each member of the group or community has an equal chance of being chosen when using probability sampling. According to probability-based statistical theory, this indicates that the sample is more likely to match the larger population, allowing for the drawing of more precise conclusions about the latter.

Yes, the quota sampling process occurs when the available or accessible people or material are selected. Due to large population size, Sampling process is preferred.

Since, Statistics convey characteristics of data to us. So yes, The sample is weighted so that predetermined characteristics are represented.

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Answer:

Step-by-step explanation:

Answer:

x = 7/10

Step-by-step explanation:

You multiply both sides by "x", to get 7 = 10x. Then divide both sides by 10 to get 7/10 = x, or 0.7 = x.

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F(x)= -ln(-x3+3x-1) is a particular solution to the differential equation that passes through (1, 0).  An equation for the tangent line to the graph of f at the point (1,0) = -3.

b.[tex]\frac{dy}{e^y} = (3x^2-6x)dx\\[/tex]

∫[tex]e^{-y} dy =[/tex] ∫[tex](3x^2-6x)dx[/tex]

[tex]-1e^{-y} = x^3-3x^2+C\\e^{-y} = -x^3+3x^2+C_{2}\\ -y= ln(-x^3+3x^2+C_{2}) \\y=-ln(-x^3+3x^2+C_{2}[/tex]

Given (1,0)

[tex]0= -ln (-1+3+C)\\0=ln_{c} (2+C)\\e^{0} = 2+C\\-1=C\\so f(x)= -ln(-x^3+3x^2-1)\\[/tex]

f(1.2)=-.465 as the actual value.

c. tangent line slope at (1,0).[tex]= e^0 (3(1)^2-6(1))\\[/tex]

[tex]=-3[/tex]

Line equation: y= 3(x-1) or y= 3x + 3

with f(1,2)=-3(1.2)+3 =-.6

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We utilize a two factors, independent measurements ANOVA, where, factor has 2 level and a factor likewise has 2 levels.

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

Factors and multiples are a part of our daily life. For example, they are employed in arranging objects in a box, handling money, recognizing patterns in numbers, solving ratios, and working with expanding

A number totally divides the provided number without leaving any residual is said to be the factor of that number.

The components of a number might be positive or negative. For example, let us find the factors of 8. Since 8 is divisible by 1, 2, 4, and 8, we may list the positive factors of 8 as, 1, 2, 4, and 8. Apart from this, 8 has negative elements as well, which might be stated as, -1, -2, -4,

According to our question-

Degrees of freedom for the F-test of the two way ANOVA

In this case, we utilize an ANOVA with two independent variables and two factors, each with two levels.

So, here,

= 2 for the number of layers of A

= B's level count is 2,

Moreover, n = sample size in each treatment condition is equal to 10.

So we have,

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of interaction effect (A x B) = ( - 1)( - 1) ( - 1)

= (2-1)(2-1) (2-1)

= 1

And = df of within variation (i.e. error variation) =

= 2 x 2 x (10 - 1) (10 - 1)

= 36

Consequently, the df value for the F-ratio measuring factors-primary A's impact is

= () ()

= (1, 36) (1, 36)

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The volume of the given solid, with the boundaries, is given as follows:

661.5 cubic units.

The volume of the solid is obtained using a double integral.

The equation for the solid is given as follows:

7x + 9y + z = 63.

z = 63 - 7x - 9y.

The coordinate planes bound the plane, hence:

Hence the double integral that is used to obtain the volume of the solid is given as follows:

[tex]V = \int_{0}^{9}\int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dydx[/tex]

The inner integral is given as follows:

[tex]I = \int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dy[/tex]

Which, applying the Fundamental Theorem of Calculus, has the result given as follows:

[tex]I = -98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441[/tex]

Then the volume of the solid is given by the outer integral as follows:

[tex]V = \int_{0}^{9} \left(-98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441\right) dx[/tex]

Which has a numeric value of:

661.5 cubic units.

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Answer:

C) 9/40

Step-by-step explanation:

1 - [tex]\frac{2}{5}[/tex] - [tex]\frac{3}{8}[/tex]     Make equivalent fractions with 40 as the denominator

[tex]\frac{2}{5}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{16}{40}[/tex]   Another name for [tex]\frac{8}{8}[/tex] is one.  This is how we can make equivalent fractions.

[tex]\frac{3}{8}[/tex] x [tex]\frac{5}{5}[/tex] = [tex]\frac{15}{40}[/tex]

1 can also be written [tex]\frac{40}{40}[/tex]

[tex]\frac{40}{40}[/tex] - [tex]\frac{16}{40}[/tex] - [tex]\frac{15}{40}[/tex] = [tex]\frac{9}{40}[/tex]