Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times.
Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of odds is different from 50%
(a) H0:p=0.5H0:p=0.5; Ha:p≠0.5Ha:p≠0.5, which is a two-tailed test.
(b) Use Excel to test whether the true proportion of odds is different from 50% Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

If Avis Company earns $2.50 per share and today, the stock is trading at $18.99.  the price-earnings ratio. is 7.6 and yield on the stock is 0.013.

a. Price-earnings ratio

Using this formula to find the Price-earnings ratio

Price-earnings ratio =Share price/ Earning per share

Let plug in the formula

Price-earnings ratio = $18.99/ $2.50 per share

Price-earnings ratio = 7.596

Price-earnings ratio = 7.6 (Approximately)

b. Yield on stock

Using this formula to find the yield on stock

Yield on stock = Annual divided / Stock price per share

Let plug in the formula

Yield on stock = $0.25 / $18.99

Yield on stock = 0.013

Therefore the  Price-earnings ratio is 7.6 and yield on stock is 0.013.

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Answer:

-----------------------------------

Simplify the equation by distribution, then substitute the value of d and solve for c:

The equation of the regression line is defined as follows:

y = 0.71x + 8.27.

The estimates are given as follows:

a) x = 140 cm: 107.67 cm.

b) x = 172 cm: 130.39 cm.

c) x = 164 cm: 124.71 cm.

d) x = 158 cm: 120.45 cm.

The linear regression equation is obtained inserting the points of the data-set into a linear regression calculator.

From the table given in this problem, the points are given as follows:

(138, 106), (168, 130), (151, 116), (144, 105), (160, 124), (159, 119), (125, 103), (137, 103), (154, 120), (147, 110), (146, 108), (147, 110).

Inserting these points into a calculator, the equation is given as follows:

y = 0.71x + 8.27.

Then the estimates are obtained replacing x into the equation and obtaining the value of y, for example, for x = 140 cm:

y = 0.71(140) + 8.27 = 107.67 cm.

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Answer:

75

Step-by-step explanation:

60+55+x=180

All triangles equal 180 so if you add 60 and 55 you get 105 then subtract that from 180 to get 75.

Answer:

x = 65

Step-by-step explanation:

= 60 +55 =115 ( exterior < property)

x = 180 -115 = 65 (linear pair)

The Probability of carcking the six digit code is 0.00139

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

We need to use Permutation to find total number of outcomes

6P6 = 6! = 6*5*4*3*2*1 = 720 outcomes

But only one outcome is correct

Probability is 1/720

Probability = 0.0013899 = 0.00139 (approx)

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We are given the following data set:

10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20

Standard deviation = 8.043

Confidence level = 1 - Significance Level = 1 - 99.74% = 4.56% = 0.0456

Answer:

24 / 16

Step-by-step explanation:

divide and do the thing

The population of the country in 2003 is, 368.3 million.

What is population?

The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.

Given:

The exponential model a = 368.3e^0.002t describes the population,

'a' is the population of a country in millions,

t years after 2003.

We have to find the population of country in 2003.

At 2003, t = 0.

So plug t = 0 in above exponential model.

a = 368.3e^0.002(0)

a = 368.3e^0

a = 368.3

Hence, the population of the country in 2003 is, 368.3 million.

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Since the upper value is 104.75 + 1.5 * 13.75 = 125.37500, the last observation, 130, is an outlier.

A collection of information, whether numerical or not, can take any shape and is referred to as data in mathematics. Calculable information, such as student test scores, employee salaries, football team member heights, etc., is known as numerical data and is always gathered in numerical form.

here the explanation,

Five points in brief

Min=91, Q1=94, Q2=99, and Q3=104.75, with a maximum of 130 B] Outlier values are those that are either below or above Q1-1.5*IQR (IQR = Q3-Q1=104.75-91=13.75).

Reduced value: 94-1.5*13.75 = 73.37500

Since the upper value is 104.75 + 1.5 * 13.75 = 125.37500, the last observation, 130, is an outlier.

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The least squares estimated regression line is  0.5x+1.667

If your data shows a linear relationship between the X and Y variables, you will want to find the line that best fits that relationship. That line is called a Regression Line and has the equation ŷ= a + b x. The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance (the sum of squares of the errors).

Data rarely fit a straight line exactly. Usually, it is satisfactory with rough predictions. Typically, you have a set of data whose scatter plot appears to “fit” a straight line. This is called a Line of Best Fit or Least-Squares Line.

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The equation that can be used to solve the first problem is [tex]0.60 x = 30\\[/tex] and the equation that can be used to solve the second problem is  [tex]\frac{x}{y} = \frac{1}{8}[/tex].

There are two problems given to us -

(a) 60 percent of what number is 30

(b) which fraction is equivalent to one-eighth

We have to find out the equations that can be used to solve the two problems.

(a) Let us say that the number to be considered is x

According to the information given for the first problem, we can say that -

60% of x = 30

[tex]= > \frac{60}{100} x = 30\\ = > 0.60 x = 30\\[/tex]

We can now solve the equation to find out the value of x as -

[tex]0.60 x = 30\\= > x = 50[/tex]

Thus, the problem of "60 percent of what number is 30?" can be represented by the equation [tex]0.60 x = 30\\[/tex].

(b) Let us say that the fraction to be considered is represented as [tex]\frac{x}{y}[/tex].

According to the information given for the second problem, we can say that -

[tex]\frac{x}{y} = \frac{1}{8}\\= > y = 8x[/tex]

For every value of the numerator x, the value of denominator y can be found out through the above equation and vice-versa.

Thus, the problem of "which fraction is equivalent to one-eighth?" can be represented by the equation [tex]\frac{x}{y} = \frac{1}{8}[/tex].

Therefore, the equation that can be used to solve the first problem is [tex]0.60 x = 30\\[/tex] and the equation that can be used to solve the second problem is  [tex]\frac{x}{y} = \frac{1}{8}[/tex].

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The sum of two interior angles other than the adjacent angle of extended length will be equal to the external angle of extended length thus m∠PQR will be 18°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus. The identical endpoint of the two rays known as the vertex is referenced as an angle's sides.

In any triangle, the sum of two interior angles other than the adjacent angle of extended length will be equal to the external angle of extended length.

In the given triangle,

m∠PQR = m∠OPQ + m∠POQ

4x - 10 = x + 9 + x - 5

4x - 10 = 2x + 4

2x = 14

x = 7

So,

m∠PQR = 4(7) - 10 = 18°

Hence the measure of m∠PQR will be 18° for the given triangle.

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Answer:

8

Step-by-step explanation:

28/3.5=8

The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

As per the given graph of a function,

The time period is the time interval after curves repeat their behavior.

The given graph repeats after 1 + 1 + 1 + 1 = 4 thus period will be 4.

Hence "The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4".

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The option that would be an appropriate procedure for this experiment is option A) The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients.

Random assignment is seen as a method of assigning participants from your sample to various groups in experimental research by using randomization. By using this technique, each sample member has a known or equal chance of being assigned to either the control group or the experimental group.

Note that with the goal of making the groups equal at the start of the study, random assignment is a method used in experiments to divide participants into multiple study groups that include those who share similar traits.

Therefore, in regards to the work of the doctor in the above case, any observed differences in the two groups' cholesterol levels would most likely be brought on by the new medication because the subjects' variability would be evenly distributed between the two groups. Hence option A is correct.

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Hence, the measure of the angles are

∠q = 65°

∠r = 65°

∠s = 50°

∠t = 65°

∠b = 64°

From the question, we are to determine the measure of the angles.

Calculating the measure of angle q

∠q + 65° + (180° - 130°) = 180° (Sum of angles in a triangle)

∠q + 65° + 50° = 180°

∠q + 115° = 180°

∠q = 180° - 115°

∠q = 65°

Calculating the measure of angle r

∠r = ∠q (Corresponding angles)

Therefore,

∠r = 65°

Calculating the measure of angle s

∠s + ∠r + 65° = 180° (Sum of angles on a straight line)

∠s + 65° + 65° = 180°

∠s + 130° = 180°

∠s = 180° - 130°

∠s = 50°

Calculating the measure of angle t

∠t = ∠r (Vertically opposite angles)

Therefore,

∠t = 65°

Second diagram

Calculating the measure of angle b

∠b = ∠a (Corresponding angles)

Therefore,

∠b = 64°

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Answer:

true

Step-by-step explanation:

the author compares the color of the water to the color of the sky. so that makes it figurative language.

hope this helps.

Area: [tex]3.14*3^2=28.26 cm^2\\[/tex]

Circumference: [tex]2*3.14*3=18.84cm[/tex]

To get 80% percentage you need to attempt 20 question

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

For example, 45% (read as "forty-five per cent") is equal to the fraction

45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.

now we need to find  80% of a 25 question test

80% of 25 can be written as 80% × 25

= 80/100 × 25

= 20

To get 80% you need to attempt 20 question

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The correct option is (d) i.e; MD = 3 with s2 = 20 for the difference scores because it generates a repeated-measures study's population mean difference with the widest 90% confidence interval.

Given that,

Which of the following will result in the widest 90% confidence interval for the population mean difference for a repeated-measures research, provided the sample size is kept constant?

MD = 3 with s2 = 20 for the difference scores.

Therefore, the correct choice is MD = 3 with s2 = 20 for the difference scores because it produces the widest 90% confidence interval for the population mean difference for a repeated-measures study.

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Answer:

55.13 I'm sure is the answer

There are 714 women out of the total 1295 students:

    [tex]\dfrac{714}{1295}\approx0.551351351351351[/tex]

About 55.14% of the students are women.

Answer:

B. Find the area of the base and multiply it by the height of the cylinder.

Step-by-step explanation:

πr^2h is the formula for finding the volume of a cylinder.

You find the area of the base by squaring the radius, then do pi times base area times height to get the volume.

The fraction 2/5 added by 3/4 will be 1 3/20.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

The fraction will be illustrated thus:

=✓2/5 + 3/4

= 8/20 + 15/20

= 23/20

= 1 3/20

The value is 1 3/20.

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Answer:

Before we declare what happens, we must have an understanding of outliers and standard deviation. Outliers are certain points that are x deviations away from the mean. Standard deviation is a measurement of dispersion in relations to the mean you are identifying. Given this information, when outliers are removed, the standard deviation becomes a lower amount, because you have to think of standard deviation as a population measurement in a way. So imagine the outliers are a prestigious group of people, and if they leave the community, the population is indeed lower. Outliers affect deviation by a measure of extremity. The more extreme an outlier, the more or less a standard deviation will be affected. When outliers are removed, they will lower the standard deviation, which changes the data in respect to population. A high outlier, however, will increase both mean and median no matter what.

Hope this helps!

There is insufficient evidence to say that the population proportion has decreased from 28%.

"Information available from the question"

In the question:

The significance level, α =.01

The sample size, n = 1122

The number of success, x = 291

What are the null and alternative hypotheses?

Now, According to the question;

Let's know:

Significance Level:

The significance level is the area of the rejection region in the hypothesis test. The larger the significance level, the easier is to reject the null hypothesis. The most common significance level used is 5% but in cases where high precision is required significance level is reduced.

[tex]H_0[/tex] : p [tex]\geq[/tex] 0.28

[tex]H_\alpha[/tex] : p < 0.28

The significance level, α =.01

The sample size, n = 1122

The number of success, x = 291

So,

The sample proportion:

p(cap) = x/ n

          = 291/1122

         =  0.2594

Test Statistics:

z = [tex]\frac{p_c_a_p - p }{\sqrt{p\frac{(1-p)}{n} } }[/tex]

z = [tex]\frac{0.2594 - 0.28}{\sqrt{0.28\frac{(1-0.28)}{1122} } }[/tex]

z = -0.0206/0.0003396

z = -0.2591

Decision rule:

Reject the null if,

p- value [tex]\leq[/tex] [tex]\alpha[/tex]

We can use a z-distribution table, an online tool, or the following excel command to calculate the p-value using excel.

p - value = P(z <  -0.2591)

              = 0.79635

p - value ≈ 0.79635 > [tex]\alpha[/tex] = 0.01

Fail to reject the null.

Conclusion:

There is insufficient evidence to say that the population proportion has decreased from 28%.

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Answer:

Step-by-step explanation:

Your question

After solving, the regular singular points are x=0, 5i, -5i.

We have to determine the singular points of the given differential equation. Classify each singular point as regular or irregular.

(x^3+25x)y"–5xy'+6y = 0

On comparing with the equation P(x)y''+Q(x)y'+R(x)y=0

P(x) = (x^3+25x)

P(x)=0

x^3+25x = 0

x=0, 5i, –5i be the singular point.

Now write equation 1 in the standard form

Divide by x^3+25x on both side, we get;

y"–5x/(x^3+25x) y'+6/(x^3+25x) y = 0

y"–5/(x^2+25) y'+6/x(x^2+25) y = 0

Comparing with the standard form of equation;

y''+P(x)y'+Q(x)y = 0

P(x) = –5/(x^2+25)      Q(x)=6/x(x^2+25)

We know that if [tex]\lim_{x \to x_{o}}(x-x_{o})p(x)\text{ and }\lim_{x \to x_{o}}(x-x_{o})^2q(x)[/tex] exist finite. Then the singular point [tex]x_{o}[/tex] is regular singular point else irregular singular point.

(a) At [tex]x_{o}[/tex]=0

[tex]\lim_{x \to 0}(x-0)p(x)=\lim_{x \to 0}\frac{-5x}{x^2+25}[/tex]

[tex]\lim_{x \to 0}(x-0)p(x)[/tex] = 0 (Finite)

[tex]\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x^2}{x(x^2+25)}[/tex]

[tex]\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x}{(x^2+25)}[/tex]

[tex]\lim_{x \to 0}(x-0)p(x)[/tex] = 0 (Finite)

So x=0 is a regular singular point.

(b) At [tex]x_{o}[/tex]=5i

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5(x-5i)}{(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5}{(x+5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)[/tex] = -1/i (Finite)

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)^2}{x(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)}{x(x+5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)[/tex] = 0 (Finite)

So x=5i is a regular singular point.

(c) At [tex]x_{o}[/tex]=-5i

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5(x+5i)}{(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5}{(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)[/tex] = 1/i (Finite)

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)^2}{x(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)}{x(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)[/tex] = 0 (Finite)

So x=-5i is a regular singular point.

Hence, the regular singular points are x=0, 5i, -5i.

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The sphere with 16 inches diameter would hold 2144in^3 of air.

A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.

The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point.

The radius of spere = diameter / 2 which is 16/2

radius = 8 inches.

The volume(V) of a sphere is 4/3 πr^3

where r = radius of sphere,  π = constant = 3.14

V = 4/3 x 3.14 x (8)^3

V = 2144 in^3

In conclusion the sphere can hold 2144in^3 of air

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Answer:

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes

Three main categories of probability exist:

The first team will be a team of all males :

Total number of Outcomes = 13C6 = 1716

Number of favourable outcomes = 7C6 = 7

Probability that all member of the first team will be male is =

Number of favourable outcomes/Total number of Outcomes

= 7/1716

the second team is all females, given the first team is all males

Total number of Outcomes = 7C6= 7

Number of favourable outcomes = 1

the probability the second team is all females, given the first team is all males = (Number of favourable outcomes/Total number of Outcomes)

= 1/7.

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The function that is represented on the given graph is;

y = arccos x

We know in trigonometry that sine and cosine are expressed as;

cos 0 = 1

cos (π/2) = 0

cos π = -1

cos (π/4) = 0.7071

sin 0 = 0

sin (π/2) = 1

sin π = 0

sin (π/4) = 0.7071

Looking at the graph attached, we see that when x = 1, y = 0 and from earlier we saw that cos 0 = 1.

Similarly, on the graph, when x = 0, y = π/2 which fits with cos  (π/2) = 0. Thus, it is clear that the graph is the inverse of cosine which is arc cos x

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