Write an equation about the movement of a Ferris wheel.As a Ferris wheel turns , the distance a rider is above the ground varies sinusoidally with time. The highest point on the wheel is 43 feed above the ground. The wheel makes a full circle every 8 seconds and has a diameter of 40 feet. Sketch a graph of your height as a rider as a function of time.a. What is an equation for your graph?b. Use this equation to predict your height above the ground at 4.5 seconds.

The distance between the base of the ladder and the wall is approximately 3.57 meters.

To find the distance between the base of the ladder and the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the base of the ladder represents one side of the triangle, the height of the ladder represents another side, and the distance between the base of the ladder and the wall represents the hypotenuse.

Using the given information, we can calculate the distance as follows:

d^2 = 5^2 - 3.5^2

d^2 = 25 - 12.25

d^2 = 12.75

d ≈ √12.75

d ≈ 3.57m

Therefore, the distance between the base of the ladder and the wall is approximately 3.57 meters.

Question is not proper;Proper question is given below;

Noah has a total of 47 video games. he only buys action games and sports games. He has 21 more action games than sports games. how many action games, a, and sports games, s, does he own?

Answer:

Noah has 34 action games and 13 sports games.

Step-by-step explanation:

Given:

Total number of games he has = 47

Let the number of action games be 'a'.

Let the number of sports game be 's'.

So we can say that;

Total number of games he has is equal to sum of the number of action games and the number of sports games.

framing in equation form we get;

[tex]a+s = 47 \ \ \ \ \ eqaution \ 1[/tex]

Also Given:

He has 21 more action games than sports games.

so we can say that;

[tex]a=s+21 \ \ \ equation\ 2[/tex]

Now Substituting equation 2 in equation 1 we get;

[tex]a+s=47\\\\s+21+s=47\\\\2s+21=47[/tex]

Subtracting both side by 21 we get;

[tex]2s+21-21=47-21\\\\2s = 26[/tex]

Dividing both side by 2 we get;

[tex]\frac{2s}{2}=\frac{26}{2}\\\\s=13[/tex]

Now Substituting the value of 's' in equation 2 we get;

[tex]a=s+21=13+21=34[/tex]

Hence Noah has 34 action games and 13 sports games.

Answer:the veterinarian made the first error in step 3

Step-by-step explanation:

the number of milligrams, m, varies directly with the weight of the dog, w.

Assuming constant of variation is k, then,

m = kw

k = m/w = 0.5/50 = 0.01

Therefore,

m = 0.01w

In step 3, Substituting 10 into the equation to find the dosage for a 10-pound dog like 10 = 0.01w was error.

The correct step is

m = 0.01 × 10

m = 0.1 milligrams

Answer:

3.93

Step-by-step explanation:

Let x is the number of hours of television watched per week by six students.

X 8 10 5 14 3 6

Standard deviation for sample data is

[tex]Standard deviation=S=\sqrt\frac{{sum(x-xbar)^2} }{n-1}[/tex]

[tex]xbar=\frac{sum(x)}{n}[/tex]

[tex]xbar=\frac{8+10+5+14+3+6}{6}[/tex]

[tex]xbar=\frac{46}{6}[/tex]

xbar=7.67

[tex]sum(x-xbar)^2=(8-7.67)^2+(10-7.67)^2+(5-7.67)^2+(14-7.67)^2+(3-7.67)^2+(6-7.67)^2[/tex][tex]sum(x-xbar)^2=0.11+5.44+7.11+40.11+21.78+2.78=77.33[/tex]

[tex]Standard deviation=S=\sqrt\frac{{(77.33)} }{5}[/tex]

[tex]S=\sqrt15.466[/tex]

S=3.93

Answer:

The answer to your question is the second option

Step-by-step explanation:

Process

Simplify using exponents laws, first inside the parentheses and then outside the parentheses.

                             [tex][\frac{a^{-2}b^{2}}{a^{2}b^{-1}} ]^{-3}[/tex]

a) Simplify a

                        a⁻² a⁻² = a⁻⁴

b) Simplify b

                        b² b¹ = b³

c) Write the result

                        [tex][\frac{b^{3}}{a^{4}}]^{-3}[/tex]

d)                      [tex][\frac{a^{4}}{b^{3}}]^{3}[/tex]

e) Simplify

                       [tex]\frac{(a^{4})^{3}}{(b^{3})3}[/tex]

f) Result

                      [tex]\frac{a^{12}}{b^{9}}[/tex]

Answer:

8 weeks

Step-by-step explanation:

$125*8 = $1000

Answer:it will take you 8 weeks to have $1,000 in your savings account

Step-by-step explanation:

If you want to comeplete baby step 1 so that you have $1,000 in your savings account, and you are able to put in $125 a week. It means that the number of weeks that it will take you to have $1000 in your savings account would be

1000/125 = 8 weeks.

Answer:

See explanation.

Step-by-step explanation:

Let us first analyze some principle theory. By definition we know that the velocity ( [tex]v[/tex] ) is a function of a distance  ( [tex]d[/tex] ) covered in some time  ( [tex]t[/tex] ), whilst acceleration ( [tex]a[/tex] ) is the velocity achieved in some time. These can also been expressed as:

[tex]v = \frac{d}{t}\\[/tex] and [tex]a=\frac{v}{t}[/tex]

We also know that both velocity and acceleration are vectors (therefore they are characterized by both a magnitude and a direction). Finally we know that given a position vector we can find the velocity and the acceleration, by differentiating the vector with respect to time, once and twice, respectively.

Let us now solve our problem. Here we are givine the Position vector of a particle P (in two dimensional space of [tex]i-j[/tex] ) as:

[tex]r=(3t^3-t+3)i+(2t^2+2t-1)j[/tex]         Eqn.(1)

Let us solve.

Part (a) Velocity: we need to differentiate Eqn.(1) with respect to time as:

[tex]v(t)=\frac{dr}{dt}\\\\ v(t)=[(3)3t^2-1]i+[(2)2t+2]j\\\\v(t)=(9t^2-1)i+(4t+2)j[/tex]            Eqn.(2)

Part (b) Acceleration: we need to differentiate Eqn.(2) with respect to time as:

[tex]a(t)=\frac{dv}{dt}\\ \\a(t)=[(2)9t]i+4j\\\\a(t)=(18t)i+4j[/tex]

Thus the expressions for the velocity and the acceleration of particle P in terms of t are

[tex]v(t)=(9t^2-1)i+(4t+2)j[/tex]   and   [tex]a(t)=(18t)i+4j[/tex]

Answers:

1) [tex]x^{8} y^{8}[/tex]

2) [tex]y^{3} \sqrt{y}[/tex]

3) [tex]5x^{4} \sqrt{6}[/tex]

4) [tex]\sqrt{7}[/tex]

5) [tex]\frac{\sqrt{z}}{z}[/tex]

Step-by-step explanation:

1) [tex]\sqrt{x^{16} y^{36}}[/tex]

Rewriting the expression:

[tex](x^{16} y^{36})^{\frac{1}{2}}[/tex]

Multiplying the exponents:

[tex]x^{\frac{16}{2}} y^{\frac{36}{2}}[/tex]

Simplifying:

[tex]x^{8} y^{8}[/tex]

2) [tex]\sqrt{y^{7}}[/tex]

Rewriting the expression:

[tex]\sqrt{y^{6} y}=(y^{6} y)^{\frac{1}{2}}[/tex]

Multiplying the exponents:

[tex]y^{\frac{6}{2}} y^{\frac{1}{2}}[/tex]

Simplifying:

[tex]y^{3} y^{\frac{1}{2}}=y^{3} \sqrt{y}[/tex]

3) [tex]\sqrt{150 x^{8}}[/tex]

Rewriting the expression:

[tex]\sqrt{(6)(25) x^{8}}[/tex]

Since [tex]\sqrt{25}=5[/tex]:

[tex]5x^{4}\sqrt{6}[/tex]

4) [tex]\frac{7}{\sqrt{7}}[/tex]

Multiplying numerator and denominator by [tex]\sqrt{7}[/tex]:

[tex]\frac{7}{\sqrt{7}} (\frac{\sqrt{7}}{\sqrt{7}})=\frac{7}{7\sqrt{7}}[/tex]

Simplifying:

[tex]\sqrt{7}[/tex]

5) [tex]\frac{5z}{\sqrt{25 z^{3}}}[/tex]

Rewriting the expression:

[tex]\frac{5z}{5z \sqrt{z}}[/tex]

Simplifying:

[tex]\frac{1}{\sqrt{z}}[/tex]

Since we do not want the square root in the denominator, we can multiply numerator and denominator by [tex]\sqrt{z}[/tex]:

[tex]\frac{1}{\sqrt{z}}(\frac{\sqrt{z}}{\sqrt{z}})[/tex]

Finally:

[tex]\frac{\sqrt{z}}{z}[/tex]

Subtracting a value from the input x shifts the graph that number of units to the right.

The answer would be C.

y=2.50 units

Step-by-step explanation:

Given that angle ∠Y=75°, ∠Z=50°, side XY=2 units, and side XZ is y then applying the sine rule for this case,

x/sin ∠x =y/sin y =z/sin z

2/sin 50°=y/sin 75°

2 sin 75° =y sin 50°

y= 2 sin 75°/sin 50°

y=2.50 units

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Answer:

C

Step-by-step explanation:

I just finished the test :)

Final answer:

Increasing the sample size from 800 to 1,300 for estimating the mean weight of carry-on bags keeps the bias the same but decreases the variance, meaning that the sample will have lower variability around the true population mean.

Explanation:

When researchers working to estimate the mean weight of carry-on bags increase the sample size from 800 to 1,300, the correct effect on the bias and variance of the estimator is that the bias will remain the same and the variance will decrease. Bias is a measure of the systematic error of an estimator, and changing the sample size does not generally affect the estimator's systematic error if the estimator is unbiased to begin with. On the other hand, increasing the sample size leads to a decrease in variance which measures the spread of the sample means around the true population mean. Therefore, the larger the sample size, the closer the sampling distribution of the mean will be to the population mean, thus reducing variability, as indicated by a smaller standard deviation and a narrower confidence interval. Therefore, the correct answer is (C): The bias will remain the same and the variance will decrease.

Answer:

[tex]m = \dfrac{a^2-99}{2a}[/tex]

Step-by-step explanation:

on a number line, m is the point that is the midpoint of two other points.

the distance between each of the points to the midpoint is 10 units..

if a is the point 10 units less than m

and b is the point 10 units greater than m,

then,

[tex]m = a+10[/tex]

[tex]m = b-10[/tex]

we can add the two equations to form the midpoint formula.

[tex]2m = a+b[/tex]

we also know that the product of both numbers equal -99.

[tex]ab = -99[/tex]

we can substitute either 'a' or 'b' to the equation of m.

[tex]2m = a-\dfrac{99}{a}[/tex]

[tex]m = \dfrac{a^2-99}{2a}[/tex]

and this is the equation for the midpoint of the two numbers.

Answer:

c

Step-by-step explanation:

Answer:

a)[tex]P(X>300)=P(\frac{X-\mu}{\sigma}>\frac{300-\mu}{\sigma})=P(Z>\frac{300-300}{25})=P(z>0)= 0.5[/tex]

[tex]P(X>335)=P(\frac{X-\mu}{\sigma}>\frac{335-\mu}{\sigma})=P(Z>\frac{335-300}{25})=P(z>1.4)=0.0808[/tex]

b)[tex]P(\bar X>300)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{300-\mu}{\sigma_{\bar x}})=P(Z>\frac{300-300}{17.5})=P(z>0)= 0.5[/tex]

[tex]P(\bar X>335)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{335-\mu}{\sigma_{\bar x}})=P(Z>\frac{335-300}{17.5})=P(z>2)=0.0228[/tex]

Step-by-step explanation:

Assuming the following questions:

a) Choose one twelfth-grader at random. What is the probability that his or her score is higher than 300? Higher than 335?

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(300,35)[/tex]  

Where [tex]\mu=300[/tex] and [tex]\sigma=35[/tex]

We are interested on this probability

[tex]P(X>300)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X>300)=P(\frac{X-\mu}{\sigma}>\frac{300-\mu}{\sigma})=P(Z>\frac{300-300}{25})=P(z>0)= 0.5[/tex]

We find the probabilities with the normal standard table or with excel.

And for the other case:

[tex]P(X>335)=P(\frac{X-\mu}{\sigma}>\frac{335-\mu}{\sigma})=P(Z>\frac{335-300}{25})=P(z>1.4)=0.0808[/tex]

b) Now choose an SRS of four twelfth-graders. What is the probability that his or her mean score is higher than 300? Higher than 335?

For this case since the distribution for X is normal then the distribution for the sample mean is also normal and given by:

[tex] \bar X = \sim N(\mu = 300, \sigma_{\bar x} = \frac{35}{\sqrt{4}}=17.5)[/tex]

The new z score is given by:

[tex]z=\frac{\bar X -\mu}{\sigma_{\bar x}}[/tex]

And using the formula we got:

[tex]P(\bar X>300)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{300-\mu}{\sigma_{\bar x}})=P(Z>\frac{300-300}{17.5})=P(z>0)= 0.5[/tex]

We find the probabilities with the normal standard table or with excel.

And for the other case:

[tex]P(\bar X>335)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{335-\mu}{\sigma_{\bar x}})=P(Z>\frac{335-300}{17.5})=P(z>2)=0.0228[/tex]

Answer: 21.9 pounds of his weight is made up of fat.

Step-by-step explanation:

The total weight of the individual is 129 pounds. The individual has a body fat percentage of 17.7%.

Therefore, the number of pounds of his body that is made up of fat would be

17.7/100 × 129 = 0.177 × 129 = 21.93 pounds.

Approximating to the nearest tenth, it becomes 21.9 pounds.

The distance of a dog from a post and the cost of buying apples can be represented by functions. We can find the values of these functions by substituting specific values and calculating the corresponding outputs.

In this question, we are given a function that represents the distance of a dog from a post as a function of time. To find the value of f(20), we substitute 20 into the function and calculate the corresponding distance. To find the value of f(140), we do the same thing, substituting 140 into the function.

f(20) = 20 feet

f(140) = 140 feet

In the second part of the question, we are given a function C that represents the cost of buying n apples. To find the meaning of each expression or equation, we substitute the given value of n and calculate the corresponding cost.

C(8) = $4.50

C(2) represents the cost of buying 2 apples.

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Answer:the first equation can be multiplied by 5 and the second equation by 3

Step-by-step explanation:

The operation that would create an equivalent system of equations with opposite like terms is that the first equation can be multiplied by 5 and the second equation by 3, the correct option is A.

The system of equation is set of equations which have a common solution.

The equations are

3x-3y = 3

4x+5y = 13

The value of x and y can be determined using Elimination Method.

In elimination method like terms have to be created to make an equivalent system,

The first equation can be multiplied by 5 and the second equation by 3 to solve the equations.

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Answer:

in the year 2023

Step-by-step explanation:

Initial population of China = 1.355  billion

Initial population of India = 1.255  billion

Annual population growth rate of China = 0.44% = 0.0044

Annual population growth rate of India = 1.25% = 0.0125

Now,

Final population = P₀ [tex]\times e^{\text{rate}\times t}[/tex]

Here,

P₀ = initial population

t = time

Thus,

Population of India > Population of China

1.255[tex]\times e^{\text{0.0125}\times t}[/tex]  > 1.355[tex]\times e^{\text{0.0044}\times t}[/tex]  

or

[tex]e^{0.0081t}[/tex] > 1.07968

taking natural log both sides

0.0081t > ln (1.07968 )

or

0.0081t > 0.0766

or

t > 9.465

Hence,

9.465 year after 2014

i.e

in 2014 + 9.465 = 2023.46

in the year 2023

Using the formula for exponential growth and the provided population data for China and India, we can approximate that India's population will exceed China's in roughly 20 years.

In order to determine when India's population will exceed that of China, we can use the formula for exponential growth, which is P = P_0 * ert , where P is the future population, P_0 is the initial population, r is the growth rate, and t is time. As per the data provided, for China, P = 1.355 billion, r = 0.44%, and for India, P = 1.255 billion, r = 1.25%. We have to find time t when population of India will exceed that of China. This requires solving the equation: 1.355 * e0.0044t = 1.255 * e0.0125t.

This equation can be solved using algebra and logarithms. However, by making some approximations and using a spreadsheet or calculator, we can find that the population of India will exceed that of China after approximately 20 years, based on the growth rates provided.

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Answer:

4m width and 9m length

Step-by-step explanation:

Let the width of the rectangle be x

Length is 1 more than twice width= 1 + 2x

Area of rectangle is L * B

x(2x + 1) = 36

2x^2 + x = 36

2x^2 + x -36 = 0

2x^2 + 9x - 8x -36 = 0

Solving this:

(2x+9)(x - 4) = 0

X = 4 or -4.5

Distance cannot be negative, so x = 4m

The length is thus 2(4) + 1 = 9m

Final answer:

The width of the plot is 4 meters and the length is 9 meters.

Explanation:

To solve this problem, we can let the width of the plot be x meters. According to the problem, the length of the plot is one more than twice its width, so the length would be 2x + 1 meters. The area of a rectangle is given by the formula A = length * width. So we have the equation (2x + 1) * x = 36. Expanding and rearranging, we get 2x² + x - 36 = 0.

Factoring this quadratic equation, we get (2x + 9)(x - 4) = 0. Setting each factor equal to zero and solving for x, we find x = -4/2 and x = 4. Since the width cannot be negative, we discard x = -4/2 and conclude that the width of the plot is 4 meters. Substituting this value back into the equation for the length, we find the length is 2(4) + 1 = 9 meters.

Answer:

Step-by-step explanation:

Answer:

Option 2) [tex]a_n = -6(a_{n-1})[/tex]            

Step-by-step explanation:

We are given the following sequence in the question:

[tex]1, -6, 36, -216, ...[/tex]

We have to find the recursive relation for the sequence.

[tex]a_1 =1\\a_2 = -6 = -6(1) = -6(a_1)\\a_3 = 36 = -6(-6) = -6(a_2)\\a_4 = -216 = -6(36) = -6(a_3)[/tex]

Thus, continuing in the following manner, we get,

[tex]a_n = -6(a_{n-1})[/tex]

Thus, the recursive rule is given by

Option 2) [tex]a_n = -6(a_{n-1})[/tex]

Answer:

Step-by-step explanation:

Answer:

The answer to your question is

                       Number of stickers = number of days + 3

Step-by-step explanation:

- To find the equation of the line that represents the situation, first, find the slope.

Slope = m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

             m = [tex]\frac{4 - 3}{1 - 0} = \frac{1}{1} = 1[/tex]

- Find the equation of the line

                      y - y1 = m(x - x1)

                      y - 4 = 1(x - 1)

                      y - 4 = x - 1

                           y = x - 1 + 4

                           y = x + 3

y = number of stickers

x = days

                     Number of stickers = number of days + 3

Answer:

is x = y + 3

Step-by-step explanation:

Answer:

The weight of grapefruit is now 80 pound.

Step-by-step explanation:

Consider the provided information.

Let the x is the weight loss. The weight of grapefruit is 100 pounds and water is 92%. After evaporation water is 90%.

Thus the weight loss is:

[tex]0.92\times100-0.90(100 - x) = x[/tex]

[tex]92-90+0.90x=x[/tex]

[tex]2=x-0.90x[/tex]

[tex]2=0.1x[/tex]

[tex]x=20[/tex]

Hence, the weight loss is 80 pounds.

Therefore,  New weight is 100 - 20 = 80 pounds

The weight of grapefruit is now 80 pound.

Answer:

Therefore the equation of the required line is y = [tex]\frac{-1}{2}[/tex]x + 2 or 2y + x = 4.

Step-by-step explanation:

i) when x = -2 then y = 3 so the line from x = -2 to x = 2 has the point (-2, 3)

ii)when x = 2 then y = 1 so the line from x = -2 to x = 2 has the point (2, 1)

iii) if two points in a line are given then slope of equation passing through the lines is given by

slope m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{1 - 3}{2 - (-2)}[/tex] = [tex]\frac{-2}{4}[/tex]  =  [tex]\frac{-1}{2}[/tex]

So from the general equation of a line y = mx + c

we get y = [tex]\frac{-1}{2}[/tex]x + c and substituting for x and y with (-2, 3) respectively we get

3 = 1 + c. Therefore c = 2.

Therefore the equation of the required line is y = [tex]\frac{-1}{2}[/tex]x + 2 or 2y + x = 4.

The number of orange cans of paint is 6

Solution:

Given that,

[tex]\text{Number of cans of red paint } = 3\frac{1}{4}\\\\\text{Number of cans of yellow paint } = 3\frac{2}{12}[/tex]

Let us convert the mixed fractions to improper fractions

Multiply the whole number part by the fraction's denominator.

Add that to the numerator.

Then write the result on top of the denominator

[tex]\rightarrow 3\frac{1}{4} = \frac{4 \times 3 + 1}{4} = \frac{13}{4}\\\\\rightarrow 3\frac{2}{12} = \frac{12 \times 3 + 2}{12} = \frac{38}{12}[/tex]

Now we have to add red cans of paint and yellow cans of paint to get orange cans of paint

[tex]\text{Number of cans of orange paint } = \frac{13}{4} + \frac{38}{12}[/tex]

Take L.C.M for denominators

The prime factors of 4 = 2 x 2

The prime factors of 12 = 2 x 2 x 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 = 12

[tex]\text{Number of cans of orange paint } = \frac{13}{4} + \frac{38}{12}[/tex]

[tex]\text{Number of cans of orange paint } = \frac{13 \times 3}{4 \times 3} + \frac{38}{12}\\\\\text{Number of cans of orange paint } = \frac{39}{12} + \frac{38}{12}\\\\\text{Number of cans of orange paint } = \frac{77}{12} = 6.4 \approx 6[/tex]

Thus the number of orange cans of paint is 6

The value of [tex]\( x \) i[/tex]s irrelevant; the relationship between the areas remains constant regardless of its value.

To find the value of[tex]\(x\), let's denote the length of the ad as \(L\) and the width as \(W\). The area of the entire ad is \(L \times W\). Since the area of the photo is half the area of the ad, its area is \(\frac{1}{2} \times L \times W\).[/tex]

Now, we're given a diagram indicating that the length of the photo is [tex]\(x\) and its width is \(\frac{1}{2}W\). Therefore, the area of the photo is \(x \times \frac{1}{2}W\)[/tex].

We set up an equation based on the given information:

[tex]\[\frac{1}{2} \times L \times W = x \times \frac{1}{2}W\][/tex]

We cancel out the common factor of[tex]\(\frac{1}{2}W\) from both sides:\[L = x\][/tex]

This means that the length of the ad is equal to [tex]\(x\). Since we're not given any specific measurements or constraints on \(x\), its value could be any positive real number. Thus, the value of \(x\) is irrelevant to the relationship between the areas of the photo and the entire ad. Regardless of \(x\)[/tex], the area of the photo will always be half the area of the ad.

Answer:

a. is symmetric but not reflexive and transitive

b. is reflexive and transitive but not symmetric

c. is reflexive, symmetric and transitive

Step-by-step explanation:

The cases are missing in the question.

Let the cases be as follows:

a. R = {(1, 3), (3, 1), (2, 2)}

b. R = {(1, 1), (2, 2), (3, 3), (1, 2)}

c. R = ∅

R is defined on the set {1, 2, 3}

a.  R = {(1, 3), (3, 1), (2, 2)} is

b. R = {(1, 1), (2, 2), (3, 3), (1, 2)} is

is reflexive because (1, 1), (2, 2), (3, 3) is in R

is not symmetric because for (1,2) (2,1) is not in R

is transitive becaue for (1,1) and (1,2) we have (1,2) in R

c. R = ∅ is

reflexive, symmetric and transitive because it satisfies the definitions since there is no counter example.

Answer:

20

Step-by-step explanation:

The question states that the sample size is 16 and standard deviation of sampling distribution of sample mean also known as standard error is 5. This information can be written as

σxbar=standard error=5 ,n=sample size=16.

We have to find population standard deviation σ.

We know that

[tex]Standard error=\frac{population standard deviation}{\sqrt{n} }[/tex]

[tex]population standard deviation=\sqrt{n} *(standard erorr)[/tex]

[tex]\sqrt{n} =\sqrt{16} =4[/tex]

Population standard deviation=σ=4*5=20

The minimum force required to open the jar using the wrench is 41.5 N, calculated based on the given torque of 8.9 N∙m and the effective radius of 0.2145 m.

Calculate the minimum force required to open the jar using the jar wrench:

1. Identify the torque required:

The problem states that the torque required to open the jar is 8.9 N∙m. This means that you need to apply a force that creates a twisting moment of 8.9 N∙m to overcome the friction between the lid and the jar.

2. Determine the effective radius:

The effective radius is the distance from the center of rotation (the center of the lid) to the point where the force is applied (the end of the wrench handle).

In this case, the effective radius is the sum of:

The length of the wrench handle (17 cm = 0.17 m)

Half the diameter of the lid (4.45 cm = 0.089 m / 2, assuming a circular lid)

So, the effective radius is 0.17 m + 0.0445 m = 0.2145 m.

3. Apply the torque formula:

The formula for torque is: τ = rF

τ = torque (in N∙m)

r = effective radius (in meters)

F = force (in Newtons)

You can rearrange this formula to solve for force: F = τ / r

4. Calculate the force:

Plug in the values: F = 8.9 N∙m / 0.2145 m

Calculate: F = 41.5 N

Therefore, the minimum force required to open the jar using the wrench is 41.5 N.

Answer: None of the above

Step-by-step explanation:

Each of the presented points helps to describe how to collect and summarize data and how to make appropriate scientific inferences.

It provides a guide on how to use biostatistical principles with grounded mathematical and probability theory. It aims is to help understand and to interpret biostatistical analysis generally.

Answer:the difference between the cost of one evening ticket and one day time ticket s $1.8

Step-by-step explanation:

The cost of four evening movie tickets is $33.40. This means that the cost of one evening ticket would be

33.4/4 = $8.35

The cost of 6 daytime tickets is 39.30. This means that the cost of one daytime ticket would be

39.30/6 = $6.55

Therefore, the difference between the cost of one evening ticket and one day time ticket would be

8.35 - 6.55 = $1.8