each day the earth completes one full rotation in twenty-four hours. at the equator, the circumference of the earth is 40,075 kilometeres and there are 0.6214 miles in a kilometer. if a person is standing at the equator, how many miles would he or she travel in five hours?

Answer:

Step-by-step explanation:

Answer:

[tex]y = 6x - 4[/tex]

Step-by-step explanation:

To find the equation of the line that passes through the given points (-1, -10) and (3, 14), first find the slope by inputting the points into the slope formula.

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Let (x₁, y₁) = (-1, -10)

Let (x₂, y₂) = (3, 14)

Therefore, the slope of the equation is:

[tex]\implies m=\dfrac{14-(-10)}{3-(-1)}=\dfrac{14+10}{3+1}=\dfrac{24}{4}=6[/tex]

Now that we have determined the slope of the line, we can input the found slope and either of the two given points into the point-slope formula to create the equation of the line.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substituting m = 6 and (x₁, y₁) = (-1, -10) into the point-slope formula:

[tex]\implies y-(-10)=6(x-(-1))[/tex]

Simplifying:

[tex]\implies y+10=6(x+1)[/tex]

[tex]\implies y+10=6x+6[/tex]

[tex]\implies y=6x-4[/tex]

Therefore, the equation of the line that passes through (-1,-10) and (3,14) is:

[tex]\boxed{y = 6x - 4}[/tex]

Answer:

6x - y - 4 = 0

Step-by-step explanation:

To find:-

Solution:-

We are here given two lines and we are interested in finding out the equation of the line passing through the given points.

Firstly here we will find out the slope of the line as ,

[tex]:\implies \sf m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]

Now on substituting the respective values, we have;

[tex]:\implies \sf m =\dfrac{-10-14}{-1-3} \\[/tex]

[tex]:\implies \sf m = \dfrac{-24}{-4}\\[/tex]

[tex]:\implies \sf\pink{ m = 6}\\[/tex]

Now we can use the point slope form of the line to find out the equation of the line . The point slope form of the line is ,

[tex]:\implies \sf \pink{ y - y_1 = m(x_2-x_1)}\\[/tex]

Take any one of the given points for (x₁,y₁) . Here i am taking (3,14) .

Now finally substitute the respective values,

[tex]:\implies \sf y - 14= 6(x -3 )\\[/tex]

[tex]:\implies \sf y- 14= 6x - 18 \\[/tex]

[tex]:\implies \sf 6x - y - 18 + 14 = 0\\[/tex]

[tex]:\implies \sf\pink{ 6x - y -4 = 0 }\\[/tex]

Hence the required equation of the line in standard form is 6x - y - 4 = 0 .

The probability that more than a fifth (i.e. 6 or more) of the 10 buyers would prefer green is 0.3981.

To conduct a study of the color preferences of new car buyers, a researcher wishes to conduct a research. Suppose that 30% of the population prefers green. If ten buyers are selected at random, what is the probability that more than a fifth of the buyers will prefer green?

The random variable X represents the number of buyers who prefer green. When n = 10 and p = 0.3, this is a binomial probability experiment. P(X > 2) is the probability that more than a fifth of the buyers would prefer green.P(X > 2) = 1 - P(X ≤ 2)P(X > 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]P(X > 2) = 1 - [C(10,0) (0.3)^0 (0.7)^10 + C(10,1) (0.3)^1 (0.7)^9 + C(10,2) (0.3)^2 (0.7)^8]P(X > 2) = 1 - [1(0.7)^10 + 10(0.3)(0.7)^9 + 45(0.3)^2 (0.7)^8]P(X > 2) = 0.2743

Therefore, the probability that more than a fifth of the buyers would prefer green is 0.2743, rounded to four decimal places.

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Red-green color blindness is controlled by an x-linked gene in humans. The allele that causes color blindness is rare and recessive to the allele for normal vision. A man and woman both with normal vision had color-blind fathers. If this man and woman have a child, Therefore, the probability of a child being color-blind is 25%.

Red-green color blindness is an X-linked recessive disorder. This means that the gene for the disorder is found on the X chromosome. Because males have only one X chromosome (inherited from their mother), they will develop color blindness if they inherit the allele from their mother. On the other hand, females need to inherit two copies of the allele, one from each parent, to develop the disorder.A man with normal vision will have the genotype XY, and the woman will have the genotype XX.

Each child of the couple will receive one X chromosome from the mother and one Y chromosome from the father. The probability of the child inheriting the allele for color blindness from its father is 0 because he has no alleles for color blindness.

The probability of the child inheriting the allele for color blindness from its mother is 1/2 because the mother's X chromosome has a 1/2 probability of carrying the allele. Because the mother is a carrier, the probability of the child receiving the allele is 1/2.

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a) Time taken to reach maximum height is 0.5 sec.

b) Highest point is 484 feet

c) Time to hit the water is 6 sec.

A statement proving the equality of two mathematical expressions is known as an equation.

a) h(t) = - 16t² +16t + 480

Differentiation with respect to t, we get,

h(t)' = - 32t + 16

Again differentiation with respect to t, we get,

h(t)" = -32 is less than 0

Then maximum value of height,

h(t)' = 0

- 32t + 16= 0

t = 1/2 = 0.5

Therefor, Time taken to reach maximum height is 0.5 sec.

b) for highest point; Put value of t in equation

h(0.5) = -16(0.5)²+16(0.5)+480 = 484

Highest point is equal to 484 feet

c) 0 =  -16t² + 16t + 480

0 =  -16 ( t² - t - 30 )

( t - 6 ) ( t + 5) = 0

t = 6, t = -5        (negative value is neglect)

Time to hit the water is 6 sec.

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Answer:

6

Step-by-step explanation:

imagine that EF continues through F and ends on AB. this point, that is on segment AB, is what i will call G.

AFG is similar to CFE.

the length of segment GF is 18-4=14.

now we know 2 side lengths of triangle GAF: FA is 21 and FG is 14.

FE is similar to GF with a factor of 4/14 = 2/7.

FE is similar to FC with this same ratio: (2/7) * 21 = 6

therefore, the length of FC is 6.

A chi-squared statistic provides strong evidence in favor of the alternative hypothesis if its value is A.  a large positive number.

Chi-squared statistics or chi-squared test is a statistical method used to find out if there is a significant difference between the expected and observed frequencies in one or more categories of a contingency table. This test is used to determine whether the null hypothesis can be rejected or not. Chi-squared statistics are a non-parametric test that helps to determine whether the data is close to what is expected or not. This test is used when the data is ordinal or nominal.

Chisquare test is often used for: Testing if the observed frequencies of a nominal variable are significantly different from the expected frequencies Assessing if two or more distributions are the same. The chi-squared statistic provides evidence for or against the null hypothesis. A large positive value of the chi-squared statistic indicates that the null hypothesis can be rejected.

Therefore, option A. a large positive number, is the correct answer.

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A grouped frequency table (grouped frequency conveyance) is an approach to coordinating an enormous arrangement of information into additional reasonable gatherings.

The grouped frequency table

________________________________________________________

 Width (in mm) C.F. Class Interval Frequency ________________________________________________________

 ≥ 20 50 20 - 30 50 - 44

= 6 ≥ 30 44 30 - 40 44 - 28

= 16

 ≥ 40 28 40 - 50 28 - 20

= 8

 ≥ 50 20 50 - 60 20 - 15

= 5

 ≥ 60 15 60 - 70 15 - 0

= 15

_____________________________________________________

                                                                                          ∑f = 50

The gatherings that we arrange the mathematical information into are called class intervals. They can have something similar or different class widths and should not cover.

The principal segment is for the gatherings where we compose the class intervals.

The center section is for the count marks.

The last segment is the frequency section where we can include the count marks.

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the complete question is:

The widths of 50 leaves of a plant were measured in mm and their cumulative frequency distribution is shown in the following table. Make frequency distribution table for this . CLASS FREQUENCY >20 50 >30 44 >40 28 >50 20 ​>60 15

Answer:

h(x) = (x^2 - 64)

Step-by-step explanation:

If the solutions to h of x = 0 are x = -8 and 8, then h(x) must be a quadratic function with roots at x = -8 and x = 8.

One way to write the quadratic function that satisfies these conditions is:

h(x) = (x+8)(x-8)

where a is some non-zero constant that determines the shape of the parabola.

Expanding the above equation, we get:

h(x) = (x^2 - 64)

Therefore, one possible quadratic function that could represent h is:

h(x) = (x^2 - 64)

where a is any non-zero constant.

Answer: $2240.59

Step-by-step explanation:

To calculate the compound interest paid when an amount is borrowed at 5% p.a for 26 years and compounded monthly, you can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the amount of money you will have after t years

P = the principal amount (the amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years) for which the money is borrowed

In this case, we have:

P = the amount borrowed (not given in the question)

r = 5% p.a, or 0.05 as a decimal

n = 12 (since the interest is compounded monthly)

t = 26 years

We need to find the amount of compound interest paid, so we need to find the difference between the amount of money you will have after 26 years (A), and the amount you borrowed (P).

Let's assume the amount borrowed (P) is $1000. Then, we can substitute these values into the formula:

A = 1000(1 + 0.05/12)^(12*26)

A = 1000(1.004167)^312

A = 1000(3.240590)

A = $3240.59

So, after 26 years, the amount of money you will have is $3240.59. The compound interest paid is the difference between the amount borrowed and the final amount:

Compound interest paid = $3240.59 - $1000

Compound interest paid = $2240.59

Therefore, the compound interest paid if the amount is borrowed at 5% p.a for 26 years and compounded monthly is $2240.59.

A = $36,594.00

A = P + I

where

P (principal) = $10,000.00

I (interest) = $26,594.00

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 10,000.00(1 + 0.05/12)(12)(26)

A = 10,000.00(1 + 0.0041666666666667)(312)

A = $36,594.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 5% per year compounded 12 times per year over 26 years is $36,594.00.

Creating a rule y=f(x) by applying transformations to the fundamental function f(x) = √x  The rule that would produce the given graph is f(x) = 2√(x-1) + 1.

To transform the basic square root function f(x) = √x to the given graph, we can use the following transformations:

1. Horizontal shift to the right by 1 unit: f(x-1) = √(x-1)

This will move the point (1, 1) on the basic function to (2, 1) on the new graph.

2. Vertical stretch by a factor of 2: 2f(x-1) = 2√(x-1)

This will result in a two-fold vertical stretch of the graph.

3. Vertical shift upward by 1 unit: 2f(x-1) + 1 = 2√(x-1) + 1

This will move the entire graph upward by 1 unit.

Therefore, the rule that would produce the given graph is f(x) = 2√(x-1) + 1.

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Answer:

D) x=20

Step-by-step explanation:

On the spinner we have numbers from 0 to 9.

It is 10 numbers and we hit only 0,1, 2 and 3 (4 f them)

Lateya have propability [tex]\frac{4}{10}[/tex] to hit those numbers.

[tex]\frac{4}{10} *50=4*5=20[/tex]

When you take a strip of paper, put two half twists in it, and glue the ends together and then cut it lengthwise along the center core line, it results in two interlocked loops.What you get is two interlocked loops when you cut it lengthwise along the center core line. This occurs because the paper strip has been twisted twice. The twist that was made in the paper strip produces two loops that are intertwined after it is cut down the center line.Paper is quite a flexible substance. When it's twisted, it retains its new shape. Because of this, when you twist a strip of paper, it retains its new form. When the strip is bent and connected to form a loop, the twisted part becomes embedded in the paper's core. This produces two loops that are interconnected. When the loop is sliced down the middle, the two loops remain interconnected since the twists in the strip have become embedded in the core.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=19\\ V=4100 \end{cases}\implies 4100=\pi r^2(19)\implies \cfrac{4100}{19\pi }=r^2 \\\\\\ \sqrt{\cfrac{4100}{19\pi }}=r\implies 8.29\approx r[/tex]

The statement is False. At a significance level of alpha equal to .05, if your model has a p-value close to 0 for the overall f test, but none of the individual variables in the model have a p-value <0.05, then you do not have an issue with multi-collinearity. Therefore the given statement is false.

A p-value is a measure of the strength of evidence against the null hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis.

When the p-value is less than or equal to the significance level alpha, then we reject the null hypothesis. In general, when the overall F-test has a low p-value and none of the individual variables in the model have a p-value less than 0.05, it is an indication of multi-collinearity.

Multi-collinearity is a situation in which two or more independent variables in a multiple regression model are highly correlated with each other. It can lead to unstable estimates of the regression coefficients and make it difficult to interpret the results of the model.

In conclusion, at a significance level of alpha equal to .05, if your model has a p-value close to 0 for the overall f test, but none of the individual variables in the model have a p-value <0.05, then you do not have an issue with multi-collinearity. The statement is false.

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Answer:

D (D)

Step-by-step explanation:

We can know from the question that each face has two A, two B, and two C, two D, and two E. And these three faces are the sides of the triangular pyramid (Each face vertex is D).

∴ We can get the picture of the fourth face.

∴ There are two A, two B, two C, one D, and two E in the picture.

∴ The middle of the fourth face is D.

*See the attachment*

Answer:

D

Step-by-step explanation:

When two objects are massive and close to each other, the gravitational force between them is strong.

Gravity is a fundamental force of nature that exists between any two objects in the universe. The strength of the gravitational force depends on two factors: the masses of the two objects and the distance between them.

The larger the masses of the two objects, the greater the gravitational force between them. Likewise, the closer the objects are to each other, the stronger the gravitational force.

This relationship is described by Newton's Law of Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

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Answer:

the star , the down arrow (3rd one), the stop sign

Answer:

  6 inches

Step-by-step explanation:

You want to know the radius of a cylinder with volume 72π in³ and height 2 in.

The given numbers can be put in the given formula, and the equation solved for r.

  V = πr²h

  72π in³ = πr²(2 in)

  36 in² = r²

  r = √(36 in²) = 6 in

The radius of the cylinder is 6 inches.

The interquartile range (IQR) of the given data set is 16.

To find the interquartile range (IQR), we first need to calculate the first and third quartiles of the data set:

Arrange the data set in order from smallest to largest:

22, 26, 28, 30, 32, 35, 35, 42, 45, 49, 50

Find the median (middle value) of the lower half of the data set (the first quartile, Q1):

22, 26, 28, 30, 32, 35

The median of this set is 29, which is halfway between 28 and 30.

Find the median (middle value) of the upper half of the data set (the third quartile, Q3):

35, 42, 45, 49, 50

The median of this set is 45.

Calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1

   = 45 - 29

   = 16

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The skier needs to go at least 65.4 miles/hour to beat the person in first place.

What is trigonometry?

It is the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

To solve this problem, we need to use trigonometry to find the horizontal distance the skier needs to cover in order to beat the person in first place, and then use this distance and the time it took the first-place skier to calculate the required speed.

A represents the skier's starting point, B represents the end of the slope where the person in first place finished, and C represents the top of the mountain. The angle of depression is labeled θ and is equal to 60 degrees.

Using trigonometry, we can calculate the horizontal distance AB using the tangent function:

tan θ = opposite/adjacent

where opposite = h = 10000 ft (the height of the mountain) and adjacent = AB (the horizontal distance we want to find).

Substituting θ = 60 degrees and h = 10000 ft, we get:

tan 60 = AB/10000

√3 = AB/10000

AB = 10000√3 ≈ 17321.17 ft

So the skier needs to cover a horizontal distance of about 17321.17 feet in order to beat the person in first place.

To find the required speed, we need to convert this distance to miles and divide by the time it took the first-place skier (3 minutes):

17321.17 ft = 17321.17/5280 miles ≈ 3.28 miles

Speed = distance/time = 3.28 miles / 3 minutes = 1.09 miles/minute

To convert miles/minute to miles/hour, we need to multiply by 60 (the number of minutes in an hour):

Speed = 1.09 miles/minute x 60 minutes/hour ≈ 65.4 miles/hour

Therefore, the skier needs to go at least 65.4 miles/hour to beat the person in first place.

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Answer:

Step-by-step explanation:

1. -(5/x^6)

2. 4398046511104

3. 65536

4. 1/100

5. 1/5764801

The binomial is (a² + 4)

We can rewrite this as follows:

[tex]-a^2*(a^2 + 4) + (a^2 + 4)[/tex]

You can think of the a squared plus 4 thing as a common factor because it appears in both terms, then we can rewrite this as:

[tex]-a^2*(a^2 + 4) + (a^2 + 4)\\-a^2*( a^2 + 4 + 1)\\-a^2*(a^2 + 5)[/tex]

That is the expression factorized.

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Answer: 56

Step-by-step explanation:

I guess and checked all the numbers that add up to 11

Answer:

The radius of the hubcap is half of its diameter, which is:

r = d/2 = 26/2 = 13 cm

The area of the hubcap, in square centimeters, is given by the formula:

A = πr²

Substituting the value of r, we get:

A = 3.14 x 13²

A = 3.14 x 169

A = 530.66

Therefore, the area of the hubcap is approximately 530.66 square centimeters.

Step-by-step explanation:

I did this question and the correct answer is 169π.

Step-by-step explanation:

If the budget were to increase to $3000, allowing us to survey many more people from a simple random sample, the test statistic would likely be more accurate and reliable.

As per the given scenario,

if we have a limited budget of $500, we can only survey 50 people from a simple random sample. In order to study the relationship between social class and voting preferences, the budget must be increased to $3000.

On increasing the budget, we can survey more people from a simple random sample, which would lead to a better representation of the population.
Due to the small budget, the test statistic would be less accurate as only a small number of people are being surveyed. However, if the budget increases to $3000, it would allow for a larger sample size and therefore the test statistic would be more accurate.

This would result in a narrower confidence interval and a higher level of confidence in the accuracy of the results.
Moreover, with a larger budget, it would be possible to use more sophisticated sampling techniques such as stratified random sampling, which could further increase the accuracy of the test statistic.

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the area of the equilateral triangle using the formula for the area of a regular polygon: 43.5 units squared

The area of a customary polygon is given as:

[tex]=\frac{1}{2} ap[/tex]

'a' is the apothem and 'p' is the edge.

The edge of the equilateral triangle is 3×10=30 units.

The apothem is given by:

[tex]a= \frac{8}{\sqrt[2]{3} }\\ \\a= \frac{10}{\sqrt[2]{3} } \\\\a=2.9[/tex]

Consequently, the area is

1/2 * 2.9 * 30 = 43.5

On the off chance that all the polygon sides and inside points are equivalent, they are known as ordinary polygons. Instances of standard polygons are square, equilateral triangle, and so forth. In standard polygons, not exclusively are the sides consistent however the points are as well. That means they are equiangular.

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the complete question is:

Bianca calculated the height of the equilateral triangle with side lengths of 10. tangent (30) = StartFraction 5 Over h EndFraction An equilateral triangle with side lengths of 10 is shown. A bisector is drawn to split the side into 2 equal parts and splits the angle into 2 30 degree segments. Then, she used the formula for area of a triangle to approximate its area, as shown below. A = one-half b h. = one-half (10) (8.7). = 43.5 units squared. Calculate the area of the equilateral triangle using the formula for area of a regular polygon, and compare it to Bianca's answer. The apothem, rounded to the nearest tenth, is units. The perimeter of the equilateral triangle is units. Therefore, the area of the equilateral triangle is , or approximately 43.5 units2. The calculated areas are .

Answer: x^2-22x+121

I believe this is correct.

The given statement, "the margin-of-error refers to the number of percentage points by which survey results may vary" is true because the margin of error is an important factor to consider when interpreting the results of a poll.

In a poll, the margin of error refers to the amount of random sampling error that is expected to be present in the results of the survey. It is a measure of the statistical uncertainty associated with using a sample of a population to make inferences about the opinions or characteristics of the entire population.

The margin of error is typically reported as a plus or minus percentage, such as "plus or minus 3 percentage points," and it represents the range of values within which the true population parameter is likely to fall with a certain level of confidence. For example, if a poll has a margin of error of plus or minus 3 percentage points with a 95% level of confidence, this means that if the poll were conducted 100 times, the results would be expected to fall within plus or minus 3 percentage points of the true population parameter in 95 of those surveys.

Therefore, the margin of error is an important factor to consider when interpreting the results of a poll and helps to provide a measure of the precision and reliability of the survey findings.

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