Suppose a student named Marcus wants to learn about the sleeping habits of students in his class. Marcus wants to collect data from his classmates to learn how many hours of sleep his classmates get. He then wants to process this data with a computer and visualize it in a Histogram. Which of the following would be the best technique for Marcus to collect this data

John has 5 red balls and 8 blue balls. What is the ratio of red balls to blue balls? Answer: The ratio of red balls to blue balls is 5:8.

We can solve this problem by using a ratio. Ratios are two values that are compared to each other. In this case, we need to compare the number of red balls to the number of blue balls. We are given that there are 5 red balls and 8 blue balls. To find the ratio, we need to write the numbers as a fraction. The fraction for red balls is 5/8 and the fraction for blue balls is 8/5. We can then simplify the fractions to get the ratio of 5:8. This means that there is a ratio of 5 red balls to 8 blue balls.

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Null Hypothesis: The jeeps have an mpg rating of 34.9

Alternative Hypothesis: The jeeps have an mpg rating that is less than 34.9

Calculate the test statistic.

Test Statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)

Test Statistic = (34.6 - 34.9) / (2.0 / √16)

Test Statistic = -1.5 / 0.5

Test Statistic = -3

Calculate the critical value.

Critical Value = -2.960 Compare the test statistic with the critical value

Test Statistic = -3

Critical Value = -2.960

Since the test statistic is lower than the critical value, we reject the null hypothesis.

Make a conclusion The jeeps have an mpg rating that is less than 34.9

At the 0.025 level, there is enough proof to conclude that Jeeps do not get the claimed mpg.

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The value of  zα for the following is :

(a)  α = 0.0089 is 2.37

(b) α = 0.09 is 1.34

(c)  α = 0.707 is -0.545

zα is the inverse function of the standard normal CDF.

(a) Central limit c= 1-α

for α = 0.0089 , c=1-0.0089

∴ c=0.9911

Hence confidence level in percentage= 99.5%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.9911)

zα =2.37

(b) Central limit c= 1-α

for α = 0.09 , c=1-0.09

∴ c=0.91

Hence confidence level in percentage= 91%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.91)

zα=1.34

(c) Central limit c= 1-α

for α = 0.707 , c=1-0.707

∴ c=0.293

Hence confidence level in percentage= 29.3%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.707)

zα= -0.545

Therefore zα value for 0.0089 is 2.37, for 0.09 is 1.34 and for 0.707 it is -0.545.

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Answer:

Step-by-step explanation:

none of these the corrct answer is 5

The value of x is: x=88.

Here, given that, 36% of the letters in Pythagoras's alphabet soup are vowels.

33 1/3% of those vowels are "os."

To calculate the percentage of letters that are "os," we first need to find 33 1/3% of 36%.

33 1/3% is equivalent to 1/3. So, we can calculate the percentage of "os" as follows:

Percentage of "os" = (36% * 1/3) = 12%

Now, we know that 12% of the letters in the soup are "os."

Next, Pythagoras removes all the "os" from his soup.

This means that what remains are the non-"os" letters, which are the remaining vowels and consonants.

To calculate the percentage of the original letters that remain, we need to subtract the percentage of "os" from 100%:

Percentage of original letters remaining = 100% - Percentage of "os"

Percentage of original letters remaining = 100% - 12% = 88%

Therefore, x% of the original letters remain, and x is equal to 88.

Hence, The value of x is: x=88.

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Random mean assignment involves randomly assigning participants to different groups, so that each group is similar in terms of characteristics such as age, gender, race, etc. This ensures that the groups are as similar as possible, reducing the chance of bias in the experiment.

Random mean assignment is an important procedure used in experiments to reduce experimenter and participant bias. This involves randomly assigning participants to different groups in the experiment, so that the groups are as similar as possible in terms of characteristics such as age, gender, race, etc. This ensures that any differences observed in the results are due to the experimental variables, rather than any pre-existing differences between the groups. Random assignment also ensures that any experimenter bias is minimized, as the experimenter is not able to select which participants go into which group. Random assignment is therefore a key procedure used to reduce the chance of bias in experiments, and ensure that the results are more reliable and valid.

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Answer: 51

Step-by-step explanation: 24^2+45^2=C

24*24=576

45*45=2025

576+2025=2601

Square root of 2601 is 51

Emma has been saving up to go on a big summer trip, visiting the United States and Russia. Emma should spend $2951.46 while in the United States.

Generally, To maximize the amount of cash Emma has in Russia, she should spend all of her money in the United States before entering Russia. First, we convert the Ruble limit to USD:

32,285 Rubles / 129.35 =249.594 USD.

Next, we convert Emma's savings from pounds to USD:

£2500 x 1.28 = $3200.

Finally, we subtract the Ruble limit from Emma's total savings in USD: $3200 - $248.54 = $2951.46.

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quadratic model; y = 0.13x2 – 2.38x + 12.27 is the best to fit the regression model for the data.

ax2+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

For the given Dataset

Sum of X = 27

Sum of Y = 22

Mean X = 5.4

Mean Y = 4.4

Sum of squares (SSX) = 45.2

Sum of products (SP) = -42.3

Regression Equation = ŷ = bX + a

b = SP/SSX = -42.3/45.2 = -0.93584

a = MY - bMX = 4.4 - (-0.94*5.4) = 9.45354

ŷ = -0.93584X + 9.45354

Thus Given linear Equation is not the best fit

Since the graph is decreasing Option b and c are also not possible

Therefore, the best to fit the regression model for the data is the quadratic model; y = 0.13x2 – 2.38x + 12.27.

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Answer:

1. Pt. A: -6               3. Pt. C: 3               5. Pt. E: 0

2. Pt. B: -2              4. Pt. D: 5

Step-by-step explanation:

By looking at the number line, you can see that a few points are labled from letter A to letter E.

In order to know the value of each point, you just have to look at their placement in the number line. For example, we can see that Point B is plotted at -2 on the number line, this means that the value of Point B is -2.

I hope this helps! :)

Answer:

y = 4/3x - 1

Step-by-step explanation:

(3, 3) and (0, -1)

m = -1-3 / 0-3

m = -4/-3

m = 4/3

y = 4/3x + b

-1 = 4/3(0) + b

-1 = 0 + b

b = -1

y = 4/3x - 1

A = P(1+r/n)(nt), where P is the original principal, r is the annual interest rate, n is the number of times the interest is compounded annually, and t is the number of years the money has been held, is the formula for compound interest.

To calculate the final amount of money in the account:

 First, divide the 8% annual interest rate by 100 to get a decimal value: 0.08.

Find the number of times the interest is compounded annually. Since it is done quarterly, the answer is n = 4.

Put these values into the formula now, along with the $1200 principle sum and the number of years, 5, to complete it:

A = $1200(1+(0.08/4))^(4*5) = $2490.07

  to determine how long it will take for the initial sum to double to $2400.

 Divide the final sum by the starting sum: 2400/1200 = 2

 Take the natural logarithm of 2: ln(2) = 0.693

Decimalize the result and divide it by the interest rate: 0.693 / 0.08 = 8.66 years

 Therefore, the time it will take for the initial sum of money to double to $2400 is 8.66 years.

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The probability is 8/33 is already in its simplest form as the numerator and denominator share no common factors.

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The probability is 8/33 is already in its simplest form as the numerator and denominator share no common factors.

Probability is a measure of the likelihood of an event occurring, represented as a decimal or fraction between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

(Probability of choosing a green pen on the first draw) x (Probability of choosing a blue pen on the second draw, given that a green pen was chosen on the first draw)

= (4/12) * (8/11)

= (1/3) * (8/11)

= 8/33

So the probability is 8/33. This is already in its simplest form as the numerator and denominator share no common factors.

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System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.

1. Algebra: This is the study of equations and their solutions, as well as the manipulation of symbols and operations.

2. geometry: This involves the study of shapes and the properties of space, such as angles and distances.

3. Calculus: This involves understanding the rate of change of a function and the area under a curve.

4. Trigonometry: This involves the study of angles and their relationships to one another and to other types of measurements.

5. Number Theory: This involves the study of the properties of numbers, such as divisibility, primes, and multiplicative functions.

System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.

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The number of extra men required to erect 2 additional cottages is; 5 men

Let us use;

M = men

D = Days

C = Cottages

Thus;

5M * 21D = 2C

105MD = 2C

To erect 2 cottages in 21days, 5 men are required

To erect 2 more cottages or 4 cottages in 21 days;

(4 * 5)/2 = 10 men

Thus, we conclude that is the number of men required to erect 2 additional cottages which is 5 extra men

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Nonvisual language is used to describe the visual world verbally. It can lead people around a museum, help an audience member find their way around an artwork, or provide them access to the visual elements of a performance.

It was in 1981 when Dr. Margaret Pfanstiehl, founder and president of The Metropolitan Washington Ear Inc., and her husband Cody perfected the art and practice of verbal description.

Standard information found on a label, such as an artist's name, nationality, the title of the artwork, date, dimensions or size of the piece, media, and method, can be found in a spoken description as well. In addition, a vocal description can offer a broad overview of the work's subject matter and structural elements.

1. Lines

2. Planes

3. Hyperboloids

4. Lines

5. Spheres

6. Ellipsoids

7. Paraboloids

8. Hyperbolas

9. Ellipses

10. Hyperbolas

11. Circles

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Answer:

0.00746696035

Step-by-step explanation:

3.39/454 = 0.00746696035

Rounded that would only be 1 cent per kg.  Hummmppp....

The requried value of given expression when a = 7 and b = 28 is 125.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
Given expression,
(a + b)² = a² + b² + 2ab
We have,
a = 7 and b = 28
(7 + 28)² = 7² + 28² + 2 × 7 × 28
35² = 49 + 786+ 392
125 = 125

Thus, the requried value of given expression when a = 7 and b = 28 is 125.

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The area of the surface is  S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

Now, According to the question:

The given equation is:

[tex]z = \frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2} )[/tex],

0 ≤ x ≤ 1 , 0 ≤ y ≤ 1

Let's know:

Surface Area:

To surface area of a solid E, defined by z = f(x , y) can be found by integrating[tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex] where R is the rectangular region

[0,1] × [0, 1] and [tex]z_x,z_y[/tex] corresponds to the partials of z w.r.t x and y.

Now,

[tex]\sqrt{(z_x)^2+(z_y)^2+1}[/tex] = [tex]\sqrt{1+(\sqrt{x} )^2+(\sqrt{y} )^2}[/tex] = [tex]\sqrt{1+x+y}[/tex]

S = [tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex]

  = [tex]\int\limits^1_0\int\limits^1_0 \sqrt{x+y+1}dy dx[/tex]

  [Integrate with respect to y ]

    =  [tex]\int\limits^1_0 (\frac{2}{3}(x + y + 1)^\frac{3}{2} )|^1_0 dx[/tex]                        

  = [tex]\int\limits^1_0 (\frac{2}{3}(x + (1) + 1)^\frac{3}{2}-\frac{2}{3}(x + (0) + 1)^\frac{3}{2} )dx[/tex]

 = [tex]\int\limits^1_0 ((\frac{2}{3}(x +2)^\frac{3}{2} ) - (\frac{2}{3}(x +1)^\frac{3}{2} ) , dx[/tex]

  =  [tex]\int\limits^1_0 (\frac{2}{3}((x +2)^\frac{3}{2} - (x +1)^\frac{3}{2} )) , dx[/tex]

  [Integrate with respect to x ]

   = [tex]\frac{2}{3} (\frac{2}{5}(x + 2)^\frac{5}{2} - \frac{2}{5}(x +1)^\frac{5}{2} )|^1_0[/tex]

    = [tex]\frac{2}{3}(\frac{2}{5}((1)+2 )^\frac{5}{2}-\frac{2}{5}((1)+1)^\frac{5}{2})-\frac{2}{3}(\frac{2}{5}((0)+2 )^\frac{5}{2} -\frac{2}{5}((0)+1)^\frac{5}{2}[/tex]

    = [tex]\frac{2}{3}(\frac{18\sqrt{3}}{5} -\frac{8\sqrt{2} }{5} )-\frac{2}{3} (\frac{8\sqrt{2} }{5} -\frac{2}{5} )[/tex]

     = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

Hence, The area of the surface is  S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

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The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:

x = log3(12)

The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:

x = ∛12

The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.

The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.

As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.

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The object will travel 639.36 yards in one minute.

Formula: Yards = Feet x 0.3333

The question is asking how many yards an object will travel in one minute when it is moving at a constant rate of 32 feet per second.

We can use the formula above to calculate the number of yards the object will travel in one minute. We know that the object is traveling at a rate of 32 feet per second.  To find the number of yards traveled in one minute, we need to multiply 10.6667 yards per second by 60 seconds in a minute. Therefore, in one minute (60 seconds), the object will travel 32 x 60 = 1920 feet. We can now use the formula to convert this to yards: Yards = 1920 x 0.3333 = 639.36 yards. Therefore, the object will travel 639.36 yards in one minute.

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Therefore , the solution of the given problem of speed comes out to be

he needs to drive at 77.77 mph.

How quickly something is traveling is determined by its speed from a distance. How far an object moves in a certain length of time depends on its speed. Speed is calculated as follows: velocity = range x time. The most used units for expressing speed are meters per second (m/s), kilometers per hour (km/h), and kilometers per second (mph) (mph).

Here,

70 + 50 = 120 miles is indeed the total distance.

You would need 2.4 hours to travel the 120 miles at such an approximate speed of 50 mph.

However, you are already on the road for 1.5 hours, so you must finish the trip in 0.9 hours.

You need to travel at a speed of 77.77 mph to complete the final 70 miles approximately 0.9 hours.

Therefore , the solution of the given problem of speed comes out to be

he needs to drive at 77.77 mph.

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a) An inequality that can determine x the number of outfits Keiland can purchase while staying within her total budget of $660 is 529.59 + 37.26x ≤ 660.

b) The inequality solution shows that x cannot be more than 3.

An inequality is a mathematical statement that two or more mathematical expressions are unequal or not equivalent.

Inequalities are depicted as follows:

These inequality symbols are usually written between two numbers or algebraic expressions.

The total spending budget Keilantra has = $660

The cost of a new bicycle = $488.20

The cost of 2 reflectors = $22.34 ($11.17 x 2)

The cost of a pair of bike gloves = $19.05

The total costs for the above three items = $529.59

The unit cost of new biking outfits = $37.26

The number of outfits Keilantra can purchase = x

529.59 + 37.26x ≤ 660

37.26x ≤ 660 - 529.59

37.26x ≤ 130.41

x ≤ 3.5

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Two sets of possible dimensions for the rectangular pyramid that uses the same amount of clay as the rectangular prism are 2 inches base and 1.5 inches height, and 3 inches by a 1-inch base and 1-inch height.

The volume of the rectangular prism is 6 inches * 1 inch * 1/2 inch = 3 cubic inches. To determine the possible dimensions for the pyramid, we need to find the dimensions that will give us the same volume.

One set of possible dimensions for the pyramid would be a base that is 2 inches by 2 inches, and a height of 1.5 inches. This would give a volume of 2 inches * 2 inches * 1.5 inches / 3 = 2 cubic inches, which is the same as the original rectangular prism.

Another set of possible dimensions would be a base that is 3 inches by 1 inch and a height of 1 inch. This would give a volume of 3 inches * 1 inch * 1 inch / 3 = 1 cubic inch, which is the same as the original rectangular prism.

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Answer:

y = 3x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

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

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = 3x + 1 ← equation of line

The completed statement using the integers that are closest to the number in the middle is 3<-√14<4

The statement: <-√14< can be interpreted as the set of all real numbers that are less than the square root of 14, which is approximately 3.74166.

The integers closest to this number are 3 and 4, so the set of integers that are closest to the number in the middle can be represented as:

(-∞, 3) U (4, ∞)

The statement says that the value of the square root of 14, when multiplied by -1 (the square root of a negative number), is between 3 and 4. The closest integers to the value of the square root of 14 are -3 and -4.

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The probability that exactly 4 of the 8 diamonds picked from the bag are real diamonds is 28/256 or 11.1%.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 meaning the event is impossible and 1 meaning the event is certain to occur. Probability theory is used to make predictions and calculate the chances of different outcomes in order to make decisions. Probability theory can also be applied to understand the behavior of complex systems.

This is calculated by first determining the total amount of possible outcomes. Out of the 8 diamonds picked, there are 8C4 = 70 ways in which the 4 real diamonds can be chosen. With 8 real diamonds and 7 fake diamonds, the probability of a real diamond being chosen is 8/15, and the probability of a fake diamond being chosen is 7/15. Therefore, the probability of having exactly 4 real diamonds is 70 x (8/15)^4 x (7/15)^4 = 28/256.

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