A coin is tossed and a standard number cube is rolled list all of the possible outcomes in a sample space.

The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).

Mean time that employees spend on personal issues each week(M) = 4.9 hours

Standard deviation = 0.35 hours

The following formula is used to get the confidence interval for the sample mean and standard deviation given:

μ = M ± t(sM)

where; M = sample mean

t = T-statistic based on confidence interval

Degree of freedom = n - 1

From the question, n = 55

Degree of freedom = 55 - 1

Degree of freedom = 54

(Standard errors)sM = √(s^2/n)

Now putting the value

sM = √(0.352/55)

sM = 0.05

t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)

Now the confidence interval

μ = M ± t(sM)

μ = 4.9 ± 2.005 × 0.05

μ = 4.9 ± 0.095

μ = (4.9 - 0.095, 4.9 + 0.095)

μ = (4.805, 4.95)

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The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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The formula for work is Work=Force × Distance, i.e., W=(F)x(d). Where F represents Force and d represents Distance.

Work is created by applying force and moving in the force's direction. Force and displacement are two vectors, and work is their dot product. Work is a scalar quantity as a consequence. The joule (J) is the SI unit of work. Also we can derive the formula as W = (F cos θ)d, where d represents the magnitude of distance.

Work may be estimated if the force acting along the path is constant by multiplying the length of the path by the component of the force acting along the path. To quantitatively express this concept, the work W is equal to the force f times the distance d, or W=(F)x(d). If the force is applied at an angle to the displacement, the work is W = (F cosθ)d.

Therefore, it is all about the work formula.

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Answer: The number is 106.4

Step-by-step explanation:

Let the number be x

Mar halves the number becomes = x x 1/2  to get 53.2

The equation to solve this problem is  x/ 2 = 53.2

Such that to find x

x/2= 53.2

x =  2 x 53.2= 106.4

The number is 106.4

There are 24 sticks in pattern 6. The diagram indicates that one pattern is made up of one box built from four sticks.

A geometric pattern is a pattern made out of geometric forms that are generally repeated, much like a wallpaper design.

The given figure shows that one pattern consists of one box formed from the 4 sticks.

Pattrern 1 = 1 box  

Pattern 2 = 2 box

Pattern 6 = 6 box

1 box = 4 stick

Pattern 6 = 6 box = 6 ×4 = 24 sticks

Hence,there are 24 sticks in pattern 6.

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The diameter of the circle pen for the sheep of the farmer is 68 yards.

The total length of the fencing used for the preparation of the fencing for sheep is 213.52 yards.

Thus,

circumference = 213.52 yards

The formula for the calculation of the circumference of circle is,

circumference = 2πr,

In which,

π = 3.14  and radius r.

Thus,

213.52 = 2πr

r = 213.52 / 2π

r = 34

Diameter = 2 x radius

Diameter = 2 x 34

Diameter = 68 yards.

Thus, the diameter of the circle pen for the sheep of the farmer is 68 yards.

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The cost per person if number of students is 100 given the inverse variation is $46.75

C = k / n

where,

If n = 55 and C = $85

C = k / n

85 = k / 55

85 × 55 = k

4,675 = k

Find C if n = 100

C = k / n

= 4,675 / 100

C = $46.75

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The probability of the sum of two integers is greater than the product is equal to 2 / 5.

Let 'A' be the set of positive integers less than or equal to 5.

A = { 1, 2, 3, 4, 5}

Sum of two numbers is greater than the product of the numbers.

1 × 1 = 1  and 1 + 1 = 2

1 × 2 = 2 and 1 + 2 = 3

1 × 3 = 3 and 1 + 3 = 4

1 × 4 = 4 and 1 + 4 = 5

1 × 5 = 5 and 1 + 5 = 6

2 × 1 = 2 and 2 + 1 = 3

3 × 1 = 3 and 3 + 1 = 4

4 × 1 = 4 and 4 + 1 = 5

5 × 1 = 5 and 5 + 1 = 6

2 × 2 = 4 and 2 + 2 = 4

Total possibilities = 5 × 5

                             = 25

Favourable outcomes = 10

Total number of outcomes = 25

Probability of sum of two numbers greater than the product

= 10 / 25

= 2 / 5

Therefore, the probability of the sum of two numbers is greater than the product is equal to 2/ 5.

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Answer:73

Step-by-step explanation:

45

+28

73

Answer:

9/6

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

when k=99

=>99=100-4n

=>4n=100-99

=>4n=1

=>n=1/4

Answer:

\(( - 1,2 \frac{1}{2} )\)

Step-by-step explanation:

\(\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}\)

Thus, midpoint

\( = ( \frac{4 - 6}{2} , \frac{8 - 3}{2} ) \\ = (\frac{ - 2}{2} , \frac{5}{2} ) \\ = ( - 1,2 \frac{1}{2} )\)

To find the exponential function given the points (0, 3) and (3, 375), we can use the form y = a * e^(bx), where 'a' represents the initial value and 'b' represents the growth/decay rate.

Let's denote the exponential function as y = a * e^(bx). Plugging in the point (0, 3), we get the equation 3 = a * e^(b * 0), which simplifies to 3 = a * e^0. Since any number raised to the power of 0 is equal to 1, we have 3 = a * 1, which gives us a = 3.

Next, we can use the point (3, 375) to find the value of 'b'. Substituting these values into the equation, we have 375 = 3 * e^(3b). Dividing both sides by 3, we get 125 = e^(3b). To solve for 'b', we take the natural logarithm (ln) of both sides, resulting in ln(125) = 3b. Simplifying further, we have b = ln(125) / 3.

Finally, substituting the values of 'a' and 'b' back into the original exponential function, we obtain the equation y = 3 * e^((ln(125)/3) * x). Thus, the exponential function that passes through the given points is y = 3 * e^((ln(125)/3) * x).

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Nick sold twice as many songs as Bianca since 4x10^6 is twice as much as 8x10^5. To explain this further, we can break down the numbers and compare them. Bianca sold 8x10^5 downloads, which is the same as 800,000 downloads. Nick sold 4x10^6 downloads, which is the same as 4,000,000 downloads.

To find out how many times as much Nick sold compared to Bianca, we can divide the number of Nick's downloads by the number of Bianca's downloads:

4,000,000 / 800,000 = 5

So Nick sold five times as many songs as Bianca.

It's important to note that the original question asked how many times as much the number of songs Nick sold as compared to Bianca, not the amount of money they made from selling their songs. While Nick sold more songs than Bianca, it's possible that Bianca made more money from her sales if her songs were higher in price. However, based solely on the number of downloads, Nick sold five times as many songs as Bianca.

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To find out how many times as much Nick sold compared to Bianca, we can divide the number of Nick's downloads by the number of Bianca's downloads:

4,000,000 / 800,000 = 5

So Nick sold five times as many songs as Bianca.

It's important to note that the original question asked how many times as much the number of songs Nick sold as compared to Bianca, not the amount of money they made from selling their songs. While Nick sold more songs than Bianca, it's possible that Bianca made more money from her sales if her songs were higher in price. However, based solely on the number of downloads, Nick sold five times as many songs as Bianca.

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The factor of 2 is 1 and 2.

What is a factor?

In mathematics, an integer m that can be multiplied by another integer to create n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.

Factors are also known as divisors. This means they can divide evenly into the number they're a factor of.

Here,

We have to find the possible factors of 2.

We concluded that the factor of 2 is 1 and itself.

Factors of 2 are all the numbers which on multiplying give the result of 2. Factors of 2 are 1 and 2 only.

Hence, the factor of 2 is 1 and 2.

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Answer:

M = -2

Step-by-step explanation:

Your answer is -2

The total height of the Monument is 604.35 ft.

To solve for x, we can use trigonometry.

Let h be the height of the Washington Monument.

Tangent function will help get distance between Noelle's eye level and the base of the monument

tan(84.8°) = h / d

d = h / tan(84.8°)

The total distance from Noelle's eye level to the top of the monument:

50 ft + 5 ft + d = h

Substituting expression for d, we get:

50 ft + 5 ft + h / tan(84.8°) = h

h / tan(84.8°) = 55 ft

Multiplying sides by tan(84.8°)

h = 55 ft * tan(84.8°)

h = 55 ft * 10.98815

h = 604.34825

h = 604.35.

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The number of times that he misses will be 56.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Peter scored 40 goals at soccer practice his ratio of goals to misses was 5: 7.

Let 'm' be the number of miss. Then the equation is given as,

40 / m = 5 / 7

Simplify the equation, then we have

40 / m = 5 / 7

8 / m = 1 / 7

m = 7 x 8

m = 56

The number of times that he misses will be 56.

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we need a sample size of at least 676 to be 90% confident that the sample proportion is within 5% of the population proportion, assuming no preliminary estimate of the true population is available.

To determine the required sample size we can use the following formula:

n = (z^2 * p * (1 - p)) / (E^2)

where:

n is the sample size we need to determine

z is the z-score associated with the confidence level (90% confidence level has a z-score of 1.645)

p is the estimated population proportion

E is the desired margin of error (5%)

Since we don't have a preliminary estimate of the true population, we can use 0.5 as an estimate for p, which will give us the maximum sample size needed. Thus, we have:

n = (1.645^2 * 0.5 * (1 - 0.5)) / (0.05^2) = 676

Therefore, we need a sample size of at least 676 to be 90% confident that the sample proportion is within 5% of the population proportion, assuming no preliminary estimate of the true population is available.

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Answer:

Step-by-step explanation:

let duke be x years

dora be 7+x years

and emeka be 3(7+x) years

according to question ur equation is

3(7+x)+7+x+x=38

21+3x+7+2x=38

28+5x=38

5x=38-28

x=10/5

x=2

Answer:

Step-by-step explanation:

3(7+x)+7+x+x=38

21+3x+7+2x=38

28+5x=38

5x=38-28=10

D.b.s by 5

10÷5=2

The probability of rolling a number greater than 6 is 1/4, or 0.25 as a decimal, or 25% as a percentage.

The die has 8 equally likely possible outcomes, which are the numbers 1 through 8. The probability of rolling a number greater than 6 is the same as the probability of rolling a 7 or 8.

Since each of these two outcomes is equally likely, the probability of rolling a number greater than 6 is:

P(rolling a number greater than 6) = P(rolling a 7) + P(rolling an 8)

The probability of rolling a 7 is 1/8, and the probability of rolling an 8 is also 1/8. Therefore:

P(rolling a number greater than 6) = 1/8 + 1/8 = 2/8 = 1/4

So the probability of rolling a number greater than 6 is 1/4, or 0.25 as a decimal, or 25% as a percentage.

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Blake can purchase approximately 60.75 pounds of Cheese Filled Lizards and 10 dozen of Fried Frog Skins with the $432 he saved by recycling old aluminum cans.

First we need to set up some equations.

Let's denote the amount of Cheese Filled Lizards in pounds as "c" and the number of dozen Fried Frog Skins as "f". We can then set up the following system of equations:

8c + 6f = 432 (the total cost of the party is $432)

12f = k (the number of Fried Frog Skins in individual pieces, k is an unknown constant)

To solve for "c" and "f", we need to eliminate one of the variables. We can do this by solving the second equation for "f" and substituting it into the first equation:

f = k/12

8c + 6(k/12) = 432

8c + (1/2)k = 432

16c + k = 864

Now we have a single equation in two variables. We can choose one of the variables and solve for it in terms of the other. For example, solving for "k" in terms of "c", we get:

k = 864 - 16c

Substituting this expression for "k" into the equation 12f = k, we get:

12f = 864 - 16c

f = (72/4) - (4/3)c

f = 18 - (4/3)c

So we have expressed the number of Fried Frog Skins in terms of the amount of Cheese Filled Lizards. We can now substitute this expression into the cost equation:

8c + 6(18 - (4/3)c) = 432

Solving for "c", we get:

8c + 108 - 8c/3 = 432

16c/3 = 324

c = 60.75

So, Blake can purchase approximately 60.75 pounds of Cheese Filled Lizards and 10 dozen of Fried Frog Skins with the $432 he saved by recycling old aluminum cans.

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The equations of the osculating circles of the parabola y = (1/2)x^2 at the points (0,0) and (1, 1/2) are x^2 + y^2 = 0 and (x-1/2)^2 + (y-1/4)^2 = 1/16, respectively.

To find the equations of the osculating circles, we need to determine the center and radius of each circle. The osculating circle at (0,0) is tangent to the parabola at that point. Since the radius of the circle is zero, the equation is simply x^2 + y^2 = 0.

At the point (1, 1/2), the osculating circle is tangent to the parabola as well. We can start by finding the slope of the tangent line at this point, which is the derivative of the parabola. Differentiating y = (1/2)x^2 with respect to x, we get dy/dx = x. Evaluating this at x = 1 gives us the slope of the tangent line as 1.

The center of the osculating circle can be found by moving along the normal line from the point (1, 1/2) by a distance equal to the radius of the circle. Since the radius is perpendicular to the tangent line, we can use the slope of the tangent line to find the slope of the normal line, which is -1 (the negative reciprocal of 1).

Using the point-slope form of a line, we have y - (1/2) = -1(x - 1), which simplifies to y = -x + 3/2. Solving this equation simultaneously with the parabola equation, we find the intersection points of the parabola and the normal line.

Substituting y = -x + 3/2 into y = (1/2)x^2, we get (-x + 3/2) = (1/2)x^2. Rearranging this equation, we have (1/2)x^2 + x - 3/2 = 0. Solving this quadratic equation, we find x = 1/2 or x = -3.

Substituting these values back into the normal line equation, we can find the y-coordinates of the intersection points. When x = 1/2, y = -1/2 + 3/2 = 1, and when x = -3, y = 3/2.

Now, we can use the midpoint formula to find the center of the osculating circle, which is the average of the intersection points: (1/2, (1 + 3/2)/2) = (1/2, 5/4) = (0.5, 1.25).

The radius of the osculating circle can be found by the distance formula between the center and one of the intersection points: r = sqrt((1/2 - 1/2)^2 + (5/4 - 1)^2) = sqrt(1/16) = 1/4.

Putting it all together, the equation of the osculating circle at (1, 1/2) is (x - 1/2)^2 + (y - 1/4)^2 = 1/16.

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Answer:

what are x and y equivalent to?

Step-by-step explanation:

The mean sum of squares of treatment (MST) is 68.

To calculate the mean sum of squares of treatment (MST), we need the degrees of freedom (df) for the treatment and the error. From the given information, we have:

SS (Sum of Squares) for Treatment = 136

SS for Error = 416

Total SS (Sum of Squares) = ? (not provided)

The degrees of freedom for the treatment (dfTreatment) can be calculated as the number of treatment groups minus 1. In this case, there are 3 methodologies (traditional, online, mixed), so dfTreatment = 3 - 1 = 2.

The degrees of freedom for the error (dfError) can be calculated as the total number of observations minus the number of treatment groups. In this case, there are 6 classes with 10 students each, resulting in a total of 60 observations. Since there are 3 treatment groups, dfError = 60 - 3 = 57.

Now, we can calculate the mean sum of squares of treatment (MST) using the formula:

MST = SS for Treatment / df for Treatment

MST = 136 / 2

MST = 68

Therefore, the mean sum of squares of treatment (MST) is 68.

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Answer:

Vertically opposite angles

Step-by-step explanation:

Given

\(\theta = 42^\circ\)

Required

What else can measure \(\theta = 42^\circ\)

The question has missing options. So, I will give a general explanation.

Using the attached image as a point of reference.

Given that:

\(\theta = 42^\circ\)

The value of b is calculated as:

\(b = \theta\)

Because b and \(\theta\) are vertically opposite angles

This gives:

\(b = 42^\circ\)

So, one possible answer to the question is a vertically opposite angle

Answer:

$3.42

Step-by-step explanation:

the cost = 11.4 × 0.30 = $ 3.42