Zoey took 2.5 hours to bike the 60 kilometers from her house to the beach. It took her 3.5 hours to bike the same distance back to her house.

What was the total distance Zoey biked?

Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

We have ,

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

Hence, Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

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complete question:

A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?

b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?

d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?

e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?

f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?

g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?

Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.

Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.

Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.

In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.

Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.

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Answer:

400g

Step-by-step explanation:

Answer:

A. 232 in²

B. 216 in²

Step-by-step explanation:

A. Box A is a cuboid/rectangular prism.

Surface area of box A = 2(LW + LH + WH)

L = 10 in

W = 2 in

H = 8 in

Surface area = 2(10*2 + 10*8 + 2*8)

= 2(20 + 80 + 16) = 2(116)

Surface area = 232 in²

B. Surface area of B = surface area of cube

Surface area of cube = 6s²

s = 6 in

Surface area = 6(6²)

= 6(36)

= 216 in²

The percentage that equivalent to 15/50 is 30%

The given term is 15/50

The percentage is defines as a relative value indicating hundredth parts of any number. It is denoted using the percentage symbol "%". We can also say that percentage is a number or ratio expressed as a fraction of 100.

The given term is 15/50

Here the denominator is 50 and numerator is 15

To find the equivalent percentage, first we have to divide 15 by 50, then multiply the result by 100

15/50 = 0.3

Multiply the result by 100

0.3×100 = 30%

Hence, the percent that equivalent to 15/50 is 30%

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Answer:

30

Step-by-step explanation:

Using the pythagorean theorem a^2+b^2=c^2

Answer:

30

78^2 = 72^2 + x^2 pythagoras theorem

x^2 = 900

x= 30

the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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Answer:

Step-by-step explanation:

formula: SA = 2(wl+hl+hw)

SA = 2(wl+hl+hw)

SA = 2(12x16 + 10x16 + 10x12)

SA = 2(192 + 160 + 120)

SA = 2(472)

SA = 944

ANSWER: 944 square inches

The correct option is (D) A, B, C, E, G, I

What is the cube?

A cube is a three-dimensional solid shape that has six square faces of equal size. It has twelve edges and eight vertices, and all angles between the faces are right angles. The cube is a regular polyhedron, which means that all its faces are congruent and all its edges have the same length.

The net of a cube is the one that has the faces arranged in such a way that it makes a complete cubic structure

A) In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

B)  In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

C) In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

D) In the given figure, the net can be folded into a cube when its faces are folded one over the other. Therefore, it is a cube net.

Hence, The correct option is (D) A, B, C, E, G, I.

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Answer:

22222

Step-by-step explanation:

The quotient in the form q(x)+r(x)/b(x) which is equal to the  x^3 +4x +(24x +1 divided by  x^2 − 6), and the identification q(x) , r(x) , and b(x) are as follow :q(x) =   x^3 +4x

r(x) = 24x +1

b(x) = x^2 − 6

Given details in the following question are as follows:

x^5 − 2x^3 + 1 is divided by x^2 − 6

By using the divisor method :

x^5 − 2x^3 + 1 / x^2 − 6 = x3 +(4x^3+1 is divided by  x^2 − 6)

= x^3 +4x +(24x +1 divided by  x^2 − 6)

where we can see that the q(x) +r(x)/b(x) is equal to the  x^3 +4x +(24x +1 divided by  x^2 − 6)

q(x) =   x^3 +4x

r(x) = 24x +1

b(x) = x^2 − 6

The quotient in the form q(x)+r(x)/b(x) which is equal to the  x^3 +4x +(24x +1 divided by  x^2 − 6)

A divisor divides a number into equal groups. The number that is being divided is called the dividend and the number that divides it is called the divisor.

Divisor Formula

The divisor formula is formed for two situations - with or without a remainder:

If the remainder is 0, then Divisor = Dividend ÷ Quotient.

If the remainder is not 0, then Divisor = (Dividend - Remainder) ÷ Quotient

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Answer:

Step-by-step explanation:

yees

The answers are explained in the solution.

Given are right triangles, we need to find the missing lengths,

Here we will use Pythagoras theorem,

Hypotenuse² = base² + perpendicular²

1) x² = 5²+2²

x = √25+4

x = √29

2) 6² = x²+4²

x = √36-16

x = √26

3) 25² = x² + √24²

x = √625-576

x = √49

x = 7

Only the 3rd is following the rule of Pythagorean triplet.

Part 2 = The Triangle Inequality :-

The Triangle Inequality (theorem) says that in any triangle, the sum of any two sides must be greater than the third side.

a) 2, 4, 8

2+4 = 6 < 8 [not a triangle]

b) 5, 6, 7

5+6 = 11 > 7

6+7 = 13 > 5

7+5 = 12 > 6

Therefore, it is forming a triangle,

7² = 49

5²+6² = 36+25 = 61

∵ 7² < 5²+6²

Therefore, the triangle is an acute triangle.

c) 6, 8, 15

6 + 8 = 14 < 15 [not a triangle]

d) 9, 12, 15

9 + 12 = 21 > 15

12 + 15 = 27 > 9

15 + 9 = 24 > 12

Therefore, it is forming a triangle,

15² = 225

9²+12² = 81 + 144 = 225

∵ 15² = 9²+12²

Therefore, the triangle is a right triangle.

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The 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

A z-score calculates how many standard deviations an observation is from the mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative.

For the 3-year-old boy, the z-score is:

z = (43 - 38) / 2 = 2.5

The z-score for the 10-year-old girl is:

z = (57 - 54.5) / 2.5 = 1

The 3-year-old boy has a higher z-score than the 10-year-old girl, indicating that he is more unusually tall for his age and gender. This is due to his height, which is higher than the average for his age group 38 inches .

Therefore, the 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

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The buying power of a currency is indeed the number of goods and services that can be purchased with a unit of currency. Real earnings, often known as real pay, is the amount of money an individual or institution earns after accounting for inflation, and the further calculation can be defined as follows:

For point a:

\(\bold{CPI=131.9}\)

Using formula:

\(\text{Purchasing Power of dollar}=\frac{\$1}{CPI} \times 100\)

                                            \(\bold{=\frac{\$1}{131.9} \times 100} \\\\\bold{= \$\ 0.00758 \times 100 }\\\\\bold{= \$\ 0.758}\)

Therefore Purchasing Power of the dollar in 2019 compared to 2002 is $0.758

For point b:

\(\bold{2019-Income = 62,900}\\\\\bold{CPI=131.9}\\\\\)

Using formula:

\(\text{Real Income}=\frac{ \text{Income in 2019}}{CPI} \times 100 \\\\\)

                    \(\bold{=\frac{62900}{131.9}\times 100}\\\\\bold{=476.876421 \times 100}\\\\\bold{= 47687.64}\)

   Therefore Real income, relative to 2002 is 47687.64

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The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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Answer:

The  value is \(G = 0.81 \%\)

Step-by-step explanation:

From the question we are told that

    The distance between a and b is  e =   9.0 map unit

    The distance between b and  c is  f = 30 map unit

      The interference in this chromosomal region is L  = 70% =  0.7

Gnerally the  first single cross-over in this chromosomal  region  is mathematically represented as

        \(k = \frac{e}{100} \%\)

=>    \(k = \frac{9}{100} \%\)

=>    \(k = 0.09 \%\)

Gnerally the  first single cross-over in this chromosomal  region is mathematically represented as

        \(J = \frac{f}{100} \%\)

=>    \(J = \frac{30}{100} \%\)

=>    \(J = 0.30 \%\)

Gnerally the expected double cross-over in this chromosomal  region  is mathematically represented as

       \(D = k * J\)

=>   \(D = 0.09 * 0.30\)

=>   \(D = 0.027\)

Generally the coefficient of  coincidence is mathematically represented as

      \(C = 1 -L\)

=>   \(C = 1 -0.7\)

=>   \(C =0.3\)

Generally this coefficient of  coincidence can also be mathematically represented as

     \(C = \frac{G}{D}\)

Here G is  the probability of a double crossover (the observed double cross over)

So

     \(0.3 = \frac{G}{0.027}\)

=>  \(G = 0.0081\)

Converting to percentage

     \(G = 0.0081 * 100\)

     \(G = 0.81 \%\)

Answer:

Area = length x width. Solution : Area = 5 x 10. Area = 50 in². Area & Perimeter of a Rectangle calculator uses length and width of a rectangle, and calculates the perimeter, area and diagonal length of the rectangle. It is an online Geometry tool requires two length sides of a rectangle.

Step-by-step explanation:

Answer:

Sophia's airplane flew 8.6 + 2.2 = 10.8 yards.

Franco threw his airplane 1.5 times as far as Sophia's airplane, which means that Franco's airplane flew 1.5 * 10.8 = 16.2 yards.

Therefore, Franco's paper airplane flew 16.2 yards.

Answer:

Franco went 16.2 yards

Step-by-step explanation:

8.6 + 2.2 = 10.8

10.8 x 1.5 = 16.2

Answer:

The mean prior to the given set of numbers would be \(58.8\).

How So?

1. Knowing this, first order the set from least to greatest.

\(22, 35, 44, 63, 63, 71, 80,92\)

2. Then, add up all the values.

\(22+35+44+63+71+80+92=470\)

3. Finally, divide 470 by 8 (the number of values in the set).

\(470\) ÷ \(8 = 58.75\)

4. Round 58.75, leaving you with the following solution:

\(58.75=58.8\) ←Our Final Solution / Mean

______________________________________________

Hope this helps!

It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

A swimming pool has a volume of 256 yd³.The amount of water in gallons needed to completely fill the pool is 51705.344 gallons.

Given that,

A swimming pool has a volume of 256 yd³.

We have to find The amount of water in gallons needed to completely fill the pool.

What is the conversion factor defined as?

An amount is used as a conversion factor when multiplying or dividing one set of units by another.

The appropriate conversion factor must be applied when converting to an equivalent value.

For instance, 12 inches equals 1 foot when converting between inches and feet.

Regarding the given problem;

The pool has a volume of 256 yd³.

Convert the yd³ volume to gallons.

201.976 gallons are in 1 yd³.

As a result, multiply both sides by 256 to get the total volume, which is 256 yd³.

201.976 yd³ are equal to 256 gallons.

51705.344 gallons are equal to 256 yd³.

Consequently, 51705.344 gallons of water are needed to completely fill the pool.

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Answer:

Known:

• a book have front, back and 200 pages

• front= 0.7 mm

• back= 0.7 mm

• each page= 0,14 mm

ask:

calculate the minimum thickness...?

answer:

a. 200 p × 0,14 = 28 mm

b. front + back = 0.7+0.7= 1.4 mm

Thickness= 28+1,4 = 29,4 mm

I hope this helps

if u have question let me know in comments^_^

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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Answer:

25%

Step-by-step explanation:

Formula to calculate the percent change :-

Change in distance from $12 per hour to $15 per hours = 15-12=3 per hour

Previous value = $12 per hour

Now, the percent change will be :_

Hence,  the percent change for  from $12 per hour to $15 per hour= 25%

(I copied this answer from JeanaShupp from question-11653373 [no links])

Answer: The answer would be 3.91666666667

\(\huge\textsf{Hey there!}\)

\(\mathsf{4 \dfrac{2}{3} - \dfrac{3}{4}}\)

\(\mathsf{= \dfrac{4\times3+2}{3} - \dfrac{3}{4}}\)

\(\mathsf{= \dfrac{12 + 2}{3} - \dfrac{3}{4}}\)

\(\mathsf{= \dfrac{14}{3} - \dfrac{3}{4}}\)

\(\mathsf{= \dfrac{56}{11} - \dfrac{9}{12}}\)

\(\mathsf{= \dfrac{14\times4}{12 - 0}}\)

\(\mathsf{= \dfrac{56 - 9}{12}}\)

\(\mathsf{= \dfrac{47}{12}}\)

\(\mathsf{= 3 \dfrac{11}{12}}\)

\(\huge\textsf{Therefore, your answer should be: }\huge\boxed{\\\mathsf{\dfrac{47}{12} \ or\ 3 \dfrac{11}{12}}}\huge\checkmark\)

\(\huge\textsf{Good luck on your assignment \& enjoy your day!}\)

Answer:

its c or a

Step-by-step explanation:

Combining the homogeneous and the particular solutions, and applying the initial conditions, the solution to the given IVP is:

\(x(t) = -\cos{(2t)} + \frac{1}{2}\sin{(2t)}\)

The IVP is given by:

\(x^{\prime\prime} + 4x = -2\sin{(2t)} + 8\cos{(2t)}\)

First, we find the homogeneous solution, which depends on the roots of the characteristic equation, given by:

\(r^2 + 4 = 0\)

\(r^2 = -4\)

\(r = \pm \sqrt{-4}\)

\(r = \pm 2i\)

Thus:

\(x_h(t) = a\cos{(2t)} + b\sin{(2t)}\)

Then, according to the source(left-side of the equality), the particular solution has the following format:

\(x_p(t) = A\cos{(2t)} + B\sin{(2t)}\)

Applying the derivatives:

\(x_p^{\prime}(t) = -2A\sin{(2t)} + 2B\cos{(2t)}\)

\(x_p^{\prime\prime}(t) = -4A\cos{(2t)} - 4B\sin{(2t)}\)

Replacing into the IVP:

\(x^{\prime\prime} + 4x = -2\sin{(2t)} + 8\cos{(2t)}\)

\(-4A\cos{(2t)} - 4B\sin{(2t)} + 4A\cos{(2t)} + 4B\sin{(2t)} = -2\sin{(2t)} + 8\cos{(2t)}\)

\(0A\cos{(2t)} + 0B\sin{(2t)} = -2\sin{(2t)} + 8\cos{(2t)}\)

Thus, the particular solution is \(x_p(t) = 0\).

The complete solution is:

\(x(t) = x_h(t) + x_p(t)\)

\(x(t) = x_h(t)\)

\(x(t) = A\cos{(2t)} + B\sin{(2t)}\)

Applying the initial conditions:

\(x(0) = -1 \rightarrow A + 0B = -1 \rightarrow A = -1\)

\(x^{\prime}(0) = 1 \rightarrow 2B = 1 \rightarrow B = \frac{1}{2}\)

Thus, the solution is:

\(x(t) = -\cos{(2t)} + \frac{1}{2}\sin{(2t)}\)

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