Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is.



Andre wrote: 228= 2 x 28 = 56



Elena said, “No, exponents mean repeated multiplication. It should be 28 x 28, which works out to be 784.”



Who do you agree with? Could they both be correct or wrong? Explain your reasoning.

The ANOVA will depend on the total sample size.

a. False. The psychologist's reasoning is incorrect, as the critical value for evaluating the ratio of between-group mean squares to within-group mean squares for the ANOVA does not depend solely on the total sample size, but also on the number of groups being compared and the level of significance. Furthermore, a Bonferroni adjusted post-hoc test does not require the p-value for each pairwise comparison to be no more than .0083 to be considered as statistically significant.

b. True. The critical value for evaluating the ratio of between-group mean squares to within-group mean squares for the ANOVA will depend on the total sample size, as well as on the number of groups being compared and the level of significance. Therefore, if the observed means across the three conditions differ entirely due to sampling errors, the critical value for evaluating the ratio of between-group mean squares to within-group mean squares for the ANOVA will depend on the total sample size.

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The torque required to maintain motion of the rotating conical body in the oil film is 0.149 N·m.

The torque required to maintain motion of a rotating conical body in an oil film can be found using the equation T = (2πμωR^3h)/ln(R/h), where T is the torque, μ is the viscosity of the oil, ω is the angular velocity of the cone, R is the radius of the base of the cone, and h is the thickness of the oil film.

First, we need to convert the given values into the appropriate units. The diameter of the base of the cone is 18cm, so the radius is 9cm or 0.09m. The thickness of the oil film is 0.8mm, or 0.0008m. The viscosity of the oil is 4·10^-3 N·S/m^2, and the angular velocity of the cone is 37 rad/s.

Now we can plug these values into the equation:

T = (2π)(4·10^-3 N·S/m^2)(37 rad/s)(0.09m)^3/(0.0008m)

T = 0.149 N·m

Therefore, the torque required to maintain motion of the rotating conical body in the oil film is 0.149 N·m.

To select the indicated motor, we need to find a motor that can provide a torque of at least 0.149 N·m. This will ensure that the motor can maintain the constant motion of the conical body in the oil film.

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The three possible forms of any positive odd integer, as required.

According to the Euclid Division Lemma, for any two positive integers a and b, there exist unique integers q and r such that a = bq + r where 0 ≤ r < b.

We can use this lemma to show that any positive odd integer is of the form 6q + 1, 6q + 3, or 6q + 5 where q is some integer.

Let a be any positive odd integer and let b = 6. By the Euclid Division Lemma, we can write a = 6q + r where 0 ≤ r < 6. Since a is odd, r cannot be an even number. Therefore, r can only take on the values of 1, 3, or 5.

Thus, we can write a as:

a = 6q + 1
a = 6q + 3
a = 6q + 5

These are the three possible forms of any positive odd integer, as required.

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The values of x that satisfy the equation are x = -8 and x = 1.

To find all values of x that satisfy the equation x-(x+5)/(x+8)=(3)/(x+8), we can follow the steps below:

1. Multiply both sides of the equation by (x+8) to eliminate the fractions:
(x+8)(x) - (x+5) = 3

2. Distribute the (x+8) on the left side of the equation:
x^2 + 8x - x - 5 = 3

3. Combine like terms on the left side of the equation:
x^2 + 7x - 5 = 3

4. Subtract 3 from both sides of the equation to get the equation equal to zero:
x^2 + 7x - 8 = 0

5. Factor the left side of the equation:
(x+8)(x-1) = 0

6. Set each factor equal to zero and solve for x:
x+8 = 0 or x-1 = 0
x = -8 or x = 1

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The lengths of a and b are 9.4 and 12 respectively using the Pythagorean theorem.

Pythagoras theorem states for a right angled triangle that, the sum of the squares of base and altitude is the square of the hypotenuse.

Given are two right angled triangles.

For the first right angled triangle, we have to find the length of the hypotenuse.

Using Pythagoras theorem,

a² = 8² + 5²

a² = 64 + 25

a² = 89

a = √89 = 9.43398 ≈ 9.4

For the second right angled triangle, we have to find the length of the altitude.

Using Pythagoras theorem,

17² = b² + 12²

b² = 17² - 12²

b² = 145

b = √145 = 12.04159 ≈ 12

Hence the length of and b are 9.4 and 12 respectively.

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Your question is incomplete. Most probably, the complete question with the image of the triangle is given below.

Work out the lengths of sides a and b.

Give your answers to 1 decimal place.

The correct name for the polynomial -2x^(3)+5x^(4)-3x is a quartic trinomial.

The student made an error when naming the polynomial as a "cubic trinomial". A cubic polynomial is one where the highest degree is 3, and a trinomial is a polynomial with three terms.

While this polynomial does have three terms, its highest degree is actually 4, as seen in the 5x^(4) term.

Therefore, the correct name for this polynomial would be a "quartic trinomial".

To summarize, the error the student made was naming the polynomial as a cubic trinomial instead of a quartic trinomial. The correct name for the polynomial -2x^(3)+5x^(4)-3x is a quartic trinomial.

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Answer:

7:05

Step-by-step explanation:

6:46 + 19 min = 7:05

Two functions as cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9)

We can rewrite the product using a sum or difference of two functions as follows:2 sin (2x/3) sin (5x/6)In order to rewrite the product using a sum or difference of two functions, we can use the following formula:2 sin A sin B = cos (A - B) - cos (A + B)Where A and B are two angles or expressions that contain an angle.So, 2 sin (2x/3) sin (5x/6) can be written as follows:2 sin (2x/3) sin (5x/6) = cos [(5x/6) - (2x/3)] - cos [(5x/6) + (2x/3)]On simplifying the above expression, we get2 sin (2x/3) sin (5x/6) = cos [(5x/6 - 4x/9)] - cos [(5x/6 + 4x/9)]= cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9)Therefore, 2 sin (2x/3) sin (5x/6) can be rewritten using a sum or difference of two functions as cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9).

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Based on the figure, the measure of the angle GPY is 118 degrees.

Alternate angles are a pair of angles that are formed by a transversal intersecting two parallel lines.

When a transversal intersects a parallel line, it creates four angles.

Alternate angles are the pairs of angles that are on opposite sides of the transversal and on opposite sides of the parallel lines.

The key property of alternate angles is that they are congruent, meaning they have the same measure.

Here angle GPY is alternate to angle RPK.

Thus;

8p + 94 = 5p + 103

8p - 5p = 103 - 94

3p = 9

Divide both sides by 3;

p = 3

The measure of angle GPY becomes ;

= 5(3) + 103= 15 + 103= 118 degrees.

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Answer:

x=63

Step-by-step explanation:

------------------

The polynomial can be written as:

f(x) = x³ - 3x² + 4x - 2

We know that the degree is 3, and two of the roots are x = 1 and x = 1 + i.

Then the last root must be 1 - i, so the polynomial is real, then if the leading coeficient of the polynomial is a, we can write:

f(x) = a*(x - 1)*(x - (1+ i))*(x - (1 - i))

Expanding that:

f(x) = a*(x - 1)*[x² -2x + 2]

f(x) = a*(x³ - 2x² + 2x - x² + 2x - 2)

f(x) = a*(x³ - 3x² + 4x - 2)

And we know that f(0) = -2, then we need to solve:

-2 = a*(0³ - 3*0² + 4*0 - 2)

-2 = a*-2

So a = 1

The polynomial is:

f(x) = x³ - 3x² + 4x - 2

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There are a total of 32 possible sequences because there are two alternatives for each stage. Since there are more than seven distinct ways to mount the stairs, the priestess can do so every day for a week.

(a) Every day, the priestess at the temple of Horus must climb a flight of five stairs, which she can do by taking one or two steps at a time. The amount of ways she can up the stairs on any given day can be represented by a binary digit, where 1 denotes a two-step ascent and 0 denotes a one-step ascent. For each of the five steps, for instance, 00101 reflects the order of her one- and two-step climbs.

(b) The same regulations apply. The entire number of potential sequences, using the same binary digit format, is 213 = 8,192. There are therefore more than 365 possible ways to mount the grand staircase, allowing the priest to do so every day for a whole year.

In conclusion, the number of alternative binary sequences, where each digit denotes a one- or two-step climb, may be used to determine the number of ways the priestess can ascend the five-step flight of stairs and the number of ways the priest can ascend the thirteen-step grand staircase.

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When t = 5, the value οf the expοnential functiοn[tex]y = 25(1.2)^t[/tex] is apprοximately 36.7.

An expοnential functiοn is a mathematical functiοn οf the fοrm[tex]f(x) = ab^x[/tex] where a and b are cοnstants, and x is the independent variable. The base b is a pοsitive cοnstant greater than 0 and nοt equal tο 1.

In the expοnential functiοn [tex]y = 25(1.2)^t[/tex], the initial amοunt is 25, which is the value οf the functiοn when t = 0.

The rate οf grοwth is 20%, which is the value οf the base οf the expοnential functiοn minus 1, expressed as a percentage. In this case, the base is 1.2, which is 20% greater than 1.

Tο evaluate the functiοn when t = 5, we substitute t = 5 intο the functiοn and simplify:

[tex]y = 25(1.2)^t[/tex]

[tex]y = 25(1.2)^5[/tex]

[tex]y = 25(1.469)[/tex]

[tex]y = 36.73[/tex]

Rοunding tο the nearest tenth, we get y ≈ 36.7.

Therefοre, when t = 5, the value οf the expοnential functiοn [tex]y = 25(1.2)^t[/tex]is apprοximately 36.7.

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The gross profit margin of the cabinet is 50%.

Gross profit margin is the difference between the revenue and cost of an item divided by the revenue of the same item expressed as a percent.

Revenue refers to the amount a seller sells a particular units of product.

Cost refers to the amount spent by a producer to manufacture a particular unit of a product.

Revenue = $800

Cost = $400

Gross profit margin = (Revenue - Cost) / Revenue × 100

= ($800 - $400) / $800 × 100

= 400/800 × 100

= 50%

Ultimately, 50% is the gross profit margin of the item.

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Using Compound Interest, The largest balance is $7802.55, so the option A will give them the largest balance after 5 years.

Even though there are several ways to define an investor, compound interest helps investors. When banks lend money and utilize the income they earn to finance other loans, for instance, they profit from compound interest. When depositors earn interest on their bank accounts, bonds, or other investments, compound interest benefits them.

here, we have,

It's crucial to remember that although while "compound interest" includes the word "interest," the idea extends beyond the contexts in which the expression is typically employed, such as bank accounts and loans.

We will calculate compound interest in every case:

Using formula

amount = P(1+r/m)^t

option A: balance after 5 years:

7802.55

option B:

balance after 5 years:

7789.84

option C:

balance after 5 years:

7768.85

The largest balance is $7802.55, so the option A will give them the largest balance after 5 years.

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The equation of the line with slope 4 that goes through the point (-3,0) is y = 4x + 12.

The equation of the line passing through the point (-3,0) with a slope of 4 can be found using the point-slope form of a line's equation:

y - y1 = m(x - x1)

where the provided point is (x1, y1), and m is the slope.

When we change the values, we obtain:

y - 0 = 4(x - (-3))

Making the right side simpler:

y = 4x + 12

Hence, y = 4x + 12 is the equation of the line with slope 4 passing through the point (-3,0).

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Answer:

You can not find X unless there is an answer you are looking for (Ex: 2x=4 so x=2) if there is nothing its equal to x can be everything and nothing

Step-by-step explanation:

The result when 2x^(4)-7x^(3)+5x^(2)-5x+5 is divided by x-1 using synthetic division is q(x) = 2x3 - 5x2 + 3x - 2 + (r(x))/(b(x))

To find the result when 2x^(4)-7x^(3)+5x^(2)-5x+5 is divided by x-1 using synthetic division, start by expressing the polynomial as follows:

2x4 - 7x3 + 5x2 - 5x + 5

Then, write the polynomial in the form:

[x4 , x3, x2, x, 1]

Now, draw a box to write the coefficients of the polynomial:

[  2 | -7 |  5 | -5 | 5]

Underneath the coefficients, write the divisor (x-1):

[  2 | -7 |  5 | -5 | 5]

 [ 1 | -1 ]

Multiply the first coefficient by the divisor and write the result on the bottom of the box:

[  2 | -7 |  5 | -5 | 5]
   

     [ 1 | -1 ]

             2
Subtract this result from the second coefficient and write the result:

[  2 | -7 |  5 | -5 | 5]

    [ 1 | -1 ]

             2

             5

Repeat the process for the remaining coefficients and write the final result:

[  2 | -7 |  5 | -5 | 5]
    [ 1 | -1 ]

             2

             5

             3

            -2

The result when 2x^(4)-7x^(3)+5x^(2)-5x+5 is divided by x-1 using synthetic division is q(x) = 2x3 - 5x2 + 3x - 2 + (r(x))/(b(x))

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For the scale factor of a dilation is 8: 7,

''This scale factor results in an enlarged image.''

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

The scale factor of a dilation is 8: 7.

Now, We know that;

When the scale factor is between 0 and 1 the image is a reduction.

And, If the scale factor is greater than 1, the image is an enlargement.

Hence, For the scale factor of a dilation is 8: 7,

''This scale factor results in an enlarged image.''

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The volume of the parallelepiped is 15.

To determine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (3,1,-1), (6,7,1), and (-6,8,9), we need to find the scalar triple product of the three vectors formed by these vertices. The scalar triple product is given by the determinant of the matrix formed by the three vectors:
\[ \begin{vmatrix} 3 & 1 & -1 \\ 6 & 7 & 1 \\ -6 & 8 & 9 \end{vmatrix} \]
Expanding the determinant, we get:
\[ \begin{aligned} \text { Volume } &=3\left( \begin{vmatrix} 7 & 1 \\ 8 & 9 \end{vmatrix} \right)-1\left( \begin{vmatrix} 6 & 1 \\ -6 & 9 \end{vmatrix} \right)-1\left( \begin{vmatrix} 6 & 7 \\ -6 & 8 \end{vmatrix} \right) \\ &=3(63-8)-1(54+6)-1(48+42) \\ &=165-60-90 \\ &=15 \end{aligned} \]
Therefore, the volume of the parallelepiped is 15.

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The composition of the mixture is: 7.323 pounds of the variety priced at $5.77 per pound and 2.677 pounds of the variety priced at $8.87 per pound.

To solve this problem, we can use a system of equations. Let x be the number of pounds of the first variety of birdseed, and y be the number of pounds of the second variety of birdseed.

The first equation will represent the total weight of the mixture:
x + y = 10

The second equation will represent the total cost of the mixture:
5.77x + 8.87y = 6.70(10)

Now we can use the elimination method to solve for one of the variables. Multiply the first equation by -5.77 to eliminate the x variable:
-5.77x - 5.77y = -57.7

Add this equation to the second equation:
3.1y = 8.3

Solve for y:
y = 2.677

Now we can plug this value back into the first equation to solve for x:
x + 2.677 = 10
x = 7.323

So, there are 7.323 pounds of the first variety of birdseed and 2.677 pounds of the second variety of birdseed in the mixture.

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The area of the composite figure given is 39 cm²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure.

Given is a figure with dimensions, 3 cm 4 cm 6 cm 5 cm we need to find the area of the figure,

Since, we can see that the figure is a composite figure, we will first split the figure and find the area of each part separately then, add all of them,

The figure is consisting of two rectangles, with dimensions, 4 cm and 6 cm and the second one with dimensions, 5 cm and 3 cm,

so, the area of the rectangle with dimensions, 4 cm and 6 cm = 4 x 6 = 24 cm²

And,

The area of the rectangle with dimensions, 5 cm and 3 cm = 5 x 3 = 15 cm²

The area of the figure = 15 + 24 = 39 cm²

Hence, the area of the composite figure given is 39 cm²

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The complete question is attached

The simplified expression is a^(-(3)/(8)).

To simplify the expression (a^(-(1)/(2)))/(a^(-(1)/(8))), we need to use the properties of exponents. Specifically, we will use the property that states that when dividing two expressions with the same base, we can subtract the exponents.

So, in this case, we have:

(a^(-(1)/(2)))/(a^(-(1)/(8))) = a^(-(1)/(2) - (-(1)/(8)))

Simplifying the exponent:

= a^(-(4)/(8) + (1)/(8))

= a^(-(3)/(8))

In conclusion, the simplified expression of (a^(-(1)/(2)))/(a^(-(1)/(8))) is a^(-(3)/(8)).

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In the journal entries, Debit: Accounts Receivable Credit: Cash 570

Debit: Sales revenue Credit: Cash 40

May 31, 2022

Cash balance per bank statement 8,120

Add:

Deposit in transit 1,972.55

Bank error—Sheffield 390

2,362.55

10,482.55

Less: Outstanding checks 876.05

Adjusted cash balance per bank 9,606.50

Cash balance per books 8,110.50

Add: Electronic funds transfer received 2,200

10,310.50

Less:

NSF check 570

Error in deposit 40

Error in recording check (1181) 54

Check printing charge 40

704

Adjusted cash balance per book 9,606.50

Journal Entries:

Debit: Cash Credit: Accounts Receivable 2,200

Debit: Accounts Receivable Credit: Cash 570

Debit: Sales revenue Credit: Cash 40

Debit: Accounts payable Credit: Cash 54

Debit: Bank charges expense Credit: Cash 40

Note: Bank charges expense can also be titled as Miscellaneous expense.

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The rate at which the water was drained from the tank is 6 gallons of water per minute.

Given:

Draining Time (minutes)      10         30

Water in Tank (gallons)     450        330

According to the question,

Now, we calculating the rate at which water was drained at a constant rate.

Rate of water drained = [tex]\frac{Rate of change of water in Tank}{Rate of change Draining Time }[/tex]

Rate of water drained = [tex]\frac{450 - 330}{30 - 10} = \frac{120}{20} = 6[/tex]

The gallon is an important unit of measurement that continues to be used widely today. Specifically, it refers to the amount of space occupied by one US liquid gallon of water, which is equivalent to approximately 3.785 liters. The gallon is commonly used to measure liquids such as gasoline, milk, and water.

The term "gallon" has a long history, dating back to medieval England, where it was used to measure wine and beer. Over time, different countries and regions developed their own variations of the gallon, with the US liquid gallon being slightly larger than the UK imperial gallon. In addition to its use in everyday life, gallons are also used in various industries, including agriculture, manufacturing, and transportation.

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Complete Question:

A tank of water was drained at a constant rate. The table shows the number of gallons of water left in the tank after being drained for two amounts of time. Draining Time (minutes) Water in Tank (gallons) 10 450 30 330

Clara should use the 50% off coupon to save the most money on a tent originally priced at $46.


To determine which coupon will save Clara the most money, we need to calculate the final price of the tent with each coupon.

For the $24 off coupon:
Final price = Original price - Coupon amount
Final price = $46 - $24
Final price = $22

For the 50% off coupon:
Final price = Original price - (Original price x Coupon percentage)
Final price = $46 - ($46 x 0.50)
Final price = $46 - $23
Final price = $23

As we can see, the final price of the tent with the $24 off coupon is $22, while the final price with the 50% off coupon is $23. Therefore, Clara should use the $24 off coupon to save the most money.

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Answer:

If 41 grams of sugar is 14% of the normal daily allowance for sugar, we can set up a proportion to solve for the recommended amount:

41 grams / x = 14% / 100%

where x is the recommended amount of sugar.

To solve for x, we can cross-multiply and simplify:

41 / 0.14 = x / 1

x = 292.86

Rounding to the nearest gram, the recommended amount of sugar in a normal diet is approximately 293 grams.

When he rests for a few hours after coming back from ice-store he rests for 2 hours the time the plane takes off is 9:10 pm.

Total distance traveled is 151 miles.

Dave spends 25 + 10 + 55 + 25 = 115 minutes (or 1 hour and 55 minutes) on stops.

Dave rests for 2 hours.

To calculate the time the plane takes off, we need to add up all the time Dave spends on driving, stops, and rests, and then add that time to the time he starts (12:45 pm).

Time to drive from A to C and back to A: 2 * 6 / 60 = 0.2 hours

Time to drive from A to C to D to B to A: (6 + 24 + 24 + 3) / 60 = 0.95 hours

Time to drive from A to C to D to home to E to market to E: (6 + 24 + 24 + 40 + 5 + 5) / 60 = 2.33 hours

Time to rest: 2 hours

Total time spent: 0.2 + 0.95 + 2.33 + 1.92 = 5.4 hours

Time of departure: 12:45 pm + 5.4 hours = 6:25 pm

Adding 45 minutes for the luggage check and boarding, the plane takes off at 6:25 pm + 0.45 hours = 7:10 pm

Adding another 2 hours for the time zone difference, the plane takes off at 7:10 pm + 2 hours = 9:10 pm.

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Answer:

Step-by-step explanation:

No, Selena is incorrect.

answer: Even though there are six

more people than pizzas at the large table and only five more people

than pizzas at the small table, each person at the large table will get

a greater share of pizza than each person at the small table.