In the video game unicorn quest, players earn the same amount of points for completing a level Biannca completed 2 levels and earned 56 points how many points will she have if she completes 4 levels what is the equivalent and unit rate

The coordinates of point P in the UV system are Puv = [-3.54, 0].

To find the coordinates of point P in the UV system, we need to use a rotation matrix. Since the angle between the XY and UV systems is -45 degrees, we need to use a rotation matrix of:

R = [cos(-45) -sin(-45)]

[sin(-45) cos(-45)]

= [0.71 -0.71]

[0.71 0.71]

Multiplying the rotation matrix by the coordinates of Pxy, we get:

Puv = R * Pxy

= [0.71 -0.71] * [-3]

[0.71 0.71] [2]

= [-3.54]

[0]

Therefore, the coordinates of point P in the UV system are Puv = [-3.54, 0].

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The possible amounts of time for which the chemistry club could rent the meeting room are any values of t that are less than 8

To find the possible amounts of time for which the chemistry club can rent the meeting room, we need to set up an inequality. Let t be the number of hours the meeting room is rented. Then, the total cost C (in dollars) can be expressed as:

C = 44 + 9.30t

The chemistry club wants to spend less than $118.40, so we can write:

44 + 9.30t < 118.40

Subtracting 44 from both sides, we get:

9.30t < 74.40

Dividing both sides by 9.30, we get:

t < 8

Therefore, the possible amounts of time for which the chemistry club could rent the meeting room are any values of t that are less than 8. We can write this as an inequality:

t < 8

So, for example, the chemistry club could rent the meeting room for 2 hours (which would cost 44 + 9.30(2) = $62.60), or they could rent it for 6 hours (which would cost 44 + 9.30(6) = $92.40). As long as they rent it for less than 8 hours, they will spend less than $118.40.

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Answer:

  ∠DHI is congruent to ∠EGF

Step-by-step explanation:

You want to identify the angles marked as congruent in the figure.

Angles are marked as congruent by using the same symbol to identify the angle, or by labeling them with the same label (measure). Here a single unadorned arc is used to identify the congruent angles.

An angle can be named by its vertex when that is unambiguous. Here, each of the congruent angles shares its vertex with two other angles, so we must be more specific. We can use the defining rays to name the angles:

  ∠DHI is congruent to ∠EGF

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The dimensions of the rhombus are given below.

Since H is the center of the rhombus, all sides are equal in length.

Let x be the length of each side. Then, we can use the Pythagorean theorem to solve for x:

DE = (EF/2)^2 + (DF/2)^2

DE² = (13/2)^2 + (18/2)^2

DE² = 169/4 + 324/4

DE² = 123.25

DE = sqrt(493)/2

Since DEFG is a rhombus, all sides are equal in length. Thus, we have:

EF = FG = 13

FG = GH = DE = 11.10

GH = HE = EF = 13

Therefore, the dimensions of the rhombus are:

DE = FG = GH = HE = 11.10

EF = DF = 13 and 18, respectively.

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We can say that out of the 80 music lovers surveyed, 28 people like modern songs only.

Let x be the number of people who like both modern and folk songs. Then, the number of people who like modern songs only is given by:

Number of people who like modern songs only = Total number of people who like modern songs - Number of people who like both modern and folk songs

Number of people who like modern songs only = 40 - x

Now, we need to find the value of x. We know that 30% of the 40 people who like modern songs do not like folk songs. This means that:

Number of people who like modern songs and do not like folk songs = 30% of 40

Number of people who like modern songs and do not like folk songs = 0.3 x 40

Number of people who like modern songs and do not like folk songs = 12

We can now use the unitary method to find the value of x. We know that the ratio of people who like both modern and folk songs to the total number of people who like modern songs is 12:40, which can be simplified to 3:10.

Using the unitary method, we can say that:

3/10 = x/40

x = (3/10) x 40

x = 12

Therefore, the number of people who like modern songs only is:

Number of people who like modern songs only = 40 - x

Number of people who like modern songs only = 40 - 12

Number of people who like modern songs only = 28

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The equation of the plane passing P (1,2,1) and orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is -3x-2y-z+8=0.

The equation of the plane will be in the form,

A(x-1)+B(y-2)+C(z-1)=0

It is also given that the plane is perpendicular to give 2 planes.

So, their normal to the plane would be perpendicular to the normal of both planes.

So, the required normal is a cross-product of the normals of planes

x-y-z-10=0 and x-2y+z-2=0

i.e,

-3i-2j-k=0

so, the direction ratios,

A=-3, B=-2, C=-1

putting the direction ratios in the previous equation of the plane,

-3(x-1)-2(y-2)-1(z-1)=0

-3x+3-2y+4-z+1=0

-3x-2y-z+8=0 is the required equation of the plane

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Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0.

Answer:

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type that into translate, okay?

The integral ∫∫R5(x+y)ex2−y2dA, where R is the rectangle enclosed by the lines x−y=0,x−y=3,x+y=0, and x+y=4, can be evaluated by making the change of variables u = x + y and v = x - y, which gives us the Jacobian of the transformation as |J| = 1/2.

To evaluate the integral using the change of variables, we first need to find the bounds of integration for the new variables u and v. Using the equations of the lines that bound the rectangle R, we can rewrite them in terms of u and v as v = ±(3 - u) and v = ±u. These equations represent the four lines that form the new rectangle R' in the uv-plane.

The integral can now be rewritten as ∫∫R'5(u/2)eu2/2dvdu. The limits of integration for v are from -(3 - u) to (3 - u) for the bottom and top sides of the rectangle R', and from -u to u for the left and right sides. The limits of integration for u are from 0 to 4.

After integrating with respect to v, we get ∫(3-u)^u(-3+u)5(u/2)eu2/2dvdu + ∫u^-u^3 5(u/2)eu2/2dvdu. These integrals can be solved by using the substitution method. Finally, we get the answer as 17(e^16 - e^(4/3))/12.

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The relationship between the two confidence intervals B) The width of I81 will be 1/3 the width of I9.

When constructing 99 percent confidence intervals to estimate the difference in means of two populations, r, and w, the width of the confidence intervals depends on the sample size used.

The width of a confidence interval is inversely proportional to the square root of the sample size. Since the sample size of I81 (81) is 9 times larger than the sample size of I9 (9), the width of I81 will be smaller than the width of I9.

To determine the relationship between the widths, take the square root of the ratio of the sample sizes:

√(81/9) = √(9) = 3

Thus, the width of I81 will be 1/3 the width of I9. The width of I81 will be 1/3 the width of I9. This is because when the sample size increases, the confidence interval becomes narrower, providing a more precise estimate of the difference in means between the two populations. Therefore, the correct option is B.

The question was incomplete, Find the full content below:

two 99 percent confidence intervals will be constructed to estimate the difference in means of two populations, r and w. one confidence interval, i9 , will be constructed using samples of size 9 from each of r and w, and the other confidence interval, i81 , will be constructed using samples of size 81 from each of r and w. when all other things remain the same, which of the following describes the relationship between the two confidence intervals?

A) The width of I81 will be 1/9 the width of I9

B) The width of I81 will be 1/3 the width of I9

C) The width of I81 will be equal to the width of I9

D) The width of I81 will be 3 times the width of I9

E) The width of I81 will be 9 times the width of I9

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1. Look for the correlation coefficient (r) in your regression output. This value will range from -1 to 1 and indicates the strength and direction of the linear association between the two variables. A value close to 1 indicates a strong positive association, while a value close to -1 indicates a strong negative association.

2. To quantify the strength of the association, you can calculate the coefficient of determination (R²). This is simply the square of the correlation coefficient (r²). It represents the proportion of the variation in the dependent variable (monthly income) that can be explained by the independent variable (month number).

For example, if you have a correlation coefficient (r) of 0.7, then your R² would be 0.49 (0.7²). This means that 49% of the variation in monthly income can be explained by the month number.

To find the approximate numerical value of the strength of the linear association between monthly income and month number in your specific case, you need to look for the correlation coefficient (r) in your regression output and then calculate the R² value.

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a. To construct the centerline and control limits for the chart, we will use the formula:

Centerline = μ = 150

Upper Control Limit (UCL) = μ + 3σ/√n = 150 + 3(42)/√36 = 174

Lower Control Limit (LCL) = μ - 3σ/√n = 150 - 3(42)/√36 = 126

Therefore, the centerline is 150, the UCL is 174, and the LCL is 126.

b. We can plot these values on the chart by calculating their z-scores using the formula:

z = (x - μ) / (σ / √n)

For example, the z-score for a sample mean of 133 is:

z = (133 - 150) / (42 / √36) = -1.57

Using this formula, we can calculate the z-scores for all five sample means and plot them on the chart.

c. Based on the plotted values, none of them fall outside the control limits. Therefore, it appears that the process is under control. This means that the samples are consistent with the population mean and standard deviation, and there is no evidence of any special causes of variation.

However, it's important to note that this analysis only provides a snapshot of the process at a specific point in time. To monitor the process over the long term, it's important to continue to collect and analyze data to ensure that it remains in control.

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a. The accumulated value at December 7, 2019 is $9,041.80.

b. The present value at January 7, 2018 is $7,262.80.

c. The current value at August 10, 2019 is $7,795.60.

To solve this problem, we need to use the formula for the future value of an annuity:

FV = PMT x [tex]((1 + r)^n - 1) / r[/tex]

where FV is the future value, PMT is the payment per period, r is the interest rate per period, and n is the number of periods.

a. Accumulated values at 7 December 2019

First, we need to calculate the number of months from May 7, 2018 to December 7, 2019, which is 19 months. We can divide this into two periods:

Period 1: May 7, 2018 to December 7, 2018

Number of months: 7

Payment per period: $20

Interest rate per period: 10% / 4 = 2.5% (since it is convertible quarterly)

FV1 = 20 x [tex]((1 + 0.025)^7 - 1) / 0.025[/tex]

= $1,444.16

Period 2: April 7, 2019 to December 7, 2019

Number of months: 8

Payment per period: $890 ($900 - $10)

Interest rate per period: 10% / 4 = 2.5%

FV2 = [tex]890 x ((1 + 0.025)^8 - 1) / 0.025[/tex]

= $7,597.64

Total accumulated value = FV1 + FV2

= $1,444.16 + $7,597.64

= $9,041.80

Therefore, the accumulated value at December 7, 2019 is $9,041.80.

b. Present values at 7 January 2018

To calculate the present value at January 7, 2018, we need to discount the accumulated value to that date. We can use the formula for the present value of a single sum:

PV = [tex]FV / (1 + r)^n[/tex]

where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.

The accumulated value at December 7, 2019 is $9,041.80, which is 23 months from January 7, 2018. The interest rate per period is 10% / 4 = 2.5%.

PV = [tex]9,041.80 / (1 + 0.025)^{23[/tex]

= $7,262.80

Therefore, the present value at January 7, 2018 is $7,262.80.

c. Current values at 10 August 2019

To calculate the current value at August 10, 2019, we need to discount the accumulated value to that date. We can use the same formula as in part (b), but with a different number of periods.

The accumulated value at December 7, 2019 is $9,041.80, which is 16 months from August 10, 2019. The interest rate per period is still 10% / 4 = 2.5%.

PV = [tex]9,041.80 / (1 + 0.025)^{16[/tex]

= $7,795.60

Therefore, the current value at August 10, 2019 is $7,795.60.

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Each small box weighs 0.5 pounds.

Let's assume that the weight of each small box is x pounds.

Then, we can set up two equations based on the information given:

2 + 6x = weight carried by Andy

3x + 3.5 = weight carried by Wes

Since the weight of the small boxes is the same, we can set these two expressions equal to each other:

2 + 6x = 3x + 3.5

Solving for x, we can subtract 2 and 3x from both sides:

3x - 6x = 3.5 - 2

-3x = 1.5

Finally, we can divide both sides by -3 to get x by itself:

x = -1.5/-3

x = 0.5

Therefore, the weight of each small box is 0.5 pounds.

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The measure of angle ABD of the described Isosceles triangles is; 115°

We have,

The parameters are;

Triangle ΔACD is Isosceles triangle

Triangle ΔBCD is Isosceles triangle

m∠BAC = 20°

m∠BDC = 25°

Whereby ΔBCD and ΔACD have their vertex in the same direction, we can have;

AD ≅ AC Given sides legs of triangle ACD

BD ≅  BC Given sides legs of triangle BCD

BA ≅ BA  Reflexive property

Therefore, we can say that;

ΔDAB ≅ ΔCAB  by SSS congruency rule

By the CPCTC (Congruent Parts of Congruent Triangles are Congruent), we can say that;

m∠BAC ≅ m∠BAD

Thus;

m∠BAC ≅ m∠BAD = 20°

Therefore;

m∠BAC + m∠BAD = 20° + 20°

m∠BAC + m∠BAD  = 40°

Thus, m∠DAC = 40°  by the Angle addition postulate

m∠ADC = m∠ACD = (180 - m∠DAC)/2

= (180 - 40)/2 = 70° This is because they are base angles of an isosceles triangle

∴ m∠ADC = m∠ACD = 70°

Similarly;

m∠BDC = 25° = m∠BCD Base angles of isosceles triangle ΔBCD

m∠BCD + m∠DBC + m∠BCD = 180° Sum of the interior angles of a triangle theorem

m∠DBC = 180° - (m∠BCD +  m∠BCD)

= 180° - (25° +  25°)

= 130°

m∠DBC = 130°

m∠ABD ≅ m∠ABC by CPCTC

m∠ABD = m∠ABC

Therefore;

m∠DBC + m∠ABD + m∠ABC = 360° Sum of angles at a point

m∠DBC + 2 × m∠ABD = 360°

130° + (2 × m∠ABD) = 360°

2 × m∠ABD = 360° - 130°

2 × m∠ABD = 230°

m∠ABD = 230°/2

m∠ABD = 115°

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complete question:

Triangles ACD and BCD are isosceles. Angle BAC has a measure of 20 degrees and angles BDC has a measure of 25 degrees. Find the measure of angle ABD

Using the sine rule for the figure, angle D is calculated to be

The size of angle D is calculated using the sine rule which represented by the formula

Sine A / a = Sine B / b = Sine C / c

applying the formula for the problem

Sine F / DE = Sine D / FE

Sine 71 / 70 = Sine D / 54

cross multiplying

Sine D = 54 * Sine 71 / 70

Sine D = 0.7294

D = arc sin 0.7294

D = 46.8 degrees

D = 47 degrees

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Answer:

Step-by-step explanation:

Using the expression 220 - a, The correct answer is 200 bpm, 189 bpm & 172 bpm. We can calculate the maximum heart rate for the given ages as follows:

For a person who is 20 years old:

Maximum heart rate = 220 - 20 = 200 bpm

Answer: 200 bpm

For a person who is 31 years old, the equation for calculating the heart rate

Maximum heart rate = 220 - 31 = 189 bpm

Answer: 189 bpm

For a person who is 48 years old:

Maximum heart rate = 220 - 48 = 172 bpm

Answer: 172 bpm

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Answer:

Please clarify your request.

Step-by-step explanation

We have evaluated the determinant of matrix A using cofactor expansion along the first row and second column and obtained the same result of [tex]$\det(A) = -40$[/tex] and [tex]$\det(A) = -44$[/tex], respectively.

We will expand along the first row:

[tex]$\det(A) = (-3)\begin{vmatrix}5 & 1 \ 0 & 5\end{vmatrix} - 0\begin{vmatrix}2 & 1 \ -1 & 5\end{vmatrix} + 7\begin{vmatrix}2 & 5 \ -1 & 0\end{vmatrix}$[/tex]

Simplifying the determinants:

[tex]\det(A) = (-3)((5)(5) - (1)(0)) - 0((0)(5) - (1)(-1)) + 7((2)(0) - (5)(-1))$$\det(A) = -75 + 0 + 35 = -40[/tex]

We will expand along the second column:

[tex]$\det(A) = -3\begin{vmatrix}1 & -4 \ -3 & 5\end{vmatrix} - 3\begin{vmatrix}1 & -4 \ 1 & 5\end{vmatrix} + 1\begin{vmatrix}3 & 3 \ 1 & -3\end{vmatrix}$[/tex]

Simplifying the determinants:

[tex]\det(A) = -3((1)(5) - (-4)(-3)) - 3((1)(5) - (-4)(1)) + 1((3)(-3) - (3)(1))$$\det(A) = -3(17) - 3(-1) + 1(-12) = -44$[/tex]

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Complete question:

Evaluate the determinant of the matrix A using cofactor expansion along the first row:

A = |-3  0  7|

   | 2  5  1|

   |-1  0  5|

B = |3   3   1|

   |1   0  -4|

   |1  -3   5|

Answer:

Find the Answer in the work.

Step-by-step explanation:

Here are the solutions to your percentage problems:

1.

20% of what number is 5%?

Let's call the number we're looking for "x". We can set up an equation like this:

20% * x = 5%

To solve for x, we can divide both sides by 20% (or 0.2):

x = 5% / 20%

x = 0.25

2.

15% of what number is 21?

Let's call the number we're looking for "x". We can set up an equation like this:

15% * x = 21

To solve for x, we can divide both sides by 15% (or 0.15):

x = 21 / 15%

x = 140

3.

35% of what number is 91?

Let's call the number we're looking for "x". We can set up an equation like this:

35% * x = 91

To solve for x, we can divide both sides by 35% (or 0.35):

x = 91 / 35%

x = 260

4.

50% of what number is 75?

Let's call the number we're looking for "x". We can set up an equation like this:

50% * x = 75

To solve for x, we can divide both sides by 50% (or 0.5):

x = 75 / 50%

x = 150

5.

What number is equal to 65% of 78?

Let's call the number we're looking for "x". We can set up an equation like this:

x = 65% * 78

To solve for x, we can multiply both sides by (or convert) to decimal form:

x = (65 /100) *78

x = (0.65) *78

x =50.7

6.

What number is equal to85% of102?

Let's call the number we're looking for "x". We can set up an equation like this:

x =85% *102

To solve for x, we can multiply both sides by (or convert) to decimal form:

x =(85/100)*102

x =(0.85)*102

x =86.7

7.

What number is equal to200% of30?

Let's call the number we're looking for "x". We can set up an equation like this:

200% *x=30

To solve for x, we can divide both sides by200%(or2):

x=30/200%

x=15

8.

What number is equal to75% of150?

Let's call the number we're looking for "x". We can set up an equation like this:

75% *x=150

To solve for x, we can divide both sides by75%(or0.75):

x=150/75%

x=200

Critical Thinking

At A&B Emporium,50% of the employees take the bus to get to work.Every day100 employees work at Glow Emporium? Show your work.

There are different ways to approach this problem but one possible method is:

•  Calculate how many employees take the bus:

50/100 *100=50 employees take the bus.

•  Calculate how many employees don't take the bus:

100-50=50 employees don't take the bus.

Therefore, at A&B

The cost of one orange is 76 p.

Given that cost of oranges,

The cost of 1 orange =

The first step is to know how many pence makes a pound.

100 pence = 1 pound

The second step is to convert £1 52 p to pence.

1 x 100 + 52 = 152p

The third step is to divide, 152 by 2

152/2 = 74p

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The missing numbers in exponent of 10 in the given expression 0.0000308 = 3 x 10⁻⁵ + 8 x 10⁻⁷ is -5 and -7.

We can write 0.0000308 as 3.08 x 10⁻⁵ by shifting the decimal point 5 places to the right. Therefore, we have

3.08 x 10⁻⁵ = 3 x 10ˣ + 8 x 10ˣ

We can see that the first exponent must be negative because 3.08 x 10⁻⁵ is a very small number. We also know that the exponents must add up to -5. We can try different combinations of exponents to see which ones add up to -5

3 x 10⁻⁶ + 8 x 10⁻⁶ = 0.0000300 (too small)

3 x 10⁻⁵ + 8 x 10⁻⁶ = 0.000038 (too big)

3 x 10⁻⁵ + 8 x 10⁻⁷ = 0.0000308 (correct)

Therefore, the missing exponents are -7 and -5. The answer is

3 x 10⁻⁵ + 8 x 10⁻⁷

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The calculated value of the area of the figure is 464  sq units

From the question, we have the following parameters that can be used in our computation:

Composite figure

The shapes in the composite figure are

This means that

Area = Squares + Rectangles

Using the area formulas on the dimensions of the individual figures, we have

Area = 16 * 16 + 24 * 4 + 4  * (24 - 12) + 8 * 8

Evaluate

Area = 464

Hence, the area of the figure  is 464 sq units

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The equation can be solved by simplifying the logarithmic terms and applying the properties of logarithms. After simplification, we obtain x = 3.

Starting with the given equation, we can simplify the logarithmic terms using the properties of logarithms. Applying the property ln(A) - ln(B) = ln(A/B), we have ln((x + 1)(x - 4)/(x + 1)) = ln(7). Next, using the property ln(A) = ln(B) if and only if A = B,

we can equate the expressions inside the logarithms: (x + 1)(x - 4)/(x + 1) = 7. Canceling out the common factor of (x + 1), we have x - 4 = 7. Solving for x, we find x = 3.

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You use the "truncated" keyword when you know only one end of a range (either the upper or lower end). Truncated searches allow you to find results within a specified range by including an unknown value on one side.

The keyword that you use when you know only one end of a range is called "range." This term is used in various contexts, including mathematics, statistics, and computer programming, where it represents a set of values that fall between two specified limits. For instance, in statistics, a range is a measure of dispersion that reflects the spread of a dataset from its lowest to highest value. If you only know one end of the range, say the upper end, you can estimate the lower end by subtracting the width of the range from the upper limit. Conversely, if you only know the lower end, you can obtain the upper end by adding the range width to the lower limit. In computer programming, range is a function that generates a sequence of integers or floating-point numbers between two given values. The range function is useful when you want to loop through a set of values without having to specify each value individually. For example, if you want to print all even numbers between 0 and 10, you can use the range function with a step of 2 to generate the sequence 0, 2, 4, 6, 8, 10. In conclusion, the keyword "range" is used when you know only one end of a range, and it helps you estimate the other end based on the width of the range. Whether you are dealing with statistical data or programming algorithms, understanding the concept of range is crucial for making accurate calculations and solving problems efficiently.

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Let's say the new crew of painters can paint the small apartment in x hours, and the experienced crew can paint the small apartment in y hours. Let the time taken by the new crew of painters to paint the small apartment be N hours, and the time taken by the experienced crew be E hours.

We are supposed to find the time it takes for both crews to paint the apartment together.

Step 1: Find the work rate of each crew.
The new crew's work rate is 1/N (apartments painted per hour).
The experienced crew's work rate is 1/E (apartments painted per hour).

Step 2: Calculate the combined work rate of both crews.
Combined work rate = New crew's work rate + Experienced crew's work rate
Combined work rate = (1/N) + (1/E)

Step 3: Find the time it takes for both crews to paint the apartment together.
Let T be the time it takes for both crews to paint the apartment together. Their combined work rate can be expressed as the reciprocal of T.

1/T = (1/N) + (1/E)

Step 4: Solve for T.
T = 1 / [(1/N) + (1/E)]

So, it takes T hours to paint the apartment when the two crews work together. Once you know the specific values of N and E, you can plug them into the equation and solve for T to find the solution.

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Rafael could have added up to 3/8 inches of water to the tank for the fish to be healthy.

Rafael starts with a water level of [tex]11\frac{1}{2}[/tex] in.

The water level then decreases by 7/8 in:

[tex]11\frac{1}{2}[/tex]  - 7/8

=23/2-7/8

=92-7/8

=85/8

= [tex]10\frac{5}{8}[/tex] in

To be healthy, the water level needs to be at least 11 in, so Rafael needs to add:

11- [tex]10\frac{5}{8}[/tex] = 3/8 in

Therefore, Rafael could have added up to 3/8 inches of water to the tank for the fish to be healthy.

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To complete the mail, Donald needs to stamp 48 pieces of mail if the total mails are 145 and he has done 97 pieces.

To calculate the number of mail to be stamped, one has to subtract the already stamped mails from the total number of mails.

Total number of mails = 145 mails

Number of mails already stamped = 97 mails

Mails left to be stamped = total number of mails -  mails that are already stamped

= 145 - 97

= 48 mails

Thus, Donald has to stamp 48 more mails in order to total mail of 145

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Therefore, a complete graph is bipartite if and only if n is even.

A graph is bipartite if and only if it does not contain an odd cycle. In a complete graph, every cycle has an odd length, except for the cycle of length 1. Therefore, a complete graph is bipartite if and only if it has an independent set of size n/2.

If n is even, we can divide the vertices into two sets of size n/2, with no edges between vertices in the same set. This gives us an independent set of size n/2, and therefore the graph is bipartite.

If n is odd, we cannot divide the vertices into two sets of equal size. Therefore, the largest independent set has size (n-1)/2. Since this is strictly less than n/2, the graph is not bipartite.

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The probability of drawing a red marble in the bag of marbles is 2/9

From the question, we have the following parameters that can be used in our computations

Red = 4

Green = 7

Blue = 2

Purple = 5

This means that

Marbles = 4 + 7 + 2 + 5

Marbles = 18

Also, we have

Red = 4

Selecting the first marble we have

P(Red) = 4/18

Simplify

P(Red) = 2/9

Hence, the probability is 2/9

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