Kevin can clean a large aquarium tank in about 7 hours. When Kevin and Lara work together, they can


clean the tank in 3 hours. Enter and solve a rational equation to determine how long, to the nearest tenth


of an hour, it would take Lara to clean the tank if she works by herself? Complete the explanation as to


whether the answer is reasonable.


It would take Lara about 7hours to clean the tank by herself. The answer is reasonable because it


is (select) and, when substituted back into the equation, the equation is true.

Answer:

\(12+3\sqrt{5}\)

Step-by-step explanation:

\((\frac{33}{4-\sqrt{5}})(\frac{4+\sqrt{5}}{4+\sqrt{5}})=\frac{132+33\sqrt{5}}{16-5}=\frac{11(12+3\sqrt{5})}{11}=12+3\sqrt{5}\)

Answer:

B & C

Step-by-step explanation:

A) does not even have an x, but prentening the z i san x?, 9*4= 36. 36+22= 14.

B) 7*4= 28, 28-1=27

C) 8*4= 32, 46-32= 1

Answer:

B,C

Step-by-step explanation:

7(4)-1=27

28-1=27

46-8(4)=14

46-32=14

Answer:

9/50

Step-by-step explanation:

Answer:

GO WITH THE GUT. ITS D

Step-by-step explanation:

Answer:

I think 15

Step-by-step explanation:

15+16+17+18+19+20=105

if it was 14 it would equal to 99

Answer:

Step-by-step explanation:

Answer:

a=1

Step-by-step explanation:

Hi there!

We are given the proportion \(\frac{1}{a+3} =\frac{4}{16}\), and we want to solve it for the variable, a

Before we start, we can simplify 4/16 to 1/4, since 4 is the GCF of the numerator and denominator of that fraction. Simplifying the fraction will make the computation easier, as the numbers are smaller.

Therefore, the proportion will now be:

\(\frac{1}{a+3} =\frac{1}{4}\)

Because this is a proportion, we can cross multiply in order to solve for a; to do that, multiply a+3 by the expression that is on the top right (in this case, 1). Also multiply 4 by the expression that is on the top left (in this case, 1). Then, set them equal to each other, since it is still an equation :)

1(a+3)=4(1)

Multiply

a+3=4

Subtract 3 from both sides

a=1

Hope this helps!

According to the solving the length of the road in real life will be = 8 km.

The relationship (or ratio) between the distance on a map and the comparable distance on the ground is referred to as map scale. For example, on a 1:100000 scale map, 1cm on the map represents 1km on the ground.

You've probably seen maps with just a scale bar representing equal sections, each marked with kilometres or miles. These divisions have been used to calculate ground distance on a map. In other words, a map scale specifies the relationship between the map and indeed the entire or a portion of the earth's surface depicted on it.

scale on a map is 1 : 200,000.

= 1 : (200,000/(100*1000))

= 1:2

= 2km

So,

length of a road on the map is 4 cm.

= 4*2

= 8km

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Answer:

The inequality x + 3 < 12 can be used to determine the number of miles left to jog.

Step-by-step explanation:

It is given that:

Number of miles Beth has already jogged = 3 miles

She plans to join less than 12 miles.

Let,

x represent the number of miles left to jog.

x + 3 < 12

x + 3 - 3 < 12 - 3

x  < 9

Therefore,

The inequality x + 3 < 12 can be used to determine the number of miles left to jog.

Answer: 10

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

9929x9829-kk>/1.79<efk+11x3.145936982

Step-by-step explanation:

its not refghj

Answer:

  see below

Step-by-step explanation:

The "arithmetic progression rule" requires the numbers on either side of an edge make an arithmetic progression with the numbers at either end.

If we label the variables 'a', 'b', 'c' clockwise from top, then the rule means we have ...

  2a -b +2c = 1

  2a +2b -c = 7

  -a +2b +2c = -2

Solution

Adding twice the second equation to each of the other two gives ...

  2(2a +2b -c) +(2a -b +2c) = 2(7) +(1)

  6a +3b = 15 . . . . [eq4]

and

  2(2a +2b -c) +(-a +2b +2c) = 2(7) +(-2)

  3a +6b = 12 . . . . [eq5]

Subtracting [eq5] from twice [eq4] we have ...

  2(6a +3b) -(3a +6b) = 2(15) -(12)

  9a = 18

  a = 2

From [eq4], we can find b:

  b = (15 -6a)/3 = 5 -2a = 5 -2(2) = 1

From [eq2] we can find c:

  c = 2(a+b) -7 = 2(2+1) -7 = -1

These values are shown on the diagram below.

To calculate the percent of variance that age at first birth shares with highest grade completed, we can use the coefficient of determination (R-squared). R-squared measures the proportion of the total variance in one variable that can be explained by another variable.

First, we need to perform a regression analysis to obtain the R-squared value. This can be done using statistical software or tools like Excel or SPSS.

Once you have the R-squared value, you can interpret it as the percentage of variance that age at first birth shares with highest grade completed. For example, if the R-squared value is 0.5, it means that 50% of the variance in age at first birth can be explained by the highest grade completed.

In conclusion, the R-squared value obtained from the regression analysis will provide the percentage of variance that age at first birth shares with highest grade completed. The higher the R-squared value, the stronger the relationship between the two variables.

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Answer:

4y - 6 =2y + 8

4y - 2y = 8 + 6

2y = 14

y = 14 / 2

y = 7

The dimensions that maximize the cost of producing the can are  \(\[ r = \left(\frac{0.5V}{1.3 \pi}\right)^{1/4} \]\), \(\[ h = \frac{2.6 \pi^{3/2}}{(0.5V)^{1/2}} \]\). These dimensions will yield the maximum cost for producing the can, given the fixed volume V.

To find the dimensions that will maximize the cost of producing the can, we need to optimize the cost function with respect to the dimensions.

Let's assume the can has a height \(\( h \)\) and a radius \(\( r \).\) The volume of the can is given as \(\( V = 625 \, \text{cm}^3 \).\)

The cost of the top, denoted by \(\( C_{\text{top}} \)\), is given by the area of the top multiplied by the cost per unit area, which is 0.4 ¢/cm \(\(^2\).\) Since the top is a circle, its area can be calculated using the formula for the area of a circle: \(\( A_{\text{top}} = \pi r^2 \).\)

The cost of the bottom and sides, denoted by \(\( C_{\text{bottom+sides}} \),\) is given by the area of the bottom and sides multiplied by the cost per unit area, which is 0.25 ¢/cm\(\(^2\).\) The area of the bottom is also a circle with radius \(\( r \),\) so its area is \(\( A_{\text{bottom}} = \pi r^2 \).\) The area of the sides is given by the lateral surface area of a cylinder, which is \(\( A_{\text{sides}} = 2 \pi rh \).\)

The total cost \(\( C \)\) is the sum of the cost of the top and the cost of the bottom and sides:

\(\[ C = C_{\text{top}} + C_{\text{bottom+sides}} = 0.4 \cdot A_{\text{top}} + 0.25 \cdot (A_{\text{bottom}} + A_{\text{sides}}) \]\)

Substituting the expressions for the areas, we have:

\(\[ C = 0.4 \cdot \pi r^2 + 0.25 \cdot (\pi r^2 + 2 \pi rh) \]\)

To maximize the cost, we need to find the values of \(\( r \)\) and \(\( h \)\) that maximize \(\( C \).\)

Since the volume of the can is given as \(\( V = 625 \, \text{cm}^3 \), we can express \( h \) in terms of \( r \) as \( h = \frac{V}{\pi r^2} \).\)

Substituting this expression for \(\( h \)\) in the cost equation, we get:

\(\[ C = 0.4 \cdot \pi r^2 + 0.25 \cdot (\pi r^2 + 2 \pi r \cdot \frac{V}{\pi r^2}) \]\)

Simplifying further:

\(\[ C = 0.4 \cdot \pi r^2 + 0.25 \cdot (\pi r^2 + 2V/r) \]\)

Let's assume the can has a radius r and height h. The volume V of a cylinder is given by:

\(\[ V = \pi r^2 h \]\)

We can express the height h in terms of the volume V as:

\(\[ h = \frac{V}{\pi r^2} \]\)

Now, let's consider the cost function C, which consists of the cost of the material for the top and bottom of the can \((0.4πr^2)\) and the cost of the material for the cylindrical side of the can \((0.25πr^2 + 2V/r):\)

\(\[ C = 0.4 \pi r^2 + 0.25 \left(\pi r^2 + \frac{2V}{r}\right) \]\)

To find the dimensions that maximize the cost, we need to find critical points where the partial derivatives of C with respect to r and h are both zero.

Taking the partial derivative of C with respect to r:

\(\[ \frac{\partial C}{\partial r} = 0.4 \cdot 2 \pi r + 0.25 \cdot (2 \pi r - \frac{2V}{r^2}) \]\)

Simplifying:

\(\[ \frac{\partial C}{\partial r} = 0.8 \pi r + 0.5 \pi r - \frac{0.5V}{r^2} \]\)

\(\[ \frac{\partial C}{\partial r} = 1.3 \pi r - \frac{0.5V}{r^2} \]\)

Setting the partial derivative equal to zero and solving for r:

\(\[ 1.3 \pi r - \frac{0.5V}{r^2} = 0 \]\)

\(\[ 1.3 \pi r^3 = \frac{0.5V}{r} \]\)

\(\[ r^4 = \frac{0.5V}{1.3 \pi} \]\)

\(\[ r = \left(\frac{0.5V}{1.3 \pi}\right)^{1/4} \]\)

Substituting this value of r back into the equation for h:

\(\[ h = \frac{V}{\pi \left(\left(\frac{0.5V}{1.3 \pi}\right)^{1/4}\right)^2} \]\)

Simplifying:

\(\[ h = \frac{V}{\pi \left(\frac{0.5V}{1.3 \pi}\right)^{1/2}} \]\)

\(\[ h = \frac{2.6 \pi^{3/2}}{(0.5V)^{1/2}} \]\)

Therefore, the dimensions that maximize the cost of producing the can are:

\(\[ r = \left(\frac{0.5V}{1.3 \pi}\right)^{1/4} \]\)

\(\[ h = \frac{2.6 \pi^{3/2}}{(0.5V)^{1/2}} \]\)

These dimensions will yield the maximum cost for producing the can, given the fixed volume V.

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The value of a and b n the expression is

a = 6 and b = 5

Simplifying the expression:

((3n + 4)² - (3n + 2)²) / (10n + 10)

simplifying the numerator

(3n + 4)² = 9n² + 24n + 16

(3n + 2)² = 9n² + 12n + 4.

subtraction gives

(9n² + 24n + 16) - (9n² + 12n + 4.) = 12n + 12 = 12(n + 1)

simplifying the denominator

(10n + 10) = 10(n + 1)

taking back to the equation

= [12(n + 1)] / 10(n+1)

= (12) / 10

=6/5

Therefore, a = 6 and b = 5

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Answer:

i think 90

Step-by-step explanation:

No of boys = 40%

let total no. of children be as "x"

now, 40% of x= 2x/5.

and since boys differ girls by 18.

no. of girl would be x-2x/5=3x/5.

now No. of boys= 2x/5

and no. of girls= 3x/5

no. of total children would then be as = 3x/5 - 2x/5= 18

The value of "X" would then be as = 90

To find no. of boys we would do 2x/5 X 90= 36

and no. of girls = 3x/5 X 90= 54.

to prove my answer 54-36= 18

Hope it helps C":

Suppose there are X children at the childcare.

Thus :

boys + girls = X

__________________________

40% of the children are boys .

Thus :

There are 40/100 × X boys .

So : boys = 0.4X (( Ω ))

__________________________

There are 18 more girls than boys

Thus :

girls - boys = 18

girls - ( 40/100 X ) = 18

girls - 0.4X = 18

Add sides 0.4X

girls - 0.4X + 0.4X = 18 + 0.4X

girls = 18 + 0.4X (( μ ))

__________________________

Now It's time to put (( μ ))

and (( Ω )) in the above equation.

boys + girls = X

0.4X + 18 + 0.4X = X

0.8X + 18 = X

Subtract sides 0.8X

- 0.8X + 0.8X + 18 = 1X - 0.8X

18 = 0.2X

0.2X = 18

Divided sides by 0.2 (( 2/10 ))

2/10 ÷ 2/10 × X = 18 ÷ 2/10

X = 18 × 10/2

X = 18 × 5

X = 90

Thus there are 90 children at the childcare.

Done.....♥️♥️♥️♥️♥️

The volume of the smallest container that holds 370 grams of oil is

400 cm³.

Density is mass per unit volume.

We have,

The density of sunflower oil = 0.925

Mass of sunflower oil = 370 grams

Now,

Density = Mass / Volume

So,

The volume of the smallest container that holds 379 grams of oil.

= Mass of the sunflower oil / Density of the sunflower oil

= 370 / 0.925

= 400 cm³

Thus,

The volume of the container that holds 379 grams of oil is 400 cm³.

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The probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

To find the probability that a random student will be taking both Algebra 2 and Chemistry, we need to use the concept of conditional probability.

Let's denote the event of taking Algebra 2 as A and the event of taking Chemistry as C. We are given that P(A) = 0.08 (8% probability of taking Algebra 2) and P(C|A) = 0.17 (17% probability of taking Chemistry given that the student is taking Algebra 2).

The probability of taking both Algebra 2 and Chemistry can be calculated using the formula for conditional probability:

P(A and C) = P(C|A) * P(A)

Substituting the given values:

P(A and C) = 0.17 * 0.08

P(A and C) = 0.0136

Therefore, the probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

It is important to note that the probability of taking both Algebra 2 and Chemistry is determined by the intersection of the two events, which means students who are taking both courses. In this case, the probability is relatively low, as it depends on the individual probabilities of each course and the conditional probability given that a student is taking Algebra 2.

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Answer:

1 foot and 4 inches.

Step-by-step explanation:

1 feet = 12 inches

3 feet = 12*3 = 36 inches

Then:

3 feet and 2 inches = 36 + 2 = 38 inches

if the chair measured 20 inches:

36 - 20 = 16 inches

16 inches = 12inches + 4 inches

= 1 foot and 4 inches

Answer:

The system of equations =

25 + 0.05x = 12 + 0.09x

The number of stickers where the cost of both printers to be equal is 325 stickers

Step-by-step explanation:

Let the number of stickers = x

Printer 1

Pop Art Printing would charge a $25 setup fee and $0.05 per sticker.

$25 + $0.05× x

25 + 0.05x

Printer 2

Sticky Slogans would charge a $12 setup fee and $0.09 per sticker.

$12 + $0.09 × x

12 + 0.09x

We equate both equations together

The system of equations =

25 + 0.05x = 12 + 0.09x

Collect like terms

25 - 12 = 0.09x - 0.05x

13 = 0.04x

x = 13/0.04

x = 325 stickers

Therefore, the number of stickers where the cost of both printers to be equal is 325 stickers

The integral Ex2 + y2 dV, where E is the area within the cylinder x2 + y2 = 25 and between the planes z = 1 and z = 4, may be evaluated using cylindrical coordinates. The integral may be assessed as 5(2)(3) = 30 by rewriting it as 0 5 0 2 1 4 E d d dz.

Cylindrical coordinates can be used to evaluate integrals such as the one given. In cylindrical coordinates. The integral can then be written as ∫∫∫ E√x^2 + y^2 dV, where E is the region inside the cylinder \(x^2 + y^2 = 25\) and between the planes z = 1 and z = 4.Using the properties of cylindrical coordinates, the integral can be rewritten as ∫ 0 5 ∫ 0 2π ∫ 1 4 Eρ dρ dθ dz. This can be evaluated using the triple integral ∫ 0 5 ∫ 0 2π ∫ 1 4 ρ dρ dθ dz. The integral can then be evaluated as follows:

= 5(2π)(3)

= 30π

Therefore, the integral ∫∫∫ E√\(x^2 + y^2\) dV can be evaluated as 30π.

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The given task is to sort a list of 3-D points based on a given sorting order string using Python's lambda function and sorted function. The sorting order is specified as a string of any combination of 'x', 'y', and 'z', where 'x' represents the primary sorting key, 'y' represents the secondary sorting key, and 'z' represents the last priority.

In Python, we can use a lambda function to define a custom key for sorting using the `sorted()` function. We can create a tuple of the `x`, `y`, and `z` coordinates of each point and pass it as the key to the `sorted()` function. We can use the `index()` method to get the index of the corresponding letter in the sorting order string.Here's an example of the two-line solution to sort the given list of points based on the sorting order string:

```python

sorted_points = sorted(points, key=lambda p: (p[order.index('x')], p[order.index('y')], p[order.index('z')]))

print(sorted_points)

```This will print the sorted list of 3-D points based on the given sorting order string.

In summary, we can use Python's lambda function and sorted function to sort a list of 3-D points based on a given sorting order string. The lambda function creates a tuple of the `x`, `y`, and `z` coordinates for each point based on the sorting order string, and the sorted function sorts the list based on this tuple. The `index()` method is used to get the index of the corresponding letter in the sorting order string.

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The minimum possible parameter of the rectangle is 34 units.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 60 sq. units.

Area of rectangle = Length × Width = L × W = 60

We are looking for the minimum perimeter of the rectangle. Perimeter of rectangle = 2(L + W)

To find the minimum perimeter, we need to find the minimum values of L and W that satisfy the condition that the area is 60.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

If we choose L = 1 and W = 60, then the area is 1 × 60 = 60.

If we choose L = 2 and W = 30, then the area is 2 × 30 = 60.

If we choose L = 3 and W = 20, then the area is 3 × 20 = 60.

If we choose L = 4 and W = 15, then the area is 4 × 15 = 60.

If we choose L = 5 and W = 12, then the area is 5 × 12 = 60.

If we choose L = 6 and W = 10, then the area is 6 × 10 = 60.

The minimum perimeter occurs when L and W are the closest in value, which is achieved when L = 5 and W = 12. Thus, the minimum perimeter of the rectangle is:

Perimeter = 2(L + W) = 2(5 + 12) = 34

Therefore, the minimum possible parameter of the rectangle is 34 units.

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Answer:

y = x + 8

Step-by-step explanation:

For 8cm of thread, 1cm of the bracelet may be produced. therefore being y(thread) = x(bracelet) with the addition of 8 (+8). Hope this helps!

The solution to the given differential equation is \(y(x) = -x^4/25 + x^2/15 - (3/25)e^(-3x) + (1/2)x^4cos(x) + (1/2)x^2sin(x) + C1e^(-3x) + C2\), where C1 and C2 are arbitrary constants.

To solve the given differential equation using the method of undetermined coefficients, we assume a particular solution of the form \(y_p = A(x^4 + Bx^2e^(-3x) + Csin(x))\), where A, B, and C are undetermined coefficients.

Step 1:

Differentiating y_p with respect to x, we obtain \(y_p' = 4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x).\)

Taking the second derivative, we have \(y_p" = 12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x).\)

Step 2:

Substituting y_p, y_p', and y_p" into the given differential equation, we get:

\((12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x)) + 5(4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x)) = 2x^4 + x^2e^(-3x) + sin(x).\)

Simplifying the equation and grouping the like terms, we have:

\((12A + 20Ax^3) + (-6B + 10Bx)e^(-3x) + (-15Bx^2 + 9Bx^3) + (12A + 10C)cos(x) + (-C + 2Bx)sin(x) = 2x^4 + x^2e^(-3x) + sin(x).\)

Comparing the coefficients of the terms on both sides, we can determine the values of A, B, and C. Equating the coefficients of each term, we obtain:

\(12A + 20Ax^3 = 2x^4,\)

\(-6B + 10Bx = x^2e^(-3x),\)

\(-15Bx^2 + 9Bx^3 = 0,\)

12A + 10C = 0,

-C + 2Bx = sin(x).

Solving these equations, we find A = -1/25, B = 1/15, and C = 0.

Therefore, the particular solution is \(y_p = (-1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

To obtain the general solution, we add the particular solution y_p to the complementary function y_c, where y_c is the solution of the homogeneous equation y" + 5y' = 0. The general solution is given by y(x) = y_c + y_p.

The complementary function can be found by solving the homogeneous equation:

y" + 5y' = 0.

The characteristic equation associated with the homogeneous equation is r^2 + 5r = 0. Solving this quadratic equation

, we find two distinct roots: r = 0 and r = -5.

Therefore, the complementary function is \(y_c = C1e^(-5x) + C2\), where C1 and C2 are arbitrary constants.

Finally, the general solution to the given differential equation is:

\(y(x) = C1e^(-5x) + C2 - (1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

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The slope of the line containing the points ( 3, 4 ) and ( 3, - 6 ) is -8.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Its slope would be:

\(m = \dfrac{y-q}{x-p}\)

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

Given;

The two points ( 3, 4 ) and ( 3, - 6 ).

Now, to find the slope

m=-6-4/4-3

m=-8/1

m=-8

Therefore, the slope will be -8.

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Answer: 9/1

Step-by-step explanation: We can write a ratio using the word "to", using a colon, or using a fraction bar.

The problem asks us to compare the number of

adult tickets to the number of child tickets.

We know that there are 45 adult tickets

and 5 child tickets so we have 45/5.

However, 45/5 is not in lowest terms so we divide

the numerator and denominator by 5 to get 9/1.

So the ratio of adult tickets to child tickets is 9/1.

Answer:

Nearest $1: $34

Nearest $5: $35

Nearest $10: $30

Answer:

rounded to the nearest one is $40

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

3+(-3) is the same as 3-3 which =0