Reduce 22/154
to its lowest form.

The Filling time is After 25 minutes, both Aquariums will contain same amount of water.

you've fully prepared the aquarium, all you need to do is follow these quick and easy steps and safely fill your aquarium with water.

Calculate the Filling Time of the aquarium Explanation

Given,

Water in Aquarium A = 4.6 gallons

Water in Aquarium B = 54.6 gallons

Filling rate = 1.2 gallons per minute.

Draining rate = 0.8 gallons per minute.

Let,

x represents the minutes.

A(x) = 4.6 + 1.2x

(Because Luis is adding water in the tank.)

B(x) = 54.6 - 0.8x

(Isacc is draining water from the tank.)

For same amount of water;

A(x) = B(x)

4.6+1.2x=54.6-0.8x

1.2x+0.8x=54.6-4.6

2x=50

Dividing both sides by 2

2x/2=50/2

x=25

Therefore, After 25 minutes, both Aquariums will contain same amount of water.

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The evaluation of the expression a + 4 when a = 7 is 11

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

Expression: a + 4

Value a = 7

Substitute the known values in the above equation, so, we have the following representation

a + 4 = 7 + 4

Evaluate the like terms in the equation

So, we have the following representation

a + 4 = 11

Using the above as a guide, we have the following:

The solution is 11

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a. The exponential function that is good model for the country population is:

Pₙ = 8100000(1.02)ⁿ ,

b. It will take 5.27 years to reach 9 million.

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Exponential Function Formula

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent.

a. Given,  initial population P₀ = 8100000, Rate of increase R = 2%.

If a constant rate of growth be R% per annum,

then function for population after n years

Pₙ = P₀ x (1+R/100)ⁿ

Population Pₙ = 8100000 × (1+2/100)ⁿ

Pₙ = 8100000(1.02)ⁿ

b. Let after x years population will be 9 million.

then,

9000000 = 8100000 (1 + 2/100)ˣ

(1 + 2/100)ˣ = 9000000/8100000

(1.02)ˣ = 90/81

(1.02)ˣ = 1.11

Taking log on both sides

ln (1.02)ˣ = ln (1.11)

ln(a)ⁿ = n ln(a)

x ln(1.02) = ln (1.11)

x = ln(1.11)/ln(1.02)

x = 5.27 years

Hence, the population will reach 9 million in 5.27 years.

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On solving the provided question, we can say that - the each angle of pentagon is x = 108

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

since all sum of pentagon is 540

so, 5x = 540

x = 108

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Answer:

Blue:  y = x²

Red:  y = -x² + 18

Step-by-step explanation:

The blue parabola opens upwards, therefore the term in x² is positive.

The red parabola opens downwards, therefore the term in x² is negative.

The x-value of the vertices of both parabolas is x = 0.

Therefore, the equations of both parabolas will not have a term in x.

The y-intercept of the blue parabola is also the y-value its vertex: y = 0.

The y-intercept of the red parabola is also the y-value its vertex: y = 18.

Therefore, the equation for each parabola is:

To check, substitute x = ±3 into both equations:

Blue

[tex]x=3 \implies y=(3)^2=9[/tex]

[tex]x=-3 \implies y=(-3)^2=9[/tex]

Red

[tex]x=3 \implies y=-(3)^2+18=9[/tex]

[tex]x=-3 \implies y=-(-3)^2+18=9[/tex]

Answer:

y = x2

y = –x2 +18

Step-by-step explanation:

I got it right on the test.

Answer: x = 10

Step-by-step explanation:

1. To find x, you need x to be by itself and the only way for it be like that in this situation is by dividing both sides by 7.

2.  7 divided by 7 cancels out and 70 divided by 7 = 10. This means x = 10.

Answer:

10

Step-by-step explanation:

since we have 7x=70

the multiply goes and becomes divide we get 70/7

and by dividing it we get the ans 10

I don't see the image. Can you send it in the message.

Surface Area : Volume = 6 : s

A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.

Surface Area of a Cube = 6a² in a square units

Volume of cube = a³ cubic units

where a is the side length of the cube.

Given length of the cube = s

Surface Area of cube A = 6s²

Volume of cube V = s³

Ratio between Surface Area and volume:

Surface Area / Volume = 6s² / s³

Surface Area / Volume = 6 / s

Surface Area : Volume = 6 : s

Hence the ratio between Surface area and volume of cube is 6 : s.

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Answer:

2x + 1 = 29

Step-by-step explanation:

There are a lot of answers.

2x + 1 = 29

2x + 1 = 29  Subtract 1 from both sides

2x = 28  Divide both sides by s

x = 14

Start off knowing that x will be 14, then multiply 14 by some number and then add or subtract some number from that and put that on the other side of the equal sign.

x = 14

14 x 2 = 28 and then add 1 to that to get 29

2x + 1 = 29

Answer: Do you want x=14 or for it to equal 14, because I have it both ways. For x=14, an acceptable two step equation would be 2x-5=23. If you want it to equal 14, then you can write 5x-1=14

Step-by-step explanation:

For x=14:

2x-5=23

Add 5 on both sides

2x=28

x=14

For the equation to equal 14:

5x-1=14

Add one on both sides

5x=15

x=3

The given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

here,
Given expression,
an=19-7(n-1)

The above-given expression is an explicit formula for the arithmetic progression,

Comparing the given expression with general expression an = a + d[n-1]

From the above comparison, we
first term,a = 19 and
the common difference, d = -7

Thus, the given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.

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To determine whether the point [tex](1,2)[/tex] is a solution of inequality  [tex]3x - 2y - 6 > 0[/tex],  we substitute the point in the inequality and if the result is True, then it will be the solution .

What is an Inequality ?

The Inequality is defined as a relationship between two expressions or values that are not equal to each other .

The inequality in the question is given as : [tex]3x - 2y - 6 > 0[/tex] ;

the point is ⇒ [tex](1,2)[/tex] ,

to check the solution , we substitute the values in the inequality as [tex]x=1[/tex]and [tex]y=2[/tex] ;

we get , [tex]3(1) -2(2) - 6 > 0[/tex]

= [tex]3-4-6 > 0[/tex]

= [tex]3-10 > 0[/tex]

= [tex]-7 > 0[/tex],

But we know that , [tex]-7 < 0[/tex] , So , the given point is not the solution of the given inequality .

The given question is incomplete , the complete question is

How do you determine if the given point (1,2)  is a solution of each linear inequality 3x - 2y - 6 > 0  ?

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All the steps of the solution are written above. Then all the options are correct. And the solution is - 14.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

2(3y + 4) − 3 (y − 2) = 2⁢y

Simplify the equation, then we have

2(3y + 4) − 3 (y − 2) = 2⁢y

6y + 8 − 3y + 6 = 2y

3y + 14 = 2y

14 = 2y - 3y

14 = - y

y = - 14

All the steps of the solution are written above. Then all the options are correct. And the solution is - 14.

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If you know two angles and one side of a triangle, you can use the Law of Cosines to find the length of the other two sides.

The Law of Cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite to those sides, the following formula holds:

c² = a² + b² - 2ab cos(C)

Where C is the angle opposite to side c.

So, if you know the measures of two angles (A and B) and the length of one side (c), you can use the Law of Cosines to find the lengths of the other two sides (a and b) by using the following formulas:

a = √(c² + b² - 2bc cos(A))

b = √(c² + a² - 2ac cos(B))

You can use the above equations to find the sides of the triangle, if you have the measures of two angles and one side.

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If g varies inversely as the square root of h, this means that the product of g and the square root of h is constant. We can represent this relationship using the equation g*sqrt(h) = k, where k is the constant value.

We are given that g = 9 when h = 121, so we can substitute these values into the equation to find the constant:

9sqrt(121) = k

Simplifying this expression gives us:

k = 911 = 99

Now that we know the value of the constant, we can use the equation to find g when h = 81:

g*sqrt(81) = 99

Solving for g gives us:

g = 99/sqrt(81) = 99/9 = 11

Therefore, when h = 81, g = 11.

The property used in this is the commutative law of multiplication.

What is the commutative law of multiplication?

In mathematics, commutative law refers to either of two rules relating to the addition and multiplication of numbers that are expressed symbolically as a + b = b + a and ab = ba. These principles imply that rearranging the terms or factors of any finite sum or product has no effect on it.

Here, we have

Given:  5x1 = 5 = 1x5

We have to find which property of multiplication is applied here.

5x1 = 5

1x5 = 5

We concluded from the given statement that the commutative law of multiplication is applied here.

commutative law of multiplication: ab = ba

Hence, the property used in this is the commutative law of multiplication.

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Using the slope of the least-squares regression line, the interpretation will be: C) The slope is 0. 50, which means for each additional pound in weight, the child’s height will increase by 0. 5 inches.

A linear approach is linear regression, which is used to represent the relationship between a scalar answer and one or more explanatory factors in statistics. When there are many explanatory factors, multiple linear regression is employed; otherwise, simple linear regression is utilised. It is possible to predict the value of one variable using linear regression analysis and the value of another variable.

Predicting the dependent variable is what you want to do. The variable you are using to anticipate the value of the other variable is the one you are utilising as an independent variable. Lines of best fit are another name for regression lines. To demonstrate how several graph points might be connected, a line of best fit is used.

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With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

We have given,

Mean weight of Eskimo dogs is μ = 30 pound

Standard deviation of Eskimo dogs is σ = 2 pound

The range of weights would 99.7% of the dogs have,

R =  μ ± 3σ

R = 30 ± 3*2

R = 30 ± 6

R = (30 - 6) , (30 + 6 )

R = 24, 36

With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.

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Answer:

[tex]8 \frac{2}{3} \times 12 = 104[/tex]

Therefore, she spends 104 hours a year playing soccer.

Answer:

104 hours

Step-by-step explanation:

1 year = 12 months

Since 1 year equals 12 months, we multiply the time she spends in 1 month by 12 to calculate the time she spends in 1 year.

8 2/3 hours × 12

= (8 + 2/3) hours × 12

= (8 × 12 + 2/3 × 12) hours

= (96 + 8) hours

= 104 hours

Using the normal distribution, we have that diameters at the 0.34th percentile are 0.2 standard deviations, that is, 0.127 inches above the mean.

Probability is the likelihood that a particular experiment result will appear a certain number of times. It cannot be less than zero or greater than one. A 100% chance of an outcome occurring exists if the outcome is 1, for example. If the result is greater than 1, there is a greater chance that it will occur.

In a normal distribution with mean  and standard deviation , the z-score of a measure X is given by:

It measures how many standard deviations the measure X is from the mean.

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

34th percentile is X when Z has a p-value of 0.34, so X when Z = 0.6331.

It means that the diameter is 0.44 standard deviations = 0.6331x0.2 = 0.127 inches above the mean.

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Amount of pineapple juice is more in Jo's drink and amount of Orange juice is less in Jo's drink as compare than the tropical punch recipe because these are not in that ratio as in the tropical punch recipe.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.

The Number of cups of pineapple juice = 222 liters

The Number of cups of orange juice = 333 liters

Thus ,

Total number of cub of juice = 222+333

                                               = 555 cups

In Jo's drink

The Number of cups of pineapple juice = 333 liters

The Number of cups of orange juice = 444 liters

Thus Total number of cub of juice = 333+444

                                                        = 777 cups.

The ratio of amount of pineapple juice and amount of Orange juice is 2:3 in the tropical punch recipe

Whereas the ratio of amount of pineapple juice and amount of Orange juice is 3:4 in Jo's drink

Thus we can see that Amount of pineapple juice is more in Jo's drink And Amount of Orange juice is less in Jo's drink.

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The answer to the table is given below.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given:

Learn more about ratios here: Jerome’s brother told him to add one cup of water for every cup of drink mix he added to keep the ratio of water to drink mix the same and still increase the total amount of energy drink. We get the following table using the constraints given in the question

Drink mix     3     4     5      6    7

water cups   8     9     10     11   12

Hence, The complete table is shown above.

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The smallest number with the factors 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24 is 232792560.

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Answer:

ye

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

A perfect square is a number from a number system that can be shown as the square of the number in the given number system. 4 can be written as 2 x 2 Making 4 a perfect square. In other words, if a number can be multiplied by its self and equal the number you are trying to square, then it is a perfect square.

Answer: 294 feet^2

Step-by-step explanation:

Find the volume of the cube.

Find the cube root of the volume.

Plug this answer into the formula for finding the surface area of a cube.

(area = 6 · s2)

Answer:

294cm[tex]^{2}[/tex]

Step-by-step explanation:

A cube has 6 faces

To find out the area of one face, you'd have to do 7x7 (7[tex]^{2}[/tex]).

To find out the total surface area of the cube, use this equation to help you:

AREA= 6(the amount of faces of the cube) × 7[tex]^{2}[/tex](the area of ONE face)

so in other words...

AREA=6×7[tex]^{2}[/tex]

AREA= 294cm[tex]^{2}[/tex]

hope this helped:)

The length of the cuboid is 56 cm.

The breadth of the cuboid is 40 cm.

The height of the cuboid is 16 cm.

A cuboid is a three-dimensional shape where the volume is given by

Length x width x height.

We have,

Volume of a cuboid = 35840 cm³

The ratio of length, breadth, and height of the cuboid = 7:5:2

This means,

Length = 7x

Breadth = 5x

Height = 2x

Now,

(7x)(5x)(2x) = 35840

70x³ = 35840

x³ = 512

x = ∛512

x = 8

Now,

Length = 7x = 7 x 8 = 56 cm

Breadth = 5x = 5 x 8 = 40 cm

Height = 2x = 2 x 8 = 16 cm

Thus,

The length, breadth, and height of the cuboid are 56cm, 40cm, and 16 cm.

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Answer:

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

According the the table the slope is:

Use slope-intercept form:

And substitute one of the ordered pairs, to find the value of b:

The y-intercept is (0, 8).

the probability that the card is either a queen or a diamond is: 4/13

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.

Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.

Number of cards, n(S) = 52

Let E = Event of getting a diamond

F = Event of getting a queen

(E ∩ F) = Event of getting a diamond of queen.

Then, n(E) = 13

n(F) = 4 ,

n (E ∩ F)=1

P(E) = 13/52 = 1/4

P (F) = 4/52 = 1/13

P (E ∩ F) = 1/52

(E or F) = P(E ∪ F) = P(E) + P(F) × P(E ∩ F)

P (E or F) = 1/4 + 1/13 - 1/52

P (E or F) = (13 + 4 - 1)/52

P (E or F) = 16/52

P (E or F) = 4/13

The required probability of getting either diamond or a queen is 4/13

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Answer:

Mark the sides BC and DF as congruent---------------------------------------------------We are given a side and an adjacent angle and need to identify the missing side or angle for proof by SAS .SAS is side-angle-side and requires two sides and the included angle to be congruent on both triangles.The missing bit is the other side of the marked angle B and D:sides BC or DF.

Step-by-step explanation:

Triangle ABC is translated to triangle EFG because a vertical translation of 10 units and a horizontal translation of 5 units maps triangle ABC onto triangle EFG.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

Triangle ABC.

A = (-9, -2)

B = (-9, -7)

C = (-7, -7)

Triangle EFG.

E = (-4, 8)

F = (-4, 3)

G = (-2, 3)

Now,

With a vertical translation of 10 units up on triangle ABC and 5 units right of the horizontal translation will give us triangle EFG.

i.e,

(-9, -2) = (-9 + 5, - 2 + 10) = (-4, 8)

(-9, -7) = (-9 + 5, -7 + 10) = (-4, 3)

(-7, -7) = (-7 + 5, -7 + 10) = (-2, 3)

Thus,

Vertical translation of 10 units up and horizontal translation of 5 units right.

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Answer:

1: Congruent

2: 10

3: 5

Step-by-step explanation: