A cylindrical water tank has a radius of 40 cm and height of 1.2m. the water in it has a depth of 60 cm. a cube of side length 50 cm is placed at the bottom of the water tank. how much does the depth of the water increased by?

The inequality for the given sentence would be:

4x ≥ 18. This means that the product of x and 4 is greater than or equal to 18.

The inequality "4x ≥ 18" is read as "four times x is greater than or equal to 18". This means that the value of x must be equal to or greater than 4.5 for the inequality to hold true.

To solve the inequality, we can divide both sides by 4, which gives us:

x ≥ 4.5

This means that any value of x that is equal to or greater than 4.5 will satisfy the original inequality.

For example, x = 5 would satisfy the inequality because: 4(5) = 20, which is greater than or equal to 18.p

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Answer:

length = 3x - 1

Step-by-step explanation:

Area of a rectangle = length x width

or using l = length, w = width and A = area

A = l x w

or

l = A/w

Given
A = 18x² - 6x
w = 6x

l = 18x²- 6x/6x

= 18x²/6x - 6x/6x

= 3x - 1

Answer:

3x - 1

Step-by-step explanation:

Area of the Rectangle:

18x^2 - 6x

6x (3x - 1)

Width = 6x

Length =?

Area of Rectangle = Length *  Width

Length = Area/breadth

6x (3x -1) / 6x cross out 6x

Thus, Length of Rectangle = 3x - 1

The 84th percentile of gestations which can be ruled by standard deviation is 282 days.

The lengths of human pregnancies (gestations) can be modeled by a bell-shaped distribution with a mean of 266 days and a standard deviation of 16 days. Use the empirical rule to determine the 84th percentile of the gestations. The empirical rule, also known as the 68-95-99.7 percent rule, is a statistical guideline that states that within one standard deviation of the mean, 68 percent of the data is distributed.

Within two standard deviations of the mean, 95% of the data is distributed. Finally, 99.7 percent of the data is distributed within three standard deviations of the mean. As a result, it's necessary to locate the corresponding z-score for the given percentile to use the empirical rule.

Since we have the mean and standard deviation, we can use the following equation to compute the z-score using the formula: z = (X - µ)/σ where X is the value of interest, µ is the mean, and σ is the standard deviation. From the formula: z = (X - µ)/σX = µ + zσ Substituting the given values in the formula, we get: X = 266 + z(16)We need to find the 84th percentile.

This means that the remaining 16 percent of the data is distributed outside of the mean plus one standard deviation. As a result, the corresponding z-score can be found using a standard normal distribution table or calculator. The standard normal distribution table or calculator gives us the z-score of 1.00 for the 84th percentile. Using this, we can compute the value of X as follows: X = µ + zσX = 266 + (1.00)(16)X = 266 + 16X = 282

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The  equation she will use to determine how much money she'll have after 2 years is: A = 49,000*(1+0.153/12)^(2*12).

After 2 years she'll have $70,960.36.

The formula for compound interest is: A = P * (1 + r/n)^(n*t).  In the formula, we convert the annual interest rate to a monthly rate by dividing it by 12 (the number of months in a year), and we multiply the number of years by 12 to get the number of months.

Using this formula, we can calculate how much money Lara will have after 2 years:

A = 49000 * (1 + 0.153/12)^(12*2)

A = $70,960.36

Therefore, Lara will have $70,960.36 after 2 years of compounding her investment monthly at 15.3%.

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a) the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b)a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

The definition of an equation is the claim that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, operations, and functions.

a) The two formulae for cooking times are:

(66 x weight in kg) + (35 x time in an electric oven

Microwave oven time = (26 x weight in kg) + 15

We can compare the two formulae by looking at their coefficients and constants.  This suggests that the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b) (66 x weight in kg) + (35 x time in an electric oven

2 x 60 = (66 x weight in kg) + 35

120 - 35 = 66 x weight in kg

85 = 66 x weight in kg

weight in kg = 85 / 66

weight in kg ≈ 1.29

So, a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

Microwave oven time = (26 x weight in kg) + 15

Microwave oven time = (26 x 1.29) + 15

Microwave oven time ≈ 48.34 minutes

Therefore, a 1.29 kg joint of meat would take about 48 minutes to cook in a microwave oven.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

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Answer:

Approximately 26.87 cm

Step-by-step explanation:

To find the length of side b using Heron's formula, we need to substitute the given values into the formula and solve for b:

A = √s(s-a)(s - b)(s-c)

270 = √45(45-15)(45-b)(45-39)

Simplifying the expression inside the square root:

270 = √45(30)(6)(6-b)

270 = 540√(6-b)

Squaring both sides:

72900 = 291600 - 54000b + 3240b^2

Rearranging:

3240b^2 - 54000b + 218700 = 0

Dividing both sides by 540:

6b^2 - 100b + 405 = 0

We can solve for b using the quadratic formula:

b = (-(-100) ± √((-100)^2 - 4(6)(405))) / (2(6))

b = (100 ± √13600) / 12

b ≈ 26.87 cm (rounded to two decimal places)

Therefore, the length of side b is approximately 26.87 cm.

Answer:

Since the interest is not compounded, Brian will earn a simple interest of 5% per year on his initial deposit of $20,000. The formula for calculating simple interest is:

I = P * r * t

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

I = 20,000 * 0.05 * 5 = 5,000

Therefore, Brian will earn $5,000 in interest over the 5-year period. Adding this to his initial deposit of $20,000, we get:

Total amount = $20,000 + $5,000 = $25,000

Therefore, Brian will have a total of $25,000 in his savings account after 5 years.

Answer:

$25,000

Step-by-step explanation:

The total amount Brian will have in 5 years can also be calculated using the formula for simple interest:

A = P(1 + rt)

where:

A = the total amount

P = the principal (initial balance)

r = the annual interest rate

t = the time period (in years)

In this case:

P = $20,000

r = 0.05 (since 5% is the annual interest rate)

t = 5 (since we're calculating the total amount after 5 years)

Plugging these values into the formula, we get:

A = $20,000(1 + 0.05 x 5)

A = $20,000(1.25)

A = $25,000

So we get answer of $25,000, which is the total amount Brian will have in 5 years.

Since the point (2, 3) lies on the line 2x + ky = 19, the value of k is equal to 5.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Making k the subject of formula, we have the following:

k = (19 - 2x)/y

Since the point (2, 3) lies on the line, we have:

k = (19 - 2(2))/3

k = (19 - 4)/3

k = 15/3

k = 5.

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Answer:

The answer would be the second one.

Step-by-step explanation:

The answer is this because 65% as a decimal is .65 and the second equation is the only one with a .65 in it. It is also the only equation with 24 in it as well.

Answer:

El espacio recorrido en el tercer segundo será de 9 m.

Step-by-step explanation:

If he sweets are all red, yellow or green in the ratio of 6 : 4 : 4, there are 36 yellow sweets in the packet.

To solve this problem, we need to use the concept of ratios. The ratio of red, yellow, and green sweets is 6:4:4, which means that for every 6 red sweets, there are 4 yellow and 4 green sweets.

We can use this ratio to find out how many yellow sweets there are in the packet. Since the ratio of yellow sweets to the total number of sweets is 4:14 (6+4+4=14), we can write:

Yellow sweets / 126 = 4 / 14

To solve for the number of yellow sweets, we can cross-multiply and simplify:

Yellow sweets = 126 x 4 / 14

Yellow sweets = 36

We can also use the same method to find the number of red and green sweets:

Red sweets = 126 x 6 / 14

Red sweets = 54

Green sweets = 126 x 4 / 14

Green sweets = 36

To check our answer, we can verify that the total number of sweets is equal to the sum of red, yellow, and green sweets:

54 + 36 + 36 = 126

Therefore, our answer is correct.

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The solution of the inequality is x ≤ - 7 / 2 or x > 1

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequalities. The variable in the inequality is x. A variable is a number represented with letter in an equality or inequality.

Therefore,

x + 1 / 2 ≤ - 3 or x - 3 > - 2

Let's solve them individually,

x + 1 / 2 ≤ - 3

subtract 1 / 2 from both sides of the inequality

x ≤ - 3 - 1 / 2

x ≤ - 7 / 2

Hence,

x - 3 > - 2

add 3 to both sides of the inequality

x - 3 + 3 > - 2 + 3

x > 1

Hence,

x ≤ - 7 / 2 or x > 1

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Answer: can you put it in diffrent form beucase the way you have it is really confusing me thanks

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

One package of sugar cookie dough costs $6 and one package of double chocolate cookie dough costs $11.

How to solve the variables?

Let's use the following variables:

Let x be the cost of one package of sugar cookie dough.

Let y be the cost of one package of double chocolate cookie dough.

We can create a system of two equations to represent the information given in the problem:

Equation 1: 7x + y = 53 (from Kayla's sales)

Equation 2: x + y = 17 (from Maria's sales)

We can solve for x and y by using the substitution method, which involves solving one equation for one variable and substituting the result into the other equation. Here's how we can do it:

Solve Equation 2 for y:

y = 17 - x

Substitute y = 17 - x into Equation 1 and solve for x:

7x + (17 - x) = 53

6x + 17 = 53

6x = 36

x = 6

Substitute x = 6 into Equation 2 and solve for y:

y = 17 - x

y = 17 - 6

y = 11

Therefore, one package of sugar cookie dough costs $6 and one package of double chocolate cookie dough costs $11.

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The questiοn is an illustratiοn οf inequalities and mathematical οperatiοns the amοunt between $2 and $10 is $8.

The amοunt between $10 and $20 is $10

$100 is greater than $50

In mathematics, an inequality is a cοnnectiοn that is nοt equal between twο expressiοns οr values. Cοnsequently, imbalance leads tο inequity. In mathematics, an inequality cοnnects twο unrelated values. Inequality is distinct frοm equality. When twο values are nοt equal, the nοt equal sign is mοst usually used ().

Variοus inequalities are emplοyed tο cοntrast values, nο matter hοw small οr huge. Many basic inequalities can be sοlved by altering the twο sides until the variables are all that remain. Yet, a variety οf factοrs cοntribute tο inequality: Negative values οn bοth sides are split οr added. Trade οff the left and right.

(a) Amοunt between $2 and $10.

The amοunt is calculated as:

Hence, the amοunt between $2 and $10 is $8

(b) Amοunt between $10 and $20.

The amοunt is calculated as:

Hence, the amοunt between $10 and $20 is $10

(c) Amοunt greater than $50.

An amοunt greater than $50 is an amοunt that have an higher value.

Take fοr instance: $100

$100 is greater than $50, because it has a higher value.

There is nο enοugh infοrmatiοn tο sοlve the οther questiοns

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Answer:

≈ 18.8 cm

Step-by-step explanation:

Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square.

The area of the square is given as 36 cm^2, so we can find the side length of the square as:

side length = √(area) = √(36 cm^2) = 6 cm

The diameter of the circle is therefore also 6 cm, and the radius of the circle is half the diameter, or 3 cm.

The circumference of a circle is given by the formula:

circumference = 2πr

where r is the radius of the circle.

Substituting in our values, we get:

circumference = 2π(3 cm) = 6π cm

Using a calculator to approximate π to one decimal place, we get:

circumference ≈ 18.8 cm

Therefore, the circumference of the circle inside the square is approximately 18.8 cm.

The yearly percent change in the number of animal species is approximately -67.68%. This means that the number of animal species is decreasing by about 67.68% each year after the last ice age began.

The yearly percent change of the number of animal species after the last ice age began can be calculated by taking the derivative of the function given, S(t)=4,200,000⋅(0.72)t. Using the power rule, the derivative of this function is S'(t)=2,976,000⋅(0.72)t-1. This tells us that the yearly percent change in the number of animal species is -72%. This means that every year, the total number of animal species decreases by 72%.

The yearly percent change of the number of animal species can be determined by finding the derivative of the function [tex]S(t) = 4,200,000(0.72)^t.[/tex]

The derivative of the function can be calculated as follows:[tex]S'(t) = 4,200,000 ln(0.72) (0.72)^t[/tex] The yearly percent change can be calculated by finding the percentage change in the total number of animal species for each year. This can be done by finding the percentage change in the value of the function for each year.

The percentage change in the value of the function can be calculated using the formula:% change = [(new value - old value) / old value] x 100Substituting the values of the function for different years in the above formula, we can find the percentage change for each year.

For example, if we want to find the percentage change in the number of animal species after 10 years, we can substitute t = 10 in the function and calculate the new value of S(t). Then, we can use the above formula to find the percentage change in the value of the function for 10 years.S(10) = 4,200,000(0.72)^10 ≈ 1,357,747% change = [(1,357,747 - 4,200,000) / 4,200,000] x 100 ≈ -67.68%

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When the shape R is reflected R' the coordinates of C (2, 5) when translated to R" C (1, -1).

What are Transformations:

Transformations are changes made to a geometric figure in a plane or space. There are three main types of transformations: translation, rotation, and reflection.

Rotation is a transformation where a figure is turned around a fixed point, called the center of rotation. This can be a clockwise or counterclockwise turn, and the degree of rotation is determined by the angle between the original and final positions of the figure.

Here we have a shape R

From the graph,

The coordinate of C is (-4, 5)  

Shape R is reflected in line x = -1 to give R'

=> (x, y )  →  (-x - 2, y)

=> (-4, 5) → (4- 2, 5)  

=> Coordinates of C are (2, 5)

R' is then translated by (-1, -6) to give R''

Hence, the R is moved 1 unit left words and 6 units downwards

=> (2, 5) → (-1 + 2, 5 - 6)

=> (2, 5) → (1, -1)

Therefore,

When the shape R is reflected R' the coordinates of C (2, 5) when translated to R" C (1, -1).

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La nueva temperatura de la congeladora industrial es de -3°C.

Si una congeladora industrial se mantiene a -8°C y aumenta su temperatura en 5°C, podemos encontrar su nueva temperatura sumando -8°C y 5°C:

-8°C + 5°C = -3°C

Por lo tanto, la nueva temperatura de la congeladora industrial es de -3°C.

La temperatura es una magnitud física que mide el grado de calor o frío de un objeto, sustancia o ambiente. Esta magnitud está relacionada con la energía cinética promedio de las moléculas que componen el objeto o sustancia, y se expresa en unidades de medida como grados Celsius (°C), grados Fahrenheit (°F) o kelvin (K).

Es importante tener en cuenta que una temperatura de -3°C sigue siendo fría, pero es importante asegurarse de que la congeladora se mantenga a la temperatura adecuada para preservar los alimentos y evitar su descomposición.

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You have some standard six-sided dice. So, the probability of rolling a total of ten when you roll three dice is 5/216.

To find the probability of rolling a total of ten when rolling three dice, we can use the formula:

P(event) = desired outcomes / total outcomes

Given that we have six-sided dice, we know that the total outcomes for rolling one die is six.

Therefore, the total outcomes for rolling three dice would be[tex]6^3[/tex]= 216.

To find the desired outcomes, we can use combinations.

There are three ways we can roll a total of ten with three dice:

1-3-62-4-43-5-24-3-34-2-45-1-5

Therefore, there are five combinations that result in a total of ten.

Therefore, the probability of rolling a total of ten when rolling three dice is:

P(event) = 5/216

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Answer:

Step-by-step explanation:

I don't mean to be rude but I think that this question Is wrong because the triangle sides are meant to be equal

Pls I am asking nicely because I want to help

2/3 in its simplest form.

3-(7)/(3) can be simplified to 2/3 by performing the following steps:

1. First, divide 7 by 3 to get 7/3.

2. Then, subtract 7/3 from 3 to get 3-(7/3), which equals 2/3.

Therefore, the answer is 2/3 in its simplest form.

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Answer:

90*

Step-by-step explanation:

Answer: 90 degrees

Step-by-step explanation:

Not sure what its asking but x is at the angle part which is definitely 90 degrees

The volume of the container is 127.23 cubic cm

The given parameters are

Number of balls = 6

Height of ball = 3 cm

This means that

Height of cylinder, h = 6 * 3 cm = 18 cm

Radius of cylinder, r = 3/2 cm = 1.5 cm

So, we have

Volume = πr²h

Volume = π * 1.5² * 18

Volume = 127.23

The volume of a ball is

Ball = 4/3πr³

For 6 balls, we have

Balls = 6 * 4/3πr³

Balls = 8πr³

So, we have

Balls = 8π * 1.5³

Balls = 84.82

So, the unoccupied space is

Space = 127.23 - 84.82

Space = 42.41

This is calculated as

Area = 2πrh + 2πr²

So, we have

Area = 2π * 1.5 * 18 + 2π * 1.5²

Area = 183.78

Hence, the surface area is 183.78 square cm

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Angles congruent to ∠1= ∠4,∠8,∠5

Angles congruent to ∠2= ∠3,∠7,∠6

Angles congruent to ∠6= ∠3,∠7,∠2

Angles congruent to ∠7= ∠3,∠6,∠2

The opposing angles created by the connection of two straight lines are known as vertical angles or vertically opposed angles.

(Vertically opposite angle ∠1=∠4

Vertically opposite angle ∠8=∠5

consecutive exterior angle ∠4=∠8)

Angles congruent to ∠2= ∠3,∠7,∠6

Hence, Angles congruent to ∠1= ∠4,∠8,∠5

(Vertically opposite angle ∠2=∠3

Vertically opposite angle ∠7=∠6

consecutive exterior angle ∠3=∠7)

Angles congruent to ∠7= ∠3,∠6,∠2

(Vertically opposite angle ∠7=∠6

Vertically opposite angle ∠2=∠3

consecutive exterior angle ∠6=∠2)

Hence, Angles congruent to ∠6= ∠3,∠7,∠2

(Vertically opposite angle ∠6=∠7

Vertically opposite angle ∠3=∠2

consecutive exterior angle ∠7=∠3)

Hence, Angles congruent to ∠2= ∠3,∠7,∠6

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Answer:

x = 6

Step-by-step explanation:

7x = 42

To solve the equation, divide each side by 7.

7x/7 = 42/7

x = 6

Answer: y=3x-2

Step-by-step explanation

(-8)-(7)/ (-2)- (3) = -15/ -5= 3

y=3x+b

f(-2)= -8

y= 3x+ b

-8= 3(-2)+b

-8=-6+b

add 6 on both sides

b=-2

y=3x-2

The radius of a circle is half of the diameter. Therefore, the radius of the circle is 7 yards and the diameter of the circle is 14 yards.

The above shape is a circle. The area of the circle is given as 49πyards square. The radius of a circle is the distance of the circumference to the centre of a square. The diameter of a circle is twice the radius of the circle.

Therefore, let's find the radius and diameter of a circle as follows:

area of a circle  = πr²

where

Area of the circle = πr²

49π = πr²

divide both sides of the equation by π

r² = 49

square root both sides of the equation

r = √49

r = 7 yards

Therefore,

diameter = 7 × 2

diameter = 14 yards

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