A process that repeats a series of steps over and over until the desired outcome is obtained.

On solving for (x), we get -

x = ±i√(a/72).

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the equation as -

- 72x² = a

The given equation is -

- 72x² = a

x² = -a/72

x = ±i√(a/72)

Therefore, on solving for (x), we get -

x = ±i√(a/72).

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The temperature in Helena at 6 a.m. the next morning is 24∘C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

The temperature in Helena, MT was 0∘C at 6 a.m. on Tuesday morning.

The temperature rose at a rate of 78∘C per hour for 12 hours, then fell at a rate of 76∘C per hour for 12 hours.

Now,

Temperature first after 12 hours= 78*12=936

Temperature second after 12 hours= 76*12=912

=936-912

=24

Therefore, the answer will be 24∘C.

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The inequality that represents the graph is given as follows:

x < 4.

The four inequality symbols, along with their meaning, are presented as follows:

The numbers to the right of 4 that are shaded on the number line are the numbers that are less than 4, with an open interval, due to the open circle at x = 4, hence the inequality is given as follows:

x < 4.

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Answer:

0.25%

Step-by-step explanation:

Answer:

0.25%

Step-by-step explanation: you`re welcome :)

It will cost $2353.05 to pour concrete for the entire driveway

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

Dimension = 15 3/4 yards by 3 yards.

Concrete costs $49.80 per square yar

The cost is calculated as

Total = Area * Cost

So, we have

Total = (15 3/4 * 3) * 49.8

Evaluate

Total = 2353.05

Hence, the cost is $2353.05

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Answer:

Rhonda's: 32$ Joel's: 128$ Joel has 96 more dollars than Rhonda.

Step-by-step explanation:

4+1=5

5x=160

x=32

Rhonda's: 32$

Joel's: 128$

Joel has 96 more dollars than Rhonda.

Since it's a rhombus, the the diagonal intersection point is the middle point, so the diagonal should be

d1=5x2=10cm

d2=2x2=4cm

area=(d1xd2)/2=(10x4)/2=20cm^2

240 gallons of a 50% antifreeze solution must be mixed with 80 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

Let's call the amount of 50% antifreeze solution that we want to mix with the 80 gallons of 10% antifreeze "x".

The total volume of the mixture after mixing x gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution is given by (x + 80) gallons.

The concentration of antifreeze in the mixture is given by the weighted average of the antifreeze concentrations in the two solutions, where the weight for each solution is proportional to its volume:

(0.5x) + (0.1 * 80) = (0.4 * (x + 80))

Expanding and solving for x, we get:

0.5x + 8 = 0.4x + 32

0.1x = 24

x = 240

Therefore, we need to mix 240 gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution to get a mixture that is 40% antifreeze.

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Answer:

1.5748 in

Step-by-step explanation:

Answer:

1 inch = 2.54 cm

4 / 2.54 = 1.5748031496 inches

Step-by-step explanation:

The acceleration due to gravity of a falling object is +9.8 m/s²

The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. m/s² is its SI unit. Its nature which includes both magnitude and direction—makes it a vector quantity.

Given:

A linear expression we have

y= k x,

Here, Variation's constant is constant, or k.

The acceleration caused by gravity is stated to be the variational constant in the statement.

So, the linear expression becomes

y = g x, where g is a proportionality constant.

Now, Work is not done against gravity since an object falling downwards accelerates due to gravity at a rate of +9.8 m/s².

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The angle is 144°.

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays. A shared terminal between two rays (half-lines) is joined to create an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

Thus;

∠AOC + ∠COD + ∠BOD = 180°

Since AOB is a straight line:

⇒3x-10+50+x+20=180

⇒4x = 120°

⇒x = 30°

Thus, ∠AOC = 3x - 18

∠AOC = 3 × 30° - 18

∠AOC = 72°

2(72) = 144°

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The required ratio of trombones to all the brass section members is 3 : 7.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The total number of members in the brass section of the jazz band is:

4 trumpets + 3 trombones = 7 members

The ratio of trombones to all the brass section members can be expressed as,

= 3 trombones / 7 brass section members

This ratio cannot be simplified further because the numbers are relatively prime.

Therefore, the ratio of trombones to all the brass section members is 3 : 7.

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The solutions to the equations are;

(-3, 8) and (34/10, 156/16)

1) We can see that;

2x+y=2  ---- (1)

5x+3y =  9 ----- (2)

Multiply (1) by 5 and (2) by (2)

10x + 5y = 10 --- (3)

10x + 6y = 18 ----- (4)

Subtract 3 from 4

y = 8

Now substitute y =8 in (1)

2x + 8 = 2

x = 2 - 8/2

x = -3

Solution is; (-3, 8)

For question 2;

5x - 2y = -2 ---- (1)

3x + 4y =  30 ---- (2)

Multiply 1 by 3 and 2 by 5

15x - 6y = -6 ---- (3)

15x + 20y = 150 ----- (4)

Subtract (3) from (4)

16y = 156

y = 156/16

5x - 2(156/16) = -2

5x - 156/8 = -2

5x = -2 + 156/8

x = 34/10

Solution; (34/10, 156/16)

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Answer: 13.5, 3.5, and 119

Step-by-step explanation:

To find these percentages, we can use the formula:percentage = (percentage value / 100) x (original value)Using this formula, we can calculate:30% of 45:

percentage = (30 / 100) x 45

percentage = 0.3 x 45

percentage = 13.5

5% of 70:

percentage = (5 / 100) x 70

percentage = 0.05 x 70

percentage = 3.5

35% of 340:

percentage = (35 / 100) x 340

percentage = 0.35 x 340

percentage = 119

Answer:

Answers below :D

Step-by-step explanation:

1. 30% of 45:

Write 30% as 30/100

Since, finding the fraction of a number is same as multiplying the fraction with the number-

30/100 of 45 = 30/100 × 45

Therefore, the answer is 13.5.

2. 5% of 70:

Write 5% as 5100

Use same reason above to multiply-

5/100 of 70 = 5/100 × 70

Therefore, the answer is 3.5.

3. 35% of 340:

Write 35% as 35/100

Multiply-

35/100 of 340 = 35/100 × 340

Therefore, the answer is 119.

The fraction of water Libby drinks is 1 6/8 more liters of water than Jack.

In mathematics, a fraction is represented by a numerical value that designates a portion of an entire. A fraction is a piece or section of a whole, where the whole can be any number, a particular value, or an object. Let's use an example to better comprehend this idea. A pizza cut into 8 equal pieces is depicted in the following diagram. Now, to describe a single portion of the pizza, we may use the notation 1/8, which indicates that, out of 8 equally sized portions, we are speaking of one portion.

Given that, Libby drinks 2 7/8 liters of water.

Coverting the mixed fraction into improper fraction:

2 7/8 = 2(8) + 7/ 8 = 23/8

Jack drinks 1 1/8 liters of water.

Coverting the mixed fraction into improper fraction:

1 1/8 = 8 + 1/8 = 9/8

The difference between is:

D = 23/8 - 9/8 = 14/8

14/8 = 1 6/8

Hence, Libby drinks 1 6/8 more liters of water than Jack.

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The graph of the inequality is added as an attachment

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

y < -1/2x + 4 1/2

3x - 4y ≥ 12

The above expressions are linear inequality

Next, we plot the graph

See attachment for the graph of the inequality

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The percent of mice whose response time was 0.8 seconds or more is; Choice B; 50%.

As evident on the box plot; The response time, 0.8 seconds corresponds to the median of the plot.

Since the median represents the 2nd quartile of a distribution or otherwise termed , the 50th percentile;

It can be inferred that the percent of mice who responded in 0.8 seconds or more is; Choice B; 50%.

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Answer:

Arc Length=∫ba√1+[f′(x)]2dx. Note that we are integrating an expression involving f′(x), so we need to be sure f′(x) is integrable. This is why we require f(x) to be smooth.

Step-by-step explanation:

have a nice day

For {K} = 12, the image will remain preserved.

Given is the scale factor of {K} = 12.

We can write the scale factor as -

reduction  {for K < 1}

enlargement  {for K > 1}

preserved  {for K = 1}

For {K} = 12, the image will remain preserved.

Therefore, for {K} = 12, the image will remain preserved.

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This is exponential growth

==========================================================

Explanation:

The exponential rule we need is:  a^(b*c) = (a^b)^c

Apply that rule and do a bit of rearranging:

y = 2(1.06)^(9t)

y = 2( (1.06)^9 )^t

y = 2( 1.68948 )^t

y = 2( 1 + 0.68948 )^t

y = 2( 1 + 0.69 )^t

The last equation fits the format of  y = a(1+r)^t  which tells us that...

Since r is positive, we have exponential growth. If r was negative, then we'd have exponential decay.

For length of 50 yards , the width is 60 yards, for length of 40 yards , the width is 75 yards, for length of 48 yards, the width is 62.5 yards , for length of 36 yards, the width is 83.33 yards, they are inversely proportional.

The formula for the area of a rectangle is: Area = Length * Width.

So, for the given case, we have:

Area = 3000 square yards

Length = 50 yards, 40 yards, 48 yards, or 36 yards

Therefore, the width of the plot in each case can be calculated as:

For Length = 50 yards,

Width = Area / Length

= 3000 / 50

= 60 yards

For Length = 40 yards,

Width = Area / Length

= 3000 / 40

= 75 yards

For Length = 48 yards,

Width = Area / Length

= 3000 / 48

= 62.5 yards

For Length = 36 yards,

Width = Area / Length

= 3000 / 36

= 83.33 yards

Therefore, the width of the plot depends on the length chosen and they are inversely proportional. When the length increases, the width decreases, and when the length decreases, the width increases.

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The number of chocolates in the jar is given by the equation n = 21 chocolates

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Let the number of chocolates be n

Substituting the values in the equation , we get

The number of strawberries in the jar = 18

The number of cherries in the jar = 24

The number of lime candies in the jar = 19

The total number of candies in the jar = 82 candies

So , the equation will be

Number of strawberries in the jar + number of cherries in the jar + number of candies in the jar + number of chocolates = 82

Substituting the values in the equation , we get

18 + 24 + 19 + n = 82

On simplifying the equation , we get

n + 61 = 82

Subtracting 61 on both sides of the equation , we get

n = 21 chocolates

Hence , the equation is n = 21 chocolates

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Answer:

B. 20x + 4

Step-by-step explanation:

Perimeter of a rectangle = 2 × (Length + Width)

                                         = 2 × [(4x + 2) + 6x]

Expand the brackets and bring like terms together:
                                         = 2 × [4x + 2 + 6x]

                                         = 2 × [4x + 6x + 2]
                                         = 2 × [10x + 2]

Expand the brackets by applying the Distributive Law:

                                        = 20x + 4

                                        Option B.

The option that does not describe the Line GE is; B: Centroid

A triangle has three sides, three angles, and three vertices.

The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

The sum of the length of any two sides of a triangle is greater than the length of the third side.

The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians.

In this case, we see that the line GE divides DF into two equal parts and as such we can call this the median, perpendicular bisector or even angular bisector because it divides angle e into 2 equal angles for specific values of y.

Thus, this line cannot be the centroid

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Answer:

Step-by-step explanation:

To determine how many crates Tom needs to put 1000 bottles into, we can divide the number of bottles by the number of bottles that fit into one crate.

So,

number of crates = 1000 bottles / 24 bottles per crate = 1000 / 24 = 41.67 (approximately 42 crates)

Therefore, Tom needs 42 crates to put 1000 bottles into.

If a data set has an outlier, the median would be the best measure of central tendency to use as it is less sensitive to extreme values compared to the mean.

The presence of an outlier can heavily skew the mean in the direction of the outlier, causing it to become an inaccurate representation of the center of the data. On the other side, the median is less sensitive to extreme values and represents the middle value of the dataset. It is calculated by finding the middle value in a dataset after arranging it in numerical order.

Therefore using the median as the measure of central tendency in a dataset with an outlier can provide a better indication of the typical value compared to the mean.

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The required number Justin could have bought 1 pair of jeans and 3 t-shirts.

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Let's assume Justin bought x pairs of jeans and y t-shirts.

We know that the cost of each pair of jeans is $40 and the cost of each t-shirt is $20.

So, the total cost of Justin's purchase can be represented as:

Total cost = 40x + 20y

We also know that Justin bought a total of 4 items. So:

x + y = 4

Now we can use these two equations to solve for x and y:

40x + 20y = 100 (divide both sides by 20)

2x + y = 5 (subtract x from both sides)

Now we have two equations with two variables. We can solve for y in the second equation:

y = 5 - 2x

And substitute this into the first equation:

40x + 20(5-2x) = 100

Simplifying, we get:

40x + 100 - 40x = 100

100 = 100

This equation is true for any value of x and y that satisfy the condition x + y = 4.

So, Justin could have bought 1 pair of jeans and 3 t-shirts.

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Median would be a better measure of central tendency to use in the employees perspective, the mean of data set is 12.5 and median is 10, and

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us find the mean and median of the given data set {11,6,32,7,18,4,9,1,15,9,5,27}.

To find mean, we add up all the numbers and divide by the total number of numbers:

(11 + 6 + 32 + 7 + 18 + 4 + 9 + 1 + 15 + 9 + 5 + 27) / 12 = 12.5

So the mean number of years of employment is 12.5.

To find the median, we first need to put the numbers in order:

1, 4, 5, 6, 7, 9, 9, 11, 15, 18, 27, 32

Since there are 12 numbers, the median is the average of the middle two numbers, which are 9 and 11.

So the median is (9 + 11) / 2 = 10.

The median would be a better measure of central tendency to use, because it is less sensitive to extreme values than the mean

Hence, the mean of data set is 12.5 and median is 10, and median would be a better measure of central tendency to use in the employees perspective.

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The missing numerator are 7, 3, 6, 6, and 2

The Numerator is the number the at top of a fraction.

From the question, the numerators are

21) 2/3 x 7/5 = 14/15

The missing numerator here is 7

22) 5/6 X 3/7 = 5/14

The missing numerator here is 3

23) 3/4 X 6/7 = 9/14

The missing numerator here is 6

24) 6/9 X 2/4 = 1/2

The missing numerator here is 6

25) 9/10 X 2/3 = 3/5

The missing numerator here is 2

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Answer:

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

Substitute ? with x and solve each equation.

21)

22)

23)

24)

25)

Answer:!(I think)! the answer might be 0

Step-by-step explanation:

6( 2 - 6o) = -24

6 times (2 - 6o) = -24

Answer:

x=1

Step-by-step explanation:

open bracket

12-36x=-24

-36x=-24-12

-36x=-36

divide both sides by -36

x=1