What conclusion can you make about the result of adding a rational and an irrational number?

If one-third of a number, x, is greater than five less than twice the number, which of the following is true?​ x < 3, x > -3, x > -3/5, x < 3/5

Option A

The true inequality is x < 3

Let the number be "x"

One third of number means that,

[tex]\rightarrow \frac{1}{3} \text{ of number } = \frac{1}{3} \times x = \frac{x}{3}[/tex]

Thus from given statement,

one-third of a number x is greater than five less than twice the number

[tex]\text{ one-third of a number x } > \text{ five less than twice the number x }[/tex]

[tex]\frac{x}{3} > 2x - 5[/tex]

Solve the above inequality

Multiply both sides of inequality by 3

[tex]\frac{x}{3} \times 3 > (2x - 5) \times 3[/tex]

[tex]x > 3(2x-5)[/tex]

Solve for brackets in R.H.S

[tex]x > 6x - 15[/tex]

Add -6x on both sides of inequality

[tex]x - 6x > 6x - 15 -6x\\\\-5x>-15[/tex]

Multiply both sides of inequality by -1

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign

[tex]5x < 15[/tex]

Divide both sides of inequality by 5

[tex]x < 3[/tex]

Thus the true inequality is x < 3

Final answer:

The inequality one-third of a number x being greater than five less than twice the number translates to x < 3 after solving the inequality properly.

Explanation:

If one-third of a number, x, is greater than five less than twice the number, we can write this as an inequality. To solve for x, we can set up the following expression:

Now, we need to solve for x. First, we'll get all the x terms on one side and the constants on the other:

The statement that is true is that x is less than 3. This means all solutions for x are numbers that are less than 3.

Answer:

  7

Step-by-step explanation:

In general, the point of an inverse function is to show you the value that gives a particular function value. That is, ...

  [tex]f^{-1}(22)=7\\\\f^{-1}(f(x))=x\\\\f^{-1}(f(7))=7[/tex]

The inverse function  [tex]f^{-1}[/tex]essentially 'undoes' the operation of the function f. Given that f(7) is 22, applying the inverse function [tex]f^{-1}(f(7))[/tex] will return us to the original input, which is 7.

The question is discussing the concept of inverse functions in mathematics. A function has an inverse if it can be 'undone' or 'reversed'. In the notation  [tex]f^{-1}[/tex], it signifies the inverse function of f. The value of [tex]f^{-1}(f(7))[/tex] indicates that we have first applied the function f to the input 7 and then applied the inverse function [tex]f^{-1}[/tex] The result would be the original input before function f was applied.

Given that f(7) is equal to 22, applying the inverse function f^-1 to this result will return us to the original input. Hence, [tex]f^{-1}(f(7))[/tex]equals 7.

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Answer: 24

Step-by-step explanation:

245-28= 217

217÷9= 24.1

The equation can be set up as 245 = ?(9) + 28

Solving for the ?, we subtract 28 from the entire equation: 217 = ?(9)

Divide by 9: 24.11111 or, rounded, $24 each week.

Answer:

58 degrees

Step-by-step explanation:

180-87-35= 58

Answer:

She put the negative sign for the 32 outside the parentheses

Step-by-step explanation:

in the formula the negitive is supposed to be inside the parentheses

The first error that Cara made was seen in the second step where she used "minus" (32) squared instead of "plus" (32).

Population variance (σ²) describes the way data points in a given population are distributed. It is the aggregate of the distances from each data set in the population towards the mean squared.

The population variance is a population parameter that is independent of research methodologies or sampling practices.

Mathematically, The correct calculation can be done by using the formula:

[tex]\mathbf{\sigma^2 = \dfrac{ \sum(x_i-\bar x)^2}{N}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{ (87-78)^2 + (46-78)^2+ (90-78)^2+(78-78)^2+(89-78)^2}{5}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{ (9)^2 + (-32)^2+ (12)^2+(0)^2+(11)^2}{5}}[/tex]  

We can now see that the minus 32 is supposed to be in the bracket.

[tex]\mathbf{\sigma^2 = \dfrac{81+1024+ 44+0+121}{5}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{1270}{5}}[/tex]

[tex]\mathbf{\sigma^2 = 254}[/tex]

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Answer:

Step-by-step explanation:

G-8=25

+8. +8

G= 33

Answer:

36 = (w+5)w = w^2 + 5w

Step-by-step explanation:

The equation to find the dimensions of the window is w*(w + 5) = 36, where w represents the width of the window.

The subject of this question is Mathematics. This problem is a classic example of a quadratic equation in algebra, where you are given the area of a rectangle and a relationship between its length and width. In this case, the length of the rectangle is 5 feet more than its width (w). So, the length can be represented as w + 5. The area of a rectangle is calculated as length times width, so we can set up the following equation where the area is 36 square feet: w*(w + 5) = 36.

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If 81km = 9L, then 9km = 1L.

So ?km = 22L.

With 22L, Amanda can drive 198km.

Mafalda's save percentage improved by 0.153.

Solution:

Given that, Mafalda has a save percentage of 0.7380 so far this hockey season

Last season, her save percentage was 0.5850

To find: Percentage improved

To find improvement in Mafalda's save percentage we will subtract last season's save percentage from this season's save percentage.

From given,

Last season save percentage = 0.5850

This season save percentage = 0.7380

Percentage improved = This season save percentage - Last season save percentage

[tex]Percentage\ Improved = 0.7380-0.5850\\\\Percentage\ Improved =0.153[/tex]

Thus Mafalda's save percentage improved by 0.153.

Final answer:

Maria and her sister's meal total cost is $13.60 before tip. With a 20% tip of $2.72 added, the total meal cost becomes $16.32.

Explanation:

First, we need to calculate the total cost of Maria and her sister's meal before tip. Each salad costs $5.40 and each drink costs $1.40. Given they both had a salad and a drink, we calculate the cost for each person as $5.40 + $1.40 = $6.80. Thus, for both Maria and her sister, the total cost of the meal is $6.80 x 2 = $13.60.

To calculate the total cost including a 20% tip, we first need to work out the amount of the tip. A 20% tip can be calculated by converting the percentage to a decimal (0.20) and multiplying it by the meal cost. So, the tip amount is 0.20 x $13.60 = $2.72.

Finally, to find the total cost of the meal including a 20% tip, we add the tip to the original meal cost: $13.60 + $2.72 = $16.32. Therefore, the total cost of the meal with a 20% tip is $16.32.

Answer:

Infinitely many solutions.

Step-by-step explanation:

7x+3=3+7x

7x-7x+3=3

3=3

Answer: the answer would be 720

Step-by-step explanation:

Answer:

Step-by-step explanation:

direct proportion

100:5 = x : 36

Product of mean = 5*x

Product of extremes = 100*36

Product of mean = Product of extremes

5*x=100*36

x = 100*36/5

= 20*36 = 720

720 quarts could be made in 36 hours.

Answer:

The amount of butter used by baker this month is 294 kilograms.

Step-by-step explanation:

The amount of butter used last month by the baker = 210 kilograms

Now, according to the question:

The amount of butter used this month

= Previous months's amount +  40% of previous month's usage

Calculating 40% of 210 kg:

[tex]\frac{40}{100} \times 210 = 84[/tex]

⇒40% of 210 kilograms  = 84 kilograms

⇒ The amount of butter used this month  

= 210 kg +  84 kg = 294 kg

Hence,the amount of butter used by baker this month is 294 kilograms.

The baker used 40% more butter this month than last month. To find this month's usage, calculate 40% of last month's usage (84 kilograms) and add it to last month's usage. The baker used 294 kilograms of butter this month.

To answer this question, we can first calculate how much 40% of the butter used last month is. 40% of 210 kilograms is 84 kilograms. This is the amount of butter the baker used additionally this month than the previous month. If we add this to the amount of butter that was used last month (210 kilograms), we get the total amount of butter used this month. 210 kilograms + 84 kilograms = 294 kilograms. So the baker used 294 kilograms of butter this month.

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Answer:

yes

Step-by-step explanation:

Given the 2 equations

y = [tex]\frac{3}{4}[/tex] x + 6 → (1)

y = - [tex]\frac{3}{4}[/tex] x + 5 → (2)

Substitute y = [tex]\frac{3}{4}[/tex] x + 6 into (2)

[tex]\frac{3}{4}[/tex] x + 6 = - [tex]\frac{3}{4}[/tex] x + 5 ( add [tex]\frac{3}{4}[/tex] to both sides )

[tex]\frac{3}{2}[/tex] x + 6 = 5 ( subtract 6 from both sides )

[tex]\frac{3}{2}[/tex] x = - 1 ( divide both sides by [tex]\frac{3}{2}[/tex] )

x = [tex]\frac{-1}{\frac{3}{2} }[/tex] = - [tex]\frac{2}{3}[/tex] ← one solution

To find the cost of renting a canoe for 7 hours, we can set up a linear equation using the given information. Using the point-slope form, we can find the equation of the line. Substituting x = 7 into the equation gives us the cost for 7 hours. The cost of renting a canoe for 7 hours is $100.25.

To find the cost of renting a canoe for 7 hours, we can set up a linear equation using the given information. Let's define the variables:

x = number of hours

y = cost of renting a canoe for x hours

From the given information, we know that it cost $12 per hour to rent a canoe. Nate and his friends rented a canoe for 4 hours and paid $68. This gives us the first point on the line: (4, 68).

To find the equation, we can use the point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Using the slope formula, we can find the slope: m = (y2 - y1) / (x2 - x1) = (68 - 25) / (4 - 0) = 43 / 4 = 10.75.

Now we can plug in the values into the point-slope form: y - 68 = 10.75(x - 4).

To find the cost for 7 hours, we substitute x = 7 into the equation and solve for y: y - 68 = 10.75(7 - 4), y - 68 = 10.75 * 3, y - 68 = 32.25, y = 32.25 + 68, y = 100.25.

Therefore, the cost of renting a canoe for 7 hours is $100.25.

Final answer:

To calculate the cost of renting a canoe for 7 hours, first find the fixed cost by using the known rental time and cost. The equation is y = 12x + 20, where y is the total cost and x is the number of hours. For 7 hours, the cost is $104.

Explanation:

We are given that the cost to rent a canoe at Eagle Bay is $12 per hour. Nate and his friends rented the canoe for 4 hours, and they paid a total of $68. To find the equation, we need to consider that there might be a fixed cost in addition to the hourly charge. First, let's define our variables: let x be the number of hours the canoe is rented, and let y be the total cost.

Based on the information provided, we can create the equation y = 12x + b, where b is the possible fixed cost.

To find the fixed cost, we use the information that renting the canoe for 4 hours cost $68: 68 = 12(4) + b. Solving for b, we find:

68 = 48 + b
b = 68 - 48
b = 20

So, the fixed cost is $20, and the equation becomes y = 12x + 20. To find the cost of renting the canoe for 7 hours, we substitute 7 for x in our equation:

y = 12(7) + 20
y = 84 + 20
y = $104

The cost to rent the canoe for 7 hours would be $104.

Answer:

3/4

Step-by-step explanation:

1/2 divided by 4/6= 1/2 divided by 2/3

We can use reciprocals.

1/2 divided by 2/3= 1/2*3/2=3/4

Answer:

4 and 6

Step-by-step explanation:

4 + 6 = 10

4 x 6 = 24

Answer:

i have solved the question in the picture above. I used factorization to solve the quadratic equation I can also solve using quadratic formula or completing the square method if you want just comment below and I will solve it thank you

Answer:

x = 3

Step-by-step explanation:

We should know that:

A straight segment joining the middle of two sides in a triangle is parallel to the third side and equal to half of it.

So,

3x + 1 = (1/2) * 20 = 10

3x = 10 - 1 = 9

x = 9/3 = 3

So, the value of x = 3

Answer 5

Step-by-step explanation:

6/12=.5

.5*10=5

Final answer:

Mindy bought 10 grapefruits at a rate of $6.00 per dozen. By calculating the cost per grapefruit at 50 cents and multiplying by 10, we find that she paid a total of $5.00 for the grapefruits.

Explanation:

Calculating the Cost of Grapefruits

Mindy bought 10 grapefruits at the rate of $6.00 per dozen. To find out how much she paid for the grapefruits, we need to calculate the cost per grapefruit and then multiply by the number she bought.

A dozen grapefruits cost $6.00, so each grapefruit costs $6.00 divided by 12, which is 50 cents per grapefruit. Since Mindy bought 10 grapefruits, the total cost will be 10 grapefruits multiplied by 50 cents each.

Performing the multiplication, we get:

10 grapefruits × 50 cents per grapefruit = 500 cents

Since there are 100 cents in a dollar, 500 cents is the same as $5.00.

Therefore, Mindy paid $5.00 for the grapefruits.

Answer:

6x^2-4a-2x-2

Step-by-step explanation:

Answer: 4 x + 13 y + 11

Step-by-step explanation:

Distribute:

=5+(2)(6y)+(2)(3)+4x+y

=5+12y+6+4x+y

Combine Like Terms:

=5+12y+6+4x+y

=(4x)+(12y+y)+(5+6)

=4x+13y+11

Answer:

=4x+13y+11

Answer:

soda:3.75      burger: 1.25

Step-by-step explanation:

Answer:

C. The difference of the medians is 4 times the interquartile range.

Step-by-step explanation:

The diagram show two box plots.

Mahoney's box plot:

Median [tex]=33[/tex]

Interquartile range [tex]=34-32=2[/tex]

Martin's box plot:

Median [tex]=41[/tex]

Interquartile range [tex]=42-40=2[/tex]

The interquartile ranges are the  same.

The difference of the medians [tex]=41-33=8[/tex]

Hence, the difference of the medians is 4 times the interquartile range.

There is no standard relationship stating that the difference of medians is a certain multiple of the interquartile range. The median and interquartile range measure different aspects of a dataset (central tendency and dispersion, respectively), so comparing them in this way is not universally applicable.

The question is asking about a theoretical relationship between the median and the interquartile range (IQR) in a set of data. However, in statistics, there's no standard relationship that states the difference of medians is a certain multiple of the interquartile range. The median is a measure of central tendency, or a 'middle' value of a dataset, while the interquartile range is a measure of dispersion, indicating the variability within the data. The difference between two medians or the comparison of a median to the interquartile range would be specific to a certain dataset, and it's not a universal relationship.

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Without a clear graph or a well-defined inequality, it is not possible to determine which inequality is graphed. An inequality and its graph on the coordinate plane represent solutions to the inequality, such as regions to the right of a vertical line for x > 2.

The student has asked which inequality is graphed. Unfortunately, the provided information is insufficient to determine the inequality or the graph in question. Moreover, the data given appears to be disorganized or incorrectly transcribed, making it impossible to provide a specific answer. For a proper response, one would need either a clear description of the graph or the correct functional form of the inequality.

To demonstrate inequalities and their graphs, one might typically use coordinate axes where solutions to the inequality are represented by regions of the plane. For example, the inequality x > 2 would be represented graphically by a shaded region to the right of the line x = 2 on a number line, or in two dimensions, to the right of the vertical line x = 2.

If the student can provide a clear and accurate description of the graph or the inequality they are inquiring about, a more precise answer could be given.

Answer:

$700

Step-by-step explanation:

Given:

The ratio of taxes to profits is 7:3.

The taxes and profits total $1000.

Question asked:

Amount of taxes = ?

Solution:

Let ratios = [tex]x[/tex]

And amount of taxes = [tex]7x[/tex]

Then amount of profit = [tex]3x[/tex]

Sum of amount of taxes and profits = $1000.(given)

                                                           [tex]= 7x + 3x = 1000\\= 10x = 1000\\[/tex]

by dividing both side by 10

                                                         [tex]x = 100[/tex]

Thus, amount of taxes = [tex]7x[/tex] = [tex]7\times100[/tex] = [tex]700[/tex]

Thus, amount of profits [tex]= 3x = 3\times100 = 300[/tex]

Answer:

The potential energy of the ball having 2kg mass would be [tex]392[/tex] J

Step-by-step explanation:

I am assuming the ball has a mass of 2 kg, as you have not mentioned the mass of a ball.

Considering the formula for calculating the gravitational potential energy

[tex]G.P.E\:=\:m.g.h[/tex]

As

[tex]m = 2[/tex] kg

Acceleration of gravity = g = 9.8 [tex]ms^{-2}[/tex]

As the ball is on the height = h = 20 meters

So,

[tex]G.P.E\:=\:(2)(9.8)(20)[/tex]

[tex]G.P.E\:=392[/tex] J

Therefore, the potential energy of the ball = [tex]392[/tex] J

Keywords: potential energy, Gravitation potential energy

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Answer:

i agree

Step-by-step explanation:

Hope it will help u.........