Does each box at the fruit stand contain a different fruit? set all_different to true if each box contains a different fruit or to false if multiple boxes contain the same fruit.

well, tis noteworthy that whenever we have an absolute value equation is really a piece-wise function in disguise, namely the absolute expression is really two in disguise.

[tex]8x=2|6x-2|\implies \cfrac{8x}{2}=|6x-2|\implies 4x=|6x-2|\implies \begin{cases} 4x=+(6x-2)\\ 4x=-(6x-2) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=+(6x-2)\implies 4x=6x-2\implies 0=2x-2 \\\\\\ 2=2x\implies \cfrac{2}{2}=x\implies \boxed{1=x} \\\\[-0.35em] ~\dotfill\\\\ 4x=-(6x-2)\implies 4x=-6x+2\implies 10x=2\implies x=\cfrac{2}{10}\implies \boxed{x=\cfrac{1}{5}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x= \begin{cases} 1\\[1em] \frac{1}{5} \end{cases}~\hfill[/tex]

Answer:

1:27pm

Step-by-step explanation:

52 + 8 = 1 hour

29 - 8 = 21

1 hour and 21 minutes

2:48 - 1:21

1:27pm

Answer:

No

Step-by-step explanation:

If Q is the midpoint of PR, then PQ=QR.

[tex]5(x+2)=8x-3 \\ \\ 5x+10=8x-3 \\ \\ 3x=13 \\ \\ x=\frac{13}{3} \\ \\ \implies PQ=5\left(\frac{8}{3} +2 \right) \neq 36[/tex]

This means PQ + QR = PR isn't 72, and thus Q is not the midpoint of PR.

The radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.

We have that:

Radius of the water pipe = 0.74 cm

r = 0.74 cm

It fills a 12 L bucket in 4 minutes

1 L = 1000 cm³

12 L = 12,000 cm³

Volume of water put in the pool = 12,000 cm³

Height of the pool that rise = 5 mm = 0.5 cm.

H = 0.5 cm

Let the radius of the pool be R.

Volume = π r² h

Substituting the values, we get that:

12,000 = ( 22 / 7 ) R² ( 0.5 )

R² = 7636.36

R = 87.39 cm

Therefore, we get that, the radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.

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Using the mean concept, it is found that LeBron scored 10 more points per game on his last two games than on his first two.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For his first two games, he scored 20 + 15 = 35 points, hence the mean is:

35/2 = 17.5 points per game.

For his last two games, he scored 25 + 30 = 55 points, hence the mean is:

55/2 = 27.5 points per game.

The difference is:

27.5 - 17.5 = 10.

On average, LeBron scored 10 more points per game on his last two games than on his first two.

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Quadratic equations are all those equations that can be reformulated in a standard format (αx² + bx + c(=0) where the value of x is unknown and the values of the coefficients (a, b and c) are unknown.

These equations can always be solved using the quadratic formula, although sometimes it is also possible to use factorization or isolation of variables.

Expand squared

It is distributed

Combine like terms.

Move terms to the left

Subtract the numbers

Use the quadratic formula.

                        [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a} \end{gathered}$}[/tex]

In standard form we identify "a", "b" and "c" from the original equation and add to the quadratic formula.

                      [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-(-14)\pm\sqrt{(-14)^{2}-4\cdot1\cdot41 } }{2\cdot1} \end{gathered}$}[/tex]

Simplify

                                         [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14\pm4\sqrt{2} }{2} \end{gathered}$}[/tex]

Separate equations

To solve for the unknown variants, we split the equation into two: one with a plus sign and the other with a minus sign.

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14+4\sqrt{2} }{2} \end{gathered}$}[/tex]

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14-4\sqrt{2} }{2} \end{gathered}$}[/tex]

Solve

Order and isolate the variant to find each solution.

                                            [tex]\large\displaystyle\text{$\begin{gathered}\sf x=7+2\sqrt{2} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x=7-2\sqrt{2} \end{gathered}$}[/tex]

                            [tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\blue{Answer \ \ \longmapsto \ \ x=7\pm2\sqrt{2} }} \end{gathered}$}}}[/tex]

The all four angles are ∠AEC=40o, ∠BEC=140o, ∠AED=140o, ∠BED=40o.

What are vertically  angles?

Vertical  angles are formed when two lines cross at a point. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles.

Given that

∠BOC+∠AOC=280o   (AB and CD intersect at point E)

we know that, ∠AED and ∠BEC are vertically opposite angles ∠AED=∠BEC

we know that, ∠AED=∠BEC

so it can be written as

∠AED+∠AED=180o,

2∠AED=280o,

∠AED= 140o,

∠AED=∠BEC=140o

we know that ∠AEC and ∠AEC form a linear pair

So it can be written as

∠AEC+∠AED=180

substituting the values

∠AEC+140o=180o

∠AEC=40o

we know that ∠AEC and ∠BED are vertically opposite angles

∠AEC=∠BED=40o

Therefore, ∠AEC=40o, ∠BEC=140o, ∠AED=140o, ∠BED=40

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Answer:

The last one -4÷0 cannot be answered

Step-by-step explanation:

Answer:

-4/0

Step-by-step explanation:

This is an undefined answer, due to the fact that it would come out as:

0.00000e00000

This would be an undefined problem.

Answer:

#1 = -2

Step-by-step explanation:

First, we need to make -2 2/3 an improper fraction. An improper fraction is a fraction whose numerator is bigger than its denominator.

you first multiply the whole number (ignoring the negative sign for now) by the denominator:

2*3=6

then you add the numerator:

6+2=8

finally you put that number over the denominator and then put the negative sign back:

-8/3

Next, you can use keep change flip to solve the division

You keep the first fraction, change the division sign to a multiplication sign, and flip the numerator and the denominator of the second fraction:

-8/3 divided by 4/3 becomes -8/3 x 3/4

finally you multiply across as you would normally and simplify

-8/3 x 3/4= -24/12

-24/12 simplified is -2

:D

if you need help with the rest just comment on this response and I'll try to answer as soon as I can

Answer:

Step-by-step explanation:

7(i)

[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=\frac{dx}{dx} *(3x-5)^\frac{5}{3}+x*\frac{d}{dx} \{(3x-5)^\frac{5}{3} \}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=1*(3x-5)^\frac{5}{3} +x*\frac{5}{3}*(3x-5)^{\frac{5}{3} -1}*\frac{d}{dx} \{(3x-5)\}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +\frac{x*5*(3x-5)^{\frac{2}{3}}*3 }{3} \\\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +5x*(3x-5)^\frac{2}{3} \\\\[/tex]

[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3}*((3x-5)^{\frac{5}{3}-\frac{2}{3}} + 5x)\\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5)^\frac{3}{3}+5x) \\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5+5x)\\\ \frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(8x-5)*(3x-5)^\frac{2}{3}[/tex]

7(ii)

[tex]\int\limits {(x*(3x-5)^\frac{2}{3}) } \, dx \\Let\ \sqrt[3]{3x-5} =u\\Hence,\\(\sqrt[3]{3x-5})^3=u^3\\ 3x-5=u^3\\3x-5+5=u^3+5\\3x=u^3+5\\[/tex]

Divide both parts of the equation by 3:

[tex]\displaystyle\\x=\frac{u^3+5}{3}\\\\dx=\frac{d}{du} \{\frac{u^3+5}{3}\} \\dx=\frac{3u^2}{3} du=\\\\dx=u^2du\\Hence,\\\\\int\limits {\frac{u^3+5}{3}* u^2*u^2} \, du =\\\\\int\limits {\frac{u^3+5}{3} *u^4} \, du =\\\\\int\limits {\frac{u^7+5u^4}{3} } \, du =\\\\\frac{1}{3} \int\limits {u^7} \, du +\frac{1}{3}\int\limits {5u^4} \, dxu =\\\\[/tex]

The general term of the function is y = 4000 + 100x

The given parameters are

Guaranteed = $4000

Monthly raise = $100

Let the number of months be x, and the total earning be y

So, we have:

y = Guaranteed + Monthly raise * x

This gives

y = 4000 + 100 * x

Evaluate

y = 4000 + 100x

Hence, the general term of the function is y = 4000 + 100x

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The slope of the lines containing the following points (-2, 1) & (-5,5) is [tex]\frac{-4}{3}[/tex].

As per the question statement, two points lie (-2, 1) & (-5,5) on a line.

We are supposed to find the slope of the line.

To solve this question, we need to know the formula to calculate the Slope of line passing through two points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] which is given by

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Since given in the question statement, our concerned points are (-2, 1) & (-5,5), we can consider [tex][x_{1}=(-2)] , [x_{2}=(-5)], [y_{1}=1][/tex] and [tex][y_{2}=5][/tex].

Using these values into above mentioned formula, we get,

Slope (m) = [tex]\frac{5-1}{[(-5)-(-2)]}=\frac{4}{-3}=\frac{-4}{3}[/tex].

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Answer:  onever

Step-by-step explanation:

4x-8>1+4(x+3)

4x-8>1+4(x)+4(3)

4x-8>1+4x+12

4x-8>4x+13

4x-8-4x>4x+13-4x

-8>13

Hence, inequality is never true

Answer:

118

Step-by-step explanation:

The key piece of information to focus on is that there are around 120 fruits. 15 is the biggest of the given divisors, and the gaps between multiples of 15 is the greatest (compared to 4 and 6) which will narrow down our options. Therefore we can first try approaching the problem by finding multiples of 15 that are close to 120.

The question says that when the number (let's call it A) is divided by 15, it leaves 13. Therefore we can express A as such:

A-13 = 15x OR 15x + 13 = A

Where 'x' represents a whole number showing that the number is divisible by 15.

The closest multiples of 15 to 120 are 105 (15*7), 120 (15*8), and 135 (15*9).

A is one of these numbers + 13, let's see which ones are closest:

105+13 = 118, 120+13 = 133, 135+13 = 148

118 is very close to 120, so let's check it with the other numbers:

118/4 = 29 r 2

118/6 = 19 r 4

The exact number of fruits is 118.

Hope this helped!

Answer:

118

Step-by-step explanation:

We are told that there are about 120 fruits.

Fruits divided equally among 4 students

Multiples of 4:  4, 8, 12, ... 112, 116, 120, 124, ...

Therefore, 116, 120 and 124 are closest to 120.

Add the given remainder of 2 to these numbers:

Fruits divided equally among 6 students

Multiples of 6:  6, 12, 18, ... 108, 114, 120, 126 ...

Therefore, 114, 120 and 126 are closest to 120.

Add the given remainder of 4 to these numbers:

Fruits divided equally among 15 students

Multiples of 15:  15, 30, 45, ... 105, 120, 135, ...

Therefore, 105, 120 and 135 are closest to 120.

Add the given remainder of 13 to these numbers:

Therefore, as the total of 118 fruits is common to all three groups the exact number of fruits is 118.

Check

Divide 118 by each group of students:

As the remainders concur with the given amount of fruit left over for each group of students, this verifies that the exact number of fruits is 118.

Answer:

Step-by-step explanation:

perimeter of rectangular: 2(a+b)

we know from the graph, assume that a = 2x b = x+ 3

so the perimeter (C) in terms of x is C = 2(2x + x +3) = 6x + 6

The inequality notation for the given interval is -∞ < x ≤ -11 and -8 ≤ x < ∞

Disclaimer:

Considering the given interval as (-∞, -11] ∪ [-8, ∞).

Given interval is a union of two intervals.

The first interval denotes the set of all real numbers which are less than or equal to -11.

And the second interval denotes the set of all real numbers which are greater than or equal to -8.

The inequalities can be written as below:

(-∞, -11] ⇒ x ≤ -11 (or) -∞ < x ≤ -11

[-8, ∞) ⇒ x ≥ -8 (or) -8 ≤ x < ∞

And there is a union symbol between these two intervals.

So, x should satisfy both inequalities.

x ≤ -11 and x ≥ -8

or the above can be written as

-∞ < x ≤ -11 and -8 ≤ x < ∞

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The name of the segment in the scaled copy that corresponds to segment AB is segment EF

The given parameters are:

Polygon EFGH is a scaled copy of Polygon ABCD.

This means that the corresponding points are

E = A

F = B

G = C

H = D

Remove points C and D

So, we have

E = A

F = B

Hence, the name of the segment in the scaled copy that corresponds to segment AB is segment EF

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Answer:

(2,7), (6,-2),

Step-by-step explanation:

After finding the points you plug them in to the distance formula:

d=√((x2-x1)²+(y2-y1)²)

d=√[(6-2)²+(-2-7)²]

The equation to represent the situation is given as $2h -$10 = 0

We have been given that

    Money earned by Shane for babysitting =  $8 per hour

    Money earned by Shane for walking dogs = $6 per hour

Let the number of hours spent by Shane be h hours

Tips she received for babysitting = $12

Tip she received for walking dogs = $10

Total amount earned by Shane for babysitting = $8*h + $12

Also Shane worked two more hours for walking dogs then the amount will be = 2*$6 = $12

Total amount earned by Shane for walking dogs = $6*h + $12 + $10

                                                                                  = $6h + $22

As she earned the same total amount of job the equation will be given as

  $8h + $12 = $6h + $22

  $2h -$10 = 0

Which is the required equation

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Answer:

203 1/3  calories

Step-by-step explanation:

I make a proportion for inches of pizza to calories

[tex]\frac{6}{610}[/tex] = [tex]\frac{16}{x}[/tex]  I know that a 6 inch pizza has 610 calories, so I am trying to figure out how many calories are in a 16 inch pizza.

I can cross multiply to get

6x = (16)(610)

6x = 9760  Divide both sides by 6

x = 1626 [tex]\frac{2}{3}[/tex]  This is how many calories are in a whole pizza.  Now I want to know how many calories are in 1 slice.  I would take this number and divide by 8.

1626 2/3 as an improper fraction would be

[tex]\frac{4880}{3}[/tex] ÷ 8 Which is the same as

[tex]\frac{4880}{3}[/tex] x [tex]\frac{1}{8}[/tex] =[tex]\frac{4880}{24}[/tex]=203 [tex]\frac{1}{3}[/tex]

Answer: A=32 B=19

Step-by-step explanation:

The volume of the water filled in the cylinder A is 141.77  cm³.

A cylinder is a 3 solid that contains two parallel bases connected at a fixed distance by a curved surface.

The formula for the volume of the cylinder is;

Volume = πr²h

Where, π = 3.14,

radius r = 3 cm.

height h = 10 cm.

Put the values and obtain the volume.

Volume = (3.14)(3)²(10)

Volume = 282.74  cm³.

As, the cylinder is half filled with water;

Water volume = 282.74/2  cm³

Water volume = 141.77  cm³

Thus, the volume of water filled in cylinder A is 141.77  cm³.

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The correct question is-

Cylinder A has radius 3 cm and height 10 cm. Cylinder A is half full of water.

Work out the volume of water in Cylinder A.

The ratio strength of the final product is 1:0.4.

One technique to indicate concentration is through ratio strength, which uses a ratio to characterize drug concentration. In this context, concentration is defined as the quantity of a solute that makes up one unit in the whole volume of a solution or combination. You should be an expert in ratio strength calculations as a pharmacy student. Ratio strength uses a ratio to describe the medication concentration. So, what it implies is, you have one unit of solute contained in the complete amount of preparation and so generally your ratio strength is expressed as one is to something. In the case of a weight-in-weight, volume-in-volume, or weight-in-volume situation, you would interpret a ratio of 1:2,000 differently.

Drug strength = 800mg

whole volume =2ltrs

The ratio of the solution in 1 ltr is = 400 mg

The ratio strength of the solutions is = 1:0.4

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I have two answers depending on the format. I'm not sure if the entire function is to the 2ndpower or not. Either way, it's either 256 or 4.

Answer:

Bar A : 266 calories; Bar B : 251 calories

Step-by-step explanation:

Assume bar A's caloric content is "a" and bar B's caloric content is "b".

1. a + 2b = 768

2. 2a + b = 783

Add both equations together.

3. 3a + 3b = 1551

Divide both sides by 3.

4. a + b = 517

Subtract equation 4 from equation 1.

5. a + 2b - a - b = 768 - 517

Evaluate.

6. b = 251

Subtract b's value from equation 2.

7. 2a + b - b = 783 - 251

Evaluate.

8. 2a = 532

Divide both sides by 2.

9. a = 266

The area of the triangle is 1200√5 cm².

Given that, the sides of the triangle are 70cm,80cm and 90cm.

We need to find the area of a triangle using Heron's formula.

As per Heron's formula, the value of the area of any triangle having lengths, a, b, c, perimeter of the triangle, P, and semi-perimeter of the triangle as 's' is determined using the below-given formula:

Area of triangle = √s(s-a)(s-b)(s-c), where s = Perimeter/2 = (a + b + c)/2

Now, semi perimeter = (70+80+90)/2=120

Area of triangle=√120(120-70)(120-80)(120-90)

=√120×50×40×30

=√40×3×2×25×40×30

=40×5√3×2×3×2×5

=40×5×3×2√5

=1200√5 cm²

Therefore, the area of the triangle is 1200√5 cm².

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