An intelligent trader travels from 1 place to another carrying 3 sacks having
30 coconuts each. No sack can hold more than 30 coconuts. On the way
he passes through 30 checkpoints and on each checkpoint he has to give 1
coconut for each sack he is carrying. How many coconuts are left in the
end? *

Answer:

4x - 4

Step-by-step explanation:

4 × x = 4x

4 × -1 = -4

4x - 4

Answer:

4x-4

Step-by-step explanation:

Answer:

i.) (-0.25, 0), (1.25, 0)

ii.) (0.5, 2), (1.5, 2)

Step-by-step explanation:

For i, it is asking for the roots of the quadratic, or where the graph crosses the x-axis.

For ii, it is asking for the x-values when y = 2.

Answer:

39.936 ( not rounded )

Step-by-step explanation:

Use Pythagorean theorem

a^2 + 6.4^2 = 9^2

height = 6.24 (rounded to nearest hundredth)

1/2 * base * height = area

1/2 * 12.8 * 6.24

= 39.936 ( not rounded )

Answer:

See below.

Step-by-step explanation:

[tex](5x^2y^3)^0\div(-2x^{-3}y^5)^{-2}[/tex]

First, note that everything to the zeroth power is 1. Thus:

[tex]=1\div(-2x^{-3}y^5)^{-2}=\frac{1}{(-2x^{-3}y^5)^{-2}}[/tex]

Distribute using Power of a Power property:

[tex]=\frac{1}{(-2)^{-2}(x^{-3})^{-2}(y^5)^{-2})}[/tex]

Make the exponents positive by putting them to the numerator:

[tex]=\frac{(-2)^2(x^{-3})^2(y^5)^2}{1}[/tex]

[tex]=\frac{4x^{-6}y^{10}}{1}[/tex]

Make the exponent positive by this time putting it to the denominator:

[tex]=\frac{4y^{10}}{x^6}[/tex]

Answer:   e

Step-by-step explanation: 12/16          6/8    3/4

Answer:

B and E.

Step-by-step Explanation:

B: 6/8

    6*2=12

    8*2=16

    12/16

E: 3/4

    3*4=12

    4*4=16

    12/16

Hope this helps!!!!!

Answer:

The function f(x) = 4e* when evaluated for f(2) is:

Step-by-step explanation:

Its slope must be m= f'(0).

f'(x) = 8e2x ⇒ m = f'(0) = 8

y - y1 = m(x - x1)

m = 8

y1 = 10

x1 = 0

cause

Answer:

Option (3)

Step-by-step explanation:

To prove ΔULV ≅ ΔKLY,

                 Statements                    Reasons

1). VL ≅ LY                                1). Radii of a circle are equal

2). UL ≅ KL                              2). Radii of a circle are equal

3). ∠ULV ≅ ∠KLY                    3). Vertical angles are equal

4). ΔULV ≅ ΔKLY                    4). SAS property of congruence

Therefore, property (3) given in the options will be used to prove the triangles congruent.

Answer:

P(A|B) = 8/15

Step-by-step explanation:

Mathematically;

P(A|B) = P(A ∩ B)/P(B)

Thus we have

P(A|B) = 1/5 divided by 3/8

= 1/5 * 8/3 = 8/15

In the 5th year

For the first year, the salary is 1.2million = 1,200,000

For the second year, the salary is 1.2million + 75000 = 1,200,000 + 75,000 = 1,275,000

.

.

.

For the last year, the salary is 1.5million = 1,500,000

This gives the following sequence...

1,200,000 1,275,000  .   .   . 1,500,000

This follows an arithmetic progression with an increment of 75,000.

Remember that,

The last term, L, of an arithmetic progression is given by;

L = a + (n - 1)d           ---------------(i)

Where;

a = first term of the sequence

n = number of terms in the sequence (which is the number of years)

d = the common difference or increment of the sequence

From the given sequence,

a = 1,200,000                          [which is the first salary]

d = 75,000                               [which is the increment in salary]

L = 1,500,000                          [which is the maximum salary]

Substitute these values into equation (i) as follows;

1,500,000 = 1,200,00 + (n - 1) 75,000

1,500,000 - 1,200,000 = 75,000(n-1)

300,000 = 75,000(n - 1)

[tex]\frac{300,000}{75,000} = n - 1[/tex]

4 = n - 1

n = 5

Therefore, in the 5th year the maximum salary will be reached.

*The dot plot is shown in the attachment below

Answer:

2

Step-by-step explanation:

Interquartile range is the difference between the upper median (Q3) and the lower median (Q1).

First, let's write out each value given in the data. Each dot represents a data point.

We have:

2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7

=>Find the median:

Our median is the middle value. The middle value is the 6th value = 4

==>Upper median Q3) = the middle value of the set of data we have from the median to our far right.

2, 3, 3, 4, 4, |4,| 4, 5, [5], 6, 7

Our upper median = 5

==>Lower median(Q1) = the middle value of the data set we have from our median to our far left.

2, 3, [3], 4, 4, |4,| 4, 5, 5, 6, 7

Lower median = 3

==>Interquartile range = Q3 - Q1 = 5-3 = 2

Answer:

2

Step-by-step explanation:

Answer:

[tex]-7[/tex]

Step-by-step explanation:

[tex]5(x+9) = 10[/tex]

[tex]5x+45=10[/tex]

[tex]5x = -35[/tex]

[tex]x=-7[/tex]

Hope this helps.

Answer:

-7

Step-by-step explanation:

5(x + 9) = 10

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

...and is your order of operation.

First, divide 5 from both sides:

(5(x + 9))/5 = (10)/5

x + 9 = 10/5

x + 9 = 2

Next, isolate the variable x, by subtracting 9 from both sides:

x + 9 (-9) = 2 (-9)

x = 2 - 9

x = -7

x = -7 is your answer.

~

Answer:

∆y = 95 ft

the vertical distance the shark travels is 95 ft

Step-by-step explanation:

Given;

Initial position y1= 80 ft below the surface of water = -80ft

Final Position y2 = 15 ft above the surface = +15ft

The vertical distance travelled by the shark is;

∆y = y2 - y1 = 15 - (-80) ft

∆y = 15 +80 ft

∆y = 95 ft

the vertical distance the shark travels is 95 ft

Answer:

Lies in the shaded regions of both the top and bottom inequalities.

Step-by-step explanation:

The point of solution for BOTH systems of inequalities must work for both equations. Therefore, the point has to lie in both top and bottom shaded regions or it won't work for both, but just one.

Answer:

C: Lies in the shaded regions of both the top and bottom inequalities.

Step-by-step explanation:

Hope this helps!

Answer:

Length of MN = 48 units

Step-by-step explanation:

AB is the diameter of the larger circle which is perpendicular to both the chords PQ (chord of the smaller circle) and MN(chord of the larger circle).

Theorem says,

"Radius or a diameter of a circle which is perpendicular to the chord divides the chord in two equal parts."

Therefore, MO ≅ ON

m(MO) = m(ON)

7x - 4 = 6x

7x - 6x = 4

x = 4

m(MN) = m(MO) + m(ON)

           = (7x - 4) + (6x)

           = 13x - 4

           = (13 × 4) - 4

           = 52 - 4

           = 48

Length of chord MN will be 48 units.

Answer:

8.8

Step-by-step explanation:

set up a system

let x be sour keys and y be chocolate bars

2.65=15x+2y

3.35=10x+3y

then solve

X turns out to be 0.05

y turns out to be 0.95

multiply : 24*0.05=1.2

multiply : 0.95*8=7.6

add : 1.2+7.6 = 8.8

Answer:

[tex]Y\approx 84^\circ $(to the nearest angle)[/tex]

Step-by-step explanation:

The lengths of the sides of the scalene triangle are 6, 11, and 12.

We want to use the law of cosines to find the largest angle.

Note that the largest angle is always opposite the largest side.

Therefore:

[tex]1. 12^2 = 11^2 + 6^2-2(11)(6)\cos(Y) \\\\2. 144 = 121 + 36-(132)\cos(Y) \\\\3. 144 = 157 - (132)\cos(Y) \\\\4. -13 = -(132)\cos(Y)\\\\\\5. \cos(Y) = \dfrac{-13}{-132} \\\\6. Y = \arccos \left ( \dfrac{13}{132}\right)\\\\7. Y=84.35^\circ\\\\8. Y\approx 84^\circ $(to the nearest angle)[/tex]

The largest angle is 84 degrees to the nearest angle.

The function with the lowest output values as x approaches infinity is A.

The function with the greatest output values as x approaches infinity is B

Answer:

D,xy=-12

Step-by-step explanation:

y=x²+x-2

x+y=1

or x+x²+x-2=1

x²+2x-3=0

x²+3x-x-3=0

x(x+3)-1(x+3)=0

(x+3)(x-1)=0

either x=-3

or x=1

when x=-3

x+y=1

-3+y=1

y=1+3=4

one solution is (-3,4)

xy=-3×4=-12

if x=1

1+y=1

y=0

second solution is (1,0)

xy=1×0=0

Answer: A

Step-by-step explanation:

Answer:

336 feet²

Step-by-step explanation:

If we have a rectangle that is 30 by 20 feet, that means the area of that rectangle would be 20 × 30 feet squared, which is 600 ft².

If there is a 3 feet sidewalk surrounding it, that means that the end of the sidewalk will extend 3 feet extra around each side of plot. Since there are two ends to one side, that means an extra six feet is added on to each dimension. Therefore, 36 × 26 are the dimensions of the sidewalk+plot. 36 × 26 = 936 ft².

To find the area of the sidewalk itself, we subtract 600 ft² from 936 ft². This gets us with 336 ft².

Hope this helped!

Answer:

B. f(x) = 1 - x²

Step-by-step explanation:

Since we are dealing with only vertical movement, all we change is the constant. Since the red graph is up one from the reflected parent graph, we know our graph is f(x) = -x² + 1 or f(x) = 1 - x².

Answer:

B. F(x) = 1 - x^2

Step-by-step explanation:

The red graph is the blue graph translated 3 units down. It has a vertical translation of -3 units.

F(x) = G(x) - 3

F(x) = 4 - x^2 - 3

F(x) = 1 - x^2

*The box plots are shown in the attachment

Answer/Step-by-step explanation:

Range is the difference between the largest value of a data set and the lowest value in that data set.

In a box plot, the highest value is located at the end of the whisker to our right, while the lowest value is located at the beginning of the whisker of the box plot at our left.

For Crackers, the range = 100-70 = 30

For Cookies, the range = 115-70 = 45

Therefore, we can conclude that the range value of the number of calories in crackers (30) is less/lower than that of cookies (45).

Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer:  The total number of vehicles in the bar graph does not add up to 30.

The spacing between the bars should be equal.  

It would be helpful to put the number of each type at the top of its bar.

It may be useful to give the location and time/date of the observation in the title of the graph.

Step-by-step explanation:  The total 12 + 8 + 6 = 26.

My other observations would depend on the purpose of the graph. Many people use color to make the graph more visually appealing.

Answer:

The matched pairs are:

(A, 4), (B, 1), (C, 2) and (D, 3)

Step-by-step explanation:

The complete question is:

Match each description of an algebraic expression with the symbolic form of that expression :

A. 2 terms; variables = x and y

B. 3 terms; variables = x and y; constant = 3

C. 2 terms; variable = x; constant = 4.5

D. 3 terms; variables = x and y; constant = 2

1. x - 2y + 3

2. 4.5 - 2x

3. 4.5x + 2 - 3y

4. 4.5y - 2x

Solution:

A. 2 terms; variables = x and y  ⇒ 4. 4.5y - 2x

B. 3 terms; variables = x and y; constant = 3  ⇒ 1. x - 2y + 3

C. 2 terms; variable = x; constant = 4.5  ⇒ 2. 4.5 - 2x

D. 3 terms; variables = x and y; constant = 2 ⇒ 3. 4.5x + 2 - 3y

Answer:

3 and 5/12

Step-by-step explanation:

To find how much flour you need, subtract how much sugar you need from how much total you need of sugar and flower. To do this, turn both numbers into improper fractions. This means 3 and 2/3 turns into 11/3 as there are 3 thirds per whole, and there are three wholes plus the 2 thirds, equaling 11/3. The 1/4 is already an improper fraction, so you can move on.

Now you just covert them to have the same denominator by multiply 11/3 by 4 on top and bottom and 1/4 by 3 on both the top and bottom to get 44/12 and 3/12. Now you just subtract 44/12-3/12 and get 41/12. Made into a mixed number that is 3 and 5/12.

The recipe will require three and five-twelfths (3 5/12) fraction cups of flour.

A fraction is a portion of a whole or, more broadly, any number of equal pieces.

It is written in the form p/q, read as "p by q", where p is called the numerator and q is called the denominator, and the fraction p/q represents p number of equal parts from q number of equal parts.

Fractions are of two types:

In the question, we are informed that a recipe calls for a total of 3 and two-thirds cups of flour and sugar.

We are asked if the recipe calls for One-fourth cup of sugar, then how much flour is needed.

We suppose the quantity of flour required to be x cups.

We know the quantity of sugar required = One-fourth cup.

This can be written as a fraction = 1/4 cup.

We know the total sugar and flour is three and two-thirds cups.

This can be written as a fraction = 3 2/3 cup = 11/3 cup.

Now, we know quantity of sugar + quantity of flour = total quantity

or, 1/4 + x = 11/3

or, x = 11/3 - 1/4 = (44 - 3)/12 = 41/12 = 3 5/12.

Therefore, the recipe will require three and five-twelfths (3 5/12) fraction cups of flour.

Learn more about fractions at

https://brainly.com/question/11562149

#SPJ2

Answer:she earned 196$ in a week in which she worked 28 hours. she earned 784$ in a month which she worked 112 hours.

196$ and 784$ are your answers

Step-by-step explanation:

Answer:

[tex]c.\hspace{3}x=12[/tex]

Step-by-step explanation:

Isosceles triangles are a type of triangles in which two of their sides have an identical length. It should be noted that the angles opposite the sides that are the same length are also the same. This means that these triangles not only have two equal sides, but also two equal angles.

You can solve this problem using different methods, I will use pythagorean theorem. First take a look at the picture I attached.  As you can see:

[tex]x=2a[/tex]

And we can find a easily using pythagorean theorem:

[tex](\sqrt{45} )^{2} =3^{2} +a^{2}[/tex]

Solving for a:

[tex]a^{2} =(\sqrt{45} )^{2} -3^{2} \\\\a^{2} =45-9\\\\[/tex]

[tex]a^{2} =36\\\\a=\sqrt{36} \\\\a=6[/tex]

Therefore:

[tex]x=2a\\\\x=2(6)\\\\x=12[/tex]

Answer:

Step-by-step explanation:

Probability is expressed as

Number of favorable outcomes/total number of possible outcomes

From the information given,

Total number of outcomes = 16

Starting from 1, the multiples of 3 between 1 and 16 are 3, 6, 9, 12 and 15

This means that the number of favorable outcomes is 5

Therefore, the probability that the card has a multiple of 3 on it is

5/16 = 0.3125

Answer:

A. The side opposite the 60° angle has a length of √3/2

C.Sin(60°)=√3/2

E.The other acute angle of the triangle is 30°

Step-by-step explanation:

The diagram has been attached to the answer

A. The side opposite the 60° angle has a length of

B. The side opposite the 60° angle has a length of .

C. sin(60°) =

D. sin(60°) =

E. The other acute angle of the triangle is 30°.

Answer

The side opposite the 60° angle has a length of the square root of 3/2

Opposite side of the 60° angle has a length of √3/2

sin(60°) = the square root of 3/2

Sin(60°)=√3/2

The other acute angle of the triangle is 30°

Proof:

Total angle in a triangle=180°

180°-60°-90°

=30°

Answer:

A, D, E

Step-by-step explanation:

I do is big smart

Answer:

The ratio 1.8 : 2.4 can be rewritten as 3 : 4. We have to solve:

3 : 4 = x : 42

3 * 42 = 4x

x = 3 * 42 / 4 = 31.5