The elephants at the zoo eat 3 1/6 buckets of bananas each day. The zookeeper bought 6 1/3 buckets of bananas. How many days will the bananas last?

Write your answer as a fraction or as a whole or mixed number.

Answer:

2 2/4 + 1 3/4 + 2/4 = 4 3/4

4 3/4

Answer:

4 and 3/4

Step-by-step explanation:

2 1/2

+1 3/4

+   1/2

_____

4 and 3/4

The various algebraic properties used for each of the given expressions are;

1) Symmetric property of equality.

2) Distributive property of equality.

3) Addition property of equality.

4) Division property of equality.

5) Addition property of equality.

6) Transitive property of equality.

7) Associative property of equality.

8) Multiplication property of equality

9) Commutative property of equality.

There are different properties of equality or algebra such as;

1)  If AB=CD, then CD=AB; Property used here is Symmetric property of equality because it suits the definition.

2) 5(x-4) = 5x-20; Property used here is Distributive property of equality because it suits the definition.

3) 3x - 17 = 8, then 3x = 25; Property used here is Addition property of equality because it suits the definition.

4) 22m=440, then m=20; Property used here is Division property of equality because it suits the definition.

5) :(2a+3a)-4a=7a+55, then (5a)-4a=7a+55; Property used here is Addition property of equality because it suits the definition.

6) If GH=2x+17, and 2x+17=JK, then GH=JK; Property used here is Transitive property of equality because it suits the definition.

7) 2b+(b-7)=17, then (2b+b)-7=17; Property used here is Associative property of equality because it suits the definition.

8) (x+7)/3=13, then x+7=39.; Property used here is Multiplication property of equality because it suits the definition.

9) m 10:4+x=13, then x+4=13; Property used here is Commutative property of equality because it suits the definition.

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Answer:

4.

5.

Step-by-step explanation:

Relationships in a right triangle:

The sine of an angle is the length of the opposite side to the angle divided by the hypotenuse.

The cosine of an angle is the length of the adjacent side to the angle divided by the hypotenuse

The tangent of an angle is the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

Question 4:

hypotenuse is 5.

AB is adjacent to an angle of 45º. So

Applying cross multiplication:

Question 5:

Hypotenuse is 10.

BC is opposite to an angle of 60. So

Answer:

T1 = P2 * V2 / T2 * P1 * V1

ANSWER

EXPLANATION

The area of a triangle using two given sides and the included angle is given as:

where a and b are the sides and C is the included angle.

Therefore, we have to find C given that:

Therefore, we have that:

That is the measure of the included angle.

PLUG IN 2 IN THE PLACE OF X IN THE FUNCTION THEN SIMPLIFY

f(2)= |5×2|

f(2)=|10|

[tex]f(2) = 10[/tex]

ATTACHED IS THE SOLUTION

Answer:

[tex]\rm f(2)=|5\;^*\;2|=|10|=10[/tex]

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol.  "Absolute value" means how far a value is from zero.   Therefore, the absolute value of a number is its positive numerical value.

Given absolute value function:

[tex]f(x)=|5x|[/tex]

To find f(2), substitute x = 2 into the given function:

[tex]\begin{aligned}\implies f(2)&=|5 \cdot 2|\\&=|10|\\&=10\end{aligned}[/tex]

Using the Fundamental Counting Theorem, the number of possible plates is given as follows:

1,000,000.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is given according to the following rule:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this question, the plate is composed by six independent digits, hence the parameters are given as follows:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = 10[/tex]

(as there are 10 possible digits, from 0 to 9).

Hence the number of possible plates is calculated as follows:

N = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10^6 = 1,000,000.

This problem is incomplete, hence we suppose that it asks for how many plates can be built.

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Answer:

x-intercept: (-0.5,0)

y-intercept: (0,1)

Slope: 2

Domain: All real values

Range: All real values

Step-by-step explanation:

x-intercept:

The x-intercept is the value of x when y = 0. In this graphic, we have that when y = 0, x = -0.5. So the x-intercept is given by: (-0.5,0)

y-intercept:

The y-intercept is the value of y when x = 0. In this graphic, we have that when x = 0, y = 1. So the y-intercept is given by: (0,1).

Slope:

To find the slope, we select two points. The slope is given by the division of the change in y by the change in x.

Two points: (-0.5, 0) and (0,1)

Change in y: 1 - 0 = 1

Change in x: 0 - (-0.5) = 0 + 0.5 = 0.5

Slope: 1/0.5 = 2

Domain and range:

In a line, the domain is all real values, the same for the range.

Answer:

75.40 cubic meters

Explanation:

Given:

• The diameter of a cylinder is 4 m.

• The height is triple the radius

We want to find the volume of the cylinder.

First, determine the radius of the cylinder.

Next, we find the height.

Substitute these values into the formula for the volume of a cylinder:

The value closest to the volume of the cylinder is 75.40 cubic meters.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. The value of P(A) = 1/9.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Total number of 2-digit terms =(99 - 10) + 1 = 90

n(s) = 90

Number of 2 digits that have 4 in tens place = 40, 41, 42 ......49

n(a) = 10

P(A) = n(a)/n(s)

Substituting the values in the above equation, we get

P(A) = 10/90

P(A) = 1/9

The value of P(A) = 1/9.

Therefore, the correct answer is option (d) 1/9.

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Let's simplify the following equation

The point-slope form of a line is given by:

y - k = m ( x - h)

Where m is the slope of the line and (h, k) is a point through which the line passes.

We are given the values of m = 1/4 and the point (0, -1).

Substituting:

SOLUTION

A coin was flipped.

A = probability of it landing on a head

B = probability of it landing on a tail.

We are asked P(A and B), that means probability of landing on a head and on a tail.

A coin can only land on a head or it can land on a tail. It can't land on a head and a tail at the same time.

Therefore the probability of landing on a head and a tail is 0.

Hence, the answer is 0.

Answer:

Perimeter = 65.12 inches, Area = 292.48 square inches

Step-by-step explanation:

Perimeter:

Total perimeter = perimeter of semicircle + perimeter of rectangle (note: excluding the shared line, since that is not on the outside of the shape).

= [tex]\frac{1}{2} 2\pi r[/tex]

= [tex]\frac{1}{2} *2*3.14*8[/tex]

= 25.12

Perimeter = 25.12 + 12 + 12 + 16 = 65.12 inches

Area:
Total area = area of semicircle + area of rectangle

Area of semicircle = [tex]\frac{1}{2} \pi r^{2}[/tex]

= [tex]\frac{1}{2} *3.14* 8^{2}[/tex]

= 100.48

Area of rectangle = l * w

= 16 * 12

= 192

Total area = 100.48 + 192 = 292.48

Final Exam accounts for 65% of total.

The rest is 100 - 65 = 35%

On the 35%, he has 74% or 74 out of 100.

Let's say the final exam is out of 100 and we want to find how much he can afford to get to take him to "B".

Let's say his score needs to be "x" in order to get B.

The overall weighted average of the course would be counted as:

Breaking it down:

74 out of 100 means WHAT out of 35? (let's call the unknown "y")

y would be:

So, he currently has 25.9 out of 35.

He would need 83 to get overall average to 83%.

He would need:

83 - 25.9 = 57.1 out of 65

That is:

Basically he would need a percentage of 87.85% (MINIMUM) on the final exam to make his overall average to 83% (which is the bare minimum for a B grade).

Notice that [tex](x,y,-z)[/tex] is a gradient field:

[tex]\nabla f(x,y,z) = (x,y,-z) \implies \begin{cases} f_x = x \\ f_y = y \\ f_z = -z \end{cases}[/tex]

That is, there exists a scalar function [tex]f(x,y,z)[/tex] whose gradient is the given vector field. Solve for [tex]f[/tex].

[tex]\displaystyle \int f_x \, dx = \int x \, dx \implies f(x,y,z) = \frac12 x^2 + g(y,z)[/tex]

[tex]f_y = g_y = y \implies \displaystyle \int g_y \, dy = \int y \, dy \implies g(y,z) = \frac12 y^2 + h(z)[/tex]

[tex]f_z = h_z = -z \implies \displaystyle \int h_z \, dz = - \int z \, dz \implies h(z) = -\frac12 z^2 + C[/tex]

[tex]\implies f(x,y,z) = \dfrac{x^2+y^2-z^2}2 + C[/tex]

By the gradient theorem, it follows that

[tex]\displaystyle \int_{(1,0,-3)}^{(6,4,8)} x \, dx + y \, dy - z \, dz = f(6,4,8) - f(1,0,-3) = \boxed{-2}[/tex]

A)

If the dress costs x and the pair of pants cost $25 dollars less, the cost of the pants will be:

B)

We know that the dress costs x and the pants cost x-25. Molly bought 2 dresses and 3 pairs of pants, with the total amount of $675. Thus:

If x is the dress cost, so the dress will cost $150. And the pants:

The pants will cost $125.

The farmer put a total of 47 potatoes in one sack.

Here, we are given that a farmer harvested 192 pounds of Yukon Gold potatoes and 138 pounds of russet potatoes.

He divided the Yukon Gold potatoes evenly among 8 baskets.

Thus, the number of pounds of potatoes in each basket = 192/8

= 24

Similarly, he divided the russet potatoes evenly among 6 baskets.

Thus, the number of pounds of  russet potatoes in each basket = 138/6

= 23

Now, he fills a sack with one basket of Yukon Gold potatoes and one basket of russet potatoes.

n = the number of pounds of potatoes the farmer put in the sack

Thus, n = 24 + 23

n = 47

Thus, the farmer put a total of 47 pounds of potatoes in one sack.

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Answer:

3x + y = -3

Step-by-step explanation:

(-4, 9), (2, -9)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁      -9 - 9          -18          -18

m = ----------- = ----------- = ---------- = ------- = -3

       x₂ - x₁        2 - (-4)      2 + 4        6

y - y₁ = m(x - x₁)

y - 9 = -3(x - (-4)

y - 9 = -3(x + 4)

y - 9 = -3x - 12

   +9           +9

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

y = -3x - 3

Standard Form:

-3x + y = -3

I hope this helps!

x = 10 is the solution to the equation -8 - x = -3( 2x - 4 ) + 3x using DCMAM method.

Given the equation in the question;

First, apply the distributive property to eliminate the parenthesis.

-8 - x = -3( 2x - 4 ) + 3x

-8 - x = -3×2x -3×-4 + 3x

Multiply -3 × 2x

-8 - x = -6x -3×-4 + 3x

Multiply -3 × -4

-8 - x = -6x + 12 + 3x

Next, combine like terms.

Add -6x and 3x

-8 - x = -3x + 12

Next, move variable to one side and constant terms to the other.

-x + 3x =  12 + 8

Add -x and 3x

2x =  12 + 8

Add 12 and 8

2x = 20

Divide both sides by 2

2x/2 = 20/2

x = 20/2

x = 10

Therefore, the value of x is 10.

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Consider the given unbalanced equation which says " 16 divided by 8 " in the Left Hand Side, while it says " 16 divided by 8 then minus one ". This can be represented as,

Consider two things. First, acording to BODMAS rule, division is dprferred over subtraction. Second,

This is a combination of the form:

So:

Answer:

21

ANSWER :

EXPLANATION :

The first step to this problem is finding the amount of butterfat there are in the 385 gallons milk with 5% of butterfat in it. To do that we need to multiply the percentage by the total amount of milk. This is done below:

There are 19.25 gallons of butterfat on the final mixture, the amount of butterfat from each of the milks we are going to mix need to be equal to that. The first milk contains 8% of butterfat, while the second milk contains 1%. So we have:

Where "x" is the number of gallons from the first milk and "y" is the number of gallons from the second milk. The number of gallons of each milk, when added, should be equal to the number of gallons on the final milk, so we have:

The same is valid for the amount of butterfat.

We have now created a system of equations as shown below:

To solve this system we will multiply the first equation by "-0.01":

Now we need to add both equations.

To find the value of "y" we will use the first equation:

We need 220 gallons from the 8% butterfat milk and 165 gallons from the 1% butterfat milk.

Answer:

y = -16 (x - 1)^2 + 112

The object lands on the ground in approximately 3.6s

Explanation:

The equation given is that of a parabola.

Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.

The vertex form of a parabola is

where (h, k) is the vertex.

The only question is, what is the vertex for our function h(t)?

Remember that if we have an equation of the form

then the x-coordinate of the vertex is

Now in our case b = 32 and a = -16; therefore,

We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get

Hence, the y-coordindate is k = 112.

Therefore, the vertex of the parabola is (1, 112).

With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.

The only problem is that we don't know what the value of a is. How do we find a?

Note that the point (0, 96) lies on the parabola. In other words,

Therefore, the vertex form of the parabola must also contain the point (0, 96).

Putting in t = 0, h = 96 into the vertex form gives

subtracting 112 from both sides gives

With the value of a in hand, we can finally write the equation of the parabola on vertex form.

Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.

We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.

Thus we solve,

Now subtracting 112 from both sides gives

Dividing both sides by -16 gives

taking the square root of both sides gives

adding 1 to both sides gives

Hence, the two solutions we get are

Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.

Therefore, it takes about 3.6 seconds for the object to hit the ground.

We can subtract 5x from 7x - 6 like this:

7x - 6 - 5x

Now, we just have to combine like terms, in this case, the terms that have the x variable, like this:

7x - 5x - 6

2x - 6

Then, after subtracting 5x from 7x - 6 we get 2x - 6

The graph of the linear function and it's inverse is given at the end of the answer.

The inverse function is: [tex]h^{-1}(x) = -6x + 55[/tex]

To find the inverse function, we exchange x and y in the original function, then isolate y.

In the context of this problem, first we have to find the function h(x), which is a linear function going through points (1,9) and (3,2), hence the slope is given by:

m = (2 - 1)/(3 - 9) = -1/6.

Then:

y = -x/6 + b.

When x = 1, y = 9, hence we can find the intercept b as follows:

9 = -1/6 + b

b = 54/6 + 1/6

b = 55/6.

Then the equation is:

h(x) = -x/6 + 55/6

Then:

y =  -x/6 + 55/6

6y = -x + 55

6x = -y + 55

y = -6x + 55.

Hence the inverse function is:

[tex]h^{-1}(x) = -6x + 55[/tex]

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In an ordered pair (x,y), x denotes the domain of the relation, and y denotes the range of the relation.

Knowing this, the three ordered pairs that will form a relation with a range of {-3, 4, 7} are

(-1, -3), (0, 4), and (2,7).

Answer: The number is 4,000.

Step-by-step explanation:

        First, we will turn 0.2% into a decimal.

0.2% / 100 = 0.002

        Next, we will set up an equation. Let x be equal to "what number:"

0.2% of what number is 8 ➜ 0.002x = 8

        Lastly, we will solve by dividing both sides by 0.02.

0.002x = 8

x = 4,000

        If we wish to, we can check our answer.

4,000 * 0.002 = 8

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