Arthur has blended coffee worth 95 pesos per kilogram with coffee worth 115 pesos per kilogram to make 50 kilograms of coffee that will be sold at 107 pesos per kilogram. How many kg each kind did he blend?

Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

Answer:

\(\frac{4}{5}\)

0.8

Step-by-step explanation:

Happy to help:)

The equivalent expression using the properties of logarithms is log2(zx^2/y^2) + log9(y^4x^12)

The logarithmic expression is given as:

log2z + 2log2x + 4log9y + 12log9x − 2log2y

Regroup the terms of the expression according to their base

log2z + 2log2x − 2log2y + 4log9y + 12log9x

Rewrite some of the terms as exponents

log2z + log2x^2 − log2y^2 + log9y^4 + log9x^12

Apply the sum and quotient law of indices

log2(z * x^2/y^2) + log9(y^4 * x^12)

Evaluate the products

log2(zx^2/y^2) + log9(y^4x^12)

Hence, the equivalent expression using the properties of logarithms is log2(zx^2/y^2) + log9(y^4x^12)

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Answer:

y is 0,3

Step-by-step explanation:

To find the x-intercept, substitute in

0

for

y

and solve for

x

. To find the y-intercept, substitute in

0

for

x

Answer:

(0,3)

Step-by-step explanation:

Two methods:

Method 1:  General method for any equation

Method 2: Method specific for parabolas in standard form

Method 1:  General method for any equation

For any two-variable equation to be graphed, the y-intercept is the point where the graph crosses the y-axis.  The y-axis is a vertical line through the origin (0,0).

Any y-intercept is on that line, and to get to that point starting from the origin, one can't travel left or right to get to the y-intercept point (without moving back to the y-axis).  The only movement would be up or down.

Since no left-right movement will happen, the x-coordinate is zero.

For any two-variable equation, the x and y coordinates of any point on the graph are linked by the equation.  If it is known that the x-value is zero, the y-value associated with that x-value is given by substituting zero into the equation everywhere there is an "x", and solving for "y".

\(y=-4x^2-x+3\)

\(y=-4(0)^2-(0)+3\)

Order of operations requires exponents before multiplication, or addition & subtraction...

\(y=-4(0)-(0)+3\)

multiplication...

\(y=0-0+3\)

addition & subtraction, from left to right...

\(y=3\)

So, when the x-value is zero, the y-value is three.  Therefore, the ordered pair representing that point is (0,3).

Method 2: Method specific for parabolas in standard form

The given equation is the equation for a parabola (as stated in the question), and it is given in "standard form": \(y=ax^2+bx+c\), where a, b, and c are real numbers (and a isn't equal to zero, because then the x-squared term would be zero, and the equation would really just be a linear equation).

Note that for our equation, it is in standard form if we rewrite the equation to only use addition, \(y=-4x^2+-1x+3\), where \(a=-4, ~b=-1 ~ \text{and}~c=3\)

For a parabola in standard form, the y-intercept is always at a height of "c".

So, the y-intercept would be (0,3).

Answer:

3/100 × 30000 is the answer to your question.

Answer:

-5

Step-by-step explanation:

(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5

Answer:

  s = -6

Step-by-step explanation:

Combining terms, we get ...

  (5/4)s = -15/2

Multiplying by 4/5 gives ...

  s = (4/5)(-15/2)

  s = -6

Let's denote the three numbers A, B, and C.

Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.

Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.

Let's list the possible combinations:

These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).

Answer:

A

Step-by-step explanation:

The correct answer is A

Answer:

1 1/4

Step-by-step explanation:

7 1/2 divided by 6

Answer:

so the answer is+$:$_1;28_6(4?3926$54;2(the 35$$-(3836252;3(837353+3(383635;33(836$-

Step-by-step explanation:

thanks me later

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

it is incomplete question isnt it??

Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

8 possible sequences in total. Thus, A tree with 8 outcomes, option 1 is correct.

A diagram with a structure of branching connecting lines, representing different processes and relationships.

Here is a tree diagram showing all the possible outcomes of Sandra tossing a coin three times:

In the diagram, each branch represents the outcome of one toss of the coin. The letters "H" and "T" represent "heads" and "tails," respectively. Each path from the top of the tree to a bottom node represents a possible sequence of coin tosses, and there are 2³ = 8 possible sequences in total.

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Complete question:

Sandra tossed a coin 3 times. Which tree diagram shows al the possible outcomes of the coin landing heads up or tails up.

A tree with 8 outcomes

A tree with 12 outcomes

A tree with 9 outcomes

A tree with 6 outcomes

Answer:

I think its C

Step-by-step explanation:

Answer: +5

Step-by-step explanation:

-6 + 5 = -1

-1 + 5 = 4

4 + 5 = 9

9 + 5 = 14

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

Answer:

B is greater than A by 1/4 of A

Step-by-step explanation:

Let's use the information given in the problem to write expressions for the values of a and b:

a = b - (1/5)b = (4/5)b

b is greater than a by the difference:

b - a = b - (4/5)b = (1/5)b

To express this difference as a fraction of a, we divide by a:

(b - a)/a = ((1/5)b)/((4/5)b) = 1/4

Therefore, b is greater than a by 1/4 of a.

Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

The points of the line for the problem is (8, -4).

For the given question;

The equation of the line in point slope form is given as;

(y + 4) = (1/3)(x - 8)

The standard form of equation of line in point slope form is;

y - y1 = m(x - x1)

where, m is the slope and (x1, y1) is the points.

Thus, by comparing the given equation with the standard form.

(x1, y1) = (8, -4)

Thus, the points of the given equation of the line is (8, -4).

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Answer:

8+9=17

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

If a sum of a number and 9 is 17 that means that a number plus 9 equals 17 you could write this out in mathematical form as

x + 9 = 17

You probably don't have to use algebra to solve this but I'll show you how just in case

subtract 9 from both sides

x + 9 = 17

-9       -9

x = 8

this is your solution, hope this helped :)

Given:

The point is (-6,5).

It is on the terminal side of theta.

To find:

The values of \(\sin\theta\) and \(\cos \theta\).

Solution:

In the point (-6,5),

x-coordinate : x=-6

y-coordinate : y=5

So, \(r=\sqrt{x^2+y^2}\)

\(r=\sqrt{(-6)^2+(5)^2}\)

\(r=\sqrt{36+25}\)

\(r=\sqrt{61}\)

Now,

\(\sin \theta=\dfrac{y}{r}\)

\(\sin \theta=\dfrac{5}{\sqrt{61}}\)

\(\cos \theta=\dfrac{x}{r}\)

\(\cos \theta=\dfrac{-6}{\sqrt{61}}\)

Therefore, the required values are \(\sin \theta=\dfrac{5}{\sqrt{61}}\) and \(\cos \theta=-\dfrac{6}{\sqrt{61}}\).

Answer:

15(16+3) is the right answer

Step-by-step explanation:

mark me brainliest PLS

Answer:

Its 2/8

Step-by-step explanation:

2/8 simplified is 1/4

Answer:

The answer will be 2/8 because if you think about it 4/8 is 1/2 and 1/2 of 4/8 is 2/8 and since 1/2 4/8 is 2/4 which is actually 1/2 of 1/2 so that makes it 1/4 hope this helps!!

(to make it clear the answer is 2/8)

Answer:

a. \(B+S = 1 \)

\(0.06B+0.1S \geq 0.075 \)

\(B \geq 0.3 \)

Objective function:

\(R=0.06B+0.1S\)

b) See Attached picture

30% in bonds and 70% in stocks

Step-by-step explanation:

a.

In order to solve the first part of the problem we need to take into account that the problem wants us to determine the percentage that should be allocated to each of the possible investment alternatives. In that case, the sum of the percentages must be equal to 1 (which means that we will have 100 of the trust fund)

so that gives us our first restriction for the problem.

B+S=1

Next, the problem tells us that the projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. It also states that he wants to select a mix that will enable him to obtain a total return of at least 7.5%, so we can take this information and get the second restriction from it:

\(0.06B+0.1S \geq 0.075 \)

Next, the problem tells us that whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund, so that's where the last restriction comes from:

\(B \geq 0.3 \)

now, the idea is to optimize the investment, this is get the greatest amount of money out of the trust fund, so the objective function is:

\(R=0.06B+0.1S\)

which represents the return on the investment.

b)

For part b we can start by graphing each of the restrictions:

\(B+S = 1 \)

This will be a single line, you can draw the line by setting B=0 first so you get:

0+S=1

S=1

So the first point to plot will be (0,1)

next, we can set s=0 to get:

B+0=1

B=1

so the second point to plot will be (1,0)

so you can plot the two points and connect them with a straight line. This is the green line on the uploaded graph.

Next we can graph the second restriction:

\(0.06B+0.1S \geq 0.075 \)

we can use the same procedure we used for the previous graph, in this case the points would be:

(0 , 0.75) and (1.25, 0)

and again connect the two points with a straight line. Next we need to decide which region of the graph to shade for which we can pick two arbitrary points on each side of the line, for example we can pick:

(0,0) and (2,2) and see which one makes the inequality true:

for (0,0) we get:

\(0.06B+0.1S \geq 0.075 \)

\(0.06(0)+0.1(0) \geq 0.075 \)

\(0 \geq 0.075 \)

Which is false, therefore we need to shade the other region of the graph:

for (2,2) we get:

\(0.06B+0.1S \geq 0.075 \)

\(0.06(2)+0.1(2) \geq 0.075 \)

\(0.32 \geq 0.075 \)

Which is true, so we shade the region of the graph that contains that point. (see red graph)

now we graph the third restriction:

\(B \geq 0.3 \)

In order to graph this third restriction we just need to draw a vertical line at B=0.3 and shade everything to the right of that line. (Blue graph)

Now, we can analyze the graph, in this case we need to locate the points where the green line crosses the red and the blue line which gives us the following coordinates:

(0.3, 0.7) and (0.625, 0.375)

these two points can be found by setting the first restriction equal to each of the other two restrictions if you are to do it algebraically. If you are using a graphing device, you can directly read them from the graphs.

So once we got those points, we can see which one gives us the greatest percentage of return.

let's test the first point (0.3, 0.7)

\(R=0.06B+0.1S\)

\(R=0.06(0.3)+0.1(0.7)\)

R=0.088

so this distribution gives us 8.8% in return, let's test the second point:

(0.625, 0.375)

\(R=0.06B+0.1S\)

\(R=0.06(0.625)+0.1(0.375)\)

R=0.075

so this distribution gives us 7.5% in return.

In this case the best distribution for us is 30% in bonds and 70% in the stock fund to get a return of 8.8%