A fruit punch that contains 10% fruit juice is combined with 100% fruit juice. How many ounces of each should be used to make 51oz of a mixture that is 70% fruit juice?

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Explanation:

For any two vectors defined as follows

u = <a,b>

v = <c,d>

the dot product is computed by

u dot v = a*c + b*d

If the dot product of the vectors is 0, then the vectors are orthogonal. Meaning they are perpendicular to one another.

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Let's find the dot product of these two given vectors

u = < 2, -4 >

v = < 6, 3 >

u dot v = 2*6 + (-4)*3

u dot v = 12 - 12

u dot v = 0

Therefore, these two vectors form a right angle and are orthogonal

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Extra info:

If we can show that u = <a, b> and v = <ka, kb> for some real number k, then we have shown that vectors u and v are parallel.

Answer:

what do u want exactly or it us a theorem

Answer  

Step-by-step explanation:

Answer:

yes that's correct

Step-by-step explanation:

let's say a question was given with the base of a triangle as 5cm and the height triangle as 8cm.

you will go by

solution

area = 1/2 * b * h

area = 1/2 (5 * 8)

area = 1/2 (40)

area = 20cm²

hope this helps

Answer:

The correct answer is - 332 pages.

Step-by-step explanation:

Given:

number of articles submissions - 75

number of pages in the yearbook on current plan = 156

pages required for two articles = 13 pages.

The number of pages to add = ?

Solution:

1 article takes pages in the yearbook = 13/2

= 6.5

the number of pages required for 75 articles = 75*6.5

= 487.5

The number of pages to add in the yearbook = 487.5 - 156

= 331.5 or 332.

Thus, the correct answer is - 332 pages.

Answer:

D

Step-by-step explanation:

Have a nice day :)

9514 1404 393

Answer:

Step-by-step explanation:

A Hamiltonian circuit visits each node once and returns to its start. There is no simple way to determine if such a circuit exists.

__

For graph 2, if there were a circuit, paths ACB, ADB, and AEB would all have to be on it. Inclusion of all of those requires visiting nodes A and B more than once, so the circuit cannot exist.

__

For graph 3, the circuit must include paths BAD and DFE. That only leaves node C, which can be reached from both nodes B and E, so path ECB completes the circuit.

Answer:

5

Step-by-step explanation:

Answer:

15,140,170,220,310,370,475,520,580,720

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

jjjj

Answer:

Step-by-step explanation:

Given,

Sides of a square is = 7 + 3x

Therefore,

Perimeter of a square = 4 × side

= 4 × (7 + 3x )

= 28 + 12x (Ans)

Answer:

its would be a and d

Step-by-step explanation:

6 times 5

Answer:

b

Step-by-step explanation:

ive done it before

Answer:

0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.

Step-by-step explanation:

For each test, there are only two possible outcomes. Either it is positive, or it is negative. The probability of a test being positive or negative is independent of any other test, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability of an individual blood sample testing positive for the virus is 0.06.

This means that [tex]p = 0.06[/tex]

If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture.

It will be positive if at least one of the tests is positive, that is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.06)^{0}.(0.94)^{3} = 0.8306[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8306 = 0.1694[/tex]

0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.

Answer:

A. Qualitative - Column chart

Step-by-step explanation:

Data could either be qualitative or quantitative. Quantitative data are usually given in a definite number, i.e it can be counted. While qualitative deals with characteristics, i.e it can be collected either by the use of questionnaires, or any similar method.

Therefore for the given question, the data survey is qualitative. And since the result would be presented as a graph showing the percentage users for each application, a column chart would be appropriate.

Thus for the data and its presentation, the answer is A. Quantitative - Column chart

Answer:

[tex]\frac{80}{45} =k[/tex]

Step-by-step explanation:

image/actual=  8/4.5

8(10)/4.5(10)= 80/45

Answer:

B and C

Step-by-step explanation:

Using the Pythagorean theorem a²+b²=c², those are the correct answers

Answer:

763.41 ft

Step-by-step explanation:

Answer:

15/240 = 5/80= 1:16. helpful answer

Answer:

1+4=60

5=60

60/5

12#

Step-by-step explanation:

or,let it be X

1x+4x=60

5x=60

X=60/5

there fore

X=12#

Answer:

B

Step-by-step explanation:

they said 2 hours for each final

Hi there!  

»»————-　★　————-««

I believe your answer is:  

x = -4

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x':}}\\\\2(x-7)=10x+18\\------------\\\rightarrow 2x-14 = 10x + 18\\\\\rightarrow 2x - 14 + 14 = 10x + 18 + 14\\\\\rightarrow 2x = 10x + 32\\\\\rightarrow 2x-10x=10x-10x+32\\\\\rightarrow-8x=32\\\\\rightarrow\frac{-8x=32}{-8}\\\\\rightarrow \boxed{x=-4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

[tex]C = 29.53x[/tex]

Step-by-step explanation:

Given

[tex]Unit\ cost = \$29.53[/tex]

Required

The cost of fencing (C)

The cost is calculated as:

[tex]C = Unit\ Cost * Perimeter\ of fencing[/tex]

Let:

[tex]x \to Perimeter\ of fencing[/tex]

So, we have:

[tex]C = Unit\ Cost * x[/tex]

[tex]C = 29.53 * x[/tex]

[tex]C = 29.53x[/tex]

The question cannot be solved further since the dimension of the fence is not given

If you know the dimension, calculate the fence perimeter and substitute the value for x

The answer is attached. I hope this helps answer your question!

Answer:

The equation of the parabola is y = x²/4

Step-by-step explanation:

The given focus of the parabola = (0, 1)

The directrix of the parabola is y = -1

A form of the equation of a parabola is presented as follows;

(x - h)² = 4·p·(y - k)

We note that the equation of the directrix is y = k - p

The focus = (h, k + p)

Therefore, by comparison, we have;

k + p = 1...(1)

k - p = -1...(2)

h = 0...(3)

Adding equation (1) to equation (2) gives;

On the left hand side of the addition, we have;

k + p + (k - p) = k + k + p - p = 2·k

On the right hand side of the addition, we have;

1 + -1 = 0

Equating both sides, gives;

2·k = 0

∴ k = 0/2 = 0

From equation (1)

k + p = 0 + 1 = 1

∴ p = 1

Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;

(x - 0)² = 4 × 1 × (y - 0)

∴ x² = 4·y

The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;

y = x²/4.

Answer:

We know that the height equation is given by:

H(t) = -16*t^2 + 108*t + 28

in ft.

First, we want to find the maximum height of the ball.

The first thing we can see is that the leading coefficient of the quadratic equation is negative, this means that the arms of the graph will open downwards, so the vertex of the quadratic equation is the maximum.

We also know that the ball will reach its maximum height when its velocity is zero (this means that the object stops going upwards at this point).

To get the velocity equation we need to derivate the above equation, we will get:

V(t) = 2*(-16)*t + 1*108

V(t) = -32*t + 108

We need to find the value of t such that this is zero, we will get:

V(t) = 0 =  -32*t + 108

        32*t = 108

             t = 108/32 = 3.375

So the ball reaches its maximum height after 3.375 seconds.

Then the maximum height is given by the height equation evaluated in that time, we will get:

H(3.375) =  -16*(3.375)^2 + 108*3.375 + 28 = 210.25

Then the maximum height of the ball is 210.25 ft

The ball will hit the ground when:

H(t) = 0

Then we just need to solve:

0 =  -16*t^2 + 108*t + 28

Using the Bhaskara's equation we can find that the two solutions for t are:

[tex]t = \frac{-108 \pm \sqrt{(108)^2 - 4*(-16)*28} }{2*(-16)} = \frac{-108 \pm 116}{-32}[/tex]

So the two solutions are:

t = (-108 + 116)/-32 = -0.25

t = (-108 - 116)/-32 = 7

Because t represents time, we should take only the positive value of time (as t = 0 is the time when the ball is thrown).

Then we can conclude that the ball hits the ground after 7 seconds.

Answer:

B) 18.610

Step-by-step explanation:

Using SOHCAHTOA (trig ratios), the tangent of 28° is the ratio of its opposite length to its adjacent.

in this scenario, the side opposite to 28°, and the side adjacent to it is 35°

tan 28° = y/35

Using inverse operations, multiply both sides by 35

y = 35 * tan 28

Solve your answer using your calculator.

I attached a picture that can help you later to recognize what function to use depending on the sides given.

Answer:

there are no real number solutions

Step-by-step explanation:

2x² + 8 = 0

x² + 4 = 0

x² = -4

these solutions all involve "i", the imaginary or complex numbers, as normally the square of any number has to be positive (and cannot be negative).

Answer:

A. 42½ units

Step-by-step explanation:

the volume = 5×2×4¼ = 10×4¼ = 42½

Answer:

Number is 36

Step-by-step explanation:

Let the number be x

one half  of the number is  [tex]\frac{1}{2} x[/tex]

6 subtracted from one half is 12, That is,

                                                             [tex]\frac{1}{2} x - 6 = 12\\\\\frac{1}{2}x = 12 +6 \\\\x = 18 \times 2 = 36[/tex]

[tex]30.87[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \frac{926}{30} \\ = 30 \frac{26}{30} \\ ( \: or \: ) \\ = 30.8666 \\ = 30.87 [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]