Ms. Albero decided to make juice to serve along with the pizza at the Student Government party. The directions said to mix 2 scoops of powdered drink mix with a half a gallon of water to make each pitcher of juice. One of Ms. Albero’s students said she will mix 8 scoops with 2 gallons of water to get 4 pitchers. How can you use the concept of proportion to decide whether the student is correct?

Step-by-step explanation:

a=

[tex] a = \sqrt{b + 16} \\ a { }^{2} = b + 16 \\ b = a {}^{2} - 16[/tex]

Answer:

28 Weeks

Step-by-step explanation:

8÷2=4

4×7=28

28 Weeks

Answer:

6.25 is the answer, I really dfon't know how to figure out which would be the procedure becuase I'm a little oxidated

Step-by-step explanation:

102*100=10200

10200÷126=80.95

So the third one is correct

Answer:1

6

−

9

Step-by-step explanation:there you go

Answer:

(C) 8 x 10,000 + 3 x 1,000 + 7 x 100 + 3 x 10 + 4 x 1 + 2 x 0.1 + 1 x 0.01

Step-by-step explanation:

8 x 10,000 + 3 x 1,000 + 7 x 100 + 3 x 10 + 4 x 1 + 2 x 0.1 + 1 x 0.01=

80,000 + 3,000 + 700 + 30 + 4 + 0.2 + 0.01=

83,734.21.

I hope this helps!

Answer:

15= -3m-9

15+9 = -3m

24 = -3m

-8= m

Therefore the m value is -8

Answer:

2:1

Step-by-step explanation:

average age of both = 40

average age of teachers = 35

average age of professors = 50

35 + 35 + 50 = 120

120 / 3 = 40

Answer:-2(9+32n)

Step-by-step explanation:

Answer:

never

Step-by-step explanation:

Answer: Hello! My guess would be 7. Sorry, if I'm wrong.

Step-by-step explanation: Count the jumps between A and C.

Answer: 1 1/2

Step-by-step explanation:

Answer:

B C

Step-by-step explanation:

because imagine that you have a huge doll house and you're wondering if you can get it in your room but you aren't sure what will happen if you try and push it through your door

[tex]\dfrac{1}{8}\cdot \dfrac{1}{8} = \dfrac{1}{8^2} = \left(\dfrac{1}{8}\right)^2 = \left(\dfrac{1}{8}\cdot 1\right)^2 = \left(\dfrac{1}{8}\cdot \dfrac{2}{2}\right)^2 = \left(\dfrac{2}{16}\right)^2[/tex]

Answer:

a. 10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.

b. 0.2457 = 24.57% probability 10 of the problems can be resolved today

c. 0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today

d. 0.5017 = 50.17% probability more than 10 of the problems can be resolved today

Step-by-step explanation:

For each case, there are only two possible outcomes. Either they are solved, or they are not. Cases are independent of each other. So we use the binomial probability distribution 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 expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

It can resolve customer problems the same day they are reported in 80% of the cases.

This means that [tex]p = 0.8[/tex]

Sample of 13 cases:

This means that [tex]n = 13[/tex]

a. How many of the problems would you expect to be resolved today? What is the standard deviation?

Expected:

[tex]E(X) = np = 13*0.8 = 10.4[/tex]

Standard deviation:

[tex]\sqrt{V(X)} = \sqrt{13*0.8*0.2} = 1.44[/tex]

10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.

b. What is the probability 10 of the problems can be resolved today?

This is [tex]P(X = 10)[/tex]. So

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

[tex]P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457[/tex]

0.2457 = 24.57% probability 10 of the problems can be resolved today.

c. What is the probability 10 or 11 of the problems can be resolved today?

This is [tex]p = P(X = 10) + P(X = 11)[/tex]. So

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

[tex]P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457[/tex]

[tex]P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680[/tex]

[tex]p = P(X = 10) + P(X = 11) = 0.2457 + 0.2680 = 0.5137[/tex]

0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today.

d. What is the probability more than 10 of the problems can be resolved today?

This is

[tex]P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13)[/tex]. So

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

[tex]P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680[/tex]

[tex]P(X = 12) = C_{13,12}.(0.8)^{12}.(0.2)^{1} = 0.1787[/tex]

[tex]P(X = 13) = C_{13,13}.(0.8)^{13}.(0.2)^{0} = 0.0550[/tex]

[tex]P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) = 0.2680 + 0.1787 + 0.0550 = 0.5017[/tex]

0.5017 = 50.17% probability more than 10 of the problems can be resolved today

Answer:

Chart nº 2

Step-by-step explanation:

Just match each points you will see which one is actually on the diagram!

Answer:

32 degrees

Step-by-step explanation:

The total angle formed is 90 degrees because there is a right angle.

So, 90 - 58 = g

      32 degrees = g

A PARALLEL line has the same angular coeficient, so:

[tex]f(x) = 2x+b[/tex]

[tex]f(4) = 5[/tex]

[tex]5 = 2\cdot 4 +b[/tex]

[tex]b = 5-8[/tex]

[tex]b = -3[/tex]

The line asked is:

[tex]f(x) = 2x-3[/tex]

Answer:

-2x+y=-3

Step-by-step explanation:

Choose a point (4,5) that the parallel line will pass through.

Find the slope m=2

To find an equation that is parallel to   y=2x-4 the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.

y-y1=m(x-x1) if m=2 and x1=4 and y1=5

y-5=2(x-4)

y-5=2x-8

Solve for  y --- > y=2x-3

-2x+y=-3

(-2x+y=-3)*-1

2x-y=3

Answer:

31

Step-by-step explanation:

31

Answer:

y=3

Step-by-step explanation:

-12+6=-6

-6/-2=3

Answer:

[tex] - \frac{1}{5 \sqrt{y} } [/tex]

Answer:

option 1

Step-by-step explanation:

[tex]\sqrt{y} =y^{\frac{1}{2}}\\\\(\frac{1}{\sqrt{y} })^{\frac{-1}{5}} =(\frac{1}{y^{\frac{1}{2}}})^{\frac{-1}{5}}\\\\= (y^{\frac{-1}{2}})^{\frac{-1}{5}}\\\\=y^{\frac{-1}{2}*\frac{-1}{5}}\\\\= y^{\frac{1}{10}}\\\\=\sqrt[10]{y}[/tex]

Answer:

The polynomial is:

[tex]p(x) = x^3 + 2x^2 - 3x + 20[/tex]

Step-by-step explanation:

A third degree polynomial can be written in function of it's zeros [tex]x_1, x_2, x_3[/tex] the following way:

[tex]p(x) = a(x - x_1)(x - x_2)(x - x_3)[/tex]

In which a is the leading coefficient.

Integer coefficient that have zeros: 1+2i, 1-2i, -4

Leading coefficient: 1

So

[tex]p(x) = 1(x - (1+2i))(x - (1-2i))(x - (-4))[/tex]

[tex]p(x) = (x - 1 -2i)(x - 1 + 2i)(x + 4)[/tex]

[tex]p(x) = ((x-1)^2 - (2i)^2)(x + 4)[/tex]

[tex]p(x) = (x^2 - 2x + 1 - 4i^2)(x + 4)[/tex]

Since [tex]i^2 = -1[/tex]

[tex]p(x) = (x^2 - 2x + 1 + 4)(x + 4)[/tex]

[tex]p(x) = (x^2 - 2x + 5)(x + 4)[/tex]

[tex]p(x) = x^3 + 4x^2 - 2x^2 - 8x + 5x + 20[/tex]

[tex]p(x) = x^3 + 2x^2 - 3x + 20[/tex]

Answer:2869

I kno :)

Answer:

-5

Step-by-step explanation:

becuses look at where the slope intersecs the y axis. Its -5

EZ

Answer:

its

3.6

Step-by-step explanation:

trust me

Answer:

522

Step-by-step explanation:

8x34=272+tips=522

Answer:

24

Step-by-step explanation:

Put it in Desmos, and it’ll show you

The reasonable domain of the function is 8 ≤ x ≤ 24.7.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -0.5x² + 16x – 96

The function represents the height of a rocket as a function of its horizontal position.

It is reasonable to assume that the rocket is launched from the ground

(x = 0) and that it has some minimum height (above ground level) before it is launched.

Now,

We can find this minimum height by finding the vertex of the parabola, which is given by.

x = -b / (2a)

where a = -0.5 and b = 16.

Plugging in these values, we get.

x = -16 / (2(-0.5))

x = 16

Now,

The vertex occurs at x = 16.

To find the minimum height, we can plug this value into the function.

f(16) = -0.5(16)² + 16(16) - 96

       = 128

Therefore,

The rocket has a minimum height of 128 feet above ground level before it is launched.

To find the reasonable domain of the function.

Since the rocket is launched from the ground at x = 0 and has a minimum height of 128 feet, it is reasonable to assume that the rocket will remain above ground level for all values of x greater than or equal to 8, since the rocket must clear a height of 128 feet by the time it reaches x = 8.

Now,

We can find the x-value where the rocket reaches ground level

(i.e., its height is zero) by setting f(x) = 0.

Solving for x.

-0.5x² + 16x - 96 = 0

Using the quadratic formula.

x = ( -16 ± √(16² - 4(-0.5)(-96)) ) / (2(-0.5))

x = ( -16 ± √(1216) ) / (-1)

x ≈ 24.7 or x ≈ 7.3

Since the rocket is launched from the ground at x = 0, it is not reasonable to consider values of x less than 0.

Therefore,

The reasonable domain of the function is 8 ≤ x ≤ 24.7

This means,

The rocket will remain above ground level for all values of x between 8 and approximately 24.7.

Thus,

The reasonable domain of the function is 8 ≤ x ≤ 24.7.

Learn more about functions here:

https://brainly.com/question/28533782

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