1 Susie wants to make some hot cereal for breakfast. The directions say to use 3 cups
of water with 1 cup of cereal to make 4 servings. Susie only wants 1 serving.
a
How much cereal should she use?
b How much water should she use?

Answer:

1/4

Step-by-step explanation:

[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]

Assuming the number cube has faces number 1 through 6, the probability of rolling any of the number is 1/6.

Therefore,

P(odd number) = P(1) or P(3) or P(5)

                         = 1/6 + 1/6 + 1/6

                         = 3/6

                         = 1/2

Similarly,

P(even number) = P(2) or P(4) or P(6)

                           = 1/6 + 1/6 + 1/6

                           = 3/6

                           = 1/2

⇒ P(odd) AND P(even) = 1/2 × 1/2 = 1/4

I can give you a hint. So when we do the composition of functions, if we plug 2 functions into each other and get x by itself, that means the functions are inversely related.

For this problem, simply find the inverse of f(x).

If you are stuck, I could provide you with a solution below...

f(x) = 8x³ - 2

y = 8x³ - 2

y + 2 = 8x³

(y + 2)/8 = x³

cube root((y + 2)/8) = x

g(x) = cube root((x + 2)/8)

The value of function g(x) after solving will be ∛(x + 2) / 2.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The value of function,

f(x) = 8x³ − 2

And, f(g(x)) = x and g(f(x)) = x

Now,

Since, f(g(x)) = x

And, f(x) = 8x³ − 2

The substitute x = g (x) in above equation we get;

f (g(x)) = 8 (g(x))³ - 2

x = 8 (g(x))³ - 2

Add 2 both side;

x + 2 = 8 (g(x))³  

Divide by 8;

(x + 2)/8 = (g(x))³

Take cube root both side;

∛(x + 2)/8 = g(x)

g(x) = ∛(x + 2) / 2

So, The value of function g(x) after solving will be ∛(x + 2) / 2.

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \:b(b + 12) = 0[/tex]

Here, we have two cases :

[tex]\qquad \sf  \dashrightarrow \:b = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \:b + 12 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \:b = - 12[/tex]

Hence, 0 and -12 are the only possible solutions for given equation.

Answer:

4

Step-by-step explanation:

(12y2-2y+18)/(4y2-y+6)=3-2+3=4

Answer:

Final answer -

[tex]d(FD) = \sqrt{65 } \: units[/tex]

hope helpful :D

Answer:

A on edge

Step-by-step explanation:

:)

A triangle is a three-edged polygon with three vertices. The length of QS is equal to 17 units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Given that the Line l is a perpendicular bisector of line segment RQ and bisects it at point T. Therefore, the length of the two lines is,

RT = QT

Now, in ΔRST and ΔQST,

RT ≅ QT

ST ≅ ST {Common side}

Now, since the two triangles are the right-angled triangle, therefore, the two triangles are congruent. Thus, we can write,

RS = SQ

Given that the Line segment, RS is 3x+2. Line segment SQ is 5x-8.

RS = SQ

3x + 2 = 5x - 8

2 + 8 = 5x - 3x

10 = 2x

x = 5

QS = 5x - 8

     = 5(5) - 8

     = 25 - 8

     = 17 units

Hence, the length of QS is equal to 17 units.

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Answer:

Any ratio where the original sides are both multiplied by the same number.

For example,

4 : 5  (your ratio)

4 x 2 : 5 x 2  (multiply both sides by a number)

8 : 10   (equivalent ration)

Answer:

2/5 :)

Step-by-step explanation:

Answer:

.................

216cm^2

Step-by-step explanation:

brainliest please

Answer:

15500

Step-by-step explanation:

Solution

here

price of tv after discount: 13950

discount : 10%

now,

Answer:

Step-by-step explanation:

Use law of cosine to calculate the other side.

c² = a² + b² -2ab Cos C

Here, c  is the length of the side which is  opposite side to ∠E

a = 29   ; b = 25  and C = 109

c² = 29² + 25² - 2*29*25*Cos 107

    = 841 + 625 - 1450* (-0.2923)

     = 1466 + 423.835

     = 1889.835

c =√1889.835

c = 43.47 ≈ 43

No, find ∠D using again use law of cosine

[tex]Cos \ \beta = \dfra{a^{2}+c^{2}}-b^{2}{2ac}\\\\\\ = \dfrac{29^{2}+43^{2}-25^{2}}{2*29*43}\\\\\\Cos \ \beta =\dfrac{841+1849-625}{2494}=\dfrac{2065}{2494}\\\\Cos \ \beta = 0.828\\\\\beta =Cos^{-1} \ 0.828\\\\[/tex]

β = ∠C = 34°

α = 180 - (34 +107)

α = ∠D = 39

Other angles are

∠C = 34°     and  ∠D°39

Answer:

48/24

Step-by-step explanation:

You didn't say which one is line BC so I'm going to give you the answer 48 for the entire line but if you are asking for the middle point to end point then it is 24.

Answer:

$168

Step-by-step explanation:

x + 3x = 672

4x = 672

x = 672 / 4

x = 168

Farah has $168

Answer:

[tex]2x^3 +x^2 -5x+9 -\frac{17}{x+2}[/tex]

Step-by-step explanation:

See picture for explanation

Answer:

π/2 : 1 or π : 2

Step-by-step explanation:

In the attachments I have a picture of a square inscribed in a circle.

Call the side of the square a. Therefore, the area of the square is a^2.

We can also see that the diagonal of the square is the circle's diameter.

Using the Pythagorean Theorem we find that the diagonal/diameter of the circle is a√2. Thus the radius is that divided by 2, which is (a√2)/2.

We also know that the formula for a circle's area is πr^2, so the area of the circle is π((a√2)/2)^2 --> π(a^2)(2)/4 --> π(a^2)/2.

Hence the ratio of the circle to the square is π(a^2)/2 to a^2 which is π/2 to 1 or π to 2.

Answer:

Step-by-step explanation:

To get one portion of soup, each ingredient should be divided by 3

Quantity of onion required=  180 ÷ 3 = 60 g

Quantity of carrots required = 120 ÷ 3 = 60 g

Oil = 3 ÷ 3 = 1 table spoon

Quantity of tomatoes required = 600 ÷ 3 = 300 g

Vegetable stock = 1.2 ÷ 3 = 0.4 litres

Answer:

Light

Step-by-step explanation:

Light can travel approximately 186,000 miles per second so the answer we are looking for in here is light.

Mikhail is 9

Step-by-step explanation:

Divide 27 by 3 because G is 2 times than Mik. So G=2 Mik=1. and 27 divided 3 is 9

Answer: 70 degrees

Step-by-step explanation:

Answer:

1 gallon / 600 sq ft

Step-by-step explanation:

As we can see, we are given that 600 sq ft uses one gallon to cover, therefore one gallon covers 600 sq ft (just vice versa of what's given).

Answer:

6/11

Each time you spin the pointer there is a 3/8 for each of the two spins. That means there is a 6/11 chance of the pointer landing on blue for both times the pointer is spun.

Step-by-step explanation:

Each spin there are 8 possible sections the spinner can land on. The circle has 3 blue sections. The question asks what is the probability of the spinner landing on blue for BOTH spins. This means that you would have to show the denominator as 16. Each time you spin the pointer there is a 3/8 chance it will touch blue. When you spin it two times there is a 6/16 probability that the spinner will land on blue for each of the times the pointer is spun.

Have a great rest of your day
#TheWizzer

Answer:

home

Step-by-step explanation:

I'm not sure I'm just guessing honestly

5-3x=-128

LHS = RHS

(5 - 3) x A = -128

( 2 ) x A = -128

2A / 2 = -128 / 2

A = -64

Answer:

A Translation 2 units left and 1 unit down

Step-by-step explanation:

[tex]2800(0.95)^t~~ = ~~2800(b)^{\frac{t}{10}}\implies \cfrac{2800(0.95)^t}{2800}=b^{\frac{t}{10}}\implies 0.95^t=b^{\frac{t}{10}} \\\\\\ (0.95)^{\frac{10t}{10}}=b^{\frac{t}{10}}\implies (0.95^{10})^{\frac{t}{10}}=b^{\frac{t}{10}}\implies (0.5987)^{\frac{t}{10}}\approx b^{\frac{t}{10}}\implies 0.5987 \approx b \\\\[-0.35em] ~\dotfill\\\\ ~\hfill f(t)\approx 2800(0.5987)^{\frac{t}{10}}~\hfill[/tex]

The x-intercepts of the quadratic equation are given by x = -2 and x = 30.

A quadratic equation is modeled by:

y = ax² + bx + c.

The x-intercepts are the values of x when y = 0, given by:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the equation is:

y = 60 + 28x - x².

Hence the coefficients are a = -1, b = 28, c = 60.

Then:

[tex]\Delta = 28^2 - 4(-1)(60) = 1024[/tex]

[tex]x_1 = \frac{-28 + \sqrt{1028}}{-2} = -2[/tex]

[tex]x_2 = \frac{-28 - \sqrt{1028}}{-2} = 30[/tex]

The x-intercepts of the quadratic equation are given by x = -2 and x = 30.

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The equation x^2−2x+c=0 is an illustration of a quadratic equation

The value of c is 1

The equation is given as:

x^2 -2x + c = 0

A quadratic equation is represented as:

ax^2 + bx+ c = 0

When the quadratic equation  has two roots of one sign, the following equation is true

b^2 =4ac

So, we have:

(-2)^2 =4 * 1 * c

Evaluate the exponent and the product

4 = 4c

Divide both sides by 4

c= 1

Hence, the value of c is 1

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The answer to this problem is:

0<c<1

The surface area of a cone with circumference base of 24π inches and slant height of 20 inches is 384π inches² in terms of π.

surface area = πr(r + l)

where

Therefore,

l = 20 inches

24π = 2πr

r = 12

Therefore,

surface area  = π(12)(12 + 20)

surface area = 12π(12 + 20)

surface area = 12π × 32

surface area = 384π inches²

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Answer:

B)  384 π square inches

Step-by-step explanation:

E2020

Answer:

y=2x-3

Step-by-step explanation:

Hi there!

We are given the points  (0, –3) and (4, 5)

We want to find the equation of the line between these points

There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

To write the equation of the line in this way, we need to first find the slope of the line
The slope can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We already have 2 points, but let's label their values to avoid confusion and mistakes when calculating.

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{5--3}{4-0}[/tex]

Simplify

m=[tex]\frac{5+3}{4-0}[/tex]

m=[tex]\frac{8}{4}[/tex]

Divide

m=2

We found the slope of the line.

Here is the equation of the line so far:

y=2x+b

Now let's find b

As stated before, b is the y intercept of the line, which is the point where the line passes through the y axis; the value of x at the y intercept is 0

One of the points we were given (0, -3) is actually the y intercept of the line!

The value of b is the value of y at the y intercept; in this case, b is equal to -3

Now substitute -3 as b in the equation.

y=2x-3

Hope this helps!

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Answer:

Step-by-step explanation:

I think this is the answer because Triangle A, has a unique that all sides have a measure of 60 degrees. And I also think that Triangle B is unique because It's an Equilateral triangle, which means that all sides have the same length.

So hence, I think the answer is A and B

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Thanks!

:D