A brownie recipe requires 2 1/2 of sugar to 1 cup of chocolate chips. If 3 1/3 of sugar is used, what quantity of chocolate chips will be needed?

Answer:

16 tricycles

Step-by-step explanation:

First, let's make a chart:

Bicycles- x bicycles and 2x wheels

tricycles- y tricycles and 3x wheels

Four wheeled vehicles- 2 bikes (given), 8 wheels

Since the total amout of bikes is 40, that means that x+y+8=40

You can simplify that to x+y=38.

now, we're going to form another equations dealing with the number of wheels.

Since we know that four wheeled vehicles already have only 8 wheels, then that means 2x+3y=92

Solve the system of equations:

2x+3y=92

x+y=38

y will be 16

An equation is formed of two equal expressions. There are a total of 16 tricycles.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the total number of bicycles be represented by x, while the total number of tricycles is represented by y.

The total number of vehicles is 40. Therefore, we can write the equation as,

x + y + 2= 40

x + y = 38

Solving the equation for x,

x = 38-y

Also, given that the total number of wheels is 100, also, the number of four-wheelers is 2. Therefore, the total number of wheels can be written as,

2x + 3y + 2(4) = 100

2x+ 3y = 92

Substitute the value of x from the above equation,

2(38 - y) + 3y = 92

76 - 2y + 3y = 92

y = 16

Hence, there are a total of 16 tricycles.

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Answer:

[tex]\huge\boxed{x\neq4\to x\in\mathbb{R}\backslash\{4\}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x-3}{2x-8}[/tex]

We know: the denominator must be different than 0.

Therefore

[tex]2x-8\neq0[/tex]        add 8 to both sides

[tex]2x-8+8\neq0+8[/tex]

[tex]2x\neq8[/tex]             divide both sides by 2

[tex]\dfrac{2x}{2}=\dfrac{8}{2}\\\\x\neq4[/tex]

The domain of the rational expression is x≠4.

It is required to find the domain of the rational expression.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The given expression

x-(3/2x) - 8

So, the domain is all real number except zero.

2x-8 ≠0

Add 8 to both sides we get,

2x-8 +8≠0+8

2x≠8

Divide both sides by 2 we get,

x≠4

But more likely you meant  (x-3)/(2x-8),  then the domain is all real numbers except 4.

The domain does not include any number that makes the denominator = 0.

Therefore, the domain of the rational expression is x≠4.

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Answer:

Reflexive property

Step-by-step explanation:

Answer:

[tex] \boxed{\huge {\sf y = 4a}} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: y: \\ \sf \implies 4y - 3a = 13a \\ \\ \sf Add \: 3a \: to \: both \: sides: \\ \sf \implies 4y + ( \boxed{ \sf 3a} - 3a) = \boxed{ \sf 3a} + 13a \\ \\ \sf 3a - 3a = 0 : \\ \sf \implies 4y = 3a + 13a \\ \\ \sf 3a + 13a = 16a : \\ \sf \implies 4y = 16a \\ \\ \sf Divide \: both \: sides \: by \: 4: \\ \sf \implies \frac{4y}{ \boxed{ \sf 4}} = \frac{16a}{ \boxed{ \sf 4}} \\ \\ \sf \frac{4y}{4} = \frac{ \cancel{ \sf 4}}{\cancel{ \sf 4}} \times y = y : \\ \sf \implies y = \frac{16a}{4} \\ \\ \sf \frac{16a}{4} = \frac{\cancel{ \sf 4} \times 4a}{\cancel{ \sf 4}} = 4a : \\ \sf \implies y = 4a[/tex]

Answer:

Table 2.

Step-by-step explanation:

Input x as 0, the output y should be 4.

y = -2(0) + 4

y = 0 + 4

y = 4

Input x as 1, the output y should be 2.

y = -2(1) + 4

y = -2 + 4

y = 2

Input x as 2, the output y should be 0.

y = -2(2) + 4

y = -4 + 4

y = 0

Answer:

The radius of the circle 'r' = 5

Equation of the circle

            (x - 2 )²  + (y+1)²  = (5)²

center of the circle ( h,k) = (2 , -1) , 'r' = 5

Step-by-step explanation:

Step(i):-

Given circle is  x² - 4 x + y² + 2 y - 20 =0

                   x² - 2(2) x + (2)²-(2)²+ y² + 2 y(1) +(1)²-(1)² - 20 = 0

We know that

          (a+b)² = a²+2 a b+b²

          (a-b)² = a² -2 a b+b²

               ⇒(x - 2 )² - 4 + (y+1)² -21 =0  

              ⇒ (x - 2 )²  + (y+1)²  = 25

Step(ii):-

Equation of the circle form

                     ( x- h)² + (y -k)² = r²

Given circle   (x - 2 )²  + (y+1)²  = (5)²

          center of the circle ( h,k) = (2 , -1)

          radius of the circle 'r' = 5

Answer:

x = 11º

Step-by-step explanation:

1. Notice Parallel Lines

2. Understand Angle Relationships When Parallel Lines Are Present (e.g., alternate interior/exterior)

3. ∠CAB ≅ ∠DCA ∴ m∠CAB = 33º

4. Use exterior angle theorem: the sum of non-adjacent angles of the same triangle which the exterior angle is drawn is equal to the measure of that angle.

5. Therefore write and solve the equation 2x + 33º (sum of non-adjacent interior angles) = 5x (exterior angle).

Answer:

11 degrees

Step-by-step explanation:

Ur welcome

Answer:

A = 25 units²

Step-by-step explanation:

First, figure out where the lines intersect.

Let's start with x = 0 and y = x:

because x = 0, substitute x in y = x    

    y = 0 so the intersection point of these two lines is (0,0)

With, x + y = 10 (or y = 10 - x) and x = 0:

  substitute x again y = 10 - 0, so y = 10 and the intersection point is (0,10)

The last point has to be found by setting y = x and x + y = 10 (y = 10 - x) equal to each other: x = 10 - x

solve for x: x = 10 - x

                  2x = 10

                    x = 5

find y: y = 10 - 5

          y = 5 and the intersection point is (5,5)

Now that you have the vertices of the triangle, you can find the area. (0,0) and (0,10) are on the y-axis and has a length of 10 units; this is your base. To find the height, you need to picture the triangle on the coordinate plane. Point (5,5) lines up with the midpoint (0,5) of the side with (0,0) and (0,10). From this, you can see that the height is  5 units.

Use the triangle area formula: A = 0.5bh

A = 0.5(10)(5)

  = 0.5 × 50

A = 25 units²

Answer:

A = 25 units²

Step-by-step explanation:

Answer:

The half life of Pa-234 is approximately 0.0701656609 days

Step-by-step explanation:

The formula for half life is calculated as:

t½ = t.In(2)/In(No/Nt)

Where:

t½ = Half life of the substance in days

t = Time elapsed in days

No = Beginning amount

Nt = End Amount

In the question,

t = Time elapsed = 10 days

No = Beginning amount = 5.14 × 10²²

Nt = End Amount = 6.43 × 10²¹

t½ = t.In(2)/In(No/Nt)

t½ = 10.In(2)/In(5.14 × 10²²/6.43 × 10²¹)

t½ = 6.9314718056/98.78723754

t½ = 0.0701656609 days

The half life of Pa-234 is approximately 0.0701656609 days

Answer:

[tex]Probability = \frac{6}{29}[/tex]

Step-by-step explanation:

Given

------------------------------Has a brother | Does not have a brother

Has a sister --------------------------- 6 ----------------- 8

Does not have a sister  -----------2 ------------------ 13

Required

Probability of having a sister and a brother

First, the total number of students has to be calculated;

Total = 6 + 2+ 8 + 13

Total = 29

Number of students that have a sister and a brother is represented with data in row 1 and column 1 i.e. 6

At this point, the probability can then be calculated;

Probability = Number of students that have a sister and a brother divided by Total number of students

[tex]Probability = \frac{6}{29}[/tex]

Answer:

b

Step-by-step explanation:

Let's find the area of the adjacent side.

Applying Pythagoras' Theorem,

(adjacent side)²= 18² -9²

adjacent side[tex] = \sqrt{243} [/tex]

adjacent side= 15.588 m (5 s.f.)

Area of triangle= ½ ×base ×height

Area of traingle

[tex] = \frac{1}{2} \times15.588 \times 9 \\ = 70.1m \: (nearest \: tenth)[/tex]

The nearest answer is B.

*If you rounded of to the nearest tenth for the adjacent side first then use the formula for area of traingle, the result would be exactly 70.2 m.

Answer:

The answer above me is correct

Step-by-step explanation:

Answer: 2 <= X <= 5

Step-by-step explanation:

Answer: 2 <= X <= 5

Step-by-step explanation:

Given that a factory can work its employees no more than 5 days a week, that is, less than or equal to 5 days.

And no less than 2 days per week. That is, greater than or equal to 2 days.

Let X be the number of days employee can work. Then, according to the first statement, X <= 5 and according to the second statement, X >= 2

An inequality to represent the range of days an employee can work will be

2 <= X <= 5

Therefore, an employee can work for 2 days, 3 days, 4 days and 5 days

Answer:

A. and C. are true i think :/

Step-by-step explanation:

im not 100% sure though but again, good lucks!

Answer:

3 6/8

Step-by-step explanation:

5 = 5

10/8 = 1 2/8

5 - 1 = 4

4 - 2/8 = 3 6/8

Answer:

3 [tex]\frac{6}{8}[/tex]

Step-by-step explanation:

Let's turn [tex]\frac{10}{8}[/tex] into a mixed number. Divide the numerator by the denominator.

10 ÷ 8 = 1 with a remainder of 2

Write down the whole number followed by the remainder over the denominator.

[tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex]

Now subtract.

5 - 1 = 4

4 - [tex]\frac{2}{8}[/tex] = 3 [tex]\frac{6}{8}[/tex]

Answer:

3/5

Step-by-step explanation:

Sine = opp/hypotenuse

The opposite of a is 3, and the hypotenuse is 5. Therefore, the sine is 3/5.

Hope this helps :)

Answer: <MQR to be 15 degrees

The value of RQ = 9, from the given details, using the sine rule and other properties of triangles.

According to the sine rule, in a triangle ABC,

a/sin A = b/sin B = c/sin C

where a = BC, b = AC, and c = AB.

In the question, we are given a diagram and the following details:

∆PQR, m ∠R = 90° m ∠PQR = 75°, m ∠MQR = 60° M ∈ PR , MP = 18. We are asked to find the value of RQ.

Now, since m ∠PQR = 75° and m ∠MQR = 60°,

we can say that m ∠PQM = m ∠PQR - m ∠ MQR = 75° - 60° = 15°.

In Δ MQR,

m ∠R = 90°, m ∠Q = 60°.

∴ m ∠M = 180° - (m ∠R + m ∠Q) = 180° - (90° + 60°) = 30°. {using angle sum property of triangle}

At point M, m ∠RMQ + m ∠ QMP = 180° {Adjacent angles}

or, 30° + m ∠ QMP = 180° {∵ m ∠RMQ = 30°, calculated above}

or, m ∠ QMP = 180° - 30° = 150°.

Now, in ΔPQM,

m ∠P + m ∠Q + m ∠M = 180°.

or, m ∠P + 15° + 150° = 180°

or, m ∠P + 165° = 180°,

or, m ∠P = 15°.

Since, m ∠P = m ∠Q, Δ QPM is an isosceles triangle, with MP = MQ = 18 {Since, MP = 18 is given}.

Now in ΔRQM, by applying the sine rule, we can say that:

MQ/sin R = RQ/sin M,

or, 18/sin 90° = RQ/sin 30°,

or, RQ = (18*sin 30°)/sin 90° = (18*0.5)/1 {Since, sin 30° = 0.5 and sin 90° = 1},

or, RQ = 9.

Therefore, RQ = 9, using the sine rule.

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Answer:

The midpoint is (2.5, 3.5)

Step-by-step explanation:

The midpoint is the average of the coordinates

x = (x1+x2)/2  and y =(y1+y2)/2

x = (2+3)/2 = 5/2 = 2.5

y = (3+4)/2 = 7/2 = 3.5

The midpoint is (2.5, 3.5)

Answer:

(2.5, 3.5)

Step-by-step explanation:

The midpoint is found by taking the average of the x-coordinates and the average of the y-coordinates.

Here, the average of the x-coordinates is (2 + 3)/2 = 5/2 = 2.5.

The average of the x-coordinates is (3 + 4)/2 = 7/2 = 3.5.

The answer is thus (2.5, 3.5).

~ an aesthetics lover

Answer: 793

Step-by-step explanation:

1 + 8 = 9

9 + 8 = 17

17 + 8 = 25

If 25 is the fourth term in the sequence, and the formula is + 8 for every term, then you need to find 96 more terms with + 8.

96 * 8 = 768

768 + 25 = 793

Answer:

The 100th term is 793.

Step-by-step explanation:

Notice that this arithmetic sequence has first term [tex]a_1=1[/tex]

and common difference [tex]d=8[/tex] (since each consecutive term is built by adding "8" to the previous one)

Recall the general formula for the nth term of a sequence:

[tex]a_n=a_1\,+(n-1)\,d[/tex]

therefore, for our articular case, the term 100th can be obtained with:

[tex]a_n=a_1\,+(n-1)\,d\\a_{100}=1\,+(100-1)\,8\\a_{100}=1\,+(99)\,8\\a_{100}=1\,+792\\a_{100}=793[/tex]

Answer:

x = √21.

Step-by-step explanation:

Triangles ADB and BCD are similar.

So their corresponding sides are in the same ratio:

x / 7 = 3 / x

x^2 = 21

x = √21.

Answer:

D. 1

Step-by-step explanation:

Step 1: Find g of f(x)

g(f(x)) = (x²) - 3

Step 2: Plug in -2 as x

g(f(x))(-2) = (-2)² - 3

g(f(x))(-2) = 4 - 3

g(f(x))(-2) = 1

Answer: The min value of Q is Q = 84 and it happens when x = 4 and y = 3

===========================================================

Explanation:

x+y = 7 turns into y = 7-x after subtracting x from both sides

Replace y with 7-x in the other equation to get

Q = 3x^2 + 4y^2

Q = 3x^2 + 4( y )^2

Q = 3x^2 + 4(7-x)^2

Q = 3x^2 + 4(49 - 14x + x^2)

Q = 3x^2 + 196 - 56x + 4x^2

Q = 7x^2 - 56x + 196

We have a function with one variable. Graphing 7x^2-56x+196 produces a parabola in which the vertex point is what we're after

Anything in the form p(x) = ax^2+bx+c will have a vertex (h,k) such that

h = -b/(2a)

k = p(h)

Let's find the x coordinate of the vertex

h = -(-56)/(2*7)

h = 4

Use this to find the y coordinate of the vertex

k = p(h)

p(x) = 7x^2-56x+196

p(h) = 7h^2-56h+196

p(4) = 7(4)^2-56(4)+196

p(4) = 84

The vertex is the lowest point in this case (since a = 7 is positive) and the vertex is (4,84)

Therefore, the minimum value of Q is Q = 84 and this happens when x = 4 and y = 3. Recall that y = 7-x.

We can see that,

Q = 3x^2 + 4y^2

Q = 3(4)^2 + 4(3)^2

Q = 3(16) + 4(9)

Q = 48 + 36

Q = 84

Which helps us verify we have the right Q value.

Answer: 600 milliliters per child

Step-by-step explanation:

Hi, to answer this question we simply have to divide the amount of soda (6 liters) by the number of people (6).

Mathematically speaking:

6 /10 = 0.6 liters per child

Since 1 liter = 1000 milliliters

0.6 x 1000 = 600 milliliters per child

Feel free to ask for more if needed or if you did not understand something.  

Answer:

0.73

Step-by-step explanation:

The decimal 0.73 is already in decimal form.

Answer:

73/100

Step-by-step explanation:

I put it down as 100

So 73/100 is the answer

Answer:

a. 0 is the correct answer.

Step-by-step explanation:

We are the given the function:

[tex]y = sin q[/tex]

If we refer to the attached graph, it represents [tex]\theta[/tex] on the x axis and y value on y axis.

i.e. the graph represents:

[tex]y =sin\theta[/tex]

For different values of [tex]\theta[/tex] (on x axis), different values of [tex]sin\theta[/tex] are shown on the y axis.

Various points that we can observe from the graph:

[tex]\theta = 0, y =0\\\theta=\dfrac{\pi}{2}, y =1\\\theta=\pi, y =0[/tex]

Here we have to find the value of:

[tex]y=sinq[/tex] where q = [tex]\pi[/tex] radians

i.e. we have to find the value of [tex]y=sin\pi[/tex]

Please refer to the graph attached in the answer area.

Point is marked as P which shows the point ([tex]\pi,0[/tex]).

So, [tex]y=sinq[/tex] where q = [tex]\pi[/tex] radians is 0.

So, correct answer is option a. 0

Answer:

1.08*10^11

Step-by-step explanation:

how many more it means you need to subtract :

in year 1965 : 7.2*10^10

in 1995 :1.8*10^11

(1.8*10^11)-(7.2*10^10)

18*10^10-(7.2*10^10)=

10.8*10^10 or 1.08*10^11

Answer:

ax² + bx + c

Step-by-step explanation:

The form of a quadratic equation that is easy to use when finding the maximum or minimum value of the function is ax² + bx + c.

Suppose a quadratic function:

f(x) = 2x² - 8x + 9

Use ( -b/2a ,  f(-b/2a) ).

-b/2a

a = 2

b = -8

-(-8)/2(2)

8/4

= 2

f(2) = 2(2)² - 8(2) + 9

f(2) = 2(4) - 8(2) + 9

f(2) = 8 - 16 + 9

f(2) = 1

The minimum value of this quadratic function is (2, 1).

It represents a minimum value because a > 0.

Answer:

Vertex form

Step-by-step explanation:

There are several forms of the quadratic equation

Standard form: y = ax^2 + bx + c which is useful for the quadratic equation and the axis of symmetry

Factored form: y = (ax - c)(bx - d)   which will give us the zeros

and

Vertex form: y = a(x - h)2 + k where ( h,k) is the vertex

The maximum and minimum would be the value of k

It would be maximum when a >0 and minimum when a<0

Answer:

answer should be 52.4 mins

Step-by-step explanation:

find the midpoint for each time:

1. 15mins = 7students

2. 45mins = 27 students

3. 75mins = 12 students

4. 100 = 4students

Then, do the normal mean calculation by adding up all the values and dividing it by 50.

7*15 + 27*45 + 12*75 + 100*4 = 2620

2620/50 = 52.4mins

Answer:

a = 95

Step-by-step explanation:

a+ 35+ 50 = 180

Combine like terms

a+ 85 = 180

Subtract 85 from each side

a+85-85 = 180-85

a = 95