A recipe for flapjacks uses only syrup sugar butter and oats in the ratio 1:2:2:4 Using this recipe 250g of syrup are needed to make 12 flapjacks find the quantity of oats needed to make 18 of these flapjacks?

The value of the number is -13/3

Algebraic expressions are defined as expressions that are composed of arithmetic operations such as subtraction, multiplication, division, addition, bracket and parentheses.

These expressions are also made up of variables, terms, coefficients, constants and factors.

From the information given, we have that;

The number = x

3x + 4 = -9

collect like terms

3x = -9 - 4

subtract the like terms

3x = -13

Make 'x' the subject

x = -13/3

Hence, the value is -13/3

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The Approximate values of the five number summary are ;

(i) the Minimum is 10 ,

(ii) the First quartile is 30 ,

(iii) the Third Quartile is 80 ,

(iv) the Median is  55 ,

(v) the Maximum is  100 .

The values of the data set are : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 ,55 ,60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;

The Five number summary consists of the minimum , maximum , first quartile , third quartile and the median .

(i) the Minimum of the data set is = 10 ;

(ii)  we split the data set into , 2 halves ;

that means ;  {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 }  and {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;

the first quartile lies in the lower half : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 }  ;

So , first quartile (Q₁) = 30 ;

(iii) the third quartile (Q₃) lies in the upper half : {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;

So , Q₃ = 80 ;

(iv) the total number of terms in the set is = 19 ;

So , the median is = tenth term = 55 ;

(v) the maximum of the data set is = 100 .

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The solution set of the system of equations is {(2,2), (4,-2)}

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

4x+2y =12------>(1)

Take some random values for x. Find the corresponding y  values

Example: when x=0

(1) => 4(0)+2y = 12

  =>  0+2y = 12

  =>      2y =12

 =>     y= 12/2 = 6

The point obtained is (x,y) = (0,6)

This way, we get a line when we graph the equation 4x+2y =12.

Similarly, when we graph the equation  y= -x² + 4x -2 , we get a parabola

Graph is attached:

In the graph, both graphs intersect at the points (2,2) and (4,-2)

Thus, the solution set of the system of equations is {(2,2), (4,-2)}

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PLEASE GIVE BRAINLIEST!

thank you and have a good day :)

Answer:

b^5

Step-by-step explanation:

When you are multiplying exponents with the same letter base, you simply just add the exponents.

for example, x^2 * x^3 = x^5

another example, y^6 * y^8 = y^14

An expression equivalent to b^3 * b^2 would be b^5

I hope this helps!

The order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].

Using the given information, we can find the common ratio of the geometric sequence A.

First, we can use the equation T₂² = T₁ T4 to find T4. Substituting n = 4, we get:

T₂² = T₁ T4

20² = T₁ T4

T4 = 400/T₁

Next, we can use the equation T5 = 20 to find T₁r⁴:

T5 = T₁r⁴

20 = T₁r⁴

We can now substitute T4 in terms of T₁ in the equation above:

20 = T₁r⁴

20 = T₁(400/T₁)r⁴

20 = 400r⁴

r⁴ = 1/20

Therefore, the common ratio r = (1/20)^(1/4) = 0.5.

To find the order of the first term whose value is greater than 106, we can use the formula for the nth term of a geometric sequence:

Tn = T₁r^(n-1)

We want to find the smallest value of n such that Tn > 106. Substituting r = 0.5 and rearranging, we get:

T₁(0.5)^(n-1) > 106

T₁ > 212(0.5)^(1-n)

Since T₁ > 0, we can take the logarithm base 0.5 of both sides:

log(0.5)(T₁) < log(0.5)(212) + (n-1)

Solving for n, we get:

n > 1 + [log(0.5)(T₁) - log(0.5)(212)]

Therefore, the order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].

Note that the exact value of this order depends on the value of T₁, which was not given in the original problem statement.

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Answer: B quadrant 2 or quadrant 3  

Step-by-step explanation:

The length of the tree remaining sides are 18 inches, 29 inches and 29 inches.

A kite is an object with four sides. It length of the two adjacent sides are of equal length. No pair of sides in a kite are parallel. The perimeter of a kite is the sum of the length of the four sides of the kite.

Perimeter of a kite = 2( a + b)

94 = 2(18 + b)

94 / 2 = 18 + b

47 = 18 + b

b = 47 - 18

b = 29 inches

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Answer: 4.5

Step-by-step explanation:

Answer:

9.09%

(⬇Read my notes⬇)

Notes:

Hi there,

I know this answer is going to be incorrect on RSM, but it is the correct answer. Everyone has been saying that it's 9.09%, and I even found that as well. So I don't know why RSM is saying that it's wrong, because it should be correct.

- 201600823

The value of x in the diagram is given as follows:

x = 10.

Similar triangles share these two features:

Considering the similar triangles, the proportional relationship for the side lengths is given as follows:

6/(6 + x) = (x - 1)/(2x + 4).

Applying cross multiplication, the value of x is obtained as follows:

(x - 1)(x + 6) = 6(2x + 4)

x² + 5x - 6 = 12x + 24

x² - 7x - 30 = 0.

Factoring, we obtain the solutions are follows:

(x - 10)(x + 3) = 0.

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The expression is constant for b = -7.5, and the constant is 49.5.

A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that, The expression 3(5x - 1) + b(2x - 7) is constant

It means the expression doesn't consist of a variable. So, we need to find the 'b' such that the variable 'x' need to be eliminated.

The co-efficient of the 'x' should be '0'.

3(5x - 1) + b(2x - 7)

= 15x - 3 + 2bx - 7b

= (15 + 2b)x - 3 - 7b

Now, 15 + 2b = 0

2b = -15

b = -7.5

On substituting the value of 'b' in the expression,

= -3 - 7 * (-7.5)

= 52.5 - 3

= 49.5

Therefore, The expression is constant for b = -7.5, and the constant is 49.5

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In the linear equation y=2x+3, if x increases by 4 points, the y will increase by 8 points.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation's graph will always be a straight line. A linear equation is expressed using the linear equation formula. There are numerous ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form. 

According to that,

y=2x+3 is the linear equation.

x will now rise by 4 points.

According to the data given, the calculation is as follows:

x = x + 4

So = 2(x)

= 2(x + 4) + 3

= (2x + 3) + 8

= y + 8

Eight points should be added to the y.

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The inverse of f(x) is restricted to the domain x ≥ 1, since this is when[tex]x^2 − 2x + 1[/tex] is always greater than 0.

To find the inverse function of f(x), we must first determine the domain of f(x). We can do this by finding the values of x where f(x) is greater than or equal to 0.

We can start by setting f(x) to 0 and solving for x:

[tex]x^2 − 2x + 1 = 0[/tex]

[tex]x^2 − 2x + 1 − 1 = 0 − 1[/tex]

[tex]x^2 − 2x = -1[/tex]

(x − 1)(x − 1) = -1

x = 1

Therefore, the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.

The inverse of a function f(x) is a function that "undoes" f(x). In order to find the inverse of a function, the domain of the function must first be identified. This is done by solving f(x) = 0 and determining which values of x make the equation equal to 0.In the case of f(x) =[tex]x^2[/tex] − 2x + 1, the equation is equal to 0 when x = 1. This means that the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.Once the domain of the function is restricted, the inverse function can be found by switching the x and y values, and solving for the new equation. This process can be used to find the inverse of any function, as long as the domain is appropriately restricted.

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For given geometrical shape, The angles which we need to find are  ∠z=115° and y=21.

What are geometric shapes, exactly?

Geometric shapes are mathematical figures that reflect the shape of objects we see in our daily lives. Shapes are geometric shapes that have boundary lines, angles, and surfaces. There are several types of 2d and 3d shapes.

Shapes are also classified according to their regularity or homogeneity. A symmetrical regular form, such as a square or circle, is common. Asymmetry can take on irregular shapes. They're also referred to as organic forms or freeform shapes. A tree, for example, has an irregular or organic shape.

In plane geometry, two-dimensional forms are flat shapes and closed figures such as circles, squares, rectangles, rhombuses, and so on. In solid geometry, the three-dimensional shapes are the cube, cuboid, and sphere.

Now,

In given figure ∠z+65°=180°    (Sum of two interior angles)

then ∠z=115°

and ∠z=∠6y-11   (vertically opposite angles)

6y-11=115

6y=126

y=21

Hence,

           For given geometrical shape, ∠z=115° and y=21.

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As the university is sending out questionnaires, the data collection method the university is using is a survey

The term "survey" describes the method of gathering data on a certain subject generally by employing questionnaires. In order to understand more about a certain topic, a survey is a method of data collection that involves asking a sample of respondents a number of questions. In the given case, the university is using a survey as a tool for gathering data. 

Here, the institution is distributing a survey to undergraduate students to learn more about their study habits and what they believe to be the most effective method of studying. In order to efficiently gather data from a large number of participants quickly and effectively, surveys are frequently employed in research investigations.

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P(A)=1/5, P(B)=7/20, P(A and B)= 7/100. The events A and B are independent.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

1) P(A)=1/5, P(B)=7/20, P(A and B)= 7/100

Here, P(A and B)= P(A)×P(B)

= 1/5 × 7/20

= 7/100

So, the events A and B are independent.

2) P(A)=13/20, P(B)=13/20, P(A and B)= 169/400

Here, P(A and B)= P(A)×P(B)

= 13/20 × 13/20

= 169/400

So, the events A and B are independent.

3) P(A)=7/10, P(B)=2/5, P(A and B)= 21/100

Here, P(A and B)= P(A)×P(B)

= 7/10 × 2/5

= 14/50

So, the events A and B are not independent.

2) P(A)=1/5, P(B)=1/5, P(A and B)= 1/25

Here, P(A and B)= P(A)×P(B)

= 1/5 × 1/5

= 1/25

So, the events A and B are independent.

Therefore, options 1, 2 and 4 are correct answers.

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Answer:

5 pounds

Step-by-step explanation:

$20/$4 = 5 pounds

HOPE IT HELPS!

The average rate of change is 2.The rate of change of the function is its gradient or slope.

To get the average rate of change, divide the change in y-values by the change in x-values.Knowing the average rate of change is necessary to detect changes in observable metrics like average speed or average velocity.

It displays the typical rate of change of the function for each unit during that time. It is determined using the slope of the line connecting the ends of the interval in the function graph.

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Let b be the initial number of boys, and let g be the initial number of girls. We know that the total number of students at the canteen is 342, so:

b + g = 342

After 51 boys and an equal number of girls returned to their classroom, there were three times the number of boys than girls in the canteen. This means that the number of girls remaining in the canteen is:

g - 51

And the number of boys remaining in the canteen is:

b - 51

Since there were three times as many boys as girls, we can write:

b - 51 = 3(g - 51)

Now we have two equations and two unknowns. We can solve for one variable in terms of the other in the first equation, and substitute into the second equation:

b + g = 342

g = 342 - b

b - 51 = 3(g - 51)

b - 51 = 3(342 - b - 51)

b - 51 = 3(291 - b)

b - 51 = 873 - 3b

4b = 924

b = 231

So there were 231 boys in the canteen at first. To check our answer, we can substitute into the first equation:

b + g = 342

231 + g = 342

g = 111

Therefore, there were 231 boys and 111 girls in the canteen at first.

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Answer:

$2.12

Step-by-step explanation:

First, let's find the area of Jennifer's envelope: 20 cm x 12 cm = 240 square cm.

Since the area needs to be rounded up to the next multiple of 50 square cm, we will round up 240 square cm to 250 square cm.

Next, let's round up the weight of the letter to the next multiple of 40 grams: 125 grams rounded up to 140 grams.

Now that we have the rounded up values for both weight and area, we can use the formula to find the postage charge:

20 cents per 50 square cm x (250 square cm ÷ 50) = 100 cents

32 cents per 40 grams x (140 grams ÷ 40) = 112 cents

So the total postage charge will be 100 cents + 112 cents = 212 cents = $2.12.

Therefore, the postage charge for Jennifer's letter will be $2.12.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

y = 2/5x +24/5, is the equation  which represents a line that passes through (-2, 4) and has a slope of 2/5.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The slope intercept form of a line is

y = mx+b

where m is the slope and b is the y intercept

y = 2/5 x +b

Substitute the point (-2,4) into the equation and solve for b

4 = 2/5(-2)+b

4 = -4/5 +b

Add 4/5 to each side

20/5 +4/5 = b

24/5 = b

Hence, y = 2/5x +24/5, is the equation  which represents a line that passes through (-2, 4) and has a slope of 2/5.

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The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 1.25 units.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

The line AB has the following coordinates.

A = (1, 4)

B = (6, 4)

The distance between AB is given as:

AB = √(6 - 1)² + (4 - 4)²

AB = √(5)²

AB = 5

The slope of AB = 0.

For the dilated rectangle the slope remains the same.

The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 5/4 = 1.25 units.

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The correct question is:

8-3√11 is the expression which is equivalent to √11+√64-2√44.

The combination of variables, numbers and operators is called as expression.

The given expression is √11+√64-2√44

Square root of 11 plus square root of sixty four minus two square root of forty four.

Let us find the equivalent expression of √11+√64-2√44

The expressions in which the expressions look different but have save same value are Equivalent

√11+√64-2√44

√11+8-2√4×11

√11+8-4√11

Combine like terms

8-3√11

Hence, 8-3√11 is the expression which is equivalent to √11+√64-2√44.

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Which expression is equivalent to √11+√64-2√44

A. 8-4√44

B. 5√3-4√11

C. 8-3√11

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

Work Shown:

n = number of nickels

22-n = number of dimes

5n = value of the nickels in cents

10(22-n) = value of the dimes in cents

5n+10(22-n) = total value in cents

5n+10(22-n) = 180

5n+220-10n = 180

-5n+220 = 180

-5n = 180-220

-5n = -40

n = -40/(-5)

n = 8 is the number of nickels

22-n = 22-8 = 14 is the number of dimes

-----------------

Check:

8 nickels = 8*5 = 40 cents

14 dimes = 14*10 = 140 cents

8 nickels + 14 dimes = 40 cents + 140 cents = 180 cents = $1.80

8 nickels + 14 dimes = 22 coins total

The answers are confirmed.

Using, the mathematical inequalities, we can conclude that the total number of occupied rooms on Friday is 10.

Number of rooms in the inn = 10

It is given that One-half of the rooms are reserved for Friday which means 5 rooms were initially reserved on Friday.

Now, 12 more rooms are reserved for Friday.

So, the Initial reservation for Friday = 5

Final reservations for Friday = 5 + 12 = 17

Now, Final reservations for Friday(17) > Total number of rooms in the inn(10).

As the reservation exceeds the capacity of the hotel, 7 reservations will be cancelled and all 10 rooms will be occupied on Friday.

Hence, the total number of occupied rooms on Friday is 10.

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