A baker had 24 cupcakes and wanted to divide them equally among 8 friends. How many cupcakes would each friend receive?
The problem can be represented by 8/3 ÷ 4, where 8 represents the number of friends, 3 represents the number of cupcakes each friend should receive, and 4 represents the number of groups the cupcakes should be divided into.
The division makes sense because first, we need to find out how many cupcakes each friend should receive, which is 24 ÷ 8 = 3. Then, we divide the number of cupcakes each friend should receive by the number of groups to find out how many cupcakes each group should receive, which is 3 ÷ 4 = 0.75 cupcakes per group.
Apple crumble is made using the following ingredients.
a) Farid makes apple crumble for 16 people.
How much flour does he need?
b) Amal makes apple crumble for 2 people.
How much sugar does she need?
g
g
Serves 8 people
700g apple
240g sugar
180g flour
40 g
butter
c) Shahina has 550 g of apples and plenty of the other ingredients.
Can she make apple crumble for 6 people? Yes/No
Explain how you got your answer.
Show your working
|+
Answer: a) To make apple crumble for 16 people, Farid will need to double the ingredients as compared to serving 8 people. Hence, he will need:
700g * 2 = 1400g of apples
240g * 2 = 480g of sugar
180g * 2 = 360g of flour
So, Farid needs 360g of flour to make apple crumble for 16 people.
b) To make apple crumble for 2 people, Amal will need to use 1/8 of the ingredients as compared to serving 8 people. Hence, she will need:
700g / 8 = 87.5g of apples
240g / 8 = 30g of sugar
So, Amal needs 30g of sugar to make apple crumble for 2 people.
c) To make apple crumble for 6 people, Shahina will need to adjust the ingredients based on the apples she has available. To calculate the amount of sugar and flour required, she can use the ratio of sugar and flour to apples as follows:
Sugar: 700g / 8 = 87.5g per serving * 6 people = 525g
Flour: 700g / 8 = 87.5g per serving * 6 people = 525g
Since Shahina has plenty of the other ingredients, including butter, she can make apple crumble for 6 people with the amount of apples she has available. So, the answer is Yes, Shahina can make apple crumble for 6 people.
Step-by-step explanation:
Which of the following is the first step to rewriting the formula P = 2l + 2w to solve for l
A)
B)
C)
D)
b) Subtract [tex]2w[/tex] from both sides
5 inches : 2 feet. If the gym is 170 inches wide in the drawing, how wide is the actual gym?
Answer:
68
Step-by-step explanation:
170/5=34 34*2=68
Which of the following sets of numbers could not represent the three sides of a triangle?
{
10
,
17
,
27
}
{10,17,27}
{
9
,
22
,
30
}
{9,22,30}
{
6
,
16
,
19
}
{6,16,19}
{
4
,
7
,
9
}
{4,7,9}
The set {10,17,27} does not represent the three sides of a triangle,
What are triangles?Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Given the sets for the triangles,
property of triangles says that,
The length of a triangle's two longest sides added together is longer than the third side.
Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.
1: given sides are 10, 17, 27
according to the property sum of 10 and 17 should be greater than 27 but sum is equal to 27,
10 + 17 = 27,
so the sides do not represent the triangle
2: sides are 9, 22, 30
here 9 + 22 > 30
the set represents the triangle.
3: sides 6, 16, 19
6 + 16 > 19
the set represents the triangle.
4: sides 4, 7, 9
4 + 7 > 9
set represents the triangle.
Hence option A is correct.
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Which table represents a linear function?
Which table represents a linear function? - 1
A linear equation is an equation in which each term has at max one degree. The table that represents a linear function is Table 1. Thus, the correct option is A.
What is a linear equation?A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.
For the table to represent a linear function, the function must have a constant slope between any two points.
For the first table, the slope between the first two points is,
m = (7-3)/(2-1) = 4
The slope between the last two points is,
m = (15-11)/(4-3)
Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.
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You are the chief scientist of Neo Medtech Inc. Your company produces 3 types of devices to detect Covid-19, namely, A, B, and C. There are 3 different type of Materials used for production, namely, M1, M2 and M3.
To produce one unit of A requires 3 units of M1, 2 units of M2 and 6 units of M3. To produce one unit of B requires 3 units of M1, 2 units of M2, and 4 units of M3. To produce one unit of C requires 4 units of M3, 5 units of M1, and 7 units of M2. The manufacturer has an everyday available quantity of 71 thousand units of M1, 81 thousand units of M2 and 92 thousand units of M3.
a. Form a system of linear equations from the information above.
b. Write a matrix equation for the system of linear equations obtained in (b).
c. Use the inverse matrix method, find the quantity of A, B and C.
d. The production cost is RM0.70 for a unit of A, RM0.50 for a unit of B, and RM0.90 for a unit of C, find, using matrix method, the daily cost for these 3 types of medicine.
The answers to all parts shown below.
What is Matrix?A set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.
Given:
a) The system of linear equations
3A + 2B + 6C = 71, 000
3A + 2B +4C = 81, 000
5A + 7B + 0C= 92, 000
B) The equation for the system of linear equations
Y = [tex]\left[\begin{array}{ccc}3&2&6\\3&2&4\\5&7&0\end{array}\right][/tex] , Z = [tex]\left[\begin{array}{ccc}71000\\81000\\92000\end{array}\right][/tex]
So, YX = Z
X = Z[tex]Y^{-1[/tex]
C) The inverse matrix method
14/11 21/11 -2/11
= 1/22 10/11 -15/11 3/11
1/2 -1/2 0
= 7/ 121 21/ 242 -1/121
5/121 -15/242 3/242
1/44 -1/44 0
and, X = Z[tex]Y^{-1[/tex]
X = [tex]\left[\begin{array}{ccc}71000\\81000\\92000\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}7/ 121 &21/ 242& -1/121\\ 5/121&-15/242&3/242\\1/44&-1/44&0\end{array}\right] \\[/tex]
A= 10,376.03
B = 946.28
C= 227.72
d) The production for A = RM 7,263.221
The production for B = RM 473.14
The production for C = RM 204.948
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Factor the expression.
(blankq^2-r^2s)(blankq^4+blankq^2r^2+blankr^4s^2)
The value of the expression is q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3
How to factor the expressionFrom the question, we have the following parameters that can be used in our computation:
(blankq^2-r^2s)(blankq^4+blankq^2r^2+blankr^4s^2)
Express properly
So, we have
(q^2-r^2s)(q^4+ q^2r^2 + r^4s^2)
Open the brackets
q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3
There are no like terms in the expression
So, the solution is q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3
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HELP
_________________________________
Answer: It's the fourth option; f^-1(x)=x^3/125 -7
Please help I need this
1 Find the measure of angle BOC. I
2 Find the measure of angle DOE.
3 Find the measure of angle AOE
Answer:
see below
Step-by-step explanation:
60+75=135
BOC =180 -135 =45
DOE = BOA =60
AOE =180-DOE =120
A water sport shop rents tubes, kayaks, canoes, skis, and rafts. The circle graph below shows the rentals from June.
There were 300 items rented in June. Based on the circle graph, how many of those rentals were tubes or rafts?
A.
180
B.
120
C.
150
D.
225
The required, 180 items rentals were tubes or rafts of 300 items.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The circle graph shows that tubes and rafts made up 60% of the total rentals. If there were 300 items rented in June, then 60% of those rentals were tubes or rafts:
300 items × 60% = 180 items
So the answer is A. 180.
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You are applying fondant to the exterior edges of a large rectangular cake. If the cake's dimensions are 21.9 inches long by 18.3 inches wide, how many inches of fondant do you need?
Answer:
Step-by-step explanation: A rectangle's perimeter formula is P=2(l+w), therefore,
P=2(21.9+18.3)
P=2(40,2)
P=80,4
You will need 80,4 inches of fondant to cover all the edges of the cake
Find the domain of the following piece wise function.
[4,8)
(2,8]
[2,8)
(4,8]
The domain is the second option:
(2, 8]
Which is the domain of the piece wise function?For a function y = f(x), we define the domain as the set of the possible inputs for the function.
Here we have a piecewise function that is defined in the 3 regions:
2 < x ≤ 4
4 < x < 8
x ≥ 8
So the domain is the set of any value larger than 2, and we can write that as:
(2, 8]
We end it at "8" becase is the last defined value and that is the only option that makes sense.
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Need help here with solution please
The solution is Option D.
The derivative of the function is given by the equation f' ( x ) = -x / ( √5-x² )
What is implicit differentiation?In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately
Given data ,
Let the function be represented as f ( x )
Substituting the values in the equation , we get
f ( x ) = √ ( 5 - x² )
Now , the derivative of the function is f' ( x )
f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( d/dx ) ( -x² )
On simplifying the equation , we get
f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( -2x )
On further simplification , we get
f' ( x ) = ( -2x/2 ) 1 / √( 5 - x² )
f' ( x ) = -x / ( √5-x² )
Hence , the derivative of the function is f' ( x ) = -x / ( √5-x² )
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Please help ASAP
Find the area of the rectangle
What is the area of the rectangle?
Find the coordinates of the point on the unit circle at an angle of 225∘.
Give your answer in the form (x,y) and leave any fractions in fraction form.
The unit circle has the co-ordinates (-√2/2, -√2/2)
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: The unit circle and the point makes an angle of 225
we know the co-ordinates of any point on the unit circle is given by
x=cost and y=sint where t is the angle that line passing through the origin containing the point makes with x-axis
Thus x=cos225
=-√2/2
and y=sin225
=-√2/2
Hence, The required point is given by co-ordinates (-√2/2, -√2/2)
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draw a design that uses three equilateral triangles and two isosceles triangles. label the vertices. list all the congruent sides and angles
In geometry, an equilateral triangle is one with three equal-length sides. In the traditional Euclidean geometry, an equilateral triangle is also equiangular, which means that each of the three internal angles is 60 degrees and that they are all congruent with one another.
What is internal angle?A shape's interior can contain angles. The closed, side-and-vertex-containing shapes are known as polygons. All of the internal angles of a regular polygon are equal. For instance, the inner angles of a square are all exactly 90 degrees, or the right angle.Interior angle of a polygon is equal to the sum of interior angles divided by the number of sides, according to the following formula. A polygon has a total of 360° in its outside angles. Exterior angle of a polygon is equal to 360 divided by the number of sides, according to the following formula. An interior angle is one that is located inside a polygon. As an illustration, a triangle has three interior angles.To learn more about internal angle, refer to:
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The design using three equilateral triangles and two isosceles triangles is shown using the vertices.
What are equilateral triangles?Any triangle with three equal sides is said to be equilateral. The third side of this particular isosceles triangle is also equal. ABC has the formula AB = BC = CA. An equilateral triangle has the following qualities:
It has three equal sides. The three angles are equal. Every angle of an equilateral triangle is 60 degrees since the sum of the interior angles is 180 degrees.
It has three regular sides and is a polygon.
What are isosceles triangle?Regardless of which way the triangle's apex points, an isosceles triangle is one that has two equal sides. Angle determination can be done using isosceles triangles. AB Equals AC in the isosceles triangle ABC. Likewise, PQ Equals PR in the triangle PQR. The isosceles triangle's base is represented by the uneven sides BC and QR, while vertices A and P are regarded as the triangle's peaks. Among its attributes are:
There are equal sides on it. The basis angles are two equal angles that make up the object. A triangle is referred to as a right isosceles triangle when the third angle is 90 degrees.
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Y=x-2 and y=3x +5 what does x and y =
Answer:
x = - 3.5 , y = - 5.5
Step-by-step explanation:
y = x - 2 → (1)
y = 3x + 5 → (2)
substitute y = 3x + 5 into (1)
3x + 5 = x - 2 ( subtract x from both sides )
2x + 5 = - 2 ( subtract 5 from both sides )
2x = - 7 ( divide both sides by 2 )
x = - 3.5
substitute x = - 3.5 into either of the 2 equations for y
substituting into (1)
y = x - 2 = - 3.5 - 2 = - 5.5
then x = - 3.5 and y = - 5.5
The perimeter of a rectangular red sticker is 14 millimeters. The sticker is 4 millimeters wide. How tall is it?
Answer:
3 millimeters
Step-by-step explanation:
The formula for finding perimeter: 2W+2L=P
W= width
L= length
P= Permiter
So just substitute the numbers in the equation
4 millimeters is the width
14 millimeters is the perimeter
So this is your equation
2*4+2L=14
8+2L=14
Subtract 8 from both sides
2L=6
Divide both sides by 2
L=3
So your length is 3 millimeters
To check:
(2*4)+(2*3)=14
8+6=14
14=14
In parallelogram LMNP if PQ=21 find QM.
5 stars and like
Answer: The diagonals of a parallelogram bisect each other, then. QM = PQ = 21. Explore all similar answers.
Step-by-step explanation: got do the d
GIVING BRAINLIEST! CHECK IMAGE. is it possible for this function to have a degree of 5 and a positive leading coefficient? explain please!
Which number is rational?
A. 4√2 B. √15 C. √3 D. √16
Please explain thank you
Answer: D
Step-by-step explanation:
Think about it this way, 3 squared is 3x3 correct? that equals 9. 4 squared is 16 so there you go. Sorry if this isn't answered clearly.I'm trying my best to help
Find the scale factor.
ABCD~EFGH
The scale factor for the given quadrilateral would be 1.5.
A scale factor is a numerical value that is used to represent an object's enlarged or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its original size. It aids in altering the figure's size but not its shape.
Given that the two quadrilaterals are similar to each other and are dilated by some scale factor.
The scale factor will be calculated as:-
Scale factor = 15 / 10
Scale factor = 1.5
Hence, the scale factor will be 1.5.
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Let A(7,10) and B(-5,5). What is the length of AB
The length of segment AB is determined as 13 units.
What is distance between two points?The distance between two points is the length of the line segment that connects the two points in a plane.
here, we have,
The length of segment AB is the distance between point A and point B, which is calculated as follows;
|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]
where;
x₁ is the x - component of point A
x₂ is the x - component of point B
y₁ is the y - component of point A
y₂ is the y- component of the point B
|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]
|AB| = √[(-5 - 7)² + (5 - 10)²]
|AB| = √[144+25]
|AB| = 13 units
Thus, the length of segment AB is the distance between point A and B.
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If yk how to do this pls help me
The linear function for the population in t years after 2000 is given as follows:
P(t) = 2200t + 44000.
The estimate for the population in 2010 is given as follows:
66,000.
How to obtain the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial value.Two points for the function are given as follows:
(5, 55000) and (8, 61600).
Dividing the change in the output by the change in the input, the slope m is given as follows:
m = (61600 - 55000)/(8 - 5)
m = 2200.
Hence:
P(t) = 2200t + b.
When x = 5, y = 55000, hence the intercept b is given as follows:
55000 = 2200(5) + b
b = 55000 - 2200(5)
b = 44000.
Hence the function is:
P(t) = 2200t + 44000.
2010 is 10 years after 2000, hence the estimate is given as follows:
P(10) = 2200(10) + 40000
P(10) = 66,000.
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PLEASE HELP ME ANSWER
Answer: D)12 units
Step-by-step explanation:
Because, your y axis travels from 34 to 22, in that case you have to take away 22 from 34 which you get 12.
The reader can tell that this excerpt is part of the poem’s resolution, because the speaker
finally feels a sense of belonging.
finally learns how to play baseball.
no longer wants to get home before dusk.
no longer tries to catch the ball.
Answer:
A
Step-by-step explanation:
Divide the polynomials.
The form of your answer should either be p(x) or p(x) +
x
is an integer.
5x³ 22x²
x
-
5
17x +11
k
where p(x) is a polynomial and k
5
The division expression is (5x³ - 22x² - 17x + 11)/(x - 5) = 5x² + 3x - 2 + (2/(x - 5))
How to divide the polynomialFrom the question, we have the following parameters that can be used in our computation:
(5x³ - 22x² - 17x + 11)/(x - 5)
Using a synthetic setup, we have
x - 5 = 0
This gives
x = 5
So, the set up becomes
5 | 5 -22 -17 11
The synthetic division is then carried out as follows
5 | 5 -22 -17 11
25 15 -10
5 3 -2 1
So, we have
Quotient = 5 3 -2
Remainder = 1
Introduce the variable
Quotient = 5x² + 3x - 2
Remainder = 2
Hence, the quotient is 5x² + 3x - 2 and the remainder is 2
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The number of Barnes & Noble bookstores has increased, then decreased through the years. The piecewise function () given below shows how “pieces of” two functions can help determine the number of Barnes & Noble stores for particular intervals of years. Use =6 for the year 2006, =7 for the year 2007, etc. ()= { −3.692 +65.28+437.30 6≤ <12 −10.17+691 ≥12 a. According to (), how many Barnes & Noble stores were there in 2009?
The required number of Barnes & Noble stores in 2009 is 725.28.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
To determine the number of Barnes & Noble stores in 2009, we need to evaluate the piecewise function for t = 2009.
Since 2009 is between the interval 6 ≤ t < 12, the number of stores is given by the first piece of the function:
y = -3.692 × x² + 65.28 × x + 437.30
put x = 9 for the year 2009
y = -3.692 × 9² + 65.28 × 9 + 437.30 = 725.28
So, there were 725.28 Barnes & Noble stores in 2009.
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Is (1, -1) a solution to this system of equations?
y= –6x + 5
y= x – 2
The solution to the system of equations is ( 1 , -1 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
y = -6x + 5 be equation (1)
Let the second equation be represented as B
Now , the value of B is
y = x - 2 be equation (2)
On simplifying the equations , we get
Substitute the value of y from equation (2) in equation (1) , we get
x - 2 = -6x + 5
Adding 6x on both sides of the equation , we get
7x - 2 = 5
Adding 2 on both sides of the equation , we get
7x = 7
Divide by 7 on both sides of the equation , we get
x = 1
Substitute the value of x in equation (2) , we get
y = 1 - 2
y = -1
Hence , the value of x and y is 1 and -1 respectively
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rewrite the expression without absolute value bars
The expression without absolute value bars is 3.84.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
|√10 - 7 |
= | 3.16 - 7 |
= | -3.84 |
= 3.84
Thus,
The value of the expression is 3.84.
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