The cost of one packet of biscuit is £1.60.
What is the cost of one packet of biscuit?The total amount that Aisha paid for the items she purchased is a function of the total cost of bread rolls, ketchup and biscuits.
Total cost of the items purchased = total cost of bread rolls + total cost of biscuits + total cost of ketchup
Total cost of bread rolls = cost per packet x number of packets bought
2 x £1.20 = £2.40
Total cost of ketchup = cost of one bottle x number of bottles bought
1 x £2.10 = £2.10
Total cost of biscuits = cost of one packet x number of packets bought
3 x b = 3b
Total cost = £2.40 + £2.10 + 3b = £4.50 + 3b
Total amount paid by Aisha = note given - change received
£10 - 70p
£10 - £0.70 = £9.30
Total amount paid by Aisha = total cost
£9.30 = £4.50 + 3b
£9.30 - £4.50 = 3b
£4.80 = 3b
b = £4.80 / 3
b = £1.60
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A triangle has vertices on a coordinate grid at R(-3,3)R(−3,3), S(-3,-9)S(−3,−9), and T(-9,-9).T(−9,−9). What is the length, in units, of \overline{RS}
RS
?
The length of the side RS in triangle RST as required to be determined in the task content is; 12 units.
What is the distance between two points?The distance between two points defined by pairs of coordinates on the Cartesian plane can be determined by a modification of the Pythagoras theorem.
Hence, the distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:
AB= √{(y₂ - y₁)² + (x₂ - x₁)²}
Given that the vertices R and S of the triangle is at R(−3,3), S(-3,-9), hence:
RS= {( -9-3 )² + ( -3-(-3))² } = 12 units.
The length of the side RS in triangle RST is 12 units.
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what is greatest common denominator of 72 and 159)
Answer:
3
Step-by-step explanation:
The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b (Wikipedia)
To find out which is the GCD of 72 and 159, keep factoring both until they cannot be factored any more
Then take the factors common to both list of factors; the greatest among them is the GCD
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 159 are: 1, 3, 53, 159
The common factors are 1, 3
So GCD is 3
Three cars are shown below, along with
their original prices.
The price of each car is then rounded to
the nearest £100.
a) Work out which car's price changes the
most.
b) By how much does this car's price
change?
Car X
£13,420
MATHS X
Car Y
£17,590
MATHS Y
Car Z
£12,860
MATHS Z
In linear equation , the car y's price changes the most.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.According to the question
a) Car x : £ 10320 ≈ £ 10300 10320 - 10300 = 20
Car y : £ 15430 ≈ £ 15400 15430 - 15400 = 30
Car z : £ 17490 ≈ £ 17500 17490 - 17500 = 10
10 < 20 < 30
so the car y's price changes the most.
b) this car's price change £ 30
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According to the empirical rule, ________ will be within two standard deviations of the mean.
According to the empirical rule, 95% will be within two standard deviations of the mean.
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean. Three-sigma limits that follow the empirical rule are used to set the upper and lower control limits in statistical quality control charts and in risk analysis such as VaR.
The empirical rule is used often in statistics for forecasting final outcomes. After calculating the standard deviation and before collecting exact data, this rule can be used as a rough estimate of the outcome of the impending data to be collected and analyzed.
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If m<2=9x+7 and m<3 = 5x + 5, what is m<1?
The value of m<1 is 65 degrees
How to determine the angleFrom the diagram shown, we have that;
m<2=9x+7 m<3 = 5x + 5It is important to note that angles on a straight line sum up to 180 degrees
Also, corresponding angles are equal
Then, we have that;
m<2 + m<3 = 180°
Substitute the values
9x + 7 + 5x + 5 = 180
collect like terms
14x = 180 - 12
14x = 168
Make 'x' the subject
x = 168/ 14
x = 12
We have that;
m<3 = 5x + 5 = 5(12) + 5 = 60 + 5 = 65
But m<3 = m<1
m<1 = 65
Thus, the value of m<1 is 65 degrees
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Choose the definition for the function.
(-x+ 2
a. y = x + 1
(-x+ 2
b. y = x + 1
{
x < 1
x ≥ 1
x ≤1
x> 1
S-x+ 2
x+1
c. y = {
(-x+ 2
d. y = x + 1
x > 1
x ≤ 1
x ≥ 1
x < 1
Enter
Answer:
can you add a photo of the questions? So it's easier to see
Evelyn is getting older and feels like she should donate her collection of stuffed animals to children who are less fortunate. She has 18 stuffed cats and 12 stuffed dogs, which she wants to divide into identical groups, with no stuffed animals left over. What is the greatest number of groups Evelyn can place her stuffed animals into?
The greatest number of groups Evelyn can place her stuffed animals into
= 6 Groups.
We have been given that
Evelyn should donate her collection of stuffed animals in which
No. of stuffed cats = 18
No. of stuffed dogs = 12.
We have to find out number of groups with no stuffed animals left over.
for solving this question we can use GCF
What is GCF (Greatest Common Factor)?
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
How can we find GCF?
The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number.
18 and 12 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 12.
The common factors of 12 and 18 are 1, 2, 3 and 6. The greatest common factor of them is 6.
In each groups no. of cats and dogs are (3cats , 2 dogs)
Hence , 6 is the greatest number of groups Evelyn can place her stuffed animals into.
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Solve
please show all steps
Answer:
10m + 100 = 15m
20 movies
Step-by-step explanation:
Hello!
Let the number of movies watched be m.
The equation for the first movie club would be 10m + 100, as you pay 10 dollars per movie (10*m) and you add the original membership fee (100).
The equation for the second movie club is 15m, 15 dollars per movie. Set the equations equal to each other and solve for m, the number of movies, so the price would be equal.
Solve for m10m + 100 = 15m 100 = 5m (subtract 10m)20 = m (Divide by 5)Therefore, you would need to watch 20 movies in each movie club for the total price to be equal.
Plane H contains four points. Points A, C, and D form a diagonal line on the left. Point B is to the right of point C.
Which points are coplanar and noncollinear?
points A and D
points C and D
points A, C, and D
points A, B, and D
Answer:
Points A B D
Step-by-step explanation:
I am assuming in the plane, all the points are inside. For it to be non- collinear, I am pretty sure there has to be points not on the line. In this Case, only A C D are actually on a line. Since B is to the right of C, I don't think that will make a good line. So that is the answer I am going with.
Answer:
d)a ,b,d
Step-by-step explanation:
Simplify each number. 32¹.²
The result of simplifying the number 32¹.² using the exponent rules is 1024
To solve this exercise we have to resolve algebraic operations following the exponent rules.
Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
(32¹)²
32⁽¹*²⁾ =
32² =
32 * 32 =
1024
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Trapezoid WXYZ has vertices at W(–5, –1), X(–3, –1), Y(–2, 1), and Z(–6, 1). Trapezoid WXYZ is translated so that the coordinates of Y' are (0, 3). What will be the coordinates for W′?
Solution :
the coordinates for W′ = (-1,3)
Trapezoid :
A trapezoid is necessarily a convex quadrilateral in Euclidean geometry. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases). A scalene trapezoid is a trapezoid with no sides of equal measure
Y = (-2,1)
Y' = (0,3)
Unit shift for Y to Y'
By distance formula :
yy' = [tex]\sqrt{{(x2-x1})^{2} +( y2-y1)^{2} }\\[/tex]
= root of (2)^2 +(2^2)
= root of 4+4
Root of 16
= root of 4
Unit shift for Y to Y' = 4
then
w = (-5,-1)
shift by adding 4
W' = (-5+4, -1+4)
W' = (-1,3)
the coordinates for W′ = (-1,3)
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Write each expression in simplest form. 5+√3 / 2-√3
The simplest form of the expression [tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex] is [tex]13+7\sqrt{3}[/tex].
The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).
In elementary algebra, the procedure of rationalization is performed to get rid of the irrational number in the denominator. There are several methods for rationalizing the denominator.
An expression comprises a variable, a number, or a combination of a number, a variable, and operation symbols. An equation is created by joining two expressions with an equal sign.
Consider the expression,
[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex]
Rationalizing the denominator,
[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} } = \frac{5+\sqrt{3} }{2-\sqrt{3} } \times \frac{2+\sqrt{3} }{2+\sqrt{3}}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{(5+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}[/tex]
Using the identity,
( a + b )( a - b ) = a² - b²
Therefore,
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{5 \times 2 + 5 \times \sqrt{3} + \sqrt{3} \times 2 + (\sqrt{3} )^{2}}{(2)^{2}-(\sqrt{3} )^{2}}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{10+7\sqrt{3}+3}{4-3}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{13+7\sqrt{3}}{1}[/tex]
[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = 13+7\sqrt{3}[/tex]
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<, >, or =
-3.625 ___ -3.62
Answer:
-3.625 < -3.62
Step-by-step explanation:
calculate the area of ABC and the area of ABDE for each of these diagrams
Step-by-step explanation:
ED || AB
E is the midpoint of AC.
therefore, D is the midpoint of BC, and AB is 2×ED.
but also the height of ABC is 2×height of EDC.
now, we know, the area of a triangle is
baseline × height / 2
area EDC = baseline × height / 2 = 18 cm²
area ABC = 2×baseline × 2×height /2 =
= 4 × (baseline × height / 2) =
= 4 × area EDC = 4 × 18 = 72 cm²
the area of ABDE = area ABC - area EDC =
= 72 - 18 = 54 cm²
Write and solve an inequality to find the possible values of x. (Please answer ASAP)
The inequality is: 14.2 + 14.2 + x < 51.3
x < 22.9
How to Solve an Inequality?We are given the following:
Perimeter of the triangle < 51.3 in.
The sides are 14.2 in., x in., and 14.2 in.
Therefore, we would have the following inequality:
14.2 + 14.2 + x < 51.3
Solve for x
28.4 + x < 51.3
x < 51.3 - 28.4
x < 22.9
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Marcelo plays a carnival game six times he spent three tokens to play each game and he won 7 tokens each game write two different expressions that can be used to find the total profit in tokens that Marcelo made
The expressions that can be used to find the total profit in tokens that Marcelo made is (7 × 6) - (3 × 7) and 42 - 21.
How to illustrate the information?From the information, Marcelo plays a carnival game six times he spent three tokens to play each game and he won 7 tokens each game.
The appropriate expression will be:
= (7 × 6) - (3 × 7)
= 42 - 21
= 21
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Based on the results express the probability that the next chew Lamonte removes from the bag will be apple chew as a percent to the nearest whole number
An apple chew was selected 13 times.
A strawberry chew was selected 6 times.
A like chew was selected 15 times.
Bob has a window that is 114 square feet. The window is in the shape of a square. Which of the following expresses the length of one of the sides of the window? A 1142 B √57 C √114 D√111 E 1143 answer as soon as possible :)
The expression of the length of one of the sides of the window is √114
What are areas?The area of a shape is the amount of space on the shape
Which of the following expresses the length of one of the sides of the window?The area of the window is given as
Area = 114 square feet
The shape of the window is a square
The area of a square is calculated as
Area = Length^2
So, we have
114 = Length^2
Take the square root of both sides
Length = √114
Hence, the expression of the length of one of the sides of the window is √114
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For each pair of functions, find f(g(x)) and g(f(x)) .
f(x)=x+3, g(x)=x-5
A composite function exists as a function that depends on another function. The value of f(g(x)) = x-8 and g(f(x)) = x-2.
What is meant by composition function?In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.
Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.
Let the two functions be f(x) = x+3 and g(x) = x-5
f(g(x)) = f(x-5)
simplifying the above equation, we get
f(x-5) = x-5+3
f(g(x)) = x-8
g(f(x)) = g(x+3)
simplifying th above equation, we get
g(x+3) = x+3-5
g(x+3) = x-2
Therefore, the value of f(g(x)) = x-8 and g(f(x)) = x-2.
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Already did the gradient a , just stuck on gradient B
The gradient of line B is (-1).
What is gradient?The gradient of a line is used to calculate the steepness of a line and determines how much it is inclined with reference to the x-axis. To calculate the gradient of any line, the x and y coordinates of a line are used. In other words, it is the ratio of the change in the y-axis to the change in the x-axis.
The gradient is the measure of the steepness of a straight line.
Given:
coordinates taken from line B is (5, 0) and (-2, 7)
we have [tex]y_2[/tex]= 7, [tex]y_1[/tex]= 0, [tex]x_1[/tex]= 5, [tex]x_2[/tex] =-2
now, substituting the values then,
The gradient is
=[tex]( y_2- y_1)/ (x_2 - x_1)[/tex]
=(7-0) / (-2 - 5)
=7 /(-7)
=-1
Hence, the gradient is -1
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If x is a binomial random variable with n = 20 and p = 0.25, the expected value of x is:_________
The expected value with a sample size of 20 and a probability of 0.25 will be 5.
What is the expected value?The anticipated value is an extension of the weighting factor in statistical inference. Informally, the anticipated value is the simple average of a significant number of outcomes of a randomly selected variable that was separately chosen.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
If x is a binomial random variable with n = 20 and p = 0.25. Then the expected value is given below.
E(x) = 20 x 0.25
E(x) = 5
The expected value with n = 20 and p = 0.25 will be 5.
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2 nm = _____ cm
WHAT IS THE FORMULA I CANT --
2nm = 2e-7 cm or written out 0.0000002 cm
To convert nm to cm, you have to divide the value by 1e+7 (10000000).
How can you express 5 1/3 + -7 2/3 as the sum of its integer and fractional parts
The sum of its integer and fractional parts is 5 + (-7) + 1/3 + 2/3. Option D
What are fractions?Fractions are defined as part of a whole.
The types of fractions include:
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsGiven the expression;
5 1/3 + -7 2/3
The integers are:
5 and -7
The fractions are;
1/3 and 2/3
The sum of the integers and fractional parts are;
5 + (-7) + 1/3 + 2/3
Thus, the sum of its integer and fractional parts is 5 + (-7) + 1/3 + 2/3. Option D
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The response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes.
The standard deviation of the response time is 1.2755 minutes.
How to illustrate the information?Based on the information, the response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes.
The standard deviation of the response time will be illustrated thus:
It should be noted that the area under the one tailed standard normal curve is given as:
P(0 <= Z <= 1.96) = 0.475
The standards deviation will be:
= 2.5 / 1.96
= 1.2755
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The response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes. What is the standard deviation of the response time?
Given f(x)=2x²+4, find the value of f(−1)
Answer:6
Step-by-step explanation:
when x is -1 y is 6. input -1 as x in the equation and solve, otherwise graph.
Solve please and thanks
Answer: (10, 8)
Step-by-step explanation:
To solve a substitution question, you have to make sure either x or y is alone on the other side of equal sign.
-x + y = -2
^^^this becomes y = -2 + x
Now, since you know what "y" is, you simply replace "y" with our new equation in the other equation.
-x - 2(-2+x) = -26
Then, you do order of operations to get the answer.
First, do distributive property.
-x + 4 - 2x = -26
Next, solve the equation.
-3x + 4 = -26
-3x = -30
x = 10
Since you found what "x" is, you substitute "x" and in one of your equations to find "y", it doesn't matter which one.
-(10) + y = -2
-10 + y = -2
y = 8
Finally, after you got "x" which is 10, and "y" which is 8, you put them in an ordered pair (x, y) which is (10, 8).
P.S. I use Sora and Deltamath too!
Order the numbers from smallest to largest:
\large \mid4\mid,\sqrt{9},-3,\mid-5\mid,-3^2,2^3
Reorder answers
1.
\large -3
Reorder answers
2.
\large -3^2
Reorder answers
3.
\large \sqrt{9}
Reorder answers
4.
\large \mid4\mid
Reorder answers
5.
\large \mid-5\mid
Reorder answers
6.
\large 2^3
The rational numbers ordered from smallest to largest are given as follows:
-3², -3, sqrt(3), 4, 5, 2³.
What are rational numbers?Rational numbers are numbers that can be represented by fractions, such as integers and terminating or repeating decimals.
They are ordered as follows:
negative infinity, ..., -5, ..., -3, ..., 0, ..., 3, ..., 5, ..., positive infinity.
That is, large negative are the smallest, and large positives are the greatest.
For this problem, the numbers are given as follows:
4.sqrt(9) = 3.-3.5.-3² = -9(as it is not inside the parenthesis, only 3 is squared and the negative sign stays).2³ = 8.Hence the ordering, from least to greatest, of the numbers is given as follows:
-3², -3, sqrt(3), 4, 5, 2³.
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the quotient of y and 27
y ÷ 27
27 ÷ y
y ÷ 27 + y
y × 27
im literally so confused pls explain how you got the answer bc someone told me and means multiplication and math but apparently it doesnt so
It should be noted that the quotient of y and 27 will be y ÷ 27. The correct option is A.
How to illustrate the information?It should be noted that quotient simply means the quantity that's produced when two numbers are divided. A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio. The quotient is the result of dividing two numbers by each other. As in the case of 8 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8, while the divisor is 4.
When we divide a number, the result we ultimately get is the quotient. The mathematical symbol (÷ ) denotes division, a technique for allocating items equally among groups.
In their case, the quotient of y and 27 simply means the division of the numbers. This will be y ÷ 27.
Therefore, the correct option is A.
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If 8x+7y=6 is a true equation, what would be the value of 5+8x+7y?
If the equation 8x+7y=6 is a true equation, then the value of the equation 5+8x+7y is 11
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of the equation?The equation is given as
8x + 7y = 6
The above equation is said to be true
The next step is to add 5 to both sides of the equation 8x + 7y = 6
So, we have
5 + 8x + 7y = 6 + 5
Evaluate the sum of the like terms
So, we have
5 + 8x + 7y = 11
Hence, if the equation 8x+7y=6 is a true equation, then the value of the equation 5+8x+7y is 11
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here are the first two terms of some different arithmetic sequences
The best there terms of the sequence will be:
a. 10, 16
b. 211, 311
c. 10 , 12.5
d. -13, -22
How to illustrate the information?It should be noted that in an arithmetic sequence, there is a constant difference, which is the difference between a term and the previous term.
We find the constant difference for each sequence, and we add it to the second term to find the third term. Then we add the constant difference to the third term to find the fourth term.
a. 4 - (-2) = 6
3rd term: 4 + 6 = 10
4th term: 10 + 6 = 16
b. 111 - 11 = 100
3rd term: 111 + 100 = 211
4th term: 211 + 100 = 311
c. 7.5 - 5 = 2.5
3rd term: 7.5 + 2.5 = 10
4th term: 10 + 2.5 = 12.5
d. -4 - 5 = -9
3rd term: -4 + (-9) = -13
4th term: -13 + (-9) = -22
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Here are the first two terms of some different arithmetic sequences:
a. -2,4
b. 11, 111
C. 5, 7.5
d. 5,-4
What are the next three terms of each sequence?