Answer:
£11.50
Step-by-step explanation:
7litres of petrol cos t £3.50. The cost of 1 liter will be:
= £3.50/7
= £0.50
The cost of 23 litres of petrol of the same grade will be:
= £0.50 × 23
= £11.50
7. Ms. Vickory assigned the problem: 8/9-4/6. Three of her students' responses are below. Who completed the problem correctly? What common mistakes did the other two students make?
The three students
Sue- 8/9-4/6=4/3 or 1 1/3
Jim- 8/6 - 4/6 = 48/54 - 36/54= 12/54 or 2/9
Bob- 8/9- 4/6 = 8/54-4/54= 4/54 = 2/27
Answer:
Jim: 2/9
Step-by-step explanation:
8/9-4/6
48/54-36/54 [Convert each fraction to a common denominator: 54
Multiply (8/9)*(6/6)=48/54; Multiply (4/6)*(9/9) = 36/54]
48/54-36/54 = 12/54
12/54 can be reduced to 2/9
Jim also has 2/9
Sue- 8/9-4/6=4/3 or 1 1/3: Sue subtracted both the numerator and denominator. This is not correct.
Jim- 8/6 - 4/6 = 48/54 - 36/54= 12/54 or 2/9: Good Job Jim
Bob- 8/9- 4/6 = 8/54-4/54= 4/54 = 2/27: Bob converted both denominators to 54, but did not multiply the numerators by the same numbers. Bad Bob.
One of the solutions to x² - 2x - 15 = 0 is x = -3. What is the other solution?
O x=-5
O x=-1
O x = 1
O x = 5
Answer:
x= 5
Step-by-step explanation:
factorised the equation is (x-5) (x+3)
x=5 x=-3
\In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur. The climate in which these mice live has slowly gotten colder.
How will this change in the environment most likely affect the mouse population?
The adaptation of thinner fur will be selected over thicker fur, and the population will remain unchanged.
The adaptation of thicker fur will be selected over thinner fur, and the population will remain unchanged.
The adaptation of thinner fur will be selected over thicker fur, and the population will evolve.
The adaptation of thicker fur will be selected over thinner fur, and the population will evolve.
The adjustment of thicker fur will be selected over thinner fur, and the population will develop. Then the correct option is D.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur.
The climate in which these mice live has slowly gotten colder.
The change in the environment most likely affect the mouse population will be
The adjustment of thicker fur will be selected over thinner fur, and the population will develop.
Then the correct option is D.
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Could use help asap please
Observe the diagram below with indexes on the shapes.
The transformations are:
Shape I is given a 90° clockwise rotation about the origin and then a reflection across the x-axis.Identify the equation with an x-intercept of 3 and a y-intercept of -2.
The equation of line is 2x - 3y = 6.
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
The x-intercept is 3 and the y-intercept is -2.
So, the line passes through the points (3, 0) and (0, -2)
Now, slope of line is
m= -2-0/ 0-3 = 2/3
Equation of line is
y = 2/3 x - 2
y = 2x-6 /3
3y= 2x -6
2x - 3y = 6
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find the value of a from the following 1. sin3a=cos3a
✏Answer:
Sin3A=Cos3A
Cos(90-3A)=Cos3A
90-3A=3A
90=3A+3A
90=6A
90/6=A
A=15^•^
The answer is A=15
Julie invests money in an account that pays compound intrestof 5% per annum after 3 years julie has 2778.30 how much did julie initially invest
Answer:
[tex]\huge\boxed{2400}[/tex]
Useful Information:
The formula for compound interest is: [tex]initial.amount*interest.rate^{no.years}[/tex]
Step-by-step explanation:
To work this out, you would first have to convert the percentage into a decimal. You can do this by dividing the percentage of 5% by 100, which gives you 0.05. This is because percentages are out of 100.
The next step is to add 1 to 0.05, this gives you 1.05. This is because you are working out the percentage increase.
The next step is to substitute the values into the formula. This gives you[tex]initial.amount*1.05^{3}=2778.30[/tex]
To work out the initial value, you would divide the final amount of 2778.30 by [tex]1.05^3[/tex], which gives you 2400. This is because you are rearranging the formula to find the initial investment.
1) Divide 5 by 100.
[tex]\frac{5}{100}=0.05[/tex]
2) Add 1 to 0.05.
[tex]1+0.05=1.05[/tex]
3) Substitute the values into the formula.
[tex]initial.amount*1.05^{3}=2778.30[/tex]
4) Divide 2778.30 by [tex]1.05^3[/tex].
[tex]\frac{2778.30}{1.05^3}=2400[/tex]
give me da answer.........................................................................
Answer:
Ok ya sure I would love to. :)
Step-by-step explanation:
Oh wait….
*Crickets chirping*
I need this answer . I would be happy if I got it .
Answer:
15cm
Step-by-step explanation:
PC = 15
BR = 15
.
............................................
The selling price of an article is Rs 270. If the article was sold at 10 % discount from the marked price, find the marked price.
Answer:
s. p = 270 Rs
discount = 10%
mp.= ?
Mp = s. p + discount
= 270 + 10/100*270
= 270 + 27
= 297 Rs
297 Rs is the marked priceAnswer:
[tex]\huge\boxed{\sf Rs.\ 297}[/tex]
Step-by-step explanation:
Selling Price = Rs. 270
Discount = 10%
Discount in Rs.:= 10% of 250
[tex]\displaystyle =\frac{10}{100} \times 270[/tex]
= 1 × 27
= Rs. 27
Marked Price:= Selling Price + Discount
= 270 + 27
= Rs. 297
[tex]\rule[225]{225}{2}[/tex]
How many sulotions does this system have? 6x-y=-1 6x+y=-1
Answer:
6/6
Step-by-step explanation:
6/6 not equal -1/1 so these lines intersect each other at only one point hence these have only one solution.
Answer:
I can give you the answer if you can answer a question
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
/
Find the value of x.
A.
4
B.
5
C.
6
D.
9
Please select the best answer from the choices provided
A
B
C
D
The value of x will be 4 , Option A is the answer.
What is a Right Angled Triangle ?A triangle that has one angle as 90 degree is called a Right angled Triangle.
In a right angled triangle
the length of the sides can be determined using Pythagoras Theorem
The length of the side is given in the image attached as
x-2 , x , √20
Hypotenuse ² = Perpendicular² + Base²
(√20)² = x² + (x-2)²
20 = x² + x² +4 -4x
2x²-4x -16 = 0
x² -2x -8 = 0
x² - 4x +2x -8 = 0
x (x-4) +2(x-4) = 0
(x+2)(x-4) = 0
x = -2 , 4
The value of x will be 4 .
Therefore Option A is the answer.
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x + 3y > –3 and y < One-halfx + 1?
The complete question is
"Which is the graph of the system x + 3y > –3 and y < One-halfx + 1?"
The solution is the intersection region of all the solutions in the system of inequalities.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
We know that the lines are given as;
x + 3y = -3
y = 1/2 x + 1
Solving for "y" from the first line;
3y = -3 - x
y = -1 - x/3
For the line x + 3y = -3 the x-intercepts;
y = 0
y = -1 - x/3
0 = -1 - x/3
x/3 = -1
x = -3
And the y-intercept;
y = -1
For the line y = 1/2 x + 1 the x-intercepts;
y = 0
0= 1/2 x + 1
1/2x = -1
x = -2
And the y-intercept
x = 0
y = 1
Now we can graph both lines,
The solution is the intersection region of all the solutions in the system of inequalities.
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How do I answer this question pls help me
Answer:
14.7 quarts
Step-by-step explanation:
Use the given equivalence figures to write a proportion. Solve the proportion for the unknown value.
__
quarts/liters = x/14 = 1/0.95 . . . . . the conversion is given as 1 qt = 0.95 L
Multiply by 14 to find x.
x = 14(1/0.95) ≈ 14.7
There are about 14.7 quarts in 14 liters.
_____
Additional comment
You are given a value in liters (14 liters) and asked for the equivalent in quarts. That means you want to change the units from liters to quarts. To do that, you can multiply the given value (14 liters) by a conversion factor that has quarts in the numerator and liters in the denominator. That is what the fraction 1/0.95 is in the above. You will note that units of liters cancel in this equation.
[tex](14\text{ liters})\times\dfrac{1\text{ quart}}{0.95\text{ liter}}=\dfrac{14}{0.95}\text{ quarts}\approx14.7\text{ quarts}[/tex]
This rule, "use a conversion factor that divides by the units you don't want and multiplies by the units you do want" applies to any units conversion problem. The conversion factor you use should always have equal quantities in the numerator and denominator. (Here, the equal quantities are 1 quart and 0.95 liters.)
You will notice that we treat units just like any variable. They can be multiplied, divided, cancelled, raised to a power. Only terms with like units can be added or subtracted.
If t = 0 in 1980, find the value for t in 1990
The value of t is 6.65
What is exponential function?An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is a variable, and a is a constant called the base of the function.
Given:
A= 210 million
P= A e^(kt)
225 = 210 * e ^ (0.0069t)
225/210= e ^ (0.0069t)
1.07 = e ^ (0.0069t)
Taking log on both side
log 1.047 = 0.0069 t log e
[tex]\frac{0.0069t\ln \left(e\right)}{0.0069\ln \left(e\right)}=\frac{\ln \left(1.047\right)}{0.0069\ln \left(e\right)}[/tex]
t= log ( 1.047) / 0.0069
t= 6.65
Hence, value of t is 6.65.
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Answer:
Step-by-step explanation:
. All the students in SS3 of a named school take either Mathematics (M), or Physics (P) or Chemistry (C). 40 take Mathematics, 42 take physics, 38 take Chemistry, 20 take Mathematics and Physics, 28 take Physics and Chemistry while 25 take mathematics and chemistry.
How many take
(a) All the three subject:
(b) Mathematics, but neither Physics nor Chemistry
(c) Physics, but neither Mathematics nor Chemistry
Answer:
(a) = 13
(b) = 8
(c) = 5
Step-by-step explanation:
Addition theorems on sets are
Theorem 1 :
n(AuB) = n(A) + n(B) - n(AnB)
Theorem 2 :
n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
Total number of students in the school is not given
so let there are 60 students in the school
using theorem 2
n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry
so putting values,
60 = 40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)
60 +73 -120 = n(AnBnC)
13 = n(AnBnC)
therefore, there are total 13 students who take all three subjects
Number of students who had taken only Mathematics =
n(A) - n(AnB) - n(AnC) + n(AnBnC)
40 - 20 - 25 + 13
53 - 45 = 8 students
Number of students who had taken only Physics =
n(B) - n(BnA) - n(BnC) + n(AnBnC)
42 - 20 - 28 + 13
53 - 48 = 5 students
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Solve using a proportion.
A carpet store charges $150 to install 12 square yards of carpet. How much should it cost to
install 24 square yards?
A. $250
B. $300
C. $3,600
D. $192
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling?
1 mile = 5,280 feet
45 miles per hour
46 miles per hour
47 miles per hour
48 miles per hour
Answer:
48 miles per hour I hope I helped you have a nice day
express the set x < 1 using interval notation
Answer:
(−∞,1)
Step-by-step explanation:
Let the numbers below represent the lengths of the sides of a triangle. Which of the triangles is a right triangle?
I. 4, 5, 6
II. 6, 8, 10
III. 5, 13, 14
IV. 7, 11, 13
A
I
B
II
C
III
D
IV
Answer:
B. II (6, 8, 10)
Step-by-step explanation:
A set of triangle side lengths will form a right triangle if they satisfy the Pythagorean theorem. The sum of squares of the shortest two sides must equal the square of the longest side.
__
Pythagorean triplesSets of integers that satisfy the Pythagorean theorem are called "Pythagorean triples." Some of these for smaller integers are ...
(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)
If small integer side lengths are not one of these triples, or a multiple of one of these triples, they will not form a right triangle.
I. not a match to any triple
II. matches (3, 4, 5) multiplied by 2 -- a right triangle
III. not a match to any triple
IV. not a match to any triple
_____
Pythagorean equationOf course, you can actually compute the squares to see if they satisfy the Pythagorean theorem:
I. 4² +5² = 41 ≠ 6² (acute triangle)
II. 6² +8² = 100 = 10² -- right triangle
III. 5² +13² = 194 ≠ 14² (obtuse triangle)
IV. 7² +11² = 170 ≠ 13² (acute triangle)
__
form factorThe sum f = a² +b² -c² (where c is the longest side) can be considered to be a "form factor" for the triangle. For ...
f>0, the sides form an acute triangle f=0, the sides form a right trianglef<0, the sides form an obtuse triangleThis "form factor" is related to the largest angle (C) by ...
cos(C) = f/(2ab)
A square garden has a side length of 5 ft. What is the area of the garden?
O 5ft²
O 10ft²
O 20ft²
O 25 ft²
formula is lsquare so answer is 25ft
PLEASE ANSWER ASAP!!!!!!!
a⃗ =<5, −1> and b⃗ =<2,−2>.
Represent a⃗ +b⃗ using the head-to-tail method.
Use the Vector tool to draw a⃗ and b⃗ , complete the head-to-tail method, and draw a⃗ +b⃗
To use the Vector tool, select the initial point and then the terminal point.
(please give picture of graph)
OC represents vector a and b drawn using the head-to-tail method.
What is a Vector ?A vector is an object that has both magnitude and direction.
The given vectors are
a =<5, −1> and b =<2,−2>
Representing vector a +b using the head and tail method
Here in the image attached with the answer ,
The vector a is represented by OA and the vector b is represented by OB
By head and tail method , the OC is drawn by extending the vector a towards b and b towards a
Vector OC = Vector OA + Vector OB
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PLEASE HELP
Mary is three times as old as her son. In 12 years, Mary's age will be one year less than her son's age. How old is each now?
Answer:
Son's Age: 11
Mary's Age: 33
Step-by-step explanation:
Let set Mary and her son as variables,
M = Mary's age
S = Mary's son age
Breakdown:
"Mary is three times as old as her son"
M = 3S
"In 12 years, Mary's age will be one less than twice her son's age"
M + 12 = 2(S + 12) - 1
we add 12 to both sides as it will be in 12 years for both
We know that M = 3S, so we plug this in
3S + 12 = 2(S + 12) - 1
Now solve for S (son's age),
3S + 12 - 12 = 2(S + 12) - 1 - 12
3S = 2(S + 12) - 13
3S = 2S + 24 - 13
3S - 2S = 2S - 2S + 24 - 13
S = 24 - 13
S = 11
To find Mary age, plug in her son age ,
M = 3S
M = 3(11)
M = 33
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find the average rate of change
Answer:
[tex]\dfrac{26}{3}[/tex]
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given function: [tex]f(x)=3^{x-1}+2[/tex]
Given interval: 1 ≤ x ≤ 4
Therefore, a = 1 and b = 4
Therefore, find the value of the given function when x = 1 and x = 4:
[tex]\begin{aligned}\implies f(1) & =3^{1-1}+2\\ & = 3^0+2\\ & = 1+2\\ & = 3 \end{aligned}[/tex]
[tex]\begin{aligned} \implies f(4) & = 3^{4-1}+2 \\ & = 3^3+2\\ & = 27+2\\ & = 29 \end{aligned}[/tex]
Substitute the found values into the formula:
[tex]\begin{aligned}\implies \dfrac{f(b)-f(a)}{b-a} & =\dfrac{f(4)-f(1)}{4-1}\\\\ & =\dfrac{29-3}{4-1}\\\\ & = \dfrac{26}{3} \end{aligned}[/tex]
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal. Is Kyle's claim Incorrect or correct? In two or more complete sentences, Justify your answer.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal. Kyle's claim is Incorrect.
What is a quadrilateral?It is a polygon with four sides. The total interior angle is 360 degrees.
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal.
Kyle's claim is Incorrect. Because the shapes are square and rhombus.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal.
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If with 150 grams of ground meat a tortilla is prepared to make a hamburger. How many tortillas can I make with one and a half kilograms of ground meat?
Answer:
You can make 10 tortillas with one and a half kilograms of ground meat
Step-by-step explanation:
one and a half kilograms to grams
1.5kg x 1000 = 1500g
150 grams prepared to make 1 hamburger
than, 150 x h = 1500
h = 1500 / 150
h = 10
Answer:
10 tortillas
Step-by-step explanation:
First convert kilograms to grams:
1 kg = 1000 g
⇒ 1.5 kg = 1500 g
Let x = number of tortillas made with 1500 g of meat
Set up a ratio of tortillas and meat and solve for x:
⇒ 1 tortilla : x tortillas = 150 g meat : 1500 g meat
[tex]\sf \implies \dfrac{1}{x}=\dfrac{150}{1500}[/tex]
[tex]\sf \implies 1 \cdot 1500= 150 \cdot x[/tex]
[tex]\sf \implies 1500=150x[/tex]
[tex]\implies \sf x=\dfrac{1500}{150}[/tex]
[tex]\implies \sf x=10[/tex]
Therefore, 10 tortillas can be made with 1.5 kg of ground meat.
Paolo and Monika are both travelling by train.
Paolo's train travels 70 km in 35 minutes.
Monika's train travels 684 km.
It leaves at 16:15 and arrives at 20:45.
Work out the difference, in km/h, between the average speed of their trains.
Answer:
32 km/hr
Step-by-step explanation:
Firstly, you need to find the speed of both trains in km/hr.
Paolo's train= (70km x 60hr)/35= 120 km/hr
Monika's train= 684km/4.5hr= 152 km/hr
Then find the difference in speed:
152-120=32 km/hr
A shoe making company makes 256 pairs of boots in a day how many pairs of boots do they make in 260 days
Answer:
66560 pairs
Step-by-step explanation:
let the number of pairs of boots the company makes in 260 days = X
1day -----------------256pairs
260days-------------X
cross multiplying
1×X = 260×256
X= 66560
therefore, in 260days, he makes 66560 pairs
Parallelogram EASY is drawn with diagonal ES. The measure of Angle AES is 40 degrees and the measure of Angle Y is 110
degrees.
Find the measure of Angle A, Angle YEA, Angle ESA, and Angle ESY.
Answer:
Step-by-step explanation:
Givens
Parallelogram EASY with diagonal ES
<AES = 40
<Y = 110
Solution
<AES = 40 GIVEN
<ESY = 40 Z THEOREM OF A PRALLELOGRAM
<A = <Y PROPERTY OF A PARALLELOGRAM
<A = <110 <A = 110 BECAUSE <Y = 110
<YES = 180 - <Y -<ESY EVERY TRIANGLE HAS 180o
<YES = 180 - 110 - 40 SIMPLIFY
<YES = 30
<YEA = <YES + <AES WE KNOW BOTH ANGLES ON THE RIGHT.
<YEA = 30 + 40 COMBINE
<YEA = 70
You could do <YEA by noting that consecutive angles of a Parallelogram equal 180
Consider figures 1 and 2 shown on the coordinate plane. Figure 1 has been transformed to produce figure 2. Graph shows 2 quadrilaterals plotted on a coordinate plane. Quadrilateral 1 in quadrant 1 has vertices at (1, 3), (2, 5), (5, 5), (5, 3). Quadrilateral 2 in quadrant 4 has vertices at (1, minus 3), (5, minus 3), (5, minus 5), (2, minus 5). Describe the transformation. This transformation can be described by?
Using translation concepts, it is found that this transformation can be described as a reflection across the x-axis.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, considering the vertices of quadrilateral 1 and quadrilateral 2, the transformation from quadrilateral 1 to quadrilateral 2 has the following format:
(x,y) -> (x, -y).
Which means that it can be described as a reflection across the x-axis.
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