The amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain
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 amount of petrol in Spain be = A
Let the amount of petrol in Wales be = B
Now , the total amount Sam paid for 18 Liters of petrol in Spain = 27 euros
1 euro = 0.85 pounds
So ,
Total amount Sam paid for 18 Liters of petrol in Spain = 27 x 0.85 pounds
Total amount Sam paid for 18 Liters of petrol in Spain = 22.95 pounds
So ,
The amount for 1 Liter of petrol in Spain = Total amount Sam paid for 18 Liters of petrol in Spain / 18
Substituting the values in the equation , we get
The amount for 1 Liter of petrol in Spain = 22.95 / 18
The amount for 1 Liter of petrol in Spain = £ 1.275
And ,
Now , the total amount Sam paid for 8 gallons of petrol in Wales = £ 40.80
1 gallon = 4.5 Liters
8 gallons = 4.5 x 8 Liters
8 gallons = 36 Liters
So ,
Total amount Sam paid for 36 Liters of petrol in Wales = £ 40.80
So ,
The amount for 1 Liter of petrol in Wales = Total amount Sam paid for 36 Liters of petrol in Spain / 36
Substituting the values in the equation , we get
The amount for 1 Liter of petrol in Wales = 40.80 / 36
The amount for 1 Liter of petrol in Wales = £ 1.13
£ 1.13 < £ 1.275
Therefore , the amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain
Hence , The amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain
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When Earth and Mars are farthest from each other they are about 4.01 x 100,000,000 kilometers apart. Sarah says "To right this number in standard form, I can move the decimal point 9 digits to the right because there are 9 digits in the 100,000,000." Explain and correct Sarah's answer.
To correct Sarah's answer, the standard form of the given value would be = 4.01 × 10^⁹ km.
What is a standard form?Standard form is defined as the simplified method of representation of large numericals using decimal number, between 1.0 and 10.0, which is then multiplied by a power of 10.
The distance between the earth and Mars = 4.01 x 100,000,000 kilometers.
There are 9 digits in 100,000,000,
Therefore to write the standard form of the given distance of 4.01 x 100,000,000 kilometers would be;
4.01 × 10^⁹ km.
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The roster form of the set P is; {-2, -1, 0, 1}
The builder notation of the set P is; {x : x ∈ I, −2 < x ≤ 1}
How to write set builder notations?We are told that P is the set of integers that are greater than -3 and less than or equal to 1.
Roster form of sets is done by listing the elements of the set, separated by commas, inside a set of curly brackets.
Since P is the set of integers that are greater than -3 and less than or equal to 1, then the possible numbers are; (-2, -1, 0, 1)
The roster form is; {-2, -1, 0, 1}
The builder notation of this set is;
{x : x ∈ I, −2 < x ≤ 1}
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Folgers coffee is priced at 12.88$ for 80 cups of coffee, and Seattle's best is priced at 9.00$ for 50 cups. Which brand of coffee is the better value for each cup
A graduate student is designing a research study. She is hoping to show that the results of an experiment are statistically significant. What type of p-value would she want to obtain?.
The required type of p-value would she want to obtain is small p-value.
What is hypothesis test?Hypothesis testing is a type of measurable surmising that utilizes information from an example to make inferences about a populace boundary or a populace probability distribution. Initial, a speculative supposition that is made about the boundary or dispersion.
According to question:P-value shows that the outcomes are genuinely huge.
P-value in Measurements assists with performing speculation test and it assists with deciding the meaning of the outcomes.
A little P-value commonly (P<0.05) demonstrates solid proof against the invalid speculation in this way, we reject the invalid speculation, on opposite when P-esteem is enormous we can't dismiss the invalid speculation.
Thus, required answer is small p-value.
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If a1 =2 and an =-2an-1 then find the value of a6
The value of the sixth term of the sequence will be negative 64.
What is the sequence?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
If the first term (a₁) is 2 and the relation is aₙ = -2aₙ₋₁.
The second term is given as,
a₂ = -2a₂₋₁
a₂ = -2a₁
a₂ = -2 x 2
a₂ = - 4
The third term is given as,
a₃ = -2a₃₋₁
a₃ = -2a₂
a₃ = -2 x ( - 4)
a₃ = 8
The fourth term is given as,
a₄ = -2a₄₋₁
a₄ = -2a₃
a₄ = -2 x 8
a₄ = - 16
The fifth term is given as,
a₅ = -2a₅₋₁
a₅ = -2a₄
a₅ = -2 x (- 16)
a₅ = 32
The sixth term is given as,
a₆ = -2a₆₋₁
a₆ = -2a₅
a₆ = -2 x 32
a₆ = - 64
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Answer: -64
Step-by-step explanation:
Answer the questions about the graph shown below.
Part A) What is the price per ticket?
Part B) What equation can be used to represent the line?
Part C) If the theater were to sell 328 tickets, how much money would they make?
Part D) Is this relationship proportional? How do you know?
Therefore , the price per ticket is $12,the equation used is y=12x, the theatre made $3936 by selling 328 ticket and the relationship is proportional.
What is equation?An algebraic equation is a linear equation. Each term in a linear equation is either a constant or the result of a constant plus one variable. In the case of a linear equation with two variables, the graph is a straight line.
Here,
A) From the given we can find the price per ticket
which is => y/x
=> 60/5
=>12
Therefore the price per ticket is $12
B)The equation can be used to represent the graph is
y= 12x
C) The theater were to sell 328 tickets they would make
=> 328*12=3936
Therefore the money would they make is $3936
D)The relationship proportional as we can see from the graph
Therefore , the price per ticket is $12,the equation used is y=12x, the theatre made $3936 by selling 328 ticket and the relationship is proportional.
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Which number corresponds to the number in scientific notation? 3. 21 × 104 kg = kg 2. 0 × 10-5 l = l
Number is the equivalent of the one written in scientific notation is
3. 21 × 104 kg = kg 2. 0 × 10-5 l = l
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It can also be referred to as standard form in the UK, standard index form, or scientific form.
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.
we have the number,
[tex]$0.000013$we know that$0.000013=\frac{13}{1000,000}=\frac{13}{10^6}=13 * 10^{-6}=1.3 * 10^{-5}$[/tex]
[tex]thereforethe answer is$1.3 * 10^{-5}$[/tex]
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It can also be referred to as standard form in the UK, standard index form, or scientific form.
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Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = 2x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.
x = ㏑₂8 in the logarithmic function.
What is a logarithmic function?A logarithmic function is the inverse of an exponential function.
Given function if f(x) = [tex]2^{x}[/tex],
When strength is equal to 8 pascals, f(x) = 8
Therefore, 8 = [tex]2^{x}[/tex]
Taking log on both sides:
ln8 = ln[tex]2^{x}[/tex]
ln8 = xln2
or x = ln8/ln2
x = ㏑₂8
Hence, the required function is x = ㏑₂8.
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find the slope of the line that contains the points (4,3)and(-6,27)
For which situations is it appropriate to use a sample? Select three options.
What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck?
What is the average number of rainbows each year in Honolulu?
How many pedestrians would use a walkway built over a busy road?
How many police cars are equipped with computers?
What is the most popular car color in the teachers’ parking lot?
Options B, C and D are the situations it is appropriate to use a sample.
What is a simple sample technique?Simple random sampling is a sampling technique in which each member of a population has an equal chance of being chosen, through the use of an unbiased selection method. The sample is chosen by a random method as every subject in the sample is assigned a number.
Sampling saves money by granting researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling because it lowers the cost associated with searching people and collecting data from them.
Therefore, options B, C and D are the situations it is appropriate to use a sample.
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Answer:
B,C,D
Step-by-step explanation:
solve this please......
The radius of a circle is increasing at a constant rate of 7 centimeters per minute. At the instant when the radius of the circle is 88 centimeters, what is the rate of change of the area? Round your answer to three decimal places.
The rate of change of the area is 3868.48 cm2/min
What in math is a rate?
A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents
A = A(r) (r)
r = r(t) (t)
A = A(r(t))
The chain rule can be used to resolve this kind of issue.
Rate of area change:
(dA/dr)(dr/dt) = dA/dt
A=r2 dA/dr = 2r
dr/dt [given] = 7 cm/min
(2r)(7 cm/min) = (dA/dt)
If r = 88 cm,
dA/dt = 2π (88 cm) (7 cm/min) ≅ 3868.48 cm2/min
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Please help!!! For what value of why must LMNP be a parallelogram?
Answer:
107 degrees
Step-by-step explanation:
The four angles of a parallelogram add up to 360 degrees. Any two adjacent angles of a parallelogram add up to 180 degrees. So y is equal to 180 degrees minus 73 degrees, which is equal to 107 degrees.
Why do you divide to find unit rate?
A number plus1/5 of the number can be expressed as
A number plus1/5 of the number can be expressed as n + 1/5n .
What is number ?A number is defined as it is an arithmetic value which is used to represent the given quantity or in making calculations. Hence, a number is a mathematical concept which is used to count, measure, and label it . Thus, we can say that numbers form the basis of mathematics.
n = number
A number in which we plus 1/5 of the number then it can be expressed as;
1 + 1/5 n
6/5 + n
n + 1/5 n
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Solve the nonlinear system of equations for real solutions. Y=x^2-3;6x-y=11
The required solution of the nonlinear equation is (4, 13) and (2, 1).
Given that,
To solve the nonlinear system of equations for real solutions. y =x²-3, 6x-y=11.
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,
y =x²-3 - - - - - [1]
6x-y=11
From equation 1,
6x -x² + 3 = 11
x² - 6x + 8 = 0
x = 4, and 2
Substitute this x's in equation 1
That gives for the above x's,
y = 13 and 1
Thus, The required solution of the nonlinear equation is (4, 13) and (2, 1).
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Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of
.4 miles
for 4.62 hours.
The exact distance Adam traveled was
v miles.
Rounding decimals to the nearest whole number, Adam traveled a distance of about
miles.
The exact distance Adam traveled was v miles is 334.488 miles.
What is distance ?
The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance travelled between them are not the same. Distance traveled is the total length of the path traveled between two positions. Travel distance is not a vector.
Exact = 334.488 miles
Rounded, 72 × 5 = 360
There were 3 decimal places in the factors, so after multiplying all the digits, put a decimal point 3 places from the right.
Your estimate from the rounded numbers is supposed to help confirm a reasonable answer.
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10x-22 3x+7 find x and the converse
The value of the x for the given condition will be 4.14.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that, ∠1 =10x-22, ∠2=3x+7
Since they are vertically opposite angles they are equal.
∠1 = ∠2
10x-22 = 3x+7
10x-3x=7+22
7x=29
x=29/7
x=4.14°
Thus, the value of the x for the given condition will be 4.14.
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The value of x is 15, for the given pair of parallel lines.
What is angle?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
Lines y and z are parallel,
And angles are (10x-22)° and 3x+7)°
The supplementary angle of (10x-22)° is 180° - (10x-22)°.
Since, lines y and z are parallel, therefore,
angle 180° - (10x-22)° and (3x+7)° will be equal.
180° - (10x-22)° = (3x+7)°
180° = 3x+7 + 10x - 22
180 = 13x - 15
195 = 13x
x = 15
The required value of x is 15.
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If point C divides segment AB with a ratio 2:3 , what are the coordinates of point C?
The coordinates of points C are (4,1).
The coordinates of the points D are (3, 2) respectively.
What is coordinates forumla?y = mx + c. Conversely,is the formula of coordinate that help to find satisfy to the equation y = mx + c is always lie on the line with the gradient m and y-intercept of c.
If the point C is divides AB in the ratio 2:3, then the coordinates of C are;
Xc=2(1)+3(6)/2+3
Xc=2+18/5
Xc=20/5 = 4
Yc=2(4)+3(-1)/2+3
Yc=8-3/5
Yc=5/5 = 1
The coordinates of points C are (4,1).
If the point D divides the AC in the ratio 3:2, then the coordinates of D are-
Xc= 3(1)+2(6)/3+2
Xc=3+12/5
Xc=15/5 = 3
Yc=3(4)+2(-1)/3+2
Yc=12-2/5
Yc=10/5=2
The coordinates of the point D are (3, 2).
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what is
2/4 + 2/4 - 4/7
Answer: 3/7
Step-by-step explanation:
1. We know that 2/4 + 2/4 is 1.
2. 1 can also be expressed as 7/7, because its easier to subtract 7/7 and 4/7 because they have the same denominator
3. 7/7-4/7=3/7
Answer:
3/7
Step-by-step explanation:
A music website charges x dollars for individual songs and y dollars for entire albums. Person A pays $25.92 to download 6 individual songs and 2 albums. Person B pays $33.93 to download 4 individual songs and 3 albums. Write a system of linear equations that represents this situation. How much does the website charge to download a song? an entire album???
Answer:
1/ y= -3x + 12.96
2/ $9.99 for an entire album & $0.99 for a song
Step-by-step explanation:
We know that the
The amount charged for downloading individual songs = x dollars
And the amount charged for downloading an entire album = y dollars
Let's write a function for person A first
6x + 2y = 25.92
Solve, and we will get
y = -3x + 12.96
Now to person B
4x + 3y = 33.93
Putting the value of y from the first equation in the second
4x + 3(12.96 - 3x) = 33.93
- 5x = - 4.95
x = $0.99
Then we take
y = 12.96 - 3x
= 12.96 - 2.97
= $9.99
fifteen is what percent of 5
Answer:
300%
Step-by-step explanation:
You want to know what percentage 15 is of 5.
PercentA ratio or fraction is converted to a percentage by multiplying by 100%.
[tex]\dfrac{15}{5}\times100\% = \boxed{300\%}[/tex]
15 is 300% of 5.
-x+6y= 5
2x - 12y = -10
Answer:
Step-by-step explanation:
-x+6y= 5 ----1
2x - 12y = -10 ----2
6y = x + 5
y = (x + 5)/6
2x -12(x + 5)/6 = -10
2x - 2x + 5 = -10
0 = -15
so, x and y have no value
Input (a): a number
Output (y): 8 less than 3 times x
The output will be if Input (x) = a number is y = 3x - 8, so option D is correct.
What is 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.
Given:
Input (x) = a number,
Output (y) = 8 less than 3 times x.
Assume a number x which is an input,
3 times of x = 3x,
8 less than 3 times of x = 3x - 8
Therefore, the output will be if Input (x) = a number is y = 3x - 8.
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Answer:
Hope this help :)
Step-by-step explanation:
In right triangle ABC, point D is on side BC, as shown. If BC= 5 x BD and the area of Triangle ABD is 8 in2, what is the area of Triangle ABC?
Answer: 40 in2
Step-by-step explanation:
Area of a triangle = 1/2 (base)(height)
Side AB is common to both triangles
BC = 5(BD)
Area ABD = 8, therefore Area ABC = 5(8) = 40
Match the equation to its description:
y=2x+3
2y=-3x-4
x--10
y-8
3y-2x+12
The equation of line is given below:
a) m = 2 , b = -3
b) m = -3/2 , b = -2
c) m = not defined , b = none
d) m = 0 , b = -8
e) m = [tex]\frac{2}{3}[/tex] , b = -4
What do you mean by equation of line?
A line equation is an algebraic representation of a set of points that together form a line in a coordinate system. A number of points that together form a line of axes, represented as a set of variables x,y, form an algebraic equation called the line equation.
Slope intercept form of the line is y = mx - b where m is the slope of the line and b is the x-intercept
a) y = 2x + 3
On comparing the equation with y = mx - b, we get m = 2 , b = -3
b) 2y = -3x -4
⇒ y = ( -3x -4 )/2
⇒ y = [tex]\frac{-3x}{2}[/tex] - 2
On comparing the equation with y = mx - b, we get m = -3/2 , b = -2
c) x = -10
⇒ x + 10 = 0
On comparing the equation with y = mx - b, we get m = not defined , b = none
d) y= 8
On comparing the equation with y = mx - b, we get m = 0 , b = -8
e) 3y = 2x + 12
⇒ y = (2x + 12)/3
⇒ y = [tex]\frac{2x}{3}[/tex] + 4
On comparing the equation with y = mx - b, we get m = [tex]\frac{2}{3}[/tex] , b = -4
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simplify the expression and find domain that will make it equivalent to previous expression.
[tex]\frac{1}{a^{2}+ab } +\frac{1}{ab+b^{2} }[/tex]
Step-by-step explanation:
The answer is
[tex] \frac{1}{ab} [/tex]
because
[tex] \frac{1}{a(a + b)} + \frac{1}{b(a + b)} = \frac{1}{ab} [/tex]
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4d +7e =68
-4d-6e = -72
Answer:
d=24
Step-by-step explanation:
What is the domain of this relation? (0, 2) (1,9) (-9, 6) (-4, 7)?
Answer: 5 trust me
Step-by-step explanation: trust me
Which inequality does the given graph represent?
A) y > x + 2
B) y ≤ −x − 2
C) y < x − 2
D) y ≥ x − 12
The given inequality in the graph is represented by the inequality y < x - 2. The correct option is C.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Given that the graph is attached to the question and shows one of the inequalities from the options.
When the inequalities are plotted on the desmos graph it is observed that the inequality which represents the graph is y < x − 2.
Therefore, the given inequality in the graph is represented by the inequality y < x - 2. The correct option is C.
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