Solve for y.


y =

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€9.31

total = price + tax

... tax = 0.19×price . . . . . . . meaning of 19% VAT

... total = price + 0.19×price = 1.19×price

Dividing by 1.19, we can find the price in terms of the total.

... total/1.19 = price

And we can use this to find the tax

... tax = 0.19×price = 0.19×(total/1.19) . . . . . substitute for price

... tax = 0.19/1.19 × total = 19/119 × total . . . . . . simplify

... tax = 19/119 × 58.31  . . . . . . .  put in total amount

... tax = 9.31 . . . . euros

Answer:

Hence third choice RQ, RP, PQ is correct.

Step-by-step explanation:

We know that if A, B, C are the angles of the triangle and if ∠A > ∠B

a>b   {Where “a” is side created by angle A and “b” is side created by angle B }.

We will use same property to decide which side is bigger.

In triangle PRQ,

∠P = 30 degree

∠R = 85 degree

then ∠P + ∠R + ∠Q = 180 {since sum of all three angle of triangle is 180 degree}

30 + 85 + ∠Q = 180

115 + ∠Q = 180

∠Q = 180 - 115

∠Q = 65

Now we know measure of all angles so we can do comparison using above property.

Smallest angle is ∠P so side RQ will be smallest.

Largest angle is ∠R so side PQ will be largest.

Hence we get RQ < RP < PQ.

Hence third choice RQ, RP, PQ is correct.

Answer:

the footballer's average pay would be $4 million/annum.

A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

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

[tex]a_1=3\\\\a_n=\dfrac{1}{2}a_{n-1}\to \boxed{r=\dfrac{1}{2}}[/tex]

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

Exciplit rule:

[tex]a_n=a_1r^{n-1}[/tex]

Substitute:

[tex]a_n=3\left(\dfrac{1}{2}\right)^{n-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot\left(\dfrac{1}{2}\right)^{-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot2\\\\\boxed{a_n=6\cdot\left(\dfrac{1}{2}\right)^n}[/tex]

Answer:

The answer is: a_n = 6*(1/2)^n

Answer:

41

Step-by-step explanation:

We know that complex numbers are a combination of real and imaginary numbers

Real part is x and imaginary part y is multiplied by i, square root of -1

Modulus of x+iy = [tex]\sqrt{x^2+y^2}[/tex]

Here instead of x and y are given 9 and 40

i.e. 9+40i

Hence to find modulus we square the coefficients add them and then find square root

|9+49i| =[tex]\sqrt{9^2+40^2} =\sqrt{1681}[/tex]

By long division method we find that

|9+40i| =41

Answer:  Modulus of |9+40i| =41

Step-by-step explanation:

Since we have given that

[tex]z=\mid9+40i\mid[/tex]

Here,

[tex]z=a+bi\\\\where,\\\\a=\text{real number}=9\\\\b=\text{imaginary number}=40[/tex]

We need to find the modulus of z:

[tex]\mid z\mid=\sqrt{a^2+b^2}[/tex]

[tex]\mid z\mid=\sqrt{9^2+40^2}\\\\\mid z\mid=\sqrt{81+1600}\\\\\mid z\mid=\sqrt{1681}\\\\\mid z\mid=41[/tex]

Hence, Modulus of |9+40i| =41

Answer:

Short Answer: B

Step-by-step explanation:

You want to solve for x in

Answer:

v = 15 miles / hour

Step-by-step explanation:

Given:

Distance covered by biker = s=45 miles

time taken by him = t=180 minutes

TO Find:

speed in miles per hour = v = ?

Solution:

As it is given that the distance covered is 45 miles

and time taken by him is 180 minutes

as one hour have 60 minutes

so time taken by rider = t = 180 /60

                                          = 3 hours

this step is done because we have to find speed in miles per hour

Now

The formula for finding the distance is

distance = speed * time

or

s = v * t

we have to find v

so dividing both sides by t

[tex]\frac{s}{t} = \frac{v*t}{t}[/tex]

it becomes

[tex]v = \frac{s}{t}[/tex]

Putting the values

[tex]v = \frac{45}{3}[/tex]

solving it gives

v = 15 miles / hour

which is the required speed

in the given options it is not available

The speed is 15 miles per hour, not matching any of the provided answer choices.

The question asks for the speed of the biker in miles per hour when given the distance rode over a certain amount of time. To find the speed, we can use the formula: Speed = Distance / Time.

In this case, the biker rode 45 miles in 180 minutes. Since there are 60 minutes in an hour, we first convert 180 minutes into hours by dividing by 60: 180 / 60 = 3 hours.

Next, we calculate the speed: Speed = 45 miles \/ 3 hours = 15 miles per hour. But since this isn't one of the options provided, it seems there has been a typo in the answer choices. The correct answer, which should be 15 mph, is missing in the options.

The first part of the proportion would be the known values of 32 people to 128 ounces.

The second part of the proportion is X ( the number of people) for 704 ounces.

This is written as 32/128 = X/704

To solve for X Cross multiply:

32 * 704 = 128x

Simplify:

22528 = 128x

Solve for X by dividing both sides by 128:

x = 22528 / 128

x = 176 people

Answer:

0.0625

Step-by-step explanation:

If the function f(x) varies inversely with x, then this function is of the form

[tex]f(x)=\dfrac{a}{x},[/tex]

where a is unknown number.

Since  f(x)=0.5 when x =0.3, then

[tex]0.5=\dfrac{a}{0.3},\\ \\a=0.5\cdot 0.3=0.15.[/tex]

Therefore, the function is

[tex]f(x)=\dfrac{0.15}{x},[/tex]

Now when x=2.4,

[tex]f(2.4)=\dfrac{0.15}{2.4}=\dfrac{15}{240}=\dfrac{1}{16}=0.0625.[/tex]

Answer: 10 cm

Step-by-step explanation:

Given: The volume of a solid piece of an aluminium cylindrical rod =[tex]200\cm^3[/tex]

The base area of cylinder = [tex]20\ cm^2[tex]

We know that the volume of cylinder is given by :-

[tex]\text{Volume]=\text{base area}\times \text{height}\\\\\Rightarrow200\=20\\times h\\\\\Rightarrow\ h=\frac{200}{20}=10[/tex]

Hence, the length of the piece of aluminium rod = 10 cm

To find the length of the aluminum rod with a volume of 200 cm³ and a base area of 20 cm², divide the volume by the base area. The length is 10 cm.

If a solid piece of an aluminum cylindrical rod has a volume of 200 cm3 and a base area of 20 cm2, to find the length of the aluminum rod, we can use the formula for the volume of a cylinder, which is Volume = Base Area  imes Height (or length in this case, since it's a rod). Given the volume (V) is 200 cm³ and base area (A) is 20 cm², the length (L) can be calculated as L = V / A.

When you divide 200 cm³ by 20 cm², the result is:

L = 200 cm³ / 20 cm² = 10 cm.

Therefore, the length of the aluminum rod is 10 cm.

Answer:

The author must sell 3000 books.

Step-by-step explanation:

The total amount earned  = advance + books sold * money per book

We know they want to make 7000

The advance is 2500

They earn 1.50 for each book sold

b= number of books sold

Substituting in

7000= 2500 + 1.5b

Subtract 2500 from each side

7000-2500 = 2500-2500 + 1.5 b

4500 = 1.5 b

Divide each side by 1.5

4500/1.5 = 1.5b/1.5

3000 = b

Answer: Option A is correct

(-5,3) U (3,6]

Step-by-step explanation:

Domain of a function is the complete set of values that the independent variable can assume.

In the given graphed function we can see that the minimum value of independent variable (x) is -5 and the maximum value is 6, wherein the values -5 and 3 do not belongs to x.

This set of values is represented as

(-5,3) U (3,6]

Hope it helps.

Thank you.

The domain of the graphed function is (-5,3) U (3,6].

The correct option is A.

The domain of a function is the entire range of values that the independent variable can take.

In the given graphed function, we observe that the lowest value of the independent variable (x) is -5, and the highest value is 6.

However, it is the values -5 and 3 are not included in the domain.

So, the set of values is represented as (-5,3) U (3,6].

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Answer:

if you still need the answer, its C.

Step-by-step explanation:

Answer: 28 and 18

Step-by-step explanation:

I used the guess and test strategy to find that:

28 - 10 = 18

28 + 18 = 46

To find the two numbers, we need to solve a system of equations. By assigning variables to the numbers and setting up equations based on the given information, we can use the method of substitution to find the values of x and y. The two numbers are 28 and 18.

To solve this problem, let's assign variables to the numbers. Let's say the two numbers are x and y. We are given two pieces of information: the sum of the two numbers is 46, so we can write the equation x + y = 46, and the difference between the two numbers is 10, so we can write the equation x - y = 10.

To solve this system of equations, we can use the method of substitution. Rearrange one of the equations to solve for one variable in terms of the other. For example, we can rearrange the first equation to get x = 46 - y. Substitute this expression for x in the second equation:

(46 - y) - y = 10.

Simplify the equation:

46 - 2y = 10. Subtract 46 from both sides:

-2y = -36. Divide both sides by -2 to solve for y:

y = 18. Substitute this value of y back into one of the equations to solve for x:

x + 18 = 46. Subtract 18 from both sides:

x = 28.

So the two numbers are 28 and 18.

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Answer:

f(x) = 2x

Step-by-step explanation:

Remark

What I'm about to do is probably not the best way to do this question, but it is right. The plan is to take out a common factor on the right of f(x - 2) and then derive f(x) from that.

Solution

Check

Final answer:

To find f(x), replace x - 2 with y to get f(y) = 2(y + 2) - 4, simplify to f(y) = 2y, then revert y back to x to find f(x) = 2x.

Explanation:

To find the function f(x) when you know that f(x - 2) = 2x - 4, you need to replace x - 2 with y so that x = y + 2. Therefore, f(y) = f(x - 2) = 2x - 4 becomes f(y) = 2(y + 2) - 4.

Simplifying this, we get:
f(y) = 2y + 4 - 4
f(y) = 2y.

Now, to revert back to the original function, replace y with x to get f(x) = 2x. This is the function we were looking to find.

What are the answer choices?

To find out what percent of the calories in a candy bar comes from sugar, divide the calories from sugar (132) by the total calories (220) and multiply by 100, resulting in 60% of the calories being from sugar.

To calculate what percent of the calories in the candy bar are from sugar, we can use the formula for percentage: (part / whole) x100. In this case, the part is the number of calories from sugar, and the whole is the total number of calories in the candy bar.
First, let's identify the given values:

Now, let's calculate the percentage:

Calculating this, we find:

Therefore, 60% of the calories in the candy bar are from sugar.

Answer:

B

Step-by-step explanation:

The interior of the 4 triangles in the rhombus are right angle triangles. In addition AC is bisected by BD and BD is bisected by AC. Those form the sides of the right angle triangle.

So the sides of the right angle are

The area of one right angle is

The answer is B

Answer:

B. 125.5 square units

Step-by-step explanation:

The area of a rhombus is half the product of the diagonals.

If the diagonals have lengths a and b, then the are is:

area = ab/2

area = (17)(15)/2

area = 255/2

area = 127.5

Answer: B. 125.5 square units

Answer:

the square root of 2 times the negative square root of 2 would be -2, which is a rational number.

Answer: -2

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

Draw a vertical line through 4 on the x axis. This vertical line crosses the parabola at some point (which we'll call point A). Draw a horizontal line from point A to the y axis and note how it lands on y = 12. Therefore the point (4,12) is on this parabola.

Repeat the same steps as before to find that (8,4) is also on the parabola

We need to find the slope of the line through (4,12) and (8,4)

m = (y2 - y1)/(x2 - x1)

m = (4-12)/(8 - 4)

m = -8/4

m = -2

The slope of this line is -2 meaning that the average rate of change from x = 4 to x = 8 is -2.

The line goes down 2 units each time you move to the right 1 unit.

Answer:

The numbers are 8 and 13

Step-by-step explanation:

In order to find this, we set the smaller number as x. Then we can set the larger one as x + 5, since it is 5 more than the smaller.

Given these two, we can then set them equal to 3x - 3, since the answer is three less than three times the larger.

x + x + 5 = 3x - 3

2x + 5 = 3x - 3

5 = x - 3

8 = x

Now to find the larger number, put into the larger number equation.

x + 5

(8) + 5

13

The numbers are 8 and 13.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''One number is five more than another and their sum Is there less than three times the smaller''.

Now,

Let the smaller number = x

Then, The another number = x + 5

Write the expression as;

x + x + 5 = 3x - 3

2x + 5 = 3x - 3

2x - 3x = - 3 - 5

- x = - 8

x = 8

And, The another number = x + 5

                                        = 8 + 5

                                        = 13

Thus, The numbers are 8 and 13.

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Answer:

143 miles

Step-by-step explanation:

Let the distance Karly biked be x

Then Dory biked 11x

So x+11x=156

x=156/12=13

So Dory biked 11 ⋅ 13= 143 miles

Is this correct?

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

A: 4, 12, 15

4 + 12 = 16 > 15    CORRECT :)

B: 4, 13, 15

4 + 13 = 17 > 15   CORRECT :)

C: 4, 4, 15

4 + 4 = 8 < 15   INCORRECT :(

D: 4, 15, 15

4 + 15 = 19 > 15  CORRECT :)

E: 4, 11, 15

4 + 11 = 15   INCORRECT :(

F: 4, 15, 19

4 + 15 = 19  INCORRECT :(

To find the total cost for the family to attend the baseball game, we substitute the given ticket prices into the expression 2a + 3c, where a is the cost of an adult ticket and c is the cost of a child ticket, resulting in a total cost of $70.

The student is asking about the cost for a family to attend a baseball game with the given prices for adult and child tickets.

Given the cost of an adult ticket as $17 and a child ticket as $12, we use the expression provided (2a + 3c) to calculate the total cost for the family.

Substituting the given values into the expression, we get 2(17) + 3(12), which equals 34 + 36.

Summing up these two products gives us a total of $70.

Therefore, it will cost the family $70 to attend the baseball game.

Answer:

D) y = -1/3 x+6

Step-by-step explanation:

If we want to find a line parallel to 3x+9y=7, the slopes will have to be the same because parallel lines have the same slope.  Knowing y= mx+b we need to find the slope of the old line.

3x+9y=7

Subtract 3x from each side

3x-3x +9y = -3x+7

9y = -3x+7

Divide each side by 9

9y/9 = -3x/9 + 7/9

y = -1/3 x + 7/9

We know the slope of the  old line is -1/3, so the slope of the parallel line is -1/3.

If we know the slope of the line and a point, we can use the point slope form of a line

y-y1 = m(x-x1)

y-4 = -1/3(x-6)

Distribute the -1/3

y-4 = -1/3 x -1/3*-6

y-4 = -1/3x +2

Add 4 to each side

y-4+4 = -1/3x +2+4

y = -1/3x+6

1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Wooden slates required to make 4 fence panels = 32

To find wooden required to make 1 panel, use ratio property,

4 fence panels = 32 wooden slates

1 fence panel = 8 wooden slates

Also, to find wooden required to make 8 panels, use ratio property,

4 fence panels = 32 wooden slates

8 fence panels = 64 wooden slates

1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.

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Final answer:

Gerard needs 64 slats to make 8 panels, as it is a proportional relationship.

Explanation:

To find out how many slats are needed for one panel, we simply divide the total number of slats by the number of panels. Since a builder uses 32 slats to make 4 panels, for one panel, Fatima would need:

Number of slats for one panel = Total number of slats \/ Number of panels

Number of slats for one panel = 32 / 4 = 8 slats

For Gerard's question, if 1 panel requires 8 slats, then to make 8 panels he would need:

Number of slats for 8 panels = Slats per panel x Number of panels

Number of slats for 8 panels = 8 x 8 = 64 slats

It's a straightforward example of a proportional relationship in mathematics, where the number of slats scales directly with the number of fence panels.

Answer:

Option 3rd is correct

Step-by-step explanation:

Kevin takes a survey of the ages of people in the library at 10a.m and at 6p.m on a Wednesday.

He should talk at library to new drivers on the dangers of texting and driving at the time when there are more people with the car.

So, that he can convey messages to more people in less time.

Therefore, Option 3rd is correct that is  At 10 a.m., because there are more people with cars at the library at that time

Answer:

1 is correct.

Step-by-step explanation:

I had the same question and I tried the other answer and so it was wrong. And in the correction I had, it was the first one.

This problem deals with dependent events in probability. The probability of picking two good apples in a row from a bag containing 7 good and 3 bad apples, without replacement, is calculated as (7/10)*(6/9), which equals 0.467.

The subject of this question is Mathematics, specifically probability. When Nick picks two apples without replacement, we are dealing with dependent events, since the outcome of the second event depends on the outcome of the first event. Dependent events require a different calculation for the probability.

The total apples in the bag initially are 7 good + 3 bad = 10 apples. The probability of picking a good apple on the first draw is 7/10 or 0.7. When one apple is taken out, there are now 9 apples left in the bag. If the first apple was good, the probability of picking the second good apple is now 6/9 or 2/3.

Since these are dependent events, the total probability of picking two good apples in a row would be (7/10) * (6/9) which reduces to 14/30 or approximately 0.467.

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Answer: 59/120 (choice D)

Add up the values in the "math" column and the "11th" row to find the total number of people who are either in 11th grade, in math, or in both.

So,

(12+10+8+7) + (14+5+3) = 59

represents the number of people who are in either category. This is out of 120 (given). This is where 59/120 comes from.