Mr. Layton needs to buy some oil for his central heating. He can put up to 2500 litres of oil in his oil tank. There are already 750 litres of oil in the tank. Mr. Layton is going to fill the tank with oil. The price of oil is 58.4 p per litre. Mr. Layton gets 6% off the price of the oil. How much does Mr. Layton pay for the oil he needs to buy

Answer:

Option C

Step-by-step explanation:

f(1) = -8

f(2) = -5/2×-8 = -20

f(3) = -5/2×-20 = -125

.

.

.

So option C is the answer

Answer:

C.  a1 = -8

an = an-1 * 5/2  for n >1

Step-by-step explanation:

-8, -20, -50, –125, 625,...

We need to find the common ratio

Take the second  term and divide by the first term

-20/-8 = 5/2

Take the third term and divide by the second term

-50/-20 = 5/2

The common ratio is 5/2

A geometric sequence is

an = a1 * r^(n-1)

an = -8 *(5/2)^(n-1)

We can also write a recursive formula

a1 = -8

an = an-1 * 5/2  for n >1

Answer:

4

Step-by-step explanation:

Constant of proportionality refers to the slope of the line in this case, the slope of the line is (4-0)/(1-0)=4

Answer:

x > - 8

Step-by-step explanation:

4x - 8 > - 40

4x > - 40 + 8

4x > - 32

Divide 4 on both sides,

4x / 4 > - 32 / 4

x > - 8

Step-by-step explanation:

distance of (1,0) from the origin is,

√{(1-0)²+(0-0)²}

= √1

= 1

So the radius of the circle is 1,

now for the point (2/5,y) distance from origin should be the same since it's the radius

so,

√{(2/5-0)²+(y-0)²} = 1

or, √(4/25+y²)=1

or, 4/25+y²=1

or, y² = 1-4/25

or, y²=21/25

or, y=√(21/25)

or, y=√21/5

so, the simplest form of y is,

[tex] \frac{ \sqrt{21} }{5} [/tex]

The answer is the population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]

Given that in 2014, the population of people in Ohio = [tex]11.59[/tex] million

Also given that One-hundred years earlier of the year 1914, the population =  [tex]5.109[/tex] million people

One-hundred years earlier in the year 2014 = 2014 [tex]- 100[/tex] years

One-hundred years earlier in the year 2014 = Year 1914

The scientific notation of the year 2014 population is [tex]11.59*(10)^6[/tex]

The scientific notation of the year 1914 population is [tex]5.109*(10)^6[/tex]

How much did the population grow over the hundred-year span?

Growth of the population from 1914-2014 = [tex]11.59*(10)^6 - 5.109*(10)^6[/tex]

Growth of the population from 1914-2014 = [tex]6.481*(10)^6[/tex]

Conclusion: The population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]

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Answer:

[tex]{ \tt{y = 3x + 7}}[/tex]

Step-by-step explanation:

General equation of a line:

[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]

m is the slope, and c is the y-intercept:

m = 3, and c = 7

Answer:

Step-by-step explanation:

Distance between (2,1) and (3,3) = √5

parametric equations for circle of radius √5, centered at (2,1):

x = √5cosθ+2

y = √5sinθ+1

At (3,3), θ = arccos(1/√5) ≅ 63.4°

After 45° transformation:

θ' = 63.4° + 45° = 108.4°

x' = √5cos(108.4°)+2 = 1.29

y' = √sin(108.4°)+1 = 3.12

(3,3) transformed to (1.29,3.12)

Answer:

P /16

Step-by-step explanation:

Take the total amount, P and divide by the number of people sharing, 16

P /16

Answer:

5/9

Step-by-step explanation:

y2-y1/x2-x1 = 5/9

Answer:

[tex]7w^{5}x^{2}[/tex]

Step-by-step explanation:

We can start by looking at each variable and and constant separately. In the first one, the constant part is 14 and in the second its 7. We can notice that the GCF of these two is 7. Next we have the part with w. The first one is w^5 while the second is w^6. We can notice that we can factor w^5 out of both, so it is the GCF. We can notice that only the first one has a y, so we can ignore it since it is not in common with both expressions. Lastly, we have x: the first has x^2 and the second has x^2 as well. They are the same, so the GCF would just be x^2.

Now, we can multiply the results together to get the GCF of the whole expressions:

7 * w^5 * x^2 = [tex]7w^{5}x^{2}[/tex]

Answer:

11, 14, 17, 20, ...

Step-by-step explanation:

An arithmetic sequence is one where each term increases by the same number every time. This is called the common difference and is always added to the previous term to get the current term. The only sequence that follows this is the third once. Every term increases by 3; therefore, it is an arithmetic sequence.

Answer:

2cm

Step-by-step explanation:

area of parallelogram=b*h=18cm

5*4=20

length of corresponding heights=20-18

=2cm

the length of corresponding height of the parallelogram is : 2cm

A parallelogram can be defined as a simple quadrilateral that is it possesses four sides and two pairs of parallel sides.

A opposite sides of a parallelogram are equal and the opposite angles of a parallelogram are equal.

In conclusion, the length of corresponding height of the parallelogram is : 2cm

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Answer:

a=40+8pi, p=4pi+4(sqrt of 29)

Step-by-step explanation:

rsm geometry class 122?

Answer:

angleABC=isosceles triangle

angleB=(180-50)÷2=65

angle B=angleX(alternative angle)

angleB=65degree

Answer:

16

Step-by-step explanation:

an area is always calculated by multiplying 2 dimensions.

when changing the dimensions, then the change factors for EACH dimension go into the calculation too.

therefore, when both dimensions of an area are enlarged 4 times, then the area is enlarged 4×4 = 16 times.

this just propagates to the whole surface area of an object, as each individual area of the overall surface area is enlarged by the same factor. and so, the sum of all the individual areas (= altogether the surface area of the object) is also enlarged in total by the same factor.

just think

16×a + 16×b + 16×c ... = 16×(a+b+c+...)

and you understand why.

Answer:

Step-by-step explanation:

Focus: (6,4)

Directrix lies 6 units below the focus, so the parabola opens upwards and focal length p = 6/2 = 3.

The equation of the directrix is y = -2.

The vertex is halfway between focus and directrix, at (6,1).

Equation of the parabola:

y = (1/(4p))(x-6)²+1 = (1/12)(x-6)²+1

The equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]

Parabolas are used to represent a quadratic equation in the vertex form

The given parameters are:

Focus = (6,4)

Directrix (x) = 6 units below the focus,

Start by calculating the focal length (p)

[tex]p = \frac x2[/tex]

This gives

[tex]p = \frac 62[/tex]

[tex]p = 3[/tex]

Next, calculate the vertex as follows:

[tex](h,k) = (6,2/2)[/tex]

Simplify

[tex](h,k) = (6,1)[/tex]

The equation of the parabola is then calculated a:

[tex]y = \frac{1}{4p}(x - h)^2 + k[/tex]

So, we have:

[tex]y = \frac{1}{4*3}(x - 6)^2 + 1[/tex]

Simplify

[tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]

Hence, the equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]

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The domain exists on all real numbers i.e {x∈R}∈

The range exists all on real numbers except at y = 0

Domains are all input values of a function for which the function exists while ranges are all the output values for which the function exists.

Since the x-intercept of a function exists at where y = 0, this means that the point where a function does not have any x-intercepts are all other points on the graph except at y = 0.

The following statements are therefore true;

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Solution :

a). The test is a left tailed test.

b). The sample proportion is :

[tex]$\hat p = \frac{x}{n}$[/tex]

[tex]$\hat p = \frac{17}{258}$[/tex]

  = 0.065

Determining the Z statistics using the formula :

[tex]$Z=\frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]

[tex]$Z=\frac{0.065 - 0.11}{\sqrt{\frac{0.11(1-0.11)}{258}}}$[/tex]

   = -2.31

∴ Z statistics value is -2.31

c). Using the excel function, the P-value is :

P-value = Normsdist(-2.31)

             = 0.0104441

d). The null hypothesis is [tex]$H_0: P = 0.11$[/tex]

    The level of significance is 0.01

    We fail to reject the null hypothesis as the P value is less than or equal to the significant level.

Answer:

B

Step-by-step explanation:

B . x+3 and -2x2 - 4x +47-6

B . x+3 and -2x2 - 4x +47-6

The divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]

"It is a way of dividing one polynomial by another polynomial of first degree."

"The value that is divided by another value to get the result. "

"The value that divides another number either completely or with a remainder."

For given question,

We have been given a synthetic division problem.

- 3/ 2 4 -4 6

We need to represent the divisor and the dividend for the given synthetic division problem.

We know that, to perform synthetic division, here are the steps:

- The leading coefficient of the divisor should also be 1.

- Express the dividend in standard form.

- Write the leading coefficient in the dividend.

- Place the product of the number you brought down and the number in the division box in the preceding column.

- Write the result at the bottom of the row.

So, the divisor of the given synthetic division form would be,

x - (-3) = x + 3

And the dividend of the given synthetic division form would be,

There are four leading coefficient.

This means the dividend polynomial must be of degree 3.

From the leading coefficients 2 4 -4 6

[tex]2x^3+4x^2-4x+6[/tex]

Therefore, the divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]

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Answer:

14

Step-by-step explanation:

Answer:

isosceles acute

Step-by-step explanation:

sum of angles in a triangle = 180

to find third angle, subtract 72 & 36 from 180 and you get 72

72, 36, and 72 are all less than 90 so it will be an acute triangle

It will also be isosceles bc there are 2 angles of the same measure

Answer:

Step 1: Set the expression inside the square root greater than or equal to zero. Step 2: Solve the equation found in step 1. In this case, we divided by a negative number, so had to reverse the direction of the inequality symbol. Step 3: Write the answer using interval notation.

hi

it's equal to as X = 1X  

so 1X-0.3X = 0.7X

Answer:

yes

Step-by-step explanation:

as

x - 0.3x = 1×x - 0.3x = (1-0.3)x = 0.7x

Answer:

1/25=3/30

1250=

2501

2389

5552

Answer:

27/4 units^3

Step-by-step explanation:

V= area of the base × length

V= 3 3/8 × 2

= 27/4 units^3

Answer:

6 1/4 units ^3

Step-by-step explanation:

The volume is given by

V = Bh  where B is the area of the base and h is the height

V = 3 3/8 *2

Changing to improper fractions

V = (8*3+3)/8 *2

    = 27/8 *2

    = 27 * 2/8

     =27/4

Changing back to a mixed number

    = 6 1/4

Answer:

A graph is below.

Step-by-step explanation:

Step-by-step explanation:

6a. Both the x and y coordinates are negative so this means isn't must be in the Third Quadrant.

6b. The measure of this using the unt circle is

[tex] \cos(x) - \frac{1}{2} [/tex]

[tex] \sin(x) = - \frac{ \sqrt{3} }{2} [/tex]

In the unit circle, this occurs about

an angle of 240 degrees. We can find coterminal angles within the interval of 2 pi to -2 pi. Just subtract 260 from theta.( which is 240)

[tex]240 - 360 = - 120[/tex]

So the angles in the interval is

240, -120.

6c. pi/2 is the same as 90 degrees so this means that

[tex](240 + 90) = 330[/tex]

In the unit circle, we know that at 330 degrees,

[tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]

[tex] \sin(330) = \frac{1}{2} [/tex]

So the coordinates are

(sqr root of 3/2, 1/2).

6d. pi is the same as 180 degrees so this means that

[tex](240 - 180) = 60[/tex]

In the unit circle, we know that 60 degrees,

[tex] \cos(60) = \frac{1}{2} [/tex]

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

So the coordinates are

(1/2, sqr root of 3/2)

Answer:

6 pies

Step-by-step explanation:

For 60 - 89 cherries there are 10 pies

For 90 -119 cherries there are 4 pies

10 -4 = 6

There are 6 more pies in the 60 -89 cherries category than in the 90-119 category

Answer:

Surface area = the sum of the area of all six sides:

(11 · 10) + (11 · 10) + (11 · 8) + (11 · 8) + (8 · 10) + (8 · 10)

= 110 + 110 + 88 + 88 + 80 + 80

= 220 + 176 + 160

= 556 ft²

Answer:

556 ft^2

Step-by-step explanation:

The surface area of a rectangular prism is

SA = 2(lw+wh+lh) where h is the height l is the length and w is the width

SA = 2( 11*10+10*8+11*8)

      = 2(110+80+88)

      =2(278)

     =556 ft^2