Ray invests £9000 in a savings account.
The account pays 2.4% compound interest per year.
Work out the value of his investment after 4 years.
Give your answer to the nearest penny.

Answer:

t =5

g = 15

Step-by-step explanation:

t = tennis balls

g = golf balls

70 = 5t+3g

85 = 2t+5g

Multiply the first equation by -2

-2(70 = 5t+3g)

-140 = -10t -6g

Multiply the second equation by 5

5(85 = 2t+5g)

425 = 10t + 25g

Add these new equation together to eliminate t

-140 = -10t -6g

425 = 10t + 25g

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

285=0t+19g

Divide by 19

285/19 = g

15 = g

Now find t

85 = 2t+5g

85 = 2t +5(15)

85 = 2t + 75

10= 2t

t =5

Let the cost of a can of tennis balls be $x and that of a sleeve of golf balls be $y.

5x + 3y = 70

2x + 5y = 85

(5x + 3y) x 2 = 70 x 2

10x + 6y = 140

(2x + 5y) x 5 = 85 x 5

10x + 25y = 425

10x + 25y -10x - 6y = 425 - 140

19y = 285

y = 15

2x + 5y = 85

2x + 75 = 85

2x = 10

x = 5

Therefore the cost of a sleeve of golf balls is $15 and that of a can of tennis balls is $5.

Answer:

3 kg÷ $3.49=.86

Step-by-step explanation:

3 kg÷ $3.49=.86

5 kg÷ 4.99=1.00

Answer: D

Step-by-step explanation:

Answer:

the answer is "C"

Step-by-step explanation:

i just took the test

Answer:

growth

Step-by-step explanation:

Exponential equations are in the form

y = a * b^x

a is the initial value

b is the growth or decay

b>1 is growth b-1 rate  of growth

b <1 decay  1-b rate of decay

y = 4(5.6)^x

5.6 is greater than 1 so it is growth

Answer: 18.75 pints per month

Step-by-step explanation:

Answer:

A) P(10 on three rolls) = 1/1728 = 0.0005787

B) P(10 in two of three rolls) = 11/1728 = 0.0063657

Step-by-step explanation:

Each die has 6 possible values, so a pair of dice have a total of 6*6=36 outcomes.

To find a sum of 10, the cases are:

(4,6), (5,5) and (6,4).

So to have a sum of 10 we have 3 cases among the 36 possible, therefore the probability is:

P(10) = 3/36 = 1/12

A)

If we want the sum of 10 in each of the three rolls, the probability is:

P(10 on three rolls) = P(10)^3 = (1/12)^3 = 1/1728 = 0.0005787

B)

If the sum is 10 in two of three rolls, in one roll we need the probability of the sum not being 10:

P(not 10) = 1 - P(10) = 1 - (1/12) = 11/12

So we have:

P(10 in two of three rolls) = P(10)^2 * P(not 10) = (1/12)^2 * (11/12)

P(10 in two of three rolls) = 11/1728 = 0.0063657

Answer:

  1. [tex]\dfrac{2y^3}{3}[/tex]

  2. 9,765,625

Step-by-step explanation:

The relevant exponent laws are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

  a^-b = 1/a^b

__

1)

  [tex]\dfrac{3x^3y^5\cdot 8xy^4}{(6x^2y^3)^2}=\dfrac{(3\cdot 8)x^{(3+1)}y^{5+4}}{6^2x^4y^6}=\dfrac{2}{3}x^{4-4}y^{9-6}=\boxed{\dfrac{2y^3}{3}}[/tex]

__

2)

  [tex]5^3\div 5\cdot(5^2)^4=5^3\cdot 5^{-1}\cdot 5^8=5^{3-1+8}\\\\=5^{10}=\boxed{9\,765\,625}[/tex]  

Answer:

74 reais

Step-by-step explanation:

Em uma determinada loja, o lucro obtido com a venda de fones de ouvido x, em reais, pode ser representado pela expressão algébrica 7x-17. Quanto lucro esta loja terá se vender 13 fones de ouvido?

O lucro é representado como 7x - 17

onde x = número de fones de ouvido vendidos

Se 13 fones de ouvido foram vendidos, o lucro será:

(7 * 13) - 17

= 91 - 17

= 74 reais

Answer:

x intercepts are : (1,0)(4,0),(-3,0)

Step-by-step explanation:

x intercepts are : (1,0)(4,0),(-3,0)

plot only the x values

hope it helps

Answer:

30 persons

Step-by-step explanation:

Let's create a proportion using the following setup:

persons/rice=persons/rice

We know that 12 persons can eat 8 kilograms of fried rice.

12 persons/ 8 kg of rice= persons/rice

We also know that x (unknown) persons can eat 20 kilograms of fried rice.

12 persons/ 8 kg of rice= x persons/ 20 kg of rice

12/8=x/20

x is being divided by 20. The inverse of division is multiplication. Multiply both sides of the equation by 20.

20(12/8)=(x/20)20

20*12/8=x

20*1.5=x

30=x

30 persons can eat 20 kilograms of fried rice.

Answer:

30 people

Step-by-step explanation:

1) Set up a proportion, 8kg/12 = 20kg/x

2) Do cross multiplication to solve for x

3) x = 30 people

Answer:

k = 77/10

Step-by-step explanation:

The jar consist of blue, red and green marbles . The probability of each of them can be described as follows.

probability of blue marbles = 2/7

probability of red marbles = 3/k

probability of green marbles = 5/2k

The sum of the individual probability is equals to 1. Therefore,

2/7 + 3/k + 5/2k = 1

collect like terms

(6 + 5)/2k = 1 - 2/7

11/2k =(7 - 2) /7

11/2k = 5/7

cross multiply

10k = 77

divide both sides by 10

k = 77/10

Answer:

Option (1)

Step-by-step explanation:

Coordinates of the vertices are A(-2, 1), B(2, 7), C(8, 3) and D(4, -3)

Since ABCD is a square,

Perimeter of a square = 4 × (length of a side)

                                    = 4 × (AB)

Formula to calculate the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, distance between two points A(-2, 1) and B(2, 7) will be,

AB = [tex]\sqrt{(2+2)^2+(7-1)^2}[/tex]

AB = [tex]\sqrt{4^2+6^2}[/tex]

AB = [tex]\sqrt{52}[/tex]

AB = [tex]2\sqrt{13}[/tex]

Now area of  square ABCD = 4 × [tex]2\sqrt{13}[/tex]

                                              = [tex]8\sqrt{13}[/tex] unit

Therefore, option (1) will be the answer.

Answer:

A

Step-by-step explanation:

T is the dependent variable

a dependent variable means it depends on something so if a number changes it will change the end result for T.

T is dependent on P since if the weight on the elevator changes the total weight will change. That is what makes it dependent.

Answer:

They are both dependent variables.

Step-by-step explanation:

I did this on Khan Academy and it worked.

It would be irrational.

Reasoning:

A rational number is any number that can be expressed as a fraction of two integers provided that the denominator is not zero.

π is an irrational number because its approxiamation is [tex]\frac{22}{7}[/tex] is not the exact value of π. Additionally, we know that the quotient of irrational numbers can be rational or irrational. Here is the case where we have [tex]\frac{\pi }{2}[/tex], an irrational number divided by a rational number giving a quotient that is irrational.

Answer: irrational

Step-by-step explanation:

Apart from multiplying by 0 or dividing by pi, nothing can make pi rational. pi/2 is the same thing as 1/2pi, which is irrational, because it cannot be simplified into a repeating or terminating decimal

Answer:

0

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

In order to inscribe a circle in a triangle, the circle's center must be placed at the in center of the triangle, is true. the in center also is a point where the bisectors of the angles meet.

Answer:

Step-by-step explanation:

m=[tex](5,\frac{25}{4} )[/tex]

midpoint line between A and B

The midpoint is halfway between the two end points:

Its x value is halfway between the two x values

Its y value is halfway between the two y values

Answer:

8 cm

Step-by-step explanation:

When a right triangle is circumscribed in a circle, the diameter is the hypotenuse AC.

Therefore, the smallest diameter of the wrapper will be that of the circle whose diameter has endpoints of A and C.

From the diagram:

Therefore, Triangle AED is congruent to Triangle DFC and in fact AD=DC.

Given: AD =4 cm

Therefore, the smallest diameter

AC=AD+DC

=4+4

=8 cm

Answer:

Step-by-step explanation:

[tex]\dfrac{|AC|}{\sin B}=\dfrac{|AB|}{\sin C}\\\\\dfrac{9}{\sin38^o}=\dfrac{11}{\sin C}\\\\\dfrac{\sin38^o}9=\dfrac{\sin C}{11}\\\\\sin C=\frac{11}9\sin38^o =\frac{11}9\cdot0,6157=0,7525(2)\\\\\sin C\approx0,7525\quad\iff\quad |\angle C|\approx48^o48'\\\\|\angle A|=180^o-|\angle B|-|\angle C|\\\\|\angle A|=180^o-38^o-48^o48'\\\\|\angle A|=93^o12'\approx93^o[/tex]

Answer:

Step-by-step explanation:

To factorise this, we find the equality ( common factor).

Here this is 4.

So the factores version = 4(t+11)

Answer:

i believe it would be (10,4)

Step-by-step explanation:

i did this by finding the rise and run from point C and point M. Then, i repeated it in the opposite direction to get point B.

I did this on a graph by the way so I don't know if it really makes any sense since you are not dealing with a graph, but it should still be right.

Answer:

2.5

Step-by-step explanation:

The median is the middle value of the data set. If there is no exact middle value then it is the average of the 2 values either side of the middle.

0  ,  1  ,  2  ,  3  ,  4  ,  5

                 ↑ middle of data

Thus median = [tex]\frac{2+3}{2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5

Answer:

35 (the sequence is 1,2,18,19,35)

Step-by-step explanation:

So you have 5 numbers a, b, 18, c, d ordered from low to high.

18 is given because it is the median.

If the mean is 15, the sum must be 75 (because 75/5=15).

d must be as high as possible, so the others must be as low as possible, but positive and different.

So let's say a=1 and b=2, we can't get any lower than that.

c can be no lower than 19, otherwise we'd lose the median.

That leaves for d = 75 - 19-18-2-1 = 35.

nice one

The largest possible integer for the given case is 51.

In order to find the mean, first sum all the values of the data and count the number of data then divide them.

In order to find the median, first check whether the number of data is even or odd. For even number, the median is n/2 th element of the sample and for odd number the median is (n + 1)/2 th element.

Given that,

The mean of five integers is 15.

And, the median is 18.

Since the median of n number of data in a sample when n is odd is given as,

Median = ((n+1)/2) th element.

For n = 5, the median is 3rd element.

Which implies the 3rd element is 18.

Now, sum of the five integers is given by 5 × Mean which is,

5 × 15

= 75.

Suppose the five integers are x₁, x₂, x₃, x₄ and x₅ respectively.

Then as per the question,

x ₁+ x₂ + x₃+ x₄+ x₅ = 75

And, x₃ = 18

Then,  x ₁+ x₂ + 18 + x₄+ x₅ = 75

=>  x ₁+ x₂ + x₄+ x₅ = 75 - 18

=>   x ₁+ x₂ + x₄+ x₅ = 57    

In order two find the largest possible integer, suppose the remaining three of them are 1, 2 and 3.

The equation can now be written as,

1 + 2 + 3 + x₄ = 57

=> x₄ = 51

Hence, the maximum possible value of the largest integer is 51.

To know more about Mean click on,

https://brainly.com/question/22871228

#SPJ2

Answer:

the answer would be a

Step-by-step explanation:

Answer:

6√2

Step-by-step explanation:

Gm = √a×b

= √4×18

= √72

= √36×2

= √6²×2

= 6√2

Answer:

2nd no is corret

Step-by-step explanation:

as altitude is defined as a st. line meeting its base forming 90degree angle.

Answer:

I think the second answer, JH is an altitude of GJI, is the correct answer.

Step-by-step explanation:

Having JH be an altitude of GJI means that it makes a 90 degree angle. And to prove that it's a 90 degree angle we look at where it has the little squares. The squares represent 90 degrees.

Hope this helps!

Answer: C

Step-by-step explanation:

Simplify(Subtract 2)

x > 0

Greater than is represented by a open circle with an arrow pointing right.  Because x is greater than 0, the point must be on 0.

Hope it helps <3

Answer:

C

Step-by-step explanation:

The inequality is x+2 > 2

x > 0 means that x is positive

so the graph must start from 0 and then should grow towrd the positive value

since we have x > 0 then 0 should be excluded

the graph that fits our solution is c where 0 is excluded

Answer:  The answers are in the steps

Step-by-step explanation:

x         y        value of y/x

-3        -3            1

1           1             1

3           3             1

Answer: x = -3/4 can not be a rational zero of the polynomial.

Step-by-step explanation:

We have the polynomial:

6x^5 + ax^3 -bx -12 = 0.

The theorem says that:

If P(x) is a polynomial with integer coefficients, and p/q is a zero of P(x) then p is a factor of the constant term (in this case the constant term is -12) and q is a factor of the leading coefficient (in this case the leading coefficient is 6.).

The factors of -12  (different than itself) are (independent of the sign).

1, 2, 3, 4 and 6.

So p can be: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6.

The factors of 6 are:

1, 2 and 3, so q can be 1, -1, 2, -2, 3, -3.

Then the option that can not be a zero of the polynomial is

x = -3/4

because the number in the denominator must be a factor of the leading coefficient, and 4 is not a factor of six.