Albert has £500 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 5 years. How much interest will he have earned after 5 years?

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

There are 36 total possible combinations with 2 number cubes. Only 3 of these combinations add up to 10 (4 and 6, 5 and 5, 6 and 4).

[tex]\frac{3}{36} =\frac{1}{12}[/tex], so the probability is [tex]\frac{1}{12}[/tex].

Answer:

1/12

Step-by-step explanation:

Answer:

(6, - 5)

Step-by-step explanation:

The equation of circle in centre radius form is:

[tex](x - h)^{2} + (y - k)^{2} = {r}^{2} \\ plugging \: h = 3 \: \: k = - 9 \: and \: r = 5 \\ (x - 3)^{2} + \{y - ( - 9) \}^{2} = {5}^{2} \\ (x - 3)^{2} + (y + 9)^{2} = 25 \\ let \: us \: plug \: x = 6 \: and \: y = - 5 \: in \: lhs \\ lhs = (6 - 3) ^{2} + ( - 5 + 9) ^{2} \\ = (3) ^{2} + ( 4) ^{2} \\ = 9 + 16 \\ = 25 \\ = rhs \\ hence \: (6, \: \: - 5) \: is \: on \: the \: circle.[/tex]

Answer:

Answer is option b) (6,-5)

Step-by-step explanation:

[tex]given \: that \: \\ centr e\: of \: circle \: is(3, - 9) \\ and \: radius \: is \: 5 \\ when \: \: we \: calculate \: the \: distance \: between \: (3, - 9) \: and \: (6, - 5) \\ distance \: = \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ here \: x1 = 3 \: \: y1 = - 9 \\ x2 = 6 \: \: \: \: y2 = - 5 \\ on \: substituting \: the \: values \\ = \sqrt{(3 - 6) + {( - 9 + 5)}^{2} }^{2 } \\ = \sqrt{ { - 3}^{2} + { - 4}^{2} } \\ = \\ = \sqrt{9 + 16} \\ = \sqrt{25} \\ = 5[/tex]

(6 -5) is a point on the circle.

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Answer:

253.5

Step-by-step explanation:

basically i had the same question so yeah! and im a pro at math

Answer:

Yup, It's 253.5 :)

Step-by-step explanation:

I checked it. It was right ^^

The hourly growth rate is 2%

An exponential growth is in the form:

y = abˣ;

where y, x are variables, a is the initial value of y and b > 1

Let y represent the number of bacteria after x hours.

There was initially 2200 bacteria, hence a = 2200. The equation becomes:

[tex]y=2200(b)^x\\\\\\After\ 1.5\ hours,y=2300:\\\\\\2300=2200(b)^{1.5}\\\\\\b^{1.5}=1.045\\\\1.5lnb=ln(1.045)\\\\ln(b)=0.0296\\\\b=1.02[/tex]

Therefore the hourly growth rate is 1.02 - 1 = 0.02 = 2%

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Answer:

(10, -20) because y=_5x + 30x=10 and there are only 2 answers with 10 in the beginning so also 20 is greater than 40.

Step-by-step explanation:

B

Answer:

Step-by-step explanation:

Answer:

x^2+x-20

Step-by-step explanation:

x = 4

x - 4 = 0

x = -5

x + 5 = -5

(x + 5)(x - 4)

x^2+x-20

The quadratic function with zeros 4 and -5 is f(x) = x² + x - 20.

To write a quadratic function f(x) whose zeros are 4 and -5, we can use the fact that the zeros of a quadratic function correspond to the values of x that make the function equal to zero.

A quadratic function can be represented in the form:

f(x) = a(x - r1)(x - r2)

where r1 and r2 are the zeros of the function.

Given zeros are 4 and -5. Substituting these into the formula, we get:

f(x) = a(x - 4)(x + 5)

Expanding this, we obtain:

f(x) = a(x² + x - 20)

To simplify, we can choose a value for a, usually 1 for simplicity:

f(x) = x² + x - 20

This is the quadratic function with zeros at 4 and -5.

Answer:

$8.48

Step-by-step explanation:

Total of Items:

Add up the prices of all the items he bought

soup+oranges+newspaper

1.99+3.49+2.50=7.98

$7.98

Sales Tax:

Multiply his total by the sales tax rate

7.98*6.25%

Convert 6.25% to a decimal

6.25/100=0.0625

7.98*0.0625=0.49875

0.49875

Total With Tax

Add the tax to his total without tax

7.98+0.49875=8.47875

Round to the nearest cent, or hundreth

$8.48

[tex]y=4-x^2\\x-y=2 \\ \\ y = 4 - {x}^{2} \\ x = 2 + y \\ \\ y = 4 - {(2 + y)}^{2} \\ {y}^{2} + 5y = 0 \\ y(y + 5) = 0 \\ y = 0 \\ y = - 5[/tex]

[tex]x = 2 + 0 = 2[/tex]

[tex]x = 2 + ( - 5) = -3[/tex]

Answer:

It lies between three and four.

Step-by-step explanation:

Answer:

First, find the square root of 12

√12=3.46410161514

Whole numbers are: 0,1,2,3,4,5...

So, the 2 whole numbers √12 lies between are 3 and 4

Final answer:

To calculate Payne's annual contribution, multiply the annual premium by 20% and subtract that amount from the annual premium.

Explanation:

To calculate Payne's annual contribution, we need to determine 20% of the total cost of the health insurance premium and then subtract that amount from the annual premium.

Step 1: Find 20% of $6,486. Multiply $6,486 by 0.2 to get $1,297.20.

Step 2: Subtract the 20% contribution from the annual premium. $6,486 - $1,297.20 = $5,188.80.

Payne's annual contribution is $5,188.80.

Step-by-step explanation:

A factor is the number in a multiplication problem.

Answer:

if I'm correct it's 22 don't quote me on it

Answer:

Surface area = 942.688

Answer:

x = 3y

Step-by-step explanation:

In this question, we are asked to model an equation that clearly mimics what we have in the question using certain type of variables.

Now initially, we are told that we have 2 bunnies having 6 babies. what does this tell us?

Looking at this, we can see that the number of babies is exactly 3 times the number of bunnies. More like saying 3 times the number of bunnies equal the number of babies.

so leveraging in this finding and applying the variable, we can say each of the 2 bunnies has 3 babies per month.

Mathematically, this is same as x bunnies = 3y babies per month

Answer:

option b and c are true ...

Answer:

4.38

Step-by-step explanation:

Answer:

Its 4.38

Step-by-step explanation:

Its because 4.377¨s hundredth place is the 7 near the 7 so rounding a digit with a number of 5 or greater would lead to changing the hunderedth place into a bigger number.

Answer:

=-80-5√5

this is the answer

hope this helps

Answer:

4

Step-by-step explanation:

13497/1250

12500 + 997/1250

12500 + 0.7976

12500.7976

Answer:

4 places of decimals.

Step-by-step explanation:

13497.1250 = 10.7976.

Answer:

45%

Step-by-step explanation:

Diego's time is 20 and a whole is 100% so multiply 9 by 5 because 20 x 5 is 100 9x5=45. This means Noah's time is 45% of Diego's time

Answer:

45% or 45 percent

Step-by-step explanation:

Yes oof

Answer:

8.2 ft

.Step-by-step explanation:

Sketch this situation.  Label the 55° angle.  The adjacent side is the distance from the stake to the bottom center of the tree.  The opposite side is the distance from the ground to the connection point of the wire on the tree.  The wire length represents the hypotenuse of this triangle.  We want to find the length of the side opposite the 55° angle.  Thus, we write

sin 55° = (opposite side)/(hypotenuse), or

(hypotenuse)(sin 55°) = (10 ft)(0.819) = 8.2 ft

Using trigonometry and the sine function, we can calculate the height of the tree as 10 ft * sin(55), which equals approximately 8.19 ft.

This problem can be solved using trigonometry, specifically the sine function. In a right triangle, the sine of an angle is defined as the length of the opposite side divided by the length of the hypotenuse. In this case, the tree forms the opposite side of our triangle, the support wire forms the hypotenuse and the angle of elevation is 55 degrees.

To express this mathematically, we can write: sin(55) = height / 10 ft. Solving this equation for height gives us: height = 10 ft * sin(55). Using a calculator, we find that sin(55) is approximately 0.81915, so the height is around 8.19 ft. Therefore, the connection point of the wire to the tree is at approximately 8.19 ft high.

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Answer: Sammi's work:

107d=1,773.4

1773.4 divided by 107 = 16.2

Step-by-step explanation:

The value of d for the given expression will be d = 16.2.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is  107d = 1,733.4. The value of d will be calculated as:-

107d=1,773.4

To calculate the value of d the number 1773.4 is divided by 107.

107d=1,773.4

d = 1,773.4 / 107

d = 16.2

Hence, the value of d will be 16.2.

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The value of the number 'n' that has the digit 0 five times and the digit 9 six times will be 59.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Range of the number             Times of '0'             Time of '9'

             1 - 9                                   0                               1

           10 - 19                                  1                               1

          20 - 29                                 1                               1

          30 - 39                                 1                               1

          40 - 49                                 1                               1

          50 - 59                                 1                               1

           Total                                   5                               6

Then the value of the number 'n' that has the digit 0 five times and the digit 9 six times will be 59.

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Answer:

The answer to your question is the letter A.    (4, -8)   and  (1, -5)

Step-by-step explanation:

Data

                x + y = -4              Equation l

                y = x² - 6x             Equation ll

Process

1.- Substitute equation ll in equation l

              x + x² - 6x = -4

2.- Solve the quadratic equation

                  x² - 5x + 4 = 0

Factor        (x - 4)(x - 1) = 0

-Solve for x

                   x₁ - 4 = 0         x₂ - 1 = 0

                   x₁ = 4               x ₂ = 1

3.- Substitute x₁ and x₂ in equation l

         4 + y₁ = -4                     1 + y₂ = -4

              y₁ = -4 - 4                      y₂ = -4 - 1

              y₁ = -8                           y₂ = -5

4.- Solutions

             (4, -8)   and  (1, -5)

Answer:

$80 + $60h =C

Step-by-step explanation:

$80 is the amount charged to come out

$60 times h (h is the number of hours)

add them together for total cost

The equation C = 80 + 60h describes Chris's total cost.

Independent variable: Hours of work, represented by h.

Dependent variable: Total cost, represented by C.

Equation: C = 80 + 60h

Y-intercept: $80, as it is the initial charge when no hours are worked.

Slope: $60 per hour, indicating the rate at which the cost increases per hour of work.

Answer:

Any dimensions can make a triangle, however

this does not make a right angled triangle.

Step-by-step explanation:

Determine the length of the hypotenuse of a right angle triangle with side lengths 5ft and 9ft by using the formula:

[tex]a^2+b^2=c^2\\[/tex]

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

[tex]c=10.29[/tex]

This is not equal to 14ft.

Answer: No, those measurements cannot make a triangle

Why not? Because of the fact that the first two sides (5 and 9) add to 5+9 = 14, which is exactly as long as the third side. I recommend you using a ruler to measure out 5 inches, 9 inches and 14 inches. Mark all three as separate segments on a piece of paper. Then cut out those segments to form strips of paper with the given lengths. Then try to form a triangle. You'll find that it is impossible since the smaller segments combine perfectly to get the longest segment. Instead of a triangle, you'll only have a line segment forming.

As a rule, when you add any two sides of a triangle, they must add to something larger than the third side. The rule more formally is

For any triangle with sides a,b,c, the following three inequalities must hold true

Answer:

0.0487 = 4.87%

Step-by-step explanation:

The probability of one mail being returned is 1.5% = 0.015, so the probability of the mail not being returned is 1 - 0.015 = 0.985. If we want 0 mails returned from a total of 200 mails, we have 0 mails returned (probabilitity of 0.015) and 200 mails not returned (probability of 0.985), then the final probability is calculated as follows:

Probability = (0.985)^200 * (0.015)^0 = 0.0487 = 4.87%

To find the probability that none of the 200 mailings will be returned because of incorrect or incomplete addresses, we can calculate the probability of an individual mailing not being returned and multiply it by itself 200 times.

To find the probability that none of the 200 mailings will be returned, we need to calculate the probability that each individual mailing is not returned. Given that 1.5% of mailings are returned, the probability of an individual mailing not being returned is 1 - 0.015 = 0.985. We can then find the probability that none of the mailings are returned by multiplying this probability by itself 200 times.

P(no mailings returned) = (0.985)200

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Answer:

134 degrees

Step-by-step explanation:

Because all triangles add up to 180 degrees, the missing degree inside the triangle would be 46 degrees. The 46 degrees are the missing side for the line and since all lines equal 180 degrees, 180 - 46 = 134

Answer:

4 boxes

48/12 = 4

Step-by-step explanation:

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Answer:

4 boxes

Step-by-step explanation:

This problem is fairly simple all you need to do is divide 48 by 12 and you should get 4. If that is too hard than you can see what 12 multiplyes by to get 48.

Hope that Helped :)

Answer: The actual distance is 142 miles.  

Step-by-step explanation:

First, you multiply the 3.375 inches by 42 miles since you are trying to scale. It equals 141.75. If you round it to the nearest mile, it equals 142 miles.

Answer:

1 4/5 = peanuts

1 1/5 = raisins

3/5 = chocolate chips

Step-by-step explanation:

3 ÷ 1 1/4 = 2 2/5

2 2/5 × 3/4 = 1 4/5

2 2/5 × 1/2 = 1 1/5

2 2/5 × 1/4 = 3/5

To keep proportions with 3 cups of granola, Darcia would need 1 ½ cups of peanuts, 1 ¼ cups of raisins, and 3/5 cup of chocolate chips in her snack mix.

Darcia has increased her granola measurement to 3 cups, which is 2.4 times more than the original 1 ¼ cups used in the snack mix recipe (since 3 ÷ 1.25 equals 2.4). To keep the other ingredients proportional to the new quantity, we need to multiply their original amounts by the same factor of 2.4

Therefore, if she used 3 cups of granola, she would use 1 ½ cups of peanuts, 1 ¼ cups of raisins, and 3/5 cup of chocolate chips to maintain the proportions in her snack mix.

Answer:

it depends what country you are referring to

In order to find a place's temperature, you have to have the continent and the place you are looking for. Temperatures are different every hour. Hope this helps! Stay safe and have a great day!

- Dhruva :)