Brian invests £2300 into his bank account.
He receives 10% per year simple interest.
How much will Brian have after 2 years?
Give your answer to the nearest penny where appropriate.

The distance between A(7,-7) and B(13,0) is 9.2 units

The formula for calculating the distance between two point is expressed as;

D = √(x₋₂-x₁)²+(y₂-y₁)²

Given the coordinate points A(7,-7) and B(13,0).

Substitute

AB = √(13-7)²+(0-7)²

AB = = √(6)²+(-7)²

AB = √36+ 49

AB = √85

AB = 9.2 units

Hence the distance between A(7,-7) and B(13,0) is 9.2 units

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Answer: $4.55

Step-by-step explanation:

Just subtract $10.00 from $5.45 and you will get $4.55

Answer:

$4.55

Step-by-step explanation:

To find the change, we have to subtract the money they give you ($10) with the guest total ($5.45).

10 - 5.45

= $4.55

$4.55 is your answer.

Take care and have a lovely rest of your day! :)

The Absolute error of the engineer's estimate is 14 pounds and the percent error is 4.89 % .

Absolute Error is defined as the difference between The Actual value and the estimated value .

Percent Error is defined as the difference between The Actual value and the estimated value in comparison to actual value expressed in percent .

[tex]Percent Error=\frac{|Estimated Value-Actual value|}{Actual Value} *100[/tex]

Given that the Estimated value =300 pounds

Actual Value=286 pounds

Absolute Error=300-286=14 pounds

Percent Error=[tex]\frac{|300-286|}{286} *100[/tex]

=[tex]\frac{14}{286} *100=4.89[/tex]%

Therefore , The Absolute error of the engineer's estimate is 14 pounds and the percent error is 4.89 % .

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Answer:

the answer is 2^x-7 = 1/3x+-1/3

graph it to 1-3 and negative 1-3 figure it out i don't really good at explaining

Answer:

Both sentences are false.

Step-by-step explanation:

Let's solve for x:

2x + 4y - 31 = 123

2x = 123 - 4y + 31

2x = 154 - 4y

x = 77 - 2y

Let's solve for y:

x = 77 - 2y

2y = 77 - x

y = 38.5 - 0.5x

Answer:

12/15

Step-by-step explanation:

Answer:

yes it can be bc it is repeating

The standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.

The population of individuals is always smaller than the entire population, therefore the possibilities for variances will be lower with the sample than with the population. The higher the population, the greater the chances for deviation from the mean.

Therefore, the standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.

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The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).

It follows from the task content that the circle in discuss has a center at the origin, (0,0).

Hence, the since the square of the radius is; = 89.

It follows that the point which fits into the equation of the circle; x² + y² = r² is;

Choice C; (5)² + (-8)² = 25 + 64 = 89.

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The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).

It follows from the task content that the circle in discuss has a center at the origin, (0,0).

Hence, the since the square of the radius is; = 89.

It follows that the point which fits into the equation of the circle; x² + y² = r² is;

Choice C; (5)² + (-8)² = 25 + 64 = 89.

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Measure of angle 1 is 50° and that of angle 2 is 130°

The sum of all the angles on a straight line is equal to 180°.

Here, we are given two angles ∠1 and ∠2

Also, we are given that

m∠1 = (x+24)°

and m∠2 = 5x°

As we can see from the given figure, ∠1 and ∠2 lie on a straight line

⇒ m∠1 + m∠2 = 180

⇒ (x+24) + 5x = 180

x + 24 + 5x = 180

x + 5x + 24 = 180

6x + 24 = 180

6x = 180 - 24

6x = 156

x = 156/ 6

x = 26

Therefore,

m∠1 = 26 + 24

= 50

and m∠2 = 5(26)

= 130

Thus, the measure of the two angles is 50° and 130°

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Your question was incomplete. Check for the missing figure below.

hi

a ( b +c) =  a*b +a*c

here a = -3  

        b = -4x

        c = +5

so :  

-3 ( -4x +5)  =  -3*-4x + -3* 5  

                   =  -12x + (-15)

                  = -12x -15

as I cannot add  -12x and  -15   ( they are two differents sort of figures )

so it's done

Answer:

12x - 15

Step-by-step explanation:

What you need to do for this is -3 · -4x + -3 · 5 = 12x+(-15). Which simplifies to 12x - 15.

Answer:

Step-by-step explanation:

The line passes through the points:

Since all x- coordinates are same, the line is vertical and its equation is:

The total money that will be cost for Mrs. Herrera to purchase candy for her is $10.9889

Given, Number of students that 100% attendance in the class is √196 -1 that is equal to

14-1 = 13.

So, number of students is 13.

Cost of one candy = $0.79+7%(tax)

Cost of one candy = $0.79 + (7% of 0.79)

Cost of one candy = $ 0.79 + 0.0553

Cost of one candy = $0.8453

So , total cost that Mrs. Herrera to purchase candy will be

Total cost = Number of student X Cost of one candy

Total cost = 13 X $0.8453

Total cost  = $ 10.9889

Hence, The total cost for Mrs. Herrera to purchase candy for her is $10.9889

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Answer:

Step-by-step explanation:

[tex]\frac{4}{6} + \frac{2}{4} + \frac{3}{5} = \frac{80}{120} + \frac{60}{120} + \frac{72}{120} = \frac{212}{120}[/tex]

simplest form : [tex]\frac{53}{30}[/tex]

The required function is d = 360 - 35h, 0 ≤ h ≤ 10.29.

We know that distance travelled is equalled to speed multiplied by time.

Let d be the distance from the destination.

Let d₁ be the distance travelled in h hour.

And h be the number of hours driven.

Given that the average speed is 35 miles per hour.

Therefore, we have d₁ = 35h

And the initial distance from the destination is 360 miles.

Note at time h= 0 the distance from the destination is the maximum which is 360 miles.

Therefore, we have d₁ = 35h

Distance from the destination is 360 - d₁.

⇒ d = 360 - d₁

⇒ d = 360 - 35h

Time taken to reach destination = d/v = 360/35 = 10.29 hours

Therefore the required function is d = 360 - 35h, 0 ≤ h ≤ 10.29

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Answer:

ok is the corr!ctewwwdeeecceeeeecrrr\g

Answer:

The multiple of 3 between 5 and 64 are 6+9+12+15+18+21+24+27+30+33+36+39+42+ 45+48+51+54+57+60+63

=690

The weighted average of the given coordinates weights is; 3

We are given that;

Coordinate of -5 has a weight of 3

Coordinate of 3 has a weight of 1

Now, we are given the formula to calculate the weighted average as;

WA = Sum of the Weighted Values/Sum of the Weights

Thus;

WA = ((-5 * 3) + (3 * 1))/(3 + 1)

WA = (-15 + 3)/4

WA = -12/4

WA = -3

We will take the absolute value which is; WA = 3

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Answer: No solution

Step-by-step explanation:

5r + 5 = 3(5r - 4) - 10r  Do multiplication

5r + 5 = 15r - 12 - 10r  combine like terms

5r + 5 = 5r - 12        This is impossible. 5r cannot equal 5 and 12 meaning there is no value of r that makes this equation true so there's No Solution.

You could continue

5r + 17 = 5r

-5r       =-5r

17=0 which is also not true

The measurement that is closest to the volume of the cylinder in cubic feet is: 15.7 Feet. (Option B)

Recall that volume is

V = πr²h

Given:

h = 5 feet

r = 2/2 = 1

Hence

V = 5 x 1 x 22/7

= 15.7142857143

Hence, the cylinders volume in cubic feet is given as:

[tex]$\approx$[/tex] 15.7 ft

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Answer: 15.7 ft3

Step-by-step explanation:

Answer:

∠ A = 42° , ∠ G = 85°

Step-by-step explanation:

the measure of an inscribed angle is half the measure of its intercepted arc.

(3)

∠ A is an inscribed angle , so

∠ A = [tex]\frac{1}{2}[/tex] BC = [tex]\frac{1}{2}[/tex] × 84° = 42°

(4)

∠ G is an inscribed angle but we require arc DF

the sum of the arcs in a circle = 360°

FG + GD + FD = 360°

70° + 120° + FD = 360°

190° + FD = 360° ( subtract 190° from both sides )

FD = 170°

Then

∠ G = [tex]\frac{1}{2}[/tex] DF = [tex]\frac{1}{2}[/tex] × 170° = 85°

The length of both the triangle's base and height in feet.

length of base = 32ft

height = 14 ft.

The base of a triangle can be any of its  sides. The term "base" refers to the both the side and the length (the measurement). The comparable height is really the length of a perpendicular segment from either the base to the opposing vertex.

Given that perhaps the cross-section of the lean-to shelter is a triangle, its area is a triangle.

A = ¹/₂bh

b = length of base

h = height

the base of the triangle is 10 feet more than twice its height, we have that

b = 2h + 10

A = ¹/₂bh

A =  ¹/₂(2h + 10)h

A = h² + 5h

Since the area of the triangle is A = 126 ft², we have that;

h² + 5h = 126

h² + 5h - 126 = 0

h² +(14h -9h) - 126 = 0

h² +14h -9h - 126  = 0

h(h + 14) -9(h + 14) = 0

(h + 14)(h - 9) = 0

Hight cant be negative:

h = 14

Length of the base is b = 2h + 10

b = 2h + 10

b = 2(14) + 10

b = 28 + 10

b = 35 ft

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Answer:

x=15

Step-by-step explanation:

-x+5

-15+5

= 10

As given Paul's Bikes rents bikes for $11 plus $4 per hour and  Amanda paid $31 to rent a bike shows she rent the bike for 5hours.

As given in the question,

Let 'h' represents the number of hours

Paul's Bikes rents bikes for $11 plus $4 per hour

Amanda paid $31 to rent a bike

Required equation is:

31 = 11 + 4h

⇒4h = 20

⇒h = 5hours

Therefore, as given Paul's Bikes rents bikes for $11 plus $4 per hour and  Amanda paid $31 to rent a bike shows she rent the bike for 5hours.

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A differential equation with some initial conditions is used to solve an initial value problem.

The required particular solution is given by the relation:

[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]

An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.

Let the given equation be [tex]$y^{1/2} dy\ dx y^{3/2} = 1[/tex], y(0) = 9

[tex]$(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1[/tex] …..(1)

Divide the given equation (1)  by [tex]$\sqrt{ y} $[/tex]  giving

[tex]$y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$[/tex], which is in Bernoulli's form.

Put [tex]$u=y^{(1+1 / 2)}=y^{(3 / 2)}$[/tex]

Then [tex]$(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$[/tex].

Multiply (2) by [tex]$\sqrt{ } y$[/tex] and we get

[tex]y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1[/tex]

(2/3) [tex]u^{\prime}+u=1$[/tex] or [tex]$u^{\prime}+(3 / 2) y=3 / 2$[/tex],

which is a first order linear equation with an integrating factor

exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is

[tex]u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$[/tex]  or

[tex]\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}[/tex]

To obtain the particular solution satisfying y(0) = 4,

put x = 0, y = 4, then

8 = (9/4) + c

c = (23/4)

Hence, the required particular solution is given by the relation:

[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]

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The change of Mandy's score is 600 points.

Here,

Mandy is playing a game.

Early in the game she had - 250 points.

Now, Mandy has 350 points.

We have to find the change of Mandy's score.

What is difference of two number?

To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.

Now,

Early in the game she had - 250 points.

And, now Mandy has 350 points.

So, The change of Mandy's score = 350 - (-250) = 350 + 250 = 600

Hence, The change of Mandy's score is 600 points.

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Answer: x=6  y=6

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{4x-3y=6} \atop {6x-5y=6}} \right.\\[/tex]

Since the right parts of the equation are equal, therefore the left parts of the equation are also equal:

[tex]4x-3y=6x-5y\\4x-3y+5y=6x-5y+5y\\4x+2y=6x\\4x+2y-4x=6x-4x\\2y=2x\\[/tex]

Divide both parts of the equation by 2:

[tex]y=x\\Hence,\\4x-3x=6\\x=6\\Thus,\\x=y=6[/tex]

The equation for the line that connects the locations is y = 2x + 5.

The slope of a line, commonly known as the gradient, is defined as the value of the steepness or direction of a line in a coordinate plane. Slope can be determined using many ways given the equation of either a line or the coordinates of points on the straight line. . The slope is defined mathematically as "climb overrun" (change in y divided by change in x).

x₁ = 1

y₁ = 7

x₂ = -3

y₂ = -1

To obtain the equation of a line, we must first determine its slope. This is computed as:

m = [y₂ - y₁ ]/[x₂ - x₁]

Substituting the value we get:

m = [(-1) - 7 )/((-3) - 1)]

  = -8/-4

   = 2

The slope of the line = 2.

The line's intercept is:

The slope is the next step toward solving for  a such equation of the line.

A typical linear equation is presented as:

y = mx + c

Let us substitute the slope and intercept values.

y = 2x + 5

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