Pedro invests £800 in a bank account that pays 3% simple interest per year. How much money will he have in his account after 3 years?

Answer:

You may or may not need to include the units.

A = 18x - 18

P = 6x + 6

Graph is attached below. (2, 18)

Step-by-step explanation:

Substitute the information we need, "l" and "w", into the formulas.

l is for length, 6cm.

w is for width, (3x - 3)cm.

Use the formula for area of a rectangle.

A = lw

A = (6)(3x-3)cm²

A = (18x - 18)cm²  or 18x - 18

Use the formula for perimeter of a rectangle.

P = 2(l + w)

P = 2(6 + (3x - 3))cm

P = 2(3x + 3)cm

P = (6x + 6)cm  or 6x + 6

Linear equations are written in the form y = mx + b, so we do not need to factor or further simplify the formulas.

To graph, first turn the "m" value into a fraction form.

8 -> 8/1

6 -> 6/1

You need two points to graph each line.

For each equation, the first point is on the y-axis at the "b" value. Then use the "m" in the equation to count the number of units up (numerator) and to the right (denominator).

The solution is (2,18)

Answer:

189

Step-by-step explanation:

Answer:

A. 90.5 cubic meters pet second.

B. 3.77 square meters per second.

C.  [tex]\frac{dV}{dS} = \frac{r}{2}[/tex]

Step-by-step explanation:

The radius of a sphere is increasing at a constant rate of 0.05 meters per second.

Therefore, [tex]\frac{dr}{dt} = 0.05[/tex] ......... (1)

A. Now, volume of the sphere is given by  

[tex]V = \frac{4}{3}\pi  r^{3}[/tex]

Now, differentiating both sides with respect to t we get,

[tex]\frac{dV}{dt} = \frac{4}{3}\pi (3r^{2}) \frac{dr}{dt} = 4\pi r^{2} \frac{dr}{dt}[/tex]

Then at r = 12 meters, the rate of increase in volume will be

[tex]\frac{dV}{dt} = 4 \times (\frac{22}{7}) \times 12^{2} \times 0.05 = 90.5[/tex] cubic meters pet second. {From equation (1)}

B. When the volume of the sphere is 36π cubic meters, then  

[tex]\frac{4}{3}\pi r^{3} = 36\pi[/tex]

⇒ [tex]r^{3} = 27[/tex]

⇒ r = 3 meters.

Now, surface area of a sphere is given by  

S = 4πr² .......... (2)

Differentiating both sides with respect to time (t) we get,

[tex]\frac{dS}{dt} = 8\pi r\frac{dr}{dt} = 8 \times (\frac{22}{7}) \times 3 \times 0.05 = 3.77[/tex] square meters per second. {From equation (1)}

C. Now, [tex]V = \frac{4}{3}\pi  r^{3}[/tex] and S = 4πr²

⇒ [tex]V = \frac{1}{3} (4\pi r^{2})r = \frac{Sr}{3}[/tex]

Now, differentiating with respect to S both sides we get,

[tex]\frac{dV}{dS} = \frac{r}{3} + \frac{S}{3} \frac{dr}{dS}[/tex] ......... (3)

Now, we have, S = 4πr²

Differentiating with respect to S both sides, we get

[tex]1 = 8\pi r\frac{dr}{dS}[/tex]

⇒ [tex]\frac{dr}{dS} = \frac{1}{8\pi r }[/tex] ......... (4)

Now, from equations (2), (3) and (4) we get,

[tex]\frac{dV}{dS} = \frac{r}{3} + \frac{4\pi r^{2} }{3} \times \frac{1}{8\pi r }[/tex]

⇒ [tex]\frac{dV}{dS} = \frac{r}{3} + \frac{r}{6}[/tex]

⇒ [tex]\frac{dV}{dS} = \frac{r}{2}[/tex] (Answer)

Question:

C. Express the rate at which the volume of the sphere changes with respect to the surface are of the sphere (as a function of r)

Step-by-step explanation:

Here's how you solve part C of this question.

Start with what you know:

dV/dt = 4pir^2 x (dr/dt)

(dr/dt) = 0.05

S(r) = (Surface Area) = 4pir^2

So, since S(r) is equal to 4pir^2, we replace 4pir^2 with S(r). We also know that (dr/dt) = 0.05, so we replace (dr/dt) with 0.05.

Now the equation should look like this:

dV/dt = 0.05 x S(r) <----- (your answer).

Hope this helped!! :)

Answer:

Step-by-step explanation:

x=2and y=−1

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Answer:

x=2, y = -1

Step-by-step explanation:

Given the system of equation;

5x + y = 9 ... (1)

3x + 2y = 4 ...(2)

We will solve it simultaneously to get variables x and y.

Using substitution method,

From equation 1, y = 9-5x ...(3)

Substituting equation 3 into 2 we will have;

3x + 2(9-5x) = 4

3x + (18-10x) = 4

3x + 18 -10x = 4

3x-10x+18 = 4

-7x+18 = 4

-7x = 4-18

-7x =-14

Dividing both sides by -7, we will have;

-7x/-7 = -14/-7

x = 2

Substituting x = 2 into equation 1 to get y we will have;

5x+y= 9

5(2) + y = 9

10+y = 9

y = 9-10

y = -1

Therefore x = 2 and y = -1 is the solution to the simultaneous equation.

The statements which are true are:

(6, 6) is the midpoint of CD

(4, 3) is the intersection point of diagonals of parallelogram

Solution:

The mid point (x,y) = [tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

A(-2, -1) and B(6, 1)

[tex]\text{ midpoint of AB } = (\frac{-2+6}{2} , \frac{-1+1}{2})\\\\\text{ midpoint of AB } = (2, 0)[/tex]

Thus statement 1 is wrong

B(6, 1) and C(10, 7)

[tex]\text{ midpoint of BC } = (\frac{6+10}{2} , \frac{1+7}{2})\\\\\text{ midpoint of BC } = (8, 4)[/tex]

Thus statement 2 is wrong

Here ,

[tex]x_1[/tex] = 10

[tex]x_2[/tex]= 2

[tex]y_1[/tex]= 7

[tex]y_2[/tex]=5

now substituting these values,

mid point of CD  = [tex](\frac{10+2}{2},\frac{7+5}{2})[/tex]

mid point of CD  = [tex](\frac{12}{2},\frac{12}{2})[/tex]  

mid point of CD  = [tex](6, 6)[/tex]

Therefore (6, 6) is the midpoint of CD

Statement 3 is correct

A = (-2, -1) and D = (2, 5)

[tex]\text{ mid point of AD } = (\frac{-2+2}{2} , \frac{-1+5}{2})\\\\\text{ mid point of AD } = (0, 2)[/tex]

Thus statement 4 is wrong

Let AC and BD be the diagonals of parallelogram

The diagonals of a parallelogram bisect each other, therefore, the point of intersection is the midpoint of either.

Midpoint of AC:

A = (-2, -1) and C(10, 7)

[tex]\text{ Midpoint of AC } = (\frac{-2+10}{2} , \frac{-1+7}{2})\\\\\text{ Midpoint of AC } = (4,3)[/tex]

Thus statement 5 is correct

Answer:

215

Step-by-step explanation:

215

3

647

6

04

 3

 17

 15

   2

hope this helped

Answer:

3x ≥ 2 + 2x

Step-by-step explanation:

Given:

[tex]x\geq 2[/tex]

Solution:

Now, we have to write an inequality with x on both sides whose solution is x is greater than or equal to 2.

[tex]x\geq 2[/tex]

Now we add 2x on both side.

[tex]x + 2x\geq 2 + 2x[/tex]

[tex]3x\geq 2 + 2x[/tex]

Therefore, the inequality which has a solution x ≥ 2 is:

3x ≥ 2 + 2x

Each friend should contribute $196.5 towards the party supplies.

To solve this problem, we need to follow these steps:

1. Calculate the total cost of all party supplies:

  - 100 balloons cost $720

  - 100 plates cost $475

  - 100 cups cost $5.45 each

  - 100 napkins cost $2.09 each

  - 10 invitations cost $1.60 each

  - We need to find the cost of the plastic punchbowl.

2. Find the cost of the plastic punchbowl:

  - To find the cost of the plastic punchbowl, we subtract the total cost of the known items from the total cost of all party supplies.

3. Calculate the total cost of all party supplies:

  - Calculate the cost of 100 cups: [tex]\(100 \times \$5.45\)[/tex]

  - Calculate the cost of 100 napkins: [tex]\(100 \times \$2.09\)[/tex]

  - Sum up the costs of all known items.

4. Find the cost per friend:

  - Once we have the total cost of all party supplies, we divide this total by the number of friends (10) to find out how much each friend should contribute equally.

Let's calculate step by step:

1. Calculate the total cost of all party supplies:

  - Cost of 100 balloons: $720

  - Cost of 100 plates: $475

  - Cost of 100 cups: [tex]\(100 \times \$5.45\)[/tex]

  - Cost of 100 napkins: [tex]\(100 \times \$2.09\)[/tex]

  - Cost of 10 invitations: [tex]\(10 \times \$1.60\)[/tex]

  - Total cost of known items [tex]= \(720 + 475 + (100 \times 5.45) + (100 \times 2.09) + (10 \times 1.60)\)[/tex]

2. Find the cost of the plastic punchbowl:

  - Total cost of all party supplies - Total cost of known items = Cost of plastic punchbowl

3. Calculate the total cost of all party supplies:

  - [tex]\(100 \times \$5.45 = \$545\)[/tex]

  - [tex]\(100 \times \$2.09 = \$209\)[/tex]

  - [tex]\(10 \times \$1.60 = \$16\[/tex]

  - Total cost of known items = [tex]\(720 + 475 + 545 + 209 + 16\)[/tex]

4. Find the cost per friend:

  - Total cost of all party supplies / Number of friends = Cost per friend

Let's compute these steps to find the solution.

Let's calculate step by step:

1. Calculate the total cost of all party supplies:

  - Cost of 100 balloons: $720

  - Cost of 100 plates: $475

  - Cost of 100 cups: [tex]\(100 \times \$5.45 = \$545\)[/tex]

  - Cost of 100 napkins: [tex]\(100 \times \$2.09 = \$209\)[/tex]

  - Cost of 10 invitations: [tex]\(10 \times \$1.60 = \$16\)[/tex]

  - Total cost of known items = [tex]\(720 + 475 + 545 + 209 + 16 = \$1965\)[/tex]

2. Find the cost of the plastic punchbowl:

  - Total cost of all party supplies - Total cost of known items = Cost of plastic punchbowl

  - Total cost of all party supplies  - $1965 = Cost of plastic punchbowl

3. Calculate the total cost of all party supplies:

  - Total cost of all party supplies = [tex]720 + 475 + (100 \times 5.45) + (100 \times 2.09) + (10 \times 1.60)[/tex] = 720 + 475 + 545 + 209 + 16 = $1965

4. Find the cost per friend:

  - Total cost of all party supplies / Number of friends = Cost per friend

  - [tex]\( \frac{\$1965}{10} = \$196.5 \)[/tex]

So, each friend should contribute $196.5 towards the party supplies.

the complete Question is given below:

For a party, 10 friends are buying 100 cups, 100 plates, a punchbowl, and 200 balloons. If the friends share the cost equally, how much should each friend contribute? Party Supplies 100 balloons $720 100 plates $475 100 cups $5.45 100 napkins $2.09 What steps do you need 10 invitations $1.60 to solve to find the plastic punchbowl

Final answer:

The given equation has no solution because it leads to a contradiction.

Explanation:

To determine whether the given equation has one solution, no solution, or infinitely many solutions, we need to simplify the equation and see if it leads to a contradiction or identity. Simplifying the equation:

2/3x = 9 - 2(-1/3x + 3)

We can start by distributing the -2 to (-1/3x + 3):

2/3x = 9 + 2/3x - 6

Combining like terms:

2/3x - 2/3x = 9 - 6

0 = 3

Since we have a contradiction (0 cannot equal 3), there is no solution to the equation. Therefore, the correct answer is no solution.

Answer: The nearest whole number to 6.58 would be 7.

Step-by-step explanation: The whole number 7 is closer to 6.58 than any other whole number. Hence, 6.58 rounded to the nearest whole number would be 7.

Answer:2³*3²

Step-by-step explanation:

The shoot would last eight hours, and the cost would be $699 whether the photographer hires Craig or Kaya.

This question can be solved using algebra, particularly the concept of system of equations, where we set two linear cost equations equal to each other to find out when they cost the same. Given: Craig's cost is $195 + $63p, and Kaya's cost is $171 + $66p, we form an equation $195 + $63p = $171 + $66p. Subtracting $171 and $63p from both sides leaves us with $24 = $3p. So, dividing both sides by $3, we get p = 8.

This means the photo shoot would last 8 hours, and the cost would be either Craig's or Kaya's cost for 8 hours, which is $195 + $63*8 = $699 or  $171 + $66*8 = $699.

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The cost for the photo shoot would be $699, and the duration of the shoot would be 8 hours.

Let's denote:

- [tex]\( C_C \)[/tex]: Total cost if the photographer hires Craig.

- [tex]\( C_K \)[/tex]: Total cost if the photographer hires Kaya.

- [tex]\( h \)[/tex]: Number of hours of the photo shoot.

Given the charges:

- Craig charges $195 for showing up, plus $63 per hour.

- Kaya charges $171 for showing up, plus $66 per hour.

The equations for the total cost [tex]\( C_C \)[/tex] and [tex]\( C_K \)[/tex] are:

[tex]\[ C_C = 195 + 63h \][/tex]

[tex]\[ C_K = 171 + 66h \][/tex]

The photographer realizes that the costs are the same, so:

[tex]\[ C_C = C_K \][/tex]

Substitute the expressions:

[tex]\[ 195 + 63h = 171 + 66h \][/tex]

Now, solve for [tex]\( h \)[/tex]:

[tex]\[ 195 - 171 = 66h - 63h \][/tex]

[tex]\[ 24 = 3h \][/tex]

[tex]\[ h = \frac{24}{3} \][/tex]

[tex]\[ h = 8 \][/tex]

So, the duration of the photo shoot is 8 hours.

Now, substitute [tex]\( h = 8 \)[/tex] back into either equation to find the cost:

Using [tex]\( C_C \)[/tex]:

[tex]\[ C_C = 195 + 63 \cdot 8 \][/tex]

[tex]\[ C_C = 195 + 504 \][/tex]

[tex]\[ C_C = 699 \][/tex]

Using [tex]\( C_K \)[/tex]:

[tex]\[ C_K = 171 + 66 \cdot 8 \][/tex]

[tex]\[ C_K = 171 + 528 \][/tex]

[tex]\[ C_K = 699 \][/tex]

Answer: Doubling the radius.

Step-by-step explanation:

The volume of a cone can be found with the following formula:

[tex]V=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height of the cone.

Let's find the volume of the conical tent with a radius of 10.4 feet and a height of 8.4 feet.

Identifiying that:

[tex]r=10.4\ ft\\\\h=8.4\ ft[/tex]

You get this volume:

[tex]V_1=\frac{1}{3}\pi (10.4\ ft)^2(8.4\ ft)\\\\V_1=951.43\ ft^3[/tex]

If you double the radius, the volume of the conical tent will be:

[tex]V_2=\frac{1}{3}\pi (2*10.4\ ft)^2(8.4\ ft)\\\\V_2=3,805.70\ ft^3[/tex]

When you divide both volumes, you get:

[tex]\frac{3,805.70\ ft^3}{951.43\ ft^3}=4[/tex]

Therefore, doubling the radius will quadruple the volume of the tent.

Answer:

[tex]\large \boxed{\math{8\frac{1}{4}}\text{ km}}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{lcll}2\frac{1}{5} \times 3\frac{3}{4} & = & \dfrac{11}{5} \times \dfrac{15}{4} & \text{Converted the mixed numbers to improper fractions}\\\\& = & 11 \times\dfrac{3}{4}& \text{Cancelled the 5s}\\\\& = & \dfrac{33}{4}& \text{Multiplied numerators and denominators}\\\\& = &\mathbf{8\frac{1}{4}} & \text{Converted the mixed number to a fraction}\\\end{array}\\\text{The length of the road is }\large \boxed{\mathbf{8\frac{1}{4}}\textbf{ km}}}[/tex]

Answer:

The scale factor is 2.

Step-by-step explanation:

Take the vertical sides of the 2 triangles.

Their length is 3 and 6 so the scale factor is 6/3 = 2.

Also we see than the horizontal lines are in the same ratio 4 : 2  = 2:1.

Answer:

There are 7 chairs in each row.

Step-by-step explanation:

Hue is arranging some number of chairs. If she arranges them in 6 rows of equal lengths then there will be 3 chairs leftover, or she arranges them in 8 rows of that same length then she requires 11 more chairs.

Let us assume that there are P numbers of chairs and there are x chairs in each row.

Therefore, we can write that  

6x + 3 = P ....... (1) and  

8x = P + 11  

⇒ 8x - 11 = P ........ (2)

Now, from equations (1) and (2) we get,

6x + 3 = 8x - 11

⇒ 2x = 14

⇒ x = 7

Therefore, there are 7 chairs in each row. (Answer)

Answer: B. on e2020

Step-by-step explanation:

The transformation of parent function to h(x) = - ∛x + 3 is such that it is reflected over the horizontal axis, and then translated up 3 units.

The correct option is B.

Transformations are changes done in the shapes on a coordinate plane by rotation or reflection or translation.

Given function,

h(x) = - ∛x + 3

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis

Parent Function: f(x) = ∛x

Horizontal Shift: None

Vertical Shift: Up 3 Units

Reflection about the x-axis:

f(x) → -f(x)

∛x → - ∛x  

Reflection of the function is over x - axis.

Hence, the transformation from the parent equation to given function can be found  by reflecting over X- axis and translate up 3 units.

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The coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

To find the image of ∆CDE for a glide reflection, we must first perform a translation. The translation is (x, y) → (x, y – 3). This means that each point of ∆CDE will be moved 3 units down.

Therefore, the coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

Next, we need to reflect ∆CDE across the line x = 0. This me The vertices of ∆CDE are C(–5, 3), D(–6, 1), and E(–1.5, 2). Which figure shows the image of ∆CDE for a glide reflection where the translation is (x, y) → (x, y – 3) and the line of reflection is x = 0?

To find the image of ∆CDE for a glide reflection, we must first perform a translation. The translation is (x, y) → (x, y – 3). This means that each point of ∆CDE will be moved 3 units down.

Therefore, the coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

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Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

(x+4)/3=6

Multiply by 3 on both sides

x+4=18

Subtract 4 from both sides

x=14

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Answer:

altitude

Step-by-step explanation:

√12x^3÷√6x

Factor 6 out of both the numerator and denominator:

√2x^3÷√x

Cancel out common factors to get:

√2x^2

Pull the terms out from under the radical to get:

D. x√2

Step-by-step explanation:

equation -

(X+7) (x-1) =0

equation = x2 -x -7x -7 = x2 -8x -7

standard form = x2 -8x -7

factor form = (x+7) (x-1)

Answer: 301

Step-by-step explanation:

the least amount one of the wrestlers could weigh is 301.

The term standard deviation refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given that,

Mean μ = 265,

Standard deviation σ = 28 lbs.

Let the least amount one of the wrestlers could weigh is x.

To find x such that P(X≥x) = 0.10

1 - P(X<x) = 0.10

P(X<x) = 1 - 0.10

P(X<x) = 0.90

z for area = 0.90 in equal to 1.28 in statistical table,

z = 1.28

Use  formula, to find the value of x,

x = μ + z × σ

x = 265 + 1.28 × 28

x = 265 + 35.84

x = 300.84

x = 301(Rounded to the nearest integer)

The required value of x is 301.

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There are triangles ΔABC, ΔFDE, and ΔGIH must be congruent. The correct answer is option A.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

In the given information, we can see that AB is congruent to both DF and GI, and BC is congruent to HI. Also, we know that ∠B is congruent to both ∠D and ∠G.

Using these properties, we can conclude that triangles ABC and FDE are congruent by the Side-Angle-Side (SAS) congruence theorem, since AB is congruent to DF, BC is congruent to DE, and ∠B is congruent to ∠D.

Similarly, we can conclude that triangles ABC and GIH are congruent by the Side-Side-Side (SSS) congruence theorem since AB is congruent to GI, BC is congruent to HI, and AC is congruent to GH.

Therefore,  ΔABC, ΔFDE, and ΔGIH must be congruent.

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Each student worked on 115 math problems.

Step-by-step explanation:

Given,

Problems solved in 4 hours = 8970

Number of students in competition = 78

As each student solved same number of problems, we will divide the total problems solved by number of students to find the amount of problems solved by one student.

Problems solved by one student = [tex]\frac{8970}{78}[/tex]

Problems solved by one student = 115

Each student worked on 115 math problems.

Keywords: division

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Each student works 115 problems.

Explanation:

I'm going to copy and paste the question here, and bold important info.

"Rayville Elementary sponsors a math competition for 78 students. During the competition, the students work a total of 8,970 math problems in 4 hours. Each student works the same number of problems. How many problems does each student work?"

Now everything not bolded? Forget about it. All you need to know is that there are 78 students. They all do 8,970 # of problems. And all the students do the same amount. Now you just have to divide the # of probs. by the amount of students in the competition, and you have your answer.

8970÷78=115

Hope that helped!

Answer:

Circumcenter describes the point equidistant to the refrigerator, stove and the sink

Step-by-step explanation:

The basic construction of the circumcenter is to identify the midpoints of the original triangle. This circumcenter is the point where all the perpendicular bisector of the sides of the triangle intersects. For an triangle that is  acute-angled, its circumcenter will lie inside the triangle. For an obtuse-angled triangle, the circumcenter lies outside of the triangle

, In a right-angled triangle, Circumcenter lies at the midpoint of the hypotenuse side of triangle.

To Find the circumcenter of the triangle

Answer:

Circumcenter

Step-by-step explanation:

Answer:

Total price of the glass is = $904.78

Step-by-step explanation:

Let's start by finding what is the surface area (in square meters) of the circular piece of glass. The information we have is that the radius of it is 8.0 meters. So we recall the formula for the area of the circle in terms of its radius (the product of the number [tex]\pi[/tex] times the square of the circle's radius):

Area of circle = [tex]\pi \,r^2[/tex]

Therefore, since the circle we need to investigate has radius 8 meters, the formula now becomes:

Area of circle = [tex]\pi \,r^2=\pi\,\,(8\,m)^2=201.062\,m^2[/tex]

Now, since they charge the glass per square meter ($4.50 per square meter), we just multiply the number of square meters we found for the glass' surface times the price per square meters, and get:

Total price = $4.50 * 201.062 = $904.78

Max needs to run 15 laps around the track.

Step-by-step explanation:

Given,

Distance Max wants to run = 512 miles

Length around the track = 34 mile

34 miles = 1 lap

1 mile = [tex]\frac{1}{34}\ laps[/tex]

512 miles = [tex]\frac{1}{34}*512[/tex]

512 miles = 15.06 laps

Rounding off to nearest whole number;

512 miles = 15 laps

Max needs to run 15 laps around the track.

Keywords: unit rate, division

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Answer:

r=-2

Step-by-step explanation:

difference in y/difference in x =slope

-r-8/1-2=-9

-r-8=-9*-1

-r=10+8

r=-2

Answer:

Let's find out!

Step-by-step explanation:

15 ounces / 2.49 dollars

≈ 6.024 ounces per dollar

20 ounces / 3.32 dollars

≈ 6.024 ounces per dollar

Your answer is:

C) The unit rates are equal

The amount of ounces per dollar is the same, so your answer MUST be C).

Answer:

C) The unit rates are equal.

Step-by-step explanation: