During her first year of college, Sara put $2000 in the bank to save for a trip to Italy after graduation. The money earned 3% simple annual interest. After 4 years, how much money did she have in the bank for her trip?

Answer:

8/27  is the solution and the alternative form is 0.296 or 2/3 to the power of 3

The equation of the line that has a slope of 1/3 and passes through the point (-2, 1) is y = 1/3x + 5/3.

The subject of this question is the representation of a line in the form of an equation, specifically a line that has a slope of 1/3 and passes through a given point, (-2, 1). We can use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Substituting the given values, we have y - 1 = 1/3(x - (-2)). Or simplified to y - 1 = 1/3(x + 2). From here, we can rearrange this into slope-intercept form (y = mx + b) by distributing the 1/3 to x and 2, thus giving us y = 1/3x + 2/3 + 1. Finally, simplifying the equation gives y = 1/3x + 5/3, which is the equation of the line that has a slope of 1/3 and passes through the point (-2, 1).

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Answer:

Step-by-step explanation:

[tex]-15=(3x-10)-5x\\\\-15=3x-10-5x\qquad\text{combine like terms}\\\\-15=(3x-5x)-10\\\\-15=-2x-10\qquad\text{add 10 to both sides}\\\\-15+10=-2x-10+10\\\\-5=-2x\qquad\text{divide both sides by (-2)}\\\\\dfrac{-5}{-5}=\dfrac{-2x}{-2}\\\\2.5=x\to x=2.5[/tex]

Answer:

exact form x=5/2 decimal form2.5 mixed number form 2 1/2

Step-by-step explanation:

Answer: It should be 3,500

Step-by-step explanation: If the number behind it is 5 or greater, then you round up, meaning the 3 would change to 4, but since it is lower than 2, it would stay the same (5) for it is closer to 3,500.

The coordinates of the image after dilation are

A (-12 , -12) , B (6 , -3) , C (3 , 3) ⇒ answer B

Step-by-step explanation:

A dilation is a transformation that produces an image that is the

same shape as the original, but in a different size

When you dilate a figure, with

Then the coordinates of each point of the figure is multiplied by k

to find the image of the figure after dilation

∵ ABC has coordinates of A (-8 , -8), B (4 , -2), and C (2 , 2)

∵ ABC is dilated by scale factor 1.5

∵ The center of dilation is the origin

- Multiply the coordinates of points A, B, and C by 1.5

∴ The image of point A = (-8 × 1.5 , -8 × 1.5) = (-12 , -12)

∴ The image of point B = (4 × 1.5 , -2 × 1.5) = (-6 , -3)

∴ The image of point C = (2 × 1.5 , 2 × 1.5) = (3 , 3)

The coordinates of the image after dilation are

A (-12 , -12) , B (6 , -3) , C (3 , 3)

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Answer:

Step-by-step explanation:

The answer is 16

Final answer:

The probability of rolling an even number on a 9-sided die is 4/9.

Explanation:

To find the probability of rolling an even number on a 9-sided die, we need to determine the number of favorable outcomes (even numbers) and divide it by the total number of possible outcomes.

In this case, there are 4 even numbers on the die: 2, 4, 6, and 8. The total number of possible outcomes is 9 (since there are 9 sides on the die).

Therefore, the probability of rolling an even number is 4/9.

Answer:

23,490

Step-by-step explanation:

10% = 0.1

234900 x 0.1 = 23490

Is that it on the description? No question of nothing?

Answer:

parallel lines

Answer:

lines

Step-by-step explanation:

Answer:

m = [tex]\frac{-2}{5}[/tex]

Step-by-step explanation:

2m + 1 = -3m - 1 (Given)

2m + 1 + 1 = -3m - 1 + 1 (Addition Property of Equality)

2m + 2 = -3m (Simplify)

2m - 2m + 2 = -3m - 2m (Subtraction Property of Equality)

2 = -5m (Simplify)

[tex]\frac{2}{-5} = \frac{-5m}{-5}[/tex] (Division Property of Equality)

[tex]\frac{-2}{5}[/tex] = m (Simplify)

m = [tex]\frac{-2}{5}[/tex] (Symmetric Property of Equality)

The answer is:

Work/explanation:

Combine like terms on each side:

[tex]\sf{2m+1=-3m-1}[/tex]

Make sure all terms that contain m are on the left side and all constant terms are on the right. Don't forget to use the opposite sign when moving terms from one side to the other one.

[tex]\sf{2m+3m=-1-1}[/tex]

[tex]\sf{5m=-2}[/tex]

Divide each side by 5

[tex]\sf{m=-\dfrac{2}{5}}[/tex]

It will take the snail 9.6 minutes to travel 24cm.

Step-by-step explanation:

Distance covered in 4 minutes = 10 cm

Ratio of distance to time = 10:4

New distance = 24cm

Let,

x be the time period

Ratio of new distance to time = 24:x

Using proportions;

Ratio of distance to time :: Ratio of new distance to time

[tex]10:4::24:x[/tex]

Product of mean = Product of extreme

[tex]24*4=10*x\\96=10x\\10x=96[/tex]

Dividing both sides by 10

[tex]\frac{10x}{10}=\frac{96}{10}\\x=9.6\ minutes[/tex]

It will take the snail 9.6 minutes to travel 24cm.

Keywords: ratio, proportion

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Answer:

b

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

0.30 * x = 240

x = 240/0.30 = 800

0.50 * 800 = 400

Answer:

The value of 50 % of number is 400  .

Step-by-step explanation:

Given as :

Let The number be x

According to statement

30 percent of a number is 240

I.e 30 % of x = 240

Or, [tex]\frac{30}{100}[/tex] × x = 240

Or, 0.3 × x = 240

So.  x = [tex]\frac{240}{0.3}[/tex]

∴     x = 800

SO, The number is 800 .

Now again 50 percent of that number = y

I.e y = 50 % of x

or, y =  50 % of 800

Or, y =  [tex]\frac{50}{100}[/tex] × 800

Or, y = 0.5 × 800

∴    y = 400

Hence The value of 50 % of number is 400  . Answer

Answer:

Option A) 4, 2

Step-by-step explanation:

We are given that quadrilateral ABCD is a  parallelogram with sides:

[tex]AB = 3 + x\\DC = 4x\\AD = y + 1\\BC = 2y[/tex]

Since the opposite sides of a parallelogram are equal, we can write:

[tex]AB = DC\\AD=BC[/tex]

Equating the sides we get,

[tex]\Rightarrow 3+x = 4x\\4x-x = 3\\3x = 3\\x = 1\\\Rightarrow y + 1 = 2y\\y = 1[/tex]

Putting the values of x and y, we get:

[tex]AB = 3 + x =4\\DC = 4x =4\\AD = y + 1=2\\BC = 2y=2[/tex]

Thus, the lengths of the opposite side pairs is 4,2.

Answer:

that is too....much? it's n = 5

Step-by-step explanation:

60/12 = 12n/12

5 = n

Answer:

The area of the square lawn is [tex]784\ m^2[/tex]

Step-by-step explanation:

Part 7)

Let

x ----> the length side of the square lawn in meters

we know that

The area of the path is equal to

[tex]A=(x+2+2)^2-x^2[/tex]

[tex]A=(x+4)^2-x^2[/tex] ----> equation A

[tex]A=240\ m^2[/tex] ----> equation B

so

[tex]240=(x+4)^2-x^2[/tex]

Solve for x

[tex]240=(x^2+8x+16)-x^2[/tex]

[tex]240=8x+16[/tex]

[tex]8x=240-16[/tex]

[tex]8x=224[/tex]

[tex]x=28\ m[/tex]

The area of the square lawn is

[tex]A=x^2[/tex]

substitute the value of x

[tex]A=28^2=784\ m^2[/tex]

Answer:

8 17/20

Step-by-step explanation:

177/20=8 17/20

Because 8*20=160 and 177-160=17.

Final answer:

To convert 177 divided by 20 into a mixed number, divide 177 by 20. The quotient is the whole number part and the remainder is the fractional part.

Explanation:

To convert 177 divided by 20 into a mixed number, we need to find the quotient and the remainder. The quotient represents the whole number part of the mixed number, while the remainder represents the fractional part.

When we divide 177 by 20, we get a quotient of 8 and a remainder of 17. Therefore, the mixed number representation of 177 divided by 20 is 8 and 17/20.

So, 177 divided by 20 is equal to 8 and 17/20.

Answer: 1/3

Step-by-step explanation:

5/15 divided both by 5 is 1/3

Answer:

The prepaid phone plan will have a steeper line and lower y-intercept.

I hope this is right

Step-by-step explanation:

prepaid phone plan y = .20x

contracted phone plan y = .02x + 50

The prepaid and the contracted plans are illustrations of linear functions, where the prepaid phone plan has a steeper line and lower y-intercept.

We have:

Prepaid

[tex]Rate = 0.20[/tex]

[tex]Monthly = 0[/tex]

Contracted

[tex]Monthly = 50[/tex]

[tex]Rate = 0.02[/tex]

For both plans, the cost function (y) is:

[tex]y =Monthly + Rate \times x[/tex]

Where:

[tex]x \to[/tex] Number of minutes

[tex]Rate \to[/tex] Steepness

So, we have:

Prepaid

[tex]y =0 + 0.20 \times x[/tex]

[tex]y =0.20x[/tex]

The y intercept (i.e. when x = 0) is

[tex]y = 0.20 \times 0 = 0[/tex]

Contracted

[tex]y = 50 + 0.02 \times x[/tex]

[tex]y = 50 + 0.02x[/tex]

The y intercept is:

[tex]y = 50 + 0.02 \times 0 = 50[/tex]

By comparing the steepness and the y-intercepts,

Hence, (a) is correct

See attachment for the graphs of both plans

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Answer:

Option B.) 45 units

Step-by-step explanation:

see the attached figure with letter to better understand the problem

step 1

Determine the coordinates of the corners of the rectangle

Let

A(4,5),B(1,8),C(14,21) and D(17,18)

step 2

we know that

The formula to calculate the perimeter of rectangle is equal to

[tex]P=2(AB+BC)[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the length side AB

[tex]A(4,5),B(1,8)[/tex]

substitute in the formula

[tex]d=\sqrt{(8-5)^{2}+(1-4)^{2}}[/tex]

[tex]d=\sqrt{(3)^{2}+(-3)^{2}}[/tex]

[tex]d_A_B=\sqrt{18}\ units[/tex]

Find the length side BC

[tex]B(1,8),C(14,21)[/tex]

substitute in the formula

[tex]d=\sqrt{(21-8)^{2}+(14-1)^{2}}[/tex]

[tex]d=\sqrt{(13)^{2}+(13)^{2}}[/tex]

[tex]d_B_C=\sqrt{338}\ units[/tex]

Find the perimeter

[tex]P=2(AB+BC)[/tex]

substitute the values

[tex]P=2(\sqrt{18}+\sqrt{338})[/tex]

[tex]P=45\ units[/tex]

Answer:

B) 45 units

Step-by-step explanation:

D = dx2 + dy2

W = (1-4)2 + (8-5)2

W = (-3)2 + (3)2 = 4.24264

L = (1-14)2 + (8-21)2

L = (-13)2 + (-13)2 = 18.38478

A = 2L+2W = 2(18.38478)+2(4.24264)= 45.3 units

Answer:

For this set of numbers, we have a range of 82, a mean of 145, a variance of 618.86 and a standard deviation of 24.88.

Step-by-step explanation:

1. Let's find the range for the set of numbers given:

Don't forget that range is a measure of dispersion and is the difference between the lowest and highest values in this set of numbers.

Range = 193 - 111

Range = 82

2. For calculating the standard deviation, we should calculate first the mean and the variance, this way:

Mean = Sum of all the terms / Number of the terms of the set

Mean = (111 + 122 + 134 + 146 + 150 + 159 + 193)/ 7

Mean = 1,015/7

Mean = 145

Now, we proceed to calculate the variance this way:

Variance= Sum of the squared distances of each term in the set from the mean/ Number of terms of the set or sample

Let's calculate the squared distances of each term in the set from the mean:

111 - 145 = - 34 ⇒ - 34² = 1,156

122 - 145 = - 23 ⇒ - 23² = 529

134 - 145 = - 11 ⇒ - 11² = 121

146 - 145 = 1 ⇒ 1² = 1

150 - 145 = 5 ⇒ 5² = 25

159 - 145 = 14 ⇒ 14² = 196

193 - 145 = 48 ⇒ 48² = 2,304

Now replacing with the real values:

Variance = (1,156 + 529 + 121  1+ 25 + 196 + 2,304)/7

Variance = 4,332/7

Variance = 618.86 (Rounding to two decimal places)

Finally, we can calculate easily the standard deviation:

Standard deviation = √Variance

Standard deviation = √ 618.86

Standard deviation = 24.88 (Rounding to two decimal places)

Answer:

343

Step-by-step explanation:

-(-7^3)=-(-7*-7*-7)=-(-343)=343

Answer:

Step-by-step explanation:

-(-7 to the power 3)

=-(-7×-7×-7)= -(-343)

=343

Answer:

Step-by-step explanation:

2 • (xy - 4cs)

The factors are: x-5 and x+3

Step-by-step explanation:

Given

[tex]x^2-2x-15 = 0[/tex]

Simplifying

[tex]x^2-5x+3x-15 = 0\\x(x-5) + 3(x-5) = 0\\(x+3)(x-5) = 0[/tex]

Let us define the zero product property first

The zero product property states that

if ab=0 then either a=0 or b=0

So,

[tex]x+3 = 0\\x+3-3 = 0-3\\x = -3\\AND\\x-5 = 0\\x-5+5 = 0+5\\x = 5[/tex]

Hence,

the factors are: x-5 and x+3

Keywords: Factorization, Zero product property

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Answer:

[tex]\displaystyle 6x + y = 4[/tex]

Step-by-step explanation:

In the Linear Standard Formula [Ax + By = C], C represents the y-intercept, and since the instructions say "parallel line", you keep your '6' the same, and just alter 5 to 4.

* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], which was why 6 remained the way it was.

I am joyous to assist you anytime.

Answer:

Infinitely many solutions

Step-by-step explanation:

-6(4x+3)=6(-4x-3)

-24x-18=-24x-18

infinitely many solutions

Answer:

This over here

Step-by-step explanation:

This over that

Answer:

5/6

Step-by-step explanation:

Add the fractions by finding the common denominator.

1/2 + 1/3

3/6 + 2/6

5/6

Answer:

Step-by-step explanation:

answer is W = 7 and A = 43.

The rate of the plane in still air is 43 miles per hour and the rate of the wind is 7 miles per hour.

Given that, Togo flew his ultralight plane to a landing field 30 miles away.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Let x represent the rate of the plane in still air.

Let y represent the rate of wind.

We know that, Distance = Speed × Time

Speed of flight with wind is x+y miles per hour

Speed of flight against wind is x-y miles per hour

With the wind, the flight took 3/5 hours.

Now, 30=3/5 (x+y)

50=x+y --------(I)

Returning against the wind, the flight took 5/6 hours.

30=5/6 (x-y)

36=x-y --------(II)

Add equation (I) and (II), we get

x+y+x-y=50+36

⇒ 2x=86

⇒ x=43 miles per hour

Substitute x=43 in equation (I), we get

43+y=50

⇒ y=7 miles per hour

Therefore, the rate of the plane in still air is 43 miles per hour and the rate of the wind is 7 miles per hour.

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