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Dad is 3 times as old as his son, Jim. In 20 years, Dad's age will be 2 years less than twice Jim's age. How old is Jim?

If D = dad's age now and J = Jim's age now, which of the following systems could be used to solve the problem?


D = 3J and D + 20 = 3J - 2
D = 3J and D + 20 = 2(3J + 20) - 2
D = 3J and D + 20 = 2(J + 20) - 2
D = 3J and D + 20 = 3J + 20 - 2

Answer:

Step-by-step explanation:

min: 8

max: 28

median: 22

1st Q: 12

3rd Q:26

Answer:

288 in3

Step-by-step explanation:

Volume of a cube is 216 in3, in cube, l=w=h so its' length, width, and height are equal to 6 in. Its' height is 2 inches longer than its width so it is equal to 8. 6 x 6 x 8 = 288 (in3)

The straight line distance between the start and finish point is required.

The straight line distance is 5.7 miles.

a = Distance traveled north = 4 miles

b = Distance traveled east = 4 miles

c = Straight line distance

The angle between the two paths is ninety degrees so, the Pythagoras theorem can be applied here.

Applying the Pythagoras theorem

[tex]c=\sqrt{a^2+b^2}\\\Rightarrow c=\sqrt{4^2+4^2}\\\Rightarrow c=4\sqrt{2}\\\Rightarrow c=5.7\ \text{miles}[/tex]

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Answer:

58 and 12

Step-by-step explanation:

CHECK:

58 + 12 = 70

70 - 58 = 12

NOW GO LISTEN TO ALEC BENJAMINS NEW SONG, THE WAY YOU FELT

Answer:

x is 41 and y is 29

Step-by-step explanation:

x plus y is 70 and x minus y is 12

subtract 2 from 1

2y=58

y is 29 and x is

29 plus x is 70 so.....x is41

Answer: I need help

Step-by-step explanation:

Answer: 0.50

Step-by-step explanation:

Given:

Total number of students = 27

Students who play basketball = 7

Student who play baseball = 18

Students who play neither sports = 7

To find:

The probability the student chosen at randomly from the class plays both basketball and base ball.

Solution:

Let the following events,

A : Student plays basketball

B : Student plays baseball

U : Union set or all students.

Then according to given information,

[tex]n(U)=27[/tex]

[tex]n(A)=7[/tex]

[tex]n(B)=18[/tex]

[tex]n(A'\cap B')=7[/tex]

We know that,

[tex]n(A\cup B)=n(U)-n(A'\cap B')[/tex]

[tex]n(A\cup B)=27-7[/tex]

[tex]n(A\cup B)=20[/tex]

Now,

[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]

[tex]20=7+18-n(A\cap B)[/tex]

[tex]n(A\cap B)=7+18-20[/tex]

[tex]n(A\cap B)=25-20[/tex]

[tex]n(A\cap B)=5[/tex]

It means, the number of students who play both sports is 5.

The probability the student chosen at randomly from the class plays both basketball and base ball is

[tex]\text{Probability}=\dfrac{\text{Number of students who play both sports}}{\text{Total number of students}}[/tex]

[tex]\text{Probability}=\dfrac{5}{27}[/tex]

Therefore, the required probability is [tex]\dfrac{5}{27}[/tex].

Answer:

[tex](a)\ (1 + 3x)^6 = 728x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1[/tex]

[tex](b)\ (1 + 3(-0.01))^6 = 0.8330[/tex]

Step-by-step explanation:

Given

[tex](1 + 3x)^6[/tex]

Solving (a): Expand

To do this, we make use of pascal triangle

When the exponent is 6, the factors are: 1, 6, 15, 20, 15, 6 and 1

As a rule, the exponent of 1 will start from 0 and then increase by 1 in each term while the exponent of 3x will start from 6 and then decrease by 1 in each term.

So, we have:

[tex](1 + 3x)^6 = 1 * 1^0 * (3x)^6 + 6 * 1^1 * (3x)^5 + 15 * 1^2 * (3x)^4 + 20 * 1^3 * (3x)^3 + 15 * 1^4 * (3x)^2 + 6 * 1^5 * (3x)^1 + 1 * 1^6 * (3x)^0[/tex]

Expand

[tex](1 + 3x)^6 = 1 * (3x)^6 + 6 * (3x)^5 + 15 * (3x)^4 + 20 * (3x)^3 + 15 * (3x)^2 + 6 * (3x)^1 + 1 * (3x)^0[/tex]

[tex](1 + 3x)^6 = 1 * 728x^6 + 6 * 243x^5 + 15 * 81x^4 + 20 * 27x^3 + 15 * 9x^2 + 6 * 3x + 1[/tex]

[tex](1 + 3x)^6 = 728x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1[/tex]

Solving (b): (0.97)^6

Rewrite as:

[tex](0.97)^6 = (1 - 0.03)^6[/tex]

Express -0.03 as 3 * -0.01

[tex](0.97)^6 = (1 + 3(-0.01))^6[/tex]

So, by comparing:

[tex](1 + 3x)^6[/tex] and [tex](1 + 3(-0.01))^6[/tex]

[tex]x = -0.01[/tex]

Recall that:

[tex](1 + 3x)^6 = 728x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1[/tex]

This gives:

[tex](1 + 3(-0.01))^6 = 728(-0.01)^6 + 1458(-0.01)^5 + 1215(-0.01)^4 + 540(-0.01)^3 + 135(-0.01)^2 + 18(-0.01) + 1[/tex]

Using a calculator

[tex](1 + 3(-0.01))^6 = 0.000000000728 -0.0000001458+ 0.00001215 -0.00054 + 0.0135 -0.18 + 1[/tex]

[tex](1 + 3(-0.01))^6 = 0.83297200492[/tex]

[tex](1 + 3(-0.01))^6 = 0.8330[/tex] --- approximated

If function f(x)= x² then g(x) is  -x² - 3 , option A is correct.

A relation is a function if it has only One y-value for each x-value.

The reflection in the x-axis changes the sign of the y-coordinate. So, the reflection of f(x) = x² in the x-axis is g(x) = -x².

Secondly, the downward shift of 3 units means subtracting 3 from the y-coordinate.

So, the transformation applied to f(x) to get g(x) is reflection in the x-axis followed by a downward shift of 3 units.

g(x) = -x² - 3 is the result of applying a reflection in the x-axis followed by a downward shift of 3 units to the function f(x) = x².

Hence, if function f(x)= x² then g(x) is  -x² - 3 , option A is correct.

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Answer:

16

Step-by-step explanation:

if 5 white cups and 8 green 10 white cups and 16 green

5 × 2 = 10

8 × 2 = 16

Answer:

16

Step-by-step explanation:

Because 5*2=10 so 8*2=16.

Have a great day. And be you.

Answer:

i didnt pray for these baguettes i prayed for better days

Step-by-step explanation:

you know?

Answer:

36

Step-by-step explanation:

You coun the base there has 10 square.

Then the two side is 13 and 13

So add up three of it so the answer is 36

Answer:

C = 65.94 ft and A = 346.185 ft^2

Step-by-step explanation:

r = d/2 = 21/2 = 10.5

let [tex]\pi[/tex] = 3.14

C = 2[tex]\pi[/tex]r

C = 2(3.14)(10.5) = 65.94 ft

A = [tex]\pi[/tex]r^2

A = (3.14)(10.5)^2 = 346.185 ft^2

The solution is: the circumference of the circle is C = 65.94 ft and, the area of the circle A = 346.185 ft^2.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

given that,

diameter of the circle = 21

so, we have,

r = d/2

 = 21/2

 = 10.5

let  

π= 3.14

we know that,

the circumference of the circle is:

C = 2rπ

C = 2(3.14)(10.5)

   = 65.94 ft

the area of the circle is:

A =π r^2

A = (3.14)(10.5)^2

  = 346.185 ft^2

Hence, The solution is: the circumference of the circle is C = 65.94 ft and, the area of the circle A = 346.185 ft^2.

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Answer:

[tex]Q_n=(2000)-(20)P_n[/tex]

Step-by-step explanation:

From the question we are told that:

Initial Quantity demanded Q_1= 200 units

Initial demand price [tex]P_1=\$90[/tex]

Final Quantity demanded [tex]Q_2= 1200 units[/tex]

Final demand price [tex]P_2=\$40[/tex]

Generally the  Demand Equation is mathematically given by

 [tex]Q_n=a-bP_n[/tex]

Where

a=Other factors affecting price

b=Slope of the demand curve

Therefore

 [tex]Q_1=a-bP_1[/tex]

 [tex]200=a-b(90)[/tex]

 [tex]Q_2=a-bP_2[/tex]

 [tex]1200=a-b(40)[/tex]

Comparing both above equations

  [tex]a=2000[/tex]

  [tex]b=20[/tex]

Therefore the  Demand Equation is mathematically given by

  [tex]Q_n=(2000)-(20)P_n[/tex]

Answer:

D $175

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the tree goes up, meaning it is positive 3. the others represent things being below or decreasing, meaning they are negative.

Answer:

c i think

Step-by-step explanation:

im sorry if its wrong

So sorry I messed it up I let you down :(

Answer:

55 cm²

Step-by-step explanation:

In a parallelogram, the top base is equal to the bottom base (and the sides are equal to each other too!)

So the top and bottom base are both 9, and the left and right sides are both 5.

So, to solve, we need to use the equation:

(4 + 1) * (9 + 2) = 5 * 11 = 55 cm²

Answer:

376*74=

Step-by-step explanation:

[tex]376 \times 74 = 27824 \\[/tex]

Answer:

4 in.

Step-by-step explanation:

The surface area of a cube is the area of one of the faces times 6 for each face.

96/6=16

16 is the area of one face of the cube.

The side of the face is the square root of the area of the face.

√16=4

Answer:

4in

Step-by-step explanation:

I had the same problem but revirsed

Answer:

[tex]2\frac{1}{10}[/tex]

Step-by-step explanation:

Answer:

2 1/10

Step-by-step explanation:

Answer:

[tex]y=\frac{1}{2} x+8[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

Perpendicular lines will always have slopes that are negative reciprocals of each other. For example, two perpendicular lines might have slopes of 3 and -1/3.

After observing the equation y=-2x-5, we can conclude that the slope is -2. Therefore, a line perpendicular to this line would have a slope of 1/2. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{1}{2} x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{1}{2} x+b[/tex]

Plug in the given point (-4,6)

[tex]6=\frac{1}{2}(-4)+b\\6=-2+b[/tex]

Add 2 to both sides

[tex]6+2=-2+b+2\\8=b[/tex]

Therefore, the y-intercept is 8. Plug this back into [tex]y=\frac{1}{2} x+b[/tex]:

[tex]y=\frac{1}{2} x+8[/tex]

I hope this helps!

Answer:

V≈ 2521.91 mm cubed

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

201.06

Step-by-step explanation:

3.14 * 8^2= 201.06

(pi * radius ^ squared)

Answer:

A turtle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you deposit $7300 into an account paying 100% annual interest compounded yearly , how much money will be in the account after 15 years?

Result:

The amount is $239206400.

Explanation:

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

Answer:

15341

Step-by-step explanation:

\text{Doubling Formula:}

Doubling Formula:

y=a(2)^{\frac{t}{d}}

y=a(2)  

d

t

​  

a=7300\hspace{40px}d=14\hspace{40px}t=15

a=7300d=14t=15

d is the doubling time

\text{Plug in:}

Plug in:

y=7300(2)^{\frac{15}{14}}

y=7300(2)  

14

15

​  

y=15341.0469243

y=15341.0469243

Answer:

The highest observation =20

The lowest observation = 1

Range of the data = 20-1

= 19(ans)

Answer:

The range is 19

Step-by-step explanation:

To calculate the range of a set of data, you order the numbers from highest to lowest (ex; 20,20,19,18,16,12,12,10,8,8,7,6,4,4,3,1,1) then you subtract the highest number from the lowest number (ex; 20 - 1)

Answer:

D is the right graph