MATHEMATICS COLLEGE

The length of a rectangular field is 4 m longer than its breadth. If the perimeter of the field is 44 m calculate:i) breadth
ii) the area of the field

Answers

Answer 1
Answer:

Step-by-step explanation:

Breadth = 8m

Length = 8m + 4m = 12m

Area of the rectangle = length × breadth, 12m × 8m = 96m square.

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QuestionCalculate the arc length for a circle whose radius is 6 with a central angle θ=135°. S=

Answers

9514 1404 393

Answer:

  S = 4.5π ≈ 14.14 units

Step-by-step explanation:

The arc length is given by ...

  s = rθ . . . . . r = radius; θ = central angle in radians

The angle 135° is ...

 135° = 135°(π/180°) = 3π/4 radians

The arc of interest has length ...

  s = 6×3π/4 = 9/2π ≈ 14.14 . . . units

A new car is purchased for 23,900 dollars. The value of the car depreciates at a rate of 6.4% per year. Which equation represents the value of the car after 4 years? Answer Multiple Choice Answers V, equals, 23, comma, 900, left bracket, 0, point, 9, 3, 6, right bracket, left bracket, 0, point, 9, 3, 6, right bracket, left bracket, 0, point, 9, 3, 6, right bracket, left bracket, 0, point, 9, 3, 6, right bracketV=23,900(0.936)(0.936)(0.936)(0.936) V, equals, 23, comma, 900, left bracket, 1, plus, 0, point, 0, 6, 4, right bracket, to the power 4V=23,900(1+0.064) 4 V, equals, 23, comma, 900, left bracket, 1, minus, 0, point, 0, 6, 4, right bracket, left bracket, 1, minus, 0, point, 0, 6, 4, right bracketV=23,900(1−0.064)(1−0.064) V, equals, 23, comma, 900, left bracket, 0, point, 0, 6, 4, right bracket, to the power 4V=23,900(0.064) 4

Answers

Answer:

V = 23,900(0.936)(0.936)(0.936)(0.936)

Step-by-step explanation:

AI-generated answer

The equation that represents the value of the car after 4 years is:

V = 23,900(0.936)(0.936)(0.936)(0.936)

Let's break it down step by step:

1. The initial value of the car is $23,900.

2. The car depreciates at a rate of 6.4% per year. This means that after each year, the car's value decreases by 6.4%.

3. To find the value of the car after 1 year, we multiply the initial value by 0.936 (100% - 6.4% = 93.6%).

4. To find the value of the car after 2 years, we multiply the value after 1 year by 0.936 again.

5. We repeat this process for 4 years, multiplying the value after each year by 0.936.

Therefore, the equation V = 23,900(0.936)(0.936)(0.936)(0.936) represents the value of the car after 4 years, taking into account the 6.4% annual depreciation rate.

Note: The other options given in the multiple-choice answers do not accurately represent the correct equation for calculating the value of the car after 4 years.

Roy is 11 years old and his uncle is 59 years old. How many years ago was Roy’s uncle 7 times as old as Roy?

Answers

Answer:

answer : 3 years ago

Step-by-step explanation:

Let x years ago.

59−x=7(11−x)

59−x=77−7x

6x=18

x=3

=3 years ago

Molly is at the Ice Cream Store. To get there, she went 1 unit right and 7 units down. Which location did Molly start from?

Answers

Answer:

To get to the ice cream store, Molly went 1 unit right and 7 units down. This means that she moved 1 unit to the right from her original position and 7 units down from her original position.

So, to find Molly's starting position, we need to move 1 unit to the left from the ice cream store and 7 units up from the ice cream store.

Therefore, Molly started from a location that is 1 unit to the left and 7 units up from the Ice Cream Store.

Step-by-step explanation:

A basketball player is 6ft 8in tall. A model of the basketball player is 5 inches tall. What is the scale factor

Answers

Answer:

1 ft. = 16 in.

Step-by-step explanation:

6 ft. 8 in. is 80 in.

then you would divide 80 by 5 to get 16.

not sure what scale factor you were looking for, so i did ft. to in.

not 100% sure though

best of luck!

The data set shows the number of practice free throws players in a basketball competition made and the number of free throws they made in a timed competition.Practice throws 312 614 2 710 8Free throws 10 22 9 35 4 11 28 20A. Use technology to find the equation AND coefficient of determination for each type of regression model. Use the number of practice throws for the input variable and the number of free throws for the output variable. Round all decimal values to three places. Equation of regression modelCoefficient of determinationLinear model Quadratic model Exponential model B. EXPLAIN, using the information you found above, which model best fits the data set. How did you come to your conclusion?Note: write exponents like this x^2 if you need to.

Answers

Let

x -----> number of practice throws

y -----> the number of free throws

Part A

Linear Model

Using a Linear Regression Calculator

we have

ŷ = 2.352X - 0.852

see the attached figure

Remember that

With linear regression, the coefficient of determination is equal to the square of the correlation between the x and y variables

the coefficient r=0.919

Quadratic model

Using a Quadratic regression Calculator

we have

y=0.073x^2+1.205x+2.555

correlation coefficient r=0.925 ------> strong correlation

see the attached figure

Exponential model

Using an Exponential Regression Calculator

we have

y=4.229(1.17)^x

Correlation:r=0.913

see the attached figure

Part B

The model that best fits the data is the Quadratic model because its value of r is greater than the linear model and greater than the exponential model
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