Assume that you are starting a retirement annuity that pays 4.5% annual interest compounded monthly. You

The first floor of a house consists of a kitchen, playroom, and dining room. The areas of the kitchen, playroom, and dining room

lozanna [386]

Answer: See explanation

Step-by-step explanation:

From the question, we are informed that the areas of the kitchen, playroom, and dining room are in the ratio 4 : 3 : 2 and that the combined area of these three rooms is 189 square feet.

Therefore, Kitchen area = 4/(4+3+2) × 189 = 4/9 × 189 = 84 square feet

Playroom area = 3/(4+3+2) × 189 = 3/9 × 189 = 63 square feet

Dining room area = 2/(4+3+2) × 189 = 2/9 × 189 = 42 square feet

5 0

3 years ago

Find the average rate of change of the function y=f(x)=1/(x-1)^2-8 with respect to x on the interval -2≤x≤0

Verdich [7]

Answer:

The average rate of change is (f(3)-f(0))/3=(7-0)/3=7/3.

Step-by-step explanation:

8 0

3 years ago

The table below shows the number of pencils and pens three friends have in their backpacks.

anyanavicka [17]

Answer:

Angel has a greater ratio of pencils to pens.

i.e. Angle's pencils to pens = 3 / 2 or 63/42

Thus, option (B) is true.

Step-by-step explanation:

Considering the table

Lydia's Number of Pencils = 10

Lydia's Number of Pens = 7

Lydia's Pencils to Pens ratio = 10/7

Angel's Number of Pencils = 9

Angel's Number of Pens = 6

Angels's Pencils to Pens ratio = 9/6 = 3 / 2

Elizabeth's Number of Pencils = 12

Elizabeth's Number of Pens = 9

Elizabeth's Pencils to Pens ratio = 12/9 = 4 / 3

So, We get the inputs ratios such as:

Lydia's ratio: Angels's ratio: Elizabeth's ratio

10/7 : 3 / 2 : 4 / 3

As the least common denominator (LCD) is: 42

Rewriting as equivalent fractions with the LCD:

10/7 : 3 / 2 : 4 / 3

60 / 42 : 63/42 : 56/42

Sorting from least to greatest:

Sorting this table by the numerators of the equivalent fractions in order from least to greatest:

Elizabeth's ratio : Lydia's ratio : Angels's ratio:

4/3 : 10 /7 : 3 / 2

56/42 : 60 / 42 : 63/42

Therefore, Angel has a greater ratio of pencils to pens.

i.e. Angle's pencils to pens = 3 / 2 or 63/42

Thus, option (B) is true.

8 0

3 years ago

Cindy works at Jurassic Park and has been tasked to design a container in the shape of a

vichka [17]

The amount Cindy should increase for each dimension of the scaled model will be 12 meters.

<h3>What is the scale factor?</h3>

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Given that:-

The scaled model of the container has dimensions of 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model.

The scale model will be solved as follows:-

Present volume = 2 x 4 x 6 = 48 cubic meters

Let the lengths be increased by x meters now the new volume will be:-

( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84

( x² + 6x + 8 ) ( 6 + x ) = 48 x 84

( x³ + 44x + 12x² - 3984 ) = 0

By solving the cubic equation we will get the value of x = 12 meters.

Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.

To know more about scale factors follow

brainly.com/question/25722260

#SPJ1

8 0

2 years ago

I have been stuck on this forever can you please help

Aneli [31]

6 acts as the base. 15 acts as the height, because it extends from the base to meet vertex opposite the base at a 90° angle.

General formula for triangle area
a = 1/2 × b × h

plug in the numbers
a = 1/2 × 6 × 15
a = 90/2
a = 45

The area of the triangle is 45 units²

8 0

4 years ago