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The diameter of a sphere is 42 centimeters. find the surface area to the nearest tenth

Mademuasel [1]

A ~ 5541.77cm squared

8 0

3 years ago

PLEASE HELP WILL GIVE BRAINLIEST Which of the following scale factors will result in an enlargement? A. k < –1 B. –1 < k &

Sergio [31]

Answer: OPTION A.

Step-by-step explanation:

By definition, a dilation can be an enlargement or a reduction of the shape.

An enlargement is when dilation creates a larger image and a reduction is when dilation creates a smaller image.

When, the scale factor is greater than 1, the image is an enlargement and when the scale factor is between 0 and 1, the image is a reduction.

It is important to know that with a negative scale factor the enlargement will will be inverted and it will also be on the other side of the center of dilation.

Knowing this, we can say that the scale factor that will result in an enlargement is:

$k$

5 0

2 years ago

$500 are deposited into an account semiannuallysemiannually for six years at an interest rate of 7.2% compounded semiannually.

kobusy [5.1K]

Each year 107.2%increase of budget
first year 500 * 1.072 = 536
second year 536 * 1.072 = 574.592
third year 574.592 * 1.072 = 615.962624
..
..
sixth year 707.854392 * 1.072 = 758.819908

or you can just (1.072)^6 * 500 = 1.517639816659862 * 500 = 758.8199083299308

bingo........

8 0

2 years ago

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The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the pris

Georgia [21]

Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume = 80 tan 36° × 16 = 1280 tan 36° = 1280 × 0.726542528

volume = 929.974435847 cm³

volume ≈ 930 cm³ (nearest cubic cm)

5 0

3 years ago

A box contains 75 red and 25 green light bulbs. it is found that 20 bulbs in the box are defective, of which 2 are red. what is

Afina-wow [57]

Answer:

15 bulbs are red.

Step-by-step explanation: Because 75 is 3 times as big as 25 so every 1 green light bulb 3 red light bulbs will be deflective.

8 0

2 years ago