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hammer [34]
3 years ago
7

Pls help i really am confused :/

Mathematics
1 answer:
madreJ [45]3 years ago
6 0

Answer:

x = 5

Step-by-step explanation:

x/40 = 7/56

Reduce the right fraction.

x/40 = 1/8

Now cross multiply.

8x = 40

Divide both sides by 8.

x = 5

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The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank?
posledela
S-Sam's\ age\\H-Hank's\ age\\\\  \left\{\begin{array}{ccc}\frac{S}{H}=\frac{5}{3}\\S+H=24&\to S=24-H\end{array}\right\\\\substitute\ S=24-H\ to\ \frac{S}{H}=\frac{5}{3}\\\\\frac{24-H}{H}=\frac{5}{3}\\\\cross\ multiply\\\\5H=3(24-H)\\5H=72-3H\\5H+3H=72\\8H=72\ \ \ /:8\\H=9\\\\Answer:Hank\ is\ 9\ years\ old.
7 0
3 years ago
(b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per
daser333 [38]

The question is incomplete. Below is the complete question:

A pill has the shape of a cylinder with a hemisphere at each end. The height of the cylindrical portion 11

mm and the overall height is 18 mm.

(a) Find the volume of the pill in cubic millimeters. Round to the nearest cubic

millimeter.

(b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per

cubic millimeter? Round to the nearest tenth of a cubic millimeter.

Answer:

a. 603 cubic millimetre

b. 1.7 mg/mm^3

Step-by-step explanation:

The since the pill has the shape of a cylinder and 2 hemispheres at both ends of the cylinder, if we are to calculate the volume, we will need the formula for calculating the volume of a cylinder and the volume of a hemisphere:

a. The volume of a cylinder = π×r^2×h and the volume of a hemisphere = 2×π×r^3.

The total height of the pill is 18mm but that of the cylinder specifically is 11cm, so 18 - 11 = 7mm.

This becomes the combined radius of the two hemispheres. We will now split it into 2:

7/2 = 3.5mm

This becomes the radius of each of the 2 hemispheres and will be used for calculating their respective volumes. The cylinder too will share same radius with the spheres (3.5mm). Let us take π as 3.14

Volume of the pill is then:

V =[2× (2/3 × π×r^3)] + π×r^2×h

V = [2×[(2/3) × 3.14 × 3.5^3]] + 3.14 × (3.5^2) × 11

[2 × (89.752)] + 423.115

179.504 + 423.115

= 602.619

= 603mm^3 (nearest cubic millimetre)

b. In order to find out how much vitamin C the pill will contain per cubic millimetre if it is to contain 1000mg of vitamin C, we will simply divide 1,000mg by the already calculated volume:

= 1000/63

= 1.658

= 1.7 mg/mm^3 (nearest tenth)

4 0
3 years ago
Triangle ABC has been reflected over the x-axis to create triangle A'B'C'. Which of the following statements is true?
Leto [7]

Answer:

A ' = (-2, -3)

B ' = (0, -3)

C ' = (-1, 1)

=======================================================

Explanation:

To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.

Algebraically, the reflection rule used can be written as

Applying this rule to the three given points will mean....

Point A = (-2, 3) becomes A ' = (-2, -3)

Point B = (0, 3) becomes B ' = (0, -3)

Point C = (-1, -1) becomes C ' = (-1, 1)

The diagram is provided below.

Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.

Step-by-step explanation:

7 0
2 years ago
11,12,15 please I am confuuuuused
mars1129 [50]

Answer:

11.x>50

12.y is greater than or equal to 8

15. z<8

Step-by-step explanation:

6 0
3 years ago
After the expression is simplified as much as possible, x is raised to what exponent?
IrinaVladis [17]
The answer to the question

7 0
3 years ago
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