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3 years ago

The ratio of Rogers age to his sons is 7:3. If the sum of their ages are 60 how old is Rogers son

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

5 0

Answer:24

Step-by-step explanation:

Sum of their ages is 60 yr. As such

7x + 3x = 60

10x = 60

x = 60 / 10

x = 6

The rationale is 6, therefore

Father's age is 7x = 7 × 6= 42 years

Son's age is 3x = 3 × 6 = 18 years

Difference in their ages

42 - 18 = 24 years

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2 years ago

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The diameter of a circle is 3 ft. Find its area to the nearest tenth.

tatiyna

Answer:

A= 7.07ft squared

Step-by-step explanation:

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2 years ago

8. Is the following statement true or false? Justify your conclusion. If a and b are nonnegative real numbers and a + b =0, then

atroni [7]

Answer:

If $a + b = 0$ then $a = 0$ and $b =0$

a | b | a + b (answer)

0 | 0 | 0

0 | 1 | 1

0 | 2 | 2

1 | 0 | 1

2 | 0 | 2

1 | 1 | 2

2 | 1 | 3

Step-by-step explanation:

Considering the following conditions for the real numbers:

$a\geq 0\\b\geq 0$

Following the rules of these in-equations, it is possible to deduce:

$a + b \geq 0$

Then, if the proposed statement is:

$a + b = 0$

The conditions above shall comply the requirements established, but first, analyzing the statement:

If $a \geq 0$ and $b \geq 0$ then $a + b \geq a$ , $a + b \geq b$ and $a + b \geq 0$ .

If $a = 0$ and b a non negative real number, then $a + b \geq b$ , but because to $a = 0$ , then $a + b = b$ . Due to the commutative property of sums, the same behavior will be presented if $b = 0$ and a a non negative real number.

According to that, if $a + b = 0$ , then $a = 0$ and $b = 0$ .

7 0

3 years ago

Listed below are prices in dollars for one night at different hotels in a certain region. Find the range, variance, and standar

Artyom0805 [142]

Answer:

Range = 115$

Standard Deviation = 43.76$

Variance = 1915.142$

Option A) The measures of variation are not very useful because when searching for a room, low prices, location, and good accommodations are more important than the amount of variation in the area.

Step-by-step explanation:

We are given the data for prices in dollars for one night at different hotels in a certain region.

234, 160, 119, 131, 218, 207, 146, 141

Range:

Sorted data: 119, 131, 141, 146, 160, 207, 218, 234

$\text{Range} = 234-119 = 115\$$

Standard Deviation:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1356}{8} = 169.5$

Sum of squares of differences = 4160.25 + 90.25 + 2550.25 + 1482.25 + 2352.25 + 1406.25 + 552.25 + 812.25 = 13406

$\sigma = \sqrt{\dfrac{13406}{7}} = 43.76\$$

Variance =

$\sigma^2 = 1915.142\$$

Measure of variance for someone searching for room:

Option A) The measures of variation are not very useful because when searching for a room, low prices, location, and good accommodations are more important than the amount of variation in the area.

5 0

3 years ago

The Capacity of a 1 cm cube is 1 mL. How many 1 cm ice cubes do you need to melt to fill a 1.5 L jar.

Svetach [21]

1500 ice cubes need to fill 1.5 L jar

Solution:

1 cm = 1 ml

Capacity of ice cube = 1 cm

= 1 ml

Capacity of jar = 1.5 L

1 L = 1000 ml

1.5 L = 1.5 × 1000

= 1500 ml

Capacity of jar = 1500 ml

$$\text{Number of ice cubes} =\frac{\text{Capacity of ice cube}}{\text{Capacity of jar}}$

$$=\frac{1500}{1}$

= 1500

Therefore 1500 ice cubes need to fill 1.5 L jar.

8 0

3 years ago