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3 years ago

39. The ratio of new houses to antique houses in a village is 4:5. If there are

Mathematics

1 answer:

jeyben [28]3 years ago

7 0

Step-by-step explanation:

☄ $\underline{ \underline{ \text{Question }}}:$ The ratio of new houses to antique houses in a village is 4 : 5 . If there are 12 new houses , how many antique houses are there ?

☄ $\underline{ \underline{ \text{Solution}}} :$

✏ Let , the number of antique houses in a village be ' x ' .

Then , According to the question :

$\sf{ \frac{Number \: of \: new \: houses}{Number \: of \: antique \: houses} \: = \: \frac{4}{5}}$

⤑ $\sf{ \frac{12}{x} = \frac{4}{5}}$

Apply cross product property

⤑ $\sf{4 \times x = 12 \times 5}$

⤑ $\sf{4x = 60}$

⤑ $\sf{ \frac{4x}{4} = \frac{60}{4}}$

⤑ $\sf{x = 15}$

So, The number of antique houses in a village is 15.

$\red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \bold{15}}}}}}$

Hope I helped ! ♡

Have a wonderful day / night ツ

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Bond [772]

Answer:

(a) Attached to this response.

(b)

(i) 0 cups = 0.275

(ii) 4 cups = 0.125

(iii) 8 cups = 0.025

Step-by-step explanation:

(a) The frequency and relative frequency table has been attached to this response.

i. The first column, labelled x, is the number of cups of coffee consumed per day.

ii. The second column, labelled f, is the number of people that consumed x cups of coffee per day. It is found by counting the number of occurrences (i.e frequency) of the numbers of the first column, x, in the given data.

For example, 0 in first column appears 11 times in the given data. Also, 5 in the first column appears 4 times in the given data.

iii. The third column, labelled r, is the relative relative frequency of the number of cups of coffee. It is calculated by dividing the frequency of the cups of coffee by the total number of people that consumed it. As shown on the table, it is calculated by dividing the each of the values on the second column by the sum of the values on that same column (second column).

For example, the relative frequency of 2 cups of coffee is given by:

r = 7 ÷ 40 = 0.175

Also, the relative frequency of 4 cups of coffee is given by;

r = 5 ÷ 40 = 0.125

(b) The probability (Pₓ) that a randomly selected person consumed x cups of coffee is given by;

Pₓ = frequency of x ÷ total frequency

This is also the relative frequency of x

Therefore,

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the relative frequency of 0 = 0.275

(ii) The probability (P₄) that a randomly selected person consumed 4 cups of coffee is given by;

the relative frequency of 4 = 0.125

(iii) The probability (P₈) that a randomly selected person consumed 8 cups of coffee is given by;

the relative frequency of 8 = 0.025

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3 years ago

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Step-by-step explanation:

Just so you know, there is a thing called calculator

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3 years ago

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Answer:

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Step-by-step explanation:

A linear relationship is a relationship of the form y = mx + b, where y and x are the linear variables, m is the rate of change and b is the value of y when x = 0.

Gym A:

Let x represent the month and y represent the total cost for the gym. From the table, we can represent the values in the form (x, y) as (1,70), (2, 90) and (3, 110). We can find the relationship between x and y using the formula:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\Let \ us\ use\ the\ points\ (1,70)\ and\ (3,110),hence:\\\\y-70=\frac{110-70}{3-1}(x-1)\\\\y-70=20(x-1)\\\\y=20x-20+70 \\\\y=20x+50\\\\For\ 10\ months(i.e.\ x=10):\\\\y=20x+50\\\\y=20(10)+50\\\\y=\$250$

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We can represent the values from the table as (1,55), (2, 80) and (3, 105). We can find the relationship between x and y using the formula:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\Let \ us\ use\ the\ points\ (1,55)\ and\ (3,105),hence:\\\\y-55=\frac{105-55}{3-1}(x-1)\\\\y-55=25(x-1)\\\\y=25x-25+55 \\\\y=25x+30\\\\For\ 10\ months(i.e.\ x=10):\\\\y=25x+30\\\\y=25(10)+30\\\\y=\$28 0$

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