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3 years ago

Kevin is 3 times as old as Daniel. 4 years ago, Kevin was 5 times as old as Daniel. How old is Daniel now

Mathematics

1 answer:

matrenka [14]3 years ago

7 0

K = 3D. K - 4 = 5(D - 4). K - 4 = 5D - 20. K = 5D - 16. 3D = 5D - 16. 16 = 2D. D = 8. K = 3 x 8. K = 24.

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One tank is filling at a rate of 5/8 gallon per 7/10 hour. A second tank is filling at a rate of 5/9 gallon per 2/3 hour. Which

anzhelika [568]

First recognize that the unit rate we're finding is gallons per hour, or $\frac{g}{h}$ .

rate for Tank 1 = x gallons per hour = a gallons / b hours

$T_{1}=\frac{\frac{5}{8}}{\frac{7}{10}}\\\\T_{1}=\frac{5}{8}*\frac{10}{7}\\\\T_{1}=\frac{50}{56}\\\\\\Fill\ rate\ of\ Tank\ 1=\frac{25}{28}$

rate for Tank 2 = y gallons per hour = c gallons / d hours

$T_{2}=\frac{\frac{5}{9}}{\frac{2}{3}}\\\\T_{2}=\frac{5}{9}*\frac{3}{2}\\\\T_{2}=\frac{15}{18}\\\\T_{2}=\frac{15}{18}\\\\\\Fill\ rate\ of\ Tank\ 2=\frac{5}{6}$

3 0

3 years ago

In which atmosphere layer do humans live most of their lives?

icang [17]

Answer:

Troposphere

Step-by-step explanation:

We humans live in the troposphere, and nearly all weather occurs in this lowest layer. Most clouds appear here, mainly because 99% of the water vapor in the atmosphere is found in the troposphere.

5 0

3 years ago

Please answer this with explanation. Please I really am struggling. I will mark you brainalist. Please solve it Please

Hatshy [7]

Answer:

13, 11, 4, 16, 6, 22

Step-by-step explanation:

Let the second digit be x and the last digit be y

Given:

Data set: 13, x, 4, 16, 6, y
Mean = 12
y = 2x or x = 2y

The mean of the data is the average. The average can be calculated by determining the sum of the terms and dividing it by the total digits.

$\implies \text{Mean of data:} \ \dfrac{13 + x + 4 + 16 + 6 + y}{6} = 12$

Let us substitute the value of y (2x) in the data.

$\implies \dfrac{13 + x + 4 + 16 + 6 + 2x}{6} = 12$

Now, add all the terms in the data and simplify.

$\implies \dfrac{39 + x +2x}{6} = 12$

$\implies \dfrac{39 + 3x}{6} = 12$

Distribute the denominators and simplify.

$\implies \dfrac{39}{6} + \dfrac{3x}{6} = 12$

$\implies \dfrac{13}{2} + \dfrac{x}{2} = 12$

$\implies 6.5 + \dfrac{x}{2} = 12$

Subtract 6.5 both sides and simplify.

$\implies 6.5 + \dfrac{x}{2} - 6.5 = 12 - 6.5$

$\implies \dfrac{x}{2} = 5.5$

Use cross multiplication and simplify.

$\implies x= 5.5 \times 2$

$\implies x= 11$

To determine the value of "y", simply substitute the value of "x" into the expression that represents the value of "y".

$\implies y = 2x$

$\implies y = 2(11)$

$\implies y = 22$

When the x and y values are substituted in the data, we get;

⇒ 13, 11, 4, 16, 6, 22

Therefore, the data is 13, 11, 4, 16, 6, 22.

8 0

2 years ago

Please hepl with math

Ivenika [448]

Answer:

$\dfrac{5^{n+2}-6\times 5^{n+1}}{13 \times5^{n}-2\times5^{n+1}} = -\dfrac{5}{3}$

Step-by-step explanation:

We are given the expression to be simplified:

$\dfrac{5^{n+2}-6\times 5^{n+1}}{13 \times5^{n}-2\times5^{n+1}}$

Let us take common a term with a power of 5 from the numerator and the denominator of the given expression.

We know that:

$a^{p+q} = a^p \times a^q$

Let us use it to solve the powers of 5 in the given expression.

$\therefore$ we can write:

$5^{n+2} = 5^{n+1}\times 5= 5^n\times 5^{2}$

$5^{n+1} = 5^n\times 5$

The given expression becomes:

$\dfrac{5^{n+1} \times 5-6\times 5^{n+1}}{13 \times5^{n}-2\times5^{n}\times 5}$

Taking common $5^{n+1}$ from the numerator and

Taking common $5^{n}$ from the denominator

$\Rightarrow \dfrac{5^{n+1} (5-6)} {5^{n}(13-2\times5)}\\\Rightarrow \dfrac{5^{n+1} (-1)} {5^{n}(13-10)}\\\Rightarrow -\dfrac{5^{n+1}} {5^{n}\times3}\\\Rightarrow -\dfrac{5^{n}\times 5} {5^{n}\times3}\\\Rightarrow -\dfrac{5}{3}$

$\therefore$ The answer is:

$\dfrac{5^{n+2}-6\times 5^{n+1}}{13 \times5^{n}-2\times5^{n+1}} = -\dfrac{5}{3}$

6 0

3 years ago

This looks pretty easy... I just am not sure how to figure it out....What is the value of the x variable in the solution to the

kakasveta [241]

Express x from the secondequation: x=3+y.
Then substitude it in first equation:

4(3+y)+2y=12,
4·3+4y+2y=12,
12+6y=12,
6y=12-12,
6y=0,
y=0 and x=3+0=3
Answer: (3,0)

8 0

3 years ago