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3 years ago

the age of Jane is 80% of the age of Alice. If we add both ages the result is 45. Find the age of Jane and Alice

Mathematics

1 answer:

inysia [295]3 years ago

5 0

Answer:

Age of Alice=25 years

Age of Jane=20 years

Step-by-step explanation:

We are given that the age of Jane is 80 % of the age Alice.

We have to find the age of Jane and Alice.

Let x be the age of Alice

According to question

Age of Jane=80% of Alice=80% of x= $\frac{80}{100}\times x=\frac{4x}{5}$

$x+\frac{4x}{5}=45$

$\frac{5x+4x}{5}=45$

$\frac{9x}{5}=45$

$x=\frac{45\times 5}{9}=25$

Age of Alice=25 years

Age of Jane= $\frac{4}{5}\times 25=20 years$

Age of Jane=20 years

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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

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Answer:

B) 25

Step-by-step explanation:

Given exponential function:

$f(x)=3(5)^x$

The growth factor between $x=1$ and $x=3$ is 25.

To find the growth factor between $x=5$ and $x=7$

Solution:

The growth factor of an exponential function in the interval $x=a$ and $x=b$ is given by :

$G=\frac{f(b)}{f(a)}$

We can check this by plugging in the given points.

The growth factor between $x=1$ and $x=3$ would be calculated as:

$G=\frac{f(3)}{f(1)}$

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$f(1)=3(5)^1$

Plugging in values.

$G=\frac{3(5)^3}{3(5)^1}$

$G=\frac{(5)^3}{(5)^1}$ (On canceling the common terms)

$G=(5)^{(3-1)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

Similarly the growth factor between $x=5$ and $x=7$ would be:

$G=\frac{f(7)}{f(5)}$

$f(7)=3(5)^7$

$f(5)=3(5)^5$

Plugging in values.

$G=\frac{3(5)^7}{3(5)^5}$

$G=\frac{(5)^7}{(5)^5}$ (On canceling the common terms)

$G=(5)^{(7-5)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

Thus, the growth factor remains the same which is =25.

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2 years ago

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2 years ago

It takes 1/5 a cup of flour to make one small pizza. How many small pizzas could be 7/10 made with

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3 1/2 small pizzas

Step-by-step explanation:

1/5 = 1 pizza

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2 years ago

A fruit market equally divided 80 red apples into 8 containers, and equally divided 54 green apples into 6 containers. Natalie b

Goryan [66]

Answer:

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Step-by-step explanation:

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7 0

2 years ago

can someone pls help me? i have no idea what to do. pls show the work steps for the questions. i will mark u as

tiny-mole [99]

Ok, so the question is based on geometric progression. Remember, the formula for calculating the nth-term of a geometric progression is: $a*r^{n-1}$ . The a in the expression stands for the 1st term of the sequence, and r is the common ratio of the elements of the sequence. Now let's take a look at the problem.

"A ping pong ball has a 75% rebound ration". We can infer that our common ratio, r, is 75% which is 0.75.

"When you drop it from a height of k feet...", this means the first height you drop it from, a.k.a, the first term.

Now going back to the expression, the nth-term = $a*r^{n-1}$ , we can substitute our common ration, 0.75 with r, and our 1st term, k, with a. This becomes: $k * 0.75^{n-1}$ . This becomes our expression.

a. The highest height achieved by the ball after six bounces. Our nth-term here is 6, so let's use our expression to find the 6th term. $n_{6} = 235 * 0.75^{6-1} = 235*0.75^{5} = 235*0.2373 = 55.7655ft$

b. The total distance travelled by the ball when it strikes the ground for the 12th time. This involves the use of the sum of elements in the geometric progression. The formula for that is $\frac{a(1 - r^{n})}{1-r}$ , provided that r is less than 1, which it is in this case, since 0.75 is less than one. Our nth-term here is 12, so we substitute.

$\frac{235(1-0.75^{12})}{(1-0.75)} = 910.2242ft$

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2 years ago