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2 years ago

A 120-liter solution that is 5% salt is mixed with an

1 answer:

vladimir2022 [97]2 years ago

4 0

Let’s add the solution and salt first
120 liter + 80 liter = 200
5% + 15% = 20%

The ratio is 20:200

20/200 = .10

The answer is 10% salt

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A group of vendors in a city determines that the equation yˆ=11.984x+15.341 models the total number of shorts they will sell eac

Virty [35]

Given the equation of a line of the form: y = mx + c, where m is the slope and c is the y-intercept.
y is the dependent variable while x is the independent variable.

The value c represents the initial value of the situation represented by the line. i.e. the value of the dependent variable (y) when the independent variable (x) is 0.

The value m is the slope and represents the amount with hich the dependent variable increases for each additional increase in the value of the independent variable.

Thus, given the equation: y=11.984x+15.341,
where: y represents the total number of shorts sold each day, and x represents the day’s high temperature in °F.

The slope is 11.984 or approximately 12 and it represents the increase in the number of shorts sold for each additional increase in temperature.

Therefore, the slope of the equation represents in context of the situation that 'The vendors will sell an additional 12 pairs of shorts for every 1° increase in temperature.' (option B)

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2 years ago

Read 2 more answers

Jason collects baseball cards. He bought one card for $25. Its current value is represented by the expression 25(1.02)t, where t

ki77a [65]

Is Jason’s baseball card going up by 2% every year for example

Jason’s baseball card after 1 year is
25×(1.02)^(1)=25.5
It increased by 0.5 in amount after one year

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2 years ago

G identify the solution of the recurrence relation an = 6an − 1 – 8an − 2 for n ≥ 2 together with the initial conditions a0 = 4,

maksim [4K]

Via the generating function method, let

$G(x)=\displaystyle\sum_{n\ge0}a_nx^n$

Then take the recurrence,

$a_n=6a_{n-1}-8a_{n-2}$

multiply everything by $x^n$ and sum over all $n\ge2$ :

$\displaystyle\sum_{n\ge2}a_nx^n=6\sum_{n\ge2}a_{n-1}x^n-8\sum_{n\ge2}a_{n-2}x^n$

Re-index the sums or add/remove terms as needed in order to be able to express them in terms of $G(x)$ :

$\displaystyle\sum_{n\ge2}a_nx^n=\sum_{n\ge0}a_nx^n-(a_0-a_1x)=G(x)-4-10x$

$\displaystyle\sum_{n\ge2}a_{n-1}x^n=\sum_{n\ge1}a_nx^{n+1}=x\sum_{n\ge1}a_nx^n=x\left(G(x)-a_0\right)=x(G(x)-4)$

$\displaystyle\sum_{n\ge2}a_{n-2}x^n=\sum_{n\ge0}a_nx^{n+2}=x^2\sum_{n\ge0}a_nx^n=x^2G(x)$

So the recurrence relation is transformed to

$G(x)-4-10x=6x(G(x)-4)-8x^2G(x)$
$(1-6x+8x^2)G(x)=4-14x$
$G(x)=\dfrac{4-14x}{1-6x+8x^2}=\dfrac{4-14x}{(1-4x)(1-2x)}=\dfrac1{1-4x}+\dfrac3{1-2x}$

For appropriate values of $x$ , we can express the RHS in terms of geometric power series:

$G(x)=\displaystyle\sum_{n\ge0}(4x)^n+3\sum_{n\ge0}(2x)^n=\sum_{n\ge0}\bigg(4^n+3\cdot2^n\bigg)x^n$

which tells us that

$a_n=4^n+3\cdot2^n$

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2 years ago

Sergio has ppp paintings in his art collection. He and other local painting collectors agreed to donate a total of 484848 painti

Crazy boy [7]

Answer:

484848

121212

±________

606,606

8 0

2 years ago

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The equation A(t) = 900(0.85)t represents the value of a motor scooter t years after it was purchased. Which statements are also

ValentinkaMS [17]

Answer:

When new, the scooter cost $900

Step-by-step explanation:

The complete question in the attached figure

we have

$A(t)=900(0.85)^t$

This is a exponential function of the form

$A(t)=a(b)^t$

where

A(t) ----> represent the value of a motor scooter

t ----> the number of years after it was purchased

a ---> represent the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

b=(1+r)

In this problem we have

$a=\$900\\b=0.85$

The base b is less than 1

That means ----> is a exponential decay function (is a decreasing function)

Find the percent rate of change

$b=(1+r)\\0.85=1+r\\r=0.85-1\\r=-0.15$

Convert to percentage (multiply by 100)

$r=-15\%$ ---> negative means is a decreasing function

Verify each statements

case A) When new, the scooter cost $765.

The statement is false

Because the original value of the scooter was $900

case B) When new, the scooter cost $900

The statement is true (see the explanation)

case C) The scooter’s value is decreasing at a rate of 85% each year

The statement is false

Because the scooter’s value is decreasing at a rate of 15% each year (see the explanation)

case D) The scooter’s value is decreasing at a rate of 0.15% each year

The statement is false

Because the scooter’s value is decreasing at a rate of 15% each year (see the explanation)

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2 years ago