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2 years ago

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When jeremy gets his allowance he agrees to save part of it his savings and expenses are in the ratio of 7:5 if his daily allowa

nce is $3,find how much he saves each day?

1 answer:

nignag [31]2 years ago

8 0

He saves $ 1.75 each day from his allowance.

<u><em>Explanation</em></u>

The ratio of his savings and expenses is 7 : 5

Lets assume, his savings = 7x dollar and his expenses is 5x dollar

Given that, his daily allowance is $3. So....

$7x+5x=3\\ \\ 12x=3\\ \\ x=\frac{3}{12}= \frac{1}{4}= 0.25$

So, the amount of his savings each day $=7x= (7*0.25)dollar= 1.75 dollar$

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When converting a linear equation into Slope Intercept form, what is our main goal? Vour answer

Eddi Din [679]

Answer:

You have to make sure the y= is always on the left side and so it looks like ,y=mx+b. m=slope, x=independent variable and b = y intercept.

Step-by-step explanation:

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2 years ago

A number y increased by 5 is at least -21

gayaneshka [121]

- - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - -

$\diamond\large\blue\textsf{\textbf{\underline{\underline{Given question:-}}}}$

❖ A number y increased by 5 is at least -21.

$\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}$

❖ First, if you come across the word "increased" it means we

"increase" a number, or add something to that number, like

y increased by 5 $\longmapsto$ $\sf{y+5}$

Now, we are also given that this expression is at least -21, which means it can't be -21; it can be -21 or it can be greater than -21.

So we have

$\longmapsto\sf{y+5\geq -21}}$

<em>Solving for y</em>

<em></em>

Subtract 5 on both sides:-

$\longmapsto\sf{y\geq -21-5}$

$\longmapsto\sf{y\geq -26}$

So the values of y greater than or equal to -26 will make this inequality true.

<h3>Good luck with your studies.</h3>

$\rule{300}{1}$

7 0

1 year ago

Read 2 more answers

Jeremy spent $33 on 3 cds. At this rate, how much would 5 cds cost?

natita [175]

$55

$33= 3CDs

$11= 1CD (divide by 3)

$55= 5CDs (times 1 by 5)

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3 years ago

A repair person is scheduled to be at your apartment between 9:00am to 12:00pm but you have to leave at 11:30 to help out a frie

barxatty [35]

The answer is
C. 83.3%

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2 years ago

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Find n for which the nth iteration by the Bisection Method guarantees to approximate the root of f(x) = 2x^2 − 3x − 2 on [−2, 1]

Lady_Fox [76]

Answer:

n = 29 iterations would be enough to obtain a root of $f(x)=2x^2-3x-2$ that is at most $10^{-8}$ away from the correct solution.

Step-by-step explanation:

You can use this formula which relates the number of iterations, n, required by the bisection method to converge to within an absolute error tolerance of ε starting from the initial interval (a, b).

$n\geq \frac{log(\frac{b-a}{\epsilon} )}{log(2)}$

We know

a = -2, b = 1 and ε = $10^{-8}$ so

$n\geq \frac{log(\frac{1+2}{10^{-8}} )}{log(2)}\\n \geq 29$

Thus, n = 29 iterations would be enough to obtain a root of $f(x)=2x^2-3x-2$ that is at most $10^{-8}$ away from the correct solution.

<u>You can prove this result by doing the computation as follows:</u>

From the information given we know:

$f(x)=2x^2-3x-2$
$\epsilon = 10^{-8}$

This is the algorithm for the Bisection method:

Find two numbers <em>a</em> and <em>b</em> at which <em>f</em> has different signs.
Define $c=\frac{a+b}{2}$
If $b-c\leq \epsilon$ then accept c as the root and stop
If $f(a)f(c)\leq 0$ then set <em>c </em>as the new<em> b</em>. Otherwise, set <em>c </em>as the new <em>a</em>. Return to step 1.

We know that $f(-2)=2(-2)^2-3(-2)-2=12$ and $f(1)=2(1)^2-3(1)-2=-3$ so we take $a=-2$ and $b=1$ then $c=\frac{-2+1}{2} =-0.5$

Because $1-(-0.5)\geq 10^{-8}$ we set $c=-0.5$ as the new <em>b.</em>

The bisection algorithm is detailed in the following table.

After the 29 steps we have that $6\cdot 10^{-9}\leq 10^{-8}$ hence the required root approximation is c = -0.50

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2 years ago