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3 years ago

Please help! provide thorough explanation and use elimination method!!

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

8 0

Multiply both sides of the second equation by 100 to get rid of the decimals:

0.05n + 0.10d = 1.50

==> 5n + 10d = 150

Multiply both sides of the first equation by -5:

n + d = 21

==> -5n - 5d = -105

Add the two equations together:

(5n + 10d) + (-5n - 5d) = 150 + (-105)

Notice that the terms containing n get eliminated and we can solve for d :

(5n - 5n) + (10d - 5d) = 150 - 105

5d = 45

d = 45/5 = 9

Plug this into either original equation to solve for n. Doing this with the first equation is easiest:

n + 9 = 21

n = 21 - 9 = 12

So Donna used 12 nickels and 9 dimes.

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The confidence interval based on the two-sample design is wider because there is considerable variation in mileage between the c

vovikov84 [41]

Answer:

The confidence interval based on the paired design is wider because there is little variation in mileage between the cars.

Step-by-step explanation:

The sample size randomly collected is matched sample and since the confidence interval is based on the paired design is large and wide. There is small variation between the mileage of the two cars indicating the cars have mileage based on the fuel.

5 0

3 years ago

Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$

4 0

2 years ago

Plz help if you can Thank ya

koban [17]

Answer:

$90\pi$

Step-by-step explanation:

The first step is to find the slant height of the cone. Using the pythagorean theorem, you can find that $\sqrt{12^2+5^2}=13$ cm. Plugging this into the equation, you get $\pi \cdot 5 \cdot 13=90\pi$ . Hope this helps!

3 0

3 years ago

Write the number that is 1 more than 8,325

borishaifa [10]

The answer is to this question is 8,326

3 0

3 years ago

Read 2 more answers

I’ve done this 3 different way and I’m still getting it wrong someone help I feel dumb

Olegator [25]

<h3>Answer: 13,011.11 dollars</h3>

note: remember to take the comma out or ignore it. I put it in there to help make the number more readable

===========================================

Explanation:

Let x be the value of the sale in dollars.

x-1900 represents the leftover amount that is over 1900

eg: if x = 2200, then x-1900 = 2200-1900 = 300 is the the leftover amount

taking 9% of (x-1900) leads to the expression 0.09(x-1900) and this expression must be 1000 since this is the extra amount of money the salesman needs (he already has $1000 in base pay)

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

Solve for x

0.09(x-1900) = 1000

x-1900 = 1000/0.09

x-1900 = 11,111.11111 approximately

x = 11,111.11111 + 1900

x = 13011.1111

x = 13,011.11 rounding to the nearest cent

4 0

3 years ago