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ivanzaharov [21]

3 years ago

9

Samantha is making some floral arrangements. The table show the prices 1/2 dozen of each type of flower.

1 answer:

adelina 88 [10]3 years ago

5 0

Working:
$5.29 + ((2/3) x 3.59) + ((4/3) x 4.79)
= $14.07 (to 2d.p.)

So, she estimated correctly that she will spend around $14 on the flowers but slightly more than $14, so I don't really know if you should say that she estimated correctly or not

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When using 3 six sided dice, what is the probability of getting a 1 on one die, a 2 on the other, and a 3 on the last die.

Semmy [17]

Answer:

1/6 is the probability for each event, so P of all three = 1/(6^3)=1/216

Step-by-step explanation:

5 0

3 years ago

Find x and y, given that line WS and line VT are parallel. Show all work!

bulgar [2K]

In the given diagram, the traingles USW and UTV are similar triangles and thus the following ratio equality applies to them.

$\frac{VT}{WS} =\frac{VU}{WU}=\frac{TU}{SU}$ ..........(Equation 1)

Checking the diagram given, we see that:

VT=y, WS=22, VU=8, ST=x-2

WU=WV+VU=12+8=20

TU=5

SU=ST+TU=(x-2)+5=x+3

Thus, substituting the required values in (Equation 1) we get:

$\frac{y}{22}=\frac{8}{20}=\frac{5}{x+3}$

Now, as can be clearly seen, to find y we will use the first two ratios as:

$\frac{y}{22}=\frac{8}{20}$

$y=\frac{8\times 22}{20}=8.8$

In a similar manner, to find the value of x we can use the last two ratios:

$\frac{8}{20}=\frac{5}{x+3}$

After cross multiplication we get:

$5\times 20=8(x+3)$

Which can be simplified as:

$x+3=\frac{100}{8} =12.5$

Thus, $x=12.5-3=9.5$

Therefore, the required answer is:

x=9.5 and y=8.8

7 0

3 years ago

A woman has 21 total coins in her pocket, all of which are either dimes or quarters. If the total value of her change is $3.90,

Elza [17]

Answer with Step-by-step explanation:

Let there be d dimes and q quarters

A woman has 21 total coins in her pocket.

⇒ d+q=21 ------(1)

1 dime=$ 0.1

1 quarter=$ 0.25

The total value of her change is $3.90

⇒ 0.1d+0.25q=3.90

Multiplying both sides by 100,we get

10d+25q=390 --------(2)

(2)-10×(1)

10d+25q-10d-10q=390-210

15q=180

Dividing both sides by 15, we get

q=12

Putting value of q in (1),we get

d=9

Hence, Number of dimes=9

and number of quarters=12

Write the number of dimes, then the number of quarters separated by a comma.

9,12

8 0

3 years ago

Read 2 more answers

Write an expression that uses subtraction and division that has a value of 3.

Strike441 [17]

Answer:

12/2-3

Step-by-step explanation:

12/2-3

3 0

2 years ago

Find the derivative of f(x) = 12x^2 + 8x at x = 9.

zvonat [6]

Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

$(f+g)'=f'+g'$ Sum rule.

$(cf)'=cf'$ Constant multiple rule.

$(x^n)'=nx^{n-1}$ Power rule.

$(x)'=1$ Slope of y=x is 1.

$f(x)=12x^2+8x$

$f'(x)=(12x^2+8x)'$

$f'(x)=(12x^2)'+(8x)'$ by sum rule.

$f'(x)=12(x^2)+8(x)'$ by constant multiple rule.

$f'(x)=12(2x)+8(1)$ by power rule.

$f'(x)=24x+8$

Now we need to find the derivative function evaluated at x=9.

$f'(9)=24(9)+8$

$f'(9)=216+8$

$f'(9)=224$

In case you wanted to use the formal definition of derivative:

$f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

Or the formal definition evaluated at x=a:

$f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$

Let's use that a=9.

$f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}$

We need to find f(9+h) and f(9):

$f(9+h)=12(9+h)^2+8(9+h)$

$f(9+h)=12(9+h)(9+h)+72+8h$

$f(9+h)=12(81+18h+h^2)+72+8h$

(used foil or the formula (x+a)(x+a)=x^2+2ax+a^2)

$f(9+h)=972+216h+12h^2+72+8h$

Combine like terms:

$f(9+h)=1044+224h+12h^2$

$f(9)=12(9)^2+8(9)$

$f(9)=12(81)+72$

$f(9)=972+72$

$f(9)=1044$

Ok now back to our definition:

$f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}$

$f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}$

Simplify by doing 1044-1044:

$f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}$

Each term has a factor of h so divide top and bottom by h:

$f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}$

$f'(9)=\lim_{h \rightarrow 0}(224+12h)$

$f'(9)=224+12(0)$

$f'(9)=224+0$

$f'(9)=224$

8 0

3 years ago