Calculate the exact value of 0.428 ×2.75

The product of two mixed numbers x and y is 10. If x= _ 2/3 and y=_ 3/4 , find x and y?

Akimi4 [234]

Answer:

x = 2 2/3
y = 3 3/4

Step-by-step explanation:

There may be other ways to do this. Here's the approach I took. Let the integer part of x be represented by "a", and the integer part of y be represented by "b". Now, we have ...

(a +2/3)(b +3/4) = 10

Multiplying by 12, this becomes ...

(3a +2)(4b +3) = 120

There are only 16 divisors of 120, so they can be easily enough checked one at a time.

120 = 1·120 = 2·60 = 3·40 = 4·30 = 5·24 = 6·20 = 8·15 = 10·12

Of these divisors, the ones that are of the form 3a+2 are ...

2, 5, 8, 20 . . . . a=0, 1, 2, 6

The ones that are of the form 4b+3 are ...

3, 15 . . . . b = 0, 3

The factor pair that consists of a number on the first list and a number on the second list is ...

120 = 8·15

corresponding to a=2 and b=3. So, the mixed numbers you want are ...

x = 2 2/3

y = 3 3/4

_____

Check

(2 2/3)·(3 3/4) =2·3 +2·3/4 +2/3·3 +2/3·3/4 = 6 +6/4 +2 +2/4 = 8+8/4 = 10

6 0

3 years ago

Bank A is lending money at 6.4% interest compounded annually. The rate at Bank B is 6.3% compounded monthly, and the rate at Ban

Ad libitum [116K]

Answer:

$1596

$1597.28

$1598.33

bank A

Step-by-step explanation:

The formula for calculating compound interest:

FV = P (1 + r/m)^mn

FV = Future value

P = Present value

R = interest rate

N = number of years

m = number of compounding

Bank A = $1500(1.064) = $1596

Bank B = $1500( 1 + 0.063/12)^12 = 1597.28

Bank C = $1500( 1 + 0.0635/365)^365 = $1598.33

Bank A pays the least amount of interest

8 0

3 years ago

The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs a minimum number o

SCORPION-xisa [38]

Answer:

The significance level is $\alpha=0.01$ and since we are conducting a right tailed test we need to find a critical value who accumulate 0.01 of the area in the right of the normal standard distribution and we got:

$z_{\alpha/2}= 2.326$

So we reject the null hypothesis is $z>2.326$

Step-by-step explanation:

For this case we define the random variable X as the number of entry-level swimmers and we are interested about the true population mean for this variable . On specific we want to test this:

Null hypothesis: $\mu \leq 15$

Alternative hypothesis: $\mu > 15$

And the statistic is given by:

$z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

The significance level is $\alpha=0.01$ and since we are conducting a right tailed test we need to find a critical value who accumulate 0.01 of the area in the right of the normal standard distribution and we got:

$z_{\alpha/2}= 2.326$

So we reject the null hypothesis is $z>2.326$

7 0

3 years ago

A lake near the Arctic Circle is covered by a 222-meter-thick sheet of ice during the cold winter months. When spring arrives, t

Ivanshal [37]

S(t) = 3.82 - 0.2t

Step-by-step explanation:

After 7 weeks, the ice is 2.42 meters thick. The ice loses 0.2 meters of thickness per week; this means on the 7th week, it has lost 7(0.2) = 1.4 meters of thickness.

This means the ice started at 2.42+1.4 = 3.82 meters thick.

Our function will start at the original thickness of the ice, 3.82 meters.

Since the ice is losing thickness, we will subtract; it loses at a rate of 0.2 meters per week (t), which gives us 0.2t. This is subtracted from the original, 3.82 meters, giving us

S(t) = 3.82 - 0.2t

7 0

3 years ago

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Keith used the following steps to find the inverse off, but he thinks he made an error

Sholpan [36]

Answer:

Option D In step 4 Keith should have subtracted 5 from each side

Step-by-step explanation:

step 1

we have

f(x)=7x+5 -----> given

step 1 is correct

step 2

Change f(x) to y

y=7x+5

so

step 2 is correct

step 3

Exchange x for y and y for x

x=7y+5

so

step 3 is correct

step 4

Subtract 5 each side

x-5=7y+5-5

x-5=7y

step 4 is not correct

step 5

Divide by 7 each side

(x-5)/7=y

step 6

Change y to g(x)

(x-5)/7=g(x)

step 7

switch sides of the equation

g(x)=(x-5)/7

therefore

In step 4 Keith should have subtracted 5 from each side

5 0

3 years ago

Read 2 more answers