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3 years ago

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Robert is putting money into his bank account every week when he gets his pay check. He has $200 in his account already. If he p

uts $50 in each week, how long will it take him to reach $5,000? what is the equation?

1 answer:

astra-53 [7]3 years ago

4 0

You can set up a porportion of 200/50 then x/5000 so then 200 x 5000= 1,000,000 divided by 200 then it will equal 500 so the answer is 500

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marshall27 [118]

The topics you should learn are equating denominators and fractions. This is summing up simple fractions.

So we have to make denominators' numbers the same in order to sum up them all (we can sum fractions if the denominators are the same) , and we did it by cross product (that thing on the picture)

Equating by lcm (least common multiple) is the easiest way, because you might see bigger numbers on other questions, and cross product will bring much bigger numbers, so this technic might confuse you.

By the way lcm of 4 and 5 is already 20

Hope it helps!

5 0

2 years ago

The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth

Art [367]

Answer:

a) $N_0=250\; k=0.15$

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies $t=0$ . And $N(0)=N_0$ . The process is:

$N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250$

b) After 2 days means $t=48$ . So, we just replace and operate:

$N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}$

c) $N(t_1)=4000; \;t_1=?$

$N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\ \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h$

d) $t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)$

$N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h$

6 0

3 years ago

Which is equivalent to x?<br> *image included below*

Assoli18 [71]

Answer:

$\bigodot B.\:\: 31\sqrt 3$

Step-by-step explanation:

$\huge x= 62.\cos 30\degree$

$\huge x= 62.\frac{\sqrt 3}{2}$

$\huge x= 31\sqrt 3$

8 0

2 years ago

Enter the value of p so that the expression 4 (n+8) is equivalent to (n+p)4

Vladimir [108]

Sick my dock is the answer

7 0

2 years ago

What is an equation of the line that passes through the point(2,−2) and is parallel to the line 5x-2y=4

mixer [17]

Answer:

y = 5/2x - 7

Step-by-step explanation:

5x - 2y = 4

5x - 4 = 2y

y = 5/2x - 2

Slope = 5/2

Point (2,-2)

y-intercept: -2 - (5/2)(2) = -2 - 5

= -7

3 0

2 years ago