in each rectangle what is the fraction that shows the area of one of the parts what is the area of each part

Solve the question: (-4)+(-1)+2+5+...+x=437

Alex Ar [27]

The sequence is an arithmetic sequence with
a₁ = -4

d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3

an = x

Sn = 437

General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)

We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7

Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x - 4) = 874
xn - 4n = 874

Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.

Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50

The solution is 50

6 0

3 years ago

7) At the beginning of the weekend a swimming pool contains 1,800 gallons of water. Every hour 7 gallons are splashed

Free_Kalibri [48]

Answer:

b

Step-by-step explanation:

it bbbbbbbbbbbbbbb yeah b or d

3 0

3 years ago

Calculate the pay for the following day of a weekly time card given a wage of $12.50/hr.

Elenna [48]

The one day pay is $106.25 rounded to the nearest hundredth.

Step-by-step explanation:

From the table shown :

The timing shown in the morning is from 8:00 to 12:15
The number of hours worked in the morning = 4 hours 15 minutes.

It is given that, the pay is $12.5 per hour.

Therefore, the pay earned in the morning = No.of hours × pay per hour.

⇒ 4 hours × 12.5 = $50

⇒ (15 mins / 60 mins) × 12.5 = $3.125

⇒ 50+3.125

⇒ 53.125

The timing shown in the afternoon is from 8:00 to 12:15
The number of hours worked in the morning = 4 hours 15 minutes.

Therefore, the pay earned in the afternoon = No.of hours × pay per hour.

⇒ 4 hours × 12.5 = $50

⇒ (15 mins / 60 mins) × 12.5 = $3.125

⇒ 50+3.125

⇒ 53.125

The pay for 1 day = pay earned in the morning section + pay earned in the afternoon section.

⇒ 53.125 + 53.125

⇒ 106.25

∴ The one day pay is $106.25 rounded to the nearest hundredth.

7 0

2 years ago

HELLOOOO HELP PLEASE

MA_775_DIABLO [31]

Answer:

$2*log(x)+log(y)$

Step-by-step explanation:

So, there are two logarithmic identities you're going to need to know.

Logarithm of a power:

$log_ba^c=c*log_ba$

So to provide a quick proof and intuition as to why this works, let's consider the following logarithm: $log_ba=x\implies b^x=a$

Now if we raise both sides to the power of c, we get the following equation: $(b^x)^c=a^c$

Using the exponential identity: $(x^a)^c=x^{a*c}$

We get the equation: $b^{xc}=a^c$

If we convert this back into logarithmic form we get: $log_ba^c=x*c$

Since x was the basic logarithm we started with, we substitute it back in, to get the equation: $log_ba^c=c*log_ba$

Now the second logarithmic property you need to know is

The Logarithm of a Product:

$log_b{ac}=log_ba+log_bc$

Now for a quick proof, let's just say: $x=log_ba\text{ and }y=log_bc$

Now rewriting them both in exponential form, we get the equations:

$b^x=a\\b^y=c$

We can multiply a * c, and since b^x = a, and b^y = c, we can substitute that in for a * c, to get the following equation:

$b^x*b^y=a*c$

Using the exponential identity: $x^{a}*x^b=x^{a+b}$ , we can rewrite the equation as:

$b^{x+y}=ac$

taking the logarithm of both sides, we get:

$log_bac=x+y$

Since x and y are just the logarithms we started with, we can substitute them back in to get: $log_bac=log_ba+log_bc$

Now let's use these identities to rewrite the equation you gave

$log(x^2y)$

As you can see, this is a log of products, so we can separate it into two logarithms (with the same base)

$log(x^2)+log(y)$

Now using the logarithm of a power to rewrite the log(x^2) we get:

$2*log(x)+log(y)$

3 0

1 year ago

If there were 5 million births in a particular country and 3 comma 375 sets of naturally occurring triplets, what is the experi

IgorLugansk [536]

Answer:

$Probablity =P=6.75*10^-^4$

Step-by-step explanation:

The experimental probability can be defined as the ratio of the number of times any particular event has occurred to the total number of times that event has taken place.

Experimental probability = P = No. of event occurrences / total number of occurrences.

In our question statement,

No of naturally occurring triplets are = 3375

Total number of births = 5 million = 5,000,000

Putting values in equation.

$P=3375/5000000$

$P = 0.000675\\P=6.75*10^-^4$

4 0

3 years ago