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How many solutions does the following equation have 3(X + 9) = 2x + 54

kotykmax [81]

Answer:

One solution.

Step-by-step explanation:

3(x + 9) = 2x + 54

3x + 27 = 2x + 54

3x + 27 - 2x = 2x + 54 - 2x

x + 27 = 54

x + 27 - 27 = 54 - 27

x = 27

8 0

3 years ago

8 + 3 • 5 - 20 ÷ 4 = ? Please use the order of operations

nalin [4]

We must multiply and divide before adding and subtracting here. Working from left to right, we get:

8 + 15 - 5 = ?

8 + 10 = ?

18 (answer)

8 0

2 years ago

Read 2 more answers

Precalculus

kodGreya [7K]

Answer:

$24.35

Step-by-step explanation:

We will use the compound interest formula provided to solve this problem:

$A=P(1+\frac{r}{n} )^{nt}$

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 1% into a decimal:

1% -> $\frac{1}{100}$ -> 0.01

Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:

$A=800(1+\frac{0.01}{12})^{12(3)}$

$A=824.35$

Lastly, subtract A from the principal to get the interest earned:

$824.35 - 800 = 24.35$

8 0

3 years ago

Each morning, Hungry Harry eats some eggs. On any given morning, the number of eggs he eats is equally likely to be 1, 2, 3, 4,

mamaluj [8]

Answer:

Mean = 35

Variance = 291.7

Step-by-step explanation:

Data provided in the question:

X : 1, 2, 3, 4, 5, 6

All the data are independent

Thus,

The mean for this case will be given as:

Mean, E[X] = $\frac{\textup{Sum of all the observations}}{\textup{Total number of observations}}$

or

E[X] = $\frac{\textup{1+2+3+4+5+6}}{\textup{6}}$

or

E[X] = 3.5

For 10 days, Mean = 3.5 × 10 = 35

And,

variance = E[X²] - ( E[X] )²

Now, for this case of independent value,

E[X²] = $\frac{1^2+2^2+3^2+4^2+5^2+6^2}{\textup{6}}$

or

E[X²] = $\frac{1+4+9+16+25+36}{\textup{6}}$

or

E[X²] = $\frac{91}{\textup{6}}$

or

E[X²] = 15.167

Therefore,

variance = E[X²] - ( E[X] )²

or

variance = 15.167 - 3.5²

or

Variance = 2.917

For 10 days = Variance × Days²

= 2.917 × 10²

= 291.7

3 0

3 years ago

Find the distance between the pair of points.

SVEN [57.7K]

Answer:

Distance is $\sqrt{290}$ units

Step-by-step explanation:

Use the distance formula which is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ where $d$ is the distance between points $(x_1,y_1)$ and $(x_2,y_2)$

We are given that $(x_1,y_1)$ is $(-6,-23)$ and $(x_2,y_2)$ is $(-23,-24)$ , therefore the distance between the two points is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$d=\sqrt{(-23-(-6))^2+(-24-(-23))^2}$

$d=\sqrt{(-23+6))^2+(-24+23))^2}$

$d=\sqrt{(-17)^2+(-1)^2}$

$d=\sqrt{289+1}$

$d=\sqrt{290}$

Therefore, the distance between $(-6,-23)$ and $(-23,-24)$ is $\sqrt{290}$ units.

3 0

2 years ago