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3 years ago

A circular plot of land has a diameter of 16 yards. What is the area of the land? Use 3.14 for pi.

Mathematics

2 answers:

Ivan3 years ago

7 0

Answer:

Step-by-step explanation:

Aliun [14]3 years ago

5 0

Here's the solution :

radius = 8 yards ( half the diameter )

now, we know,

$\boxed{area = \pi {r}^{2} }$

let's solve,

$3.14 \times 8 \times 8$

$200.96 \: \: yd {}^{2}$

so, correct option is B.

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Solving a Two-Step Matrix Equation<br> Solve the equation:

Cloud [144]

Answer:

$\boxed {x_{1} = 3}$

$\boxed {x_{2} = -4}$

Step-by-step explanation:

Solve the following equation:

$\left[\begin{array}{ccc}3&2\\5&5\\\end{array}\right] \left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right] + \left[\begin{array}{ccc}1\\2\\\end{array}\right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right]$

-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:

-First equation:

$3x_{1} + 2x_{2} + 1 = 2$

-Second equation:

$5x_{1} + 5x_{2} + 2 = -3$

-Choose one of the two following equations, which I choose the first one, then you solve for $x_{1}$ by isolating

$3x_{1} + 2x_{2} + 1 = 2$

-Subtract $1$ to both sides:

$3x_{1} + 2x_{2} + 1 - 1 = 2 - 1$

$3x_{1} + 2x_{2} = 1$

-Subtract $2x_{2}$ to both sides:

$3x_{1} + 2x_{2} - 2x_{2} = -2x_{2} + 1$

$3x_{1} = -2x_{2} + 1$

-Divide both sides by $3$ :

$3x_{1} = -2x_{2} + 1$

$x_{1} = \frac{1}{3} (-2x_{2} + 1)$

-Multiply $-2x_{2} + 1$ by $\frac{1}{3}$ :

$x_{1} = \frac{1}{3} (-2x_{2} + 1)$

$x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}$

-Substitute $-\frac{2x_{2} + 1}{3}$ for $x_{1}$ in the second equation, which is $5x_{1} + 5x_{2} + 2 = -3$ :

$5x_{1} + 5x_{2} + 2 = -3$

$5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3$

Multiply $-\frac{2x_{2} + 1}{3}$ by $5$ :

$5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3$

$-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3$

-Combine like terms:

$-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3$

$\frac{5}{3}x_{2} + \frac{11}{3} = -3$

-Subtract $\frac{11}{3}$ to both sides:

$\frac{5}{3}x_{2} + \frac{11}{3} - \frac{11}{3} = -3 - \frac{11}{3}$

$\frac{5}{3}x_{2} = -\frac{20}{3}$

-Multiply both sides by $\frac{5}{3}$ :

$\frac{\frac{5}{3}x_{2}}{\frac{5}{3}} = \frac{-\frac{20}{3}}{\frac{5}{3}}$

$\boxed {x_{2} = -4}$

-After you have the value of $x_2$ , substitute for $x_{2}$ onto this equation, which is $x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}$ :

$x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}$

$x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}$

-Multiply $-\frac{2}{3}$ and $-4$ :

$x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}$

$x_{1} = \frac{8 + 1}{3}$

-Since both $\frac{1}{3}$ and $\frac{8}{3}$ have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:

$x_{1} = \frac{8 + 1}{3}$

$x_{1} = \frac{9}{3}$

$\boxed {x_{1} = 3}$

5 0

3 years ago

The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of

mrs_skeptik [129]

Answer:

The percentage of the bank's customers carry daily balances between $700 and $1,000 is 65.7%.

The minimum daily balance on which it should be willing to pay interest is $1,198.

Step-by-step explanation:

We have a normal distribution with mean = $800 and standard deviation = $150.

a) We can calculate this value with the standard normal distribution, calculating the z-value for $700 and $1,000.

$z_1=\frac{x-\mu}{\sigma} =\frac{700-800}{150}= \frac{-100}{150} =-0.67\\\\\\z_2=\frac{1,000-800}{150}=\frac{200}{150}=1.33\\\\\\P(700$

The percentage of the bank's customers carry daily balances between $700 and $1,000 is 65.7%.

b) We must calculate from what amount only 6% of the accounts remain.

This is done by solving:

$P(z>x)=0.06$

This happens for a z-value of z=2.652.

This corresponds to a amount of $1,198.

$x=\mu+z*\sigma=800+2.652*150=800+398=1,198$

The minimum daily balance on which it should be willing to pay interest is $1,198.

8 0

4 years ago

A low correlation coefficient implies that

docker41 [41]

Correlation coefficients whose magnitude are between 0.3 and 0.5 indicate variables which have a low correlation.<span> Correlation coefficients whose magnitude are less than 0.3 have little if any (linear) correlation.</span>

5 0

3 years ago

HELLLLLLLLLPPPPPPPPP , mathhhhhhhhhhhhhhh

madreJ [45]

i think it's 6 because that's how many y points shifted from when x = 0 and to x = 1

8 0

4 years ago

2x+3y is greater than or equal to 4, x+2y is less than or equal to 3

Amanda [17]

Answer:

Step-by-step explanation:

2x+3y=6xy

x+2y=2xy

The first one is grater than 4 and the second one is less than 3.

4 0

3 years ago