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3 years ago

7

Find the area of a circle with a diameter of six. Either enter an exact answer in terms of pie or use 3.14 for pie and enter you

r answer as a decimal

1 answer:

miss Akunina [59]3 years ago

4 0

Answer:

The area of the circle is 28.26

The area of the circle in terms of pi is 9π

Step-by-step explanation:

radius = half of diameter

d = 6

r = 6/2 = 3

To solve this problem we need to use the area formula of a circle:

a = area

r = radius = 3

π = pi

a = π * r²

we replace with the known values

a = π * (3)²

a = π * 9

a = 9π

The area of the circle in terms of pi is 9π

9 * 3.14 = 28.26

The area of the circle is 28.26

You might be interested in

Medicare would like to test the hypothesis that the average monthly rate for one-bedroom assisted-living facility is equal to $3

aliina [53]

Answer:

C) more than the absolute value of the critical value, we can conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.

Step-by-step explanation:

Hello!

Interest hypothesizes is " the average monthly rate for one-bedroom assisted-living facility is equal to $3300" symbolically: μ = 3300

The study variable is:

X: Monthly rate for a one-bedroom assisted-living facility.

Since there is no information about the distribution of the variable, to be able to study the population mean, I'll assume that the variable has a normal distribution.

The hypothesis is:

H₀: μ = 3300

H₁: μ ≠ 3300

α: 0.05

The statistic to use, considering that there is no known population information and the sample size, is a Student t:

t= <u> X[bar] - μ </u> ~ $t_{n-1}$

S/√n

n= 12

X[bar]= $3690

S= $530

Using the sample data, calculate the statistic value:

t= <u> 3690 - 3300 </u> = 2.549

530/√12

The rejection region for this test is two-tailed, with critical values:

$t_{n-1; \alpha /2} = t_{11; 0.025} = -2.201$

$t_{n-1;1-\alpha /2} = t_{11; 0.975} = 2.201$

The decision rule is:

Reject the null hypothesis if t ≤ -2.201 or if t ≥ 2.201

Not reject the null hypothesis if -2.201 < t < 2.201

Since the calculated value (2.549) is greater than the right critical value (2.201) the decision is to reject the null hypothesis.

With a signification level of 5%, there is enough evidence to reject the null hypothesis. This means that the population mean of the monthly rate for a one-bedroom assisted living facility is different from $3300.

I hope it helps!

7 0

2 years ago

Aiden's mom calculated that in the previous month, their family had used 40% of the monthly income for

Natali5045456 [20]

Answer:

The money left after gasoline expenses was <u>$622.50</u>.

Step-by-step explanation:

Given:

Last month, family had used 40% of the monthly income for gasoline, and 63% of that gasoline was consumed by the family's SUV.

The family's SUV used $261.45 worth of gasoline previous month.

Now, to find the money left of the family monthly income after gasoline expenses.

Let the total money spend on gasoline be $g.$

As, given:

The family's SUV used $261.45 worth of gasoline, which was 63% of the gasoline that was consumed.

According to question:

$63\%\ of\ g=$261.45.\\\\$

$\frac{63}{100} \times g=261.45\\\\0.63\times g=261.45$

<em>Dividing both sides 0.63 we get:</em>

$g=\$415.$

<u><em>The total money spend on gasoline = $415.</em></u>

Now, 40% of the monthly income is used for gasoline.

Let the total monthly income be $x.$

So, to get the monthly income we put an equation:

$40\%\ of\ x=\$415\\\\\frac{40}{100}\times x=415\\\\0.40\times x=415$

<em>Dividing both sides by 0.40 we get:</em>

$x=\$1037.50.$

<u><em>The total monthly income = $1037.50.</em></u>

Now, to get the money left after gasoline expenses we subtract the total money spend on gasoline from the total monthly income:

$\$1037.50-\$415\\\\=\$622.50.$

Therefore, the money left after gasoline expenses was $622.50.

6 0

3 years ago

What are the real and complex solutions of the polynomial equation? x^4-41x^2=-400. *work needed*

pickupchik [31]

<h3>Answer: x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>

Step-by-step explanation:

Given the polynomial equation $x^4-41x^2=-400$ .

Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get

$x^4-41x^2+400=-400+400$ .

$x^4-41x^2+400=0$ .

Factoring by product sum rule.

We need product of 400 and sum upto -41.

We can see that 400 = -25 × -16 = 400 and -25-16 = -41.

Therefore,

$x^4-25x^2-16x^2+400=0$

Making it into two groups, we get

$(x^4-25x^2)+(-16x^2+400)=0$

Factoring out GCF of each group, we get

$x^2(x^2-25)-16(x^2-25)=0$

$(x^2-25)(x^2-16) =0$

Factoring out $(x^2-25)$ and $(x^2-16)$ separately by difference of the squares identity $a^2-b^2=(a-b)(a+b)$ , we get

$(x^2-25) = x^2-5^2= (x-5)(x+5)$ and

$x^2-16 = x^2-4^2 =(x-4)(x+4)$ .

Therefore,

$(x-5)(x+5)(x-4)(x+4) =0$

Applying zero product rule,

x-5=0

x+5=0

x-4=0 and

x+4=0.

Therefore,

<h3>x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>

6 0

3 years ago

I I know that it's already circled, but I'm just not sure what the right answer is.

Nimfa-mama [501]

Answer:

I think it is D. You might need to ask somebody else to be positive!!

Step-by-step explanation:

6 0

3 years ago

The product of a number, x, and 18 is 113.4. Which equation and value of x represent this relationship?

KIM [24]

Answer:

42

Step-by-step explanation:

5 0

3 years ago