Complete each statement using the words or algebraic expressions listed in the word bank below.
1. The length of the
of
the rectangular region
approximates the length of
the
of the circle.
2. The
of the rectangle
approximates the length of
one-half of the
circumference of the
circle.
3. The circumference of the circle is _______________________.
4. The _________________ of the ___________________ is 2.
5. The ratio of the circumference to the diameter is ______.
6. Area (circle) = Area of (_____________) =
1
2
∙ circumference ∙ =
1
2
(2) ∙ = ∙ ∙ = _____________.
Word bank
radius height base
diameter circle rectangle
�

Answer:

3) Not equivalent

4) Equivalent multiply by 2

5) Equivalent multiply by 2

Answer:

[tex]512\ \text{in}^2[/tex]

Step-by-step explanation:

x = Length and width of base

y = Height of box

Volume of the box is [tex]16384\ \text{in}^3[/tex]

[tex]x^2y=16384\\\Rightarrow y=\dfrac{16384}{x^2}[/tex]

Surface area is given by

[tex]s=x^2+4y\\\Rightarrow s=x^2+4\times \dfrac{16384}{x^2}\\\Rightarrow s=x^2+\dfrac{65536}{x^2}[/tex]

Differentiating with respect to x we get

[tex]s'=2x-\dfrac{131072}{x^3}[/tex]

Equating with 0 we get

[tex]0=2x^4-131072\\\Rightarrow x=(\dfrac{131072}{2})^{\dfrac{1}{4}}\\\Rightarrow x=16[/tex]

[tex]s''=2+\dfrac{393216}{x^4}[/tex]

at [tex]x=16[/tex]

[tex]s''=2+\dfrac{393216}{16^4}=8>0[/tex]

So the function is minimum at x = 16

[tex]y=\dfrac{16384}{x^2}=\dfrac{16384}{16^2}\\\Rightarrow y=64[/tex]

The material required is

[tex]s=x^2+4y=16^2+4\times 64\\\Rightarrow s=512\ \text{in}^2[/tex]

The minimum amount of material required is [tex]512\ \text{in}^2[/tex].

Answer:

I believe it is C

Step-by-step explanation:

the answer is supposed to be 3/2 but i dont know

Answer: 6000+700+00+0

I hope that helps you

Answer:

[tex]3.6 * 10^{3} \\\\[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distance = 6 miles

Time = 3 hours

Speed = Distance ÷ Time

Speed = 6 ÷ 3

Speed = 2 miles/hour

....................................................

Speed = 2 miles/hour

Distance = 7.5 miles

Time = Distance ÷ Speed

Time = 7.5 ÷ 2

Time = 3.75 hours

3.75 hours = 3 hours & 45 minutes

Answer:

Step-by-step explanation:

Time taken to travel 6 miles = 3 hours

Time taken to travel 1 mile = 3 ÷ 6 = [tex]\frac{3}{6}=\frac{1}{2} hour[/tex] = 30 minutes

Time taken to travel 7.5 miles = 30 * 7.5 = 225 minutes = 3.45 hours

Answer: 4 hours and 48 minutes

Step-by-step explanation:

120 miles divided by 25 mph

= 4.8

= 4 hours

0.8 x 60

= 48 mins

0 x 60 = 0

Answer:

The answer is the third one, 1,176

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

3 occurs the most in this data set

Answer:

The mode is 3.

Step-by-step explanation:

Answer:

20.83 yard

Step-by-step explanation:

Calculate Cubic Yards

Calculate your area

Calculate your volume: Multiply area times the depth to get volume in cubic feet

Calculate your cubic yards: Divide cubic feet by 27 to convert to cubic yards and this is your answer

Where ft2 = square foot, ft3 = cubic foot, yd3 = cubic yard

Total yards = 5[x] + x + 8  

Solve

133 = 6x + 8

6x = 125

x = 20.83 yard

Therefore, the Cyclone cleared 20.83 yards on the first day.

Answer:

0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Mean of 4 minutes

This means that [tex]m = 4, \mu = \frac{1}{4} = 0.25[/tex]

Find the probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot:

This is:

[tex]P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2)[/tex]

In which

[tex]P(X \leq 132) = 1 - e^{-0.25*132} = 1[/tex]

[tex]P(X \leq 2) = 1 - e^{-0.25*2} = 0.393469[/tex]

[tex]P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2) = 1 - 0.393469 = 0.606531[/tex]

0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.

Answer:

The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

A random sample of 80 college students showed that 44 had driven a car during the day before the survey was conducted.

This means that [tex]n = 80, \pi = \frac{44}{80} = 0.55[/tex]

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.479[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.621[/tex]

The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).

Answer

its confusing

Step-by-step explanation:

Answer:

see bottom

Step-by-step explanation:

divide through by 4

x2 - 2x - 3 = 0

x2 - 3x + x - 3 = 0

(x2 - 3x) + (x - 3) = 0

x(x - 3) + 1(x - 3) = 0

(x + 1) (x - 3) = 0

x + 1 = 0 and x - 3 = 0

x = -1 and x = 3

Answer:

5 i think

Step-by-step explanation:

Answer:

a triangle that may not have the same dimensions as the bases

Step-by-step explanation:

The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.

Answer:

60

Explanation:

The new superset list is

2, 2, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 5 = 60

In exponential form:

LCM = 22 x 31 x 51 = 60

LCM = 60

Therefore,

LCM(4, 5, 6) = 60

Answer:7 quarters and 6 dimes

Step-by-step explanation:

Answer:

Frederick Winslow Taylor

Step-by-step explanation:

Answer:

∠4 = 22

Step-by-step explanation:

Hello There!

The angles shown are consecutive interior angles

If you didn't know consecutive interior angles are supplementary angles meaning that the sum of the two angles is 180

So we can find the missing angle by subtracting the given angle (158 in this case) from 180

180 - 158 = 22

so we can conclude that ∠4 = 22

180.timr3fzgncvdfccfxdfdxxfhk

180-158=22

the measure is 44

Answer:

The statement that is accurate is csc(θ)=1.06

Step-by-step explanation:

Looking at the reference angle in this triangle, we can see that the side that is 47 units is opposite of it, the side that is 50 units is the hypotenuse, and the side that is 17 units is adjacent to it.

Because we know this, we can plug our sides into the formula for cscθ, secθ, and cotθ.

So:

cotθ=adjacent/opposite = 17/47= 0.36

cscθ=hypotenuse/opposite = 50/47=1.06

Now without even looking at the other statements, we can see that the second one is correct as cscθ=hypotenuse/opposite = 50/47=1.06

Therefore, the statement that is accurate is csc(θ)=1.06.

Answer:

6:5

Step-by-step explanation:

Step 1: we need to match the b portions of each ration, use a lcm calculator, we see that the least common factor of 1 and 2 is 2

Step 2: For our a:b ratio of 3:1 we need to multiply each portion of the ration by 2 divided by 1 is 2

2 times 3:2 times 1 = 6: 2 our new a b ratio

Step 3: for our bc ratio of 2: 5 we need to multiply each portion of the ratio by 2 divided by 2 equals 1

1 times 2: 1 times 5 = 2:5 our new b:c ratio

since the b portions of each ratio match, we just take a: c = 6:5

GOOD LUCK!

Answer:

theres no question to match an answer to, bud..

Step-by-step explanation:

Answer:

plz send full question

Step-by-step explanation:

ok

The rate of change for the interval between 0 and 2 for the quadratic equation f(x) = 2x^2 + x - 3, represented in the table, is 6.

To find the rate of change for the interval between 0 and 2 for the quadratic equation f(x) = 2x^2 + x - 3, we can use the values provided in the table.

First, let's calculate the values of f(x) for x = 0 and x = 2:

For x = 0: f(0) = 2(0)^2 + 0 - 3 = -3

For x = 2: f(2) = 2(2)^2 + 2 - 3 = 9

Now, we can find the rate of change by calculating the difference in the values of f(x) divided by the difference in x for the interval [0, 2]:

Rate of change = (f(2) - f(0)) / (2 - 0)

Substituting the values we found:

Rate of change = (9 - (-3)) / (2 - 0)

= (9 + 3) / 2

= 12 / 2

= 6

for more such questions on quadratic equation

https://brainly.com/question/1214333

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Answer:

C

Step-by-step explanation:

Instead of how much she should've had left it should've asked how much did she use.

Given:

Consider the below figure attached with this question.

The given data set is:

66, 65, 66, 70, 66, 68, 63, 60, 66, 68, 63, 65

To find:

The correct box plot for the given data set.

Solution:

We have,

66, 65, 66, 70, 66, 68, 63, 60, 66, 68, 63, 65

Arrange the data set in ascending order.

60, 63, 63, 65, 65, 66, 66, 66, 66, 68, 68, 70

Divide the data set in 4 equal parts by using the parenthesis.

(60, 63, 63), (65, 65, 66), (66, 66, 66), (68, 68, 70)

Minimum value = 60

First quartile: [tex]Q_1=\dfrac{63+65}{2}[/tex]

[tex]Q_1=64[/tex]

Median: [tex]M=\dfrac{66+66}{2}[/tex]

[tex]M=66[/tex]

Third quartile: [tex]Q_3=\dfrac{66+68}{2}[/tex]

[tex]Q_3=67[/tex]

Maximum value = 70

It means the end points of the box plot are 60 and 70. The box lies between 64 and 67. Line inside the box at 66.

The box plot in option A is the only box plot that satisfy the above conditions.

Therefore, the correct option is A.

Answer:

The average daily maximum temperature in March is of 61 degrees.

Step-by-step explanation:

The average daily maximum temperature in his hometown in x months after January is given by:

[tex]f(x) = 12.2\cos{(\frac{\pi x}{6})} + 54.9[/tex]

What is the average daily maximum temperature in March?

March is 3 - 1 = 2 months after January, so this is f(2).

[tex]f(2) = 12.2\cos{(\frac{\pi*2}{6})} + 54.9 = 61[/tex]

The average daily maximum temperature in March is of 61 degrees.

Answer:

least to greatest is how number appear on a number line. numbers less than 0 or indicated with a negative number. if the number is greater than 0 it's indicated without the negative as the plus is implied.

-11, -5, -2 ,4 , 7