Solve the quadratic equation by completing the square. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
x2 + 8x + 14 = 0

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:1. How can you tell by looking at each graph that a proportional relationship exists between the quantities?

relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

2. Find the constant of proportionality for each graph. Write your answer as y = kx.

y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.

Step-by-step explanation:

Answer:

12 square feet

Step-by-step explanation:

A=Area

b=Base

h=Height

To find the area of an triangle, you use the formula A=1/2bh

you plug in the the area and the height to get:

48=1/2xbx8

you do the maths and you get

b=12

1Answer:

12 sqft

Step-by-step explanation:

Answer:

4/15 of an inch

Step-by-step explanation:

A worm wriggled forward 4/5 of an inch in 3 minutes.

=> At that rate, the distance the worm would go in 1 minute is:

D = (4/5)/3 = 4/(5x3) = 4/15 of an inch

Hope this helps!

The worm would go 0.267 inches in 1 minute.

How far would the worm go in 1 minute?

By Unitary method,we can solve this problem.

But now question is what is the use of Unitary method ?

By some examples we can understand this concept.

Let cost of 5 book is 500 rupees.

By Unitary method, cost of 1 book is

\(\frac{500}{5} \\ = 100 \: rupees\)

Cost of 100 books is \((100 \times 100) = 10000 \: rupees\)

Again for another example let length of 1 rope is 5 m

Then by Unitary method length of 5 rope is \((5 \times 5) = 25 \: m\)

Given,a worm wriggled forward 4/5 of an inch in 3 minutes.

So,in 3 minutes the worm can cover 4/5 of an inch

\( = \frac{4}{5} \times 1 \: inch \\ = \frac{4}{5} \: inch\)

Now we want to find how far would the worm go in 1 minute ?

In 3 minutes the worm covers 4/5 inche

By Unitary method, in 1 minute the worm covers

\( \frac{4}{5} ÷ 3 = \frac{4}{15} = 0.267 \: inches\)

Therefore,the worm would go 2.4 inches in 1 minute

This is a Unitary method related problem.

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Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Answer:

41/140 or approximately 29.29%

Step-by-step explanation:

Divide 41 by 140 to get 0.29285714285, and round it to the nearest hundredths.

Answer:

Step-by-step explanation:

b= buttons

z= zips

b∩z'=41

b'∩z=48

b'∩z'=25

b=?

b= b∩z+b∩z' (law of total probability)

140=b∩z+b∩z'+b'∩z+b'∩z'  (if this is confusing draw a venn diagram)

140=b∩z+41+48+25

b∩z=26

26+41= 67

67/140= .478571429

Answer:

its b

Step-by-step explanation:

i took the test

Answer: its b cause i took the test and got it right

Answer:

hlohhwwhwuwhwwhwywuyeyeyhee

Answer:

Step-by-step explanation:

132 + 106 + 81 + x = 360

319 + x = 360

x = 41

The true statement is A, for x < 0 the function is negative.

On the image we can see the graph of the parent cube root function.

y = ∛x

And we want to see which statements are true. Remember that the function is negative if the graph is below the x-axis and positive if it is above, using that we can analyze the graph.

First, notice that for x < 0 the graph is below the x-axis, then the first statement is true.

When x < 0, the function is negative.

So the only correct option is A.

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Answer:

The food preferences among vole species are independent of one another.

Step-by-step explanation:

The hypothesis can be defined as follows:

H₀: The food preferences among vole species are independent of one another.

Hₐ: There is a relationship between voles and food preference.

The data provided is:

                                           meadow voles            common voles

                 apple slices                15                                   21

peanut butter-oatmeal               25                                    16

A Chi-square test for the Goodness of fit will be used.

The expected values are computed using the formula:

\(E_{i}=\frac{\text{ith Row Total}\times \text{jth Column Total}}{N}\)

Consider the Excel sheet attached.

The Chi-square statistic value is 2.861.

Compute the degrees of freedom as follows:

df = (r - 1)(c - 1)

   = (2 - 1)(2 - 1)

   = 1

Compute the p-value as follows:

\(p-value=P(\chi^{2}_{(1)}>2.861)=\text{CHISQ.DIST.RT(2.861,1)}=0.091\)

The p-value = 0.091 > α = 0.05

The null hypothesis will not be rejected.

Thus, it can be concluded that the food preferences among vole species are independent of one another.

The matrix representing the profit from the sales of book A for each store is:

[  $4  ]

[  $4  ]

[  $4  ]

To represent the profit from the sales of book A for each store, we can use a matrix where the rows correspond to the stores (X, Y, Z) and the columns correspond to the book A.

The matrix representing the profit from the sales of book A for each store is as follows:

Store Book A

X $4

Y $4

Z $4

Therefore, the matrix representing the profit from the sales of book A for each store is:

[  $4  ]

[  $4  ]

[  $4  ]

Each element in the matrix represents the profit from the sales of book A in a specific store, which is $4 for all stores (X, Y, Z).

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Hope it helped

Answer:

m<wzx = 71

Step-by-step explanation:

Assuming these are interior angles of a triangle.

The sum of all three interior angles of a triangle is always 180 degrees, therefore:

m<xyz + m<wxz + m<wzx = 180

Substitute our values:

58 + 51 + m<wzx = 180

m<wzx = 180 - 58 - 51

m<wzx = 71

Answer:

200 cm

Step-by-step explanation:

2*100= 200

Answer: 200 centimeters

Step-by-step explanation:

100 centimeters = 1 meter

? centimeters = 2 meters

100 x 2 = 200

200/1 = 200 centimeters

Answer:

35.235

Step-by-step explanation:

because 78.3*0.45 = 35.235

The meaning of the y-intercept in this situation is ,

''For every additional mile the cab travels, the total fee increases by $12.00.''

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

From the table, we have the following parameters:

Points (x, y) = (2, 5) and (15.00, 19.50)

So, we would calculate the slope as follows:

Slope = (19.50 - 5)/(15.00 - 2)

Slope = 14.50/13

Slope = 1.11

Hence, We get;

Fixed fee = $15 - (1.12 x 2)

               = $15 - 2.24 ≈ $12.00

So, We get;

For every additional mile the cab travels, the total fee increases by $12.00.

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Answer:

The margin of error is of 4.22 minutes.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.2622

The margin of error is:

\(M = T\frac{s}{\sqrt{n}}\)

In which s is the standard deviation of the sample and n is the size of the sample.

We have that \(s = 6, n = 10\). So

\(M = T\frac{s}{\sqrt{n}} = 2.2622\frac{6}{\sqrt{10}} = 4.22\)

The margin of error is of 4.22 minutes.

Part A)

Part B)

Part A:

(1) The area of the circle is A = πr², where r is the radius (half the diameter) of the circle. So, the radius is 3/2 = 1.5. Therefore, the area of the circle is A = π(1.5)² ≈ 7.07.

The area of the square is 9² = 81. The probability of hitting the circle is the ratio of the area of the circle to the area of the square, so:

P(hit circle) = A(circle) / A(square) = 7.07 / 81 ≈ 0.0873

(2) I would classify the answer as unlikely to happen, since the probability is relatively low.

Part B:

(1) The probability of NOT hitting the circle is the complement of the probability of hitting the circle, so:

P(not hit circle) = 1 - P(hit circle) = 1 - 0.0873 = 0.9127

(2) I would classify the answer as likely to happen, since the probability is relatively high.

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Answer:

The third one.

Step-by-step explanation:

The perimeter of the larger triangle is 51

Here, we want to calculate the perimeter of the larger triangle

From the smaller triangle, we can see that its shortest side is 4

The shortest side of the larger triangle is 12

This shows that the scale of the larger to the smaller is 3 to 1

Mathematically, what this means is that, by multiplying the length of the smaller triangle by 3, we can get the sides of the larger

Hence, what we have at this point is that the sides of the larger triangle are 12 by 18 by 21

Mathematically, the perimeter of a triangle can be calculated by adding the length of the sides together

With respect to this question, the perimeter of the larger triangle will be;

12 + 18 + 21 = 51

The solution to the inequality equation \(x^{2}\) – 9x < –18 is 3 < X < 6

Inequality equation means a mathematical expression in which the sides are not equal to each other

\(x^{2}\) – 9x < –18

Rewrite in standard form

x^2 -9x +18 < 0

Factorise the equation

\(x^{2}\)  - 3x -6x +18 < 0

x (x - 3) - 6 (x - 3) < 0

(x - 3) ( x- 6) < 0

(x - 3) < 0

x < 3

( x- 6) < 0

x < 6

3 < X < 6

Therefore, the solution to the inequality is 3 < X < 6

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Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

Answer:

help u in what please ask the question so we can anwser

Yes the relation is a function because each input value has only one output value

Function is a type of relation, or rule, that maps one input to specific single output.

The x circle contains the numbers -6, -1, 4, and 0. The y circle contains the numbers -2, -1, and 3.

The mapping is of numbers from x to numbers from y. There are arrows going from 6 to -1, from -1 to 2, from 4 to 3, and from 0 to 3.

Thus, we conclude that yes the relation is a function because for each element of the set X there is only one correspondent element in the set Y.

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Answer: c

Step-by-step explanation: i did the test C:

Answer:

12

Step-by-step explanation:

Listing the weeks he will attend each item

Class  4,8,12,16

Chess 2,4,6,8,10,12

Fencing 3,6,9,12

Starting today at week 0, he will attend all 3 again at week 12

Answer:

12 weeks

Step-by-step explanation:

We know that Salvatore attends class every 4 week, chess club every 2 weeks, and fencing lessons every 3 weeks.

If he attended all today, to find out when he will attend all again,we just need to find the least common multiple (LCM) of 3, 4, and 2.

The LCM of 3, 4, and 2 is 12.

So, he will attend all classes again after 12 weeks.

Answer:

Step-by-step

i) a² - 2ab + b² = (a + b)²

a² = p² ;     a  = p

b² = 16 = 4²  ;        b = 4

2ab = 2*p*4 = 8p

p² - 8p + 16 = (p - 4)²

ii) a² + 2ab + b² = (a +b)²

a² = 121x² = (11x)²                 ;  b² = 4y² = (2y)²

2ab = 2 * 11x * 2y = 44xy

121x² + 44xy + 4y² = (11x + 2y)²