two segments from P are tangent to circle O. If the measure of and P is 60 and the radius of circle O is 12 feet, find the length of each tangent.

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?

Hello!

y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

\(\hrulefill\)

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

\(\hrulefill\)

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

The average rate of change of the function over the interval is 4

From the question, we have the following parameters that can be used in our computation:

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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Answer:

25

Step-by-step explanation:

\(0.09a=75\\a=\frac{75}{0.09} \\0.03*a=0.03*\frac{75}{0.09} =25\)

Answer:

both are 79

Step-by-step explanation:

The perimeter of the figure with side length of 5 units is 50 units

From the question, we have the following parameters that can be used in our computation:

Shape = rectangle

Smaller shapes = squares

Side lengths = 5 units

The perimeter of the figure is calculated as

Perimeter  = Number of visible sides * Side length of the square shape

In this case, we have

Number of visible sides = 10

Substitute the known values in the above equation, so, we have the following representation

Perimeter  = 10 * 5

Evaluate the products

Perimeter  = 50 units

Hence, the perimeter is 50 units

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Answer:

\(\large\boxed{x = -8}\)

Step-by-step explanation:

-6 = x + 2

Subtract 2 from both sides of the equation

\(\large\boxed{x = -8}\)

Hope this helps :)

Answer:

x=-8

Step-by-step explanation:

-x=2+6

calculate

-x=8

change the signs

there ya go x=-8

hope that helped

Answer:

Step-by-step explanation:

It looks like 25, but I have to check it some more.

It looks like there are 25, but I can only give you the answer. I cannot give you a proof

Samples

12821

40604

51215

Answer:a

Step-by-step explanation:

The point (-2, -6) lies on the graph of a function f(x) if the f(x) = 3x^3 + 8x^2 + 5x – 4 divided by x + 2 and found the remainder was r = -6 option fourth is correct.

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)

Let's suppose the divisor is Q

Then from the remainder theorem:

f(x) = (x+2)Q -6

\(\rm 3x^3+8x^2+5x-4=(x+2)Q-6\)

If we put x = -2, then

\(\rm 3(-2)^3+8(-2)^2+5(-2)-4=(-2+2)Q-6\)

\(\rm 3\times-8+8\times4-10-4=-6\)

-24 + 32 -10 -4 = -6

-6 = -6

It means (-2, -6) lies on the function(also refer the graph of the function)

Thus, the point (-2, -6) lies on the graph of a function f(x) if the f(x) = 3x^3 + 8x^2 + 5x – 4 divided by x + 2 and found the remainder was r = -6 option fourth is correct.

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The cuboid in question has a surface area of 202 square units.

We must sum together the areas of all six faces to determine a cuboid's surface area.

The dimensions of the given cuboid are:

length (l) = 9 units

width (w) = 5 units

height (h) = 4 units

The area of each face is given by:

Top and bottom faces:\(lw = 9 * 5 = 45\) square units each

Front and back faces: \(lh = 9 *4 = 36\) square units each

Left and right faces: \(wh = 5 * 4 = 20\) square units each

Therefore, the total surface area of the cuboid is:

\(2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units\)

Hence, the surface area of the given cuboid is 202 square units.

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Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Michelle was paid for that month is $ 4021.625

A linear equation is an algebraic equation of the form y=mx+b. regarding only a regular and a first-order (linear) time period, in which m is the slope and b is the y-intercept. on occasion, the above is called a "linear equation of two variables," where y and x are the variables.

Calculation:-

Percentage of commission = 10.5%

per week paid = $495.50

a. Equation of Michelle paid = 10.5/100X + 495.50

b. The total value of the kayaks she sold was $19 425.

  Michelle was paid for that month = 19 425 × 10.5/100 + 4 × 495.50

                                                          = 2039.625 + 1982

                                                          = $ 4021.625

A linear equation bureaucracy is an immediate line on a graph. A nonlinear equation paperwork an S-curve, bell curve, or any other nonlinear form on a graph. experts in mathematics and physics view linear equations as simple. specialists in mathematics and physics view nonlinear equations as complex.

A linear equation in a single variable is an equation wherein there is handiest one variable present. it is of the form Ax + B = 0, wherein A and B are any real numbers and x is an unknown variable that has the handiest one answer. for instance, 9x + 78 = 18 is a linear equation in one variable.

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Answer:

the area of the rectangle is A=L•W

The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m

A=L-W

27m²=(2W-3m)-W

27m2=2w2-3m-W

2w2-3wm-27m2=0

....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)

W=

2-2

w=(3m± √9m²+216m²)

w=(3m+ √225m²)

W=(3m± 15m...you need only positive root because width cannot be negative

W= 3m+15m

4

W=. 4

18m

W=4.5m ......now find the L

L=2.4.5m-3m

L=9m-3m

L=6m

Answer:

W = 4.5cm

L = 6cm

Step-by-step explanation:

Work Shown:

Complementary angles add to 90 degrees.

A+B = 90

(3x+18)+(2x+17) = 90

5x+35 = 90

5x = 90-35

5x = 55

x = 55/5

x = 11

Then we can determine each angle:

As a check: A+B = 51+39 = 90 to confirm the answer.

Answer:

49.97% probability of getting one child of each sex

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The sex of a children is independent of other children, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The probability that a couple’s first child is a boy is 0.512.

This means that \(p = 0.512\)

The will have two children:

This means that \(n = 2\)

(a) What is the probability of getting one child of each sex?

This is P(X = 1).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 1) = C_{2,1}.(0.512)^{1}.(0.488)^{1} = 0.4997\)

49.97% probability of getting one child of each sex

Answer:

Yes

Step-by-step explanation:

If you simplify the 1st equation,

5x + 9 - 2x = 12

Add like terms

3x + 9 = 12  

Subtract the 9 from both sides

3x = 3

It gives you the same equation as the other one

Answer:

yes they both equal 1

Step-by-step explanation:

Answer:kbef;eohrjkvoubwe

cv bojbDetectives are unsure whether Kendall Postwell will be able to testify at her trial. They say it is a question of competence. What does this MOST likely mean?

A.

Kendall might be determined to be insane and not qualified to testify.

B.

The evidence in Kendall’s case is inconclusive and doesn’t prove anything.

C.

Kendall is an expert witness who has testified many times before.

D.

The police think it will hurt their case if Kendall chooses to testify.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Arc length= \(\frac{interior angle}{360} 2\pi r\)

Answer: A

f(x)=(x-4)^(2)

Step-by-step explanation:

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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Answer:

taena mo bobo mo sa math hindi ka mag kakajowa sa February 14 hahahhahahah

The points that we would find on the graph for |x| + 1 < 3 are -1, 0, and 1.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal= ≥

We have,

|x| + 1 < 3 _____(1)

We will find the value of x which will satisfy the given inequality (1).

For x = -2

|-2| + 1 < 3

2 + 1 < 3

3 < 3 This is not true.

For x = -1

|-1| + 1 < 3

1 + 1 < 3

2 < 3 This is true.

For x = 0

|0| + 1 < 3

1 < 3 This is true.

For x = 1

|1| + 1 < 3

2 < 3 This is true.

For x = 2

|2| + 1 < 3

3 < 3 This is not true.

We see that,

The x values at -1, 0, and 1 satisfy the inequality |x| + 1 < 3.

Thus,

The points that we would find on the graph for |x| + 1 < 3 are -1, 0, and 1.

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1) The value of AA is \(\left[\begin{array}{ccc}25&0&0\\0&4&0\\0&0&16\end{array}\right]\). 2) By solving the matrix equation, we got \(\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right]\) = \(\left[\begin{array}{ccc}-131 \\-1\\7\end{array}\right]\). 3) The value of x and y is -4 and 18

1) A = \(\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right]\)                

AA =  \(\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right]\)   \(\left[\begin{array}{ccc}-5&0&0\\0&-2&0\\0&0&-4\end{array}\right]\)  

AA = \(\left[\begin{array}{ccc}(-5)^2&0&0\\0&(-2)^2&0\\0&0&(-4)^2\end{array}\right]\)

AA = \(\left[\begin{array}{ccc}25&0&0\\0&4&0\\0&0&16\end{array}\right]\)

2)We are given            x₁ - 2x₂ + 3x₃ = 24

                                      -x₁ + 3x₂ - x₃ = -11

                                   2x₁ - 5x₂ + 5x₃ = 24

Now, AX = B

\(\left[\begin{array}{ccc}1&-2&3\\-1&3&-1\\2&-5&5\end{array}\right]\) \(\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right]\) = \(\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right]\)

As, AX = B => X = BA⁻¹      --(1)

Here A⁻¹ = (1/|A|)adjA

Where adjA is Adjoint of matrix A

|A| = 1

AdjA = \(\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right]\)

Therefore, A⁻¹ = \(\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right]\)

Using (1)

X = \(\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right]\)\(\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right]\)

\(\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right]\) = \(\left[\begin{array}{ccc}24 \\-11\\42\end{array}\right]\)\(\left[\begin{array}{ccc}10&7&-7\\3&-1&-2\\-1&1&1\end{array}\right]\)

\(\left[\begin{array}{ccc}x_{1} \\y_{2}\\z_{3}\end{array}\right]\) = \(\left[\begin{array}{ccc}-131 \\-1\\7\end{array}\right]\)

3)  \(\left[\begin{array}{ccc}x+2&6&-5\\7&2y&2x\\2x+6&6&-5\end{array}\right]\) = \(\left[\begin{array}{ccc}2x+6&6&-5\\7&18&-8\\3&-8&11\end{array}\right]\)

So, x + 2 = 2x + 6

       2x - x = 2 - 6

              x = -4

     2y = 18

       y = 9

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The fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

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Answer:

13.5

Step-by-step explanation:

c = 2πr

42.3 = 2(3.14)r

42.3 = 6.28r

6.74 = r

d = r + r

d = 6.74 + 6.74

d = 13.5

Answer:

Step-by-step explanation:

Answer:

33 is the answer for this ez math

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.