Which term describes the figure? Please help

Answer:

23. C

24. B

Step-by-step explanation:

The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))

To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.

The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.

The total number of possible arrangements is given by the factorial of the total number of letters:

Total arrangements = 10!

However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:

Total arrangements = 10! / (2!)

To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.

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If \(f^{-1}(x)\) is the inverse of \(f(x)\), then

\(f\left(f^{-1}(x)\right) = x\)

We're given a domain for \(f(x)\) of \(x\ge0\), so \(f\left(f^{-1}(x)\right) = x\) is valid only for \(f^{-1}(x)\ge0\).

Now,

\(f\left(f^{-1}(x)\right) = \left(f^{-1}(x) + 1\right)^2 + 2 = x\)

Solve for the inverse :

\(\left(f^{-1}(x) + 1\right)^2 = x - 2 \\\\ \sqrt{\left(f^{-1}(x)+1\right)^2} = \sqrt{x-2} \\\\ \left|f^{-1}(x) + 1\right| = \sqrt{x-2}\)

Since \(f^{-1}(x)\ge0 \implies f^{-1}(x)+1 \ge0\), by definition of absolute value we have

\(\left|f^{-1}(x)+1\right| = f^{-1}(x) + 1\)

Then we end up with

\(f^{-1}(x) + 1 = \sqrt{x-2} \\\\ \boxed{f^{-1}(x) = \sqrt{x-2}-1}\)

The length of the hypotenuse is 12.52 yards.

Given that a right triangle, we need to find the value of the hypotenuse x,

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.

We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.

We know that, the cosine of the angle is the ratio of the base to the hypotenuse,

So,

Cos 37° = 10 / x

x = 10 / Cos 37°

x = 12.52

Hence the length of the hypotenuse is 12.52 yards.

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Let n be an odd integer. By definition, n must be an integer not divisible by 2. Hence, when n2 is divided by 8, the remainder must be 1.

Let n be an odd integer. First, we can express n as 2k+1, where k is an integer. Next, when we square n, we get (2k+1)2. Expanding this gives 4k2+4k+1. Dividing this by 8 gives 4k2+k as the quotient and 1 as the remainder. This proves that the square of an odd integer always have a remainder of 1 when divided by 8.

To summarize, when an odd integer n is squared, the remainder when the result is divided by 8 is always 1. This is because an odd integer is not divisible by 2, and so the quotient will not be a whole number when divided by 8.

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Answer:

-1/2 + 2.

Step-by-step explanation:

Using the length formula we know that the length of the given arc is 30.144 miles.

In mathematics, an arc is a portion of the boundary of a circle or curve. It is sometimes referred to as an open curve.

The measurement around a circle that determines its edge is called the circumference, often known as the perimeter.

So, the formula to find the length of the arc is:

Length of an Arc = θ × r

Now, insert values and calculate as follows:

Length of an Arc = θ × r

Length of an Arc = 4π/5 × 12

Length of an Arc = 4π/5 × 12

Length of an Arc = 12.56/5 * 12

Length of an Arc = 2.512 * 12

Length of an Arc =  30.144

Therefore, using the length formula we know that the length of the given arc is 30.144 miles.

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The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:( 175/6)

Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35

Answer:

1. 0.75

2. 0.15

3. 1

Step-by-step explanation:

1. P(student is female) = 1 - 0.25 = 0.75

2. P(student is male and does not walk to school) = 0.25 × 0.6 = 0.15

3. P(student walks to school or does not walk to school) = 0.4 + 0.6 = 1

Answer:

The sum of the probabilities of all possible outcomes is 1.

Given:

Therefore:

Part (a)

\(\begin{aligned}\sf P(\textsf{female}) & = 1 - 0.25\\ & = 0.75\\ & = 75\%\end{aligned}\)

Part (b)

\(\begin{aligned}\sf P(\textsf{does not walk to school}) & = 1 - 0.4\\ & = 0.6\\ & = 60\%\end{aligned}\)

\(\begin{aligned}\implies\sf P(\textsf{student is male and does not walk to school}) & = 0.25 \times 0.6\\ & = 0.15\\ & = 15\%\end{aligned}\)

Part (c)

\(\begin{aligned}\implies\sf P(\textsf{student walks to school or does not walk to school}) & = 0.4+0.6\\ & = 1\\ & = 100\%\end{aligned}\)

Answer:

x = 27 , ∠ EAF = 27°

Step-by-step explanation:

∠ GAF = 90° , then

∠ GAC + ∠ CAF = ∠ GAF , that is

x + 63 = 90 ( subtract 63 from both sides )

x = 27

∠ DAE = 90°

since CD is a straight angle of 180° , then

∠ CAE = 90° , so

∠ CAF + ∠ EAF = ∠ CAE , that is

63° + ∠ EAF = 90° ( subtract 63° from both sides )

∠ EAF = 27°

Answer:

Domain: 0, 1, 2, 3, 4,

Range: 1, 2, 3, 4, 5,

Step-by-step explanation:

Based on the graph the domain of the function is 0, 1, 2, 3, 4, and the range is 1, 2, 3, 4, 5,  therefore, the answer is:

The two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.

What is combination ?

Combination refers to the number of ways a selection of items can be made from a larger set of items without regard to their arrangement. In other words, combinations are a way to calculate the total number of possible groups of items that can be formed, regardless of the order in which the items are selected. The formula for calculating the number of combinations is nCr, where n is the total number of items and r is the number of items being selected.

According to the question:
Let's start by finding the possible prices of the pie. Since the price must be an exact number of pence, we can convert the price range to pence by multiplying each value by 100:

£1.30 = 130 pence

£2.99 = 299 pence

We know that the price plus the 24% tip must be an exact number of pence. If we let x be the price of the pie in pence, then we can write this as:

x + 0.24x = 1.24x

Since 1.24 is not divisible by 5 (which we'll need for the change), we need to find two values of x that differ by a multiple of 5. One way to do this is to start with the lower bound and add multiples of 5 until we get a valid value:

x = 130: 1.24x = 161.2

x = 135: 1.24x = 167.4

x = 140: 1.24x = 173.6 (valid)

x = 145: 1.24x = 179.8

x = 150: 1.24x = 186.0 (valid)

x = 155: 1.24x = 192.2

x = 160: 1.24x = 198.4

So the possible prices of the pie are 140p and 150p. To find the possible amounts of change, we need to subtract each price from 500p (the value of the £5 note) and express the result as a combination of coins. For example:

Price = 140p, change = 360p = 3 x £1 + 1 x 50p + 1 x 10p

Price = 150p, change = 350p = 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p

Therefore, the two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.

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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: Well this one is simple too.

ATQ Angle 4 is 73° so the vertically opposite angle that is angle to will be the same, 73°.

now for the rest two.

lets find angle 1 first. If we find any one from this we can automatically get the other as they are vertically opposite angles.

Angle 1= 180 - Angle 4

Angle 1 = 180-73=107°

We found this coz the Angle 1 and 4 are on the same line which will form a straight angle.

hence, Angle 4 and 2 = 73°

Angle 1 and 3= 107°

Hope it helps. Pls mark brainliest

Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

Answer:

I need to go and take my shower now.

Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)

Answer:

we can do it again and I am a great time with you and your family and friends and family is not good

Answer:

There should be 12 questions

Step-by-step explanation:

Mental Math

Answer:

ln t^5s^6.

Step-by-step explanation:

5In t + 6In s

= ln t^5 + ln s^6

= ln (t^5*s^6)

= ln t^5s^6.

The CDF at P(X > 1)  is 1/16.

CDF stands for the cumulative distribution function. It is a function that maps each possible value of a random variable X to the probability that X takes a value less than or equal to that value.

The cdf given is:

F(x) =0 for x < 0

x^2/16 for 0 <= x < 1

1 - (3-x)^2/16 for 1 <= x < 4

1 for x >= 4

P(X <= 1)

Using the definition of the cdf, we have:

P(X <= 1) = F(1)

Since 0 <= 1 < 1, we have:

F(1) = 1^2/16 = 1/16

So, P(X <= 1) = F(1) = 1/16.

P(X > 2)

Using the definition of the cdf, we have:

P(X > 2) = 1 - P(X <= 2)

Since 0 <= 2 < 4, we have:

P(X <= 2) = F(2) = 2^2/16 = 1/4

Therefore:

P(X > 2) = 1 - P(X <= 2)

=> 1 - 1/4

=> 3/4.

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The required simplified value of the f⁻¹(f(x)) is given as x.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Property of function states that function of function would be x, if the last function is an inverse function of its substituting function or vice versa. So,

f⁻¹(f(x)) = f(f⁻¹(x)) = x

Thus, the required simplified value of the f⁻¹(f(x)) is given as x.

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As per the given details, the value of ff.ds over the region V bounded by the planes x = 0, y = 0, z = 0, z = 4, and the surface of the cylinder x² + y² = 9 in the first octant, where F = xî + xyj + 2k, is 81π.

The divergence theorem relates a flux fundamental across a closed floor S to a triple crucial over strong E enclosed by way of the surface.

It states that for a vector field F and a closed floor S that encloses a solid area E, the outward flux of F across S is equal to the triple necessary of the divergence of F over E.

Mathematically, the divergence theorem can be written as:

∫∫ F · dS = ∭ div(F) dV

To examine ff.Ds over the vicinity V bounded by using the planes x = zero, y = zero, z = zero, z = 4, and the floor of the cylinder x² + y² = 9 within the first octant, in which F = xî + xyj + 2k, we can use the divergence theorem. The first step is to locate the divergence of F:

div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 1 + x

Next, we want to discover the volume enclosed via the surface. The cylinder x² + y² = 9 inside the first octant is a round cylinder with radius 3 and top 4. Therefore, the volume enclosed with the aid of the floor is:

V = ∫∫R (4 - z) dA

= ∫0^3 ∫0^(2π) (4 - z) r dr dθ

= 18π

So,

∫∫S F · dS = ∭V div(F) dV

= ∭V (1 + x) dV

= ∫0^4 ∫0^3 ∫0^(2π) (1 + x) r dθ dz dr

= 81π

Therefore, the value of ff.Ds over the place V bounded through the planes x = 0, y = 0, z = zero, z = four, and the surface of the cylinder x² + y² = 9 inside the first octant, where F = xî + xyj + 2k, is 81π.

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Step-by-step explanation:

Erin is selling books for $12 each. She wants to make more than $180 in book sales.

Write an inequality that can be used to determine the number of books b, she must sell in order to meet her goal, then solve for b.​

12b > 180

12b > 180

divide both sides by 12:

12b/12 > 180/12

b > 15

Erin must sell more than 15 books or a minimum of 16 books.  

Answer:

12b>180

b>15

Step-by-step explanation:

we multiply 12 by b since each book is $12 and then set it to greater than since she wants to make over $180

12b>180
now to solve for b we divide both sides by 12

12b>180
/12.  /12

b>15

Hopes this helps please mark brainliest

SOLUTION AND EXPLANATION

The giving function are

The function h(x) which represent the total monthly revenue is the sum of F(x) and g(x)

Then we rearrange the terms according to their degrees and simplify them

Answer:

34 people. (extremely sorry if this is wrong! please tell me if it is.)

Step-by-step explanation:

197 people were in the survey. First we can subtract 57 from 197 because 57 people dont like cats or dogs.

197-57 = 140

and to find the number of people that chose cats but not dogs, we subtract 106 from 140 which leaves us with 34 people.