find the arc length of a central angle of 90° in a circle whose radius is 4 inches

The inverse of the function f(x) = 15x + 3 is found by swapping x and f(x) in the equation and solving for f^-1(x), which leads to f^-1(x) = (x - 3) / 15.

To find the inverse of the function f(x) = 15x + 3, it is necessary to first swap x and f(x) in the function equation. This results in x = 15f^-1(x) + 3. Secondly, solving for f^-1(x) means isolating this on one side of the equation. That results in f^-1(x) = (x - 3) / 15.

So, the inverse function of f(x) = 15x + 3 is f^-1(x) = (x - 3) / 15.

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There are total 56 ways to fill the open spot .

A combination is a way for determining the number of possible arrangements in a collection of items where the order of selection does not matter.

[tex]C(n, r) =\frac{n!}{(n - r)!r!}[/tex]

where,

n is the number of items in set.

r is the number of items selected from the set.

According to the question we have,

Number of altos, n = 8

Number of  open spots, r = 3

Therefore, the number of ways to fill open spots = C(8, r)

Number of ways = [tex]\frac{8!}{3!(8-3)!}[/tex]

Number of ways = [tex]\frac{8!}{5!3!}[/tex][tex]= \frac{(8)(7)(6)(5!)}{5!3!}[/tex] = [tex]\frac{(8)(7)(6)}{(3)(2)} =8(7) = 56[/tex]

Hence, there are total 56 ways to fill the open spot .

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Answer:

x=4

Step-by-step explanation:

Answer:

.C

Step-by-step explanation:

Final answer:

There are 88 different ways of choosing one man and one woman for a committee.

Explanation:

In order to find the number of different ways of choosing one man and one woman for a committee, we can use the concept of combinations. The number of ways of choosing one item from a group of n items is denoted by n C 1, which is equal to n. So, the number of ways of choosing one man from a group of 11 men is 11, and the number of ways of choosing one woman from a group of 8 women is 8. To find the total number of ways, we multiply these two numbers:

Total number of ways = 11 * 8 = 88

Therefore, there are 88 different ways of choosing one man and one woman for a committee.

The value of y in the table is 165 more than the value of y in the graph

The points on the table are represented as:

So, the equation of the table is calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]

This gives

[tex]y = \frac{280 - 210}{4 - 3} (x - 3) + 210[/tex]

[tex]y = 70(x - 3) + 210[/tex]

Expand

[tex]y = 70x - 210 + 210[/tex]

[tex]y = 70x [/tex]

When x = 11,

We have:

[tex]y = 70 \times 11[/tex]

[tex]y = 770[/tex]

The points on the graph are represented as:

So, the equation of the graph is calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]

This gives

[tex]y = \frac{220 - 110}{4 - 2} (x - 2) + 110[/tex]

[tex]y = 55 (x - 2) + 110[/tex]

Expand

[tex]y = 55x - 110 + 110[/tex]

[tex]y = 55x[/tex]

When x = 11,

We have:

[tex]y = 55 \times 11[/tex]

[tex]y = 605[/tex]

Calculate the difference between the y-values

[tex]y_2 - y_2 =770 - 605[/tex]

[tex]y_2 - y_2 =165[/tex]

Hence, the value of y in the table is 165 more than the value of y in the graph

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Let us say that the intersection point of lines AB and CD is called point E. The lines AB and CD are perpendicular to each other which also means that the triangle CEB is a right triangle.

Where the line CB is the radius of the circle while the side lengths are half of the whole line segment:

EB = 0.5 AB = 0.5 (8 ft) = 4 ft

CE = 0.5 CD = 0.5 (6 ft) = 3 ft

Now using the hypotenuse formula since the triangle is right triangle, we can find for the radius or line CB:

CB^2 = EB^2 + CE^2

CB^2 = (4 ft)^2 + (3 ft)^2

CB^2 = 16 ft^2 + 9 ft^2

CB^2 = 25 ft^2

CB = 5 ft = radius

Answer:

5ft

Step-by-step explanation:

Answer:

The independent variable is time.

Step-by-step explanation:

Given,

The original number of pigs on the island = 20,

Also, the number of pigs doubled each year,

After 1 year the pigs = 20(2),

After 2 years = 20(2)²,

After 3 years = 20(2)³,

......................., so on...

Similarly, the number of pigs after t years would be,

[tex]y=20.2^t[/tex]

⇒ The value of y depends upon t,

⇒ The number of pigs depends upon the time ( in years ),

Since, the variable in which the other variable depends is called independent variable,

Hence, the independent variable must be time.

Doing this, we get that 32 feet are needed.

Square:

The area of a square of side s is:

[tex]A = s^2[/tex]

And the perimeter is:

[tex]P = 4s[/tex]

Area of 64 square feet

This means that:

[tex]s^2 = 64[/tex]

[tex]s = \sqrt{64}[/tex]

[tex]s = 8[/tex]

The side of the square is of 8 feet.

Perimeter:

Side of 8 feet, so:

[tex]P = 4s = 4(8) = 32[/tex]

32 feet of chain fence are needed.

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the 2 parallel lines mean that the lines are equal

 SO since BD = 18, DC is also 18

Answer: D. 1816214400

Step-by-step explanation:

When we select r things from n things in order we apply permutations and the number of ways to select r things = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]

Given : Total player = 15

Required number of players for Batting order = 9

Then the number of different ways to select 9 person batting order so that he arrange the players in the lineup would be [tex]^{15}P_9=\dfrac{15!}{(15-9)!}[/tex]

[tex]=\dfrac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6!}{6!}[/tex]

[tex]=1816214400[/tex]

∴ The number of different ways can he arrange the players in the lineup = 1816214400

Hence, the correct answer is D. 1816214400

To solve this problem, we use the combination equation to find for the possible groups of answer to the questions. Since we are looking for at least 5 correct answers out of 10 questions, therefore we find for 10 ≥ r ≥ 5. We use the formula for combination:

nCr = n! / r! (n – r)!

Where,

n = total number of questions = 10

r = questions with correct answers

For 10 ≥ r ≥ 5:

10C5 = 10! / 5! (10 – 5)! = 252

10C6 = 10! / 6! (10 – 6)! = 210

10C7 = 10! / 7! (10 – 7)! = 120

10C8 = 10! / 8! (10 – 8)! = 45

10C9 = 10! / 9! (10 – 9)! = 10

10C10 = 10! / 10! (10 – 10)! = 1

Summing up all combinations will give the total possibilities:

Total possibilities = 252 + 210 + 120 + 45 + 10 + 1 = 638

Answer: 638

To find out when the car and truck will pass each other, set up an equation where the sum of the distances covered by each at their respective speeds equals 305 miles. After solving, it's determined they will pass each other at 4:00 p.m.

To determine at what time the car and truck will pass each other, we need to calculate how far each vehicle will have traveled before they meet. The car leaves St. Louis at 1:00 p.m., while the truck leaves Chicago at 2:00 p.m., one hour later. We assume they meet after the car has been traveling for t hours and the truck for t - 1 hours.

The distance the car travels is the product of its speed and time, which can be calculated as 65 miles per hour times t hours. The truck's distance is 55 miles per hour times (t - 1) hours. Since the total distance between St. Louis and Chicago is 305 miles, we combine these distances to form the equation:

65t + 55(t - 1) = 305

Solving this equation:

Since the car has been traveling for 3 hours after 1:00 p.m., the two vehicles will pass each other at 4:00 p.m.

T = total cost

X= number of rides

T=4.00x+9.00

The quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.

In the given diagram, overline PN serves as the perpendicular bisector of overline AB, implying that point N lies on the midpoint of segment AB.

Additionally, overline PN functions as the angle bisector of ∠CPD. Since ∠CPD measures x degrees, by the angle bisector theorem, ∠DPN and ∠DPB each measure x/2 degrees.

Now, to determine sin ∠DPB, we consider the right triangle DPN. By definition, sin θ = opposite/hypotenuse.

In this triangle, the opposite side to ∠DPB is overline DN, and the hypotenuse is overline DP.

Therefore, sin ∠DPB = DN/DP.

Since ∠DPN = x/2, applying trigonometric ratios in right triangle DPN, sin(x/2) = DN/DP.

Hence, the quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.

The probable question may be:

In the diagram, overline PN is the perpendicular bisector of overline AB and is also the angle bisector of ∠ CPD If m∠ CPD=x , which quantity is equal to sin ∠ DPB ?

A. sin π /2

B. sin x/2

C. cos x/2

D. cos π /3