A circle has a radius of 3 feet. What is the arc length subtended a central angle of 90 degrees?

Answer: 8

Step-by-step explanation:

32/4

Answer: $2.52

Step-by-step explanation:

Since 4.5% = 0.045 we can just take that and multiply by the item cost, $56, and get $2.52. Therefore that is the fee.

Answer: sometimes

Step-by-step explanation:

sometimes

The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. ... All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.

Answer:

A- The point-slope form of a line parallel to another line is given by y - y1 = m(x - x1), where m is the slope of the original line. The slope of the line x+2y=6 is -1/2. So, the equation of the line parallel to x+2y=6 through (8,3) is y - 3 = -1/2 (x - 8), which can be written in standard form as -2x + y = -11.

B- The point-slope form of a line perpendicular to another line is given by y - y1 = -1/m(x - x1), where m is the slope of the original line. The slope of the line x+2y=6 is -1/2. So, the equation of the line perpendicular to x+2y=6 through (8,3) is y - 3 = 1/2 (x - 8), which can be written in standard form as 2x + y = 15.

C- To graph the three lines, we can plot the x- and y-intercepts of each line and then draw a line through the points.

The x-intercepts are (-11/2,0), (0,-15), (0,-11) and the y-intercepts are (0,3), (0,7.5) and (0,5.5) respectively.

For a more detailed graph you can use a graphing software or calculator.

Answer:

Biased

Step-by-step explanation:

Asking people about their opinions on the park while in the park would give biased results. To get unbiased results, Kyle would have to ask people outside the park their opinions.

Answer:

¡Hola! Su escritura a mano es ilegible para leer.

Answer:

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

Step-by-step explanation:

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The value of x in the following diagram in which the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8, is 3.5 units.

The line which is drawn from the center of the circle perpendicular to  the chord in the circle bisect the chord into two equal shape.

In the given, diagram the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8.

These both the lines are equal in length as both are drawn from the center of the circle and has a perpendicular bisector for the 15 units length chord in the circle. Thus,

\(3x+1=x+8\\3x-x=8-1\\2x=7\\x=\dfrac{7}{2}\\x=3.5\)

Thus, the value of x in the following diagram in which the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8, is 3.5 units.

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Answer:

4

Step-by-step explanation:

Given

2y + 3 ≤ 11 ( subtract 3 from both sides )

2y ≤ 8 ( divide both sides by 2 )

y ≤ 4

Since y has to be less than or equal to 4

Then the largest value y could be is 4

The annual interest rate is approximately 4.68%.

To find the annual interest rate, we can use the formula for compound interest:

\(A = P(1 + r/n)^(nt)\)

Where:

A = Final account balance ($92,501.14)

P = Principal amount ($12,000)

r = Annual interest rate (to be determined)

n = Number of times interest is compounded per year (monthly, so n = 12)

t = Number of years (18)

We can rearrange the formula to solve for the annual interest rate (r):

\(r = (A/P)^(1/(n*t)) - 1\)

Substituting the given values:

r = ($\(92,501.14/$12,000)^(1/(12*18)) - 1\)

Calculating this expression, we find:

r ≈ 0.0468

To convert this decimal value to a percentage, we multiply by 100:

r ≈ 4.68%

Therefore, the annual interest rate is approximately 4.68%.

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The option (A) x → -∞, f(x) → ∞ and x → ∞, f(x) → -∞ if the polynomial function is  f(x) = -x⁵ + 9x⁴ - 18x³.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The polynomial function is:

f(x) = -x⁵ + 9x⁴ - 18x³

After plotting the graph of the polynomial function:

From the graph;

x → -∞, f(x) → ∞

x → ∞, f(x) → -∞

Thus, the option (A) x → -∞, f(x) → ∞ and x → ∞, f(x) → -∞ if the polynomial function is  f(x) = -x⁵ + 9x⁴ - 18x³.

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Answer:

C.) 2x+3 = 12

Step-by-step explanation:

x+x=2x

2x-(-3) is 2x+3

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The 30th partial sum of the sequence 5x-12 = 1965

To derive the 30th partial sum of the sequence 5x -12, we need to add up to the first 30 terms of the sequence.

Th e nth term of the sequence will be:

5 -12

the first 30th terms are:

5(1) -12 = -7

5(2) -12 = -2

5(3) -12 = -3

5(4)  -12 = -8

and so on

So to get the 30th partial sum, we write:
-7 + (-2) = 3+ 8 ...... + (5(30)-12

If simplified, this expression will given us:

S = (n/2) (a+l)

In this case,

s is the sum of the n terms
A is the first term and
L is the last term.

In this ase, a = -7 (the first term) and L= 5(30) -12 = 138 (the 30th term) So  for the partial sum we say:

S30 = (30/2) (-7 + 138) = 30(131)/2
S30 = 1965

Thus, the partial sum of the sequence 5x-12) is 1965

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Step-by-step explanation:

8

y

Find

x

when

y

=

3

and

R

=

5

Give your answer as an improper fraction in its simplest form.

The range of value of x in the inequality x/7 ≥ -6 is x≥ -42

Inequality, is a statement of an order relationship. Some terms used in inequality are ,greater than, greater than or equal to, less than, or less than or equal to. They are used between two numbers or algebraic expressions.

greater than has the sign >

greater than or equal to has the sign ≥

less than has the sign < and

less than or equal to has ≤

solving the range of value of x in the inequality x/7 ≥- 6

multiply both sides by 7

x ≥ -42

Therefore the range of value of x is x ≥ -42

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It is important to know that the shaded area refers to the difference between the large rectangle and the smaller. So, let's find the area of each rectangle.

Then, we subtract

Answer:

The new interest rate is about 0.1038.

As a percent, this is about 10.4%.

Step-by-step explanation:

We are given:

\(\displaystyle A=250(1.1)^t\)

From this, we can determine that the interest rate is compounded annually at 10%.

We want a new equation that keeps A and P but the interest rate is compounded quarterly.

Compound interest is given by:

\(\displaystyle A=P(1+\frac{r}{n})^{nt}\)

Since we are compounding quarterly, n = 4. Since the rate is 10%, r = 0.1. P stays at 250. Therefore:

\(\displaystyle A=250(1+\frac{0.1}{4})^{4t}\)

Add:

\(\displaystyle A=250(1.025)^{4t}\)

Rewrite:

\(A=250((1.025)^4)^t\)

So:

\(A\approx 250(1.1038)^t\)

Therefore, the approximate new interest rate is 1.1038 - 1 or about 0.1038.

As a percent, this will be 0.1038 or about 10.4%.

Answer:

Step-by-step explanation:

You can just check the values:

A.  x = 2, y = 8

x + 3y = 2 + 3×8 = 26 not <16  ⇒  NOT these values

B.   x = 9, y = 2

x + 3y = 9 + 3×2 = 15  <16

x + y = 9 + 2 = 11  >10

YES, x = 9, y = 2 are solutions of the  system of inequalities

C.  x = 1, y = 5

x + 3y = 1 + 3×5 = 16 not <16  ⇒  NOT these values

D.  x = 7, y = 2

x + 3y = 7 + 3×2 = 13  <16

x + y = 7 + 2 = 9 not >10  ⇒  NOT these values

Answer:

The correct answer is A and C.

1. 45 out of the 105 tiles to be vowels.

2. 10 out of the 20 cards to have flowers on them.

1. The expected number of vowels among the 105 tiles, we can multiply the proportion of vowels by the total number of tiles:

Expected number of vowels

= Proportion of vowels x Total number of tiles

= (3/7) x 105

= (3/7) x 105

= 45

Therefore, you would expect 45 out of the 105 tiles to be vowels.

2. Now, to find the expected number of cards with flowers among the 20 cards, we can multiply the proportion of cards with flowers by the total number of cards:

Expected number of cards with flowers

= Proportion of cards with flowers x Total number of cards

= (2/4) x 20

= 10

Therefore, you would expect 10 out of the 20 cards to have flowers on them.

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Answer:

Cosine is the x-coordinate of an angle. For example, cosine of 2pi is 1, because at cosine 2pi lies the point (1,0) on the unit-circle. Another example of cosine is that the cosine of pi/4 is sqrt(2)/2.

Answer:

238

Step-by-step explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

given

3 | 2x - 9 | + 7 ( substitute x = - 34 )

= 3 | 2(- 34) - 9 | + 7

= 3 | - 68 - 9 | + 7

= 3 | - 77 | + 7

= 3 | 77 | + 7

= 3 × 77 + 7

= 231 + 7

= 238

We can convert the equation of the line in vector form by imposing i cap ,j cap and k cap with direction ratios.

The movement of an object from one place to another is described using vectors. Vectors can be represented as points in a coordinate system in the cartesian system. Similar to this, a "n" tuple can be used to represent vectors with "n" dimensions.

In physics, a vector is a quantity with both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity. Simply subtract the starting point from the terminal point to determine the vector in component form given the initial and terminal points.

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The area of the shaded diagonal plane is  17.5 square units.

The area of the shaded diagonal plane is calculated as follows:

Using Pythagoras' theorem, let the hypotenuse formed by the diagonal be x

x² = 3² + 5²

x² = 9 + 25

x² = 34

x = √34

The shape of the shaded plane is a rectangle.

The area of the rectangle will be:

Area = length * width

Area = √34 * 3

Area do the shaded plane = 17.5 square units

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Answer:

6 ^ 6

Step-by-step explanation:

hope this helps!

\(\implies {\blue {\boxed {\boxed {\purple {\sf { \: C. \:{6}^{5} }}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( {6}^{2} \times {6}^{3} \)

➺\( \: {6}^{2 + 3} \)

➺\( \: {6}^{5} \)

\( {a}^{m} \times {a}^{n} = {a}^{m + n} \)

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♬}}}}}\)

Answer:

f(4) = 13

Step-by-step explanation:

f(4) = 2(4)+5
f(4) = 13

Answer:

13

Step-by-step explanation:

f ( x ) = 2x + 5

To find : f ( 4 )

f ( 4 ) = f ( x )

Here,

x = 4

So,

f ( 4 ) = 2 ( 4 ) + 5

        = 2*4 + 5

        = 8 + 5

f ( 4 ) = 13

Hey there!

“Write 9 1/12 as a decimal”

9(12) + 1 / 12

9(12) = 108

108 + 1/ 12

108 + 1 = 109

109/12

109/12 = 9.083

Answer: 9.083

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The Probability that exactly one light bulb is defective is approximately 0.251.

The probability of exactly one light bulb being defective can be calculated using combinations and the concept of probability.

In this case, we have a total of 15 light bulbs, of which 5 are defective. We want to select 6 light bulbs at random, and we want exactly one of them to be defective.

The number of ways to choose one defective bulb from the 5 defective bulbs is given by "5C1" (read as 5 choose 1), which is equal to 5.

The number of ways to choose the remaining 5 non-defective bulbs from the 10 non-defective bulbs is given by "10C5" (read as 10 choose 5), which is equal to 252.

The total number of ways to choose any 6 bulbs from the 15 available bulbs is given by "15C6" (read as 15 choose 6), which is equal to 5005.

To calculate the probability of exactly one bulb being defective, we divide the number of favorable outcomes (where exactly one bulb is defective) by the total number of possible outcomes.

So, the probability can be calculated as:

P(exactly one defective) = (5C1 * 10C5) / 15C6

                         = (5 * 252) / 5005

                         = 1260 / 5005

                         ≈ 0.251

Therefore, the probability that exactly one light bulb is defective is approximately 0.251.

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