Find the length of an arc when the radius is 15 feet and the measure of the central angle 135 degrees. Round to nearest hundredth.

The inverse property of multiplication states that if you multiply a number by its reciprocal, also called the multiplicative inverse, the product will be 1.

So the reciprocal of 2 is 1/2 because 2*1/2=1

Therefore , the solution of the given problem of equation comes out to be k1 = - 0.67 and k2 = -0.1.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A scientific statement that verifies the equality of two formalisms is known as an equation in algebra. For instance, the pieces ptdc + 6 and 12 are separated by an equal sign in the solution obd + 6 = 12. The relationship between the two phrases on either flank of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 4x – 4 = 0.

Here,

If y varies in this case simply also as square of x

k is the proportionality constant, and

y = kx² in mathematics.

Considering y = -54 and x = 9,

y = kx²

k = y/ x²

k = -54/ 9²

k = -54/81

k1 = - 0.67

Moreover, if y=-11/3 and x=6,

k = y/x²

k = -3.667/ (6)²

k = -3.667/36

k2 = -0.1

Therefore , the solution of the given problem of equation comes out to be k1 = - 0.67 and k2 = -0.1.

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Answer:

36

Step-by-step explanation:

do x to the second power then multiply 4 to get your answer

Answer:

B.

Step-by-step explanation:

Relate a vertical line test to understanding functions.

B. Each vertical line drawn through the graph will

intersect a function in many locations

intersect a function in only one location

The vertex, focus, and directrix of the parabola x^2 = 2y are Vertex: (0, 0), Focus: (0, 1/2), Directrix: y = -1/2

The given equation is x^2 = 2y, which is a parabola with vertex at the origin.

The general form of a parabola is y^2 = 4ax, where a is the distance from the vertex to the focus and to the directrix.

Comparing the given equation x^2 = 2y with the general form, we get 4a = 2, which gives us a = 1/2.

Hence, the focus is at (0, a) = (0, 1/2), and the directrix is the horizontal line y = -a = -1/2.

Therefore, the vertex, focus, and directrix of the parabola x^2 = 2y are:

Vertex: (0, 0)

Focus: (0, 1/2)

Directrix: y = -1/2

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Answer:

350 miles per week

Step-by-step explanation:

That'd be 70 miles each day for 5 days, or 350 miles per week.

Answer:

A

Step-by-step explanation:

In a slope-intercept equation, the format goes like this:

M = Slope

B = Y-intercept

In the equation, y = 6/9x + 3:

The slope is 6/9

The y-intercept is 3.

So what the question means by "cross the y-axis" is when the line on the graph is going through the y-intercept point.

Because the y-intercept is 3, the ordered pair would look like this:

(0, 3)

Note: The y-intercept is when the x-intercept has a value of 0 and the y-intercept is only on the y-axis, never the x-axis.

Therefore, the answer would be Option A. (0, 3)

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

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

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

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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QUESTION A

Player E has 3.1 free throw attempts and 10.4 points.

This is represented by the point labelled D in the image.

QUESTION B

The point (2.1, 18.6) can be compared to the table.

When we do so, we can see that player B has the same values for free throw attempts and points.

Thus, that point represents the data for player B.

QUESTION C

Player O scored 14.3 points and 4.8 free throw attempts. This can be shown in the

The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

Step 1: Simplify both sides of the equation.

0.4(12−3x)=0.3(12x−16)

(0.4)(12)+(0.4)(−3x)=(0.3)(12x)+(0.3)(−16)(Distribute)

4.8+−1.2x=3.6x+−4.8

−1.2x+4.8=3.6x−4.8

Step 2: Subtract 3.6x from both sides.

−1.2x+4.8−3.6x=3.6x−4.8−3.6x

−4.8x+4.8=−4.8

Step 3: Subtract 4.8 from both sides.

−4.8x+4.8−4.8=−4.8−4.8

−4.8x=−9.6

Step 4: Divide both sides by -4.8.

−4.8x /−4.8  =  −9.6 /−4.8

x = 2

The final expression is 20(5x - 1)2 + 2x + 8.

The given expression is (20x2-12x+8)+ (2x+8). We are required to simplify the given expression.To do that, we will first simplify the expressions inside the parentheses followed by the addition.(20x2-12x+8) can be written as 4 * 5x2-3x+2. This is because we can take 4 as the GCF (Greatest Common Factor) from the given expression. 4 is also a perfect square so we can write 4 * 5x2-3x+2 as 2 * 2 * 5x2-3x+2.

This expression can further be simplified using the (a + b)2 formula which is a2 + 2ab + b2. In this case, a is 5x and b is 1. Hence, we can write 2 * 2 * 5x2-3x+2 as 2 * 2 * (5x - 1)2. Now, the given expression becomes 2 * 2 * (5x - 1)2 + (2x + 8).We will simplify this expression further by distributing the factor 2 on the right-hand side of the addition. Therefore, the given expression becomes 2 * 2 * (5x - 1)2 + 2x + 2 * 4. This can be simplified to get the following expression:20(5x - 1)2 + 2x + 8We have now successfully simplified the given expression.

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Answer:

Step-by-step explanation:

Plant A growth over 2 weeks:

Average rate of change after 2 weeks or 14 days:

If you need it in inches, then convert as below:

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

let distance=d

d²=4²+(2+4)²=16+36=52=4×13

d=2√13

a) Rocky Mountain should order 200 tires each time it places an order.

b) The total cost of this policy is $17,160.

a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:

If fewer than 200 tires are ordered: The purchase price is $25 per tire.

If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.

If 8,000 or more tires are ordered: The purchase price is $13 per tire.

Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.

b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:

Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200

Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950

Therefore, the total cost of this policy is $40,950.

Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.

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In cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. One such method is called standardization.

Cluster analysis is a data mining approach that is widely utilized in data processing, image analysis, and other data-based analytics applications. It groups items that have comparable characteristics into clusters by separating them from other objects that do not share the same features.

Standardization is the process of converting variables with various scales to a common scale so that they can be compared fairly.

Standardization involves transforming all of the variables into comparable units of measurement by converting them into z-scores. This allows for the comparison of values without being affected by the different units of measurement.

The method that can be used to reduce bias due to the difference in units of measurement in cluster analysis is standardization, which converts variables with various scales to a common scale so that they can be compared fairly. This ensures that each variable contributes equally to the distance between the clusters.

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The  required answer is the angle between vectors a and b is 44.8 degrees.

To find the angle θ between two vectors a and b, we use the dot product formula:
a · b = |a| |b| cos θ

where |a| and |b| are the magnitudes of vectors a and b, respectively.
First, let's calculate the dot product of a and b:
a · b = (9)(2) + (-1)(0) + (-5)(-8) = 18 + 40 = 58
Variable  were explicit numbers solve a range of problems in a single computation. The quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula. A variable is either a symbol representing an unspecified term of the theory , or a basic object of the theory that is manipulated ,without referring to its possible intuitive interpretation.
Next, let's calculate the magnitudes of vectors a and b:
|a| = sqrt(9^2 + (-1)^2 + (-5)^2) = sqrt(107)
|b| = sqrt(2^2 + 1^2 + (-8)^2) = sqrt(69)
the angle θ by taking the inverse cosine of the cosine value: θ = (57 / (√107 * √69)
Now we can substitute these values into the dot product formula to solve for θ:
58 = sqrt(107) sqrt(69) cos θ
cos θ = 58 / (sqrt(107) sqrt(69))
θ = cos^-1(58 / (sqrt(107) sqrt(69)))
Now you have the angle θ between the two vectors a and b.
Using a calculator, we find that θ is approximately 44.8 degrees.

Therefore, the angle between vectors a and b is 44.8 degrees.

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Answer:

5y+11

Step-by-step explanation:

y+3+4(y+2)

Use the distributive property to multiply 4 by y+2.

y+3+4y+8

Combine y and 4y to get 5y.

5y+3+8

Add 3 and 8 to get 11.

Answer:

3332 green beads

Step-by-step explanation:

There are 1428 more green beads than red beads.

There are 3,332 greed beads in the box

Given :

A box contains red, purple and green beads in the ratio 4:6:7

From the given ratio,

number of red beads = 4x

number of purple beads= 6x

number of green beads= 7x

There are 1428 more green beads than red beads.

green  beads =1428 + red beads

\(7x=1428+4x\\3x=1428\\x=476\)

we know that number of green beads= 7x

number of green beads= \(7(476)=3332\)

There are 3,332 greed beads in the box

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Answer:

n + 32 = 59.13

Step-by-step explanation:

n + 32 = 59.13

Answer:

32+n=59.13?

Step-by-step explanation:

I hope this helps im bad at math ;-;

The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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Answer:

\(n\)

Step-by-step explanation:

The expression \(n+1\) represents infinite numbers, because \(n\) can be all positive numbers, all negative numbers, or can be an element of the whole number field.

So, generally speaking, the numbers less than \(n+1\) are \(n\), because \(n<n+1\).

Therefore, an expression less than the given one is \(n\)

Answer:

n+1

Step-by-step explanation:

The given polynomial is

30x^3 + 83x^2 + 37x - 30

We want to divide it by 3x + 5. We would apply the method of long division. The steps are shown below

The result of dividing 30x^3 + 83x^2 + 37x - 30 by 3x + 5 = 10x^2 + 11x - 6

This is a quadratic polynomial. We would simplify this quadratic polynomial by applying the method of factorisation. The first step is to multiply 10x^2 with - 6. It becomes - 60x^2. We would find two terms such that their sum or difference is 11x and their product is - 60x^2. The terms are 15x and - 4x. By replacing 11x with 15x - 4x, we have

10x^2 + 15x - 4x - 6

We would factorise by grouping. We have

5x(2x + 3) - 2(2x + 3)

Since 2x + 3 is common, it becomes

(2x + 3)(5x - 2)

The other two factors are (2x + 3)(5x - 2)

a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

To write a rational number as a decimal, you need to divide the numerator by the denominator. Let's go through each option to determine which decimal is repeating or terminating.

a. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

b. 0: This decimal is also terminating because there are no numbers after the decimal point. The rational number is 0.

c. 0.16 overbar: This decimal has a line over the 16, indicating that it is repeating. The rational number is 0.161616...

d. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

So, to summarize:

a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

.

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Step-by-step explanation:

For the first question, let's add the %'s

37% + 13% + 25% + 25% = 100%

So it looks like you have a 100% chance to win a prize.

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

For the second question

It cost $2 to play

Soda - $1

Candy Bar - $1

Toy - $3

Mega Win - $40

It looks like 2 out of 4 (50%) cost more than the price to play.

So we add the % of the Toy and Mega since those are the ones more than $2

25% + 13% = 38% chance to win a prize more than the cost to play

Option B. The value of the data set that measures the average value of all the elements of the data set. The mean is the average of all the values in the data set.

The mean is a measure of central tendency that is used to calculate the average value of a data set. In order to calculate the mean, all of the values in the data set are added together and then divided by the number of values in the data set. The mean is a good measure of central tendency to use when the data set is symmetrical.

This is because the mean is calculated by adding all of the values in the data set together and then dividing by the number of values in the data set. This gives each value in the data set an equal weight.

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Answer:

the first one x = -2

Step-by-step explanation:

Let's solve your equation step-by-step.

4x−6=10x−3

Step 1: Subtract 10x from both sides.

4x−6−10x=10x−3−10x

−6x−6=−3

Step 2: Add 6 to both sides.

−6x−6+6=−3+6

−6x=3

Step 3: Divide both sides by -6.

Answer:

x = -1/2

Step-by-step explanation:

4x - 6 = 10x - 3

    +6           +6

  4x = 10x + 3

-10x   -10x

-6x = 3

3 / -6 = -1/2