Determine the equation of the cirele with center (2, 3) containing the point (7, 15).

The polynomial function in factored form with roots x = 7, x = -10, and x = 3, each with a multiplicity of 1, is  [tex]f(x) = x^3 - 76x + 210.[/tex]

To write a polynomial function in factored form with the given roots, we can use the factored form equation:

f(x) = (x - r1)(x - r2)(x - r3)...

Where r1, r2, r3 represent the roots of the polynomial.

Given the roots x = 7, x = -10, and x = 3, we can write the factored form equation as:

f(x) = (x - 7)(x + 10)(x - 3)

Expanding this equation will give us the polynomial function in factored form:

[tex]f(x) = (x - 7)(x + 10)(x - 3)[/tex]

[tex]= (x^2 - 7x + 10x - 70)(x - 3)[/tex]

[tex]= (x^2 + 3x - 70)(x - 3)[/tex]

[tex]= x^3 - 3x^2 + 3x^2 - 9x - 70x + 210[/tex]

[tex]= x^3 - 76x + 210[/tex]

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Answer: 2916 cubic feet

Step-by-step explanation:

V=(4/3)*3*(9^3)

V=(4/3)*3*729

V=2916

The straight-line distance from your starting point at the end of driving is approximately 24.4 miles.

To find the straight-line distance from your starting point, we can use the Pythagorean states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance you drove west and turned left forms two sides of a right triangle, and the straight-line distance from the starting point will be the hypotenuse.

Given:

Distance driven west = 20 miles

Distance driven south = 14 miles

Using the Pythagorean:

Hypotenuse² = (Distance driven west)² + (Distance driven south)²

Hypotenuse² = 20² + 14²

Hypotenuse² = 400 + 196

Hypotenuse² = 596

To find the length of the hypotenuse (straight-line distance), we take the square root of both sides:

Hypotenuse = √596

Hypotenuse ≈ 24.4 miles (rounded to the nearest tenth)

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Answer:

The answer is number 2

The mode of the data is 0

Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.

It provides an accurate description of the entire data.

The three major measures of central tendency are given as;

The mode is defined as the measure of central tendency representing the most occurring number in a given data set

From the information given, we have;

0, 4 , 3, 4, 0, 9, 1

Then, the mode is 0

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Answer:

Sin θ = 3/5 cos θ = 4/5 tan θ= 3/4

The angle that has been formed and is shown as x is shown as 52.1°.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. The tangent function is denoted as tan.

We can see that we need to find the tangent of the angle;

Tan x = 36/28

x = Tan-1(36/28)

x = 52.1°

Thus it is clear from the calculation that we have done above that the angle that is marked x is 52.1°.

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Answer:

Angles 1 and 8 are alternate exterior angles.

Answer:

We can start by finding the value of the expression inside the tangent function: tan(1/2 (0 + π/2)) = tan(π/4) = 1

Now we can substitute this value into the original equation and simplify:

y = -3 + tan(1/2 (0 + π/2))

y = -3 + 1

y = -2

The vertical shift of the graph is the constant term in the equation, which is -2. Since this value is negative, the graph is shifted downwards. Therefore, the correct answer is (A) 3 units down

Answer:

70cm^2

Step-by-step explanation:

10×5=50cm^2 is the area of the rectangle

18-10=8 is the height of the triangle

8×2.5=20

20÷2=10 is area of half the triangle

10+10=20cm^2 is the area of the triangle

50cm^2+20cm^2=70cm^2

Answer:

Question 3:    5

Question 4:    91

Step-by-step explanation:

[tex](x+5)2-y[/tex]

[tex]x = -2[/tex]

[tex]y =1[/tex]

[tex](-2 + 5)2 - 1[/tex]

[tex](3)2-1[/tex]

[tex]6-1 = 5[/tex]

[tex]3x +4y^2[/tex]

[tex]x = -3[/tex]

[tex]y=5[/tex]

[tex]3(-3)+4(5)^2[/tex]

[tex]-9 + 100[/tex]

[tex]=91[/tex]

Step-by-step explanation:

One rectangle  10 x 6 = 60 cm^2

Two sqaures     2 *    4x4 =  32 cm^2      Total = 92 cm^2

Answer:

The Answer is 80√3 or 138.56 to 2d.p

Step-by-step explanation:

sin 60=L/8

L=sin60×8

L=4√3

Area of rectangle =L×W

A=20×4√3

A=80√3=138.56 to 2d.p

The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

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Answer: [tex]x\approx 6.2[/tex]

Step-by-step explanation:

Detailed explanation is attached below.

Answer:

Step-by-step explanation:

Answer:

  (c)  0 < a < 1

Step-by-step explanation:

You want to know the value of 'a' in y = a·cot(x) that will cause a vertical compression without reflection.

When a function value is multiplied by a factor greater than 1, its graph is expanded vertically. When that factor is less than 1, the graph is compressed, as in the attachment.

If the scale factor is negative, the graph will be reflected across the x-axis.

Here, you want compression without reflection. That requires a positive scale factor less than 1.

  0 < a < 1

The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

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The statement which is true is he has enough of each type of juice to make 1 recipe, the correct option is B.

We are given that;

Orange juice cup= 6

Pineapple juice cup=3

Now,

PART A: To answer this question, we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Felicia has pineapple juice in fluid ounces. We can use the fact that 1 cup = 8 fluid ounces to convert Felicia’s amount of pineapple juice to cups:

32 fluid ounces = 32 / 8 cups = 4 cups

The recipe requires 3 cups of pineapple juice, so Felicia has more than enough pineapple juice. The correct answer is B.

PART B: we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Jared has each type of juice in pints. We can use the fact that 1 pint = 2 cups to convert Jared’s amounts of juice to cups:

8 pints = 8 * 2 cups = 16 cups

Jared has 16 cups of each type of juice. The recipe requires 6 cups of orange juice, 3 cups of pineapple juice, and 1 cup of cranberry juice. This adds up to 10 cups of juice for one recipe. So, Jared has enough of each type of juice to make one recipe and have some left over. However, he does not have enough of each type of juice to make two recipes, since that would require 20 cups of juice in total. T

Therefore, by unitary method the answer will be He has enough of each type of juice to make 1 recipe.

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The calculated value of the conditional probability P(Not A | Not B) is 0.8125

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

The table of values

The probability P(Not A | Not B ) is calculated as

P(Not A | Not B ) = (Not A and Not B)/(Not B)

Using the above as a guide, we have the following:

(Not A and Not B) = 0.65

(Not B) = 0.80

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

P(Not A | Not B ) = 0.65/0.80

Evaluate

P(Not A | Not B) = 0.8125

Hence, the probability P(Not A | Not B) is 0.8125

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Answer:

Part A: The data that Zoe would expect to collect from this question is the amount of time each student spends playing video games. She could collect this data by asking each student how many hours per week they spend playing video games.

Part B: This is not a statistical question because it is asking for a specific answer. A statistical question would be asking for a distribution of the data, such as the average amount of time students spend playing video games or the range of times students spend playing video games.

To make this question statistical, Zoe could ask the following question:

How much time do students in my class spend playing video games per week?

This question is statistical because it is asking for a distribution of the data. Zoe could then collect the data and use it to create a histogram or other graph to show the distribution of the data.

The solution is: 100! different ways can you draw all of the names from the hat.

Here, we have,

if we have n object, and as we know that arrangement given by = n!. (Permutation)

A permutation is a mathematical technique for determining the number of possible arrangements in a sentence where the order of arrangements is important. A common math problem involves choosing some items in a particular order from a set of items.

A permutation also called an "order number" or "sequence", is the rearrangement of the elements of an ordered list so that they correspond one-to-one with themselves. (Faculty; Ouspensky 1937, p. 18). Permutations are said to be ordered combinations. The number of permutations r of n objects acquired simultaneously is determined by the following formula: P(n,r)=n!(n-r)!

Hereafter taking each unique name, we will arrange it in raw, so we can say this problem is equivalently permutation problem, So we can say the way of drawing all names can be done in 100! Way.

So ANSWER IS 100!

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Answer:

The length of the second book is 10.5 inches, while the first book's thickness is in a ratio of 2:1.5, which simplifies to 4:3. Similarly, the length of the first book is also in a ratio of 4:3 with the second book. Hence, we can calculate the second book's length as 14 divided by 4, multiplied by 3, which equals 10.5 inches.

Answer:

Use systems of equations to solve.

Let x represent the cost per pound of the espresso coffee beans and

y represent the cost per pound of the vanilla coffee beans.

6x + 5y = 77.50

20x + 13y = 234.50, both of these are given.

Rewrite these equations so you can eliminate one of the variables;

60x + 50y = 775, Multiply both sides of the equation by 10

60x + 39y = 703.5, Multiply both sides of the equation by 3

Now Subtract equation 2 from equation 1,

11y = 71.5

y = 6.5

Solve for x,

6x + 5(6.50)= 77.50

x = 7.50

Therefore, the cost per pound of the espresso coffee beans is $7.50, and

the cost per pound of the vanilla coffee beans is $6.50.

Answer:

[tex]\huge\boxed{\sf 0.00008\ km}[/tex]

Step-by-step explanation:

= 8 cm

= 8 / 100,000 km

[tex]\rule[225]{225}{2}[/tex]

Answer:

0.00008

80 cm is 0.0008 so you know I just assumed

the solution to the equation log2x + log4x + log16 = 7  the logarithms using the properties of Logarithms is x ≈ 53.408.

To solve the equation log2x + log4x + log16 = 7, we can simplify the logarithms using the properties of logarithms.

First, we can use the property loga + logb = log(ab) to combine the logarithms:

log2x + log4x + log16 = log(2x * 4x * 16)

Next, we simplify the expression inside the logarithm:

log(2x * 4x * 16) = log(32x^3)

Now, our equation becomes:

log(32x^3) = 7

To eliminate the logarithm, we can rewrite the equation in exponential form:

32x^3 = 10^7

Simplifying further:

32x^3 = 10,000,000

Now, we can solve for x by dividing both sides of the equation by 32:

x^3 = 10,000,000 / 32

x^3 = 312,500

To find the value of x, we take the cube root of both sides:

x = ∛312,500

x ≈ 53.408

Therefore, the solution to the equation log2x + log4x + log16 = 7 is x ≈ 53.408.

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Answer:

The odd numbers between 1 and 7 are 1, 3, 5, and 7. There are four of them.

The total number of balls in the bag is 7.

Therefore, the probability of picking an odd number is:

number of odd numbers / total number of balls = 4/7

So the probability of picking an odd number is 4/7

The transformations to the parent function are given as follows:

The parent function for this problem is given as follows:

y = 1/x.

The transformed function for this problem is given as follows:

y = 3/(x + 5) - 3.

Hence the  transformations to the parent function are given as follows:

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