If a chord of a circle is 6 and is twice as far from the center chord of length 12, how long is the radius of the circle?

The cubic function obtained after a vertical stretch by a factor of 6 and a translation 3 units left from the parent function y = x³ is y = 6x³ + 54x² + 162x + 162.

To determine the cubic function obtained from the parent function y = x³ after the given transformations (vertical stretch by a factor of 6 and a translation 3 units left), we can apply the transformations to the parent function step by step.

Vertical stretch by a factor of 6:

The vertical stretch multiplies the function by a factor of 6. Therefore, the resulting function becomes y = 6x³.

Translation 3 units left:

The translation of 3 units left shifts the function horizontally to the left. To achieve this, we replace x with (x + 3) in the function obtained from the previous step.

Thus, the final cubic function after the transformations is:

y = 6(x + 3)³

Simplifying the expression further, we can expand the cube:

y = 6(x + 3)(x + 3)(x + 3)

y = 6(x² + 6x + 9)(x + 3)

y = 6(x³ + 9x² + 27x + 27)

Hence, the cubic function obtained after a vertical stretch by a factor of 6 and a translation 3 units left from the parent function y = x³ is y = 6x³ + 54x² + 162x + 162.

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Answer:

Step-by-step explanation:

divide the \(x-x_{1}\) from the right side to isolate the m.

The probability that none of them are between 46 cm and 48 cm is 0.422

From the given data,

A botanist wanted to know if the stem lengths of daffodils differed depending on which side of a building they grew on.

South side of the building

First quartile Q1 = 43

Median Q2 = 46

Third quartile Q3 = 48

As we know that first quartile Q1 is 25% mark , Median id 50% mark and third quartile Q3 is 75% mark

25% data's lie between Q1 and Q2 and next 25% between Q2 and Q3.

So the percentage data point lying between median and Q3 is 25% or 0.25.

In a sample of 3 let X be the random variable defining numbers of daffodils lying between 46 cm and 48 cm.

Then X follows Binomial (3 P=0.25)

So, P(X=0)=\({ }^3 \mathrm{C}_0 \times 0.25^0 \times(1-0.25)^3=\frac{3 !}{3 !} \times 1 \times 0.75^3=0.421875 \approx 0.422$\)

Therefore, the probability that none of them are between 46 cm and 48 cm is 0.422

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Answer:

See below.

Step-by-step explanation:

When there is a double negative, it converts the operation into an addition sign.

6--1 is actually 6+1, which is 7.

-hope it helps

Answer:

Step-by-step explanation:

In case you were wondering, a double negative is an addition problem.

In this case:

Answer:

V = x³ - 3x² + 3x - 1

Step-by-step explanation:

The volume (V) of a cube is calculated as

V = s³ ( s is the measure of the side )

Here s = x - 1 , thus

V = (x - 1)³

   = (x - 1)(x - 1)(x - 1) ← expand the second pair using FOIL

   = (x - 1)(x² - 2x + 1) ← distribute

   = x³ - 2x² + x - x² + 2x - 1 ← collect like terms

   = x³ - 3x² + 3x - 1

Answer:

Step-by-step explanation:

yeah

Answer:

i think that the answer is 7 units

Step-by-step explanation:

let me know if im wrong

Answer:

5

Step-by-step explanation:

it was correct for me

The correctanswer is-the percentage of the pieces that will meet the length specs is 98.78%.

The given data may be a random variable that takes after the normal distribution with mean μ=64 and standard deviation σ=0.1

The required value is to discover the rate of the pieces that will meet the length specs which is between 63.76 and 64.24 inches.

To find the required percentage, standardize the given limits as follows: Lower Limit: (63.76 - μ) / σ= (63.76 - 64) / 0.1 = -2.4

Upper Limit: (64.24 - μ) / σ= (64.24 - 64) / 0.1 = 2.4

Using the Standard Normal Distribution Table, the probability that the value will fall between -2.4 and 2.4 is found to be 0.9878.

The required percentage is then found by multiplying the probability by 100, which is: Percentage = 0.9878 x 100% = 98.78%

Therefore, the percentage of the pieces that will meet the length specs is 98.78%.

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Answer:

-13/3

Step-by-step explanation:

y2 - y1 / x2 - x1

6 - (-7) / -1 - 2

13 / -3

= -13/3

Hello !

Answer:

\( \boxed{\sf None \: of \: the \: options \text{:} \: \: m =- \dfrac{13}{3}} \)

Step-by-step explanation:

The slope m of a line passing through two points can be calculated using the following formula:

\( \sf m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1} \)

\( \\ \)

Let (x₁ , y₁) = (2 , -7)

Let (x₂ , y₂) = (-1 , 6)

Substitute these values into our formula:

\( \sf m =\dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{6 - (-7) }{-1 - 2 } = \dfrac{13}{-3}\\ \\ \implies \boxed{\sf m = -\dfrac{13}{3}} \)

Have a nice day ;)

Answer: The nth term of the sequence whose integers are between 1 -9 such that there is the permission of repetition but no two consecutive digits must be even is 1.834 x \(10^{21}\)

Step-by-step explanation:

Given data,

Two people pair up to create a sequence. Each of them pick five random digits from 1 to 9.

Define Consecutive numbers :

Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers. In a set of consecutive numbers, theme an and the median are Equal. If n is a number, then n, n+1, and n+2 would be consecutive numbers Examples. 1, 2, 3, 4, 5.

The numbers that are given:

Now, suppose a (n) denotes the number of n-digit positive integers as stated in the question, thereby using:

              = (9!) x (8!) x (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

             = 362880 x 40320 x 5040 x 720 x 120 x 24 x 6 x 2 x 1

            \(n^{th}\) = 1.834 x \(10^{21}\)

Therefore,

The nth term of the sequence whose integers are between 1 -9 such that there is the permission of repetition but no two consecutive digits must be even is 1.834 x \(10^{21}\).

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The possible length, in inches, of the third side of the triangle is modeled by the inequality 9/4 < c < 15/4 inches.

The length of the third side of a triangle is always greater than the difference of the length of the other two sides and always less than the sum of the length of the other two sides.

let

Difference:

= 3 inches - 3/4 inches

= (12-3) / 4

= 9/4 inches

Sum:

3 + 3/4 inches

= (12+3) / 4

= 15/4 inches

So,

9/4 < c < 15/4 inches.

Therefore, 9/4 < c < 15/4 inches is the inequality that can be used to represent the third side of the triangle.

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Answer:

Mike

Step-by-step explanation:

17% = .17

.7 = .70

All that's left is to compare the amounts of oi for each person and decide who has the most, which would be Mike. Hope this helps! (Rate brainliest!)

Answer:

Brett used the most

Step-by-step explanation:

Martha used = 17%

Brett used = 0.18 = 18/100 = 18%

Mike used = 0.7 × 100/8 = 8.75% (he only used 0.7 of ONE of the gallons in the can, not of the total oil in the can)

Therefore, Brett used the greatest amount of oil.

To make Px(x) = cx² a legitimate probability mass function:

a. We set c = 1/30 to ensure that the sum of all probabilities equals 1.

b. The probability of X being less than or equal to 3 is 7/15.

To make c  Px(x) = cx² a legitimate probability mass function, we set c = 1/30.

a. To make Px(x) a legitimate probability mass function, the sum of all probabilities must equal 1.

We can find the value of c by summing up Px(x) for all possible values of x and setting it equal to 1:

∑ Px(x) = ∑ cx² = c(1²) + c(2²) + c(3²) + c(4²) = c(1 + 4 + 9 + 16) = 30c

Setting 30c equal to 1, we have:

30c = 1

Solving for c:

c = 1/30

Therefore, to make Px(x) a legitimate probability mass function, we set c = 1/30.

b. The probability of X being less than or equal to 3 can be calculated by summing the probabilities for x = 1, 2, and 3:

P(X ≤ 3) = P(1) + P(2) + P(3)

        = (1/30)(1²) + (1/30)(2²) + (1/30)(3²)

        = (1/30)(1 + 4 + 9)

        = (1/30)(14)

        = 14/30

        = 7/15

Therefore, the probability that X is less than or equal to 3 is 7/15.

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The expression of the verbal statement is 15 + 0.15m

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

The sum of 15 and 15% of a number m

15% of a number m means 0.15m

So, we have the following representation

The sum of 15 and 0.15m

Sum  mean plus

So, we have

15 + 0.15m

We can get the equivalent expression

So, we have the following representation

(30 + 0.3m)/2

Hence, the expression is 15 + 0.15m

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Answer:

187.0 inches^2

Step-by-step explanation:

A paper has two sides so would double the value for computed surface area of the rectangle business letter paper.

By definition, area of a rectangle is length time width.  We are given the length of 8.5 inches and width of 11 inches.

So the computed area for one side of paper is 8.5 inches x 11 inches.

The resulting answer for one side of paper area is 93.5 inches^2.

Now we would need to double that value to get the total surface area for the paper and the final answer is 187.0 inches^2

8) The percent of people that said that Pinocchio was their favorite Disney Movie is of: 28%.

9) The percent of people that said that Pinocchio or Cars was their favorite Disney movie is of: 39%.

10) The two movies that about half the people say were their favorite is of: Pinocchio and Toy Story.

From the pizza graph, the sum of all the percentages must be of 100%, hence the Pinocchio percentage is obtained as follows:

10 + 11 + 14 + 15 + 22 + P = 100

72 + P = 100

P = 100 - 72

P = 28%.

Then the percentage for Pinocchio or Cars is of:

28 + 11 = 39%.

The percentage for Pinocchio or Toy Story is of:

28 + 22 = 50%.

(about half).

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Answer: 2.5, 5.4

Step-by-step explanation:

\(-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4\)

The amount of the investment at the end of 12 years for the following compounding methods when $400 is invested at an interest rate of 5.5% per year will be as follows:

Annual compounding Interest = 5.5%

Investment = $400

Time = 12 years

The formula for annual compounding is,A = P(1 + r / n)^(n * t)  

Where,P = $400

r = 5.5%

= 0.055

n = 1

t = 12 years

Substituting the values in the formula,

A = 400(1 + 0.055 / 1)^(1 * 12)  

A = 400(1.055)^12  

A = $812.85  

Hence, the amount of the investment at the end of 12 years for the annual compounding method will be $812.85.

Rate = 5.5%

Compound Interest = 400 * (1 + 0.055)^12

= $813 (rounded to the nearest cent).  

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Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.

Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.

Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.

To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.

If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.

The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.

These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.

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2 solutions (2 intersection points)

and the solutions

(4 ; 5) and (0 ; - 3)

Answer:

75

Step-by-step explanation:

its right

Answer:

75 degrees

Step-by-step explanation:

delta math told me

The answer of the question based on the angles statements the answer is

always true based on condition.

Range is the difference between highest and lowest values.

Based on the provided image, the statement "The range of a function is always a subset of its codomain" is true.

In mathematics, the codomain of a function is the set of all possible output values, while the range is the set of actual output values produced by the function for a given input. Since the range is a subset of the codomain, the statement is true.

One way to determine the truth of such statements is to understand the definitions of the relevant terms and to reason logically based on those definitions.

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9=5-x÷2

x=23

23-5=18÷2=9

Answer:

Graph A passes THrough the Center making it proportional when graph B is not passing

Step-by-step explanation:

Answer:

that is y

Step-by-step explanation:

Graph A is proportional because it runs thru the origin while the other doesn't

Answer: x²+3x-4 i

Step-by-step explanation: pretty sure its A

Answer:

12

Step-by-step explanation: