The following table gives a partial set of values of a polynomial function. x −2 −1 0 1 2 3 g(x) 14 2 0 4 6 −2 Between which two values would a relative minimum most likely occur? (2 points) −2 and 0 0 and 2 −1 and 1 1 and 3

Answer:

100*100/23+(24/8)

100*100/23+3

100*4.37+3

43.7+3

46.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think it’s -5

Answer:

He will make 55,000 dollars a year

Step-by-step explanation:

\(300\) × \(50 = 15000\)

\(15000 + 40000 = 55000\)

\(\large\underline{\underline{\red{\sf \blue{\longmapsto} Step-by-step\: Explanation:-}}}\)

Given to points to us are :-

Now , we can use Distance Formula , which is :-

\(\boxed{\purple{\tt Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}\)

Here ,

→ Substituting the respective values ,

⇒ Distance = √ [ ( 6 - 1)² + ( 3 +9)² ] .

⇒ Distance = √ 5² + 12²

⇒ Distance = √ 25 + 144

⇒ Distance = √ 169 .

⇒ Distance = 13 units .

Hence the distance between two points is 13u.

A slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

The slope of a linear relationship represents the rate of change between two variables. In this case, a slope of b = 0.007 suggests a weak positive relationship between the variables. The positive sign indicates that as the independent variable increases, the dependent variable also tends to increase. However, the small value of 0.007 indicates that the increase in the dependent variable is relatively small for each unit increase in the independent variable.

To illustrate, let's consider an example where the independent variable represents time and the dependent variable represents the number of customers in a store. With a slope of 0.007, it means that for every unit increase in time (e.g., one hour), we can expect a small increase of 0.007 customers on average. This indicates a weak positive relationship, as the increase in customers is relatively modest for each unit increase in time.

In summary, a slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

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The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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The value of q is -27.

Recall Vieta's Formulas, which state that for a quadratic equation \(ax^2\) + bx + c = 0 with zeroes alpha and beta, the sum of the zeroes is equal to -b/a, and the product of the zeroes is equal to c/a.

In our equation \(x^2\) - 3x + q, the sum of the zeroes alpha and beta is -(-3)/1 = 3.

We are given that 2 alpha + 3 beta = 15. Substitute alpha = (15 - 3 beta)/2 into the equation.

Replace the value of alpha in the sum of zeroes equation: (15 - 3 beta)/2 + beta = 3.

Simplify the equation by multiplying both sides by 2: 15 - 3 beta + 2 beta = 6.

Combine like terms: 15 - beta = 6.

Subtract 15 from both sides: -beta = -9.

Multiply both sides by -1 to solve for beta: beta = 9.

Substitute the value of beta into the sum of zeroes equation: alpha = (15 - 3 * 9)/2 = -3.

Since we have the values of alpha and beta, we can find q using the product of the zeroes formula: q = alpha * beta = -3 * 9 = -27.

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The APR, or stated rate, is calculated as the annualized interest rate expressed as a percentage.

The APR, or stated rate, represents the annualized interest rate on a loan or investment, expressed as a percentage.

To calculate the APR, we need to consider the nominal interest rate and the compounding frequency. The formula to calculate the APR is:

APR = (1 + nominal interest rate/compounding periods)^(compounding periods) - 1

The nominal interest rate is the stated rate without taking compounding into account.

The compounding periods refer to the number of times interest is compounded in a year, typically based on daily, monthly, or quarterly periods.

By applying the formula and considering the appropriate compounding periods, we can determine the APR.

The APR is an important metric as it allows for easy comparison of interest rates across different financial products.

It helps consumers and investors understand the true cost or yield associated with a loan or investment and enables them to make informed decisions.

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Answer:

vertex is (6, -11)

Step-by-step explanation:

Given equation
f(x) = x² - 12x + 25

is that of an upward-facing parabola(since the coefficient of x² is positive).

The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x

f'(x) = d/dx(x² - 12x + 25)

= 2x - 12

f'(x) = 0 ==> 2x - 12 = 0

2x = 12

x = 6

Substitute x = 6 in f(x) to get

f(6) = 6² - 12(6) + 25

= 36 - 72 + 25

= -11

So the vertex is at (6, -11)

Step-by-step explanation:

let eqn be y = mx + b.

m = (9 - 1)/(2 - 4) = -4

sub (4, 1):

1 = -4(4) + b

b = 17

therefore, it's y = -4x + 17

Topic: coordinate geometry

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As the number of people visiting each day is the same 404 people visited on Sunday.

We have,

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday and the number of people who visited on each day is the same.

As the number of visitors is same on each day and the total number of days is three each they the number of people visited is,

= (1212/3).

= 404.

So, On Sunday 404 visitors were there.

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complete question:

The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday. If the same number of people visited each day, how many visitors were there on Sunday

All of the study participants make up the experimental units.

The object about which a researcher seeks to draw conclusions from the sample is known as the experimental unit. As a result, this is the entity that requires proper replication. The number of experimental units per group is the sample size.

From a sample of 50 people who had a cold, the researcher assigned 25 people to take the supplement each day. the other 25 people were asked to drink water each day and were not given the supplement. The researcher recorded the number of days the cold lasted for each person.

All of the study participants make up the experimental units.

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The percent of change in the cost of gasoline from $1.30 to $2.95 is approximately 126.92%. This means that the price of gasoline has increased by 126.92% from its initial value.

To calculate the percent of change, we use the formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

In this case, the old value (initial cost) is $1.30, and the new value is $2.95. Plugging these values into the formula, we get:

Percent Change = (($2.95 - $1.30) / $1.30) * 100 = $1.65 / $1.30 * 100 = 126.92%

This means that the cost of gasoline has increased by 126.92% from $1.30 to $2.95. The percentage indicates the relative increase in the price. In other words, the new price is 126.92% higher than the initial price. This significant increase in the cost of gasoline reflects the change in market conditions, such as fluctuations in crude oil prices, supply and demand dynamics, and other factors that influence the pricing of fuel products.

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The correct option will be A that is t=(A-P)/Pr by the simplification of equation, "an equation is a mathematical statement that shows that two mathematical expressions are equal ".

In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, an equation is a relationship of equality between two expressions written on both sides of the equal to sign. 3y = 16 is an example of an equation. Some examples of important equations are:

Here,

A=P+Prt

A-P=Prt

t=(A-P)/Pr

The answer is A, which is t=(A-P)/Pr using the equation's simplified form. An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.

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Step-by-step explanation:

Look here answer with steps

hope it helps

The vertex and range are (-2, -3) and y >= -3 respectively

The equation is given as:

y = |x +2| - 3

The above equation is an absolute value equation

An absolute value equation is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (-2, -3)

Also, we have

a = 1

Since a is positive, then the vertex is a minimum

Hence, the vertex and range are (-2, -3) and y >= -3 respectively

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Answer:

12:8= 18: x+6

Step-by-step explanation:

12:8=1.5

18:x+6=1.5

x+6=18:1.5=12

x=12-6

x=6

The mean of the sampling distribution of p is 0.40 and the standard deviation of the sampling distribution of p is 0.0409.

Standard deviation is a measure of how spread out the values in a data set are from the mean. It is calculated by taking the square root of the variance of the data set. It is a commonly used measure to assess the variability in a data set.

The mean of the sampling distribution of p is 0.40, which is the same as the proportion of supporters in the population of Okeechobee County. This is due to the fact that the sample proportion estimates the population proportion. The standard deviation of the sampling distribution of p is equal to the square root of the product of p (0.40) and q (1-p, or 0.60) divided by the sample size (135). In this case, the standard deviation of the sampling distribution of p is 0.0409.

The mean and standard deviation of the sampling distribution of p can be used to understand what values of p are likely when samples of size n = 135 are drawn from the population of Okeechobee County. If a sample is drawn from the population, the sample proportion of supporters is likely to be close to 0.40, which is the mean of the sampling distribution of p. Furthermore, most of the sample proportions of supporters are likely to be within two standard deviations (or 0.0818) of the mean. This means that the sample proportion of supporters is likely to be between 0.3182 and 0.4818 when samples of size n = 135 are drawn from the population.

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The relation which we see between the orders of the elements of a group and the order of the group is smallest positive power.

G = U(20), order of each element of G = ?

The smallest positive power of an element that gives you your identity is the order of the element in a group. Three instances are covered: complex numbers, a 2x2 rotation matrix, and real number elements of finite order.

G = U(20) = {1,3,7,9,11,13,17,19}

⇒ 3° ≡ 1, 3¹ ≡ 3, 3² ≡ 9, 3³ ≡ 7, 3¹ ≡ 1(20)

∴ order of 3 = 4

7⁴ ≡ 1 (mod 20) → order (7) = 4

9² ≡ 1 (mod 20) → order (9) = 2

11² ≡ 1 (mod 20) → order (11) = 2

13² ≡ 9(mod 20) → 13⁴ ≡ 81(mod 20) → 13⁴ ≡ 1 (mod 20)

⇒ order (13) = 4

order  07 = 4

17 ≡-3(mod 20) ⇒ 17² ≡ yy (mod 20)

⇒ 17⁴ ≡ 81 (mod 20) ≡ 1 (mod 20) ⇒

19 = -1 (mod 20)

19² ≡ 1 (mod 20) ⇒ order (19) = 2

Hence we get the requires answer.

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The sequence \({1- (-1)"}\)diverges in R for the given details

Given that the sequences, (a)\({(-1)"}. and (b) {1- (-1)"}\).We need to show that both the sequences diverge in R.(a) {(-1)"}Here, the terms of the sequence alternate between +1 and -1.Hence, the sequence does not converge as the terms of the sequence do not approach a particular value.

A sequence is a list of numbers or other objects in mathematics that is arranged according to a pattern or rule. Every component of the sequence is referred to as a term, and each term's place in the sequence is indicated by its index or position number. Sequences may have an end or an infinity. While infinite sequences never end, finite sequences have a set number of terms. Sequences can be created directly by generating each term using a formula or rule, or recursively by making each term dependent on earlier terms. Numerous areas of mathematics, including calculus, number theory, and discrete mathematics, all study sequences.

Instead, the sequence oscillates between two values.Therefore, the sequence {(-1)"} diverges in R.(b) {1- (-1)"}Here, the terms of the sequence alternate between 0 and 2.

Hence, the sequence does not converge as the terms of the sequence do not approach a particular value.Instead, the sequence oscillates between two values.

Therefore, the sequence {1- (-1)"} diverges in R.

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Answer: 51 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cost of renting bowling alley = $ 100

Additional cost of renting bowling alley per person = $ 4

⇒ Total Cost for n no. of people = 100 + 4 × n

So, Cost for 15 people = Fix $100 for bowling alley

                                          + $4 for each 15 people

                                      = 100 + 4 × 15

                                    = 100 + 60

                                    = 160

Therefore, The cost for 15 people equals to $ 160.

The initial monthly payment on the mortgage loan is $971.35.

To find the initial monthly payment, we can use the formula for calculating the monthly payment on a mortgage loan:

PV = PMT/i[1 - {1/(1+i)ⁿ]

where:

PMT = monthly payment

PV = principal (loan amount)

i = monthly interest rate (annual rate divided by 12)

n = total number of payments (the number of years multiplied by 12)

For the initial fixed period of five years, the interest rate is 4.25%.

So the monthly interest rate is 4.25%/12 = 0.00354.

The total number of payments is 30 years x 12 months/year = 360.

Plugging in the values, we get:

M = 197500 [ 0.00354(1 + 0.00354)³⁶⁰ ] / [ (1 + 0.00354)³⁶⁰ – 1]

M ≈ $971.350054812

M = $971.35

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The statement sqrt((x-3)^2) = 3 - x is true only when x is not equal to 3. Therefore, option 1) "x is not equal to 3" is the correct answer.

When we simplify sqrt((x-3)^2), we get |x-3|, which represents the absolute value of (x-3). On the other hand, the expression 3 - x represents the negation of x subtracted from 3.

For x ≠ 3, both |x-3| and 3 - x can be positive or negative depending on the value of x. They are not always equal to each other.

However, if we consider x = 3, the expression sqrt((x-3)^2) becomes sqrt(0^2) = 0, and 3 - x becomes 3 - 3 = 0. In this case, both sides of the equation are equal.

Therefore, the equation sqrt((x-3)^2) = 3 - x is not true for all values of x. It is true when x is not equal to 3, but false when x = 3.

Regarding option 2) "-x|x| > 0", it is unrelated to the given equation and does not provide any information about the validity of the equation sqrt((x-3)^2) = 3 - x.

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For A and B to be independent, the value of P(B) should be ≈ 1.224

For events A and B to be independent, the probability of their intersection (A ∩ B) must be equal to the product of their individual probabilities (P(A) * P(B)).

In this case, we have the following information:

P(A) = 0.49

P(A ∩ Bc) = 0.4

We need to determine the value of P(B) for which A and B are independent.

We can use the following equation:

P(A ∩ B) = P(A) * P(B)

However, we don't have the direct value of P(A ∩ B), but we have P(A ∩ Bc) and we can use the complement rule to obtain P(A ∩ B):

P(A ∩ B) = 1 - P(A ∩ Bc)

Now, substituting the known values:

1 - P(A ∩ Bc) = P(A) * P(B)

1 - 0.4 = 0.49 * P(B)

0.6 = 0.49 * P(B)

0.6 / 0.49 = P(B)

Approximately, P(B) = 1.224

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To find the largest four-digit value of t such that the expression is an integer, we need to set up an equation and solve for t.

Let's denote the given expression as x:

x = √(t - √(t - √(t - √(t - ...)))

To simplify the expression, we notice that the inner square root can be represented by x itself. So we can rewrite the equation as:

x = √(t - x)

Squaring both sides to eliminate the square root:

x^2 = t - x

Rearranging the equation:

x^2 + x - t = 0

To find the largest four-digit value of t, we can iterate through the values of t starting from 9999 and solve the quadratic equation for x. We are looking for a positive integer solution for x. Once we find the largest value of t that satisfies this condition, we have our answer.

By solving the quadratic equation for different values of t, the largest four-digit value of t that satisfies the condition is 9985.

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