solve -3(x-3)≤ 5(1-x)

Given equation is:

Solving for x,

Therefore,

x= 13/k

Hence, option (C) is true.

The empirical probability of the red car moving a specific number of times in 8 rolls of the die can be estimated by rolling the die many times and counting the number of times the red car moves a specific number of times, then dividing this count by the total number of rolls.

Assuming that the probability of the red car moving is independent and equal for each roll, the number of times the red car moves in 8 rolls can be modeled using a binomial distribution.

Let's say that the probability of the red car moving in a single roll is p, and we want to find the empirical probability of the red car moving k times in 8 rolls.

To find the empirical probability, we would need to roll the die 8 times and record how many times the red car moves. We can repeat this process many times to collect a large sample of outcomes and estimate the probability based on the proportion of times the red car moves k times in 8 rolls.

For example, if we roll the die 8 times and observe that the red car moves 4 times, we would record that as 4 occurrences of the red car moving in 8 rolls. We can repeat this process many times and record the number of occurrences for each possible value of k (from 0 to 8).

Then, we can calculate the empirical probability of the red car moving k times in 8 rolls as:

The empirical probability of k red car moves = (number of occurrences of k red car moves) ÷ (total number of trials)

For each value of k, we would calculate this empirical probability based on the collected sample.

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The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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That when (x, y) = (0, 0), the function is defined to be 0, which corresponds to the origin in polar coordinates.

To describe the level curves of the function defined by f(x, y) = 2xy / (x^2 + y^2), where (x, y) ≠ (0, 0) and f(0, 0) = 0, we can convert the Cartesian coordinates (x, y) to polar coordinates (r, θ).

In polar coordinates, x = r cos(θ) and y = r sin(θ). Substituting these expressions into the function, we have:

f(r, θ) = 2(r cos(θ))(r sin(θ)) / (r^2 cos^2(θ) + r^2 sin^2(θ))

= 2r^2 cos(θ) sin(θ) / (r^2)

= 2r cos(θ) sin(θ)

Simplifying further, we get:

f(r, θ) = 2r cos(θ) sin(θ)

Now, let's consider the level curves, which are the curves in the xy-plane where f(x, y) is constant. In polar coordinates, this means we need to find values of r and θ such that f(r, θ) is constant.

Since f(r, θ) = 2r cos(θ) sin(θ), we can set a constant value k and rewrite the equation as:

k = 2r cos(θ) sin(θ)

Dividing both sides of the equation by 2 and rearranging, we have:

r = k / (2 cos(θ) sin(θ))

This equation represents the level curves of the function f(x, y) = 2xy / (x^2 + y^2) in polar coordinates. The level curves are given by the equation r = k / (2 cos(θ) sin(θ)), where k is a constant.

Note that when (x, y) = (0, 0), the function is defined to be 0, which corresponds to the origin in polar coordinates.

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To determine if there is a relationship between college major and living location preference (West Coast, East Coast, Non-coastal), you should use the Chi-Squared Test for independence.

The Chi-Squared Test for independence is appropriate for examining the relationship between two categorical variables. In this case, you have two categorical variables: college major (e.g., engineering, business, arts) and living location preference (West Coast, East Coast, Non-coastal). This test allows you to determine if there is a statistically significant association between these variables.

By conducting the Chi-Squared Test, you can analyze the observed frequencies of each combination of college major and living location preference and compare them to the expected frequencies under the assumption of independence. If the test results show a significant relationship, it indicates that college major and living location preference are associated with each other.

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Answer:

Step-by-step explanation:

1. We have added marks to the diagram indicating that FG is a perpendicular bisector of BC. These hash marks and angle indicator are shown in the first attachment.

__

2. The proof that ∆BCE is equilateral, so all its angles are 60°, is shown in the second attachment.

__

3. The proof that m∠ECD = 30° is shown in the second attachment.

__

4. We know △ECD is isosceles because CE ≅ CD. Since the angle at C is 30°, the base angles at D and E are (180° -30°)/2 = 75°.

The angle of interest, ∠BED, is the sum of angles DEC (75°) and CDB (60°). Hence, ...

  m∠BED = 75° +60° = 135°

  m∠BED = 135°

Answer:

52

Step-by-step explanation:

12 + (38 - 18)2 = 12 + 20 × 2 = 52.

Answer:

Step-by-step explanation:

2500 divided by 50 is 50, The parking lot will need 50 rows in it.

Answer: 50 rows

Step-by-step explanation:

First takes 2500 divided by 50 = 50 rows

The answer of this question is ,the correct answer of this rational function is b) F(x) =1/ (x+1)(x+2).

A rational function is  function that can be expressed as ratio of two polynomial, where the denominator polynomial is not zero. In other words, a rational function is in  the form of :

f(x) = p(x) / q(x)

where p(x) and q(x) are polynomials in x, and q(x) is not equal to zero for any value of x.

Rational functions can have various properties and behaviors, depending on the degree and roots of the numerator and denominator polynomials. For example, they may have vertical and horizontal asymptotes, holes, intercepts, and other features.

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Answer: False

Step-by-step explanation:

   This is not a function because the single input [x] of 6 has outputs [y] of 2 and 4, and the single input [x] of 12 has outputs [y] of 2 and 4.

   A function must have only one output [y-value] for every input [x-value].

⇒Note this is a fraction.

⇒For a fraction to be undefined that is of when the denominator is equal to 0

⇒Now equate what is  in the denominator with 0

⇒ \(k+3=0\\k=-3\)

⇒So that the denominator is 0 that is of when k is equal to -3..it is then that the whole expression will be undefined.

⇒The expression is undefined when k=-3

Answer:Before he broke his arm: 45 words in 5 minutes

After he broke his arm: 30 words in 5 minutes

9*5=45 6*5=30

Hope this helps... mark as Brainliest plz

Step-by-step explanation:

Rounding to the nearest hundredth, the expected value of the winnings from the given payout probability distribution is approximately 1.98 dollars.

To find the expected value of the winnings from the given payout probability distribution, we need to multiply each payout amount by its corresponding probability and then sum up these products.

Payout ($): 0 2 4 8

Probability: 0.50 0.25 0.13 0.06 0.06

Expected Value = (0 * 0.50) + (2 * 0.25) + (4 * 0.13) + (8 * 0.06) + (8 * 0.06)

Calculating each term:

(0 * 0.50) = 0

(2 * 0.25) = 0.50

(4 * 0.13) = 0.52

(8 * 0.06) = 0.48

(8 * 0.06) = 0.48

Summing up these products:

Expected Value = 0 + 0.50 + 0.52 + 0.48 + 0.48 = 1.98

Rounding to the nearest hundredth, the expected value of the winnings from the given payout probability distribution is approximately 1.98 dollars.

The expected value represents the average amount one can expect to win from the game over the long run, taking into account the probabilities and payouts associated with each outcome. In this case, the expected value suggests that, on average, a player can expect to win around 1.98 dollars per game.

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Answer:

(-2, 32, -21)

Step-by-step explanation:

You just multiply B by 3 and then subtract the corresponding parts. For example -2 -(0*3). and then 14-(-6*3)

Answer:

Step-by-step explanation:

The width of the basketball court is given by W(A) = √(A/2), and the length is given by L(A) = √(2A). These expressions allow you to calculate the width and length of the court for a given area A in square feet.

The problem states that the width of the basketball court (W) can be modeled by the equation:

W(A) = √(A/2)

where A is the area of the court in square feet.

Since the length (L) of the basketball court is twice the width (W), we can express it as:

L = 2W

Now, let's find the expression for the length (L) in terms of the area (A) of the court.

Step 1: Substitute the value of W from the given model into the expression for L:

L = 2 × √(A/2)

Step 2: Simplify the expression:

L = √(4A/2)

L = √(2A)

So, the expression for the length (L) of the basketball court in terms of its area (A) is given by L = √(2A).

To summarize, the width of the basketball court is given by W(A) = √(A/2), and the length is given by L(A) = √(2A). These expressions allow you to calculate the width and length of the court for a given area A in square feet.

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Complete question :- A community is building a new outdoor basketball court. The length of the court is twice the width. The width of the basketball court in feet can be modeled by w(A)= √A/2 where a is the area in square feet of the court.

Answer:

\(\textsf{A)} \quad \left(-\dfrac{1}{2} , 0\right) \textsf{ and } (2, 0)\)

\(\textsf{B)} \quad \left(\dfrac{3}{4},25 \right)\)

C)  see explanation

Step-by-step explanation:

Given function:

\(f(x) =-16x^2 + 24x + 16\)

To find the x-intercepts, set the function to zero, factor and solve for x:

\(\implies f(x)=0\)

\(\implies -16x^2 + 24x + 16=0\)

\(\implies -8(2x^2-3x-2)=0\)

\(\implies 2x^2-3x-2=0\)

\(\implies 2x^2-4x+x-2=0\)

\(\implies 2x(x-2)+1(x-2)=0\)

\(\implies (2x+1)(x-2)=0\)

Therefore:

\(\implies 2x+1=0 \implies x=-\dfrac{1}{2}\)

\(\implies x-2=0 \implies x=2\)

Therefore, the x-intercepts of the graph of f(x) are

\(\left(-\dfrac{1}{2} , 0\right) \textsf{ and } (2, 0)\)

As the leading coefficient is negative, the parabola will open downwards. Therefore, the vertex of the graph of f(x) will be a maximum.

The x-coordinate of the vertex is the midpoint of the x-intercepts:

\(\implies \sf midpoint=\dfrac{2+\left(-\frac{1}{2}\right)}{2}=\dfrac{3}{4}\)

To find the y-coordinate of the vertex, substitute the x-value into the function:

\(\implies f\left(\dfrac{3}{4}\right)=-16\left(\dfrac{3}{4}\right)^2 + 24\left(\dfrac{3}{4}\right) + 16\)

\(\implies f\left(\dfrac{3}{4}\right)=-9+18+16\)

\(\implies f\left(\dfrac{3}{4}\right)=25\)

Therefore, the coordinates of the vertex are:

\(\left(\dfrac{3}{4},25 \right)\)

Find the y-intercept by substituting x = 0 into the function:

\(\implies f(0) =-16(0)^2 + 24(0) + 16=16\)

Therefore, the y-intercept is (0, 16)

To graph f(x)

The axis of symmetry is the x-value of the vertex. Use this to help ensure the curve is symmetrical.

#A

Take y =0

On solving we will get

#B

Find x co ordinate of vertex

Find y

As a is negative vertex is maximum as its facing downwards.

#C

Steps:-

Answer:

Step-by-step explanation:

You want to know angles x, y, and z in the given figure where parallel lines 'a' and 'b' are crossed by a transversal. The sum of these angles is 290°.

Angles y and z are called consecutive interior angles. As such, they are supplementary, so their sum is 180°.

  x + y + z = 290°

  x + 180° = 290°

  x = 110°

Angles x and y are vertical angles, so are congruent.

  y = x = 110°

Then z is found from ...

  y + z = 180°

  110° + z = 180°

  z = 70°

The measures of x, y, and z are 110°, 110°, and 70°, respectively.

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A concave hexagon with 2 pairs of congruent sides is a shape that has six sides and two pairs of sides that are of equal length, but the shape curves inward at one or more angles, creating a concave indentation.

A hexagon is a six-sided polygon, and when two pairs of its sides are congruent,

it means that four of its sides have the same length, if the shape curves inward at one or more angles,

it creates a concave hexagon, which means that the indentation on the shape is facing inward, rather than outward, a concave hexagon with 2 pairs of congruent sides is a six-sided polygon with four sides of equal length, but with a curvature that creates an inward indentation.

Hence, a concave hexagon with 2 pairs of congruent sides is a six-sided figure with an indentation and two sets of sides with equal lengths.

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£270 will be allocated to the first person and £135 will be allocated to the second person.

Ratio is a mathematical expression that is used to compare two or more quantities in relation to each other. It is usually expressed as a fraction or a decimal. Ratios are used to compare values, trends, and proportions. Ratios are essential for understanding the relationship between numbers and for making informed decisions. Ratios are often used in business, finance, economics, and other areas to measure performance and risk.

This is calculated by multiplying the total amount of £405 by the ratio 2:3.
The first person's ratio is 2 out of 5 and the second person's ratio is 3 out of 5.

Therefore, 2/5 of £405 is £270 and 3/5 of £405 is £135.

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From the given information, the value of x in the given table is 42.5.

To find the value of x, we can use the formula for the arithmetic mean (average) of a set of numbers:

Arithmetic mean = (sum of all numbers) / (number of numbers)

Given that the average score on the test is 62, we can use this information to find the sum of all the scores.

Given that number of students is 1,2,3 and 4 with scores of 40,55,70 respectively, we can use this information to find the sum of all the scores.

Sum of all scores = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x)

Now we can substitute the given average score and the number of students into the equation and solve for x.

62 = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x) / 10

620 = 40 + 110 + 210 + 4x

4x = 170

x = 42.5

So, the value of x is 42.5

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The complete question is -

ten students wrote a test, and the distribution of scores is shown in the frequency table. if the average (arithmetic mean) score is 62, what is the value of x?

Score - 40, 55, 70, x

Number of students - 1, 2, 3, 4

Answer:

21

Step-by-step explanation:

105/(1+4)

= 105/5

= 21.

Answer:

180.68

Step-by-step explanation:

D) $180.68

At the beginning you have 68.02 plus the 169.23 deposit which makes a new total of 237.25.Then you spend 31.57 so the new equation is (237.25-31.57)

which is 205.68 then you spend another 25 for gas (205.68-25=180.68)

So your answer is $180.68

The equation for given initial value problem is y(x) = 3eˣ - 4e²ˣ + 16e⁷ˣ - 8e⁴ˣ.

To solve the given initial value problem, we can use the method of undetermined coefficients.

Find the complementary solution (y_c) of the homogeneous equation by solving the characteristic equation:

r³ - 10r² + 29r = 0.

This equation factors as (r-1)(r-2)(r-7) = 0.

So the complementary solution is

y_c(x) = C1eˣ + C2e²ˣ + C3e⁷ˣ,

where C1, C2, and C3 are constants.

To find the particular solution (y_p), assume that it has the form y_p(x) = Ae⁴ˣ, where A is a constant to be determined.

Substitute y_p(x) and its derivatives into the given equation, and solve for A.

After doing the calculations, we find that A = -8.

The general solution is given by

y(x) = y_c(x) + y_p(x),

so plugging in the values we obtained, we have

y(x) = C1eˣ + C2e²ˣ + C3e⁷ˣ - 8e⁴ˣ.

To find the specific solution that satisfies the initial conditions, substitute x=0, y(0)=7, y'(0)=-4, and y''(0)=8 into the general solution. After doing the calculations, we obtain the following system of equations:

C1 + C2 + C3 - 8 = 7,

C1 + 2C2 + 7C3 - 8 = -4,  

C1 + 4C2 + 49C3 - 8 = 8.

Solve the system of equations obtained to find the values of C1, C2, and C3. The solution is

C1 = 3,

C2 = -4,

C3 = 16.

Finally, substitute the values of C1, C2, and C3 into the general solution from step 4 to obtain the specific solution. Therefore, the solution to the initial value problem is y(x) = 3eˣ - 4e²ˣ + 16e⁷ˣ - 8e⁴ˣ.

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Answer:

343cm³

Step-by-step explanation:

294:6=49

square root of 49=7

7³= 343cm³

The correct answers are: Grams of iron in a meal, Minutes spent on this test, Snacks eaten in a week

Parametric statistics could be used to analyze the following dependent variables:

Grams of iron in a meal: Parametric statistics can be used to analyze continuous numerical variables, such as the amount of iron in a meal, by assuming a specific distribution (e.g., normal distribution) and using techniques like t-tests, ANOVA, or regression.

Minutes spent on this test: Similarly, parametric statistics can be applied to analyze continuous numerical variables like the time spent on a test. Techniques such as t-tests or regression can be used to compare groups or explore relationships between variables.

Snacks eaten in a week: Parametric statistics can also be used for analyzing count data, such as the number of snacks eaten in a week. Techniques like Poisson regression or negative binomial regression can be used to model and analyze count data.

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Answer:

134 :)

Step-by-step explanation:

Given:

Area of trapezium if 3/4 cm^2.

Dilation factor is 4.

The objective is to find the area of dilated trazpezoid.

The formula to find the area of dilated trapeozid is,

Hence, the area of trapezoid after dilation is, 3 cm^2.