which graph is a function of x?
​

Answer:

13/3

Step-by-step explanation:

Try it

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

Answer: 58

Step-by-step explanation: you divide 290 into 5

U(7, 7)

U'(-3,7)

Explanation:

reflecting upon the value of x=2 that means we reflect over y- axis.

*for reflections the distance from the line of reflection to the object is equal to the distance to the image point.

d = 2 + 2 = 4 units.

7 - 4 = 3(since reflection is done towards the negative side)

x' = -3.

9514 1404 393

Answer:

  ∠4 = 145°

  ∠5 = ∠6 = 35°

Step-by-step explanation:

Angles 5 and 35° are corresponding angles, so are congruent.

Angles 5 and 6 are vertical angles, so are congruent.

Angles 4 and 35° are a linear pair, so are supplementary.

  ∠4 = 180° -35°

  ∠4 = 145°

  ∠5 = ∠6 = 35°

In the given scenario, where there is one infinitely long track and overtaking is impossible, the initial situation consists of three equally spaced trains, each moving at a different speed. The trains have the capability to link up when one catches up to the other, resulting in a single train moving at the speed of the slower train.

As the trains move, they will eventually reach a configuration where the fastest train catches up to the middle train. At this point, the fastest train will link up with the middle train, forming a single train moving at the speed of the middle train. The remaining train, which was initially the slowest, continues to move independently at its original speed. Over time, the process continues as the new single train formed by the fastest and middle trains catches up to the remaining train. Once again, they link up, forming a single train moving at the speed of the remaining train. This process repeats until all the trains eventually merge into a single train moving at the speed of the initially slowest train. In summary, on this strange railway line, where trains can only link up and cannot overtake, the initial configuration of three equally spaced trains results in a sequence of mergers where the trains progressively combine to form a single train moving at the speed of the initially slowest train.

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In regression analysis, if the dependent variable is measured in dollars, the independent variable can be units.

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Answer:

The three Rational between 3 and 4

A rational number between 3 and 4 is 1/2 (3 + 4) = 7/2. Hence, 13/4, 7/2 and 15/4 are the three rational numbers lying between 3 and 4.

Step-by-step explanation:

The range of the function is f(x) <= 4

The attached graph is the missing piece in the question

The function f(x) is given as:

The above means that, the value of the function do not exceed y = 4

Hence, the range of the function is f(x) <= 4

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The correct choice for the second set in the pyramiding method of dynamic resistance training would typically be a weight that allows the client to perform fewer repetitions than in the first set, typically around 6 to 8 repetitions of their 12-RM weight.

In the pyramiding method, the goal is to gradually increase the weight lifted while decreasing the number of repetitions. This helps to progressively overload the muscles and stimulate strength gains. Starting with a weight that allows the client to perform 10 to 12 repetitions of their 12-RM weight in the first set ensures that they are working at an appropriate intensity to promote muscle adaptation.

For the second set, the weight should be increased to a level that challenges the client's muscles further. By reducing the number of repetitions to 6 to 8, the load becomes more challenging, leading to greater muscle recruitment and strength development. This gradual increase in intensity and decrease in repetitions can help to maximize the benefits of the training session.

It's important to note that the specific recommendations for sets, repetitions, and weights may vary depending on the individual's fitness level, goals, and training program. Working with a qualified fitness professional can help ensure that the pyramiding method is tailored to the client's needs and abilities for safe and effective training.

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Answer:

x=-16

Step-by-step explanation:

2/3x+1=1/6x-7.

Subtract 1/6x.

1/2x+1=-7

subtract 1.

1/2x=-8

divide by 1/2.

x=-16.

Hope this helps plz hit the crown :D

Step-by-step explanation:

\( \frac{2}{3} x + 1 = \frac{1}{6}x - 7 \\ \frac{4}{6} x - \frac{1}{6} x = - 7 - 1 \\ \frac{3}{6} x = - 8 \\ \frac{1}{2} x = - 8 \\ \boxed{ x = - 16}\)

Answer:

y

=

−

1

3

(

x

+

3

)

Step-by-step explanation:

The point-slope form of a linear equation is:  

(

y

−

y

1

)

=

m

(

x

−

x

1

)

Where  

(

x

1

,

y

1

)

is a point on the line and  

m

is the slope.

Substituting the values from the point in the problem and the slope provided in the problem gives:

Answer:

y=-1/2x

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=-1/2(x-4)

y+2=-1/2x+4/2

y+2=-1/2x+2

y=-1/2x+2-2

y=-1/2x

Answer:

ans: option 1st

Step-by-step explanation:

in similar triangle, corresponding sides are proportional to each other

Answer:

The actual dimensions of the kitchen are  12 feet by 14  feet

Step-by-step explanation:

The kitchen's real measurements are 12 feet by 14 feet.

Detailed explanation:

4 / 0.8 = 5, 7 / 1.4 = 5. The actual drawing ratio is a 5:1 ratio.

Consequently, 2.4 inches multiplied by 5 is 12 feet and 2.8 inches multiplied by 5 equals 14 feet.

12 ft. x 14 ft.

Find the scale of the drawing

\(\frac{0.8}{4} \frac{in}{ft.} = \frac{1.4}{7} = 0.2 \frac{in}{ft.}\)

To determine the precise dimensions subtract 0.2 from the measurements on the scale illustration to get 12 feet (2.4/0.2).

2.8/0.2 = 14 ft

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Answer:

Dude sorry  I’d undo

Step-by-step explanation:

Please forgive me

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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Answer:

x=6

Step-by-step explanation:

By the Product Rule of Logarithms, the logarithm of the product of numbers is the sum of the logarithms of the numbers.

\( log(x) + log(x - 1) = log(x(x - 1)) = log( {x}^{2} - x ) = log(3x + 12) \)

Raise both sides to the power of 10 to eliminate the logs, obtaining:

\( {x}^{2} - x = 3x + 12\)

\( {x}^{2} - 4x - 12 = 0\)

\((x - 6)(x + 2) = 0\)

x = -2 or x = 6. Since x = -2 is extraneous, it follows that x = 6.

Answer:

It is 3 or 8

Step-by-step explanation:

Answer:

The most likely result is that there will be no winners in the stadium.

Step-by-step explanation:

The odds of winning are 1 in 1 million, which means that there is a 99.9999% chance that any given person will not win. If there are 100,000 people in attendance at the game, then the expected number of winners is 0.1.

Answer: w=20/3

Step-by-step explanation: start by multiplying -3/2 by 2 and multiply -10 by 2 as well. you would get -3w = -20. divide both sides by -3 and you’ll get 20/3.

To the nearest tenth, the value of AC in triangle ABC is approximately 8.2 m.

Hence, AC ≈ 8.2 m.

To find the value of AC in triangle ABC, given that BC = 10.5 m, we can use the Law of Sines. The Law of Sines relates the lengths of the sides of a triangle to the sines of its corresponding angles.

According to the Law of Sines:

AC / sin(B) = BC / sin(A)

Substituting the given values, we have:

AC / sin(30°) = 10.5 m / sin(40°)

Now, let's solve for AC. First, find the value of sin(30°) and sin(40°):

sin(30°) ≈ 0.5

sin(40°) ≈ 0.643

Plugging in the values:

AC / 0.5 = 10.5 m / 0.643

Now, cross-multiply and solve for AC:

AC = (10.5 m * 0.5) / 0.643

AC ≈ 8.174 m

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Answer:

The ratio of their surface areas would 1:9 and the ratio of their volumes would be 1:27

Step-by-step explanation:

Given Info: The sides of two cubes are in ratio of 1:3. We can assign one square x and the other square 3x.

We know that the area of a square is its side squared, and that a cube has 6 sides. So thus if we assign one side of the cube x we can assume that surface area is 6x^2:

Surface Area of Cube #1= 6x^2

Surface Area of Cube #2= 6((3x)^2) = 6(9x^2) = 54x^2

Ratio of Surface Area: 6x^2 : 54x^2 = 6:54 = 1:9

Now for the volume we know that it is equivalent to one side cubed. So after assigning x to one cube, we can assume that volume would be x^3.

Volume of Cube #1= x^3

Volume of Cube #2= (3x)^3 = 27x^3

Ratio of Volume: x^3: 27x^3 = 1:27

Hope this helps!

Evaluating the distribution sample surveyed and comparing the long run state of the market of the three companies

i) The distribution of sample as at the beginning month of August is :

  Benfel limited =  5000 customers

  Cromwell Ltd  =   7167 customers

  Samtec  Ltd   =   4400 customers

ii) In the long run Benfel limited will have more customers than Cromwell and Samtec because they both lose more customers to Benfel limited than Benfel loses to them. also Benfel keeps a higher percentage of its customer

i) At the Beginning of the month of August the sample size for each company respectively will be

X * 70/100 = 3500 ∴ x ( sample size at August ) = 5000  ( Benfel )

y * 60/100 = 4300 ∴ y ( sample size at August ) = 7167   ( Cromwell )

z * 50/100 = 2200 ∴ z ( sample size at August ) = 4,400  ( Samtec )

ii) In the long run Benfel limited will have more customers than Cromwell and Samtec because they both lose more customers to Benfel limited than Benfel loses to them. also Benfel keeps a higher percentage of its customers

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Answer: The length of the room on blueprint = 10 feet.

Step-by-step explanation:

Given: On blueprint,

\(\dfrac14\) inch = 2 feet

i.e. 1 actual feet = \(2\times\dfrac 14 =\dfrac12\text{ inch}\)

If the actual length of 20 feet, the length of a room on blueprint = \(20\times\dfrac12\text{ feet}\)

= 10 feet.

Hence, the length of the room on blueprint = 10 feet.

The centre line of a control chart is calculated by computing the average (mean) of the data for every period.

In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.

The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.

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From the given density function, we see that f(y1, y2) = 6(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere. Therefore,f1(y1) = ∫0

Given that the joint probability density function of y1 and y2 is f(y1, y2) = 6(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere. The task is to find the marginal density function for Y1.The marginal probability density function for Y1 can be found as follows:The marginal probability density function for Y1 is obtained by integrating the joint probability density function over all possible values of Y2.

Thus we can write f1(y1) as follows:f1(y1) = ∫f(y1, y2)dy2From the given density function, we see that f(y1, y2) = 6(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere. Therefore,f1(y1) = ∫0.

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The statement that best describes the sampling distribution of sample means is normal with a mean of 625 and a standard deviation of 4.45. So, correct option is A.

The sampling distribution of sample means is the distribution of all possible sample means that could be obtained from a population of a given size. The Central Limit Theorem (CLT) states that if the sample size is sufficiently large (usually n > 30), the sampling distribution of sample means will be approximately normal, regardless of the distribution of the population.

In this case, the population is the distribution of SAT math scores of students taking Calculus I with a mean of 625 and a standard deviation of 44.5. If random samples of 100 students are repeatedly taken, the sampling distribution of sample means will also be normal due to the CLT.

The mean of the sampling distribution of sample means will be the same as the population mean of 625, while the standard deviation of the sampling distribution of sample means will be the population standard deviation divided by the square root of the sample size, which is 44.5/√100 = 4.45.

Therefore, correct option is A.

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(a) Please refer to the accompanying diagram for the visual representation of triangle ABC.

(b) Angle C ≈ 50.57°, Angle A ≈ 41.84°, Angle B ≈ 87.59°

(c) The area of triangle ABC ≈ 80 square units.

(a) To draw the triangle ABC, we need to follow the given information: b = 12 cm, a = 19 cm, and c = 15 cm.

First, draw a line segment AB of length 19 cm. This will be the base of the triangle.

Next, place point C on the line segment AB, at a distance of 12 cm from point A.

Finally, draw a line segment AC of length 15 cm, connecting points A and C.

The resulting triangle ABC should have side lengths of 19 cm, 15 cm, and 12 cm.

(b) To solve the triangle ABC, we will use the Law of Cosines and the Law of Sines to find the remaining angles and sides.

Let's start by finding angle C using the Law of Cosines:

\(\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]\)

\(\[ 15^2 = 19^2 + 12^2 - 2 \cdot 19 \cdot 12 \cdot \cos(C) \]\)  

Solving for cos(C):

\(\[ \cos(C) = \frac{19^2 + 12^2 - 15^2}{2 \cdot 19 \cdot 12} \]\)

\(\[ \cos(C) \approx 0.625 \]\)

Using the inverse cosine function:

\(\[ C \approx \cos^{-1}(0.625) \]\)

\(\[ C \approx 50.57^\circ \]\)

Next, we can find angle A using the Law of Sines:

\(\[ \frac{\sin(A)}{a} = \frac{\sin(C)}{c} \]\)

\(\[ \frac{\sin(A)}{19} = \frac{\sin(50.57^\circ)}{15} \]\)

Solving for sin(A):

\(\[ \sin(A) = \frac{19 \cdot \sin(50.57^\circ)}{15} \]\)

\(\[ \sin(A) \approx 0.662 \]\)

Using the inverse sine function:

\(\[ A \approx \sin^{-1}(0.662) \]\)

\(\[ A \approx 41.84^\circ \]\)

To find angle B, we can use the fact that the sum of the angles in a triangle is 180 degrees:

\(\[ B = 180^\circ - A - C \]\)

\(\[ B \approx 87.59^\circ \]\)

(c) To calculate the area of the triangle ABC, we can use Heron's formula:

\(\[ \text{Area} = \sqrt{s(s - a)(s - b)(s - c)} \]\)

where s is the semiperimeter of the triangle, given by:

\(\[ s = \frac{a + b + c}{2} \]\)

Substituting the given values:

\(\[ s = \frac{19 + 12 + 15}{2} = 23 \]\)

Plugging the values into the formula:

\(\[ \text{Area} = \sqrt{23(23 - 19)(23 - 12)(23 - 15)} \]\)

\(\[ \text{Area} = \sqrt{23 \cdot 4 \cdot 11 \cdot 8} \]\)

\(\[ \text{Area} = \sqrt{6448} \]\)

\(\[ \text{Area} \approx 80 \]\)

Therefore, the area of the triangle ABC is approximately 80 square units.

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