Variable y varies directly with variable x. If x = 12, then y = 3. What is the value of y
when x = 8?

Using the speed - distance relationship, the time left before the appointed time is 27 minutes.

Recall :

At 10mph :

At 12 mph :

Equate (1) and (2) :

10t + 30 = 12t - 24

Collect like terms

10t - 12t = - 24 - 30

-2t = - 54

Divide both sides by - 2

t = 54 / 2

t = 27

Hence, the time left before the appointed time is 27 minutes.

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Answer:

7

Step-by-step explanation:

Answer:

the answer of the question is 25

The solutions for θ in the interval [0, 2π) where cos(θ) = -√3/2 are θ = 2π/3 and θ = 4π/3.

The graph of f(θ) is shifted and stretched when compared to the graph of f(2θ).

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the trigonometric functions that describe those relationships.

Part A:

To find when the pogo stick's spring will be equal to its non-compressed length, we need to solve for when f(θ) = 0.

f(θ) = 2cos(θ) + √3 = 0

2cos(θ) = -√3

cos(θ) = -√3/2

The solutions for θ in the interval [0, 2π) where cos(θ) = -√3/2 are θ = 2π/3 and θ = 4π/3.

Part B:

If we double the angle, θ becomes 2θ, and the function becomes:

f(2θ) = 2cos(2θ) + √3

Using the double angle formula for cosine, we can rewrite this as:

f(2θ) = 2(2cos²(θ) - 1) + √3

f(2θ) = 4cos²(θ) - 2 + √3

Substituting cos(θ) = -√3/2, we get:

f(2θ) = 4(-3/4) - 2 + √3

f(2θ) = -3 + √3

So the solutions for 2θ in the interval [0, 2π) where f(2θ) = 0 are:

2θ = π/6 and 2θ = 11π/6

Dividing by 2, we get the solutions for θ:

θ = π/12 and θ = 11π/12

These solutions are different from the solutions in Part A, and the graph of f(θ) is shifted and stretched when compared to the graph of f(2θ).

Part C:

To find when the lengths of the springs are equal, we need to solve the equation f(θ) = g(θ).

2cos(θ) + √3 = 1 - sin²(θ) + √3

2cos(θ) = 1 - sin²(θ)

Using the identity sin²(θ) + cos²(θ) = 1, we can rewrite this as:

2cos(θ) = cos²(θ)

cos(θ)(cos(θ) - 2) = 0

The solutions for θ in the interval [0, 2π) where the lengths of the springs are equal are:

θ = 0, θ = π/3, θ = 2π/3, θ = π, θ = 4π/3, θ = 5π/3

We can check that f(θ) = g(θ) at each of these values.

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Answer:

mn(5mn² + 9) ;

2mn(1 - 1/2mn²)

Step-by-step explanation:

Given:

5m²n³ +9mn

(8mn - 4m²n³ ÷ 4)​

5m²n³ + 9mn

mn(5mn² + 9)

(8mn - 4m²n³ ÷ 4)​

8mn/ 4 - 4m²n³ / 4

2mn - m²n³

2mn(1 - 1/2mn²)

The 83rd percentile contains intervals which are 50 and 100 thousand kilometers.

What is a histogram ?

A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals.

It is given that , data for most recent 23 vehicles is shown in the histogram.

On the x-axis distance driven in thousands of kilometers and on the y-axis frequency is represented in the histogram.

For 23 vehicles , we have different ranges of distance driven i.e., 0 - 50 , 50 - 100 , 150 - 200 . 200 - 250 , 250 - 300.

We know that the 83rd percentile meant the distance driven is greater than or equal to 83 %.

i.e.,

Here , 83 lies between 50 - 100 , so , 83rd percentile contains intervals which are 50 and 100 thousand kilometers.

Therefore , 83rd percentile contains intervals which are 50 and 100 thousand kilometers.

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Answer:

(x + 1)(x + 2) is divisible by 3.

Step-by-step explanation:

Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.

Case 1: r = 1

If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)

= (3k + 2)(3k + 3)

= 3(3k^2 + 5k + 2)

We can see that (x + 1)(x + 2) is divisible by 3.

Case 2: r = 2

If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)

= (3k + 3)(3k + 4)

= 3(3k^2 + 7k + 4)

We can see that (x + 1)(x + 2) is divisible by 3.

Hence, the statement is proven.

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The probability that the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is approximately 82.38%.

Assuming the sample of 30 Americans is representative of the population, we can calculate the sample proportion as the number of individuals in the sample who agree divided by the total sample size. Let's assume that the sample proportion is p'.

To calculate the probability of the proportion exceeding 35%, we need to find the z-score of the value 0.35 using the formula:

z = (p' - p) / √[p * (1 - p) / n]

where p is the population proportion (which we don't know), and n is the sample size (30 in this case). We can use p' as an estimate of p.

Once we find the z-score, we can use a standard normal distribution table or a calculator to find the probability that the z-score is greater than the value we calculated. This probability is the probability that the proportion of Americans who agree that climate change is an immediate threat to humanity exceeds 35%.

For example, if p' = 0.4, then the z-score is:

z = (0.4 - 0.35) /√ [0.35 * (1 - 0.35) / 30] = 1.03

Using a standard normal distribution table, we can find that the probability of a z-score being greater than 1.03 is approximately 0.8238, or about 82.38%.

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Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

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Answer:

9 and 17

Step-by-step explanation:

Let the two numbers by x and y.

We are told that x - y = 8

And we learn that (x+y)/2 = 13

Rearrange the first equation to isolate x (or y):

x - y = 8

x = 8+y

Use this expression for x in the second equation:

(x+y)/2 = 13

((8+y)+y)/2 = 13

Solve for y:

(2y+8)/2 = 13

y + 4 = 13

y = 9

If y = 9, x is:

x - y = 8

x - (9) = 8

x = 17

The difference between 17 and 9 is 8

The average is (9+17)/2 =  13                                                                                                                                                                                                          

Answer:

9 and 17

Step-by-step explanation:

let x and y be the 2 numbers , x > y , then

x - y = 8 → (1)

\(\frac{x+y}{2}\) = 13 ( multiply both sides by 2 )

x + y = 26 → (2)

add both equations term by term to eliminate y

2x + 0 = 34

2x = 34 ( divide both sides by 2 )

x = 17

substitute x = 17 into (1) and solve for y

17 - y = 8 ( subtract 17 from both sides )

- y = - 9 ( multiply both sides by - 1 )

y = 9

The 2 numbers are 9 and 17

Answer:

-31 c + 13

Step-by-step explanation:

-13c+8-18c+5

combine like terms

-18c and -13c combined is -31c

8 + 5 = 13

-31 c + 13

Answer

-31c+13 is your answer (see explanation below!)

Step-by-step explanation:

1) Add the numbers:

\(-13c + 8 - 18c + 5\\-13c + 13 -18c\\\)

2) Combine like terms:

\(-13c+13-18c\\-31c+13\\\)

\(A: -31c+13\)

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Answer:

(12, 190). This represents that after selling 12 ice creams, I gain $190.

Step-by-step explanation:

I just found a scatter plot online. Ignore the current label on the x-axis that says TemperatureC, I just changed that to ice creams. You can change the title of the graph to whatever you want.

Answer:

144

Step-by-step explanation:

24  

______

30   x6=  180    

24x6= 144

7h-15h+40=-72

40+72=15h-7h

112=8h

h=14

Answer:

110°

Step-by-step explanation:

Given:

Since AB has the same side length measure as AD, ΔABD is an isosceles triangle. In an isosceles triangle, the base angles are the same measure.

In ΔABD, the base angles of the triangle are angle B and angle D. Since angle B = 35° and ∠B = ∠D, thus, angle D is also 35°. Now, apply the 180° triangle property and solve for the measure of angle A, which is said to be x°.

Therefore, the measure of ∠A is 110°. (x = 110°)

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Answer:

The value of n that best fits to show the length of a fingernail as 1.2 x 10^-1 mm, which is option (a).

The ratio of the heights is 5, the ratio of the surface areas is 25, and the ratio of the volumes is 125

Step-by-step explanation:

We can use the fact that similar pyramids have the same shape, but possibly different sizes. Let's denote the height of pyramid a by h_a, the height of pyramid b by h_b, and the scale factor between the two pyramids by k. Then, we have:

The ratio of the heights is k, since the height is scaled up by the same factor as the base length. That is, k = h_b / h_a.

The ratio of the surface areas is k^2, since the surface area is proportional to the square of the base length and the height. That is, k^2 = (side length of b / side length of a)^2 = (25 / 5)^2 = 5^2 = 25.

The ratio of the volumes is k^3, since the volume is proportional to the cube of the base length and the height. That is, k^3 = (side length of b / side length of a)^3 = (25 / 5)^3 = 5^3 = 125.

Therefore, the ratio of the heights is 5, the ratio of the surface areas is 25, and the ratio of the volumes is 125.

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Answer:

height ratio- 1:5   surface area- 1:25  volume- 1:125

Step-by-step explanation:

To Prove:-

JK=IJ

JK= ½IK = IJ= ½IK

JK= IJ(Equal Distance)

GK//HI (Parallel)

Therefore, JK congruent IJ

Hope This Helps

The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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The ZGYS + ZSYA = 90 degrees.

The given diagram is as follows: \(\text{Given:}\) Gray is a rectangle.

Conclusions: \(\text{Conclusion 1: }\)If S is the midpoint of GA, then \(\text{Reason: }\) S is the midpoint of GA and according to the Midpoint theorem, the line segment joining any two midpoints of a triangle is parallel to the third side. Therefore, GA is parallel to RY. \(\text

{Conclusion 2: }\)If GA bisects RY, then \(\text{Reason: }\) GA bisects RY and if a line segment is bisected by a line, then two halves of the line segment will be equal. Therefore, GY = RY. \(\text

{Conclusion 3: }\)If GR is perpendicular to RA, then \(\text{Reason: }\) GR is perpendicular to RA and if a line segment is perpendicular to another, then they will form right angles. Therefore, ZGRA = 90 degrees. \(\text

{Conclusion 4: }\)If ZGRA and ZRAY are supplementary angles, then \(\text{Reason: }\) ZGRA and ZRAY are supplementary angles and if two angles are supplementary, then their sum will be 180 degrees. Therefore, ZGRA + ZRAY = 180 degrees. \(\text

{Conclusion 5: }\)If ZGYS and ZSYA formed a right angle, then \(\text{Reason: }\) ZGYS and ZSYA form a right angle and if two angles form a right angle, then their sum will be 90 degrees.

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ACTIVITY 3: TEST YOURSELF!1. If S is the midpoint of GA, then the length of SG is equal to the length of GA.2. If D is the midpoint of EF, then the length of DE is equal to the length of EF.3.

If A is the midpoint of BC, then the length of AB is equal to the length of AC.4. If M is the midpoint of PQ, then the length of MP is equal to the length of MQ.5. If ZGYS and ZSYA formed a right angle, then ZGYS is a right angle.Thus, we can say that midpoint bisects the line segment into two equal halves.

In the given question, we have to identify the relationship between different points of a triangle. We have to identify whether the given line segment is the midpoint of the other line segment or not.In the first question, we have been given a triangle and a point S. We have to check if S is the midpoint of GA or not. To check that we need to measure the length of SG and GA. If the length of both the line segments is equal, then S is the midpoint of GA. In the fifth question, we have been given a triangle and two line segments. We need to check whether they form a right angle or not. If they form a right angle, then the given angle is a right angle.

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C. True. Every matrix equation Ax=b can be written as a vector equation x1a1 + x2a2 + ··· + xnan = b, where a1, a2, ..., an are the columns of A and x and b are vectors of appropriate dimensions. This vector equation has the same solution set as the matrix equation.

The vector equation is obtained by expressing each element of the matrix equation as a linear combination of the columns of A. Specifically, if Ax = b, then we can write x1a1 + x2a2 + ··· + xnan = b, where x1, x2, ..., xn are the entries of the vector x and ai,j is the (i, j)-th entry of the matrix A.

Conversely, given a vector equation x1a1 + x2a2 + ··· + xnan = b, we can express it in matrix form as Ax = b, where A is the matrix whose columns are a1, a2, ..., an, and x and b are vectors of appropriate dimensions.

Therefore, the matrix equation Ax = b corresponds to the vector equation x1a1 + x2a2 + ··· + xnan = b, and they have the same solution set.

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For the given statement "Every matrix equation Ax b corresponds to a vector equation with the same solution set." the correct answer is option (C). True.

The matrix equation Ax-b is simply another notation for the vector equation x1a1 + x2a2 +·.. + xnan-b, where al.

The given statement is true. Every matrix equation Ax-b corresponds to a vector equation with the same solution set.

Let's consider a system of linear equations:

Let A be an n×m matrix, and let x and b be column vectors in ℝn and ℝm, respectively. Then the system of linear equations Ax=b is equivalent to the vector equation below:x1a1 + x2a2 + ... + xnan=b

In this equation, the columns of the matrix A are represented by ai, and the coefficients of the unknowns x are represented by xi. For example, for a 2×2 matrix A, the vector equation Ax=b can be rewritten as follows:

x1a1 + x2a2=b

The system of linear equations Ax=b can also be written in matrix notation as:

Ax=b

Thus, every matrix equation Ax-b corresponds to a vector equation with the same solution set. Therefore, option (C) is the correct answer.

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The rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0 is zero.

Given that,

Seawater has a density of 1025 kg/m³ and moves at a constant velocity field defined by the equations v = yi + xj, where x, y, and z are measured in meters and the components of V are expressed in meters per second.

We have to find the rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0.

We know that,

v= yi + xj, and density = 1025 kg/m³

F=1025(yi + xj)

After solving the R(u,v) we get zero.

Therefore, the rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0 is zero.

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Answer:

Step-by-step explanation:

1st picture on left: no solution

2nd picture on right infinitely many solutions

Answer:

The answer is E

Step-by-step explanation:

Answer: the common number is 8 for 151 and 152

Step-by-step explanation: hope this helps

The distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

The distribution of X, representing the IQ of an individual from the ruling species on the faraway planet, is a normal distribution with a mean (μ) of 106 and a standard deviation (σ) of 18. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

In this distribution, the majority of IQ values will cluster around the mean of 106. The standard deviation of 18 indicates the average amount of variation or dispersion from the mean. The normal distribution is symmetric, which means that the probabilities of IQ values being above or below the mean are equal.

The shape of the normal distribution is bell-shaped, with the highest point being at the mean. As we move away from the mean, the probability of observing extreme values decreases. The spread of the distribution is determined by the standard deviation, where a larger standard deviation indicates a wider spread of IQ values.

the distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet.

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On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.  What is the distribution of X? X ~ N( 106 , 18 )  

The standard error for the sample was 0.5.

Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.

SE = SD / √n

where SE = standard error

SD = sample standard deviation = 10

n = sample size = 400

Standard error multiply by a critical value at the confidence interval will give the margin of error.

To solve for the standard error, plug in the values to the formula.

SE = SD / √n

SE = 10 / √400

SE = 0.5

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The time it takes for a rocket following the path h(x)= -4x² + 16x to hit the ground is 4 seconds.

How to find the time for a rocket to hit the ground?

The given path equation is a function of x which is a time variable here. When the rocket hits ground, height of the rocket gets zero.

Hence equating the equation of height to zero and solving for x will give the time required for the rocket to hit the ground.

According to the given question:

We are given equation for height as

h(x) = -4x² + 16x

where x is the time in seconds

When object hits the ground the height becomes 0

So, we can set h(x) = 0 and then we can solve for x

-4x² + 16x = 0

Dividing by -4x from both sides

x - 4 = 0

x = 4 sec

So, the time it takes for a rocket  to hit the ground is 4 seconds.

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The correct correlation between the heights of husbands and wives in the U.S. is around -0.3. The correlation between the heights of husbands and wives in the U.S. is not as strong as some might assume. It is about -0.3.

This is not a strong negative correlation, but it is still a negative one, indicating that as the height of one partner increases, the height of the other partner decreases. This relationship may be seen in married partners of all ages. It's important to note that the correlation may not be consistent among various populations, and it may vary in different places. The correlation between husbands and wives' heights is -0.3, which is a weak negative correlation.

It indicates that as the height of one partner increases, the height of the other partner decreases. When there is a weak negative correlation, the two variables are inversely related. That is, when one variable increases, the other variable decreases, albeit only slightly. The correlation is not consistent across all populations, and it may differ depending on where you are. Nonetheless, when compared to other correlations, such as a correlation of -0.9 or 0.9, the correlation between husbands and wives' heights is a weak negative one.

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The time 0 value of a $500 perpetuity at a 7 percent discount rate is $7,142.86, calculated using the formula Present Value = Cash Flow / Discount Rate.

To calculate the present value of a perpetuity, you can use the formula:
Present Value = Cash Flow / Discount Rate
In this case, the cash flow is $500, and the discount rate is 4.5 percent. However, you mentioned a discount rate of 7 percent in the beginning. I will assume that you want to calculate the present value using a discount rate of 7 percent.
Using the formula:
Present Value = $500 / (0.07)
Present Value = $500 / 0.07
Present Value = $7,142.86
Therefore, the time 0 value of a $500 perpetuity at an interest rate of 7 percent is $7,142.86.

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