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solve the system of equations 10x+12y=380
6x+8y=244​

Answer:

120

Step-by-step explanation:

6!=1x2x3x4x5x6

3!=1.2.3

Rate at which volume of the snowball decreasing when the radius is 12 cm is 180.864 cm^3/min

Given:

a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. at what rate is the volume of the snowball decreasing when the radius is 12 cm.

Let r be the radius of the spherical snowball

Radius is decreasing at rate of 0.1 cm/min.=> dr/dt = -0.1

(negative sign indicates decreasing)

Volume v = 4/3πr^3

dv/dt = 4/3 π 3r^2*dr/dt

= 12π/3*r^2*(-0.1)

= 4π*12^2*(-0.1)

= 4π*144*-1/10

= 4π*(-14.4)

= -57.6π

= 180.864 cm^3/min

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If a nonhomogeneous system of linear equations is underdetermined, it can have either infinitely many solutions or no solutions.

A nonhomogeneous system of linear equations is represented by the equation Ax = b, where A is the coefficient matrix, x is the vector of unknowns, and b is the vector of constants. When the system is underdetermined, it means that there are more unknown variables than equations, resulting in an infinite number of possible solutions. In this case, there are infinitely many ways to assign values to the free variables, which leads to different solutions.

To determine if the system has a solution or infinitely many solutions, we can use techniques such as row reduction or matrix methods like the inverse or pseudoinverse. If the coefficient matrix A is full rank (i.e., all its rows are linearly independent), and the augmented matrix [A | b] also has full rank, then the system has a unique solution. However, if the rank of A is less than the rank of [A | b], the system is underdetermined and can have infinitely many solutions. This occurs when there are redundant equations or when the equations are dependent on each other, allowing for multiple valid solutions.

On the other hand, it is also possible for an underdetermined system to have no solutions. This happens when the equations are inconsistent or contradictory, leading to an impossibility of finding a solution that satisfies all the equations simultaneously. Inconsistent equations can arise when there is a contradiction between the constraints imposed by different equations, resulting in an empty solution set.

In summary, when a nonhomogeneous system of linear equations is underdetermined, it can have infinitely many solutions or no solutions at all, depending on the relationship between the equations and the number of unknowns.

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\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$9600\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{16}{100}\dotfill &0.16\\ t=years\dotfill &5 \end{cases} \\\\\\ 9600=P(0.16)(5)\implies 9600=0.8P\implies \cfrac{9600}{0.8}=P\implies 12000=P\)

The expected gain or loss from playing the game 15 times is -$75.00, indicating an expected loss of $75.00.

To determine the expected gain or loss from playing the game 15 times, we need to calculate the expected value.

The probability of getting three tails (winning) in a single coin toss is (1/2) * (1/2) * (1/2) = 1/8, since each coin toss is independent and has a 1/2 probability of landing tails.

The probability of losing in a single coin toss is 1 - 1/8 = 7/8.

If we play the game 15 times, the expected number of wins is (1/8) * 15 = 15/8, and the expected number of losses is (7/8) * 15 = 105/8.

The amount gained from winning is $10, and the amount lost from losing is $2.

Therefore, the expected gain or loss can be calculated as follows:

Expected gain or loss = (Expected number of wins * Amount gained) - (Expected number of losses * Amount lost)

= (15/8 * $10) - (105/8 * $2)

Simplifying this expression, we find:

Expected gain or loss = $187.50 - $262.50

= -$75.00

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Answer:

Simple b is 2

Step-by-step explanation:

1.5(2)= 3

Answer:

2

Step-by-step explanation:

So you need to find how many times to multiply 1.5 to make 3.

Divide 3 by 1.5 and you will get 2.

Hope this helps! :D

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nonononononononononononononononononononononononononononononononononononononono

Given

Which of the following is NOT equivalent to the formula d=rt?

Procedure

A. d/r=t is equivalent d=rt

B. r=dt is not equivalent

C. d/t=r is equivalent d=rt

D. d/rt=1 is equivalent d=rt

The answer is option B. r=dt that is NOT equivalent to the formula d=rt

The output obtained after executing the java code snippet,

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

will be 4.

As per the question statement, we are provided with a java code snippet, which goes as:

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

We are required to determine the output, that we will obtain on executing the above mentioned code.

That is, on executing the code

public static void main(string[] args)

{

int value = 3;

value++;

system.out.println(value);
}

We will obtain an output of 4, as "++" is the post increment function.

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An equation of this line I in the form y = mx + c is y = 2x + 3.

Mathematically, the standard form of the equation of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would determine the slope of this line by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (11 - 3)/(4 - 0)

Slope, m = 8/4

Slope, m = 2

From the point (0, 3), the y-intercept (c) is equal to 3. Therefore, the equation of this line is given by;

y = mx + c

y = 2x + 3

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The number line is missing, so i have attached it.

Answer:

Point C

Step-by-step explanation:

From calculator, square root of 5 gives us; √5 = 2.236

Now, looking at the number line attached, the point that best represents the value of the square root value of 2.236 will be point C because is lies between 2 and 3 which corresponds to our calculated value of 2.236

the height of the firecracker after 4 seconds from launch is 68 feet.

To find the height of the firecracker after 4 seconds from launch, we need to plug in t = 4 into the equation h(t) =\(-t^2\) + 19t + 14. This gives us h(4) =\(-4^2\) + 19(4) + 14 = -16 + 76 + 14 = 68 feet. Therefore, the height of the firecracker after 4 seconds from launch is 68 feet.

To find the height of the firecracker after 4 seconds from launch, we need to use the equation h(t) =\(-t^2\) + 19t + 14. This equation models the path of the firecracker, with h(t) being the height in feet of the firecracker at any given time, t. When we plug in t = 4, we get h(4) = \(-4^2\) + 19(4) + 14 = -16 + 76 + 14 = 68 feet. So, the height of the firecracker 4 seconds after launch is 68 feet. This equation allows us to calculate the height of the firecracker at any given time, making it a useful tool for predicting the trajectory of the firecracker.

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The probability P(x > 18) is equal to 1 minus the probability P(x < 18) for a normally distributed variable x with mean μ = 100 inches.

In a normal distribution, the area under the curve represents the probability of observing a certain value or a range of values. The probability P(x > 18) represents the probability of observing a value greater than 18 for the variable x. Conversely, the probability P(x < 18) represents the probability of observing a value less than 18 for the variable x.

Since the total area under the normal distribution curve is equal to 1, we can say that the sum of the probabilities of all possible events is equal to 1. Therefore, the probability of an event occurring (P(x > 18)) plus the probability of the event not occurring (P(x < 18)) is equal to 1.

Mathematically, we can express this relationship as:

P(x > 18) = 1 - P(x < 18)

So, the probability P(x > 18) is related to P(x < 18) by subtracting the latter from 1.

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Answer:

x=6

Step-by-step explanation:

(5x+30)+80=140

5x+110=140

5x=30

x=6

answer: B

Answer:

The box-and-whisker plot of this distribution is presented in the attached image to this solution.

Step-by-step explanation:

A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.

A box and whiskers plot shows 5 major information about the distribution of data. It shows:

- The maximum variable.

- The minimum variable.

- The Median.

- The first quartile.

- The third quartile.

Further info such as the range and Inter quartile range can then be obtained from this 5-number summary.

The elements of the box plot are described thus;

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.

The horizontal line inside the box is the median.

The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.

The required boxplot for this question is given in the attached image to this solution.

The median for the boxplot isn't provided, but it was assumed to be midway between the first and third quartile.

Hope this Helps!!!

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis, we can use the method of cylindrical shells.

First, let's determine the limits of integration. The region is bounded by x = 1 and x = 5, so our limits of integration will be from x = 1 to x = 5.

Next, we consider a small vertical strip at an arbitrary x-value within this interval. The height of the strip is given by the difference between the y-values of the two curves: y = 5/x and y = 0. Thus, the height of the strip is h = 5/x - 0 = 5/x.

The circumference of the strip is 2πr, where r is the x-value. Therefore, the circumference is 2πx.

Now, we can calculate the volume of the strip by multiplying the height, the circumference, and a small width dx. Hence, the volume of the strip is dV = 2πx * (5/x) * dx = 10π dx.

To find the total volume, we integrate the expression for dV from x = 1 to x = 5:

V = ∫(1 to 5) 10π dx.

Integrating, we get:

V = [10πx] (from 1 to 5)

= 10π(5 - 1)

= 40π.

Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 5/x, y = 0, x = 1, and x = 5 about the x-axis is 40π cubic units.

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a) For the events a and b to be mutually exclusive, the value of p(b) must be 0.5. and b) For the events a and b to be independent, the value of p(b) must be 0.5.

a) When two events are mutually exclusive, they cannot occur at the same time. This means that the probability of their intersection (a and b occurring together) is zero.

In this case, we know that p(a U b) = 0.5, which means that the probability of either a or b occurring is 0.5. If a and b are mutually exclusive, then the probability of their intersection is zero, so p(b) = 0.5 - p(a) = 0.5 - 0.5 = 0.

b) When two events are independent, the occurrence of one event does not affect the probability of the other event occurring. In this case, we know that p(a U b) = 0.5, which means that the probability of either a or b occurring is 0.5.

If a and b are independent, then the probability of their intersection is the product of their individual probabilities, i.e., p(a and b) = p(a) * p(b). Since p(a and b) = 0 when a and b are mutually exclusive, p(a) * p(b) = 0.5 * p(b) = 0.5, which gives us the value of p(b) = 1.

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Answer:

653005 = 653,005 in the International System of Numeration, the number is (Six hundred fifty-three thousand and five)

Answer:

It is C

Step-by-step explanation: The explanation says that he subtracted 10 by 20 and divided by 5 so the real answer is 18 but the answer in your page is C

Your Welcome :)

The solution in which the dependent variable is expressed solely in terms of the independent variable and constants is called an explicit solution.

A solution in which the dependent variable is expressed solely in terms of the independent variable and constants is said to be an explicit solution.

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Answer:

D

Step-by-step explanation:

CD is an angle bisector and divides the opposite side into segments which are proportional to the other 2 sides, that is

\(\frac{BC}{AC}\) = \(\frac{BD}{AD}\) , substitute values

\(\frac{4}{3}\) = \(\frac{x}{2.25}\) ( cross- multiply )

3x = 9 ( divide both sides by 3 )

x = 3 → D

Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.

A rigid transformation, also called isometry,  is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:

1. Reflection

→  is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.  

The figure is reflected across \(x-\) or \(y-\) axis, and then change \(x-\) or \(y-\) coordinate.

2. Rotation

→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.

The figure is rotated by a degree (ex: 90°), and then change \(x-\) or \(y-\) coordinate. Meanwhile, a point's center rotation stays at the same.

3. Translation

→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right),  or vertical reflections (make a figure up or down).

Vertical translation is shifting the graph along  \(y-\) axis

Horizontal translation is shifting the graph along  \(x-\) axis.

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Roads that are well-maintained, dry, and free from hazards are generally less likely to result in traction loss.

The likelihood of losing traction depends on various factors such as road conditions, weather, vehicle type, and driver behavior. However, in general, roads that are well-maintained, dry, and free from debris or hazards are less likely to result in traction loss. Additionally, roads with good grip surfaces, such as asphalt or concrete, tend to provide better traction compared to unpaved or slippery surfaces. It's important to drive cautiously and adapt to the specific conditions of the road to minimize the risk of losing traction.

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There were 16 ounces of oil in the lantern at noon.

Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.

We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:

x - rt = y

where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:

x - 2r = 12

And at 4 pm:

x - 4r = 8

Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:

2r = 4

r = 2

Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:

x - 2(2) = 12

x - 4 = 12

x = 16

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An estimate of the change in f between the two points is approximately 1.96. To estimate the change Δf = f(2.03, 0.95) − f(2,1), we need to use the equation Δf ≈ fx (a, b)Δx + fy(a, b)Δy, where fx and fy represent the partial derivatives of f with respect to x and y, evaluated at the point (a, b).

First, let's find the partial derivatives of f:

fx(x,y) = 3x^2y^-4
fy(x,y) = -4x^3y^-5

Next, we need to evaluate fx and fy at the point (a,b) = (2,1):

fx(2,1) = 3(2)^2(1)^-4 = 3(4) = 12
fy(2,1) = -4(2)^3(1)^-5 = -32

Now we can use the equation:

Δf ≈ fx(2,1)Δx + fy(2,1)Δy

To find Δx and Δy, we subtract the x and y values of the two points:

Δx = 2.03 - 2 = 0.03
Δy = 0.95 - 1 = -0.05

Substituting the values we have:

Δf ≈ 12(0.03) - 32(-0.05)
Δf ≈ 0.36 + 1.6
Δf ≈ 1.96

Therefore, an estimate of the change in f between the two points is approximately 1.96.

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Independent-samples t test. This test is used to compare the means of two independent groups. The correct answer is a.

In this case, the average number of matching characteristics reported by the fingerprint analysts and the average number of matching characteristics calculated by the defense attorney. The standard deviation of s = 1.2 would be used in the calculation of the t-statistic.
To determine whether the average number of matching characteristics the defense attorney observed (M = 9.8) differs significantly from that reported by fingerprint analysts (16 matching characteristics), she should use a "Single-sample t test".
Here's why:
- The defense attorney is comparing a sample (her 30 cases) to a known population mean (16 matching characteristics).
- The standard deviation of the sample is provided (s = 1.2), but the population standard deviation is not known.
- An Independent-samples t test would be used if comparing two independent groups, which is not the case here.
So, the correct answer is c. Single-sample t test.

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Answer:

The general equation of the cost of the billboard can be represented as follows:

y = 25 + 15x

In this equation:

"y" represents the cost of the billboard

"x" represents the number of days that your advertisement remains on the billboard

The fixed cost of $25 is added to the product of the daily cost of $15 and the number of days "x" that the advertisement is up.

Please note that this equation assumes a linear relationship between the number of days and the cost.

For a significance level of 0.100, with a sample correlation of 0.61 and 13 stations, the test statistic is 1.808. We fail to reject the null hypothesis, suggesting no evidence of a positive correlation.


a. The decision rule for a significance level of 0.100 (10%) is to reject the null hypothesis if the test statistic is greater than the critical value from the t-distribution with n-2 degrees of freedom.

b. To compute the test statistic, we can use Fisher’s z-transformation. The formula is z = (0.5 * ln((1 + r) / (1 – r))) * √(n – 3), where r is the sample correlation coefficient and n is the sample size. Calculating the test statistic with r = 0.61 and n = 13, we find z ≈ 1.808.

c. Since the test statistic of 1.808 does not exceed the critical value at a significance level of 0.100, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the correlation in the population is greater than zero.

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Answer:

It's all of them

Step-by-step explanation:

All the options given above are true.

the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

According to our study,

All the options given above are true.

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The required solution for the hypothesis testing is shown.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
Part A:

The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.

The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.

H0: p ≤ 0.05

Ha: p > 0.05

where p represents the proportion of defective batteries.

Part B:

A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.

A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.

Part C:

If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.

Part D:

If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.

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