W= 32-0.05n
Andrei has a glass tank. First, he wants to put some marbles in it, all of the same volume. Then,
he wants to fill the tank with water until it's completely full. The equation shown above
describes the volume of water, W, measured in liters, that Andrei should use when there are n
marbles. What is the volume of the glass tank, in liters?
Answer:

The image of point K after GHK is rotated 90° counterclockwise about point G is (1,8).

What is counterclockwise ?

Counterclockwise is a rotational direction opposite to the direction that the hands on a clock move. It is also known as anticlockwise or counter-clockwise. In mathematical contexts, counterclockwise usually refers to a rotation direction in a Cartesian coordinate system where the positive direction of rotation is opposite to the positive direction of the x-axis.

According to the question:
To rotate point K 90° counterclockwise about point G, we can follow these steps:

Translate the image so that the center of rotation is at the origin (0,0). We can do this by subtracting the coordinates of G from each point:

G' = (1-1, 3-3) = (0,0)

K' = (6-1, 3-3) = (5,0)

H' = (6-1, 0-3) = (5,-3)

Rotate the image 90° counterclockwise. This can be done using the following formula for a 2D rotation:

(x', y') = (-y, x)

So, for each point:

K'' = (-0, 5) = (0,5)

Translate the image back to its original position by adding the coordinates of G:

K''' = (0+1, 5+3) = (1,8)

Therefore, the image of point K after GHK is rotated 90° counterclockwise about point G is (1,8).


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To solve equations with fractions and variables in the denominator, we need to eliminate it by moving it to the other side. To do this, we multiply both sides of the equation by the term in the denominator. This will cancel out the fraction and leave us with a simpler equation to solve.

For example, suppose we have the equation (3 + x) / x = 2. To get rid of the fraction, we multiply both sides by x. This gives us: x * (3 + x) / x = x * 2. The x in the numerator and denominator cancel out, leaving us with:

3 + x = 2x. Now we can solve for x by subtracting x from both sides: 3 = x

This is the solution of the equation.

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Answer:

higher education

Step-by-step explanation:

it makes most sence if you choose mine

Generally, the more education you receive, the higher your lifetime earnings.

Formal education is a type of social institution where an individual is though the morals , manners and ethics of the society. The individual's use of logic while making decisions and integration with others is amplified.

The importance of education to the life of an individual include the following:

Therefore, the more education you receive, the higher your lifetime earnings and achievements.

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The correct response is c. scatter plot. An essential sort of data visualization that demonstrates the correlations between variables is the scatter plot.

In a scatter plot, dots are used to show the values for two different numerical variables (also known as a scatter chart or scatter graph). The position of each dot on the horizontal and vertical axes indicates the values for each data point. Frequency distributions are used to show how variables are linked to each other. The scatterplot shows how two numerical variables that were evaluated for the same individuals correlate with one another. On the horizontal axis, one variable's values are displayed, and on the vertical axis, the values of the other variable. On the graph, each data point represents a unique person. The correlation between the two variables, or the strength of the association, increases with the approach of a straight line to which the data points can be plotted.

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what plot will show it to you?

The formula for the Volume(V) of the cylinder is given as,

Given:

Therefore,

Hence, the volume of the cylinder is

The means of the 10 possible samples of size 2 from the population {2, 4, 6, 6, 8} are 3, 4, 4, 5, 5, 5, 6, 6, 7, and 7.

To list all possible samples of size 2 from the given population of 5 values, we can use combinations. The possible combinations of two values from a set of five are:

{2, 4}, {2, 6}, {2, 6}, {2, 8}, {4, 6}, {4, 6}, {4, 8}, {6, 6}, {6, 8}, {6, 8}

To compute the mean of each sample, we add the two values in the sample and divide by 2. The mean of each sample, rounded to 1 decimal place, is:

{2, 4}: (2 + 4)/2 = 3

{2, 6}: (2 + 6)/2 = 4

{2, 6}: (2 + 6)/2 = 4

{2, 8}: (2 + 8)/2 = 5

{4, 6}: (4 + 6)/2 = 5

{4, 6}: (4 + 6)/2 = 5

{4, 8}: (4 + 8)/2 = 6

{6, 6}: (6 + 6)/2 = 6

{6, 8}: (6 + 8)/2 = 7

{6, 8}: (6 + 8)/2 = 7

Therefore, the means of the 10 possible samples of size 2 from the population {2, 4, 6, 6, 8} are 3, 4, 4, 5, 5, 5, 6, 6, 7, and 7.

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Evaluating f(t) when t=2 and t=5 yields different values. When t=2, f(t) simplifies to \(2e^2 + 20\). When t=5, f(t) simplifies to \(25e^5 - 6e^3 - 80\).

To evaluate f(t) at t=2, we substitute the value of t into the given expression. Using the unit step function [u(t)], we have 2⋅[u(2)] which evaluates to 2 since the unit step function is 1 for positive arguments. The term -5(t-3)⋅[u(t+1)] becomes -5(2-3)⋅[u(2+1)] = -5⋅(-1)⋅[u(3)] = 5⋅[u(3)] = 5. The term 5\(e^t\)⋅[δ(t+2)] simplifies to 5\(e^2\)⋅[δ(2+2)] = 5\(e^2\)⋅[δ(4)] = 5\(e^2\)⋅0 = 0 since the Dirac delta function is zero for non-zero arguments. The term (\(t^2\) + 2)⋅[u(t-3)] evaluates to (\(2^2\) + 2)⋅[u(2-3)] = 4⋅[u(-1)] = 4⋅0 = 0. Lastly, the term \(e^{-t}e^3.[u(t-1)]\) becomes \(e^{-2}e^3\)⋅[u(2-1)] = \(e^{-2}e^3\)⋅[u(1)] = \(e^{-2}e^3\)⋅1 = \(e^{-2}e^3\).

Thus, when t=2, f(t) simplifies to 2e^2 + 20.

Now let's evaluate f(t) when t=5. Following a similar process, we substitute t=5 into the given expression. The term 2⋅[u(5)] evaluates to 2 since the unit step function is 1 for positive arguments. The term -5(t-3)⋅[u(t+1)] becomes -5(5-3)⋅[u(5+1)] = -10⋅[u(6)] = -10. The term 5\(e^t\)⋅[δ(t+2)] simplifies to \(5e^5\)⋅[δ(5+2)] = 5\(e^5\)⋅[δ(7)] = 0. The term (\(t^2\) + 2)⋅[u(t-3)] evaluates to (5^2 + 2)⋅[u(5-3)] = 27⋅[u(2)] = 27 since the unit step function is 1 for positive arguments. Lastly, the term e^(-t)e^3⋅[u(t-1)] becomes \(e^{-5}e^3\)⋅[u(5-1)] = \(e^{-5}e^3\)⋅[u(4)] = \(e^{-5}e^3\).

Therefore, when t=5, f(t) simplifies to 25e^5 - 6e^3 - 80.

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The number of possible paths a basketball can take to go into the basket depends on the range of possible angles at which it is thrown. Each angle corresponds to a unique trajectory, and the number of possible angles will determine the total number of paths.

When a basketball is thrown, it follows a parabolic trajectory due to the force of gravity. The angle at which it is thrown determines the initial velocity components in the horizontal and vertical directions. Let's assume the initial velocity magnitude, denoted as V, is fixed.

To analyze the motion of the basketball, we can use the equations of projectile motion. The horizontal and vertical motions are independent of each other. In the horizontal direction, the velocity remains constant, and in the vertical direction, the velocity changes due to the acceleration caused by gravity.

The range of possible angles at which the basketball can be thrown will determine the number of paths it can take. For example, if the angles are limited to discrete values, such as 0°, 10°, 20°, and so on, then there will be a finite number of paths. However, if the angles can vary continuously between 0° and 90°, then there will be infinitely many paths. The total number of possible paths will depend on the specific range or set of angles allowed.

In conclusion, the number of paths a basketball can take to go into the basket depends on the range of angles at which it is thrown. The more angles that are allowed, the greater the number of possible paths. The exact number of paths can vary depending on the specific conditions and constraints given for the problem.

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For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96. The statement is false.

The statement is incorrect. For a one-tailed test with a 0.05 level of significance, the critical z statistic is indeed 1.645. However, the critical t statistic value depends on the degrees of freedom (df), which is not provided in the statement. The 1.96 value mentioned is actually the critical z statistic for a two-tailed test with a 0.05 level of significance.

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The table of values is

n | f(n)

0 | 42

2 | 56

4 | 70

6 | 84

From the question, we have the following parameters that can be used in our computation:

f(n) = 7n + 42

We have the n values to be

x = 0, 2 4 and 6

Substitute the known values in the above equation, so, we have the following representation

f(0) = 7(0) + 42 = 42

f(2) = 7(2) + 42 = 56

f(4) = 7(4) + 42 = 70

f(6) = 7(6) + 42 = 84

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All correct proportions include the following:

A. \(\frac{AC}{CE} =\frac{BD}{DF}\)

D. \(\frac{CE}{DF} =\frac{AE}{BF}\)

In Mathematics and Geometry, two geometric figures are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Hence, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar.

Since line segment AB is parallel to line segment CD and parallel to line segment EF, we can logically deduce that they are congruent because they can undergo rigid motions. Therefore, we have the following proportional side lengths;

\(\frac{AC}{CE} =\frac{BD}{DF}\)

\(\frac{CE}{DF} =\frac{AE}{BF}\)

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Answer:

x = -1 + ⟌17

Step-by-step explanation:

You want to solve the equation for x by finding a, b, and c of the quadratic formula

A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Answer:

1.    =0.01

2.  =0.0001  

3.  =10,000

4. =0.000001

Step-by-step explanation:

Answer: A) √35

Step-by-step explanation:

Answer:

c.

Step-by-step explanation:

when an equation doesn't have a y-intercept. That means it is proportional.

We have to find the value of  `(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)`

Let's find all trigonometric ratios:

We can say that:

\($$\tan \theta= \frac{opp}{adj}= \frac{-4}{3}$$$$\text\)

{Using the Pythagorean Theorem we can find the hypotenuse }

\($$$$\text{Hypotenuse = } \sqrt{(-4)^2+(3)^2}\)

\(= \sqrt{16+9}\)

= \(\sqrt{25}\)

=\(5$$$$\)

Substituting the values of sinθ, cosθ and tanθ in `

\(= \frac{\frac{3}{5} + \frac{-4}{5} - \frac{-4}{3}}{\frac{-4}{5} + \frac{5}{3} - \frac{-3}{4}}$$$$\)

\(=\frac{\frac{9}{15} + \frac{-12}{15} + \frac{20}{15}}{\frac{-16}{20} + \frac{25}{12} + \frac{3}{4}}$$$$\)

\(=\frac{\frac{17}{15}}{\frac{-14}{15}}$$$$\)

\(=-\frac{17}{14}$$\)

Therefore, \(`(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)\)` is equal to

`-17/14` when `tanθ=−43` (Quadrant II).

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Speed = distance / time

Speed = 40 miles / 10 seconds

Speed = 4 miles per second.

The equation of  line of reflection that transforms shape P into shape Q is y=7.

a reflection is known as a flip. A reflection is a mirror image of its shape. An image will reflect through the line, known as the line of reflection. Every point in a figure is said to mirror the other figure when they are all equally spaced apart from one another.

In the given figure, Shape P and Shape Q touches the line y=7 and Shape Q forms exact reflection of Shape P

Hence, the equation of the line of reflection that

transforms shape P into shape Q. is y=7.

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Answer: Creo que es correcto

Step-by-step explanation: Porque si realmente lo piensas, probablemente lo entenderías, así que sí, y espero haberte ayudado.

Answer:

Point slope form is the best form to use for this particular question.

We reflect point slope form as:  \(y-y_{1} =m(x-x_1)\)

M reflects the slope, and the X and Y values are the coordinates given.

M = -2, X = 4, Y = 2

This should result in an equation that looks like this:

\(y-2=-2(x-4)\)

Now, if we want to turn this equation into slope-intercept form, we have to do some calculations. First of all, we have to multiply -2 with (x-4) to get

\(y-2=-2x+8\)

Next, we add two on both sides to isolate the Y variable.

Therefore, the slope-intercept equation would be: \(y=-2x+10\)

The statement ''A frequency polygon is a very useful graphic technique when comparing two or more distributions'' is true because a frequency polygon is a very useful graphic technique for comparing two or more distributions.

A frequency polygon is a line graph that shows the distribution of a dataset.

It is created by plotting the frequency of each data value or interval on the y-axis and the corresponding values or intervals on the x-axis, and then connecting the points with line segments.

By using frequency polygons, it becomes easy to compare the shapes and spread of two or more distributions. We can overlay different frequency polygons on the same graph and compare them.

This helps to identify similarities and differences between the data sets.

For instance, frequency polygons can help identify which data set has a higher mean or median, and which distribution has a greater variance.

In summary, frequency polygons are a useful visual tool for comparing distributions and identifying patterns in data.

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The triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

The Angle-Side-Angle (ASA) Congruence Theorem is a postulate in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.

Triangle YXZ is formed from a reflection and then a dilation of the triangle WVZ, then the relations between the angles are given as follows:

The side lengths WV and YZ, which are the side lengths between these two angles, form a proportional relationship, hence the triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

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Answer:

-1/3

Step-by-step explanation:

hope it helps thanks

Answer:

-1/3

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Triangle proportionality theorem: when you draw a line parallel to one side of a triangle, it'll intersect the other two sides of the triangle and divide them proportionally

\(\frac{26}{39}=\frac{18}{x}\)

Cross multiply and you get 702=26x

x=27

Answer:

x=27

Step-by-step explanation:

-We can use the triangle proportionality theorem: if line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.

-we write the proportion and solve for x

\(\frac{39}{26} =\frac{x}{18}\)

\(x= \frac{39*18}{26}\)

x= 27

Answer:

1/100

Step-by-step explanation:

From 1 to 10 there are 10 numbers, so the fraction would be:

# / 10

Since you are putting the cards back into the deck, the denominator will never change.

The chances of getting " 1 " are 1 / 10.

And the chances of getting " 2 " are also 1 / 10

To find the odds of getting one-after-the-other, you multiply these 2 chances.

( 1 / 10 ) x ( 1 / 10 ) = ( 1 / 100 )

There is a 1 / 100 chance that you will draw 1, then 2 if you put the cards back after drawing.

The solution to the differential equation \(y{"+ 2y'+ y = -7e^{(-t)\) is \(y = (a + bt)e^{(-t)} + (7/2)e^{(-t)\), where 'a' and 'b' are constants of integration.

To find the particular solution (yp) of the given second-order linear homogeneous differential equation: \(y{"+ 2y'+ y = -7e^{(-t)\)

We first find the homogeneous solution (yh) by setting the right-hand side equal to zero: y′′ + 2y′ + y = 0

The characteristic equation for this homogeneous equation is:\(r^2 + 2r + 1 = 0\)

We solve the characteristic equation: \((r + 1)^2 = 0\)

r + 1 = 0

r = -1

Since we have a repeated root, the homogeneous solution is of the form:

\(yh = (a + bt)e^{(-t)\)

where 'a' and 'b' are constants of integration.

Now, let's find the particular solution (yp). We assume the particular solution has a form similar to the right-hand side of the equation: \(yp = Ae^{(-t)\)

where 'A' is a constant to be determined.

Differentiating yp with respect to 't', we find: \(yp' = -Ae^{(-t)\)

Differentiating again, we have: \(yp'' = Ae^{(-t)\)

Substituting these derivatives into the original differential equation:

\(Ae^{(-t) }+ 2(-Ae^{(-t)}) + Ae^{(-t) }= -7e^{(-t)\)

Simplifying: \(-2Ae^{(-t)} = -7e^{(-t)}\)

Dividing by \(-2e^{(-t)\): A = 7/2

Therefore, the particular solution is: \(yp = (7/2)e^{(-t)\)

Finally, the complete solution is the sum of the homogeneous and particular solutions: y = yh + yp

\(y = (a + bt)e^{(-t)} + (7/2)e^{(-t)\) where 'a' and 'b' are constants of integration.

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The complete question is:

Find a solution to  \(y{"+ 2y'+ y = -7e^{(-t)\). Use a and b for the constants of integration associated with the homogeneous solution. y=yh​+yp​=

Answer: x^-4

Step-by-step explanation:

x^-10 · x^6

When you're multiplying exponents, use the first rule: add powers together when multiplying like bases.

-10 + 6 = -4

x^-4