Clay has a bag that contains 4 white marbles and 10 black marbles. Clay chooses a marble from the bag without looking, records the color, replaces it, then
chooses another marble. What is the theoretical probability that Clay chooses a white marble both times?
• 2.04%
O 8.16%
0 28.57%
O 51.02%
!!

Answer:

0.68 inches

Step-by-step explanation:

The interior diameter of the old pipe is 0.63 inches, and the plumbing tape will fill 0.15 inches of the space between the old pipe and the new pipe. Therefore, the total diameter that the new pipe must fit inside is:

0.63 inches + 0.15 inches = 0.78 inches

The new pipe must be 0.1 inches smaller than this diameter to ensure a proper fit. Therefore, the diameter of the new pipe should be:

0.78 inches - 0.1 inches = 0.68 inches

So, the new pipe must have an interior diameter of 0.68 inches to fit correctly inside the old pipe with the plumbing tape.

If Peter mows 7 lawns in 11 hours, then the number of lawns Peter can mow in 55 hours is 35.

The first step is to determine how many lawns Peter can mow in 1 hour. To do this, divide 7 by 11.

Division is the process of determining the quotient of two or more numbers. It entails putting a number into equal groups using another number.

To determine the number of lawns that can be mowed in 55 hours, multiply the fraction derived in the previous step by 55.

Multiplication is the process of determining the product of two or more numbers.

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(1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.

What is Scatter Plot ?

A scatter plot is a graph that shows the relationship between two sets of data. Each dot on the plot represents a single data point, and the position of the dot corresponds to the values of the two variables being plotted.

In this specific scatter plot, we have 10 data points represented by dots. To find the two points that a line of best fit would go through, we want to look for a pattern or trend in the data. Ideally, the line of best fit should pass as close as possible to all of the data points, but this is not always possible.

One common method for finding the line of best fit is to choose two points that seem to be close to the middle of the data and that the line passes through. This is because we want the line to be a good representation of the overall trend in the data.

Looking at the scatter plot provided, we can see that there is a general trend of the data points sloping downward from left to right. If we draw a line that passes through the points (3, 7) and (9, 1), we can see that it closely follows the trend of the data points. Therefore, these are the two points that a line of best fit would go through to best fit the data.

Therefore, (1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.

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The 90% confidence interval for the population mean salary is 4650 + 45.24. The correct answer is option f.

To find the 90% confidence interval for the population mean salary, we need to use the formula:

CI = x ± z(s/√n)

Where:
- CI = confidence interval
- x = sample mean
- z = z-score for the desired confidence level
- s = sample standard deviation
- n = sample size

Plugging in the given values, we get:

CI = 4650 ± 1.645(165/√36)

CI = 4650 ± 1.645(165/6)

CI = 4650 ± 1.645(27.5)

CI = 4650 ± 45.2375

CI = 4650 ± 45.24

Therefore, the 90% confidence interval for the population mean salary is 4650 ± 45.24 or (4604.7625, 4695.2375).

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The solution set of inequality " for 9t+27 <4t-18" in interval notation is (-∞, -9).

To solve the inequality 9t + 27 < 4t - 18, we need to isolate the variable t on one side of the inequality. Here are the steps:

1. Subtract 4t from both sides: 9t - 4t + 27 < -18
2. Simplify: 5t + 27 < -18
3. Subtract 27 from both sides: 5t < -45
4. Divide both sides by 5: t < -9

Now we can write the solution set in interval notation: (-∞, -9)

So the solution set is all values of t that are less than -9.

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The coordinates of R are (-15, 8). The solution has been obtained by using Mid point formula.

What is Mid point formula?

The centre point of a straight line can be located using the midpoint formula. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.

We are given that Q is the midpoint of segment PR and point P is (11,-2) and point Q is (-2,3).

Let the coordinates of R be (x₂, y₂)

Using Mid point formula, we get

⇒Point Q = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

⇒(-2,3) = ((11 + x₂) / 2, (-2 + y₂) / 2)

So,

⇒-2 = (11 + x₂) / 2

⇒-4 = 11 + x₂

⇒x₂ = -15  

Similarly,

⇒3 = (-2 + y₂) / 2

⇒6 = -2 + y₂

⇒y₂ = 8

Hence, the coordinates of R are (-15, 8).

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Substituting Q = 30 degrees, we get:

Q' = 30 degrees + 45 degrees

Q' = 75 degrees

Therefore, the measure of angle Q' is 75 degrees.

Acute angles are those that range in degree from 0 to 90. Obtuse angles (90°–180°) are those that fall within this range. • A right angle is one with an angle of 90 degrees (= 90°).

If angle Q measures 30 degrees and is rotated 45 degrees, we can find the measure of the new angle Q' as follows:

Q' = Q + 45 degrees

Substituting Q = 30 degrees, we get:

Q' = 30 degrees + 45 degrees

Simplifying, we get:

Q' = 75 degrees

Therefore, the measure of angle Q' is 75 degrees.

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plt.plot(x, y_sine)
plt.plot(x, y_cosine)

To compute the x and y coordinates for points on sine and cosine curves, you need to use the trigonometric functions sine and cosine. To plot the sine and cosine graphs in the same figure, you need to create a subplot grid using the plt.subplot() function. This function takes in the number of rows, columns and the active plot you want to plot the graphs in.

To create a subplot grid that has height 2 and width 1 and set the first subplot as active, the code will look like this:
plt.subplot(2, 1, 1)

You can then plot the sine and cosine graphs by using the x and y coordinates calculated from the sine and cosine functions. The code for plotting the graphs will look like this:
plt.plot(x, y_sine)
plt.plot(x, y_cosine)

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Answer:

Step-by-step explanation: So first, you're gonna distribute the 4/5 to the b and the -5, by doing that u will get 3.2=4/5b - 4. Then you're gonna cancel out the -4 by adding it on both sides - 3.2+4=4/5b, you get 7.2=4/5b.  Multiply by the reciprocal of 4/5 which is 5/4 on both sides. 7.2 x 5/4 = b. you get 9 = b

The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.

here, we have,

given that,

Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3)

and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)."

now, we now that,

distance formula:

d=√(x2−x1)^2+(y2−y1)^2

so, we get,

length of AB = 3√2

and, length of XY = 3

so, scale factor = AB/XY

                          =3√2/3

                          =√2

Hence, The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.

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(a) The standard error is 1.17. (b) IT is a two-sided test. (c) If a = 0.05, it can be concluded that we can reject the null hypothesis and accept the alternative hypothesis. (d) A 90% two-sided CI on the difference in means is (0.33, 4.37).

(a) The missing value for the standard error of the difference in sample means can be calculated using the formula:

Standard error = (Difference in sample means) / (Test statistic) = 2.35 / 2.01 = 1.17

(b) This is a two-sided test because the P-value is given for a two-sided test. If it were a one-sided test, the P-value would be half of the given value, or 0.0149.

(c) If a = 0.05, we can conclude that the difference in sample means is statistically significant because the P-value (0.0298) is less than a (0.05). This means that we can reject the null hypothesis and accept the alternative hypothesis that there is a difference in the means.

(d) A 90% two-sided CI on the difference in means can be calculated using the formula:

CI = (Difference in sample means) ± (t-value) × (Standard error)

The t-value for a 90% two-sided CI with 18 degrees of freedom is 1.734. So the CI is:

CI = 2.35 ± 1.734 × 1.17 = (0.33, 4.37)

Therefore, the 90% two-sided CI on the difference in means is (0.33, 4.37).

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The radius of the first circle is 14.67 cm and the radius of the second circle is 8.11 miles.

The radius of a circle can be found by using the formula s = rθ, where s is the length of the arc, r is the radius, and θ is the central angle in radians. Rearranging the formula, we can find the radius by dividing the length of the arc by the central angle: r = s/θ.

For the first part of the question, we are given an arc length of 88 cm and a central angle of 6 radians. Plugging these values into the formula, we can find the radius:

r = 88 cm / 6 radians = 14.67 cm

For the second part of the question, we are given an arc length of 17 miles and a central angle of 120°. However, we need to convert the central angle from degrees to radians before plugging it into the formula. We can do this by multiplying the angle in degrees by π/180:

120° × π/180 = 2π/3 radians

Now we can plug the values into the formula to find the radius:

r = 17 miles / (2π/3) radians = 8.11 miles

So the radius of the first circle is 14.67 cm and the radius of the second circle is 8.11 miles.

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AB is indeed the zero matrix, and we have found a 2 x 2 matrix B such that AB is the zero matrix.

When multiplying two matrices, we use the dot product of the rows of the first matrix and the columns of the second matrix to obtain the entries of the resulting matrix. In order for the product of two matrices to be the zero matrix, the dot product of each row of the first matrix with each column of the second matrix must be zero.

Let's construct a 2 x 2 matrix B such that AB is the zero matrix. We can use two different nonzero columns for B to obtain the zero matrix. Let's start with the first column of B:

B = [b1 b3]
   [b2 b4]

We need to find values for b1, b2, b3, and b4 such that the dot product of each row of A with each column of B is zero. Let's start with the first row of A and the first column of B:

-12b1 + 4b2 = 0

We can rearrange this equation to solve for b2 in terms of b1:

b2 = 3b1

Now let's look at the second row of A and the first column of B:

15b1 - 5b2 = 0

Substituting the value of b2 from the first equation gives us:

15b1 - 5(3b1) = 0

Simplifying gives us:

0 = 0

This equation is always true, so we can choose any value for b1 and find the corresponding value for b2. Let's choose b1 = 1:

b2 = 3(1) = 3

Now let's look at the first row of A and the second column of B:

-12b3 + 4b4 = 0

We can rearrange this equation to solve for b4 in terms of b3:

b4 = 3b3

Now let's look at the second row of A and the second column of B:

15b3 - 5b4 = 0

Substituting the value of b4 from the first equation gives us:

15b3 - 5(3b3) = 0

Simplifying gives us:

0 = 0

This equation is always true, so we can choose any value for b3 and find the corresponding value for b4. Let's choose b3 = 2:

b4 = 3(2) = 6

Now we have the values for all of the entries of B:

B = [1 2]
   [3 6]

Let's check our work by multiplying A and B:

AB = [-12 4] [1 2]
    [ 15 -5] [3 6]

 = [(-12)(1) + (4)(3)  (-12)(2) + (4)(6)]
    [(15)(1) + (-5)(3)  (15)(2) + (-5)(6)]

 = [0 0]
    [0 0]

So AB is indeed the zero matrix, and we have found a 2 x 2 matrix B such that AB is the zero matrix.

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The length of the diagonal is between 3 and 4; it is closer to 3.

In Mathematics, the diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.

In any rectangle, each of the two (2) opposite sides are equal and parallel and the two (2) diagonals are equal.

Based on the information provided about the diagonal, we have:

Diagonal = √18

Diagonal = √9 × √2

Diagonal = 3√2 units.

In conclusion, we can logically deduce that the diagonal is closer to 3 units.

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we can graph s=s(t),v=v(t), and a=a(t) by plotting the equations for s, v, and a as functions of t. The graph of s=s(t) is a sinusoidal curve with a linear trend. The graph of v=v(t) is a sinusoidal curve with a constant value. The graph of a=a(t) is a sinusoidal curve with a zero value.

The velocity v of the pendulum is the first derivative of the distance s with respect to time t. That is, \[ v=v(t)=\frac{ds}{dt} \] Similarly, the acceleration a of the pendulum is the first derivative of the velocity v with respect to time t. That is, \[ a=a(t)=\frac{dv}{dt} \] We can find the velocity v and acceleration a by taking the derivatives of the given equation for the distance s. \[ s=s(t)=0.04 \sin (2 t)+3 t \] The first derivative of s with respect to t is \[ v=v(t)=\frac{ds}{dt}=0.08 \cos (2 t)+3 \] The second derivative of s with respect to t is \[ a=a(t)=\frac{dv}{dt}=-0.16 \sin (2 t) \] Now, we can find the velocity v and acceleration a at the given times t= 8π ,t= 4π , and t= 2π by plugging in the values of t into the equations for v and a. \[ v( 8π )=0.08 \cos (2( 8π ))+3=3 \quad \text{m/s} \] \[ v( 4π )=0.08 \cos (2( 4π ))+3=3 \quad \text{m/s} \] \[ v( 2π )=0.08 \cos (2( 2π ))+3=3 \quad \text{m/s} \] \[ a( 8π )=-0.16 \sin (2( 8π ))=0 \quad \text{m/s}^2 \] \[ a( 4π )=-0.16 \sin (2( 4π ))=0 \quad \text{m/s}^2 \] \[ a( 2π )=-0.16 \sin (2( 2π ))=0 \quad \text{m/s}^2 \] Finally, we can graph s=s(t),v=v(t), and a=a(t) by plotting the equations for s, v, and a as functions of t. The graph of s=s(t) is a sinusoidal curve with a linear trend. The graph of v=v(t) is a sinusoidal curve with a constant value. The graph of a=a(t) is a sinusoidal curve with a zero value.

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Due to length restrictions, we kindly invite to read the explanation to see the lenghts of each 30-60-90 right triangles.

In this problem we find six cases of 30-60-90 right triangles, that is, right triangles whose inner angles have the following measures: 30°, 60°, 90°. The length of sides can be found by the following relationships:

Now we proceed to determine the missing length:

Case 1:

PV = 4 / (1 / 2)

PV = 8

VT = √3 · 4

VT = 4√3

Case 2:

PT = 2 / √3

PT = 2√3 / 3

PV = 2 / (√3 / 2)

PV = 4√3 / 3

Case 3:

PT = (1 / 2) · 3

PT = 3 / 2

VT = 3√3 / 2

Case 4:

PT = 7 / √3

PT = 7√3 / 3

PV = 7 / (√3 / 2)

PV = 14√3 / 3

Case 5:

VT = √3 · (1 / 2)

VT = √3 / 2

PV = (1 / 2) / (1 / 2)

PV = 1

Case 6:

PV = 100

PT = 50

VT = 50√3

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We can use the two-point form to find the equation of the line passing through the two given points:

y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)

where (x1, y1) = (1, 7) and (x2, y2) = (3, 3).

Substituting the values, we get:

y - 7 = ((3 - 7)/(3 - 1))(x - 1)

Simplifying the equation, we get:

y - 7 = (-2/2)(x - 1)

y - 7 = -x + 1

Adding 7 to both sides, we get:

y = -x + 8

Therefore, the equation of the line passing through the points (1, 7) and (3, 3) is y = -x + 8.

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Alternate interior angles = ∠7 and ∠9.

Corresponding angles = ∠1 and ∠7

Vertical angles = ∠4 and ∠11

∠7 = 60°

∠8 = 120°

∠9 = 60°

When two lines meet, they intersect at an angle. By using the symbol, we may symbolise an angle.

Two lines meet at the common vertex of an angle, which has one common leg. A straight line's one side always has a total angle of 180 degrees. On the other hand, a point's surrounding angles are always added up to 360 degrees.

Here,

We can see that the Alternate interior angles = ∠7 and ∠9.

Corresponding angles = ∠1 and ∠7

Vertical angles = ∠4 and ∠11

Given, ∠1 = 60°

Now similarly, using the angles properties we can ind the rest of the angles.

∠7 = 60°

∠8 = 120°

∠9 = 60°

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The line which is not transversal to LR would be Line TK.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

Properties of Parallel Lines Cut by a Transversal

The corresponding angles are equal and the vertically opposite angles are equal.

The alternate interior angles are equal and the alternate exterior angles are equal.

Also, pair of interior angles on the same side of the transversal is supplementary.

Since we know that transversal is a line that intersects two or more other lines at different points.

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Line TK is not transversal to line LR.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines. We can also say Parallel lines meet at infinity.

Given,

Line PR and KT are parallel

By the figure,
PR = LR

and KT = TK
PR || KT

∴ LR || TK

Hence, TK is the line, that is not the transversal line to LR.

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The zeros in the given graph. (the one where its curved pointing downwards) is {-3,1}.

The solutions to the equation p(x) = 0, where p(x) stands for the polynomial, are the zeros of a polynomial. If we plot this polynomial as y = p, we can see that these are the values of x where y = 0. (x). In other words, these are the x-intercepts of the graph.

The polynomial's zeros can be found by locating the locations where its graph contacts or crosses the x-axis.

When f(x) = 0, or when the graph's y-coordinate is equal to 0, the zeroes of the graph are determined.

From the graph we see that, at y = 0 we have the values of x as:

1. x = -3 and x = 1

Hence, the zeros in the given graph. (the one where its curved pointing downwards) is {-3,1}.

2. Roots of the graph are - x = - 2 and x = 4, {-2, 4}

3. solutions to x² + 10x = 24,

x² + 10x - 24 = 0

x² + 12x - 2x - 24

x(x + 12) -2 (x + 12)

(x - 2) (x + 12)

x = 2 or x = -12

{-12,2}

4. solutions to x² + 18x = 4x - 49

x² + 14x + 49

x² + 7x + 7x + 49

x(x + 7) + 7 (x + 7)

(x + 7)(x + 7)

x = -7

{-7}

5.  zeros of x² - 9x = 0

x(x - 9) = 0

Either x = 0 or x = 9,

{0,9}

6. roots of 4x² - 24 = 20x

4x² - 20x - 24 = 0

x² - 5x - 6 = 0

x² -6x + x - 6 = 0

x(x - 6) + 1(x - 6) = 0

(x + 1) (x - 6)

x = -1 and x = 6

{-1,6}

7. correct option is y = x² - x - 6

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The composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).

Given functions are \( f(x)=6x−5 \) and \( g(x)=x^2−6x+3 \). Let's find the composition of functions below:\((f\circ g)(x)\)First, we need to substitute \( g(x) \) in place of \( x \) in \( f(x) \). Hence,\( (f\circ g)(x) = f(g(x)) \)\( f(g(x)) = 6g(x) - 5 \)Substitute \( g(x) \) in the above equation,\( (f\circ g)(x) = 6(x^2-6x+3) - 5 \)\( (f\circ g)(x) = 6x^2 - 36x + 13 \)\((g\circ f)(x)\)First, we need to substitute \( f(x) \) in place of \( x \) in \( g(x) \). Hence,\( (g\circ f)(x) = g(f(x)) \)We are given that \( f(x)=6x−5 \) , substitute this in the above equation,\( (g\circ f)(x) = g(6x-5) \)Substitute this in the function \( g(x) \),\( (g\circ f)(x) = (6x-5)^2 - 6(6x-5) + 3 \)\( (g\circ f)(x) = 36x^2 - 72x + 29 \)Hence, the composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).

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The probability of drawing a King, Queen, or Jack from a standard deck of 52 cards is 3/13.

The probability of drawing a King, Queen, or Jack in a standard deck of 52 cards can be calculated by using the formula for the probability of an event happening: P(E) = number of favorable outcomes / total number of possible outcomes.

In this case, the number of favorable outcomes is the total number of Kings, Queens, and Jacks in the deck, which is 4 + 4 + 4 = 12. The total number of possible outcomes is the total number of cards in the deck, which is 52.

So, the probability of drawing a King, Queen, or Jack is:

P(E) = 12 / 52

Simplifying this fraction gives us:

P(E) = 3 / 13

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okay i will answer it for you yes

The white ball is transferring its momentum to the red ball.
The missing blank is "transferring".

The statement "the white ball is transferring its momentum to the red ball" is based on the law of conservation of momentum.

According to this law, the total momentum of a closed system (in which no external forces act on the system) is conserved. This means that the momentum lost by one object in the system must be gained by another object in the system.

So we can conclude that, in the picture, the white ball and the red ball together form a closed system, and the collision between them causes the white ball to transfer some of its momentum to the red ball, in accordance with the law of conservation of momentum.

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Answer: 210 ( it hope this is a best answer)

Step-by-step explanation:

2 hours and 20 minutes is 2 and a third hours. Multiply 90 by 2 and a third.

90 × 2.333

209.999

If you round to the nearest kilometer, the answer is 210 km

The value of the fractions will be:

a. 1/3 + 1/4 = 7/12

b. 1/3 + 2/7 = 13/21

c. 1/2 + 2/9 = 13/18

d. 3/4 + 1/5 = 19/20

e. 1/3 + 4/9 = 7/9

f. 1/6 + 3/4 = 11/12

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The value of the fractions will be:

a. 1/3 + 1/4

= 4/12 + 3/12

= 7/12

b. 1/3 + 2/7

= 7/21 + 6/21

= 13/21

c. 1/2 + 2/9

= 9/18 + 4/18

= 13/18

d. 3/4 + 1/5

= 15/20 + 4/20

= 19/20

e. 1/3 + 4/9 = 7/9

f. 1/6 + 3/4 = 11/12

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Step-by-step explanation:

The circumference of the bike tire above is 82.268 inches.

What is the radius of the bike tire? (Use 3.14 for .)

A.

26.2 in

B.

13.1 in

C.

41.13 in

D.

258.32 in

Ps=the answer is B

The area of the trapezoid is 335 square inches.

What is Trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The distance between the bases is called the height or altitude of the trapezoid.

First, we need to convert the lengths of the bases and the perpendicular distance to the same units. Let's convert 6 feet to inches:

6 feet = 6 x 12 inches = 72 inches

Now we can calculate the area of the trapezoid using the formula:

Area = (a + b) * h / 2

where a and b are the lengths of the bases and h is the perpendicular distance between them.

Substituting the given values, we get:

Area = (62 + 72) * 5 / 2

Area = 134 * 5 / 2

Area = 670 / 2

Area = 335 square inches

Therefore, the area of the trapezoid is 335 square inches.

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Answer: 23 kg

Step-by-step explanation:

Let's begin by using algebra to solve the problem.

Let x be the number of kilograms of salmon the fish-shop owner bought at the market.

We know that the total cost of the salmon was $400, so we can write:

400 = x * c

where c is the cost per kilogram of salmon.

We also know that all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. So the price per kilogram of salmon at the fish shop was c + 10.

The total revenue from the sale of the fish was $540, so we can write:

540 = (x - 2) * (c + 10)

Now we can use these two equations to solve for x.

First, we can use the first equation to solve for c:

c = 400 / x

Then we can substitute this expression for c into the second equation:

540 = (x - 2) * (400/x + 10)

Simplifying this equation:

540 = 4000/x + 10x - 20 - 80/x

Multiplying both sides by x:

540x = 4000 + 10x^2 - 20x - 80

10x^2 - 20x - 4600 = 0

Dividing both sides by 10:

x^2 - 2x - 460 = 0

We can solve for x using the quadratic formula:

x = [2 ± sqrt(4 + 4*460)] / 2

x = [2 ± 44] / 2

Discarding the negative solution, we get:

x = (2 + 44) / 2

x = 23

Therefore, the fish-shop owner bought 23 kilograms of salmon at the market.

There are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]

To find the real solutions, we can use the zero product property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. In this case, we can set each of the factors equal to zero and solve for x:

[tex]2(x-1)^(2)=02x+3=0(x+5)^(3)=0[/tex]

Solving each of these equations gives us the following solutions:
[tex]x=1x=-3/2x=-5[/tex]

However, we need to check each of these solutions to see if they satisfy the original equation. Plugging each solution back into the equation gives us:

[tex]2(1-1)^(2)(2(1)+3)(1+5)^(3)=.0012(-3/2-1)^(2)(2(-3/2)+3)(-3/2+5)^(3)=.0012(-5-1)^(2)(2(-5)+3)(-5+5)^(3)=.001[/tex]

The first and third solutions do not satisfy the equation, but the second solution does. Therefore, there are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]

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