3. What is the angle of rotation for the following figure?

45°

60°

90°

120°​

Answer:

0.5*13*15 = 97.5 square units

Step-by-step explanation:

If the diagonals of the rhombus are 13 and 15 then its area is 0.5*13*15 = 97.5 square units

The area of the rhombus is,

A. 97.5 square units

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Rhombus ABCD with the following dimensions:

diagonal 1 (d1) = BD = 15

diagonal 2 (d2) = AC = 13

AB = 9.9

Hence, Area of the rhombus;

Since we know the length of the 2 diagonals, area of the rhombus can be calculated using;

A = 1/2 × d1 × d2

A = 1/2 × 15 × 13

A = 1/2 × 195

A = 97.5 square units

Thus, The area of the rhombus is,

A. 97.5 square units

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It would take Bethany and Mandy approximately 1 hour and 38 minutes (or 1.64 hours) to proof the chapter together.

To determine how long it would take Bethany and Mandy to proof the chapter together, we can use the concept of work rates.

Let's denote the time it takes for them to proof the chapter together as "t" (in hours).

Bethany's work rate is 1 chapter per 2 hours, which can be expressed as 1/2 chapter per hour.

Mandy's work rate is 1 chapter per 9 hours, which can be expressed as 1/9 chapter per hour.

When they work together, their work rates are additive. Therefore, the combined work rate of Bethany and Mandy is:

1/2 + 1/9 = 9/18 + 2/18 = 11/18 chapter per hour.

To find the time it takes for them to proof the chapter together, we can set up the equation:

(11/18) * t = 1 (representing the entire chapter).

Simplifying the equation:

11t/18 = 1

Cross-multiplying:

11t = 18

Dividing by 11:

t = 18/11

Therefore, together, Bethany and Mandy could proofread the chapter in about 1 hour and 38 minutes (or 1.64 hours).

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The quotient of 4.082 and 10,000 is 0.000004082.

To find the quotient of 4.082 and 10,000, we need to divide 4.082 by 10,000. However, dividing a decimal by another decimal can be tricky, so we need to move the decimal point of the dividend (4.082) and the divisor (10,000) to make the division easier.

We can move the decimal point of 4.082 four places to the left to obtain 0.04082. This is because moving the decimal point to the left makes the number smaller. For example, moving the decimal point in 4.082 one place to the left gives us 0.4082, which is ten times smaller than 4.082. Moving the decimal point four places to the left gives us a number that is 10,000 times smaller than 4.082.

Similarly, we can move the decimal point of 10,000 four places to the right to obtain 100,000,000. This is because moving the decimal point to the right makes the number larger. For example, moving the decimal point in 10,000 one place to the right gives us 1,000, which is ten times larger than 10,000. Moving the decimal point four places to the right gives us a number that is 10,000 times larger than 10,000.

Now we can divide 0.04082 by 100,000,000, which gives us the quotient of 0.000004082. Therefore, to find the quotient of 4.082 and 10,000, we need to move the decimal point in 4.082 four places to the left and move the decimal point in 10,000 four places to the right, and then divide the resulting numbers.

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Answer:

7·35=245

Step-by-step explanation:

Answer:

Hi,

Step-by-step explanation:

x>=0

y>=0

x+y-5<=0 line passing through (0,5)  and (5,0) with (0,0) in minus region

2x-y-8<=0 line passing trough (0,-8) and (4,0) with (0,0) in minus region

Answer C

The approximate amount of gallons used per person with the population of  2.34 x 10¹⁵ people is 2283 gallons.

We were given the  total amount of water used in a the town as 5.342 x 10¹⁸

We were also told that the total number of the people in that town is 2.34 x 10¹⁵ people.

Then we can determine the amount of gallons used per person by making the division of the total amount of the water used by the total number of the people in the town as :

( 5.342 x 10¹⁸)/(2.34 x 10¹⁵ )

= 2283 gallons.

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Answer:

c if lsrt lstr name two congruent segments

When testing the differences between means, the research hypothesis suggests that population means are not equal.  (Option B)

Hypothesis refers to a concept or explanation for a trend that is based on known facts but has not yet been proved. A research hypothesis, also known as scientific hypothesis, is a statement about the expected result of a study. It is the proposed answer to the research question and generally includes an explanation (e.g., x affect y because …). It introduces a research question and proposes an expected result. It illustrates the relationship between two variables - an independent and dependent variable. Hence, when testing the difference between means, the hypothesis that suggests that population means are not equal is a research hypothesis.

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The intensity and the threshold of the noise are illustrations of rates

The decibel measurement of a quiet room is 28

From the graph that completes the question, we have the following point

(Decibel, Intense) = (28,500)

This means that, the decibel measurement is 28

Hence, the decibel measurement of a quiet room is 28

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Answer:

B or 28

Step-by-step explanation:

edge 22

Answer:

E': (-3, 3)

F': (-1, 2)

G': (0,0)

H': (-2, 1)

Step-by-step explanation:

Answer:

song of mulan

Step-by-step explanation:

why my reflection show who I am insidee

the equation (\(x^2 + 3x - 10 = 0\)) has both 2 and -5 as solutions. Therefore the correct option is a.

To determine which equation(s) have both 2 and -5 as solutions, substitute these values into each equation and see if they satisfy the equation. Let's check each option:

a. \(x^2 + 3x - 10 = 0\)

Substituting x = 2:

\((2)^2 + 3(2) - 10 = 4 + 6 - 10 = 0\)

Substituting x = -5:

\((-5)^2 + 3(-5) - 10 = 25 - 15 - 10 = 0\)

Both 2 and -5 satisfy the equation, so option a has both 2 and -5 as solutions.

b. \(x^2 - 3x - 10 = 0\)

Substituting x = 2:

\((2)^2 - 3(2) - 10 = 4 - 6 - 10 = -12\)

Substituting x = -5:

\((-5)^2 - 3(-5) - 10 = 25 + 15 - 10 = 30\)

Neither 2 nor -5 satisfy the equation, so option b does not have both 2 and -5 as solutions.

c. \(x^2 + 7x + 10 = 0\)

Substituting x = 2:

\((2)^2 + 7(2) + 10 = 4 + 14 + 10 = 28\)

Substituting x = -5:

\((-5)^2 + 7(-5) + 10 = 25 - 35 + 10 = 0\)

Only -5 satisfies the equation, so option c does not have both 2 and -5 as solutions.

d. \(x^2 - 7x + 10 = 0\)

Substituting x = 2:

\((2)^2 - 7(2) + 10 = 4 - 14 + 10 = 0\)

Substituting x = -5:

\((-5)^2 - 7(-5) + 10 = 25 + 35 + 10 = 70\)

Only 2 satisfies the equation, so option d does not have both 2 and -5 as solutions.

In conclusion, the equation in option a (\(x^2 + 3x - 10 = 0\)) has both 2 and -5 as solutions.

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The answers are as follows:

a) C. The mean fat content is probably higher for beef hot dogs.

b) A. The difference in the two sample means is significant.

c) 0.11

a) The fact that the endpoints of the confidence interval are positive numbers indicates that the mean fat content for beef hot dogs is likely higher than the mean fat content for meat hot dogs. Since the confidence interval does not include zero, it suggests that there is a statistically significant difference in the mean fat content between the two types of hot dogs.

Therefore, option C, which states that the mean fat content is probably higher for beef hot dogs, is the correct choice.

b) The fact that the confidence interval does not contain zero indicates that the difference in the two sample means is statistically significant. If the confidence interval included zero, it would suggest that there is no significant difference between the mean fat content of beef hot dogs and meat hot dogs. However, since the interval does not contain zero, it provides evidence to support the presence of a significant difference between the two samples.

Therefore, option A, which states that the difference in the two sample means is significant, is the correct choice.

c) The corresponding alpha level can be determined by subtracting the confidence level (1 - 0.89 = 0.11) from 1. In this case, the confidence level is 89%, which corresponds to an alpha level of 0.11. The alpha level represents the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.

Therefore, the corresponding alpha level for this confidence interval is 0.11.

In summary, the confidence interval indicates a likely higher mean fat content for beef hot dogs compared to meat hot dogs. The absence of zero in the confidence interval suggests a significant difference between the two samples. The corresponding alpha level for this confidence interval is 0.11, representing the probability of making a Type I error in the hypothesis test.

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The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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The triangle having sides 12, 40, and 50 is acute angled triangle.

The given that,

For a triangle,

length of sides:

a = 12,

b = 40,

c = 50

Now squaring each sides then

a² = 144

b² = 1600

c² = 2500

We know that the Pythagoras theorem for a right angled triangle:

(Hypotenuse)²= (Perpendicular)² + (Base)²

Then we have following three conditions also,

(1) If sides of triangle are satisfy:

a² = b² + c²

The the triangle is right angled triangle

(2) If sides of triangle are satisfy:

a² > b² + c²

The the triangle is obtuse angled triangle

(3) If sides of triangle are satisfy:

a² > b² + c²

The the triangle is acute angled triangle.

Therefore check for conditions,

since 144 < 1600 +2500

Hence,

The triangle is acute angled triangle.

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Answer:

17a - 16

7b

Step-by-step explanation:

Given the following expressions

3a+4(5a - 4)=

Expand

3a + 4(5a)- 4(4)

= 3a + 20a - 16

= 17a - 16

For the expression

5b -2(5a -b) + 10a

Expand

5b - 2(5a)-2(-b) + 10a

5b - 10a  + 2b + 10a

= 5b + 2b -10a + 10a

= 7b + 0

= 7b

The system of equations is consistent and has a unique solution at (-4, 1).

To solve the system of equations by graphing, we can plot the lines represented by each equation on a coordinate plane and find their point of intersection.

The given system of equations is:

1) 3x + y = -3

2) 6x - 6y = -30

Let's graph these equations:

For equation 1, 3x + y = -3, we can rewrite it as y = -3x - 3.

For equation 2, 6x - 6y = -30, we can simplify it to x - y = -5, and then y = x + 5.

Now, let's plot these lines on a graph:

The line for equation 1, y = -3x - 3, has a slope of -3 and y-intercept of -3. It will have a negative slope, and we can plot two points on the line: (0, -3) and (-1, 0).

The line for equation 2, y = x + 5, has a slope of 1 and y-intercept of 5. We can plot two points on this line as well: (0, 5) and (-5, 0).

Plotting these lines on a graph, we can see that they intersect at the point (-4, 1).

Now, let's analyze the system:

Since the lines intersect at a single point, the system is consistent. The solution to the system is the coordinates of the point of intersection, which is (-4, 1).

In summary, the system of equations is consistent and has a unique solution of x = -4 and y = 1.

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Given:

The equation of a circle is

\(x^2+y^2=10\)

A tangent line l to the circle touches the circle at point P(1,3).

To find:

The equation of the line l.

Solution:

Slope formula: If a line passes through two points, then the slope of the line is

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Endpoints of the radius are O(0,0) and P(1,3). So, the slope of radius is

\(m_1=\dfrac{3-0}{1-0}\)

\(m_1=\dfrac{3}{1}\)

\(m=3\)

We know that the radius of a circle is always perpendicular to the tangent at the point of tangency.

Product of slopes of two perpendicular lines is always -1.

Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.

\(m\times m_1=-1\)

\(m\times 3=-1\)

\(m=-\dfrac{1}{3}\)

The slope of line l is \(-\dfrac{1}{3}\) and it passs through the point P(1,3). So, the equation of line l is

\(y-y_1=m(x-x_1)\)

\(y-3=-\dfrac{1}{3}(x-1)\)

\(y-3=-\dfrac{1}{3}(x)+\dfrac{1}{3}\)

Adding 3 on both sides, we get

\(y=-\dfrac{1}{3}x+\dfrac{1}{3}+3\)

\(y=-\dfrac{1}{3}x+\dfrac{1+9}{3}\)

\(y=-\dfrac{1}{3}x+\dfrac{10}{3}\)

Therefore, the equation of line l is \(y=-\dfrac{1}{3}x+\dfrac{10}{3}\).

Answer:

0.5

Step-by-step explanation:

6+ 4x = 8

or, 4x = 8-6

or, 4x = 2

x = 0.5

Answer: 475

Step-by-step explanation: i am in middle school so I think its this

The general solution to the differential equation y'' + 16y = 0 is y(x) = (c₁ + c₂) * cos(4x)

To solve the differential equation y'' + 16y = 0 using reduction of order, we'll assume a second solution of the form y₂(x) = u(x) * y₁(x), where y₁(x) is a known solution and u(x) is an unknown function.

Given y₁(x) = cos(4x), we'll differentiate it to find y₁'(x) and y₁''(x):

y₁'(x) = -4sin(4x)

y₁''(x) = -16cos(4x)

Now we substitute y₂(x) = u(x) * y₁(x) into the original differential equation:

y'' + 16y = 0

(-16cos(4x)) + 16(u(x) * cos(4x)) = 0

Simplifying the equation:

-16cos(4x) + 16u(x) * cos(4x) = 0

cos(4x)(-16 + 16u(x)) = 0

For this equation to hold for all values of x, we must have (-16 + 16u(x)) = 0.

Solving for u(x):

-16 + 16u(x) = 0

16u(x) = 16

u(x) = 1

Now we have the second solution:

y₂(x) = u(x) * y₁(x)

y₂(x) = 1 * cos(4x)

y₂(x) = cos(4x)

Therefore, the general solution to the differential equation y'' + 16y = 0 is:

y(x) = c₁ * y₁(x) + c₂ * y₂(x)

y(x) = c₁ * cos(4x) + c₂ * cos(4x)

y(x) = (c₁ + c₂) * cos(4x)

Where c₁ and c₂ are arbitrary constants.

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The rectangular prism has a length of 9 units, a width of 10 units (since width = 90 / length), and a height of 5 units (since height = (5/9) length).

What is the area of a rectangle?

A rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides that are parallel and congruent (equal in length). The area of a rectangle is defined as the amount of space that is enclosed by its two-dimensional shape, and it can be calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is:

Based on the given information, we can determine the dimensions of the rectangular prism as follows:

Cross section A has an area of 90 square units, which is equal to the area of the base of the prism. Since the base of the prism is a rectangle, we can use the formula for the area of a rectangle to find its dimensions:

90 = length x width

Cross section B has an area of 50 square units, which is equal to the area of one of the sides of the prism. Since the sides of the prism are also rectangles, we can use the formula for the area of a rectangle to find its dimensions:

50 = height x width

Cross section C has an area of 45 square units, which is equal to the area of the front of the prism. Since the front of the prism is also a rectangle, we can use the formula for the area of a rectangle to find its dimensions:

45 = length x height

We now have three equations with three unknowns, which we can solve for to find the dimensions of the prism:

90 = length x width

50 = height x width

45 = length x height

Solving for width in the first equation gives us:

width = 90 / length

Substituting this into the second equation gives us:

50 = height x (90 / length)

Solving for height gives us:

height = 50 x (length / 90) = (5/9) length

Substituting this into the third equation gives us:

45 = length x (5/9) length = (5/9) length²

Solving for length gives us:

length² = (9/5) x 45 = 81

length = √(81) = 9

Therefore, the rectangular prism has a length of 9 units, a width of 10 units (since width = 90 / length), and a height of 5 units (since height = (5/9) length).

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4.25 light years is 2.4984x10¹³ miles

What is light years?

A light-year, sometimes spelt light year, is a huge measure of length used in astronomy that is comparable to approximately 9.46 trillion kilometers (9.461012 kph) or 5.88 trillion miles (5.881012 mi). A light-year, as defined by the International Astronomical Union (IAU), is the distance that light travels in a vacuum in one Julian year (365.25 days). The phrase light-year is frequently misconstrued as a unit of time since it contains the time-measurement word "year." The light-year is most commonly used in non-specialist contexts and popular scientific publications to indicate distances to stars and other cosmic distances.

1 light years is = 5.8786x10¹² miles

4.25 light years = 5.8786x10¹²x4.25 = 2.4984x10¹³ miles

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The probability that the sample proportion of households spending more than $125 a week is less than 0.35 is 0.9884.

Using the given information, the population proportion of households spending more than $125 a week is 0.34. The sample size is 196 households.

Population proportion (p) = 0.34

Sample size (n) = 196

Sample proportion (p') = 0.35

Standard error of proportion (p') = √[p*(1-p)/n] = √[(0.34*0.66)/196] = 0.044

To find the probability that the sample proportion is less than 0.35, we need to find the z-score and then find the area to the left of that z-score using a standard normal distribution table.

z-score = (p' - p) / σp' = (0.35 - 0.34) / 0.044 = 2.27 (approx)

Using a standard normal distribution table, the area to the left of the z-score 2.27 is 0.9884.

Therefore, there is a roughly 0.9884 percent chance that the sample proportion of households paying more than $125 per week is less than 0.35.

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Answer:

Step-by-step explanation:

\(\tan(29.4^o)=\dfrac{?}{56.8}\\\\\tan(29.4^o)\times56.8=?\\\\?\approx0,563471\times56.8\approx32\)

Yes, it is possible.

To determine if there is a way to choose some of the n items to make the total weight exactly equal to w, you can use the following step-by-step approach:

1. List the weights of each of the n items.
2. Create a table with columns representing the weights from 0 to w, and rows representing the items from 0 to n.
3. Initialize the first row (representing item 0) with "True" for weight 0 and "False" for all other weights.
4. Loop through each item (i) from 1 to n:
  a. Loop through each possible weight (j) from 0 to w:
     i. If the item's weight is less than or equal to the current weight (j), check if the remaining weight (j minus the item's weight) can be obtained using the previous items (row i-1). If yes, mark the current cell as "True".
     ii. If the current item's weight is greater than the current weight (j) or the remaining weight can't be obtained using the previous items, copy the value from the cell above (row i-1) in the table.
5. Check the last cell in the table (cell [n][w]). If it is marked "True", it is possible to choose some of the n items to make the total weight exactly equal to w. If it's "False", it's not possible.

This approach uses dynamic programming to efficiently solve the problem. If the last cell in the table is "True", you can backtrack through the table to find the exact items that contribute to the total weight of w.

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Answer:

so the Domain:

{5, -5, 6,−6}

Range:  {1,4,2,8,3}

functon no

Since x=−5 produces y=4 and y=3, the relation (5,1),(−5,4),(6,2),(−6,8),(−5,3)is not function.

Step-by-step explanation:

domain is normally x and range in most the time y, this is what i was taught and i hope it helps and is right

After solving the given expression → F = - m + B/q³  for  [B], we get -

B = q³(F + M).

We have the following equation -

F = - m + B/q³

We have the following equation -

F = - m + B/q³

On solving for [B], we get -

F + M = B/q³

B = q³(F + M)

Therefore, the given expression after solving for [B], we get -

B = q³(F + M).

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The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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